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+Project Gutenberg (https://www.gutenberg.org) public repository for
+eBook #68991 (https://www.gutenberg.org/ebooks/68991)
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-The Project Gutenberg eBook of Giant brains; or Machines that think,
-by Edmund Callis Berkeley
-
-This eBook is for the use of anyone anywhere in the United States and
-most other parts of the world at no cost and with almost no restrictions
-whatsoever. You may copy it, give it away or re-use it under the terms
-of the Project Gutenberg License included with this eBook or online at
-www.gutenberg.org. If you are not located in the United States, you
-will have to check the laws of the country where you are located before
-using this eBook.
-
-Title: Giant brains; or Machines that think
-
-Author: Edmund Callis Berkeley
-
-Release Date: September 14, 2022 [eBook #68991]
-
-Language: English
-
-Produced by: Tim Lindell and the Online Distributed Proofreading Team at
-             https://www.pgdp.net (This book was produced from images
-             made available by the HathiTrust Digital Library.)
-
-*** START OF THE PROJECT GUTENBERG EBOOK GIANT BRAINS; OR MACHINES
-THAT THINK ***
-
-
-
-
-
-Transcriber’s Notes:
-
-  Underscores “_” before and after a word or phrase indicate _italics_
-    in the original text.
-  A single underscore after a symbol indicates a subscript.
-  Small capitals have been converted to SOLID capitals.
-  Illustrations have been moved so they do not break up paragraphs.
-  Typographical and punctuation errors have been silently corrected.
-
-
-
-
-                  GIANT BRAINS
-                       OR
-               MACHINES THAT THINK
-
-             EDMUND CALLIS BERKELEY
-
-         Consultant in Modern Technology
-    President, E. C. Berkeley and Associates
-
-        JOHN WILEY & SONS, INC., NEW YORK
-         CHAPMAN & HALL, LIMITED, LONDON
-
-                 Copyright, 1949
-                       by
-             EDMUND CALLIS BERKELEY
-
-              _All Rights Reserved_
-
-     _This book or any part thereof must not
-        be reproduced in any form without
-    the written permission of the publisher._
-
-         Second Printing, February, 1950
-     Printed in the United States of America
-
-                 To my friends,
-           whose help and instruction
-             made this book possible
-
-
-
-
-PREFACE
-
-The Subject, Purpose, and Method of this Book
-
-
-The subject of this book is a type of machine that comes closer to
-being a brain that thinks than any machine ever did before 1940. These
-new machines are called sometimes mechanical brains and sometimes
-sequence-controlled calculators and sometimes by other names.
-Essentially, though, they are machines that can handle information with
-great skill and great speed. And that power is very similar to the
-power of a brain.
-
-These new machines are important. They do the work of hundreds of human
-beings for the wages of a dozen. They are powerful instruments for
-obtaining new knowledge. They apply in science, business, government,
-and other activities. They apply in reasoning and computing, and, the
-harder the problem, the more useful they are. Along with the release of
-atomic energy, they are one of the great achievements of the present
-century. No one can afford to be unaware of their significance.
-
-In this book I have sought to tell a part of the story of these new
-machines that think. Perhaps you, as you start this book, may not agree
-with me that a machine can think: the first chapter of this book is
-devoted to the discussion of this question.
-
-My purpose has been to tell enough about these machines so that we
-can see in general how they work. I have sought to explain some
-giant brains that have been built and to show how they do thinking
-operations. I have sought also to talk about what these machines can do
-in the future and to judge their significance for us. It seems to me
-that they will take a load off men’s as great as the load that printing
-took off men’s writing: a tremendous burden lifted.
-
-We need to examine several of the new mechanical brains: Massachusetts
-Institute of Technology’s differential analyzer, Harvard’s IBM
-automatic sequence-controlled calculator, Moore School’s ENIAC
-(Electronic Numerical Integrator and Calculator), and Bell Laboratories’
-general-purpose relay calculator. These are described in the sequence in
-which they were finished between the years 1942 and 1946.
-
-We also have to go on some excursions—for instance, the nature of
-language and of symbols, the meaning of thinking, the human brain and
-nervous system, the future design of machinery that can think, and a
-little algebra and logic. I have also sought to discuss the relations
-between machines that think and human society—what we can foresee as
-likely to happen or be needed as a result of the remarkable invention
-of machines that can think.
-
-
-READING THIS BOOK
-
-This book is intended for everyone. I have sought to put it together in
-such a way that any reader can select from it what he wants.
-
-Perhaps at first reading you want only the main thread of the story.
-Then read only what seems interesting, and skip whatever seems
-uninteresting. The subheadings should help to tell you what to read and
-what to skip. Nearly all the chapters can be read with little reference
-to what goes before, although some reference to the supplements in the
-back may at times be useful.
-
-Perhaps your memory of physics is dim, like mine. The little knowledge
-of physics needed is explained here and there throughout the book, and
-the index should tell where to find any explanation you may want.
-
-Perhaps it is a long time since you did any algebra. Then Supplement
-2 on mathematics may hold something of use to you. Two sections (one
-in Chapter 5 and one in Chapter 6) labeled as containing some rather
-mathematical details may be skipped with no great loss.
-
-Perhaps you are unacquainted with logic that uses symbols—the branch of
-logic called mathematical logic. In fact, very few people are familiar
-with it. No discussion in the book hinges on understanding this
-subject, except for Chapter 9 where a machine that calculates logical
-truth is described. In all other chapters you may freely skip all
-references to mathematical logic. But, if you are curious about the
-subject and how it can be usefully applied in the field of mechanical
-brains, then begin with the introduction to the subject in Chapter 9,
-and note the suggestions in the section entitled “Algebra of Logic” in
-Supplement 2.
-
-In any case, glance at the table of contents, the chapter headings and
-subheadings, and the supplements at the back. These should give an idea
-of how the book is put together and how you may select what may be
-interesting to you.
-
-Please do not read this book straight from beginning to end unless
-that way proves to be congenial to you. If you are not interested in
-technical details, skip most of the middle chapters, which describe
-existing mechanical brains. If, on the other hand, you want more
-details than this book contains, look up references in Supplement
-3. Here are listed, with a few comments, over 250 books, articles,
-and pamphlets related to the subject of machinery for computing and
-reasoning. These cover many parts of the field; some parts, however,
-are not yet covered by any published information.
-
-There are no photographs in this book, although there are over 80
-drawings. Photographs of these complicated machines can really show
-very little: panels, lights, switches, wires, and other kinds of
-hardware. What is important is the way the machine works inside. This
-cannot be shown by a photograph but may be shown by schematic drawings.
-In the same way, a photograph of a human being shows almost nothing
-about how he thinks.
-
-
-UNDERSTANDING THIS BOOK
-
-I have tried to write this book so that it could be understood. I have
-attempted to explain machinery for computing and reasoning without
-using technical words any more than necessary. To do this seemed to be
-easy in some places, much harder in others. As a test of this attempt,
-a count has been made of all the different words in the book that have
-two syllables or more, that are used for explaining, and that are
-not themselves defined. There are fewer than 1800 of these words. In
-Supplement 1, entitled “Words and Ideas,” I have digressed to discuss
-further the problem of explanation and understanding.
-
-Every now and then in the book, along comes a word or a phrase that
-has a special meaning, for example, the name of something new. When it
-first appears, it is put in italics and is explained or defined. In
-addition, all the words and phrases having special meaning appear again
-in the index, and next to each is the page number of its explanation or
-definition.
-
-In many places, I have talked of mechanical brains as if they were
-living. For example, instead of “capacity to store information” I have
-spoken of “memory.” Of course, the machines are not living; but they do
-have individuality, responsiveness, and other traits of living beings,
-just as a political party pictured as a living elephant does. Besides,
-to treat things as persons is a help in making any subject vivid and
-understandable, as every song writer and cartoonist illustrates.
-We speak of “Old Man River” and “Father Time”; we may speak of a
-ship or a locomotive as “she”; and the crew on the first Harvard
-sequence-controlled calculator has often called her “Bessy, the Bessel
-engine.”
-
-Let us pause a little longer on the subject of understanding. What
-is the understanding of something new? It is a state of knowing, a
-process of knowing more and more. The more we know about something
-new, the better we understand it. It is possible for almost anybody to
-understand almost anything, I believe. What is mainly needed in order
-to grasp an idea is a good collection of true statements about it and
-some practice in using those statements in situations. For example,
-no one has ever seen or touched the separate scraps of electricity
-called electrons. But electrons have been described and measured;
-hundreds of thousands of people work with electrons; they know and use
-true statements about electrons. In effect, these people understand
-electrons.
-
-Probably the hardest task of an author is to make his statements
-understandable yet accurate. It is too much to hope for complete
-success. I shall be very grateful to any reader who points out to me
-the statements that he has not understood or that are in error.
-
-As to the views I have expressed, I do not expect every reader to agree
-with me. In fact, I shall be glad if many a reader disagrees with
-me. For then someone else may say to both of us, “You’re both right
-and both wrong—the truth lies atwixt and atween you.” Thoughtful and
-tolerant disagreement is the finest climate for scientific progress.
-
-
-BASIC FACTS
-
-Many of the mechanical brains described in this book will do good work
-for years; but their design is already out of date. Many organizations
-are hard at work finding new tricks in electronics, materials, and
-engineering and making new mechanical brains that are better and faster.
-
-In spite of future developments, though, the basic facts about
-mechanical brains will endure. These basic facts are drawn from the
-principles of thinking, of mathematics, of science, of engineering,
-etc. These facts govern all handling of information. They do not depend
-very much on human or mechanical energy. They do not depend very much
-on signs. They do not depend very much on the century, or the language,
-or the country. For example, “II et III V sunt,” the Romans may have
-said; “deux et trois font cinq,” say the French; “2 + 3 = 5,” say the
-mathematicians; and we say, “two and three make five.” The main effort
-in this book has been to make clear the basic facts about mechanical
-brains, for they are now a masterly instrument for obtaining new
-knowledge.
-
-                                    EDMUND CALLIS BERKELEY
-
-    New York 11, N. Y.
-    _June 30, 1949_
-
-
-
-
-ACKNOWLEDGMENTS
-
-
-This book has been over seven years in the making and has evolved
-through many different plans for its contents. It springs essentially
-from the desire to see human beings use their knowledge better: we
-know enough, but how are we to use what we know? Machines that handle
-information, that make knowledge accessible, are a long step in the
-direction of using what we know.
-
-For help in causing this desire to come to fruition, I should like
-to express my indebtedness especially to Professor (then Commander,
-U.S.N.R.) Howard H. Aiken of Harvard University, whose stimulus, while
-I was stationed for ten months in 1945-46 in his laboratory, was very
-great.
-
-I should also like to express my appreciation to Mr. Harry J. Volk,
-whose vision and enthusiasm greatly encouraged me in the writing of
-this book.
-
-For careful reviews and helpful comments on the chapters dealing with
-existing mechanical brains, I am especially grateful to Dr. Franz
-L. Alt, Mr. E. G. Andrews, Professor Samuel H. Caldwell, Dr. Grace
-M. Hopper, Mr. Theodore A. Kalin, and Dr. John W. Mauchly, who are
-experts in their fields. Dr. Ruth P. Berkeley, Dr. Rudolf Flesch, Mr.
-J. Ross Macdonald, Dr. Z. I. Mosesson, Mr. Irving Rosenthal, Mr. Max
-S. Weinstein, and many others have been true friends in reading and
-commenting upon many parts of the manuscript. Mr. Frank W. Keller
-devoted much time and skill to converting my rough sketches into
-illustrations. Mr. Murray B. Ritterman has been of invaluable help in
-preparing and checking much of the bibliography. Miss Marjorie L. Black
-has helped very greatly in turning scraps of paper bearing sentences
-into an excellent manuscript for the printer.
-
-For permission to use the quotations on various pages in Chapters 11
-and 12, I am indebted to the kindness of:
-
-    E. P. Dutton & Co., for quotations from
-        _Frankenstein_, by Mary W. Shelley,
-        Everyman’s Library, No. 616.
-
-    Samuel French, for quotations from _R. U. R._,
-        by Karel Čapek.[1]
-
-    _Modern Industry_, for a quotation from the
-        issue of February 15, 1947.
-
-[1] Copyright 1923 by Doubleday, Page and Co.; all rights reserved;
-quotations reprinted by permission of Karel Čapek and Samuel French.
-
-Responsibility for the statements and opinions expressed in this book
-is solely my own. These statements and opinions do not necessarily
-represent the views of any organization with which I may be or have
-been associated. To the best of my knowledge and belief no information
-contained in this book is classified by the Department of Defense of
-the United States.
-
-    EDMUND CALLIS BERKELEY
-
-
-
-
-CONTENTS
-
-
-    1. CAN MACHINES THINK?
-          What Is a Mechanical Brain?                                1
-
-    2. LANGUAGES:
-          Systems for Handling Information                          10
-
-    3. A MACHINE THAT WILL THINK:
-          The Design of a Very Simple Mechanical Brain              22
-
-    4. COUNTING HOLES:
-          Punch-Card Calculating Machines                           42
-
-    5. MEASURING:
-          Massachusetts Institute of Technology’s Differential
-          Analyzer No. 2                                            65
-
-    6. ACCURACY TO 23 DIGITS:
-          Harvard’s IBM Automatic Sequence-Controlled Calculator    89
-
-    7. SPEED—5000 ADDITIONS A SECOND:
-          Moore School’s ENIAC (Electronic Numerical Integrator
-          and Calculator)                                          113
-
-    8. RELIABILITY—NO WRONG RESULTS:
-          Bell Laboratories’ General-Purpose Relay Calculator      128
-
-    9. REASONING:
-          The Kalin-Burkhart Logical-Truth Calculator              144
-
-    10. AN EXCURSION:
-          The Future Design of Machines That Think                 167
-
-    11. THE FUTURE:
-          Machines That Think, and What They Might Do for Men      180
-
-    12. SOCIAL CONTROL:
-           Machines That Think, and How Society May Control Them   196
-
-        SUPPLEMENTS
-           1. Words and Ideas                                      209
-           2. Mathematics                                          214
-           3. References                                           228
-
-        INDEX                                                      257
-
-
-
-
-Chapter 1
-
-CAN MACHINES THINK?
-
-WHAT IS A MECHANICAL BRAIN?
-
-
-Recently there has been a good deal of news about strange giant
-machines that can handle information with vast speed and skill. They
-calculate and they reason. Some of them are cleverer than others—able
-to do more kinds of problems. Some are extremely fast: one of them does
-5000 additions a second for hours or days, as may be needed. Where they
-apply, they find answers to problems much faster and more accurately
-than human beings can; and so they can solve problems that a man’s life
-is far too short to permit him to do. That is why they were built.
-
-These machines are similar to what a brain would be if it were made of
-hardware and wire instead of flesh and nerves. It is therefore natural
-to call these machines _mechanical brains_. Also, since their powers
-are like those of a giant, we may call them _giant brains_.
-
-Several giant mechanical brains are now at work finding out
-answers never before known. Two are in Cambridge, Mass.; one is
-at Massachusetts Institute of Technology, and one at Harvard
-University. Two are in Aberdeen, Md., at the Army’s Ballistic Research
-Laboratories. These four machines were finished in the period 1942
-to 1946 and are described in later chapters of this book. More giant
-brains are being constructed.
-
-Can we say that these machines really think? What do we mean by
-thinking, and how does the human brain think?
-
-
-HUMAN THINKING
-
-We do not know very much about the physical process of thinking in the
-human brain. If you ask a scientist how flesh and blood in a human
-brain can think, he will talk to you a little about nerves and about
-electrical and chemical changes, but he will not be able to tell you
-very much about how we add 2 and 3 and make 5. What men know about the
-way in which a human brain thinks can be put down in a few pages, and
-what men do not know would fill many libraries.
-
-Injuries to brains have shown some things of importance; for example,
-they have shown that certain parts of the brain have certain duties.
-There is a part of the brain, for instance, where sights are recorded
-and compared. If an accident damages the part of the brain where
-certain information is stored, the human being has to relearn—haltingly
-and badly—the information destroyed.
-
-We know also that thinking in the human brain is done essentially by a
-process of storing information and then referring to it, by a process
-of learning and remembering. We know that there are no little wheels
-in the brain so that a wheel standing at 2 can be turned 3 more steps
-and the result of 5 read. Instead, you and I store the information that
-2 and 3 are 5, and store it in such a way that we can give the answer
-when questioned. But we do not know the register in our brain where
-this particular piece of information is stored. Nor do we know how,
-when we are questioned, we are able automatically to pick up the nerve
-channels that lead into this register, get the answer, and report it.
-
-Since there are many nerves in the brain, about 10 billion of them, in
-fact, we are certain that the network of connecting nerves is a main
-part of the puzzle. We are therefore much interested in nerves and
-their properties.
-
-
-NERVES AND THEIR PROPERTIES
-
-A single nerve, or _nerve cell_, consists of a _cell nucleus_ and
-a _fiber_. This fiber may have a length of anything from a small
-fraction of an inch up to several feet. In the laboratory, successive
-impulses can be sent along a nerve fiber as often as 1000 a second.
-Impulses can travel along a nerve fiber in either direction at a rate
-from 3 feet to 300 feet a second. Because the speed of the impulse
-is far less than 186,000 miles a second—the speed of an electric
-current—the impulse in the nerve is thought by some investigators to be
-more chemical than electrical.
-
-We know that a nerve cell has what is called an _all-or-none response_,
-like the trigger of a gun. If you stimulate the nerve up to a certain
-point, nothing will happen; if you reach that point, or cross
-it,—bang!—the nerve responds and sends out an impulse. The strength of
-the impulse, like the shot of the gun, has no relation whatever to the
-amount of the stimulation.
-
-[Illustration: FIG. 1. Scheme of a nerve cell.]
-
-The structure between the end of one nerve and the beginning of the
-next is called a _synapse_ (see Fig. 1). No one really knows very much
-about synapses, for they are extremely small and it is not easy to tell
-where a synapse stops and other stuff begins. Impulses travel through
-synapses in from ½ to 3 thousandths of a second. An impulse travels
-through a synapse only in one direction, from the head (or _axon_) of
-one nerve fiber to the foot (or _dendrite_) of another. It seems clear
-that the activity in a synapse is chemical. When the head of a nerve
-fiber brings in an impulse to a synapse, apparently a chemical called
-_acetylcholine_ is released and may affect the foot of another fiber,
-thus transmitting the impulse; but the process and the conditions for
-it are still not well understood.
-
-It is thought that nearly all information is handled in the brain
-by groups of nerves in parallel paths. For example, the eye is
-estimated to have about 100 million nerves sensitive to light, and the
-information that they gather is reported by about 1 million nerves to
-the part of the brain that stores sights.
-
-Not much more is yet known, however, about the operation of handling
-information in a human brain. We do not yet know how the nerves are
-connected so that we can do what we do. Probably the greatest obstacle
-to knowledge is that so far we cannot observe the detailed structure of
-a living human brain while it performs, without hurting or killing it.
-
-
-BEHAVIOR THAT IS THINKING
-
-Therefore, we cannot yet tell what thinking is by observing precisely
-how a human brain does it. Instead, we have to define thinking by
-describing the kind of behavior that we call thinking. Let us consider
-some examples.
-
-When you and I add 12 and 8 and make 20, we are thinking. We use our
-minds and our understanding to count 8 places forward from 12, for
-example, and finish with 20. If we could find a dog or a horse that
-could add numbers and tell answers, we would certainly say that the
-animal could think.
-
-With no trouble a machine can do this. An ordinary 10-column adding
-machine can be given two numbers like 1,378,917,766 and 2,355,799,867
-and the instruction to add them. The machine will then give the answer,
-3,734,717,633, much faster than a man. In fact, the mechanical brain at
-Harvard can add a number of 23 digits to another number of 23 digits
-and get the right answer in ³/₁₀ of a second.
-
-Or, suppose that you are walking along a road and come to a fork. If
-you stop, read the signpost, and then choose left or right, you are
-thinking. You know beforehand where you want to go, you compare your
-destination with what the signpost says, and you decide on your route.
-This is an operation of logical choice.
-
-A machine can do this. The mechanical brain now at Aberdeen which was
-built at Bell Laboratories can examine any number that comes up in the
-process of a calculation and tell whether it is bigger than 3 (or any
-stated number) or smaller. If the number is bigger than 3, the machine
-will choose one process; if the number is smaller than 3, the machine
-will choose another process.
-
-Now suppose that we consider the basic operation of all thinking: in
-the human brain it is called learning and remembering, and in a machine
-it is called storing information and then referring to it. For example,
-suppose you want to find 305 Main Street in Kalamazoo. You look up a
-map of Kalamazoo; the map is information kindly stored by other people
-for your use. When you study the map, notice the streets and the
-numbering, and then find where the house should be, you are thinking.
-
-A machine can do this. In the Bell Laboratories’ mechanical brain, for
-example, the map could be stored as a long list of the blocks of the
-city and the streets and numbers that apply to each block. The machine
-will then hunt for the city block that contains 305 Main Street and
-report it when found.
-
-A machine can handle information; it can calculate, conclude, and
-choose; it can perform reasonable operations with information. A
-machine, therefore, can think.
-
-
-THE DEFINITION OF A MECHANICAL BRAIN
-
-Now when we speak of a machine that thinks, or a mechanical brain, what
-do we mean? Essentially, a _mechanical brain_ is a machine that handles
-information, transfers information automatically from one part of the
-machine to another, and has a flexible control over the sequence of its
-operations. No human being is needed around such a machine to pick up
-a physical piece of information produced in one part of the machine,
-personally move it to another part of the machine, and there put it in
-again. Nor is any human being needed to give the machine instructions
-from minute to minute. Instead, we can write out the whole program to
-solve a problem, translate the program into machine language, and put
-the program into the machine. Then we press the “start” button; the
-machine starts whirring; and it prints out the answers as it obtains
-them. Machines that handle information have existed for more than 2000
-years. These two properties are new, however, and make a deep break
-with the past.
-
-How should we imagine a mechanical brain? One way to think of a
-mechanical brain is shown in Fig. 2. We see here a railroad line with
-four stations, marked _input_, _storage_, _computer_, and _output_.
-These stations are joined by little gates or switches to the main
-railroad line. We can imagine that numbers and other information move
-along this railroad line, loaded in freight cars. _Input_ and _output_
-are stations where numbers or other information go in and come out,
-respectively. _Storage_ is a station where there are many platforms and
-where information can be stored. The _computer_ is a special station
-somewhat like a factory; when two numbers are loaded on platforms 1 and
-2 of this station and an order is loaded on platform 3, then another
-number is produced on platform 4.
-
-[Illustration: FIG. 2. Scheme of a mechanical brain.]
-
-We see also a tower, marked _control_. This tower runs a telegraph line
-to each of its little watchmen standing by the gates. The tower tells
-them when to open and when to shut which gates.
-
-Now we can see that, just as soon as the right gates are shut, freight
-cars of information can move between stations. Actually the freight
-cars move at the speed of electric current, thousands of miles a
-second. So, by closing the right gates each fraction of a second,
-we can flash numbers and information through the system and perform
-operations of reasoning. Thus we obtain a mechanical brain.
-
-In general, a mechanical brain is made up of:
-
-    1. A quantity of registers where information (numbers and
-       instructions) can be stored.
-
-    2. Channels along which information can be sent.
-
-    3. Mechanisms that can carry out arithmetical and logical
-       operations.
-
-    4. A control, which guides the machine to perform a sequence
-       of operations.
-
-    5. Input and output devices, whereby information can go
-       into the machine and come out of it.
-
-    6. Motors or electricity, which provide energy.
-
-
-THE KINDS OF THINKING A MECHANICAL BRAIN CAN DO
-
-There are many kinds of thinking that mechanical brains can do. Among
-other things, they can:
-
-     1. Learn what you tell them.
-     2. Apply the instructions when needed.
-     3. Read and remember numbers.
-     4. Add, subtract, multiply, divide, and round off.
-     5. Look up numbers in tables.
-     6. Look at a result, and make a choice.
-     7. Do long chains of these operations one after another.
-     8. Write out an answer.
-     9. Make sure the answer is right.
-    10. Know that one problem is finished, and turn to another.
-    11. Determine _most_ of their own instructions.
-    12. Work unattended.
-
-They do these things much better than you or I. They are fast. The
-mechanical brain built at the Moore School of Electrical Engineering at
-the University of Pennsylvania does 5000 additions a second. They are
-reliable. Even with hundreds of thousands of parts, the existing giant
-brains have worked successfully. They have remarkably few mechanical
-troubles; in fact, for one of the giant brains, a mechanical failure
-is of the order of once a month. They are powerful. The big machine
-at Harvard can remember 72 numbers each of 23 digits at one time and
-can do 3 operations with these numbers every second. The mechanical
-brains that have been finished are able to solve problems that have
-baffled men for many, many years, and they think in ways never open to
-men before. Mechanical brains have removed the limits on complexity of
-routine: the machine can carry out a complicated routine as easily as
-a simple one. Already, processes for solving problems are being worked
-out so that the mechanical brain will itself determine more than 99 per
-cent of all the routine orders that it is to carry out.
-
-But, you may ask, can they do any kind of thinking? The answer is no.
-No mechanical brain so far built can:
-
-    1. Do intuitive thinking.
-    2. Make bright guesses, and leap to conclusions.
-    3. Determine _all_ its own instructions.
-    4. Perceive complex situations outside itself and interpret them.
-
-A clever wild animal, for example, a fox, can do all these things; a
-mechanical brain, not yet. There is, however, good reason to believe
-that most, if not all, of these operations will in the future be
-performed not only by animals but also by machines. Men have only just
-begun to construct mechanical brains. All those finished are children;
-they have all been born since 1940. Soon there will be much more
-remarkable giant brains.
-
-
-WHY ARE THESE GIANT BRAINS IMPORTANT?
-
-Most of the thinking so far done by these machines is with numbers.
-They have already solved problems in airplane design, astronomy,
-physics, mathematics, engineering, and many other sciences, that
-previously could not be solved. To find the solutions of these
-problems, mathematicians would have had to work for years and years,
-using the best known methods and large staffs of human computers.
-
-These mechanical brains not only calculate, however. They also remember
-and reason, and thus they promise to solve some very important human
-problems. For example, one of these problems is the application of what
-mankind knows. It takes too long to find understandable information
-on a subject. The libraries are full of books: most of them we can
-never hope to read in our lifetime. The technical journals are full of
-condensed scientific information: they can hardly be understood by you
-and me. There is a big gap between somebody’s knowing something and
-employment of that knowledge by you or me when we need it. But these
-new mechanical brains handle information very swiftly. In a few years
-machines will probably be made that will know what is in libraries and
-that will tell very swiftly where to find certain information. Thus
-we can see that mechanical brains are one of the great new tools for
-finding out what we do not know and applying what we do know.
-
-
-
-
-Chapter 2
-
-LANGUAGES:
-
-SYSTEMS FOR HANDLING INFORMATION
-
-
-As everyone knows, it is not always easy to think. By _thinking_,
-we mean computing, reasoning, and other handling of information. By
-_information_ we mean collections of ideas—physically, collections of
-marks that have meaning. By _handling_ information, we mean proceeding
-logically from some ideas to other ideas—physically, changing from
-some marks to other marks in ways that have meaning. For example, one
-of your hands can express an idea: it can store the number 3 for a
-short while by turning 3 fingers up and 2 down. In the same way, a
-machine can express an idea: it can store information by arranging some
-equipment. The Harvard mechanical brain can store 132 numbers between
-0 and 99,999,999,999,999,999,999,999 for days. When you want to change
-the number stored by your fingers, you move them: perhaps you need a
-half second to change the number stored by your fingers from 3 to 2,
-for example. In the same way, a machine can change a stored number by
-changing the arrangement of some equipment: the electronic brain Eniac
-can change a stored number in ¹/₅₀₀₀ of a second.
-
-
-LANGUAGES
-
-Since it is not always easy to think, men have given much attention to
-devices for making thinking easier. They have worked out many _systems
-for handling information_, which we often call _languages_. Some
-languages are very complete and versatile and of great importance.
-Others cover only a narrow field—such as numbers alone—but in this
-field they may be remarkably efficient. Just what is a language?
-
-Every language is both a _scheme for expressing meanings_ and _physical
-equipment_ that can be handled. For example, let us take _spoken
-English_. The scheme of spoken English consists of more than 150,000
-words expressing meanings, and some rules for putting words together
-meaningfully. The physical equipment of spoken English consists of
-(1) sounds in the air, and (2) the ears of millions of people, and
-their mouths and voices, by which they can hear and speak the sounds
-of English. For another example, let us take numbers expressed in
-the _Arabic numerals_ and the rules of arithmetic. The scheme of
-this language contains only ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
-or their equivalents, and some rules for combining them. Sufficient
-physical equipment for this language might very well be a ten-column
-desk calculating machine with its counter wheels, gears, keys, etc. If
-we tried to exchange the physical equipment of these two languages, we
-would be blocked: the desk calculating machine cannot possibly express
-the meaningful combinations of 150,000 words, and sounds in the air
-are not permanent enough to express the steps of division of one large
-number by another.
-
-
-SCHEMES FOR EXPRESSING MEANINGS
-
-If we examine languages that have existed, we can observe a number of
-schemes for expressing meanings. In the table on pp. 12-13 is a rough
-list of a dozen of them. From among these we can choose the schemes
-that are likely to be useful in mechanical brains. Schemes 11 and 12
-are the schemes that have been predominantly used in machinery for
-computing. Scheme 12 consisting of combinations of just two marks,
-✓, ✕, provides one of the best codes for mechanical handling of
-information. This scheme, called _binary coding_ (see Supplement 2), is
-also useful for measuring the quantity of information.
-
-
-QUANTITY OF INFORMATION
-
-How should we measure the quantity of information? The smallest unit
-of information is a “yes” or a “no,” a check mark (✓) or a cross (✕),
-an impulse in a nerve or no impulse, a 1 or a 0, black or white,
-good or bad, etc. This twofold difference is called a _binary digit_
-of information (see Supplement 2). It is the convenient _unit of
-information_.
-
-
-SCHEMES FOR EXPRESSING MEANINGS
-
-                                      EXAMPLE:
-                        /————————————————^—————————————————\
-         PRINCIPLE      SIGN       USED IN      SIGNIFICANCE    NAME OF
-    NO.  OF SCHEME                                              SCHEME
-    (1)    (2)           (3)         (4)            (5)          (6)
-                                      _Sounds_
-     1. Sound of new  Bobwhite[2] Spoken        kind of quail, Imitative;
-        word is like              English         so called      bowwow
-         sound of                               from its note    theory
-         referent
-
-     2. An utterance  Pooh![2]    Spoken        The speaker     Pooh-pooh
-         becomes a                English        expresses       theory
-         new word                                 disdain
-
-     3. New word is   Chortle[2] Spoken         “Chuckle”      Analogical
-        like another             English;          and
-          word                   invented by     “snort”
-                                 Lewis Carroll,  blended
-                                    1896
-
-     4. Word has      Mother[2]  Spoken          Female        Historical
-        been used                English         parent
-        through
-        the ages
-
-                                      _Sights_
-     5. Picture       [picture   Egyptian;       Picture of  Imitative;
-        is like         of eye]   Ojibwa          eye and    pictographic
-        referent                (American        tears, to
-                                  Indian)        mean grief
-
-     6. Pattern is      5         English;       Five;      Ideographic;
-         symbol of                French;        cinq;      mathematical;
-          an idea                 German;        fünf;       symbolic;
-                                    etc.          etc.        numeric
-
-                                  _Mapping of Sounds_
-     7. Object        [picture    Possible       Picture of   Rebus-
-        pictured       of knot]    English       a knot to      writing;
-         has the                                 mean “not”  phonographic
-         wanted
-         sound
-
-     8. Pattern is    [picture    Ancient        Sign for     Syllable-
-        symbol for     of star]   Cypriote         the          writing
-         a large                (island of       syllable
-        sound unit                Cyprus)        _mu_
-
-
-     9. Pattern is      Ʒ       International     The sound    Phonetic
-        symbol for                 Phonetic       _zh_, as       writing
-         a small                 Alphabet of       _s_ in      alphabetic
-        sound unit              87 characters     “measure”      writing;
-
-                             _Mapping of Sights or Symbols_
-    10. Systematic    ENIAC     Abbreviations,    Initial     Alphabetic
-       combinations                 etc.          letters      coding
-          of 26                                    of a
-         letters                                  5-word
-                                                   title
-
-    11.  Systematic    135-03-1228  Abbreviations,  Social    Numeric
-        combinations                nomenclature,  Security   coding
-        of 10 digits                    etc.        No. of
-                                                   a person
-
-    12.  Systematic   ✓,✕,✕,✓,✓ Checking       “yes,”     Binary
-         combinations                lists,         “no,”     coding
-         of 2 marks                   etc.          “no,”
-                                                    “yes,”
-                                                    “yes,”
-                                                  respectively
-
-[2] The preceding word is the spoken word, not the written one.
-
-With 2 units of information or 2 binary digits (1 or 0) we can
-represent 4 pieces of information:
-
-    00, 01, 10, 11
-
-With 3 units of information we can represent 8 pieces of information:
-
-    000, 001, 010, 011, 100, 101, 110, 111
-
-With 4 units of information we can represent 16 pieces of information:
-
-    0000 0001 0010 0011
-    0100 0101 0110 0111
-    1000 1001 1010 1011
-    1100 1101 1110 1111
-
-Now 4 units of information are sufficient to represent a _decimal
-digit_ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and allow 6 possibilities to be
-left over; 3 units of information are not sufficient. For example, we
-may have:
-
-    0 0000      5 0101
-    1 0001      6 0110
-    2 0010      7 0111
-    3 0011      8 1000
-    4 0100      9 1001
-
-We say, therefore, that a decimal digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is
-_equivalent_ to 4 units of information. Thus a table containing 10,000
-numbers, each of 10 decimal digits, is equivalent to 400,000 units of
-information.
-
-One of the 26 letters of the alphabet is equivalent to 5 units
-of information, for, 5 binary digits (1 or 0) have 32 possible
-arrangements, and these are enough to provide for the 26 letters. Any
-printed information in English can be expressed in about 80 characters
-consisting of 10 numerals, 52 capital and small letters, and some 18
-punctuation marks and other types of marks; 6 binary digits (1 or 0)
-have 64 possible arrangements, and 7 binary digits (1 or 0) have 128
-possible arrangements. Each character in a printed book, therefore, is
-roughly equivalent to 7 units of information.
-
-It can be determined that a big telephone book or a big reference
-dictionary stores printed information at the rate of about 1 billion
-units of information per cubic foot. If the 10 billion nerves in the
-human brain could independently be impulsed or not impulsed, then the
-human brain could conceivably store 10 billion units of information.
-The largest library in the world is the Library of Congress, containing
-7 million volumes including pamphlets. It stores about 100 trillion
-units of information.
-
-We can thus see the significance of a _quantity of information_ from
-1 unit to 100 trillion units. No distinction is here made between
-information that reports facts and information that does not. For
-example, a book of fiction about persons who never existed is
-still counted as information, and, of course, much instruction and
-entertainment may be found in such a source.
-
-
-PHYSICAL EQUIPMENT FOR HANDLING INFORMATION
-
-The first thing we want to do with information is _store_ it. The
-second thing we want to do is _combine_ it. We want equipment that
-makes these two processes easy and efficient. We want equipment for
-handling information that:
-
-    1. Costs little.
-
-    2. Holds much information in little space.
-
-    3. Is _permanent_, when we want to keep the information.
-
-    4. Is _erasable_, when we want to remove information.
-
-    5. Is _versatile_, holds easily any kind of information,
-       and allows operations to be done easily.
-
-The amount of human effort needed to handle information correctly
-depends very much on the properties of the physical equipment
-expressing the information, although the laws of correct reasoning are
-independent of the equipment. For example, the great difficulty with
-spoken sounds as physical equipment for handling information is the
-trouble of storing them. The technique for doing so was mastered only
-about 1877 when Thomas A. Edison made the first phonograph. Even with
-this advance, no one can glance at a soundtrack and tell quickly what
-sounds are stored there; only by turning back the machine and listening
-to a groove can we determine this. It was not possible for the men of
-2000 B.C. to wait thousands of years for the storing of spoken sounds.
-The problem of storing information was accordingly taken to other types
-of physical equipment.
-
-
-PHYSICAL EQUIPMENT FOR HANDLING INFORMATION
-
-        PHYSICAL  ARRANGED   OPERATED OR  LOW   LITTLE PERM-  ERAS- VERS-
-    NO. OBJECTS   IN OR ON   PRODUCED BY  COST? SPACE? ANENT? ABLE? ATILE?
-    (1)   (2)      (3)          (4)        (5)   (6)    (7)    (8)   (9)
-
-                              _Mind_
-     1. Nerve     Human      Body           ✕    ✓✓    ✓     ✓   ✓✓
-        cells     brain
-
-                              _Sounds_
-     2. Sounds    Air        Voice          ✓✓  ✓✓   ✕✕   ✓✓  ✓✓
-
-     3. Sound-    Wax        Machines       ✓     ✓    ✓✓   ✕   ✓✓
-        tracks    cylinders,   and
-                  phonograph  motors
-                  records
-
-                               _Sights_
-     4. Marks     Sand       Stick          ✓     ✕     ✓   ✓✓   ✕
-
-     5. Colored   Cave       Paintbrush     ✕     ✕     ✓   ✕   ✕✕
-        painting  walls,     and paints
-                               canvases,
-                                  etc.
-
-     6. Marks,    Clay,      Stylus,        ✕✕    ✓   ✓✓   ✕✕   ✓
-       inscript-  stone      chisel
-        ions
-
-     7. Marks     Slate      Chalk          ✓      ✕   ✓    ✓✓    ✓
-
-     8. Marks     Paper,     Pen            ✓✓    ✓   ✓    ✕     ✓✓
-                  parchment, and ink,
-                   etc.      pencil
-
-     9. Letters,  Paper,     Printing       ✓✓   ✓✓  ✓✓  ✕✕   ✓✓
-         etc.     books,       press,
-                   etc.      movable
-                               type,
-                             motor,
-                              and hands
-
-    10. Photo-    Film,      Camera         ✓    ✓✓    ✓   ✕✕   ✓✓
-         graphs   prints,
-                   etc.
-
-    11. Letters,  Paper,     Typewriter     ✓    ✓✓    ✓    ✕    ✓✓
-          etc.    mimeograph    and
-                  stencil,    fingers
-                    etc.
-                                _Body_
-    12. Gestures  Space      Body           ✓    ✕     ✕✕   ✓✓  ✕✕
-
-    13. Fingers   Hands      Body           ✕    ✕     ✕✕   ✓✓  ✕✕
-
-                               _Objects_
-    14. Pebbles   Slab       Hands          ✓✓   ✓     ✓     ✓   ✕✕
-
-    15. Knots     String     Hands          ✓✓   ✓     ✓     ✓   ✕✕
-
-    16. Tallies,  Stick      Knife          ✓✓   ✓    ✓✓   ✕✕  ✕✕
-        notches
-
-    17. Beads     Rods in    Hands          ✓     ✓     ✓    ✓✓  ✕✕
-                  a frame,
-                  abacus
-
-    18. Ruled     Rulers,    Hands,         ✓     ✓     ✓    ✓    ✓
-        lines,    scales,    pressure,
-        pointers  dials       etc.
-
-                              _Machines_
-    19. Counter   Desk       Motor          ✓     ✓     ✓   ✓✓   ✓
-         wheels, calculating  and
-         gears,   machines,   hands
-         keys,  fire-control
-        lights, instruments,
-          etc.      etc.
-
-    20. Punched   Punch card Motor          ✓✓   ✓✓   ✓    ✕   ✓✓
-         cards    machinery, and
-          and     teletype,  input
-         paper      etc.    instructions
-          tape
-
-    21. Relays    Dial       Motor          ✕     ✓    ✓    ✓✓  ✓✓
-                  telephone, and
-                  other      input
-                  machinery instructions
-
-    22. Elect-    Machinery   Motor         ✓    ✓     ✓   ✓✓   ✓✓
-          ronic               and
-          tubes              input
-                             instructions
-
-    23. Magnetic  Machinery   Motor         ✓✓  ✓✓   ✓✓  ✓✓  ✓✓
-       surfaces:              and
-          wire,              input
-          tape,              instructions
-          discs
-
-    24. Delay     Machinery   Motor         ✕    ✓     ✕   ✓✓  ✓✓
-          lines:              and
-       electric,             input
-       acoustic              instructions
-
-    25. Electro-  Machinery   Motor         ✕   ✓✓    ✕  ✓✓  ✓✓
-          static              and
-        storage              input
-         tubes               instructions
-
-        ✓✓  yes, very.
-        ✓    yes, adequately.
-        ✕    not generally.
-        ✕✕  not at all.
-
-What are the types of physical equipment for handling information, and
-which are the good ones? In the table on pp. 16-17 is a rough list of
-25 types of physical equipment for handling information. ✓✓ means “yes,
-very;” ✓ means “yes, adequately;” ✕ means “not generally;” ✕✕ means
-“not at all.”
-
-For example, our _fingers_ (see No. 13) as a device for handling
-information are very expensive for most cases. They take up a good deal
-of space. Certainly they are very temporary storage; any information
-they may express is very erasable; and what we can express with them
-alone is very limited. Yet, with a _typewriter_ (see No. 11), our
-fingers become versatile and efficient. In fact, our fingers can make
-4 strokes a second; we can select any one of about 38 keys; and, since
-each key is equivalent to 5 or 6 units of information, the effective
-speed of our fingers may be about 800 units of information a second.
-
-
-LANGUAGES OF PHYSICAL OBJECTS
-
-The use of pebbles (see No. 14) for keeping track of numerical
-information is shown in the history of the words containing the
-root _calc_-of the word _calculate_. The Latin word _calcis_ meant
-pertaining to lime or limestone, and the Latin word _calculus_ derived
-from it meant first a small piece of limestone, and later any small
-stone, particularly a pebble used in counting. All three of these
-meanings have left descendants: “chalk,” “calcite,” “calcium,” relating
-in one way or another to lime; in medicine, “calculus,” referring to
-stones in the kidneys or elsewhere in the body; and in mathematics,
-“calculate,” “calculus,” referring to computations, once done with
-pebbles.
-
-The pebbles, and the slab (for which the ancient Greek word is _abax_)
-on which they were arranged and counted, were later replaced, for ease
-in handling, by groups of beads strung on rods and placed in a frame
-(see No. 17). These constituted the _abacus_ (see Supplement 2 and the
-figure there). This was the first calculating machine. It is still
-used all over Asia; in fact, even today more people use the abacus for
-accounting than use pencil and paper. The skill with which the abacus
-can be used was shown in November 1946 in a well-publicized contest
-in Japan. Kiyoshi Mastuzaki, a clerk in the Japanese communications
-department, using the abacus, challenged Private Thomas Wood of the U.
-S. Army, using a modern desk calculating machine, and defeated him in a
-speed contest involving additions, subtractions, multiplications, and
-divisions.
-
-The heaps of small pebbles, the notches in sticks, and the abacus had
-the advantage of being visible and comparatively permanent. Storing
-and reading were relatively easy. They were rather compact and easy
-to manipulate, certainly much easier than spoken words. But they were
-subject to disadvantages also. Moving correctly from one arrangement
-to another was difficult, since there was no good way for storing
-intermediate steps so that the process could be easily verified.
-Furthermore, these devices applied to specified numbers only. Also,
-there was no natural provision for recording what the several numbers
-belonged to. This had to be recorded with the help of another language,
-writing.
-
-The language of physical objects was picked up from obscurity by
-the invention of motors and the demands of commerce and business.
-Commencing in the late 1800’s, _desk calculating machines_ (see No. 19)
-were constructed to meet mass calculation requirements. They would add,
-subtract, multiply, and divide specific numbers with great accuracy
-and speed. But until recently they still were adjuncts to the other
-languages, for they provided figures one at a time for insertion in the
-spaces on the ledger pages or calculation sheets where figures were
-called for.
-
-Beginning in the 1920’s, a remarkable change has taken place. Instead
-of performing single operations, machines have been developed to
-perform chains of operations with many kinds of information. One
-of these machines is the _dial telephone_: it can select one of 7
-million telephones by successive sorting according to the letters
-and digits of a telephone number. Another of these machines is a
-_fire-control instrument_, a mechanism for controlling the firing
-of a gun. For example, in a modern anti-aircraft gun the mechanism
-will observe an enemy plane flying at several hundred miles an hour,
-convert the observations into gun-aiming directions, and determine the
-aiming directions fast enough to shoot down the plane. _Punch-card
-machinery_, machines handling information expressed as punched holes
-in cards, enable the fulfillment of social security legislation, the
-production of the census, and countless operations of banks, insurance
-companies, department stores, and factories. And, finally, in 1942 the
-first _mechanical brain_ was finished at Massachusetts Institute of
-Technology.
-
-
-THE CRUCIAL DEVICES FOR MECHANICAL BRAINS
-
-Let us consider the two modern physical devices for handling
-information which make mechanical brains possible. These are _relays_
-and _electronic tubes_ (Nos. 21 and 22). The last three kinds of
-equipment listed in the table (_magnetic surfaces_, No. 23; _delay
-lines_, No. 24; and _electrostatic storage tubes_, No. 25) were not
-included in any mechanical brains functioning by the middle of 1948.
-The discussion of them is therefore put off to Chapter 10, where we
-talk about the future design of mechanical brains.
-
-[Illustration: FIG. 1. Relay]
-
-Figure 1 shows a simple relay. There are two electrical circuits
-here. One has two terminals—Pickup and Ground. The other has three
-terminals—Common, Normally Open, and Normally Closed. When current
-flows through the coil of wire around the iron, it makes the iron
-a magnet; the magnet pulls down the flap of iron above, overcoming
-the force of the spring. When there is no current through the coil,
-the iron is not a magnet, and the flap is held up by the spring. Now
-suppose that there is current in Common. When there is no current in
-Pickup, the current from Common will flow through the upper contact, to
-the terminal marked Normally Closed. When there is current in Pickup,
-the current from Common will flow through the lower contact, to the
-terminal marked Normally Open. Thus we see that a relay expresses a
-“yes” or a “no,” a 1 or 0, a binary digit, a unit of information. A
-relay costs $5 to $10. It is rather expensive for storing a single unit
-of information. The fastest it can be changed from 1 to 0, or vice
-versa, is about ¹/₁₀₀ of a second.
-
-[Illustration: FIG. 2. Electronic tube.]
-
-Figure 2 shows a simple electronic tube. It has three parts—the
-Cathode, the Grid, and the Plate. The Grid actually is a coarse net
-of metal wires. Electrons can flow from the Cathode to the Plate,
-provided the voltage on the Grid is such as to permit them to flow.
-So we can see that an electronic tube is a very simple on-off device
-and expresses a “yes” or a “no,” a 1 or 0, a binary digit, a unit of
-information. A simple electronic tube suitable for calculating purposes
-costs 50 cents to a $1, only ⅒ the cost of a relay. It can be changed
-from 1 to 0, or back again, in 1 millionth of a second.
-
-Relays have been widely used in the mechanical brains so far built, and
-electronic tubes are the essence of Eniac.
-
-In the next chapter, we shall see how physical equipment for handling
-information can be put together to make a simple mechanical brain.
-
-
-
-
-Chapter 3
-
-A MACHINE THAT WILL THINK:
-
-THE DESIGN OF A VERY SIMPLE MECHANICAL BRAIN
-
-
-We shall now consider how we can design a very simple machine that will
-think. Let us call it Simon, because of its predecessor, Simple Simon.
-
-
-SIMON, THE VERY SIMPLE MECHANICAL BRAIN
-
-By designing Simon, we shall see how we can put together physical
-equipment for handling information in such a way as to get a very
-simple mechanical brain. At every point in the design of Simon, we
-shall make the simplest possible choice that will still give us a
-machine that: handles information, transfers information automatically
-from one part of the machine to another, and has control over the
-sequence of operations. Simon is so simple and so small, in fact, that
-it could be built to fill up less space than a grocery-store box, about
-4 cubic feet. If we know a little about electrical work, we will find
-it rather easy to make Simon.
-
-What do we do first to design the very simple mechanical brain, Simon?
-
-
-SIMON’S FLESH AND NERVES—REPRESENTING INFORMATION
-
-The first thing we have to decide about Simon is how information will
-be represented: as we put it into Simon, as it is moved around inside
-of Simon, and as it comes out of Simon. We need to decide what physical
-equipment we shall use to make Simon’s flesh and nerves. Since we are
-taking the simplest convenient solution to each problem, let us decide
-to use: _punched paper tape_ for putting information in, _relays_ (see
-Chapter 2) and wires for storing and transferring information, and
-_lights_ for putting information out.
-
-[Illustration: TWO-HOLED TAPE READER: Simon’s left ear that listens to
-numbers and operations.
-
-FOUR-HOLED TAPE READER: Simon’s right ear that listens to instructions.
-
-LIGHT BULBS: Simon’s eyes that wink answers.
-
-FIG. 1. Simon, the very simple mechanical brain.]
-
-For the equipment inside Simon, we could choose either electronic tubes
-or relays. We choose relays, although they are slower, because it is
-easier to explain circuits using relays. We can look at a relay circuit
-laid out on paper and tell how it works, just by seeing whether or not
-current will flow. Examples will be given below. When we look at a
-circuit using electronic tubes laid out on paper, we still need to know
-a good deal in order to calculate just how it will work.
-
-How will Simon perceive a number or other information by means of
-punched tape, or relays, or lights? With punched paper tape having, for
-example, 2 spaces where holes may be, Simon can be told 4 numbers—00,
-01, 10, 11. Here the binary digit 1 means a hole punched; the binary
-digit 0 means no hole punched. With 2 relays together in a register,
-Simon can remember any one of the 4 numbers 00, 01, 10, and 11. Here
-the binary digit 1 means the relay picked up or energized or closed; 0
-means the relay not picked up or not energized or open. With 2 lights,
-Simon can give as an answer any one of the 4 numbers 00, 01, 10, 11. In
-this case the binary digit 1 means the light glowing; 0 means the light
-off. (See Fig. 1.)
-
-We can say that the two lights by which Simon puts out the answer
-are his _eyes_ and say that he tells his answer by _winking_. We can
-say also that the two mechanisms for reading punched paper tape are
-Simon’s _ears_. One tape, called the _input tape_, takes in numbers
-or operations. The other tape takes in instructions and is called the
-_program tape_.
-
-
-SIMON’S MENTALITY—POSSIBLE RANGE OF INFORMATION
-
-We can say that Simon has a _mentality_ of 4. We mean not age 4 but
-just the simple fact that Simon knows only 4 numbers and can do only 4
-operations with them. But Simon can keep on doing these operations in
-all sorts of routines as long as Simon has instructions. We decide that
-Simon will know just 4 numbers, 0, 1, 2, 3, in order to keep our model
-mechanical brain very simple. Then, for any register, we need only 2
-relays; for any answer, we need only 2 lights.
-
-Any calculating machine has a _mentality_, consisting of the whole
-collection of different ideas that the machine can ever actually
-express in one way or another. For example, a 10-place desk calculating
-machine can handle numbers up to 10 decimal digits without additional
-capacity. It cannot handle bigger numbers.
-
-[Illustration: FIG. 2. Four directions.]
-
-What are the 4 _operations with numbers_ which Simon can carry out?
-Let us consider some simple operations that we can perform with just 4
-numbers. Suppose that they stood for 4 directions in the order east,
-north, west, south (see Fig. 2). Or suppose that they stood for a turn
-counterclockwise through some right angles as follows:
-
-    0: Turn through   0°, or no right angles.
-    1: Turn through  90°, or  1 right angle.
-    2: Turn through 180°, or  2 right angles.
-    3: Turn through 270°, or  3 right angles.
-
-Then we could have the operations of _addition_ and _negation_, defined
-as follows:
-
-        ADDITION           NEGATION
-    _c_ = _a_ + _b_       _c_ = -_a_
-
-     _b_: 0 1 2 3          _a_|_c_
-    _a_ +—————————        ————+————
-     0  | 0 1 2 3           0 | 0
-     1  | 1 2 3 0           1 | 3
-     2  | 2 3 0 1           2 | 2
-     3  | 3 0 1 2           3 | 1
-
-For example, the first table says, “1 plus 3 equals 0.” This means
-that, if we turn 1 right angle and then turn in the same direction 3
-more right angles, we face in exactly the same way as we did at the
-start. This statement is clearly true. For another example, the second
-table says, “2 is the negative of 2.” This means that, if we turn to
-the left 2 right angles, we face in exactly the same way as if we turn
-to the right 2 right angles, and this statement also is, of course,
-true.
-
-With only these two operations in Simon, we should probably find him a
-little too dull to tell us much. Let us, therefore, put into Simon two
-more operations. Let us choose two operations involving both numbers
-and logic: in particular, (1) finding which of two numbers is greater
-and (2) selecting. In this way we shall make Simon a little cleverer.
-
-It is easy to teach Simon how to find which of two numbers is the
-greater when all the numbers that Simon has to know are 0, 1, 2, 3. We
-put all possible cases of two numbers _a_ and _b_ into a table:
-
-     _b_: 0 1 2 3
-    _a_+—————————
-     0 |
-     1 |
-     2 |
-     3 |
-
-Then we tell Simon that we shall mark with 1 the cases where _a_ is
-greater than _b_ and mark with 0 the cases where _a_ is not greater
-than _b_:
-
-    GREATER THAN
-
-     _b_: 0 1 2 3
-    _a_+—————————
-     0 |  0 0 0 0
-     1 |  1 0 0 0
-     2 |  1 1 0 0
-     3 |  1 1 1 0
-For example, “2 is greater than 3” is false, so we put 0 in the table
-on the 2 line in the 3 column. We see that, for the 16 possible cases,
-_a_ is greater than _b_ in 6 cases and _a_ is not greater than _b_ in
-10 cases.
-
-There is a neat way of saying what we have just said, using the
-language of _mathematical logic_ (see Chapter 9 and Supplement 2).
-Suppose that we consider the statement “_a_ is greater than _b_” where
-_a_ and _b_ may be any of the numbers 0, 1, 2, 3. We can say that the
-_truth value p_ of a _statement P_ is 1 if the statement is true and
-that it is 0 if the statement is false:
-
-    _p_ = 1 if _P_ is true, 0 if _P_ is false
-
-The truth value of a statement _P_ is conveniently denoted as _T_(_P_)
-(see Supplement 2):
-
-    _p_ = _T_(_P_)
-
-Now we can say that the table for the operation _greater than_ shows
-the truth value of the statement “_a_ is greater than _b_”:
-
-    _p_ = _T_(_a_ > _b_)
-
-Let us turn now to the operation _selection_. By _selecting_ we mean
-choosing one number _a_ if some statement _P_ is true and choosing
-another number _b_ if that statement is not true. As before, let _p_
-be the truth value of that statement _P_, and let it be equal to 1 if
-_P_ is true and to 0 if _P_ is false. Then the operation of selection
-is fully expressed in the following table and logical formula (see
-Supplement 2):
-
-    SELECTION _c_ = _a_·_p_ + _b_·(1 - _p_)
-
-     _p_: 0 0 0 0  1 1 1 1
-     _b_: 0 1 2 3  0 1 2 3
-    _a_+——————————————————
-     0 |  0 1 2 3  0 0 0 0
-     1 |  0 1 2 3  1 1 1 1
-     2 |  0 1 2 3  2 2 2 2
-     3 |  0 1 2 3  3 3 3 3
-
-For example, suppose that _a_ is 2 and _b_ is 3 and the statement _P_
-is the statement “2 is greater than 0.” Since this statement is true,
-_p_ is 1, and
-
-    _a_·_p_ + _b_·(1 - _p_) = 2(1) + 3(0) = 2
-This result is the same as selecting 2 if 2 is greater than 0 and
-selecting 3 if 2 is not greater than 0.
-
-Thus we have four operations for Simon that do not overstrain his
-mentality; that is, they do not require him to go to any numbers other
-than 0, 1, 2, and 3. These four operations are: addition, negation,
-greater than, selection. We label these operations also with the
-numbers 00 to 11 as follows: addition, 00; negation, 01; greater than,
-10; selection, 11.
-
-
-SIMON’S MEMORY—STORING INFORMATION
-
-The _memory_ of a mechanical brain consists of physical equipment
-in which information can be stored. Usually, each section of the
-physical equipment which can store one piece of information is called
-a _register._ Each register in Simon will consist of 2 relays. Each
-register will hold any of 00, 01, 10, 11. The information stored in
-a register 00, 01, 10, 11 may express a number or may express an
-operation.
-
-[Illustration: S1-2 Relay energized]
-
-[Illustration: S1-1 Relay not energized
-
-FIG. 3. Register _S_1 storing 10.]
-
-How many registers will we need to put into Simon to store information?
-We shall need one register to read the input tape and to store the
-number or operation recorded on it. We shall call this register the
-_input register I_. We shall need another register to store the number
-or operation that Simon says is the answer and to give it to the output
-lights. We shall call this register the _output register O_. We shall
-need 5 registers for the part of Simon which does the computing, which
-we shall call the _computer_: we shall need 3 to store numbers put into
-the computer (_C_1, _C_2, _C_3), 1 to store the operation governing the
-computer (_C_4), and 1 to store the result (_C_5). Suppose that we
-decide to have 8 registers for storing information, so as to provide
-some flexibility for doing problems. We shall call these registers
-_storage registers_ and name them _S_1, _S_2, _S_3, ··· _S_8. Then
-Simon will have 15 registers: a memory that at one time can hold 15
-pieces of information.
-
-How will one of these registers hold information? For example, how
-will register _S_1 hold the number 2 (see Fig. 3)? The number 2 in
-machine language is 10. Register _S_1 consists of two relays, _S_1-2
-and _S_1-1. 10 stored in register _S_1 means that relay _S_1-2 will be
-energized and that relay _S_1-1 will not be energized.
-
-
-THE CONTROL OF SIMON
-
-So far we have said nothing about the control of Simon. Is he docile?
-Is he stubborn? We know what his capacity is, but we do not know how to
-tell him to do anything. How do we connect our desires to his behavior?
-How do we tell him a problem? How do we get him to solve it and tell
-us the answer? How do we arrange control over the sequence of his
-operations? For example, how do we get Simon to add 1 and 2 and tell us
-the answer 3?
-
-On the outside of Simon, we have said, there are two ears: little
-mechanisms for reading punched paper tape. Also there are two eyes
-that can wink: light bulbs that by shining or not shining can put out
-information (see Fig. 1). One of the ears—let us call it the _left
-ear_—takes in information about a particular problem: numbers and
-operations. Here the _problem tape_ or _input tape_ is listened to.
-Each line on the input tape contains space for 2 punched holes. So, the
-information on the input tape may be 00, 01, 10, or 11—either a number
-or an operation. The other ear—let us call it the _right ear_—takes in
-information about the sequence of operations, the program or routine
-to be followed. Here the _program tape_ or _routine tape_ or _control
-tape_ is listened to. Each line on the program tape contains space for
-4 punched holes. We tell Simon by _instructions_ on the program tape
-what he is to do with the information that we give him on the input
-tape. The information on the program tape, therefore, may be 0000,
-0001, 0010, ···, 1111, or any number from 0 to 15 expressed in binary
-notation (see Supplement 2).
-
-How is this accomplished? In the first place, Simon is a machine, and
-he behaves during time. He does different things from time to time.
-His behavior is organized in _cycles_. He repeats a cycle of behavior
-every second or so. In each cycle of Simon, he listens to or reads the
-input tape once and he listens to or reads the program tape twice.
-Every complete instruction that goes on the program tape tells Simon a
-register from which information is to be sent and a register in which
-information is to be received. The first time that he reads the program
-tape he gets the name of the register that is to receive certain
-information, the _receiving register_. The second time he reads the
-program tape he gets the name of the register from which information is
-to be sent, the _sending register_. He finishes each cycle of behavior
-by transferring information from the sending register to the receiving
-register.
-
-For example, suppose that we want to get an answer out of Simon’s
-computer into Simon’s output lights. We put down the instruction
-
-    Send information from _C_5 into _O_
-
-or, more briefly,
-
-    _C_5 → _O_
-
-But he does not understand this language. We must translate into
-machine language, in this case punched holes in the program tape.
-Naturally, the punched holes in the program tape must be able to
-specify any sending register and any receiving register. There are 15
-registers, and so we give them punched hole _codes_ as follows:
-
-    REGISTER     CODE             REGISTER      CODE
-      _I_        0001               _C_1        1010
-      _S_1       0010               _C_2        1011
-      _S_2       0011               _C_3        1100
-      _S_3       0100               _C_4        1101
-      _S_4       0101               _C_5        1110
-      _S_5       0110               _O_         1111
-      _S_6       0111
-      _S_7       1000
-      _S_8       1001
-
-To translate the direction of transfer of information, which we showed
-as an arrow, we put on the program tape the code for the receiving
-register first—in this case, output, _O_, 1111—and the code for the
-sending register second—in this case, _C_5, 1110. The instruction
-becomes 1111, 1110. The first time in any cycle that Simon listens with
-his right ear, he knows that what he hears is the name of the receiving
-register; and the second time that he listens, he knows that what he
-hears is the name of the sending register. One reason for this sequence
-is that any person or machine has to be prepared beforehand to absorb
-or take in any information.
-
-Now how do we tell Simon to add 1 and 2? On the input tape, we put:
-
-    Add   00
-     1    01
-     2    10
-
-On the program tape, we need to put:
-
-      _I_  →  _C_4
-      _I_  →  _C_1
-      _I_  →  _C_2
-    _C_5   →  _O_
-
-which becomes:
-
-    1101, 0001;
-    1010, 0001;
-    1011, 0001;
-    1111, 1110
-
-
-THE USEFULNESS OF SIMON
-
-Thus we can see that Simon can do such a problem as:
-
-    Add 0 and 3. Add 2 and the negative of 1.
-    Find which result is greater.
-    Select 3 if this result equals 2; otherwise select 2.
-
-To work out the coding for this and like problems would be a good
-exercise. Simon, in fact, is a rather clever little mechanical brain,
-even if he has only a mentality of 4.
-
-It may seem that a simple model of a mechanical brain like Simon
-is of no great practical use. On the contrary, Simon has the same
-use in instruction as a set of simple chemical experiments has: to
-stimulate thinking and understanding and to produce training and skill.
-A training course on mechanical brains could very well include the
-construction of a simple model mechanical brain as an exercise. In this
-book, the properties of Simon may be a good introduction to the various
-types of more complicated mechanical brains described in later chapters.
-
-The rest of this chapter is devoted to such questions as:
-
-    How do transfers of information actually take place
-      in Simon?
-
-    How does the computer in Simon work so that calculation
-      actually occurs?
-
-    How could Simon actually be constructed?
-
-What follows should be skipped unless you are interested in these
-questions and the burdensome details needed for answering them.
-
-
-SIMON’S THINKING—TRANSFERRING INFORMATION
-
-The first basic thinking operation for any mechanical brain is
-transferring information automatically. Let us see how this is done in
-Simon.
-
-[Illustration: FIG. 4. Scheme of Simon.]
-
-Let us first take a look at the scheme of Simon as a mechanical brain
-(see Fig. 4). We have 1 input, 8 storage, 5 computer, and 1 output
-registers, which are connected by means of transfer wires or a transfer
-line along which numbers or operations can travel as electrical
-impulses. This transfer line is often called the _bus_, perhaps because
-it is always busy carrying something. In Simon the bus will consist of
-2 wires, one for carrying the right-hand digit and one for carrying the
-left-hand digit of any number 00, 01, 10, 11. Simon also has a number
-of neat little devices that will do the following:
-
-    When any number goes into a register, the coils of the
-      relays of the register will be connected with the bus.
-
-    When any number goes out of a register, the contacts of
-      the relays of the register will be connected with the bus.
-
-For example, suppose that in register _C_5 the number 2 is stored. In
-machine language this is 10. That means the left-hand relay (_C_5-2) is
-energized and the right-hand relay (_C_5-1) is not energized. Suppose
-that we want to transfer this number 2 into the output register _O_,
-which has been cleared. What do we do?
-
-Let us take a look at a circuit that will transfer the number (see
-Fig. 5). First we see two relays in this circuit. They belong to the
-_C_5 register. The _C_5-2 relay is energized since it holds 1; current
-is flowing through its coil, the iron core becomes a magnet, and the
-contact above it is pulled down. The _C_5-1 relay is not energized
-since it holds 0; its contact is not pulled down. The next thing we
-see is two _rectifiers_. The sign for these is a triangle. These are
-some modern electrical equipment that allow electrical current to
-flow in only one direction. In the diagram, the direction is shown by
-the pointing of the triangle along the wire. Rectifiers are needed to
-prevent undesired circuits. Next, we see the bus, consisting of two
-wires. One carries the impulses for left-hand or 2 relays, and the
-other carries impulses for the right-hand or 1 relays. Next, we see
-two relays, called the _entrance relays_ for the _O_ register. Current
-from Source 1 may flow to these relays, energize them, and close their
-contacts. When the first line of the program tape is read, specifying
-the receiving register, the code 1111 causes Source 1 to be energized.
-This fact is shown schematically by the arrow running from the program
-tape code 1111 to Source 1. Finally, we see the coils of the two
-relays for the Output or _O_ register. We thus see that we have a
-circuit from the contacts of the _C_5 register through the bus to the
-coils of the _O_ register.
-
-[Illustration: FIG. 5. Transfer circuit.]
-
-We are now ready to transfer information when the second line of the
-program tape is read. This line holds 1110 and designates _C_5 as the
-sending register and causes Source 2 to be energized. This fact is
-shown schematically by the arrow running from the second line of the
-program tape to Source 2. When the second line is read, current flows:
-
-    1. From Source 2.
-
-    2. Through the contacts of the _C_5 register if closed.
-
-    3. Through the rectifiers.
-
-    4. Through the bus.
-
-    5. Through the entrance relay contacts of the _O_ register.
-
-    6. Through the coils of the _O_ register relays, energizing
-       such of them as match with the _C_5 closed contacts; and
-       finally
-
-    7. Into the ground.
-
-Thus relay _O_-2 is energized; it receives current because contact
-_C_5-2 is closed. And relay _O_-1 is not energized; it receives no
-current since contact _C_5-1 is open. So we have actually transferred
-information from the _C_5 register to the _O_ register.
-
-The same process in principle applies to all transfers:
-
-    The pattern of electrical impulses, formed by the positioning
-    of one register, is produced in the positioning of another
-    register.
-
-
-SIMON’S COMPUTING AND REASONING
-
-Now so far the computing registers in Simon are a mystery. We have said
-that _C_1, _C_2, and _C_3 take in numbers 00, 01, 10, 11, that _C_4
-takes in an operation 00, 01, 10, 11, and that _C_5 holds the result.
-What process does Simon use so that he has the correct result in
-register _C_5?
-
-Let us take the simplest computing operation first and see what sort of
-a circuit using relays will give us the result. The simplest computing
-operation is _negation_. In negation, a number 00, 01, 10, 11 goes into
-the _C_1 register, and the operation 01 meaning negation goes into the
-_C_4 register, and the correct result must be in the _C_5 register. So,
-first, we note the fact that the _C_4-2 relay must not be energized,
-since it contains 0, and that the _C_4-1 relay must be energized, since
-it contains 1.
-
-Now the table for negation, with _c_ =-_a_, is:
-
-    _a_ | _c_
-    ————+————
-     0  |  0
-     1  |  3
-     2  |  2
-     3  |  1
-
-Negation in machine language will be:
-
-    _a_ | _c_
-    ————+————
-     00 | 00
-     01 | 11
-     10 | 10
-     11 | 01
-
-Now if _a_ is in the _C_1 register and if _c_ is in the _C_5 register,
-then negation will be:
-
-    _C_1 | _C_5
-    —————+—————
-     00  |  00
-     01  |  11
-     10  |  10
-     11  |  01
-
-But each of these registers _C_1, _C_5 will be made up of two relays,
-the left-hand or 2 relay and the right-hand or 1 relay. So, in terms of
-these relays, negation will be:
-
-    _C_1-2 _C_1-1 | _C_5-2 _C_5-1
-    ——————————————+——————————————
-      0      0    |   0      0
-      0      1    |   1      1
-      1      0    |   1      0
-      1      1    |   0      1
-
-Now, on examining the table, we see that the _C_5-1 relay is energized
-if and only if the _C_1-1 relay is energized. So, in order to energize
-the _C_5-1 relay, all we have to do is transfer the information from
-_C_1-1 to _C_5-1. This we can do by the circuit shown in Fig. 6. (In
-this and later diagrams, we have taken one more step in streamlining
-the drawing of relay contacts: the contacts are drawn, but the coils
-that energize them are represented only by their names.)
-
-[Illustration: FIG. 6. Negation—right-hand digit.]
-
-[Illustration: FIG. 7. Negation—left-hand digit.]
-
-Taking another look at the table, we see also that the _C_5-2 relay
-must be energized if and only if:
-
-    _C_1-2     AND     _C_1-1
-     HOLDS:             HOLDS:
-       0                  1
-       1                  0
-
-A circuit that will do this is the one shown in Fig. 7. In Fig. 8 is a
-circuit that will do all the desired things together: give the right
-information to the _C_5 relay coils if and only if the _C_4 relays hold
-01.
-
-[Illustration: FIG. 8. Negation circuit.]
-
-Let us check this circuit. First, if there is any operation other than
-01 stored in the _C_4 relays, then no current will be able to get
-through the _C_4 contacts shown and into the _C_5 relay coils, and the
-result is blank. Second, if we have the operation 01 stored in the _C_4
-relays, then the _C_4-2 contacts will not be energized—a condition
-which passes current—and the _C_4-1 contacts will be energized—another
-condition which passes current—and:
-
-    IF THE NUMBER                                  AND THE _C_5 RELAYS
-     IN _C_1 IS:    THEN _C_1-1:    AND _C_1-2:      ENERGIZED ARE:
-          0        does not close  does not close     neither
-          1        closes          does not close    _C_5-2, _C_5-1
-          2        does not close  closes            _C_5-2 only
-          3        closes          closes            _C_5-1 only
-
-Thus we have shown that this circuit is correct.
-
-We see that this circuit uses more than one set of contacts for several
-relays (_C_1-2, _C_4-1, _C_4-2); relays are regularly made with 4, 6,
-or 12 sets of contacts arranged side by side, all controlled by the
-same pickup coil. These are called 4-, 6-, or 12-_pole_ relays.
-
-[Illustration: FIG. 9. Addition circuit.]
-
-[Illustration: FIG. 10. Greater-than circuit.]
-
-Circuits for _addition_, _greater than_, and _selection_ can also be
-determined rather easily (see Figs. 9, 10, 11). (_Note_: By means of
-the _algebra of logic_, referred to in Chapter 9 and Supplement 2, the
-conditions for many relay circuits, as well as the circuit itself, may
-be expressed algebraically, and the two expressions may be checked by
-a mathematical process.) For example, let us check that the addition
-circuit in Fig. 9 will enable us to add 1 and 2 and obtain 3. We take
-a colored pencil and draw closed the contacts for _C_1-1 (since _C_1
-holds 01) and for _C_2-2 (since _C_2 holds 10). Then, when we trace
-through the circuit, remembering that addition is stored as 00 in the
-_C_4 relays, we find that both the _C_5 relays are energized. Hence
-_C_5 holds 11, which is 3. Thus Simon can add 1 and 2 and make 3!
-
-[Illustration: FIG. 11. Selection Circuit.]
-
-
-PUTTING SIMON TOGETHER
-
-In order to put Simon together and make him work, not very much is
-needed. On the outside of Simon we shall need two small mechanisms for
-reading punched paper tape. Inside Simon, there will be about 50 relays
-and perhaps 100 feet of wire for connecting them. In addition to the 15
-registers (_I_, _S_1 to _S_8, _C_1 to _C_5, and _O_), we shall need a
-register of 4 relays, which we shall call the _program register_. This
-register will store the successive instructions read off the program
-tape. We can call the 4 relays of this register _P_8, _P_4, _P_2, _P_1.
-For example, if the _P_8 and _P_2 relays are energized, the register
-holds 1010, and this is the program instruction that calls for the 8th
-plus 2nd, or 10th, register, which is _C_1.
-
-For connecting receiving registers to the bus, we shall need a relay
-with 2 poles, one for the 2-line and one for the 1-line, for each
-register that can receive a number from the bus. For example, for
-entering the output register, we actually need only one 2-pole relay
-instead of the two 1-pole relays drawn for simplicity in Fig. 5. There
-will be 13 2-pole relays for this purpose, since only 13 registers
-receive numbers from the bus; registers _I_ and _C_5 do not receive
-numbers from the bus. We call these 13 relays the _entrance relays_ or
-_E relays_, since _E_ is the initial letter of the word entrance.
-
-[Illustration: FIG. 12. Select-Receiving-Register circuit.]
-
-The circuit for selecting and energizing the _E_ relays is shown in
-Fig. 12. We call this circuit the _Select-Receiving-Register_ circuit.
-For example, suppose that the _P_8 and _P_2 relays are energized. Then
-this circuit energizes the _E_10 relay. The _E_10 relay closes the
-contacts between the _C_1 relay coils and the bus; and so it connects
-the _C_1 register to receive the next number that is sent into the bus.
-This kind of circuit expresses a classification and is sometimes called
-a _pyramid circuit_ since it spreads out like a pyramid. A similar
-pyramid circuit is used to select the sending register.
-
-We shall need a relay for moving the input tape a step at a time. We
-shall call this relay the _MI relay_, for _m_oving _i_nput tape. We
-also need a relay for moving the program tape a step at a time. We
-shall call this relay the _MP relay_ for _m_oving _p_rogram tape. Here
-then is approximately the total number of relays required:
-
-          RELAYS                        NAME                NUMBER
-    _I_, _S_, _C_, _O_    Input, Storage, Computer, Output    30
-    _P_                   Program                              4
-    _E_                   Entrance                            13
-    _MI_                  Move Input Tape                      1
-    _MP_                  Move Program Tape                    1
-                                                             ————
-                              Total                           49
-
-A few more relays may be needed to provide more contacts or poles. For
-example, a single _P_1 relay will probably not have enough poles to
-meet all the need for its contacts.
-
-[Illustration: FIG. 13. Latch relay.]
-
-Each cycle of the machine will be divided into 5 equal _time intervals_
-or _times_ 1 to 5. The timing of the machine will be about as follows:
-
-    TIME                                ACTION
-     1  Move program tape. Move input tape if read out of in last
-        cycle.
-     2  Read program tape, determining the receiving register.
-        Read through the computing circuit setting up the
-        _C_5 register.
-     3  Move program tape. Energize the _E_ relay belonging
-        to the receiving register.
-     4  Read program tape again, determining the sending register.
-     5  Transfer information by reading through the
-        Select-Sending-Register circuit and the
-        Select-Receiving-Register circuit.
-
-In order that information may remain in storage until wanted, register
-relays should hold their information until just before the next
-information is received. This can be accomplished by keeping current in
-their coils or in other ways. There is a type of relay called a _latch
-relay_, which is made with two coils and a latch. This type of relay
-has the property of staying or latching in either position until the
-opposite coil is impulsed (see Fig. 13). This type of relay would be
-especially good for the registers of Simon.
-
-If any reader sets to work to construct Simon, and if questions arise,
-the author will be glad to try to answer them.
-
-
-
-
-Chapter 4
-
-COUNTING HOLES:
-
-PUNCH-CARD CALCULATING MACHINES
-
-
-When we think of counting, we usually think of saying softly to
-ourselves “one, two, three, four, ···.” This is a good way to find the
-total of a small group of objects. But when we have a large group of
-objects or a great many groups of objects to be counted, a much faster
-way of counting is needed. A very fast way of sorting and counting is
-_punch-card calculating machinery_. This is machinery which handles
-information expressed as holes in cards. _Punch-card machines_ can:
-
-    Sort, count, file, select, and copy information,
-    Make comparisons, and choose according to instructions,
-    Add, subtract, multiply, and divide,
-    List information, and print totals.
-
-For example, in a life insurance company, much routine handling of
-information about insurance policies is necessary:
-
-    Writing information on newly issued policies.
-
-    Setting up policy-history cards.
-
-    Making out notices of premiums due.
-
-    Making registers of policies in force, lapsed, died, etc.,
-      for purposes of valuation as required by law or good
-      management.
-
-    Calculating and tabulating premium rates, dividend rates,
-      reserve factors, etc.
-
-    Computing and tabulating expected and actual death rates;
-      and much more.
-
-All these operations can be done almost automatically by punch-card
-machines.
-
-
-ORIGIN AND DEVELOPMENT
-
-When a census of the people of a country is taken, a great quantity of
-sorting and counting is needed: by village, county, city, and state;
-by sex; by age; by occupation; etc. In 1886, the census of the people
-of the United States which had been taken in 1880 was still being
-sorted and counted. Among the men then studying census problems was
-a statistician and inventor, Herman Hollerith. He saw that existing
-methods were so slow that the next census (1890) would not be finished
-before the following census (1900) would have to be begun. He knew
-that cards with patterns of holes had been used in weaving patterns
-in cloth. He realized that the presence or absence of a property, for
-example employed or unemployed, could be represented by the presence
-or absence of a hole in a piece of paper. An electrical device could
-detect the hole, he believed, since it would allow current to flow
-through, whereas the absence of the hole would stop the current. He
-experimented with sorting and counting, using punched holes in cards,
-and with electrical devices to detect the holes and count them. A
-definite meaning was given to each place in the card where a hole might
-be punched. Then electrical devices handled the particular information
-that the punches represented. These devices either counted or added,
-singly or in various combinations, as might be desired.
-
-More than 50 years of development of punch-card calculating machinery
-have since then taken place. Several large companies have made
-quantities of punch-card machines. A great degree of development has
-taken place in the punch-card machines of International Business
-Machines Corporation (IBM), and for this reason these machines will
-be the ones described in this chapter. What is said here, however,
-may also in many ways apply to punch-card machines made by other
-manufacturers—Remington-Rand, Powers, Control Instrument, etc.
-
-
-GENERAL PRINCIPLES
-
-To use punch-card machines, we first convert the original information
-into patterns of holes in cards. Then we feed the cards into the
-machines. Electrical impulses read the pattern of holes and convert
-them into a pattern of timed electrical currents. Actually, the
-reading of a hole in a column of a punch card is done by a brush of
-several strands of copper wire pressed against a metal roller (Fig.
-1). The machine feeds the card (the bottom edge first, where the 9’s
-are printed) with very careful timing over the roller; and, when the
-punched hole is between the brush and the roller, an electrical circuit
-belonging to that column of the card is completed. The machine responds
-according to its general design and its wiring for the particular
-problem: it punches new cards, or it prints new marks, or it puts
-information into new storage places. Clerks, however, move the cards
-from one machine to another. They wait on the machines, keep the card
-feeds full, and empty the card hoppers as they fill up. A human error
-of putting the wrong block of cards into a machine may from time to
-time cause a little trouble, especially in sorting. Actually, in a
-year, billions of punch cards are handled precisely.
-
-[Illustration: FIG. 1. Reading of punch cards.]
-
-The _punch card_ is a masterpiece of engineering and standardization.
-Its exact thickness matches the knife-blade edges that feed the cards
-into slots in the machines, and matches the channels whereby these
-cards travel through the machines. The standard card is 7⅜ inches long
-and 3¼ inches wide, and it has a standard thickness of 0.0065 inch and
-other standard properties with respect to stiffness, finish, etc.
-
-[Illustration: FIG. 2. Scheme of standard punch card. (Note: Positions
-11 and 12 are not usually marked by printed numbers or letters.)]
-
-The standard IBM punch card of today has 80 _columns_ and 12
-_positions_ for punching in each column (Fig. 2). A single punched
-hole in each of the positions known as 0 to 9 stands for each of the
-digits 0 to 9 respectively. The remaining 2 single punch positions
-available in any column are usually called the _11 position_ and _12
-position_ (though sometimes called the numerical _X position_ and _Y
-position_). These two positions do not behave arithmetically as 11 and
-12. Actually, in the space between one card and the next card as they
-are fed through the machines, more positions occur. For example, there
-may be 4 more: a 10 position preceding the 9, and a 13, a 14, and a
-15 position following the 12. The 16 positions in total correspond to
-a full turn, 360°, of the roller under the brush, and to a complete
-_cycle_ in the machine; and a single position corresponds to ¹/₁₆ of
-360°, or 22½°. In some machines, the total number of positions may be
-20. A pair of punches stands for each of the letters of the alphabet,
-according to the scheme shown.
-
-    A    12-1        J    11-1     Unused  0-1
-    B    12-2        K    11-2        S    0-2
-    C    12-3        L    11-3        T    0-3
-    D    12-4        M    11-4        U    0-4
-    E    12-5        N    11-5        V    0-5
-    F    12-6        O    11-6        W    0-6
-    G    12-7        P    11-7        X    0-7
-    H    12-8        Q    11-8        Y    0-8
-    I    12-9        R    11-9        Z    0-9
-
-For example, the word MASON is shown punched in Fig. 3.
-
-[Illustration: FIG. 3. Alphabetic punching.]
-
-[Illustration: FIG. 4. Single-panel plugboard.]
-
-To increase the versatility of the machines and provide them with
-instructions, many of them have _plugboards_ (Fig. 4). These are
-standard interchangeable boards filled with prongs on one side and
-holes or terminals called _hubs_ on the other side. The side with the
-prongs connects to the ends of electrical circuits in the punch-card
-machine, which are brought together in one place for the purpose.
-On the other side of the board, using plugwires, we can connect the
-hubs to each other in different ways to produce different results.
-The single-panel plugboard is 10 inches long and 5¾ inches wide. It
-contains 660 hubs in front and 660 corresponding prongs in the back.
-A double-panel plugboard or a triple-panel plugboard applies to some
-machines. In less time than it takes to describe it, we can take one
-wired-up plugboard out of a machine and put in a new wired-up plugboard
-and thus change completely the instructions under which the machine
-operates. Many of the machines have a number of different switches that
-we must also change, when going from one kind of problem to another.
-
-The numbers that are stored or sorted in punch-card machines may be
-of any size up to 80 digits, one in each column of the punch card. In
-doing arithmetic (adding, subtracting, multiplying, and dividing),
-however, the largest number of digits is usually 10. Beyond 10 digits,
-we can work out tricks in many cases.
-
-
-TYPES OF PUNCH-CARD MACHINES
-
-The chief IBM punch-card machines are: the _key punch_, the _verifier_,
-the _sorter_, the _interpreter_, the _reproducer_, the _collator_, the
-_multiplying punch_, the _calculating punch_, and the _tabulator_. Of
-these 9 machines, the last 6 have plugboards and can do many different
-operations as a result.
-
-There is a flow of punch cards through each of these machines. The
-machines differ from each other in the number and relation of the
-paths of flow, or _card channels_, and in the number and relation of
-the momentary stopping places, or _card stations_, at which cards are
-read, punched, or otherwise acted on. We can get a good idea of what a
-machine is from a picture of these card channels.
-
-
-Key Punch
-
-We use a key punch (Fig. 5) to punch original information into
-blank cards. In the key punch there is one card channel; it has one
-entrance, one station, and one exit. At the card station, there are
-12 _punching dies_, one for each position in the card column, and
-each card column is presented one by one for punching. The numeric
-_keyboard_ (Fig. 6) for the key punch has 14 keys:
-
-    One key for each of the
-      punches 0 to 9, 11, and 12,
-
-    A _space key_, which allows a
-      column of the punch card to
-      go by with no punch in it,
-
-    A _release key_, which ejects the
-      card and feeds another card.
-
-[Illustration: FIG. 5. Key punch.]
-
-[Illustration: FIG. 6. Keyboard of key punch.]
-
-Of course, in using a key punch, we must punch the same kind of
-information in the same group of columns. For example, if these cards
-are to contain employees’ social security numbers, we must punch that
-number always in the same card columns, numbered, say, 15 to 23, or 70
-to 78, etc.
-
-
-Verifier
-
-The verifier is really the same machine as the key punch, but it has
-dull punching dies moving gently instead of sharp ones moving with
-force. It turns on a red light and stops when there is no punched hole
-in the right spot to match with a pressed key.
-
-
-Sorter
-
-The sorter is a machine for sorting cards, one column at a time (Fig.
-7). The sorter has a card channel that forks; it has one entrance,
-one station, and 13 exits. Each exit corresponds to: one of the 12
-punch positions 0 to 9, 11, and 12; or _reject_, which applies when the
-column is nowhere punched. It has one card station where a brush reads
-a single column of the card. We can turn a handle and move the brush to
-any column.
-
-[Illustration: FIG. 7. Sorter.]
-
-
-Interpreter
-
-The interpreter takes in a card, reads its punches, prints on the card
-the marks indicated by the punches, and stacks the card. We call this
-process _interpreting_ the card, since it translates the punched holes
-into printed marks. The interpreter (Fig. 8) has one card channel, with
-one entrance, 2 card stations, and one exit. What the machine does at
-the second card station depends on what the machine reads at the first
-card station and on what we have told the machine by switches and
-plugboard wiring to do.
-
-[Illustration: FIG. 8. Interpreter.]
-
-
-Reproducer
-
-The reproducer or reproducing punch can:
-
-    _Reproduce_, or copy the punches in one group of
-        cards into another group of cards (in the same or
-        different columns).
-
-    _Compare_, or make sure that the punches in two
-         groups of cards agree (and shine a red light if
-         they do not).
-
-    _Gang punch_, or copy the punches in a _master card_
-         into a group of _detail cards_.
-
-    _Summary punch_, or copy totals or summaries obtained
-         in the tabulator into blank cards in the reproducer.
-
-[Illustration: FIG. 9. Reproducer.]
-
-The reproducer (Fig. 9) has 2 independent card channels, the cards not
-mingling in any way, called the _reading channel_ and the _punching
-channel_. We can run the machine with only the punching channel
-working; in fact, IBM equips some models only with the punching
-channel, particularly for “summary punch” operation. The machine
-is timed so that, when any card is at the middle station in either
-channel, then the next preceding card is at the latest station, and
-the next following card is at the earliest station. At 5 stations, the
-machine reads a card. At the middle station of the punching channel,
-the machine punches a card. Using a many-wire cable, we can connect
-the tabulator to the reproducer and so cause the tabulator to give
-information electrically to the reproducer. This connection makes
-possible the “summary punch” operation. Here is an instance with
-punch-card machines where, in order to transfer information from one
-machine to another, we are not required to move cards physically from
-one machine to another.
-
-
-Collator
-
-The collator is a machine that arranges or _collates_ cards. It is
-particularly useful in selecting, matching, and merging cards. The
-collator (Fig. 10) has 2 card channels which join and then fork into 4
-channels ending in pockets called _Hoppers_ 1, 2, 3, and 4. The 2 card
-feeds are called the _Primary Feed_ and the _Secondary Feed_. Cards
-from the Primary Feed may fall only into the first and second hoppers.
-Cards from the Secondary Feed may fall only into the second, third, and
-fourth hoppers. The collator has 3 stations at which cards may be read.
-
-[Illustration: No.1--Selected primaries
-
-No.2--Merged cards and unselected primaries
-
-No.3--Separate secondaries not selected
-
-No.4--Selected secondaries
-
-FIG. 10. Collator.]
-
-IBM can supply additional wiring called the _collator counting device_.
-With this we can make the collator count cards as well as compare them.
-For example, we could put 12 blank cards from the Secondary Feed behind
-each punched-card from the Primary Feed in order to prepare for some
-other operation.
-
-
-Calculating Punch
-
-The calculating punch was introduced in 1946. It is a versatile machine
-of considerable capacity. It adds, subtracts, multiplies, and divides.
-It also has a control over a sequence of operations, in some cases up
-to half a dozen steps.
-
-This machine (Fig. 11) has one card channel with 4 stations called,
-respectively, _control brushes_, _reading brushes_, _punch feed_, and
-_punching dies_. At station 1, there are 20 brushes; we can set these
-by hand to read any 20 of the 80 card columns. At station 2 there are
-80 regular reading brushes. At station 3 the card waits for a part
-of a second while the machine calculates, and, when that is done,
-the card is fed into station 4, where it is punched or verified. The
-multiplying punch is an earlier model of the calculating punch, without
-the capacity for division.
-
-[Illustration: FIG. 11. Calculating punch.]
-
-
-Tabulator
-
-The tabulator can select and list information from cards. Also, it can
-total information from groups of cards in _counters_ of the tabulator
-and can print the totals.
-
-[Illustration: FIG. 12. Tabulator.]
-
-The tabulator (Fig. 12) has one card channel with two stations where
-cards may be read, called the _Upper Brushes_ and _Lower Brushes_.
-When the Lower Brush station is reading one card, the Upper Brush
-station is reading the next card. The tabulator also has another
-channel, which is for endless paper (and sometimes separate sheets or
-cards). This channel has one station; here printing takes place. Unlike
-the typewriter, the tabulator prints a whole row at a time. It can
-print up to 88 numerals or letters across the sheet in one stroke. The
-cards flowing through the card channel and the paper flowing through
-the paper channel do not have to move in step; in fact, we need many
-different time relations between them, and the number of rows printed
-on the paper may have almost any relation to the number of punch cards
-flowing through the card channel.
-
-At the station where paper is printed, we can put on the machine a
-mechanism called the _automatic carriage_. This is like a typewriter
-carriage, which holds the paper for a typewriter, but we can control
-the movement of paper through the automatic carriage by plugboard
-wiring, switch settings, and holes in punch cards. Thus we can arrange
-for headings, spacing, and feeding of new sheets to be controlled by
-the information and the instructions, with a great deal of versatility.
-
-
-HANDLING INFORMATION
-
-We have now described briefly the chief available punch-card machines
-as of the middle of 1948. The next question is: How do we actually get
-something done by means of punch cards? Let us go back to the census
-example, even though it may not be a very typical example, and see what
-would be done if we wished to compile a census by punch cards.
-
-The first thing we do is plan which columns of the punch card will
-contain what information about the people being counted. For example,
-the following might be part of the plan:
-
-                         NO. OF
-     INFORMATION      POSSIBILITIES   COLUMNS
-    State                    60          1- 2
-    County                1,000          3- 5
-    Township             10,000          6- 9
-    City or village      10,000         10-13
-    Sex                       2            14
-    Age last birthday       100         15-16
-    Occupation          100,000         17-21
-    ...                   ...            ...
-
-Under the heading state, we know that there are 48 states, the District
-of Columbia, and several territories and possessions—all told, perhaps
-60 possibilities. So, 2 punch-card columns are enough: they will allow
-100 different sets of punches from 00 to 99 to be put in them. We then
-assign the _code_ 00 to Maine, 01 to New Hampshire, 02 to Vermont,
-etc., or we might assign the code 00 to Alabama, 01 to Arizona, 02
-to Arkansas, etc.—whichever would be more useful. Under the other
-headings, we do the same thing: count the possibilities; assign codes.
-In this case, it will be reasonable to use numeric codes 0 to 9 in each
-column in all places because we shall have millions of cards to deal
-with and numeric codes can be sorted faster than alphabetic codes.
-Alphabetic codes require 2 punched holes in each column, and sorting
-any column takes 2 operations.
-
-The punch cards are printed with the chosen headings. We set up
-the codes in charts and give them to clerks. Using key punches and
-verifiers, they punch up the cards and check them. They work from the
-original information collected by the census-taker in the field. Since
-the original information will come in geographically, probably only one
-geographic code at a time will be needed, and it will be simple to keep
-track of. As to occupation, however, it may be useful to assign other
-clerks full-time to examining the original information and specifying
-the right code for the occupation. Then the clerks who do the punching
-will have only copying to do.
-
-The great bulk of the work with the census will be sorting, counting,
-and totaling. The original punch cards will be summarized into larger
-and larger groups. For example, the cards for all males age 23 last
-birthday living in the state of Massachusetts are sorted together. This
-group of cards may be put into a tabulator wired to a summary punch.
-When the tabulator has counted the last card of this group, the summary
-punch punches one card, showing the total number in this group. Some
-time later a card like this will be ready for every state. Then the
-whole group of state cards may be fed into the tabulator wired to the
-reproducer acting as summary punch. When totaled, the number of males
-age 23 last birthday in the United States will be punched into a single
-card. After more compiling, a card like this will be ready for all
-males in the United States at each age. Then this group of cards may
-be fed into the tabulator wired to the summary punch. Each card may
-be listed by the tabulator on the paper flowing through it, showing
-the age and the number of males living at that age. At the end of the
-listing, the tabulator will print the total number of all males in the
-list, and the summary punch will punch a card containing this total.
-
-
-ARITHMETICAL OPERATIONS
-
-Punch-card machines can perform the arithmetical operations of
-counting, adding, subtracting, multiplying, dividing, and rounding off.
-
-
-Counting
-
-Counting can be done by the sorter, the tabulator, and the collator.
-The tabulator can print the total count. The tabulator and summary
-punch wired together can put the total count automatically into another
-punch card. The sorter shows the count in dials.
-
-
-Adding and Subtracting
-
-Adding and subtracting can be done by the tabulator, the calculating
-punch, and the multiplying punch. In the calculating and multiplying
-punches, the sum or difference is usually punched into the same card
-from which the numbers were first obtained. The tabulator, however,
-obtains the result first in a counter; from the counter, it can be
-printed on paper or punched into a blank card with the aid of the
-summary punch.
-
-Numbers are handled as groups of decimal digits, and the machines
-mirror the properties of digits in the decimal system. Negative numbers
-are usually handled as _complements_ (see Supplement 2). For example,
-if we have in the tabulator a counter with a capacity of six digits,
-the number-000013 is stored in the counter as the complement 999987.
-We cannot store in the counter the number +999987, since we cannot
-distinguish it from-000013. In other words, if a counter is to be used
-for both positive and negative numbers, its capacity is actually one
-digit less, since in the last decimal place on the left 0 will mean
-positive and 9 will mean negative.
-
-
-Multiplying and Dividing
-
-Multiplying is done in the calculating and multiplying punches. In
-both cases, the multiplication table is built into the circuits of
-the machine, and the system of _left-hand components_ and _right-hand
-components_ is used (see Supplement 2).
-
-Dividing is done in the calculating punch and is carried out in that
-machine much as in ordinary arithmetic. By means of an estimating
-circuit the calculating punch guesses what multiple of the divisor will
-go into the dividend. Then it determines that multiple and tries it.
-
-
-Rounding Off
-
-Rounding off may be done in 3 punch-card machines, the calculating
-and multiplying punches, and the tabulator. For example, suppose we
-have the numbers 49.1476, 68.5327, and we wish to round them off to
-2 decimal places. The results will be 49.15 and 68.53. For the first
-number, we raise the .0076, turning .1476 into .15, since .0076 is more
-than .005. For the second number, we drop the .0027 since it is less
-than .005.
-
-Each of these punch-card machines provides what is called a _5 impulse_
-in each machine cycle. When the number is to be rounded off, the 5
-impulse is plugged into the first decimal place that is to be dropped,
-and it is there added. If the figure in the decimal place to be dropped
-is 0 to 4, the added 5 makes no difference in the last decimal place
-that is to be kept. But, if the figure in the decimal place to be
-dropped is 5 to 9, then the added 5 makes a carry into the last decimal
-place that is to be kept, increasing it by 1, and this is just what is
-wanted for rounding off.
-
-
-LOGICAL OPERATIONS
-
-Punch-card machines do many operations of reasoning or logic that do
-not involve addition, subtraction, multiplication, or division. Just
-as we can write equations for arithmetical operations, so we can write
-equations for these logical operations using mathematical logic (see
-Chapter 9 and Supplement 2). If any reader, however, is not interested
-in these logical equations, he should skip each paragraph that begins
-with “in the language of logic,” or a similar phrase.
-
-
-Translating
-
-Reading and writing are operations perhaps not strictly of reasoning
-but of _translating_ from one language to another. Basically these
-operations take in a mark in one language and give out a mark with the
-same meaning in another language. For example, the interpreter takes in
-punched holes and gives out printed marks, but the holes and the marks
-have the same meaning.
-
-The major part of sorting is done by a punch-card sorting machine and
-can be considered an operation of translating. In sorting a card, the
-machine takes in a mark in the form of a punched hole on a punch card
-and specifies a place bearing the same mark where the card is put. The
-remaining part of sorting is done by human beings. This part consists
-of picking up blocks of cards from the pockets of the sorter and
-putting the blocks together in the right sequence.
-
-
-Comparing
-
-[Illustration: FIG. 13. Comparer.]
-
-The first operation of reasoning done by punch-card machines is
-_comparing_. For an example of comparing in the operation of the
-tabulator, let us take instructing the machine when to pick up a total
-and print it. As an illustration, suppose that we are making a table
-by state, county, and township of the number of persons counted in a
-census. Suppose that for each township we have one punch card telling
-the total number of persons. If all the cards are in sequence, then,
-whenever the county changes, we want a minor total, and, whenever the
-state changes, we want a major total. What does the machine do?
-
-The tabulator has a mechanism that we shall call a _comparer_ (Fig.
-13). A comparer has 2 inputs that may be called _Previous_ and
-_Current_ and one output that may be called _Unequal_. The comparer
-has the property of giving out an impulse if and only if there is a
-difference between the 2 inputs.
-
-In the language of the algebra of logic (see Supplement 2 and Chapter
-9), let the pieces of information coming into the comparer be _a_ and
-_b_, and let the information coming out of the comparer be _p_. Then
-the equation of the comparer is:
-
-    _p_ = _T_(_a_ ≠ _b_)
-
-where “_T_ (···)” is “the truth value of ···” and “···” is a statement,
-and where the truth value is 1 if true and 0 if false.
-
-In wiring the tabulator so that it can tell when to total, we use the
-comparer. We feed into it the county from the current card and the
-county from the previous card. Out of the comparer we get an impulse if
-and only if these two pieces of information are different. This is just
-what happens when the county changes. The impulse from the comparer is
-then used in further wiring of the tabulator: it makes the counter that
-is busy totaling the number of persons in the county print its total
-and then clear. In the same way, another comparer, which watches state
-instead of county, takes care of major totals when the state changes.
-
-
-Selecting
-
-The next operation of reasoning which punch-card machines can do
-is _selecting_. The tabulator, collator, interpreter, reproducer,
-and calculating punch all may contain mechanisms that can select
-information. These mechanisms are called _selectors_.
-
-For example, suppose that we are using the tabulator to make a table
-showing for each city the number of males and the number of females.
-In the table we shall have three columns: first, city; second, males;
-third, females. Suppose that each punch card in columns 30 to 36 shows
-the total of males or females in a city. Suppose that, if and only if
-the card is for females, it has an X punch (or 11 punch) in column 79.
-What do we want to have happen? We want the number in columns 30 to 36
-to go into the second column of the table if there is no X in column
-79, and we want it to go into the third column of the table if there is
-an X in column 79. This is just another way of saying that we want the
-number to go into the males column if it is a number of males, and into
-the females column if it is a number of females. We make this happen by
-using a selector.
-
-A selector (Fig. 14) is a mechanism with 2 inputs and 2 outputs. The
-2 inputs are called _X Pickup_ and _Common_. The 2 outputs are called
-_X_ and _No X_. The X Pickup, as its name implies, watches for X’s.
-The Common takes in information. What comes out of X is what goes into
-Common if and only if an X punch is picked up; otherwise nothing comes
-out. What comes out of No X is what goes into Common if and only if an
-X punch is not picked up; otherwise nothing comes out. From the point
-of view of ordering punch-card equipment, we should note that there are
-two types of selectors: _X selectors_ or _X distributors_, which have a
-selecting capacity of one column—that is, one decimal digit—and _class
-selectors_, which ordinarily have a selecting capacity of 10 columns or
-10 decimal digits. But we shall disregard this difference here, as we
-have disregarded most other questions of capacity in multiplication,
-division, etc.
-
-[Illustration: FIG. 14. Selector.]
-
-In the language of logic (see Chapter 9 and Supplement 2), if _p_,
-_a_, _b_, _c_ are the information in X Pickup, Common, X, and No X,
-respectively, then the equations for a selector are:
-
-    _b_ = _a_·_p_
-
-    _c_ = _a_·(1 - _p_)
-
-Returning now to the table we wish to make, we connect columns 30 to
-36 of the punch card to Common. We connect column 79 of the punch card
-to the X Pickup. We connect the output No X to the males column of the
-table. We connect the output X to the females column of the table. In
-this way we make the number in the punch card appear in either one of
-two places in the table according to whether the number counts males or
-females.
-
-We might mention several more properties of selectors. A selector can
-be used in the reverse way, with X Pickup, X, and No X as inputs and
-Common as output (Fig. 15). What will come out of Common is (1) what
-goes into input No X if there is no X punch in the column to which
-input X Pickup is wired, and (2) what goes into input X if there is an
-X punch in the column to which input X Pickup is wired.
-
-In this case the logical equation for the selector is:
-
-    _a_ = _bp_ + _c_(1 - _p_)
-
-Also, selectors can be used one after another, so that selecting based
-on 2 or 3 X punches can be made.
-
-[Illustration: FIG. 15. Selector.]
-
-In the language of logic, if _p_, _q_, _r_ are the truth values of
-“there is an X punch in column _i_, _j_, _k_,” respectively, then by
-means of selectors we can get such a function as:
-
-    _c_ = _apq_ + _b_(1 - _q_)(1 - _r_)
-
-Also, a selector may often be energized not only by an X punch but
-also by a punch 0, 1, 2, ···, 9 and 12. In this case, the selector is
-equipped with an additional input that can respond to any digit. This
-input is called the Digit Pickup.
-
-
-Digit Selector
-
-Something like an ordinary selector is another mechanism called a
-_digit selector_ (Fig. 16). This has one input, Common, and 12 outputs,
-0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12. This mechanism is often included
-in the tabulator and may be included in other punch-card machines. For
-example, suppose that we want to do something if and only if column 62
-of a punch card contains a 3 or a 4 or a 9. Then we connect a brush
-that reads column 62 of the punch card to the Common input of the digit
-selector. And we connect out from the digit selector jointly from
-outputs 3, 4, and 9.
-
-[Illustration: FIG. 16. Digit selector.]
-
-In the language of logic, if _a_ is the digit going into Common, and if
-_p_ is the impulse coming out of the digit selector, then the equation
-of the mechanism in this case is:
-
-    _p_ = _T_(_a_ = 3, 4, 9)
-
-
-Sequencer
-
-A fourth operation of reasoning done by punch-card machines is finding
-that one number is greater than, or equal to, or less than another.
-This operation is done in the collator and may be called _sequencing_.
-For example, suppose that we have a file of punch cards for cities,
-showing in columns 41 to 48 the number of people. Suppose that we wish
-to pick out the cards for cities over 125,000 in population. Now the
-collator has a mechanism that has 2 inputs and 3 outputs (Fig. 17). We
-may call this mechanism a _sequencer_, since it can tell the sequence
-of two numbers. What goes into the _Primary_ input is a number: let us
-call it _a_. What goes into _Secondary_ is another number: let us call
-it _b_. An impulse comes out of _Low Primary_ if _a_ is less than _b_.
-An impulse comes out of _Equal_ if _a_ equals _b_. An impulse comes out
-of _Low Secondary_ if _a_ is greater than _b_.
-
-[Illustration: FIG. 17. Sequencer.]
-
-In the language of logic, if _p_, _q_, _r_ are the three indications in
-Low Primary, Equal, and Low Secondary, then:
-
-    _p_ = _T_(_a_ < _b_)
-
-    _q_ = _T_(_a_ = _b_)
-
-    _r_ = _T_(_a_ > _b_)
-
-Returning to our example, we punch up a card with 125,000 in columns 43
-to 48, and we put this card into the Secondary Feed. We take the punch
-cards for cities and put them into the Primary Feed. In the plugboard,
-we connect the hubs of the Secondary Brushes (that read the card in
-the Secondary Feed), columns 43 to 48, to the Secondary input of the
-Sequencer. We connect the hubs of the Primary Brushes (that read the
-card in the Primary Feed), columns 41 to 48, to the Primary input of
-the Sequencer. Then we connect the Low Primary output of the Sequencer
-to a device that causes the city card being examined to fall into
-pocket 1. We connect Equal output and Low Secondary output to a device
-that causes the city card being examined to fall into pocket 2. Then,
-when the card for any city comes along, the machine compares the number
-of people in the city with 125,000. If the number is greater than
-125,000, the card will fall into pocket 1; otherwise the card will fall
-into pocket 2. At the end of the run, we shall find in pocket 1 all the
-cards we want.
-
-
-NEW DEVELOPMENTS
-
-We may expect to see over the next few years major developments in
-punch-card machinery. It would seem likely that types of punch-card
-machines like the following might be constructed:
-
-    A punch-card machine that performs any arithmetical or
-      logical operation at high speed and may perform a dozen
-      such operations in sequence during the time that a punch
-      card passes through the machine.
-
-    A punch-card machine that uses loops of punched paper
-      tape, which express either a sequence of values in a table
-      that the machine can consult or a sequence of instructions
-      that govern the operations of the machine.
-
-    Punch-card machinery that uses a larger card than the
-      80-column card.
-
-    A punch-card machine that may have a fairly large amount
-      of internal memory, perhaps 30 or 40 registers where
-      numbers or words may be stored and referred to.
-
-
-SPEED
-
-The speed of various operations with present IBM punch-card machines is
-about as shown in the table.
-
-       MACHINE             OPERATION                     TIME IN SECONDS
-    Key punch          Punch 80 columns                   About 20 to 40
-    Verifier           Check 80 columns                   About 20 to 40
-    Sorter             Sort 1 card on 1 column                 0.15
-    Interpreter        Print 1 line                            0.8
-    Reproducer         Reproduce a card, all 80 columns        0.6
-    Collator           Merge 2 cards                           0.25
-    Multiplying punch  Multiply by 8 digits                    5.6
-    Calculating punch  Add                                     0.3
-    Calculating punch  Multiply by 8 digits                    3.6
-    Calculating punch  Divide, obtaining 8 quotient digits     9.0
-    Tabulator          Print 1 line, numbers only              0.4
-    Tabulator          Print 1 line, letters included          0.75
-    Tabulator          Add numbers from 1 card                 0.4
-
-
-COST
-
-Punch-card machines may be either rented or purchased from some
-manufacturers but only rented from others. If we take the cost of a
-clerk as $120 to $150 a month, the monthly rent of most punch-card
-machines ranges from ⅒ of the cost of a clerk for the simplest type
-of machine, such as a key punch, to 3 times the cost of a clerk for a
-complicated and versatile type of machine, such as a tabulator with
-many attachments. The rental basis is naturally convenient for many
-kinds of jobs.
-
-
-RELIABILITY
-
-The reliability of work with punch cards and punch-card machines is
-often much better than 99 per cent: in 10,000 operations, failures
-should be less than 2 or 3. This is, of course, much better than with
-clerical operations.
-
-There are a number of causes for machine or card failures. Sometimes
-cards may be warped and may not feed into the machines properly. Or,
-the air in the room may be very dry, and static electricity may make
-the cards stick together. Or, the air may be too humid; the cards may
-swell slightly and may jam in the machine. A punch may get slightly
-out of true alignment, and punches in the cards may be slightly off. A
-relay may get dust on its contact points and, from time to time, fail
-to perform in the right way. Considerable engineering effort has been
-put into remedying these and other troubles, with much success.
-
-To make sure that we have correct results from human beings working
-with punch-card machines, we may verify each process. Information
-that is punched on the key punch may be verified on the verifier.
-Multiplications done with multiplicand _a_ and multiplier _b_ may be
-repeated and compared with multiplications done with multiplicand _b_
-and multiplier _a_. Cards that are sorted on the sorter may be put
-through the collator to make sure that their sequence is correct. It
-is often good to plan every operation so that we have a proof that the
-result is right.
-
-It is standard practice to have the machines inspected regularly in
-order to keep them operating properly. On the average, for every 50 to
-75 machines, there will be one full-time service man maintaining them
-and taking care of calls for repairs. Of course, as with any machinery,
-some service calls will be a result of the human element; for example,
-a problem may have been set up wrongly on a machine.
-
-
-GENERAL USEFULNESS
-
-Punch-card calculations are much faster and more accurate than hand
-calculations. With punch cards, work is organized so that all cases
-are handled at the same time in the same way. This process is very
-different from handling each case separately from start to finish. As
-soon as the number of cases to be handled is more than a hundred and
-each item of information is to be used five or more times, punch cards
-are likely to be advantageous, provided other factors are favorable.
-Vast quantities of information have been handled very successfully by
-punch-card machines. Over 30 scientific and engineering laboratories in
-the United States are doing computation by punch cards. Over a billion
-punch cards, in fact, are used annually in this country.
-
-
-
-
-Chapter 5
-
-MEASURING:
-
-MASSACHUSETTS INSTITUTE OF TECHNOLOGY’S
-
-DIFFERENTIAL ANALYZER NO. 2
-
-
-In the previous chapter we talked about machines that move information
-expressed as holes in cards. In this chapter we shall talk about
-machines that move information expressed as measurements.
-
-
-ANALOGUE MACHINES
-
-A simple example of a device that uses a measurement to handle
-information is a doorpost. Here the height of a child may be marked
-from year to year as he grows (Fig. 1). Or, suppose that we have a
-globe of the world and wish to find the shortest path between Chicago
-and Moscow. We may lay a piece of string on the globe, pull it tight
-between those points, and then measure the string on a scale to see
-about what distance it shows (Fig. 2).
-
-Machines that handle information as measurements of physical quantities
-are called _analogue_ machines, because the measurement is _analogous_
-to, or like, the information. A common example of analogue machine
-is the _slide rule_. With this we calculate by noting the positions
-of ruled lines on strips that slide by each other. These strips are
-made of fine wood, or of plastic, or of steel, in such fashion that
-the ruled lines will hold true positions and not warp. If we space
-the rulings so that 1, 2, 3, 4, 5, 6 ··· are equally spaced, then the
-slide rule is useful for addition (Fig. 3). But if we space the rulings
-so that _powers_ (for example, powers of two—1, 2, 4, 8, 16, 32 ···)
-(Fig. 4) are equally spaced, we can do multiplication. The spacings
-are then according to the _logarithms_ of numbers (see Supplement 2).
-Multiplication is more troublesome than addition, and so more slide
-rules are made for multiplication than for addition.
-
-[Illustration: FIG. 1. Measurement by doorpost.]
-
-[Illustration: FIG. 2. Measurement by string.]
-
-[Illustration: FIG. 3. Slide Rule for adding.]
-
-[Illustration: FIG. 4. Slide Rule for multiplying.]
-
-During World War II, the aiming and firing of guns against hostile
-planes was done by machine. After sighting a plane, these machines
-automatically calculated how to direct fire against it. They were
-much better and faster than any man. These _fire-control instruments_
-were analogue machines with steel and electrical parts built to fine
-tolerances. With care we can get accuracy of 1 part in 10,000 with
-analogue machines, but greater accuracy is very hard to get.
-
-
-PHYSICAL QUANTITIES
-
-Suppose that we wish to make an analogue machine. We need to represent
-information by a measurement of something. What should we select?
-What physical thing to be measured should we choose to put into the
-machine? Different amounts of this _physical quantity_ will match with
-different amounts of the measurement being expressed. In the case of
-the doorpost, the string, and the slide rule, the physical quantity
-is distance. In many fire-control instruments, the physical quantity
-is the _amount of turning of a shaft_ (Fig. 5). Many other physical
-quantities have from time to time been used in analogue machines,
-such as electrical measurements. The speedometer of an automobile
-tells distance traveled and speed. It is an analogue machine. It uses
-the amount of turning of a wheel, and some electrical properties.
-It handles information by means of measurements. The basic physical
-quantity that it measures is the amount of turning of a shaft.
-
-[Illustration: FIG. 5. Measurement by amount of turning of a shaft.]
-
-
-DIFFERENTIAL ANALYZER
-
-The biggest and cleverest mechanical brain of the analogue type which
-has yet been built is the _differential analyzer_ finished in 1942
-at Massachusetts Institute of Technology in Cambridge, Mass. The
-fundamental physical quantity used in this machine is the amount of
-turning of a shaft. The name _analyzer_ means an apparatus or machine
-for analyzing or solving problems. It happens that the word “analyzer”
-has been used rather more often in connection with analogue machines,
-and so in many cases the word “analyzer” carries the meaning “analogue”
-as well. The word “differential” in the phrase “differential analyzer”
-refers to the main purpose of the machine: it is specially adapted for
-solving problems involving _differential equations_. Now what is a
-differential equation?
-
-
-DIFFERENTIAL EQUATIONS
-
-In order to explain what a differential equation is, we need to use
-certain ideas. These ideas are: _equation_; _formula_; _function_;
-_rate of change_; _interval_; _derivative_; and _integral_. In the
-next few paragraphs, we shall introduce these ideas briefly, with
-some explanation and examples. It is entirely possible for anyone to
-understand these ideas rather easily, by collecting true statements
-about them; no one should feel that because these ideas may be new they
-cannot be understood readily.
-
-
-PHYSICAL PROBLEMS
-
-In physics, chemistry, mechanics, and other sciences there are many
-problems in which the behavior of distance, of time, of speed, heat,
-volume, electrical current, weight, acceleration, pressure, and many
-other _physical quantities_ are related to each other. Examples of such
-problems are:
-
-[Illustration: FIG. 6. Paths of a shot from a gun, trajectories.]
-
-    What are the various angles to which a gun should be raised
-    in order that it may shoot various distances? (See Fig. 6.)
-    (The paths of a shot from a gun are called _trajectories_.)
-
-    If a plane flies in a direction always at the same angle from
-    the north, how much farther will it travel than if it flew
-    along the shortest path? (See Fig. 7.) (A path always at the same
-    angle from the north is called a _loxodrome_, and a shortest
-    path on a globe is called a _great circle_.)
-
-    How should an engine be designed so that it will have the least
-    vibration when it moves fast?
-
-In _physical problems_ like these, the answer is not a single number
-but a _formula_. What we want to do in any one of these problems is
-find a formula so that any one of the quantities may be calculated,
-given the behavior of the others. For example, here is a familiar
-problem in which the answer is a formula and not a number:
-
-[Illustration: FIG. 7. Paths of a flight.]
-
-[Illustration: FIG. 8. Room formulas.]
-
-    How are the floor area of a room, its length,
-    and its width related to each other? (See Fig. 8.)
-
-The answer is told in any one of three _equations_:
-
-
-    (_floor area_) EQUALS (_length_) TIMES (_width_)
-
-    (_length_) EQUALS (_floor area_) DIVIDED BY (_width_)
-
-    (_width_) EQUALS (_floor area_) DIVIDED BY (_length_)
-
-The first equation shows that the floor area depends on the length of
-the room and also on the width of the room. So we say floor area is a
-_function_ of length and width. This particular function happens to be
-_product_, the result of multiplication. In other words, floor area is
-equal to the product of length and width.
-
-Now there is another kind of function called a _differential function_
-or _derivative_. A _differential function_ or _derivative_ is an
-_instantaneous rate of change_. An instantaneous rate of change
-is the result of two steps: (1) finding a rate of change over an
-_interval_ and then (2) letting the interval become smaller and smaller
-indefinitely. For example, suppose that we have the problem:
-
-    How are speed, distance, and time related to each other?
-
-One of the answers is:
-
-    (_speed_) EQUALS THE INSTANTANEOUS RATE OF CHANGE OF (_distance_)
-              WITH RESPECT TO (_time_)
-
-Or we can say, and it is just the same thing in other words:
-
-    (_speed_) EQUALS THE DERIVATIVE OF (_distance_)
-              WITH RESPECT TO (_time_)
-
-Now we can tell what a differential equation is. It is simply an
-equation in which a derivative occurs, such as the last example.
-Perhaps the commonest kind of equation in physical problems is the
-differential equation.
-
-
-SOLVING PHYSICAL PROBLEMS
-
-Now we were able to change the equation about floor area into other
-forms, if we wanted to find length or width instead of floor area. When
-we did this, we ran into the _inverse_ or opposite of multiplication:
-division.
-
-In the same way, we can change the equation about speed into other
-forms, if we want to find distance or time instead of speed. If we
-do this, we run into a new idea, the inverse or opposite of the
-derivative, called _integral_. The two new equations are:
-
-    (_distance_) EQUALS THE INTEGRAL OF (_speed_)
-                 WITH RESPECT TO (_time_)
-
-    (_time_) EQUALS THE INTEGRAL OF [ONE DIVIDED BY (_speed_)]
-             WITH RESPECT TO (_distance_)
-
-These equations may also be called differential equations.
-
-An integral is the result of a process called _integrating_. To
-integrate speed and get distance is the result of three steps: (1)
-breaking up an interval of time into a large number of small bits, (2)
-adding up all the small distances that we get by taking each bit of
-time and multiplying by the speed which applied in that bit of time,
-and (3) letting the bits of time get smaller and smaller, and letting
-the number of them get larger and larger, indefinitely.
-
-In other words,
-
-    (_total distance_) EQUALS THE SUM OF ALL THE SMALL (_distances_),
-       EACH EQUAL TO: A BIT OF (_time_)
-       MULTIPLIED BY THE (_speed_) APPLYING TO THAT BIT
-
-This is another way of saying as before,
-
-    (_distance_) EQUALS THE INTEGRAL OF (_speed_)
-                 WITH RESPECT TO (_time_)
-
-To solve a differential equation, we almost always need to integrate
-one or more quantities.
-
-
-ORIGIN AND DEVELOPMENT OF THE DIFFERENTIAL ANALYZER
-
-For at least two centuries, solving differential equations to answer
-physical problems has been a main job for mathematicians. Mathematics
-is supposed to be logical, and perhaps you would think this would
-be easy. But mathematicians have been unable to solve a great many
-differential equations; only here and there, as if by accident, could
-they solve one. So they often wished for better methods in order to
-make the job easier.
-
-A British mathematician and physicist, William Thomson (Lord Kelvin),
-in 1879 suggested solving differential equations by a machine. He went
-further: he described mechanisms for integrating and other mathematical
-processes, and how these mechanisms could be connected together in a
-machine. No such machine was then built; engineering in those years
-was not equal to it. In 1923, a machine of this type for solving the
-differential equations of trajectories was proposed by L. Wainwright.
-
-In 1925, at Massachusetts Institute of Technology, the problem of a
-machine to solve differential equations was again being studied by Dr.
-Vannevar Bush and his associates. Dr. Bush experimented with mechanisms
-that would integrate, add, multiply, etc., and methods of connecting
-them together in a machine. A major part of the success of the machine
-depended on a device whereby a very small turning force would do a
-rather large amount of work. He developed a way in which the small
-turning force, about as small as a puff of breath, could be used to
-tighten a string around a drum already turning with a considerable
-force, and thus clutch the drum, bring in that force, and do the work
-that needed to be done. You may have watched a ship being loaded, seen
-a man coil a rope around a _winch_, and watched him swing a heavy load
-into the air by a slight pull on the rope (Fig. 9). If so, you have
-seen this same principle at work. The turning force (or _torque_) that
-pulls on the rope is greatly increased (or _amplified_) by such a
-mechanism, and so we call it a _torque amplifier_.
-
-[Illustration: FIG. 9. Increasing turning force; winch, or torque
-amplifier.]
-
-By 1930, Dr. Bush and his group had finished the first differential
-analyzer. It was entirely mechanical, having no electrical parts except
-the motors. It was so successful that a number of engineering schools
-and manufacturing businesses have since then built other machines of
-the Bush type. Each time, some improvements were made in accuracy and
-capacity for solving problems. But, if you changed from one problem
-to another on this type of machine, you had to do a lot of work with
-screwdrivers and wrenches. You had to undo old mechanical connections
-between shafts and set up new ones. Accordingly, in 1935, the men at
-MIT started designing a second differential analyzer. In this one you
-could make all the connections electrically.
-
-MIT finished its second differential analyzer in 1942, but the fact
-was not published during World War II, for the machine was put to work
-on important military problems. In fact, a rumor spread and was never
-denied that the machine was a white elephant and would not work. The
-machine was officially announced in October 1945. It was the most
-advanced and efficient differential analyzer ever built. We shall
-talk chiefly about it for the rest of this chapter. A good technical
-description of this machine is in a paper, “A New Type of Differential
-Analyzer,” by Vannevar Bush and Samuel H. Caldwell, published in the
-_Journal of the Franklin Institute_ for October 1945.
-
-
-GENERAL ORGANIZATION OF MIT DIFFERENTIAL ANALYZER NO. 2
-
-A differential analyzer is basically made up of shafts that turn.
-When we set up the machine to solve a differential equation, we
-assign one shaft in the machine to each quantity referred to in the
-equation. It is the job of that shaft to keep track of that quantity.
-The total amount of turning of that shaft at any time while the
-problem is running measures the size of that quantity at that time.
-If the quantity decreases, the shaft turns in the opposite direction.
-For example, if we have speed, time, and distance in a differential
-equation, we label one shaft “speed,” another shaft “time,” and another
-shaft “distance.” If we wish, we may assign 10 turns of the “time”
-shaft to mean “one second,” 2 turns of the “distance” shaft to mean
-“one foot,” and 4 turns of the “speed” shaft to mean “one foot per
-second.” These are called _scale factors_. We could, however, use any
-other convenient units that we wished.
-
-By just looking at a shaft or a wheel, we can tell what part of a
-full turn it has made—a half, or a quarter, or some other part—but we
-cannot tell by looking how many full turns it has made. In the machine,
-therefore, there are mechanisms that record not only full turns but
-also tenths of turns. These are called _counters_. We can connect a
-counter to any shaft. When we want to know some quantity that a shaft
-and counter are keeping track of, we read the counting mechanism.
-
-The second differential analyzer, which MIT finished in 1942, went a
-step further than any previous one. In this machine, a varying number
-can be expressed either (1) mechanically as the amount of turning of
-a shaft, or (2) electrically as the amount of two _voltages_ in a
-pair of wires. The MIT men did this by means of a mechanism called an
-_angle-indicator_.
-
-Angle indicators have essentially three parts: a _transmitter_, a
-_receiver_, and switches. The transmitter (Fig. 10) can sense the exact
-amount that a shaft has turned and give out a voltage in each of two
-wires which tells exactly how much the shaft has turned (Fig. 11). The
-receiving device (Fig. 12), which has a motor, can take in the voltages
-in the two wires and drive a second shaft, making it turn in step with
-the first shaft. By means of the switchboard (Fig. 13), the two wires
-from the transmitter of any angle-indicator can lead anywhere in the
-machine and be connected to the receiver of any other angle indicator.
-
-[Illustration: FIG. 10. Scheme of angle-indicator transmitter.]
-
-[Illustration: FIG. 11. Indication of angle.]
-
-[Illustration: FIG. 12. Scheme of angle-indicator receiver.]
-
-In a differential analyzer, we can connect the shafts together in many
-different ways. For example, suppose that we want one shaft _b_ to
-turn twice as much as another shaft _a_. For this to happen we must
-have a mechanism that will connect shaft _a_ to shaft _b_ and make
-shaft _b_ turn twice as much as shaft _a_. We can draw the scheme of
-this mechanism in Fig. 14: a box, standing for any kind of simple or
-complicated mechanism; a line going into it, standing for input of
-the quantity _a_; a line going out of it, standing for output of the
-quantity _b_; and a statement saying that _b_ equals 2_a_.
-
-[Illustration: FIG. 13. Switchboard.]
-
-One mechanism that will make shaft _b_ turn twice as much as shaft _a_
-is a _pair of gears_ such that: (1) they mesh together and (2) the gear
-on shaft _a_ has twice as many teeth as the gear on shaft _b_ (Fig.
-15). On the mechanical differential analyzer that MIT finished in 1930,
-a pair of gears was the mechanism actually used for doubling. To make
-one shaft turn twice as much as another by this device, we would: go
-over to the machine with a screwdriver; pick out from a box two gears,
-one with twice as many teeth as the other; slide them onto the shafts
-that are to be connected; make the gears mesh together; and screw them
-tight on their shafts.
-
-[Illustration: FIG. 14. Scheme of a doubling mechanism.]
-
-[Illustration: FIG. 15. Example of a doubling mechanism.]
-
-On the MIT differential analyzer No. 2, however, we are better off. A
-much more convenient device for doubling is used. We make use of: a
-_gearbox_ in whichthere are two shafts that may be geared so that one
-turns twice as much as the other, and two angle-indicator transmitters
-and receivers. Looking at the drawing (Fig. 16), we can see that: shaft
-_a_ drives shaft _c_ to turn in step, shaft _c_ drives shaft _d_ to
-turn twice as much, and shaft _d_ drives shaft _b_ to turn in step.
-Here we can accomplish doubling by closing the pairs of switches that
-connect to the gearbox shafts.
-
-[Illustration: Angle indicators: T, transmitters, and R, receivers
-
-FIG. 16. Another example of a doubling mechanism.]
-
-Above, we have talked about a mechanism with gears that would multiply
-the amount of turning by the _constant ratio_ 2. But, of course, in a
-calculation, any ratio, say 7.65, 3.142, ···, might be needed, not only
-2. In order to handle various constant ratios, gearboxes of two kinds
-are in differential analyzer No. 2. The first kind is a _one-digit
-gearbox_. It can be set to give any of 10 ratios, 0.1, 0.2, 0.3, ···,
-1.0. The second kind is a _four-digit gearbox_. It can be set to give
-any one of more than 11 thousand ratios, 0.0000, 0.0001, 0.0002, ···,
-1.1109, 1.1110. We can thus multiply by constant ratios.
-
-
-Adders
-
-We come now to a new mechanism, whose purpose is to add or subtract the
-amount of turning of two shafts. It is called an _adder_. The scheme
-of it is shown in Fig. 17: an input shaft with amount of turning _a_,
-another input shaft with amount of turning _b_, and an output shaft
-with amount of turning _a_ + _b_. The adder essentially is another
-kind of gearbox, called a _differential gear assembly_. This name is
-confusing: the word “differential” here has nothing to do with the
-word “differential” in “differential analyzer.” This mechanism is very
-closely related to the “differential” in the rear axle of a motor car,
-which distributes a driving thrust from the motor to the two rear
-wheels of the car.
-
-[Illustration: FIG. 17. Scheme of an adder mechanism.]
-
-[Illustration: FIG. 18. Example of an adding mechanism (differential
-gear assembly).]
-
-A type of differential gear assembly that will add is shown in Fig. 18.
-This is a set of 5 gears _A_ to _E_. The 2 gears _A_ and _B_ are input
-gears. The amount of their turning is _a_ and _b_, respectively. They
-both mesh with a third gear, _C_, free to turn, but the axis of _C_
-is fastened to the inside rim of a fourth, larger gear, _D_. Thus _D_
-is driven, and the amount of its turning is (_a_ + _b_)/2. This gear
-meshes with a gear _E_ with half the number of teeth, and so the amount
-of turning of _E_ is _a_ + _b_.
-
-We can subtract the turning of one shaft from the turning of another
-simply by turning one of the input shafts in the opposite direction.
-
-
-Integrators
-
-Another mechanism in a differential analyzer, and the one that makes
-it worth while to build the machine, is called an _integrator_. This
-mechanism carries out the process of integrating, of adding up a very
-large number of small changing quantities. Figure 19 shows what an
-integrator is. It has three chief parts: a _disc_, a little _wheel_,
-and a _screw_. The round disc turns horizontally on its vertical shaft.
-The wheel rests on the disc and turns vertically on its horizontal
-shaft. The screw goes through the support of the disc; when the screw
-turns, it changes the distance between the edge of the wheel and the
-center of the disc.
-
-[Illustration: FIG. 19. Mechanism of integrator.]
-
-Now let us watch this mechanism move. If the disc turns a little bit,
-the wheel pressing on it must turn a little bit. If the screw turns a
-small amount, the distance between the edge of the wheel and the center
-of the disc changes. The amount that the wheel turns is doubled if its
-distance from the center of the disc is doubled, and halved if that
-distance is halved. So we see that:
-
-    (_the total amount that the wheel turns_) EQUALS
-       THE SUM OF ALL THE SMALL (_amounts of turning_),
-       EACH EQUAL TO: A BIT OF (_disc turning_)
-       MULTIPLIED BY THE (_distance from the center
-       of the disc to the edge of the wheel_) APPLYING
-       TO THAT BIT
-
-If we look back at our discussion of integrating (p. 72), we see that
-the capital words here are just the same as those used there. Thus we
-have a mechanism that expresses integration:
-
-    (_the total amount that the wheel turns_) EQUALS THE INTEGRAL OF
-         (_the distance from the center of the disc to the wheel_)
-         WITH RESPECT TO (_the amount that the disc turns_)
-
-The scheme of this mechanism is shown in Fig. 20.
-
-For example, suppose that the screw measures the speed at which a car
-travels and that the disc measures time. The wheel, consequently, will
-measure distance traveled by the car. The mechanism INTEGRATES speed
-with respect to time and gives distance.
-
-[Illustration: FIG. 20. Scheme of integrator.]
-
-This mechanism is the device that Lord Kelvin talked about in 1879 and
-that Dr. Bush made practical in 1925. The mechanical difficulty is to
-make the friction between the disc and the wheel turn the wheel with
-enough force to do other work. In the second differential analyzer, the
-angle indicator set on the shaft of the wheel solves the problem very
-neatly.
-
-[Illustration: FIG. 21. Graph of air resistance coefficient.]
-
-
-Function Tables
-
-The behavior of some physical quantities can be described only by a
-series of numbers or a graphic curve. For example, the _resistance_ or
-_drag_ of the air against a passing object is related to the speed of
-the object in a rather complicated way. Part of the relation is called
-the _drag coefficient_ or _resistance coefficient_; a rough graph of
-this is shown in Fig. 21. This graph shows several interesting facts:
-(1) when the object is still, there is no air resistance; (2) as it
-travels faster and faster, air resistance rapidly increases; (3) when
-the object travels with the speed of sound, resistance is very great
-and increases enormously; (4) but, when the object starts traveling
-with a speed about 20 per cent faster than sound, the drag coefficient
-begins to decrease. This drawing or _graph_ shows in part how air
-resistance depends on speed of object; in other words, it shows the
-drag coefficient as a _function_ of speed (see Supplement 2).
-
-[Illustration: FIG. 22. Pointer following graph.]
-
-Now we need a way of putting any function we wish into a differential
-analyzer. To do this, we use a mechanism called a _function table_. We
-draw a careful graph of the function according to the scale we wish to
-use, and we set the graph on the outside of a large drum (Fig. 22).
-For example, we can put the resistance coefficient graph on the drum;
-the speed (or _independent variable_) goes around the drum, and the
-resistance coefficient (or _dependent variable_) goes along the drum.
-The machine slowly turns the drum, as may be called for by the problem.
-A girl sits at the function table and watches, turning a handwheel
-that keeps the sighting circle of a pointer right over the graph. The
-turning of the handwheel puts the graphed function into the machine.
-Instead of employing a person, we can make one side of the graph black,
-leaving the other side white, and put in a _phototube_ (an electronic
-tube sensitive to amount of light) that will steer from pure black or
-pure white to half and half (see Fig. 23).
-
-We do not need many function tables to put in information, because we
-can often use integrators in neat combinations to avoid them. We shall
-say more about this possibility later.
-
-We can also use a function table to put out information and to draw a
-graph. To do so, we disconnect the handwheel; we connect the shaft of
-the handwheel to the shaft that records the function we are interested
-in; we take out the pointer and put in a pen; and we put a blank sheet
-of graph paper around the drum.
-
-[Illustration: FIG. 23. Phototube following graph.]
-
-We have now described the main parts of the second MIT differential
-analyzer. They are the parts that handle numbers. We can now tell the
-capacity of the differential analyzer by telling the number of main
-parts that it holds:
-
-    Shafts                About 130
-    One-digit gearboxes          12
-    Four-digit gearboxes         16
-    Adders                About  16
-    Integrators                  18
-    Function tables               3
-
-On a simpler level, we can say that the machine holds these physical
-parts:
-
-    Miles of wire        About  200
-    Relays               About 3000
-    Motors               About  150
-    Electronic tubes     About 2000
-
-
-INSTRUCTING THE MIT DIFFERENTIAL ANALYZER NO. 2
-
-Besides the function tables for putting information into the machine,
-there are three mechanisms that read punched paper tape. The three
-tapes are called the _A tape_, the _B tape_, and the _C tape_. From
-these tapes the machine is set up to solve a problem.
-
-Suppose that we have decided how the machine is to solve a problem.
-Suppose that we know the number of integrators, adders, gearboxes,
-etc., that must be used, and know how their inputs and outputs are
-to be connected. To carry out the solution, we now have to put the
-instructions and numbers into the machine.
-
-The _A_ tape contains instructions for connecting shafts in the
-machine. Each instruction connects a certain output of one type
-of mechanism (adder, etc.) to a certain input of another type of
-mechanism. When the machine reads an instruction on this tape, it
-connects electrically the transmitting angle-indicator of an output
-shaft to the receiving angle-indicator of another input shaft.
-
-Now the connecting part of the differential analyzer behaves as if
-it were very intelligent: it assigns an adder or an integrator or a
-gearbox, etc., to a new problem only if that mechanism is not busy. For
-example, if a problem tape calls for adder 3 (in the list belonging to
-the problem), the machine will assign the first adder that is not busy,
-perhaps adder 14 (in the machine), to do the work. Each time that adder
-3 (in the problem list) is called for in the _A_ tape, the machine
-remembers that adder 14 was chosen and assigns it over again. This
-ability, of course, is very useful.
-
-The _B_ tape contains the ratios at which the gearboxes are to be set.
-For example, suppose that we want gearbox 4 (in the problem list) to
-change its input by the ratio of 0.2573. The machine, after reading the
-_A_ tape, has assigned gearbox 11 (in the machine list). Then, when the
-machine reads the _B_ tape, it sets the ratio in gearbox 11 to 0.2573.
-
-The answer to a differential equation is different for different
-starting conditions. For example, when we know speed and time and wish
-to find distance traveled and where we have arrived, we must know the
-point at which we started. We therefore need to arrange the machine so
-that we can put in different starting conditions (or different _initial
-conditions_, as the mathematician calls them).
-
-The _C_ tape puts the initial conditions into the machine. For example,
-reading the _C_ tape for the problem, the machine finds that 3000
-should, at the start of the problem, stand in counter 4. The machine
-then reads the number at which counter 4 actually stands, say 6728.3.
-It subtracts the two numbers and remembers the difference, -3728.3.
-And whenever the machine reads that counter later, finding, say, 9468.4
-in it, first the 3728.3 is subtracted, and then the answer 5740.1 is
-printed.
-
-
-ANSWERS
-
-Information may come out of the machine in either one of two ways: in
-printed numbers or in a graph. In fact, the same quantity may come out
-of the machine in both ways at the same time. To obtain a graph, we
-change a function table from input to output, put a pen on it, and have
-it draw the graph.
-
-The machine has 3 electric typewriters. The machine will take numerical
-information out of the counters at high speed even while they are
-turning, and it will put the information into relays. Then it will read
-from the relays into the typewriter keys one by one while they type
-from left to right across the page.
-
-
-HOW THE DIFFERENTIAL ANALYZER CALCULATES
-
-Up to this point in this chapter, the author has tried to tell the
-story of the differential analyzer in plain words. But for reading
-this section, a little knowledge of calculus is necessary. (See also
-Supplement 2.) If you wish, skip this section, and go on to the next
-one.
-
-We have described how varying quantities, or _variables_, are operated
-on in the machine in one way or another: adding, subtracting,
-multiplying by a constant, referring to a table, and integrating. What
-do we do if we wish to multiply 2 variables together? A neat trick is
-to use the formula:
-
-    _xy_ = ⌠_x dy_ + ⌠_y dx_
-           ⌡         ⌡
-
-To multiply in this way requires 2 integrators and 1 adder. The
-connections that are made between them are as follows:
-
-    Shaft _x_           To Integrator 1, Screw
-    Shaft _x_           To Integrator 2, Disc
-    Shaft _y_           To Integrator 1, Disc
-    Shaft _y_           To Integrator 2, Screw
-    Integrator 1, Wheel      To Adder 1, Input 1
-    Integrator 2, Wheel      To Adder 1, Input 2
-    Adder 1, Output          To Shaft expressing _xy_
-
-A product of 2 variables _under the integral sign_ can be obtained a
-little more easily, because of the curious powers of the differential
-analyzer. Thus, if it is desired to obtain ∫_xy dt_, we can use the
-formula:
-
-                      ┌          ┐
-    ⌠           ⌠     │ ⌠        │
-    │_xy dt_ =  │_x d_│ │ _y dt_ │
-    ⌡           ⌡     │ ⌡        │
-                      └          ┘
-
-and this operation does not require an adder. The connections are as
-follows:
-
-    Shaft _t_               To Integrator 1, Disc
-    Shaft _y_               To Integrator 1, Screw
-    Integrator 1, Wheel          To Integrator 2, Disc
-    Shaft _x_               To Integrator 2, Screw
-    Integrator 2, Wheel     To Shaft expressing ∫_xy dt_
-
-In order to get the quotient of 2 variables, _x_/_y_, we can use some
-more tricks. First, the _reciprocal_ 1/_y_ can be obtained by using the
-two _simultaneous equations_:
-
-    ⌠   1                  ⌠     1
-    │ ———— _dy_ = log _y_, │ - ———— _d_(log _y_) = _y_
-    ⌡  _y_                 ⌡    _y_
-
-The connections are as follows:
-
-    Shaft _y_       To Integrator 1, Disc AND TO Integrator 2, Wheel
-    Shaft log _y_   To Integrator 1, Wheel AND TO Integrator 2, Disc
-    Shaft 1/_y_     To Integrator 1, Screw, AND NEGATIVELY
-                                            TO Integrator 2, Screw
-
-In order to get _x_/_y_, we can then multiply _x_ by 1/_y_. We see that
-this setup gives us log _y_ for nothing, that is, without needing more
-integrators or other equipment. Clearly, other tricks like this will
-give sin _x_, cos _x_, _eˣ_, _x²_, and other functions that satisfy
-simple differential equations.
-
-An integral of a reciprocal can be obtained even more directly. Suppose
-that
-
-          ⌠   1
-    _y_ = │ ————— _dt_
-          ⌡  _x_
-
-                  1
-    Then _Dₜy_ = —————, _D{_y} t_ = _x_,
-                 _x_
-
-              ⌠
-    and _t_ = │_x dy_
-              ⌡
-
-The connections therefore are:
-
-    Shaft _t_   To Integrator, Wheel
-    Shaft _x_   To Integrator, Screw
-    Shaft _y_   To Integrator, Disc
-
-The light wheel then drives the heavy disc. Clearly only the
-angle-indicator device makes this possible at all. Naturally, the
-closer the wheel gets to the center of the disc, that is, _x_
-approaching zero, the greater the strain on the mechanism, and the more
-likely the result is to be off. Mathematically, of course, the limit of
-1/_x_ as _x_ approaches zero equals infinity, and this gives trouble in
-the machine.
-
-There is no standard mathematical method for solving any differential
-equation. But the machine provides a standard direct method for
-solving all differential equations with only one independent variable.
-First: assign a shaft for each _term_ that appears in the equation.
-For example, the highest derivative that appears and the independent
-variable are both assigned shafts. The integral of the highest
-derivative is easily obtained, and the integral of that integral, etc.
-Second: connect the shafts so that all the mathematical relations are
-expressed. Both _explicit_ and _implicit_ equations may be expressed.
-Third: for any shaft there must be just one _drive_, or source of
-torque. A shaft may, however, drive more than one other shaft. Fourth:
-choose _scale factors_ so that the limits of the machine are not
-exceeded yet at the same time are well used. For example, the most
-that an integrator or a function table can move is 1 or 2 feet. Also,
-the number of full turns made by a shaft in representing its variable
-should be large, often between 1000 and 10,000.
-
-Of course, as with all these large machines, anyone would need some
-months of actual practice before he could put on a problem and get an
-answer efficiently.
-
-
-AN APPRAISAL OF THE MACHINE
-
-The second MIT differential analyzer is probably the best machine
-ever built for solving most differential equations. It regularly has
-an accuracy of 1 part in 10,000. This is enough for most engineering
-problems. If greater accuracy is needed, the second differential
-analyzer cannot provide it. Once in a while the machine can reach an
-accuracy of 1 part in 50,000; but, to balance this, it is sometimes
-less accurate than 1 part in 10,000.
-
-The MIT differential analyzer No. 2 can find answers to problems very
-quickly. The time for setting up a problem to be run on the machine
-ranges from 5 to 15 minutes. The time for preparing the tapes that
-set up the problem is, of course, longer; but the punch for preparing
-the tape is a separate machine and does not delay the differential
-analyzer. The time for the machine to produce a single solution to a
-problem ranges usually from 3 minutes to a half-hour. It is easy to
-put on a problem, run a few solutions, take the problem off, study the
-results, change a few numbers, and then put the problem back on again.
-This virtue is a great help in a search in a new field. While the study
-is going on, time is not wasted, for the machine can be busy with a
-different problem.
-
-Running a problem a second time is a good check on the reliability of
-an answer. For, when the problem is run the second time, we can arrange
-that the machine will route the problem to other mechanisms.
-
-The machine has a control panel. Here the operator watching the machine
-can tell what units are doing what parts of what problems. If a unit
-gives trouble or needs to be inspected, the clerk can throw a “busy”
-switch. Then the machine cannot choose that unit for work to be done.
-The machine contains many protecting signals and alarms. It is idle for
-repairs less than 5 per cent of the time.
-
-It is not easy to determine the total cost of the machine, for it was
-partially financed by several large gifts. Also, much of the labor
-was done by graduate students in return for the instruction that they
-gained. The actual out-of-pocket cost was about $125,000. If the
-machine were to be built by industry, the cost would likely be more
-than 4 times as much. A simple differential analyzer, however, can be
-cheap. Small scale differential analyzers have been built for less than
-$1000; their accuracy has been about 1 part in 100.
-
-There are many things that this machine cannot do; it was not built
-to do them. (1) It cannot choose methods of solution. (2) It cannot
-perform steps in solving a problem that depend on results as they
-are found. (3) It cannot solve differential equations containing two
-or more independent variables. Such equations are called _partial
-differential equations_; they appear in connection with the flow of
-heat or air or electricity in 2 or 3 dimensions, and elsewhere. (4)
-It cannot solve problems requiring 6 or more digits of accuracy. (5)
-The machine, while running, can store numbers only for an instant,
-since it operates on the principle of smoothly changing quantities;
-however, when the machine stops, the number last held by each device is
-permanently stored.
-
-None of these comments, however, are criticisms of the machine.
-Instead they show avenues of development for future machines. As was
-said before, for solving most differential equations, this machine
-has no equal to date. The range of problems which any differential
-analyzer can do depends mostly on the number of its integrators. The
-second differential analyzer has 18 and provides for expansion to 30.
-The machine is constructed, also, so that it can be operated in 3
-independent sections, each working to solve a different problem. The
-differential analyzer can operate unattended. After it has been set up
-and the first few results examined, it can be left alone to grind out
-large blocks of answers.
-
-An interesting example of the experimental use of a differential
-analyzer in a commercial business is the following: In Great Britain,
-R. E. Beard of the Pearl Assurance Company built a differential
-analyzer with 6 integrators. He applied this machine to compute to 3
-figures certain insurance values known as _continuous annuities_ and
-_continuous contingent insurances_. He has described the machine and
-the application he made in a paper published in the _Journal of the
-Institute of Actuaries_, Vol. 71, 1942, pp. 193-227.
-
-
-
-
-Chapter 6
-
-ACCURACY TO 23 DIGITS:
-
-HARVARD’S IBM AUTOMATIC
-
-SEQUENCE-CONTROLLED CALCULATOR
-
-
-One of the first giant brains to be finished was the machine in the
-Computation Laboratory at Harvard University called the _IBM Automatic
-Sequence-Controlled Calculator_. This great mechanical brain started
-work in April 1944 and has been running 24 hours a day almost all the
-time ever since. It has produced quantities of information for the
-United States Navy. Although many problems that have been placed on it
-have been classified by the Navy as confidential, the machine itself
-is fully public. The way it was working on Sept. 1, 1945, has been
-thoroughly described in a 540-page book published in 1946, Volume I of
-the Annals of the Harvard Computation Laboratory, entitled _Manual of
-Operation of the Automatic Sequence-Controlled Calculator_. Since then
-the machine has been improved in many ways.
-
-This machine does thousands of calculating steps, one after another,
-according to a scheme fixed ahead of time. This property is what gives
-the machine its name: _automatic_, since the individual operations are
-automatic, once the punched tape fixing the chain of operations has
-been put on the machine, and _sequence-controlled_, since control over
-the sequence of its operations has been built into the machine.
-
-
-ORIGIN AND DEVELOPMENT
-
-More than a hundred years ago, an English mathematician and actuary,
-Charles Babbage (1792-1871), designed a machine—or _engine_ as
-he called it—that would carry out the sequences of mathematical
-operations. In the 1830’s he received a government grant to build
-an _analytical engine_ whereby long chains of calculations could be
-performed. But he was unsuccessful, because the refined physical
-devices necessary for quantities of digital calculation were not
-yet developed. Only in the 1930’s did these physical devices become
-sufficiently versatile and reliable for a calculator of hundreds of
-thousands of parts to be successful.
-
-The Automatic Sequence-Controlled Calculator at Harvard was largely the
-concept of Professor Howard H. Aiken of Harvard. It was built through
-a partnership of efforts, ideas, and engineering between him and the
-International Business Machines Corporation, in the years 1937 to
-1944. The calculator was a gift from IBM to Harvard University. Some
-very useful additional control units, named the _Subsidiary Sequence
-Mechanism_, were built at the Harvard Computation Laboratory in 1947
-and joined to the machine.
-
-[Illustration: FIG. 1. Scheme of Harvard IBM Automatic
-Sequence-Controlled Calculator.]
-
-
-GENERAL ORGANIZATION
-
-The machine (see Fig. 1) is about 50 feet long, 8 feet high, and about
-2 feet wide. It consists of 22 panels; 17 of them are set in a straight
-line, and the last 5 are at the rear of the machine. In the scheme of
-the machine shown in Fig. 1, the details you would see in a photograph
-have been left out. Instead you see the sections of the machine that
-are important because of what they do: _input_, _memory_, _control_,
-and _output_. Why do we not see a section labeled “computer”? Because
-in this mechanical brain the computing part of the machine is closely
-joined to the memory: every storage register can add and subtract. We
-shall soon discuss these sections of the machine more fully.
-
-
-PHYSICAL DEVICES
-
-Now in order for any brain to work, _physical devices_ must be used.
-For example, in the human body, a nerve is the physical device that
-carries information from one part of the body to another. In the
-Harvard machine, an insulated _wire_ is the physical device that
-carries information from one part of the machine to another. One side
-of every panel in the Harvard machine is heavily laden with a great
-network of wires. Between the panels, you can see in many places cables
-as thick as your arm and containing hundreds of wires. More than 500
-miles of wire are used.
-
-The physical devices in the Harvard machine are numerous, as we would
-expect. It is perhaps not surprising that this machine has more than
-760,000 parts. But, curiously enough, there are only 7 main kinds of
-physical devices in the major part of the machine. They are: wire,
-_two-position switches_, _two-position relays_ (see Chapter 2),
-_ten-position switches_, _ten-position relays_, _buttons_, and _cam
-contacts_ (see below). These are the devices that handle information
-in the form of electrical impulses. They can be combined by electrical
-circuits in a great variety of ways. There are, of course, other kinds
-of physical devices that are important, but they are not numerous,
-and they have rather simple duties. Looking at the machine, you can
-see three examples easily. Physical devices of the first kind convert
-punched holes into electrical impulses: 2 _card feeds_, 4 _tape feeds_.
-Those of the second kind convert electrical impulses into punched
-holes: 1 _card punch_, 1 _tape punch_. Those of the third kind convert
-electrical impulses into printed characters: 2 _electric typewriters_.
-We can think of a fourth kind of physical device that would be a help,
-but, at present writing, it does not yet exist: a device that converts
-printed characters into electrical impulses.
-
-The Harvard machine, of course, is complicated. But it is complicated
-because of the variety of ways in which relatively simple devices have
-been connected together to make a machine that thinks.
-
-
-Switches
-
-A _two-position switch_ (see Fig. 2) turned by hand connects a wire to
-either one of 2 others. These 2 positions may stand for “yes” and “no,”
-0 and 1, etc. There are many two-position switches in the machine. A
-_ten-position switch_ or _dial switch_ (see Fig. 3) turned by hand
-connects the wire running into the center of the switch with a wire at
-any one of ten positions 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 around the edge.
-There are over 1400 dial switches in the machine. How does turning the
-pointer on the top of the dial make connection between the center wire
-and the edge wire? Under the face of the dial is the part that works, a
-short rod of metal fastened to the pointer (shown with dashes in Fig.
-3). When the pointer turns, this rod also turns, making the desired
-connection.
-
-[Illustration: FIG. 2. Two-position switch.]
-
-[Illustration: FIG. 3. Dial switch.]
-
-
-Relays
-
-_Two-position relays_—more often called just _relays_ (see Chapter
-2)—do the automatic routing of the electrical impulses that cause
-computing to take place. Each relay may take 2 positions, open or
-closed, and these positions may stand for 0 and 1. There are more than
-3000 relays in the Harvard machine.
-
-A magnet pulling one way and a spring pulling the other way are
-sufficient in an ordinary relay to give 2 positions, “on” and “off,”
-“yes” and “no,” 0 and 1. But how do we make a relay that can hold any
-one of 10 positions? Figure 4 shows one scheme for a _ten-position
-relay_. The _arm_ can take any one of 10 positions, connecting the
-contact _Common_ to any one of the contacts O, 1, 2, 3, 4, 5, 6, 7, 8,
-and 9 so that current can flow. The _gear_ turns all the time. When
-an impulse comes in on the _Pickup_ line, the _clutch_ connects the
-arm to the gear. When an impulse comes in on the _Drop-out_ line, the
-clutch disconnects the arm from the gear. For example, suppose that the
-ten-position relay is stopped at contact 2, as shown. Suppose that we
-now pick up the relay, hold it just long enough to turn 3 steps, and
-then drop it out. The relay will now rest at contact 5.
-
-[Illustration: FIG. 4. Scheme of a ten-position relay, or counter
-position.]
-
-[Illustration: FIG. 5. Scheme of a counter wheel.]
-
-In the Harvard machine, the ten-position relays, much like the scheme
-shown, do the same work as _counter wheels_ (Fig. 5) in an ordinary
-desk calculating machine, and so they are often spoken of as _counter
-positions_ in the Harvard machine. They are very useful in the machine
-not only because they express the 10 decimal digits 0, 1, 2, 3, 4,
-5, 6, 7, 8, 9 but also because adding and subtracting numbers is
-accomplished by turning them through the proper number of steps. In
-fact, an additional impulse is provided when the counter position turns
-from 9 to 0, for purposes of carry. A group of 24 counter positions
-makes up each _storage counter_—or _storage register_—in the machine.
-There are 2200 of these counter positions. Each is connected to a
-continuously running gear on a small shaft (Fig. 6). All these shafts
-are connected by other gears and shafts to a main drive shaft, and they
-are driven by a 5-horsepower motor at the back of the machine. When
-a counter position is supposed to step, a clutch connects the drive
-to the running gear, and the counter position steps. When the counter
-position is supposed to stay unchanged, the clutch is disconnected
-and the driving gear runs free. In fact, when you first approach the
-Harvard machine, about the first thing you are aware of is the running
-of these gears and the intermittent whirring and clicking of the
-counter positions as they step. The machine gives a fine impression of
-being busy!
-
-[Illustration: FIG. 6. Scheme of counter 16.]
-
-
-Timing Contacts
-
-A _button_ (see Fig. 7) is a device for closing an electric circuit
-when and only when you push it. A simple example is the button for
-ringing a bell: you push the button, a circuit is closed, and something
-happens. When you let go, the circuit is opened. The Harvard machine
-has a button for starting, a button for stopping, and many others.
-
-[Illustration: FIG. 7. Button.]
-
-[Illustration: FIG. 8. Cam, with 5 lobes and contact.]
-
-A _cam contact_ (see Fig. 8) is an automatic device for closing an
-electric circuit for just a short interval of time. When the lobes
-on the cam strike the contact, it closes and current flows. When the
-lobes have gone by, the spring pushes open the contact, and no current
-flows. Just as a two-position relay is the automatic equivalent of
-a two-position switch, and a ten-position relay is the automatic
-equivalent of a ten-position switch, so a cam contact is the automatic
-equivalent of a button.
-
-All the cams in the machine have 20 pockets where small round metal
-lobes may or may not be inserted. Each cam makes a full turn once in
-³/₁₀ of a second and is in time with all the others. Thus we can time
-all the electrical circuits in the machine in units of ³/₂₀₀ of a
-second.
-
-
-NUMBERS
-
-Numbers in the machine regularly consist of 23 decimal digits. The 24th
-numerical position at the left in any register contains only 0 for a
-positive number and only 9 for a negative number. _Nines complements_
-(see Supplement 2) are used for negative numbers. For example,-00284 is
-represented as 999715, supposing that we had 5-digit numbers instead
-of 23-digit numbers. The sum of two nines complements is automatically
-corrected so that it is still a correct nines complement. The device
-that accomplishes this is called _end-around-carry_ (see Supplement 2).
-The decimal point is fixed for each problem; in other words, in any
-problem, the decimal point is consistently kept in one place, usually
-between the 15th and 16th decimal columns from the right.
-
-
-HOW INFORMATION GOES INTO THE MACHINE
-
-Numerical information may go into the machine in any one of 3 ways: (1)
-by regular IBM punch cards, using standard IBM card feeds (panel 16);
-(2) by hand-set dial switches (panels 1, 2); and (3) by long loops of
-punched tape placed on the value tape feeds (panels 12 to 14). Three
-sets of 24 columns each punched on a regular IBM punch card can be
-used to send 3 numbers and their signs into the machine in one machine
-cycle. This is the fastest way for giving numbers to the machine, but
-the most limited; for the cards must be referred to in order and can
-be referred to automatically only once. Also, there is the risk that
-they may be out of order. A card may be passed through the machine
-without reading; this saves some sorting in preparing cards for the
-machine. Machines for preparing the cards are regular IBM key punches,
-and machines for sorting them after preparation are regular IBM card
-sorters.
-
-In panels 1 and 2 there are 60 registers by which unchanging numbers
-like 1, or 3.14159265···, or 7.65 may be put into the machine. These
-are called the _constant registers_. Each constant register consists of
-24 dial switches and contains 23 digits and a sign, 0 if positive and
-9 if negative. Whenever the mathematician says a certain constant is
-needed for a problem, the operator of the machine walks over to these
-panels, and, while the machine is turned off, sets the dial switches
-for the number, one by one, by hand. If we need 40 constants of 10
-digits each for a problem, then the operator sets 400 dial switches by
-hand and makes certain that the remaining 14 switches in each of the 40
-constant registers used are either at 0 or 9, depending on the sign of
-the number. Only then can he return to start the machine.
-
-[Illustration: FIG. 9. Value tape code.]
-
-The third means by which numerical information can be put into the
-machine is the _value tape feeds_, in panels 12, 13, and 14. Here the
-machine can consult tables of numbers. The numbers are punched on paper
-tape 24 holes wide, made of punch-card stock. Tapes for the value tape
-feeds may be prepared by hand or by the machine itself using punch
-cards or machine calculation. The tapes use equally spaced _arguments_
-(see Supplement 2). The tape punch changes the decimal digits in its
-keyboard into the following punching code (see Fig. 9):
-
-    0  0000      5  1100
-    1  1000      6  1010
-    2  0100      7  1001
-    3  0010      8  0110
-    4  0001      9  0101
-
-Here the 1 denotes a punched hole and 0 no punched hole, and the 4
-columns from left to right of the code correspond to 4 rows of the
-paper tape from bottom to top. To make sure the value tape is correct,
-the machine itself can read the value tape and check it mathematically
-or compare it with punch-card values.
-
-
-HOW INFORMATION COMES OUT OF THE MACHINE
-
-Information comes out of the machine in any one of three ways: (1) by
-punching on IBM cards with a regular IBM card punch that is built into
-the machine (panel 17), (2) by typing on paper sheets with electric
-typewriters (panels 16 and 17), and (3) by punching paper tape 24 holes
-wide of the same kind as is fed into the machine.
-
-Usually, one of the electric typewriters is used to print a result for
-a visual check and to print it before the machine makes a specified
-check of the value. Then, about 10 seconds later, after the result has
-been checked as specified in the machine, the checked result is printed
-by the second typewriter. In the second typewriter, a special one-use
-carbon ribbon of paper is used to produce copy for publication by a
-photographic process.
-
-The card punch writes a number more rapidly than an electric
-typewriter. This extra speed is sometimes very useful. However, the
-punch’s chief purpose is to record intermediate results on punch cards.
-Then, if there is a machine failure, and if the problem has been well
-organized, the problem may be run over from these intermediate results,
-instead of requiring a return to the original starting information.
-The tape punch used for preparing tape by hand can also be operated by
-cable from the machine.
-
-
-HOW INFORMATION IS HANDLED IN THE MACHINE
-
-The machine is a mechanical brain. So, between taking in information
-and putting out information, the machine does some “thinking.” It
-does this thinking according to instructions. The instructions go
-into the machine as: (1) the setting of switches, or (2) the pressing
-of buttons, or (3) the wiring of plugboards, or (4) feeding in tape
-punched with holes. The instructions are remembered in the machine in
-these 4 ways, and we can call these sets of devices the control of the
-machine.
-
-To illustrate: One of the buttons pressed for every problem is the
-Start Key: when you press it, the machine starts to work on the
-problem. One of the switches with which you give instructions is
-a switch that turns electric typewriter 1 on or off. One of the
-plugboards contains some hubs by which you can tell the machine how
-many figures to choose in the quotient when dividing, for clearly you
-do not need a quotient of 23 figures every time the machine divides.
-You can have 5 choices in any one problem; you can specify them by
-plugging, and you can call for any one of 5 choices of quotient size
-from time to time during the problem. In many cases, when we wish
-the machine to do the same thing for all of a single problem and do
-it whenever the occasion arises, we can put the instruction into the
-wiring of a plugboard. We use plugboard wiring, for example, in fixing
-the decimal point in multiplication, so that the product will read out
-properly, and in guiding the operation of the typewriters, so that
-printing will take place in the columns where we want it.
-
-
-Sequence of Steps
-
-The most important part of the control of the machine is the
-_sequence-tape feed_ and its _sequence-control tape_. These tell the
-machine a great part of what operations are to be performed.
-
-[Illustration: FIG. 10. Sequence-control tape code.]
-
-At the end of the room where the machine is, there is the special tape
-punch mentioned above. It holds a big spool of card stock that is thin,
-flexible, smooth, and tough. With one keyboard we may prepare value
-tape. With another keyboard we prepare the sequence-control tape.
-The tape (see Fig. 10) contains places for 24 round punched holes in
-each row. Some and only some of these holes are punched. Each row of
-punched holes is equivalent to an instruction to the machine and is
-called a _line of coding_ or _coding line_. In general, the instruction
-has the form:
-
-    Take a number out of Register _A_; put the number
-      into Register _B_; and perform operation _C_.
-
-The first group of 8 holes at the left is called the _A field_ or the
-_out-field_. Here we tell the machine where a number is to be taken
-from. The middle group of 8 holes is called the _B field_ or the
-_in-field_. Here we tell the machine where a number is to be put. The
-last group of 8 holes is called the _C field_ or the _miscellaneous
-field_. Here we tell the machine part or all of the operation that is
-to be performed.
-
-To illustrate (see Fig. 10), we have holes 3, 2, 1 punched in the _A_
-field, holes 3, 2 punched in the _B_ field, and hole 7 punched in the
-_C_ field. Now 321 is the _code_—or machine language, or machine call
-number—for storage counter 7; 32 is the code for storage counter 6;
-and 7 in the _C_ field is the code (in this case, and generally) for
-“Add, and read the next line of coding.” So, if we punch out this line
-of coding and put the tape on the machine, we tell the machine to read
-the number in counter 7, add it into counter 6, and proceed to the next
-line of coding and read that.
-
-The holes in each group of 8 holes from left to right are numbered: 8,
-7, 6, 5, 4, 3, 2, 1. The code 631, for example, means that holes 6, 3,
-1 are punched and that no holes are punched at 8, 7, 5, 4, 2. Since it
-is more natural, the code is read from left to right, or 631, instead
-of from right to left in the sequence 136.
-
-The devices in the machine have _in-codes_, used in the in-field, and
-_out-codes_, used in the out-field. For each of the 72 regular storage
-counters, the in-code and the out-code are the same. The first 8
-storage counters have the codes 1, 2, 21, 3, 31, 32, 321, 4, 41; the
-last 2 storage counters, the 71st and the 72nd, have the codes 7321, 74.
-
-The constant registers—often called _constant switches_, or just
-_switches_—naturally have only out-codes, since numbers can be entered
-into the constant registers only by setting dial switches by hand.
-The first 8 constant registers have the out-codes 741, 742, 7421, 743,
-7431, 7432, 74321, 75, and the 59th and 60th constant registers have
-the out-codes 821, 83.
-
-
-Transferring, Adding, and Clearing
-
-Each storage counter has the property that any number transferred into
-it is added into it. For example, the instruction
-
-    Take the number in switch 741; transfer it into storage register 321
-
-is coded:
-
-    741, 321, 7
-
-The 7 in the third column is an instruction to the sequence-tape feed
-to turn up to the next coding line and read it. If any number is
-already stored in register 321, the content of 741 will be added to it,
-and the total will then be stored in 321.
-
-Resetting or clearing a regular storage register is accomplished by a
-coding that is a departure from the usual scheme of “out” and “in.” The
-instruction
-
-    Clear register 321; read the next coding line
-
-is coded:
-
-    321, 321, 7
-
-Similarly, you can clear any other regular storage register if you
-repeat its code in the out-and in-fields. However, a few of the storage
-registers in the machine have special reset codes, and these may occur
-in any of the three fields _A_, _B_, _C_.
-
-As the result of a recent modification of the machine, you can easily
-double the number in any storage register. For example, the instruction
-
-    Double the number in register 321; read the next coding line
-
-is coded:
-
-    321, 321, 743
-
-
-Subtracting
-
-If the number in switch 741 is to be subtracted from the number in
-storage counter 321, the instruction is changed into:
-
-    Take the negative of the number in switch 741; transfer
-      it into storage register 321; read the next line of coding
-
-The coding line becomes:
-
-    741, 321, 732
-
-By putting 32 in the _C_ field, we cause the number in switch 741 to be
-subtracted from whatever number is in register 321.
-
-We have 2 more choices in adding and subtracting. The value of the
-number without regard to sign—in other words, its _absolute value_ (see
-Supplement 2)—may be added or subtracted. The instruction
-
-    Add the absolute value of
-
-is expressed by a _C_ field code 2, and the instruction
-
-    Add the negative of the absolute value of
-
-is expressed by a _C_ field code 1.
-
-
-Multiplying
-
-When we wish to multiply one number by another and get a product, we
-have 3 numbers. We tell the machine about each of these numbers on
-a separate line of coding. Multiplication is signaled by sending a
-number into the _multiplicand counter_. The multiplicand counter has an
-in-code 761. If the multiplicand is in 321, the instruction is:
-
-    Take the number in 321; enter it as multiplicand; read the
-    next coding line
-
-The coding is:
-
-    321, 761, 7
-
-On the third following coding line, the multiplier is sent into
-the _multiplier counter_. If the multiplier is in switch 741, the
-instruction is:
-
-Take the number in 741; enter it as multiplier; read the next coding
-line
-
-The coding is:
-
-    741, ——, 7
-
-We do not punch anything in the middle field: the machine is “educated”
-and “knows” that it has started a multiplication and needs a
-multiplier, and it expects this multiplier in the third coding line. To
-have no code for the multiplier counter is, of course, a departure from
-the general rule, but it saves some punching and permits the use of
-this space for certain other codes, thus saving some operating time.
-
-We need not confuse the 761 in-code for the multiplicand counter with
-the 761 out-code, which happens to be the out-code of the 25th constant
-register, because neither can occur in the other’s field. We may, of
-course, use other registers besides 321 and 741 for supplying the
-multiplicand and multiplier.
-
-To get the product and put it into any storage counter _D_, we use two
-lines of coding one right after the other:
-
-     ——    ——   6421
-    8761   _D_   ——
-
-The _product counter_ has the out-code 8761. When the product is
-desired, it is called for, transferred into counter _D_, and the
-multiplication unit is automatically cleared. It takes time, however,
-for the machine to perform a multiplication. That is the reason for
-the preceding coding line and the 6421 in the _C_ field. While the
-multiplication is going on, we can instruct the machine to do other
-things that we want done. We can insert or _interpose_ coding lines in
-between the multiplier line and the product line. For example, if we
-have a multiplier of 10 digits, we can insert 8 coding lines and maybe
-more. The 6421 code essentially tells the machine to finish both the
-multiplication and the interposed instructions, and, as soon as the
-later one of these two tasks is finished, to transfer out the product
-to counter _D_.
-
-Up to the middle of 1946, the wiring of the machine was a little
-different and less convenient. When the product was obtained by the
-multiplication unit, it had to be accepted and transferred at once into
-one of the 72 storage registers.
-
-
-Dividing
-
-Division is called for by first sending the divisor into the _divisor
-counter_, and this has a code 76 in the _B_ field. If the divisor is in
-counter 321, the instruction may be:
-
-    Take the number in 321; enter it as divisor; read the next
-      coding line
-
-The coding will then be:
-
-    321, 76, 7
-
-Three coding lines later, the dividend is called for, and the coding,
-if the dividend is in switch 7431, is:
-
-    7431, ——, 7
-
-We can send the quotient, when ready, into any desired counter _Q_ by
-the following two lines of coding:
-
-    ——    ——   642
-    876   _Q_   ——
-
-In the same way as with multiplication, we can insert a number of
-coding lines in between the dividend line and the first quotient line.
-
-Both multiplication and division are carried out in the same unit of
-the machine, the _multiply-divide unit_. The machine first constructs
-a table of the multiples of the multiplicand or divisor: 1 times, 2
-times, 3 times, ···, 9 times. In multiplication this table is then used
-by selecting multiples according to the digits of the multiplier one
-after another. In division the table is used by comparing multiples of
-the divisor against the dividend and successive remainders, finding
-which will go and which will not. Since the numbers in the machine are
-normally of 15 to 23 digits, any particular multiple will be used,
-on the average, several times, and so this process is relatively
-efficient. Actually the multiplicand and the divisor go into the same
-counter. Division, however, has the code 76 and multiplication the code
-761, and so the difference is essentially an operation code not in the
-third or _C_ field.
-
-
-Consulting a Table
-
-When we desire the machine to consult a table of values (i.e., a
-_function_—see Supplement 2), we punch the table with its arguments and
-function values on a tape, and we put the tape on a value tape feed
-mechanism. The instruction to the machine may be:
-
-    Take the number in register _A_; find the value of the
-      function for this number, and enter it in register _B_.
-
-The coding is:
-
-    ——       ——       73
-    _A_     7654      61
-    ——       ——      762
-    ——       ——      543
-    ——       ——    75431
-    841     7654     ——
-    _A_      763    6421
-    8762      _B_     73
-    ——      8763       7
-
-Without explaining this coding line by line, we can say that this is
-what happens:
-
-    The machine reads the argument in register _A_.
-      The machine reads the argument in the table at which
-      the value tape feed is resting.
-
-    It subtracts them, and thereby determines how far away
-      the desired argument is.
-
-    The machine then turns the tape that required distance.
-
-    It checks that the new argument is the wanted argument.
-
-    It reads the value of the function entered at that
-      point on the function tape.
-
-
-Selecting
-
-There is a storage counter in the machine that is called the _selection
-counter_. The selection counter is counter 70 and has the code 732. It
-has all the properties of an ordinary storage counter and, in addition,
-one extra property: depending on the sign of the number stored in the
-selection counter, it is possible to select whether some other number
-shall be treated positively or negatively. In other words, addition of
-a number anywhere in the machine may take place either positively or
-negatively, if the number stored in the selection counter is positive
-or negative, respectively.
-
-For example, suppose that _x_ is the number in the selection counter.
-Suppose that _y_ is the number in some other counter _A_. Suppose that
-_z_ is the number in counter _B_. Suppose that we use the coding:
-
-    _A_, _B_, 7432
-
-What we get in _B_, because of the 7432 in the third or _C_ field, is
-_z_ plus _y_ if _x_ is positive or zero, and _z_ minus _y_ if _x_ is
-negative. In the language of the algebra of logic (see Chapter 9 and
-Supplement 2), where _T_( ...) is “the truth value of ...,” the number
-in _b_ equals:
-
-    _z_ + _y_·_T_(_x_ ≥ 0) - _y_·_T_(_x_ < 0)
-
-(The nines complement of 0, namely 999···9 to 24 digits, is treated by
-the machine as negative.)
-
-Why do we need an operation like this in a mechanical brain? Among
-other reasons, what we want to do with a number, in mathematics, often
-depends on its sign. It may happen that a table is, for negative
-arguments, the negative of what it is for positive arguments; in
-other words, _F_(-_x_) =-_F_(_x_). This is true, for instance, for a
-table of _cubes_ {_F_(_x_) = _x_³} or for a table of _trigonometric
-tangents_ (see Supplement 2). If so, we certainly do not want to take
-the time and trouble to list the whole table. We put down only half
-the table and then, if _x_ is negative, use the negative of the value
-in the table. In order to apply such a time-saving rule when using the
-machine, we need the selection counter or its equivalent.
-
-
-Checking
-
-There is another special counter in the machine that is called the
-_check counter_. It also has all the properties of an ordinary storage
-counter and, in addition, one extra property: If the sign of the number
-stored in the check counter on a certain coding line is negative, then
-on the next coding line the machine may be stopped. In other words,
-suppose that the check counter stores a certain tolerance _t_. Suppose,
-under the instructions we give the machine, that it calculates a
-positive number _x_ that ought to be less than this tolerance. Suppose
-that something may go wrong and that _x_ actually may be greater than
-_t_. Then we put a check into our instructions. We tell the machine:
-
-    When you have found _x_, subtract it from _t_.
-
-    If the result is positive, go ahead.
-
-    If the result is negative or zero, _stop_!
-
-Here is the coding. Suppose that the tolerance _t_ is in switch 751.
-Suppose that the number _x_ to be checked is in counter 4321. Then the
-instructions and coding are:
-
-
-    Clear the check counter                                   —    —    7
-    Put in the tolerance, from switch 751                     751  74   7
-    Subtract the absolute value of the number to be checked  4321  74  71
-    Stop, O Mechanical Brain, if your result be negative!      —    —  64
-
-An operation like this is very useful in a mechanical brain. It
-enables the calculation to be interrupted if something has gone
-wrong. Of course, other operations of checking besides this one are
-used—for example, inspecting for reasonableness the results printed on
-typewriter 1.
-
-
-Other Operations
-
-There are other operations in the machine. There are two pairs of
-storage registers that can be _coupled_ together so that we can handle
-problems requiring numbers of 46 digits instead of 23. Registers 64
-and 65 can be coupled, and registers 68 and 69 can be coupled. There
-is another storage counter, No. 71, that has an extra property. We can
-read out the number it holds times 1, or times 10¹², or times 10⁻¹²,
-as may be called for. As a result of this counter, we can do problems
-requiring 144 registers storing numbers of 11 digits each, instead of
-72 registers storing 23 digits each. Bigger statistical problems can be
-handled, for example.
-
-There are some minor sequences of operations, or _subroutines_, that
-can be called for by a single code. The subroutine may be a whole set
-of additions, subtractions, multiplications, divisions, and choices,
-having a single purpose: to compute some number by a _process of rapid
-approximation_ (see Supplement 2). There are built-in subroutines for
-some special mathematical functions: the _logarithm_ of a number to the
-base 10, the _exponential_ of a number to the base 10, and the _sine_
-of a number. (See Supplement 2.)
-
-There are also 10 changeable subroutines, each of 22 coding lines,
-which can be called in, when wanted, by the main sequence-control tape
-or by each other. These subroutines constitute the Subsidiary Sequence
-Mechanism, and are extremely useful. They have _A_, _B_, and _C_ fields
-just like the main sequence-control, but they are given information by
-plugging with short lengths of wire instead of by feeding punched paper
-tape.
-
-
-RAPID APPROXIMATION FOR A LOGARITHM
-
-Up to this point in this chapter the author has tried to tell the facts
-about the Harvard machine in plain words. But for reading this section,
-a little knowledge of calculus is necessary. (See also Supplement 2.)
-If you wish, skip this section and go on to the next one.
-
-What is the process that the machine uses to compute any desired
-logarithm to 23 digits? Suppose that we take for an example the process
-by which the machine computes log_{10} 49.3724. We choose a 6-digit
-number for simplicity; the machine would handle a 23-digit number in
-the same way. The process uses 2 fundamental equations involving the
-logarithm: the sum relation
-
-    log (_a_·_b_·_c_···) = log _a_ + log _b_ + log _c_···
-
-and the series relation
-
-                          _h_²   _h_³   _h_⁴
-    logₑ(1 + _h_) = _h_ - ———— + ———— - ———— + ···, │_h_│ < 1
-                           2      3      4
-
-The error in this series is less than the first neglected term. Now,
-the machine stores the base 10 logarithms (to 23 decimal places) of the
-following 36 numbers:
-
-     1   1.1  1.01  1.001
-     2   1.2  1.02  1.002
-    ...  ...   ...   ...
-     9   1.9  1.09  1.009
-
-First, the number 49.3724 is examined in a counter called the
-_Logarithm-In-Out counter_, and the position of the decimal point is
-determined, giving the _characteristic_ of the logarithm. The number
-49.3724 has the characteristic 1. Next, 4 successive divisions are
-performed, in which the 4 divisors are (1) the first digit of the
-number, (2) the first 2 digits of the quotient, (3) the first 3 digits
-of the next quotient, and (4) the first 4 digits of the subsequent
-quotient; thus,
-
-    4.93724/4 = 1.23431
-
-    1.23431/1.2 = 1.02860
-
-    1.02860/1.02 = 1.00843
-
-    1.00843/1.008 = 1.00043
-
-For simplicity we have kept only 6 digits, although the machine, of
-course, would keep 23. It is interesting to note that the machine is
-able to sense digits and thus determine the 4 divisors; this is an
-arithmetical and numerical process and one that cannot be done in
-ordinary algebra. We now have:
-
-    log₁₀ 49.3724 = 1 + log₁₀ 4 + log₁₀ 1.2 + log₁₀ 1.02
-                      + log₁₀ 1.008 + log₁₀ 1.00043
-
-To compute log₁₀ 1.00043 to 21 decimals we use
-
-               (      _h_²    _h_³     _h_⁴    _h_⁵   _h_⁶ )
-    log₁₀_e_ · (_h_ - ————— + —————  - ———— + ————— - —————)
-               (       2       3         4      5      6   )
-
-with _h_ = 0.00043. Only 6 terms of the series relation are needed.
-For, the error is less than _h_⁷/7, which is less than 10⁻²¹/7, since
-_h_ < ¹/₁₀₀₀. The machine uses the series relation in the form
-
-    log₁₀ (1 + _h_) = {([{(_c_₆_h_ + _c_₅)_h_ + _c_₄}_h_
-
-                        + _c_₃]_h_ + _c_₂)_h_ + _c_₁}_h_
-    where
-
-    _c_₁ = _M_, _c_₂ = -_M_/2, _c_₃ = _M_/3, ···,
-
-    and _M_ = log₁₀__e_= 0.434294···.
-
-The 6 values of the _c_’s are also stored in the machine. When any
-logarithm is to be computed, the sum of the characteristic, of the 4
-logarithms of the successive divisors, and of the first 6 terms of the
-series relation gives the logarithm. The maximum time required is 90
-seconds.
-
-
-AN APPRAISAL OF THE CALCULATOR
-
-The IBM Automatic Sequence-Controlled Calculator at Harvard is a
-landmark in the development of machines that think. Its capacity for
-many problems for which it is suited is far beyond the capacity of a
-hundred human computers.
-
-
-Speed
-
-The time required in the machine for adding, subtracting, transferring,
-or clearing numbers is ³/₁₀ of a second. This is the time of one
-machine cycle or of reading one coding line. Multiplication takes at
-the most 6 seconds, and an average of 4 seconds. Division takes at the
-most 16 seconds, and an average of 11 seconds. Each, however, requires
-only 3 lines of coding, or ⁹/₁₀ of a second’s attention from the
-sequence mechanism; interposed operations fill the rest of the time.
-To calculate a logarithm, an exponential, or a sine to the full number
-of digits obtainable by means of the automatic subroutine takes at
-the most 90, 66, and 60 seconds, respectively. To get three 24-digit
-numbers from feeding a punch card takes ⅓ second. To punch a number
-takes from ½ second up to 3 seconds. To print a number takes from 1½
-seconds up to 7 seconds.
-
-
-Cost and Value
-
-The cost of the machine was somewhere near 3 or 4 hundred thousand
-dollars, if we leave out some of the cost of research and development,
-which would have been done whether or not this particular machine had
-ever been built. A staff of 10 men, consisting of 4 mathematicians,
-4 operators, and 2 maintenance men, are needed to keep the machine
-running 24 hours a day. This might represent, if capitalized, another
-1 or 2 hundred thousand dollars. If a capital value of $500,000 is
-taken as equivalent to $50,000 a year, then the cost of the machine in
-operation 24 hours a day is in the neighborhood of $150 a day or $6 an
-hour.
-
-The value of the machine, however, is very much greater. If 100 human
-beings with desk calculators were set to work 8 hours a day at $1.50 an
-hour, the cost would be $1200 a day, or 8 times as much. Yet it is very
-doubtful that the work they could produce would equal that turned out
-by the machine, either in quality or quantity, when the machine is well
-suited to the problem.
-
-
-Reliability
-
-By reliability we mean the extent to which the results produced by the
-machine can be relied on to be right. The machine contains no built-in
-device for making its operations reliable. So, if we wish to check a
-multiplication, for example, we can do the multiplication a second
-time, interchanging the multiplier and the multiplicand. But if, say,
-digit 16 of the product were not transferring correctly, we would get
-the same wrong result both ways and we would not have a sufficient
-check. Thus, when we set up a problem for the machine to do, one of the
-big tasks we have is checking. We have to work out ways of making sure
-that the result, when we get it, is right and ways of instructing the
-machine to make the tests we want. This is not a new task. Whenever
-you or I set out to solve a problem, we have to make sure—usually by
-doing the problem twice, and preferably by doing it a different way the
-second time—that our answer, when we get it, is correct. One of the
-chief tasks for the mathematician, in making a sequence-control tape
-for the machine, is to put into it sufficient checks to make sure that
-the results are correct.
-
-We can use a number of different kinds of partial checks: the check
-counter; _differences_, and _smoothness_ (see Supplement 2); watching
-the results printed on typewriter 1; mathematical checks; comparison
-with known specific values; etc.
-
-In actual experience on the machine, human failures, such as failure
-to state the problem exactly or failure to put it on the machine
-correctly, have given about as much trouble as mechanical failures. The
-machine operates without mechanical failure about 90 to 95 per cent
-of the time. The balance of the time the machine is idle while being
-serviced or repaired. The machine is serviced by mechanics trained and
-supervised at Harvard.
-
-Often when we change the machine from one problem to another problem,
-we find some kind of trouble. Consequently, we need to work out in
-detail the first part of any calculation placed on the machine. We
-then compare the results step by step with the results produced by the
-machine. Any mathematician working with the machine needs considerable
-training in order to diagnose trouble quickly and guide the maintenance
-men to the place where repair or replacement is needed. Once you find
-the trouble, you can fix it easily. Without disturbing the soldered
-connections, you can easily pull out from its socket a relay that is
-misbehaving and plug in a new relay. With a screwdriver you can change
-a counter position—detach it from its socket and replace it by another
-one that is working correctly.
-
-One “bug” that will long be remembered around the Laboratory was a case
-involving a 5 that would incorrectly come in to a number every now
-and then. It did not happen often—only once in a while. After a week
-of search the bug was finally located: the insulation on a wire that
-carried a 5 had worn through in one spot, and once in a while this wire
-would shake against a post that could carry current and took in the 5!
-
-
-Efficiency
-
-In many respects, this machine is efficient and well-balanced. Its
-reading and writing speed is close to its calculating speed. We can
-punch or print a result on the average for every 10 additions or 1½
-multiplications. The memory of 72 numbers in the machine is extremely
-useful; a smaller memory is a serious limitation on the achievements of
-a computing machine. The machine can do many kinds of arithmetic and
-logic. It is well educated and can compute automatically some rather
-complicated mathematical functions, like logarithm or sine. It has done
-difficult and important problems. It has computed and tabulated (see
-Supplement 2) _Bessel functions_, _definite integrals_, etc. It can
-solve _differential equations_ (see Chapter 5) and many other problems
-in mathematics, physics, and engineering.
-
-On the other hand, no calculator will ever again be built just like
-this one, useful though it is. Electronic computing is easily 100 times
-as fast as relay computing; nearly every future calculator will do
-its computing electronically. Many other improvements will be made.
-For example, in this calculator, there are 72 addition-subtraction
-mechanisms, yet only one of these can be used at a time. Also, the
-machine has only one combined multiply-divide unit. So we have to
-organize any computation with few multiplications, and with still fewer
-divisions, for they take longer still.
-
-Until 1947, we had to organize any computation in this calculator into
-one single fixed sequence of operations. In other words, there was
-no way to move from one subroutine to another subroutine depending
-on some indication that turned up in our computation. Recently, the
-Harvard Computation Laboratory decided to remedy this condition and
-provided the Subsidiary Sequence Mechanism equivalent to 10 subroutines
-of 22 lines of coding each. These are on relays and plug wires and
-may be called for by the sequence-control tape or by each other. This
-provision has added greatly to the efficiency of the calculator.
-
-Whatever else can be said about the Harvard IBM Automatic
-Sequence-Controlled Calculator, it must be said that this was the first
-general-purpose mechanical brain using numbers in digit form and able
-to do arithmetic and logic in hundreds of thousands of steps one after
-another. And great credit must go to Professor Howard H. Aiken of
-Harvard and the men of International Business Machines Corporation who
-made this great mechanical brain come into existence.
-
-
-
-
-Chapter 7
-
-SPEED—5000 ADDITIONS A SECOND:
-
-MOORE SCHOOL’S ENIAC
-
-(ELECTRONIC NUMERICAL INTEGRATOR AND CALCULATOR)
-
-
-Another of the giant brains that has begun to work is named _ENIAC_.
-This name comes from the initial letters of the full name, _Electronic
-Numerical Integrator and Calculator_. Eniac was born in 1942 at
-the Moore School of Electrical Engineering, of the University of
-Pennsylvania, in Philadelphia. Eniac’s father was the Ordnance
-Department of the U. S. Army, which provided the funds to feed and rear
-the prodigy.
-
-In the short space of four years, Eniac grew to maturity, and in
-February 1946 he began to earn his own living by electronic thinking.
-Eniac promptly set several world’s records. He was the first giant
-brain to use electronic tubes for calculating. He was the first one to
-reach the speed of 5000 additions a second. He was the first piece of
-electronic apparatus containing as many as 18,000 electronic tubes all
-functioning together successfully. As soon as Eniac started thinking,
-he promptly made relay calculators obsolete from the scientific point
-of view, for they have a top speed of perhaps 10 additions a second.
-
-At the age of 5, he moved to Maryland at a cost of about $90,000, and
-his permanent home is now the Ballistic Research Laboratories at the U.
-S. Army’s Proving Ground at Aberdeen, Md.
-
-
-ORIGIN AND DEVELOPMENT
-
-In the Department of Terrestrial Magnetism in the Carnegie Institution
-of Washington, a great deal of information about the earth is studied.
-Many kinds of physical observations are there gathered and analyzed:
-electricity in the atmosphere, magnetism in the earth, and the weather,
-for example. In 1941, a physicist, Dr. John W. Mauchly, was thinking
-about the great mass of numerical information they had to handle. He
-became convinced that much swifter ways of handling these numbers were
-needed. He was certain electronic devices could be used for computing
-at very high speeds, yet he found no one busy applying electronics in
-this field. With hopes of finding some way of developing electronic
-computing, he joined the staff of the Moore School of Electrical
-Engineering in the autumn of 1941.
-
-The Moore School in 1934 and 1935 had built a differential analyzer;
-and, from that time on, the school had made a number of improvements
-in it. In 1941, with war imminent, the differential analyzer was put
-hard at work calculating tables for the Army’s Ballistic Research
-Laboratories. These tables were mostly firing tables, tables of the
-paths along which projectiles travel when fired—_trajectories_;
-obviously, you cannot fire a gun usefully, unless you know how to aim
-it. The amount of calculation of trajectories was so huge that Dr.
-Mauchly suggested that a machine using electronic tubes be constructed
-to calculate them. A good deal of discussion took place between men at
-the Moore School, men at the Ballistic Research Laboratories, and men
-from the Ordnance Department in Washington. A contract for research
-into an electronic trajectory computer was concluded with the Ordnance
-Department of the U. S. Army. Mauchly and one of the young electronics
-engineers studying at Moore School, J. Presper Eckert, Jr., set to work
-on the design.
-
-Gradually the design of a machine took form, and the crucial
-experiments on equipment were completed. In 1943, the design was
-settled as a special-purpose machine to calculate trajectories. Later
-on, the group modified the plans here and there to enable the machine
-to calculate a very wide class of problems. A group of Moore School
-electronics engineers and technicians during 1944 and 1945 built the
-machine, using as much as possible standard radio tubes and parts.
-Here, again, in spite of the successful progress of the electronic
-machine, the rumor that it was a “white elephant” was allowed to spread
-in order to protect the work from prying enemy ears.
-
-
-GENERAL ORGANIZATION
-
-The main part of Eniac consists of 42 _panels_, which are placed along
-the sides of a square U. Each of these panels is 9 feet high, 2 feet
-wide, and 1 foot thick. They are of sheet steel, painted black, with
-switches, lights, etc., mounted on them. At the tops of all the panels
-are air ducts for drawing off the hot air around the tubes. Large
-motors and fans above the machine suck the heated air away through the
-ducts. There are also 5 pieces of equipment which can be rolled from
-place to place and are called _portable_, but there is no choice as to
-where they can be plugged in. We shall call this equipment panels 43 to
-47.
-
-
-Panels
-
-Now what are these panels, and what do they do? Each panel is an
-assembly of some equipment. The names of the panels are shown in the
-accompanying table. The arrangement of Eniac at the Ballistic Research
-Laboratories as shown in the table is slightly different from the
-arrangement of Eniac at Moore School.
-
-NAMES OF PANELS OF ENIAC
-
-     PANEL NO.  NAME (AND ADDITIONAL NAMES IN SOME CASES)
-
-         1       Initiating Unit
-         2       Cycling Unit
-      3, 4       Master Programmer, panels 1, 2
-         5       Accumulator 1
-         6       Accumulator 2
-         7       Accumulator 3
-         8       Accumulator 4 (Quotient)
-         9       Divider-Square-Rooter
-        10       Accumulator 5 (Numerator I)
-        11       Accumulator 6 (Numerator II)
-        12       Accumulator 7 (Denominator—Square Root I)
-        13       Accumulator 8 (Denominator—Square Root II)
-        14       Accumulator 9 (Shift I)
-        15       Accumulator 10 (Shift II)
-        16       Blank panel for new unit (Converter)
-        17       Accumulator 11 (Multiplier)
-        18       Accumulator 12 (Multiplicand)
-     19-21       Multiplier, panels 1, 2, 3
-        22       Accumulator 13 (Left-Hand Partial Products I)
-        23       Accumulator 14 (Left-Hand Partial Products II)
-        24         Accumulator 15 (Right-Hand Products I)
-        25         Accumulator 16 (Right-Hand Products II)
-        26         Blank panel for new unit (100 Registers)
-        27         Accumulator 17
-        28         Accumulator 18
-        29         Accumulator 19
-        30         Accumulator 20
-    31, 32     Function Table 1, panels 1, 2
-    33, 34     Function Table 2, panels 1, 2
-    35, 36     Function Table 3, panels 1, 2
-     37-39      Constant Transmitter, panels 1, 2, 3
-     40-42      Printer, panels 1, 2, 3
-     43-45      Portable Function Tables _A_, _B_, and _C_
-        46         IBM Card Reader
-        47         IBM Summary Punch
-
-     _Note_: The accumulators from which a number can be sent
-                  to the printer are now accumulators 1, 2, and
-                  15 to 20.
-
-In reading over the table, we find a number of words that need
-explaining. Some of the explanation we can give in the summary of the
-units of Eniac:
-
-SUMMARY OF UNITS OF ENIAC
-
-    QUANTITY       DEVICE                        SIGNIFICANCE
-
-    20  Accumulators           Store, add, and subtract numbers
-    1   Multiplier             Multiplies
-    1   Divider-Square-Rooter  Divides, and obtains twice the _square
-                                 root_ of a number (see Supplement 2)
-    3   Function Tables        Part of the memory, for referring to
-                                 tables of numbers
-    1   Constant Transmitter   Stores numbers from the card reader and
-                                 from hand-set switches
-    1   Printer                Punches machine results into cards
-    1   Cycling Unit           Controls the timing of the various parts
-                                 of the machine
-    1   Initiating Unit        Has controls for starting a calculation,
-                                 for clearing, etc.
-    1   Master Programmer      Holds the chief controls for coordinating
-                                  the various parts of the machine
-
-An _accumulator_ is a storage counter. It can hold a number; it
-can clear a number; it can transmit a number either positively or
-negatively; and it can receive a number by adding the number in and
-thus holding the sum of what it held before and the number received.
-Eniac when first built had only 20 accumulators, and so it could
-remember only 20 numbers at one time (except for constant numbers set
-in switches). This small memory was the most serious drawback of Eniac;
-panel 26 was designed, therefore, to provide a great additional memory
-capacity.
-
-The _divider-square-rooter_, as its name tells, is a mechanism that
-can divide and that can find twice the square root of a number. Eniac
-is one of the several giant brains that have had square root capacity
-built into them, particularly since square root is needed for solving
-trajectories.
-
-Many panels of Eniac have double duty and some have triple duty.
-For example, panel 24 is an accumulator, but it also (1) stores the
-right-hand partial products (see Supplement 2) of the multiplier
-and (2) was a register, when Eniac was at Moore School, from which
-information to be punched in the printer could be obtained. Clearly, if
-we have a multiplication to do, we cannot also use this accumulator for
-storing a number that is to remain unchanged during the multiplication.
-
-
-Parts
-
-The total number of parts in Eniac is near half a million, even if
-we count electronic tubes as single parts. There are over 18,800
-electronic tubes in the machine. It is interesting to note that only 10
-kinds of electronic tubes are used in the calculating circuits and only
-about 60 kinds of _resistors_ and 30 kinds of _capacitors_. A resistor
-is a device that opposes the steady flow of electric current through
-it to a certain extent (called _resistance_ and measured in _ohms_). A
-capacitor is a device that can store electrical energy up to a certain
-extent (called _capacitance_ and measured in _farads_). All these tubes
-and parts are standard parts in radios. All types are identified by the
-color labels established in standard radio manufacturing. It is the
-combinations of these parts, like the combinations of pieces in a chess
-game, that give rise to the marvelous powers of Eniac.
-
-The combinations of parts at the first level are called _plug-in
-units_. A plug-in unit is a standard box or tray or chassis made
-of sheet steel containing a standard assembly of tubes, wires, and
-other parts. It can be pushed in or pulled out of a standard socket
-with many connections. An example of a plug-in unit is a _decade_,
-or, more exactly, an _accumulator decade_. This is just a counter
-wheel or decimal position expressed in Eniac language: it can express
-successively all the digits from 0 to 9 and then pass from 9 to 0,
-giving rise to a carry impulse. It is striking that a mechanical
-counter to hold 10 digits can be made up of 10 little wheels, ¼ inch
-wide and an inch high. But an accumulator in Eniac, to hold 10 digits,
-is a set of 10 decades each 2 inches wide and 2½ feet high.
-
-There are only about 20 kinds of plug-in units altogether. Each plug-in
-unit is interchangeable with any other of the same kind. So, if a
-decade, for example, shows trouble, you can pull it out of its socket
-and plug in a spare decade instead.
-
-
-Numbers
-
-Numbers in Eniac are of 10 decimal digits with a sign that may be plus
-or minus. The decimal point is fixed. However, when you are connecting
-one accumulator with another, you can shift the decimal point if you
-want to. Also, 2 accumulators may be coupled together so as to handle
-numbers of 20 digits.
-
-
-HOW INFORMATION GOES INTO THE MACHINE
-
-There are three ways by which information—numbers or instructions—can
-go into the Eniac. Numbers can be put into the machine by means of
-punch cards fed into the Card Reader, panel 46, or switches on the
-Constant Transmitter, panels 37 to 39. Numbers or instructions can
-also go into the machine by means of the Function Tables, panels 43 to
-45. Here there are dial switches, which are set by hand. Instructions
-can also go into the machine by setting the switches, plugging the
-inputs and outputs, etc., of the wires or lines along which numbers and
-instructions travel.
-
-
-HOW INFORMATION COMES OUT OF THE MACHINE
-
-There are two ways by which numerical information can come out of
-the machine. Numbers can come out of the machine punched on cards by
-the Summary Punch, panel 47. They are then printed in another room by
-means of a separate IBM tabulator. Also, numbers can be read out of
-the machine by means of the lights in the _neon bulbs_ mounted on each
-accumulator. You can read in the lights of a panel the number held by
-the accumulator, if the panel is not computing.
-
-
-HOW INFORMATION IS MANIPULATED IN THE MACHINE
-
-Eniac handles information rather differently from any other of the big
-brains. Instead of having only one bus or “railroad line” along which
-numbers can be sent, Eniac has more than 10 such lines. They are called
-_digit trays_ and labeled A, B, C, ···. Each contains 11 _digit trunk
-lines_ or _digit trunks_—10 to carry the digits of a number, and the
-11th to carry the sign. Instead of having only one telegraph line along
-which instructions can be sent, Eniac has more than 100 such lines.
-They are called _program trunk lines_ or _program trunks_ and labeled
-A1, A2, ···, A11, B1, B2, ···, B11, ···, etc. They are assembled in
-groups of 11 to a tray; the _program trays_, in fact, look just like
-the digit trays, except for their connectors and their purpose, which
-are different. Below, we shall make clear how the program trays carry
-control information.
-
-Now, actually, Eniac has many more trunk lines than we have just
-stated, for each of the lines we have mentioned can be divided into
-numerous separate sections by the removal of plug connections. How
-we choose to do this depends on the needs of the problem, the space
-between the panels, the time when the line is used, etc.
-
-
-Transferring Numbers, Adding, and Subtracting
-
-Basically, a number is represented in Eniac by an arrangement of on
-and off electronic tube elements in pairs, called _flip-flops_. There
-is one flip-flop enclosed in a single tube (type 6SN7) for each value
-0, 1, 2, 3, 4, 5, 6, 7, 8, 9 for each of the 10 digits stored in an
-accumulator. So we have at least 100 flip-flops for each accumulator,
-and thus at least 100 electronic tubes are required to store 10 digits.
-Actually, an accumulator needs 550 electronic tubes. So we see that
-there is not very much of a future in this type of arrangement. The
-newer electronic brains use different devices for storage of numbers.
-
-In order to show what number is stored in an accumulator, there are 100
-little neon bulbs mounted on the face of each accumulator panel. Each
-bulb glows when the flip-flop that belongs to it is on. For example,
-suppose that the 4th decade in Accumulator 11 holds the digit 7. Then
-the 7th flip-flop in that decade will be on, and all the others will be
-off. The 7th neon bulb for that decade will glow.
-
-Now suppose that the number 7 is in the 4th decade in Accumulator 11
-and is to be added into, say, the 4th decade in Accumulator 13. And
-suppose that it is to be subtracted from the 4th decade in Accumulator
-16. What do we do, and what will Eniac do?
-
-First, we pick out 2 digit trays, say B and D. Accumulator 11 has 2
-outputs, called the _add output_ and the _subtract output_. We plug B
-into the add output and D into the subtract output. Then we go over to
-Accumulators 13 and 16. They have 5 inputs, that is, 5 ways of being
-plugged to receive numbers from digit trunks. These inputs are named
-with _Greek letters_, α, β, γ, δ, ε. We choose one input, say γ, for
-Accumulator 13, and we plug B into that input. We choose one input, say
-ε, for Accumulator 16, and we plug D into that input.
-
-Now we have the “railroad” switching for numbers accomplished. We
-have set up a channel whereby the number in Accumulator 11 will be
-routed positively into Accumulator 13 and negatively into Accumulator
-16. Now let us suppose that, at some definite time fixed by the
-control, Accumulator 11 is stimulated to transmit and Accumulators
-13 and 16 are conditioned to receive. When this happens, a group of
-10 _pulses_ comes along a direct trunk from the cycling unit, and a
-group of 9 pulses comes along another trunk. We can think of each
-pulse as a little surge of electricity lasting about 2 millionths
-of a second. The _ten-pulses_, as the first group is called, are 10
-millionths of a second apart. The _nine-pulses_, as the second group
-is called, are also 10 millionths of a second apart but are sandwiched
-between the ten-pulses. When the 1st ten-pulse comes along, the 7th
-flip-flop in Accumulator 11 goes off, the 8th flip-flop goes on, the
-following nine-pulse goes through and goes out on the subtract line to
-Accumulator 16. Then the 2nd ten-pulse comes along, the 8th flip-flop
-goes off, the 9th flip-flop goes on, and the next nine-pulse goes out
-on the subtract line to Accumulator 16. Now the decade sits at 9,
-and for this reason the next ten-pulse changes an electronic switch
-(actually another flip-flop) so that all later nine-pulses will go
-out on the add line. This ten-pulse also turns off the 9th flip-flop
-and turns on the 0th flip-flop without causing any carry. Now the 4th
-of the ten-pulses comes along, turns the 0th flip-flop off, and turns
-the 1st flip-flop on, and the next nine-pulse goes out on the add line
-to Accumulator 13. The next 6 of the ten-pulses then come along and
-change Accumulator 11 back to the digit 7 as before, and the next 6
-of the nine-pulses go out to Accumulator 13. Thus Eniac has added 7
-into Accumulator 13, has added 2, the _nines complement_ of 7 (see
-Supplement 2), into Accumulator 16, and has left Accumulator 11 holding
-the same number as before. This is just the result that we wanted.
-
-In this way, the nines complement of any digit in a decade is
-transferred out along the subtract line, and the digit unchanged is
-transmitted out along the add line. As the pulses arrive at any other
-accumulator, they add into that accumulator.
-
-
-Multiplying and Dividing
-
-Eniac performs multiplication by a built-in table of the products in
-the 10-by-10 multiplication table, using the method of _left-hand
-components_ and _right-hand components_ (see Supplement 2). For
-example, suppose that the 3rd digit of the multiplier is 7 and that the
-5th digit of the multiplicand is 6. Then, when Eniac attends to the
-3rd digit of the multiplier, the right-hand digit of the 42 = 6 × 7 is
-gathered in one accumulator, and the left-hand digit 4 is gathered in
-another accumulator. After Eniac has attended to all the digits of the
-multiplier, then Eniac performs one more addition and transfers the sum
-of the left-hand digits into the right-hand digits accumulator.
-
-Eniac does division in rather a novel way. First, the divisor is
-subtracted over and over until the result becomes negative or 0. Then
-the machine shifts to the next column and adds the divisor until the
-result becomes positive or 0. It continues this process, alternating
-from column to column. For example, suppose that we divide 3 into 84 in
-this way. We have:
-
-      ______  _
-    3 ) 84 ( 32
-       -3
-       ——
-       +54
-       -3
-       ——
-       +24
-       -3
-       ——
-        -6
-        +3
-        ——
-        -3
-        +3
-        ——
-         0
-
-After we subtract 3 the third time, the result becomes negative,-6;
-in the next column, after we add 3 twice, the result becomes 0. The
-quotient is
-
-     _
-    32, which is the same as 30 - 2, or 28;
-
-and 3 × 28 is 84. Thus the process checks.
-
-
-Consulting a Table
-
-Eniac has three Function Tables. Here you can store numbers or
-instructions for the machine to refer to. Each Function Table has
-104 _arguments_ (see Supplement 2). For each argument, you can store
-12 digits and 2 signs that may be plus or minus. This capacity can
-be devoted to one 12-digit number with a sign, or to two 6-digit
-numbers each with a sign, or to six 2-digit instructions. The three
-Function Tables are panels 43, 44, and 45. To put in the numbers or
-instructions, you have to go over to these panels and set the numbers
-or instructions, digit by digit, turning dial switches by hand. It is
-slow and hard to do this right, but once it is done, Eniac can refer
-to any number or instruction in any table in ¹/₁₀₀₀ of a second. This
-is much faster than the table reference time in any other of the giant
-brains built up to 1948.
-
-
-Programming
-
-We said above that Eniac has over 100 control lines or program trunks
-along which instructions can be sent. These instructions are expressed
-as pulses called _program pulses_. Now how do we make these pulses do
-what we want them to do? For example, how can we instruct Accumulator
-11 to add what it holds into Accumulator 13?
-
-On each unit of Eniac there are plug hubs or sockets (called
-_program-pulse input terminals_) to which a program trunk may be
-connected. A program pulse received here can make the unit act in some
-desired way. On each accumulator of Eniac, we find 12 program-pulse
-input hubs. Corresponding to each of these hubs, there is a nine-way
-switch, called a _program-control switch_. The setting of this switch
-determines what the accumulator will do when the program-pulse input
-hub belonging to the switch receives a program pulse. For instance,
-there are switch settings for: receive input on the α line, receive
-input on the β line, etc.; and transmit output on the add line, etc.
-There is even a switch setting that instructs the accumulator to do
-nothing, and this instruction may be both useful and important.
-
-Now, in order that Accumulator 11 may transfer a number to Accumulator
-13, we need: (1) a digit tray, say B, for the number to travel along;
-(2) a program trunk line, say G3, to tell Accumulator 11 when to send
-the number and Accumulator 13 when to receive it; and (3) certain
-plugging as follows:
-
-    1. We plug from program trunk G3 into a program-pulse
-       input hub, say No. 5, of Accumulator 11;
-
-    2. We plug from the same program trunk G3 into a
-       program-pulse input hub, say No. 7, of Accumulator 13;
-
-    3. We set program-control switch No. 5 of Accumulator
-       11 to “add”;
-
-    4. We set program-control switch No. 7 of Accumulator
-       13 to some input, say γ.
-
-    5. We plug from digit tray B into the add output of
-       Accumulator 11.
-
-    6. We plug from digit tray B into the γ input of
-       Accumulator 13.
-
-Now, when the program pulse comes along line G3, it makes Accumulator
-13 transmit additively along digit tray B into Accumulator 13. And that
-is the result that we wanted.
-
-As each mechanism of Eniac finishes what it is instructed to do, it
-may or may not put out a program pulse. This pulse in turn may be
-plugged into any other program trunk line and may stimulate another
-mechanism to act. Then, when this mechanism finishes, it too may or may
-not put out a program pulse, and so on.
-
-In general, there are two different ways to instruct Eniac to do a
-problem. One way is to set all the switches, plug all the connections,
-etc., for the specific problem. This is a long and hard task. Very
-often, even with great care, it is done not quite correctly, and
-then the settings must be carefully checked all over again. A second
-method (called the _von Neumann programming method_) is to store all
-the instructions for a problem in one or two function tables of Eniac
-and then tell Eniac to read the function tables in sequence and to do
-what they say. The rest of the machine is then wired up in a standard
-fashion. This method of instructing Eniac was proposed by Dr. John von
-Neumann of the Institute of Advanced Study at Princeton, N. J. Eniac
-has been modified to the slight extent needed so that this method can
-be used when desired. In this method, each instruction is a selected
-one of 60 different standard instructions or orders—one of them, for
-example, being “multiplication.” Each standard order is expressed by
-2 decimal digits. The 60 standard orders are sufficient so that Eniac
-can do any mathematical problem that does not overstrain its capacity.
-Since each of the 3 Function Tables can hold 600 2-digit instructions,
-the machine can hold a program of 1800 instructions under the von
-Neumann programming method.
-
-
-AN APPRAISAL OF ENIAC AS A COMPUTER
-
-As a general-purpose calculating machine, Eniac suffers from unbalance.
-That is to say, Eniac operates rapidly and successfully in some
-respects, and slowly and troublesomely in other respects. This is
-altogether to be expected, however, in a calculator as novel as Eniac
-and made to so large an extent out of standard radio parts. It was
-certainly better to finish a calculator like this one and then start
-on a new one, as the Moore School of Electrical Engineering did, than
-to prolong design and construction indefinitely in order to make
-improvements.
-
-
-Speed
-
-Eniac adds or subtracts very swiftly at the rate of 5000 a second.
-Eniac multiplies at the rate of 360 to 500 a second. Division,
-however, is slow, relatively; the rate is about 50 a second. Reading
-numbers from punched cards, 12 a second for 10-digit numbers, is even
-slower. As a result of these rates, you find, when you put a problem
-on Eniac, that one division delays you as long as 100 additions or
-8 multiplications. Division might have been speeded somewhat by
-(1) _rapidly convergent approximation_ (see Supplement 2) to the
-_reciprocal_ of the divisor and (2) multiplying by the dividend; this
-might have taken 5 or 6 multiplication times instead of 8. Also, the
-use of a standard IBM punch-card feed and card punch slows the machine
-greatly. One way to overcome this drawback might be to install one or
-two additional sets of such equipment, which might increase input and
-output speed.
-
-
-Ease of Programming
-
-Eniac has a very rapid and flexible automatic control over the
-programming of operations. Eniac has more than 10 channels along which
-numbers can be transferred and more than 100 channels along which
-program-control pulses can be transferred. There are many ways for
-providing subroutines. Eniac has the additional advantage that there
-is no delay in giving the machine successive instructions: all the
-instructions the machine may need at any time are ready at the start of
-the problem, and indications occurring in the calculation can change
-the routine completely.
-
-All these advantages, however, are paid for rather heavily by the
-slow methods for changing programming. You have to plug large numbers
-of program trunk lines and digit trunk lines, or you have to set
-large numbers of switches, or both. Also, when you wish to return to
-a previous problem, you must do all the plugging and switch setting
-over again. Many delays in the operation of the machine are due to
-human errors in setting the machine for a new problem. Here again, we
-must remember that Eniac was originally designed as a special-purpose
-machine for solving trajectories. To calculate a large family of
-trajectories very little changing of wires and switches would be
-needed.
-
-
-Memory
-
-The most severe limitation on the usefulness of Eniac was, at the
-outset, the fact that it had only 20 registers for storing numbers.
-There are large numbers of problems that cannot be simply handled with
-so small an internal memory. Even the Harvard IBM calculator (see
-Chapter 6) is often strained during a problem because of the number of
-intermediate results that must be stored for a time before combining.
-The Ballistic Research Laboratories, however, contracted for extensions
-to Eniac to provide more memory and easier changing of instructions.
-
-
-Reliability
-
-Checking results with Eniac is not easy. There is no built-in guarantee
-that Eniac’s results are correct. A large calculator can and does make
-both constant and intermittent errors. Ways for checking with Eniac are:
-
-    Mathematical, if and when available, and this will be
-      seldom.
-
-    Running the problem a second time, and this will, at
-      most, prove consistency.
-
-    Deliberate testing of small parts of the problem,
-      which is very useful and is standard practice but
-      leads only to a probability that the final result is
-      correct.
-
-You can operate Eniac one addition at a time, and even one pulse at a
-time, and see what the machine shows in its little neon bulbs. This is
-a very useful partial check.
-
-
-Cost
-
-The cost of Eniac is higher than that of some of the other large
-mechanical brains—over half a million dollars. Because some of the
-work was done at the Moore School by students, the cost was probably
-less than it otherwise would have been. The largest part of the cost
-was the designing of the machine and the construction of the panels;
-the tubes were only a small portion of the cost. The tubes used in
-the calculating circuits cost only 20 to 90 cents. However, no later
-electronic calculator need cost as much, for many improvements can now
-be seen.
-
-The power required for Eniac is about 150 kilowatts or about 200
-horsepower, most of which is used for the heaters of the electronic
-tubes. The largest number of electronic tubes mentioned for future
-electronic calculators is about 3000, so we can see that they are
-likely to use less than a quarter of the power needed for Eniac.
-
-Eniac will doubtless give a number of years of successful operation
-and be extremely useful for problems that employ its assets and are
-not excluded by its limitations. In fact, at the Ballistic Research
-Laboratories, for a typical week of actual work, Eniac has already
-proved to be equal to 500 human computers working 40 hours with desk
-calculating machines, and it appears that soon two or three times as
-much work may be obtained from Eniac.
-
-
-
-
-Chapter 8
-
-RELIABILITY—NO WRONG RESULTS:
-
-BELL LABORATORIES’ GENERAL-PURPOSE RELAY CALCULATOR
-
-
-In 1946, Bell Telephone Laboratories in New York finished two
-_general-purpose relay calculators_—mechanical brains. They were twins.
-One was shipped in July 1946 to the National Advisory Committee for
-Aeronautics at Langley Field, Virginia. The other, after some months of
-trial operation, was shipped in February 1947 to the Ballistic Research
-Laboratories at the U. S. Army’s Proving Ground, Aberdeen, Md.
-
-Each machine is remarkably reliable and versatile. It can do a wide
-variety of calculations in a great many different ways. Yet the machine
-never takes a new step without a check that the old step was correctly
-performed. There is, therefore, a chance of better than 99.999,999,999
-per cent that the machine will not let a wrong result come out. The
-automatic checking, of course, does not prevent (1) human mistakes—for
-example, instructing the machine incorrectly—or (2) mechanical
-failures, in which the machine stops dead in its tracks, letting no
-result at all come out.
-
-
-ORIGIN AND DEVELOPMENT
-
-In Bell Telephone Laboratories the telephone system of the country is
-continually studied. Their research produced the common type of dial
-telephone system: a masterly machine for selecting information.
-
-Now when a telephone engineer studies an electric circuit, he often
-finds it very convenient to use numbers in pairs: like 2, 5 or-4,-1.
-Here the comma is a separation sign to keep the two numbers in the pair
-separate and in sequence. Mathematicians call numbers of this kind, for
-no very good reason, _complex numbers_; of course, they are far less
-complex than why the sun shines or why plants grow.
-
-When Bell Laboratories test the design of new circuits, girl computers
-do arithmetic with complex numbers. Addition and subtraction are
-easy: each means two operations of addition or subtraction of
-ordinary numbers. For example, 2, 5, plus-4,-1 equals 2-4, 5-1, which
-equals-2, 4. And 2, 5 minus-4,-1 is the same as 2, 5 plus 4, 1; and
-this equals 2 + 4, 5 + 1, which equals 6, 6. Multiplication of two
-complex numbers, however, is more work. If _a_, _b_ and _c_, _d_ are
-two complex numbers, then the formula for their product is (_a_ ×
-_c_)-(_b_ × _d_), (_a_ × _d_) + (_b_ × _c_). To get the answer, we
-need 4 multiplications, 1 subtraction, and 1 addition. Division of two
-complex numbers requires even more work. If _a_, _b_ and _c_, _d_ are
-two complex numbers, the formula for the quotient of _a_, _b_ divided
-by _c_, _d_ is:
-
-    [(_a_ × _c_) + (_b_ × _d_)] ÷ [(_c_ × _c_) + (_d_ × _d_)],
-
-    [(_b_ × _c_) - (_a_ × _d_)] ÷ [(_c_ × _c_) + (_d_ × _d_)]
-
-For example,
-
-    (2, 5) ÷ (-4, -1) = [(2 × -4 = -8) + (5 × -1 = -5)]
-           ÷ [(-4 × -4 = 16) + (-1 × -1 = 1)],
-
-    [(5 × -4 = -20) - (2 × -1 = -2)] ÷ [16 + 1] = -(¹³/₁₇), -(¹⁸/₁₇)
-
-Thus, division of one complex number by another needs 6
-multiplications, 2 additions, 1 subtraction, and 2 divisions of
-ordinary numbers—and always in the same pattern or sequence.
-
-
-The Complex Computer
-
-About 1939, an engineer at Bell Telephone Laboratories in New York, Dr.
-George R. Stibitz, noticed the great volume of this pattern arithmetic.
-He began to wonder why telephone switching equipment could not be used
-to do the multiplications and divisions automatically. He decided it
-could. All that was necessary was that the _relays_ (see Chapter 2)
-used in regular telephone equipment should have a way of remembering
-and calculating with numbers. Regular telephone equipment would take
-care of the proper sequence of operations. Regular equipment known as
-_teletypewriters_ would print the numbers of the answer when it was
-obtained. A teletypewriter consists essentially of a typewriter that
-may be operated by electrical impulses. It has a keyboard that may
-produce electrical impulses in sets corresponding to letters; and it
-can receive or transmit over wires.
-
-Dr. Stibitz _coded_ the numbers: each decimal digit was matched up with
-a group of four relays in sequence, and each of these relays could be
-open or closed. If 0 means open and 1 means closed, here is the pattern
-or code that he used:
-
-    DECIMAL DIGIT   RELAY CODE
-          0          0 0 1 1
-          1          0 1 0 0
-          2          0 1 0 1
-          3          0 1 1 0
-          4          0 1 1 1
-
-          5          1 0 0 0
-          6          1 0 0 1
-          7          1 0 1 0
-          8          1 0 1 1
-          9          1 1 0 0
-
-With regular telephone relays and regular telephone company techniques,
-Dr. Stibitz and Bell Telephone Laboratories designed and constructed
-the machine. It was called the _Complex Computer_ and was built just
-for multiplying and dividing complex numbers. Six or eight panels of
-relays and wires were in one room. Two floors away, some of the girl
-computers sat in another room, where one of the teletypewriters of
-the machine was located. When they wished, they could type into the
-machine’s teletypewriter the numbers to be multiplied or divided. In a
-few seconds back would come the answer. In fact, there were two more
-computing rooms where teletypewriters of the machine were stationed. To
-prevent conflicts between stations, the machine had a circuit like the
-busy signal from a telephone.
-
-In 1940, a demonstration of the Complex Computer took place: the
-computing panels remained in New York, but the teletypewriter
-input-output station was set up at Dartmouth College in Hanover, N. H.
-Mathematicians gave problems to the machine in Dartmouth, it solved
-them in New York, and it reported the answers in Dartmouth.
-
-
-Special-Purpose Computers
-
-With this as a beginning, Bell Laboratories developed another machine
-for a wide variety of mathematical processes called _interpolating_
-(see Supplement 2). Then, during World War II, Bell Laboratories made
-more special-purpose computing machines. They were used in military
-laboratories charged with testing the accuracy of instruments for
-controlling the fire of guns. These computers took in a set of
-gun-aiming directions put out by the _fire-control instrument_ in
-some test. They also took in the set of observations that went into
-the fire-control instrument on that test. Then they computed the
-differences between the gun-aiming produced by the fire-control
-instrument and the gun-aiming really required by the observations.
-Using these differences, the fire-control instrument could be adjusted
-and corrected. These special-purpose computers were also useful in
-checking the design of new fire-control instruments and in checking
-changes due to new types of guns or explosives.
-
-Regularly, after each of these special-purpose computers was finished,
-people began to put other problems on it. It seemed to be fated that,
-as soon as you had made a machine for one purpose, you wanted to use
-it for something else. Accordingly, in 1944, two agencies of the U. S.
-Government together made a contract with Bell Telephone Laboratories
-for two general-purpose relay computers. These two machines were
-finished in 1946 and are twins.
-
-
-ORGANIZATION OF THE GENERAL-PURPOSE COMPUTER
-
-When a man sits down at a desk to work on a computation, he has six
-things on his desk to work with: a work sheet; a desk calculator, to
-add, subtract, multiply, and divide; some rules to be followed; the
-tables of numbers he will need; the data for the problem; and an answer
-sheet. In his head, he has the capacity to make decisions and to do
-his work in a certain sequence of steps. These seven subdivisions of
-calculation are all found in the Bell Laboratories’ general-purpose
-relay computer. The general-purpose computer is a computing system, in
-fact, more than it is a single machine. The part of the system which
-does the actual calculating is called, in the following paragraphs,
-the _computer_, or else, since it is in two halves, _Computer 1_ and
-_Computer 2_.
-
-
-Physical Units
-
-The computing system delivered to the Ballistic Research Laboratories
-fills a room about 30 by 40 feet and consists of the following:
-
-    2 _computers_: panels of relays, wiring, etc.,
-      which add, subtract, multiply, divide, select,
-      decide, control, etc.
-
-    4 _problem positions_: tables each holding 12
-      mechanisms for feeding paper tape, which read numbers
-      and instructions punched on tape and convert them
-      into electrical impulses.
-
-    2 _hand perforators_: keyboard devices for
-      punching instructions and numbers on paper tape.
-
-    1 _processor_: a table holding mechanisms for
-      feeding 2 paper tapes and punching a third paper
-      tape, used for checking numbers and instructions
-      punched on tape.
-
-    2 _recorders_: each a table holding a
-      teletypewriter, a tape punch, and a tape feed, used
-      for recording answers and, if necessary, consulting
-      them again.
-
-The 2 computers correspond to the work sheet, the desk calculator,
-and the man’s capacity to make decisions and to carry out a sequence
-of steps. The 4 problem positions correspond to the problem data, the
-rules, and the tables of numbers. The 2 recorders correspond to the
-answer sheet. The 2 hand perforators and the processor are auxiliary
-machines: they translate the ordinary language of arithmetic into the
-machine language of punched holes in paper tape.
-
-This is the computing system as organized for the Ballistic Research
-Laboratories at Aberdeen. The one for the National Advisory Committee
-for Aeronautics has only 3 problem positions. The computer system may,
-in fact, be organized with 1 to 10 computers and with 1 to 20 problem
-positions.
-
-The great bulk of this computing system, like the mechanical brains
-described in previous chapters, is made up of large numbers of
-identical parts of only a few kinds. These are: standard telephone
-relays; wire; and standard _teletype transmitters_, mechanisms that
-read punched paper tape and produce electrical impulses.
-
-
-Numbers
-
-The numbers that the Bell machine contains range from 0.1000000 to
-0.9999999 times a _power_ of 10 varying from 10,000,000,000,000,000,000
-to 0.000,000,000,000,000,000,1, or, in other words, from 10¹⁹ to 10⁻¹⁹.
-The machine also contains zero and _infinity_: zero arises when the
-number is smaller than 10⁻¹⁹, and infinity arises when the number is
-equal to or greater than 9,999,999,000,000,000,000. (See Supplement 2.)
-
-The system used in the machine to represent numbers on relays is called
-_biquinary_—the _bi_-, because it is partly twofold like the hands, and
-the -_quinary_ because it is partly fivefold like the fingers. This
-system is used in the abacus (see Chapter 2 and Supplement 2). In the
-machine, for each decimal digit, 7 relays are used. These relays are
-called the 00 and 5 relays, and the 0, 1, 2, 3, and 4 relays. If, as
-before, 0 indicates a relay that is not energized and 1 indicates a
-relay that is energized, then each decimal digit is represented by the
-positioning of the 7 relays as follows:
-
-    DECIMAL DIGIT        RELAYS
-
-                    00 5   0 1 2 3 4
-
-          0          1 0   1 0 0 0 0
-          1          1 0   0 1 0 0 0
-          2          1 0   0 0 1 0 0
-          3          1 0   0 0 0 1 0
-          4          1 0   0 0 0 0 1
-
-          5          0 1   1 0 0 0 0
-          6          0 1   0 1 0 0 0
-          7          0 1   0 0 1 0 0
-          8          0 1   0 0 0 1 0
-          9          0 1   0 0 0 0 1
-
-Then, for any decimal digit, one and only one of the 00 and 5 relays
-is energized, and one and only one of the 0, 1, 2, 3, and 4 relays
-is energized. If more or less than exactly one relay in each set is
-energized, then the machine knows that it has made a mistake, and it
-stops dead in its tracks. Thus any accidental failure of a relay is at
-once caught, and the chance of two compensating failures occurring at
-the same time is extremely small.
-
-
-HOW INFORMATION GOES INTO THE MACHINE
-
-In order to put a problem into this machine—just as with the other
-machines—first a mathematician who knows how the problem is to be
-solved, and who knows how to organize it for the machine, lays out
-the scheme of calculation. Then, a girl goes to one of the hand
-perforators. Sitting at the keyboard, she presses keys and punches out
-feet or yards of paper tape expressing the instructions and numbers
-for the calculation. Each character punched—digit, letter, or sign—has
-one or more of a maximum of 6 holes across the tape. Another girl,
-using the other hand perforator, also punches out the instructions and
-numbers for the calculation. If she wishes to erase a wrong character,
-she can press an _erase key_ that punches all 6 holes, and then the
-machine will pass by this row as if it were not there.
-
-Three kinds of tapes are produced for the machine:
-
-    _Problem tapes_, which contain information
-       belonging to the particular problem.
-
-    _Table tapes_, which contain tables of numbers to
-       be referred to from time to time.
-
-    _Routine tapes_, which contain the program, or
-       routine, or sequence of steps that the machine is to
-       carry out.
-
-In each of these tapes one character takes up ⅒ of an inch along the
-tape. In the case of a table tape, however, an ordinary 1-digit number
-requires 4 characters on the tape, and a 7-digit number requires 11
-characters on the tape. On a table tape there will be on the average
-about 1 inch of tape per number.
-
-
-The Processor
-
-The two paper tapes prepared on the perforator should agree. But
-whether or not they agree, a girl takes them over to the processor and
-puts them both in. The processor has two tape feeds, and she puts one
-tape on each and starts the machine. The processor compares them row by
-row, making sure that they agree, and punches a new tape row by row.
-If the two input tapes disagree, the processor stops. You can look to
-see which tape is right, and then you can put the correct punch into
-the new tape with a keyboard mounted on the processor. As the processor
-compares the two input tapes, it also converts any number written in
-the usual way into machine language. For example, the processor will
-automatically translate 23,188 into +.231 8800 × 10⁺⁵. The processor
-also puts in certain safeguards. If you want it to, the processor will
-also make a printed record of a tape. Also, when a tape becomes worn
-from use in the machine, you can put it into the processor and make a
-fresh copy.
-
-
-The Problem Positions
-
-Next, the girl takes the punched tape made by the processor over to a
-problem position that is idle. Two of the problem positions are always
-busy guiding the two computers. The other two problem positions stand
-by, ready to be loaded with problems.
-
-A problem position looks like a large covered-over table. Under
-the covers are 12 tape feeds, or _tape transmitters_. All these
-transmitters look exactly alike except for their labels and consist
-of regular teletype transmitters. Six-hole paper tape can be fed into
-any transmitter. Six metal fingers sense the holes in the paper tape
-and give out electrical impulses at proper times. At the front of the
-problem position is a small group of switches that provide complete
-control over the problem while it is on the machine. These are switches
-for starting, disconnecting, momentary stop, etc.
-
-One tape transmitter is the problem tape transmitter. It takes in
-all the data for the problem such as the starting numbers. The first
-thing it does at the start of a problem is to check (by comparing tape
-numbers) that the right tapes are in the right feeds.
-
-Five transmitters are routine tape transmitters. Each of these takes
-in the sequence of computing steps. The routine tapes also contain
-information for referring to table tapes and instructions for printing
-and punching tape. The machine can choose according to instructions
-between the five routine tapes and can choose between many different
-sections on each tape. Therefore, we can use a large number of
-different routines in a calculation, and this capacity makes the
-machine versatile and powerful.
-
-Six transmitters are table tape transmitters. They read tables of
-numbers when directed to. A table tape can be as long as 100 feet and
-will hold numbers at the rate of 1 inch per number, so that about 1200
-numbers of seven decimal digits can be stored on a table tape.
-
-When we look up a number in a table, such as the following,
-
-          2½       3      3½   ···
-       +————————————————————————————
-     1 |1.02500 1.03000 1.03500
-     2 |1.05063 1.06090 1.07123
-     3 |1.07689 1.09273          ···
-     4 |1.10381   ···     ···
-     5 |1.13141   ···
-     6 |1.15969
-     7 |                  ···
-     8 |          ···
-     9 |  ···
-    10 |
-    ···|  ···
-
-we look along the top and down the side until we find the column and
-row of the number we are looking for. These are called the _arguments_
-of the _tabular value_ that we are looking for (see Supplement 2).
-Now when we put this table on a tape to go into the Bell Laboratories
-machine, we write it all on one line, one figure after another, and we
-punch it as follows:
-
-    2-½   1-5     1.02500    1.05063    1.07689   1.10381    1.13141
-      6-10    1.15969      ···      11-15   ···    ···      ···    3
-      1-5   1.03000    1.06090    ···    ···    3½     1-5   1.03500
-    ···
-
-You will notice that the column labels 2½, 3, 3½ have been put on the
-tape, each in front of the group of numbers they apply to. The row
-labels 1 to 5, 6 to 10, ··· have also been put on the tape, each in
-front of the group of numbers they apply to. The appropriate column
-and row numbers, or arguments, must be put often on every table tape,
-so that it is easy for the machine to tell what part of the table tape
-it is reading.
-
-In the Bell Laboratories machine, we do not need to put equal _blocks_
-of arguments like 1-5, 6-10 ··· on the table tape. Instead we can put
-individual arguments like 1, 2, 3, 4 ···, or, if we wish, we can use
-blocks of different sizes, like 1-3, 4-15, 16-30···. For some tables,
-such as income tax tables, it is very useful to have varying-sized
-blocks of arguments. The machine, when hunting for a certain value in
-the table, makes a comparison at each block of arguments.
-
-The machine needs about 6 seconds to search a foot of tape. If we want
-to set up a table economically, therefore, we need to consider the
-average length of time needed for searching.
-
-[Illustration: FIG. 1. Scheme of a recorder.]
-
-HOW INFORMATION COMES OUT OF THE MACHINE
-
-At either one of the two recorders (Fig. 1), information comes out of
-the machine, either in the form of printed characters or as punched
-tape. The recorder consists of a _printer_, a _reperforator_, and
-a tape transmitter. One recorder table belongs to each computer
-and records the results it computes. The printer is a regular
-teletypewriter connected to the machine. It translates information
-produced by the machine as electrical impulses and prints the
-information in letters and digits on paper. The reperforator is an
-automatic tape punch. It translates information produced by the machine
-in the form of electrical impulses and punches the information on
-paper tape. Next to the tape punch is a tape transmitter. After the
-tape comes through the punch, it is fed into the transmitter. Here the
-machine can hunt for a previous result punched in the tape, read that
-result, and use it again.
-
-
-HOW INFORMATION IS MANIPULATED IN THE MACHINE
-
-The main part of the computing system consists of 27 large frames
-loaded with relays and wiring, called the _computer_, or _Computer 1_
-and _Computer 2_. In this “telephone central station,” all the “phone
-calls” from one number to another are attended to. There are 8 types of
-these frames in the computer:
-
-     FRAMES             NUMBER
-
-    Storing register frames         6
-    Printer frames                  2
-    Problem frames                  2
-    Position frames                 2
-    Calculator frames               6
-    Control frames                  2
-    Routine frames                  4
-    BTL (Block-Trig-Log) frames     2
-    Permanent table frames          1
-                                   ——
-      Total                        27
-
-In most but not quite all respects, the two halves, _Computer 1_ and
-_Computer 2_, can compute independently. The _storing register frames_
-hold enough relays to store 30 numbers. The registers for these
-numbers are named _A, B, C, D_, ···, _M, N, O_ in two groups of 15
-each. One group belongs to Computer 1 and the other to Computer 2. In
-each Computer, the _calculator frames_ hold enough relays for storing
-two numbers (held in the _X_ and _Y_ registers) and for performing
-addition, subtraction, multiplication, division, and square root. In
-each Computer, the _problem frame_ stores the numbers that are read off
-the problem tape and the table tapes, and the _printer frame_ stores
-the numbers that are read into the printer. The printer frame also
-stores indications, for example, the signs of numbers, plus or minus,
-for purposes of combining them. These frames also hold the relays that
-control the printer, the problem tape, and the table tapes. Jointly for
-both Computers, the _position frames_ connect a problem in some problem
-position to a Computer that becomes idle. For example, one problem
-may finish in the middle of the night; the machine automatically and
-unattended switches to another problem position and proceeds with the
-instructions there contained. A backlog of computing on hand can be
-stored in two of the problem positions, while the other two control the
-two Computers. In each Computer, the _routine frames_ hold the relays
-that make the Computer follow the routine instructions. Jointly for
-both Computers, the remaining frames—the _control frames_, the _BTL
-frames_, and the _permanent table frames_—hold the relays that control:
-the alarms and lights for indicating failures; some circuits called the
-BTL controls; the tape processor; and the mathematical tables that are
-permanently wired into the machine. The permanent table frames hold the
-following mathematical functions (see Supplement 2): _sine_, _cosine_,
-_antitangent_, _logarithm_, and _antilogarithm_.
-
-
-Storing
-
-Numbers can be stored in the machine in the 30 regular storing
-registers of both Computers together. They can also be stored, at the
-cost of tying up some machine capacity, in the other registers: the 4
-calculator registers, the 2 problem registers, the 2 table registers,
-and the 2 printer registers. Numbers can also be punched out on tape,
-in either of the two printers, and later read again from the tape.
-Labels identifying the numbers can also be punched and read again from
-the tape.
-
-Each register in the machine stores a number in the biquinary notation,
-as explained above. In programming the machine, after mentioning a
-register it is necessary—as a part of the scheme for checking—to tell
-the machine specifically whether to hold the number in the register or
-to clear it.
-
-
-Addition and Subtraction
-
-The calculator frames can add two numbers together, if so instructed in
-the routine tape. Suppose that the two numbers are in the registers
-_B_ and _D_ and that we wish to put the sum in register _F_. Suppose
-that we wish to clear the _D_ number but hold the _B_ number after
-using them. The code on the routine tape is _B H_ + _D C_ = _F_. _H_
-and _C_ coming right after the names of the registers always designate
-“hold” and “clear,” respectively.
-
-The calculator frames can, likewise, subtract a number. The routine
-instruction _B H_-_D C_ = _F_ means:
-
-    Take the number in register _B_ (hold it); subtract the
-      number in _D_ (clear it); put the result in _F_
-
-
-Multiplication and Division
-
-The calculator frames perform multiplication by storing the digits of
-the multiplier, adding the multiplicand over and over, and shifting,
-until the product is obtained. However, if the multiplier is 1989, for
-example, the calculator treats it as 2000-11. This short-cut applies
-to digits 6, 7, 8, 9 and cuts the time required for multiplying. The
-routine instruction is _B H_ × _D C_ = _F_.
-
-The calculator performs division by repeated subtraction. The routine
-instruction is _B H_ ÷ _D C_ = _F_. The operation signs +,-, ×, ÷
-actually appear on the keyboard of the perforator and on the printed
-tape produced by the printer.
-
-
-Discrimination
-
-_Discrimination_ is the term used in the Bell Laboratories computer for
-what we have previously called selection, or comparison, or sequencing.
-The _discriminator_ is a part of the calculator that compares or
-selects or decides—“discriminates.” The discriminator can decide
-whether a number is zero or not zero. In the language of the _algebra
-of logic_ (see Chapter 9 and Supplement 2), if _a_ is a number, the
-discriminator can find _T_(_a_ = 0). The discriminator can also decide
-whether a number is positive or negative. In the language of logic, it
-can find _T_(_a_ > 0) or _T_(_a_ < 0). The actions that a discriminator
-can cause to be taken are:
-
-    Stop the machine.
-    Stop the problem, and proceed to another problem.
-    Stop the routine going on, and proceed with a new routine.
-    Permit printing, or prevent printing; etc.
-
-In this way the discriminator can:
-
-    Distinguish between right and wrong results.
-    Tell that a certain result is impossible.
-    Recognize a certain result to be the answer.
-    Control the number of repetitions of a formula.
-    Change from one formula to another formula.
-    Check a number against a tolerance; etc.
-
-
-PROBLEMS
-
-Among the problems that have been placed on the machine successfully
-are: solving the _differential equation_ of a _trajectory_ (see Chapter
-5) and solving 32 _linear simultaneous equations_ in 32 _unknowns_ (see
-Supplement 2). In the second case, the routine tapes were designed to
-apply equally well to 11 to 100 linear equations in 11 to 100 unknowns.
-However, the machine can do a very broad class of problems, including,
-for example, computing a personal income tax. This calculation with all
-its complexity of choices cannot be placed on any of the mechanical
-brains described in previous chapters. The machine can, of course, be
-used to calculate any tables that we may wish to refer to.
-
-
-AN APPRAISAL OF THE CALCULATOR
-
-The Bell Telephone Laboratories general-purpose relay computer is
-probably the best mechanical brain made up to the end of 1947, in
-regard to the two important factors of reliability and versatility.
-
-
-Reliability
-
-The machine produces results that are practically 100 per cent
-reliable, for the machine checks each step before taking the next
-one. The checking principle is that exactly a certain number of
-relays must be energized. For example, as we said before, for each
-decimal digit there are 7 relays. Exactly 2 of these relays must be
-energized—no more, no less. If this does not happen, the machine stops
-at once without losing any numbers. Lights shine for many circuits
-in the control panel, and, if you compare what they ought to show
-with what they do show, you can usually find at once the location of
-the mistake. The trouble may be a speck of dirt between two contact
-points on a relay, and, when it is brushed away, the machine can go
-right ahead from where it stopped. According to a statement by Franz
-L. Alt, director of the computing laboratory at the Ballistic Research
-Laboratories, in December 1947, “the Bell machine had not given a
-single wrong result in eight months of operation, except when operators
-interfered with its normal running.”
-
-To guard against the risk of putting tapes in the wrong transmitters,
-the machine will check by the instructions contained in the tapes that
-the right tapes are in the right places.
-
-
-Time Required
-
-The time required to do problems on this mechanical brain is perhaps
-longer than on the others. The numbers are handled digit by digit on
-the input tapes, and the typewriter in the recorder moves space by
-space in order to get to the proper writing point. These are slow
-procedures. The speeds of numerical operation are: addition, ³/₁₀
-second; multiplication, 1 second on the average; division, 2.7 seconds
-on the average; square root, 4.5 seconds on the average; logarithm,
-about 15 seconds.
-
-
-Staff
-
-In order to operate the machine, the staff required is: one maintenance
-man; one mathematical engineer; about six girls for punching tape,
-etc., depending on the number of problems to be handled at the rate of
-about one problem per week per girl. Unlike any of the other mechanical
-brains built by the end of 1947, this machine will run unattended.
-
-
-Maintenance
-
-The relays in the machine will operate for years with no failure; they
-have the experience of standard telephone techniques built into them.
-Under laboratory conditions this type of relay had by 1946 operated
-successfully much more than 100 million times. The tape feeding and
-reading equipment in the machine may be maintained by periodic
-inspection and service. The total number of teletype transmitters in
-the machine is 38. If one fails, it is easy to plug in a spare.
-
-The total power required for the machine is about 28 horsepower.
-Batteries are furnished so that, if the power supply should be
-interrupted, the machine can still operate for as long as a half-hour.
-
-
-Cost
-
-The cost of production of this machine in the size of 4 problem
-positions and 2 computers has been roughly estimated as half a million
-dollars. This cost includes material, manufacture, installation, and
-testing. No development cost is included in this figure. Instead, the
-cost of development has been reckoned as squaring with patents and
-other contributions of the work to the telephone switching art.
-
-It is unlikely that the general-purpose relay computer will be
-manufactured generally. The pressure of orders for telephones, the
-need to catch up with the backlog of demand, and the development of
-electronic computers—all indicate that the Bell system will hardly
-go further with this type of computer. In an emergency, however, the
-Bell system would probably construct such machines for the government,
-if requested. In the meantime, many principles first used in the
-general-purpose relay computer are likely to find applications in
-telephone system work. In fact, a present major development being
-pursued in the telephone sections of Bell Laboratories is the
-application of the computer principles to the automatic computation of
-telephone bills.
-
-
-
-
-Chapter 9
-
-REASONING:
-
-THE KALIN-BURKHART LOGICAL-TRUTH CALCULATOR
-
-
-So far we have talked about mechanical brains that are mathematicians.
-They are fond of numbers; their main work is with numbers; and the
-other kinds of thinking they do are secondary. We now come to a
-mechanical brain that is a logician. It is fond of reasoning—logic; its
-main work is with what is logically true and what is logically false;
-and it does not handle numbers. This mechanical brain was finished in
-June 1947. It is called the _Kalin-Burkhart Logical-Truth Calculator_.
-As its name tells, it calculates _logical truth_. Now what do we mean
-by that?
-
-
-TRUTH
-
-To be true or false is a property of a statement. Usually we say that
-a statement is true when it expresses a fact. For example, take the
-statement “Salt dissolves in water.” We consider this statement to be
-true because it expresses a fact. Actually, in this case we can roughly
-prove the fact ourselves. We take a bowl, put some water in it, and put
-in a little salt. After a while we look into the water and notice that
-no salt whatever is to be seen.
-
-Of course, this statement, like many another, occurs in a _context_
-where certain things are understood. One of the understandings here,
-for example, is “a small amount of salt in a much larger amount of
-water.” For if we put a whole bag full of salt in just a little water,
-not all the salt will dissolve. Nearly every statement occurs in a
-context that we must know if we are to decide whether the statement is
-true or false.
-
-
-LOGICAL TRUTH
-
-Logical truth is different from ordinary truth. With logical truth
-we appeal not to facts but to suppositions. Usually we say that a
-statement is logically true when it follows logically from certain
-suppositions. In other words, we play a game that has useful, even
-wonderful, results. The game starts with “if” or “suppose” or “let us
-assume.” While the game lasts, any statement is logically true if it
-follows logically from the suppositions.
-
-For example, let us take five statements:
-
-    1. “The earth is flat like a sheet of paper.”
-
-    2. “The earth is round like a ball.”
-
-    3. “John Doe travels as fast as he can, without turning
-        to left or to right, for many days.”
-
-    4. “John Doe will fall off the earth.”
-
-    5. “John Doe will arrive back at his starting point.”
-
-Let us also take a certain context in which: We know what we mean
-by such words as “earth,” “flat,” “falling,” etc.; we have other
-statements and understandings such as “if John Doe walks off the edge
-of a cliff, he will fall,” “a flat sheet of paper has an edge,” etc.
-In this context, if statements 1 and 3 are supposed, then statement
-4 is logically true. On the other hand, if statements 2 and 3 are
-supposed, then statement 5 is logically true. Of course, for many
-centuries, nearly all men believed statement 1; and the importance of
-the years 1492 to 1521 (Columbus to Magellan) is linked with the final
-proof that statement 2 expresses a fact. So, depending on the game, or
-the context, whichever we wish to call it, almost any statement can
-be logically true. What we become interested in, therefore, is the
-connections between statements which make them _follow logically_.
-
-
-LOGICAL PATTERNS
-
-Perhaps the most familiar example of “following logically” is a pattern
-of words like the following:
-
-    1. All igs are ows.
-    2. All ows are umphs.
-    3. Therefore, all igs are umphs.
-
-If statements 1 and 2 are supposed, then statement 3 is logically true.
-In other words, statement 3 logically follows from statements 1 and 2.
-This word pattern is logically true, no matter what substitutions we
-make for igs, ows, and umphs. For example, we can replace igs by men,
-ows by animals, and umphs by mortals, and obtain:
-
-    4. All men are animals.
-    5. All animals are mortals.
-    6. Therefore, all men are mortals.
-
-The invented words “igs,” “ows,” “umphs” mark places in the _logical
-pattern_ where we can insert any names we are interested in. The words
-“all,” “are,” “therefore” and the ending s mark the logical pattern. Of
-course, instead of using invented words like “igs,” “ows,” “umphs” we
-would usually put _A_’s, _B_’s, _C_’s. This logical pattern is called a
-_syllogism_ and is one of the most familiar. But there are even simpler
-logical patterns that are also familiar.
-
-
-THE SIMPLEST LOGICAL PATTERNS
-
-Many simple logical patterns are so familiar that we often use them
-without being conscious of doing so. The simple logical patterns are
-marked by words like “and,” “or,” “else,” “not,” “if,” “then,” “only.”
-In the same way, simple arithmetical patterns are marked by words like
-“plus,” “minus,” “times,” “divided by.”
-
-Let us see what some of these simple logical patterns are. Suppose that
-we take two statements about which we have no factual information that
-might interfere with logical supposing:
-
-1. John Doe is eligible for insurance.
-
-2. John Doe requires a medical examination.
-
-In practice, we might be concerned with such statements when writing
-the rules governing a plan of insurance for a group of employees. Here,
-we shall play a game:
-
-    (1) We shall make up some new statements from
-        statements 1 and 2, using the words “and,”
-         “or,” “else,” “not,” “if,” “then,” “only.”
-
-    (2) We shall examine the logical patterns that we can make.
-
-    (3) We shall see what we can find out about their
-        logical truth.
-
-Suppose we make up the following statements:
-
-    3. John Doe is not eligible for insurance.
-
-    4. John Doe does not require a medical examination.
-
-    5. John Doe is eligible for insurance and requires a medical
-       examination.
-
-    6. John Doe is eligible for insurance, and John Doe is eligible
-       for insurance.
-
-    7. John Doe is eligible for insurance, or John Doe requires
-       a medical examination.
-
-    8. If John Doe is eligible for insurance, then he requires
-       a medical examination.
-
-    9. John Doe requires a medical examination if and only if
-       he is eligible for insurance.
-
-    10. John Doe is eligible for insurance or else he requires
-        a medical examination.
-
-Now clearly it is troublesome to repeat quantities of words when we
-are interested only in the way that “and,” “or,” “else,” “not,” “if,”
-“then,” “only” occur. So, let us use just 1 and 2 for the two original
-statements, remembering that “1 AND 2” means here “statement 1 AND
-statement 2” and does not mean 1 plus 2. Then we have:
-
-     3: NOT-1
-     4: NOT-2
-     5: 1 AND 2
-     6: 1 AND 1
-     7: 1 OR 2
-     8: IF 1, THEN 2
-     9: 1 IF AND ONLY IF 2
-    10: 1 OR ELSE 2
-
-Here then are some simple logical patterns that we can make.
-
-
-CALCULATION OF LOGICAL TRUTH
-
-Now what can we find out about the logical truth of statements 3 to
-10? If we know something about the truth or falsity of statements
-1 and 2, what will logically follow about the truth or falsity of
-statements 3 to 10? In other words, how can we calculate the logical
-truth of statements 3 to 10, given the truth or falsity of statements 1
-and 2?
-
-For example, 3 is NOT-1; that is, statement 3 is the negative or the
-_denial_ of statement 1. It follows logically that, if 1 is true, 3 is
-false; if 1 is false, 3 is true. Suppose that we use _T_ for logically
-true and _F_ for logically false. Then we can show our calculation of
-the logical truth of statement 3 in Table 1.
-
-       Table 1         Table 2
-
-     1  | NOT-1 = 3    2  | NOT-2 = 4
-        |                 |
-    _T_ |    _F_      _T_ |    _F_
-    _F_ |    _T_      _F_ |    _T_
-
-Our rule for calculation is: For _T_ put _F_; for _F_ put _T_. Of
-course, exactly the same rule applies to statements 2 and 4 (see Table
-2). The _T_ and _F_ are called _truth values_. Any meaningful statement
-can have truth values. This type of table is called a _truth table_.
-For any logical pattern, we can make up a truth table.
-
-Let us take another example, “AND.” Statement 5 is the same as
-statement 1 AND statement 2. How can we calculate the logical truth of
-statement 5? We can make up the same sort of a table as before. On the
-left-hand side of this table, there will be 4 cases:
-
-    1. Statement 1 true, statement 2 true.
-    2. Statement 1 false, statement 2 true.
-    3. Statement 1 true, statement 2 false.
-    4. Statement 1 false, statement 2 false.
-
-On the right-hand side of this table, we shall put down the truth
-value of statement 5. Statement 5 is true if both statements 1 and
-2 are true; statement 5 is false in the other cases. We know this
-from our common everyday experience with the meaning of “AND” between
-statements. So we can set up the truth table, and our rule for
-calculation of logical truth, in the case of AND, is shown on Table 3.
-
-          Table 3
-
-     1   2  | 1 AND 2 = 5
-            |
-    _T_ _T_ |     _T_
-    _F_ _T_ |     _F_
-    _T_ _F_ |     _F_
-    _F_ _F_ |     _F_
-
-“AND” and the other words and phrases joining together the original two
-statements to make new statements are called _connectives_, or _logical
-connectives_. The connectives that we have illustrated in statements 7
-to 10 are: OR, IF ··· THEN, IF AND ONLY IF, OR ELSE.
-
-Table 4 shows the truth table that applies to statements 7, 8, 9, and
-10. This truth table expresses the calculation of the logical truth or
-falsity of these statements.
-
-                            Table 4
-
-                                     1 IF AND
-             1 OR 2   IF 1, THEN 2   ONLY IF 2   1 OR ELSE 2
-     1   2  |  = 7         = 8           = 9         = 10
-            |
-    _T_ _T_ |  _T_         _T_           _T_          _F_
-    _F_ _T_ |  _T_         _T_           _F_          _T_
-    _T_ _F_ |  _T_         _F_           _F_          _T_
-    _F_ _F_ |  _F_         _T_           _T_          _F_
-
-The “OR” (as in statement 7) that is defined in the truth table is
-often called the _inclusive “or”_ and means “AND/OR.” Statement 7,
-“1 OR 2,” is considered to be the same as “1 OR 2 OR BOTH.” There is
-another “OR” in common use, often called the _exclusive “or,”_ meaning
-“OR ELSE” (as in statement 10). Statement 10, “1 OR ELSE 2,” is the
-same as “1 OR 2 BUT NOT BOTH” or “EITHER 1 OR 2.” In ordinary English,
-there is some confusion over these two “OR’s.” Usually we rely on
-the context to tell which one is intended. Of course, such reliance
-is not safe. Sometimes we rely on a necessary conflict between the
-two statements connected by “OR” which prevents the “both” case from
-being possible. In Latin the two kinds of “OR” were distinguished by
-different words, _vel_ meaning “AND/OR,” and _aut_ meaning “OR ELSE.”
-
-The “IF ··· THEN” that is defined in the truth table agrees with our
-usual understanding that (1) when the “IF clause” is true, the “THEN
-clause” must be true; and (2) when the “IF clause” is false, the “THEN
-clause” may be either true or false. The “IF AND ONLY IF” that is
-defined in the truth table agrees with our usual understanding that (1)
-if either clause is true, the other is true; and (2) if either clause
-is false, the other is false.
-
-In statement 6, there are only two possible cases, and the truth table
-is shown in Table 5.
-
-        Table 5
-
-     1  | 1 AND 1 = 6
-        |
-    _T_ |      _T_
-    _F_ |      _F_
-
-We know that 6 is true if and only if 1 is true. In other words, the
-statement “1 AND 1 IF AND ONLY IF 1” is true, no matter what statement
-1 may refer to. It is because of this fact that we never use a
-statement in the form “1 and 1”: it can always be replaced by the plain
-statement “1.”
-
-
-LOGICAL-TRUTH CALCULATION BY EXAMINING CASES AND REASONING
-
-Now you may say that this is all very well, but what good is it? Almost
-anybody can use these connectives correctly and certainly has had a
-great deal of practice using them. Why do we need to go into truth
-values and truth tables?
-
-When we draft a contract or a set of rules, we often have to consider
-several conditions that give rise to a number of cases. We must avoid:
-
-    1. All _conflicts_, in which two statements that disagree
-       apply to the same case.
-
-    2. All _loopholes_, in which there is a case not covered
-       by any statement.
-
-If we have one statement or condition only, we have to consider 2
-possible cases: the condition satisfied or the statement true;
-the condition not satisfied or the statement false. If we have 2
-conditions, we have to consider 4 possible cases: true, true; false,
-true; true, false; false, false. If we have 3 conditions, we have to
-consider 8 possible cases one after the other (see Table 6).
-
-
-Table 6
-
-    CASE   1ST CONDITION   2ND CONDITION   3RD CONDITION
-
-     1          _T_             _T_             _T_
-     2          _F_             _T_             _T_
-     3          _T_             _F_             _T_
-     4          _F_             _F_             _T_
-
-     5          _T_             _T_             _F_
-     6          _F_             _T_             _F_
-     7          _T_             _F_             _F_
-     8          _F_             _F_             _F_
-
-Instead of _T_’s and _F_’s, we would ordinarily use _check-marks_ (✓)
-and _crosses_ (✕), which, of course, have the same meaning. We may
-consider and study each case individually. In any event, we must make
-sure that the proposed contract or set of rules covers all the cases
-without conflicts or loopholes.
-
-The number of possible cases that we have to consider doubles whenever
-one more condition is added. Clearly, it soon becomes too much work
-to consider each case individually, and so we must turn to a second
-method, thoughtful classifying and reasoning about classes of cases.
-
-Now suppose that the number of conditions increases: 4 conditions give
-rise to 16 possible cases; 5, 6, 7, 8, 9, 10, ··· conditions give rise
-to 32, 64, 128, 256, 512, 1024, ··· cases respectively. Because of the
-large number of cases, we soon begin to make mistakes while reasoning
-about classes of cases. We need a more efficient way of knowing whether
-all cases are covered properly.
-
-
-LOGICAL-TRUTH CALCULATION BY ALGEBRA
-
-One of the more efficient ways of reasoning is often called the
-_algebra of logic_. This algebra is a part of a new science called
-_mathematical logic_. Mathematical logic is a science that has the
-following characteristics:
-
-    It studies chiefly nonnumerical reasoning.
-
-    It seeks accurate meanings and necessary consequences.
-
-    Its chief instruments are efficient symbols.
-
-Mathematical logic studies especially the logical relations expressed
-in such words as “or,” “and,” “not,” “else,” “if,” “then,” “only,”
-“the,” “of,” “is,” “every,” “all,” “none,” “some,” “same,” “different,”
-etc. The algebra of logic studies especially only the first seven of
-these words.
-
-The great thinkers of ancient Greece first studied the problems
-of logical reasoning as these problems turned up in philosophy,
-psychology, and debate. Aristotle originated what was called _formal
-logic_. This was devoted mainly to variations of the logical pattern
-shown above called the syllogism. In the last 150 years, the fine
-symbolic techniques developed by mathematicians were applied to
-the problems of the calculation of logical truth, and the result
-was mathematical logic, much broader and much more powerful than
-formal logic. A milestone in the development of mathematical logic
-was _The Laws of Thought_, written by George Boole, a great English
-mathematician, and published in 1854. Boole introduced the branch of
-mathematical logic called the algebra of logic, also called _Boolean
-algebra_. In late years, all the branches of mathematical logic have
-been improved and made easier to use.
-
-We can give a simple numerical example of Boolean algebra and how it
-can calculate logical truth. Suppose that we take the truth value of a
-statement as 1 if it is true and 0 if it is false. Now we have numbers
-1 and 0 instead of letters _T_ and _F_. Since they are numbers, we can
-add them, subtract them, and multiply them. We can also make up simple
-numerical formulas that will let us calculate logical truth. If _P_
-and _Q_ are statements, and if _p_ and _q_ are their truth values,
-respectively, we have Table 7.
-
-
-Table 7
-
-        STATEMENT             TRUTH VALUE
-    NOT-_P_                   1 - _p_
-    _P_ AND _Q_               _pq_
-    _P_ OR _Q_                _p_ + _q_ - _pq_
-    IF _P_, THEN _Q_          1 - _p_ + _pq_
-    _P_ IF AND ONLY IF _Q_    1 - _p_ - _q_ + 2_pq_
-    _P_ OR ELSE _Q_           _p_ + _q_ - 2_pq_
-
-For example, suppose that we have two statements _P_ and _Q_:
-
-    _P_: John Doe is eligible for insurance.
-
-    _Q_: John Doe requires a medical examination.
-
-To test that the truth value of “_P_ OR _Q_” is _p_ + _q_-_pq_, let us
-put down the four cases, and calculate the result (see Table 8).
-
-
-Table 8
-
-    _p_ _q_ | _p_ + _q_ - _pq_
-                      |
-     1   1  | 1 + 1 - 1 = 1
-     0   1  | 0 + 1 - 0 = 1
-     1   0  | 1 + 0 - 0 = 1
-     0   0  | 0 + 0 - 0 = 0
-
-Now we know that _P_ or _Q_ is true if and only if either one or both
-of _P_ and _Q_ are true, and thus we see that the calculation is
-correct.
-
-The algebra of logic (see also Supplement 2) is a more efficient way of
-calculating logical truth. But it is still a good deal of work to use
-the algebra. For example, if we have 10 conditions, we shall have 10
-letters like _p_, _q_ to handle in calculations. Thus we need a still
-more efficient way.
-
-
-CALCULATION OF CIRCUITS BY THE ALGEBRA OF LOGIC
-
-In 1937 a research assistant at Massachusetts Institute of Technology,
-Claude E. Shannon, was studying for his degree of master of science.
-He was enrolled in the Department of Electrical Engineering. He was
-interested in automatic switching circuits and wondered why an algebra
-should not apply to them. He wrote his thesis on the answer to this
-question and showed that:
-
-    (1) There is an algebra that applies to switching circuits.
-
-    (2) It is the algebra of logic.
-
-A paper, based on his thesis, was published in 1938 in the
-_Transactions of the American Institute of Electrical Engineers_ with
-the title “A Symbolic Analysis of Relay and Switching Circuits.”
-
-[Illustration: FIG. 1. Switches in series.]
-
-For a simple example of what Shannon found out, suppose that we have
-two switches, 1, 2, in series (see Fig. 1). When do we get current
-flowing from the source to the sink? There are 4 possible cases and
-results (see Table 9).
-
-
-Table 9
-
-    SWITCH 1 IS CLOSED   SWITCH 2 IS CLOSED   CURRENT FLOWS
-           Yes                  Yes                Yes
-           No                   Yes                No
-           Yes                  No                 No
-           No                   No                 No
-
-Now what does this table remind us of? It is precisely the truth table
-for “AND.” It is just what we would have if we wrote down the truth
-table of the statement “Switch 1 is closed AND switch 2 is closed.”
-
-[Illustration: FIG. 2. Switches in parallel.]
-
-[Illustration: FIG. 3. Switch open—current flowing.]
-
-Suppose that we have two switches 1, 2 in parallel (see Fig. 2). When
-do we get current flowing from the source to the sink? Answer: when
-either one or both of the switches are closed. Therefore, this circuit
-is an exact representation of the statement “Switch 1 is closed or
-switch 2 is closed.”
-
-Suppose that we have a switch that has two positions, and at any time
-must be at one and only one of these two positions (see Fig. 3).
-Suppose that current flows only when the switch is open. There are two
-possible cases and results (see Table 10).
-
-
-Table 10
-
-    SWITCH 1 IS CLOSED   CURRENT FLOWS
-
-           Yes                No
-           No                 Yes
-
-This is like the truth table for “NOT”; and this circuit is an exact
-representation of the statement “Switch 1 is NOT closed.” (_Note_:
-These examples are in substantial agreement with Shannon’s paper,
-although Shannon uses different conventions.)
-
-We see, therefore, that there is a very neat correspondence between the
-algebra of logic and automatic switching circuits. Thus it happens that:
-
-    1. The algebra of logic can be used in the calculation of
-       some electrical circuits.
-
-    2. Some electrical circuits can be used in the calculations
-       of the algebra of logic.
-
-This fact is what led to the next step.
-
-
-LOGICAL-TRUTH CALCULATION BY MACHINE
-
-In 1946 two undergraduates at Harvard University, Theodore A. Kalin
-and William Burkhart, were taking a course in mathematical logic.
-They noticed that there were a large number of truth tables to be
-worked out. To work them out took time and effort and yet was a rather
-tiresome automatic process not requiring much thinking. They had had
-some experience with electrical circuits. Knowing of Shannon’s work,
-they said to each other, “Why not build an electrical machine to
-calculate truth tables?”
-
-They took about two months to decide on the essential design of the
-machine:
-
-    1. The machine would have dial switches in which logical
-       connectives would be entered.
-
-    2. It would have dial switches in which the numbers of
-       statements like 1, 2, 3 ··· would be entered.
-
-    3. It would scan the proper truth table line by line by
-       sending electrical pulses through the dial switches.
-
-    4. It would compute the truth or falsehood of the whole
-       expression.
-
-
-CONSTRUCTION AND COMPLETION OF THE KALIN-BURKHART LOGICAL-TRUTH
-CALCULATOR
-
-With the designs in mind, Kalin and Burkhart bought some war surplus
-materials, including relays, switches, wires, lights, and a metal
-box about 30 inches long by 16 inches tall, and 13 inches deep. From
-March to June, 1947, they constructed a machine in their spare time,
-assembling and mounting the parts inside the box. The total cost of
-materials was about $150. In June the machine was demonstrated in
-Cambridge, Mass., before several logicians and engineers, and in August
-it was moved for some months to the office of a life insurance company.
-There some study was made of the possible application of the machine in
-drafting contracts and rules.
-
-
-GENERAL ORGANIZATION OF THE MACHINE
-
-The logical-truth calculator built by Kalin and Burkhart is not giant
-in size, although giant in capacity. Like other mechanical brains,
-the machine is made up of many pieces of a rather small number of
-different kinds of parts. The machine contains about 45 dial switches,
-23 snap switches (or two-position switches), 85 relays, 6 push buttons,
-less than a mile of wire, etc. The lid of the metal box is the front,
-vertical panel of the machine.
-
-
-UNITS OF THE MACHINE
-
-The machine contains 16 units. These units are listed in Table 11, in
-approximately the order in which they appear on the front panel of the
-machine—row by row from top to bottom, and from left to right in each
-row.
-
-
-Table 11
-
-UNITS, THEIR NAMES, AND SIGNIFICANCE
-
-    UNIT ROW   PART       NO. MARK      NAME            SIGNIFICANCE
-
-     1    1 Small red     12  —   _Statement truth-_  Output: glows if
-            lights                   _value lights_      statement is
-                                                         assumed true
-                                                         in the case
-     2    1 2-position    12   ~   _Statement denial_  Input: if up,
-            snap switches            _switches_          statement
-                                                         is denied
-     3    2 14-position   12  _V_  _Statement_         Input of
-            dial switches            _switches_          statements
-     4    3 4-position    11  _k_  _Connective_        Input of
-            dial switches           _switches_           connectives:
-                                                       ∧ (and),
-                                                       ∨ (or),
-                                                       ▲ (if-then),
-                                                       ▼ (if and only if)
-     5    4 11-position   11  _A_  _Antecedent_        Input of
-            dial switches           _switches_           antecedents
-     6    5 11-position   11  _C_  _Consequent_        Input of
-            dial switches           _switches_           consequents
-     7    6 2-position    11  _S_  _Stop switches_     Input: if up,
-            snap switches                                associates
-                                                         connective to
-                                                         main truth-value
-                                                         light
-     8    6 2-position    11   ~   _Connective denial_ Input: if up,
-            snap switches            _switches_          statement
-                                                         produced by
-                                                         connective is
-                                                         denied
-     9    7 Red light and  1 Start _Automatic start_   Input: causes the
-            large button                                 calc. to start
-                                                         down a
-                                                         truth table
-                                                         automatically
-    10    7 Red light and  1 Start  _Power switch_     Input: turns the
-            2 buttons        Stop                        power on or off
-    11    7 2-position     1 Stop  “_Stop-on-true-or-_  Input: causes the
-            snap switch              _false_” _switch_   calc.to stop
-            and red                                      either on true
-            button                                       cases or on
-                                                         false cases
-    12    7 Yellow light   1  —   _Main truth-value_  Output: glows if
-                                     _light_             the statement
-                                                         produced by the
-                                                         main connective
-                                                         is true for the
-                                                         case
-    13    7 Large button   1 Man.  _Manual pulse_      Input: causes the
-                  Pulse              _button_            calc. to go
-                                                         to the next line
-                                                         of a truth table
-    14    7 11-position    1 _kⱼ_  _Connective check_  Output: glows when
-            dial switch            _switch and light_    any specified
-                                                         connective is
-                                                         true
-    15    7 13-position    1  TT  “_Truth-table-row-_ Input: causes the
-            dial switch       Row   _stop_” _switch_    calc. to stop on
-                              Stop                       last row of the
-                                                         the truth table
-    16 Be-   Continuous    1  —   _Timing control_    Input: controls the
-       tween dial knob                _knob_              speed at which
-       6 & 7 and button                                   the calculator
-                                                          scans rows of
-                                                          the truth table
-
-Some of the words appearing in this table need to be defined.
-_Connective_ here means “AND,” “OR,” “IF ··· THEN,” “IF AND ONLY IF.”
-Only these four connectives appear on the machine; others when needed
-can be constructed from these. The symbols used for these connectives
-in mathematical logic are ∧, ∨, ▲, ▼. These signs serve as labels
-for the connective switch points. In this machine, when there is a
-connective between two statements, the statement that comes before is
-called the _antecedent_ and the statement that comes after is called
-the _consequent_.
-
-
-HOW INFORMATION GOES INTO THE MACHINE
-
-Of the 16 units 13 are input units. They control the setup of the
-machine so that it can solve a problem. Of the 13 input units, those
-that have the most to do with taking in the problem are shown in Table
-12.
-
-
-Table 12
-
-          Name of                               KIND OF
-    UNIT  SWITCHES   MARK   SWITCH          SWITCH SETTINGS
-
-     3   Statement  _V_₁ to  Dial    Statements 1 to 12 or constant
-                     _V_₁₂                 _T_ or _F_
-     2   Statement     ~     Snap     Affirmative (down) or negative
-           denial                               (up)
-     4   Connective _k_₁ to  Dial    ∧ (AND),
-                     _k_₁₁           ∨ (OR),
-                                      ▲ (IF-THEN),
-                                      ▼ (IF AND ONLY IF)
-     8   Connective      ~   Snap     Affirmative (down) or negative
-           denial                              (up)
-     5   Antecedent _A_₁ to  Dial     _V_ or various _k_’s
-                     _A_₁₁
-     6   Consequent _C_₁ to  Dial     _V_ or various _k_’s
-                     _C_₁₁
-     7   Stop       _S_₁ to  Snap     Not connected (down) or
-                     _S_₁₁               connected (up)
-
-The first step in putting a problem on the machine is to express the
-whole problem as a single compound statement that we want to know the
-truth or falsity of. We express the single compound statement in a form
-such as the following:
-
-    _V k V k V k V k V k V k V k V k V k V k V k V_
-
-where each _V_ represents a statement, each _k_ represents a
-connective, and we know the grouping, or in other words, we know the
-antecedent and consequent of each connective.
-
-For example, let us choose a problem with an obvious answer:
-
-    PROBLEM. Given: statement 1 is true; and if statement 1 is true,
-    then statement 2 is true; and if statement 2 is true, then statement
-    3 is true; and if statement 3 is true, then statement 4 is true.
-    Is statement 4 true?
-
-How do we express this whole problem in a form that will go on the
-machine? We express the whole problem as a single compound statement
-that we want to know the truth or falsity of:
-
-If [1 and (if 1 then 2) and (if 2 then 3) and (if 3 then 4)], then 4
-
-The 8 statements occurring in this problem are, respectively: 1 1 2 2
-3 3 4 4. These are the values at which the _V_ switches (the statement
-dial switches, Unit 2) from _V_₁ to _V_₈ are set. The 7 connectives
-occurring in this problem are, respectively: AND, IF-THEN, AND,
-IF-THEN, AND, IF-THEN, IF-THEN. These are the values at which the _k_
-switches (the connective dial switches, Unit 4) from _k_₁ to _k_₇ are
-set.
-
-A grouping (one of several possible groupings) that specifies the
-antecedent and consequent of each connective is the following:
-
-    1 AND 1 IF-THEN 2 AND 2 IF-THEN 3 AND 3 IF-THEN 4 IF-THEN 4
-          |         |     |         |     |         |
-          +—————————+     +—————————+     +—————————+
-             _k_₂            _k_₄            _k_₆
-    |               |     |                         |
-    +———————————————+     +—————————————————————————+
-     _k_₁                            _k_₅
-    |                                               |
-    +———————————————————————————————————————————————+
-                     _k_₃
-    |                                                         |
-    +—————————————————————————————————————————————————————————+
-                                                        _k_₇
-
-The grouping has here been expressed graphically with lines but may be
-expressed in the normal mathematical way with parentheses and brackets
-as follows:
-
-    {[1 AND (1 IF-THEN 2)] AND [(2 IF-THEN 3) AND
-       (3 IF-THEN 4)]} IF-THEN 4.
-
-So the values at which the antecedent and consequent dial switches are
-set are as shown in Table 13.
-
-
-Table 13
-
-                ANTECEDENT          CONSEQUENT
-    CONNECTIVE    SWITCH    SET AT    SWITCH     SET AT
-       _k_₁        _A_₁       _V_      _C_₁        _k_₂
-       _k_₂        _A_₂       _V_      _C_₂        _V_
-       _k_₃        _A_₃       _k_₁     _C_₃        _k_₅
-       _k_₄        _A_₄       _V_      _C_₄        _V_
-       _k_₅        _A_₅       _k_₄     _C_₅        _k_₆
-       _k_₆        _A_₆       _V_      _C_₆        _V_
-       _k_₇        _A_₇       _k_₃     _C_₇        _V_
-
-In any problem, statements that are different are numbered one after
-another 1, 2, 3, 4 ···. A statement that is repeated bears always the
-same number. In nearly all cases that are interesting, there will be
-repetitions of the statements. If any statement appeared with a “NOT”
-in it, we would turn up the denial switch for that statement (Unit 2).
-
-The different connectives available on the machine are “AND,” “OR,” “IF
-··· THEN,” “IF AND ONLY IF.” If a “NOT” affected the compound statement
-produced by any connective, we would turn up the denial switch for that
-connective (Unit 8).
-
-The last step in putting the problem on the machine is to connect the
-main connective of the whole compound statement to the yellow light
-output (Unit 12). In this problem the last “IF-THEN,” _k_₇, is the
-main connective, the one that produces the whole compound statement.
-So we turn Stop Switch 7 (in Unit 7) that belongs to _k_₇ into the
-up position. There are a few more things to do, naturally, but the
-essential part of putting the information of the problem into the
-machine has now been described.
-
-
-HOW INFORMATION COMES OUT OF THE MACHINE
-
-Of the 16 units listed in Table 11, 3 are output units, and only 2 of
-these are really important, as shown in Table 14.
-
-
-Table 14
-
-    UNIT       NAME OF LIGHT          MARK       KIND OF LIGHT
-      1     Statement truth value  _V_₁ to _V_₁₂   Small, red
-     13     Main truth value                       Large, yellow
-
-The answer to a problem is shown by a pattern of the lights of Units
-1 and 13. The pattern of lights is equivalent to a row of the truth
-table. Each little red light (Unit 1) glows when its statement is
-assumed to be true, and it is dark when its statement is assumed to
-be false. The yellow light (Unit 13) glows when the whole compound
-statement is calculated to be logically true, and it is dark when the
-whole compound statement is calculated to be logically false.
-
-The machine turns its “attention” automatically to each line of the
-truth table one after the other, and pulses are fed in according to the
-pattern of assumed true statements. We can set the machine to stop on
-true cases or on false cases or on every case, so as to give us time
-to copy down whichever kind of results we are interested in. When we
-have noted the case, we can press a button and the machine will then go
-ahead searching for more cases.
-
-
-A COMPLETE AND CONCRETE EXAMPLE
-
-The reader may still be wondering when he will see a complete and
-concrete example of the application of the logical-truth calculator. So
-far we have given only pieces of examples in order to illustrate some
-explanation. Therefore, let us consider now the following problem:
-
-    PROBLEM. The A. A. Adams Co., Inc., has about
-    1000 employees. About 600 of them are insured under a
-    contract for group insurance with the I. I. Insurance
-    Co. Mr. Adams decides that more of his employees ought
-    to be insured. As a part of his study of the change, he
-    asks his manager in charge of the group insurance plan,
-    “What are the possible statuses of my employees who are
-    not insured?”
-
-    The manager replies, “I can tell you the names of the
-    men who are not insured, and all the data you may want
-    to know about them.”
-
-    Mr. Adams says, “No, John, that won’t be enough, for I
-    need to know whether there are any groups or classes
-    that for some basic reason I should exclude from the
-    change I am considering.”
-
-    So the manager goes to work with the following 5 statuses and
-    the following 5 rules, and he produces the following answer.
-    Our question is, “Is he right, or has he made a mistake?”
-
-    _Statuses._ A status for any employee is a report about
-    that employee, answering all the following 5 questions with
-    “yes” or “no.”
-
-    1. Is the employee eligible for insurance?
-
-    2. Has the employee applied for insurance?
-
-    3. Has the employee’s application for insurance been approved?
-
-    4. Does the employee require a medical examination for insurance?
-
-    5. Is the employee insured?
-
-_Rules._ The rules applying to employees are:
-
-    _A._ Any employee, to be insured, must be eligible
-      for insurance, must make application for insurance,
-      and must have such application for insurance approved.
-
-    _B._ Only eligible employees may apply for
-      insurance.
-
-    _C._ The application of any person eligible
-      for insurance without medical examination is
-      automatically approved.
-
-    _D._ (Naturally) an application can be approved
-      only if the application is made.
-
-    _E._ (Naturally) a medical examination will not be
-      required from any person not eligible for insurance.
-
-    _Answer by the Manager._ There are 5 possible
-      combinations of statuses for employees who are not
-      insured, as shown in Table 15.
-
-
-Table 15
-
-
-     POSSIBLE                         STATUS 3,   STATUS 4,
-    COMBINATION  STATUS 1, STATUS 2, APPLICATION EXAMINATION  STATUS 5,
-    OF STATUSES  ELIGIBLE   APPLIED   APPROVED    REQUIRED     INSURED
-
-          1        Yes       Yes        Yes          Yes         No
-          2        Yes       Yes        Yes          No          No
-          3        Yes       Yes        No           Yes         No
-          4        Yes       No         Yes          No          No
-          5        No        No         No           No          No
-
-The question may be asked why employees who are eligible, who have
-applied for insurance, who have had their applications approved, and
-who require no medical examination (combination 2) are yet not insured.
-The answer is that the rules given do not logically lead to this
-conclusion. As a matter of fact, there might be additional rules, such
-as: any sick employee must first return to work; or any period from
-date of approval of application to the first of the following month
-must first pass.
-
-The first step in putting this problem on the Kalin-Burkhart
-Logical-Truth Calculator is to rephrase the rules, using the language
-of the connectives that we have on the machine. The rules rephrased are:
-
-    _A._ If an employee is insured, then he is
-      eligible, he has applied for insurance, and his
-      application has been approved.
-
-    IF 5, THEN 1 AND 2
-      AND 3
-
-    _B._ If an employee has applied (under these
-      rules) for insurance, then he is eligible.
-
-    IF 2, THEN 1
-
-    _C._ If an employee is eligible for insurance, has
-      applied, and requires no medical examination, his
-      application is automatically approved.
-
-    IF 1 AND 2 AND
-      NOT-4, THEN 3
-
-    _D._ If an employee’s application has been
-      approved, then he has applied.
-
-    IF 3, THEN 2
-
-    _E._ If an employee is not eligible, then he does
-      not require a medical examination (under these rules).
-
-    IF NOT-1, THEN NOT-4
-
-To get the answer we seek, we must add one more rule _for this answer
-only_:
-
-    _F._ The employee is not insured.
-          NOT-5
-
-We now have a total of 4 + 2 + 4 + 2 + 2 + 1 occurrences of statements,
-or 15 occurrences. This is beyond the capacity of the existing machine.
-But fortunately Rule _F_ and Rule _A_ cancel each other; they may both
-be omitted; and this gives us 10 occurrences instead of 15. In other
-words, all the possible statuses under “Rule _B_ AND Rule _C_ AND Rule
-_D_ AND Rule _E_” will give us the answer we seek.
-
-The rephrasing and reasoning we have done here is perhaps not easy. For
-example, going from the logical pattern
-
-Only igs may be ows to the logical pattern
-
-    If it is an ow, then it is an ig
-
-as we did in rephrasing Rule _B_, deserves rather more thought and
-discussion than we can give to the subject here. A person who is
-responsible for preparing problems for the Logical-Truth Calculator
-should know the algebra of logic.
-
-Choosing an appropriate grouping, we now set on the machine:
-
-    {(IF 2, THEN 1) AND [IF (1 AND 2) AND NOT-4, THEN 3]} AND
-    [(IF 3, THEN 2) AND (IF NOT-1, THEN NOT-4)]
-
-The setting is as shown in Table 16. After this setting, the machine is
-turned on and set to stop on the “true” cases. The
-
-
-Table 16
-
-SETTING OF THE PROBLEM ON THE LOGICAL-TRUTH CALCULATOR
-
-    UNIT
-      3    Statement Dial No.         _V_₁ _V_₂ _V_₃ _V_₄ _V_₅ _V_₆
-      3    Statement Dial Setting      2    1    1    2    4    3
-      2    Statement Denial Switch
-             Setting                   —    —    —    —    up   —
-      4    Connective Dial No.        _k_₁ _k_₂ _k_₃ _k_₄ _k_₅ _k_₆
-      4    Connective Dial Setting     ▲    ∧   ∧   ∧    ▲   ∧
-      8    Connective Denial Switch
-             Setting                   —    —    —    —    —    —
-      5    Antecedent Dial No.        _A_₁ _A_₂ _A_₃ _A_₄ _A_₅ _A_₆
-      5    Antecedent Dial Setting    _V_  _k_₁ _V_  _k_₃ _k_₄ _k_₂
-      6    Consequent Dial No.        _C_₁ _C_₂ _C_₃ _C_₄ _C_₅ _C_₆
-      6    Consequent Dial Setting    _V_  _k_₅ _V_  _V_  _V_  _k_₈
-      7    Stop Switches, associating
-             connective to Main
-             Truth-Value Light         —    —    —    —    —    up
-     -----------------------------------------------------------------
-      3    Statement Dial No.         _V_₇ _V_₈ _V_₉ _V_₁₀ _V_₁₁ _V_₁₂
-      3    Statement Dial Setting      3    2    1    4    _F_   _F_
-      2    Statement Denial Switch
-             Setting                   —    —    up   up    —     —
-      4    Connective Dial No.        _k_₇ _k_₈ _k_₉ _k_₁₀ _k_₁₁
-      4    Connective Dial Setting     ▲    ∧   ▲   off   off
-      8    Connective Denial Switch
-             Setting                   —    —    —    —     —
-      5    Antecedent Dial No.        _A_₇ _A_₈ _A_₉ _A_₁₀ _A_₁₁
-      5    Antecedent Dial Setting    _V_  _k_₇ _V_  off   off
-      6    Consequent Dial No.        _C_₇ _C_₈ _C_₉ _C_₁₀ _C_₁₁
-      6    Consequent Dial Setting    _V_  _k_₉ _V_  off   off
-      7    Stop Switches, associating
-             connective to Main
-             Truth-Value Light         —    —    —    —     —
-possible statuses of employees who are not insured are shown in
-Table 17. As we look down the last column in Table 17, we observe 6
-occurrences of _T_, instead of 5 as the manager determined (see Table
-15). Thus, when we compare the manager’s result with the machine
-result, we find an additional possible combination to be reported to
-Mr. Adams, combination 7:
-
-    Employee eligible, employee has not applied, employee’s
-      application not approved, employee requires a medical
-      examination, employee not insured.
-
-
-Table 17
-
-SOLUTION OF THE PROBLEM BY THE CALCULATOR
-
-      LEGEND:
-      {A} THE EMPLOYEE IS ELIGIBLE FOR INSURANCE
-      {B} THE EMPLOYEE HAS APPLIED FOR INSURANCE
-      {C} THE EMPLOYEE’S APPLICATION FOR INSURANCE HAS BEEN APPROVED
-      {D} THE EMPLOYEE REQUIRES A MEDICAL EXAMINATION
-      {E} THE EMPLOYEE IS INSURED
-      {F} CASE, OR COMBINATION NO.
-      {G} THE COMBINATION DOES NOT CONTRADICT THE RULES,
-             I.E., THE YELLOW LIGHT IS ON
-
-             {A}   {B}   {C}   {D}   {E}   {F}   {G}
-    _Status_: 1     2     3     4     5
-             _T_   _T_   _T_   _T_   _F_    1    _T_
-             _F_   _T_   _T_   _T_   _F_    2    _F_
-             _T_   _F_   _T_   _T_   _F_    3    _F_
-             _F_   _F_   _T_   _T_   _F_    4    _F_
-
-             _T_   _T_   _F_   _T_   _F_    5    _T_
-             _F_   _T_   _F_   _T_   _F_    6    _F_
-             _T_   _F_   _F_   _T_   _F_    7    _T_
-             _F_   _F_   _F_   _T_   _F_    8    _F_
-
-             _T_   _T_   _T_   _F_   _F_    9    _T_
-             _F_   _T_   _T_   _F_   _F_   10    _F_
-             _T_   _F_   _T_   _F_   _F_   11    _F_
-             _F_   _F_   _T_   _F_   _F_   12    _F_
-
-             _T_   _T_   _F_   _F_   _F_   13    _F_
-             _F_   _T_   _F_   _F_   _F_   14    _F_
-             _T_   _F_   _F_   _F_   _F_   15    _T_
-             _F_   _F_   _F_   _F_   _F_   16    _T_
-
-Because of the medical examination, this additional class of employee
-would need to be considered rather carefully in any change of the group
-insurance plan.
-
-
-AN APPRAISAL OF THE CALCULATOR
-
-In appraising the Kalin-Burkhart Logical-Truth Calculator, we must
-remember that this is a first model. It was the only machine of its
-kind up to the end of 1948; and it worked.
-
-The cost of the machine, as stated before, was about $150 of parts and
-perhaps $1000 of labor. This is less than ¹/₁₀₀ of the cost of the
-other giant brains described in previous chapters. Yet we can properly
-call this machine a mechanical brain because it transfers information
-automatically from one part to another of the machine, has automatic
-control over the sequence of operations, and does certain kinds of
-reasoning.
-
-The machine is swift. It can check up to a 100 cases against a set of
-rules in less than 1 minute. It can check: 128 cases for 7 conditions
-in 1¼ minutes, 256 cases for 8 conditions in 2½ minutes, and 4096 cases
-for 12 conditions in 38 minutes. That is the limit of the present
-machine. Of course, setting up the machine to do a problem takes some
-more time.
-
-The programming of this machine to do a problem is less complicated
-than the programming of most of the big machines previously described.
-Of course, in order to prepare a problem for the machine, the preparer
-needs to know a fair amount of the algebra of logic. This, however, is
-not very hard. As to reliability, the machine has in practice been out
-of order less than 2 per cent of operating time.
-
-The big barrier to wide use of the machine, of course, is lack of
-understanding of the field of problems in which it can be applied.
-Even in this modern world of ours, we are in rather a primitive stage
-in regard to recognizing problems in logical truth and knowing how to
-calculate it. Here, however, is an electrical instrument for logical
-reasoning, and it seems likely that its applications will multiply.
-
-
-
-
-Chapter 10
-
-AN EXCURSION:
-
-THE FUTURE DESIGN OF MACHINES THAT THINK
-
-
-In the previous chapters we have described four giant mechanical
-brains finished by the end of 1946: Massachusetts Institute of
-Technology’s Differential Analyzer No. 2, Harvard’s IBM Automatic
-Sequence-Controlled Calculator, Moore School of Electrical
-Engineering’s Electronic Numerical Integrator and Calculator (Eniac),
-and Bell Telephone Laboratories’ General-Purpose Relay Computer. All
-these brains have actually worked long enough to have demonstrated
-thoroughly some facts of great importance.
-
-
-WHAT EXISTING MACHINES HAVE PROVED
-
-The existing mechanical brains have proved that information can be
-automatically transferred between any two registers of a machine.
-No human being is needed to pick up a physical piece of information
-produced in one part of the machine, personally move it to another part
-of the machine, and there put it in again. We can think of a mechanical
-brain as something like a battery of desk calculators or punch-card
-machines all cabled together and communicating automatically.
-
-The existing mechanical brains have also proved that flexible,
-automatic control over long sequences of operations is possible. We can
-lay out the whole routine to solve a problem, translate it into machine
-language, and put it into the machine. Then we press the “start”
-button; the machine starts whirring and prints out the answers as it
-obtains them. Mechanical brains have removed the limits on complexity
-of routine: the machine can carry out a complicated routine as easily
-as a simple one.
-
-The existing giant brains have shown that a machine with hundreds of
-thousands of parts will work successfully. It will operate accurately,
-it will run unattended, and it will have remarkably few mechanical
-troubles.
-
-These machines have shown that enormous speeds can be realized: 5000
-additions a second is Eniac’s record. High speed is needed for many
-problems in science, government, and business. In fact, there are
-economic and statistical problems, now settled by armchair methods,
-for which high-speed mechanical brains may make it possible to compute
-answers rather than guess them.
-
-Also, these machines have been shown to be reasonable in cost. The cost
-of each of the large calculators is in the neighborhood of $250,000 to
-$500,000. If we assume a ten-year life, which is conservative, the cost
-is about $3 to $6 an hour for 24-hour operation. Since each mechanical
-brain can, for problems for which it is suited, do the work of a
-hundred human computers, such a machine can save its cost half a dozen
-times. And these machines are only engineers’ models, built without the
-advantages of production-line assembly.
-
-The cost of giant mechanical brains under design in 1947 and 1948
-is in the neighborhood of $100,000 to $200,000. The main reason for
-the reduction from the previous cost is the use of cheaper automatic
-memory. As designs improve and charges for research and development are
-paid off, the cost should continue to go down.
-
-
-NEW DEVICES FOR HANDLING INFORMATION
-
-In the laboratories working on new mechanical and electronic brains,
-scientists are doing a lot of thinking about new devices for handling
-information. Research into devices for storing information shows that
-_magnetic wire_ as used in sound recording is a rather good storage
-medium.
-
-
-Magnetic Wire
-
-For example, on a hundredth of an inch of fine steel wire we
-can “write” a _magnetized spot_ by means of a small “writing”
-_electromagnet_. The electromagnet is simply some copper wire coiled
-around some soft iron shaped in a U. When current flows through the
-coil, the iron becomes a magnet, and the tips of the U magnetize the
-little section of the wire between them. The magnetized spot can be of
-two kinds, say north-south or south-north, depending on which way the
-current flows. We can “read” this difference by means of another small
-“reading” electromagnet. We can erase the spot by means of a stronger
-“erasing” magnet that produces a uniform magnetic state throughout the
-wire. The difference between north-south and south-north corresponds
-to the difference between 1 and 0, or “yes” and “no,” etc., and is
-a _unit of information_ (see Chapter 2). Many other variations are
-possible. For example, the presence or absence of a magnetized spot may
-be the unit of information, or the “writing,” “reading,” and “erasing”
-electromagnets all may be the same.
-
-Magnetic wire sound recordings made in the 1890’s are still good.
-This fact shows that magnetic wire may be a more permanent medium for
-storing information than is paper. Stray magnetic forces are likely
-to have no harmful effect on information stored on magnetic wire, for
-these forces would not be strong enough or detailed enough to change
-greatly the difference between the magnetized spot and its neighboring
-neutral area.
-
-A reel of magnetic wire a mile long and ³/₁₀₀₀ of an inch thick costs
-about $5. At 80 magnetized spots to the inch, a mile of wire can store
-about 5 million units of information. Hence, the cost of storing one
-unit of information is about ¹/₁₀₀₀₀ of a cent. The time needed for
-changing a magnetized spot from 1 to 0 or from 0 to 1 is about ¹/₁₀₀₀₀
-of a second.
-
-
-Magnetic Tape
-
-There is, however, a storage device that may be even more useful, and
-this is _magnetic tape_ (see Fig. 1). The usual size of such tape is ¼
-inch wide and 2 or 3 thousandths of an inch thick. Magnetic tape may be
-made of plastic with magnetic powder all through it, or it may be of
-paper coated with magnetic powder, or it may be of stainless steel or
-a magnetic alloy, or it may be of brass or a nonmagnetic alloy coated
-with a magnetic plating.
-
-Magnetic tape has the added advantage that from 4 to 20 channels across
-the tape can be filled with magnetized spots, and the cost then becomes
-about ¹/₁₀₀₀₀₀ of a cent per spot. It seems possible that 1000 units
-of information can be stored in a quarter of a square inch of magnetic
-tape. This means that more than 1 million units of information can be
-stored in a cubic inch of space filled with magnetic tape, and about 2
-billion units of information in a cubic foot, except that some of the
-space should be allotted to the reels and other equipment that hold
-the tape (see Fig. 2). This is closer packing than printed information
-in the telephone book, and yet with magnetic tape we can get to the
-information automatically.
-
-[Illustration: FIG. 1. Magnetic tape.]
-
-[Illustration: FIG. 2. Tape reels.]
-
-Think of the enormous files in libraries, government, and business.
-Think of the problems of space and cost and access which these files
-imply. We can then see that this new development may well be of
-extraordinary importance.
-
-
-Mercury Tanks
-
-[Illustration: FIG. 3. Mercury tank.]
-
-Scientists are investigating other storage devices having still more
-remarkable properties, but these have the disadvantage that, when the
-power goes off, the information vanishes. One of these new storage
-devices is called a _mercury tank_ (see Fig. 3). It consists mainly
-of a section of iron or steel pipe filled with mercury. At each end
-of this pipe, touching the mercury, is a thin slab of a crystal of
-_quartz_. Quartz, which is a common stone, and which nearly all sand
-is made of, changes its shape when pulsed with electricity. We put a
-pattern of electrical pulses into the quartz slab at one end of the
-mercury tank; for example, we could have the pattern 1101 meaning
-“pulse, pulse, no pulse, pulse.” The electrical pulses going into the
-quartz slab make the quartz vibrate. Thus ripples are produced in the
-mercury, and waves in the pattern 1101 meaning “wave, wave, no wave,
-wave” travel down the tank and strike the quartz slab at the far end.
-The quartz slab there changes its shape in the rhythm 1101, and it
-converts the waves back into electrical pulses in the same pattern.
-Then we take the pulses out of the far end along a wire, make them
-stronger again with an amplifier, give them the right form again, and
-feed them back into the front end of the mercury tank. The mercury tank
-is a clever use of the principle of an _echo_, as when you call across
-a valley and the rocks answer you back. We can store a pattern of 400
-pulses (each a unit of information, a 1 or a 0, and each a millionth
-of a second in duration), in a mercury tank about 20 inches long. A
-mercury tank and an echo are examples of _delay lines_—“lines” along
-which waves are “delayed.”
-
-
-Electrostatic Storage Tube
-
-Another of the memory devices being developed is called an
-_electrostatic storage tube_ (see Fig. 4). This is a big electronic
-tube with a _screen_ across one end. The screen may be of two layers:
-one of copper, which conducts electricity, and one of _mica_, a
-material that does not. In the other end of the tube is a _beam_ of
-electrons, which we can turn on and off and shoot at any of 2 or 3
-thousand specific points or _spots_ on the screen.
-
-[Illustration: FIG. 4. Electrostatic storage tube.]
-
-There are two sizes of _electric charge_ or quantity of electrons; we
-can call these 1 and 0. In about a millionth of a second, we can put
-either size of charge on one of the spots of the screen. With other
-circuits we can keep it there as long as we want, if the power does
-not flicker off. We can “remember” perhaps 2 or 3 thousand units of
-information in one of these electronic tubes. We can read, write, or
-erase any unit of information in a few millionths of a second.
-
-Neither the mercury tank nor the electrostatic storage tube had, by the
-end of 1947, been put into a working mechanical brain. But there is
-good reason to believe that they will be successful devices and will
-open up a new era of speed in storing and referring to information.
-In fact, several laboratories are developing electronic calculating
-circuits using these devices which will perform up to 100,000 additions
-a second or 10,000 multiplications a second. Our minds certainly
-stagger at the thought of such speeds.
-
-
-NEW OPERATIONS
-
-Many kinds of combining operations have already been built into one or
-more mechanical brains. The operations may be arithmetical: addition,
-subtraction, multiplication, division, looking up numbers in tables,
-etc. Or the operations may be logical: comparing, selecting, checking,
-etc. Additional logical operations will be built into some of the
-mechanical brains now being constructed: sorting, collating, matching,
-merging, etc.
-
-
-NEW IDEAS IN PROGRAMMING
-
-_Programming_—the way to give instructions to machines—is also being
-studied in the laboratories. Several new ideas of importance have
-developed as a result.
-
-One idea is that the machine should be able to store its instructions
-or _program_ or _routine_ in its memory in just the same physical ways
-as it stores numbers. There is basically no reason why numbers only
-should be stored in some registers, and instructions only stored in
-other registers.
-
-Another idea is that the machine should have in its permanent memory
-any subroutine it may need. For example, a subroutine should always be
-available in the machine for finding _square root_. At any time when a
-square root was needed, we would only have to call on the machine for
-the subroutine of square root. The machine would then consult the right
-part of its memory and carry out the subroutine for square root.
-
-A third idea, and one of the most interesting, is that the machine
-should be able to compute its own instructions. For example, consider a
-program for finding the product of two _matrices_ (see Supplement 2),
-each of 100 terms in an array of 10 columns and 10 rows, resulting in a
-new _matrix_ of 100 terms. The whole program can be made to consist of
-about 50 orders. Only one of them is “multiply,” and only one of them
-is “add”; the other orders consist of how to choose expressions to be
-multiplied or added, etc.
-
-Such problems as these are often fascinating to mathematicians, who
-love to play with the intricate ideas needed.
-
-
-NEW IDEAS IN RELIABILITY
-
-Reliability has a number of aspects:
-
-    1. No wrong results allowed out of the machine.
-
-    2. Few failures.
-
-    3. Rapid location of failures.
-
-    4. Quick repair or replacement of parts that fail.
-
-    5. Easy maintenance.
-
-    6. Unattended operation overnight.
-
-For example, Bell Laboratories proved that mechanical brains can be
-built so that no wrong results are allowed to come out. In other words,
-the machine checks itself all the time as it goes along and stops at
-once if the check shows that something is wrong. This is likely to be a
-standard feature of new automatic thinking machinery.
-
-The frequency of failures in the machinery being designed in the
-laboratories may be of the order of one or two mechanical failures
-a week. For any type of failure an alarm circuit and trouble lights
-will show what part of the machine needs attention. Plug-in parts for
-replacement are already in use in at least two of the four mechanical
-brains described and should be available in all the new machines. It is
-possible to build a machine that will automatically change from failing
-equipment to properly functioning equipment. For some years though,
-this may be too expensive to be reasonable.
-
-The use of magnetic tape for storage reduces greatly the number of
-parts and so increases reliability. For example, instead of 18,000
-electronic tubes in an electronic brain, there may be less than 3000.
-
-A final degree of reliability is gained when most of the time the
-machine operates unattended. Then, there is no human operator standing
-by who may fail to do the correct thing at the moment when the machine
-needs some attention. In fact, the motto for the room housing a
-mechanical brain should become, “Don’t think; let the machine do it
-for you.” Unattended operation from the end of one working day to
-the beginning of the next, with the machine changing itself from one
-problem to another problem, has already been proved possible on the
-Bell Laboratories machine.
-
-
-AUXILIARY DEVICES
-
-In order to use a mechanical brain, we have to give it and take from it
-language that it understands, _machine language_. A mechanical brain
-that can do 10,000 additions a second can very easily finish almost
-all its work at once. How can we, slow as we are, keep our friend,
-the giant brain, busy? We have found so far several answers to this
-question, none of them yet very good.
-
-Devices for preparing input will be very important. For each brain, we
-shall need a great many of these devices. For, at best, we type at a
-rate, say, of 4 characters a second, selecting any one of some 38 keys,
-each of which is equivalent to about 6 units of information. This is
-about 800 units of information per second. The machine, however, is
-likely to be able to gulp information from its input mechanism at the
-amazing rate of 60,000 units of information per second, equal to 75
-people typing with no mistakes and no resting. Fortunately, at least
-some of the time the machine will be busy computing!
-
-For an input-preparation device, we may get something that can be
-fastened to an ordinary typewriter and that will produce magnetic
-tape agreeing with what is printed by the typewriter. Since the input
-information must be carefully verified, we shall need a second magnetic
-tape device such as exists for paper tape on the Bell Laboratories
-machine: the _processor_. The processor takes two hand-prepared tapes,
-compares them, reports any differences, and produces a third tape. The
-third tape copies the two original tapes if they agree, and it receives
-corrected information as furnished by a girl at a keyboard if the two
-original tapes disagree.
-
-For information already on punch cards, we need an input device that
-will read punch cards and write on magnetic tape. Where information is
-on punched paper tape, we need a machine that will read punched paper
-tape and write on magnetic tape.
-
-Problem data, tables of numbers, and routine instructions will go
-into the mechanical brain. They will all be prepared on regular input
-devices. The machine will accept information in the form in which it is
-most convenient for you and me to prepare it. Then, the machine will
-be instructed to change the information into the form with which it is
-most convenient for the machine to operate.
-
-Many output devices will also be needed, since the machine will be able
-to produce information very swiftly. These output devices might be
-cabled to the machine. A kind of traffic control system would govern
-them. Each will have a magnetic tape that will be loaded up swiftly
-with information. Then the output device will unload its information
-more slowly, in any form that we may desire: printing, graphs, film,
-punch cards, or punched paper tape.
-
-The machine is likely to be able to put out information on magnetic
-tape at the same high speed of 60,000 units of information per
-second or 10,000 characters per second. But the best printing speed
-of an electric typewriter is about 10 or 12 characters a second.
-Card-punching speed is about 130 characters a second. Punch-card
-tabulator speed can reach a maximum of about 200 characters a second.
-Thus we see that here, too, we may be snowed under with the information
-that the giant brain puts out, if we fail to ask the giant only for
-what we really want.
-
-
-MECHANICAL BRAINS UNDER CONSTRUCTION
-
-This chapter would not be complete without mention of the great
-mechanical brains that were actually under construction at the end of
-1947. In power they are intermediate between the machinery now being
-designed, described in this chapter, and the earlier machines described
-in the previous chapters of this book.
-
-The mechanical brains under construction on December 31, 1947, were:
-
-    Harvard’s Sequence-Controlled Relay Calculator _Mark
-      II_, constructed at the Harvard Computation
-      Laboratory, tested there July 1947 to January 1948,
-      and delivered to the Naval Proving Ground, Dahlgren,
-      Va., in 1948.
-
-    The _IBM Selective-Sequence Electronic
-      Calculator_, constructed in the IBM laboratories,
-      Endicott, N. Y., and installed in 1947 at the office
-      of International Business Machines, 590 Madison Ave.,
-      New York, N. Y.
-
-    Moore School of Electrical Engineering’s _EDVAC_
-      (Electronic Digital Variable Automatic Computer)
-      being constructed partly at Moore School and partly
-      elsewhere, and to be delivered to the Ballistic
-      Research Laboratories, Aberdeen, Md.
-
-    Harvard’s Sequence-Controlled Electronic Calculator
-      _Mark III_, being constructed at the Harvard
-      Computation Laboratory, and to be delivered to the
-      Naval Proving Ground, Dahlgren, Va.
-
-We shall cover briefly (and perhaps a little technically) some of the
-main features of the first two of these machines; for, during 1948,
-they began to do problems. The other two had not been finished by
-the end of 1948 and so would be difficult to describe correctly, for
-mechanical brains _grow_, and design changes go on until they are
-finished—and even afterwards.
-
-Some information about these machines can be obtained from the
-organizations referred to above and from reports that should appear
-from time to time in some of the journals mentioned in Supplement
-3. There is also a regular section entitled “Automatic Computing
-Machinery” in the quarterly _Mathematical Tables and Other Aids to
-Computation_, where it is likely that current information may be found.
-
-
-Harvard’s Mark II
-
-The Harvard Sequence-Controlled Calculator Mark II began to do problems
-under test during July 1947. This machine is at least twelve times as
-powerful as Mark I (see Chapter 6) and was constructed entirely by
-the Harvard Computation Laboratory. The machine contains about 13,000
-relays of a new type that will operate reliably within ¹/₁₀₀ of a
-second.
-
-Numbers in the machine are regularly of 10 decimal digits between
-1.000,000,000 and 9.999,999,999, inclusive, multiplied by a power of 10
-between 1,000,000,000,000,000 and 0.000,000,000,000,001, inclusive.
-
-For storage of numbers, the machine has 100 relay registers totaling
-about 1200 decimal digits. Also, it can consult any one of 8 tape feeds
-for numbers and any one of 4 tape feeds for instructions. Effectively,
-the machine can read one number and one instruction from paper tape in
-¹/₃₀ of a second.
-
-The machine performs all arithmetical and most logical operations.
-In every second it can carry out 4 multiplications, 8 additions (or
-subtractions), and 12 transfers. Division is performed by rapid
-approximation using the other operations.
-
-In each second the machine can perform 30 instructions. An instruction
-is expressed by 6 digits between 0 and 7 which you can select and, in
-effect, by 3 more digits fixed by the time (within the second) when the
-machine reads the instruction. For example, in the 9th instruction of
-the 30 instructions in each second, we can specify a multiplicand. But,
-if we do not want to multiply right then—a rare event if we are coding
-wisely—we leave the 9th instruction empty. The machine may operate as a
-whole, attending to one problem; or the machine may be separated into
-halves, and each half will attend to its own problem.
-
-
-The IBM Selective-Sequence Electronic Calculator
-
-The IBM Selective-Sequence Electronic Calculator was announced publicly
-on January 27, 1948, after some months of trial running. It is a large
-and powerful mechanical brain, and it is the intention of International
-Business Machines to devote it to solving scientific problems. The
-staff of the Watson Scientific Computing Laboratory in New York will be
-mainly in charge of the machine.
-
-The machine contains about 12,500 electronic tubes and about 21,500
-relays. Numbers in the machine are regularly of either 14 or 19
-decimal digits. Instructions are expressed as numbers. For storage of
-information, the machine has a capacity of 8 registers totaling 160
-decimal digits of very rapid memory in electronic tubes. Also, it has
-about 150 registers totaling 3000 decimal digits of less rapid memory
-in relays. Also, it can consult any one of 66 paper tape feeds; each
-row on a paper tape can hold up to 78 punched holes or 19 decimal
-digits, and the machine can consult 25 rows on one tape in one second.
-These paper tapes together give the machine about 400,000 decimal
-digits of memory.
-
-For arithmetical and logical operations, the machine has an
-arithmetical unit using electronic tubes. This unit can carry out about
-50 multiplications or about 250 additions per second, including the
-transfers of numbers. In each second the machine can read and perform
-50 instructions, and each instruction consists, usually, of getting
-two numbers out of two relay registers, performing an operation, and
-putting the result into a third relay register.
-
-
-Eckert-Mauchly’s Binac
-
-As this book went to press, another mechanical brain, the Electronic
-Binary Automatic Computer, or BINAC, was announced on August 22,
-1949. This machine was constructed by the Eckert-Mauchly Computer
-Corporation, Philadelphia, Pa., for Northrop Aircraft, Inc., Hawthorne,
-Calif.
-
-This machine has some remarkable properties. It does addition or
-subtraction at the rate of 3500 per second. It does multiplication or
-division at the rate of 1000 per second. The input is from a keyboard
-or magnetic tape; the output is to magnetic tape or an electric
-typewriter. Binac has 512 registers of very rapid memory in mercury
-tanks, and each register holds 30 binary digits. The machine actually
-is a pair of twins: the storage, the computing element, and the control
-are double, and each twin runs in step with the other and checks
-every operation of the other. In tests in July the machine ran over
-10 consecutive hours with no error. Each twin has only 700 electronic
-tubes. Binac handles all numbers in binary notation, except that the
-keyboard and the typewriter express numbers in _octal notation_ (see
-Supplement 2). Finally, Binac is only 5 feet high, 4 feet long, and one
-foot wide.
-
-
-
-
-Chapter 11
-
-THE FUTURE:
-
-MACHINES THAT THINK, AND WHAT THEY MIGHT DO FOR MEN
-
-
-The pen is mightier than the sword, it is often said. And if this is
-true, then the pen with a motor may be mightier than the sword with a
-motor.
-
-In the Middle Ages, there were few kinds of weapons, and it was easy
-for a man to protect himself against most of them by wearing armor.
-As gunpowder came into use, a man could no longer carry the weight of
-armor that would protect him, and so armor was given up. But in 1917,
-armor, equipped with a motor and carrying the man and his weapons, came
-back into service—as the tank.
-
-In much the same way, in the Middle Ages, there were few books, and it
-was easy for a man to handle nearly all the information that was in
-books. As the printing press came into use, man’s brain could no longer
-handle all recorded information, and the effort to do so was given
-up. But in 1944, a brain to handle information, equipped with a motor
-and supporting the man and his reasoning, came into existence—as the
-sequence-controlled calculator.
-
-In previous chapters we have examined some of the giant mechanical
-brains that have been finished; we have also considered the design
-of such machines. Now in this chapter we shall discuss the future
-significance of machines that think, of motorized information. We shall
-discuss what we can foresee if we look with imagination into the future.
-
-There are two questions we need to ask: What types of machines that
-think can we foresee? What types of problems to be solved by these
-machines can we foresee?
-
-
-FUTURE TYPES OF MACHINES THAT THINK
-
-The machines that already exist show that some processes of thinking
-can already be performed very quickly:
-
-    Calculating: adding, subtracting,...
-    Reasoning: comparing, selecting,...
-    Referring: looking up information in lists,...
-
-We can expect other processes of thinking to come up to high speed
-through the further development of thinking machines.
-
-
-Automatic Address Book
-
-Nowadays when we wish to send out announcements of an event, like going
-to South America for a year, we may copy the addresses of our friends
-onto the envelopes by hand. In the future, we can see our address book
-as a spool of magnetic tape. When we wish to send out announcements,
-we put a stack of blank envelopes into the machine that will read the
-magnetic tape, and we press a button. Out will come the envelopes
-addressed.
-
-If we wish to select only those friends of ours whose last names we put
-down on a list, we can write the list on another magnetic tape, place
-it also in the machine, and set a few switches. Then the machine will
-read the names on the list, find their addresses in the address-book
-tape, and prepare only the envelopes we want. If a friend’s address
-changes, we can notify the machine. It will find his old address, erase
-it, and enter the new address.
-
-
-Automatic Library
-
-We can foresee the development of machinery that will make it possible
-to consult information in a library automatically. Suppose that you
-go into the library of the future and wish to look up ways for making
-biscuits. You will be able to dial into the catalogue machine “making
-biscuits.” There will be a flutter of movie film in the machine. Soon
-it will stop, and, in front of you on the screen, will be projected
-the part of the catalogue which shows the names of three or four books
-containing recipes for biscuits. If you are satisfied, you will press
-a button; a copy of what you saw will be made for you and come out of
-the machine.
-
-After further development, all the pages of all books will be available
-by machine. Then, when you press the right button, you will be able to
-get from the machine a copy of the exact recipe for biscuits that you
-choose.
-
-We are not yet at the end of foreseeable development. There will be
-a third stage. You will then have in your home an automatic cooking
-machine operated by program tapes. You will stock it with various
-supplies, and it will put together and cook whatever dishes you desire.
-Then, what you will need from the library will be a program or routine
-on magnetic tape to control your automatic cook. And the library,
-instead of producing a pictorial copy of the recipe for you to read and
-apply, will produce a routine on magnetic tape for controlling your
-cooking machine so that you will actually get excellent biscuits!
-
-Of course, you may have other kinds of automatic producing machinery in
-your home or office. The furnishing of routines to control automatic
-machinery will become a business of importance.
-
-
-Automatic Translator
-
-Another machine that we can foresee would be used for translating from
-one language to any other. We can call it an _automatic translator_.
-Suppose that you want to say “How much?” in Swedish. You dial into the
-machine “How much?” and press the button “Swedish,” and the machine
-will promptly write out “Hur mycket?” for you. It also will pronounce
-it, if you wish, for there would be little difficulty in recording on
-magnetic tape the pronunciation of the word as spoken by a good speaker
-of the language. The machine could be set to repeat the pronunciation
-several times so that the student could really learn the sound. He
-could learn it better, probably, by hearing it and trying to say it
-than he could by using any set of written symbols.
-
-
-Automatic Typist
-
-We now come to a possible machine that uses a new principle. This
-principle is that of being able to _recognize_ signs. This machine
-would perceive writing on a piece of paper and recognize that all the
-_a_’s that appear on the paper are cases of _a_, and that all the _b_’s
-that appear on it are instances of _b_, and so forth. The machine could
-then control an electric typewriter and copy the marks that it sees.
-The first stage of this machine would be one in which only printed
-characters of a high degree of likeness could be recognized. In later
-stages, handwriting, even rather illegible handwriting, might be
-recognizable by the machine. We can call it an _automatic typist_.
-
-The elements of the automatic typist would be the following:
-
-    1. _Phototubes_ (electronic tubes sensitive to
-        the brightness of light), which could sense the
-        difference between black and white (these already
-        exist).
-
-    2. A memory of the shapes of 52 letters, 10 digits,
-        and punctuation marks. Fine distinctions would be
-        required of this memory in some cases—like the
-        difference between the numeral 5 and the capital
-        letter S.
-
-    3. A control that would cause the machine to
-        _tune_ itself, so that a good matching between
-        the marks it observed and the shapes it remembered
-        would be reached.
-
-    4. A _triggering control_ so that, when the
-        machine had reached good enough matching between
-        its observations and its memory, the machine would
-        proceed to identify the marks, read them, and
-        transfer them.
-
-    5. An electric typewriter, which would respond to
-        the transferred instructions. (This also already
-        exists.)
-
-This machine is perhaps not so farfetched as it might seem. During
-World War II, gun-aiming equipment using the new technique _radar_
-reached a high stage of development. Many shots that disabled and sank
-enemy ships were fired in total darkness by radar-controlled guns.
-On the glowing screen in the control room, there were two spots, one
-that marked the target and one that reported the point at which the
-gun was aimed. These two spots could be brought almost automatically
-into agreement. In the same way, a report from a phototube telling
-the shape of an observed mark and a report from the memory of the
-machine telling the shape of a similar mark could be compared by the
-machine for likeness and, if judged enough alike, could be approved as
-identical.
-
-Even the phrase “enough alike” can be applied by a machine. During
-World War II, tremendous advances were made in machinery for
-deciphering enemy messages. Machines observed various features and
-patterns in enemy messages, swiftly counted the frequency of these
-features, and carried out statistical tests. Then the machines selected
-those few cases in which the patterns showed meaning instead of
-randomness.
-
-A machine like the automatic typist, if made flexible enough, would
-be, of course, extremely useful. A great load of dull office work is
-now being thrown on clerks whose task is to translate from writing and
-typing into languages that machines can read, such as punch cards.
-At the present time, if punch-card machines are widely used in a big
-company, the company must employ large numbers of girls whose sole
-duty is to read papers and punch up cards. A still bigger chore is the
-work of typists in all kinds of businesses whose main duty is to read
-handwriting, etc., and then copy the words on a typewriter.
-
-[Illustration: Each square in the grill is watched by a phototube.
-
-FIG. 1. Scheme for distinguishing _A_ and _H_ by 15
-phototubes.]
-
-Research has already begun on various features of the automatic typist
-because of its obvious labor-saving value. For example, many patents
-have been issued on schemes for dividing the area occupied by a letter
-or a digit into an array of spots, with a battery of phototubes
-each watching a spot. The reports from the phototubes together will
-distinguish the letter or digit. For example, if we consider _A_ and
-_H_ placed in a grill of fifteen spots, 5 long by 3 wide (see Fig.
-1), then the phototubes can distinguish between _A_ and _H_ by sensing
-black or white in the spot in the middle of the top row. When we
-consider how easily and swiftly a human being does this, we can once
-more marvel at the recognizing machine we all carry around with us in
-our heads.
-
-
-Automatic Stenographer
-
-Another development that we can foresee is one that we can call the
-_automatic stenographer_. This is a machine that will listen to sounds
-and write them down in properly spelled English words. The elements of
-this machine can be outlined:
-
-        1. Microphones, which can sense spoken sounds (these
-            already exist).
-
-        2. A memory storing the 40 (more or less) phonetic
-            units or sounds that make up English, such as the
-            23 consonant sounds,
-
-        _p_    _b_    _l_    _ng_
-        _f_    _v_    _m_    _th_
-        _t_    _d_    _n_    _r_
-        _s_    _z_    _h_    _y_
-        _k_    _g_           _w_
-        _ch_   _j_
-        _sh_   _zh_ (heard in “pleasure”)
-
-    and the 17 vowel sounds,
-
-              LONG            SHORT           OTHER
-        _A_  (“ate”)    _a_  (“cat”)    _ar_ (“are”)
-        _E_  (“eat”)    _e_  (“end”)    _aw_ (“awe”)
-        _I_  (“isle”)   _i_  (“in”)     _er_ (“err”)
-        _O_  (“owe”)    _o_  (“on”)     _ow_ (“owl”)
-        _U_  (“cute”)   _u_  (“up”)     _oi_ (“oil”)
-        _OO_ (“roof”)   _oo_ (“book”)
-
-        3. A collection of the rules of spelling in English,
-            containing many statements like
-
-        The sound _b_ is always spelled _b_
-
-        The sound _sh_ may be spelled _sh_ (ship), _s_ (sugar),
-            _ti_ (station), _ci_ (physician), _ce_ (ocean) or
-            _tu_ (picture) and other statements based on context,
-            word lists, derivation, etc. These are the statements
-            by means of which a good English speller knows how to
-            spell even words that he hears for the first time.
-
-        4. A triggering control so that, when the machine
-            reaches good enough matching between its
-            observations of sounds, its memory of sounds, and
-            its knowledge of spelling rules, the machine will
-            identify groups of sounds as words, determine their
-            spelling, and report the letters determined.
-
-        5. An electric typewriter, which would type the
-            reported letters.
-
-With this type of machine, you would dictate your letters into a
-machine (now existing) that would record your voice. Then the record
-would be placed on the automatic stenographer, and out would come your
-letters written and spaced as they should be.
-
-
-Automatic Recognizer
-
-We can foresee a recognizing machine with very general powers. Suppose
-that we call it an _automatic recognizer_ (see Fig. 2). It will have
-the following elements:
-
-    1. _Input._ This element will consist of a set
-        of observing instruments, capable of perceiving
-        sights, sounds, etc. There will be ways of
-        positioning or _tuning_ these instruments.
-
-    2. _Memory._ This element will store knowledge.
-        It may store the patterns of observations that we
-        are interested in; or it may store general rules on
-        how to find patterns of observations that we will
-        be interested in. It will contain knowledge about
-        acceptable groups of patterns, about actions to be
-        performed in response to patterns, etc.
-
-    3. _Program 1._ The element “Program 1” performs
-        a set of standard instructions. Under these
-        instructions, the machine:
-
-    Compares group after group of observations with the
-        information in the memory.
-
-    Compares these groups with patterns furnished, or seeks
-        to organize the observations into patterns.
-
-    Counts cases and tests frequencies.
-
-    Finds out how much matching with patterns there is.
-
-    Tunes the observing instruments in ways to increase
-        matching.
-
-[Illustration: FIG. 2. Scheme of an automatic recognizer.]
-
-    4. _Program 2._ The element “Program 2” performs
-        another set of standard instructions. Under these
-        instructions, the machine, if it is tuned well,
-        matches sets of observations one after another with
-        the patterns and so reads them.
-
-    5. _Triggering Control._ This element shifts the
-        control of the machine from Program 1 to Program
-        2. It does this when the machine reaches “good
-        matching.” We shall set the meaning of this into
-        the machine in much the same way as we set “warm”
-        into a thermostat.
-
-    6. _Output._ This element performs any action
-        that we want, depending on recognized patterns read
-        and any other knowledge or instructions stored in
-        the memory.
-
-The automatic recognizer will be capable of extraordinary tasks. With
-microphones and a large memory, this type of machine would be able to
-hear a foreign language spoken and translate it into spoken or written
-English. With phototubes and with an expanded filtering and decoding
-capacity as in deciphering machines, the automatic recognizer should be
-able to read a dead language, even those (such as Minoan or Etruscan)
-that have so far resisted efforts to read it. The machine would derive
-rules for the translation of the language and translate any sample.
-
-An automatic recognizer could perhaps be equipped with many sensitive,
-tiny observing instruments that could be placed around or in the brain
-and nervous systems of animals. Then the machine might enable us to
-find out what activity in the nervous system corresponds with what
-activity in the animal.
-
-
-TYPES OF PROBLEMS THAT MACHINES WILL SOLVE IN THE FUTURE
-
-We turn now to the second question regarding the future of machines
-that think: What types of problems can we foresee as solved by these
-machines?
-
-
-Problems of Control
-
-Probably the foremost problem which machines that think can solve is
-automatic control over all sorts of other machines. This involves
-controlling a machine that is running so that it will do the right
-thing at the right time in response to information. For example,
-suppose that you are mowing a lawn with a mowing machine. You watch
-the preceding strip so as to stay next to it. You watch the ends of
-the strips, where you turn around. If a stick is caught in the cutting
-blade, you stop and take it out. Now it is entirely possible to put
-devices on the mowing machine so that all these things will be taken
-care of automatically. In fact, in the case of plowing a large field,
-a tractor-plow can be equipped with a device that guides it next to
-the preceding furrow. Thus, once the first furrow around the edge has
-been made, riderless tractors will plow a whole field and stop in the
-middle.
-
-For another example, take a gas furnace for heating steam to keep a
-house warm. Such a furnace has automatic controls, which respond to the
-following information whenever reported:
-
-    House too warm.
-    House not warm enough.
-    Too much steam pressure.
-    Not enough water in boiler.
-    Gas flame not lit.
-    Daytime.
-    Nighttime.
-
-In fact, your own meaning of “warm” can be put into the control system:
-you set the dial on your thermostat at the temperature that “warm” is
-to be for you.
-
-In the future many kinds of automatic control will be common. We shall
-have automatic pilots for flying and landing airplanes. We shall
-have automatic missiles for destructive purposes, such as bombing
-and killing, and for constructive purposes, such as delivering mail
-and fast freight. An article in the magazine _Fortune_ for November
-1946 described the automatic factory (see Supplement 3). This is a
-factory in which there would be automatic arms for holding stuff being
-manufactured, and automatic feed lines for supplying material just
-where it is needed. All this factory would be controlled by machines
-that handle information automatically and produce actions that respond
-to information.
-
-This prospect fills us with concern as well as with amazement. How
-shall we control these automatic machines, these robots, these
-Frankensteins? What will there be left for us to do to earn our living?
-But more of this in the next chapter.
-
-
-Problems of Science
-
-Other problems for which we can foresee the use of machines that think
-are the understanding, and later the controlling, of nature. One of
-these problems is weather forecasting and weather control.
-
-
-The Weather Brain
-
-We can imagine the following type of machine—a _weather brain_. A
-thousand weather observatories all over the country observe the weather
-at 8 A.M. The observations are fed automatically through a countrywide
-network of communication lines into a central station. Here a giant
-machine, containing a great deal of scientific knowledge about the
-weather, takes in all the data reported to it. At 8:15 the weather
-brain starts to calculate; in half an hour it has finished, having
-produced an excellent forecast of the weather for the whole country.
-Then it proceeds to transmit its forecast all over the country. By 8:50
-every weather station, newspaper, radio station, and airport in the
-country has the details. In October 1945, Dr. V. K. Zworykin of the
-Princeton Laboratories of the Radio Corporation of America proposed
-solving the problem of weather forecasting in this way by a giant brain.
-
-The weather brain will have a second stage of application. From time to
-time and here and there, the weather is unstable: it can be triggered
-to behave in one way or another. For example, recently, pellets of
-_frozen carbon dioxide_—often called Dry Ice—have been dropped from
-planes and have caused rain. In fact, a few pounds of Dry Ice have
-apparently caused several hundred tons of rain or snow. In similar
-ways, we may, for example, turn away a hail storm so that hail will
-fall over a barren mountain instead of over a farming valley and
-thus protect crops. Or we may dispel conditions that would lead to a
-tornado, thus avoiding its damage. Both these examples involve local
-weather disturbances. However, even the greatest weather disturbances,
-like hurricanes and blizzards, may eventually be directed to some
-extent. Thus the weather may become to some degree subject to man’s
-control, and the weather brain will be able to tell men where and when
-to take action.
-
-
-Psychological Testing
-
-Another scientific problem to which new machinery for handling
-information applies is the problem of understanding human beings and
-their behavior. This increased understanding may lead to much wiser
-dealing with human behavior.
-
-For example, consider tests of aptitudes. If you take one of these
-tests, you may be asked to mark which word out of five suggested ones
-is nearest in meaning to a given word. Or your test may be 40 simple
-arithmetical problems to be solved in 25 minutes. Or you may be given
-a sheet with 20 circles, and be asked to put 3 dots in the first, 7
-dots in the second, 4 dots in the third, 11 dots in the fourth, and
-so on, irregularly; you may be given a total of 45 seconds to do this
-as well as you can. Now, if a vocational counselor gives you one of
-these tests, and if you get 84 out of 100 on it, he needs to know just
-what he has measured about you. Also, he needs to know whether he can
-reasonably forecast that, as a result of your grade of 84, you will
-be good at writing articles, or good at supervising the work of other
-people, or good at designing in a machine shop. He needs to know the
-records of people with scores of about 84 on this test and to have
-evidence supporting his forecasts.
-
-If we wish to make the most use of the tests, we need to carry out a
-good deal of statistics, mathematics, and logic. For example, it will
-turn out that answers to some questions are much more significant
-than answers to others, and so we can greatly improve the quality of
-the tests by keeping only the more significant questions. Powerful
-machinery for handling calculations will be very useful in the field of
-aptitude testing.
-
-But, you may ask, what if the person analyzing your answers has to use
-interpretations and judgments? If the judgments and interpretations can
-be expressed in words, and if the words can be translated into machine
-language, then the machine can carry out the analysis. Usually the
-difference between a rule and a judgment is simply this: a rule in a
-case in which it is hard to express all the factors being considered is
-called a judgment.
-
-
-Psychological Trainer
-
-It is conceivable that machines that think can eventually be applied
-in the actual treatment of mental illness and maladjustment. Consider
-what a physician does. In treating a psychiatric case, such as a
-_neurosis_, a physician uses words almost entirely. He asks questions.
-He listens to the patient’s answers. Each answer takes the physician
-nearer and nearer to a diagnosis. By and by the physician knows what
-most of the difficulty is. Then he must present his knowledge slowly
-to the patient, gradually guiding the patient to understanding. It is
-a psychological truth that telling a man in ten minutes what is wrong
-with him does not cure him. The physician seeks to free the patient
-from the tormenting circles of habit and worry in which he has been
-trapped. Often the diagnosis is short and the treatment is long; the
-reasons for the neurosis may soon be clear to the physician, but they
-may take months to become clear to the patient.
-
-Now let us consider the following kind of machine as an aid to the
-physician. We might call this kind of machine a _psychological
-trainer_, for in many ways it is like the training machines used in
-World War II for training a pilot to fly an airplane. The psychological
-trainer would have the following properties:
-
-    1. The machine is able to show sound movies—produce
-        pictures and utter words.
-
-    2. It is able to put before the patient: situations,
-        problems, questions, experiences, etc.
-
-    3. It is able to take in responses from the patient.
-
-    4. It is able to receive a program of instructions
-        from the physician.
-
-    5. Depending on the responses of the patient and on
-        the program from the physician, the training
-        machine can select more material to put before the
-        patient.
-
-    6. The training machine produces a record of what it
-        presented and of how the patient responded, so that
-        the physician and the patient can study the record
-        later.
-
-What sort of films would the machine hold? The machine could be loaded
-with a number of films which would help in the particular type of
-neurosis from which the patient was suffering.
-
-What sort of responses could the patient make? The patient might have
-buttons in front of him which he could press to indicate such answers
-as:
-
-    Yes       I don’t know      Repeat
-    No        It depends        Go ahead
-
-Also, the patient might hold a device—like a lie detector,
-perhaps—which would report his state of tenseness, etc., and so report
-what he really felt.
-
-Where would the machine’s questions come from? From one or more
-physicians very clever in the treatment of mental illness.
-
-Suppose that the patient is inconsistent in his answers? The machine,
-discovering the inconsistencies, could return to the subject and ask
-related questions in a different way. As soon as several questions
-related to the same point are answered consistently, the machine could
-exclude groups of questions that no longer apply and could proceed to
-other questions that would still apply.
-
-Patients would vary in their ability to go as fast as the machine
-could. So from time to time the machine would ask questions to test
-the effect of what it had presented; and, depending on the answers,
-the machine would go faster or would bring in additional material to
-clarify some point.
-
-This machine might have a few advantages over ordinary treatment. For
-example, with the machine, treatment does not depend on the physician’s
-making the right answer in a split second, as it may in a personal
-interview. Also, the patient might be franker with the machine than
-with the physician, for it might be arranged that the patient could
-review his record, and then decide whether to confess it to his
-physician.
-
-Such a machine would enable physicians to treat many more patients
-than they now can. In fact, it is estimated that nearly 50 per cent of
-persons who consult physicians are suffering only from mental illness.
-Such a machine would therefore be a great help.
-
-
-Problems of Business
-
-Another large group of problems for which we can foresee the use of
-machines that think is found in business and economics.
-
-For example, consider production scheduling in a business or a factory.
-The machine takes in a description of each order received by the
-business and a description of its relative urgency. The machine knows
-(that is, has in its memory) how much of each kind of raw material is
-needed to fill the order and what equipment and manpower are needed
-to produce it. The machine makes a schedule showing what particular
-men and what particular equipment are to be set to work to produce the
-order. The machine turns out the best possible production schedule,
-showing who should do what when, so that all the orders will be filled
-in the best sequence. What is the “best” sequence? We can decide what
-we think is the best sequence, and we can set the machine for making
-that kind of selection, in the same way as we decide what is “warm” and
-set the thermostat to produce it!
-
-On a much larger scale, we can use mechanical brains to study economic
-relations in a society. Everything produced in a society is made by
-consuming some materials, labor, equipment, and skill. The output
-produced by one man or factory or industry becomes the input for
-other men, factories, industries. In this way all economic units are
-linked together by many different kinds and degrees of dependence. The
-situation is, of course, complicated: it changes as time goes on and
-as people want different things produced. Economists have already set
-up simple models of economic societies and have studied them. But with
-machines that think, it will be possible to set up and study far more
-complicated models—models that are very much like the society we live
-in. We can then answer questions of economics by calculation instead of
-by arguments and counting noses. We shall be able to solve definitely
-such problems as: “How will a rise in the price of steel affect the
-farming industry?” “How much money must be paid out as wages and
-salaries so that consumer purchasing power will buy back what industry
-produces?”
-
-
-Machines and the Individual
-
-What about the ordinary everyday effects of these machines upon you
-and me as an individual? We can see that the new machinery will apply
-on a small scale even to us. Small machines using a few electronic
-tubes—much like a radio set, for example—and containing spools of
-magnetic wire or magnetic tape will doubtless be available to us. We
-shall be able to use them to keep addresses and telephone numbers, to
-figure out the income tax we should pay, to help us keep accounts and
-make ends meet, to remember many things we need to know, and perhaps
-even to give us more information. For there are a great many things
-that all of us could do much better if we could only apply what the
-wisest of us knows.
-
-We can even imagine what new machinery for handling information may
-some day become: a small pocket instrument that we carry around with
-us, talking to it whenever we need to, and either storing information
-in it or receiving information from it. Thus the brain with a motor
-will guide and advise the man just as the armor with a motor carries
-and protects him.
-
-
-
-
-Chapter 12
-
-SOCIAL CONTROL:
-
-MACHINES THAT THINK AND HOW SOCIETY MAY CONTROL THEM
-
-
-It is often easier for men to create a device than to guide it well
-afterwards: it is often easier for a scientist to study his science
-than to study the results for good or evil that his discoveries may
-lead to. But it is not right nor proper for a scientist, a man who is
-loyal to truth as an ideal, to have no regard for what his discoveries
-may lead to.
-
-This principle is now being widely recognized. Many scientists
-today—both as individuals and as groups, and especially the atomic
-scientists—are considering the results of their scientific discoveries;
-and they are sharing in the effort to render those results truly useful
-to humanity.
-
-It would be easy to leave out of this book any discussion of how
-machines that think may be controlled, any consideration of how they
-may be made truly useful to humanity. But that would be hardly right
-or proper. In concluding a book such as this one, that touches on many
-aspects of machines that think, we need to consider what can and should
-be done to make such machines of true benefit to all of humanity.
-
-So, we come to the most important of all our questions: What sort of
-control over machines that think do we need in human society?
-
-
-MACHINE THAT BOTH THINKS AND ACTS
-
-From a narrow point of view, a machine that only thinks produces
-only information. It takes in information in one state, and it puts
-out information in another state. From this viewpoint, information
-in itself is harmless; it is just an arrangement of marks; and
-accordingly, a machine that thinks is harmless, and no control is
-necessary.
-
-Although it is true that the information produced only becomes good or
-evil after other machinery or human beings act on the information, in
-reality a machine with the power to produce information is constructed
-only for the reason of its use. We want to know what such machines can
-tell us only because we can then proceed to act much more efficiently
-than before. For example, a guided missile needs a mechanical brain
-only because then it can reach its target. In all cases mechanical
-brains are inseparable from their uses.
-
-For the purposes of this chapter, the narrow view will be rejected
-because it dodges the issue. We shall be much concerned with the
-combination of a machine that thinks with another machine that acts;
-and we shall often call this combination the _robot machine_.
-
-
-READING THIS CHAPTER
-
-Now, before launching further into the discussion, we need to say
-that the conclusions suggested in this chapter are not final. Even
-if they are expressed a little positively in places, they are
-nevertheless subject to change as more information is discovered and
-as the appraisal of information changes with time. Also, almost any
-conclusions about social control—including, certainly, the conclusions
-in this chapter—are subject to controversy. But controversy is good:
-it leads to thought. The more minds that go to work on solving the
-problem of social control over robot machines and other products of
-the new technology—which is rushing upon us from the discoveries of
-the scientists—the better off we all will be. If, while stimulating
-disagreement, the ideas expressed in this chapter should succeed in
-stimulating thought and deliberation, the purpose of this chapter will
-be well fulfilled.
-
-Up to this point in this book, the emphasis has been on possibilities
-of benefits to humanity that may arise from machines that think. In
-this chapter, devoted as it is to the subject of control, the emphasis
-is on possibilities for harm. Both possibilities are valid, and the
-happening of either depends upon the actions of men. In much the same
-way, atomic energy is a great possibility for benefit and for harm. It
-is the nature of control to put a fence around danger; and so it is
-natural in this chapter that the weight of attention should shift to
-the dangerous aspects of machines that think.
-
-Perhaps a reader may feel that a chapter of this kind is rather out of
-place in a book, such as this one, that seeks to be scientific. If so,
-he is reminded that, in accordance with the general suggestions for
-reading this book stated in the preface, he should omit this chapter.
-
-
-FRANKENSTEIN
-
-Perhaps the first study of the consequences of a machine that thinks is
-a prophetic novel called _Frankenstein_, written more than a hundred
-years ago, in 1818. The author, then only 21 years old, was Mary W.
-Godwin, who became the wife of the poet Percy Bysshe Shelley.
-
-According to the story, a young Swiss, an ardent student of physiology
-and chemistry, Victor Frankenstein, finds the secret of life. He makes
-an extremely ugly, clever, and powerful monster, with human desires.
-Frankenstein promptly flees from his laboratory and handiwork. The
-monster, after seeking under great hardships for a year or two to earn
-fair treatment among men, finds himself continually attacked and harmed
-on account of his ugliness, and he becomes embittered. He begins to
-search for his creator for either revenge or a bargain. When they meet:
-
-    “I expected this reception,” said the daemon.
-
-    “All men hate the wretched; how then must I be hated
-    who am miserable beyond all living things! Yet you my
-    creator detest and spurn me, thy creature, to whom thou
-    art bound by ties only dissoluble by the annihilation
-    of one of us. You purpose to kill me. How dare you
-    sport thus with life? Do your duty towards me, and I
-    will do mine towards you and the rest of mankind. If
-    you will comply with my conditions, I will leave them
-    and you at peace; but if you refuse, I will glut the
-    maw of death, until it be satiated with the blood of
-    your remaining friends.”
-
-Frankenstein starts to comply with the main condition, which is to
-make a mate for the monster; but Frankenstein cannot bring himself
-to do it. So the monster causes the death one after another of all
-Frankenstein’s family and closest friends; and the tale finally ends
-with the death of Frankenstein and the disappearance of the monster.
-
-As the dictionary says about Frankenstein, “The name has become a
-synonym for one destroyed by his own works.”
-
-
-ROSSUM’S UNIVERSAL ROBOTS
-
-Perhaps the next study of the consequences of a machine that thinks
-is a remarkable play called _R.U.R._ (for Rossum’s Universal Robots),
-first produced in Prague in 1921. Karel Čapek, the Czech dramatist who
-wrote it, was then only 31. The word “robot” comes from the Czech word
-“robota,” meaning compulsory service.
-
-According to the play, Rossum the elder, a scientist, discovered a
-“method of organizing living matter” that was “more simple, flexible,
-and rapid” than the method used by nature. Rossum the younger, an
-engineer, founded a factory for the mass production of artificial
-workmen, robots. They had the form of human beings, intelligence,
-memory, and strength; but they were without feelings.
-
-In the first act, the factory under Harry Domin, General Manager, is
-busy supplying robots to purchasers all over the world—for work, for
-fighting, for any purpose at all, to anyone who could pay for them.
-Domin declares:
-
-    “... in ten years, Rossum’s Universal Robots will
-    produce so much corn, so much cloth, so much everything
-    that things will be practically without price. There
-    will be no poverty. All work will be done by living
-    machines. Everybody will be free from worry and
-    liberated from the degradation of labor. Everybody will
-    live only to perfect himself.... It’s bound to happen.”
-
-In the second act, ten years later, it turns out that Domin and the
-others in charge of the factory have been making some robots with
-additional human characteristics, such as the capacity to feel pain.
-The newer types of robots, however, have united all the robots against
-man, for the robots declare that they are “more highly developed than
-man, stronger, and more intelligent, and man is their parasite.”
-
-In the last act, the robots conquer and slay all men except one—an
-architect, Alquist, who in the epilogue provides a final quirk to the
-plot.
-
-
-FACT AND FANCY
-
-Now what is fact and what is fancy in these two warnings given to us a
-hundred years apart?
-
-Of course, it is very doubtful that a Frankenstein monster or a Rossum
-robot will soon be constructed with nerves, flesh, and blood like an
-animal body. But we know that many types of robot machines can even now
-be constructed out of hardware—wheels, motors, wires, electronic tubes,
-etc. They can handle many kinds of information and are able to perform
-many kinds of actions, and they are stronger and swifter than man.
-
-Of course, it is doubtful that the robot machines, by themselves and
-of their own “free will,” will be dangerous to human beings. But as
-soon as antisocial human beings have access to the controls over robot
-machines, the danger to society becomes great. We want to escape that
-danger.
-
-
-Escape from Danger
-
-A natural longing of many of us is to escape to an earlier, simpler
-life on this earth. Victor Frankenstein longed to undo the past. He
-said:
-
-    “Learn from me, if not by my precepts, at least by my
-    example, how dangerous is the acquirement of knowledge,
-    and how much happier that man is who believes his
-    native town to be the world, than he who aspires to
-    become greater than his nature will allow.”
-
-Any sort of return to the past is, of course, impossible. It is
-doubtful that men could, even if they wanted to, stop the great flood
-of technical knowledge that science is now producing. We all must
-now face the fact that the kind of world we used to live in, even so
-recently as 1939, is gone. There now exist weapons and machines so
-powerful and dangerous in the wrong hands that in a day or two most of
-the people of the earth could be put to death. Giant brains are closely
-related to at least two of these weapons: scientists have already used
-mechanical brains for solving problems about atomic explosives and
-guided missiles. In addition, thinking mechanisms designed for the
-automatic control of gunfire were an important part of the winning of
-World War II. They will be a still more important part of the fighting
-of any future war.
-
-Nor can we escape to another part of the earth which the new weapons
-will not reach. At 300 miles an hour, any spot on earth can be reached
-from any other in less than 48 hours. A modern plane exceeds this
-speed; a rocket or guided missile doubles or trebles it.
-
-Nor can we trust that some kind of good luck will pull us through and
-help men to escape the consequences of what men do. Both Frankenstein
-and Domin reaped in full the consequences of what they did. The history
-of life on this earth that is recorded in the rocks is full of evidence
-of races of living things that have populated the earth for a time
-and then become extinct, such as the dinosaurs. In that long history,
-rarely does a race survive. In our own day, insects and fungi rather
-than men have shown fitness to survive and spread over the earth:
-witness the blight that destroyed the chestnut trees of North America,
-in spite of the best efforts of scientists to stop it.
-
-There seems to be no kind of escape possible. It is necessary to
-grapple with the problem: How can we be safe against the threat of
-physical harm from robot machines?
-
-
-UNEMPLOYMENT
-
-The other chief threat from robot machines is against our economic
-life. Harry Domin, in _R.U.R._, you remember, prophesied: “All work
-will be done by living machines.” As an example, in the magazine
-_Modern Industry_ for Feb. 15, 1947, appeared a picture of a machine
-for selling books, and under the picture were the words:
-
-    _Another new product in robot salesmen_—Latest in
-    the parade of mechanical vending machines is this book
-    salesman.... It is designed for use in hospitals, rail
-    terminals, and stores. It offers 15 different titles,
-    selected manually, and obtained by dropping quarter in
-    slot. Cabinet stores 96 books.
-
-Can you feel the breath of the robot salesman, workman, engineer,—--,
-on the back of your neck?
-
-At the moment when we combine automatic producing machinery and
-automatic controlling machinery, we get a vast saving in labor and
-a great increase in technological unemployment. In extreme cases,
-perhaps, the effect of robot machines will be the disappearance of men
-from a factory. Such a factory will be like a modern power plant that
-turns a waterfall into electricity: once the machinery is installed,
-only one watchman is ordinarily needed. But, in most cases, this will
-be the effect: in a great number of factories, mines, farms, etc., the
-labor force needed will be cut by a great proportion. The effect is not
-different in quality, because the new development is robot machinery;
-but the amount of technological unemployment coming from robot machines
-is likely to be considerably greater than previously.
-
-The robot machine raises the two questions that hang like swords over
-a great many of us these days. The first one is for any employee: What
-shall I do when a robot machine renders worthless all the skill I have
-spent years in developing? The second question is for any businessman:
-How shall I sell what I make if half the people to whom I sell lose
-their jobs to robot machines?
-
-
-SOCIAL CONTROL AND ITS TWO SIDES
-
-The two chief harmful effects upon humanity which are to be expected
-from robot machines are physical danger and unemployment. These are
-serious risks, and some degree of social control is needed to guard
-against them.
-
-There will also be very great advantages from robot machines. The
-monster in _Frankenstein_ is right when he says, “Do your duty towards
-me, and I will do mine towards you and the rest of mankind.” And Harry
-Domin in _R.U.R._ is right as to possibility when he says, “There will
-be no poverty.... Everybody will be free from worry.” Social control
-must also be concerned with how the advantages from robot machines are
-to be shared.
-
-The problem of social control over men and their devices has always had
-two sides. The first side deals with what we might plan for control
-if men were reasonable and tolerant. This part of the problem seems
-relatively easy. The other side deals with what we must ordinarily
-arrange, since most men are often unreasonable and prejudiced and, as a
-result, often act in antisocial ways. This part of the problem is hard.
-Let us begin with the easier side first.
-
-
-TYPES OF CONTROL—IF MEN WERE REASONABLE
-
-In seeking to fulfill wants and achieve safety, men have used hundreds
-of types of control. The main types are usually called political and
-economic systems, but there are always great quantities of exceptions.
-The more mature and freer the society, the greater the variety of types
-of control that can be found in it.
-
-Probably the most widely used type of control in this country is
-private and public control working together, as private ownership
-and public regulation—for example, railroads, banks, airlines, life
-insurance companies, telephone systems, and many others. It would be
-reasonable to expect private ownership and public regulation of a
-great many classes of robot machines, to the end that they would never
-threaten the safety of people.
-
-Another common type of control is public ownership and operation;
-examples are toll bridges, airports, city transit systems, and
-water-supply systems. Atomic energy was so clearly fraught with
-serious implications that in 1946 the Congress of the United States
-placed it entirely under public control expressed as the Atomic
-Energy Commission. There is a class of robot machinery which has
-already reached the stage of acute public concern: guided missiles and
-automatic fire-control. It would be reasonable that in this country
-all activity in this subdivision should be under close control by the
-Department of Defense.
-
-In the international arena, again, the problem becomes soluble if
-we assume men to be reasonable. An international agency, such as an
-organ of the United Nations, would take over inspection and control of
-robot machine activities closely affecting the public safety anywhere
-in the world. Particularly, this agency would concern itself with
-guided missiles, robot pilots for planes, automatic gunfire control,
-etc. Much manufacturing skill is needed to make such products as
-these: the factories where they could be manufactured would thereby
-be determined. Also, a giant brain is a useful device for solving
-scientific problems about weapons of mass destruction. So the agency
-would need to inspect the problems being solved on such machines. This
-agency would be responsible to a legislature or an executive body
-representing all the people in the world—if men were reasonable.
-
-In regard to the effects of robot machines on unemployment, again,
-if men were reasonable, the problem would be soluble. The problem is
-equivalent to the problem of abundance: how should men distribute the
-advantages of a vast increase in production among all the members of
-society in a fair and sensible way? A vast increase in production is
-not so impossible as it may seem. For example, in 1939, with 45 million
-employed, the United States index of industrial production was at 109,
-and, in 1943, with 52½ million employed, the index of production was at
-239.
-
-If men were reasonable, the net profits from robot machinery would
-be divided among (1) those who had most to do with devising the new
-machinery, and (2) all of society. A rule would be adopted (probably
-it could be less complicated than some existing tax rules) which would
-take into account various factors such as rewards to the inventors,
-incentives to continue inventing, adequate assistance to those made
-unemployed by the robot machines, reduction of prices to benefit
-consumers, and contributions to basic and applied scientific research.
-
-In fact, under the assumption “if men were reasonable,” it would hardly
-be necessary to devote a chapter to the problem of social control over
-robot machines!
-
-
-OBSTACLES
-
-The discussion above of how robot machines could be controlled
-supposing that men were reasonable, seems, of course, to be glaringly
-impractical. Men are not reasonable on most occasions most of the time.
-If we stopped at this point, again we would be dodging the issue. What
-are the obstacles to reasonable control?
-
-There are, it seems, two big obstacles and one smaller one to
-reasonable types of social control over robot machines. The smaller
-one is ignorance, and the two big obstacles are prejudice and a narrow
-point of view.
-
-
-Ignorance
-
-By ignorance we mean lack of knowledge and information. Now mechanical
-brains are a new and intricate subject. A great many people will,
-through no fault of their own, naturally remain uninformed about
-mechanical brains and robot machines for a long time. However, there is
-a widespread thirst for knowledge these days: witness in magazines, for
-example, the growth of the article and the decline of the essay. There
-is also a fairly steady surge of knowledge from the austere scientific
-fountain of new technology. We can thus see both a demand and a supply
-for information in such fields as mechanical brains and robot machines.
-We can expect, therefore, a fairly steady decline in ignorance.
-
-
-Prejudice
-
-Prejudice is a much more serious obstacle to reasonable control over
-robot machines. It will be worth our while to examine it at length.
-
-Prejudice is frequent in human affairs. For example, in some countries,
-but not in all, there is conflict among men, based on their religious
-differences. Again, in other countries, but not in all, there is
-wide discrimination among men, based on the color of their skin.
-Over the whole world today, there is a sharp lack of understanding
-between conservatives, grading over to reactionaries, on the one
-hand, and liberals, grading over to radicals, on the other hand. All
-these differences are based on men’s attitudes, on strongly held
-sets of beliefs. These attitudes are not affected by “information”;
-the “information” is not believed. The attitudes are not subject to
-“judgment”; they come “before judgment”: they are prejudices. Even
-in the midst of all the science of today, prejudice is widespread.
-In Germany, from 1933 to 1939, we saw one of the most scientific of
-countries become one of the most prejudiced.
-
-Prejudice is often difficult to detect. We find it hard to recognize
-even in ourselves. For a prejudice always seems, to the person who
-has it, the most natural attitude in the world. As we listen to other
-people, we are often uncertain how to separate information, guesses,
-humor, prejudice, etc. Circumstances compel us to accept provisionally
-quantities of statements just on other people’s say-so. A good test
-of a statement for prejudice, however, is to compare it with the
-scientific view.
-
-Prejudice is most dangerous for society. Its more extreme
-manifestations are aggressive war, intolerance (especially of strange
-people and customs), violence, race hatred, etc. In the consuming
-hatred that a prejudiced man has towards the object of his prejudice,
-he is likely to destroy himself and destroy many more people besides.
-In former days, the handy weapon was a sword or a pistol; not too much
-damage could be done when one man ran amuck. But nowadays a single use
-of a single weapon has slain 70,000 people (the atom bomb dropped at
-Hiroshima), and so a great many people live anxious and afraid.
-
-What is prejudice? How does it arise? How can it be cured, and thus
-removed from obstructing reasonable control over robot machines and the
-rest of today’s amazing scientific developments?
-
-Prejudice is a disease of men’s minds. It is infectious. The cause and
-development of the disease are about as follows: Deprive someone of
-something he deeply needs, such as affection, food, or opportunity.
-In this way hurt him, make him resentful, hostile; but prevent him
-from expressing his resentments in a reasonable way, giving him
-instead false outlets, such as other people to hurt, myths to believe,
-hostile behavior patterns to imitate. He will then break out with
-prejudices as if they were measles. The process of curing the disease
-of prejudice is about as follows: Make friends with the patient; win
-his trust. Encourage him to pour out his half-forgotten hates. Help him
-to talk them over freely, by means of questions but not criticisms,
-until finally the patient achieves insight, sees through his former
-prejudices, and drops them.
-
-In these days prejudice is a cardinal problem of society. It is
-perhaps conservative to say that a chief present requirement for the
-survival of human society—with the atom bomb, bacterial warfare, guided
-missiles, etc., near at hand—is cure of prejudice and its consequences,
-irrational and unrestrained hate.
-
-
-Narrow Point of View
-
-A narrow point of view regarding what is desirable or good is the third
-obstacle to rational control over robot machines. What do we mean by
-this?
-
-Our point of view as a two-year-old is based on pure self-interest.
-If we see a toy, we grab it. There is no prejudice about this; it is
-entirely natural—for two-year-olds. As we grow older, our point of
-view concerning what is good or desirable rapidly broadens: we think
-of others and their advantage besides our own. For example, we may
-become interested in a conservation program to conserve birds, or soil,
-or forests, and our point of view expands, embraces these objectives,
-which become part of our personality and loyalties.
-
-Unfortunately, it seems to be true that the expanding point of view,
-the expanding loyalties, of most people as they grow up are arrested
-somewhere along the line of: self, family, neighborhood, community,
-section of country, nation. An honorable exception is the scientists’
-old and fine tradition of world-wide unity and loyalty in the search
-for objective truth.
-
-Now the problem of rational control over robot machines and other
-parts of the new technology is no respecter of national boundaries. To
-be solved it requires a world-wide point of view, a loyalty to human
-society and its best interests, a social point of view.
-
-Almost all that you and I have and do and think is the result of a long
-history of human society on this earth. All men on the earth today are
-descendants of other men who lived 1000, 2000, 3000 ... years ago,
-whether they were Romans or Chinese or Babylonians or Mayas or members
-of any other race. To ride in a subway or an airplane, to talk on the
-telephone, to speak a language, to calculate, to survive smallpox or
-the black death, etc.—all these privileges are our inheritance from
-countless thousands of other human beings, of many countries, and
-nearly all of whom are now dead. During our lives we pass on to our own
-children an inheritance in which our own contribution is remarkably
-small. Since each person is the child of two others, the number of
-our forefathers is huge, and we are all undoubtedly blood cousins.
-Because of this relationship, and because we owe to the rest of
-society nearly all that we are, we have a social responsibility—we need
-to hold a social point of view. Each of us needs to accept and welcome
-a world-wide social responsibility, as a member of human society, as
-a beneficiary and trustee of our human inheritance. Otherwise we are
-drones, part of the hive without earning our keep. The social point of
-view is equitable, it is inspiring, and it is probably required now in
-order for human beings to survive. We need to let go of a narrow point
-of view.
-
-
-CONCLUSION
-
-We have now outlined the problem of social control over robot machines,
-supposing that human beings were reasonable. We have also discussed the
-practical obstacles that obstruct reasonable control.
-
-It is not easy to think of any yet organized group of people anywhere
-that would have both the strength and the vision needed to solve this
-problem through its own efforts. For example, a part of the United
-Nations might have some of the vision needed, but it does not have the
-power. Consequently, it is necessary and desirable for individuals
-and groups everywhere to take upon themselves an added load of social
-responsibility—just as they tend to do in time of war. People often
-“want to do their share.” Through encouragement and education, the
-basic attitude of a number of people can contain more of “This is our
-business; we have a responsibility for helping to solve this problem.”
-We also need public responsibility; we need a public body responsible
-for study, education, advice, and some measure of control. It might
-be something like an Atomic Energy Commission, Bacterial Defense
-Commission, Mental Health Commission, and Robot Machine Commission, all
-rolled into one.
-
-When, at last, there is an effective guarantee of the two elements
-physical safety and adequate employment, then at last we shall all
-be free from the threat of the robot machine. We can then welcome
-the robot machine as our deliverer from the long hard chores of many
-centuries.
-
-
-
-
-Supplement 1
-
-WORDS AND IDEAS
-
-
-The purpose of this book is to explain machines that think, without
-using technical words any more than necessary. This supplement is a
-digression. Its purposes are to consider how to explain in this way and
-to discuss the attempt made in this book to achieve simple explanation.
-
-
-WORDS AS INSTRUMENTS FOR EXPLAINING
-
-Words are the chief instruments we use for explaining. Of course, many
-other devices—pictures, numbers, charts, models, etc.—are also used;
-but words are the prime tools. We do most of our explaining with them.
-
-Words, however, are not very good instruments. Like a stone arrow-head,
-a word is a clumsy weapon. In the first place, words mean different
-things on different occasions. The word “line,” for example, has more
-than fifty meanings listed in a big dictionary. How do we handle the
-puzzle of many meanings? As we grow older we gather experience and we
-develop a truly marvelous capacity to listen to a sentence and then
-fit the words together into a pattern that makes sense. Sometimes we
-notice the time lag while our brain hunts for the meaning of a word we
-have heard but not grasped. Then suddenly we guess the needed meaning,
-whereupon we grasp the meaning of the sentence as a whole in much the
-same way as the parts of a puzzle click into place when solved.
-
-Another trouble with words is that often there is no good way to tell
-someone what a word means. Of course, if the word denotes a physical
-object, we can show several examples of the object and utter the word
-each time. In fact, several good illustrations of a word denoting a
-physical thing often tell most of its meaning. But the rest of its
-meaning we often do not learn for years, if ever. For instance, two
-people would more likely disagree than agree about what should be
-called a “rock” and what should be called a “stone,” if we showed them
-two dozen examples.
-
-In the case of words not denoting physical objects, like “and,” “heat,”
-“responsibility,” we are worse off. We cannot show something and say,
-“That is a ···.” The usual dictionary is of some help, but it has a
-tendency to tell us what some word _A_ means by using another word _B_,
-and when we look up the other word _B_ we find the word _A_ given as
-its meaning. Mainly, however, to determine the meanings of words, we
-gather experience: we soak up words in our brains and slowly establish
-their meanings. We seem to use an unconscious reasoning process: we
-notice how words are used together in patterns, and we conclude what
-they must mean. Clearly, then, words being clumsy instruments, the
-more experience we have had with a word, the more likely we are to be
-able to use it, work with it, and understand it. Therefore explanation
-should be based chiefly on words with which we have had the most
-experience. What words are these? They will be the well-known words. A
-great many of them will be short.
-
-
-SET OF WORDS FOR EXPLAINING
-
-Now what is the set of all the words needed to explain simply a
-technical subject like machines that think? For we shall need more
-words than just the well-known and short ones. This question doubtless
-has many answers; but the answer used in this book was based on the
-following reasoning. In a book devoted to explanation, there will be
-a group of words (1) that are supposed to be known already or to be
-learned while reading, and (2) that are used as building blocks in
-later explanation and definitions. Suppose that we call these words the
-_words for explaining._ There are at least three groups of such words:
-
-    _Group 1._ Words not specially defined that are so
-        familiar that every reader will know all of them;
-        for example, “is,” “much,” “tell.”
-
-    _Group 2._ Words not specially defined that are
-        familiar, but perhaps some reader may not know some
-        of them; for example, “alternative,” “continuous,”
-        “indicator.”
-
-    _Group 3._ Words that are not familiar, that many
-        readers are not expected to know, and that are
-        specially defined and explained in the body of the
-        book; for example, “abacus,” “trajectory,” “torque.”
-
-In writing this book, it was not hard to keep track of the words in the
-third group. These words are now listed in the index, together with
-the page where they are defined or explained. (The index, of course,
-also lists phrases that are specially defined.)
-
-But what division should be made between the other two groups? A
-practical, easy, and conservative way to separate most words between
-the first and second groups seemed to be on the basis of number of
-syllables. All words of one syllable—if not specially defined—were put
-in Group 1. Also, if a word became two syllables only because of the
-addition of one of the endings “-es,” “-ed,” “-ing,” it was kept in
-Group 1, for these endings probably do not make a word any harder to
-understand. In addition, there were put into Group 1:
-
-    1. Numbers; for example, “186,000”; “³/₁₀”.
-
-    2. Places: “Philadelphia”; “Massachusetts”.
-
-    3. Nations, organizations, people, etc.: “Swedish”; “Bell”.
-
-    4. Years and dates: “February”; “1946”.
-
-    5. Names of current books or articles and their authors.
-
-Of course, not all these words would be familiar to every reader (for
-example, “Maya”), but in the way they occur, they are usually not
-puzzling, for we can tell from the context just about what they must
-mean.
-
-All remaining words for explaining—chiefly, words of two or more
-syllables and not specially defined—were put in Group 2 and were
-listed during the writing of this book. Many Group 2 words, of course,
-would be entirely familiar to every reader; but the list had several
-virtues. No hard words would suddenly be sprung like a trap. The
-same word would be used for the same idea. Every word of two or more
-syllables was continually checked: is it needed? can it be replaced by
-a shorter word? It is perhaps remarkable that there were fewer than
-1800 different words allowed to stay in this list. This fact should be
-a comfort to a reader, as it was to the author.
-
-Now there are more words in this book than _words for explaining_. So
-we shall do well to recognize:
-
-    _Group 4._ Words that do not need to be known or learned
-       and that are not used in later explanation and definitions.
-
-These words occur in the book in such a way that understanding them,
-though helpful, is not essential. One subdivision of Group 4 are names
-that appear just once in the book, as a kind of side remark, for
-example, “a chemical, called _acetylcholine_.” Such a name will also
-appear in the index, but it is not a _word for explaining_. Another
-subdivision of Group 4 are words occurring only in quotations. For
-example, in the quotation from _Frankenstein_ on page 198, a dozen
-words appear that occur nowhere else in the book, including “daemon,”
-“dissoluble,” “maw,” “satiate.” Clearly we would destroy the entire
-flavor of the quotation if we changed any of these words in any way.
-But only the general drift of the quotation is needed for understanding
-the book, and so these words are Group 4 words.
-
-In this way the effort to achieve simple explanation in this book
-proceeded. But even supposing that we could reach the best set of words
-for explaining, there is more to be done. How do we go from simple
-explanation to understanding?
-
-
-UNDERSTANDING IDEAS
-
-_Understanding_ an idea is basically a standard process. First, we
-find the name of the idea, a word or phrase that identifies it. Then,
-we collect true statements about the idea. Finally, we practice using
-them. The more true statements we have gathered, and the more practice
-we have had in applying them, the more we understand the idea.
-
-For example, do you understand zero? Here are some true statements
-about zero.
-
-    1. Zero is a number.
-    2. It is the number that counts none or nothing.
-    3. It is marked 0 in our usual numeral writing.
-    4. The ancient Romans, however, had no numeral for it.
-        Apparently, they did not think of zero as a number.
-    5. 0 is what you get when you take away 17 from 17, or
-        when you subtract any number from itself.
-    6. If you add 0 to 23, you get 23; and if you add 0 to
-        any number, you get that number unchanged.
-    7. If you subtract 0 from 48, you get 48; and if you
-        subtract 0 from any number, you get that number
-        unchanged.
-    8. If you multiply 0 by 71, you get 0; and if you
-        multiply together 0 and any number, you get 0.
-    9. Usually you are not allowed to divide by 0: that is
-        against the rules of arithmetic.
-    10. But if you do, and if you divide 12 by 0, for
-        example—and there are times when this is not
-        wrong—the result is called _infinity_ and is
-        marked ∞, a sign that is like an 8 on its side.
-
-This is not all the story of zero; it is one of the most important of
-numbers. But, if you know these statements about zero, and have had
-some practice in applying them, you have a good _understanding_ of
-zero. Incidentally, a mechanical brain knows all these statements about
-zero and a few more; they must be built into it.
-
-For us to understand any idea, then, we pursue three aims:
-
-    1. We find out what it is called.
-    2. We collect true statements about it.
-    3. We apply those statements—we use them in situations.
-
-We can do this about any idea. Therefore, we can understand any idea,
-and the degree of our understanding increases as the number of true
-statements mastered increases.
-
-Perhaps this seems to be a rash claim. Of course, it may take a good
-deal of time to collect true statements about many ideas. In fact, a
-scientist may spend thirty years of his life trying to find out from
-experiment the truth or falsehood of one statement, though, when he has
-succeeded, the fact can be swiftly told to others. Also, we all vary in
-the speed, perseverance, skill, etc., with which we can collect true
-statements and apply them. Besides, some of us have not been taught
-well and have little faith in our ability to carry out this process:
-this is the greatest obstacle of all. But, there is in reality no idea
-in the field of existing science and knowledge which you or I cannot
-understand. The road to understanding lies clear before us.
-
-
-
-
-Supplement 2
-
-MATHEMATICS
-
-
-In the course of our discussion of machines that think, we have had to
-refer without much explanation to a number of mathematical ideas. The
-purpose of this supplement is to explain a few of these ideas a little
-more carefully than seemed easy to do in the text and, at the end of
-the supplement, to put down briefly some additional notes for reference.
-
-
-DEVICES FOR MULTIPLICATION
-
-Suppose that we have to multiply 372 by 465. With the ordinary school
-method, we write 465 under the 372 and proceed about as follows: 5
-times 2 is 10, put down the 0 and carry the 1; 5 times 7 is 35, 35 and
-1 is 36, put down the 6 and carry the 3; 5 times 3 is 15, 15 and 3 is
-18, put down the 8 and carry the 1; ... The method is based mainly on a
-well-learned subroutine of continually changing steps:
-
-    1. Select a multiplicand digit.
-    2. Select a multiplier digit.
-    3. Refer to the multiplication table with these digits.
-    4. Obtain the value of their product, called a _partial product_.
-    5. Add the preceding carry.
-    6. Set down the right-hand digit.
-    7. Carry the left-hand digit.
-
-We can, however, simplify this subroutine for a machine by delaying the
-carrying. We collect in one place all the right-hand digits of partial
-products, collect in another place all the left-hand digits, and delay
-all addition until the end.
-
-For example, let us multiply 372 by 465 with this method:
-
-
-    RIGHT-HAND      LEFT-HAND       USUAL METHOD,
-      DIGITS          DIGITS       FOR COMPARISON
-
-        372             372               372
-      × 465           × 465             × 465
-     ——————          ——————            ——————
-        550            131               1860
-       822            141               2232
-      288            120               1488
-      —————          —————             ——————
-      37570          13541             172980
-
-            FINAL ADDITION
-
-                   37570
-                + 13541
-                ————————
-                  172980
-
-
-37570 is called the _right-hand component_ of the product. It is
-convenient to fill in with 0 the space at the end of 13541 and to call
-135410 the _left-hand component_ of the product.
-
-This process is called _multiplying by right- and left-hand components_.
-It has the great advantage that no carrying is necessary to complete
-any line of the original multiplications. Some computing machines
-use this process. Built into the hardware of the machine is a
-multiplication table up to 9 × 9. The machine, therefore, can find
-automatically the right-hand digit and the left-hand digit of any
-partial product. In a computing machine that uses this process, all
-the left-hand digits are automatically added in one register, and
-all the right-hand digits are added in another register. The only
-carrying that is needed is the carrying as the right-hand digits are
-accumulated and as the left-hand digits are accumulated. At the end of
-the multiplication, one of the registers is automatically added into
-the other, giving the product.
-
-Another device used in computing machines for multiplying is to change
-the multiplier into a set of digits 0 to 5 that are either positive or
-negative. For example, suppose that we want to multiply 897 by 182. We
-note that 182 equals 200 minus 20 plus 2, and so we can write it as
-
-     _
-    222.
-
-The minus over the 2 marks it as a _negative digit_ 2. Then to multiply
-we have:
-
-        897
-         _
-        222
-       ————
-       1794
-    - 1794
-     1794
-     ——————
-     163254
-
-The middle 1794 is subtracted. This process is usually called
-_short-cut multiplication_. Everybody discovers this trick when he
-decides that multiplying by 99 is too much work, that it is easier to
-multiply by 100 and subtract once.
-
-
-BINARY OR TWO NUMBERS
-
-We are well accustomed to decimal notation in which we use 10 decimal
-digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and write them in combinations
-to designate decimal numbers. In _binary notation_ we use two binary
-digits 0, 1 and write them in combinations to designate _binary
-numbers_. For example, the first 17 numbers, from 0 to 16 in the
-decimal notation, correspond with the following numbers in binary
-notation:
-
-    DECIMAL   BINARY     DECIMAL  BINARY
-       0           0
-       1           1        9      1001
-       2          10       10      1010
-       3          11       11      1011
-       4         100       12      1100
-       5         101       13      1101
-       6         110       14      1110
-       7         111       15      1111
-       8        1000       16     10000
-
-In decimal notation, 101 means one times a hundred, no tens, and one.
-In binary notation, 101 means one times four, no twos, and one. The
-successive digits in a decimal number from right to left count 1, 10,
-100, 1000, 10000, ...—successive _powers_ of 10 (for this term, see the
-end of this supplement). The successive digits in a binary number from
-right to left count 1, 2, 4, 8, 16, ...—powers of 2.
-
-The decimal notation is convenient when equipment for computing has ten
-positions, like the fingers of a man, or the positions of a counter
-wheel. The binary notation is convenient when equipment for computing
-has just two positions, like “yes” or “no,” or current flowing or no
-current flowing.
-
-Addition, subtraction, multiplication, and division can all be carried
-out unusually simply in binary notation. The addition table is simple
-and consists only of four entries.
-
-    +   0   1
-      +——————
-    0 | 0   1
-      |
-    1 | 1  10
-
-The multiplication table is also simple and contains only four entries.
-
-    ×   0  1
-      +——————
-    0 | 0  0
-      |
-    1 | 0  1
-
-Suppose that we add in binary notation 101 and 1001:
-
-    BINARY ADDITION   CHECK
-
-           101          5
-        + 1001          9
-        ——————         ———
-          1110         14
-
-We proceed: 1 and 1 is 10; write down 0 and carry 1; 0 and 0 is 0, and
-1 to carry is 1; and 1 and 0 is 1; and then we just copy the last 1. To
-check this we can convert to decimal and see that 101 is 5, 1001 is 9,
-and 1110 is 14, and we can verify that 5 and 9 is 14.
-
-One of the easiest ways to subtract in binary notation is to add a
-_ones complement_ (that is, the analogue of the nines complement)
-and use end-around-carry (for these two terms, see the end of this
-supplement). A ones complement can be written down at sight by just
-putting 1 for 0 and 0 for 1. For example, suppose that we subtract 101
-from 1110:
-
-                          SUBTRACTION BY
-      DIRECT               ADDING ONES
-    SUBTRACTION   CHECK     COMPLEMENT
-
-        1110        14          1110
-       - 101        -5        + 1010
-       —————       ————       ——————
-        1001         9       (1)1000
-                              ↓
-                               ⎯→  1
-                              ——————
-                                1001
-
-Multiplication in the binary notation is simple. It amounts to (1)
-adding if the multiplier digit is 1 and not adding if the multiplier
-digit is 0, and (2) moving over or shifting. For example, let us
-multiply 111 by 101:
-
-    BINARY MULTIPLICATION   CHECK
-
-              111              7
-            × 101            × 5
-            ——————
-              111
-            111
-           ——————            ———
-           100011             35
-
-The digit 1 in the 6th (or _n_th) _binary_ place from the right in
-100011 stands for 1 times 2 to the 5th (or _n_-1 th) power, 2 × 2 × 2
-× 2 × 2 = 32. The result 100011 is translated into 32 plus 2 plus 1,
-which equals 35 and verifies.
-
-Division in the binary notation is also simple. It amounts to (1)
-subtracting (yielding a quotient digit 1) or not subtracting (yielding
-a quotient digit 0), and (2) shifting. We never need to try multiples
-of the divisor to find the largest that can be subtracted yet leave a
-positive remainder. For example, let us divide 1010 (10 in decimal)
-into 10001110 (142 in decimal):
-
-             1110 (14 in decimal)
-        ——————————
-    1010)10001110
-          1010
-         ——————
-           1111
-           1010
-           —————
-            1011
-            1010
-            —————
-               10 (remainder, 2 in decimal)
-
-In decimal notation, digits to the right of the decimal point count
-powers of ⅒. In binary notation, digits to the right of the _binary
-point_ count powers of ½: ½, ¼, ⅛, ¹/₁₆.... For example, 0.1011 equals
-½ + ⅛ + ¹/₁₆, or ¹¹/₁₆.
-
-If we were accustomed to using binary numbers, all our arithmetic
-would be very simple. Furthermore, binary numbers are in many ways
-much better for calculating machinery than any other numbers. The main
-problem is converting numbers from decimal notation to binary. One
-method depends on storing the powers of 2 in decimal notation. The rule
-is: subtract successively smaller powers of 2; start with the largest
-that can be subtracted, and count 1 for each power that goes and 0 for
-each power that does not. For example, 86 in decimal becomes 1010110 in
-binary:
-
-    86
-    64   64 goes         1
-    ———
-    22   32 does not go  0
-    16   16 goes         1
-    ———
-     6    8 does not go  0
-     4    4 goes         1
-    ———
-     2    2 goes         1
-     2    1 does not go  0
-    ———
-     0
-
-It is a little troublesome to remember long series of 1’s and 0’s; in
-fact, to write any number in binary notation takes about 3⅓ times as
-much space as decimal notation. For this reason we can separate binary
-numbers into triples beginning at the right and label each triple as
-follows:
-
-    TRIPLE   LABEL
-     000       0
-     001       1
-     010       2
-     011       3
-     100       4
-     101       5
-     110       6
-     111       7
-
-For example, 1010110 would become 1 010 110 or 126. This notation is
-often called _octal notation_, because it is notation in the scale of
-eight.
-
-
-BIQUINARY OR _TWO-FIVE_ NUMBERS
-
-Another kind of notation for numbers is _biquinary notation_, so called
-because it uses both 2’s and 5’s. Essentially this notation is very
-like Roman numerals, ancient style. By ancient style we mean, for
-example, VIIII instead of IX. In the following table we show the first
-two dozen numbers in decimal, biquinary, and ancient Roman notation:
-
-    DECIMAL   BIQUINARY   ROMAN
-       0           0
-       1           1      I
-       2           2      II
-       3           3      III
-       4           4      IIII
-       5          10      V
-       6          11      VI
-       7          12      VII
-       8          13      VIII
-       9          14      VIIII
-      10         100      X
-      11         101      XI
-      12         102      XII
-      13         103      XIII
-      14         104      XIIII
-      15         110      XV
-      16         111      XVI
-      17         112      XVII
-      18         113      XVIII
-      19         114      XVIIII
-      20         200      XX
-      21         201      XXI
-      22         202      XXII
-      23         203      XXIII
-
-The biquinary columns alternate in going from 0 to 4 and from 0 to 1.
-The digits from 0 to 4 are not changed. The digits from 5 to 9 are
-changed into 10 to 14. We see that the _biquinary digits_ are 0 to 4 in
-odd columns and 0, 1 in even columns, counting from the right.
-
-This is the notation actually expressed by the _abacus_. The beads of
-the abacus show by their positions groups of 2 and 5 (see Fig. 1).
-
-[Illustration: FIG. 1. Abacus and notations.]
-
-
-SOME OPERATIONS OF ALGEBRA
-
-One of the operations of algebra that is important for a mechanical
-brain is _approximation_, the problem of getting close to the right
-value of a number. Take, for example, finding _square root_ (see the
-end of this supplement). The ordinary process taught in school is
-rather troublesome. We can set down another process, however, using a
-desk calculator to do division, which gives us square root with great
-speed.
-
-Suppose that we want to find the square root of a number _N_, and
-suppose that we have _x_₀ as a guessed square root correct to one
-figure. For example, _N_ might be 67.2 and _x_₀ might be 8, chosen
-because 8 × 8 is 64, and 9 × 9 is 81, and it seems as if 8 should be
-near the square root of 67.2. Here is the process:
-
-    1. Divide _x_₀ into _N_, and obtain _N_/_x_₀.
-
-    2. Multiply _x_₀ + _N_/_x_₀ by 0.5 and call the result _x_₁.
-
-Now repeat:
-
-    1. Divide _x_₁ into _N_ and obtain _N_/_x_₁.
-
-    2. Multiply _x_₁ + _N_/_x_₁ by 0.5 and call the result _x_₂.
-
-Every time this process is repeated, the new _x_ comes a great deal
-closer to the correct square root. In fact it can be shown that, if
-_x_₀ is correct to one figure, then:
-
-    APPROXIMATION   IS CORRECT TO ··· FIGURES
-       _x_₁                  2
-       _x_₂                  4
-       _x_₃                  8
-       _x_₄                 16
-
-Let us see how this actually works out with 67.2 and a 10-column desk
-calculator.
-
-    Round 1: 8 divided into 67.2 gives 8.4. One half of 8
-      plus 8.4 is 8.2. This is _x_₁.
-
-    Round 2: 8.2 divided into 67.2 gives 8.195122. One half
-      of 8.2 plus 8.195122 is 8.197561. This is _x_₂.
-
-    Round 3: 8.197561 divided into 67.2 gives 8.197560225.
-      One half of 8.197561 and 8.197560225 is 8.1975606125.
-      This is _x_₃.
-
-    Checking _x_₃, we find that 8.1975606125 divided
-      into 67.2 gives 8.1975606126 approximately.
-
-In this case, then, _x_₃ is correct to more than 10 figures. In other
-words, with a reasonable guess and two or three divisions we can
-obtain all the accuracy we can ordinarily use. This process is called
-_rapid approximation_, or _rapidly convergent approximation_, since it
-_converges_ (points or comes together) very quickly to the number we
-are seeking.
-
-Another important operation of algebra is _interpolation_, the problem
-of putting values smoothly in between other values. For example,
-suppose that we have the table:
-
-    _x        y_
-      5      26
-      6      37
-      7      50
-      8      65
-      9      82
-
-Suppose that we want to find the value that _y_ (or _yₓ_) ought to have
-when _x_ has the value of 7.2. This is the problem of _interpolating y_
-so as to find _y_ at the value of 7.2, _y_₇ˌ₂.
-
-One way of doing this is to discover the formula that expresses _y_ and
-then to put _x_ into that formula. This is not always easy. Another
-way is to take the difference between _y_₇ and _y_₈, 15, and share
-the difference appropriately over the distance 7 to 7.2 and 7.2 to 8.
-We can, for example, take ²/₁₀ of 15 = 3, add that to _y_₇ = 50, and
-obtain an estimated _y_₇ˌ₂ = 53. This is called _linear interpolation_,
-since the difference 0.2 in the value of _x_ is used only to the first
-power. It is a good practical way to carry out most interpolation
-quickly and approximately.
-
-Actually here _y_ = _x_² + 1, and so the true value of _y_₇ˌ₂ is (7.2 ×
-7.2) + 1, or 52.84, which is rather close to 53. Types of interpolation
-procedures more accurate than linear interpolation will come much
-nearer still to the true value.
-
-
-ALGEBRA OF LOGIC
-
-We turn now to the _algebra of logic_. The first half of Chapter
-9, “Reasoning” (through the section “Logical-Truth Calculation by
-Algebra”), introduces this subject. There the terms _truth values_,
-_truth tables_, _logical connectives_, and _algebra of logic_ are
-explained. The part of Chapter 3, “A Machine That Will Think,” that
-discusses the operations _greater-than_ and _selection_, also explains
-some of the algebra of logic. It introduces, for example, the formula
-
-    _p_ = _T_(_a_ > _b_) = 1, 0
-
-This is a way of saying briefly that the truth value of the statement
-“_a_ is greater than _b_” equals _p_; _p_ is 1 if the statement is true
-and 0 if the statement is false. The truth value 1 corresponds with
-“yes.” The truth value 0 corresponds with “no.”
-
-With mechanical brains we are especially interested in handling
-mathematics and logic without any sharp dividing line between them.
-For example, suppose that we have a register in which a ten-digit
-number like 1,765,438,890 may be stored. We should be able to use
-that register to store a number consisting of only 1’s and 0’s, like
-1,100,100,010. Such a number may designate the answers to 10 successive
-questions: yes, yes, no, no, yes, no, no, no, yes, no. Or it may
-tell 10 successive binary digits. The register then is three times
-as useful: it can store either decimal numbers or truth values or
-binary digits. We need, of course, a way to obtain from the register
-any desired digit. For this purpose we may have two instructions to
-the machine: (1) read the left-hand end digit; (2) shift the number
-around in a circle. The second instruction is the same as multiplying
-by 10 and then putting the left-most digit at the right-hand end.
-For example, suppose that we want the 3rd digit from the left in
-1,100,100,010. The result of the first circular shift is 1,001,000,101;
-the result of the second circular shift is 0,010,001,011; and reading
-the left-most digit gives 0. A process like this has been called
-_extraction_ and is being built into the newest mechanical brains.
-
-Using truth values, we can put down very neatly some truths of ordinary
-algebra. For example:
-
-    (the _absolute value_ of _a_) =
-        _a_ × (the truth of _a_ greater than or equal to 0)
-      - _a_ × (the truth of _a_ less than 0)
-
-    ⎮_a_⎮ = _a_ · _T_(_a_ ≥ 0) - _a_ · _T_(_a_ < 0)
-
-For another example:
-
-    Either _a_ is greater than _b_,
-      or else _a_ equals _b_,
-      or else _a_ is less than _b_
-
-    _T_(_a_ > _b_) + _T_(_a_ = _b_) + _T_(_a_ < _b_) = 1
-
-Many common logical operations, like selecting and comparing, and
-the behavior of many simple mechanisms, like a light or a lock, can
-be expressed by truth values. Chapter 4, on punch-card mechanisms,
-contains a number of examples.
-
-       *       *       *       *       *
-
-
-pronoun, variable
-
-In ordinary language, a _pronoun_, like “he,” “she,” “it,” “the
-former,” “the latter,” is a word that usually stands for a noun
-previously referred to. A pronoun usually stands for the last preceding
-noun that the grammar allows. In mathematics, a _variable_, like “_a_,”
-“_b_,” “_x_,” “_m₁_,” “_m₂_” closely resembles a pronoun in ordinary
-language. A variable is a symbol that usually stands for a number
-previously referred to, and usually it stands for the same number
-throughout a particular discussion.
-
-
-multiplicand, dividend, augend, etc.
-
-       IN THE           THE NAME       THE NAME    THE NAME
-      EQUATION:        OF _a_ IS:     OF _b_ IS:   OF _c_ IS:
-
-    _a_ + _b_ = _c_    augend         addend       sum
-    _a_ - _b_ = _c_    minuend        subtrahend   remainder
-    _a_ × _b_ = _c_    multiplicand   multiplier   product
-    _a_ ÷ _b_ = _c_    dividend       divisor      quotient
-
-
-_Augend_ and _addend_ are names of registers in the Harvard Mark II
-calculator (see Chapter 10).
-
-
-subtraction by adding, nines complement
-
-Two digits that add to 9 (0 and 9, 1 and 8, 2 and 7, 3 and 6, 4 and 5)
-are called _nines complements_ of each other. The _nines complement_ of
-a number _a_ is the number _b_ in which each digit of _b_ is the nines
-complement of the corresponding digit of _a_; for example, the nines
-complement of 173 is 826. Ordinary subtraction is the same as addition
-as of the nines complement, with a simple correction; for example, 562
-less 173 (equal to 389) is the same as 562 plus 826 (equal to 1388)
-less 1000 plus 1.
-
-
-end-around-carry
-
-The correction “less 1000 plus 1” of the foregoing example may be
-thought of as carrying the 1 (in the result 1388) around from the
-left-hand end to the right-hand end, where it is there added. So the 1
-is called _end-around-carry_.
-
-
-tens complement
-
-Two digits that add to 10 are called _tens complements_ of each other.
-The _tens complement_ of a number _a_, however, is equal to the nines
-complement of the number plus 1. For example, the tens complement of
-173 is 827. When subtracting by adding a tens complement, the left-most
-digit 1 in the result is dropped. For example, 562 less 173 (equal to
-389) is the same as 562 plus 827 (equal to 1389) less 1000.
-
-
-power, square, cube, reciprocal, etc.
-
-A _power_ of any number _a_ is _a_ multiplied by itself some number
-of times. _a_ × _a_ × _a_ ... × _a_ where _a_ appears _b_ times is
-written _a_ᵇ and is read _a_ to the _b_th power. _a_², a to the 2nd
-power, is _a_ × _a_ and is called _a squared_ or the _square_ of _a_.
-_a_³, _a_ to the 3rd power, _a_ × _a_ × _a_, is called _a cubed_, or
-the _cube_ of _a_. _a_⁰, _a_ to the zero power, is equal to 1 for every
-_a_. _a_¹, _a_ to the power 1, is _a_ itself. The first power is often
-called _linear_. _a_ to some negative power is the same as 1 divided
-by that power; that is, _a_⁻ᵇ = 1/_a_ᵇ. _a_⁻¹, _a_ to the power minus
-1, is 1/_a_, and is called the _reciprocal_ of _a_. _a_¹ᐟ², _a_ to
-the one-half power, is a number _c_ such that _c_ × _c_ = _a_, and is
-called the _square root_ of _a_ and often denoted by √_a_.
-
-
-table, tabular value, argument, etc.
-
-An example of a _table_ is:
-
-        0.025     0.03
-      +——————————————————
-    1 | 1.02500   1.03000
-      |
-    2 | 1.05063   1.06090
-      |
-    3 | 1.07689   1.09273
-
-The numbers in the body of the table, called _tabular values_, depend
-on or are determined by the numbers along the edge of the table, called
-_arguments_. In this example, if 1, 2, 3 are choices of a number _n_,
-and if 0.025, 0.03 are choices of a number _i_, then each tabular value
-_y_ is equal to 1 plus _i_ raised to the _n_th power. _n_ and _i_ are
-also called _independent variables_, and _y_ is called the _dependent
-variable_. The table expresses a _function_ or _formula_ or _rule_. The
-rule could be stated as: add _i_ to 1; raise the result to the _n_th
-power.
-
-
-constant
-
-A number is said to be a _constant_ if it has the same value under
-all conditions. For example, in the formula: (area of a circle) = π ×
-(radius)², π is a constant, equal to 3.14159 ..., applying equally well
-to all circles.
-
-
-infinity
-
-Mathematics recognizes several kinds of infinity. One of them occurs
-when numbers become very large. For example, the quotient of 12 divided
-by a number _x_, as _x_ becomes closer and closer to 0, becomes
-indefinitely large, and the limit is called _infinity_ and is denoted ∞.
-
-
-equation, simultaneous, linear
-
-An example of two linear simultaneous _equations_ is:
-
-    7_x_ + 8_t_ = 22
-
-    3_x_ + 5_t_ = 11
-
-_x_ and _t_ are called _unknowns_—that is, unknown variables—because
-the objective of solving the equations is to find them. These equations
-are called _simultaneous_ because they are to be solved together,
-at the same time, for values of _x_ and _t_ which will fit in both
-equations. The equations are called _linear_ because the only powers
-of the unknowns that appear are the first power. Values that solve
-equations are said to _satisfy_ them. It is easy to solve these two
-equations and find that _x_ = 2 and _t_ = 1 is their solution. But
-it is a long process to solve 10 linear simultaneous equations in 10
-unknowns, and it is almost impossible (without using a mechanical
-brain) to solve 100 linear simultaneous equations in 100 unknowns.
-
-
-derivative, integral, differential equation, etc.
-
-See the sections in Chapter 5 entitled “Differential Equations,”
-“Physical Problems,” and “Solving Physical Problems.” There these
-ideas and, to some extent, also the following ideas were explained:
-formula, equation, function, differential function, instantaneous rate
-of change, interval, inverse, integrating. See also a textbook on
-calculus. If _y_ is a function of _x_, then a mathematical symbol for
-the derivative of _y_ with respect to _x_ is _Dₓ y_, and a symbol for
-the integral of _y_ with respect to _x_, is ∫_y dx_. An integral with
-given initial conditions (see p. 83) is a _definite integral_.
-
-
-exponential
-
-A famous mathematical function is the _exponential_. It equals
-the constant _e_ raised to the _x_ power, _eˣ_, where _e_ equals
-2.71828.... The exponential lies between the powers of 2 and the powers
-of 3. It can be computed from:
-
-                       _x_²      _x_³
-    _eˣ_ = 1 + _x_ + —————— + ————————— + ...
-                      1 · 2   1 · 2 · 3
-
-It is a solution of the differential equation _Dₓy_ = _y_. See also a
-textbook on calculus. The _exponential to the base 10_ is 10ˣ.
-
-
-logarithm
-
-Another important mathematical function is the _logarithm_. It is
-written log _x_ or logₑ _x_ and can be computed from the two equations:
-
-    log _uv_ = log _u_ + log _v_
-
-                          _x_²     _x_³
-    log(1 + _x_) = _x_ - —————— + —————— - ..., _x_² < 1
-                           2        3
-
-It is a solution of the differential equation _Dₓy_ = 1/_y_. If _y_
-is the logarithm of _x_, then _x_ is the _antilogarithm_ of _y_. The
-_logarithm to the base 10_ of _x_, log₁₀ _x_, equals the _logarithm to
-the base e_ of _x_, logₑ _x_, divided by logₑ 10. See also textbooks on
-algebra and calculus.
-
-
-sine, cosine, tangent, antitangent
-
-These also are important mathematical functions. The _sine_ and
-_cosine_ are solutions of the differential equation _Dₓ_(_Dₓy_) =-_y_
-and are written as sin _x_ and cos _x_. They can be computed from
-
-                     _x_³       _x_⁵
-    sin _x_ = _x_ - —————— + ————————— - ...
-                    1·2·3    1·2·3·4·5
-
-                   _x_²      _x_₄
-    cos _x_ = 1 - —————— + —————— - ...
-                   1·2     1·2·3·4
-
-The _tangent_ of _x_ is simply sine of _x_ divided by cosine of _x_. If
-_y_ is the tangent of _x_, then _x_ is the _antitangent_ of _y_. See
-also references on trigonometry and on calculus. _Trigonometric_ tables
-include sine, cosine, tangent, and related functions.
-
-
-Bessel functions
-
-These are mathematical functions that were named after Friedrich W.
-Bessel, a Prussian astronomer who lived from 1784 to 1846. Bessel
-functions are found as some of the solutions of the differential
-equation
-
-    _x_² _Dₓ_(_Dₓy_) + x _Dₓy_ + (_x_² - _n_²)_y_ = O
-
-This equation arises in a number of physical problems in the fields of
-electricity, sound, heat flow, air flow, etc.
-
-
-matrix
-
-A _matrix_ is a table (or _array_) of numbers in rows and columns, for
-which addition, multiplication, etc., with similar tables is specially
-defined. For example, the matrix
-
-          ⎮1  2⎮
-          ⎮    ⎮
-          ⎮3  4⎮
-
-    plus the matrix
-
-          ⎮5    20⎮
-          ⎮       ⎮
-          ⎮60  100⎮
-
-    equals the matrix
-
-          ⎮6    22⎮
-          ⎮       ⎮
-          ⎮63  104⎮.
-
-(Can you guess the rule defining addition?)
-
-Calculations using matrices are useful in physics, engineering,
-psychology, statistics, etc. To add a _square matrix_ of 100 terms in
-an array of 10 columns and 10 rows to another such matrix, 100 ordinary
-additions of numbers are needed. To multiply one such matrix by
-another, 1000 ordinary multiplications and 900 ordinary additions are
-needed. See references on matrix algebra and matrix calculus.
-
-
-differences, smoothness, checking
-
-On p. 221, a sequence of values of _y_ is shown: 26, 37, 50, 65, 82.
-Suppose, however, the second value of _y_ was reported as 47 instead
-of 37. Then the _differences_ of _y_ as we pass down the sequence
-would not be 11, 13, 15, 17 (which is certainly regular or _smooth_)
-but 21, 3, 15, 17 (which is certainly not smooth). The second set of
-differences would strongly suggest a mistake in the reporting of _y_.
-The _smoothness_ of differences is often a useful check on a sequence
-of reported values.
-
-
-
-
-Supplement 3
-
-REFERENCES
-
-
-A book like the present one can cover only a part of the subject of
-machines that think. To obtain more information about these machines
-and other topics to which they are related there are many references
-that may be consulted. There are still few books directly on the
-subject of machines that think, but there are many articles and papers,
-most of them rather specialized.
-
-The purpose of this supplement is to give a number of these references
-and to provide a brief, general introduction to some of them. The
-references are subdivided into groups, each dealing with a branch of
-the subject. The references in each group are in alphabetical order
-by name of author (with “anonymous” last), and under each author they
-are in chronological order by publication date. Some publications,
-especially a forum or symposium, are listed more than once, according
-as the topic discussed falls in different groups. In this supplement,
-the sign three dots ( ...) next to the page numbers for an article
-indicates that the article is continued on later, nonconsecutive pages.
-
-It seemed undesirable to try to make the group of references dealing
-with a subject absolutely complete, so long as enough were given to
-provide a good introduction to the subject. It proved impractical
-to try to make the citation of every single reference technically
-complete, so long as enough citation was given so that the reference
-could certainly be found. Furthermore, in a list of more than 250
-references, errors are almost certain to occur. If any reader should
-send me additions or corrections, I shall be more than grateful.
-
-
-THE HUMAN BRAIN
-
-No one yet knows specifically how particular ideas are thought about
-in the human brain. The references listed in this section, however,
-contain some information about such topics as:
-
-    The structural differences, development, and evolution
-      of the brains of animals, apes, primitive man, and
-      modern man.
-    The effect on the brain of blood composition, body
-      temperature, supply of oxygen, and other biochemical
-      factors.
-    The structure and physiology of the brain, the nervous
-      system, and nerve impulses.
-    The theory of learning, intelligence, and memory.
-
-    BARCROFT, JOSEPH, _The Brain and Its
-        Environment_, New Haven: Yale University Press,
-        1948, 117 pp.
-
-    BEACH, FRANK A., Payday for Primates,
-        _Natural History_, vol. 56, no. 10, Dec. 1947,
-        pp. 448-451.
-
-    BEACH, FRANK A., Can Animals Reason?
-        _Natural History_, vol. 57, no. 3, Mar. 1948,
-        pp. 112-116 ...
-
-    BERRY, R. J. A., _Brain and Mind, or the
-        Nervous System of Man_, New York: The Macmillan
-        Co., 1928, 608 pp.
-
-    BORING, EDWIN G., _A History of Experimental
-        Psychology_, New York: Century Co., 1929, 699 pp.
-
-    FRANZ, SHEPHERD I., _The Evolution of
-        an Idea; How the Brain Works_, Los Angeles:
-        University of California, 1929, 35 pp.
-
-    HERRICK, C. JUDSON, _The Thinking
-        Machine_, Chicago: University of Chicago Press,
-        1929, 374 pp.
-
-    HERRICK, C. JUDSON, _Brains of Rats and
-        Men_, Chicago: University of Chicago Press,
-        1930, 382 pp.
-
-    LASHLEY, KARL S., _Brain Mechanisms and
-        Intelligence_, Chicago: University of Chicago
-        Press, 1929, 186 pp.
-
-    PIERON, HENRI, _Thought and the Brain_,
-        London: Kegan, Paul, Trench, Trübner & Co., 1927,
-        262 pp. Also New York: Harcourt, Brace & Co.
-
-    SCHRÖDINGER, ERWIN, _What is Life?_,
-        New York: The Macmillan Co., 1945, 90 pp.
-
-    SHERRINGTON, CHARLES S., _The Brain and Its
-        Mechanism_, Cambridge, England: The University
-        Press, 1933, 35 pp.
-
-    TILNEY, FREDERICK, _The Brain from Ape to
-        Man_, New York: P. B. Hoeber, Inc., 1928,
-        2 vol., 1075 pp.
-
-    WIENER, NORBERT, _Cybernetics, or
-        Control and Communication in the Animal and the
-        Machine_, New York: John Wiley & Sons, 1948, 194 pp.
-
-    ANONYMOUS, Ten Billion Relays,
-        _Time_, Feb. 14, 1949, p. 67.
-
-
-MATHEMATICAL BIOPHYSICS
-
-There has recently been another approach to the problem: How does
-a brain think? A group of men, many of them in and near Chicago,
-have been saying: “We know the properties of nerves, nerve impulses,
-and simple nerve networks. We know the activity of the brain. What
-mathematical model of nerve networks is necessary to account for the
-activity of the brain?” These men have used mathematics, statistics,
-and mathematical logic in the effort to attack this problem, and they
-support a _Bulletin of Mathematical Biophysics_.
-
-    HOUSEHOLDER, ALSTON S., A Neural Mechanism for
-        Discrimination, _Psychometrika_, vol. 4, no.
-        1, Dec. 1939, pp. 45-58.
-
-    HOUSEHOLDER, ALSTON S., and Herbert D.
-        Landahl, _Mathematical Biophysics of the Central
-        Nervous System_, Bloomington, Ind.: Principia
-        Press, 1945.
-
-    LANDAHL, HERBERT D., Contributions to the
-        Mathematical Biophysics of the Central Nervous
-        System, _Bulletin of Mathematical Biophysics_,
-        vol. 1, no. 2, June 1939, pp. 95-118.
-
-    LANDAHL, HERBERT D., WARREN S.
-        MCCULLOCH, and WALTER PITTS, A
-        Statistical Consequence of the Logical Calculus
-        of Nervous Nets, _Bulletin of Mathematical
-        Biophysics_, vol. 5, no. 4, Dec. 1943,
-        pp. 135-137.
-
-    LANDAHL, HERBERT D., A Note on the
-        Mathematical Biophysics of Central Excitation
-        and Inhibition, _Bulletin of Mathematical
-        Biophysics_, vol. 7, no. 4, Dec. 1945,
-        pp. 219-221.
-
-    LETTVIN, JEROME Y., and WALTER PITTS,
-        A Mathematical Theory of the Affective Psychoses,
-        _Bulletin of Mathematical Biophysics_, vol. 5,
-        no. 4, Dec. 1943, pp. 139-148.
-
-    MCCULLOCH, WARREN S., and WALTER
-        PITTS, A Logical Calculus of the Ideas
-        Immanent in Nervous Activity, _Bulletin of
-        Mathematical Biophysics_, vol. 5, no. 4,
-        Dec. 1943, pp. 115-133.
-
-    RASHEVSKY, N., _Mathematical Biophysics_,
-        Chicago: University of Chicago Press. Revised
-        edition, 1948, 669 pp.
-
-    RASHEVSKY, N., Mathematical Biophysics of
-        Abstraction and Logical Thinking, _Bulletin of
-        Mathematical Biophysics_, vol. 7, no. 3,
-        Sept. 1945, pp. 133-148.
-
-    RASHEVSKY, N., Some Remarks on the Boolean
-        Algebra of Nervous Nets in Mathematical Biophysics,
-        _Bulletin of Mathematical Biophysics_, vol. 7,
-        no. 4, Dec. 1945, pp. 203-211.
-
-    RASHEVSKY, N., A Suggestion for Another
-        Statistical Interpretation of the Fundamental
-        Equations of the Mathematical Biophysics of the
-        Central Nervous System, _Bulletin of Mathematical
-        Biophysics_, vol. 7, no. 4, Dec. 1945,
-        pp. 223-226.
-
-    RASHEVSKY, N., The Neural Mechanism of
-        Logical Thinking, _Bulletin of Mathematical
-        Biophysics_, vol. 8, no. 1, Mar. 1946, pp. 29-40.
-
-
-LANGUAGES: WORDS AND SYMBOLS FOR THINKING
-
-Hardly any field of techniques for thinking is more fascinating than
-language. The following list of references, of course, is short; it is
-meant chiefly as an introduction pointing out a number of different
-paths into the field of language and languages. Such topics as the
-following are introduced by the references in this list:
-
-    The origin of languages and alphabets.
-    The languages of the world, and speech communities.
-    The comparison of words and structure from language to language.
-    The significance of grammar and syntax.
-    The problem of clear meanings.
-    Writing and speaking that is easy to understand.
-
-    BLOOMFIELD, LEONARD, _Language_,
-        New York: Henry Holt & Co., 1933, 564 pp.
-
-    BODMER, FREDERICK, and LAUNCELOT
-        HOGBEN, _The Loom of Language_, New York:
-        W. W. Norton & Co., 1944, 692 pp.
-
-    FLESCH, RUDOLF, _The Art of Plain Talk_,
-        New York: Harper & Brothers, 1946, 210 pp.
-
-    GRAFF, WILLEM L., _Language and Languages:
-        An Introduction to Linguistics_, New York:
-        D. Appleton & Co., 1932, 487 pp.
-
-    HAYAKAWA, S. I., _Language in Action_,
-        New York: Harcourt, Brace & Co., 1941, 345 pp.
-
-    JESPERSEN, OTTO, _The Philosophy of
-        Grammar_, New York: Henry Holt & Co., 1929
-        (third printing), 359 pp.
-
-    JESPERSEN, OTTO, _Analytic Syntax_,
-
-    In this book, by means of a well-contrived system of letters
-    and signs, the great linguistic scholar Jespersen depicts all
-    the important inter-relations of English words and parts of
-     words in connected speech.
-
-    OGDEN, C. K., _The System of Basic
-        English_, New York: Harcourt, Brace & Co., 1934,
-        320 pp.
-
-    SCHLAUCH, MARGARET, _The Gift of
-        Tongues_, New York: Modern Age Books, 1942,
-        342 pp.
-
-    WALPOLE, HUGH R., _Semantics: The Nature
-        of Words and Their Meanings_, New York:
-        W. W. Norton & Co., 1941, 264 pp.
-
-
-LANGUAGES: MACHINES FOR THINKING
-
-For many years, nearly all references about machines as a language for
-thinking have been specialized and limited. Colleges with scholars
-who write textbooks usually have not had a variety of expensive and
-versatile computing machinery. As a result, the main environment for
-stimulating possible authors has until recently been missing. The list
-of references is accordingly brief.
-
-    AIKEN, HOWARD H., and others, _Proceedings
-        of a Symposium on Large-Scale Digital Calculating
-        Machinery_, Cambridge, Mass.: Harvard University
-        Press, 1948, 302 pp.
-
-    COMRIE, JOHN LESLIE, The Application of
-        Commercial Calculating Machines to Scientific
-        Computing, _Mathematical Tables and Other Aids
-        to Computation_, vol. 2, no. 16, Oct. 1946,
-        pp. 149-159.
-
-    CREW, E. W., Calculating Machines, _The
-        Engineer_, vol. 172, Dec. 1941, pp. 438-441.
-
-    FRY, MACON, _Designing Computing
-        Mechanisms_, Cleveland, Ohio: Penton Publishing
-        Co., 1946, 48 pp. (Reprinted from _Machine
-        Design_, Aug. 1945 through Feb. 1946.)
-
-    HARTREE, D. R., _Calculating Machines:
-        Recent and Prospective Developments and Their
-        Impact on Mathematical Physics_, Cambridge,
-        England: The University Press, 1947, 40 pp.
-
-    HORSBURGH, E. H., _Modern Instruments and
-        Methods of Calculation_, London: G. Bell and
-        Sons, Ltd., 1914, 343 pp.
-
-    LILLEY, S., Mathematical Machines,
-        _Nature_, vol. 149, Apr. 25, 1942, pp. 462-465.
-
-    MURRAY, FRANCIS J., _The Theory of
-        Mathematical Machines_, New York: King’s Crown
-        Press, 1947, 116 pp.
-
-    The author states that a mathematical machine is a mechanism
-    that provides information concerning the relationships among
-    a specified set of mathematical concepts.
-
-    TURCK, J. A. V., _The Origin of Modern
-        Calculating Machines_, Chicago: Western Society
-        of Engineers, 1921.
-
-    Recently, however, some magazine and newspaper publishers
-    have seen news value in machines that think, and some good
-    general articles with appeal to a wide audience have appeared.
-    For the references to these articles, see the section of this
-    supplement entitled “Digital Machines—Miscellaneous.”
-
-PUNCH-CARD CALCULATING MACHINES
-
-There are a few general references on punch-card calculating machines:
-
-    BAEHNE, G. WALTER, editor, and others,
-        _Practical Applications of the Punched Card
-        Method in Colleges and Universities_, New York:
-        Columbia University Press, 1935, 442 pp.
-
-    This is a collection of many contributions from a
-    number of authors, describing various applications,
-    chiefly educational.
-
-    ECKERT, W. J., _Punched-Card Methods in
-        Scientific Computation_, New York: Columbia
-        University, The Thomas J. Watson Astronomical
-        Computing Bureau, 1940, 136 pp.
-
-    This is a scientific treatise, chiefly relating to
-    the computation of orbits in astronomy.
-
-    HARTKEMEIER, HARRY PELLE, _Principles of
-        Punch-Card Machine Operation_
-       (Subtitle: _How to Operate Punch-Card Tabulating
-        and Alphabetic Accounting Machines_), New York:
-        Thomas Y. Crowell Co., 1942, 269 pp.
-
-    This is based on the author’s experience in teaching statistical
-    analysis using IBM tabulators. The book does not deal with the
-    collator or multiplying punch.
-
-    HEDLEY, K. J., _The Development of the
-        Punched-Card Method_, Actuarial Society of
-        Australasia, 1946, 20 pp.
-
-    INTERNATIONAL BUSINESS MACHINES CORPORATION,
-        _International Business Machines_ (form no.
-        A-4036-6-45), New York: International Business
-        Machines Corporation, 1945, 65 pp.
-
-    Pages 6 to 31 show pictures and brief descriptions of
-    about 20 punch-card machines, available in 1945.
-
-    SCHNACKEL, H. G., and H. C. LANG,
-        _Accounting by Machine Methods_, New York:
-        Ronald Press Co., 1939, 53 pp.
-
-    WOLF, ARTHUR W., and EDMUND C.
-        BERKELEY, _Advanced Course in Punched Card
-        Operations_, Newark, N. J.: Prudential Insurance
-        Company of America, 1942, 98 pp.
-
-    A useful and authoritative description of IBM punch-card
-    calculating machinery is the following:
-
-    INTERNATIONAL BUSINESS MACHINES CORPORATION,
-        DEPARTMENT OF EDUCATION, _Machine Methods
-        of Accounting_, Endicott, N. Y.: International
-        Business Machines Corporation, 1936-41, 385 pp.
-
-    This is a collection of 28 separate booklets telling the
-    detailed operation of IBM punch-card machinery. They were
-    written for employees of IBM and users of IBM equipment.
-    The following list of the booklets is useful in locating them:
-
-                                                                NO. OF
-                TITLE                            FORM NO.  DATE  PAGES
-    Machine Methods of Accounting—Foreword         AM      1936      6
-    Development of IBM Corporation                 AM-1-1  1936     14
-    Principles of the Electric Accounting
-      Machine Method                               AM-2    1936     12
-    The Tabulating Card                            AM-3-1  1936     20
-    Design of Tabulating Cards                     AM-4-1  1936     16
-    Preparation and Use of Codes                   AM-5    1936     28
-    Organization and Supervision of the
-      Tabulating Department                        AM-6    1936     16
-    Selection and Training of Key Punch Operators  AM-7    1936     12
-    Accounting Control                             AM-8    1936      8
-    Punches                                        AM-9    1936     12
-    Alphabetic Printing Punches                    AM-10   1936      7
-    Facts to Know about Key Punches                AM-11   1936      4
-    Verifiers                                      AM-12   1936      4
-    Gang Punches                                   AM-13   1936      8
-    Card-Operated Sorting Machines                 AM-14   1936     12
-    Facts to Know about Sorters                    AM-14a  1936      4
-    Electric Tabulating Machines                   AM-15   1936     20
-    Electric Accounting Machines
-       (Type 285 and Type 297)                     AM-16   1936     16
-    Alphabetic Direct Subtraction Accounting
-      Machine                                      AM-17   1936     28
-    Numerical Interpreters                         AM-18   1936      8
-    Electric Punched-Card Interpreter (Type 552)   AM-18a  1941      8
-    Reproducing Punches (Type 512)                 AM-19   1936     16
-    Automatic Summary Punches for Use with
-      the Numerical Accounting Machines
-      (Type 285-297)                               AM-20   1936     16
-    Automatic Summary Punches for Use with
-      the Alphabetic Accounting Machines
-      (Type 405)                                   AM-20a  1940     16
-    Multiplying Punches                            AM-21   1936     16
-    Application of Machines to Accounting
-      Functions                                    AM-22   1936     24
-    Other International Products                   AM-23-2 1936     19
-    The International Automatic Carriage
-       (Type 921)                                  AM-24   1938     15
-
-The Department of Education of IBM has begun a second series of
-booklets on the principles of operation of punch-card calculating
-machinery:
-
-    INTERNATIONAL BUSINESS MACHINES CORPORATION,
-    DEPARTMENT OF EDUCATION, _Principles of Operation_,
-    Endicott, N. Y.: International Business Machines Corporation,
-    1942 and later (except for one published in 1939).
-
-Many of the booklets in this series have good examples of machine
-operation and applications. Also, for the first time, letters and
-numbers have been used as coordinates to label the hubs on the
-plugboards. This series includes the following:
-
-                                                               NO. OF
-             TITLE                            FORM NO.   DATE  PAGES
-
-                         CARD PUNCHES AND VERIFIERS
-    Card-Punching and Verifying Machines      52-3176-0  1946   21
-    Alphabetical Verifier, Type 055           52-3295-1  1946    4
-
-                                INTERPRETERS
-    Card Interpreters, Type 550, 551, and 552 52-3178-0  1946   14
-
-                                REPRODUCERS
-    Automatic Reproducing Punch, Type 513     52-3180-0  1945   22
-    End Printing Reproducing Punch, Type 519  52-3292-1  1946   26
-
-    Electric Document-Originating Machine,               June
-    Type 519                                  52-3292-2  1948   26
-
-                                 COLLATORS
-    Collator                                  AM-25      1943   31
-    Collator Counting Device                  C.R. 9178  1942   12
-
-                             CALCULATING PUNCHES
-    Electric Multiplier, Type 601             52-3408-1  1947   47
-    Calculating Punch, Type 602               52-3409-0  1946   83
-    Calculating Punch, Type 602               52-3409-5  1947   93
-    Calculating Punch, Type 602-A
-    (Preliminary Manual)                      22-5489-0  1948   59
-    Electronic Multiplier, Type 603           52-3561-0  1946    5
-    Electronic Calculating Punch, Type 604    22-5279-0  1948   51
-
-                                  TABULATORS
-    Accounting Machine, Type 402 and 403
-    (Preliminary Manual)                      22-5654-0  1949  146
-    Alphabetical Accounting Machine, Type 404 52-3395-1  1946   96
-    Typical Applications, Alphabetical
-      Accounting Machine, Type 404,
-      with Multiple Line Printing             22-3771-1  1947   47
-    Alphabetical Accounting Machine, Type 405 AM 17 (1), 1943   90
-                                                Revised 1/1/43
-                                                         Nov.
-    Alphabetical Accounting Machine, Type 405 52-3179-2  1948   81
-
-                           AUTOMATIC PRINTING CARRIAGES
-    Bill Feed, Type 920                       52-3184-0  1945   21
-    Form Feeding Device                       52-3235-0  1946   11
-    Automatic Carriage, Type 921              52-3183-0  1945   36
-    Tape-Controlled Carriage
-     (Preliminary Manual, Revised)            22-5415-1  1948   27
-
-                               TEST SCORING MACHINE
-    Test Scoring Machine                      94-2333-0  1939   19
-                                                         May
-    Test Scoring Machine                      32-9145-1  1946   20
-    Published Tests Adapted for Use with                 June
-      the IBM Electric Test Scoring Machine   27-4286-9  1948    8
-
-In addition to the new types of punch-card machines referred to in the
-above list, an elaborate punch-card calculating machine is described in
-the following reference:
-
-    ECKERT, W. J., The IBM Pluggable Sequence
-        Relay Calculator, _Mathematical Tables and Other
-        Aids to Computation_, vol. 3, no. 23, July 1948,
-        pp. 149-161.
-
-A description of punch-card machinery in rather a light vein is
-contained in:
-
-    ANONYMOUS, Speaking of Pictures: New
-        Mechanical Monsters Ease _Life’s_ Growing Pains,
-        _Life_, Sept. 15, 1947, pp. 15-16.
-
-    ANONYMOUS, _540_, Chicago:
-        Time-Life-Fortune Magazine,
-        Subscription Fulfillment Office, 1948, 15 pp.
-
-New types of punch-card machinery are continually coming into use.
-Among them are: machines that take in punch cards and make punched
-paper tape (such as teletype tape), and vice versa—useful for
-transmitting punch-card information over wires; an electric typewriter
-operated by punch cards—useful for preparing almanacs for sea and air
-navigation, etc.; a calculator programmed by punch cards, consisting
-of an assembly of a tabulator, an electronic calculating punch, and
-an auxiliary storage unit, all cabled together—useful for some types
-of long calculation; etc. For information about such machinery, the
-manufacturers may be consulted.
-
-
-PUNCH-CARD CALCULATING MACHINERY: APPLICATIONS
-
-There are many articles in scientific journals on applications of
-punch-card calculating machinery to technical problems. The fields of
-engineering, education, indexing, mathematics, surveying, statistics,
-and others are all represented in the following list of sample
-references:
-
-    ALT, FRANZ L., Multiplication of Matrices,
-        _Mathematical Tables and Other Aids to
-        Computation_, vol. 2, no. 13, Jan. 1946,
-        pp. 12-13.
-
-    BAILEY, C. F., and others, Punch Cards for
-        Indexing Scientific Data, _Science_, vol. 104,
-        Aug. 23, 1946, p. 181.
-
-    BOWER, E. C., On Subdividing Tables, _Lick
-        Observatory Bulletin_, vol. 16, no. 455,
-        Nov. 1933, pp. 143-144.
-
-    BOWER, E. C., Systematic Subdivision of
-        Tables, _Lick Observatory Bulletin_, vol. 17,
-        no. 467, Apr. 1935, pp. 65-74.
-
-    CLEMENCE, G. M., and PAUL HERGET,
-        Optimum-Interval Punched-Card Tables,
-        _Mathematical Tables and Other Aids to
-        Computation_, vol. 1, no. 6, Apr. 1944,
-        pp. 173-176.
-
-    CULLEY, FRANK L., Use of Accounting Machines
-        for Mass-Transformation from Geographic to
-        Military-Grid Coordinates, Washington, D. C.:
-        National Research Council, _American Geophysical
-        Union Transactions of 1942_, part 2, pp. 190-197.
-
-    DEMING, W. EDWARDS, and MORRIS H.
-        HANSEN, On Some Census Aids to Sampling,
-        _Journal of the American Statistical
-        Association_, vol. 38, no. 225, Sept. 1943,
-        pp. 353-357.
-
-    DUNLAP, JACK W., The Computation of Means,
-        Standard Deviations, and Correlations by the
-        Tabulator When the Numbers Are Both Positive
-        and Negative, _Proceedings of the Educational
-        Research Forum_, International Business Machines
-        Corporation, Aug. 1940, pp. 16-19.
-
-    DWYER, PAUL S., The Use of Tables in the
-        Form of Prepunched Cards, _Proceedings of the
-        Educational Research Forum_, International
-        Business Machines Corporation, Aug. 1940,
-        pp. 125-127.
-
-    DWYER, PAUL S., Summary of Problems in
-        the Computation of Statistical Constants with
-        Tabulating and Sorting Machines, _Proceedings of
-        the Educational Research Forum_, International
-        Business Machines Corporation, Aug. 1940, pp. 20-28.
-
-    DWYER, PAUL S., and ALAN D. MEACHAM,
-        The Preparation of Correlation Tables on a
-        Tabulator Equipped with Digit Selection, _Journal
-        of the American Statistical Association_, vol.
-        32, 1937, pp. 654-662.
-
-    DYER, H. S., Making Test Score Data Effective
-        in the Admission and Course Placement of Harvard
-        Freshmen, _Proceedings of the Research Forum_,
-        International Business Machines Corporation, 1946,
-        pp. 55-62.
-
-    ECKERT, W. J., and RALPH F. HAUPT,
-        The Printing of Mathematical Tables,
-        _Mathematical Tables and Other Aids to
-        Computation_, vol. 2, no. 17, Jan. 1947,
-        pp. 196-202.
-
-    FEINSTEIN, LILLIAN, and MARTIN
-        SCHWARZCHILD, Automatic Integration of Linear
-        Second-Order Differential Equations by Means of
-        Punched-Card Machines, _Review of Scientific
-        Instruments_, vol. 12, no. 8, Aug. 1941,
-        pp. 405-408.
-
-    HOTELLING, HAROLD, Some New Methods in
-        Matrix Calculation, _The Annals of Mathematical
-        Statistics_, vol. 14, no. 1, Mar. 1943, pp. 1-34.
-
-    INTERNATIONAL BUSINESS MACHINES CORPORATION,
-        editor, and others, _Proceedings of the
-        Educational Research Forum_, Endicott, N. Y.:
-        International Business Machines Corporation, 1941.
-
-    INTERNATIONAL BUSINESS MACHINES CORPORATION,
-        editor, and others, _Proceedings of the Research
-        Forum_, Endicott, N. Y.: International Business
-        Machines Corporation, 1946, 94 pp.
-
-    KING, GILBERT W., Punched-Card Tables of the
-        Exponential Function, _Review of Scientific
-        Instruments_, vol. 15, no. 12, Dec. 1944,
-        pp. 349-350.
-
-    KING, GILBERT W., and GEORGE B.
-        THOMAS, Preparation of Punched-Card
-        Tables of Logarithms, _Review of Scientific
-        Instruments_, vol. 15, no. 12, Dec. 1944, p. 350.
-
-    KORMES, MARK, A Note on the Integration of
-        Linear Second-Order Differential Equations by
-        Means of Punched Cards, _Review of Scientific
-        Instruments_, vol. 14, no. 4, Apr. 1943, p. 118.
-
-    KORMES, MARK, Numerical Solution of the
-        Boundary Value Problem for the Potential Equation
-        by Means of Punched Cards, _Review of Scientific
-        Instruments_, vol. 14, no. 8, Aug. 1943,
-        pp. 248-250.
-
-    KORMES, MARK, and JENNIE P. KORMES,
-        Numerical Solution of Initial Value Problems by
-        Means of Punched-Card Machines, _Review of
-        Scientific Instruments_, vol. 16, no. 1,
-        Jan. 1945, pp. 7-9.
-
-    KUDER, G. FREDERIC, Use of the IBM Scoring
-        Machine for Rapid Computation of Tables of
-        Intercorrelations, _Journal of Applied
-        Psychology_, vol. 22, no. 6, Dec. 1938,
-        pp. 587-596.
-
-    MAXFIELD, D. K., Library Punched Card
-        Procedures, _Library Journal_, vol. 71,
-        no. 12, June 15, 1946, pp. 902-905 ...
-
-    MCLAUGHLIN, KATHLEEN, Adding Machines Nip AEF
-        Epidemics, New York: _New York Times_,
-        Apr. 27, 1945.
-
-    MCPHERSON, JOHN C., On Mechanical Tabulation
-        of Polynomials, _Annals of Mathematical
-        Statistics_, Sept. 1941, pp. 317-327.
-
-    MCPHERSON, JOHN C., Mathematical Operations
-        with Punched Cards, _Journal of the American
-        Statistical Association_, vol. 37, June 1942,
-        pp. 275-281.
-
-    MILLIMAN, WENDELL A., Mechanical
-        Multiplication by the Use of Tabulating Machines,
-        _Transactions of the Actuarial Society of
-        America_, vol. 35, part 2, Oct. 1934, pp.
-        253-264; for discussion see also vol. 36, part 1,
-        May 1935, pp. 77-84.
-
-    ROYER, ELMER B., A Machine Method for
-        Computing the Biserial Correlation Coefficient in
-        Item Validation, _Psychometrika_, vol. 6,
-        no. 1, Feb. 1941, pp. 55-59.
-
-    WHITTEN, C. A., Triangulation Adjustment by
-        International Business Machines, Washington, D. C.:
-        National Research Council, _American Geophysical
-        Union Transactions of 1943_, part 1, p. 31.
-
-The following bibliography may be obtained on request to the Watson
-Scientific Computing Laboratory, Columbia University, 612 West 116
-Street, New York 27, N. Y.:
-
-    WATSON SCIENTIFIC COMPUTING LABORATORY,
-        _Bibliography: The Use of IBM Machines in
-        Scientific Research, Statistics, and Education_,
-        New York: International Business Machines
-        Corporation (form no. 50-3813-0), Sept. 1947, 25 pp.
-
-The organization and equipment of this laboratory are described in:
-
-    ECKERT, W. J., Facilities of the Watson
-        Scientific Computing Laboratory, _Proceedings
-        of the Research Forum_, International Business
-        Machines Corporation, 1946, pp. 75-80.
-
-
-THE DIFFERENTIAL ANALYZER
-
-The basic scientific articles on the two differential analyzers at
-Massachusetts Institute of Technology are:
-
-    BUSH, VANNEVAR, The Differential Analyzer: A
-        New Machine for Solving Differential Equations,
-        _Journal of the Franklin Institute_, vol. 212,
-        no. 4, Oct. 1931, pp. 447-488.
-
-    BUSH, VANNEVAR, and SAMUEL H.
-        CALDWELL, A New Type of Differential Analyzer,
-        _Journal of the Franklin Institute_, vol. 240,
-        no. 4, Oct. 1945, pp. 255-326.
-
-Some of the less technical articles about the second differential
-analyzer at M.I.T. are:
-
-    CALDWELL, SAMUEL H., Educated Machinery,
-        _Technology Review_, vol. 48, no. 1,
-        Nov. 1945, pp. 31-34.
-
-    GENET, N., 100-Ton Brain at M.I.T.,
-        _Scholastic_, vol. 48, Feb. 4, 1946, p. 36.
-
-    ANONYMOUS, Mathematical Machine; New
-        Electronic Differential Analyzer, _Science News
-        Letter_, vol. 48, Nov. 10, 1945, p. 291.
-
-    ANONYMOUS, Robot Einstein: Differential
-        Analyzer at M.I.T., _Newsweek_, vol. 26,
-        Nov. 12, 1945, p. 93.
-
-    ANONYMOUS, M.I.T.’s 100-Ton Mathematical Brain
-        is Now to Tackle Problems of Peace, _Popular
-        Science_, vol. 148, Jan. 1946, p. 81.
-
-    ANONYMOUS, The Great Electro-Mechanical Brain;
-        M.I.T.’s Differential Analyzer, _Life_,
-        vol. 20, Jan. 14, 1946, pp. 73-74 ...
-
-    ANONYMOUS, All the Answers at Your Fingertips;
-        in the Laboratory of M.I.T., _Popular
-        Mechanics_, vol. 85, Mar. 1946, pp. 164-167 ...
-
-A differential analyzer was built at the Moore School of Electrical
-Engineering:
-
-    TRAVIS, IRVEN, Differential Analyzer
-        Eliminates Brain Fag, _Machine Design_, July
-        1935, pp. 15-18.
-
-A differential analyzer was built at the General Electric Company,
-Schenectady, N. Y. Instead of using a mechanical or electrical
-amplifier of the motion of the little turning wheel riding on the
-disc, this machine follows the motion using polarized light. This
-machine is described in:
-
-    BERRY, T. M., Polarized Light Servo System,
-        _Transactions of the American Institute of
-        Electrical Engineers_, vol. 63, Apr. 1944,
-        pp. 195-197.
-
-    KUEHNI, H. P., and H. A. PETERSON, A
-        New Differential Analyzer, _Transactions of the
-        American Institute of Electrical Engineers_,
-        vol. 63, May 1944, pp. 221-227.
-
-A differential analyzer has been put into use at the University of
-California:
-
-    BOELTER, L. M. K., and others, _The
-        Differential Analyzer of the University of
-        California_, Los Angeles: University of
-        California, 1947, 25 pp.
-
-A differential analyzer was built at Manchester University, England.
-It was built first from “Meccano” parts, at a total cost of about 20
-pounds, and later refined for more exact work. Some articles dealing
-with this differential analyzer are:
-
-    HARTREE, D. R., The Differential Analyzer,
-        _Nature_, vol. 135, June 8, 1935, p. 940.
-
-    HARTREE, D. R., The Mechanical Integration
-        of Differential Equations, _The Mathematical
-        Gazette_, vol. 22, 1938, pp. 342-364.
-
-    HARTREE, D. R., and A. PORTER,
-        The Construction of a Model Differential Analyser,
-        _Memoirs and Proceedings of the Manchester
-        Literary and Philosophical Society_, vol. 79,
-        July 1935, pp. 51-72.
-
-Other small scale differential analyzers built in England are covered
-in:
-
-    BEARD, R. E., The Construction of a Small
-        Scale Differential Analyser and Its Application to
-        the Calculation of Actuarial Functions, _Journal
-        of the Institute of Actuaries_, vol. 71, 1942,
-        pp. 193-227.
-
-    MASSEY, H. S. W., J. WYLIE,
-        and R. A. BUCKINGHAM, A Small Scale
-        Differential Analyser: Its Construction and
-        Operation, _Proceedings of the Royal Irish
-        Academy_, vol. 45, 1938, pp. 1-21.
-
-A differential analyzer constructed in Germany is briefly described in
-the following:
-
-    SAUER, R., and H. POESCH, Integrating
-        Machine for Solving Ordinary Differential
-        Equations, _Engineers Digest_ (American
-        Edition), vol. 1, May 1944, pp. 326-328.
-
-From the historical point of view there are some interesting papers on
-a machine for solving differential equations by Sir William Thomson
-(Lord Kelvin), including one by his brother James Thomson. They are
-in the _Proceedings of the Royal Society_, vol. 24, Feb. 1876, pp.
-262-275. The method of integration by a machine is described, but
-the state of machine tools at the time was such that no accurate
-mechanism was constructed. Another interesting paper foreshadowing the
-differential analyzer is:
-
-    WAINWRIGHT, LAWRENCE L., _A Ballistic
-        Engine_, Chicago: University of Chicago,
-        thesis for Master’s Degree, 1923, 28 pp.
-
-Some of the applications and mathematical limitations of differential
-analyzers are covered in:
-
-    BUSH, V., and S. H. CALDWELL,
-        Thomas-Fermi Equation Solution by the Differential
-        Analyzer, _Physical Review_, vol. 38, no. 10,
-        1931, pp. 1898-1902.
-
-    HARTREE, D. R., A Great Calculating Machine:
-        the Bush Differential Analyser and Its Applications
-        in Science and Industry, _Proceedings of the
-        Royal Institution of Great Britain_, vol. 31,
-        1940, pp. 151-170.
-
-    HARTREE, D. R., and A. PORTER,
-        The Application of the Differential Analyser
-        to Transients on a Distortionless Transmission
-        Line, _Journal of the Institute of Electrical
-        Engineering_, vol. 83, no. 503, Nov. 1938,
-        pp. 648-656.
-
-    HARTREE, D. R., and J. R. WOMERSLEY,
-        A Method for the Numerical or Mechanical Solution
-        of Certain Types of Partial Differential Equations,
-        _Proceedings of the Royal Society of London_,
-        series A, vol. 161, 1937, pp. 353-366.
-
-    MAGINNISS, F. J., Differential Analyzer
-        Applications, _General Electric Review_,
-        vol. 48, no. 5, May 1945, pp. 54-59.
-
-    SHANNON, CLAUDE E., Mathematical Theory of the
-        Differential Analyzer, _Journal of Mathematics
-        and Physics_, Cambridge, Mass.: Massachusetts
-        Institute of Technology, vol. 20, no. 4, 1941,
-        pp. 337-354.
-
-
-HARMONIC ANALYZERS AND SYNTHESIZERS
-
-Another branch of the analogue calculating machine is the harmonic
-analyzer and synthesizer. These are machines that study wave motions
-and related physical and mathematical functions. A brief list of
-articles on this type of machine follows:
-
-    ARCHER, R. M., Projecting Apparatus for
-        Compounding Harmonic Vibrations, _Journal of
-        Scientific Instruments_, vol. 14, 1937,
-        pp. 408-410.
-
-    BROWN, S. L., A Mechanical Harmonic
-        Synthesizer-Analyzer, _Journal of the Franklin
-        Institute_, vol. 228, 1939, pp. 675-694.
-
-    BROWN, S. L., and L. L. WHEELER,
-        A Mechanical Method for Graphical Solution
-        of Polynomials, _Journal of the Franklin
-        Institute_, vol. 231, 1941, pp. 223-243.
-
-    BROWN, S. L., and L. L. WHEELER, Use
-        of the Mechanical Multiharmonograph for Graphing
-        Types of Functions and for Solution of Pairs of
-        Non-Linear Simultaneous Equations, _Review of
-        Scientific Instruments_, vol. 13, Nov. 1942,
-        pp. 493-495.
-
-    BROWN, S. L., and L. L. WHEELER,
-        The Use of a Mechanical Synthesizer to Solve
-        Trigonometric and Certain Types of Transcendental
-        Equations, and for the Double Summations Involved
-        in Patterson Contours, _Journal of Applied
-        Physics_, vol. 14, Jan. 1943, pp. 30-36.
-
-    FÜRTH, R., and R. W. PRINGLE, A
-        New Photo-Electric Method for Fourier Synthesis
-        and Analysis, _London, Edinburgh and Dublin
-        Philosophical Magazine and Journal of Science_,
-        vol. 35, series 7, 1944, pp. 643-656.
-
-    INTERNATIONAL HYDROGRAPHIC BUREAU, _Tide
-        Predicting Machines_, International Hydrographic
-        Bureau, Special Publication 13, July 1926.
-
-    KRANZ, FREDERICK W., A Mechanical Synthesizer
-        and Analyzer, _Journal of the Franklin
-        Institute_, vol. 204, 1927, pp. 245-262.
-
-    MARBLE, F. G., An Automatic Vibration
-        Analyzer, _Bell Laboratories Record_, vol. 22,
-        Apr. 1944, pp. 376-380.
-
-    MAXWELL, L. R., An Electrical Method for
-        Compounding Sine Functions, _Review of Scientific
-        Instruments_, vol. 11, Feb. 1940, pp. 47-54.
-
-    MILLER, DAYTON C., A 32-Element Harmonic
-        Synthesizer, _Journal of the Franklin
-        Institute_, vol. 181, 1916, pp. 51-81.
-
-    MILLER, DAYTON C., The Henrici Harmonic
-        Analyzer and Devices for Extending and Facilitating
-        Its Use, _Journal of the Franklin Institute_,
-        vol. 182, 1916, pp. 285-322.
-
-    MILNE, J. R., A “Duplex” Form of Harmonic
-        Synthetiser and Its Mathematical Theory,
-        _Proceedings of the Royal Society of
-        Edinburgh_, vol. 39, 1918-19, pp. 234-242.
-
-    MONTGOMERY, H. C., An Optical Harmonic
-        Analyzer, _Bell System Technical Journal_,
-        vol. 17, no. 3, July 1938, pp. 406-415.
-
-    RAYMOND, W. J., An Harmonic Synthesizer Having
-        Components of Incommensurable Period and Any
-        Desired Decrement, _Physical Review_, vol. 11,
-        series 2, 1918, pp. 479-481.
-
-    ROBERTSON, J. M., A Simple Harmonic Continuous
-        Calculating Machine, _London, Edinburgh and
-        Dublin Philosophical Magazine and Journal of
-        Science_, vol. 13, 1932, pp. 413-419.
-
-    SOMERVILLE, J. M., Harmonic Synthesizer for
-        Demonstrating and Studying Complex Wave Forms,
-        _Journal of Scientific Instruments_, vol. 21,
-        Oct. 1944, pp. 174-177.
-
-    STRAITON, A. W., and G. K. TERHUNE,
-        Harmonic Analysis by Photographic Method,
-        _Journal of Applied Physics_, vol. 14, 1943,
-        pp. 535-536.
-
-    WEGEL, R. L., and C. R. MOORE, An
-        Electrical Frequency Analyzer, _Bell System
-        Technical Journal_, vol. 3, 1924, pp. 299-323.
-
-
-NETWORK ANALYZERS
-
-A third branch of the analogue calculating machine is the network
-analyzer. To solve problems, this machine uses the laws governing a
-network of electrical circuits. For example, an electric power company
-with a system of power lines over hundreds of miles may have a problem
-about electrical power: will an accident or a sudden demand cause a
-breakdown anywhere in the system? In the General Electric Company
-in Schenectady, N. Y., there is a machine called the A.C. Network
-Analyzer. All the properties of the power company’s network of lines
-can be fed on a small scale into the analyzer. Certain dials are turned
-and certain plugwires are connected. Then various kinds of “accidents”
-and “sudden demands” are fed into the machine, and the response of the
-system is noted. The answers given by the machine are multiplied by the
-proper scale factor, and in this way the problem of the power company
-is solved.
-
-There are two kinds of problems that network analyzers are built to
-solve: the steady state conditions and the transient conditions. For
-example, you may not overload a fuse with an electric iron when it is
-plugged in and being used, but as you pull out the cord, you may blow
-the fuse: the steady state does not overstrain the system, but the
-transient does.
-
-Some articles on network analyzers are:
-
-    ENNS, W. E., A New Simple Calculator of Load
-        Flow in A.C. Networks, _Transactions of the
-        American Institute of Electrical Engineers_,
-        vol. 62, 1943, pp. 786-790.
-
-    HAZEN, H. L., and others, _The M.I.T.
-        Network Analyzer_, Cambridge, Mass.:
-        Massachusetts Institute of Technology, Department
-        of Electrical Engineering, Serial No. 69, Apr. 1931.
-
-    KUEHNI, H. P., and R. G. LORRAINE,
-        A New A.C. Network Analyzer, _Transactions of the
-        American Institute of Electrical Engineers_,
-        vol. 57, 1938, pp. 67-73.
-
-    PARKER, W. W., Dual A.C. Network Calculator,
-        _Electrical Engineering_, May 1945,
-        pp. 182-183.
-
-    PARKER, W. W., The Modern A.C. Network
-        Calculator, _Transactions of the American
-        Institute of Electrical Engineers_, vol. 60,
-        Nov. 1941, pp. 977-982.
-
-    PETERSON, H. A., An Electric Circuit Transient
-        Analyzer, _General Electric Review_,
-        Sept. 1939, pp. 394-400.
-
-    VARNEY, R. N., An All-Electric Integrator
-        for Solving Differential Equations, _Review of
-        Scientific Instruments_, vol. 13, Jan. 1942,
-        pp. 10-16.
-
-Some of the articles on applications of network analyzers to various
-problems are:
-
-    KRON, GABRIEL, Equivalent Circuits of the
-        Elastic Field, _Journal of Applied Mechanics_,
-        vol. A11, Sept. 1944, pp. 146-161.
-
-    KRON, GABRIEL, Tensorial Analysis and
-        Equivalent Circuits of Elastic Structures,
-        _Journal of the Franklin Institute_, vol. 238,
-        Dec. 1944, pp. 399-442.
-
-    KRON, GABRIEL, Numerical Solution of Ordinary
-        and Partial Differential Equations by Means
-        of Equivalent Circuits, _Journal of Applied
-        Physics_, vol. 16, 1945, pp. 172-186.
-
-    KRON, GABRIEL, Electric Circuit Models for
-        the Vibration Spectrum of Polyatomic Molecules,
-        _Journal of Chemical Physics_, vol. 14, no. 1,
-        Jan. 1946, pp. 19-31.
-
-    KRON, G., and G. K. CARTER, A.C.
-        Network Analyzer Study of the Schrödinger Equation,
-        _Physical Review_, vol. 67, 1945, pp. 44-49.
-
-    KRON, G., and G. K. CARTER, Network
-        Analyzer Tests of Equivalent Circuits of Vibrating
-        Polyatomic Molecules, _Journal of Chemical
-        Physics_, vol. 14, no. 1, Jan. 1946, pp. 32-34.
-
-    PETERSON, H. A., and C. CONCORDIA,
-        Analyzers for Use in Engineering and Scientific
-        Problems, _General Electric Review_, vol. 48,
-        no. 9, Sept. 1945, pp. 29-37.
-
-
-MACHINES FOR SOLVING ALGEBRAIC EQUATIONS
-
-Another branch of the analogue calculating machine is a type of machine
-that will solve various kinds of algebraic equations (see Supplement
-2). A list of some articles follows. The article by Mallock describes
-a machine for solving up to 10 linear simultaneous equations in 10
-unknowns, and the article by Wilbur, a machine for solving up to 9.
-
-    DIETZOLD, ROBERT L., The Isograph—A
-        Mechanical Root-Finder, _Bell Laboratories
-        Record_, vol. 16, no. 4, Dec. 1937, pp. 130-134.
-
-    DUNCAN, W. J., Some Devices for the Solution
-        of Large Sets of Simultaneous Linear Equations,
-        _London, Edinburgh, and Dublin Philosophical
-        Magazine and Journal of Science_,
-        vol. 35, series 7, 1944, pp. 660-670.
-
-    FRAME, J. SUTHERLAND, Machines for Solving
-        Algebraic Equations, _Mathematical Tables and
-        Other Aids to Computation_, vol. 1, no. 9,
-        Jan. 1945, pp. 337-353.
-
-    HART, H. C., and IRVEN TRAVIS,
-        Mechanical Solution of Algebraic Equations,
-        _Journal of the Franklin Institute_,
-        vol. 225, Jan. 1938, pp. 63-72.
-
-    HERR, D. L., and R. S. GRAHAM, An
-        Electrical Algebraic Equation Solver, _Review of
-        Scientific Instruments_, vol. 9, Oct. 1938, pp.
-        310-315.
-
-    MALLOCK, R. R. M., An Electrical Calculating
-        Machine, _Proceedings of the Royal Society_,
-        series A, vol. 140, 1933, pp. 457-483.
-
-    MERCNER, R. O., The Mechanism of the Isograph,
-        _Bell Laboratories Record_, vol. 16, no. 4,
-        Dec. 1937, pp. 135-140.
-
-    STIBITZ, GEORGE R., Electric Root-finder,
-        _Mathematical Tables and Other Aids to
-        Computation_, vol. 3, no. 24, Oct. 1948,
-        pp. 328-329.
-
-    WILBUR, J. B., The Mechanical Solution of
-        Simultaneous Equations, _Journal of the Franklin
-        Institute_, vol. 222, Dec. 1936, pp. 715-724.
-
-
-ANALOGUE MACHINES—MISCELLANEOUS
-
-Some articles referring to various other kinds of analogue machines and
-their applications are here listed together:
-
-    BUSH, V., F. D. GAGE, and R. R.
-        STEWART, A Continuous Integraph, _Journal
-        of the Franklin Institute_, vol. 203, 1927,
-        pp. 63-84.
-
-    GRAY, T. S., A Photo-Electric Integraph,
-        _Journal of the Franklin Institute_, vol. 212,
-        1931, pp. 77-102.
-
-    HAZEN, H. L., G. S. BROWN, and W.
-        R. HEDEMAN, The Cinema Integraph: A Machine
-        for Evaluating a Parametric Product Integral (two
-        parts and appendix), _Journal of the Franklin
-        Institute_, vol. 230, July 1940, pp. 19-44,
-        and Aug. 1940, pp. 183-205.
-
-    MCCANN, G. D., and H. E. CRINER,
-        Mechanical Problems Solved Electrically,
-        _Westinghouse Engineer_, vol. 6, no. 2,
-        March 1946, pp. 49-56.
-
-    MYERS, D. M., An Integraph for the Solution
-        of Differential Equations of the Second-Order,
-        _Journal of Scientific Instruments_, vol. 16,
-        1939, pp. 209-222.
-
-    PEKERIS, C. L., and W. T. WHITE,
-        Differentiation with the Cinema Integraph,
-        _Journal of the Franklin Institute_, vol. 234,
-        July 1942, pp. 17-29.
-
-    SMITH, C. E., and E. L. GOVE,
-        An Electromechanical Calculator for
-        Directional-Antenna Patterns, _Transactions of
-        the American Institute of Electrical Engineers_,
-        vol. 62, 1943, pp. 78-82.
-
-    YAVNE, R. O., High Accuracy Contour Cams,
-        _Product Engineering_, vol. 19, part 2,
-        Aug. 1948, 3 pp.
-
-    ANONYMOUS, Electrical Gun Director
-        Demonstrated, _Bell Laboratories Record_,
-        vol. 22, no. 4, Dec. 1943, pp. 157-167.
-
-    ANONYMOUS, Development of the Electric
-        Director, _Bell Laboratories Record_, vol. 22,
-        no. 5, Jan. 1944, pp. 225-230.
-
-    ANONYMOUS, Old Field Fortune Teller:
-        Electronic Oil Pool Analyzer, _Popular
-        Mechanics_, vol. 86, Sept. 1946, p. 154.
-
-
-HARVARD IBM AUTOMATIC SEQUENCE-CONTROLLED CALCULATOR
-
-The basic scientific description of this machine as of September 1,
-1945, is contained in:
-
-    AIKEN, HOWARD H., and STAFF OF THE
-        COMPUTATION LABORATORY, _A Manual of
-        Operation for the Automatic Sequence-Controlled
-        Calculator_, Cambridge, Mass.: Harvard
-        University Press, 1946, 561 pp.
-
-The machine has changed rather a good deal since Sept. 1, 1945. Some
-circuits have been removed. Other circuits have been added. The
-capacity of the machine to do problems has been greatly increased.
-The Computation Laboratory at Harvard University is cordial towards
-scientific inquiries, and some unpublished, mimeographed information is
-available at the laboratory regarding the details of these changes.
-
-Some shorter scientific and technical descriptions of the machine are
-contained in:
-
-    AIKEN, HOWARD H., and GRACE
-        M. HOPPER, The Automatic Sequence
-        Controlled Calculator (3 parts), _Electrical
-        Engineering_, vol. 65, nos. 8, 9, and 10,
-        Aug. to Nov. 1946, p. 384 ... (21 pp.).
-
-    BLOCH, RICHARD M., Mark I Calculator,
-        _Proceedings of a Symposium on Large-Scale
-        Digital Calculating Machinery_, Harvard
-        University Press, 1948, pp. 23-30.
-
-    HARRISON, JOSEPH O., JR., The Preparation of
-        Problems for the Mark I Calculator, _Proceedings
-        of a Symposium on Large-Scale Digital Calculating
-        Machinery_, Harvard University Press, 1948,
-        pp. 208-210.
-
-    INTERNATIONAL BUSINESS MACHINES CORPORATION,
-        _IBM Automatic Sequence-Controlled
-        Calculator_, Endicott, N. Y.: International
-        Business Machines Corporation, 1945, 6 pp.
-
-Some of the less technical articles regarding the machine are:
-
-    GENET, N., Got a Problem? Harvard’s Amazing
-        New Mathematical Robot, _Scholastic_, vol. 45,
-        Sept. 18, 1944, p. 35.
-
-    TORREY, V., Robot Mathematician Knows All the
-        Answers, _Popular Science_, vol. 145,
-        Oct. 1944, pp. 86-89....
-
-    ANONYMOUS, Giant New Calculator, _Science
-        News Letter_, vol. 46, Aug. 12, 1944, p. 111.
-
-    ANONYMOUS, Mathematical Robot Presented to
-        Harvard, _Time_, vol. 44, Aug. 14, 1944, p. 72.
-
-    ANONYMOUS, World’s Greatest Machine for
-        Automatic Calculation, _Science News Letter_,
-        vol. 46, Aug. 19, 1944, p. 123.
-
-    ANONYMOUS, Superbrain, _Nation’s
-        Business_, vol. 32, Sept. 1944, p. 8.
-
-    ANONYMOUS, Robot Works Problems Never Before
-        Solved, _Popular Mechanics_, vol. 82,
-        Oct. 1944, p. 13.
-
-
-ENIAC, THE ELECTRONIC NUMERIC INTEGRATOR AND CALCULATOR
-
-There is as yet no full-scale, published scientific account of the
-Eniac. At the Ballistic Research Laboratories, Aberdeen, Md., where
-the machine now is, there are a few copies of some long mimeographed
-reports on the machine and the way it works. These were prepared by
-H. H. Goldstine and others when at the Moore School of Electrical
-Engineering, as a part of the contract under which the machine was
-constructed for the U. S. Government. It is possible that these reports
-might be consulted on request by serious students.
-
-Some scientific descriptions of the machine and its properties are:
-
-    BURKS, ARTHUR W., Electronic Computing
-        Circuits of the ENIAC, _Proceedings of the
-        Institute of Radio Engineers_, vol. 35, no. 8,
-        Aug. 1947, pp. 756-767.
-
-    CLIPPINGER, R. F., _A Logical Coding System
-        Applied to the Eniac_, B. R. L. Report No. 673,
-        Aberdeen, Md.: Ballistic Research Laboratories,
-        Sept. 29, 1948, 41 pp.
-
-    ECKERT, J. PRESPER, JR., JOHN W.
-        MAUCHLY, HERMAN H. GOLDSTINE, and
-        J. G. BRAINERD, Description of the ENIAC
-        and Comments on Electronic Digital Computing
-        Machines, Applied Mathematics Panel Report 171.2R,
-        Washington, D. C.: National Defense Research
-        Committee, Nov. 1945, 78 pp.
-
-    GOLDSTINE, HERMAN H., and ADELE
-        GOLDSTINE, The Electronic Numerical Integrator
-        and Computer (ENIAC), _Mathematical Tables and
-        Other Aids to Computation_, vol. 2, no. 15,
-        July 1946, pp. 97-110.
-
-    HARTREE, D. R., The ENIAC, an Electronic
-        Computing Machine, _Nature_, vol. 158,
-        Oct. 12, 1946, pp. 500-506.
-
-    HARTREE, D. R., _Calculating Machines:
-        Recent and Prospective Developments and Their
-        Impact on Mathematical Physics_, Cambridge,
-        England: The University Press, 1947, 40 pp.
-       (Pages 14 to 27 are devoted to the Eniac.)
-
-    TABOR, LEWIS P., Brief Description and
-        Operating Characteristics of the ENIAC,
-        _Proceedings of a Symposium on Large-Scale
-        Digital Calculating Machinery_, Harvard
-        University Press, 1948, pp. 31-39.
-
-Some of the less technical articles on Eniac are:
-
-    ROSE, A., Lightning Strikes Mathematics:
-        ENIAC, _Popular Science_, vol. 148,
-        Apr. 1946, pp. 83-86.
-
-    ANONYMOUS, Robot Calculator: ENIAC, All
-        Electronic Device, _Business Week_,
-        Feb. 16, 1946, p. 50 ...
-
-    ANONYMOUS, Answers by ENY: Electronic
-        Numerical Integrator and Computer, ENIAC,
-        _Newsweek_, vol. 27, Feb. 18, 1946, p. 76.
-
-    ANONYMOUS, Adds in ¹/₅₀₀₀ Second: Electronic
-        Computing Machine at the University of
-        Pennsylvania, _Science News Letter_, vol. 49,
-        Feb. 23, 1946, p. 113 ...
-
-    ANONYMOUS, ENIAC: at the University of
-        Pennsylvania, _Time_, vol. 47,
-        Feb. 25, 1946, p. 90.
-
-    ANONYMOUS, It Thinks with Electrons; the
-        ENIAC, _Popular Mechanics_, vol. 85,
-        June 1946, p. 139.
-
-    ANONYMOUS, Electronic Calculator: ENIAC,
-        _Scientific American_, vol. 174,
-        June 1946, p. 248.
-
-
-BELL LABORATORIES RELAY COMPUTERS
-
-As yet no full-scale scientific report is available on the Bell
-Laboratories general-purpose relay computers that went to Aberdeen and
-Langley Field. However, there is some information about these and other
-Bell Laboratories relay computing machines in the following articles:
-
-    ALT, FRANZ L., A Bell Telephone Laboratories’
-        Computing Machine (two parts), _Mathematical
-        Tables and Other Aids to Computation_, vol. 3,
-        no. 21, Jan. 1948, pp. 1-13, and vol. 3, no. 22,
-        Apr. 1948, pp. 69-84.
-
-    CESAREO, O., The Relay Interpolator, _Bell
-        Laboratories Record_, vol. 24, no. 12,
-        Dec. 1946, pp. 457-460.
-
-    JULEY, JOSEPH, The Ballistic Computer, _Bell
-        Laboratories Record_, vol. 25, no. 1,
-        Jan. 1947, pp. 5-9.
-
-    WILLIAMS, SAMUEL B., A Relay Computer
-        for General Application, _Bell Laboratories
-        Record_, vol. 25, no. 2,
-        Feb. 1947, pp. 49-54.
-
-    WILLIAMS, SAMUEL B., Bell Telephone
-        Laboratories’ Relay Computing System,
-        _Proceedings of a Symposium on Large-Scale
-        Digital Calculating Machinery_, Harvard
-        University Press, 1948, pp. 40-68.
-
-    ANONYMOUS, Complex Computer Demonstrated,
-        _Bell Laboratories Record_, vol. 19, no. 2,
-        Oct. 1940, pp. v-vi.
-
-    ANONYMOUS, _Computer Mark 22 Mod. 0:
-        Development and Description_, Navord Report
-        No. 178-45, Washington, D. C.: Navy Department,
-        Dec. 6, 1945, 225 pp.
-
-    ANONYMOUS, Relay Computer for the Army,
-        _Bell Laboratories Record_, vol. 26, no. 5,
-        May 1948, pp. 208-209.
-
-
-THE KALIN-BURKHART LOGICAL-TRUTH CALCULATOR
-
-As yet there are no published references on the Kalin-Burkhart
-Logical-Truth Calculator.
-
-Some books covering a good deal of mathematical logic are:
-
-    QUINE, W. V., _Mathematical Logic_, New
-        York: W. W. Norton & Co., 1940, 348 pp.
-
-    REICHENBACH, HANS, _Elements of Symbolic
-        Logic_, New York: The Macmillan Co., 1947, 444
-        pp.
-
-    TARSKI, ALFRED, _Introduction to Logic_,
-        New York: Oxford University Press, 1941, 239 pp.
-
-    WOODGER, J. H., _The Axiomatic Method in
-        Biology_, Cambridge, England: The University
-        Press, 1937, 174 pp.
-
-        Chapter 2, pp. 18-52, is an excellent and
-        understandable summary of the concepts of
-        mathematical logic.
-
-
-Several papers on the application of mathematical logic to the analysis
-of practical situations are:
-
-    BERKELEY, EDMUND C., Boolean Algebra
-        (The Technique for Manipulating “And,” “Or,”
-        “Not,” and Conditions) and Applications to
-        Insurance, _Record of the American Institute of
-        Actuaries_, vol. 26, Oct. 1937, pp. 373-414.
-
-    BERKELEY, EDMUND C., Conditions Affecting
-        the Application of Symbolic Logic, _Journal of
-        Symbolic Logic_, vol. 7, no. 4, Dec. 1942,
-        pp. 160-168.
-
-    SHANNON, CLAUDE E., A Symbolic Analysis of
-        Relay and Switching Circuits, _Transactions of
-        the American Institute of Electrical Engineers_,
-        vol. 57, 1938, pp. 713-723.
-
-        This paper has had a good deal of influence here
-        and there on the development of electric circuits
-        using relays.
-
-The following report discusses the solution of some problems of
-mathematical logic by means of a large-scale digital calculator:
-
-    TARSKI, ALFRED, _A Decision Method for
-        Elementary Algebra and Geometry_, Report R-109,
-        California: Rand Corporation, Aug. 1, 1948, 60 pp.
-
-
-OTHER DIGITAL MACHINES FINISHED OR UNDER DEVELOPMENT
-
-
-The Aiken Mark II Relay Calculator
-
-The Computation Laboratory of Harvard University finished during
-1947 a second large relay calculator, called the Aiken Mark II Relay
-Calculator. This machine is alluded to briefly at the end of Chapter 10
-and is described more fully in the following:
-
-    CAMPBELL, ROBERT V. D., Mark II Calculator,
-        _Proceedings of a Symposium on Large-Scale
-        Digital Calculating Machinery_, Cambridge,
-        Mass.: Harvard University Press, 1948, pp. 69-79.
-
-    FREELAND, STEPHEN L., Inside the Biggest
-        Man-Made Brain, _Popular Science_, May 1947,
-        pp. 95-100.
-
-    MILLER, FREDERICK G., Application of Printing
-        Telegraph Equipment to Large-Scale Calculating
-        Machinery, _Proceedings of a Symposium on
-        Large-Scale Digital Calculating Machinery_,
-        Cambridge, Mass.: Harvard University Press, 1948,
-        pp. 213-222.
-
-
-The Edsac
-
-The Edsac is a machine under construction in England.
-
-    WILKES, M. V., The Design of a Practical
-        High-Speed Computing Machine: the EDSAC,
-        _Proceedings of the Royal Society_, series A,
-        vol. 195, 1948, pp. 274-279.
-
-    WILKES, M. V., and W. RENWICK, An
-        Ultrasonic Memory Unit for the EDSAC, _Electronic
-        Engineering_, vol. 20, no. 245, July 1948,
-        pp. 208-213.
-
-
-The Edvac
-
-The Edvac is a machine under construction at the Moore School of
-Electrical Engineering, Philadelphia.
-
-    KOONS, FLORENCE, and SAMUEL LUBKIN,
-        Conversion of Numbers from Decimal to Binary Form
-        in the EDVAC, _Mathematical Tables and Other Aids
-        to Computation_, vol. 3, no. 26, Apr. 1949,
-        pp. 427-431.
-
-    ANONYMOUS, EDVAC Replaces ENIAC, _The
-        Pennsylvania Gazette_, Philadelphia: University
-        of Pennsylvania, vol. 45, no. 8, Apr. 1947,
-        pp. 9-10.
-
-
-The IBM Selective-Sequence Electronic Calculator
-
-The IBM Selective-Sequence Electronic Calculator was finished and
-announced in January 1948, and is alluded to briefly at the end of
-Chapter 10. More information about this machine is in the following
-references:
-
-    ECKERT, W. J., Electrons and Computation,
-        _The Scientific Monthly_, vol. 67, no. 5,
-        Nov. 1948, pp. 315-323.
-
-    INTERNATIONAL BUSINESS MACHINES CORPORATION,
-        _IBM Selective-Sequence Electronic
-        Calculator_, New York: International Business
-        Machines Corporation (form no. 52-3927-0), 1948,
-        16 pp.
-
-
-The Raytheon Computer
-
-The Raytheon Computer is a machine under construction at the Raytheon
-Manufacturing Co., Waltham, Mass.
-
-    BLOCH, R. M., R. V. D. CAMPBELL,
-        and M. ELLIS, The Logical Design of the
-        Raytheon Computer, _Mathematical Tables and Other
-        Aids to Computation_, vol. 3, no. 24, Oct. 1948,
-        pp. 286-295.
-
-    BLOCH, R. M., R. V. D. CAMPBELL, and
-        M. ELLIS, General Design Considerations
-        for the Raytheon Computer, _Mathematical Tables
-        and Other Aids to Computation_, vol. 3, no. 24,
-        Oct. 1948, pp. 317-323.
-
-
-A “System of Electric Remote-Control Accounting”
-
-During the 1930’s a system using connected punch-card machinery was
-experimented with in a department store in Pittsburgh. The purpose of
-the system was automatic accounting and analysis of sales. This system
-is described in:
-
-    WOODRUFF, L. F., A System of Electric
-        Remote-Control Accounting, _Transactions of the
-        American Institute of Electrical Engineers_,
-        vol. 57, Feb. 1938, pp. 78-87.
-
-
-The Univac
-
-The Univac is a machine under construction at the Eckert-Mauchly
-Computer Corporation, Philadelphia. A similar but smaller digital
-computer called the Binac is also being developed.
-
-    ECKERT-MAUCHLY COMPUTER CORPORATION, _The
-        Univac System_, Philadelphia: Eckert-Mauchly
-        Computer Corp., 1948, 8 pp.
-
-    ELECTRONIC CONTROL CO. (now ECKERT-MAUCHLY
-        COMPUTER CORP.), _A Tentative Instruction
-        Code for a Statistical Edvac_, Philadelphia:
-        Electronic Control Co. (now Eckert-Mauchly Computer
-        Corp.), May 7, 1947, 19 pp.
-
-    SNYDER, FRANCES E., and HUBERT M.
-        LIVINGSTON, Coding of a Laplace Boundary Value
-        Problem for the UNIVAC, _Mathematical Tables and
-        Other Aids to Computation_, vol. 3, no. 25,
-        Jan. 1949, pp. 341-350.
-
-
-The Zuse Computer
-
-The Zuse Computer is a small digital computer constructed in Germany.
-
-    LYNDON, ROGER C., The Zuse Computer,
-        _Mathematical Tables and Other Aids to
-        Computation_, vol. 2, no. 20, Oct. 1947,
-        pp. 355-359.
-
-
-THE DESIGN OF DIGITAL MACHINES
-
-Following are a number of references on various aspects of the design
-of digital computing machines:
-
-
-Organization
-
-    BURKS, ARTHUR W., Super-Electronic Computing
-        Machine, _Electronic Industries_, vol. 5,
-        no. 7, July 1946, p. 62.
-
-    BURKS, ARTHUR W., HERMAN H. GOLDSTINE
-        and JOHN VON NEUMANN, _Preliminary
-        Discussion of the Logical Design of an Electronic
-        Computing Instrument_, Princeton, N. J.:
-        Institute for Advanced Study, 2nd edition,
-        Sept. 1947, 42 pp.
-
-    ECKERT, J. PRESPER, JR., JOHN W.
-        MAUCHLY, and J. R. WEINER, An
-        Octal System Automatic Computer, _Electrical
-        Engineering_, vol. 68, no. 4, Apr. 1949, p. 335.
-
-    FORRESTER, JAY W., WARREN S. LOUD,
-        ROBERT R. EVERETT, and DAVID R.
-        BROWN, _Lectures by Project Whirlwind Staff
-        on Electronic Digital Computation_, Cambridge,
-        Mass.: Massachusetts Institute of Technology,
-        Servo-mechanisms Laboratory, Mar. and Apr. 1947,
-        149 pp.
-
-    LUBKIN, SAMUEL, Decimal Point Location in
-        Computing Machines, _Mathematical Tables and
-        Other Aids to Computation_, vol. 3, no. 21,
-        Jan. 1948, pp. 44-50.
-
-    PATTERSON, GEORGE W., editor, and others,
-        _Theory and Techniques for Design of Electronic
-        Digital Computers_ (subtitle: _Lectures
-        Given at the Moore School 8 July 1946-31
-        August 1946_), Philadelphia: The University
-        of Pennsylvania, Moore School of Electrical
-        Engineering, vol. 1, lectures 1-10, Sept. 10, 1947,
-        161 pp.; vol. 2, lectures 11-21, Nov. 1, 1947, 173
-        pp.; vol. 3 and 4 in preparation.
-
-    STIBITZ, GEORGE R., _Relay Computers_,
-        Applied Mathematics Panel Report 171.1R,
-        Washington, D. C.: National Defense Research
-        Council, Feb. 1945, 83 pp.
-
-    STIBITZ, GEORGE R., Should Automatic Computers
-        be Large or Small? _Mathematical Tables and Other
-        Aids to Computation_, vol. 2, no. 20, Oct. 1947,
-        pp. 362-364.
-
-    STIBITZ, GEORGE R., The Organization of
-        Large-Scale Calculating Machinery, _Proceedings
-        of a Symposium on Large-Scale Digital Calculating
-        Machinery_, Cambridge, Mass.: Harvard University
-        Press, 1948, pp. 91-100.
-
-    STIBITZ, GEORGE R., A New Class of Computing
-        Aids, _Mathematical Tables and Other Aids to
-        Computation_, vol. 3, no. 23, July 1948,
-        pp. 217-221.
-
-
-Input and Output Devices
-
-    ALEXANDER, SAMUEL N., Input and Output Devices
-        for Electronic Digital Calculating Machinery,
-        _Proceedings of a Symposium on Large-Scale
-        Digital Calculating Machinery_, Cambridge,
-        Mass.: Harvard University Press, 1948, pp. 248-253.
-
-    FULLER, HARRISON W., The Numeroscope,
-        _Proceedings of a Symposium on Large-Scale
-        Digital Calculating Machinery_, Cambridge,
-        Mass.: Harvard University Press, 1948, pp. 238-247.
-
-    O’NEAL, R. D., Photographic Methods for
-        Handling Input and Output Data, _Proceedings of
-        a Symposium on Large-Scale Digital Calculating
-        Machinery_, Cambridge, Mass.: Harvard University
-        Press, 1948, pp. 260-266.
-
-    TYLER, ARTHUR W., Optical and Photographic
-        Storage Techniques, _Proceedings of a Symposium
-        on Large-Scale Digital Calculating Machinery_,
-        Cambridge, Mass.: Harvard University Press, 1948,
-        pp. 146-150.
-
-    ZWORYKIN, V. K., L. E. FLORY, and
-        W. S. PIKE, Letter-Reading Machine,
-        _Electronics_, vol. 22, no. 6, June 1949,
-        pp. 80-86.
-
-    ANONYMOUS, Letter-Printing Cathode-Ray Tube,
-        _Electronics_, vol. 22, no. 6, June 1949,
-        pp. 160-162.
-
-
-Storage Devices
-
-    BRILLOUIN, LEON N., Electromagnetic Delay
-        Lines, _Proceedings of a Symposium on Large-Scale
-        Digital Calculating Machinery_, Cambridge,
-        Mass.: Harvard University Press, 1948, pp. 110-124.
-
-    FORRESTER, JAY W., High-Speed Electrostatic
-        Storage, _Proceedings of a Symposium on
-        Large-Scale Digital Calculating Machinery_,
-        Cambridge, Mass.: Harvard University Press, 1948,
-        pp. 125-129.
-
-    HAEFF, ANDREW V., The Memory Tube and
-        its Application to Electronic Computation,
-        _Mathematical Tables and Other Aids to
-        Computation_, vol. 3, no. 24, Oct. 1948,
-        pp. 281-286.
-
-    KORNEI, OTTO, Survey of Magnetic Recording,
-        _Proceedings of a Symposium on Large-Scale
-        Digital Calculating Machinery_, Cambridge,
-        Mass.: Harvard University Press, 1948, pp. 223-237.
-
-    MOORE, BENJAMIN L., Magnetic and Phosphor
-        Coated Discs, _Proceedings of a Symposium on
-        Large-Scale Digital Calculating Machinery_,
-        Cambridge, Mass.: Harvard University Press, 1948,
-        pp. 130-132.
-
-    RAJCHMAN, JAN A., The Selectron—A Tube for
-        Selective Electrostatic Storage, _Mathematical
-        Tables and Other Aids to Computation_, vol. 2,
-        no. 20, Oct. 1947, pp. 359-361 and frontispiece.
-
-    SHARPLESS, T. KITE, Mercury Delay Lines as
-        a Memory Unit, _Proceedings of a Symposium on
-        Large-Scale Digital Calculating Machinery_,
-        Cambridge, Mass.: Harvard University Press, 1948,
-        pp. 103-109.
-
-    SHEPPARD, C. BRADFORD, Transfer Between
-        External and Internal Memory, _Proceedings of
-        a Symposium on Large-Scale Digital Calculating
-        Machinery_, Cambridge, Mass.: Harvard University
-        Press, 1948, pp. 267-273.
-
-
-Programming or Coding
-
-    EVERETT, ROBERT R., _Digital Computing
-        Machine Logic_ (memorandum M-63), Cambridge,
-        Mass.: Massachusetts Institute of Technology,
-        Servo-mechanisms Laboratory, Mar. 19, 1947, 48 pp.
-
-    GOLDSTINE, HERMAN H., and JOHN VON
-        NEUMANN, _Planning and Coding of Problems
-        for an Electronic Computing Instrument_,
-        Princeton, N. J.: Institute for Advanced Study,
-        1947, 69 pp.
-
-    GOLDSTINE, HERMAN H., and JOHN VON
-        NEUMANN, _Planning and Coding of Problems
-        for an Electronic Computing Instrument_,
-        Princeton, N. J.: Institute for Advanced Study,
-        part 2, vol. 3, 1948, 23 pp.
-
-    MAUCHLY, JOHN W., Preparation of Problems for
-        Edvac-Type Machines, _Proceedings of a Symposium
-        on Large-Scale Digital Calculating Machinery_,
-        Cambridge, Mass.: Harvard University Press, 1948,
-        pp. 203-207.
-
-
-DIGITAL MACHINES—MISCELLANEOUS
-
-Many of the following articles are nontechnical and contain much
-interesting information about machines that think:
-
-    ALT, FRANZ L., New High-Speed Computing
-        Devices, _The American Statistician_, vol. 1,
-        no. 1, Aug. 1947, pp. 14-15.
-
-    BUSH, VANNEVAR, As We May Think, _Atlantic
-        Monthly_, July 1945, pp. 101-108.
-
-    CONDON, EDWARD U., _The Electronic Brain
-        Means a Better Future for You_ (broadcast),
-        Columbia Broadcasting System, Jan. 4, 1948.
-
-    DAVIS, HARRY M., Mathematical Machines,
-        _Scientific American_, vol. 180, no. 4,
-        Apr. 1949, pp. 29-39.
-
-    LAGEMANN, JOHN K., It All Adds Up,
-        _Collier’s Magazine_, May 31, 1947,
-        pp. 22-23 ...
-
-    LOCKE, E. L., Modern Calculators,
-        _Astounding Science Fiction_, vol. 52, no. 5,
-        Jan. 1949, pp. 87-106.
-
-    MACLAUGHLAN, LORNE, Electrical Mathematicians,
-        _Astounding Science Fiction_, vol. 53, no. 3,
-        May 1949, pp. 93-108.
-
-    MANN, MARTIN, Want to Buy a Brain? _Popular
-        Science_, vol. 154, no. 5, May 1949, pp. 148-152.
-
-    NEWMAN, JAMES R., Custom-Built Genius, _New
-        Republic_, June 23, 1947, pp. 14-18.
-
-    PFEIFFER, JOHN E., The Machine That Plays Gin
-        Rummy, _Science Illustrated_, vol. 4, no. 3,
-        Mar. 1949, pp. 46-48 ...
-
-    RIDENOUR, LOUIS N., Mechanical Brains,
-        _Fortune_, vol. 39, no. 5, May 1949,
-        pp. 108-118.
-
-    TUMBLESON, ROBERT C., Calculating Machines,
-        _Federal Science Progress_, June 1947, pp. 3-7.
-
-    ANONYMOUS, Almost Human, _Home Office
-        News_, Newark, N. J.: Prudential Insurance
-        Company of America, Feb. 1947, p. 8.
-
-
-APPLICATIONS OF DIGITAL MACHINES
-
-Some of the problems that mechanical brains can solve, some of the
-methods for controlling them to solve problems, and some of the
-implications of mechanical brains for future problems are covered in
-the following references:
-
-
-Solving Problems
-
-    BERKELEY, EDMUND C., Electronic Machinery for
-        Handling Information, and its Uses in Insurance,
-        _Transactions of the Actuarial Society of
-        America_, vol. 48, May 1947, pp. 36-52.
-
-    BERKELEY, EDMUND C., Electronic Sequence
-        Controlled Calculating Machinery and Applications
-        in Insurance, _Proceedings of 1947 Annual
-        Conference, Life Office Management Association_,
-        New York: Life Office Management Association, 1947,
-        pp. 116-129.
-
-    CURRY, HASKELL B., and WILLA A.
-        WYATT, _A Study of Inverse Interpolation of
-        the Eniac_, B. R. L. Report No. 615, Aberdeen,
-        Md.: Ballistic Research Laboratories, Aug. 19,
-        1946, 100 pp.
-
-    HARRISON, JOSEPH O., JR., and HELEN
-        MALONE, Piecewise Polynomial Approximation for
-        Large-Scale Digital Calculators, _Mathematical
-        Tables and Other Aids to Computation_, vol. 3,
-        no. 26, Apr. 1949, pp. 400-407.
-
-    HOFFLEIT, DORRIT, A Comparison of Various
-        Computing Machines Used in Reduction of Doppler
-        Observations, _Mathematical Tables and Other Aids
-        to Computation_, vol. 3, no. 25, Jan. 1949,
-        pp. 373-377.
-
-    LEONTIEF, WASSILY W., Computational Problems
-        Arising in Connection with Economic Analysis of
-        Interindustrial Relationships, _Proceedings of
-        a Symposium on Large-Scale Digital Calculating
-        Machinery_, Cambridge, Mass.: Harvard University
-        Press, 1948, pp. 169-175.
-
-    LOTKIN, MAX, _Inversion on the Eniac
-        Using Osculatory Interpolation_, B. R. L.
-        Report No. 632, Aberdeen, Md.: Ballistic Research
-        Laboratories, July 15, 1947, 42 pp.
-
-    LOWAN, ARNOLD N., The Computation Laboratory
-        of the National Bureau of Standards, _Scripta
-        Mathematica_, vol. 15, no. 1, Mar. 1949,
-        pp. 33-63.
-
-    MATZ, ADOLPH, Electronics in Accounting,
-        _Accounting Review_, vol. 21, no. 4, Oct.
-        1946, pp. 371-379.
-
-    MCPHERSON, JAMES L., Applications of
-        High-Speed Computing Machines to Statistical
-        Work, _Mathematical Tables and Other Aids to
-        Computation_, vol. 3, no. 22, Apr. 1948,
-        pp. 121-126.
-
-    MITCHELL, HERBERT F., JR., Inversion of a
-        Matrix of Order 38, _Mathematical Tables and
-        Other Aids to Computation_, vol. 3, no. 23,
-        July 1948, pp. 161-166.
-
-    ANONYMOUS, Revolutionizing the Office,
-        _Business Week_, May 28, 1949, no. 1030,
-        pp. 65-72.
-
-
-Speech
-
-Some of the possibilities of machines dealing with voice and speech are
-indicated in:
-
-    DUDLEY, HOMER, R. R. RIESZ, and
-        S. S. A. WATKINS, A Synthetic Speaker,
-        _Journal of the Franklin Institute_, vol. 227,
-        June 1939, pp. 739-764.
-
-        This is an article on the _Voder_, which is
-        an abbreviation of _V_oice _O_peration
-        _De_monstrator. The machine was exhibited at
-        the New York World’s Fair, 1939.
-
-    DUDLEY, HOMER, The Vocoder, _Bell
-        Laboratories Record_, vol. 18, no. 4, Dec. 1939,
-        pp. 122-126.
-
-        This is a more general type of machine than the Voder.
-        The Vocoder is both an analyzer and synthesizer of
-        human speech.
-
-    POTTER, RALPH K., GEORGE A. KOPP, and
-        HARRIET C. GREEN, _Visible Speech_,
-        New York: D. Van Nostrand Co., 1947, 441 pp.
-
-    ANONYMOUS, Pedro the Voder: A Machine that
-        Talks, _Bell Laboratories Record_, vol. 17,
-        no. 6, Feb. 1939, pp. 170-171.
-
-
-Weather
-
-Some of the possibilities of machines dealing with weather information
-are covered in:
-
-    LAGEMANN, JOHN K., Making Weather to Order,
-        _New York Herald Tribune: This Week_,
-        Feb. 23, 1947.
-
-    SHALETT, SIDNEY, Electronics to Aid Weather
-        Figuring, _The New York Times_, Jan. 11, 1946.
-
-    ZWORYKIN, V. K., _Outline of Weather
-        Proposal_, Princeton, N. J.: Radio Corporation
-        of America Research Laboratories, Oct. 1945, 11 pp.
-
-    ANONYMOUS, Weather Under Control,
-        _Fortune_, Feb. 1948, pp. 106-111 ...
-
-
-The Robot Machine
-
-    ČAPEK, KAREL, _R. U. R._ (translated from
-        the Czech by Paul Selver), New York: Doubleday,
-        Page & Co., 1923.
-
-    LAGEMANN, JOHN K., From Piggly Wiggly to
-        Keedoozle, _Collier’s Magazine_, vol. 122,
-        no. 18, Oct. 30, 1948, pp. 20-21 ...
-
-    LEAVER, E. W., and J. J. BROWN,
-        Machines Without Men, _Fortune_, vol. 34,
-        no. 5, Nov. 1946, pp. 165 ...
-
-    PEASE, M. C., Devious Weapon, _Astounding
-        Science Fiction_, vol. 53, no. 2, Apr. 1949,
-        pp. 34-43.
-
-    SHANNON, CLAUDE E., _Programming a Computer
-        for Playing Chess_, Bell Telephone Laboratories,
-        Oct. 8, 1948, 34 pp.
-
-    SHELLEY, MARY W., _Frankenstein_ (in
-        Everyman’s Library, No. 616), New York: E. P.
-        Dutton & Co., last reprinted 1945, 242 pp.
-
-    SPILHAUS, ATHELSTAN, Let Robot Work for You,
-        _The American Magazine_, Dec. 1948, p. 47 ...
-
-    ANONYMOUS, Another New Product for Robot
-        Salesmen, _Modern Industry_, vol. 13, no. 2,
-        Feb. 15, 1947.
-
-    ANONYMOUS, The Automatic Factory,
-        _Fortune_, vol. 34, no. 5, Nov. 1946,
-        p. 160 ...
-
-    ANONYMOUS, Machines Predict What Happens in
-        Your Plant, _Business Week_, Sept. 25, 1948,
-        pp. 68-69 ...
-
-
-
-
-NAME INDEX
-
-_Note: This list of persons mentioned in the text includes names of
-fictional characters. The subject index, which follows, includes all
-other names._
-
-
-    Aiken, Howard H., 90-112, 177-8, 232, 245-6
-    Alexander, Samuel N., 251
-    Alquist, 200
-    Alt, Franz L., 142, 237, 247, 253
-    Archer, R. M., 241
-    Aristotle, 152
-
-    Babbage, Charles, 89
-    Baehne, G. Walter, 232
-    Bailey, C. F., 237
-    Barcroft, Joseph, 229
-    Beach, Frank A., 229
-    Beard, R. E., 88, 240
-    Berkeley, Edmund C., 233, 248, 254
-    Berry, R. J. A., 229
-    Berry, T. M., 240
-    Bloch, Richard M., 246, 250
-    Bloomfield, Leonard, 231
-    Bodmer, Frederick, 231
-    Boelter, L. M. K., 240
-    Boole, George, 152
-    Boring, Edwin G., 229
-    Bower, E. C., 237
-    Brainerd, J. G., 247
-    Brillouin, Leon N., 252
-    Brown, David R., 251
-    Brown, G. S., 245
-    Brown, J. J., 255
-    Brown, S. L., 241-2
-    Buckingham, R. A., 240
-    Burkhart, William, 144, 155-6
-    Burks, Arthur W., 246, 251
-    Bush, Vannevar, 72, 74, 239, 241, 245, 253
-
-    Caldwell, Samuel H., 74, 239, 241
-    Campbell, Robert V. D., 249-50
-    Čapek, Karel, 199, 255
-    Carroll, Lewis, 12
-    Carter, G. K., 244
-    Cesareo, O., 248
-    Clemence, G. M., 237
-    Clippinger, R. F., 246
-    Comrie, John Leslie, 232
-    Concordia, C., 244
-    Condon, Edward U., 253
-    Crew, E. W., 232
-    Criner, H. E., 245
-    Culley, Frank L., 237
-    Curry, Haskell B., 254
-
-    Davis, Harry M., 253
-    Deming, W. Edwards, 237
-    Dietzold, Robert L., 244
-    Domin, Harry, 199
-    Dudley, Homer, 254-5
-    Duncan, W. J., 244
-    Dunlap, Jack W., 237
-    Dwyer, Paul S., 237
-    Dyer, H. S., 237
-
-    Eckert, J. Presper, Jr., 114, 178, 247, 251
-    Eckert, W. J., 233, 236-7, 239, 250
-    Edison, Thomas A., 15
-    Ellis, M., 250
-    Enns, W. E., 243
-    Everett, Robert R., 251-2
-
-    Feinstein, Lillian, 237
-    Flesch, Rudolf, 231
-    Flory, L. E., 252
-    Forrester, Jay W., 251-2
-    Frame, J. Sutherland, 244
-    Frankenstein, Victor, 198, 200
-    Franz, Shepherd I., 229
-    Freeland, Stephen L., 249
-    Fry, Macon, 232
-    Fuller, Harrison W., 252
-    Fürth, R., 242
-
-    Gage, F. D., 245
-    Genet, N., 239, 246
-    Godwin, Mary W. (Mary W. Shelley), 198, 255
-    Goldstine, Adele, 247
-    Goldstine, Herman H., 247, 251, 253
-    Gove, E. L., 245
-    Graff, Willem L., 231
-    Graham, R. S., 244
-    Gray, T. S., 245
-    Green, Harriet C., 255
-
-    Haeff, Andrew V., 252
-    Hansen, Morris H., 237
-    Harrison, Joseph O., Jr., 246, 254
-    Hart, H. C., 244
-    Hartkemeier, Harry Pelle, 233
-    Hartree, D. R., 232, 240-1, 247
-    Haupt, Ralph F., 237
-    Hayakawa, S. I., 231
-    Hazen, H. L., 243, 245
-    Hedeman, W. R., 245
-    Hedley, K. J., 233
-    Herget, Paul, 237
-    Herr, D. L., 244
-    Herrick, C. Judson, 229
-    Hoffleit, Dorrit, 254
-    Hogben, Launcelot, 231
-    Hollerith, Herman, 43
-    Hopper, Grace M., 246
-    Horsburgh, E. H., 232
-    Hotelling, Harold, 237
-    Householder, Alston S., 230
-
-    Jespersen, Otto, 231
-    Juley, Joseph, 248
-
-    Kalin, Theodore A., 144, 155-6
-    Kelvin, Lord, 72, 240
-    King, Gilbert W., 238
-    Koons, Florence, 249
-    Kopp, George A., 255
-    Kormes, Jennie P., 238
-    Kormes, Mark, 238
-    Kornei, Otto, 252
-    Kranz, Frederick W., 242
-    Kron, Gabriel, 243-4
-    Kuder, G. Frederic, 238
-    Kuehni, H. P., 240, 243
-
-    Lagemann, John K., 253, 255
-    Landahl, Herbert D., 230
-    Lang, H. C., 233
-    Lashley, Karl S., 229
-    Leaver, E. W., 255
-    Leontief, Wassily W., 254
-    Lettvin, Jerome Y., 230
-    Lilley, S., 232
-    Livingston, Hubert M., 250
-    Locke, E. L., 253
-    Lorraine, R. G., 243
-    Lotkin, Max, 254
-    Loud, Warren S., 251
-    Lowan, Arnold N., 254
-    Lubkin, Samuel, 249, 251
-    Lyndon, Roger C., 250
-
-    MacLaughlan, Lorne, 253
-    Maginniss, F. J., 241
-    Mallock, R. R. M., 244
-    Malone, Helen, 254
-    Mann, Martin, 253
-    Marble, F. G., 242
-    Massey, H. S. W., 240
-    Mastukazi, Kiyoshi, 19
-    Matz, Adolph, 254
-    Mauchly, John W., 114, 178, 247, 251, 253
-    Maxfield, D. K., 238
-    Maxwell, L. R., 242
-    McCann, G. D., 245
-    McCulloch, Warren S., 230
-    McLaughlin, Kathleen, 238
-    McPherson, James L., 254
-    McPherson, John C., 238
-    Meacham, Alan D., 237
-    Mercner, R. O., 244
-    Miller, Dayton C., 242
-    Miller, Frederick G., 249
-    Milliman, Wendell A., 238
-    Milne, J. R., 242
-    Mitchell, Herbert F., Jr., 254
-    Montgomery, H. C., 242
-    Moore, Benjamin L., 252
-    Moore, C. R., 242
-    Murray, Francis J., 232
-    Myers, D. M., 245
-
-    Newman, James R., 253
-
-    Ogden, C. K., 231
-    O’Neal, R. D., 252
-
-    Parker, W. W., 243
-    Patterson, George W., 251
-    Pease, M. C., 255
-    Pekeris, C. L., 245
-    Peterson, H. A., 240, 243-4
-    Pfeiffer, John E., 253
-    Pieron, Henri, 229
-    Pike, W. S., 252
-    Pitts, Walter, 230
-    Poesch, H., 240
-    Porter, A., 240-1
-    Potter, Ralph K., 255
-    Pringle, R. W., 242
-
-    Quine, W. V., 248
-
-    Rajchman, Jan A., 252
-    Rashevsky, N., 230
-    Raymond, W. J., 242
-    Reichenbach, Hans, 248
-    Renwick, W., 249
-    Ridenour, Louis N., 253
-    Riesz, R. R., 254
-    Robertson, J. M., 242
-    Rose, A., 247
-    Rossum, 199
-    Royer, Elmer B., 238
-
-    Sauer, R., 240
-    Schlauch, Margaret, 231
-    Schnackel, H. G., 233
-    Schrödinger, Erwin, 229
-    Schwarzchild, Martin, 237
-    Shalett, Sidney, 255
-    Shannon, Claude E., 153-5, 241, 248, 255
-    Sharpless, T. Kite, 252
-    Shelley, Mary W., 198, 255
-    Shelley, Percy Bysshe, 198
-    Sheppard, C. Bradford, 252
-    Sherrington, Charles S., 229
-    Smith, C. E., 245
-    Snyder, Frances E., 250
-    Somerville, J. M., 242
-    Spilhaus, Athelstan, 255
-    Stewart, R. R., 245
-    Stibitz, George R., 129-30, 244, 251
-    Straiton, A. W., 242
-
-    Tabor, Lewis P., 247
-    Tarski, Alfred, 248-9
-    Terhune, G. K., 242
-    Thomas, George B., 238
-    Thomson, James, 240
-    Thomson, William, 72, 240
-    Tilney, Frederick, 229
-    Torrey, V., 246
-    Travis, Irven, 239, 244
-    Tumbleson, Robert C., 253
-    Turck, J. A. V., 232
-    Tyler, Arthur W., 252
-
-    Varney, R. N., 243
-    von Neumann, John, 124, 251
-
-    Wainwright, Lawrence L., 72, 241
-    Walpole, Hugh R., 231
-    Watkins, S. S. A., 254
-    Wegel, R. L., 242
-    Weiner, J. R., 251
-    Wheeler, L. L., 241-2
-    Whitten, C. A., 238
-    Wiener, Norbert, 229
-    Wilbur, J. B., 244
-    Wilkes, M. V., 249
-    Williams, Samuel B., 248
-    Wolf, Arthur W., 233
-    Womersley, J. R., 241
-    Wood, Thomas, 19
-    Woodger, J. H., 248
-    Woodruff, L. F., 250
-    Wyatt, Willa A., 254
-    Wylie, J., 240
-
-    Yavne, R. O., 245
-
-    Zworykin, V. K., 190, 252, 255
-
-
-
-
-SUBJECT INDEX
-
-_Notes: Phrases consisting of an adjective and a noun, or of a noun
-and a noun, are entered in their alphabetical place according to the
-first word. For example, “electrostatic storage tube” is under_ e, _and
-“punch card” is under_ p.
-
-
-    _A_ field, 99
-    _A_ tape, 82-3
-    abacus, 17-9, 133, 220
-    _abax_ (Greek), 18
-    absolute value, 101, 222
-    accumulator, 115-6
-    accumulator decade, 118
-    accuracy, 67, 89
-    acetylcholine, 3
-    add output, 120
-    addend, 223
-    adder, 77
-    adder mechanism, 77-8
-    adding, 24-5, 27, 37, 55, 100, 119, 139
-    addition circuit, 37
-    Aiken Mark I Calculator, 10, 89-112, 245-6;
-      _see also_ Harvard IBM Automatic Sequence-Controlled
-                      Calculator
-    Aiken Mark II Relay Calculator, 176-8, 249
-    Aiken Mark III Electronic Calculator, 177
-    air resistance coefficient, 80-2
-    algebra of logic, 26, 36, 56-62, 105, 140, 151-2, 164, 221-3, 248
-    algebraic equations, machines for solving, 244
-    all-or-none response, 3
-    alphabet, 14
-    alphabetic coding, 13, 54
-    alphabetic punching, 46
-    alphabetic writing, 13
-    amplify, 73
-    analogous, 65
-    analogue, 65
-    analogue machines (machines that handle information
-                       expressed as measurements),        65;
-      MIT Differential Analyzer No. 2, 65-88;
-      references, 239-45
-    analytical engine, 90
-    analyzer, 68, 241-4;
-      _see also_ differential analyzer
-    and, 146-8
-    and/or, 149
-    angle-indicator, 74-5
-    animal thinking, 4, 8, 188
-    annuities, 88
-    antecedent, 158
-    antilogarithm, 139, 226
-    antitangent, 139, 226
-    approximation, 220;
-      _see also_ rapid approximation
-    aptitude testing, 190
-    argument (in a mathematical table or function),
-              96, 103-4, 122, 136, 224
-    arithmetical operations, 55-6, 173
-    armor with a motor, 180, 195
-    array, 173, 227
-    Atomic Energy Commission, 203, 208
-    attitudes, 205
-    augend, 223
-    _aut_ (Latin), 149
-    automatic address-book, 181
-    automatic carriage, 53
-    “Automatic Computing Machinery”
-           (section in _Mathematical Tables and Other Aids
-            to Computation_),                               177
-    automatic control: house-furnace, 189;
-      lawn-mower, 188;
-      tractor-plow, 188;
-      weather, 189
-    automatic cook, 181
-    automatic factory, 189
-    automatic library, 9, 181
-    automatic machinery, 182
-    automatic pilot, 189
-    automatic recognizer, 186-7
-    automatic sequence-controlled calculator, 90;
-      _see also_ Harvard IBM Automatic Sequence-Controlled
-                      Calculator
-    automatic stenographer, 185
-    automatic switching circuits, 248
-    automatic translator, 182
-    automatic typist, 182, 184
-    axon, 3
-
-    _B_ field, 99
-    _B_ tape, 82-3
-    Ballistic Research Laboratories, 1, 113-5, 127-8, 132, 142
-    base _e_, 226
-    base 10, 226
-    beam of electrons, 172
-    behavior, 4, 7-8, 29
-    Bell Telephone Laboratories, 4-5, 128-43, 247-8
-    Bell Telephone Laboratories’ general-purpose relay computer,
-              128-43, 247-8;
-      cost, 142;
-      reliability, 141;
-      speed, 142
-    Bessel functions, 111, 226
-    Binac, 179
-    binary coding, 11, 13
-    binary digit, 14
-    binary numbers, 14, 216-9
-    biophysics, 230
-    biquinary numbers, 133, 219-20
-    blocks of arguments, 137
-    Boolean algebra, 152, 248;
-      _see also_ mathematical logic
-    both, 149
-    bowwow theory, 12
-    brain evolution, 229
-    brain with a motor, 180, 195
-    BTL frames, 138-9
-    bus, 32, 119
-    button, 91, 94
-
-    _C_ field, 99
-    _C_ tape, 82-3
-    _calcis_ (Latin), 18
-    calculating punch, 47, 51-2, 235
-    calculator frames, 138
-    calculator programmed by punch cards, 236
-    cam, 94-5
-    cam contact, 91, 94-5
-    capacitance, 117
-    capacitor, 117
-    capacity: counter, 59;
-      selecting, 59
-    carbon dioxide, 190
-    card channel, 47, 52
-    card column, 48
-    card feed, 48, 91
-    card punch, 91, 97
-    card reader, 116, 118
-    card sorter, 96
-    card stacker, 48
-    card station, 47
-    Carnegie Institution of Washington, 113
-    carry impulse, 118
-    cell nucleus, 2-3
-    census, 43, 53
-    channel, 47, 52, 170
-    characteristic of a logarithm, 107
-    check counter, 105
-    check-marks, 151
-    checking, 105, 110, 179, 227
-    chess game, 117
-    chestnut blight, 201
-    chortle, 12
-    class selector, 59
-    clearing, 100
-    codes, 29, 54, 96, 99
-    coding, 30, 130, 252-3
-    coding line, 99
-    column (in a punch card), 45
-    connective, 148, 158-9
-    connective grouping, 159
-    collating, 51, 173
-    collator, 47, 51, 235
-    collator counting device, 51, 235
-    combining information, 15
-    combining operations, 173
-    Common, 59-60
-    comparer, 57-8
-    comparing, 50, 57-8
-    complement, 55;
-      _see also_ nines complement, ones complement,
-                      tens complement
-    Complex Computer, 129-30
-    complex numbers, 128-9
-    computer, 6, 27
-    Computer 1 and Computer 2, 132, 138
-    conflicts between statements, 149-50
-    consequent, 158
-    constant, 224
-    constant ratio, 77
-    constant register, 96, 99
-    constant switch, 99
-    Constant Transmitter, 116, 118
-    consulting a table, 103, 122
-    convergent, 221
-    Converter, 115
-    context, 144
-    continuous annuities, 88
-    continuous contingent insurances, 88
-    continuously running gear, 93
-    control, 6, 28, 90-1
-    control brushes, 51-2
-    control frames, 138-9
-    Control Instrument Company, 43
-    control over robot machines, 196-208
-    control tape, 28
-    controversy, 197
-    cosine, 75, 85, 139, 226
-    cost of mechanical brains, 87, 109, 126, 142, 165, 168
-    counter, 52, 74, 93-4
-    counter position, 93
-    counter wheel, 93, 118
-    counting, 55
-    coupling (numbers), 106
-    cube, 105, 224
-    Current (input of comparer), 57
-    cycle, 29, 45
-    Cycling Unit, 115-6
-    Cypriote, 13
-
-    Dartmouth College, 131
-    decade, 118
-    decimal digit, 11, 14
-    decimal position, 118
-    deciphering, 184, 188
-    decoding, 184, 188
-    definite integral, 111, 225
-    delay lines, 17, 20, 171-2
-    dendrite, 3
-    denial, 147
-    dependent variable, 81, 224
-    derivative, 68-71, 225
-    design of mechanical brains, 167-79, 251
-    desk calculating machines, 4, 11, 17, 19
-    detail cards, 50
-    dial switch, 92, 95-6
-    dial telephone, 17, 19, 128
-    differences, 110, 227
-    differential, 68, 70, 78
-    differential analyzer, 68, 72-88, 239-41
-    Differential Analyzer No. 2, 65-88;
-      accuracy, 86;
-      cost, 87;
-      reliability, 87;
-      speed, 87
-    differential equation, 68-9, 71, 111, 141, 225-6
-    differential function, 70
-    differential gear assembly, 78
-    digit, 11, 14
-    Digit Pickup, 60
-    digit selector, 60
-    digit tray, 119
-    digit trunk lines, 119
-    digit trunks, 119
-    digital machines
-       (machines that handle information expressed
-           as digits or letters):
-      Bell Laboratories’ general-purpose relay calculator, 128-43;
-      Eniac, 113-27;
-      Harvard IBM Automatic Sequence-Controlled Calculator, 89-112;
-      punch-card calculating machinery, 42-64;
-      references, 232-9, 245-55
-    directions, 24
-    disc, 78-80
-    discrimination, 140
-    discriminator, 140-1
-    distance, 68-9
-    distinguishing _A_ and _H_, 184
-    dividend, 103, 223
-    Divider-Square-Rooter, 115-7
-    dividing, 55-6, 98, 102, 121, 140
-    divisor counter, 102
-    doorpost, 65-6
-    doubling, 76-7, 100
-    doubling mechanism, 76-7
-    drafting rules, 149
-    drag coefficient, 80
-    drive, 86
-    Dry Ice, 190
-
-    echo, 171
-    Eckert-Mauchly Computer Corporation, 179, 250
-    economic relations, 194
-    Edsac, 249
-    “educated” machine, 101
-    Edvac, 177, 249
-    Egyptian, 12
-    either, 149
-    electric charge, 172
-    electric remote-control accounting, 250
-    electric typewriter, 91, 97, 236
-    electromagnet, 168
-    Electronic Binary Automatic Computer, 179
-    electronic calculating punch, 236
-    Electronic Control Company, 250
-    Electronic Numerical Integrator and Calculator (Eniac),
-               113-27, 246-7;
-      _see also_ Eniac
-    electronic tubes, 17, 20-1, 178-9;
-      Cathode, 21;
-      Grid, 21;
-      Plate, 21
-    electrostatic storage tube, 17, 20, 172
-    11 position, 45
-    11 punch, 58
-    else, 146-7
-    end-around-carry, 95, 217, 223
-    engine, 90
-    Eniac, 113-27, 246-7;
-      cost, 126;
-      panels, 115;
-      reliability, 126;
-      speed, 125;
-      unbalance, 124
-    “enough alike,” 184
-    Equal (output of sequencer), 61-2
-    equation, 68, 225
-    equivalent, 14
-    erase key, 134
-    Etruscan, 188
-    explanation, 209-13
-    explicit equation, 86
-    exponential, 85, 106, 225-6
-    extraction, 222
-
-    falsity, 147
-    farad, 117
-    fingers, 16, 18
-    fire-control instrument, 17, 19, 67, 131
-    5 impulse, 56
-    flights, 70
-    flip-flop, 119
-    following logically, 145
-    form feeding device, 236
-    formal logic, 152
-    formula, 68, 70, 224
-    Frankenstein’s monster, 198
-    function, 68, 70, 81, 103, 116, 118, 224
-    function table, 80-1, 116, 118
-
-    gang punching, 50
-    gearbox, 77-8
-    General Electric A.C. Network Analyzer, 243
-    General Electric Company, 243
-    geographic code, 54
-    giant brain, 1, 5-8
-    globe, 65-6
-    graph, 81
-    great circle, 69
-    greater-than, 25-7, 37, 222
-    greater-than circuit, 37
-    Greek letters, 120
-    guided missile, 197, 206
-    gun, 69
-
-    hail storm, 190
-    hand perforator, 132, 134
-    handling information, 10-18
-    harmonic analyzers, 241-2
-    harmonic synthesizers, 241-2
-    Harvard Computation Laboratory, 89, 176-7, 245, 249
-    Harvard IBM Automatic Sequence-Controlled Calculator (Mark I),
-               10, 89-112, 245-6;
-      cost, 109;
-      efficiency, 111;
-      reliability, 110;
-      speed, 109
-    Harvard Sequence-Controlled Electronic Calculator (Mark III), 177
-    Harvard Sequence-Controlled Relay Calculator (Mark II), 176-8, 249
-    Harvard University, 1, 4, 8, 89, 176-7, 245, 249
-    hatred, 206
-    hoppers, 51
-    hub, 46, 98
-    human brain, 2-4, 16, 229
-    humidity, 63
-
-    IBM (International Business Machines),
-               43-64, 89-90, 177, 233-9, 249-50
-    IBM Automatic Sequence-Controlled Calculator, 10, 89-112, 245-6;
-      _see also_ Harvard IBM Automatic Sequence-Controlled
-                      Calculator
-    IBM card-programmed calculator, 236
-    IBM pluggable sequence relay calculator, 236
-    IBM punch-card machinery, 43-64, 233-9
-    IBM Selective-Sequence Electronic Calculator, 177-9, 249
-    ideographic writing, 12
-    if, 146-7
-    if ... then, 149
-    ignorance, 205
-    illness, 191-2
-    imitative scheme, 12
-    in-code, 99
-    in-field, 99
-    independent variable, 81, 224
-    infinity, 86, 133, 212, 225
-    information, 10
-    initial conditions, 83, 225
-    Initiating Unit, 115-6
-    input, 6, 90-1
-    input devices, 175, 251-2
-    input register, 27
-    instantaneous rate of change, 70-1
-    Institute of Advanced Study, 124
-    instructions, 28, 83, 97, 178-9
-    insurance company, 42
-    insurance policies, 42
-    insurance values, 88
-    integral, 68, 71-2, 225
-    integral sign, 85, 225
-    integrating, 71-2, 78
-    integrator, 78-80
-    integrator mechanism, 78-9
-    International Business Machines Corporation (IBM), 43;
-      _see_ IBM
-    International Hydrographic Bureau, 242
-    International Phonetic Alphabet, 13
-    interpolating, 131, 221
-    interposing, 102
-    interpreter, 47, 49, 235
-    interpreting, 49
-    interval, 68, 70
-    intuitive thinking, 8
-    inverse, 71
-
-    judgments, 191
-
-    Kalin-Burkhart Logical-Truth Calculator, 144-66, 248;
-      cost, 165;
-      reliability, 166;
-      speed, 166
-    key punch, 47-8, 96, 235
-    keyboard, 48
-    knots, 17
-
-    language of logic, 56-62, 105, 140;
-      _see also_ mathematical logic
-    languages, 10-21, 231
-    latch relay, 40-1
-    left-hand components, 56, 121, 215
-    library, 9, 181
-    Library of Congress, 15
-    lie detector, 192
-    line of coding, 99
-    linear, 224-5
-    linear interpolation, 221
-    linear simultaneous equations, 141, 225
-    lobe, 94-5
-    logarithm, 67, 85, 106-8, 139, 225
-    Logarithm-In-Out counter, 107
-    logic, 144;
-      _see also_ mathematical logic
-    logical choice, 4;
-      _see also_ mathematical logic
-    logical connective, 148, 222
-    logical operations, 56-62, 173
-    logical pattern, 145-6
-    logical truth, 144-56, 166
-    Logical-Truth Calculator, 144-66;
-      _see_ Kalin-Burkhart Logical-Truth Calculator
-    loopholes, 149
-    Low Primary (output of sequencer), 61-2
-    Low Secondary (output of sequencer), 61-2
-    Lower Brushes, 52
-    loxodrome, 69-70
-
-    machine call number, 99
-    machine cycle, 56
-    machine language, 29, 99, 175, 191
-    machines as a language for thinking, 19-20;
-      references, 231-2
-    machines involving voice and speech, 185-6, 254
-    magnetic surfaces, 17, 20, 168-70, 179
-    magnetic tape, 169-70, 179
-    magnetic wire, 168
-    magnetized spot, 168-70
-    main connective, 160
-    many-wire cable, 50
-    Mark I (Harvard IBM Automatic Sequence-Controlled Calculator),
-               10, 89-112, 245-6;
-      _see also_ Harvard IBM Automatic Sequence-Controlled
-                      Calculator
-    Mark II (Harvard Sequence-Controlled Relay Calculator), 176-8, 249
-    Mark III (Harvard Sequence-Controlled Electronic Calculator), 177
-    Massachusetts Institute of Technology, 1, 20, 65, 72-88, 153
-    Massachusetts Institute of Technology’s Differential
-               Analyzer No. 2, 65-88;
-      accuracy, 86;
-      cost, 87;
-      reliability, 87;
-      speed, 87
-    master card, 50
-    Master Programmer, 115-6
-    matching, 173
-    mathematical biophysics, 230
-    mathematical logic, 26, 36, 56-62, 105, 140, 151-2, 164, 221-3, 248
-    matrices, 173, 227
-    matrix, 173, 227
-    meanings, 209, 231
-    measurements, 65-6, 68
-    mechanical brain, 1, 5-8, 20;
-      crucial devices for, 20
-    mechanical brains under construction, 176-9
-    memory, 27, 90-1
-    mentality, 24, 27
-    mercury tank, 171, 179
-    merging, 173
-    metal fingers, 135
-    mica, 172
-    microphone, 185
-    mimeograph stencil, 16
-    Minoan, 188
-    miscellaneous field, 99
-    mistake, 134
-    Moore School of Electrical Engineering, 7, 113-27, 177, 249
-    multiplicand, 223
-    multiplicand counter, 101
-    multiplication schemes, 214-6
-    multiplier, 115-6
-    multiplier counter, 101
-    multiply-divide unit, 103
-    multiplying, 55-6, 101, 121, 140
-    multiplying punch, 47, 52, 235
-
-    National Advisory Committee for Aeronautics, 128, 132
-    Naval Proving Ground, 177
-    negation, 24-5, 27, 34-6
-    negation circuit, 36
-    negative, 147
-    negative digit, 215
-    neon bulb, 119
-    nerve, 2-4
-    nerve cell, 2, 3, 16
-    nerve fiber, 2, 3
-    nerve networks, 230
-    nervous system, 188
-    network analyzers, 242-4
-    neurosis, 191
-    nine-pulses, 120-1
-    nines complement, 95, 121, 223
-    No X, 59
-    Northrop Aircraft, Inc., 179
-    not, 146-8
-    numeric coding, 13, 54
-    numerical X position, 45
-    numerical Y position, 45
-
-    occupation code, 54
-    octal notation, 179, 219
-    ohm, 117
-    Ojibwa, 12
-    ones complement, 217
-    only, 146-7
-    operation code, 103
-    operations with numbers, 24-7
-    or, 146-9
-    organization of digital machines, 251
-    out-code, 99
-    out-field, 99
-    output, 6, 90-1, 251-2
-    output devices, 176, 251-2
-    output register, 27
-
-    paper channel, 52
-    partial differential equations, 87
-    partial products, 115, 214
-    Pearl Assurance Company, 88
-    pebbles, 17-8
-    pen with a motor, 180, 195
-    permanent table frames, 138-9
-    personal income tax, 141
-    phonetic writing, 13
-    phonograph, 15-6
-    phonographic writing, 13
-    phototube, 81-2, 183-4
-    physical equipment for handling information, 11, 15-21, 91
-    physical problems, 69-72
-    physical quantities, 67-9
-    pictographic writing, 12
-    plugboard, 46, 98
-    plug-in units, 117-8
-    point of view, 207
-    pooh-pooh theory, 12
-    position (in a punch card), 45
-    position frames, 138-9
-    power, 43, 65, 133, 216, 224
-    prejudice, 205
-    Previous (input of comparer), 57
-    Primary (input of sequencer), 61-2
-    Primary Brushes, 51, 62
-    Primary Feed, 51, 61
-    Primary Sequence Brushes, 51
-    printer, 137
-    printer frames, 138
-    problem frames, 138
-    problem position, 132, 135
-    problem tape, 134
-    processor, 132, 134, 175
-    product, 70, 102, 223
-    product counter, 102
-    production scheduling, 193
-    program, 122, 173, 252-3
-    program-control switch, 123
-    program pulse, 122
-    program-pulse input terminal, 123
-    program register, 38
-    program tape, 28-9
-    program trays, 119
-    program trunk lines, 119
-    programming method of von Neumann, 124
-    pronoun, 223
-    psychological testing, 190
-    psychological trainer, 191-2
-    pulses, 120, 171
-    punch card, 17, 44-5, 95, 97
-    punch-card column, 45
-    punch-card machinery, 17, 20, 42-64, 232-9;
-      cost, 63;
-      reliability, 63-4;
-      speed, 62-3
-    punch feed, 51-2
-    punched paper tape, 17, 23, 82, 95
-    punching channel, 50
-    punching dies, 48, 51-2
-    pyramid circuit, 39
-
-    quantity of information, 11, 14-15
-    quartz, 171
-    quotient, 98, 103
-
-    _R.U.R._, 199
-    radar, 183
-    railroad line, 6, 119
-    rapid approximation, 106-8, 220-1
-    rate of change, 68, 70-1
-    ratio, 77, 83
-    Raytheon Computer, 250
-    reading, 57
-    reading brushes, 51-2
-    reading channel, 50
-    reading of punch cards, 44
-    reasoning, 144
-    rebus-writing, 13
-    reciprocal, 85, 224
-    recognizing, 8, 182-5
-    recorder, 132, 137
-    rectifier, 32
-    referent, 12
-    register, 27
-    reject, 49
-    relay, 17, 20-1, 23, 92, 129, 133, 178;
-      Common, 21;
-      Ground, 21;
-      Normally Closed, 21;
-      Normally Open, 21;
-      Pickup, 21
-    release key, 48
-    reliability, 63-4, 110, 126, 128, 141-2, 166, 168, 174
-    Remington-Rand, 43
-    reperforator, 137
-    rephrasing, 163-4
-    reproducer, 47, 49-50, 235
-    reproducing, 49
-    reset code, 100
-    resetting, 100
-    resistance, 80, 117
-    resistance coefficient, 80
-    resistor, 117
-    right-hand components, 56, 121, 215
-    robot machine, 197, 198-208, 255
-    robot salesman, 201
-    _robota_ (Czech), 199
-    Roman numerals, 212;
-      ancient style, 219
-    room, 70
-    Rossum’s Universal Robots, 199
-    rounding off, 55-6
-    routine, 8, 167, 173
-    routine frames, 138-9
-    routine tape, 28, 134
-    rules, 191, 224
-
-    satisfy, 225
-    scale factor, 74, 86
-    schemes for expressing meanings, 11-15
-    screen, 172
-    screw, 78
-    Secondary (input of sequencer), 61-2
-    Secondary Brushes, 51, 62
-    Secondary Feed, 61
-    Select-Receiving-Register circuit, 39
-    selecting, 26, 58, 104
-    selection, 26-7, 38, 222
-    selection circuit, 38
-    selection counter, 104
-    selector, 58-60
-    sensing digits, 108
-    separation sign, 129
-    sequence-control tape, 98
-    sequence-control-tape code, 98
-    sequence-controlled, 89
-    sequence-tape feed, 98
-    sequencer, 61
-    sequencing, 61
-    shifting, 217
-    short-cut multiplication, 215-6
-    Simon, 22-40
-    simultaneous, 225
-    simultaneous equations, 85, 225
-    sine, 75, 85, 106, 139, 226
-    sink (of a circuit), 154
-    slab, 18
-    slide rule, 65, 67
-    smoothness, 110, 227
-    social control, types, 203
-    sorter, 47-9
-    sorting, 57, 173
-    soundtracks, 16, 18
-    source (of a circuit), 154
-    space key, 48
-    speedometer, 68
-    spelling rules, 185
-    spoken English, 11
-    square, 224
-    square matrix, 227
-    square root, 116-7, 173, 220, 224
-    Start Key, 98
-    statements, 26, 144-51
-    static electricity, 63
-    storage, 6
-    storage counter, 93
-    storage devices, 252
-    storage register, 28, 93
-    storing information, 15
-    storing register frames, 138
-    storing registers, 139
-    string, 65-6
-    stylus, 16
-    subroutine, 106
-    Subsidiary Sequence Mechanism, 90, 106
-    subtract output, 120
-    subtracting, 55, 100, 119, 139, 223
-    subtracting by adding, 223
-    summary punch, 50, 116, 119
-    summary-punching, 50
-    switch open and current flowing, 154
-    switchboard, 76
-    switches in parallel, 154
-    switches in series, 154
-    switching circuits, 155
-    syllable-writing, 13
-    syllables, 211
-    syllogism, 146, 152
-    symbolic logic, 221-3, 248;
-      _see also_ mathematical logic
-    symbolic writing, 12
-    synapse, 3
-    System of Electric Remote-Control Accounting, 250
-    systems for handling information, 10
-
-    table tape, 134
-    tables (of values), 103, 136, 224
-    tabular value, 136, 224
-    tabulator, 47, 52, 119, 235
-    tallies, 17
-    tangent, 105, 226
-    tank (armored), 180, 195
-    tank (mercury tank), 171, 179
-    tape-controlled carriage, 236
-    tape feed, 91, 178-9
-    tape punch, 91, 97-8, 137
-    tape reels, 170
-    tape transmitter, 135, 137
-    telegraph line, 6, 119
-    telephone central station, 138
-    teletype, 17
-    teletype transmitter, 133, 135
-    teletypewriter, 130, 137
-    ten-position relay, 91-3
-    ten-position switch, 91-2
-    ten-pulses, 120-1
-    tens complement, 224
-    test scoring machine, 236
-    then, 146-7
-    thermostat, 187
-    thinking, 1-5, 10, 97
-    timed electrical currents, 44
-    timing contact, 94
-    tolerances, 67, 105
-    torque, 73, 86
-    torque amplifier, 73
-    trajectories, 69, 114, 141
-    transfer circuit, 33
-    transferring, 31, 34, 100, 119, 167
-    translating, 57
-    transmitter, 74
-    triggering control, 183, 186-7
-    trigonometric tables, 226
-    trigonometric tangent, 105, 226
-    truth, 144
-    truth table, 147, 155, 222
-    truth value, 26, 58, 105, 147, 222
-    tuning, 183
-    turning force, 72
-    12 position, 45
-    two-position relay, 21, 91-2;
-      _see also_ relay
-    two-position switch, 91-2
-    typewriter, 16, 18
-    typewriter carriage, 53
-
-    unattended operation, 174
-    understanding, 212-3, 231
-    unemployment, 201-2
-    Unequal (output of comparer), 57
-    unit of information, 11, 14-5, 169
-    United Nations, 203, 208
-    United States Army Ordnance Department, 113-4
-    Univac, 250
-    University of Pennsylvania, 7, 113
-    unknowns, 141
-    Upper Brushes, 52
-
-    value tape code, 96
-    value tape feed, 95-6
-    variables, 84, 223
-    _vel_ (Latin), 149
-    verifier, 47-8, 235
-    vibration, 69
-    Vocoder, 255
-    Voder, 254
-    voltage, 74
-
-    Watson Scientific Computing Laboratory, 239
-    weather control, 189, 255
-    weather forecasting, 189, 255
-    wheel (of a counter), 78
-    white elephant, 73, 114
-    winch, 73
-    words for explaining, 209-12
-
-    X, 59
-    X distributor, 59
-    X Pickup, 59
-    X punch, 45, 58
-    X selector, 59
-
-    zero, 133, 212
-    _zh_ (sound), 13, 185
-    Zuse Computer, 250
-
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-<p style='text-align:center; font-size:1.2em; font-weight:bold'>The Project Gutenberg eBook of Giant brains; or Machines that think, by Edmund Callis Berkeley</p>
-<div style='display:block; margin:1em 0'>
-This eBook is for the use of anyone anywhere in the United States and
-most other parts of the world at no cost and with almost no restrictions
-whatsoever. You may copy it, give it away or re-use it under the terms
-of the Project Gutenberg License included with this eBook or online
-at <a href="https://www.gutenberg.org">www.gutenberg.org</a>. If you
-are not located in the United States, you will have to check the laws of the
-country where you are located before using this eBook.
-</div>
-
-<p style='display:block; margin-top:1em; margin-bottom:1em; margin-left:2em; text-indent:-2em'>Title: Giant brains; or Machines that think</p>
-<p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em'>Author: Edmund Callis Berkeley</p>
-<p style='display:block; text-indent:0; margin:1em 0'>Release Date: September 14, 2022 [eBook #68991]</p>
-<p style='display:block; text-indent:0; margin:1em 0'>Language: English</p>
-  <p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em; text-align:left'>Produced by: Tim Lindell and the Online Distributed Proofreading Team at https://www.pgdp.net (This book was produced from images made available by the HathiTrust Digital Library.)</p>
-<div style='margin-top:2em; margin-bottom:4em'>*** START OF THE PROJECT GUTENBERG EBOOK GIANT BRAINS; OR MACHINES THAT THINK ***</div>
-
-<hr class="chap" />
-
-<h1>GIANT BRAINS<br /><small>OR</small><br />MACHINES THAT THINK</h1>
-
-<p class="f120 space-above2"><b>EDMUND CALLIS BERKELEY</b></p>
-
-<p class="f90">Consultant in Modern Technology<br />
-President, E. C. Berkeley and Associates</p>
-
-<p class="center space-above2">JOHN WILEY &amp; SONS, INC., NEW YORK<br />
-CHAPMAN &amp; HALL, LIMITED, LONDON</p>
-
-<p class="center space-above2">Copyright, 1949<br />by<br />
-EDMUND CALLIS BERKELEY</p>
-
-<p class="center space-above2"><i>All Rights Reserved</i></p>
-
-<p class="center space-above2"><i>This book or any part thereof must not<br />
-be reproduced in any form without<br />the written permission of the publisher.</i></p>
-
-<p class="center space-above2">Second Printing, February, 1950</p>
-
-<p class="center space-above2">Printed in the United States of America</p>
-
-<p class="center space-above2">To my friends,<br />
-whose help and instruction<br />made this book possible</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<h2 class="nobreak">PREFACE<br />
-<span class="h_subtitle">The Subject, Purpose, and Method<br />of this Book</span></h2>
-</div>
-
-<p>The subject of this book is a type of machine that comes closer to
-being a brain that thinks than any machine ever did before 1940. These
-new machines are called sometimes mechanical brains and sometimes
-sequence-controlled calculators and sometimes by other names.
-Essentially, though, they are machines that can handle information with
-great skill and great speed. And that power is very similar to the
-power of a brain.</p>
-
-<p>These new machines are important. They do the work of hundreds of human
-beings for the wages of a dozen. They are powerful instruments for
-obtaining new knowledge. They apply in science, business, government,
-and other activities. They apply in reasoning and computing, and, the
-harder the problem, the more useful they are. Along with the release of
-atomic energy, they are one of the great achievements of the present
-century. No one can afford to be unaware of their significance.</p>
-
-<p>In this book I have sought to tell a part of the story of these new
-machines that think. Perhaps you, as you start this book, may not agree
-with me that a machine can think: the first chapter of this book is
-devoted to the discussion of this question.</p>
-
-<p>My purpose has been to tell enough about these machines so that we
-can see in general how they work. I have sought to explain some
-giant brains that have been built and to show how they do thinking
-operations. I have sought also to talk about what these machines can do
-in the future and to judge their significance for us. It seems to me
-that they will take a load off men’s as great as the load that
-printing took off men’s writing: a tremendous burden lifted.</p>
-
-<p>We need to examine several of the new mechanical brains: Massachusetts
-Institute of Technology’s differential analyzer, Harvard’s IBM
-automatic sequence-controlled calculator, Moore School’s ENIAC
-<span class="pagenum" id="Page_viii">[Pg viii]</span>
-(Electronic Numerical Integrator and Calculator), and Bell
-Laboratories’ general-purpose relay calculator. These are described in
-the sequence in which they were finished between the years 1942 and 1946.</p>
-
-<p>We also have to go on some excursions—for instance, the nature of
-language and of symbols, the meaning of thinking, the human brain and
-nervous system, the future design of machinery that can think, and a
-little algebra and logic. I have also sought to discuss the relations
-between machines that think and human society—what we can foresee as
-likely to happen or be needed as a result of the remarkable invention
-of machines that can think.</p>
-
-<h3>READING THIS BOOK</h3>
-
-<p>This book is intended for everyone. I have sought to put it together in
-such a way that any reader can select from it what he wants.</p>
-
-<p>Perhaps at first reading you want only the main thread of the story.
-Then read only what seems interesting, and skip whatever seems
-uninteresting. The subheadings should help to tell you what to read and
-what to skip. Nearly all the chapters can be read with little reference
-to what goes before, although some reference to the supplements in the
-back may at times be useful.</p>
-
-<p>Perhaps your memory of physics is dim, like mine. The little knowledge
-of physics needed is explained here and there throughout the book, and
-the index should tell where to find any explanation you may want.</p>
-
-<p>Perhaps it is a long time since you did any algebra. Then <a href="#SUPPL_2">Supplement 2</a>
-on mathematics may hold something of use to you. Two sections (one
-in <a href="#CHAPTER_5">Chapter 5</a> and one in <a href="#CHAPTER_6">Chapter 6</a>)
-labeled as containing some rather mathematical details may be skipped
-with no great loss.</p>
-
-<p>Perhaps you are unacquainted with logic that uses symbols—the branch
-of logic called mathematical logic. In fact, very few people are
-familiar with it. No discussion in the book hinges on understanding
-this subject, except for <a href="#CHAPTER_9">Chapter 9</a> where a machine that
-calculates logical truth is described. In all other chapters you may freely skip
-all references to mathematical logic. But, if you are curious about the
-<span class="pagenum" id="Page_ix">[Pg ix]</span>
-subject and how it can be usefully applied in the field of mechanical
-brains, then begin with the introduction to the subject in <a href="#CHAPTER_9">Chapter 9</a>,
-and note the suggestions in the section entitled “Algebra of Logic”
-in <a href="#SUPPL_2">Supplement 2</a>.</p>
-
-<p>In any case, glance at the table of contents, the chapter headings and
-subheadings, and the supplements at the back. These should give an idea
-of how the book is put together and how you may select what may be
-interesting to you.</p>
-
-<p>Please do not read this book straight from beginning to end unless
-that way proves to be congenial to you. If you are not interested in
-technical details, skip most of the middle chapters, which describe
-existing mechanical brains. If, on the other hand, you want more
-details than this book contains, look up references in <a href="#SUPPL_3">Supplement 3</a>.
-Here are listed, with a few comments, over 250 books, articles,
-and pamphlets related to the subject of machinery for computing and
-reasoning. These cover many parts of the field; some parts, however,
-are not yet covered by any published information.</p>
-
-<p>There are no photographs in this book, although there are over 80
-drawings. Photographs of these complicated machines can really show
-very little: panels, lights, switches, wires, and other kinds of
-hardware. What is important is the way the machine works inside. This
-cannot be shown by a photograph but may be shown by schematic drawings.
-In the same way, a photograph of a human being shows almost nothing
-about how he thinks.</p>
-
-<h3>UNDERSTANDING THIS BOOK</h3>
-
-<p>I have tried to write this book so that it could be understood. I have
-attempted to explain machinery for computing and reasoning without
-using technical words any more than necessary. To do this seemed to be
-easy in some places, much harder in others. As a test of this attempt,
-a count has been made of all the different words in the book that have
-two syllables or more, that are used for explaining, and that are
-not themselves defined. There are fewer than 1800 of these words. In
-<a href="#SUPPL_1">Supplement 1</a>, entitled “Words and Ideas,” I have
-digressed to discuss further the problem of explanation and understanding.
-<span class="pagenum" id="Page_x">[Pg x]</span></p>
-
-<p>Every now and then in the book, along comes a word or a phrase that
-has a special meaning, for example, the name of something new. When it
-first appears, it is put in italics and is explained or defined. In
-addition, all the words and phrases having special meaning appear again
-in the index, and next to each is the page number of its explanation or
-definition.</p>
-
-<p>In many places, I have talked of mechanical brains as if they were
-living. For example, instead of “capacity to store information” I have
-spoken of “memory.” Of course, the machines are not living; but they do
-have individuality, responsiveness, and other traits of living beings,
-just as a political party pictured as a living elephant does. Besides,
-to treat things as persons is a help in making any subject vivid and
-understandable, as every song writer and cartoonist illustrates.
-We speak of “Old Man River” and “Father Time”; we may speak of a
-ship or a locomotive as “she”; and the crew on the first Harvard
-sequence-controlled calculator has often called her “Bessy, the
-Bessel engine.”</p>
-
-<p>Let us pause a little longer on the subject of understanding. What
-is the understanding of something new? It is a state of knowing, a
-process of knowing more and more. The more we know about something
-new, the better we understand it. It is possible for almost anybody to
-understand almost anything, I believe. What is mainly needed in order
-to grasp an idea is a good collection of true statements about it and
-some practice in using those statements in situations. For example,
-no one has ever seen or touched the separate scraps of electricity
-called electrons. But electrons have been described and measured;
-hundreds of thousands of people work with electrons; they know and use
-true statements about electrons. In effect, these people understand electrons.</p>
-
-<p>Probably the hardest task of an author is to make his statements
-understandable yet accurate. It is too much to hope for complete
-success. I shall be very grateful to any reader who points out to me
-the statements that he has not understood or that are in error.</p>
-
-<p>As to the views I have expressed, I do not expect every reader to agree
-with me. In fact, I shall be glad if many a reader disagrees with me.
-For then someone else may say to both of us, “You’re both right and
-<span class="pagenum" id="Page_xi">[Pg xi]</span>
-both wrong—the truth lies atwixt and atween you.” Thoughtful and
-tolerant disagreement is the finest climate for scientific progress.</p>
-
-<h3>BASIC FACTS</h3>
-
-<p>Many of the mechanical brains described in this book will do good work
-for years; but their design is already out of date. Many organizations
-are hard at work finding new tricks in electronics, materials, and
-engineering and making new mechanical brains that are better and faster.</p>
-
-<p>In spite of future developments, though, the basic facts about
-mechanical brains will endure. These basic facts are drawn from the
-principles of thinking, of mathematics, of science, of engineering,
-etc. These facts govern all handling of information. They do not depend
-very much on human or mechanical energy. They do not depend very much
-on signs. They do not depend very much on the century, or the language,
-or the country. For example, “II et III V sunt,” the Romans may have
-said; “deux et trois font cinq,” say the French; “2 + 3 = 5,” say the
-mathematicians; and we say, “two and three make five.” The main effort
-in this book has been to make clear the basic facts about mechanical
-brains, for they are now a masterly instrument for obtaining new
-knowledge.</p>
-
-<p class="author"><span class="smcap">Edmund Callis Berkeley</span></p>
-
-<p>New York 11, N. Y.<br />&nbsp;&emsp;<i>June 30, 1949</i></p>
-
-<p><span class="pagenum" id="Page_xii">[Pg xii]</span></p>
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_xiii">[Pg xiii]</span></p>
-<h2 class="nobreak">ACKNOWLEDGMENTS</h2>
-</div>
-
-<p>This book has been over seven years in the making and has evolved
-through many different plans for its contents. It springs essentially
-from the desire to see human beings use their knowledge better: we
-know enough, but how are we to use what we know? Machines that handle
-information, that make knowledge accessible, are a long step in the
-direction of using what we know.</p>
-
-<p>For help in causing this desire to come to fruition, I should like
-to express my indebtedness especially to Professor (then Commander,
-U.S.N.R.) Howard H. Aiken of Harvard University, whose stimulus, while
-I was stationed for ten months in 1945-46 in his laboratory, was very
-great.</p>
-
-<p>I should also like to express my appreciation to Mr. Harry J. Volk,
-whose vision and enthusiasm greatly encouraged me in the writing of
-this book.</p>
-
-<p>For careful reviews and helpful comments on the chapters dealing with
-existing mechanical brains, I am especially grateful to Dr. Franz
-L. Alt, Mr. E. G. Andrews, Professor Samuel H. Caldwell, Dr. Grace
-M. Hopper, Mr. Theodore A. Kalin, and Dr. John W. Mauchly, who are
-experts in their fields. Dr. Ruth P. Berkeley, Dr. Rudolf Flesch, Mr.
-J. Ross Macdonald, Dr. Z. I. Mosesson, Mr. Irving Rosenthal, Mr. Max
-S. Weinstein, and many others have been true friends in reading and
-commenting upon many parts of the manuscript. Mr. Frank W. Keller
-devoted much time and skill to converting my rough sketches into
-illustrations. Mr. Murray B. Ritterman has been of invaluable help in
-preparing and checking much of the bibliography. Miss Marjorie L. Black
-has helped very greatly in turning scraps of paper bearing sentences
-into an excellent manuscript for the printer.</p>
-
-<p>For permission to use the quotations on various pages in Chapters 11
-and 12, I am indebted to the kindness of:
-<span class="pagenum" id="Page_xiv">[Pg xiv]</span></p>
-
-<div class="blockquot">
-<p class="neg-indent">E. P. Dutton &amp; Co., for quotations from
-<i>Frankenstein</i>, by Mary W. Shelley, Everyman’s Library, No.
-616.</p>
-
-<p class="neg-indent">Samuel French, for quotations from <i>R.
-U. R.</i>, by Karel Čapek.<a id="FNanchor_1" href="#Footnote_1" class="fnanchor">[1]</a></p>
-
-<p class="neg-indent"><i>Modern Industry</i>, for a quotation from the
-issue of February 15, 1947.</p>
-</div>
-
-<p>Responsibility for the statements and opinions expressed in
-this book is solely my own. These statements and opinions do
-not necessarily represent the views of any organization with
-which I may be or have been associated. To the best of my
-knowledge and belief no information contained in this book is
-classified by the Department of Defense of the United States.</p>
-
-<p class="author"><span class="smcap">Edmund Callis Berkeley</span></p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_xv">[Pg xv]</span></p>
-<h2 class="nobreak">CONTENTS</h2>
-</div>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary="TOC" cellpadding="2" >
-  <tbody><tr>
-      <td class="tdr">1.</td>
-      <td class="tdl_ws1" colspan="2">CAN MACHINES THINK?</td>
-   </tr><tr>
-      <td class="tdr"> </td>
-      <td class="tdl"><span class="ws2"> </span>What Is a Mechanical Brain?</td>
-      <td class="tdr"><a href="#CHAPTER_1"> 1</a></td>
-   </tr><tr>
-      <td class="tdr">2.</td>
-      <td class="tdl_ws1" colspan="2">LANGUAGES:</td>
-   </tr><tr>
-      <td class="tdr"> </td>
-      <td class="tdl"><span class="ws2"> </span>Systems for Handling Information</td>
-      <td class="tdr"><a href="#CHAPTER_2">10</a></td>
-   </tr><tr>
-      <td class="tdr">3.</td>
-      <td class="tdl_ws1" colspan="2">A MACHINE THAT WILL THINK:</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>The Design of a Very Simple Mechanical Brain</td>
-      <td class="tdr"><a href="#CHAPTER_3">22</a></td>
-   </tr><tr>
-      <td class="tdr">4.</td>
-      <td class="tdl_ws1" colspan="2">COUNTING HOLES:</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>Punch-Card Calculating Machines</td>
-      <td class="tdr"><a href="#CHAPTER_4">42</a></td>
-   </tr><tr>
-      <td class="tdr">5.</td>
-      <td class="tdl_ws1" colspan="2">MEASURING:</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>Massachusetts Institute of Technology’s</td>
-      <td class="tdr">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>Differential Analyzer No. 2</td>
-      <td class="tdr"><a href="#CHAPTER_5">65</a></td>
-   </tr><tr>
-      <td class="tdr">6.</td>
-      <td class="tdl_ws1" colspan="2">ACCURACY TO 23 DIGITS:</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>Harvard’s IBM Automatic</td>
-      <td class="tdr">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>Sequence-Controlled Calculator</td>
-      <td class="tdr"><a href="#CHAPTER_6">89</a></td>
-   </tr><tr>
-      <td class="tdr">7.</td>
-      <td class="tdl_ws1" colspan="2">SPEED—5000 ADDITIONS A SECOND:</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>Moore School’s <b>ENIAC</b></td>
-      <td class="tdr">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>(Electronic Numerical Integrator and Calculator)</td>
-      <td class="tdr"><a href="#CHAPTER_7">113</a></td>
-   </tr><tr>
-      <td class="tdr">8.</td>
-      <td class="tdl_ws1" colspan="2">RELIABILITY—NO WRONG RESULTS:</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>Bell Laboratories’</td>
-      <td class="tdr">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>General-Purpose Relay Calculator</td>
-      <td class="tdr"><a href="#CHAPTER_8">128</a></td>
-   </tr><tr>
-      <td class="tdr">9.</td>
-      <td class="tdl_ws1" colspan="2">REASONING:</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>The Kalin-Burkhart Logical-Truth Calculator</td>
-      <td class="tdr"><a href="#CHAPTER_9">144</a></td>
-   </tr><tr>
-      <td class="tdr">10.</td>
-      <td class="tdl_ws1" colspan="2">AN EXCURSION:</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>The Future Design of Machines That Think</td>
-      <td class="tdr"><a href="#CHAPTER_10">167</a></td>
-   </tr><tr>
-      <td class="tdr">11.</td>
-      <td class="tdl_ws1" colspan="2">THE FUTURE:</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>Machines That Think, and</td>
-      <td class="tdr">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>What They Might Do for Men</td>
-      <td class="tdr"><a href="#CHAPTER_11">180</a></td>
-   </tr><tr>
-      <td class="tdr">12.</td>
-      <td class="tdl_ws1" colspan="2">SOCIAL CONTROL:</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>Machines That Think, and</td>
-      <td class="tdr">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl"><span class="ws2">&nbsp;</span>How Society May Control Them</td>
-      <td class="tdr"><a href="#CHAPTER_12">196</a></td>
-   </tr><tr>
-      <td class="tdc" colspan="3">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc" colspan="3"><b>SUPPLEMENTS</b>
-                     <span class="pagenum" id="Page_xvi">[Pg xvi]</span></td>
-   </tr><tr>
-      <td class="tdr">1.</td>
-      <td class="tdl_ws1">Words and Ideas</td>
-      <td class="tdr"><a href="#SUPPL_1">209</a></td>
-   </tr><tr>
-      <td class="tdr">2.</td>
-      <td class="tdl_ws1">Mathematics</td>
-      <td class="tdr"><a href="#SUPPL_2">214</a></td>
-   </tr><tr>
-      <td class="tdr">3.</td>
-      <td class="tdl_ws1">References</td>
-      <td class="tdr"><a href="#SUPPL_3">228</a></td>
-   </tr><tr>
-      <td class="tdr">&nbsp;</td>
-      <td class="tdl_ws1">INDEX</td>
-      <td class="tdr"><a href="#Page_257">257</a></td>
-   </tr>
- </tbody>
-</table>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_1">[Pg 1]</span></p>
-<h2 class="nobreak" id="CHAPTER_1">Chapter 1<br />
-<span class="h_subtitle">CAN MACHINES THINK?<br />WHAT IS A MECHANICAL BRAIN?</span></h2>
-</div>
-
-<p>Recently there has been a good deal of news about strange giant
-machines that can handle information with vast speed and skill. They
-calculate and they reason. Some of them are cleverer than others—able
-to do more kinds of problems. Some are extremely fast: one of them does
-5000 additions a second for hours or days, as may be needed. Where they
-apply, they find answers to problems much faster and more accurately
-than human beings can; and so they can solve problems that a man’s life
-is far too short to permit him to do. That is why they were built.</p>
-
-<p>These machines are similar to what a brain would be if it were made of
-hardware and wire instead of flesh and nerves. It is therefore natural
-to call these machines <i>mechanical brains</i>. Also, since their
-powers are like those of a giant, we may call them <i>giant brains</i>.</p>
-
-<p>Several giant mechanical brains are now at work finding out
-answers never before known. Two are in Cambridge, Mass.; one is
-at Massachusetts Institute of Technology, and one at Harvard
-University. Two are in Aberdeen, Md., at the Army’s Ballistic Research
-Laboratories. These four machines were finished in the period 1942
-to 1946 and are described in later chapters of this book. More giant
-brains are being constructed.</p>
-
-<p>Can we say that these machines really think? What do we mean by
-thinking, and how does the human brain think?
-<span class="pagenum" id="Page_2">[Pg 2]</span></p>
-
-<h3>HUMAN THINKING</h3>
-
-<p>We do not know very much about the physical process of thinking in the
-human brain. If you ask a scientist how flesh and blood in a human
-brain can think, he will talk to you a little about nerves and about
-electrical and chemical changes, but he will not be able to tell you
-very much about how we add 2 and 3 and make 5. What men know about the
-way in which a human brain thinks can be put down in a few pages, and
-what men do not know would fill many libraries.</p>
-
-<p>Injuries to brains have shown some things of importance; for example,
-they have shown that certain parts of the brain have certain
-duties. There is a part of the brain, for instance, where sights
-are recorded and compared. If an accident damages the part of the
-brain where certain information is stored, the human being has to
-relearn—haltingly and badly—the information destroyed.</p>
-
-<p>We know also that thinking in the human brain is done essentially by
-a process of storing information and then referring to it, by a process
-of learning and remembering. We know that there are no little wheels
-in the brain so that a wheel standing at 2 can be turned 3 more steps
-and the result of 5 read. Instead, you and I store the information that
-2 and 3 are 5, and store it in such a way that we can give the answer
-when questioned. But we do not know the register in our brain where
-this particular piece of information is stored. Nor do we know how,
-when we are questioned, we are able automatically to pick up the nerve
-channels that lead into this register, get the answer, and report it.</p>
-
-<p>Since there are many nerves in the brain, about 10 billion of them,
-in fact, we are certain that the network of connecting nerves is a main
-part of the puzzle. We are therefore much interested in nerves and
-their properties.</p>
-
-<h3>NERVES AND THEIR PROPERTIES</h3>
-
-<p>A single nerve, or <i>nerve cell</i>, consists of a <i>cell nucleus</i>
-and a <i>fiber</i>. This fiber may have a length of anything from a
-<span class="pagenum" id="Page_3">[Pg 3]</span>
-small fraction of an inch up to several feet. In the laboratory,
-successive impulses can be sent along a nerve fiber as often as 1000
-a second. Impulses can travel along a nerve fiber in either direction
-at a rate from 3 feet to 300 feet a second. Because the speed of
-the impulse is far less than 186,000 miles a second—the speed of
-an electric current—the impulse in the nerve is thought by some
-investigators to be more chemical than electrical.</p>
-
-<p>We know that a nerve cell has what is called an <i>all-or-none
-response</i>, like the trigger of a gun. If you stimulate the nerve
-up to a certain point, nothing will happen; if you reach that point,
-or cross it,—bang!—the nerve responds and sends out an impulse. The
-strength of the impulse, like the shot of the gun, has no relation
-whatever to the amount of the stimulation.</p>
-
-<div class="figcenter">
-  <img id="FIG_1-1" src="images/i_003.jpg" alt="" width="600" height="192" />
-  <p class="f120"><span class="smcap">Fig. 1.</span> Scheme of a nerve cell.</p>
-</div>
-
-<p>The structure between the end of one nerve and the beginning of the
-next is called a <i>synapse</i> (<a href="#FIG_1-1">see Fig. 1</a>).
-No one really knows very much about synapses, for they are extremely
-small and it is not easy to tell where a synapse stops and other stuff
-begins. Impulses travel through synapses in from ½ to 3 thousandths of
-a second. An impulse travels through a synapse only in one direction,
-from the head (or <i>axon</i>) of one nerve fiber to the foot (or
-<i>dendrite</i>) of another. It seems clear that the activity in a
-synapse is chemical. When the head of a nerve fiber brings in an
-impulse to a synapse, apparently a chemical called <i>acetylcholine</i>
-is released and may affect the foot of another fiber, thus transmitting
-the impulse; but the process and the conditions for it are still not
-well understood.</p>
-
-<p>It is thought that nearly all information is handled in the brain by
-groups of nerves in parallel paths. For example, the eye is estimated
-<span class="pagenum" id="Page_4">[Pg 4]</span>
-to have about 100 million nerves sensitive to light, and the
-information that they gather is reported by about 1 million nerves to
-the part of the brain that stores sights.</p>
-
-<p>Not much more is yet known, however, about the operation of handling
-information in a human brain. We do not yet know how the nerves are
-connected so that we can do what we do. Probably the greatest obstacle
-to knowledge is that so far we cannot observe the detailed structure of
-a living human brain while it performs, without hurting or killing it.</p>
-
-<h3>BEHAVIOR THAT IS THINKING</h3>
-
-<p>Therefore, we cannot yet tell what thinking is by observing precisely
-how a human brain does it. Instead, we have to define thinking by
-describing the kind of behavior that we call thinking. Let us consider
-some examples.</p>
-
-<p>When you and I add 12 and 8 and make 20, we are thinking. We use our
-minds and our understanding to count 8 places forward from 12, for
-example, and finish with 20. If we could find a dog or a horse that
-could add numbers and tell answers, we would certainly say that the
-animal could think.</p>
-
-<p>With no trouble a machine can do this. An ordinary 10-column adding
-machine can be given two numbers like 1,378,917,766 and 2,355,799,867
-and the instruction to add them. The machine will then give the answer,
-3,734,717,633, much faster than a man. In fact, the mechanical brain at
-Harvard can add a number of 23 digits to another number of 23 digits
-and get the right answer in ³/₁₀ of a second.</p>
-
-<p>Or, suppose that you are walking along a road and come to a fork. If
-you stop, read the signpost, and then choose left or right, you are
-thinking. You know beforehand where you want to go, you compare your
-destination with what the signpost says, and you decide on your route.
-This is an operation of logical choice.</p>
-
-<p>A machine can do this. The mechanical brain now at Aberdeen which was
-built at Bell Laboratories can examine any number that comes up in the
-process of a calculation and tell whether it is bigger than 3 (or any
-stated number) or smaller. If the number is bigger than 3, the machine
-<span class="pagenum" id="Page_5">[Pg 5]</span>
-will choose one process; if the number is smaller than 3, the machine
-will choose another process.</p>
-
-<p>Now suppose that we consider the basic operation of all thinking: in
-the human brain it is called learning and remembering, and in a machine
-it is called storing information and then referring to it. For example,
-suppose you want to find 305 Main Street in Kalamazoo. You look up a
-map of Kalamazoo; the map is information kindly stored by other people
-for your use. When you study the map, notice the streets and the
-numbering, and then find where the house should be, you are thinking.</p>
-
-<p>A machine can do this. In the Bell Laboratories’ mechanical brain, for
-example, the map could be stored as a long list of the blocks of the
-city and the streets and numbers that apply to each block. The machine
-will then hunt for the city block that contains 305 Main Street and
-report it when found.</p>
-
-<p>A machine can handle information; it can calculate, conclude, and
-choose; it can perform reasonable operations with information. A
-machine, therefore, can think.</p>
-
-<h3>THE DEFINITION OF A MECHANICAL BRAIN</h3>
-
-<p>Now when we speak of a machine that thinks, or a mechanical brain,
-what do we mean? Essentially, a <i>mechanical brain</i> is a machine
-that handles information, transfers information automatically from
-one part of the machine to another, and has a flexible control over
-the sequence of its operations. No human being is needed around such
-a machine to pick up a physical piece of information produced in
-one part of the machine, personally move it to another part of the
-machine, and there put it in again. Nor is any human being needed to
-give the machine instructions from minute to minute. Instead, we can
-write out the whole program to solve a problem, translate the program
-into machine language, and put the program into the machine. Then we
-press the “start” button; the machine starts whirring; and it prints
-out the answers as it obtains them. Machines that handle information
-have existed for more than 2000 years. These two properties are new,
-however, and make a deep break with the past.
-<span class="pagenum" id="Page_6">[Pg 6]</span></p>
-
-<p>How should we imagine a mechanical brain? One way to think of a
-mechanical brain is shown in <a href="#FIG_2-1">Fig. 2</a>. We see
-here a railroad line with four stations, marked <i>input</i>,
-<i>storage</i>, <i>computer</i>, and <i>output</i>. These stations
-are joined by little gates or switches to the main railroad line.
-We can imagine that numbers and other information move along this
-railroad line, loaded in freight cars. <i>Input</i> and <i>output</i>
-are stations where numbers or other information go in and come out,
-respectively. <i>Storage</i> is a station where there are many
-platforms and where information can be stored. The <i>computer</i> is a
-special station somewhat like a factory; when two numbers are loaded on
-platforms 1 and 2 of this station and an order is loaded on platform 3,
-then another number is produced on platform 4.</p>
-
-<div class="figcenter">
-  <img id="FIG_2-1" src="images/i_006.jpg" alt="" width="600" height="468" />
-  <p class="f120"><span class="smcap">Fig. 2.</span> Scheme of a mechanical brain.</p>
-</div>
-
-<p>We see also a tower, marked <i>control</i>. This tower runs a telegraph
-line to each of its little watchmen standing by the gates. The tower
-tells them when to open and when to shut which gates.</p>
-
-<p>Now we can see that, just as soon as the right gates are shut, freight
-<span class="pagenum" id="Page_7">[Pg 7]</span>
-cars of information can move between stations. Actually the freight
-cars move at the speed of electric current, thousands of miles a
-second. So, by closing the right gates each fraction of a second,
-we can flash numbers and information through the system and perform
-operations of reasoning. Thus we obtain a mechanical brain.</p>
-
-<p>In general, a mechanical brain is made up of:</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. A quantity of registers where information
-(numbers and instructions) can be stored.</p>
-
-<p class="neg-indent">2. Channels along which information can be
-sent.</p>
-
-<p class="neg-indent">3. Mechanisms that can carry out arithmetical and
-logical operations.</p>
-
-<p class="neg-indent">4. A control, which guides the machine to perform
-a sequence of operations.</p>
-
-<p class="neg-indent">5. Input and output devices, whereby information
-can go into the machine and come out of it.</p>
-
-<p class="neg-indent">6. Motors or electricity, which provide
-energy.</p>
-</div>
-
-<h3>THE KINDS OF THINKING A<br /> MECHANICAL BRAIN CAN DO</h3>
-
-<p>There are many kinds of thinking that mechanical brains can do. Among
-other things, they can:</p>
-
-<ul class="index no-wrap">
-<li class="isub2">&nbsp;&nbsp;1. Learn what you tell them.</li>
-<li class="isub2">&nbsp;&nbsp;2. Apply the instructions when needed.</li>
-<li class="isub2">&nbsp;&nbsp;3. Read and remember numbers.</li>
-<li class="isub2">&nbsp;&nbsp;4. Add, subtract, multiply, divide, and round off.</li>
-<li class="isub2">&nbsp;&nbsp;5. Look up numbers in tables.</li>
-<li class="isub2">&nbsp;&nbsp;6. Look at a result, and make a choice.</li>
-<li class="isub2">&nbsp;&nbsp;7. Do long chains of these operations one after another.</li>
-<li class="isub2">&nbsp;&nbsp;8. Write out an answer.</li>
-<li class="isub2">&nbsp;&nbsp;9. Make sure the answer is right.</li>
-<li class="isub2">10. Know that one problem is finished, and turn to another.</li>
-<li class="isub2">11. Determine <i>most</i> of their own instructions.</li>
-<li class="isub2">12. Work unattended.</li>
-</ul>
-
-<p>They do these things much better than you or I. They are fast. The
-mechanical brain built at the Moore School of Electrical Engineering at
-the University of Pennsylvania does 5000 additions a second. They are
-reliable. Even with hundreds of thousands of parts, the existing giant
-<span class="pagenum" id="Page_8">[Pg 8]</span>
-brains have worked successfully. They have remarkably few mechanical
-troubles; in fact, for one of the giant brains, a mechanical failure
-is of the order of once a month. They are powerful. The big machine
-at Harvard can remember 72 numbers each of 23 digits at one time and
-can do 3 operations with these numbers every second. The mechanical
-brains that have been finished are able to solve problems that have
-baffled men for many, many years, and they think in ways never open to
-men before. Mechanical brains have removed the limits on complexity of
-routine: the machine can carry out a complicated routine as easily as
-a simple one. Already, processes for solving problems are being worked
-out so that the mechanical brain will itself determine more than 99 per
-cent of all the routine orders that it is to carry out.</p>
-
-<p>But, you may ask, can they do any kind of thinking? The answer is no.
-No mechanical brain so far built can:</p>
-
-<ul class="index no-wrap">
-<li class="isub2">1. Do intuitive thinking.</li>
-<li class="isub2">2. Make bright guesses, and leap to conclusions.</li>
-<li class="isub2">3. Determine <i>all</i> its own instructions.</li>
-<li class="isub2">4. Perceive complex situations outside itself and interpret them.</li>
-</ul>
-
-<p>A clever wild animal, for example, a fox, can do all these things; a
-mechanical brain, not yet. There is, however, good reason to believe
-that most, if not all, of these operations will in the future be
-performed not only by animals but also by machines. Men have only just
-begun to construct mechanical brains. All those finished are children;
-they have all been born since 1940. Soon there will be much more
-remarkable giant brains.</p>
-
-<h3>WHY ARE THESE GIANT BRAINS IMPORTANT?</h3>
-
-<p>Most of the thinking so far done by these machines is with numbers.
-They have already solved problems in airplane design, astronomy,
-physics, mathematics, engineering, and many other sciences, that
-previously could not be solved. To find the solutions of these
-problems, mathematicians would have had to work for years and years,
-using the best known methods and large staffs of human computers.
-<span class="pagenum" id="Page_9">[Pg 9]</span></p>
-
-<p>These mechanical brains not only calculate, however. They also remember
-and reason, and thus they promise to solve some very important human
-problems. For example, one of these problems is the application of what
-mankind knows. It takes too long to find understandable information
-on a subject. The libraries are full of books: most of them we can
-never hope to read in our lifetime. The technical journals are full of
-condensed scientific information: they can hardly be understood by you
-and me. There is a big gap between somebody’s knowing something and
-employment of that knowledge by you or me when we need it. But these
-new mechanical brains handle information very swiftly. In a few years
-machines will probably be made that will know what is in libraries and
-that will tell very swiftly where to find certain information. Thus
-we can see that mechanical brains are one of the great new tools for
-finding out what we do not know and applying what we do know.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_10">[Pg 10]</span></p>
-<h2 class="nobreak" id="CHAPTER_2">Chapter 2<br />
-<span class="h_subtitle">LANGUAGES:<br />SYSTEMS FOR HANDLING INFORMATION</span></h2>
-</div>
-
-<p>As everyone knows, it is not always easy to think. By <i>thinking</i>,
-we mean computing, reasoning, and other handling of information.
-By <i>information</i> we mean collections of ideas—physically,
-collections of marks that have meaning. By <i>handling</i>
-information, we mean proceeding logically from some ideas to other
-ideas—physically, changing from some marks to other marks in ways that
-have meaning. For example, one of your hands can express an idea: it
-can store the number 3 for a short while by turning 3 fingers up and
-2 down. In the same way, a machine can express an idea: it can store
-information by arranging some equipment. The Harvard mechanical brain
-can store 132 numbers between 0 and 99,999,999,999,999,999,999,999
-for days. When you want to change the number stored by your fingers,
-you move them: perhaps you need a half second to change the number
-stored by your fingers from 3 to 2, for example. In the same way, a
-machine can change a stored number by changing the arrangement of some
-equipment: the electronic brain Eniac can change a stored number in
-¹/₅₀₀₀ of a second.</p>
-
-<h3>LANGUAGES</h3>
-
-<p>Since it is not always easy to think, men have given much attention
-to devices for making thinking easier. They have worked out many
-<i>systems for handling information</i>, which we often call
-<i>languages</i>. Some languages are very complete and versatile and of
-<span class="pagenum" id="Page_11">[Pg 11]</span>
-great importance. Others cover only a narrow field—such as numbers
-alone—but in this field they may be remarkably efficient. Just what is
-a language?</p>
-
-<p>Every language is both a <i>scheme for expressing meanings</i> and
-<i>physical equipment</i> that can be handled. For example, let us
-take <i>spoken English</i>. The scheme of spoken English consists
-of more than 150,000 words expressing meanings, and some rules for
-putting words together meaningfully. The physical equipment of spoken
-English consists of (1) sounds in the air, and (2) the ears of millions
-of people, and their mouths and voices, by which they can hear and
-speak the sounds of English. For another example, let us take numbers
-expressed in the <i>Arabic numerals</i> and the rules of arithmetic.
-The scheme of this language contains only ten digits 0, 1, 2, 3, 4, 5,
-6, 7, 8, 9 or their equivalents, and some rules for combining them.
-Sufficient physical equipment for this language might very well be a
-ten-column desk calculating machine with its counter wheels, gears,
-keys, etc. If we tried to exchange the physical equipment of these two
-languages, we would be blocked: the desk calculating machine cannot
-possibly express the meaningful combinations of 150,000 words, and
-sounds in the air are not permanent enough to express the steps of
-division of one large number by another.</p>
-
-<h3>SCHEMES FOR EXPRESSING MEANINGS</h3>
-
-<p>If we examine languages that have existed, we can observe a number of
-schemes for expressing meanings. In the table on <a href="#Page_12">pp. 12-13</a>
-is a rough list of a dozen of them. From among these we can choose
-the schemes that are likely to be useful in mechanical brains.
-Schemes 11 and 12 are the schemes that have been predominantly used
-in machinery for computing. Scheme 12 consisting of combinations of
-just two marks, ✓, ✕, provides one of the best codes for mechanical
-handling of information. This scheme, called <i>binary coding</i>
-(<a href="#SUPPL_2">see Supplement 2</a>), is also useful for measuring
-the quantity of information.</p>
-
-<h3>QUANTITY OF INFORMATION</h3>
-
-<p>How should we measure the quantity of information? The smallest unit
-of information is a “yes” or a “no,” a check mark (✓) or a cross (✕),
-an impulse in a nerve or no impulse, a 1 or a 0, black or white, good
-or bad, etc. This twofold difference is called a <i>binary digit</i> of
-information (<a href="#SUPPL_2">see Supplement 2</a>). It is the convenient
-<i>unit of information</i>.
-<span class="pagenum" id="Page_12">[Pg 12]</span></p>
-
-<p class="f120 space-above2"><b>SCHEMES FOR EXPRESSING MEANINGS</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" rules="cols">
-  <thead><tr>
-      <th class="tdc" colspan="6"><span class="smcap">Example:</span></th>
-   </tr><tr>
-      <th class="tdc" colspan="2">&nbsp;</th>
-      <th class="tdc" colspan="3">/——————^—————————\</th>
-      <th class="tdc">&nbsp;</th>
-   </tr><tr>
-      <th class="tdc"><span class="smcap">No.</span></th>
-      <th class="tdc"><span class="smcap">Principle<br />of Scheme</span></th>
-      <th class="tdc"><span class="smcap">Sign</span></th>
-      <th class="tdc"><span class="smcap">Used in</span></th>
-      <th class="tdc"><span class="smcap">Significance</span></th>
-      <th class="tdc"><span class="smcap">Name of<br />Scheme</span></th>
-   </tr><tr>
-      <th class="tdc bb">(1)</th>
-      <th class="tdc bb">(2)</th>
-      <th class="tdc bb">(3)</th>
-      <th class="tdc bb">(4)</th>
-      <th class="tdc bb">(5)</th>
-      <th class="tdc bb">(6)</th>
-    </tr>
-   </thead>
-  <tbody><tr>
-      <td class="tdc bb" colspan="6"><big><i>Sounds</i></big></td>
-   </tr><tr>
-      <td class="tdc_top">1.</td>
-      <td class="tdc_top bb">Sound of new<br />word is like<br />sound of<br />referent</td>
-      <td class="tdc_top bb">Bobwhite<a id="FNanchor_2" href="#Footnote_2" class="fnanchor">[2]</a></td>
-      <td class="tdc_top bb">Spoken<br />English</td>
-      <td class="tdc_top bb">kind of quail,<br />so called<br />from its note</td>
-      <td class="tdc_top bb">Imitative;<br />bowwow<br />theory</td>
-   </tr><tr>
-      <td class="tdc_top">2.</td>
-      <td class="tdc_top bb">An utterance<br />becomes a<br />new word</td>
-      <td class="tdc_top bb">Pooh!<a id="FNanchor_3" href="#Footnote_3" class="fnanchor">[3]</a></td>
-      <td class="tdc_top bb">Spoken<br />English</td>
-      <td class="tdc_top bb">The speaker<br />expresses<br />disdain</td>
-      <td class="tdc_top bb">Pooh-pooh<br />theory</td>
-   </tr><tr>
-      <td class="tdc_top">3.</td>
-      <td class="tdc_top bb">New word is<br />like another<br />word</td>
-      <td class="tdc_top bb">Chortle<a id="FNanchor_4" href="#Footnote_4" class="fnanchor">[4]</a></td>
-      <td class="tdc_top bb">Spoken<br />English;<br />invented by<br />Lewis Carroll,<br />1896</td>
-      <td class="tdc_top bb">“Chuckle”<br />and<br />“snort”<br />blended</td>
-      <td class="tdc_top bb">Analogical</td>
-   </tr><tr>
-      <td class="tdc_top bb">4.</td>
-      <td class="tdc_top bb">Word has<br />been used<br />through<br />the ages</td>
-      <td class="tdc_top bb">Mother<a id="FNanchor_5" href="#Footnote_5" class="fnanchor">[5]</a></td>
-      <td class="tdc_top bb">Spoken<br />English</td>
-      <td class="tdc_top bb">Female<br />parent</td>
-      <td class="tdc_top bb">Historical</td>
-   </tr><tr>
-      <td class="tdc bb" colspan="6"><big><i>Sights</i></big></td>
-   </tr><tr>
-      <td class="tdc_top">5.</td>
-      <td class="tdc_top bb">Picture<br />is like<br />referent</td>
-      <td class="tdc_top bb"><img src="images/i_012.jpg" alt="" width="100" height="103" /></td>
-      <td class="tdc_top bb">Egyptian;<br />Ojibwa<br />(American<br />Indian)</td>
-      <td class="tdc_top bb">Picture of<br />eye and<br />tears, to<br />mean grief</td>
-      <td class="tdc_top bb">Imitative;<br />pictographic</td>
-   </tr><tr>
-      <td class="tdc_top bb">6.<span class="pagenum" id="Page_13">[Pg 13]</span></td>
-      <td class="tdc_top bb">Pattern is<br />symbol of<br />an idea</td>
-      <td class="tdc bb"><big>5</big></td>
-      <td class="tdc_top bb">English;<br />French;<br />German;<br />etc.</td>
-      <td class="tdc_top bb">Five;<br />cinq;<br />fünf;<br />etc.</td>
-      <td class="tdc_top bb">Ideographic;<br />mathematical;<br />symbolic;<br />numeric</td>
-   </tr><tr>
-      <td class="tdc bb" colspan="6"><big><i>Mapping of Sounds</i></big></td>
-   </tr><tr>
-      <td class="tdc_top">7.</td>
-      <td class="tdc_top bb">Object<br />pictured<br />as the<br />wanted<br />sound</td>
-      <td class="tdc bb"><img src="images/i_013a.jpg" alt="" width="100" height="55" /></td>
-      <td class="tdc_top bb">Possible<br />English</td>
-      <td class="tdc_top bb">Picture of<br />a knot to<br />mean “not”</td>
-      <td class="tdc_top bb">Rebus-<br />writing;<br />phonographic</td>
-   </tr><tr>
-      <td class="tdc_top">8.</td>
-      <td class="tdc_top bb">Pattern is<br />symbol for<br />a large<br />ound unit</td>
-      <td class="tdc bb"><img src="images/i_013b.jpg" alt="" width="100" height="50" /></td>
-      <td class="tdc_top bb">Ancient<br />Cypriote<br />(island of<br />Cyprus)</td>
-      <td class="tdc_top bb">Sign for<br />the<br />syllable<br /><i>mu</i></td>
-      <td class="tdc_top bb">Syllable-<br />writing</td>
-   </tr><tr>
-      <td class="tdc_top bb">9.</td>
-      <td class="tdc_top bb">Pattern is<br />symbol for<br />a small<br />sound unit</td>
-      <td class="tdc bb"><big>Ʒ</big></td>
-      <td class="tdc_top bb">International<br />Phonetic<br />Alphabet of<br />87 characters</td>
-      <td class="tdc_top bb">The sound<br /><i>zh</i>, as<br /><i>s</i> in<br />“measure”</td>
-      <td class="tdc_top bb">Phonetic<br />writing<br />alphabetic<br />writing;</td>
-   </tr><tr>
-      <td class="tdc bb" colspan="6"><big><i>Mapping of Sights or Symbols</i></big></td>
-   </tr><tr>
-      <td class="tdc_top">10.</td>
-      <td class="tdc_top bb">Systematic<br />combinations<br />of 26<br />letters</td>
-      <td class="tdc bb"><b> ENIAC</b></td>
-      <td class="tdc_top bb">Abbreviations,<br />etc.</td>
-      <td class="tdc_top bb">Initial<br />letters<br />of a<br />5-word<br />title</td>
-      <td class="tdc_top bb">Alphabetic<br />coding</td>
-   </tr><tr>
-      <td class="tdc_top">11.</td>
-      <td class="tdc_top bb">Systematic<br />combinations<br />of 10 digits</td>
-      <td class="tdc bb">135-03-1228</td>
-      <td class="tdc_top bb">Abbreviations,<br />nomenclature,<br />etc.</td>
-      <td class="tdc_top bb">Social<br />Security<br />No. of<br />a person</td>
-      <td class="tdc_top bb">Numeric<br />coding</td>
-   </tr><tr>
-      <td class="tdc_top bb">12.</td>
-      <td class="tdc_top bb">Systematic<br />combinations<br />of 2 marks</td>
-      <td class="tdc bb">✓,✕,✕,✓,✓</td>
-      <td class="tdc_top bb">Checking<br />lists,<br />etc.</td>
-      <td class="tdc_top bb">“yes,” “no,”<br />“no,” “yes,”<br />“yes,”<br />respectively</td>
-      <td class="tdc_top bb">Binary<br />coding</td>
-   </tr><tr>
-      <td class="tdc" colspan="6">&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent"><span class="pagenum" id="Page_14">[Pg 14]</span>
-With 2 units of information or 2 binary digits (1 or 0) we can
-represent 4 pieces of information:</p>
-
-<p class="f120">00, 01, 10, 11</p>
-
-<p class="no-indent">With 3 units of information we can represent 8 pieces of information:</p>
-
-<p class="f120">000, 001, 010, 011, 100, 101, 110, 111</p>
-
-<p class="no-indent">With 4 units of information we can represent 16 pieces of information:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdl">0000</td>
-      <td class="tdl_ws1">0001</td>
-      <td class="tdl_ws1">0010</td>
-      <td class="tdl_ws1">0011</td>
-   </tr><tr>
-      <td class="tdl">0100</td>
-      <td class="tdl_ws1">0101</td>
-      <td class="tdl_ws1">0110</td>
-      <td class="tdl_ws1">0111</td>
-   </tr><tr>
-      <td class="tdl">1000</td>
-      <td class="tdl_ws1">1001</td>
-      <td class="tdl_ws1">1010</td>
-      <td class="tdl_ws1">1011</td>
-   </tr><tr>
-      <td class="tdl">1100</td>
-      <td class="tdl_ws1">1101</td>
-      <td class="tdl_ws1">1110</td>
-      <td class="tdl_ws1">1111</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Now 4 units of information are sufficient to
-represent a <i>decimal digit</i> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and
-allow 6 possibilities to be left over; 3 units of information are not
-sufficient. For example, we may have:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdc">0</td>
-      <td class="tdl_ws1">0000</td>
-      <td class="tdc_ws1">5</td>
-      <td class="tdl">0101</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdl_ws1">0001</td>
-      <td class="tdc">6</td>
-      <td class="tdl">0110</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdl_ws1">0010</td>
-      <td class="tdc">7</td>
-      <td class="tdl">0111</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdl_ws1">0011</td>
-      <td class="tdc">8</td>
-      <td class="tdl">1000</td>
-   </tr><tr>
-      <td class="tdc">4</td>
-      <td class="tdl_ws1">0100</td>
-      <td class="tdc">9</td>
-      <td class="tdl">1001</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">We say, therefore, that a decimal digit 0, 1, 2,
-3, 4, 5, 6, 7, 8, 9 is <i>equivalent</i> to 4 units of information.
-Thus a table containing 10,000 numbers, each of 10 decimal digits, is
-equivalent to 400,000 units of information.</p>
-
-<p>One of the 26 letters of the alphabet is equivalent to 5 units
-of information, for, 5 binary digits (1 or 0) have 32 possible
-arrangements, and these are enough to provide for the 26 letters. Any
-printed information in English can be expressed in about 80 characters
-consisting of 10 numerals, 52 capital and small letters, and some 18
-punctuation marks and other types of marks; 6 binary digits (1 or 0)
-have 64 possible arrangements, and 7 binary digits (1 or 0) have 128
-<span class="pagenum" id="Page_15">[Pg 15]</span>
-possible arrangements. Each character in a printed book, therefore, is
-roughly equivalent to 7 units of information.</p>
-
-<p>It can be determined that a big telephone book or a big reference
-dictionary stores printed information at the rate of about 1 billion
-units of information per cubic foot. If the 10 billion nerves in the
-human brain could independently be impulsed or not impulsed, then the
-human brain could conceivably store 10 billion units of information.
-The largest library in the world is the Library of Congress, containing
-7 million volumes including pamphlets. It stores about 100 trillion
-units of information.</p>
-
-<p>We can thus see the significance of a <i>quantity of information</i>
-from 1 unit to 100 trillion units. No distinction is here made
-between information that reports facts and information that does not.
-For example, a book of fiction about persons who never existed is
-still counted as information, and, of course, much instruction and
-entertainment may be found in such a source.</p>
-
-<h3>PHYSICAL EQUIPMENT FOR<br />HANDLING INFORMATION</h3>
-
-<p>The first thing we want to do with information is <i>store</i> it.
-The second thing we want to do is <i>combine</i> it. We want equipment
-that makes these two processes easy and efficient. We
-want equipment for handling information that:</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. Costs little.</p>
-
-<p class="neg-indent">2. Holds much information in little space.</p>
-
-<p class="neg-indent">3. Is <i>permanent</i>, when we want to keep the
-information.</p>
-
-<p class="neg-indent">4. Is <i>erasable</i>, when we want to remove
-information.</p>
-
-<p class="neg-indent">5. Is <i>versatile</i>, holds easily any kind of
-information, and allows operations to be done easily.</p>
-</div>
-
-<p>The amount of human effort needed to handle information correctly
-depends very much on the properties of the physical equipment
-expressing the information, although the laws of correct reasoning are
-independent of the equipment. For example, the great difficulty with
-spoken sounds as physical equipment for handling information is the
-trouble of storing them. The technique for doing so was mastered only
-about 1877 when Thomas A. Edison made the first phonograph. Even with
-this advance, no one can glance at a soundtrack and tell quickly what
-sounds are stored there; only by turning back the machine and listening
-to a groove can we determine this. It was not possible for the men of
-2000 <span class="smcap">b.c.</span> to wait thousands of years for the storing
-of spoken sounds. The problem of storing information was accordingly taken to
-other types of physical equipment.
-<span class="pagenum" id="Page_16">[Pg 16]</span></p>
-
-<p class="f120 space-above2"><b>PHYSICAL EQUIPMENT FOR<br />HANDLING INFORMATION</b></p>
-
-<table id="TABLE_PE" class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" rules="cols">
-  <thead><tr>
-      <th class="tdc"><span class="smcap">No.</span></th>
-      <th class="tdc"><span class="smcap">Physical<br />Objects</span></th>
-      <th class="tdc"><span class="smcap">Arranged<br />in or on</span></th>
-      <th class="tdc"><span class="smcap">Operated or<br />Produced by</span></th>
-      <th class="tdc"><span class="smcap">Low<br />Cost?</span></th>
-      <th class="tdc"><span class="smcap">Little<br />Space?</span></th>
-      <th class="tdc"><span class="smcap">Perma-<br />nent?</span></th>
-      <th class="tdc"><span class="smcap">Eras-<br />able?</span></th>
-      <th class="tdc"><span class="smcap">Vers-<br />atile?</span></th>
-   </tr><tr>
-      <th class="tdc bb">(1)</th>
-      <th class="tdc bb">(2)</th>
-      <th class="tdc bb">(3)</th>
-      <th class="tdc bb">(4)</th>
-      <th class="tdc bb">(5)</th>
-      <th class="tdc bb">(6)</th>
-      <th class="tdc bb">(7)</th>
-      <th class="tdc bb">(8)</th>
-      <th class="tdc bb">(9)</th>
-    </tr>
-   </thead>
-  <tbody><tr>
-      <td class="tdc bb" colspan="9"><big><i>Mind</i></big></td>
-   </tr><tr>
-      <td class="tdc_top bb">1.</td>
-      <td class="tdc_top bb">Nerve<br />cells</td>
-      <td class="tdc_top bb">Human<br />brain</td>
-      <td class="tdc bb">Body</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc bb" colspan="9"><big><i>Sounds</i></big></td>
-   </tr><tr>
-      <td class="tdc">2.</td>
-      <td class="tdc bb">Sounds</td>
-      <td class="tdc bb">Air</td>
-      <td class="tdc bb">Voice</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✕✕</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc_top bb">3.</td>
-      <td class="tdc_top bb">Sound-<br />tracks</td>
-      <td class="tdc_top bb">Wax<br />cylinders,<br />phonograph<br />records</td>
-      <td class="tdc_top bb">Machines<br />and<br />motors</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc bb" colspan="9"><big><i>Sights</i></big></td>
-   </tr><tr>
-      <td class="tdc_top">4.</td>
-      <td class="tdc bb">Marks</td>
-      <td class="tdc bb">Sand</td>
-      <td class="tdc bb">Stick</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✕</td>
-   </tr><tr>
-      <td class="tdc_top">5.</td>
-      <td class="tdc_top bb">Colored<br />painting<br />canvases,<br />etc.</td>
-      <td class="tdc_top bb">Cave<br />walls,</td>
-      <td class="tdc_top bb">Paintbrush<br />and paints</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✕✕</td>
-   </tr><tr>
-      <td class="tdc_top">6.</td>
-      <td class="tdc_top bb">Marks,<br />inscript-<br />ions</td>
-      <td class="tdc_top bb">Clay,<br />stone</td>
-      <td class="tdc_top bb">Stylus,<br />chisel</td>
-      <td class="tdc bb">✕✕</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✕✕</td>
-      <td class="tdc bb">✓</td>
-   </tr><tr>
-      <td class="tdc_top">7.</td>
-      <td class="tdc bb">Marks</td>
-      <td class="tdc bb">Slate</td>
-      <td class="tdc bb">Chalk</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓</td>
-   </tr><tr>
-      <td class="tdc_top">8.</td>
-      <td class="tdc_top bb">Marks<br />parchment,<br />etc.</td>
-      <td class="tdc_top bb">Paper,<br />and ink,<br />pencil</td>
-      <td class="tdc bb">Pen</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc_top">9.</td>
-      <td class="tdc_top bb">Letters,<br />etc.</td>
-      <td class="tdc_top bb">Paper<br />books<br />etc.</td>
-      <td class="tdc_top bb">Printing<br />press,<br />movable<br />type,<br />motor,<br />and hands</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✕✕</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc_top">10.</td>
-      <td class="tdc_top bb">Photo-<br />graphs</td>
-      <td class="tdc_top bb">Film,<br />prints,<br />etc.</td>
-      <td class="tdc_top bb">Camera</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✕✕</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc_top bb">11.</td>
-      <td class="tdc_top bb">Letters,<br />etc.</td>
-      <td class="tdc_top bb">Paper,<br />mimeograph<br />stencil,<br />etc.</td>
-      <td class="tdc_top bb">Typewriter<br />and<br />fingers</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc bb" colspan="9"><big><i>Body</i></big>
-                          <span class="pagenum" id="Page_17">[Pg 17]</span></td>
-   </tr><tr>
-      <td class="tdc_top">12.</td>
-      <td class="tdc bb">Gestures</td>
-      <td class="tdc bb">Space</td>
-      <td class="tdc bb">Body</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✕✕</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✕✕</td>
-   </tr><tr>
-      <td class="tdc_top bb">13.</td>
-      <td class="tdc bb">Fingers</td>
-      <td class="tdc bb">Hands</td>
-      <td class="tdc bb">Body</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✕✕</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✕✕</td>
-   </tr><tr>
-      <td class="tdc bb" colspan="9"><big><i>Objects</i></big></td>
-   </tr><tr>
-      <td class="tdc_top">14.</td>
-      <td class="tdc bb">Pebbles</td>
-      <td class="tdc bb">Slab</td>
-      <td class="tdc bb">Hands</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✕✕</td>
-   </tr><tr>
-      <td class="tdc_top">15.</td>
-      <td class="tdc bb">Knots</td>
-      <td class="tdc bb">String</td>
-      <td class="tdc bb">Hands</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✕✕</td>
-   </tr><tr>
-      <td class="tdc_top">16.</td>
-      <td class="tdc_top bb">Tallies,<br />notches</td>
-      <td class="tdc bb">Stick</td>
-      <td class="tdc bb">Knife</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✕✕</td>
-      <td class="tdc bb">✕✕</td>
-   </tr><tr>
-      <td class="tdc_top">17.</td>
-      <td class="tdc bb">Beads</td>
-      <td class="tdc_top bb">Rods in<br />a frame,<br />abacus</td>
-      <td class="tdc bb">Hands</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✕✕</td>
-   </tr><tr>
-      <td class="tdc_top bb">18.</td>
-      <td class="tdc_top bb">Ruled<br />lines,<br />pointers</td>
-      <td class="tdc_top bb">Rulers,<br />scales,<br />dials</td>
-      <td class="tdc_top bb">Hands,<br />pressure,<br />etc.</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-   </tr><tr>
-      <td class="tdc bb" colspan="9"><big><i>Machines</i></big></td>
-   </tr><tr>
-      <td class="tdc_top">19.</td>
-      <td class="tdc_top bb">Counter<br />wheels,<br />gears,<br />keys,<br />lights,<br />etc.</td>
-      <td class="tdc_top bb">Desk<br />calculating<br />machines,<br />fire-control<br />instruments,<br />etc.</td>
-      <td class="tdc_top bb">Motor<br />and<br />hands</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓</td>
-   </tr><tr>
-      <td class="tdc_top">20.</td>
-      <td class="tdc_top bb">Punched<br />cards<br />and<br />paper<br />tape</td>
-      <td class="tdc_top bb">Punch card<br />machinery,<br />teletype,<br />etc.</td>
-      <td class="tdc_top bb">Motor<br />and<br />input<br />instructions</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc_top">21.</td>
-      <td class="tdc bb">Relays</td>
-      <td class="tdc_top bb">Dial<br />telephone,<br />other<br />machinery</td>
-      <td class="tdc_top bb">Motor<br />and<br />input<br />instructions</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc_top">22.</td>
-      <td class="tdc_top bb">Elect-<br />ronic<br />tubes</td>
-      <td class="tdc bb">Machinery</td>
-      <td class="tdc_top bb">Motor<br />and<br />input<br />instructions</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc_top">23.</td>
-      <td class="tdc_top bb">Magnetic<br />surfaces:<br />wire,<br />tape,<br />discs</td>
-      <td class="tdc bb">Machinery</td>
-      <td class="tdc_top bb">Motor<br />and<br />input<br />instructions</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc_top">24.</td>
-      <td class="tdc_top bb">Delay<br />lines:<br />electric,<br />acoustic</td>
-      <td class="tdc bb">Machinery</td>
-      <td class="tdc_top bb">Motor<br />and<br />input<br />instructions</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc_top bb">25.</td>
-      <td class="tdc_top bb">Electro-<br />static<br />storage<br />tubes</td>
-      <td class="tdc bb">Machinery</td>
-      <td class="tdc_top bb">Motor<br />and<br />input<br />instructions</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✕</td>
-      <td class="tdc bb">✓✓</td>
-      <td class="tdc bb">✓✓</td>
-   </tr><tr>
-      <td class="tdc" colspan="9">&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<ul class="index fontsize_120">
-<li class="isub4">✓✓  &nbsp;yes, very.</li>
-<li class="isub4">✓    &nbsp;yes, adequately.</li>
-<li class="isub4">✕    &nbsp;not generally.</li>
-<li class="isub4">✕✕  not at all.</li>
-</ul>
-
-<p><span class="pagenum" id="Page_18">[Pg 18]</span>
-What are the types of physical equipment for handling information, and
-which are the good ones? In the table on <a href="#Page_16">pp. 16-17</a>
-is a rough list of 25 types of physical equipment for handling
-information. ✓✓ means “yes, very;” ✓ means “yes, adequately;” ✕ means
-“not generally;” ✕✕ means “not at all.”</p>
-
-<p>For example, our <i>fingers</i> (<a href="#TABLE_PE">see No. 13</a>)
-as a device for handling information are very expensive for most
-cases. They take up a good deal of space. Certainly they are very
-temporary storage; any information they may express is very erasable;
-and what we can express with them alone is very limited. Yet, with
-a <i>typewriter</i> (<a href="#TABLE_PE">see No. 11</a>), our fingers become
-versatile and efficient. In fact, our fingers can make 4 strokes a second; we
-can select any one of about 38 keys; and, since each key is equivalent to
-5 or 6 units of information, the effective speed of our fingers may be
-about 800 units of information a second.</p>
-
-<h3>LANGUAGES OF PHYSICAL OBJECTS</h3>
-
-<p>The use of pebbles (<a href="#TABLE_PE">see No. 14</a>) for keeping track
-of numerical information is shown in the history of the words containing the
-root <i>calc</i>-of the word <i>calculate</i>. The Latin word
-<i>calcis</i> meant pertaining to lime or limestone, and the Latin
-word <i>calculus</i> derived from it meant first a small piece of
-limestone, and later any small stone, particularly a pebble used in
-counting. All three of these meanings have left descendants: “chalk,”
-“calcite,” “calcium,” relating in one way or another to lime; in
-medicine, “calculus,” referring to stones in the kidneys or elsewhere
-in the body; and in mathematics, “calculate,” “calculus,” referring to
-computations, once done with pebbles.</p>
-
-<p>The pebbles, and the slab (for which the ancient Greek word is
-<i>abax</i>) on which they were arranged and counted, were later
-replaced, for ease in handling, by groups of beads strung on rods and
-<span class="pagenum" id="Page_19">[Pg 19]</span>
-placed in a frame (<a href="#TABLE_PE">see No. 17</a>). These constituted the <i>abacus</i>
-(<a href="#SUPPL_2">see Supplement 2</a> and the <a href="#FIG_1-S">figure</a> there).
-This was the first calculating machine. It is still used all over Asia;
-in fact, even today more people use the abacus for accounting than
-use pencil and paper. The skill with which the abacus can be used was
-shown in November 1946 in a well-publicized contest in Japan. Kiyoshi
-Mastuzaki, a clerk in the Japanese communications department, using
-the abacus, challenged Private Thomas Wood of the U. S. Army, using a
-modern desk calculating machine, and defeated him in a speed contest
-involving additions, subtractions, multiplications, and divisions.</p>
-
-<p>The heaps of small pebbles, the notches in sticks, and the abacus had
-the advantage of being visible and comparatively permanent. Storing
-and reading were relatively easy. They were rather compact and easy
-to manipulate, certainly much easier than spoken words. But they were
-subject to disadvantages also. Moving correctly from one arrangement
-to another was difficult, since there was no good way for storing
-intermediate steps so that the process could be easily verified.
-Furthermore, these devices applied to specified numbers only. Also,
-there was no natural provision for recording what the several numbers
-belonged to. This had to be recorded with the help of another language,
-writing.</p>
-
-<p>The language of physical objects was picked up from obscurity by
-the invention of motors and the demands of commerce and business.
-Commencing in the late 1800’s, <i>desk calculating machines</i>
-(<a href="#TABLE_PE">see No. 19</a>) were constructed to meet mass
-calculation requirements. They would add, subtract, multiply, and
-divide specific numbers with great accuracy and speed. But until
-recently they still were adjuncts to the other languages, for they
-provided figures one at a time for insertion in the spaces on the
-ledger pages or calculation sheets where figures were called for.</p>
-
-<p>Beginning in the 1920’s, a remarkable change has taken place. Instead
-of performing single operations, machines have been developed to
-perform chains of operations with many kinds of information. One of
-these machines is the <i>dial telephone</i>: it can select one of 7
-million telephones by successive sorting according to the letters
-and digits of a telephone number. Another of these machines is a
-<span class="pagenum" id="Page_20">[Pg 20]</span>
-<i>fire-control instrument</i>, a mechanism for controlling the firing
-of a gun. For example, in a modern anti-aircraft gun the mechanism
-will observe an enemy plane flying at several hundred miles an hour,
-convert the observations into gun-aiming directions, and determine the
-aiming directions fast enough to shoot down the plane. <i>Punch-card
-machinery</i>, machines handling information expressed as punched holes
-in cards, enable the fulfillment of social security legislation, the
-production of the census, and countless operations of banks, insurance
-companies, department stores, and factories. And, finally, in 1942 the
-first <i>mechanical brain</i> was finished at Massachusetts Institute
-of Technology.</p>
-
-<h3>THE CRUCIAL DEVICES FOR<br />MECHANICAL BRAINS</h3>
-
-<p>Let us consider the two modern physical devices for handling
-information which make mechanical brains possible. These are
-<i>relays</i> and <i>electronic tubes</i> (<a href="#TABLE_PE">Nos. 21 and 22</a>).
-The last three kinds of equipment listed in the table (<i>magnetic
-surfaces</i>, No. 23; <i>delay lines</i>, No. 24; and <i>electrostatic
-storage tubes</i>, No. 25) were not included in any mechanical brains
-functioning by the middle of 1948. The discussion of them is therefore
-put off to <a href="#CHAPTER_10">Chapter 10</a>, where we talk about the
-future design of mechanical brains.</p>
-
-<div class="figcenter">
-  <img id="FIG_1-2" src="images/i_020.jpg" alt="" width="600" height="394" />
-  <p class="f120"><span class="smcap">Fig. 1.</span> Relay</p>
-</div>
-
-<p><span class="pagenum" id="Page_21">[Pg 21]</span>
-<a href="#FIG_1-2">Figure 1</a> shows a simple relay. There are two electrical
-circuits here. One has two terminals—Pickup and Ground. The other has three
-terminals—Common, Normally Open, and Normally Closed. When current
-flows through the coil of wire around the iron, it makes the iron
-a magnet; the magnet pulls down the flap of iron above, overcoming
-the force of the spring. When there is no current through the coil,
-the iron is not a magnet, and the flap is held up by the spring. Now
-suppose that there is current in Common. When there is no current in
-Pickup, the current from Common will flow through the upper contact, to
-the terminal marked Normally Closed. When there is current in Pickup,
-the current from Common will flow through the lower contact, to the
-terminal marked Normally Open. Thus we see that a relay expresses a
-“yes” or a “no,” a 1 or 0, a binary digit, a unit of information. A
-relay costs $5 to $10. It is rather expensive for storing a single unit
-of information. The fastest it can be changed from 1 to 0, or vice
-versa, is about <big>¹/₁₀₀</big> of a second.</p>
-
-<div class="figcenter">
-  <img id="FIG_2-2" src="images/i_021.jpg" alt="" width="500" height="285" />
-  <p class="f120"><span class="smcap">Fig. 2.</span> Electronic tube.</p>
-</div>
-
-<p><a href="#FIG_2-2">Figure 2</a> shows a simple electronic tube.
-It has three parts—the Cathode, the Grid, and the Plate. The Grid
-actually is a coarse net of metal wires. Electrons can flow from the
-Cathode to the Plate, provided the voltage on the Grid is such as to
-permit them to flow. So we can see that an electronic tube is a very
-simple on-off device and expresses a “yes” or a “no,” a 1 or 0, a
-binary digit, a unit of information. A simple electronic tube suitable
-for calculating purposes costs 50 cents to a $1, only ⅒ the cost of a
-relay. It can be changed from 1 to 0, or back again, in 1 millionth of
-a second.</p>
-
-<p>Relays have been widely used in the mechanical brains so far built,
-and electronic tubes are the essence of Eniac.</p>
-
-<p>In the next chapter, we shall see how physical equipment for handling
-information can be put together to make a simple mechanical brain.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_22">[Pg 22]</span></p>
-<h2 class="nobreak" id="CHAPTER_3">Chapter 3<br />
-<span class="h_subtitle">A MACHINE THAT WILL THINK:<br />
-THE DESIGN OF A VERY SIMPLE<br /> MECHANICAL BRAIN</span></h2>
-</div>
-
-<p>We shall now consider how we can design a very simple machine that will
-think. Let us call it Simon, because of its predecessor, Simple Simon.</p>
-
-<h3>SIMON, THE VERY SIMPLE<br /> MECHANICAL BRAIN</h3>
-
-<p>By designing Simon, we shall see how we can put together physical
-equipment for handling information in such a way as to get a very
-simple mechanical brain. At every point in the design of Simon, we
-shall make the simplest possible choice that will still give us a
-machine that: handles information, transfers information automatically
-from one part of the machine to another, and has control over the
-sequence of operations. Simon is so simple and so small, in fact, that
-it could be built to fill up less space than a grocery-store box, about
-4 cubic feet. If we know a little about electrical work, we will find
-it rather easy to make Simon.</p>
-
-<p>What do we do first to design the very simple mechanical brain, Simon?</p>
-
-<h3>SIMON’S FLESH AND NERVES—<br />REPRESENTING INFORMATION</h3>
-
-<p>The first thing we have to decide about Simon is how information will
-be represented: as we put it into Simon, as it is moved around inside
-<span class="pagenum" id="Page_23">[Pg 23]</span>
-of Simon, and as it comes out of Simon. We need to decide what physical
-equipment we shall use to make Simon’s flesh and nerves. Since we
-are taking the simplest convenient solution to each problem, let us
-decide to use: <i>punched paper tape</i> for putting information in,
-<i>relays</i> (<a href="#CHAPTER_2">see Chapter 2</a>) and wires for storing
-and transferring information, and <i>lights</i> for putting information out.</p>
-
-<div class="figcenter">
-  <img id="FIG_1-3" src="images/i_023.jpg" alt="" width="600" height="323" />
-  <p class="f120"><span class="smcap">Fig. 1.</span> Simon, the very simple mechanical brain.</p>
-</div>
-
-<p>For the equipment inside Simon, we could choose either electronic tubes
-or relays. We choose relays, although they are slower, because it is
-easier to explain circuits using relays. We can look at a relay circuit
-laid out on paper and tell how it works, just by seeing whether or not
-current will flow. Examples will be given below. When we look at a
-circuit using electronic tubes laid out on paper, we still need to know
-a good deal in order to calculate just how it will work.</p>
-
-<p>How will Simon perceive a number or other information by means of
-punched tape, or relays, or lights? With punched paper tape having, for
-example, 2 spaces where holes may be, Simon can be told 4 numbers—00,
-01, 10, 11. Here the binary digit 1 means a hole punched; the binary
-digit 0 means no hole punched. With 2 relays together in a register,
-Simon can remember any one of the 4 numbers 00, 01, 10, and 11. Here
-the binary digit 1 means the relay picked up or energized or closed; 0
-means the relay not picked up or not energized or open. With 2 lights,
-Simon can give as an answer any one of the 4 numbers 00, 01, 10, 11. In
-this case the binary digit 1 means the light glowing; 0 means the light
-off. (<a href="#FIG_1-3">See Fig. 1.</a>)
-<span class="pagenum" id="Page_24">[Pg 24]</span></p>
-
-<p>We can say that the two lights by which Simon puts out the answer are
-his <i>eyes</i> and say that he tells his answer by <i>winking</i>. We
-can say also that the two mechanisms for reading punched paper tape
-are Simon’s <i>ears</i>. One tape, called the <i>input tape</i>, takes
-in numbers or operations. The other tape takes in instructions and is
-called the <i>program tape</i>.</p>
-
-<h3>SIMON’S MENTALITY—POSSIBLE RANGE<br />OF INFORMATION</h3>
-
-<p>We can say that Simon has a <i>mentality</i> of 4. We mean not age
-4 but just the simple fact that Simon knows only 4 numbers and can
-do only 4 operations with them. But Simon can keep on doing these
-operations in all sorts of routines as long as Simon has instructions.
-We decide that Simon will know just 4 numbers, 0, 1, 2, 3, in order to
-keep our model mechanical brain very simple. Then, for any register, we
-need only 2 relays; for any answer, we need only 2 lights.</p>
-
-<p>Any calculating machine has a <i>mentality</i>, consisting of the
-whole collection of different ideas that the machine can ever actually
-express in one way or another. For example, a 10-place desk calculating
-machine can handle numbers up to 10 decimal digits without additional
-capacity. It cannot handle bigger numbers.</p>
-
-<div class="figcenter">
-  <img id="FIG_2-3" src="images/i_024.jpg" alt="" width="400" height="376" />
-  <p class="f120"><span class="smcap">Fig. 2.</span> Four directions.</p>
-</div>
-
-<p>What are the 4 <i>operations with numbers</i> which Simon can carry
-out? Let us consider some simple operations that we can perform with
-just 4 numbers. Suppose that they stood for 4 directions in the order
-east, north, west, south (<a href="#FIG_2-3">see Fig. 2</a>). Or suppose that
-they stood for a turn counterclockwise through some right angles as follows:</p>
-
-<ul class="index">
-<li class="isub4">0:&emsp;Turn through&nbsp;  0°, or no right angles.</li>
-<li class="isub4">1:&emsp;Turn through&nbsp; 90°, or&nbsp; 1 right angle.</li>
-<li class="isub4">2:&emsp;Turn through 180°, or&nbsp; 2 right angles.</li>
-<li class="isub4">3:&emsp;Turn through 270°, or&nbsp; 3 right angles.</li>
-</ul>
-
-<p>Then we could have the operations of <i>addition</i> and
-<i>negation</i>, defined as follows:
-<span class="pagenum" id="Page_25">[Pg 25]</span></p>
-
-<table class="fontsize_120 no-wrap space-below1" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdc" colspan="6"><span class="smcap">Addition</span></th>
-      <th class="tdc"><span class="ws4">&nbsp;</span></th>
-      <th class="tdc" colspan="2"><span class="smcap">Negation</span></th>
-   </tr><tr>
-      <th class="tdc" colspan="6"><i>c</i> = <i>a</i> + <i>b</i></th>
-      <th class="tdc">&nbsp;</th>
-      <th class="tdc" colspan="2"><i>c</i> = -<i>a</i></th>
-    </tr>
-   </thead>
-  <tbody><tr>
-      <td class="tdc" colspan="9">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc bb"><i>b</i>:&nbsp;</td>
-      <td class="tdc bl bb">&nbsp;&nbsp;&nbsp;</td>
-      <td class="tdc bb">&nbsp;0&nbsp;</td>
-      <td class="tdc bb">&nbsp;1&nbsp;</td>
-      <td class="tdc bb">&nbsp;2&nbsp;</td>
-      <td class="tdc bb">&nbsp;3&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc"><i>a</i>:&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc bb"><i>a</i></td>
-      <td class="tdc bl bb"><i>c</i></td>
-   </tr><tr>
-      <td class="tdc">0&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">2</td>
-      <td class="tdc">3</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">0</td>
-      <td class="tdc bl">0</td>
-   </tr><tr>
-      <td class="tdc">1&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">1</td>
-      <td class="tdc">2</td>
-      <td class="tdc">3</td>
-      <td class="tdc">0</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">1</td>
-      <td class="tdc bl">3</td>
-   </tr><tr>
-      <td class="tdc">2&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">2</td>
-      <td class="tdc">3</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">2</td>
-      <td class="tdc bl">2</td>
-   </tr><tr>
-      <td class="tdc">3&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">3</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">2</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">3</td>
-      <td class="tdc bl">1</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">For example, the first table says, “1
-plus 3 equals 0.” This means that, if we turn 1 right angle and then
-turn in the same direction 3 more right angles, we face in exactly the
-same way as we did at the start. This statement is clearly true. For
-another example, the second table says, “2 is the negative of 2.” This
-means that, if we turn to the left 2 right angles, we face in exactly
-the same way as if we turn to the right 2 right angles, and this
-statement also is, of course, true.</p>
-
-<p>With only these two operations in Simon, we should probably find him a
-little too dull to tell us much. Let us, therefore, put into Simon two
-more operations. Let us choose two operations involving both numbers
-and logic: in particular, (1) finding which of two numbers is greater
-and (2) selecting. In this way we shall make Simon a little cleverer.</p>
-
-<p>It is easy to teach Simon how to find which of two numbers is the
-greater when all the numbers that Simon has to know are 0, 1, 2, 3.
-We put all possible cases of two numbers <i>a</i> and <i>b</i> into a table:</p>
-
-<table class="fontsize_120 no-wrap space-below1" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc" colspan="9">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc bb"><i>b</i>:&nbsp;</td>
-      <td class="tdc bl bb">&nbsp;&nbsp;&nbsp;</td>
-      <td class="tdc bb">&nbsp;0&nbsp;</td>
-      <td class="tdc bb">&nbsp;1&nbsp;</td>
-      <td class="tdc bb">&nbsp;2&nbsp;</td>
-      <td class="tdc bb">&nbsp;3&nbsp;</td>
-   </tr><tr>
-      <td class="tdc"><i>a</i>:&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc" colspan="4">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">0&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc" colspan="4">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">1&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc" colspan="4">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">2&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc" colspan="4">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">3&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc" colspan="4">&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Then we tell Simon that we shall mark with 1 the cases where
-<i>a</i> is greater than <i>b</i> and mark with 0 the cases where <i>a</i> is not
-greater than <i>b</i>:</p>
-
-<table class="fontsize_120 no-wrap space-below1" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdc" colspan="6"><span class="smcap">Greater Than</span></th>
-    </tr>
-   </thead>
-  <tbody><tr>
-      <td class="tdc" colspan="6">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc bb"><i>b</i>:&nbsp;</td>
-      <td class="tdc bl bb">&nbsp;&nbsp;&nbsp;</td>
-      <td class="tdc bb">&nbsp;0&nbsp;</td>
-      <td class="tdc bb">&nbsp;1&nbsp;</td>
-      <td class="tdc bb">&nbsp;2&nbsp;</td>
-      <td class="tdc bb">&nbsp;3&nbsp;</td>
-   </tr><tr>
-      <td class="tdc"><i>a</i>:&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">0&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0</td>
-   </tr><tr>
-      <td class="tdc">1&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0</td>
-   </tr><tr>
-      <td class="tdc">2&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">1</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0</td>
-   </tr><tr>
-      <td class="tdc">3&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">1</td>
-      <td class="tdc">1</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent"><span class="pagenum" id="Page_26">[Pg 26]</span>
-For example, “2 is greater than 3” is false, so we put 0 in the table
-on the 2 line in the 3 column. We see that, for the 16 possible cases,
-<i>a</i> is greater than <i>b</i> in 6 cases and <i>a</i> is not
-greater than <i>b</i> in 10 cases.</p>
-
-<p>There is a neat way of saying what we have just said, using the
-language of <i>mathematical logic</i> (see <a href="#CHAPTER_9">Chapter 9</a>
-and <a href="#SUPPL_2">Supplement 2</a>). Suppose that we consider
-the statement “<i>a</i> is greater than <i>b</i>” where <i>a</i> and
-<i>b</i> may be any of the numbers 0, 1, 2, 3. We can say that the
-<i>truth value p</i> of a <i>statement P</i> is 1 if the statement is
-true and that it is 0 if the statement is false:</p>
-
-<p class="f120"><i>p</i> = 1 if <i>P</i> is true,&emsp;0 if <i>P</i> is false</p>
-
-<p class="no-indent">The truth value of a statement <i>P</i> is
-conveniently denoted as <i>T</i>(<i>P</i>) (<a href="#SUPPL_2">see Supplement 2</a>):</p>
-
-<p class="f120"><i>p</i> = <i>T</i>(<i>P</i>)</p>
-
-<p class="no-indent">Now we can say that the table for the operation
-<i>greater than</i> shows the truth value of the statement “<i>a</i> is
-greater than <i>b</i>”:</p>
-
-<p class="f120"><i>p</i> = <i>T</i>(<i>a</i> &gt; <i>b</i>)</p>
-
-<p>Let us turn now to the operation <i>selection</i>. By <i>selecting</i>
-we mean choosing one number <i>a</i> if some statement <i>P</i> is true
-and choosing another number <i>b</i> if that statement is not true. As
-before, let <i>p</i> be the truth value of that statement <i>P</i>, and
-let it be equal to 1 if <i>P</i> is true and to 0 if <i>P</i> is false.
-Then the operation of selection is fully expressed in the following
-table and logical formula (<a href="#SUPPL_2">see Supplement 2</a>):</p>
-
-<table class="fontsize_120 no-wrap space-below1" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdc" colspan="10"><span class="smcap">Selection</span></th>
-   </tr><tr>
-      <th class="tdc" colspan="10"><i>c</i> = <i>a</i>·<i>p</i> + <i>b</i>·(1 - <i>p</i>)</th>
-    </tr>
-   </thead>
-  <tbody><tr>
-      <td class="tdc" colspan="6">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc"><i>p</i>:&nbsp;</td>
-      <td class="tdc">&nbsp;&nbsp;&nbsp;</td>
-      <td class="tdc">&nbsp;0&nbsp;</td>
-      <td class="tdc">&nbsp;0&nbsp;</td>
-      <td class="tdc">&nbsp;0&nbsp;</td>
-      <td class="tdc">&nbsp;0&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;1&nbsp;</td>
-      <td class="tdc">&nbsp;1&nbsp;</td>
-      <td class="tdc">&nbsp;1&nbsp;</td>
-      <td class="tdc">&nbsp;1&nbsp;</td>
-   </tr><tr>
-      <td class="tdc bb"><i>b</i>:&nbsp;</td>
-      <td class="tdc bb">&nbsp;&nbsp;&nbsp;</td>
-      <td class="tdc bb">&nbsp;0&nbsp;</td>
-      <td class="tdc bb">&nbsp;1&nbsp;</td>
-      <td class="tdc bb">&nbsp;2&nbsp;</td>
-      <td class="tdc bb">&nbsp;3&nbsp;</td>
-      <td class="tdl_ws1 bb">&nbsp;0&nbsp;</td>
-      <td class="tdc bb">&nbsp;1&nbsp;</td>
-      <td class="tdc bb">&nbsp;2&nbsp;</td>
-      <td class="tdc bb">&nbsp;3&nbsp;</td>
-   </tr><tr>
-      <td class="tdc"><i>a</i>:&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc" colspan="8">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">0&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">2</td>
-      <td class="tdc">3</td>
-      <td class="tdl_ws1">0</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0</td>
-   </tr><tr>
-      <td class="tdc">1&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">2</td>
-      <td class="tdc">3</td>
-      <td class="tdl_ws1">1</td>
-      <td class="tdc">1</td>
-      <td class="tdc">1</td>
-      <td class="tdc">1</td>
-   </tr><tr>
-      <td class="tdc">2&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">2</td>
-      <td class="tdc">3</td>
-      <td class="tdl_ws1">2</td>
-      <td class="tdc">2</td>
-      <td class="tdc">2</td>
-      <td class="tdc">2</td>
-   </tr><tr>
-      <td class="tdc">3&nbsp;</td>
-      <td class="tdc bl">&nbsp;</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">2</td>
-      <td class="tdc">3</td>
-      <td class="tdl_ws1">3</td>
-      <td class="tdc">3</td>
-      <td class="tdc">3</td>
-      <td class="tdc">3</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">For example, suppose that <i>a</i> is 2 and
-<i>b</i> is 3 and the statement <i>P</i> is the statement “2 is greater
-than 0.” Since this statement is true, <i>p</i> is 1, and</p>
-
-<p class="f120"><i>a</i>·<i>p</i> + <i>b</i>·(1 - <i>p</i>) = 2(1) + 3(0) = 2</p>
-
-<p><span class="pagenum" id="Page_27">[Pg 27]</span>
-This result is the same as selecting 2 if 2 is greater than 0 and
-selecting 3 if 2 is not greater than 0.</p>
-
-<p>Thus we have four operations for Simon that do not overstrain his
-mentality; that is, they do not require him to go to any numbers other
-than 0, 1, 2, and 3. These four operations are: addition, negation,
-greater than, selection. We label these operations also with the
-numbers 00 to 11 as follows: addition, 00; negation, 01; greater than,
-10; selection, 11.</p>
-
-<h3>SIMON’S MEMORY—<br />STORING INFORMATION</h3>
-
-<p>The <i>memory</i> of a mechanical brain consists of physical equipment
-in which information can be stored. Usually, each section of the
-physical equipment which can store one piece of information is called
-a <i>register.</i> Each register in Simon will consist of 2 relays.
-Each register will hold any of 00, 01, 10, 11. The information stored
-in a register 00, 01, 10, 11 may express a number or may express an operation.</p>
-
-<div id="FIG_3-3" class="figcontainer">
-  <div class="figsub">
-   <img src="images/i_027a.jpg" alt="" width="300" height="191" />
-   <p class="center">S1-2<br /> Relay energized</p>
-  </div>
-  <div class="figsub">
-   <img src="images/i_027b.jpg" alt="" width="300" height="190" />
-   <p class="center">S1-1<br /> Relay not energized</p>
-   </div>
-   <p class="f120 space-below1"><span class="smcap">Fig. 3.</span>
-                  Register <i>S</i>1 storing 10.</p>
-</div>
-
-<p>How many registers will we need to put into Simon to store information?
-We shall need one register to read the input tape and to store the
-number or operation recorded on it. We shall call this register the
-<i>input register I</i>. We shall need another register to store the
-number or operation that Simon says is the answer and to give it to
-the output lights. We shall call this register the <i>output register
-O</i>. We shall need 5 registers for the part of Simon which does the
-computing, which we shall call the <i>computer</i>: we shall need 3 to
-store numbers put into the computer (<i>C</i>1, <i>C</i>2, <i>C</i>3),
-1 to store the operation governing the computer (<i>C</i>4), and 1 to
-<span class="pagenum" id="Page_28">[Pg 28]</span>
-store the result (<i>C</i>5). Suppose that we decide to have 8
-registers for storing information, so as to provide some flexibility
-for doing problems. We shall call these registers <i>storage
-registers</i> and name them <i>S</i>1, <i>S</i>2, <i>S</i>3, ···
-<i>S</i>8. Then Simon will have 15 registers: a memory that at one time
-can hold 15 pieces of information.</p>
-
-<p>How will one of these registers hold information? For example, how
-will register <i>S</i>1 hold the number 2 (<a href="#FIG_3-3">see Fig. 3</a>)?
-The number 2 in machine language is 10. Register <i>S</i>1 consists
-of two relays, <i>S</i>1-2 and <i>S</i>1-1. 10 stored in register
-<i>S</i>1 means that relay <i>S</i>1-2 will be energized and that relay
-<i>S</i>1-1 will not be energized.</p>
-
-<h3>THE CONTROL OF SIMON</h3>
-
-<p>So far we have said nothing about the control of Simon. Is he docile?
-Is he stubborn? We know what his capacity is, but we do not know how to
-tell him to do anything. How do we connect our desires to his behavior?
-How do we tell him a problem? How do we get him to solve it and tell
-us the answer? How do we arrange control over the sequence of his
-operations? For example, how do we get Simon to add 1 and 2 and tell us
-the answer 3?</p>
-
-<p>On the outside of Simon, we have said, there are two ears: little
-mechanisms for reading punched paper tape. Also there are two eyes
-that can wink: light bulbs that by shining or not shining can put out
-information (<a href="#FIG_1-3">see Fig. 1</a>). One of the ears—let us call it
-the <i>left ear</i>—takes in information about a particular problem: numbers
-and operations. Here the <i>problem tape</i> or <i>input tape</i> is
-listened to. Each line on the input tape contains space for 2 punched
-holes. So, the information on the input tape may be 00, 01, 10, or
-11—either a number or an operation. The other ear—let us call it
-the <i>right ear</i>—takes in information about the sequence of
-operations, the program or routine to be followed. Here the <i>program
-tape</i> or <i>routine tape</i> or <i>control tape</i> is listened
-to. Each line on the program tape contains space for 4 punched holes.
-We tell Simon by <i>instructions</i> on the program tape what he is
-to do with the information that we give him on the input tape. The
-<span class="pagenum" id="Page_29">[Pg 29]</span>
-information on the program tape, therefore, may be 0000, 0001, 0010,
-···, 1111, or any number from 0 to 15 expressed in binary notation
-(<a href="#SUPPL_2">see Supplement 2</a>).</p>
-
-<p>How is this accomplished? In the first place, Simon is a machine, and
-he behaves during time. He does different things from time to time.
-His behavior is organized in <i>cycles</i>. He repeats a cycle of
-behavior every second or so. In each cycle of Simon, he listens to or
-reads the input tape once and he listens to or reads the program tape
-twice. Every complete instruction that goes on the program tape tells
-Simon a register from which information is to be sent and a register
-in which information is to be received. The first time that he reads
-the program tape he gets the name of the register that is to receive
-certain information, the <i>receiving register</i>. The second time
-he reads the program tape he gets the name of the register from which
-information is to be sent, the <i>sending register</i>. He finishes
-each cycle of behavior by transferring information from the sending
-register to the receiving register.</p>
-
-<p>For example, suppose that we want to get an answer out of Simon’s
-computer into Simon’s output lights. We put down the instruction</p>
-
-<p class="center">Send information from <i>C</i>5 into <i>O</i></p>
-
-<p class="no-indent">or, more briefly,</p>
-
-<p class="f120"><i>C</i>5 → <i>O</i></p>
-
-<p class="no-indent">But he does not understand this language. We must
-translate into machine language, in this case punched holes in the
-program tape. Naturally, the punched holes in the program tape must be
-able to specify any sending register and any receiving register. There
-are 15 registers, and so we give them punched hole <i>codes</i> as follows:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Register</span></th>
-      <th class="tdc"><span class="smcap">&nbsp;Code&nbsp;</span></th>
-      <th class="tdc"><span class="smcap">&nbsp;&nbsp;Register&nbsp;&nbsp;</span></th>
-      <th class="tdc"><span class="smcap">&nbsp;Code&nbsp;</span></th>
-  </tr>
-  </thead>
-  <tbody><tr>
-      <td class="tdc"><i>I&nbsp;</i></td>
-      <td class="tdc">0001</td>
-      <td class="tdc"><i>C</i>1</td>
-      <td class="tdc">1010</td>
-   </tr><tr>
-      <td class="tdc"><i>S</i>1</td>
-      <td class="tdc">0010</td>
-      <td class="tdc"><i>C</i>2</td>
-      <td class="tdc">1011</td>
-   </tr><tr>
-      <td class="tdc"><i>S</i>2</td>
-      <td class="tdc">0011</td>
-      <td class="tdc"><i>C</i>3</td>
-      <td class="tdc">1100</td>
-   </tr><tr>
-      <td class="tdc"><i>S</i>3</td>
-      <td class="tdc">0100</td>
-      <td class="tdc"><i>C</i>4</td>
-      <td class="tdc">1101</td>
-   </tr><tr>
-      <td class="tdc"><i>S</i>4</td>
-      <td class="tdc">0101</td>
-      <td class="tdc"><i>C</i>5</td>
-      <td class="tdc">1110</td>
-   </tr><tr>
-      <td class="tdc"><i>S</i>5</td>
-      <td class="tdc">0110</td>
-      <td class="tdc"><i>O</i></td>
-      <td class="tdc">1111</td>
-   </tr><tr>
-      <td class="tdc"><i>S</i>6</td>
-      <td class="tdc">0111</td>
-      <td class="tdc" colspan="2">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc"><i>S</i>7</td>
-      <td class="tdc">1000</td>
-      <td class="tdc" colspan="2">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc"><i>S</i>8</td>
-      <td class="tdc">1001</td>
-      <td class="tdc" colspan="2">&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent"><span class="pagenum" id="Page_30">[Pg 30]</span>
-To translate the direction of transfer of information, which we showed
-as an arrow, we put on the program tape the code for the receiving
-register first—in this case, output, <i>O</i>, 1111—and the code
-for the sending register second—in this case, <i>C</i>5, 1110. The
-instruction becomes 1111, 1110. The first time in any cycle that Simon
-listens with his right ear, he knows that what he hears is the name of
-the receiving register; and the second time that he listens, he knows
-that what he hears is the name of the sending register. One reason
-for this sequence is that any person or machine has to be prepared
-beforehand to absorb or take in any information.</p>
-
-<p>Now how do we tell Simon to add 1 and 2? On the input tape, we put:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdc">Add</td>
-      <td class="tdc">00</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdc">01</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdc">10</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">On the program tape, we need to put:</p>
-
-<p class="f120"><i>I</i>&nbsp; →&nbsp; <i>C</i>4<br />
-<i>I</i>&nbsp; →&nbsp; <i>C</i>1<br />
-<i>I</i>&nbsp; →&nbsp; <i>C</i>2<br />
-<i>C</i>5  →  <i>O</i>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p>
-
-<p class="no-indent">which becomes:</p>
-
-<p class="f120">1101, 0001;<br />1010, 0001;<br />
-1011, 0001;<br />1111, 1110&nbsp;&nbsp;</p>
-
-<h3>THE USEFULNESS OF SIMON</h3>
-
-<p>Thus we can see that Simon can do such a problem as:</p>
-
-<div class="blockquot">
-<p class="no-indent fontsize_120">Add 0 and 3.<br />Add 2 and the negative of 1.<br />
-Find which result is greater.<br />Select 3 if this result equals 2;<br />
-otherwise select 2.</p>
-</div>
-
-<p>To work out the coding for this and like problems would be a good
-exercise. Simon, in fact, is a rather clever little mechanical brain,
-even if he has only a mentality of 4.
-<span class="pagenum" id="Page_31">[Pg 31]</span></p>
-
-<p>It may seem that a simple model of a mechanical brain like Simon
-is of no great practical use. On the contrary, Simon has the same
-use in instruction as a set of simple chemical experiments has: to
-stimulate thinking and understanding and to produce training and skill.
-A training course on mechanical brains could very well include the
-construction of a simple model mechanical brain as an exercise. In
-this book, the properties of Simon may be a good introduction to the various
-types of more complicated mechanical brains described in later chapters.</p>
-
-<p>The rest of this chapter is devoted to such questions as:</p>
-
-<div class="blockquot">
-<p class="neg-indent">How do transfers of information actually take place in Simon?</p>
-
-<p class="neg-indent">How does the computer in Simon work so that calculation
-actually occurs?</p>
-
-<p class="neg-indent">How could Simon actually be constructed?</p>
-</div>
-
-<p>What follows should be skipped unless you are interested in these
-questions and the burdensome details needed for answering them.</p>
-
-<h3>SIMON’S THINKING—<br />TRANSFERRING INFORMATION</h3>
-
-<p>The first basic thinking operation for any mechanical brain is
-transferring information automatically. Let us see how this is done in Simon.</p>
-
-<div class="figcenter">
-  <img id="FIG_4-3" src="images/i_031.jpg" alt="" width="600" height="256" />
-  <p class="f120"><span class="smcap">Fig. 4.</span> Scheme of Simon.</p>
-</div>
-
-<p>Let us first take a look at the scheme of Simon as a mechanical brain
-<span class="pagenum" id="Page_32">[Pg 32]</span>
-(<a href="#FIG_4-3">see Fig. 4</a>). We have 1 input, 8 storage, 5 computer,
-and 1 output registers, which are connected by means of transfer wires
-or a transfer line along which numbers or operations can travel as
-electrical impulses. This transfer line is often called the <i>bus</i>,
-perhaps because it is always busy carrying something. In Simon the bus
-will consist of 2 wires, one for carrying the right-hand digit and one
-for carrying the left-hand digit of any number 00, 01, 10, 11. Simon
-also has a number of neat little devices that will do the following:</p>
-
-<div class="blockquot">
-<p class="neg-indent">When any number goes into a register, the coils
-of the relays of the register will be connected with the bus.</p>
-
-<p class="neg-indent">When any number goes out of a register, the
-contacts of the relays of the register will be connected with the bus.</p>
-</div>
-
-<p>For example, suppose that in register <i>C</i>5 the number 2 is
-stored. In machine language this is 10. That means the left-hand relay
-(<i>C</i>5-2) is energized and the right-hand relay (<i>C</i>5-1) is
-not energized. Suppose that we want to transfer this number 2 into the
-output register <i>O</i>, which has been cleared. What do we do?</p>
-
-<p>Let us take a look at a circuit that will transfer the number
-(<a href="#FIG_5-3">see Fig. 5</a>). First we see two relays in this circuit.
-They belong to the <i>C</i>5 register. The <i>C</i>5-2 relay is energized since
-it holds 1; current is flowing through its coil, the iron core becomes a
-magnet, and the contact above it is pulled down. The <i>C</i>5-1 relay
-is not energized since it holds 0; its contact is not pulled down.
-The next thing we see is two <i>rectifiers</i>. The sign for these
-is a triangle. These are some modern electrical equipment that allow
-electrical current to flow in only one direction. In the diagram, the
-direction is shown by the pointing of the triangle along the wire.
-Rectifiers are needed to prevent undesired circuits. Next, we see the
-bus, consisting of two wires. One carries the impulses for left-hand
-or 2 relays, and the other carries impulses for the right-hand or 1
-relays. Next, we see two relays, called the <i>entrance relays</i> for
-the <i>O</i> register. Current from Source 1 may flow to these relays,
-energize them, and close their contacts. When the first line of the
-program tape is read, specifying the receiving register, the code 1111
-causes Source 1 to be energized. This fact is shown schematically by
-the arrow running from the program tape code 1111 to Source 1. Finally,
-<span class="pagenum" id="Page_33">[Pg 33]</span>
-we see the coils of the two relays for the Output or <i>O</i> register.
-We thus see that we have a circuit from the contacts of the <i>C</i>5
-register through the bus to the coils of the <i>O</i> register.</p>
-
-<div class="figcenter">
-  <img id="FIG_5-3" src="images/i_033.jpg" alt="" width="600" height="416" />
-  <p class="f120"><span class="smcap">Fig. 5.</span> Transfer circuit.</p>
-</div>
-
-<p>We are now ready to transfer information when the second line of the
-program tape is read. This line holds 1110 and designates <i>C</i>5 as
-the sending register and causes Source 2 to be energized. This fact is
-shown schematically by the arrow running from the second line of the
-program tape to Source 2. When the second line is read, current flows:</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. From Source 2.</p>
-<p class="neg-indent">2. Through the contacts of the <i>C</i>5 register if closed.</p>
-<p class="neg-indent">3. Through the rectifiers.</p>
-<p class="neg-indent">4. Through the bus.</p>
-<p class="neg-indent">5. Through the entrance relay contacts of the <i>O</i> register.</p>
-<p class="neg-indent">6. Through the coils of the <i>O</i> register relays, energizing
-       such of them as match with the <i>C</i>5 closed contacts; and finally</p>
-<p class="neg-indent">7. Into the ground.</p>
-</div>
-
-<p class="no-indent"><span class="pagenum" id="Page_34">[Pg 34]</span>
-Thus relay <i>O</i>-2 is energized; it receives current because
-contact <i>C</i>5-2 is closed. And relay <i>O</i>-1 is not energized;
-it receives no current since contact <i>C</i>5-1 is open. So we have
-actually transferred information from the <i>C</i>5 register to the
-<i>O</i> register.</p>
-
-<p>The same process in principle applies to all transfers:</p>
-
-<p class="blockquot">The pattern of electrical impulses, formed by the
-positioning of one register, is produced in the positioning of another
-register.</p>
-
-<h3>SIMON’S COMPUTING AND REASONING</h3>
-
-<p>Now so far the computing registers in Simon are a mystery. We have
-said that <i>C</i>1, <i>C</i>2, and <i>C</i>3 take in numbers 00, 01,
-10, 11, that <i>C</i>4 takes in an operation 00, 01, 10, 11, and that
-<i>C</i>5 holds the result. What process does Simon use so that he has
-the correct result in register <i>C</i>5?</p>
-
-<p>Let us take the simplest computing operation first and see what sort
-of a circuit using relays will give us the result. The simplest
-computing operation is <i>negation</i>. In negation, a number 00, 01,
-10, 11 goes into the <i>C</i>1 register, and the operation 01 meaning
-negation goes into the <i>C</i>4 register, and the correct result must
-be in the <i>C</i>5 register. So, first, we note the fact that the
-<i>C</i>4-2 relay must not be energized, since it contains 0, and that
-the <i>C</i>4-1 relay must be energized, since it contains 1.</p>
-
-<p>Now the table for negation, with <span class="fontsize_120"><b><i>c</i> = -<i>a</i></b></span>, is:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" rules="cols" >
-  <tbody><tr>
-      <td class="tdc bb"><big><b><i>a</i></b></big></td>
-      <td class="tdc bb"><big><b><i>c</i></b></big></td>
-   </tr><tr>
-      <td class="tdc">&nbsp;0&nbsp;</td>
-      <td class="tdc">&nbsp;0&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdc">3</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdc">2</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdc">1</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Negation in machine language will be:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" rules="cols" >
-  <tbody><tr>
-      <td class="tdc bb"><big><b><i>a</i></b></big></td>
-      <td class="tdc bb"><big><b><i>c</i></b></big></td>
-   </tr><tr>
-      <td class="tdc">&nbsp;00&nbsp;</td>
-      <td class="tdc">&nbsp;00&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">01</td>
-      <td class="tdc">11</td>
-   </tr><tr>
-      <td class="tdc">10</td>
-      <td class="tdc">10</td>
-   </tr><tr>
-      <td class="tdc">11</td>
-      <td class="tdc">01</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent"><span class="pagenum" id="Page_35">[Pg 35]</span>
-Now if <i>a</i> is in the <i>C</i>1 register and if <i>c</i> is in the
-<i>C</i>5 register, then negation will be:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" rules="cols" >
-  <tbody><tr>
-      <td class="tdc bb"><big><b><i>C</i>1</b></big></td>
-      <td class="tdc bb"><big><b><i>C</i>5</b></big></td>
-   </tr><tr>
-      <td class="tdc">&nbsp;00&nbsp;</td>
-      <td class="tdc">&nbsp;00&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">01</td>
-      <td class="tdc">11</td>
-   </tr><tr>
-      <td class="tdc">10</td>
-      <td class="tdc">10</td>
-   </tr><tr>
-      <td class="tdc">11</td>
-      <td class="tdc">01</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">But each of these registers <i>C</i>1, <i>C</i>5
-will be made up of two relays, the left-hand or 2 relay and the
-right-hand or 1 relay. So, in terms of these relays, negation will be:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdc bb">&nbsp;<big><b><i>C</i>1-2</b></big>&nbsp;</td>
-      <td class="tdc bb br">&nbsp;<big><b><i>C</i>1-1</b></big>&nbsp;</td>
-      <td class="tdc bb">&nbsp;<big><b><i>C</i>5-2</b></big>&nbsp;</td>
-      <td class="tdc bb">&nbsp;<big><b><i>C</i>5-1</b></big>&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">0</td>
-      <td class="tdc br">0</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0</td>
-   </tr><tr>
-      <td class="tdc">0</td>
-      <td class="tdc br">1</td>
-      <td class="tdc">1</td>
-      <td class="tdc">1</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdc br">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdc br">1</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Now, on examining the table, we see that the
-<i>C</i>5-1 relay is energized if and only if the <i>C</i>1-1 relay is
-energized. So, in order to energize the <i>C</i>5-1 relay, all we have
-to do is transfer the information from <i>C</i>1-1 to <i>C</i>5-1. This
-we can do by the circuit shown in <a href="#FIG_6-3">Fig. 6</a>.
-(In this and later diagrams, we have taken one more step in
-streamlining the drawing of relay contacts: the contacts are drawn, but
-the coils that energize them are represented only by their names.)</p>
-
-<div class="figcontainer">
-  <div id="FIG_6-3" class="figsub">
-   <img src="images/i_035a.jpg" alt="" width="300" height="294" />
-   <p class="center"><span class="smcap">Fig. 6.</span> Negation—<br />right-hand digit.</p>
-  </div>
-  <div id="FIG_7-3" class="figsub">
-   <img src="images/i_035b.jpg" alt="" width="300" height="271" />
-   <p class="center"><br /><span class="smcap">Fig. 7.</span> Negation—<br />left-hand digit.</p>
-   </div>
-</div>
-
-<p>Taking another look at the table, we see also that the <i>C</i>5-2
-relay must be energized if and only if:
-<span class="pagenum" id="Page_36">[Pg 36]</span></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdc"><b><i>C</i>1-2<br />HOLDS:</b></td>
-      <td class="tdc">&nbsp;&nbsp;<b>AND</b>&nbsp;&nbsp;</td>
-      <td class="tdc"><b><i>C</i>1-1<br />HOLDS:</b></td>
-   </tr><tr>
-      <td class="tdc">0</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">1</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">0</td>
-   </tr>
- </tbody>
-</table>
-
-<p>A circuit that will do this is the one shown in <a href="#FIG_7-3">Fig. 7</a>.
-In <a href="#FIG_8-3">Fig. 8</a> is a circuit that will do all the desired things
-together: give the right information to the <i>C</i>5 relay coils if and only if
-the <i>C</i>4 relays hold 01.</p>
-
-<div class="figcenter">
-  <img id="FIG_8-3" src="images/i_036.jpg" alt="" width="500" height="573" />
-  <p class="f120"><span class="smcap">Fig. 8.</span> Negation circuit.</p>
-</div>
-
-<p>Let us check this circuit. First, if there is any operation other than
-01 stored in the <i>C</i>4 relays, then no current will be able to
-get through the <i>C</i>4 contacts shown and into the <i>C</i>5 relay
-coils, and the result is blank. Second, if we have the operation 01
-stored in the <i>C</i>4 relays, then the <i>C</i>4-2 contacts will not
-be energized—a condition which passes current—and the <i>C</i>4-1
-contacts will be energized—another condition which passes current—and:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdc bb"><b><span class="smcap">If the number in</span> <i>C</i>1 <span class="smcap">is</span>:</b></td>
-      <td class="tdc_bott bb"><b><span class="smcap">then</span> <i>C</i>1-1:</b></td>
-      <td class="tdc_bott bb"><b><span class="smcap">and</span> <i>C</i>1-2:</b></td>
-      <td class="tdc bb"><b><span class="smcap">and the</span> <i>C</i>5 <span class="smcap">relays energized are</span>:</b></td>
-   </tr><tr>
-      <td class="tdc">0</td>
-      <td class="tdl_ws1">does not close</td>
-      <td class="tdl_ws1">does not close</td>
-      <td class="tdl_ws1">neither</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdl_ws1">closes</td>
-      <td class="tdl_ws1">does not close</td>
-      <td class="tdl_ws1"><i>C</i>5-2, <i>C</i>5-1</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdl_ws1">does not close</td>
-      <td class="tdl_ws1">closes</td>
-      <td class="tdl_ws1"><i>C</i>5-2 only</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdl_ws1">closes</td>
-      <td class="tdl_ws1">closes</td>
-      <td class="tdl_ws1"><i>C</i>5-1 only</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Thus we have shown that this circuit is correct.</p>
-
-<p>We see that this circuit uses more than one set of contacts for several
-relays (<i>C</i>1-2, <i>C</i>4-1, <i>C</i>4-2); relays are regularly
-made with 4, 6, or 12 sets of contacts arranged side by side, all
-<span class="pagenum" id="Page_37">[Pg 37]</span>
-controlled by the same pickup coil. These are called 4-, 6-, or
-12-<i>pole</i> relays.</p>
-
-<div class="figcenter">
-  <img id="FIG_9-3" src="images/i_037a.jpg" alt="" width="500" height="419" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 9.</span> Addition circuit.</p>
-  <img id="FIG_10-3" src="images/i_037b.jpg" alt="" width="500" height="462" />
-  <p class="f120"><span class="smcap">Fig. 10.</span> Greater-than circuit.</p>
-</div>
-
-<p>Circuits for <i>addition</i>, <i>greater than</i>, and <i>selection</i>
-can also be determined rather easily (see Figs. <a href="#FIG_9-3">9</a>,
-<a href="#FIG_10-3">10</a>, <a href="#FIG_11-3">11</a>).
-(<i>Note</i>: By means of the <i>algebra of logic</i>, referred to in
-<a href="#CHAPTER_9">Chapter 9</a> and <a href="#SUPPL_2">Supplement 2</a>, the conditions
-for many relay circuits, as well as the circuit itself, may be expressed algebraically,
-and the two expressions may be checked by a mathematical process.) For example, let
-<span class="pagenum" id="Page_38">[Pg 38]</span>
-us check that the addition circuit in <a href="#FIG_9-3">Fig. 9</a>
-will enable us to add 1 and 2 and obtain 3. We take a colored pencil
-and draw closed the contacts for <i>C</i>1-1 (since <i>C</i>1 holds 01)
-and for <i>C</i>2-2 (since <i>C</i>2 holds 10). Then, when we trace
-through the circuit, remembering that addition is stored as 00 in the
-<i>C</i>4 relays, we find that both the <i>C</i>5 relays are energized.
-Hence <i>C</i>5 holds 11, which is 3. Thus Simon can add 1 and 2 and
-make 3!</p>
-
-<div class="figcenter">
-  <img id="FIG_11-3" src="images/i_038.jpg" alt="" width="600" height="461" />
-  <p class="f120"><span class="smcap">Fig. 11.</span> Selection Circuit.</p>
-</div>
-
-<h3>PUTTING SIMON TOGETHER</h3>
-
-<p>In order to put Simon together and make him work, not very much is
-needed. On the outside of Simon we shall need two small mechanisms
-for reading punched paper tape. Inside Simon, there will be about 50
-relays and perhaps 100 feet of wire for connecting them. In addition
-to the 15 registers (<i>I</i>, <i>S</i>1 to <i>S</i>8, <i>C</i>1 to
-<i>C</i>5, and <i>O</i>), we shall need a register of 4 relays, which
-we shall call the <i>program register</i>. This register will store
-the successive instructions read off the program tape. We can call the
-4 relays of this register <i>P</i>8, <i>P</i>4, <i>P</i>2, <i>P</i>1.
-For example, if the <i>P</i>8 and <i>P</i>2 relays are energized, the
-register holds 1010, and this is the program instruction that calls for
-the 8th plus 2nd, or 10th, register, which is <i>C</i>1.
-<span class="pagenum" id="Page_39">[Pg 39]</span></p>
-
-<p>For connecting receiving registers to the bus, we shall need a relay
-with 2 poles, one for the 2-line and one for the 1-line, for each
-register that can receive a number from the bus. For example, for
-entering the output register, we actually need only one 2-pole relay
-instead of the two 1-pole relays drawn for simplicity in <a href="#FIG_5-3">Fig. 5</a>.
-There will be 13 2-pole relays for this purpose, since only 13 registers
-receive numbers from the bus; registers <i>I</i> and <i>C</i>5 do not
-receive numbers from the bus. We call these 13 relays the <i>entrance
-relays</i> or <i>E relays</i>, since <i>E</i> is the initial letter of
-the word entrance.</p>
-
-<div class="figcenter">
-  <img id="FIG_12-3" src="images/i_039.jpg" alt="" width="600" height="294" />
-  <p class="f120"><span class="smcap">Fig. 12.</span> Select-Receiving-Register circuit.</p>
-</div>
-
-<p>The circuit for selecting and energizing the <i>E</i> relays is shown
-in <a href="#FIG_12-3">Fig. 12</a>. We call this circuit the
-<i>Select-Receiving-Register</i> circuit. For example, suppose that
-the <i>P</i>8 and <i>P</i>2 relays are energized. Then this circuit
-energizes the <i>E</i>10 relay. The <i>E</i>10 relay closes the
-contacts between the <i>C</i>1 relay coils and the bus; and so it
-connects the <i>C</i>1 register to receive the next number that is sent
-into the bus. This kind of circuit expresses a classification and is
-sometimes called a <i>pyramid circuit</i> since it spreads out like
-a pyramid. A similar pyramid circuit is used to select the sending
-register.</p>
-
-<p>We shall need a relay for moving the input tape a step at a time.
-We shall call this relay the <i>MI relay</i>, for <i>m</i>oving
-<i>i</i>nput tape. We also need a relay for moving the program tape
-a step at a time. We shall call this relay the <i>MP relay</i> for
-<i>m</i>oving <i>p</i>rogram tape. Here then is approximately the total
-number of relays required:
-<span class="pagenum" id="Page_40">[Pg 40]</span></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary="TOC" cellpadding="2" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Relays</span></th>
-      <th class="tdc"><span class="smcap">Name</span></th>
-      <th class="tdr"><span class="smcap">Number</span></th>
-  </tr>
-  </thead>
-  <tbody><tr>
-      <td class="tdl"><i>I</i>, <i>S</i>, <i>C</i>, <i>O</i></td>
-      <td class="tdl_ws1">Input, Storage, Computer, Output</td>
-      <td class="tdr">30</td>
-   </tr><tr>
-      <td class="tdl"><i>P</i></td>
-      <td class="tdl_ws1">Program</td>
-      <td class="tdr">4</td>
-   </tr><tr>
-      <td class="tdl"><i>E</i></td>
-      <td class="tdl_ws1">Entrance</td>
-      <td class="tdr">13</td>
-   </tr><tr>
-      <td class="tdl"><i>MI</i></td>
-      <td class="tdl_ws1">Move Input Tape</td>
-      <td class="tdr">1</td>
-   </tr><tr>
-      <td class="tdl"><i>MP</i></td>
-      <td class="tdl_ws1">Move Program Tape</td>
-      <td class="tdr">1</td>
-   </tr><tr>
-      <td class="tdl">&nbsp;</td>
-      <td class="tdc">Total</td>
-      <td class="tdr bt">49</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">A few more relays may be needed to provide more
-contacts or poles. For example, a single <i>P</i>1 relay will probably
-not have enough poles to meet all the need for its contacts.</p>
-
-<div class="figcenter">
-  <img id="FIG_13-3" src="images/i_040.jpg" alt="" width="400" height="550" />
-  <p class="f120"><span class="smcap">Fig. 13.</span> Latch relay.</p>
-</div>
-
-<p>Each cycle of the machine will be divided into 5 equal <i>time
-intervals</i> or <i>times</i> 1 to 5. The timing of the machine will be
-about as follows:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdl"><span class="smcap">Time</span></th>
-      <th class="tdl"><span class="ws8"><span class="smcap">Action</span></span></th>
-   </tr>
-  </thead>
-  <tbody><tr>
-      <td class="tdc">1</td>
-      <td class="tdl_ws1">Move program tape.</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">Move input tape if read out of in last cycle.</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdl_ws1">Read program tape, determining the receiving register.</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">Read through the computing circuit setting up the <i>C</i>5 register.</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdl_ws1">Move program tape.</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">Energize the <i>E</i> relay belonging to the receiving register.</td>
-   </tr><tr>
-      <td class="tdc">4</td>
-      <td class="tdl_ws1">Read program tape again, determining the sending register.</td>
-   </tr><tr>
-      <td class="tdc">5</td>
-      <td class="tdl_ws1">Transfer information by reading through the</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">Select-Sending-Register circuit and the</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">Select-Receiving-Register circuit.</td>
-   </tr>
- </tbody>
-</table>
-
-<p><span class="pagenum" id="Page_41">[Pg 41]</span>
-In order that information may remain in storage until wanted, register
-relays should hold their information until just before the next
-information is received. This can be accomplished by keeping current
-in their coils or in other ways. There is a type of relay called a
-<i>latch relay</i>, which is made with two coils and a latch. This type
-of relay has the property of staying or latching in either position
-until the opposite coil is impulsed (<a href="#FIG_13-3">see Fig. 13</a>).
-This type of relay would be especially good for the registers of Simon.</p>
-
-<p>If any reader sets to work to construct Simon, and if questions arise,
-the author will be glad to try to answer them.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_42">[Pg 42]</span></p>
-<h2 class="nobreak" id="CHAPTER_4">Chapter 4<br />
-<span class="h_subtitle">COUNTING HOLES:<br />
-PUNCH-CARD CALCULATING MACHINES</span></h2>
-</div>
-
-<p>When we think of counting, we usually think of saying softly to
-ourselves “one, two, three, four, ···.” This is a good way to find
-the total of a small group of objects. But when we have a large group
-of objects or a great many groups of objects to be counted, a much
-faster way of counting is needed. A very fast way of sorting and
-counting is <i>punch-card calculating machinery</i>. This is machinery which
-handles information expressed as holes in cards. <i>Punch-card machines</i> can:</p>
-
-<ul class="index no-wrap fontsize_120">
-<li class="isub2">Sort, count, file, select, and copy information,</li>
-<li class="isub2">Make comparisons, and choose according to instructions,</li>
-<li class="isub2">Add, subtract, multiply, and divide,</li>
-<li class="isub2">List information, and print totals.</li>
-</ul>
-
-<p class="no-indent">For example, in a life insurance company, much routine handling of
-information about insurance policies is necessary:</p>
-
-<div class="blockquot">
-<p class="neg-indent">Writing information on newly issued policies.</p>
-
-<p class="neg-indent">Setting up policy-history cards.</p>
-
-<p class="neg-indent">Making out notices of premiums due.</p>
-
-<p class="neg-indent">Making registers of policies in force, lapsed,
-died, etc., for purposes of valuation as required by law or good
-management.</p>
-
-<p class="neg-indent">Calculating and tabulating premium rates,
-dividend rates, reserve factors, etc.</p>
-
-<p class="neg-indent">Computing and tabulating expected and actual
-death rates; and much more.</p>
-</div>
-
-<p class="no-indent">All these operations can be done almost automatically
-by punch-card machines.
-<span class="pagenum" id="Page_43">[Pg 43]</span></p>
-
-<h3>ORIGIN AND DEVELOPMENT</h3>
-
-<p>When a census of the people of a country is taken, a great quantity of
-sorting and counting is needed: by village, county, city, and state;
-by sex; by age; by occupation; etc. In 1886, the census of the people
-of the United States which had been taken in 1880 was still being
-sorted and counted. Among the men then studying census problems was
-a statistician and inventor, Herman Hollerith. He saw that existing
-methods were so slow that the next census (1890) would not be finished
-before the following census (1900) would have to be begun. He knew
-that cards with patterns of holes had been used in weaving patterns
-in cloth. He realized that the presence or absence of a property, for
-example employed or unemployed, could be represented by the presence
-or absence of a hole in a piece of paper. An electrical device could
-detect the hole, he believed, since it would allow current to flow
-through, whereas the absence of the hole would stop the current. He
-experimented with sorting and counting, using punched holes in cards,
-and with electrical devices to detect the holes and count them. A
-definite meaning was given to each place in the card where a hole might
-be punched. Then electrical devices handled the particular information
-that the punches represented. These devices either counted or added,
-singly or in various combinations, as might be desired.</p>
-
-<p>More than 50 years of development of punch-card calculating machinery
-have since then taken place. Several large companies have made
-quantities of punch-card machines. A great degree of development has
-taken place in the punch-card machines of International Business
-Machines Corporation (IBM), and for this reason these machines will
-be the ones described in this chapter. What is said here, however,
-may also in many ways apply to punch-card machines made by other
-manufacturers—Remington-Rand, Powers, Control Instrument, etc.</p>
-
-<h3>GENERAL PRINCIPLES</h3>
-
-<p>To use punch-card machines, we first convert the original information
-<span class="pagenum" id="Page_44">[Pg 44]</span>
-into patterns of holes in cards. Then we feed the cards into the
-machines. Electrical impulses read the pattern of holes and convert
-them into a pattern of timed electrical currents. Actually, the
-reading of a hole in a column of a punch card is done by a brush of
-several strands of copper wire pressed against a metal roller (<a href="#FIG_1-4">Fig. 1</a>).
-The machine feeds the card (the bottom edge first, where the 9’s
-are printed) with very careful timing over the roller; and, when the
-punched hole is between the brush and the roller, an electrical circuit
-belonging to that column of the card is completed. The machine responds
-according to its general design and its wiring for the particular
-problem: it punches new cards, or it prints new marks, or it puts
-information into new storage places. Clerks, however, move the cards
-from one machine to another. They wait on the machines, keep the card
-feeds full, and empty the card hoppers as they fill up. A human error
-of putting the wrong block of cards into a machine may from time to
-time cause a little trouble, especially in sorting. Actually, in a
-year, billions of punch cards are handled precisely.</p>
-
-<div class="figcenter">
-  <img id="FIG_1-4" src="images/i_044.jpg" alt="" width="600" height="395" />
-  <p class="f120"><span class="smcap">Fig. 1.</span> Reading of punch cards.</p>
-</div>
-
-<p>The <i>punch card</i> is a masterpiece of engineering and
-standardization. Its exact thickness matches the knife-blade edges that
-feed the cards into slots in the machines, and matches the channels
-whereby these cards travel through the machines. The standard card is
-7⅜ inches long and 3¼ inches wide, and it has a standard thickness of
-0.0065 inch and other standard properties with respect to stiffness, finish, etc.
-<span class="pagenum" id="Page_45">[Pg 45]</span></p>
-
-<div class="figcenter">
-  <img id="FIG_2-4" src="images/i_045.jpg" alt="" width="600" height="496" />
-  <p class="f120"><span class="smcap">Fig. 2.</span> Scheme of standard punch card.</p>
-  <p class="f90">(Note: Positions 11 and 12 are not usually marked by printed numbers or letters.)</p>
-</div>
-
-<p>The standard IBM punch card of today has 80 <i>columns</i> and 12
-<i>positions</i> for punching in each column (<a href="#FIG_2-4">Fig. 2</a>).
-A single punched hole in each of the positions known as 0 to 9 stands
-for each of the digits 0 to 9 respectively. The remaining 2 single
-punch positions available in any column are usually called the
-<i>11 position</i> and <i>12 position</i> (though sometimes called
-the numerical <i>X position</i> and <i>Y position</i>). These two
-positions do not behave arithmetically as 11 and 12. Actually, in the
-space between one card and the next card as they are fed through the
-machines, more positions occur. For example, there may be 4 more: a 10
-position preceding the 9, and a 13, a 14, and a 15 position following
-the 12. The 16 positions in total correspond to a full turn, 360°,
-of the roller under the brush, and to a complete <i>cycle</i> in the
-machine; and a single position corresponds to ¹/₁₆ of 360°, or 22½°.
-In some machines, the total <span class="pagenum" id="Page_46">[Pg
-46]</span> number of positions may be 20. A pair of punches stands for
-each of the letters of the alphabet, according to the scheme shown.</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdl"><b><big>A</big></b></td>
-      <td class="tdl_ws1">12-1</td>
-      <td class="tdl_ws1"><b><big>J</big></b></td>
-      <td class="tdl_ws1">11-1</td>
-      <td class="tdc">&nbsp;&nbsp;<b>Unused</b></td>
-      <td class="tdl_ws1">0-1</td>
-   </tr><tr>
-      <td class="tdl"><b><big>B</big></b></td>
-      <td class="tdl_ws1">12-2</td>
-      <td class="tdl_ws1"><b><big>K</big></b></td>
-      <td class="tdl_ws1">11-2</td>
-      <td class="tdc"><b><big>S</big></b></td>
-      <td class="tdl_ws1">0-2</td>
-   </tr><tr>
-      <td class="tdl"><b><big>C</big></b></td>
-      <td class="tdl_ws1">12-3</td>
-      <td class="tdl_ws1"><b><big>L</big></b></td>
-      <td class="tdl_ws1">11-3</td>
-      <td class="tdc"><b><big>T</big></b></td>
-      <td class="tdl_ws1">0-3</td>
-   </tr><tr>
-      <td class="tdl"><b><big>D</big></b></td>
-      <td class="tdl_ws1">12-4</td>
-      <td class="tdl_ws1"><b><big>M</big></b></td>
-      <td class="tdl_ws1">11-4</td>
-      <td class="tdc"><b><big>U</big></b></td>
-      <td class="tdl_ws1">0-4</td>
-   </tr><tr>
-      <td class="tdl"><b><big>E</big></b></td>
-      <td class="tdl_ws1">12-5</td>
-      <td class="tdl_ws1"><b><big>N</big></b></td>
-      <td class="tdl_ws1">11-5</td>
-      <td class="tdc"><b><big>V</big></b></td>
-      <td class="tdl_ws1">0-5</td>
-   </tr><tr>
-      <td class="tdl"><b><big>F</big></b></td>
-      <td class="tdl_ws1">12-6</td>
-      <td class="tdl_ws1"><b><big>O</big></b></td>
-      <td class="tdl_ws1">11-6</td>
-      <td class="tdc"><b><big>W</big></b></td>
-      <td class="tdl_ws1">0-6</td>
-   </tr><tr>
-      <td class="tdl"><b><big>G</big></b></td>
-      <td class="tdl_ws1">12-7</td>
-      <td class="tdl_ws1"><b><big>P</big></b></td>
-      <td class="tdl_ws1">11-7</td>
-      <td class="tdc"><b><big>X</big></b></td>
-      <td class="tdl_ws1">0-7</td>
-   </tr><tr>
-      <td class="tdl"><b><big>H</big></b></td>
-      <td class="tdl_ws1">12-8</td>
-      <td class="tdl_ws1"><b><big>Q</big></b></td>
-      <td class="tdl_ws1">11-8</td>
-      <td class="tdc"><b><big>Y</big></b></td>
-      <td class="tdl_ws1">0-8</td>
-   </tr><tr>
-      <td class="tdl"><b><big>I</big></b></td>
-      <td class="tdl_ws1">12-9</td>
-      <td class="tdl_ws1"><b><big>R</big></b></td>
-      <td class="tdl_ws1">11-9</td>
-      <td class="tdc"><b><big>Z</big></b></td>
-      <td class="tdl_ws1">0-9</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">For example, the word MASON is shown punched in
-<a href="#FIG_3-4">Fig. 3</a>.</p>
-
-<div class="figcontainer">
-  <div id="FIG_3-4" class="figsub">
-   <img src="images/i_046a.jpg" alt="" width="150" height="413" />
-   <p class="center"><span class="smcap">Fig. 3.</span> Alphabetic punching.</p>
-  </div>
-  <div id="FIG_4-4" class="figsub">
-   <img src="images/i_046b.jpg" alt="" width="230" height="412" />
-   <p class="center"><span class="smcap">Fig. 4.</span> Single-panel plugboard.</p>
-   </div>
-</div>
-
-<p>To increase the versatility of the machines and provide them with
-instructions, many of them have <i>plugboards</i> (<a href="#FIG_4-4">Fig. 4</a>).
-These are standard interchangeable boards filled with prongs on one side and
-<span class="pagenum" id="Page_47">[Pg 47]</span>
-holes or terminals called <i>hubs</i> on the other side. The side
-with the prongs connects to the ends of electrical circuits in the
-punch-card machine, which are brought together in one place for the
-purpose. On the other side of the board, using plugwires, we can
-connect the hubs to each other in different ways to produce different
-results. The single-panel plugboard is 10 inches long and 5¾ inches
-wide. It contains 660 hubs in front and 660 corresponding prongs in
-the back. A double-panel plugboard or a triple-panel plugboard applies
-to some machines. In less time than it takes to describe it, we can
-take one wired-up plugboard out of a machine and put in a new wired-up
-plugboard and thus change completely the instructions under which the
-machine operates. Many of the machines have a number of different
-switches that we must also change, when going from one kind of problem
-to another.</p>
-
-<p>The numbers that are stored or sorted in punch-card machines may be
-of any size up to 80 digits, one in each column of the punch card. In
-doing arithmetic (adding, subtracting, multiplying, and dividing),
-however, the largest number of digits is usually 10. Beyond 10 digits,
-we can work out tricks in many cases.</p>
-
-<h3>TYPES OF PUNCH-CARD MACHINES</h3>
-
-<p>The chief IBM punch-card machines are: the <i>key punch</i>, the
-<i>verifier</i>, the <i>sorter</i>, the <i>interpreter</i>, the
-<i>reproducer</i>, the <i>collator</i>, the <i>multiplying punch</i>,
-the <i>calculating punch</i>, and the <i>tabulator</i>. Of these
-9 machines, the last 6 have plugboards and can do many different
-operations as a result.</p>
-
-<p>There is a flow of punch cards through each of these machines. The
-machines differ from each other in the number and relation of the paths
-of flow, or <i>card channels</i>, and in the number and relation of the
-momentary stopping places, or <i>card stations</i>, at which cards are
-read, punched, or otherwise acted on. We can get a good idea of what a
-machine is from a picture of these card channels.</p>
-
-<h4>Key Punch</h4>
-
-<p>We use a key punch (<a href="#FIG_5-4">Fig. 5</a>) to punch original information
-into blank cards. In the key punch there is one card channel; it has one entrance,
-<span class="pagenum" id="Page_48">[Pg 48]</span>
-one station, and one exit. At the card station, there are 12
-<i>punching dies</i>, one for each position in the card column, and
-each card column is presented one by one for punching. The numeric
-<i>keyboard</i> (<a href="#FIG_6-4">Fig. 6</a>) for the key punch has 14 keys:</p>
-
-<div class="blockquot">
-<p class="neg-indent">One key for each of the punches 0 to 9, 11,
-and 12,</p>
-
-<p class="neg-indent">A <i>space key</i>, which allows a column of the
-punch card to go by with no punch in it,</p>
-
-<p class="neg-indent">A <i>release key</i>, which ejects the card and
-feeds another card.</p>
-</div>
-
-<div class="figcenter">
-  <img id="FIG_5-4" src="images/i_048a.jpg" alt="" width="600" height="266" />
-  <p class="f120"><span class="smcap">Fig. 5.</span> Key punch.</p>
-  <img id="FIG_6-4" src="images/i_048b.jpg" alt="" width="400" height="392" />
-  <p class="f120"><span class="smcap">Fig. 6.</span> Keyboard of key punch.</p>
-</div>
-
-<p>Of course, in using a key punch, we must punch the same kind of
-information in the same group of columns. For example, if these cards
-are to contain employees’ social security numbers, we must punch that
-number always in the same card columns, numbered, say, 15 to 23, or 70
-to 78, etc.</p>
-
-<h4>Verifier</h4>
-
-<p>The verifier is really the same machine as the key punch, but it has
-dull punching dies moving gently instead of sharp ones moving with
-force. It turns on a red light and stops when there is no punched hole
-in the right spot to match with a pressed key.</p>
-
-<h4>Sorter</h4>
-
-<p>The sorter is a machine for sorting cards, one column at a time (<a href="#FIG_7-4">Fig. 7</a>).
-The sorter has a card channel that forks; it has one entrance, one
-<span class="pagenum" id="Page_49">[Pg 49]</span>
-station, and 13 exits. Each exit corresponds to: one of the 12 punch
-positions 0 to 9, 11, and 12; or <i>reject</i>, which applies when the
-column is nowhere punched. It has one card station where a brush reads
-a single column of the card. We can turn a handle and move the brush to
-any column.</p>
-
-<div class="figcenter">
-  <img id="FIG_7-4" src="images/i_049a.jpg" alt="" width="600" height="251" />
-  <p class="f120"><span class="smcap">Fig. 7.</span> Sorter.</p>
-</div>
-
-<h4>Interpreter</h4>
-
-<p>The interpreter takes in a card, reads its punches, prints on the
-card the marks indicated by the punches, and stacks the card. We call
-this process <i>interpreting</i> the card, since it translates the
-punched holes into printed marks. The interpreter (<a href="#FIG_8-4">Fig. 8</a>)
-has one card channel, with one entrance, 2 card stations, and one exit. What the
-machine does at the second card station depends on what the machine
-reads at the first card station and on what we have told the machine by
-switches and plugboard wiring to do.</p>
-
-<div class="figcenter">
-  <img id="FIG_8-4" src="images/i_049b.jpg" alt="" width="600" height="246" />
-  <p class="f120"><span class="smcap">Fig. 8.</span> Interpreter.</p>
-</div>
-
-<h4>Reproducer</h4>
-
-<p>The reproducer or reproducing punch can:
-<span class="pagenum" id="Page_50">[Pg 50]</span></p>
-
-<div class="blockquot">
-<p class="neg-indent"><i>Reproduce</i>, or copy the punches in one
-group of cards into another group of cards (in the same or different columns).</p>
-
-<p class="neg-indent"><i>Compare</i>, or make sure that the punches in
-two groups of cards agree (and shine a red light if they do not).</p>
-
-<p class="neg-indent"><i>Gang punch</i>, or copy the punches in a
-<i>master card</i> into a group of <i>detail cards</i>.</p>
-
-<p class="neg-indent"><i>Summary punch</i>, or copy totals or summaries
-obtained in the tabulator into blank cards in the reproducer.</p>
-</div>
-
-<div class="figcenter">
-  <img id="FIG_9-4" src="images/i_050.jpg" alt="" width="600" height="376" />
-  <p class="f120"><span class="smcap">Fig. 9.</span> Reproducer.</p>
-</div>
-
-<p>The reproducer (<a href="#FIG_9-4">Fig. 9</a>) has 2 independent
-card channels, the cards not mingling in any way, called the <i>reading
-channel</i> and the <i>punching channel</i>. We can run the machine
-with only the punching channel working; in fact, IBM equips some
-models only with the punching channel, particularly for “summary
-punch” operation. The machine is timed so that, when any card is at
-the middle station in either channel, then the next preceding card is
-at the latest station, and the next following card is at the earliest
-station. At 5 stations, the machine reads a card. At the middle station
-of the punching channel, the machine punches a card. Using a many-wire
-cable, we can connect the tabulator to the reproducer and so cause
-the tabulator to give information electrically to the reproducer.
-This connection makes possible the “summary punch” operation. Here
-is an instance with punch-card machines where, in order to transfer
-information from one machine to another, we are not required to move
-cards physically from one machine to another.
-<span class="pagenum" id="Page_51">[Pg 51]</span></p>
-
-<h4>Collator</h4>
-
-<p>The collator is a machine that arranges or <i>collates</i> cards. It
-is particularly useful in selecting, matching, and merging cards. The
-collator (<a href="#FIG_10-4">Fig. 10</a>) has 2 card channels which join
-and then fork into 4 channels ending in pockets called <i>Hoppers</i>
-1, 2, 3, and 4. The 2 card feeds are called the <i>Primary Feed</i> and
-the <i>Secondary Feed</i>. Cards from the Primary Feed may fall only
-into the first and second hoppers. Cards from the Secondary Feed may
-fall only into the second, third, and fourth hoppers. The collator has
-3 stations at which cards may be read.</p>
-
-<div class="figcenter">
-  <img id="FIG_10-4" src="images/i_051.jpg" alt="" width="600" height="236" />
-  <p class="no-indent"><b><big>No.1—Selected primaries<br />
-                       No.2—Merged cards and unselected primaries<br />
-                       No.3—Separate secondaries not selected<br />
-                       No.4—Selected secondaries</big></b></p>
-  <p class="f120"><span class="smcap">Fig. 10.</span> Collator.</p>
-</div>
-
-<p>IBM can supply additional wiring called the <i>collator counting
-device</i>. With this we can make the collator count cards as well
-as compare them. For example, we could put 12 blank cards from the
-Secondary Feed behind each punched-card from the Primary Feed in order
-to prepare for some other operation.</p>
-
-<h4>Calculating Punch</h4>
-
-<p>The calculating punch was introduced in 1946. It is a versatile machine
-of considerable capacity. It adds, subtracts, multiplies, and divides.
-It also has a control over a sequence of operations, in some cases up
-to half a dozen steps.</p>
-
-<p>This machine (<a href="#FIG_11-4">Fig. 11</a>) has one card channel
-with 4 stations called, respectively, <i>control brushes</i>,
-<i>reading brushes</i>, <i>punch feed</i>, and <i>punching dies</i>. At
-station 1, there are 20 brushes; we can set these by hand to read any
-20 of the 80 card columns. At station 2 there are 80 regular reading
-<span class="pagenum" id="Page_52">[Pg 52]</span>
-brushes. At station 3 the card waits for a part of a second while
-the machine calculates, and, when that is done, the card is fed into
-station 4, where it is punched or verified. The multiplying punch is
-an earlier model of the calculating punch, without the capacity for
-division.</p>
-
-<div class="figcenter">
-  <img id="FIG_11-4" src="images/i_052a.jpg" alt="" width="600" height="236" />
-  <p class="f120"><span class="smcap">Fig. 11.</span> Calculating punch.</p>
-</div>
-
-<h4>Tabulator</h4>
-
-<p>The tabulator can select and list information from cards. Also, it
-can total information from groups of cards in <i>counters</i> of the
-tabulator and can print the totals.</p>
-
-<div class="figcenter">
-  <img id="FIG_12-4" src="images/i_052b.jpg" alt="" width="600" height="448" />
-  <p class="f120"><span class="smcap">Fig. 12.</span> Tabulator.</p>
-</div>
-
-<p>The tabulator (<a href="#FIG_12-4">Fig. 12</a>) has one card channel with
-two stations where cards may be read, called the <i>Upper Brushes</i> and
-<span class="pagenum" id="Page_53">[Pg 53]</span>
-<i>Lower Brushes</i>. When the Lower Brush station is reading one card, the
-Upper Brush station is reading the next card. The tabulator also has
-another channel, which is for endless paper (and sometimes separate
-sheets or cards). This channel has one station; here printing takes
-place. Unlike the typewriter, the tabulator prints a whole row at a
-time. It can print up to 88 numerals or letters across the sheet in
-one stroke. The cards flowing through the card channel and the paper
-flowing through the paper channel do not have to move in step; in fact,
-we need many different time relations between them, and the number of
-rows printed on the paper may have almost any relation to the number of
-punch cards flowing through the card channel.</p>
-
-<p>At the station where paper is printed, we can put on the machine
-a mechanism called the <i>automatic carriage</i>. This is like a
-typewriter carriage, which holds the paper for a typewriter, but we
-can control the movement of paper through the automatic carriage by
-plugboard wiring, switch settings, and holes in punch cards. Thus we
-can arrange for headings, spacing, and feeding of new sheets to be
-controlled by the information and the instructions, with a great deal
-of versatility.</p>
-
-<h3>HANDLING INFORMATION</h3>
-
-<p>We have now described briefly the chief available punch-card machines
-as of the middle of 1948. The next question is: How do we actually get
-something done by means of punch cards? Let us go back to the census
-example, even though it may not be a very typical example, and see what
-would be done if we wished to compile a census by punch cards.</p>
-
-<p>The first thing we do is plan which columns of the punch card will
-contain what information about the people being counted. For example,
-the following might be part of the plan:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdl"><span class="smcap">Information</span></th>
-      <th class="tdl"><span class="smcap">No. of Possibilities</span></th>
-      <th class="tdl"><span class="smcap">&nbsp;&nbsp;Columns</span></th>
-  </tr>
-  </thead>
-  <tbody><tr>
-      <td class="tdl">State</td>
-      <td class="tdr">60<span class="ws2">&nbsp;</span></td>
-      <td class="tdc">1-2</td>
-   </tr><tr>
-      <td class="tdl">County</td>
-      <td class="tdr">1,000<span class="ws2">&nbsp;</span></td>
-      <td class="tdc">3-5</td>
-   </tr><tr>
-      <td class="tdl">Township</td>
-      <td class="tdr">10,000<span class="ws2">&nbsp;</span></td>
-      <td class="tdc">6-9</td>
-   </tr><tr>
-      <td class="tdl">City or village</td>
-      <td class="tdr">10,000<span class="ws2">&nbsp;</span></td>
-      <td class="tdc">10-13</td>
-   </tr><tr>
-      <td class="tdl">Sex</td>
-      <td class="tdr">2<span class="ws2">&nbsp;</span></td>
-      <td class="tdc">14</td>
-   </tr><tr>
-      <td class="tdl">Age last birthday</td>
-      <td class="tdr">100<span class="ws2">&nbsp;</span></td>
-      <td class="tdc">15-16</td>
-   </tr><tr>
-      <td class="tdl">Occupation</td>
-      <td class="tdr">100,000<span class="ws2">&nbsp;</span></td>
-      <td class="tdc">17-21</td>
-   </tr><tr>
-      <td class="tdl">...</td>
-      <td class="tdr">...<span class="ws3">&nbsp;</span></td>
-      <td class="tdc">...</td>
-   </tr>
- </tbody>
-</table>
-
-<p><span class="pagenum" id="Page_54">[Pg 54]</span>
-Under the heading state, we know that there are 48 states, the District
-of Columbia, and several territories and possessions—all told, perhaps
-60 possibilities. So, 2 punch-card columns are enough: they will allow
-100 different sets of punches from 00 to 99 to be put in them. We then
-assign the <i>code</i> 00 to Maine, 01 to New Hampshire, 02 to Vermont,
-etc., or we might assign the code 00 to Alabama, 01 to Arizona, 02
-to Arkansas, etc.—whichever would be more useful. Under the other
-headings, we do the same thing: count the possibilities; assign codes.
-In this case, it will be reasonable to use numeric codes 0 to 9 in each
-column in all places because we shall have millions of cards to deal
-with and numeric codes can be sorted faster than alphabetic codes.
-Alphabetic codes require 2 punched holes in each column, and sorting
-any column takes 2 operations.</p>
-
-<p>The punch cards are printed with the chosen headings. We set up
-the codes in charts and give them to clerks. Using key punches and
-verifiers, they punch up the cards and check them. They work from the
-original information collected by the census-taker in the field. Since
-the original information will come in geographically, probably only one
-geographic code at a time will be needed, and it will be simple to keep
-track of. As to occupation, however, it may be useful to assign other
-clerks full-time to examining the original information and specifying
-the right code for the occupation. Then the clerks who do the punching
-will have only copying to do.</p>
-
-<p>The great bulk of the work with the census will be sorting, counting,
-and totaling. The original punch cards will be summarized into larger
-and larger groups. For example, the cards for all males age 23 last
-birthday living in the state of Massachusetts are sorted together. This
-group of cards may be put into a tabulator wired to a summary punch.
-When the tabulator has counted the last card of this group, the summary
-punch punches one card, showing the total number in this group. Some
-time later a card like this will be ready for every state. Then the
-whole group of state cards may be fed into the tabulator wired to the
-reproducer acting as summary punch. When totaled, the number of males
-age 23 last birthday in the United States will be punched into a single
-card. After more compiling, a card like this will be ready for all
-<span class="pagenum" id="Page_55">[Pg 55]</span>
-males in the United States at each age. Then this group of cards may
-be fed into the tabulator wired to the summary punch. Each card may
-be listed by the tabulator on the paper flowing through it, showing
-the age and the number of males living at that age. At the end of the
-listing, the tabulator will print the total number of all males in the
-list, and the summary punch will punch a card containing this total.</p>
-
-<h3>ARITHMETICAL OPERATIONS</h3>
-
-<p>Punch-card machines can perform the arithmetical operations of
-counting, adding, subtracting, multiplying, dividing, and rounding off.</p>
-
-<h4>Counting</h4>
-
-<p>Counting can be done by the sorter, the tabulator, and the collator.
-The tabulator can print the total count. The tabulator and summary
-punch wired together can put the total count automatically into another
-punch card. The sorter shows the count in dials.</p>
-
-<h4>Adding and Subtracting</h4>
-
-<p>Adding and subtracting can be done by the tabulator, the calculating
-punch, and the multiplying punch. In the calculating and multiplying
-punches, the sum or difference is usually punched into the same card
-from which the numbers were first obtained. The tabulator, however,
-obtains the result first in a counter; from the counter, it can be
-printed on paper or punched into a blank card with the aid of the
-summary punch.</p>
-
-<p>Numbers are handled as groups of decimal digits, and the machines
-mirror the properties of digits in the decimal system. Negative numbers
-are usually handled as <i>complements</i> (<a href="#SUPPL_2">see Supplement 2</a>).
-For example, if we have in the tabulator a counter with a capacity of six
-digits, the number-000013 is stored in the counter as the complement
-999987. We cannot store in the counter the number +999987, since we
-cannot distinguish it from-000013. In other words, if a counter is
-to be used for both positive and negative numbers, its capacity is
-actually one digit less, since in the last decimal place on the left 0
-will mean positive and 9 will mean negative.
-<span class="pagenum" id="Page_56">[Pg 56]</span></p>
-
-<h4>Multiplying and Dividing</h4>
-
-<p>Multiplying is done in the calculating and multiplying punches. In
-both cases, the multiplication table is built into the circuits
-of the machine, and the system of <i>left-hand components</i> and
-<i>right-hand components</i> is used (<a href="#SUPPL_2">see Supplement 2</a>).</p>
-
-<p>Dividing is done in the calculating punch and is carried out in that
-machine much as in ordinary arithmetic. By means of an estimating
-circuit the calculating punch guesses what multiple of the divisor will
-go into the dividend. Then it determines that multiple and tries it.</p>
-
-<h4>Rounding Off</h4>
-
-<p>Rounding off may be done in 3 punch-card machines, the calculating
-and multiplying punches, and the tabulator. For example, suppose we
-have the numbers 49.1476, 68.5327, and we wish to round them off to
-2 decimal places. The results will be 49.15 and 68.53. For the first
-number, we raise the .0076, turning .1476 into .15, since .0076 is more
-than .005. For the second number, we drop the .0027 since it is less
-than .005.</p>
-
-<p>Each of these punch-card machines provides what is called a <i>5
-impulse</i> in each machine cycle. When the number is to be rounded
-off, the 5 impulse is plugged into the first decimal place that is to
-be dropped, and it is there added. If the figure in the decimal place
-to be dropped is 0 to 4, the added 5 makes no difference in the last
-decimal place that is to be kept. But, if the figure in the decimal
-place to be dropped is 5 to 9, then the added 5 makes a carry into the
-last decimal place that is to be kept, increasing it by 1, and this is
-just what is wanted for rounding off.</p>
-
-<h3>LOGICAL OPERATIONS</h3>
-
-<p>Punch-card machines do many operations of reasoning or logic that do
-not involve addition, subtraction, multiplication, or division. Just
-as we can write equations for arithmetical operations, so we can write
-equations for these logical operations using mathematical logic (see <a href="#CHAPTER_9">Chapter 9</a>
-and <a href="#SUPPL_2">Supplement 2</a>). If any reader, however, is
-not interested in these logical equations, he should skip each paragraph that
-begins with “in the language of logic,” or a similar phrase.
-<span class="pagenum" id="Page_57">[Pg 57]</span></p>
-
-<h4>Translating</h4>
-
-<p>Reading and writing are operations perhaps not strictly of reasoning
-but of <i>translating</i> from one language to another. Basically these
-operations take in a mark in one language and give out a mark with the
-same meaning in another language. For example, the interpreter takes in
-punched holes and gives out printed marks, but the holes and the marks
-have the same meaning.</p>
-
-<p>The major part of sorting is done by a punch-card sorting machine and
-can be considered an operation of translating. In sorting a card, the
-machine takes in a mark in the form of a punched hole on a punch card
-and specifies a place bearing the same mark where the card is put. The
-remaining part of sorting is done by human beings. This part consists
-of picking up blocks of cards from the pockets of the sorter and
-putting the blocks together in the right sequence.</p>
-
-<h4>Comparing</h4>
-
-<div class="figcenter">
-  <img id="FIG_13-4" src="images/i_057.jpg" alt="" width="600" height="176" />
-  <p class="f120"><span class="smcap">Fig. 13.</span> Comparer.</p>
-</div>
-
-<p>The first operation of reasoning done by punch-card machines is
-<i>comparing</i>. For an example of comparing in the operation of the
-tabulator, let us take instructing the machine when to pick up a total
-and print it. As an illustration, suppose that we are making a table
-by state, county, and township of the number of persons counted in a
-census. Suppose that for each township we have one punch card telling
-the total number of persons. If all the cards are in sequence, then,
-whenever the county changes, we want a minor total, and, whenever the
-state changes, we want a major total. What does the machine do?</p>
-
-<p>The tabulator has a mechanism that we shall call a <i>comparer</i>
-(<a href="#FIG_13-4">Fig. 13</a>). A comparer has 2 inputs that may be
-called <i>Previous</i> and <i>Current</i> and one output that may be
-called <i>Unequal</i>. The comparer has the property of giving out an
-impulse if and only if there is a difference between the 2 inputs.
-<span class="pagenum" id="Page_58">[Pg 58]</span></p>
-
-<p>In the language of the algebra of logic (<a href="#SUPPL_2">see Supplement 2</a>
-and <a href="#CHAPTER_9">Chapter 9</a>), let the pieces of information coming into
-the comparer be <i>a</i> and <i>b</i>, and let the information coming out of the
-comparer be <i>p</i>. Then the equation of the comparer is:</p>
-
-<p class="f120"><i>p</i> = <i>T</i>(<i>a</i> ≠ <i>b</i>)</p>
-
-<p class="no-indent">where “<i>T</i> (···)” is “the truth value of ···”
-and “···” is a statement, and where the truth value is 1 if true and 0
-if false.</p>
-
-<p>In wiring the tabulator so that it can tell when to total, we use the
-comparer. We feed into it the county from the current card and the
-county from the previous card. Out of the comparer we get an impulse if
-and only if these two pieces of information are different. This is just
-what happens when the county changes. The impulse from the comparer is
-then used in further wiring of the tabulator: it makes the counter that
-is busy totaling the number of persons in the county print its total
-and then clear. In the same way, another comparer, which watches state
-instead of county, takes care of major totals when the state changes.</p>
-
-<h4>Selecting</h4>
-
-<p>The next operation of reasoning which punch-card machines can do is
-<i>selecting</i>. The tabulator, collator, interpreter, reproducer,
-and calculating punch all may contain mechanisms that can select
-information. These mechanisms are called <i>selectors</i>.</p>
-
-<p>For example, suppose that we are using the tabulator to make a table
-showing for each city the number of males and the number of females.
-In the table we shall have three columns: first, city; second, males;
-third, females. Suppose that each punch card in columns 30 to 36 shows
-the total of males or females in a city. Suppose that, if and only if
-the card is for females, it has an X punch (or 11 punch) in column 79.
-What do we want to have happen? We want the number in columns 30 to 36
-to go into the second column of the table if there is no X in column
-79, and we want it to go into the third column of the table if there is
-an X in column 79. This is just another way of saying that we want the
-number to go into the males column if it is a number of males, and into
-the females column if it is a number of females. We make this happen by
-using a selector.
-<span class="pagenum" id="Page_59">[Pg 59]</span></p>
-
-<p>A selector (<a href="#FIG_14-4">Fig. 14</a>) is a mechanism with 2 inputs
-and 2 outputs. The 2 inputs are called <i>X Pickup</i> and
-<i>Common</i>. The 2 outputs are called <i>X</i> and <i>No X</i>.
-The X Pickup, as its name implies, watches for X’s. The Common takes
-in information. What comes out of X is what goes into Common if and
-only if an X punch is picked up; otherwise nothing comes out. What
-comes out of No X is what goes into Common if and only if an X punch
-is not picked up; otherwise nothing comes out. From the point of view
-of ordering punch-card equipment, we should note that there are two
-types of selectors: <i>X selectors</i> or <i>X distributors</i>, which
-have a selecting capacity of one column—that is, one decimal digit—and
-<i>class selectors</i>, which ordinarily have a selecting capacity of
-10 columns or 10 decimal digits. But we shall disregard this difference
-here, as we have disregarded most other questions of capacity in
-multiplication, division, etc.</p>
-
-<div class="figcenter">
-  <img id="FIG_14-4" src="images/i_059.jpg" alt="" width="600" height="182" />
-  <p class="f120"><span class="smcap">Fig. 14.</span> Selector.</p>
-</div>
-
-<p>In the language of logic (see <a href="#CHAPTER_9">Chapter 9</a> and
-<a href="#SUPPL_2">Supplement 2</a>), if <i>p</i>, <i>a</i>, <i>b</i>,
-<i>c</i> are the information in X Pickup, Common, X, and No X,
-respectively, then the equations for a selector are:</p>
-
-<p class="f120"><i>b</i> = <i>a</i>·<i>p</i></p>
-
-<p class="f120"><i>c</i> = <i>a</i>·(1 - <i>p</i>)</p>
-
-<p>Returning now to the table we wish to make, we connect columns 30 to
-36 of the punch card to Common. We connect column 79 of the punch card
-to the X Pickup. We connect the output No X to the males column of the
-table. We connect the output X to the females column of the table. In
-this way we make the number in the punch card appear in either one of
-two places in the table according to whether the number counts males or
-females.</p>
-
-<p>We might mention several more properties of selectors. A selector can
-be used in the reverse way, with X Pickup, X, and No X as inputs and
-<span class="pagenum" id="Page_60">[Pg 60]</span>
-Common as output (<a href="#FIG_15-4">Fig. 15</a>). What will come out
-of Common is (1) what goes into input No X if there is no X punch in
-the column to which input X Pickup is wired, and (2) what goes into
-input X if there is an X punch in the column to which input X Pickup is
-wired.</p>
-
-<p>In this case the logical equation for the selector is:</p>
-
-<p class="f120"><i>a</i> = <i>bp</i> + <i>c</i>(1 - <i>p</i>)</p>
-
-<p class="no-indent">Also, selectors can be used one after another,
-so that selecting based on 2 or 3 X punches can be made.</p>
-
-<div class="figcenter">
-  <img id="FIG_15-4" src="images/i_060a.jpg" alt="" width="600" height="214" />
-  <p class="f120"><span class="smcap">Fig. 15.</span> Selector.</p>
-</div>
-
-<p>In the language of logic, if <i>p</i>, <i>q</i>, <i>r</i> are the truth
-values of “there is an X punch in column <i>i</i>, <i>j</i>, <i>k</i>,”
-respectively, then by means of selectors we can get such a function as:</p>
-
-<p class="f120"><i>c</i> = <i>apq</i> + <i>b</i>(1 - <i>q</i>)(1 - <i>r</i>)</p>
-
-<p>Also, a selector may often be energized not only by an X punch but
-also by a punch 0, 1, 2, ···, 9 and 12. In this case, the selector is
-equipped with an additional input that can respond to any digit. This
-input is called the Digit Pickup.</p>
-
-<h4>Digit Selector</h4>
-
-<p>Something like an ordinary selector is another mechanism called a
-<i>digit selector</i> (<a href="#FIG_16-4">Fig. 16</a>). This has one input,
-Common, and 12 outputs, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12. This
-mechanism is often included in the tabulator and may be included in
-other punch-card machines. For example, suppose that we want to do
-something if and only if column 62 of a punch card contains a 3 or a 4
-or a 9. Then we connect a brush that reads column 62 of the punch card
-to the Common input of the digit selector. And we connect out from the
-digit selector jointly from outputs 3, 4, and 9.</p>
-
-<div class="figcenter">
-  <img id="FIG_16-4" src="images/i_060b.jpg" alt="" width="600" height="332" />
-  <p class="f120"><span class="smcap">Fig. 16.</span> Digit selector.</p>
-</div>
-
-<p><span class="pagenum" id="Page_61">[Pg 61]</span>
-In the language of logic, if <i>a</i> is the digit going into Common,
-and if <i>p</i> is the impulse coming out of the digit selector, then
-the equation of the mechanism in this case is:</p>
-
-<p class="f120"><i>p</i> = <i>T</i>(<i>a</i> = 3, 4, 9)</p>
-
-<h4>Sequencer</h4>
-
-<p>A fourth operation of reasoning done by punch-card machines is
-finding that one number is greater than, or equal to, or less than
-another. This operation is done in the collator and may be called
-<i>sequencing</i>. For example, suppose that we have a file of punch
-cards for cities, showing in columns 41 to 48 the number of people.
-Suppose that we wish to pick out the cards for cities over 125,000 in
-population. Now the collator has a mechanism that has 2 inputs and
-3 outputs (<a href="#FIG_17-4">Fig. 17</a>). We may call this mechanism
-a <i>sequencer</i>, since it can tell the sequence of two numbers.
-What goes into the <i>Primary</i> input is a number: let us call it
-<i>a</i>. What goes into <i>Secondary</i> is another number: let
-us call it <i>b</i>. An impulse comes out of <i>Low Primary</i> if
-<i>a</i> is less than <i>b</i>. An impulse comes out of <i>Equal</i> if
-<i>a</i> equals <i>b</i>. An impulse comes out of <i>Low Secondary</i>
-if <i>a</i> is greater than <i>b</i>.</p>
-
-<div class="figcenter">
-  <img id="FIG_17-4" src="images/i_061.jpg" alt="" width="600" height="187" />
-  <p class="f120"><span class="smcap">Fig. 17.</span> Sequencer.</p>
-</div>
-
-<p>In the language of logic, if <i>p</i>, <i>q</i>, <i>r</i> are the three
-indications in Low Primary, Equal, and Low Secondary, then:</p>
-
-<p class="f120"><i>p</i> = <i>T</i>(<i>a</i> &lt; <i>b</i>)</p>
-
-<p class="f120"><i>q</i> = <i>T</i>(<i>a</i> = <i>b</i>)</p>
-
-<p class="f120"><i>r</i> = <i>T</i>(<i>a</i> &gt; <i>b</i>)</p>
-
-<p>Returning to our example, we punch up a card with 125,000 in columns 43
-to 48, and we put this card into the Secondary Feed. We take the punch
-cards for cities and put them into the Primary Feed. In the plugboard,
-<span class="pagenum" id="Page_62">[Pg 62]</span>
-we connect the hubs of the Secondary Brushes (that read the card in
-the Secondary Feed), columns 43 to 48, to the Secondary input of the
-Sequencer. We connect the hubs of the Primary Brushes (that read the
-card in the Primary Feed), columns 41 to 48, to the Primary input of
-the Sequencer. Then we connect the Low Primary output of the Sequencer
-to a device that causes the city card being examined to fall into
-pocket 1. We connect Equal output and Low Secondary output to a device
-that causes the city card being examined to fall into pocket 2. Then,
-when the card for any city comes along, the machine compares the number
-of people in the city with 125,000. If the number is greater than
-125,000, the card will fall into pocket 1; otherwise the card will fall
-into pocket 2. At the end of the run, we shall find in pocket 1 all the
-cards we want.</p>
-
-<h3>NEW DEVELOPMENTS</h3>
-
-<p>We may expect to see over the next few years major developments in
-punch-card machinery. It would seem likely that types of punch-card
-machines like the following might be constructed:</p>
-
-<div class="blockquot">
-<p class="neg-indent">A punch-card machine that performs any
-arithmetical or logical operation at high speed and may perform a dozen
-such operations in sequence during the time that a punch card passes
-through the machine.</p>
-
-<p class="neg-indent">A punch-card machine that uses loops of punched
-paper tape, which express either a sequence of values in a table that
-the machine can consult or a sequence of instructions that govern the
-operations of the machine.</p>
-
-<p class="neg-indent">Punch-card machinery that uses a larger card than
-the 80-column card.</p>
-
-<p class="neg-indent">A punch-card machine that may have a fairly large
-amount of internal memory, perhaps 30 or 40 registers where numbers or
-words may be stored and referred to.</p>
-</div>
-
-<h4>SPEED</h4>
-
-<p>The speed of various operations with present IBM punch-card machines is
-about as shown in the table.
-<span class="pagenum" id="Page_63">[Pg 63]</span></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdl bb"><span class="smcap">Machine</span></th>
-      <th class="tdl_ws1 bb"><span class="smcap">&nbsp;&emsp;Operation</span></th>
-      <th class="tdl bb"><span class="smcap">Time in Seconds</span></th>
-  </tr>
-  </thead>
-  <tbody><tr>
-      <td class="tdl">Key punch</td>
-      <td class="tdl_ws1">Punch 80 columns</td>
-      <td class="tdc">About 20 to 40</td>
-   </tr><tr>
-      <td class="tdl">Verifier</td>
-      <td class="tdl_ws1">Check 80 columns</td>
-      <td class="tdc">About 20 to 40</td>
-   </tr><tr>
-      <td class="tdl">Sorter</td>
-      <td class="tdl_ws1">Sort 1 card on 1 column</td>
-      <td class="tdc">&#8199;0.15</td>
-   </tr><tr>
-      <td class="tdl">Interpreter</td>
-      <td class="tdl_ws1">Print 1 line</td>
-      <td class="tdc">0.8</td>
-   </tr><tr>
-      <td class="tdl">Reproducer</td>
-      <td class="tdl_ws1">Reproduce a card, all 80 columns</td>
-      <td class="tdc">0.6</td>
-   </tr><tr>
-      <td class="tdl">Collator</td>
-      <td class="tdl_ws1">Merge 2 cards</td>
-      <td class="tdc">&#8199;0.25</td>
-   </tr><tr>
-      <td class="tdl">Multiplying punch</td>
-      <td class="tdl_ws1">Multiply by 8 digits</td>
-      <td class="tdc">5.6</td>
-   </tr><tr>
-      <td class="tdl">Calculating punch</td>
-      <td class="tdl_ws1">Add</td>
-      <td class="tdc">0.3</td>
-   </tr><tr>
-      <td class="tdl">Calculating punch</td>
-      <td class="tdl_ws1">Multiply by 8 digits</td>
-      <td class="tdc">3.6</td>
-   </tr><tr>
-      <td class="tdl">Calculating punch</td>
-      <td class="tdl_ws1">Divide, obtaining 8 quotient digits</td>
-      <td class="tdc">9.0</td>
-   </tr><tr>
-      <td class="tdl">Tabulator</td>
-      <td class="tdl_ws1">Print 1 line, numbers only</td>
-      <td class="tdc">0.4</td>
-   </tr><tr>
-      <td class="tdl">Tabulator</td>
-      <td class="tdl_ws1">Print 1 line, letters included</td>
-      <td class="tdc">&#8199;0.75</td>
-   </tr><tr>
-      <td class="tdl">Tabulator</td>
-      <td class="tdl_ws1">Add numbers from 1 card</td>
-      <td class="tdc">0.4</td>
-   </tr>
- </tbody>
-</table>
-
-<h4>COST</h4>
-
-<p>Punch-card machines may be either rented or purchased from some
-manufacturers but only rented from others. If we take the cost of a
-clerk as $120 to $150 a month, the monthly rent of most punch-card
-machines ranges from ⅒ of the cost of a clerk for the simplest type
-of machine, such as a key punch, to 3 times the cost of a clerk for a
-complicated and versatile type of machine, such as a tabulator with
-many attachments. The rental basis is naturally convenient for many
-kinds of jobs.</p>
-
-<h4>RELIABILITY</h4>
-
-<p>The reliability of work with punch cards and punch-card machines is
-often much better than 99 per cent: in 10,000 operations, failures
-should be less than 2 or 3. This is, of course, much better than with
-clerical operations.</p>
-
-<p>There are a number of causes for machine or card failures. Sometimes
-cards may be warped and may not feed into the machines properly. Or,
-the air in the room may be very dry, and static electricity may make
-the cards stick together. Or, the air may be too humid; the cards may
-swell slightly and may jam in the machine. A punch may get slightly
-out of true alignment, and punches in the cards may be slightly off. A
-relay may get dust on its contact points and, from time to time, fail
-to perform in the right way. Considerable engineering effort has been
-<span class="pagenum" id="Page_64">[Pg 64]</span>
-put into remedying these and other troubles, with much success.</p>
-
-<p>To make sure that we have correct results from human beings working
-with punch-card machines, we may verify each process. Information
-that is punched on the key punch may be verified on the verifier.
-Multiplications done with multiplicand <i>a</i> and multiplier
-<i>b</i> may be repeated and compared with multiplications done with
-multiplicand <i>b</i> and multiplier <i>a</i>. Cards that are sorted
-on the sorter may be put through the collator to make sure that their
-sequence is correct. It is often good to plan every operation so that
-we have a proof that the result is right.</p>
-
-<p>It is standard practice to have the machines inspected regularly in
-order to keep them operating properly. On the average, for every 50 to
-75 machines, there will be one full-time service man maintaining them
-and taking care of calls for repairs. Of course, as with any machinery,
-some service calls will be a result of the human element; for example,
-a problem may have been set up wrongly on a machine.</p>
-
-<h4>GENERAL USEFULNESS</h4>
-
-<p>Punch-card calculations are much faster and more accurate than hand
-calculations. With punch cards, work is organized so that all cases
-are handled at the same time in the same way. This process is very
-different from handling each case separately from start to finish. As
-soon as the number of cases to be handled is more than a hundred and
-each item of information is to be used five or more times, punch cards
-are likely to be advantageous, provided other factors are favorable.
-Vast quantities of information have been handled very successfully by
-punch-card machines. Over 30 scientific and engineering laboratories in
-the United States are doing computation by punch cards. Over a billion
-punch cards, in fact, are used annually in this country.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_65">[Pg 65]</span></p>
-<h2 class="nobreak" id="CHAPTER_5">Chapter 5<br />
-<span class="h_subtitle">MEASURING:<br />
-MASSACHUSETTS INSTITUTE OF TECHNOLOGY’S<br />
-DIFFERENTIAL ANALYZER NO. 2</span></h2>
-</div>
-
-<p>In the previous chapter we talked about machines that move information
-expressed as holes in cards. In this chapter we shall talk about
-machines that move information expressed as measurements.</p>
-
-<h3>ANALOGUE MACHINES</h3>
-
-<p>A simple example of a device that uses a measurement to handle
-information is a doorpost. Here the height of a child may be marked
-from year to year as he grows (<a href="#FIG_1-5">Fig. 1</a>). Or,
-suppose that we have a globe of the world and wish to find the shortest
-path between Chicago and Moscow. We may lay a piece of string on the
-globe, pull it tight between those points, and then measure the string
-on a scale to see about what distance it shows (<a href="#FIG_2-5">Fig. 2</a>).</p>
-
-<p>Machines that handle information as measurements of physical quantities
-are called <i>analogue</i> machines, because the measurement is
-<i>analogous</i> to, or like, the information. A common example of
-analogue machine is the <i>slide rule</i>. With this we calculate by
-noting the positions of ruled lines on strips that slide by each other.
-These strips are made of fine wood, or of plastic, or of steel, in such
-fashion that the ruled lines will hold true positions and not warp. If
-we space the rulings so that 1, 2, 3, 4, 5, 6 ··· are equally spaced,
-then the slide rule is useful for addition (<a href="#FIG_3-5">Fig. 3</a>).
-But if we space the rulings so that <i>powers</i> (for example,
-powers of two—1, 2, 4, 8, 16, 32 ···) (<a href="#FIG_4-5">Fig. 4</a>)
-are equally spaced, we can do multiplication. The spacings are then
-according to the <i>logarithms</i> of numbers (<a href="#SUPPL_2">see Supplement 2</a>).
-Multiplication is more troublesome than addition, and so more slide
-rules are made for multiplication than for addition.
-<span class="pagenum" id="Page_66">[Pg 66]</span></p>
-
-<div class="figcenter">
-  <img id="FIG_1-5" src="images/i_066a.jpg" alt="" width="400" height="473" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 1.</span> Measurement by doorpost.</p>
-  <img id="FIG_2-5" src="images/i_066b.jpg" alt="" width="400" height="365" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 2.</span> Measurement by string.</p>
-</div>
-
-<p><span class="pagenum" id="Page_67">[Pg 67]</span></p>
-
-<div class="figcenter">
-  <img id="FIG_3-5" src="images/i_067a.jpg" alt="" width="600" height="267" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 3.</span> Slide Rule for adding.</p>
-  <img id="FIG_4-5" src="images/i_067b.jpg" alt="" width="600" height="288" />
-  <p class="f120"><span class="smcap">Fig. 4.</span> Slide Rule for multiplying.</p>
-</div>
-
-<p>During World War II, the aiming and firing of guns against hostile
-planes was done by machine. After sighting a plane, these machines
-automatically calculated how to direct fire against it. They were much
-better and faster than any man. These <i>fire-control instruments</i>
-were analogue machines with steel and electrical parts built to fine
-tolerances. With care we can get accuracy of 1 part in 10,000 with
-analogue machines, but greater accuracy is very hard to get.</p>
-
-<h3>PHYSICAL QUANTITIES</h3>
-
-<p>Suppose that we wish to make an analogue machine. We need to represent
-information by a measurement of something. What should we select? What
-<span class="pagenum" id="Page_68">[Pg 68]</span>
-physical thing to be measured should we choose to put into the machine?
-Different amounts of this <i>physical quantity</i> will match with
-different amounts of the measurement being expressed. In the case of
-the doorpost, the string, and the slide rule, the physical quantity is
-distance. In many fire-control instruments, the physical quantity is
-the <i>amount of turning of a shaft</i> (<a href="#FIG_5-5">Fig. 5</a>).
-Many other physical quantities have from time to time been used in
-analogue machines, such as electrical measurements. The speedometer
-of an automobile tells distance traveled and speed. It is an analogue
-machine. It uses the amount of turning of a wheel, and some electrical
-properties. It handles information by means of measurements. The basic
-physical quantity that it measures is the amount of turning of a
-shaft.</p>
-
-<div class="figcenter">
-  <img id="FIG_5-5" src="images/i_068.jpg" alt="" width="400" height="196" />
-  <p class="f120"><span class="smcap">Fig. 5.</span> Measurement by amount
-                  of turning of a shaft.</p>
-</div>
-
-<h3>DIFFERENTIAL ANALYZER</h3>
-
-<p>The biggest and cleverest mechanical brain of the analogue type which
-has yet been built is the <i>differential analyzer</i> finished in
-1942 at Massachusetts Institute of Technology in Cambridge, Mass. The
-fundamental physical quantity used in this machine is the amount of
-turning of a shaft. The name <i>analyzer</i> means an apparatus or
-machine for analyzing or solving problems. It happens that the word
-“analyzer” has been used rather more often in connection with analogue
-machines, and so in many cases the word “analyzer” carries the meaning
-“analogue” as well. The word “differential” in the phrase “differential
-analyzer” refers to the main purpose of the machine: it is specially
-adapted for solving problems involving <i>differential equations</i>.
-Now what is a differential equation?</p>
-
-<h3>DIFFERENTIAL EQUATIONS</h3>
-
-<p>In order to explain what a differential equation is, we need to use
-certain ideas. These ideas are: <i>equation</i>; <i>formula</i>;
-<i>function</i>; <i>rate of change</i>; <i>interval</i>;
-<span class="pagenum" id="Page_69">[Pg 69]</span>
-<i>derivative</i>; and <i>integral</i>. In the next few paragraphs,
-we shall introduce these ideas briefly, with some explanation and
-examples. It is entirely possible for anyone to understand these ideas
-rather easily, by collecting true statements about them; no one should
-feel that because these ideas may be new they cannot be understood readily.</p>
-
-<h3>PHYSICAL PROBLEMS</h3>
-
-<p>In physics, chemistry, mechanics, and other sciences there are many
-problems in which the behavior of distance, of time, of speed, heat,
-volume, electrical current, weight, acceleration, pressure, and many
-other <i>physical quantities</i> are related to each other. Examples of
-such problems are:</p>
-
-<div class="figcenter">
-  <img id="FIG_6-5" src="images/i_069.jpg" alt="" width="600" height="366" />
-  <p class="f120"><span class="smcap">Fig. 6.</span> Paths of a shot from a gun, trajectories.</p>
-</div>
-
-<div class="blockquot">
-<p>What are the various angles to which a gun should be raised in order
-that it may shoot various distances? (<a href="#FIG_6-5">See Fig. 6.</a>)
-(The paths of a shot from a gun are called <i>trajectories</i>.)</p>
-
-<p>If a plane flies in a direction always at the same angle from the
-north, how much farther will it travel than if it flew along the
-shortest path? (<a href="#FIG_7-5">See Fig. 7.</a>) (A path always at
-the same angle from the north is called a <i>loxodrome</i>, and a
-shortest path on a globe is called a <i>great circle</i>.)</p>
-
-<p>How should an engine be designed so that it will have the least
-vibration when it moves fast?</p>
-</div>
-
-<p><span class="pagenum" id="Page_70">[Pg 70]</span>
-In <i>physical problems</i> like these, the answer is not a single
-number but a <i>formula</i>. What we want to do in any one of these
-problems is find a formula so that any one of the quantities may be
-calculated, given the behavior of the others. For example, here is a
-familiar problem in which the answer is a formula and not a number:</p>
-
-<div class="figcontainer">
-  <div class="figsub">
-   <img id="FIG_7-5" src="images/i_070a.jpg" alt="" width="300" height="359" />
-   <p class="center"><span class="smcap">Fig. 7.</span> Paths of a flight.</p>
-  </div>
-  <div class="figsub">
-   <p class="space-below3">&nbsp;</p>
-   <img id="FIG_8-5" src="images/i_070b.jpg" alt="" width="300" height="195" />
-   <p class="center space-above2"><span class="smcap">Fig. 8.</span> Room formulas.</p>
-   </div>
-</div>
-
-<p>How are the floor area of a room, its length,
-and its width related to each other? (<a href="#FIG_8-5">See Fig. 8.</a>)</p>
-
-<p>The answer is told in any one of three <i>equations</i>:</p>
-
-<div class="blockquot">
-<p>(<i>floor area</i>) <span class="smcap">equals</span> (<i>length</i>)
-<span class="smcap">times</span> (<i>width</i>)</p>
-
-<p>(<i>length</i>) <span class="smcap">equals</span> (<i>floor area</i>)
-<span class="smcap">divided by</span> (<i>width</i>)</p>
-
-<p>(<i>width</i>) <span class="smcap">equals</span> (<i>floor area</i>)
-<span class="smcap">divided by</span> (<i>length</i>)</p>
-</div>
-
-<p>The first equation shows that the floor area depends on the length of
-the room and also on the width of the room. So we say floor area is a
-<i>function</i> of length and width. This particular function happens
-to be <i>product</i>, the result of multiplication. In other words,
-floor area is equal to the product of length and width.</p>
-
-<p>Now there is another kind of function called a <i>differential
-function</i> or <i>derivative</i>. A <i>differential function</i>
-or <i>derivative</i> is an <i>instantaneous rate of change</i>. An
-instantaneous rate of change is the result of two steps: (1) finding
-a rate of change over an <i>interval</i> and then (2) letting the
-interval become smaller and smaller indefinitely. For example, suppose
-that we have the problem:</p>
-
-<p class="blockquot">How are speed, distance, and time related to each other?</p>
-
-<p><span class="pagenum" id="Page_71">[Pg 71]</span>
-One of the answers is:</p>
-
-<p class="blockquot">(<i>speed</i>) <span class="smcap">equals the instantaneous
-rate of change of</span> (<i>distance</i>) <span class="smcap">with respect
-to</span> (<i>time</i>)</p>
-
-<p>Or we can say, and it is just the same thing in other words:</p>
-
-<p class="blockquot">(<i>speed</i>) <span class="smcap">equals the derivative
-of</span> (<i>distance</i>) <span class="smcap">with respect to</span>
-(<i>time</i>)</p>
-
-<p>Now we can tell what a differential equation is. It is simply an
-equation in which a derivative occurs, such as the last example.
-Perhaps the commonest kind of equation in physical problems is the
-differential equation.</p>
-
-<h3>SOLVING PHYSICAL PROBLEMS</h3>
-
-<p>Now we were able to change the equation about floor area into other
-forms, if we wanted to find length or width instead of floor area.
-When we did this, we ran into the <i>inverse</i> or opposite of
-multiplication: division.</p>
-
-<p>In the same way, we can change the equation about speed into other
-forms, if we want to find distance or time instead of speed. If we
-do this, we run into a new idea, the inverse or opposite of the
-derivative, called <i>integral</i>. The two new equations are:</p>
-
-<div class="blockquot">
-<p>(<i>distance</i>) <span class="smcap">equals the integral of</span> (<i>speed</i>)
-<span class="smcap">with respect to</span> (<i>time</i>)</p>
-
-<p>(<i>time</i>) <span class="smcap">equals the integral of [one divided by</span>
-(<i>speed</i>)<span class="smcap">] with respect to</span> (<i>distance</i>)</p>
-</div>
-
-<p class="no-indent">These equations may also be called differential equations.</p>
-
-<p>An integral is the result of a process called <i>integrating</i>. To
-integrate speed and get distance is the result of three steps: (1)
-breaking up an interval of time into a large number of small
-bits, (2) adding up all the small distances that we get by taking
-each bit of time and multiplying by the speed which applied in
-that bit of time, and (3) letting the bits of time get smaller and
-smaller, and letting the number of them get larger and larger, indefinitely.
-<span class="pagenum" id="Page_72">[Pg 72]</span></p>
-
-<p class="no-indent">In other words,</p>
-
-<p class="blockquot">(<i>total distance</i>) <span class="smcap">equals
-the sum of all the small</span> (<i>distances</i>),
-<span class="smcap">each equal to: a bit of</span> (<i>time</i>)
-<span class="smcap">multiplied by the</span> (<i>speed</i>)
-<span class="smcap">applying to that bit</span></p>
-
-<p class="no-indent">This is another way of saying as before,</p>
-
-<p class="blockquot">(<i>distance</i>) <span class="smcap">equals the
-integral of</span> (<i>speed</i>) <span class="smcap">with respect
-to</span> (<i>time</i>)</p>
-
-<p class="no-indent">To solve a differential equation, we almost always
-need to integrate one or more quantities.</p>
-
-<h3>ORIGIN AND DEVELOPMENT OF THE<br /> DIFFERENTIAL ANALYZER</h3>
-
-<p>For at least two centuries, solving differential equations to answer
-physical problems has been a main job for mathematicians. Mathematics
-is supposed to be logical, and perhaps you would think this would
-be easy. But mathematicians have been unable to solve a great many
-differential equations; only here and there, as if by accident, could
-they solve one. So they often wished for better methods in order to
-make the job easier.</p>
-
-<p>A British mathematician and physicist, William Thomson (Lord Kelvin),
-in 1879 suggested solving differential equations by a machine. He went
-further: he described mechanisms for integrating and other mathematical
-processes, and how these mechanisms could be connected together in a
-machine. No such machine was then built; engineering in those years
-was not equal to it. In 1923, a machine of this type for solving the
-differential equations of trajectories was proposed by L. Wainwright.</p>
-
-<p>In 1925, at Massachusetts Institute of Technology, the problem of a
-machine to solve differential equations was again being studied by Dr.
-Vannevar Bush and his associates. Dr. Bush experimented with mechanisms
-that would integrate, add, multiply, etc., and methods of connecting
-them together in a machine. A major part of the success of the machine
-depended on a device whereby a very small turning force would do a
-rather large amount of work. He developed a way in which the small
-<span class="pagenum" id="Page_73">[Pg 73]</span>
-turning force, about as small as a puff of breath, could be used to
-tighten a string around a drum already turning with a considerable
-force, and thus clutch the drum, bring in that force, and do the work
-that needed to be done. You may have watched a ship being loaded,
-seen a man coil a rope around a <i>winch</i>, and watched him swing
-a heavy load into the air by a slight pull on the rope (<a href="#FIG_9-5">Fig. 9</a>).
-If so, you have seen this same principle at work. The turning force
-(or <i>torque</i>) that pulls on the rope is greatly increased (or
-<i>amplified</i>) by such a mechanism, and so we call it a
-<i>torque amplifier</i>.</p>
-
-<div class="figcenter">
-  <img id="FIG_9-5" src="images/i_073.jpg" alt="" width="600" height="274" />
-  <p class="f120"><span class="smcap">Fig. 9.</span> Increasing turning force;<br />
-                    winch, or torque amplifier.</p>
-</div>
-
-<p>By 1930, Dr. Bush and his group had finished the first differential
-analyzer. It was entirely mechanical, having no electrical parts except
-the motors. It was so successful that a number of engineering schools
-and manufacturing businesses have since then built other machines of
-the Bush type. Each time, some improvements were made in accuracy and
-capacity for solving problems. But, if you changed from one problem
-to another on this type of machine, you had to do a lot of work with
-screwdrivers and wrenches. You had to undo old mechanical connections
-between shafts and set up new ones. Accordingly, in 1935, the men at
-MIT started designing a second differential analyzer. In this one you
-could make all the connections electrically.</p>
-
-<p>MIT finished its second differential analyzer in 1942, but the fact
-was not published during World War II, for the machine was put to work
-on important military problems. In fact, a rumor spread and was never
-denied that the machine was a white elephant and would not work. The
-machine was officially announced in October 1945. It was the most
-advanced and efficient differential analyzer ever built. We shall
-talk chiefly about it for the rest of this chapter. A good technical
-<span class="pagenum" id="Page_74">[Pg 74]</span>
-description of this machine is in a paper, “A New Type of Differential
-Analyzer,” by Vannevar Bush and Samuel H. Caldwell, published in the
-<i>Journal of the Franklin Institute</i> for October 1945.</p>
-
-<h3>GENERAL ORGANIZATION OF<br /> MIT DIFFERENTIAL ANALYZER NO. 2</h3>
-
-<p>A differential analyzer is basically made up of shafts that turn.
-When we set up the machine to solve a differential equation, we
-assign one shaft in the machine to each quantity referred to in the
-equation. It is the job of that shaft to keep track of that quantity.
-The total amount of turning of that shaft at any time while the
-problem is running measures the size of that quantity at that time.
-If the quantity decreases, the shaft turns in the opposite direction.
-For example, if we have speed, time, and distance in a differential
-equation, we label one shaft “speed,” another shaft “time,” and another
-shaft “distance.” If we wish, we may assign 10 turns of the “time”
-shaft to mean “one second,” 2 turns of the “distance” shaft to mean
-“one foot,” and 4 turns of the “speed” shaft to mean “one foot per
-second.” These are called <i>scale factors</i>. We could, however, use
-any other convenient units that we wished.</p>
-
-<p>By just looking at a shaft or a wheel, we can tell what part of a full
-turn it has made—a half, or a quarter, or some other part—but we
-cannot tell by looking how many full turns it has made. In the machine,
-therefore, there are mechanisms that record not only full turns but
-also tenths of turns. These are called <i>counters</i>. We can connect
-a counter to any shaft. When we want to know some quantity that a shaft
-and counter are keeping track of, we read the counting mechanism.</p>
-
-<p>The second differential analyzer, which MIT finished in 1942, went a
-step further than any previous one. In this machine, a varying number
-can be expressed either (1) mechanically as the amount of turning of a
-shaft, or (2) electrically as the amount of two <i>voltages</i> in a
-pair of wires. The MIT men did this by means of a mechanism called an
-<i>angle-indicator</i>.</p>
-
-<p>Angle indicators have essentially three parts: a <i>transmitter</i>,
-a <i>receiver</i>, and switches. The transmitter (<a href="#FIG_10-5">Fig. 10</a>)
-can sense the exact amount that a shaft has turned and give out a voltage in each of
-<span class="pagenum" id="Page_75">[Pg 75]</span>
-two wires which tells exactly how much the shaft has turned (<a href="#FIG_11-5">Fig. 11</a>).
-The receiving device (<a href="#FIG_12-5">Fig. 12</a>), which has a motor, can take in the
-voltages in the two wires and drive a second shaft, making it turn in
-step with the first shaft. By means of the switchboard (<a href="#FIG_13-5">Fig. 13</a>),
-the two wires from the transmitter of any angle-indicator can lead anywhere
-in the machine and be connected to the receiver of any other angle indicator.</p>
-
-<div class="figcenter">
-  <img id="FIG_10-5" src="images/i_075a.jpg" alt="" width="600" height="312" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 10.</span> Scheme of angle-indicator transmitter.</p>
-  <img id="FIG_11-5" src="images/i_075b.jpg" alt="" width="600" height="295" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 11.</span> Indication of angle.</p>
-  <img id="FIG_12-5" src="images/i_075c.jpg" alt="" width="600" height="211" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 12.</span> Scheme
-                            of angle-indicator receiver.</p>
-</div>
-
-<p>In a differential analyzer, we can connect the shafts together in many
-different ways. For example, suppose that we want one shaft <i>b</i>
-to turn twice as much as another shaft <i>a</i>. For this to happen
-we must have a mechanism that will connect shaft <i>a</i> to shaft
-<i>b</i> and make shaft <i>b</i> turn twice as much as shaft <i>a</i>.
-We can draw the scheme of this mechanism in <a href="#FIG_14-5">Fig. 14</a>:
-a box, standing for any kind of simple or complicated mechanism; a line
-going into it, standing for input of the quantity <i>a</i>; a line
-going out of it, standing for output of the quantity <i>b</i>; and a
-statement saying that <i>b</i> equals 2<i>a</i>.
-<span class="pagenum" id="Page_76">[Pg 76]</span></p>
-
-<div class="figcenter">
-  <img id="FIG_13-5" src="images/i_076a.jpg" alt="" width="600" height="291" />
-  <p class="f120"><span class="smcap">Fig. 13.</span> Switchboard.</p>
-</div>
-
-<p>One mechanism that will make shaft <i>b</i> turn twice as much as shaft
-<i>a</i> is a <i>pair of gears</i> such that: (1) they mesh together
-and (2) the gear on shaft <i>a</i> has twice as many teeth as the gear
-on shaft <i>b</i> (<a href="#FIG_15-5">Fig. 15</a>). On the mechanical
-differential analyzer that MIT finished in 1930, a pair of gears was
-the mechanism actually used for doubling. To make one shaft turn twice
-as much as another by this device, we would: go over to the machine
-with a screwdriver; pick out from a box two gears, one with twice as
-many teeth as the other; slide them onto the shafts that are to be
-connected; make the gears mesh together; and screw them tight on their
-shafts.</p>
-
-<div class="figcontainer">
-  <div class="figsub">
-   <p class="space-below3">&nbsp;</p>
-   <img id="FIG_14-5" src="images/i_076b.jpg" alt="" width="300" height="109" />
-   <p class="center space-above2"><span class="smcap">Fig. 14.</span> Scheme of a doubling<br /> mechanism.</p>
-  </div>
-  <div class="figsub">
-   <img id="FIG_15-5" src="images/i_076c.jpg" alt="" width="300" height="268" />
-   <p class="center"><span class="smcap">Fig. 15.</span> Example of a doubling<br /> mechanism.</p>
-   </div>
-</div>
-
-<p>On the MIT differential analyzer No. 2, however, we are better off. A
-much more convenient device for doubling is used. We make use of: a
-<span class="pagenum" id="Page_77">[Pg 77]</span>
-<i>gearbox</i> in whichthere are two shafts that may be geared so
-that one turns twice as much as the other, and two angle-indicator
-transmitters and receivers. Looking at the drawing (<a href="#FIG_16-5">Fig. 16</a>),
-we can see that: shaft <i>a</i> drives shaft <i>c</i> to turn in step,
-shaft <i>c</i> drives shaft <i>d</i> to turn twice as much, and shaft
-<i>d</i> drives shaft <i>b</i> to turn in step. Here we can accomplish
-doubling by closing the pairs of switches that connect to the gearbox shafts.</p>
-
-<div class="figcenter">
-  <p class="f120"><b>Angle indicators: T, transmitters, and R, receivers</b></p>
-  <img id="FIG_16-5" src="images/i_077a.jpg" alt="" width="600" height="149" />
-  <p class="f120"><span class="smcap">Fig. 16.</span> Another example
-                                     of a doubling mechanism.</p>
-</div>
-
-<p>Above, we have talked about a mechanism with gears that would multiply
-the amount of turning by the <i>constant ratio</i> 2. But, of course,
-in a calculation, any ratio, say 7.65, 3.142, ···, might be needed,
-not only 2. In order to handle various constant ratios, gearboxes of
-two kinds are in differential analyzer No. 2. The first kind is a
-<i>one-digit gearbox</i>. It can be set to give any of 10 ratios, 0.1,
-0.2, 0.3, ···, 1.0. The second kind is a <i>four-digit gearbox</i>. It
-can be set to give any one of more than 11 thousand ratios, 0.0000,
-0.0001, 0.0002, ···, 1.1109, 1.1110. We can thus multiply by constant ratios.</p>
-
-<h4>Adders</h4>
-
-<p>We come now to a new mechanism, whose purpose is to add or subtract
-the amount of turning of two shafts. It is called an <i>adder</i>. The
-scheme of it is shown in <a href="#FIG_17-5">Fig. 17</a>: an input shaft
-<span class="pagenum" id="Page_78">[Pg 78]</span>
-with amount of turning <i>a</i>, another input shaft with amount of
-turning <i>b</i>, and an output shaft with amount of turning <i>a</i>
-+ <i>b</i>. The adder essentially is another kind of gearbox, called
-a <i>differential gear assembly</i>. This name is confusing: the word
-“differential” here has nothing to do with the word “differential” in
-“differential analyzer.” This mechanism is very closely related to the
-“differential” in the rear axle of a motor car, which distributes a
-driving thrust from the motor to the two rear wheels of the car.</p>
-
-<div class="figcontainer">
-  <div class="figsub">
-   <p class="space-below3">&nbsp;</p>
-   <img id="FIG_17-5" src="images/i_077b.jpg" alt="" width="300" height="125" />
-   <p class="center space-above2"><span class="smcap">Fig. 17.</span> Scheme of an adder mechanism.</p>
-  </div>
-  <div class="figsub">
-   <img id="FIG_18-5" src="images/i_078.jpg" alt="" width="300" height="356" />
-   <p class="center"><span class="smcap">Fig. 18.</span> Example of an adding mechanism<br />
-                        (differential gear assembly).</p>
-   </div>
-</div>
-
-<p>A type of differential gear assembly that will add is shown in <a href="#FIG_18-5">Fig. 18</a>.
-This is a set of 5 gears <i>A</i> to <i>E</i>. The 2 gears <i>A</i> and
-<i>B</i> are input gears. The amount of their turning is <i>a</i> and
-<i>b</i>, respectively. They both mesh with a third gear, <i>C</i>,
-free to turn, but the axis of <i>C</i> is fastened to the inside rim
-of a fourth, larger gear, <i>D</i>. Thus <i>D</i> is driven, and the
-amount of its turning is (<i>a</i> + <i>b</i>)/2. This gear meshes with
-a gear <i>E</i> with half the number of teeth, and so the amount of
-turning of <i>E</i> is <i>a</i> + <i>b</i>.</p>
-
-<p>We can subtract the turning of one shaft from the turning of another
-simply by turning one of the input shafts in the opposite direction.</p>
-
-<h4>Integrators</h4>
-
-<p>Another mechanism in a differential analyzer, and the one that makes
-it worth while to build the machine, is called an <i>integrator</i>.
-This mechanism carries out the process of integrating, of adding up a
-very large number of small changing quantities. <a href="#FIG_19-5">Figure 19</a>
-shows what an integrator is. It has three chief parts: a <i>disc</i>,
-a little <i>wheel</i>, and a <i>screw</i>. The round disc turns
-horizontally on its vertical shaft. The wheel rests on the disc and
-turns vertically on its horizontal shaft. The screw goes through the
-<span class="pagenum" id="Page_79">[Pg 79]</span>
-support of the disc; when the screw turns, it changes the distance
-between the edge of the wheel and the center of the disc.</p>
-
-<div class="figcenter">
-  <img id="FIG_19-5" src="images/i_079.jpg" alt="" width="600" height="350" />
-  <p class="f120"><span class="smcap">Fig. 19.</span> Mechanism of integrator.</p>
-</div>
-
-<p>Now let us watch this mechanism move. If the disc turns a little bit,
-the wheel pressing on it must turn a little bit. If the screw turns a
-small amount, the distance between the edge of the wheel and the center
-of the disc changes. The amount that the wheel turns is doubled if its
-distance from the center of the disc is doubled, and halved if that
-distance is halved. So we see that:</p>
-
-<div class="blockquot">
-<p class="neg-indent">(<i>the total amount that the wheel turns</i>)
-<span class="smcap">equals the sum of all the small</span> (<i>amounts
-of turning</i>), <span class="smcap">each equal to: a bit of</span>
-(<i>disc turning</i>) <span class="smcap">multiplied by the</span>
-(<i>distance from the center of the disc to the edge of the
-wheel</i>) <span class="smcap">applying to that bit</span></p>
-</div>
-
-<p class="no-indent">If we look back at our discussion of integrating
-(<a href="#Page_72">p. 72</a>), we see that the capital words here
-are just the same as those used there. Thus we have a mechanism that
-expresses integration:</p>
-
-<div class="blockquot">
-<p class="neg-indent">(<i>the total amount that the wheel turns</i>)
-<span class="smcap">equals the integral of</span> (<i>the distance
-from the center of the disc to the wheel</i>) <span class="smcap">with
-respect to</span> (<i>the amount that the disc turns</i>)</p>
-</div>
-
-<p class="no-indent">The scheme of this mechanism is shown in <a href="#FIG_20-5">Fig. 20</a>.</p>
-
-<p>For example, suppose that the screw measures the speed at which a car
-<span class="pagenum" id="Page_80">[Pg 80]</span>
-travels and that the disc measures time. The wheel, consequently, will
-measure distance traveled by the car. The mechanism <span class="smcap">integrates</span>
-speed with respect to time and gives distance.</p>
-
-<div class="figcenter">
-  <img id="FIG_20-5" src="images/i_080a.jpg" alt="" width="600" height="237" />
-  <p class="f120"><span class="smcap">Fig. 20.</span> Scheme of integrator.</p>
-</div>
-
-<p>This mechanism is the device that Lord Kelvin talked about in 1879 and
-that Dr. Bush made practical in 1925. The mechanical difficulty is to
-make the friction between the disc and the wheel turn the wheel with
-enough force to do other work. In the second differential analyzer, the
-angle indicator set on the shaft of the wheel solves the problem very neatly.</p>
-
-<div class="figcenter">
-  <img id="FIG_21-5" src="images/i_080b.jpg" alt="" width="600" height="279" />
-  <p class="f120"><span class="smcap">Fig. 21.</span> Graph of air resistance coefficient.</p>
-</div>
-
-<h4>Function Tables</h4>
-
-<p>The behavior of some physical quantities can be described only
-by a series of numbers or a graphic curve. For example, the
-<i>resistance</i> or <i>drag</i> of the air against a passing object is
-related to the speed of the object in a rather complicated way. Part
-of the relation is called the <i>drag coefficient</i> or <i>resistance
-coefficient</i>; a rough graph of this is shown in <a href="#FIG_21-5">Fig. 21</a>.
-This graph shows several interesting facts: (1) when the object is
-still, there is no air resistance; (2) as it travels faster and faster,
-air resistance rapidly increases; (3) when the object travels with the
-<span class="pagenum" id="Page_81">[Pg 81]</span>
-speed of sound, resistance is very great and increases enormously;
-(4) but, when the object starts traveling with a speed about 20 per
-cent faster than sound, the drag coefficient begins to decrease. This
-drawing or <i>graph</i> shows in part how air resistance depends on
-speed of object; in other words, it shows the drag coefficient as a
-<i>function</i> of speed (<a href="#SUPPL_2">see Supplement 2</a>).</p>
-
-<div class="figcenter">
-  <img id="FIG_22-5" src="images/i_081.jpg" alt="" width="600" height="299" />
-  <p class="f120"><span class="smcap">Fig. 22.</span> Pointer following graph.</p>
-</div>
-
-<p>Now we need a way of putting any function we wish into a differential
-analyzer. To do this, we use a mechanism called a <i>function
-table</i>. We draw a careful graph of the function according to the
-scale we wish to use, and we set the graph on the outside of a large
-drum (<a href="#FIG_22-5">Fig. 22</a>). For example, we can put the
-resistance coefficient graph on the drum; the speed (or <i>independent
-variable</i>) goes around the drum, and the resistance coefficient (or
-<i>dependent variable</i>) goes along the drum. The machine slowly
-turns the drum, as may be called for by the problem. A girl sits at the
-function table and watches, turning a handwheel that keeps the sighting
-circle of a pointer right over the graph. The turning of the handwheel
-puts the graphed function into the machine. Instead of employing a
-person, we can make one side of the graph black, leaving the other side
-white, and put in a <i>phototube</i> (an electronic tube sensitive to
-amount of light) that will steer from pure black or pure white to half
-and half (<a href="#FIG_23-5">see Fig. 23</a>).</p>
-
-<p>We do not need many function tables to put in information, because we
-can often use integrators in neat combinations to avoid them. We shall
-say more about this possibility later.</p>
-
-<p>We can also use a function table to put out information and to draw a
-graph. To do so, we disconnect the handwheel; we connect the shaft of
-<span class="pagenum" id="Page_82">[Pg 82]</span>
-the handwheel to the shaft that records the function we are interested
-in; we take out the pointer and put in a pen; and we put a blank sheet
-of graph paper around the drum.</p>
-
-<div class="figcenter">
-  <img id="FIG_23-5" src="images/i_082.jpg" alt="" width="600" height="298" />
-  <p class="f120"><span class="smcap">Fig. 23.</span> Phototube following graph.</p>
-</div>
-
-<p>We have now described the main parts of the second MIT differential
-analyzer. They are the parts that handle numbers. We can now tell the
-capacity of the differential analyzer by telling the number of main
-parts that it holds:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdl">Shafts</td>
-      <td class="tdr">&nbsp;&emsp;About 130</td>
-   </tr><tr>
-      <td class="tdl">One-digit gearboxes</td>
-      <td class="tdr">12</td>
-   </tr><tr>
-      <td class="tdl">Four-digit gearboxes</td>
-      <td class="tdr">16</td>
-   </tr><tr>
-      <td class="tdl">Adders</td>
-      <td class="tdr">About  16</td>
-   </tr><tr>
-      <td class="tdl">Integrators</td>
-      <td class="tdr">18</td>
-   </tr><tr>
-      <td class="tdl">Function tables</td>
-      <td class="tdr">3</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">On a simpler level, we can say that the machine holds
-these physical parts:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdl">Miles of wire</td>
-      <td class="tdr">About  200</td>
-   </tr><tr>
-      <td class="tdl">Relays</td>
-      <td class="tdr">About  3000</td>
-   </tr><tr>
-      <td class="tdl">Motors</td>
-      <td class="tdr">About  150</td>
-   </tr><tr>
-      <td class="tdl">Electronic tubes</td>
-      <td class="tdr">&nbsp;&emsp;About  2000</td>
-   </tr>
- </tbody>
-</table>
-
-<h3>INSTRUCTING THE MIT<br />DIFFERENTIAL ANALYZER NO. 2</h3>
-
-<p>Besides the function tables for putting information into the machine,
-there are three mechanisms that read punched paper tape. The three
-tapes are called the <i>A tape</i>, the <i>B tape</i>, and the <i>C
-tape</i>. From these tapes the machine is set up to solve a problem.</p>
-
-<p>Suppose that we have decided how the machine is to solve a problem.
-Suppose that we know the number of integrators, adders, gearboxes,
-<span class="pagenum" id="Page_83">[Pg 83]</span>
-etc., that must be used, and know how their inputs and outputs are
-to be connected. To carry out the solution, we now have to put the
-instructions and numbers into the machine.</p>
-
-<p>The <i>A</i> tape contains instructions for connecting shafts in
-the machine. Each instruction connects a certain output of one type
-of mechanism (adder, etc.) to a certain input of another type of
-mechanism. When the machine reads an instruction on this tape, it
-connects electrically the transmitting angle-indicator of an output
-shaft to the receiving angle-indicator of another input shaft.</p>
-
-<p>Now the connecting part of the differential analyzer behaves as if
-it were very intelligent: it assigns an adder or an integrator or a
-gearbox, etc., to a new problem only if that mechanism is not busy. For
-example, if a problem tape calls for adder 3 (in the list belonging to
-the problem), the machine will assign the first adder that is not busy,
-perhaps adder 14 (in the machine), to do the work. Each time that adder
-3 (in the problem list) is called for in the <i>A</i> tape, the machine
-remembers that adder 14 was chosen and assigns it over again. This
-ability, of course, is very useful.</p>
-
-<p>The <i>B</i> tape contains the ratios at which the gearboxes are to be
-set. For example, suppose that we want gearbox 4 (in the problem list)
-to change its input by the ratio of 0.2573. The machine, after reading
-the <i>A</i> tape, has assigned gearbox 11 (in the machine list). Then,
-when the machine reads the <i>B</i> tape, it sets the ratio in gearbox
-11 to 0.2573.</p>
-
-<p>The answer to a differential equation is different for different
-starting conditions. For example, when we know speed and time and wish
-to find distance traveled and where we have arrived, we must know the
-point at which we started. We therefore need to arrange the machine
-so that we can put in different starting conditions (or different
-<i>initial conditions</i>, as the mathematician calls them).</p>
-
-<p>The <i>C</i> tape puts the initial conditions into the machine. For
-example, reading the <i>C</i> tape for the problem, the machine finds
-that 3000 should, at the start of the problem, stand in counter 4. The
-machine then reads the number at which counter 4 actually stands, say
-6728.3. It subtracts the two numbers and remembers the difference,
-<span class="pagenum" id="Page_84">[Pg 84]</span>
--3728.3. And whenever the machine reads that counter later, finding,
-say, 9468.4 in it, first the 3728.3 is subtracted, and then the answer
-5740.1 is printed.</p>
-
-<h3>ANSWERS</h3>
-
-<p>Information may come out of the machine in either one of two ways: in
-printed numbers or in a graph. In fact, the same quantity may come out
-of the machine in both ways at the same time. To obtain a graph, we
-change a function table from input to output, put a pen on it, and have
-it draw the graph.</p>
-
-<p>The machine has 3 electric typewriters. The machine will take numerical
-information out of the counters at high speed even while they are
-turning, and it will put the information into relays. Then it will read
-from the relays into the typewriter keys one by one while they type
-from left to right across the page.</p>
-
-<h3>HOW THE DIFFERENTIAL ANALYZER CALCULATES</h3>
-
-<p>Up to this point in this chapter, the author has tried to tell the
-story of the differential analyzer in plain words. But for reading
-this section, a little knowledge of calculus is necessary.
-(<a href="#SUPPL_2">See also Supplement 2</a>.) If you wish,
-skip this section, and go on to the next one.</p>
-
-<p>We have described how varying quantities, or <i>variables</i>, are
-operated on in the machine in one way or another: adding, subtracting,
-multiplying by a constant, referring to a table, and integrating. What
-do we do if we wish to multiply 2 variables together? A neat trick is
-to use the formula:</p>
-
-<table class="fontsize_150 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdr"><i>xy</i> =</td>
-      <td class="tdl"><big>∫</big> <i>x dy</i> +</td>
-      <td class="tdl"><big>∫</big> <i>y dx</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">To multiply in this way requires 2 integrators
-and 1 adder. The connections that are made between them are as follows:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdl">Shaft <i>x</i></td>
-      <td class="tdl">To Integrator 1, Screw</td>
-   </tr><tr>
-      <td class="tdl">Shaft <i>x</i></td>
-      <td class="tdl">To Integrator 2, Disc</td>
-   </tr><tr>
-      <td class="tdl">Shaft <i>y</i></td>
-      <td class="tdl">To Integrator 1, Disc</td>
-   </tr><tr>
-      <td class="tdl">Shaft <i>y</i></td>
-      <td class="tdl">To Integrator 2, Screw</td>
-   </tr><tr>
-      <td class="tdl">Integrator 1, Wheel</td>
-      <td class="tdl">To Adder 1, Input 1</td>
-   </tr><tr>
-      <td class="tdl">Integrator 2, Wheel&emsp;&nbsp;</td>
-      <td class="tdl">To Adder 1, Input 2</td>
-   </tr><tr>
-      <td class="tdl">Adder 1, Output</td>
-      <td class="tdl">To Shaft expressing <i>xy</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent"><span class="pagenum" id="Page_85">[Pg 85]</span>
-A product of 2 variables <i>under the integral sign</i> can be obtained
-a little more easily, because of the curious powers of the differential
-analyzer. Thus, if it is desired to obtain <big><b>∫ <i>xy dt</i></b></big>,
-we can use the formula:</p>
-
-<table class="fontsize_150 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc"><img src="images/integral_single.jpg" alt="" width="40" height="81" /></td>
-      <td class="tdl"><i>xy</i> <i>dt</i> =</td>
-      <td class="tdc"><img src="images/integral_single.jpg" alt="" width="40" height="81" /></td>
-      <td class="tdl"><i>x</i> <i>d</i>&nbsp;</td>
-      <td class="tdc"><img src="images/cbl-4.jpg" alt="" width="23" height="82" /></td>
-      <td class="tdc"><img src="images/integral_single.jpg" alt="" width="40" height="81" /></td>
-      <td class="tdl"><i>y</i> <i>dt</i></td>
-      <td class="tdc"><img src="images/cbr-4.jpg" alt="" width="23" height="82" /></td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">and this operation does not require an adder.
-The connections are as follows:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdl">Shaft <i>t</i></td>
-      <td class="tdl">To Integrator 1, Disc</td>
-   </tr><tr>
-      <td class="tdl">Shaft <i>y</i></td>
-      <td class="tdl">To Integrator 1, Screw</td>
-   </tr><tr>
-      <td class="tdl">Integrator 1, Wheel</td>
-      <td class="tdl">To Integrator 2, Disc</td>
-   </tr><tr>
-      <td class="tdl">Shaft <i>x</i></td>
-      <td class="tdl">To Integrator 2, Screw</td>
-   </tr><tr>
-      <td class="tdl">Integrator 2, Wheel&emsp;&nbsp;</td>
-      <td class="tdl">To Shaft expressing <big><b>∫<i>xy dt</i></b></big></td>
-   </tr>
- </tbody>
-</table>
-
-<p>In order to get the quotient of 2 variables, <i>x</i>/<i>y</i>, we can
-use some more tricks. First, the <i>reciprocal</i> 1/<i>y</i> can be
-obtained by using the two <i>simultaneous equations</i>:</p>
-
-<table class="fontsize_150 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc" rowspan="2"><img src="images/integral_single.jpg" alt="" width="40" height="81" /></td>
-      <td class="tdl" rowspan="2">&nbsp;</td>
-      <td class="tdc bb">&nbsp;1&nbsp;</td>
-      <td class="tdl" rowspan="2">&nbsp;<i>dy</i> = log <i>y</i>,</td>
-   </tr><tr>
-      <td class="tdc"><i>y</i></td>
-   </tr><tr>
-      <td class="tdc" rowspan="2"><img src="images/integral_single.jpg" alt="" width="40" height="81" /></td>
-      <td class="tdl" rowspan="2">&nbsp;-&nbsp;</td>
-      <td class="tdc bb">&nbsp;1&nbsp;</td>
-      <td class="tdl" rowspan="2">&nbsp;<i>d</i>(log <i>y</i>) = <i>y</i></td>
-   </tr><tr>
-      <td class="tdc"><i>y</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">The connections are as follows:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdl">Shaft <i>y</i></td>
-      <td class="tdl">To Integrator 1, Disc <span class="smcap">and to</span> Integrator 2, Wheel</td>
-   </tr><tr>
-      <td class="tdl">Shaft log <i>y</i>&nbsp;</td>
-      <td class="tdl">To Integrator 1, Wheel <span class="smcap">and to</span> Integrator 2, Disc</td>
-   </tr><tr>
-      <td class="tdl">Shaft 1/<i>y</i></td>
-      <td class="tdl">To Integrator 1, Screw, <span class="smcap">and negatively to</span> Integrator 2, Screw</td>
-   </tr>
- </tbody>
-</table>
-
-<p>In order to get <i>x</i>/<i>y</i>, we can then multiply <i>x</i> by
-1/<i>y</i>. We see that this setup gives us log <i>y</i> for nothing,
-that is, without needing more integrators or other equipment. Clearly,
-other tricks like this will give sin <i>x</i>, cos <i>x</i>, <i>eˣ</i>,
-<i>x²</i>, and other functions that satisfy simple differential equations.</p>
-
-<p>An integral of a reciprocal can be obtained even more directly. Suppose
-that</p>
-
-<table class="fontsize_150 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc" rowspan="2"><i>y</i> =</td>
-      <td class="tdc" rowspan="2"><img src="images/integral_single.jpg" alt="" width="40" height="81" /></td>
-      <td class="tdc bb">&nbsp;1&nbsp;</td>
-      <td class="tdl" rowspan="2">&nbsp;<i>dt</i></td>
-   </tr><tr>
-      <td class="tdc"><i>x</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Then</p>
-
-<table class="fontsize_150 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc" rowspan="2"><i>Dₜ y</i> =&nbsp;</td>
-      <td class="tdc bb">&nbsp;1&nbsp;</td>
-      <td class="tdl" rowspan="2">&nbsp;,&emsp;<i>D<sub>y</sub></i> <i>t</i> = <i>x</i>,</td>
-   </tr><tr>
-      <td class="tdc"><i>x</i></td>
-   </tr>
- </tbody>
-</table>
-
-<table class="fontsize_150 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdl">&nbsp;<i>t</i> =&nbsp;</td>
-      <td class="tdc"><img src="images/integral_single.jpg" alt="" width="40" height="81" /></td>
-      <td class="tdc">&nbsp;<i>x</i> <i>dy</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">The connections therefore are:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdl">Shaft <i>t</i>&emsp;&nbsp;</td>
-      <td class="tdl">To Integrator, Wheel</td>
-   </tr><tr>
-      <td class="tdl">Shaft <i>x</i></td>
-      <td class="tdl">To Integrator, Screw</td>
-   </tr><tr>
-      <td class="tdl">Shaft <i>y</i></td>
-      <td class="tdl">To Integrator, Disc</td>
-   </tr>
- </tbody>
-</table>
-
-<p><span class="pagenum" id="Page_86">[Pg 86]</span>
-The light wheel then drives the heavy disc. Clearly only the
-angle-indicator device makes this possible at all. Naturally, the
-closer the wheel gets to the center of the disc, that is, <i>x</i>
-approaching zero, the greater the strain on the mechanism, and the more
-likely the result is to be off. Mathematically, of course, the limit of
-1/<i>x</i> as <i>x</i> approaches zero equals infinity, and this gives
-trouble in the machine.</p>
-
-<p>There is no standard mathematical method for solving any differential
-equation. But the machine provides a standard direct method for solving
-all differential equations with only one independent variable. First:
-assign a shaft for each <i>term</i> that appears in the equation.
-For example, the highest derivative that appears and the independent
-variable are both assigned shafts. The integral of the highest
-derivative is easily obtained, and the integral of that integral, etc.
-Second: connect the shafts so that all the mathematical relations are
-expressed. Both <i>explicit</i> and <i>implicit</i> equations may be
-expressed. Third: for any shaft there must be just one <i>drive</i>,
-or source of torque. A shaft may, however, drive more than one other
-shaft. Fourth: choose <i>scale factors</i> so that the limits of the
-machine are not exceeded yet at the same time are well used. For
-example, the most that an integrator or a function table can move
-is 1 or 2 feet. Also, the number of full turns made by a shaft in
-representing its variable should be large, often between 1000 and
-10,000.</p>
-
-<p>Of course, as with all these large machines, anyone would need some
-months of actual practice before he could put on a problem and get an
-answer efficiently.</p>
-
-<h3>AN APPRAISAL OF THE MACHINE</h3>
-
-<p>The second MIT differential analyzer is probably the best machine
-ever built for solving most differential equations. It regularly has
-an accuracy of 1 part in 10,000. This is enough for most engineering
-problems. If greater accuracy is needed, the second differential
-analyzer cannot provide it. Once in a while the machine can reach an
-accuracy of 1 part in 50,000; but, to balance this, it is sometimes
-less accurate than 1 part in 10,000.
-<span class="pagenum" id="Page_87">[Pg 87]</span></p>
-
-<p>The MIT differential analyzer No. 2 can find answers to problems very
-quickly. The time for setting up a problem to be run on the machine
-ranges from 5 to 15 minutes. The time for preparing the tapes that
-set up the problem is, of course, longer; but the punch for preparing
-the tape is a separate machine and does not delay the differential
-analyzer. The time for the machine to produce a single solution to a
-problem ranges usually from 3 minutes to a half-hour. It is easy to
-put on a problem, run a few solutions, take the problem off, study the
-results, change a few numbers, and then put the problem back on again.
-This virtue is a great help in a search in a new field. While the study
-is going on, time is not wasted, for the machine can be busy with a
-different problem.</p>
-
-<p>Running a problem a second time is a good check on the reliability of
-an answer. For, when the problem is run the second time, we can arrange
-that the machine will route the problem to other mechanisms.</p>
-
-<p>The machine has a control panel. Here the operator watching the machine
-can tell what units are doing what parts of what problems. If a unit
-gives trouble or needs to be inspected, the clerk can throw a “busy”
-switch. Then the machine cannot choose that unit for work to be done.
-The machine contains many protecting signals and alarms. It is idle for
-repairs less than 5 per cent of the time.</p>
-
-<p>It is not easy to determine the total cost of the machine, for it was
-partially financed by several large gifts. Also, much of the labor
-was done by graduate students in return for the instruction that they
-gained. The actual out-of-pocket cost was about $125,000. If the
-machine were to be built by industry, the cost would likely be more
-than 4 times as much. A simple differential analyzer, however, can be
-cheap. Small scale differential analyzers have been built for less than
-$1000; their accuracy has been about 1 part in 100.</p>
-
-<p>There are many things that this machine cannot do; it was not built
-to do them. (1) It cannot choose methods of solution. (2) It cannot
-perform steps in solving a problem that depend on results as they
-are found. (3) It cannot solve differential equations containing two
-or more independent variables. Such equations are called <i>partial
-<span class="pagenum" id="Page_88">[Pg 88]</span>
-differential equations</i>; they appear in connection with the flow of
-heat or air or electricity in 2 or 3 dimensions, and elsewhere. (4)
-It cannot solve problems requiring 6 or more digits of accuracy. (5)
-The machine, while running, can store numbers only for an instant,
-since it operates on the principle of smoothly changing quantities;
-however, when the machine stops, the number last held by each device is
-permanently stored.</p>
-
-<p>None of these comments, however, are criticisms of the machine.
-Instead they show avenues of development for future machines. As was
-said before, for solving most differential equations, this machine
-has no equal to date. The range of problems which any differential
-analyzer can do depends mostly on the number of its integrators. The
-second differential analyzer has 18 and provides for expansion to 30.
-The machine is constructed, also, so that it can be operated in 3
-independent sections, each working to solve a different problem. The
-differential analyzer can operate unattended. After it has been set up
-and the first few results examined, it can be left alone to grind out
-large blocks of answers.</p>
-
-<p>An interesting example of the experimental use of a differential
-analyzer in a commercial business is the following: In Great Britain,
-R. E. Beard of the Pearl Assurance Company built a differential
-analyzer with 6 integrators. He applied this machine to compute to 3
-figures certain insurance values known as <i>continuous annuities</i>
-and <i>continuous contingent insurances</i>. He has described the
-machine and the application he made in a paper published in the
-<i>Journal of the Institute of Actuaries</i>, Vol. 71, 1942, pp. 193-227.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_89">[Pg 89]</span></p>
-<h2 class="nobreak" id="CHAPTER_6">Chapter 6<br />
-<span class="h_subtitle">ACCURACY TO 23 DIGITS:<br />
-HARVARD’S IBM AUTOMATIC<br />
-SEQUENCE-CONTROLLED CALCULATOR</span></h2>
-</div>
-
-<p>One of the first giant brains to be finished was the machine in
-the Computation Laboratory at Harvard University called the <i>IBM
-Automatic Sequence-Controlled Calculator</i>. This great mechanical
-brain started work in April 1944 and has been running 24 hours a
-day almost all the time ever since. It has produced quantities of
-information for the United States Navy. Although many problems
-that have been placed on it have been classified by the Navy as
-confidential, the machine itself is fully public. The way it was
-working on Sept. 1, 1945, has been thoroughly described in a 540-page
-book published in 1946, Volume I of the Annals of the Harvard
-Computation Laboratory, entitled <i>Manual of Operation of the
-Automatic Sequence-Controlled Calculator</i>. Since then the machine
-has been improved in many ways.</p>
-
-<p>This machine does thousands of calculating steps, one after another,
-according to a scheme fixed ahead of time. This property is what gives
-the machine its name: <i>automatic</i>, since the individual operations
-are automatic, once the punched tape fixing the chain of operations has
-been put on the machine, and <i>sequence-controlled</i>, since control
-over the sequence of its operations has been built into the machine.</p>
-
-<h3>ORIGIN AND DEVELOPMENT</h3>
-
-<p>More than a hundred years ago, an English mathematician and actuary,
-<span class="pagenum" id="Page_90">[Pg 90]</span>
-Charles Babbage (1792-1871), designed a machine—or <i>engine</i>
-as he called it—that would carry out the sequences of mathematical
-operations. In the 1830’s he received a government grant to build an
-<i>analytical engine</i> whereby long chains of calculations could
-be performed. But he was unsuccessful, because the refined physical
-devices necessary for quantities of digital calculation were not
-yet developed. Only in the 1930’s did these physical devices become
-sufficiently versatile and reliable for a calculator of hundreds of
-thousands of parts to be successful.</p>
-
-<p>The Automatic Sequence-Controlled Calculator at Harvard was largely the
-concept of Professor Howard H. Aiken of Harvard. It was built through
-a partnership of efforts, ideas, and engineering between him and the
-International Business Machines Corporation, in the years 1937 to
-1944. The calculator was a gift from IBM to Harvard University. Some
-very useful additional control units, named the <i>Subsidiary Sequence
-Mechanism</i>, were built at the Harvard Computation Laboratory in 1947
-and joined to the machine.</p>
-
-<div class="figcenter">
-  <img id="FIG_1-6" src="images/i_090.jpg" alt="" width="600" height="282" />
-  <p class="f120"><span class="smcap">Fig. 1.</span> Scheme of Harvard IBM Automatic<br />
-                               Sequence-Controlled Calculator.</p>
-</div>
-
-<h3>GENERAL ORGANIZATION</h3>
-
-<p>The machine (<a href="#FIG_1-6">see Fig. 1</a>) is about 50 feet long,
-8 feet high, and about 2 feet wide. It consists of 22 panels; 17 of
-them are set in a straight line, and the last 5 are at the rear of the
-machine. In the scheme of the machine shown in <a href="#FIG_1-6">Fig. 1</a>, the details you
-<span class="pagenum" id="Page_91">[Pg 91]</span>
-would see in a photograph have been left out. Instead you see the
-sections of the machine that are important because of what they do:
-<i>input</i>, <i>memory</i>, <i>control</i>, and <i>output</i>. Why do
-we not see a section labeled “computer”? Because in this mechanical
-brain the computing part of the machine is closely joined to the
-memory: every storage register can add and subtract. We shall soon
-discuss these sections of the machine more fully.</p>
-
-<h3>PHYSICAL DEVICES</h3>
-
-<p>Now in order for any brain to work, <i>physical devices</i> must be
-used. For example, in the human body, a nerve is the physical device
-that carries information from one part of the body to another. In the
-Harvard machine, an insulated <i>wire</i> is the physical device that
-carries information from one part of the machine to another. One side
-of every panel in the Harvard machine is heavily laden with a great
-network of wires. Between the panels, you can see in many places cables
-as thick as your arm and containing hundreds of wires. More than 500
-miles of wire are used.</p>
-
-<p>The physical devices in the Harvard machine are numerous, as we would
-expect. It is perhaps not surprising that this machine has more than
-760,000 parts. But, curiously enough, there are only 7 main kinds
-of physical devices in the major part of the machine. They are:
-wire, <i>two-position switches</i>, <i>two-position relays</i> (<a href="#CHAPTER_2">see Chapter 2</a>),
-<i>ten-position switches</i>, <i>ten-position relays</i>,
-<i>buttons</i>, and <i>cam contacts</i> (<a href="#FIG_4-6">see below</a>).
-These are the devices that handle information in the form of electrical
-impulses. They can be combined by electrical circuits in a great
-variety of ways. There are, of course, other kinds of physical devices
-that are important, but they are not numerous, and they have rather
-simple duties. Looking at the machine, you can see three examples
-easily. Physical devices of the first kind convert punched holes into
-electrical impulses: 2 <i>card feeds</i>, 4 <i>tape feeds</i>. Those
-of the second kind convert electrical impulses into punched holes:
-1 <i>card punch</i>, 1 <i>tape punch</i>. Those of the third kind
-convert electrical impulses into printed characters: 2 <i>electric
-typewriters</i>. We can think of a fourth kind of physical device that
-<span class="pagenum" id="Page_92">[Pg 92]</span>
-would be a help, but, at present writing, it does not yet exist: a
-device that converts printed characters into electrical impulses.</p>
-
-<p>The Harvard machine, of course, is complicated. But it is complicated
-because of the variety of ways in which relatively simple devices have
-been connected together to make a machine that thinks.</p>
-
-<h4>Switches</h4>
-
-<p>A <i>two-position switch</i> (<a href="#FIG_2-6">see Fig. 2</a>)
-turned by hand connects a wire to either one of 2 others. These 2
-positions may stand for “yes” and “no,” 0 and 1, etc. There are many
-two-position switches in the machine. A <i>ten-position switch</i>
-or <i>dial switch</i> (<a href="#FIG_3-6">see Fig. 3</a>) turned by
-hand connects the wire running into the center of the switch with a
-wire at any one of ten positions 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 around
-the edge. There are over 1400 dial switches in the machine. How does
-turning the pointer on the top of the dial make connection between the
-center wire and the edge wire? Under the face of the dial is the part
-that works, a short rod of metal fastened to the pointer (shown with
-dashes in <a href="#FIG_3-6">Fig. 3</a>). When the pointer turns,
-this rod also turns, making the desired connection.</p>
-
-<div class="figcontainer">
-  <div class="figsub">
-   <p class="space-below3">&nbsp;</p>
-   <img id="FIG_2-6" src="images/i_092a.jpg" alt="" width="300" height="153" />
-   <p class="center space-above2"><span class="smcap">Fig. 2.</span>Two-position switch.</p>
-  </div>
-  <div class="figsub">
-   <img id="FIG_3-6" src="images/i_092b.jpg" alt="" width="300" height="349" />
-   <p class="center"><span class="smcap">Fig. 3.</span> Dial switch.</p>
-   </div>
-</div>
-
-<h4>Relays</h4>
-
-<p><i>Two-position relays</i>—more often called just <i>relays</i>
-(<a href="#CHAPTER_2">see Chapter 2</a>)—do the automatic routing of the
-electrical impulses that cause computing to take place. Each relay may
-take 2 positions, open or closed, and these positions may stand for 0
-and 1. There are more than 3000 relays in the Harvard machine.</p>
-
-<p>A magnet pulling one way and a spring pulling the other way are
-sufficient in an ordinary relay to give 2 positions, “on” and “off,”
-“yes” and “no,” 0 and 1. But how do we make a relay that can hold any
-<span class="pagenum" id="Page_93">[Pg 93]</span>
-one of 10 positions? <a href="#FIG_4-6">Figure 4</a> shows one scheme
-for a <i>ten-position relay</i>. The <i>arm</i> can take any one of
-10 positions, connecting the contact <i>Common</i> to any one of the
-contacts O, 1, 2, 3, 4, 5, 6, 7, 8, and 9 so that current can flow.
-The <i>gear</i> turns all the time. When an impulse comes in on the
-<i>Pickup</i> line, the <i>clutch</i> connects the arm to the gear.
-When an impulse comes in on the <i>Drop-out</i> line, the clutch
-disconnects the arm from the gear. For example, suppose that the
-ten-position relay is stopped at contact 2, as shown. Suppose that we
-now pick up the relay, hold it just long enough to turn 3 steps, and
-then drop it out. The relay will now rest at contact 5.</p>
-
-<div class="figcenter">
-  <img id="FIG_4-6" src="images/i_093a.jpg" alt="" width="600" height="282" />
-  <p class="f120"><span class="smcap">Fig. 4.</span> Scheme of a ten-position relay,<br />
-           or counter position.</p>
-</div>
-
-<div class="figleft">
-  <img id="FIG_5-6" src="images/i_093b.jpg" alt="" width="200" height="285" />
-  <p class="f120"><span class="smcap">Fig. 5.</span> Scheme of a<br /> counter wheel.</p>
-</div>
-
-<p>In the Harvard machine, the ten-position relays, much like the scheme
-shown, do the same work as <i>counter wheels</i> (<a href="#FIG_5-6">Fig. 5</a>)
-in an ordinary desk calculating machine, and so they are often spoken of as
-<i>counter positions</i> in the Harvard machine. They are very useful
-in the machine not only because they express the 10 decimal digits
-0, 1, 2, 3, 4, 5, 6, 7, 8, 9 but also because adding and subtracting
-numbers is accomplished by turning them through the proper number of
-steps. In fact, an additional impulse is provided when the counter
-position turns from 9 to 0, for purposes of carry. A group of 24
-counter positions makes up each <i>storage counter</i>—or <i>storage
-register</i>—in the machine. There are 2200 of these counter
-positions. Each is connected to a continuously running gear on a small
-shaft (<a href="#FIG_6-6">Fig. 6</a>). All these shafts are connected by other
-gears and shafts to a main drive shaft, and they are driven by a 5-horsepower
-motor at the back of the machine. When a counter position is supposed
-<span class="pagenum" id="Page_94">[Pg 94]</span>
-to step, a clutch connects the drive to the running gear, and the
-counter position steps. When the counter position is supposed to
-stay unchanged, the clutch is disconnected and the driving gear runs
-free. In fact, when you first approach the Harvard machine, about the
-first thing you are aware of is the running of these gears and the
-intermittent whirring and clicking of the counter positions as they
-step. The machine gives a fine impression of being busy!</p>
-
-<div class="figcenter">
-  <img id="FIG_6-6" src="images/i_094a.jpg" alt="" width="600" height="240" />
-  <p class="f120"><span class="smcap">Fig. 6.</span> Scheme of counter 16.</p>
-</div>
-
-<h4>Timing Contacts</h4>
-
-<p>A <i>button</i> (<a href="#FIG_7-6">see Fig. 7</a>) is a device for
-closing an electric circuit when and only when you push it. A simple
-example is the button for ringing a bell: you push the button, a
-circuit is closed, and something happens. When you let go, the circuit
-is opened. The Harvard machine has a button for starting, a button for
-stopping, and many others.</p>
-
-<div class="figcontainer">
-  <div class="figsub">
-   <img id="FIG_7-6" src="images/i_094b.jpg" alt="" width="225" height="327" />
-   <p class="center"><span class="smcap">Fig. 7.</span> Button.</p>
-  </div>
-  <div class="figsub">
-   <img id="FIG_8-6" src="images/i_094c.jpg" alt="" width="350" height="333" />
-   <p class="center"><span class="smcap">Fig. 8.</span> Cam, with 5 lobes and contact.</p>
-   </div>
-</div>
-
-<p><span class="pagenum" id="Page_95">[Pg 95]</span>
-A <i>cam contact</i> (<a href="#FIG_8-6">see Fig. 8</a>) is an automatic
-device for closing an electric circuit for just a short interval of
-time. When the lobes on the cam strike the contact, it closes and
-current flows. When the lobes have gone by, the spring pushes open the
-contact, and no current flows. Just as a two-position relay is the
-automatic equivalent of a two-position switch, and a ten-position relay
-is the automatic equivalent of a ten-position switch, so a cam contact
-is the automatic equivalent of a button.</p>
-
-<p>All the cams in the machine have 20 pockets where small round metal
-lobes may or may not be inserted. Each cam makes a full turn once in
-³/₁₀ of a second and is in time with all the others. Thus we can time
-all the electrical circuits in the machine in units of ³/₂₀₀ of a second.</p>
-
-<h3>NUMBERS</h3>
-
-<p>Numbers in the machine regularly consist of 23 decimal digits. The
-24th numerical position at the left in any register contains only
-0 for a positive number and only 9 for a negative number. <i>Nines
-complements</i> (<a href="#SUPPL_2">see Supplement 2</a>) are used for negative
-numbers. For example,-00284 is represented as 999715, supposing that we
-had 5-digit numbers instead of 23-digit numbers. The sum of two
-nines complements is automatically corrected so that it is still a
-correct nines complement. The device that accomplishes this is called
-<i>end-around-carry</i> (<a href="#SUPPL_2">see Supplement 2</a>). The decimal
-point is fixed for each problem; in other words, in any problem, the decimal point
-is consistently kept in one place, usually between the 15th and 16th
-decimal columns from the right.</p>
-
-<h3>HOW INFORMATION GOES<br />INTO THE MACHINE</h3>
-
-<p>Numerical information may go into the machine in any one of 3 ways: (1)
-by regular IBM punch cards, using standard IBM card feeds (panel 16);
-(2) by hand-set dial switches (panels 1, 2); and (3) by long loops of
-punched tape placed on the value tape feeds (panels 12 to 14). Three
-sets of 24 columns each punched on a regular IBM punch card can be used
-to send 3 numbers and their signs into the machine in one machine cycle.
-<span class="pagenum" id="Page_96">[Pg 96]</span>
-This is the fastest way for giving numbers to the machine, but the most
-limited; for the cards must be referred to in order and can be referred
-to automatically only once. Also, there is the risk that they may be
-out of order. A card may be passed through the machine without reading;
-this saves some sorting in preparing cards for the machine. Machines
-for preparing the cards are regular IBM key punches, and machines for
-sorting them after preparation are regular IBM card sorters.</p>
-
-<p>In panels 1 and 2 there are 60 registers by which unchanging numbers
-like 1, or 3.14159265···, or 7.65 may be put into the machine. These
-are called the <i>constant registers</i>. Each constant register
-consists of 24 dial switches and contains 23 digits and a sign, 0 if
-positive and 9 if negative. Whenever the mathematician says a certain
-constant is needed for a problem, the operator of the machine walks
-over to these panels, and, while the machine is turned off, sets the
-dial switches for the number, one by one, by hand. If we need 40
-constants of 10 digits each for a problem, then the operator sets 400
-dial switches by hand and makes certain that the remaining 14 switches
-in each of the 40 constant registers used are either at 0 or 9,
-depending on the sign of the number. Only then can he return to start
-the machine.</p>
-
-<div class="figcenter">
-  <img id="FIG_9-6" src="images/i_096.jpg" alt="" width="500" height="215" />
-  <p class="f120"><span class="smcap">Fig. 9.</span> Value tape code.</p>
-</div>
-
-<p>The third means by which numerical information can be put into the
-machine is the <i>value tape feeds</i>, in panels 12, 13, and 14. Here
-the machine can consult tables of numbers. The numbers are punched
-on paper tape 24 holes wide, made of punch-card stock. Tapes for the
-value tape feeds may be prepared by hand or by the machine itself
-using punch cards or machine calculation. The tapes use equally spaced
-<i>arguments</i> (<a href="#SUPPL_2">see Supplement 2</a>). The tape punch
-changes the decimal digits in its keyboard into the following punching
-code (<a href="#FIG_9-6">see Fig. 9</a>):</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdc">&nbsp;0&nbsp;</td>
-      <td class="tdl">0000</td>
-      <td class="tdc" rowspan="5"><span class="ws2">&nbsp;</span></td>
-      <td class="tdc">&nbsp;5&nbsp;</td>
-      <td class="tdl">1100</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdl">1000</td>
-      <td class="tdc">6</td>
-      <td class="tdl">1010</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdl">0010</td>
-      <td class="tdc">7</td>
-      <td class="tdl">1001</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdl">0010</td>
-      <td class="tdc">8</td>
-      <td class="tdl">0110</td>
-   </tr><tr>
-      <td class="tdc">4</td>
-      <td class="tdl">0001</td>
-      <td class="tdc">9</td>
-      <td class="tdl">0101</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent"><span class="pagenum" id="Page_97">[Pg 97]</span>
-Here the 1 denotes a punched hole and 0 no punched hole, and the 4
-columns from left to right of the code correspond to 4 rows of the
-paper tape from bottom to top. To make sure the value tape is correct,
-the machine itself can read the value tape and check it mathematically
-or compare it with punch-card values.</p>
-
-<h3>HOW INFORMATION COMES<br />OUT OF THE MACHINE</h3>
-
-<p>Information comes out of the machine in any one of three ways: (1) by
-punching on IBM cards with a regular IBM card punch that is built into
-the machine (panel 17), (2) by typing on paper sheets with electric
-typewriters (panels 16 and 17), and (3) by punching paper tape 24 holes
-wide of the same kind as is fed into the machine.</p>
-
-<p>Usually, one of the electric typewriters is used to print a result for
-a visual check and to print it before the machine makes a specified
-check of the value. Then, about 10 seconds later, after the result has
-been checked as specified in the machine, the checked result is printed
-by the second typewriter. In the second typewriter, a special one-use
-carbon ribbon of paper is used to produce copy for publication by a
-photographic process.</p>
-
-<p>The card punch writes a number more rapidly than an electric
-typewriter. This extra speed is sometimes very useful. However, the
-punch’s chief purpose is to record intermediate results on punch cards.
-Then, if there is a machine failure, and if the problem has been well
-organized, the problem may be run over from these intermediate results,
-instead of requiring a return to the original starting information.
-The tape punch used for preparing tape by hand can also be operated by
-cable from the machine.</p>
-
-<h3>HOW INFORMATION IS HANDLED<br />IN THE MACHINE</h3>
-
-<p>The machine is a mechanical brain. So, between taking in information
-and putting out information, the machine does some “thinking.” It
-does this thinking according to instructions. The instructions go
-into the machine as: (1) the setting of switches, or (2) the pressing
-of buttons, or (3) the wiring of plugboards, or (4) feeding in tape
-<span class="pagenum" id="Page_98">[Pg 98]</span>
-punched with holes. The instructions are remembered in the machine in
-these 4 ways, and we can call these sets of devices the control of the
-machine.</p>
-
-<p>To illustrate: One of the buttons pressed for every problem is the
-Start Key: when you press it, the machine starts to work on the
-problem. One of the switches with which you give instructions is
-a switch that turns electric typewriter 1 on or off. One of the
-plugboards contains some hubs by which you can tell the machine how
-many figures to choose in the quotient when dividing, for clearly you
-do not need a quotient of 23 figures every time the machine divides.
-You can have 5 choices in any one problem; you can specify them by
-plugging, and you can call for any one of 5 choices of quotient size
-from time to time during the problem. In many cases, when we wish
-the machine to do the same thing for all of a single problem and do
-it whenever the occasion arises, we can put the instruction into the
-wiring of a plugboard. We use plugboard wiring, for example, in fixing
-the decimal point in multiplication, so that the product will read out
-properly, and in guiding the operation of the typewriters, so that
-printing will take place in the columns where we want it.</p>
-
-<h4>Sequence of Steps</h4>
-
-<p>The most important part of the control of the machine is the
-<i>sequence-tape feed</i> and its <i>sequence-control tape</i>. These
-tell the machine a great part of what operations are to be performed.</p>
-
-<div class="figcenter">
-  <img id="FIG_10-6" src="images/i_098.jpg" alt="" width="600" height="142" />
-  <p class="f120"><span class="smcap">Fig. 10.</span> Sequence-control tape code.</p>
-</div>
-
-<p>At the end of the room where the machine is, there is the special tape
-punch mentioned above. It holds a big spool of card stock that is thin,
-flexible, smooth, and tough. With one keyboard we may prepare value
-tape. With another keyboard we prepare the sequence-control tape. The
-tape (<a href="#FIG_10-6">see Fig. 10</a>) contains places for 24 round punched holes
-in each row. Some and only some of these holes are punched. Each row of punched
-<span class="pagenum" id="Page_99">[Pg 99]</span>
-holes is equivalent to an instruction to the machine and is called
-a <i>line of coding</i> or <i>coding line</i>. In general, the
-instruction has the form:</p>
-
-<ul class="index fontsize_110">
-<li class="isub3">Take a number out of Register <i>A</i>;</li>
-<li class="isub4">put the number into Register <i>B</i>;</li>
-<li class="isub4">and perform operation <i>C</i>.</li>
-</ul>
-
-<p>The first group of 8 holes at the left is called the <i>A field</i> or
-the <i>out-field</i>. Here we tell the machine where a number is to be
-taken from. The middle group of 8 holes is called the <i>B field</i>
-or the <i>in-field</i>. Here we tell the machine where a number is to
-be put. The last group of 8 holes is called the <i>C field</i> or the
-<i>miscellaneous field</i>. Here we tell the machine part or all of the
-operation that is to be performed.</p>
-
-<p>To illustrate (<a href="#FIG_10-6">see Fig. 10</a>), we have holes
-3, 2, 1 punched in the <i>A</i> field, holes 3, 2 punched in the
-<i>B</i> field, and hole 7 punched in the <i>C</i> field. Now 321 is
-the <i>code</i>—or machine language, or machine call number—for storage
-counter 7; 32 is the code for storage counter 6; and 7 in the <i>C</i>
-field is the code (in this case, and generally) for “Add, and read
-the next line of coding.” So, if we punch out this line of coding and
-put the tape on the machine, we tell the machine to read the number
-in counter 7, add it into counter 6, and proceed to the next line of
-coding and read that.</p>
-
-<p>The holes in each group of 8 holes from left to right are numbered: 8,
-7, 6, 5, 4, 3, 2, 1. The code 631, for example, means that holes 6, 3,
-1 are punched and that no holes are punched at 8, 7, 5, 4, 2. Since it
-is more natural, the code is read from left to right, or 631, instead
-of from right to left in the sequence 136.</p>
-
-<p>The devices in the machine have <i>in-codes</i>, used in the in-field,
-and <i>out-codes</i>, used in the out-field. For each of the 72 regular
-storage counters, the in-code and the out-code are the same. The first
-8 storage counters have the codes 1, 2, 21, 3, 31, 32, 321, 4, 41; the
-last 2 storage counters, the 71st and the 72nd, have the codes 7321, 74.</p>
-
-<p>The constant registers—often called <i>constant switches</i>, or just
-<i>switches</i>—naturally have only out-codes, since numbers can be
-entered into the constant registers only by setting dial switches by
-<span class="pagenum" id="Page_100">[Pg 100]</span>
-hand. The first 8 constant registers have the out-codes 741, 742, 7421,
-743, 7431, 7432, 74321, 75, and the 59th and 60th constant registers
-have the out-codes 821, 83.</p>
-
-<h4>Transferring, Adding, and Clearing</h4>
-
-<p>Each storage counter has the property that any number transferred into
-it is added into it. For example, the instruction</p>
-
-<ul class="index fontsize_110">
-<li class="isub3">Take the number in switch 741;</li>
-<li class="isub4">transfer it into storage register 321</li>
-</ul>
-
-<p class="no-indent">is coded:</p>
-
-<p class="f110">741, 321, 7</p>
-
-<p class="no-indent">The 7 in the third column is an instruction to the
-sequence-tape feed to turn up to the next coding line and read it. If
-any number is already stored in register 321, the content of 741 will
-be added to it, and the total will then be stored in 321.</p>
-
-<p>Resetting or clearing a regular storage register is accomplished by a
-coding that is a departure from the usual scheme of “out” and “in.” The
-instruction</p>
-
-<ul class="index fontsize_110">
-<li class="isub3">Clear register 321;</li>
-<li class="isub4">read the next coding line</li>
-</ul>
-
-<p class="no-indent">is coded:</p>
-
-<p class="f110">321, 321, 7</p>
-
-<p class="no-indent">Similarly, you can clear any other regular storage
-register if you repeat its code in the out-and in-fields. However, a
-few of the storage registers in the machine have special reset codes,
-and these may occur in any of the three fields <i>A</i>, <i>B</i>,
-<i>C</i>.</p>
-
-<p>As the result of a recent modification of the machine, you can easily
-double the number in any storage register. For example, the instruction</p>
-
-<ul class="index fontsize_110">
-<li class="isub3">Double the number in register 321;</li>
-<li class="isub4">read the next coding line</li>
-</ul>
-
-<p class="no-indent">is coded:</p>
-
-<p class="f110">321, 321, 743</p>
-
-<h4>Subtracting</h4>
-
-<p>If the number in switch 741 is to be subtracted from the number in
-storage counter 321, the instruction is changed into:</p>
-
-<ul class="index fontsize_110">
-<li class="isub3">Take the negative of the number in switch 741;</li>
-<li class="isub4">transfer it into storage register 321;</li>
-<li class="isub4">read the next line of coding</li>
-</ul>
-
-<p class="no-indent"><span class="pagenum" id="Page_101">[Pg 101]</span>
-The coding line becomes:</p>
-
-<p class="f110">741, 321, 732</p>
-
-<p class="no-indent">By putting 32 in the <i>C</i> field, we cause the number
-in switch 741 to be subtracted from whatever number is in register 321.</p>
-
-<p>We have 2 more choices in adding and subtracting. The value of the
-number without regard to sign—in other words, its <i>absolute
-value</i> (<a href="#SUPPL_2">see Supplement 2</a>)—may be added
-or subtracted. The instruction</p>
-
-<p class="f110">Add the absolute value of</p>
-
-<p class="no-indent">is expressed by a <i>C</i> field code 2, and the instruction</p>
-
-<p class="f110">Add the negative of the absolute value of</p>
-
-<p class="no-indent">is expressed by a <i>C</i> field code 1.</p>
-
-<h4>Multiplying</h4>
-
-<p>When we wish to multiply one number by another and get a product, we
-have 3 numbers. We tell the machine about each of these numbers on a
-separate line of coding. Multiplication is signaled by sending a number
-into the <i>multiplicand counter</i>. The multiplicand counter has an
-in-code 761. If the multiplicand is in 321, the instruction is:</p>
-
-<ul class="index fontsize_110">
-<li class="isub3">Take the number in 321;</li>
-<li class="isub4">enter it as multiplicand;</li>
-<li class="isub4">read the next coding line</li>
-</ul>
-
-<p class="no-indent">The coding is:</p>
-
-<p class="f110">321, 761, 7</p>
-
-<p class="no-indent">On the third following coding line, the multiplier
-is sent into the <i>multiplier counter</i>. If the multiplier is in
-switch 741, the instruction is:</p>
-
-<ul class="index fontsize_110">
-<li class="isub3">Take the number in 741;</li>
-<li class="isub4">enter it as multiplier;</li>
-<li class="isub4">read the next coding line</li>
-</ul>
-
-<p class="no-indent">The coding is:</p>
-
-<p class="f110">741, ——, 7</p>
-
-<p class="no-indent">We do not punch anything in the middle field: the machine
-is “educated” and “knows” that it has started a multiplication and needs a
-<span class="pagenum" id="Page_102">[Pg 102]</span>
-multiplier, and it expects this multiplier in the third coding line. To
-have no code for the multiplier counter is, of course, a departure from
-the general rule, but it saves some punching and permits the use of
-this space for certain other codes, thus saving some operating time.</p>
-
-<p>We need not confuse the 761 in-code for the multiplicand counter with
-the 761 out-code, which happens to be the out-code of the 25th constant
-register, because neither can occur in the other’s field. We may, of
-course, use other registers besides 321 and 741 for supplying the
-multiplicand and multiplier.</p>
-
-<p>To get the product and put it into any storage counter <i>D</i>, we use
-two lines of coding one right after the other:</p>
-
-<p class="f110">——   ——  6421</p>
-<p class="f110">8761    <i>D</i>    ——</p>
-
-<p class="no-indent">The <i>product counter</i> has the out-code 8761.
-When the product is desired, it is called for, transferred into counter
-<i>D</i>, and the multiplication unit is automatically cleared. It
-takes time, however, for the machine to perform a multiplication.
-That is the reason for the preceding coding line and the 6421 in the
-<i>C</i> field. While the multiplication is going on, we can instruct
-the machine to do other things that we want done. We can insert or
-<i>interpose</i> coding lines in between the multiplier line and the
-product line. For example, if we have a multiplier of 10 digits, we
-can insert 8 coding lines and maybe more. The 6421 code essentially
-tells the machine to finish both the multiplication and the interposed
-instructions, and, as soon as the later one of these two tasks is
-finished, to transfer out the product to counter <i>D</i>.</p>
-
-<p>Up to the middle of 1946, the wiring of the machine was a little
-different and less convenient. When the product was obtained by the
-multiplication unit, it had to be accepted and transferred at once into
-one of the 72 storage registers.</p>
-
-<h4>Dividing</h4>
-
-<p>Division is called for by first sending the divisor into the <i>divisor
-counter</i>, and this has a code 76 in the <i>B</i> field. If the
-divisor is in counter 321, the instruction may be:</p>
-
-<ul class="index fontsize_110">
-<li class="isub3">Take the number in 321;</li>
-<li class="isub4">enter it as divisor;</li>
-<li class="isub4">read the next coding line</li>
-</ul>
-
-<p class="no-indent"><span class="pagenum" id="Page_103">[Pg 103]</span>
-The coding will then be:</p>
-
-<p class="f110">321, 76, 7</p>
-
-<p class="no-indent">Three coding lines later, the dividend is called
-for, and the coding, if the dividend is in switch 7431, is:</p>
-
-<p class="f110">7431, ——, 7</p>
-
-<p class="no-indent">We can send the quotient, when ready, into any
-desired counter <i>Q</i> by the following two lines of coding:</p>
-
-<p class="f110">——  ——  642</p>
-<p class="f110">876       <i>Q</i>    ——</p>
-
-<p class="no-indent">In the same way as with multiplication, we can
-insert a number of coding lines in between the dividend line and the
-first quotient line.</p>
-
-<p>Both multiplication and division are carried out in the same unit
-of the machine, the <i>multiply-divide unit</i>. The machine first
-constructs a table of the multiples of the multiplicand or divisor:
-1 times, 2 times, 3 times, ···, 9 times. In multiplication this
-table is then used by selecting multiples according to the digits of
-the multiplier one after another. In division the table is used by
-comparing multiples of the divisor against the dividend and successive
-remainders, finding which will go and which will not. Since the numbers
-in the machine are normally of 15 to 23 digits, any particular multiple
-will be used, on the average, several times, and so this process is
-relatively efficient. Actually the multiplicand and the divisor go into
-the same counter. Division, however, has the code 76 and multiplication
-the code 761, and so the difference is essentially an operation code
-not in the third or <i>C</i> field.</p>
-
-<h4>Consulting a Table</h4>
-
-<p>When we desire the machine to consult a table of values (i.e., a
-<i>function</i>—<a href="#SUPPL_2">see Supplement 2</a>), we punch
-the table with its arguments and function values on a tape, and we put
-the tape on a value tape feed mechanism. The instruction to the machine
-may be:</p>
-
-<ul class="index fontsize_110">
-<li class="isub3">Take the number in register <i>A</i>;</li>
-<li class="isub4">find the value of the function for this number,</li>
-<li class="isub4">and enter it in register <i>B</i>.</li>
-</ul>
-
-<p class="no-indent"><span class="pagenum" id="Page_104">[Pg 104]</span>
-The coding is:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc_ws1">——</td>
-      <td class="tdc_ws1">——</td>
-      <td class="tdr_ws1">73</td>
-   </tr><tr>
-      <td class="tdc_ws1"><i>A</i></td>
-      <td class="tdc_ws1">7654</td>
-      <td class="tdr_ws1">61</td>
-   </tr><tr>
-      <td class="tdc_ws1">——</td>
-      <td class="tdc_ws1">——</td>
-      <td class="tdr_ws1">762</td>
-   </tr><tr>
-      <td class="tdc_ws1">——</td>
-      <td class="tdc_ws1">——</td>
-      <td class="tdr_ws1">543</td>
-   </tr><tr>
-      <td class="tdc_ws1">——</td>
-      <td class="tdc_ws1">——</td>
-      <td class="tdr_ws1">75431</td>
-   </tr><tr>
-      <td class="tdc_ws1">841</td>
-      <td class="tdc_ws1">7654</td>
-      <td class="tdr_ws1">——</td>
-   </tr><tr>
-      <td class="tdc_ws1"><i>A</i></td>
-      <td class="tdc_ws1">763</td>
-      <td class="tdr_ws1">6421</td>
-   </tr><tr>
-      <td class="tdc_ws1">8762</td>
-      <td class="tdc_ws1"><i>B</i></td>
-      <td class="tdr_ws1">73</td>
-   </tr><tr>
-      <td class="tdc_ws1">——</td>
-      <td class="tdc_ws1">8763</td>
-      <td class="tdr_ws1">7</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Without explaining this coding line by line,
-we can say that this is what happens:</p>
-
-<div class="blockquot">
-<p class="neg-indent">The machine reads the argument in register
-<i>A</i>. The machine reads the argument in the table at which the
-value tape feed is resting.</p>
-
-<p class="neg-indent">It subtracts them, and thereby determines how far
-away the desired argument is.</p>
-
-<p class="neg-indent">The machine then turns the tape that required
-distance.</p>
-
-<p class="neg-indent">It checks that the new argument is the wanted
-argument.</p>
-
-<p class="neg-indent">It reads the value of the function entered at that
-point on the function tape.</p>
-</div>
-
-<h4>Selecting</h4>
-
-<p>There is a storage counter in the machine that is called the
-<i>selection counter</i>. The selection counter is counter 70 and
-has the code 732. It has all the properties of an ordinary storage
-counter and, in addition, one extra property: depending on the sign of
-the number stored in the selection counter, it is possible to select
-whether some other number shall be treated positively or negatively.
-In other words, addition of a number anywhere in the machine may take
-place either positively or negatively, if the number stored in the
-selection counter is positive or negative, respectively.</p>
-
-<p>For example, suppose that <i>x</i> is the number in the selection
-counter. Suppose that <i>y</i> is the number in some other counter
-<i>A</i>. Suppose that <i>z</i> is the number in counter <i>B</i>.
-Suppose that we use the coding:</p>
-
-<p class="f110"><i>A</i>, <i>B</i>, 7432</p>
-
-<p class="no-indent"><span class="pagenum" id="Page_105">[Pg 105]</span>
-What we get in <i>B</i>, because of the 7432 in the third or <i>C</i>
-field, is <i>z</i> plus <i>y</i> if <i>x</i> is positive or zero, and
-<i>z</i> minus <i>y</i> if <i>x</i> is negative. In the language of the
-algebra of logic (see <a href="#CHAPTER_9">Chapter 9</a> and
-<a href="#SUPPL_2">Supplement 2</a>), where <i>T</i>( ...) is “the
-truth value of ...,” the number in <i>b</i> equals:</p>
-
-<p class="f120"><i>z</i> + <i>y</i>·<i>T</i>(<i>x</i> ≥ 0) - <i>y</i>·<i>T</i>(<i>x</i> &lt; 0)</p>
-
-<p class="no-indent">(The nines complement of 0, namely 999···9 to 24
-digits, is treated by the machine as negative.)</p>
-
-<p>Why do we need an operation like this in a mechanical brain? Among
-other reasons, what we want to do with a number, in mathematics, often
-depends on its sign. It may happen that a table is, for negative
-arguments, the negative of what it is for positive arguments; in other
-words, <big><i>F</i>(-<i>x</i>) =-<i>F</i>(<i>x</i>)</big>. This is true, for
-instance, for a table of <i>cubes</i> <big>{<i>F</i>(<i>x</i>) = <i>x</i>³}</big>
-or for a table of <i>trigonometric tangents</i> (<a href="#SUPPL_2">see Supplement 2</a>).
-If so, we certainly do not want to take the time and trouble to list the
-whole table. We put down only half the table and then, if <i>x</i> is
-negative, use the negative of the value in the table. In order to apply
-such a time-saving rule when using the machine, we need the selection
-counter or its equivalent.</p>
-
-<h4>Checking</h4>
-
-<p>There is another special counter in the machine that is called the
-<i>check counter</i>. It also has all the properties of an ordinary
-storage counter and, in addition, one extra property: If the sign of
-the number stored in the check counter on a certain coding line is
-negative, then on the next coding line the machine may be stopped. In
-other words, suppose that the check counter stores a certain tolerance
-<i>t</i>. Suppose, under the instructions we give the machine, that
-it calculates a positive number <i>x</i> that ought to be less than
-this tolerance. Suppose that something may go wrong and that <i>x</i>
-actually may be greater than <i>t</i>. Then we put a check into our
-instructions. We tell the machine:</p>
-
-<ul class="index fontsize_110">
-<li class="isub3">When you have found <i>x</i>, subtract it from <i>t</i>.</li>
-<li class="isub4">If the result is positive, go ahead.</li>
-<li class="isub4">If the result is negative or zero, <i>stop</i>!</li>
-</ul>
-
-<p><span class="pagenum" id="Page_106">[Pg 106]</span>
-Here is the coding. Suppose that the tolerance <i>t</i> is in switch
-751. Suppose that the number <i>x</i> to be checked is in counter 4321.
-Then the instructions and coding are:</p>
-
-<table class="fontsize_110 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdl">Clear the check counter</td>
-      <td class="tdr_ws1">—</td>
-      <td class="tdr_ws1">—</td>
-      <td class="tdr">7</td>
-   </tr><tr>
-      <td class="tdl">Put in the tolerance, from switch 751</td>
-      <td class="tdr_ws1">751</td>
-      <td class="tdr_ws1">74</td>
-      <td class="tdr">7</td>
-   </tr><tr>
-      <td class="tdl">Subtract the absolute value of the number to be checked&nbsp;&nbsp;</td>
-      <td class="tdr_ws1">4321</td>
-      <td class="tdr_ws1">74</td>
-      <td class="tdr">71</td>
-   </tr><tr>
-      <td class="tdl">Stop, O Mechanical Brain, if your result be negative!</td>
-      <td class="tdr_ws1">—</td>
-      <td class="tdr_ws1">—</td>
-      <td class="tdr">64</td>
-   </tr>
- </tbody>
-</table>
-
-<p>An operation like this is very useful in a mechanical brain. It
-enables the calculation to be interrupted if something has gone
-wrong. Of course, other operations of checking besides this one are
-used—for example, inspecting for reasonableness the results printed on
-typewriter 1.</p>
-
-<h4>Other Operations</h4>
-
-<p>There are other operations in the machine. There are two pairs of
-storage registers that can be <i>coupled</i> together so that we can
-handle problems requiring numbers of 46 digits instead of 23. Registers
-64 and 65 can be coupled, and registers 68 and 69 can be coupled. There
-is another storage counter, No. 71, that has an extra property. We can
-read out the number it holds times 1, or times 10¹², or times 10⁻¹²,
-as may be called for. As a result of this counter, we can do problems
-requiring 144 registers storing numbers of 11 digits each, instead of
-72 registers storing 23 digits each. Bigger statistical problems can be
-handled, for example.</p>
-
-<p>There are some minor sequences of operations, or <i>subroutines</i>,
-that can be called for by a single code. The subroutine may be a
-whole set of additions, subtractions, multiplications, divisions,
-and choices, having a single purpose: to compute some number by a
-<i>process of rapid approximation</i> (<a href="#SUPPL_2">see Supplement 2</a>).
-There are built-in subroutines for some special mathematical functions: the
-<i>logarithm</i> of a number to the base 10, the <i>exponential</i>
-of a number to the base 10, and the <i>sine</i> of a number.
-(<a href="#SUPPL_2">See Supplement 2</a>.)</p>
-
-<p>There are also 10 changeable subroutines, each of 22 coding lines,
-which can be called in, when wanted, by the main sequence-control tape
-or by each other. These subroutines constitute the Subsidiary Sequence
-<span class="pagenum" id="Page_107">[Pg 107]</span>
-Mechanism, and are extremely useful. They have <i>A</i>, <i>B</i>,
-and <i>C</i> fields just like the main sequence-control, but they are
-given information by plugging with short lengths of wire instead of by
-feeding punched paper tape.</p>
-
-<h3>RAPID APPROXIMATION FOR A LOGARITHM</h3>
-
-<p>Up to this point in this chapter the author has tried to tell the facts
-about the Harvard machine in plain words. But for reading this section,
-a little knowledge of calculus is necessary. (<a href="#SUPPL_2">See also Supplement 2</a>.)
-If you wish, skip this section and go on to the next one.</p>
-
-<p>What is the process that the machine uses to compute any desired
-logarithm to 23 digits? Suppose that we take for an example the process
-by which the machine computes log<sub>10</sub> 49.3724. We choose a 6-digit
-number for simplicity; the machine would handle a 23-digit number in
-the same way. The process uses 2 fundamental equations involving the
-logarithm: the sum relation</p>
-
-<p class="f120">log (<i>a</i>·<i>b</i>·<i>c</i>···) = log <i>a</i> + log <i>b</i> + log <i>c</i>···</p>
-
-<p class="no-indent">and the series relation</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdl" rowspan="2">logₑ(1 + <i>h</i>) = <i>h</i> -&nbsp;</td>
-      <td class="tdc bb"><i>h</i>²</td>
-      <td class="tdl" rowspan="2">+</td>
-      <td class="tdc bb"><i>h</i>³</td>
-      <td class="tdl" rowspan="2">-</td>
-      <td class="tdc bb"><i>h</i>⁴</td>
-      <td class="tdl" rowspan="2">&nbsp;+ ···, │<i>h</i>│ &lt; 1</td>
-   </tr><tr>
-
-      <td class="tdc">2</td>
-      <td class="tdc">3</td>
-      <td class="tdc">4</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">The error in this series is less than the first neglected term. Now,
-the machine stores the base 10 logarithms (to 23 decimal places) of the
-following 36 numbers:</p>
-
-<table class="fontsize_110 no-wrap" border="0" cellspacing="4" summary=" " cellpadding="4" >
-  <tbody><tr>
-      <td class="tdc">1</td>
-      <td class="tdc">1.1</td>
-      <td class="tdc">1.01</td>
-      <td class="tdc">1.001</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdc">1.2</td>
-      <td class="tdc">1.02</td>
-      <td class="tdc">1.002</td>
-   </tr><tr>
-      <td class="tdc">...</td>
-      <td class="tdc">...</td>
-      <td class="tdc">...</td>
-      <td class="tdc">...</td>
-   </tr><tr>
-      <td class="tdc">9</td>
-      <td class="tdc">1.9</td>
-      <td class="tdc">1.09</td>
-      <td class="tdc">1.009</td>
-   </tr>
- </tbody>
-</table>
-
-<p>First, the number 49.3724 is examined in a counter called the
-<i>Logarithm-In-Out counter</i>, and the position of the decimal point
-is determined, giving the <i>characteristic</i> of the logarithm. The
-number 49.3724 has the characteristic 1. Next, 4 successive divisions
-are performed, in which the 4 divisors are (1) the first digit of the
-number, (2) the first 2 digits of the quotient, (3) the first 3 digits
-of the next quotient, and (4) the first 4 digits of the subsequent
-quotient; thus,
-<span class="pagenum" id="Page_108">[Pg 108]</span></p>
-
-<table class="fontsize_110 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdc bb">4.93724</td>
-      <td class="tdc" rowspan="2">&nbsp;= 1.23431</td>
-   </tr><tr>
-      <td class="tdc">4</td>
-   </tr><tr>
-      <td class="tdc bb">1.23431</td>
-      <td class="tdc" rowspan="2">&nbsp;= 1.02860</td>
-   </tr><tr>
-      <td class="tdc">1.2</td>
-   </tr><tr>
-      <td class="tdc bb">1.02860</td>
-      <td class="tdc" rowspan="2">&nbsp;= 1.00843</td>
-   </tr><tr>
-      <td class="tdc">1.02</td>
-   </tr><tr>
-      <td class="tdc bb">1.00843</td>
-      <td class="tdc" rowspan="2">&nbsp;= 1.00043</td>
-   </tr><tr>
-      <td class="tdc">1.008</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">For simplicity we have kept only 6 digits,
-although the machine, of course, would keep 23. It is interesting to
-note that the machine is able to sense digits and thus determine the 4
-divisors; this is an arithmetical and numerical process and one that
-cannot be done in ordinary algebra. We now have:</p>
-
-<p class="f120 no-wrap">log₁₀ 49.3724 = 1 + log₁₀ 4 + log₁₀ 1.2 + log₁₀ 1.02<br />
-<span class="ws6">+ log₁₀ 1.008 + log₁₀ 1.00043</span></p>
-
-<p class="no-indent">To compute log₁₀ 1.00043 to 21 decimals we use</p>
-
-<table class="fontsize_110 no-wrap" border="0" cellspacing="4" summary=" " cellpadding="4" >
-  <tbody><tr>
-      <td class="tdl" rowspan="2">log₁₀<i>e</i> ·</td>
-      <td class="tdl" rowspan="2"><img src="images/l_paren.jpg" alt="" width="20" height="66" /></td>
-      <td class="tdl" rowspan="2"><i>h</i> -</td>
-      <td class="tdc bb"><i>h</i>²</td>
-      <td class="tdc" rowspan="2">&nbsp;+&nbsp;</td>
-      <td class="tdc bb"><i>h</i>³</td>
-      <td class="tdc" rowspan="2">&nbsp;-&nbsp;</td>
-      <td class="tdc bb"><i>h</i>⁴</td>
-      <td class="tdc" rowspan="2">&nbsp;+&nbsp;</td>
-      <td class="tdc bb"><i>h</i>⁵</td>
-      <td class="tdc" rowspan="2">&nbsp;-&nbsp;</td>
-      <td class="tdc bb"><i>h</i>⁶</td>
-      <td class="tdc" rowspan="2"><img src="images/r_paren.jpg" alt="" width="20" height="65" /></td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdc">3</td>
-      <td class="tdc">4</td>
-      <td class="tdc">5</td>
-      <td class="tdc">6</td>
-   </tr>
-</tbody>
-</table>
-
-<p class="no-indent">with <i>h</i> = 0.00043. Only 6 terms of the
-series relation are needed. For, the error is less than <big><i>h</i>⁷/7</big>,
-which is less than <big>10⁻²¹/7</big>, since <big><i>h</i> &lt; ¹/₁₀₀₀</big>. The machine
-uses the series relation in the form</p>
-
-<p class="f120 no-wrap">log₁₀ (1 + <i>h</i>) = <big>{([{(</big><i>c</i>₆<i>h</i> + <i>c</i>₅<big>)</big>
-<i>h</i> + <i>c</i>₄<big>}</big><i>h</i> + <i>c</i>₃<big>]</big><i>h</i> +
-<i>c</i>₂<big>)</big><i>h</i> + <i>c</i>₁<big>}</big><i>h</i></p>
-
-<p class="no-indent">where</p>
-
-<p class="f120 no-wrap"><i>c</i>₁ = <i>M</i>, <i>c</i>₂ = -<i>M</i>/2, <i>c</i>₃ = <i>M</i>/3, ···,</p>
-
-<p class="no-indent">and <span class="fontsize_120"><i>M</i> = log₁₀_<i>e</i>= 0.434294···.</span></p>
-
-<p class="no-indent">The 6 values of the <i>c</i>’s are also stored
-in the machine. When any logarithm is to be computed, the sum of the
-characteristic, of the 4 logarithms of the successive divisors, and
-of the first 6 terms of the series relation gives the logarithm. The
-maximum time required is 90 seconds.</p>
-
-<h3>AN APPRAISAL OF THE CALCULATOR</h3>
-
-<p>The IBM Automatic Sequence-Controlled Calculator at Harvard is a
-<span class="pagenum" id="Page_109">[Pg 109]</span>
-landmark in the development of machines that think. Its capacity for
-many problems for which it is suited is far beyond the capacity of a
-hundred human computers.</p>
-
-<h4>Speed</h4>
-
-<p>The time required in the machine for adding, subtracting, transferring,
-or clearing numbers is ³/₁₀ of a second. This is the time of one
-machine cycle or of reading one coding line. Multiplication takes at
-the most 6 seconds, and an average of 4 seconds. Division takes at the
-most 16 seconds, and an average of 11 seconds. Each, however, requires
-only 3 lines of coding, or ⁹/₁₀ of a second’s attention from the
-sequence mechanism; interposed operations fill the rest of the time.
-To calculate a logarithm, an exponential, or a sine to the full number
-of digits obtainable by means of the automatic subroutine takes at
-the most 90, 66, and 60 seconds, respectively. To get three 24-digit
-numbers from feeding a punch card takes ⅓ second. To punch a number
-takes from ½ second up to 3 seconds. To print a number takes from 1½
-seconds up to 7 seconds.</p>
-
-<h4>Cost and Value</h4>
-
-<p>The cost of the machine was somewhere near 3 or 4 hundred thousand
-dollars, if we leave out some of the cost of research and development,
-which would have been done whether or not this particular machine had
-ever been built. A staff of 10 men, consisting of 4 mathematicians,
-4 operators, and 2 maintenance men, are needed to keep the machine
-running 24 hours a day. This might represent, if capitalized, another
-1 or 2 hundred thousand dollars. If a capital value of $500,000 is
-taken as equivalent to $50,000 a year, then the cost of the machine in
-operation 24 hours a day is in the neighborhood of $150 a day or $6 an hour.</p>
-
-<p>The value of the machine, however, is very much greater. If 100 human
-beings with desk calculators were set to work 8 hours a day at $1.50 an
-hour, the cost would be $1200 a day, or 8 times as much. Yet it is very
-doubtful that the work they could produce would equal that turned out
-by the machine, either in quality or quantity, when the machine is well
-suited to the problem.
-<span class="pagenum" id="Page_110">[Pg 110]</span></p>
-
-<h4>Reliability</h4>
-
-<p>By reliability we mean the extent to which the results produced by the
-machine can be relied on to be right. The machine contains no built-in
-device for making its operations reliable. So, if we wish to check a
-multiplication, for example, we can do the multiplication a second
-time, interchanging the multiplier and the multiplicand. But if, say,
-digit 16 of the product were not transferring correctly, we would get
-the same wrong result both ways and we would not have a sufficient
-check. Thus, when we set up a problem for the machine to do, one of the
-big tasks we have is checking. We have to work out ways of making sure
-that the result, when we get it, is right and ways of instructing the
-machine to make the tests we want. This is not a new task. Whenever
-you or I set out to solve a problem, we have to make sure—usually by
-doing the problem twice, and preferably by doing it a different way the
-second time—that our answer, when we get it, is correct. One of the
-chief tasks for the mathematician, in making a sequence-control tape
-for the machine, is to put into it sufficient checks to make sure that
-the results are correct.</p>
-
-<p>We can use a number of different kinds of partial checks: the check
-counter; <i>differences</i>, and <i>smoothness</i> (<a href="#SUPPL_2">see Supplement 2</a>);
-watching the results printed on typewriter 1; mathematical checks;
-comparison with known specific values; etc.</p>
-
-<p>In actual experience on the machine, human failures, such as failure
-to state the problem exactly or failure to put it on the machine
-correctly, have given about as much trouble as mechanical failures. The
-machine operates without mechanical failure about 90 to 95 per cent
-of the time. The balance of the time the machine is idle while being
-serviced or repaired. The machine is serviced by mechanics trained and
-supervised at Harvard.</p>
-
-<p>Often when we change the machine from one problem to another problem,
-we find some kind of trouble. Consequently, we need to work out in
-detail the first part of any calculation placed on the machine. We
-then compare the results step by step with the results produced by the
-machine. Any mathematician working with the machine needs considerable
-<span class="pagenum" id="Page_111">[Pg 111]</span>
-training in order to diagnose trouble quickly and guide the maintenance
-men to the place where repair or replacement is needed. Once you find
-the trouble, you can fix it easily. Without disturbing the soldered
-connections, you can easily pull out from its socket a relay that is
-misbehaving and plug in a new relay. With a screwdriver you can change
-a counter position—detach it from its socket and replace it by another
-one that is working correctly.</p>
-
-<p>One “bug” that will long be remembered around the Laboratory was a case
-involving a 5 that would incorrectly come in to a number every now
-and then. It did not happen often—only once in a while. After a week
-of search the bug was finally located: the insulation on a wire that
-carried a 5 had worn through in one spot, and once in a while this wire
-would shake against a post that could carry current and took in the 5!</p>
-
-<h4>Efficiency</h4>
-
-<p>In many respects, this machine is efficient and well-balanced. Its
-reading and writing speed is close to its calculating speed. We can
-punch or print a result on the average for every 10 additions or 1½
-multiplications. The memory of 72 numbers in the machine is extremely
-useful; a smaller memory is a serious limitation on the achievements of
-a computing machine. The machine can do many kinds of arithmetic and
-logic. It is well educated and can compute automatically some rather
-complicated mathematical functions, like logarithm or sine. It has done
-difficult and important problems. It has computed and tabulated
-(<a href="#SUPPL_2">see Supplement 2</a>) <i>Bessel functions</i>,
-<i>definite integrals</i>, etc. It can solve <i>differential
-equations</i> (<a href="#CHAPTER_5">see Chapter 5</a>) and many other
-problems in mathematics, physics, and engineering.</p>
-
-<p>On the other hand, no calculator will ever again be built just like
-this one, useful though it is. Electronic computing is easily 100 times
-as fast as relay computing; nearly every future calculator will do
-its computing electronically. Many other improvements will be made.
-For example, in this calculator, there are 72 addition-subtraction
-mechanisms, yet only one of these can be used at a time. Also, the
-machine has only one combined multiply-divide unit. So we have to
-<span class="pagenum" id="Page_112">[Pg 112]</span>
-organize any computation with few multiplications, and with still fewer
-divisions, for they take longer still.</p>
-
-<p>Until 1947, we had to organize any computation in this calculator into
-one single fixed sequence of operations. In other words, there was
-no way to move from one subroutine to another subroutine depending
-on some indication that turned up in our computation. Recently, the
-Harvard Computation Laboratory decided to remedy this condition and
-provided the Subsidiary Sequence Mechanism equivalent to 10 subroutines
-of 22 lines of coding each. These are on relays and plug wires and
-may be called for by the sequence-control tape or by each other. This
-provision has added greatly to the efficiency of the calculator.</p>
-
-<p>Whatever else can be said about the Harvard IBM Automatic
-Sequence-Controlled Calculator, it must be said that this was the first
-general-purpose mechanical brain using numbers in digit form and able
-to do arithmetic and logic in hundreds of thousands of steps one after
-another. And great credit must go to Professor Howard H. Aiken of
-Harvard and the men of International Business Machines Corporation who
-made this great mechanical brain come into existence.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_113">[Pg 113]</span></p>
-<h2 class="nobreak" id="CHAPTER_7">Chapter 7<br />
-<span class="h_subtitle">SPEED—5000 ADDITIONS A SECOND:<br />
-MOORE SCHOOL’S <b>ENIAC</b><br />
-ELECTRONIC NUMERICAL INTEGRATOR AND CALCULATOR</span></h2>
-</div>
-
-<p>Another of the giant brains that has begun to work is named
-<i>ENIAC</i>. This name comes from the initial letters of the full
-name, <i>Electronic Numerical Integrator and Calculator</i>. Eniac was
-born in 1942 at the Moore School of Electrical Engineering, of the
-University of Pennsylvania, in Philadelphia. Eniac’s father was the
-Ordnance Department of the U. S. Army, which provided the funds to feed
-and rear the prodigy.</p>
-
-<p>In the short space of four years, Eniac grew to maturity, and in
-February 1946 he began to earn his own living by electronic thinking.
-Eniac promptly set several world’s records. He was the first giant
-brain to use electronic tubes for calculating. He was the first one to
-reach the speed of 5000 additions a second. He was the first piece of
-electronic apparatus containing as many as 18,000 electronic tubes all
-functioning together successfully. As soon as Eniac started thinking,
-he promptly made relay calculators obsolete from the scientific point
-of view, for they have a top speed of perhaps 10 additions a second.</p>
-
-<p>At the age of 5, he moved to Maryland at a cost of about $90,000, and
-his permanent home is now the Ballistic Research Laboratories at the U.
-S. Army’s Proving Ground at Aberdeen, Md.</p>
-
-<h3>ORIGIN AND DEVELOPMENT</h3>
-
-<p>In the Department of Terrestrial Magnetism in the Carnegie Institution
-<span class="pagenum" id="Page_114">[Pg 114]</span>
-of Washington, a great deal of information about the earth is studied.
-Many kinds of physical observations are there gathered and analyzed:
-electricity in the atmosphere, magnetism in the earth, and the weather,
-for example. In 1941, a physicist, Dr. John W. Mauchly, was thinking
-about the great mass of numerical information they had to handle. He
-became convinced that much swifter ways of handling these numbers were
-needed. He was certain electronic devices could be used for computing
-at very high speeds, yet he found no one busy applying electronics in
-this field. With hopes of finding some way of developing electronic
-computing, he joined the staff of the Moore School of Electrical
-Engineering in the autumn of 1941.</p>
-
-<p>The Moore School in 1934 and 1935 had built a differential analyzer;
-and, from that time on, the school had made a number of improvements
-in it. In 1941, with war imminent, the differential analyzer was put
-hard at work calculating tables for the Army’s Ballistic Research
-Laboratories. These tables were mostly firing tables, tables of the
-paths along which projectiles travel when fired—<i>trajectories</i>;
-obviously, you cannot fire a gun usefully, unless you know how to aim
-it. The amount of calculation of trajectories was so huge that Dr.
-Mauchly suggested that a machine using electronic tubes be constructed
-to calculate them. A good deal of discussion took place between men at
-the Moore School, men at the Ballistic Research Laboratories, and men
-from the Ordnance Department in Washington. A contract for research
-into an electronic trajectory computer was concluded with the Ordnance
-Department of the U. S. Army. Mauchly and one of the young electronics
-engineers studying at Moore School, J. Presper Eckert, Jr., set to work
-on the design.</p>
-
-<p>Gradually the design of a machine took form, and the crucial
-experiments on equipment were completed. In 1943, the design was
-settled as a special-purpose machine to calculate trajectories. Later
-on, the group modified the plans here and there to enable the machine
-to calculate a very wide class of problems. A group of Moore School
-electronics engineers and technicians during 1944 and 1945 built the
-machine, using as much as possible standard radio tubes and parts.
-Here, again, in spite of the successful progress of the electronic
-machine, the rumor that it was a “white elephant” was allowed to spread
-in order to protect the work from prying enemy ears.
-<span class="pagenum" id="Page_115">[Pg 115]</span></p>
-
-<h3>GENERAL ORGANIZATION</h3>
-
-<p>The main part of Eniac consists of 42 <i>panels</i>, which are placed
-along the sides of a square U. Each of these panels is 9 feet high, 2
-feet wide, and 1 foot thick. They are of sheet steel, painted black,
-with switches, lights, etc., mounted on them. At the tops of all the
-panels are air ducts for drawing off the hot air around the tubes.
-Large motors and fans above the machine suck the heated air away
-through the ducts. There are also 5 pieces of equipment which can be
-rolled from place to place and are called <i>portable</i>, but there
-is no choice as to where they can be plugged in. We shall call this
-equipment panels 43 to 47.</p>
-
-<h4>Panels</h4>
-
-<p>Now what are these panels, and what do they do? Each panel is an
-assembly of some equipment. The names of the panels are shown in the
-accompanying table. The arrangement of Eniac at the Ballistic Research
-Laboratories as shown in the table is slightly different from the
-arrangement of Eniac at Moore School.</p>
-
-<p class="f150"><b>NAMES OF PANELS OF ENIAC</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Panel<br /> No.</span></th>
-      <th class="tdc"><span class="smcap">Name<br />
-                 (and additional names in some cases)</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdc">1</td>
-      <td class="tdl_ws1">Initiating Unit</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdl_ws1">Cycling Unit</td>
-   </tr><tr>
-      <td class="tdc">3, 4</td>
-      <td class="tdl_ws1">Master Programmer, panels 1, 2</td>
-   </tr><tr>
-      <td class="tdc">5</td>
-      <td class="tdl_ws1">Accumulator 1</td>
-   </tr><tr>
-      <td class="tdc">6</td>
-      <td class="tdl_ws1">Accumulator 2</td>
-   </tr><tr>
-      <td class="tdc">7</td>
-      <td class="tdl_ws1">Accumulator 3</td>
-   </tr><tr>
-      <td class="tdc">8</td>
-      <td class="tdl_ws1">Accumulator 4 (Quotient)</td>
-   </tr><tr>
-      <td class="tdc">9</td>
-      <td class="tdl_ws1">Divider-Square-Rooter</td>
-   </tr><tr>
-      <td class="tdc">10</td>
-      <td class="tdl_ws1">Accumulator 5 (Numerator I)</td>
-   </tr><tr>
-      <td class="tdc">11</td>
-      <td class="tdl_ws1">Accumulator 6 (Numerator II)</td>
-   </tr><tr>
-      <td class="tdc">12</td>
-      <td class="tdl_ws1">Accumulator 7 (Denominator—Square Root I)</td>
-   </tr><tr>
-      <td class="tdc">13</td>
-      <td class="tdl_ws1">Accumulator 8 (Denominator—Square Root II)</td>
-   </tr><tr>
-      <td class="tdc">14</td>
-      <td class="tdl_ws1">Accumulator 9 (Shift I)</td>
-   </tr><tr>
-      <td class="tdc">15</td>
-      <td class="tdl_ws1">Accumulator 10 (Shift II)</td>
-   </tr><tr>
-      <td class="tdc">16</td>
-      <td class="tdl_ws1">Blank panel for new unit (Converter)</td>
-   </tr><tr>
-      <td class="tdc">17</td>
-      <td class="tdl_ws1">Accumulator 11 (Multiplier)</td>
-   </tr><tr>
-      <td class="tdc">18</td>
-      <td class="tdl_ws1">Accumulator 12 (Multiplicand)</td>
-   </tr><tr>
-      <td class="tdc">19-21</td>
-      <td class="tdl_ws1">Multiplier, panels 1, 2, 3</td>
-   </tr><tr>
-      <td class="tdc">22<span class="pagenum" id="Page_116">[Pg 116]</span></td>
-      <td class="tdl_ws1">Accumulator 13 (Left-Hand Partial Products I)</td>
-   </tr><tr>
-      <td class="tdc">23</td>
-      <td class="tdl_ws1">Accumulator 14 (Left-Hand Partial Products II)</td>
-   </tr><tr>
-      <td class="tdc">24</td>
-      <td class="tdl_ws1">Accumulator 15 (Right-Hand Products I)</td>
-   </tr><tr>
-      <td class="tdc">25</td>
-      <td class="tdl_ws1">Accumulator 16 (Right-Hand Products II)</td>
-   </tr><tr>
-      <td class="tdc">26</td>
-      <td class="tdl_ws1">Blank panel for new unit (100 Registers)</td>
-   </tr><tr>
-      <td class="tdc">27</td>
-      <td class="tdl_ws1">Accumulator 17</td>
-   </tr><tr>
-      <td class="tdc">28</td>
-      <td class="tdl_ws1">Accumulator 18</td>
-   </tr><tr>
-      <td class="tdc">29</td>
-      <td class="tdl_ws1">Accumulator 19</td>
-   </tr><tr>
-      <td class="tdc">30</td>
-      <td class="tdl_ws1">Accumulator 20</td>
-   </tr><tr>
-      <td class="tdc">31, 32</td>
-      <td class="tdl_ws1">Function Table 1, panels 1, 2</td>
-   </tr><tr>
-      <td class="tdc">33, 34</td>
-      <td class="tdl_ws1">Function Table 2, panels 1, 2</td>
-   </tr><tr>
-      <td class="tdc">35, 36</td>
-      <td class="tdl_ws1">Function Table 3, panels 1, 2</td>
-   </tr><tr>
-      <td class="tdc">37-39</td>
-      <td class="tdl_ws1">Constant Transmitter, panels 1, 2, 3</td>
-   </tr><tr>
-      <td class="tdc">40-42</td>
-      <td class="tdl_ws1">Printer, panels 1, 2, 3</td>
-   </tr><tr>
-      <td class="tdc">43-45</td>
-      <td class="tdl_ws1">Portable Function Tables <i>A</i>, <i>B</i>, and <i>C</i></td>
-   </tr><tr>
-      <td class="tdc">46</td>
-      <td class="tdl_ws1">IBM Card Reader</td>
-   </tr><tr>
-      <td class="tdc">47</td>
-      <td class="tdl_ws1">IBM Summary Punch</td>
-   </tr>
- </tbody>
-</table>
-
-<div class="blockquot">
-   <p class="neg-indent"><i>Note</i>: The accumulators from which a number can be sent
-                         to the printer are now accumulators 1, 2, and 15 to 20.</p>
-</div>
-
-<p>In reading over the table, we find a number of words that need
-explaining. Some of the explanation we can give in the summary of the
-units of Eniac:</p>
-
-<p class="f150"><b>SUMMARY OF UNITS OF ENIAC</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Quantity</span></th>
-      <th class="tdc"><span class="smcap">Device</span></th>
-      <th class="tdc"><span class="smcap">Significance</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdc">20</td>
-      <td class="tdl_ws1">Accumulators</td>
-      <td class="tdl_ws1">Store, add, and subtract numbers</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdl_ws1">Multiplier</td>
-      <td class="tdl_ws1">Multiplies</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdl_ws1">Divider-Square-Rooter</td>
-      <td class="tdl_ws1">Divides, and obtains twice the <i>square root</i></td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;&emsp;of a number (<a href="#SUPPL_2">see Supplement 2</a>)</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdl_ws1">Function Tables</td>
-      <td class="tdl_ws1">Part of the memory, for referring to</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;&emsp;tables of numbers</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdl_ws1">Constant Transmitter</td>
-      <td class="tdl_ws1">Stores numbers from the card reader and</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;&emsp;from hand-set switches</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdl_ws1">Printer</td>
-      <td class="tdl_ws1">Punches machine results into cards</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdl_ws1">Cycling Unit</td>
-      <td class="tdl_ws1">Controls the timing of the various parts</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;&emsp;of the machine</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdl_ws1">Initiating Unit</td>
-      <td class="tdl_ws1">Has controls for starting a calculation,</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;&emsp;for clearing, etc.</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdl_ws1">Master Programmer</td>
-      <td class="tdl_ws1">Holds the chief controls for coordinating</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;&emsp;the various parts of the machine</td>
-   </tr>
- </tbody>
-</table>
-
-<p>An <i>accumulator</i> is a storage counter. It can hold a number; it
-can clear a number; it can transmit a number either positively or
-<span class="pagenum" id="Page_117">[Pg 117]</span>
-negatively; and it can receive a number by adding the number in and
-thus holding the sum of what it held before and the number received.
-Eniac when first built had only 20 accumulators, and so it could
-remember only 20 numbers at one time (except for constant numbers set
-in switches). This small memory was the most serious drawback of Eniac;
-panel 26 was designed, therefore, to provide a great additional memory capacity.</p>
-
-<p>The <i>divider-square-rooter</i>, as its name tells, is a mechanism
-that can divide and that can find twice the square root of a number.
-Eniac is one of the several giant brains that have had square root
-capacity built into them, particularly since square root is needed for
-solving trajectories.</p>
-
-<p>Many panels of Eniac have double duty and some have triple duty.
-For example, panel 24 is an accumulator, but it also (1) stores the
-right-hand partial products (<a href="#SUPPL_2">see Supplement 2</a>) of the
-multiplier and (2) was a register, when Eniac was at Moore School, from which
-information to be punched in the printer could be obtained. Clearly, if
-we have a multiplication to do, we cannot also use this accumulator for
-storing a number that is to remain unchanged during the multiplication.</p>
-
-<h4>Parts</h4>
-
-<p>The total number of parts in Eniac is near half a million, even if
-we count electronic tubes as single parts. There are over 18,800
-electronic tubes in the machine. It is interesting to note that only 10
-kinds of electronic tubes are used in the calculating circuits and only
-about 60 kinds of <i>resistors</i> and 30 kinds of <i>capacitors</i>. A
-resistor is a device that opposes the steady flow of electric current
-through it to a certain extent (called <i>resistance</i> and measured
-in <i>ohms</i>). A capacitor is a device that can store electrical
-energy up to a certain extent (called <i>capacitance</i> and measured
-in <i>farads</i>). All these tubes and parts are standard parts in
-radios. All types are identified by the color labels established in
-standard radio manufacturing. It is the combinations of these parts,
-like the combinations of pieces in a chess game, that give rise to the
-marvelous powers of Eniac.</p>
-
-<p>The combinations of parts at the first level are called <i>plug-in
-units</i>. A plug-in unit is a standard box or tray or chassis made of
-<span class="pagenum" id="Page_118">[Pg 118]</span>
-sheet steel containing a standard assembly of tubes, wires, and other
-parts. It can be pushed in or pulled out of a standard socket with
-many connections. An example of a plug-in unit is a <i>decade</i>, or,
-more exactly, an <i>accumulator decade</i>. This is just a counter
-wheel or decimal position expressed in Eniac language: it can express
-successively all the digits from 0 to 9 and then pass from 9 to 0,
-giving rise to a carry impulse. It is striking that a mechanical
-counter to hold 10 digits can be made up of 10 little wheels, ¼ inch
-wide and an inch high. But an accumulator in Eniac, to hold 10 digits,
-is a set of 10 decades each 2 inches wide and 2½ feet high.</p>
-
-<p>There are only about 20 kinds of plug-in units altogether. Each plug-in
-unit is interchangeable with any other of the same kind. So, if a
-decade, for example, shows trouble, you can pull it out of its socket
-and plug in a spare decade instead.</p>
-
-<h4>Numbers</h4>
-
-<p>Numbers in Eniac are of 10 decimal digits with a sign that may be plus
-or minus. The decimal point is fixed. However, when you are connecting
-one accumulator with another, you can shift the decimal point if you
-want to. Also, 2 accumulators may be coupled together so as to handle
-numbers of 20 digits.</p>
-
-<h3>HOW INFORMATION GOES<br /> INTO THE MACHINE</h3>
-
-<p>There are three ways by which information—numbers or instructions—can
-go into the Eniac. Numbers can be put into the machine by means of
-punch cards fed into the Card Reader, panel 46, or switches on the
-Constant Transmitter, panels 37 to 39. Numbers or instructions can
-also go into the machine by means of the Function Tables, panels 43 to
-45. Here there are dial switches, which are set by hand. Instructions
-can also go into the machine by setting the switches, plugging the
-inputs and outputs, etc., of the wires or lines along which numbers and
-instructions travel.</p>
-
-<h3>HOW INFORMATION COMES<br /> OUT OF THE MACHINE</h3>
-
-<p>There are two ways by which numerical information can come out of the
-<span class="pagenum" id="Page_119">[Pg 119]</span>
-machine. Numbers can come out of the machine punched on cards by the
-Summary Punch, panel 47. They are then printed in another room by means
-of a separate IBM tabulator. Also, numbers can be read out of the
-machine by means of the lights in the <i>neon bulbs</i> mounted on each
-accumulator. You can read in the lights of a panel the number held by
-the accumulator, if the panel is not computing.</p>
-
-<h3>HOW INFORMATION IS MANIPULATED<br /> IN THE MACHINE</h3>
-
-<p>Eniac handles information rather differently from any other of the big
-brains. Instead of having only one bus or “railroad line” along which
-numbers can be sent, Eniac has more than 10 such lines. They are called
-<i>digit trays</i> and labeled A, B, C, ···. Each contains 11 <i>digit
-trunk lines</i> or <i>digit trunks</i>—10 to carry the digits of a
-number, and the 11th to carry the sign. Instead of having only one
-telegraph line along which instructions can be sent, Eniac has more
-than 100 such lines. They are called <i>program trunk lines</i> or
-<i>program trunks</i> and labeled A1, A2, ···, A11, B1, B2, ···, B11,
-···, etc. They are assembled in groups of 11 to a tray; the <i>program
-trays</i>, in fact, look just like the digit trays, except for their
-connectors and their purpose, which are different. Below, we shall make
-clear how the program trays carry control information.</p>
-
-<p>Now, actually, Eniac has many more trunk lines than we have just
-stated, for each of the lines we have mentioned can be divided into
-numerous separate sections by the removal of plug connections. How
-we choose to do this depends on the needs of the problem, the space
-between the panels, the time when the line is used, etc.</p>
-
-<h4>Transferring Numbers, Adding,<br /> and Subtracting</h4>
-
-<p>Basically, a number is represented in Eniac by an arrangement of on and
-off electronic tube elements in pairs, called <i>flip-flops</i>. There
-is one flip-flop enclosed in a single tube (type 6SN7) for each value
-0, 1, 2, 3, 4, 5, 6, 7, 8, 9 for each of the 10 digits stored in an
-accumulator. So we have at least 100 flip-flops for each accumulator,
-and thus at least 100 electronic tubes are required to store 10 digits.
-Actually, an accumulator needs 550 electronic tubes. So we see that
-<span class="pagenum" id="Page_120">[Pg 120]</span>
-there is not very much of a future in this type of arrangement. The
-newer electronic brains use different devices for storage of numbers.</p>
-
-<p>In order to show what number is stored in an accumulator, there are 100
-little neon bulbs mounted on the face of each accumulator panel. Each
-bulb glows when the flip-flop that belongs to it is on. For example,
-suppose that the 4th decade in Accumulator 11 holds the digit 7. Then
-the 7th flip-flop in that decade will be on, and all the others will be
-off. The 7th neon bulb for that decade will glow.</p>
-
-<p>Now suppose that the number 7 is in the 4th decade in Accumulator 11
-and is to be added into, say, the 4th decade in Accumulator 13. And
-suppose that it is to be subtracted from the 4th decade in Accumulator
-16. What do we do, and what will Eniac do?</p>
-
-<p>First, we pick out 2 digit trays, say B and D. Accumulator 11 has 2
-outputs, called the <i>add output</i> and the <i>subtract output</i>.
-We plug B into the add output and D into the subtract output. Then we
-go over to Accumulators 13 and 16. They have 5 inputs, that is, 5 ways
-of being plugged to receive numbers from digit trunks. These inputs are
-named with <i>Greek letters</i>, <big>α, β, γ, δ, ε</big>. We choose one input,
-say γ, for Accumulator 13, and we plug B into that input. We choose one
-input, say ε, for Accumulator 16, and we plug D into that input.</p>
-
-<p>Now we have the “railroad” switching for numbers accomplished. We have
-set up a channel whereby the number in Accumulator 11 will be routed
-positively into Accumulator 13 and negatively into Accumulator 16.
-Now let us suppose that, at some definite time fixed by the control,
-Accumulator 11 is stimulated to transmit and Accumulators 13 and 16 are
-conditioned to receive. When this happens, a group of 10 <i>pulses</i>
-comes along a direct trunk from the cycling unit, and a group of 9
-pulses comes along another trunk. We can think of each pulse as a
-little surge of electricity lasting about 2 millionths of a second. The
-<i>ten-pulses</i>, as the first group is called, are 10 millionths of
-a second apart. The <i>nine-pulses</i>, as the second group is called,
-are also 10 millionths of a second apart but are sandwiched between
-the ten-pulses. When the 1st ten-pulse comes along, the 7th flip-flop
-in Accumulator 11 goes off, the 8th flip-flop goes on, the following
-<span class="pagenum" id="Page_121">[Pg 121]</span>
-nine-pulse goes through and goes out on the subtract line to
-Accumulator 16. Then the 2nd ten-pulse comes along, the 8th flip-flop
-goes off, the 9th flip-flop goes on, and the next nine-pulse goes out
-on the subtract line to Accumulator 16. Now the decade sits at 9,
-and for this reason the next ten-pulse changes an electronic switch
-(actually another flip-flop) so that all later nine-pulses will go
-out on the add line. This ten-pulse also turns off the 9th flip-flop
-and turns on the 0th flip-flop without causing any carry. Now the 4th
-of the ten-pulses comes along, turns the 0th flip-flop off, and turns
-the 1st flip-flop on, and the next nine-pulse goes out on the add line
-to Accumulator 13. The next 6 of the ten-pulses then come along and
-change Accumulator 11 back to the digit 7 as before, and the next 6 of
-the nine-pulses go out to Accumulator 13. Thus Eniac has added 7 into
-Accumulator 13, has added 2, the <i>nines complement</i> of 7
-(<a href="#SUPPL_2">see Supplement 2</a>), into Accumulator 16, and has
-left Accumulator 11 holding the same number as before. This is just the
-result that we wanted.</p>
-
-<p>In this way, the nines complement of any digit in a decade is
-transferred out along the subtract line, and the digit unchanged is
-transmitted out along the add line. As the pulses arrive at any other
-accumulator, they add into that accumulator.</p>
-
-<h4>Multiplying and Dividing</h4>
-
-<p>Eniac performs multiplication by a built-in table of the products in
-the 10-by-10 multiplication table, using the method of <i>left-hand
-components</i> and <i>right-hand components</i> (<a href="#SUPPL_2">see Supplement 2</a>).
-For example, suppose that the 3rd digit of the multiplier is 7 and that the
-5th digit of the multiplicand is 6. Then, when Eniac attends to the
-3rd digit of the multiplier, the right-hand digit of the 42 = 6 × 7 is
-gathered in one accumulator, and the left-hand digit 4 is gathered in
-another accumulator. After Eniac has attended to all the digits of the
-multiplier, then Eniac performs one more addition and transfers the sum
-of the left-hand digits into the right-hand digits accumulator.</p>
-
-<p>Eniac does division in rather a novel way. First, the divisor is
-subtracted over and over until the result becomes negative or 0. Then
-the machine shifts to the next column and adds the divisor until the
-<span class="pagenum" id="Page_122">[Pg 122]</span>
-result becomes positive or 0. It continues this process, alternating
-from column to column. For example, suppose that we divide 3 into 84 in
-this way. We have:</p>
-
-<ul class="index fontsize_120">
-<li class="isub3">____&nbsp; &nbsp;_</li>
-<li class="isub2">3 ) 84 ( 32</li>
-<li class="isub3">-3</li>
-<li class="isub3 over">+54</li>
-<li class="isub3">&nbsp;-3</li>
-<li class="isub3 over">+24</li>
-<li class="isub3 u">&nbsp;-3&nbsp;&nbsp;</li>
-<li class="isub3">&nbsp;&nbsp;&nbsp;-6</li>
-<li class="isub3">&nbsp;&nbsp;+3</li>
-<li class="isub3 over">&nbsp;&nbsp;&nbsp;-3</li>
-<li class="isub3 u">&nbsp;&nbsp;+3</li>
-<li class="isub4">0</li>
-</ul>
-
-<p class="no-indent">After we subtract 3 the third time, the result
-becomes negative,-6; in the next column, after we add 3 twice, the
-result becomes 0. The quotient is</p>
-
-<ul class="index">
-<li class="isub1">&nbsp;&nbsp;_</li>
-<li class="isub1">32, which is the same as 30 - 2, or 28;</li>
-</ul>
-
-<p class="no-indent">and 3 × 28 is 84. Thus the process checks.</p>
-
-<h4>Consulting a Table</h4>
-
-<p>Eniac has three Function Tables. Here you can store numbers or
-instructions for the machine to refer to. Each Function Table has
-104 <i>arguments</i> (<a href="#SUPPL_2">see Supplement 2</a>). For
-each argument, you can store 12 digits and 2 signs that may be plus
-or minus. This capacity can be devoted to one 12-digit number with a
-sign, or to two 6-digit numbers each with a sign, or to six 2-digit
-instructions. The three Function Tables are panels 43, 44, and 45. To
-put in the numbers or instructions, you have to go over to these panels
-and set the numbers or instructions, digit by digit, turning dial
-switches by hand. It is slow and hard to do this right, but once it
-is done, Eniac can refer to any number or instruction in any table in
-¹/₁₀₀₀ of a second. This is much faster than the table reference time
-in any other of the giant brains built up to 1948.</p>
-
-<h4>Programming</h4>
-
-<p>We said above that Eniac has over 100 control lines or program trunks
-along which instructions can be sent. These instructions are expressed
-as pulses called <i>program pulses</i>. Now how do we make these pulses
-<span class="pagenum" id="Page_123">[Pg 123]</span>
-do what we want them to do? For example, how can we instruct
-Accumulator 11 to add what it holds into Accumulator 13?</p>
-
-<p>On each unit of Eniac there are plug hubs or sockets (called
-<i>program-pulse input terminals</i>) to which a program trunk may be
-connected. A program pulse received here can make the unit act in some
-desired way. On each accumulator of Eniac, we find 12 program-pulse
-input hubs. Corresponding to each of these hubs, there is a nine-way
-switch, called a <i>program-control switch</i>. The setting of this
-switch determines what the accumulator will do when the program-pulse
-input hub belonging to the switch receives a program pulse. For
-instance, there are switch settings for: receive input on the α line,
-receive input on the β line, etc.; and transmit output on the add line,
-etc. There is even a switch setting that instructs the accumulator to
-do nothing, and this instruction may be both useful and important.</p>
-
-<p>Now, in order that Accumulator 11 may transfer a number to Accumulator
-13, we need: (1) a digit tray, say B, for the number to travel along;
-(2) a program trunk line, say G3, to tell Accumulator 11 when to send
-the number and Accumulator 13 when to receive it; and (3) certain
-plugging as follows:</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. We plug from program trunk G3 into a
-program-pulse input hub, say No. 5, of Accumulator 11;</p>
-
-<p class="neg-indent">2. We plug from the same program trunk G3 into a
-program-pulse input hub, say No. 7, of Accumulator 13;</p>
-
-<p class="neg-indent">3. We set program-control switch No. 5 of
-Accumulator 11 to “add”;</p>
-
-<p class="neg-indent">4. We set program-control switch No. 7 of
-Accumulator 13 to some input, say γ.</p>
-
-<p class="neg-indent">5. We plug from digit tray B into the add output
-of Accumulator 11.</p>
-
-<p class="neg-indent">6. We plug from digit tray B into the γ input of
-Accumulator 13.</p>
-</div>
-
-<p class="no-indent">Now, when the program pulse comes along line G3,
-it makes Accumulator 13 transmit additively along digit tray B into
-Accumulator 13. And that is the result that we wanted.</p>
-
-<p>As each mechanism of Eniac finishes what it is instructed to do, it may
-<span class="pagenum" id="Page_124">[Pg 124]</span>
-or may not put out a program pulse. This pulse in turn may be plugged
-into any other program trunk line and may stimulate another mechanism
-to act. Then, when this mechanism finishes, it too may or may not put
-out a program pulse, and so on.</p>
-
-<p>In general, there are two different ways to instruct Eniac to do a
-problem. One way is to set all the switches, plug all the connections,
-etc., for the specific problem. This is a long and hard task. Very
-often, even with great care, it is done not quite correctly, and then
-the settings must be carefully checked all over again. A second method
-(called the <i>von Neumann programming method</i>) is to store all
-the instructions for a problem in one or two function tables of Eniac
-and then tell Eniac to read the function tables in sequence and to do
-what they say. The rest of the machine is then wired up in a standard
-fashion. This method of instructing Eniac was proposed by Dr. John von
-Neumann of the Institute of Advanced Study at Princeton, N. J. Eniac
-has been modified to the slight extent needed so that this method can
-be used when desired. In this method, each instruction is a selected
-one of 60 different standard instructions or orders—one of them, for
-example, being “multiplication.” Each standard order is expressed by
-2 decimal digits. The 60 standard orders are sufficient so that Eniac
-can do any mathematical problem that does not overstrain its capacity.
-Since each of the 3 Function Tables can hold 600 2-digit instructions,
-the machine can hold a program of 1800 instructions under the von
-Neumann programming method.</p>
-
-<h3>AN APPRAISAL OF ENIAC<br /> AS A COMPUTER</h3>
-
-<p>As a general-purpose calculating machine, Eniac suffers from unbalance.
-That is to say, Eniac operates rapidly and successfully in some
-respects, and slowly and troublesomely in other respects. This is
-altogether to be expected, however, in a calculator as novel as Eniac
-and made to so large an extent out of standard radio parts. It was
-certainly better to finish a calculator like this one and then start
-on a new one, as the Moore School of Electrical Engineering did, than
-to prolong design and construction indefinitely in order to make improvements.
-<span class="pagenum" id="Page_125">[Pg 125]</span></p>
-
-<h4>Speed</h4>
-
-<p>Eniac adds or subtracts very swiftly at the rate of 5000 a second.
-Eniac multiplies at the rate of 360 to 500 a second. Division,
-however, is slow, relatively; the rate is about 50 a second. Reading
-numbers from punched cards, 12 a second for 10-digit numbers, is even
-slower. As a result of these rates, you find, when you put a problem
-on Eniac, that one division delays you as long as 100 additions or
-8 multiplications. Division might have been speeded somewhat by (1)
-<i>rapidly convergent approximation</i> (<a href="#SUPPL_2">see Supplement 2</a>)
-to the <i>reciprocal</i> of the divisor and (2) multiplying by the dividend;
-this might have taken 5 or 6 multiplication times instead of 8. Also,
-the use of a standard IBM punch-card feed and card punch slows the
-machine greatly. One way to overcome this drawback might be to install
-one or two additional sets of such equipment, which might increase
-input and output speed.</p>
-
-<h4>Ease of Programming</h4>
-
-<p>Eniac has a very rapid and flexible automatic control over the
-programming of operations. Eniac has more than 10 channels along which
-numbers can be transferred and more than 100 channels along which
-program-control pulses can be transferred. There are many ways for
-providing subroutines. Eniac has the additional advantage that there
-is no delay in giving the machine successive instructions: all the
-instructions the machine may need at any time are ready at the start of
-the problem, and indications occurring in the calculation can change
-the routine completely.</p>
-
-<p>All these advantages, however, are paid for rather heavily by the
-slow methods for changing programming. You have to plug large numbers
-of program trunk lines and digit trunk lines, or you have to set
-large numbers of switches, or both. Also, when you wish to return to
-a previous problem, you must do all the plugging and switch setting
-over again. Many delays in the operation of the machine are due to
-human errors in setting the machine for a new problem. Here again, we
-must remember that Eniac was originally designed as a special-purpose
-machine for solving trajectories. To calculate a large family of
-trajectories very little changing of wires and switches would be needed.
-<span class="pagenum" id="Page_126">[Pg 126]</span></p>
-
-<h4>Memory</h4>
-
-<p>The most severe limitation on the usefulness of Eniac was, at the
-outset, the fact that it had only 20 registers for storing numbers.
-There are large numbers of problems that cannot be simply handled with
-so small an internal memory. Even the Harvard IBM calculator (<a href="#CHAPTER_6">see Chapter 6</a>)
-is often strained during a problem because of the number of
-intermediate results that must be stored for a time before combining.
-The Ballistic Research Laboratories, however, contracted for extensions
-to Eniac to provide more memory and easier changing of instructions.</p>
-
-<h4>Reliability</h4>
-
-<p>Checking results with Eniac is not easy. There is no built-in guarantee
-that Eniac’s results are correct. A large calculator can and does make
-both constant and intermittent errors. Ways for checking with Eniac are:</p>
-
-<div class="blockquot">
-<p class="neg-indent">Mathematical, if and when available, and this
-will be seldom.</p>
-
-<p class="neg-indent">Running the problem a second time, and this will,
-at most, prove consistency.</p>
-
-<p class="neg-indent">Deliberate testing of small parts of the problem,
-which is very useful and is standard practice but leads only to a
-probability that the final result is correct.</p>
-</div>
-
-<p class="no-indent">You can operate Eniac one addition at a time, and
-even one pulse at a time, and see what the machine shows in its little
-neon bulbs. This is a very useful partial check.</p>
-
-<h4>Cost</h4>
-
-<p>The cost of Eniac is higher than that of some of the other large
-mechanical brains—over half a million dollars. Because some of the
-work was done at the Moore School by students, the cost was probably
-less than it otherwise would have been. The largest part of the cost
-was the designing of the machine and the construction of the panels;
-the tubes were only a small portion of the cost. The tubes used in
-the calculating circuits cost only 20 to 90 cents. However, no later electronic
-calculator need cost as much, for many improvements can now be seen.
-<span class="pagenum" id="Page_127">[Pg 127]</span></p>
-
-<p>The power required for Eniac is about 150 kilowatts or about 200
-horsepower, most of which is used for the heaters of the electronic
-tubes. The largest number of electronic tubes mentioned for future
-electronic calculators is about 3000, so we can see that they are
-likely to use less than a quarter of the power needed for Eniac.</p>
-
-<p>Eniac will doubtless give a number of years of successful operation
-and be extremely useful for problems that employ its assets and are
-not excluded by its limitations. In fact, at the Ballistic Research
-Laboratories, for a typical week of actual work, Eniac has already
-proved to be equal to 500 human computers working 40 hours with desk
-calculating machines, and it appears that soon two or three times as
-much work may be obtained from Eniac.</p>
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_128">[Pg 128]</span></p>
-<h2 class="nobreak" id="CHAPTER_8">Chapter 8<br />
-<span class="h_subtitle">RELIABILITY—NO WRONG RESULTS:<br />
-BELL LABORATORIES’<br />GENERAL-PURPOSE RELAY CALCULATOR</span></h2>
-</div>
-
-<p>In 1946, Bell Telephone Laboratories in New York finished two
-<i>general-purpose relay calculators</i>—mechanical brains. They
-were twins. One was shipped in July 1946 to the National Advisory
-Committee for Aeronautics at Langley Field, Virginia. The other, after
-some months of trial operation, was shipped in February 1947 to the
-Ballistic Research Laboratories at the U. S. Army’s Proving Ground,
-Aberdeen, Md.</p>
-
-<p>Each machine is remarkably reliable and versatile. It can do a wide
-variety of calculations in a great many different ways. Yet the machine
-never takes a new step without a check that the old step was correctly
-performed. There is, therefore, a chance of better than 99.999,999,999
-per cent that the machine will not let a wrong result come out. The
-automatic checking, of course, does not prevent (1) human mistakes—for
-example, instructing the machine incorrectly—or (2) mechanical
-failures, in which the machine stops dead in its tracks, letting no
-result at all come out.</p>
-
-<h3>ORIGIN AND DEVELOPMENT</h3>
-
-<p>In Bell Telephone Laboratories the telephone system of the country is
-continually studied. Their research produced the common type of dial
-telephone system: a masterly machine for selecting information.</p>
-
-<p>Now when a telephone engineer studies an electric circuit, he often
-<span class="pagenum" id="Page_129">[Pg 129]</span>
-finds it very convenient to use numbers in pairs: like 2, 5 or-4,-1.
-Here the comma is a separation sign to keep the two numbers in the pair
-separate and in sequence. Mathematicians call numbers of this kind, for
-no very good reason, <i>complex numbers</i>; of course, they are far
-less complex than why the sun shines or why plants grow.</p>
-
-<p>When Bell Laboratories test the design of new circuits, girl computers
-do arithmetic with complex numbers. Addition and subtraction are easy:
-each means two operations of addition or subtraction of ordinary
-numbers. For example, 2, 5, plus-4,-1 equals 2-4, 5-1, which
-equals-2, 4. And 2, 5 minus-4,-1 is the same as 2, 5 plus 4, 1;
-and this equals 2 + 4, 5 + 1, which equals 6, 6. Multiplication of
-two complex numbers, however, is more work. If <i>a</i>, <i>b</i> and
-<i>c</i>, <i>d</i> are two complex numbers, then the formula for their
-product is <big>(<i>a</i> × <i>c</i>)-(<i>b</i> × <i>d</i>), (<i>a</i>
-× <i>d</i>) + (<i>b</i> × <i>c</i>)</big>. To get the answer, we need 4
-multiplications, 1 subtraction, and 1 addition. Division of two complex
-numbers requires even more work. If <i>a</i>, <i>b</i> and <i>c</i>,
-<i>d</i> are two complex numbers, the formula for the quotient of
-<i>a</i>, <i>b</i> divided by <i>c</i>, <i>d</i> is:</p>
-
-<p class="f120 no-wrap">[(<i>a</i> × <i>c</i>) + (<i>b</i> × <i>d</i>)]
-                     ÷ [(<i>c</i> × <i>c</i>) + (<i>d</i> × <i>d</i>)],</p>
-
-<p class="f120 no-wrap">[(<i>b</i> × <i>c</i>) - (<i>a</i> × <i>d</i>)]
-                     ÷ [(<i>c</i> × <i>c</i>) + (<i>d</i> × <i>d</i>)]</p>
-
-<p class="no-indent">For example,</p>
-
-<p class="f120 no-wrap">(2, 5) ÷ (-4, -1) = [(2 × -4 = -8) + (5 × -1 = -5)]
-                      ÷ [(-4 × -4 = 16) + (-1 × -1 = 1)],</p>
-
-<p class="f120 no-wrap">[(5 × -4 = -20) - (2 × -1 = -2)] ÷ [16 + 1] = -(¹³/₁₇), -(¹⁸/₁₇)</p>
-
-<p class="no-indent">Thus, division of one complex number by another
-needs 6 multiplications, 2 additions, 1 subtraction, and 2 divisions of
-ordinary numbers—and always in the same pattern or sequence.</p>
-
-<h4>The Complex Computer</h4>
-
-<p>About 1939, an engineer at Bell Telephone Laboratories in New York, Dr.
-George R. Stibitz, noticed the great volume of this pattern arithmetic.
-He began to wonder why telephone switching equipment could not be used
-to do the multiplications and divisions automatically. He decided it
-could. All that was necessary was that the <i>relays</i> (<a href="#CHAPTER_2">see Chapter 2</a>)
-<span class="pagenum" id="Page_130">[Pg 130]</span>
-used in regular telephone equipment should have a way of remembering
-and calculating with numbers. Regular telephone equipment would take
-care of the proper sequence of operations. Regular equipment known as
-<i>teletypewriters</i> would print the numbers of the answer when it
-was obtained. A teletypewriter consists essentially of a typewriter
-that may be operated by electrical impulses. It has a keyboard that may
-produce electrical impulses in sets corresponding to letters; and it
-can receive or transmit over wires.</p>
-
-<p>Dr. Stibitz <i>coded</i> the numbers: each decimal digit was matched up
-with a group of four relays in sequence, and each of these relays could
-be open or closed. If 0 means open and 1 means closed, here is the
-pattern or code that he used:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Decimal<br /> Digit</span></th>
-      <th class="tdr">&nbsp;<span class="smcap">Relay Code</span>&nbsp;</th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdc">0</td>
-      <td class="tdc">0011</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdc">0100</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdc">0101</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdc">0110</td>
-   </tr><tr>
-      <td class="tdc">4</td>
-      <td class="tdc">0111</td>
-   </tr><tr>
-      <td class="tdc" colspan="2">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">5</td>
-      <td class="tdc">1000</td>
-   </tr><tr>
-      <td class="tdc">6</td>
-      <td class="tdc">1001</td>
-   </tr><tr>
-      <td class="tdc">7</td>
-      <td class="tdc">1010</td>
-   </tr><tr>
-      <td class="tdc">8</td>
-      <td class="tdc">1011</td>
-   </tr><tr>
-      <td class="tdc">9</td>
-      <td class="tdc">1100</td>
-   </tr>
- </tbody>
-</table>
-
-<p>With regular telephone relays and regular telephone company techniques,
-Dr. Stibitz and Bell Telephone Laboratories designed and constructed
-the machine. It was called the <i>Complex Computer</i> and was built
-just for multiplying and dividing complex numbers. Six or eight panels
-of relays and wires were in one room. Two floors away, some of the
-girl computers sat in another room, where one of the teletypewriters
-of the machine was located. When they wished, they could type into the
-machine’s teletypewriter the numbers to be multiplied or divided. In a
-few seconds back would come the answer. In fact, there were two more
-computing rooms where teletypewriters of the machine were stationed. To
-prevent conflicts between stations, the machine had a circuit like the
-busy signal from a telephone.</p>
-
-<p>In 1940, a demonstration of the Complex Computer took place: the
-<span class="pagenum" id="Page_131">[Pg 131]</span>
-computing panels remained in New York, but the teletypewriter
-input-output station was set up at Dartmouth College in Hanover, N. H.
-Mathematicians gave problems to the machine in Dartmouth, it solved
-them in New York, and it reported the answers in Dartmouth.</p>
-
-<h4>Special-Purpose Computers</h4>
-
-<p>With this as a beginning, Bell Laboratories developed another
-machine for a wide variety of mathematical processes called
-<i>interpolating</i> (<a href="#SUPPL_2">see Supplement 2</a>). Then,
-during World War II, Bell Laboratories made more special-purpose
-computing machines. They were used in military laboratories charged
-with testing the accuracy of instruments for controlling the fire of
-guns. These computers took in a set of gun-aiming directions put out
-by the <i>fire-control instrument</i> in some test. They also took in
-the set of observations that went into the fire-control instrument on
-that test. Then they computed the differences between the gun-aiming
-produced by the fire-control instrument and the gun-aiming really
-required by the observations. Using these differences, the fire-control
-instrument could be adjusted and corrected. These special-purpose
-computers were also useful in checking the design of new fire-control
-instruments and in checking changes due to new types of guns or
-explosives.</p>
-
-<p>Regularly, after each of these special-purpose computers was finished,
-people began to put other problems on it. It seemed to be fated that,
-as soon as you had made a machine for one purpose, you wanted to use
-it for something else. Accordingly, in 1944, two agencies of the U. S.
-Government together made a contract with Bell Telephone Laboratories
-for two general-purpose relay computers. These two machines were
-finished in 1946 and are twins.</p>
-
-<h3>ORGANIZATION OF THE<br /> GENERAL-PURPOSE COMPUTER</h3>
-
-<p>When a man sits down at a desk to work on a computation, he has six
-things on his desk to work with: a work sheet; a desk calculator, to
-add, subtract, multiply, and divide; some rules to be followed; the
-tables of numbers he will need; the data for the problem; and an answer
-sheet. In his head, he has the capacity to make decisions and to do his
-<span class="pagenum" id="Page_132">[Pg 132]</span>
-work in a certain sequence of steps. These seven subdivisions of
-calculation are all found in the Bell Laboratories’ general-purpose
-relay computer. The general-purpose computer is a computing system, in
-fact, more than it is a single machine. The part of the system which
-does the actual calculating is called, in the following paragraphs, the
-<i>computer</i>, or else, since it is in two halves, <i>Computer 1</i>
-and <i>Computer 2</i>.</p>
-
-<h4>Physical Units</h4>
-
-<p>The computing system delivered to the Ballistic Research Laboratories
-fills a room about 30 by 40 feet and consists of the following:</p>
-
-<div class="blockquot">
-<p class="neg-indent">2 <i>computers</i>: panels of relays, wiring,
-etc., which add, subtract, multiply, divide, select, decide, control,
-etc.</p>
-
-<p class="neg-indent">4 <i>problem positions</i>: tables each
-holding 12 mechanisms for feeding paper tape, which read numbers
-and instructions punched on tape and convert them into electrical
-impulses.</p>
-
-<p class="neg-indent">2 <i>hand perforators</i>: keyboard devices for
-punching instructions and numbers on paper tape.</p>
-
-<p class="neg-indent">1 <i>processor</i>: a table holding mechanisms
-for feeding 2 paper tapes and punching a third paper tape, used for
-checking numbers and instructions punched on tape.</p>
-
-<p class="neg-indent">2 <i>recorders</i>: each a table holding a
-teletypewriter, a tape punch, and a tape feed, used for recording
-answers and, if necessary, consulting them again.</p>
-</div>
-
-<p class="no-indent">The 2 computers correspond to the work sheet, the
-desk calculator, and the man’s capacity to make decisions and to carry
-out a sequence of steps. The 4 problem positions correspond to the
-problem data, the rules, and the tables of numbers. The 2 recorders
-correspond to the answer sheet. The 2 hand perforators and the
-processor are auxiliary machines: they translate the ordinary language
-of arithmetic into the machine language of punched holes in paper tape.</p>
-
-<p>This is the computing system as organized for the Ballistic
-Research Laboratories at Aberdeen. The one for the National
-Advisory Committee for Aeronautics has only 3 problem positions.
-The computer system may, in fact, be organized with 1
-to 10 computers and with 1 to 20 problem positions.
-<span class="pagenum" id="Page_133">[Pg 133]</span></p>
-
-<p>The great bulk of this computing system, like the mechanical brains
-described in previous chapters, is made up of large numbers of
-identical parts of only a few kinds. These are: standard telephone
-relays; wire; and standard <i>teletype transmitters</i>, mechanisms
-that read punched paper tape and produce electrical impulses.</p>
-
-<h4>Numbers</h4>
-
-<p>The numbers that the Bell machine contains range from
-0.1000000 to 0.9999999 times a <i>power</i> of 10 varying from
-10,000,000,000,000,000,000 to 0.000,000,000,000,000,000,1, or, in
-other words, from <big>10¹⁹</big> to <big>10⁻¹⁹</big>. The machine also contains zero and
-<i>infinity</i>: zero arises when the number is smaller than <big>10⁻¹⁹</big>,
-and infinity arises when the number is equal to or greater than
-9,999,999,000,000,000,000. (<a href="#SUPPL_2">See Supplement 2</a>.)</p>
-
-<p>The system used in the machine to represent numbers on relays is called
-<i>biquinary</i>—the <i>bi</i>-, because it is partly twofold like
-the hands, and the -<i>quinary</i> because it is partly fivefold like
-the fingers. This system is used in the abacus (see <a href="#CHAPTER_2">Chapter 2</a>
-and <a href="#SUPPL_2">Supplement 2</a>). In the machine, for each decimal digit,
-7 relays are used. These relays are called the 00 and 5 relays, and the 0, 1,
-2, 3, and 4 relays. If, as before, 0 indicates a relay that is not energized
-and 1 indicates a relay that is energized, then each decimal digit is
-represented by the positioning of the 7 relays as follows:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Decimal<br /> Digit</span></th>
-      <th class="tdc" colspan="2">&nbsp;</th>
-      <th class="tdr">&nbsp;<span class="smcap">Relays</span>&nbsp;</th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;00&nbsp;</td>
-      <td class="tdc">&nbsp;5&nbsp;</td>
-      <td class="tdc">&nbsp;0 1 2 3 4&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1 0 0 0 0</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0 1 0 0 0</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0 0 1 0 0</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0 0 0 1 0</td>
-   </tr><tr>
-      <td class="tdc">4</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0 0 0 0 1</td>
-   </tr><tr>
-      <td class="tdc" colspan="2">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">5</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">1 0 0 0 0</td>
-   </tr><tr>
-      <td class="tdc">6</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0 1 0 0 0</td>
-   </tr><tr>
-      <td class="tdc">7</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0 0 1 0 0</td>
-   </tr><tr>
-      <td class="tdc">8</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0 0 0 1 0</td>
-   </tr><tr>
-      <td class="tdc">9</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-      <td class="tdc">0 0 0 0 1</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Then, for any decimal digit, one and only one of
-<span class="pagenum" id="Page_134">[Pg 134]</span>
-the 00 and 5 relays is energized, and one and only one of the 0, 1, 2,
-3, and 4 relays is energized. If more or less than exactly one relay
-in each set is energized, then the machine knows that it has made a
-mistake, and it stops dead in its tracks. Thus any accidental failure
-of a relay is at once caught, and the chance of two compensating
-failures occurring at the same time is extremely small.</p>
-
-<h3>HOW INFORMATION GOES<br /> INTO THE MACHINE</h3>
-
-<p>In order to put a problem into this machine—just as with the other
-machines—first a mathematician who knows how the problem is to be
-solved, and who knows how to organize it for the machine, lays out
-the scheme of calculation. Then, a girl goes to one of the hand
-perforators. Sitting at the keyboard, she presses keys and punches out
-feet or yards of paper tape expressing the instructions and numbers for
-the calculation. Each character punched—digit, letter, or sign—has
-one or more of a maximum of 6 holes across the tape. Another girl,
-using the other hand perforator, also punches out the instructions and
-numbers for the calculation. If she wishes to erase a wrong character,
-she can press an <i>erase key</i> that punches all 6 holes, and then
-the machine will pass by this row as if it were not there.</p>
-
-<p>Three kinds of tapes are produced for the machine:</p>
-
-<div class="blockquot">
-<p class="neg-indent"><i>Problem tapes</i>, which contain information
-belonging to the particular problem.</p>
-
-<p class="neg-indent"><i>Table tapes</i>, which contain tables of
-numbers to be referred to from time to time.</p>
-
-<p class="neg-indent"><i>Routine tapes</i>, which contain the program,
-or routine, or sequence of steps that the machine is to carry out.</p>
-</div>
-
-<p class="no-indent">In each of these tapes one character takes up
-⅒ of an inch along the tape. In the case of a table tape, however,
-an ordinary 1-digit number requires 4 characters on the tape, and a
-7-digit number requires 11 characters on the tape. On a table tape
-there will be on the average about 1 inch of tape per number.</p>
-
-<h4>The Processor</h4>
-
-<p>The two paper tapes prepared on the perforator should agree. But
-<span class="pagenum" id="Page_135">[Pg 135]</span>
-whether or not they agree, a girl takes them over to the processor and
-puts them both in. The processor has two tape feeds, and she puts one
-tape on each and starts the machine. The processor compares them row by
-row, making sure that they agree, and punches a new tape row by row.
-If the two input tapes disagree, the processor stops. You can look to
-see which tape is right, and then you can put the correct punch into
-the new tape with a keyboard mounted on the processor. As the processor
-compares the two input tapes, it also converts any number written in
-the usual way into machine language. For example, the processor will
-automatically translate 23,188 into +.231 8800 × 10⁺⁵. The processor
-also puts in certain safeguards. If you want it to, the processor will
-also make a printed record of a tape. Also, when a tape becomes worn from
-use in the machine, you can put it into the processor and make a fresh copy.</p>
-
-<h4>The Problem Positions</h4>
-
-<p>Next, the girl takes the punched tape made by the processor over to a
-problem position that is idle. Two of the problem positions are always
-busy guiding the two computers. The other two problem positions stand
-by, ready to be loaded with problems.</p>
-
-<p>A problem position looks like a large covered-over table. Under the
-covers are 12 tape feeds, or <i>tape transmitters</i>. All these
-transmitters look exactly alike except for their labels and consist
-of regular teletype transmitters. Six-hole paper tape can be fed into
-any transmitter. Six metal fingers sense the holes in the paper tape
-and give out electrical impulses at proper times. At the front of the
-problem position is a small group of switches that provide complete
-control over the problem while it is on the machine. These are switches
-for starting, disconnecting, momentary stop, etc.</p>
-
-<p>One tape transmitter is the problem tape transmitter. It takes in
-all the data for the problem such as the starting numbers. The first
-thing it does at the start of a problem is to check (by comparing tape
-numbers) that the right tapes are in the right feeds.</p>
-
-<p>Five transmitters are routine tape transmitters. Each of these takes in
-<span class="pagenum" id="Page_136">[Pg 136]</span>
-the sequence of computing steps. The routine tapes also contain
-information for referring to table tapes and instructions for printing
-and punching tape. The machine can choose according to instructions
-between the five routine tapes and can choose between many different
-sections on each tape. Therefore, we can use a large number of
-different routines in a calculation, and this capacity makes the
-machine versatile and powerful.</p>
-
-<p>Six transmitters are table tape transmitters. They read tables of
-numbers when directed to. A table tape can be as long as 100 feet and
-will hold numbers at the rate of 1 inch per number, so that about 1200
-numbers of seven decimal digits can be stored on a table tape.</p>
-
-<p>When we look up a number in a table, such as the following,</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc bb">2½</td>
-      <td class="tdc bb">3</td>
-      <td class="tdc bb">3½</td>
-      <td class="tdc bb">&nbsp;···&nbsp;</td>
-   </tr><tr>
-      <td class="tdr br">1&nbsp;</td>
-      <td class="tdc">&nbsp;1.02500&nbsp;</td>
-      <td class="tdc">&nbsp;1.03000&nbsp;</td>
-      <td class="tdc">&nbsp;1.03500&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr br">2&nbsp;</td>
-      <td class="tdc">1.05063</td>
-      <td class="tdc">1.06090</td>
-      <td class="tdc">1.07123</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr br">3&nbsp;</td>
-      <td class="tdc">1.07689</td>
-      <td class="tdc">1.09273</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">···</td>
-   </tr><tr>
-      <td class="tdr br">4&nbsp;</td>
-      <td class="tdc">1.10381</td>
-      <td class="tdc">···</td>
-      <td class="tdc">···</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr br">5&nbsp;</td>
-      <td class="tdc">1.13141</td>
-      <td class="tdc">···</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr br">6&nbsp;</td>
-      <td class="tdc">1.15969</td>
-      <td class="tdc" colspan="3">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr br">7&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">···</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr br">8&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">···</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr br">9&nbsp;</td>
-      <td class="tdc">···</td>
-      <td class="tdc" colspan="3">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr br">10&nbsp;</td>
-      <td class="tdc" colspan="4">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr br">···&nbsp;</td>
-      <td class="tdc">···</td>
-      <td class="tdc" colspan="3">&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">we look along the top and down the side until we
-find the column and row of the number we are looking for. These are
-called the <i>arguments</i> of the <i>tabular value</i> that we are
-looking for (<a href="#SUPPL_2">see Supplement 2</a>). Now when we put
-this table on a tape to go into the Bell Laboratories machine, we write
-it all on one line, one figure after another, and we punch it as follows:</p>
-
-<p class="f120">2-½   1-5     1.02500    1.05063    1.07689    1.10381     1.13141<br />
-6-10    1.15969    ···      11-15     ···     ···      ···     3   1-5<br />
- 1.03000    1.06090    ···    ···    3½     1-5     1.03500 ···</p>
-
-<p class="no-indent">You will notice that the column labels 2½, 3, 3½
-have been put on the tape, each in front of the group of numbers they
-apply to. The row labels 1 to 5, 6 to 10, ··· have also been put on
-the tape, each in front of the group of numbers they apply to. The
-<span class="pagenum" id="Page_137">[Pg 137]</span>
-appropriate column and row numbers, or arguments, must be put often on
-every table tape, so that it is easy for the machine to tell what part
-of the table tape it is reading.</p>
-
-<p>In the Bell Laboratories machine, we do not need to put equal
-<i>blocks</i> of arguments like 1-5, 6-10 ··· on the table tape.
-Instead we can put individual arguments like 1, 2, 3, 4 ···, or, if we
-wish, we can use blocks of different sizes, like 1-3, 4-15, 16-30···.
-For some tables, such as income tax tables, it is very useful to have
-varying-sized blocks of arguments. The machine, when hunting for
-a certain value in the table, makes a comparison at each block of
-arguments.</p>
-
-<p>The machine needs about 6 seconds to search a foot of tape. If we want
-to set up a table economically, therefore, we need to consider the
-average length of time needed for searching.</p>
-
-<div class="figcenter">
-  <img id="FIG_1-8" src="images/i_137.jpg" alt="" width="500" height="429" />
-  <p class="f120"><span class="smcap">Fig. 1.</span> Scheme of a recorder.</p>
-</div>
-
-<h3>HOW INFORMATION COMES<br /> OUT OF THE MACHINE</h3>
-
-<p>At either one of the two recorders (<a href="#FIG_1-8">Fig. 1</a>), information
-comes out of the machine, either in the form of printed characters or as punched
-tape. The recorder consists of a <i>printer</i>, a <i>reperforator</i>,
-and a tape transmitter. One recorder table belongs to each computer
-and records the results it computes. The printer is a regular
-teletypewriter connected to the machine. It translates information
-produced by the machine as electrical impulses and prints the
-information in letters and digits on paper. The reperforator is an
-<span class="pagenum" id="Page_138">[Pg 138]</span>
-automatic tape punch. It translates information produced by the machine
-in the form of electrical impulses and punches the information on
-paper tape. Next to the tape punch is a tape transmitter. After the
-tape comes through the punch, it is fed into the transmitter. Here the
-machine can hunt for a previous result punched in the tape, read that
-result, and use it again.</p>
-
-<h3>HOW INFORMATION IS MANIPULATED<br /> IN THE MACHINE</h3>
-
-<p>The main part of the computing system consists of 27 large frames
-loaded with relays and wiring, called the <i>computer</i>, or
-<i>Computer 1</i> and <i>Computer 2</i>. In this “telephone central
-station,” all the “phone calls” from one number to another are attended
-to. There are 8 types of these frames in the computer:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Frames</span></th>
-      <th class="tdr"><span class="smcap">Number</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdl">Storing register frames</td>
-      <td class="tdc">6</td>
-   </tr><tr>
-      <td class="tdl">Printer frames</td>
-      <td class="tdc">2</td>
-   </tr><tr>
-      <td class="tdl">Problem frames</td>
-      <td class="tdc">2</td>
-   </tr><tr>
-      <td class="tdl">Position frames</td>
-      <td class="tdc">2</td>
-   </tr><tr>
-      <td class="tdl">Calculator frames</td>
-      <td class="tdc">6</td>
-   </tr><tr>
-      <td class="tdl">Control frames</td>
-      <td class="tdc">2</td>
-   </tr><tr>
-      <td class="tdl">Routine frames</td>
-      <td class="tdc">4</td>
-   </tr><tr>
-      <td class="tdl">BTL (Block-Trig-Log) frames</td>
-      <td class="tdc">2</td>
-   </tr><tr>
-      <td class="tdl">Permanent table frames</td>
-      <td class="tdc">1</td>
-   </tr><tr>
-      <td class="tdl_ws1">&nbsp;&emsp;Total</td>
-      <td class="tdc bt">27</td>
-   </tr>
- </tbody>
-</table>
-
-<p>In most but not quite all respects, the two halves, <i>Computer 1</i>
-and <i>Computer 2</i>, can compute independently. The <i>storing
-register frames</i> hold enough relays to store 30 numbers. The
-registers for these numbers are named <i>A, B, C, D</i>, ···, <i>M, N,
-O</i> in two groups of 15 each. One group belongs to Computer 1 and the
-other to Computer 2. In each Computer, the <i>calculator frames</i>
-hold enough relays for storing two numbers (held in the <i>X</i>
-and <i>Y</i> registers) and for performing addition, subtraction,
-multiplication, division, and square root. In each Computer, the
-<i>problem frame</i> stores the numbers that are read off the problem
-tape and the table tapes, and the <i>printer frame</i> stores the
-numbers that are read into the printer. The printer frame also stores
-indications, for example, the signs of numbers, plus or minus, for
-<span class="pagenum" id="Page_139">[Pg 139]</span>
-purposes of combining them. These frames also hold the relays that
-control the printer, the problem tape, and the table tapes. Jointly
-for both Computers, the <i>position frames</i> connect a problem in
-some problem position to a Computer that becomes idle. For example,
-one problem may finish in the middle of the night; the machine
-automatically and unattended switches to another problem position and
-proceeds with the instructions there contained. A backlog of computing
-on hand can be stored in two of the problem positions, while the
-other two control the two Computers. In each Computer, the <i>routine
-frames</i> hold the relays that make the Computer follow the routine
-instructions. Jointly for both Computers, the remaining frames—the
-<i>control frames</i>, the <i>BTL frames</i>, and the <i>permanent
-table frames</i>—hold the relays that control: the alarms and lights
-for indicating failures; some circuits called the BTL controls; the
-tape processor; and the mathematical tables that are permanently
-wired into the machine. The permanent table frames hold the following
-mathematical functions (<a href="#SUPPL_2">see Supplement 2</a>):
-<i>sine</i>, <i>cosine</i>, <i>antitangent</i>, <i>logarithm</i>,
-and <i>antilogarithm</i>.</p>
-
-<h4>Storing</h4>
-
-<p>Numbers can be stored in the machine in the 30 regular storing
-registers of both Computers together. They can also be stored, at the
-cost of tying up some machine capacity, in the other registers: the 4
-calculator registers, the 2 problem registers, the 2 table registers,
-and the 2 printer registers. Numbers can also be punched out on tape,
-in either of the two printers, and later read again from the tape.
-Labels identifying the numbers can also be punched and read again from
-the tape.</p>
-
-<p>Each register in the machine stores a number in the biquinary notation,
-as explained above. In programming the machine, after mentioning a
-register it is necessary—as a part of the scheme for checking—to tell
-the machine specifically whether to hold the number in the register or
-to clear it.</p>
-
-<h4>Addition and Subtraction</h4>
-
-<p>The calculator frames can add two numbers together, if so instructed
-in the routine tape. Suppose that the two numbers are in the registers
-<span class="pagenum" id="Page_140">[Pg 140]</span>
-<i>B</i> and <i>D</i> and that we wish to put the sum in register
-<i>F</i>. Suppose that we wish to clear the <i>D</i> number but hold
-the <i>B</i> number after using them. The code on the routine tape is
-<i>B H</i> + <i>D C</i> = <i>F</i>. <i>H</i> and <i>C</i> coming right
-after the names of the registers always designate “hold” and “clear,”
-respectively.</p>
-
-<p>The calculator frames can, likewise, subtract a number. The routine
-instruction <i>B H</i>-<i>D C</i> = <i>F</i> means:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub1">Take the number in register <i>B</i> (hold it);</li>
-<li class="isub2">subtract the number in <i>D</i> (clear it);</li>
-<li class="isub2">put the result in <i>F</i></li>
-</ul>
-
-<h4>Multiplication and Division</h4>
-
-<p>The calculator frames perform multiplication by storing the digits of
-the multiplier, adding the multiplicand over and over, and shifting,
-until the product is obtained. However, if the multiplier is 1989, for
-example, the calculator treats it as 2000-11. This short-cut applies
-to digits 6, 7, 8, 9 and cuts the time required for multiplying. The
-routine instruction is <i>B H</i> × <i>D C</i> = <i>F</i>.</p>
-
-<p>The calculator performs division by repeated subtraction. The routine
-instruction is <i>B H</i> ÷ <i>D C</i> = <i>F</i>. The operation signs
-<big>+,-, ×, ÷</big> actually appear on the keyboard of the perforator and on the
-printed tape produced by the printer.</p>
-
-<h4>Discrimination</h4>
-
-<p><i>Discrimination</i> is the term used in the Bell Laboratories
-computer for what we have previously called selection, or comparison,
-or sequencing. The <i>discriminator</i> is a part of the calculator
-that compares or selects or decides—“discriminates.” The discriminator
-can decide whether a number is zero or not zero. In the language of
-the <i>algebra of logic</i> (see <a href="#CHAPTER_9">Chapter 9</a> and <a href="#SUPPL_2">Supplement 2</a>),
-if <i>a</i> is a number, the discriminator can find <i>T</i>(<i>a</i> = 0).
-The discriminator can also decide whether a number is positive or
-negative. In the language of logic, it can find <i>T</i>(<i>a</i> &gt; 0)
-or <i>T</i>(<i>a</i> &lt; 0). The actions that a discriminator can cause
-to be taken are:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">Stop the machine.</li>
-<li class="isub2">Stop the problem, and proceed to another problem.</li>
-<li class="isub2">Stop the routine going on, and proceed with a new routine.</li>
-<li class="isub2">Permit printing, or prevent printing; etc.</li>
-</ul>
-
-<p class="no-indent"><span class="pagenum" id="Page_141">[Pg 141]</span>
-In this way the discriminator can:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">Distinguish between right and wrong results.</li>
-<li class="isub2">Tell that a certain result is impossible.</li>
-<li class="isub2">Recognize a certain result to be the answer.</li>
-<li class="isub2">Control the number of repetitions of a formula.</li>
-<li class="isub2">Change from one formula to another formula.</li>
-<li class="isub2">Check a number against a tolerance; etc.</li>
-</ul>
-
-<h3>PROBLEMS</h3>
-
-<p>Among the problems that have been placed on the machine successfully
-are: solving the <i>differential equation</i> of a <i>trajectory</i>
-(<a href="#CHAPTER_5">see Chapter 5</a>) and solving 32 <i>linear simultaneous equations</i> in
-32 <i>unknowns</i> (<a href="#SUPPL_2">see Supplement 2</a>). In the second case,
-the routine tapes were designed to apply equally well to 11 to 100 linear equations
-in 11 to 100 unknowns. However, the machine can do a very broad class
-of problems, including, for example, computing a personal income tax.
-This calculation with all its complexity of choices cannot be placed
-on any of the mechanical brains described in previous chapters. The
-machine can, of course, be used to calculate any tables that we may
-wish to refer to.</p>
-
-<h3>AN APPRAISAL OF THE CALCULATOR</h3>
-
-<p>The Bell Telephone Laboratories general-purpose relay computer is
-probably the best mechanical brain made up to the end of 1947, in
-regard to the two important factors of reliability and versatility.</p>
-
-<h4>Reliability</h4>
-
-<p>The machine produces results that are practically 100 per cent
-reliable, for the machine checks each step before taking the next one.
-The checking principle is that exactly a certain number of relays must
-be energized. For example, as we said before, for each decimal digit
-there are 7 relays. Exactly 2 of these relays must be energized—no
-more, no less. If this does not happen, the machine stops at once
-without losing any numbers. Lights shine for many circuits in the
-<span class="pagenum" id="Page_142">[Pg 142]</span>
-control panel, and, if you compare what they ought to show with
-what they do show, you can usually find at once the location of the
-mistake. The trouble may be a speck of dirt between two contact points
-on a relay, and, when it is brushed away, the machine can go right
-ahead from where it stopped. According to a statement by Franz L.
-Alt, director of the computing laboratory at the Ballistic Research
-Laboratories, in December 1947, “the Bell machine had not given a
-single wrong result in eight months of operation, except when operators
-interfered with its normal running.”</p>
-
-<p>To guard against the risk of putting tapes in the wrong transmitters,
-the machine will check by the instructions contained in the tapes that
-the right tapes are in the right places.</p>
-
-<h4>Time Required</h4>
-
-<p>The time required to do problems on this mechanical brain is perhaps
-longer than on the others. The numbers are handled digit by digit on
-the input tapes, and the typewriter in the recorder moves space by
-space in order to get to the proper writing point. These are slow
-procedures. The speeds of numerical operation are: addition, ³/₁₀
-second; multiplication, 1 second on the average; division, 2.7 seconds
-on the average; square root, 4.5 seconds on the average; logarithm,
-about 15 seconds.</p>
-
-<h4>Staff</h4>
-
-<p>In order to operate the machine, the staff required is: one maintenance
-man; one mathematical engineer; about six girls for punching tape,
-etc., depending on the number of problems to be handled at the rate of
-about one problem per week per girl. Unlike any of the other mechanical
-brains built by the end of 1947, this machine will run unattended.</p>
-
-<h4>Maintenance</h4>
-
-<p>The relays in the machine will operate for years with no failure; they
-have the experience of standard telephone techniques built into them.
-Under laboratory conditions this type of relay had by 1946 operated
-successfully much more than 100 million times. The tape feeding
-and reading equipment in the machine may be maintained by periodic
-<span class="pagenum" id="Page_143">[Pg 143]</span>
-inspection and service. The total number of teletype transmitters in
-the machine is 38. If one fails, it is easy to plug in a spare.</p>
-
-<p>The total power required for the machine is about 28 horsepower.
-Batteries are furnished so that, if the power supply should be
-interrupted, the machine can still operate for as long as a half-hour.</p>
-
-<h4>Cost</h4>
-
-<p>The cost of production of this machine in the size of 4 problem
-positions and 2 computers has been roughly estimated as half a million
-dollars. This cost includes material, manufacture, installation, and
-testing. No development cost is included in this figure. Instead, the
-cost of development has been reckoned as squaring with patents and
-other contributions of the work to the telephone switching art.</p>
-
-<p>It is unlikely that the general-purpose relay computer will be
-manufactured generally. The pressure of orders for telephones, the
-need to catch up with the backlog of demand, and the development of
-electronic computers—all indicate that the Bell system will hardly
-go further with this type of computer. In an emergency, however, the
-Bell system would probably construct such machines for the government,
-if requested. In the meantime, many principles first used in the
-general-purpose relay computer are likely to find applications in
-telephone system work. In fact, a present major development being
-pursued in the telephone sections of Bell Laboratories is the
-application of the computer principles to the automatic computation
-of telephone bills.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_144">[Pg 144]</span></p>
-<h2 class="nobreak" id="CHAPTER_9">Chapter 9<br />
-<span class="h_subtitle">REASONING:<br />
-THE KALIN-BURKHART<br />LOGICAL-TRUTH CALCULATOR</span></h2>
-</div>
-
-<p>So far we have talked about mechanical brains that are mathematicians.
-They are fond of numbers; their main work is with numbers; and the
-other kinds of thinking they do are secondary. We now come to a
-mechanical brain that is a logician. It is fond of reasoning—logic;
-its main work is with what is logically true and what is logically
-false; and it does not handle numbers. This mechanical brain was
-finished in June 1947. It is called the <i>Kalin-Burkhart Logical-Truth
-Calculator</i>. As its name tells, it calculates <i>logical truth</i>.
-Now what do we mean by that?</p>
-
-<h3>TRUTH</h3>
-
-<p>To be true or false is a property of a statement. Usually we say that
-a statement is true when it expresses a fact. For example, take the
-statement “Salt dissolves in water.” We consider this statement to be
-true because it expresses a fact. Actually, in this case we can roughly
-prove the fact ourselves. We take a bowl, put some water in it, and put
-in a little salt. After a while we look into the water and notice that
-no salt whatever is to be seen.</p>
-
-<p>Of course, this statement, like many another, occurs in a
-<i>context</i> where certain things are understood. One of the
-understandings here, for example, is “a small amount of salt in a much
-larger amount of water.” For if we put a whole bag full of salt in just
-a little water, not all the salt will dissolve. Nearly every statement
-occurs in a context that we must know if we are to decide whether the
-statement is true or false.
-<span class="pagenum" id="Page_145">[Pg 145]</span></p>
-
-<h3>LOGICAL TRUTH</h3>
-
-<p>Logical truth is different from ordinary truth. With logical truth
-we appeal not to facts but to suppositions. Usually we say that a
-statement is logically true when it follows logically from certain
-suppositions. In other words, we play a game that has useful, even
-wonderful, results. The game starts with “if” or “suppose” or “let us
-assume.” While the game lasts, any statement is logically true if it
-follows logically from the suppositions.</p>
-
-<p>For example, let us take five statements:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">1. “The earth is flat like a sheet of paper.”</li>
-<li class="isub2">2. “The earth is round like a ball.”</li>
-<li class="isub2">3. “John Doe travels as fast as he can, without turning</li>
-<li class="isub4">to left or to right, for many days.”</li>
-<li class="isub2">4. “John Doe will fall off the earth.”</li>
-<li class="isub2">5. “John Doe will arrive back at his starting point.”</li>
-</ul>
-
-<p class="no-indent">Let us also take a certain context in which: We
-know what we mean by such words as “earth,” “flat,” “falling,” etc.;
-we have other statements and understandings such as “if John Doe walks
-off the edge of a cliff, he will fall,” “a flat sheet of paper has an
-edge,” etc. In this context, if statements 1 and 3 are supposed, then
-statement 4 is logically true. On the other hand, if statements 2 and 3
-are supposed, then statement 5 is logically true. Of course, for many
-centuries, nearly all men believed statement 1; and the importance of
-the years 1492 to 1521 (Columbus to Magellan) is linked with the final
-proof that statement 2 expresses a fact. So, depending on the game,
-or the context, whichever we wish to call it, almost any statement
-can be logically true. What we become interested in, therefore,
-is the connections between statements which make them <i>follow
-logically</i>.</p>
-
-<h3>LOGICAL PATTERNS</h3>
-
-<p>Perhaps the most familiar example of “following logically” is a pattern
-of words like the following:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">1. All igs are ows.</li>
-<li class="isub2">2. All ows are umphs.</li>
-<li class="isub2">3. Therefore, all igs are umphs.</li>
-</ul>
-
-<p class="no-indent"><span class="pagenum" id="Page_146">[Pg 146]</span>
-If statements 1 and 2 are supposed, then statement 3 is logically true.
-In other words, statement 3 logically follows from statements 1 and 2.
-This word pattern is logically true, no matter what substitutions we
-make for igs, ows, and umphs. For example, we can replace igs by men,
-ows by animals, and umphs by mortals, and obtain:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">4. All men are animals.</li>
-<li class="isub2">5. All animals are mortals.</li>
-<li class="isub2">6. Therefore, all men are mortals.</li>
-</ul>
-
-<p class="no-indent">The invented words “igs,” “ows,” “umphs” mark
-places in the <i>logical pattern</i> where we can insert any names we
-are interested in. The words “all,” “are,” “therefore” and the ending
-s mark the logical pattern. Of course, instead of using invented words
-like “igs,” “ows,” “umphs” we would usually put <i>A</i>’s, <i>B</i>’s,
-<i>C</i>’s. This logical pattern is called a <i>syllogism</i> and is
-one of the most familiar. But there are even simpler logical patterns
-that are also familiar.</p>
-
-<h3>THE SIMPLEST LOGICAL PATTERNS</h3>
-
-<p>Many simple logical patterns are so familiar that we often use them
-without being conscious of doing so. The simple logical patterns are
-marked by words like “and,” “or,” “else,” “not,” “if,” “then,” “only.”
-In the same way, simple arithmetical patterns are marked by words like
-“plus,” “minus,” “times,” “divided by.”</p>
-
-<p>Let us see what some of these simple logical patterns are. Suppose that
-we take two statements about which we have no factual information that
-might interfere with logical supposing:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">1. John Doe is eligible for insurance.</li>
-<li class="isub2">2. John Doe requires a medical examination.</li>
-</ul>
-
-<p class="no-indent">In practice, we might be concerned with such
-statements when writing the rules governing a plan of insurance for a
-group of employees. Here, we shall play a game:
-<span class="pagenum" id="Page_147">[Pg 147]</span></p>
-
-<div class="blockquot">
-<p class="neg-indent">(1) We shall make up some new statements from
-statements 1 and 2, using the words “and,” “or,” “else,” “not,” “if,”
-“then,” “only.”</p>
-
-<p class="neg-indent">(2) We shall examine the logical patterns that we
-can make.</p>
-
-<p class="neg-indent">(3) We shall see what we can find out about their
-logical truth.</p>
-</div>
-
-<p class="no-indent">Suppose we make up the following statements:</p>
-
-<div class="blockquot">
-<p class="neg-indent">3. John Doe is not eligible for insurance.</p>
-
-<p class="neg-indent">4. John Doe does not require a medical
-examination.</p>
-
-<p class="neg-indent">5. John Doe is eligible for insurance and
-requires a medical examination.</p>
-
-<p class="neg-indent">6. John Doe is eligible for insurance, and John
-Doe is eligible for insurance.</p>
-
-<p class="neg-indent">7. John Doe is eligible for insurance, or John
-Doe requires a medical examination.</p>
-
-<p class="neg-indent">8. If John Doe is eligible for insurance, then he
-requires a medical examination.</p>
-
-<p class="neg-indent">9. John Doe requires a medical examination if and
-only if he is eligible for insurance.</p>
-
-<p class="neg-indent">10. John Doe is eligible for insurance or else he
-requires a medical examination.</p>
-</div>
-
-<p class="no-indent">Now clearly it is troublesome to repeat quantities of words when we
-are interested only in the way that “and,” “or,” “else,” “not,” “if,”
-“then,” “only” occur. So, let us use just 1 and 2 for the two original
-statements, remembering that “1 <span class="smcap">and</span> 2” means here “statement 1
-<span class="allsmcap">AND</span> statement 2” and does not mean 1 plus 2. Then we have:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary="" cellpadding="2" >
-  <tbody><tr>
-      <td class="tdr">3:</td>
-      <td class="tdl_ws1"><span class="smcap">not</span>-1</td>
-   </tr><tr>
-      <td class="tdr">4:</td>
-      <td class="tdl_ws1"><span class="smcap">not</span>-2</td>
-   </tr><tr>
-      <td class="tdr">5:</td>
-      <td class="tdl_ws1">1 <span class="smcap">and</span> 2</td>
-   </tr><tr>
-      <td class="tdr">6:</td>
-      <td class="tdl_ws1">1 <span class="smcap">and</span> 1</td>
-   </tr><tr>
-      <td class="tdr">7:</td>
-      <td class="tdl_ws1">1 <span class="smcap">or</span> 2</td>
-   </tr><tr>
-      <td class="tdr">8:</td>
-      <td class="tdl_ws1"><span class="smcap">if</span> 1, <span class="smcap">then</span> 2</td>
-   </tr><tr>
-      <td class="tdr">9:</td>
-      <td class="tdl_ws1">1 <span class="smcap">if and only if</span> 2</td>
-   </tr><tr>
-      <td class="tdr">10:</td>
-      <td class="tdl_ws1">1 <span class="smcap">or else</span> 2</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Here then are some simple logical patterns that we can make.</p>
-
-<h3>CALCULATION OF LOGICAL TRUTH</h3>
-
-<p>Now what can we find out about the logical truth of statements 3 to 10?
-<span class="pagenum" id="Page_148">[Pg 148]</span>
-If we know something about the truth or falsity of statements 1 and 2,
-what will logically follow about the truth or falsity of statements
-3 to 10? In other words, how can we calculate the logical truth of
-statements 3 to 10, given the truth or falsity of statements 1 and 2?</p>
-
-<p>For example, 3 is <span class="smcap">not</span>-1; that is, statement 3 is the negative
-or the <i>denial</i> of statement 1. It follows logically that, if 1
-is true, 3 is false; if 1 is false, 3 is true. Suppose that we use
-<i>T</i> for logically true and <i>F</i> for logically false. Then we
-can show our calculation of the logical truth of statement 3 in Table 1.</p>
-
-<table id="TABLE_1-2" class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc" colspan="2"><b>Table 1</b></td>
-      <td class="tdc" rowspan="5"><span class="ws2">&nbsp;</span></td>
-      <td class="tdc" colspan="2"><b>Table 2</b></td>
-   </tr><tr>
-      <td class="tdr br">1&nbsp;</td>
-      <td class="tdl">&nbsp;<span class="smcap">not</span>-1 = 3</td>
-      <td class="tdr br">2&nbsp;</td>
-      <td class="tdl">&nbsp;<span class="smcap">not</span>-2 = 4</td>
-   </tr><tr>
-      <td class="tdr br">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;</td>
-      <td class="tdr br">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr br"><i>T</i>&nbsp;</td>
-      <td class="tdl">&nbsp;<i>F</i></td>
-      <td class="tdr br"><i>T</i>&nbsp;</td>
-      <td class="tdl">&nbsp;<i>F</i></td>
-   </tr><tr>
-      <td class="tdr br"><i>F</i>&nbsp;</td>
-      <td class="tdl">&nbsp;<i>T</i></td>
-      <td class="tdr br"><i>F</i>&nbsp;</td>
-      <td class="tdl">&nbsp;<i>T</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Our rule for calculation is: For <i>T</i> put
-<i>F</i>; for <i>F</i> put <i>T</i>. Of course, exactly the same rule
-applies to statements 2 and 4 (<a href="#TABLE_1-2">see Table 2</a>).
-The <i>T</i> and <i>F</i> are called <i>truth values</i>. Any
-meaningful statement can have truth values. This type of table is
-called a <i>truth table</i>. For any logical pattern, we can make up a
-truth table.</p>
-
-<p>Let us take another example, “<span class="smcap">and</span>.” Statement 5 is the same
-as statement 1 <span class="smcap">and</span> statement 2. How can we calculate the
-logical truth of statement 5? We can make up the same sort of a table
-as before. On the left-hand side of this table, there will be 4 cases:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">1. Statement 1 true, statement 2 true.</li>
-<li class="isub2">2. Statement 1 false, statement 2 true.</li>
-<li class="isub2">3. Statement 1 true, statement 2 false.</li>
-<li class="isub2">4. Statement 1 false, statement 2 false.</li>
-</ul>
-
-<p class="no-indent">On the right-hand side of this table, we shall
-put down the truth value of statement 5. Statement 5 is true if both
-statements 1 and 2 are true; statement 5 is false in the other cases.
-We know this from our common everyday experience with the meaning of
-“<span class="smcap">and</span>” between statements. So we can set up
-the truth table, and our rule for calculation of logical truth, in the
-case of <span class="smcap">and</span>, is shown on <a href="#TABLE_3">Table 3</a>.
-<span class="pagenum" id="Page_149">[Pg 149]</span></p>
-
-<p id="TABLE_3" class="f150"><b>Table 3</b></p>
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc">&nbsp;&nbsp;1&nbsp;&nbsp;</td>
-      <td class="tdr br">&nbsp;&nbsp;2&nbsp;&nbsp;</td>
-      <td class="tdl">&nbsp;&nbsp;1 <span class="smcap">and</span> 2 = 5</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc br">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdr br"><i>T</i>&nbsp;</td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdr br"><i>T</i>&nbsp;</td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdr br"><i>F</i>&nbsp;</td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdr br"><i>F</i>&nbsp;</td>
-      <td class="tdc"><i>F</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p>“<span class="smcap">and</span>” and the other words and phrases joining together
-the original two statements to make new statements are called <i>connectives</i>,
-or <i>logical connectives</i>. The connectives that we have
-illustrated in statements 7 to 10 are: <span class="smcap">or</span>,
-<span class="smcap">if</span> ··· <span class="smcap">then</span>, <span class="smcap">if
-and only if</span>, <span class="smcap">or else</span>.</p>
-
-<p><a href="#TABLE_4">Table 4</a> shows the truth table that applies to
-statements 7, 8, 9, and 10. This truth table expresses the calculation
-of the logical truth or falsity of these statements.</p>
-
-<p id="TABLE_4" class="f150"><b>Table 4</b></p>
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc br">&nbsp;</td>
-      <td class="tdc_ws1">1 <span class="smcap">or</span> 2</td>
-      <td class="tdc_ws1"><span class="smcap">if</span> 1, <span class="smcap">then</span> 2</td>
-      <td class="tdc_ws1">1 <span class="smcap">if and only if</span> 2</td>
-      <td class="tdc_ws1">1 <span class="smcap">or else</span> 2</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;&nbsp;1&nbsp;&nbsp;</td>
-      <td class="tdc br">&nbsp;&nbsp;2&nbsp;&nbsp;</td>
-      <td class="tdc">= 7</td>
-      <td class="tdc">= 8</td>
-      <td class="tdc">= 9</td>
-      <td class="tdc">= 10</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc br">&nbsp;</td>
-      <td class="tdc" colspan="4">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc br"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc br"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc br"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc br"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">The “<span class="smcap">or</span>” (as in statement 7) that is
-defined in the truth table is often called the <i>inclusive “or”</i> and means
-“<span class="smcap">and/or</span>.” Statement 7, “1 <span class="smcap">or</span> 2,” is considered to
-be the same as “1 <span class="smcap">or</span> 2 <span class="smcap">or both</span>.” There is another
-“<span class="smcap">or</span>” in common use, often called the <i>exclusive “or,”</i>
-meaning “<span class="smcap">or else</span>” (as in statement 10). Statement 10, “1
-<span class="smcap">or else</span> 2,” is the same as “1 <span class="smcap">or</span> 2 <span class="smcap">but not
-both</span>” or “<span class="smcap">either</span> 1 <span class="smcap">or</span> 2.” In ordinary English,
-there is some confusion over these two “<span class="smcap">or</span>’s.” Usually we rely
-on the context to tell which one is intended. Of course, such reliance
-is not safe. Sometimes we rely on a necessary conflict between the
-two statements connected by “<span class="smcap">or</span>” which prevents the “both”
-case from being possible. In Latin the two kinds of “<span class="smcap">or</span>” were
-distinguished by different words, <i>vel</i> meaning “<span class="smcap">and/or</span>,”
-and <i>aut</i> meaning “<span class="smcap">or else</span>.”
-<span class="pagenum" id="Page_150">[Pg 150]</span></p>
-
-<p>The “<span class="smcap">if</span> ··· <span class="smcap">then</span>” that is defined in the truth table
-agrees with our usual understanding that (1) when the “<span class="smcap">if</span>
-clause” is true, the “<span class="smcap">then</span> clause” must be true; and (2) when
-the “<span class="smcap">if</span> clause” is false, the “<span class="smcap">then</span> clause” may be
-either true or false. The “<span class="smcap">if and only if</span>” that is defined in
-the truth table agrees with our usual understanding that (1) if either
-clause is true, the other is true; and (2) if either clause is false,
-the other is false.</p>
-
-<p>In statement 6, there are only two possible cases, and the truth table
-is shown in <a href="#TABLE_5">Table 5</a>.</p>
-
-<p id="TABLE_5" class="f150"><b>Table 5</b></p>
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdr br">&nbsp;&nbsp;1&nbsp;&nbsp;</td>
-      <td class="tdl">&nbsp;&nbsp;1 <span class="smcap">and</span> 1 = 6</td>
-   </tr><tr>
-      <td class="tdc br">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc br"><i>T</i></td>
-      <td class="tdc"><i>T</i>&nbsp;</td>
-   </tr><tr>
-      <td class="tdc br"><i>F</i></td>
-      <td class="tdc"><i>F</i>&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">We know that 6 is true if and only if 1 is true. In other
-words, the statement “1 <span class="smcap">and</span> 1 <span class="smcap">if
-and only if</span> 1” is true, no matter what statement 1 may refer to.
-It is because of this fact that we never use a statement in the form “1
-and 1”: it can always be replaced by the plain statement “1.”</p>
-
-<h3>LOGICAL-TRUTH CALCULATION BY<br /> EXAMINING CASES AND REASONING</h3>
-
-<p>Now you may say that this is all very well, but what good is it? Almost
-anybody can use these connectives correctly and certainly has had a
-great deal of practice using them. Why do we need to go into truth
-values and truth tables?</p>
-
-<p>When we draft a contract or a set of rules, we often have to consider
-several conditions that give rise to a number of cases. We must avoid:</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. All <i>conflicts</i>, in which two statements
-that disagree apply to the same case.</p>
-
-<p class="neg-indent">2. All <i>loopholes</i>, in which there is a case
-not covered by any statement.</p>
-</div>
-
-<p class="no-indent">If we have one statement or condition only, we have to
-consider 2 possible cases: the condition satisfied or the statement true;
-<span class="pagenum" id="Page_151">[Pg 151]</span>
-the condition not satisfied or the statement false. If we have 2
-conditions, we have to consider 4 possible cases: true, true; false,
-true; true, false; false, false. If we have 3 conditions, we have to
-consider 8 possible cases one after the other (<a href="#TABLE_6">see Table 6</a>).</p>
-
-<p id="TABLE_6" class="f150"><b>Table 6</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc"><span class="smcap">Case</span></td>
-      <td class="tdc"><span class="smcap">1st<br />&nbsp;Condition&nbsp;</span></td>
-      <td class="tdc"><span class="smcap">2nd<br />&nbsp;Condition&nbsp;</span></td>
-      <td class="tdc"><span class="smcap">3rd<br />&nbsp;Condition&nbsp;</span></td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc">4</td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc" colspan="4">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">5</td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc">6</td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc">7</td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc">8</td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Instead of <i>T</i>’s and <i>F</i>’s, we would
-ordinarily use <i>check-marks</i> <big>(✓)</big> and <i>crosses</i>
-<big>(✕)</big>, which, of course, have the same meaning. We may
-consider and study each case individually. In any event, we must make
-sure that the proposed contract or set of rules covers all the cases
-without conflicts or loopholes.</p>
-
-<p>The number of possible cases that we have to consider doubles whenever
-one more condition is added. Clearly, it soon becomes too much work
-to consider each case individually, and so we must turn to a second
-method, thoughtful classifying and reasoning about classes of cases.</p>
-
-<p>Now suppose that the number of conditions increases: 4 conditions give
-rise to 16 possible cases; 5, 6, 7, 8, 9, 10, ··· conditions give rise
-to 32, 64, 128, 256, 512, 1024, ··· cases respectively. Because of the
-large number of cases, we soon begin to make mistakes while reasoning
-about classes of cases. We need a more efficient way of knowing whether
-all cases are covered properly.</p>
-
-<h3>LOGICAL-TRUTH CALCULATION<br />BY ALGEBRA</h3>
-
-<p>One of the more efficient ways of reasoning is often called the
-<i>algebra of logic</i>. This algebra is a part of a new science called
-<i>mathematical logic</i>. Mathematical logic is a science that has the
-following characteristics:
-<span class="pagenum" id="Page_152">[Pg 152]</span></p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">It studies chiefly nonnumerical reasoning.</li>
-<li class="isub2">It seeks accurate meanings and necessary consequences.</li>
-<li class="isub2">Its chief instruments are efficient symbols.</li>
-</ul>
-
-<p class="no-indent">Mathematical logic studies especially the logical
-relations expressed in such words as “or,” “and,” “not,” “else,” “if,”
-“then,” “only,” “the,” “of,” “is,” “every,” “all,” “none,” “some,”
-“same,” “different,” etc. The algebra of logic studies especially only
-the first seven of these words.</p>
-
-<p>The great thinkers of ancient Greece first studied the problems
-of logical reasoning as these problems turned up in philosophy,
-psychology, and debate. Aristotle originated what was called <i>formal
-logic</i>. This was devoted mainly to variations of the logical
-pattern shown above called the syllogism. In the last 150 years, the
-fine symbolic techniques developed by mathematicians were applied to
-the problems of the calculation of logical truth, and the result was
-mathematical logic, much broader and much more powerful than formal
-logic. A milestone in the development of mathematical logic was
-<i>The Laws of Thought</i>, written by George Boole, a great English
-mathematician, and published in 1854. Boole introduced the branch of
-mathematical logic called the algebra of logic, also called <i>Boolean
-algebra</i>. In late years, all the branches of mathematical logic have
-been improved and made easier to use.</p>
-
-<p>We can give a simple numerical example of Boolean algebra and how it
-can calculate logical truth. Suppose that we take the truth value of a
-statement as 1 if it is true and 0 if it is false. Now we have numbers
-1 and 0 instead of letters <i>T</i> and <i>F</i>. Since they are
-numbers, we can add them, subtract them, and multiply them. We can also
-make up simple numerical formulas that will let us calculate logical
-truth. If <i>P</i> and <i>Q</i> are statements, and if <i>p</i> and
-<i>q</i> are their truth values, respectively, we have <a href="#TABLE_7">Table 7</a>.</p>
-
-<p id="TABLE_7" class="f150"><b>Table 7</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Statement</span></th>
-      <th class="tdc"><span class="smcap">Truth Value</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdl"><span class="smcap">not</span>-<i>P</i></td>
-      <td class="tdl">1 - <i>p</i></td>
-   </tr><tr>
-      <td class="tdl"><i>P</i> <span class="smcap">and</span> <i>Q</i></td>
-      <td class="tdl"><i>pq</i></td>
-   </tr><tr>
-      <td class="tdl"><i>P</i> <span class="smcap">or</span> <i>Q</i></td>
-      <td class="tdl"><i>p</i> + <i>q</i> - <i>pq</i></td>
-   </tr><tr>
-      <td class="tdl"><span class="smcap">if</span> <i>P</i>, <span class="smcap">then</span> <i>Q</i></td>
-      <td class="tdl">1 - <i>p</i> + <i>pq</i></td>
-   </tr><tr>
-      <td class="tdl"><i>P</i> <span class="smcap">if and only if</span> <i>Q</i><span class="ws2">&nbsp;</span></td>
-      <td class="tdl">1 - <i>p</i> - <i>q</i> + 2<i>pq</i></td>
-   </tr><tr>
-      <td class="tdl"><i>P</i> <span class="smcap">or else</span> <i>Q</i></td>
-      <td class="tdl"><i>p</i> + <i>q</i> - 2<i>pq</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent"><span class="pagenum" id="Page_153">[Pg 153]</span>
-For example, suppose that we have two statements <i>P</i> and <i>Q</i>:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2"><i>P</i>: John Doe is eligible for insurance.</li>
-<li class="isub2"><i>Q</i>: John Doe requires a medical examination.</li>
-</ul>
-
-<p class="no-indent">To test that the truth value of “<i>P</i>
-<span class="smcap">or</span> <i>Q</i>” is <i>p</i> + <i>q</i>-<i>pq</i>,
-let us put down the four cases, and calculate the result (<a href="#TABLE_8">see Table 8</a>).</p>
-
-<p id="TABLE_8" class="f150"><b>Table 8</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdc">&nbsp;&nbsp;<i>p</i>&nbsp;&nbsp;</td>
-      <td class="tdc br">&nbsp;&nbsp;<i>q</i>&nbsp;&nbsp;</td>
-      <td class="tdc">&nbsp;&nbsp;<i>p</i> + <i>q</i> - <i>pq</i></td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc br">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdc br">1</td>
-      <td class="tdc">&nbsp;&nbsp;1 + 1 - 1 = 1</td>
-   </tr><tr>
-      <td class="tdc">0</td>
-      <td class="tdc br">1</td>
-      <td class="tdc">&nbsp;&nbsp;0 + 1 - 0 = 1</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdc br">0</td>
-      <td class="tdc">&nbsp;&nbsp;1 + 0 - 0 = 1</td>
-   </tr><tr>
-      <td class="tdc">0</td>
-      <td class="tdc br">0</td>
-      <td class="tdc">&nbsp;&nbsp;0 + 0 - 0 = 0</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Now we know that <i>P</i> or <i>Q</i> is true if
-and only if either one or both of <i>P</i> and <i>Q</i> are true, and
-thus we see that the calculation is correct.</p>
-
-<p>The algebra of logic (<a href="#SUPPL_2">see also Supplement 2</a>)
-is a more efficient way of calculating logical truth. But it is still
-a good deal of work to use the algebra. For example, if we have 10
-conditions, we shall have 10 letters like <i>p</i>, <i>q</i> to handle
-in calculations. Thus we need a still more efficient way.</p>
-
-<h3>CALCULATION OF CIRCUITS BY<br />THE ALGEBRA OF LOGIC</h3>
-
-<p>In 1937 a research assistant at Massachusetts Institute of Technology,
-Claude E. Shannon, was studying for his degree of master of science.
-He was enrolled in the Department of Electrical Engineering. He was
-interested in automatic switching circuits and wondered why an algebra
-should not apply to them. He wrote his thesis on the answer to this
-question and showed that:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">(1) There is an algebra that applies to switching circuits.</li>
-<li class="isub2">(2) It is the algebra of logic.</li>
-</ul>
-
-<p class="no-indent">A paper, based on his thesis, was published in
-1938 in the <i>Transactions of the American Institute of Electrical
-Engineers</i> with the title “A Symbolic Analysis of Relay and
-Switching Circuits.”
-<span class="pagenum" id="Page_154">[Pg 154]</span></p>
-
-<div class="figcenter">
-  <img id="FIG_1-9" src="images/i_154a.jpg" alt="" width="600" height="138" />
-  <p class="f120"><span class="smcap">Fig. 1.</span> Switches in series.</p>
-</div>
-
-<p>For a simple example of what Shannon found out, suppose that we have
-two switches, 1, 2, in series (<a href="#FIG_1-8">see Fig. 1</a>). When
-do we get current flowing from the source to the sink? There are 4
-possible cases and results (<a href="#TABLE_9">see Table 9</a>).</p>
-
-<p id="TABLE_9" class="f150"><b>Table 9</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdl"><span class="smcap">&nbsp;Switch 1<br />&nbsp;is closed&nbsp;</span></th>
-      <th class="tdl"><span class="smcap">&nbsp;&nbsp;Switch 2&nbsp;&nbsp;<br />&nbsp;&nbsp;is closed&nbsp;&nbsp;</span></th>
-      <th class="tdl"><span class="smcap">&nbsp;Current&nbsp;<br />&nbsp;&nbsp;flows</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdc">Yes</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">Yes</td>
-   </tr><tr>
-      <td class="tdc">No</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">No</td>
-   </tr><tr>
-      <td class="tdc">Yes</td>
-      <td class="tdc">No</td>
-      <td class="tdc">No</td>
-   </tr><tr>
-      <td class="tdc">No</td>
-      <td class="tdc">No</td>
-      <td class="tdc">No</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Now what does this table remind us of? It is
-precisely the truth table for “<span class="smcap">and</span>.” It
-is just what we would have if we wrote down the truth table of the
-statement “Switch 1 is closed <span class="smcap">and</span>
-switch 2 is closed.”</p>
-
-<div class="figcenter">
-  <img id="FIG_2-9" src="images/i_154b.jpg" alt="" width="600" height="277" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 2.</span> Switches in parallel.</p>
-  <img id="FIG_3-9" src="images/i_154c.jpg" alt="" width="600" height="225" />
-  <p class="f120"><span class="smcap">Fig. 3.</span> Switch open—current flowing.</p>
-</div>
-
-<p>Suppose that we have two switches 1, 2 in parallel (<a href="#FIG_2-9">see Fig. 2</a>).
-When do we get current flowing from the source to the sink?
-<span class="pagenum" id="Page_155">[Pg 155]</span>
-Answer: when either one or both of the switches are closed. Therefore,
-this circuit is an exact representation of the statement “Switch 1 is
-closed or switch 2 is closed.”</p>
-
-<p>Suppose that we have a switch that has two positions, and at any time
-must be at one and only one of these two positions (<a href="#FIG_3-9">see Fig. 3</a>).
-Suppose that current flows only when the switch is open. There are two
-possible cases and results (<a href="#TABLE_10">see Table 10</a>).</p>
-
-<p id="TABLE_10" class="f150"><b>Table 10</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdl"><span class="smcap">&nbsp;Switch 1<br />&nbsp;is closed&nbsp;</span></th>
-      <th class="tdl"><span class="smcap">&nbsp;Current&nbsp;<br />&nbsp;&nbsp;flows</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdc">Yes</td>
-      <td class="tdc">No</td>
-   </tr><tr>
-      <td class="tdc">No</td>
-      <td class="tdc">Yes</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">This is like the truth table for “<span
-class="smcap">not</span>”; and this circuit is an exact representation
-of the statement “Switch 1 is <span class="smcap">not</span> closed.”
-(<i>Note</i>: These examples are in substantial agreement with
-Shannon’s paper, although Shannon uses different conventions.)</p>
-
-<p>We see, therefore, that there is a very neat correspondence between the
-algebra of logic and automatic switching circuits. Thus it happens that:</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. The algebra of logic can be used in the
-calculation of some electrical circuits.</p>
-
-<p class="neg-indent">2. Some electrical circuits can be used in the
-calculations of the algebra of logic.</p>
-</div>
-
-<p class="no-indent">This fact is what led to the next step.</p>
-
-<h3>LOGICAL-TRUTH CALCULATION<br /> BY MACHINE</h3>
-
-<p>In 1946 two undergraduates at Harvard University, Theodore A. Kalin
-and William Burkhart, were taking a course in mathematical logic.
-They noticed that there were a large number of truth tables to be
-worked out. To work them out took time and effort and yet was a rather
-tiresome automatic process not requiring much thinking. They had had
-some experience with electrical circuits. Knowing of Shannon’s work,
-they said to each other, “Why not build an electrical machine to
-calculate truth tables?”</p>
-
-<p>They took about two months to decide on the essential design
-of the machine:
-<span class="pagenum" id="Page_156">[Pg 156]</span></p>
-
-<div class="blockquot">
-<p class="neg-indent">1. The machine would have dial switches in which
-logical connectives would be entered.</p>
-
-<p class="neg-indent">2. It would have dial switches in which the
-numbers of statements like 1, 2, 3 ··· would be entered.</p>
-
-<p class="neg-indent">3. It would scan the proper truth table line by
-line by sending electrical pulses through the dial switches.</p>
-
-<p class="neg-indent">4. It would compute the truth or falsehood of the
-whole expression.</p>
-</div>
-
-<h3>CONSTRUCTION AND COMPLETION OF THE<br /> KALIN-BURKHART LOGICAL-TRUTH
-CALCULATOR</h3>
-
-<p>With the designs in mind, Kalin and Burkhart bought some war surplus
-materials, including relays, switches, wires, lights, and a metal
-box about 30 inches long by 16 inches tall, and 13 inches deep. From
-March to June, 1947, they constructed a machine in their spare time,
-assembling and mounting the parts inside the box. The total cost of
-materials was about $150. In June the machine was demonstrated in
-Cambridge, Mass., before several logicians and engineers, and in August
-it was moved for some months to the office of a life insurance company.
-There some study was made of the possible application of the machine in
-drafting contracts and rules.</p>
-
-<h3>GENERAL ORGANIZATION<br /> OF THE MACHINE</h3>
-
-<p>The logical-truth calculator built by Kalin and Burkhart is not giant
-in size, although giant in capacity. Like other mechanical brains,
-the machine is made up of many pieces of a rather small number of
-different kinds of parts. The machine contains about 45 dial switches,
-23 snap switches (or two-position switches), 85 relays, 6 push buttons,
-less than a mile of wire, etc. The lid of the metal box is the front,
-vertical panel of the machine.</p>
-
-<h3>UNITS OF THE MACHINE</h3>
-
-<p>The machine contains 16 units. These units are listed in
-<a href="#TABLE_11">Table 11</a>, in approximately the order in which they
-appear on the front panel of the machine—row by row from top to bottom,
-and from left to right in each row.
-<span class="pagenum" id="Page_157">[Pg 157]</span></p>
-
-<p id="TABLE_11" class="f150"><b>Table 11</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" rules="cols">
-  <thead><tr>
-      <th class="tdc bb" colspan="7">UNITS, THEIR NAMES, AND SIGNIFICANCE</th>
-   </tr><tr>
-      <th class="tdc bb"><span class="smcap">Unit</span></th>
-      <th class="tdc bb"><span class="smcap">Row</span></th>
-      <th class="tdc bb"><span class="smcap">Part</span></th>
-      <th class="tdc bb"><span class="smcap">No.</span></th>
-      <th class="tdc bb"><span class="smcap">Mark</span></th>
-      <th class="tdc bb"><span class="smcap">Name</span></th>
-      <th class="tdc bb"><span class="smcap">Significance</span></th>
-    </tr>
-   </thead>
-  <tbody><tr>
-      <td class="tdc_top">1</td>
-      <td class="tdc_top">1</td>
-      <td class="tdc_top">Small red<br />lights</td>
-      <td class="tdc_top">12</td>
-      <td class="tdc_top">—</td>
-      <td class="tdc_top"><i>Statement truth-<br />value lights</i></td>
-      <td class="tdl_top">Output: glows if<br />&nbsp;statement is<br />&nbsp;assumed true<br />&nbsp;in the case</td>
-   </tr><tr>
-      <td class="tdc_top">2</td>
-      <td class="tdc_top">1</td>
-      <td class="tdc_top">2-position<br />snap switches</td>
-      <td class="tdc_top">12</td>
-      <td class="tdc_top"><big>~</big></td>
-      <td class="tdc_top"><i>Statement denial<br />switches</i></td>
-      <td class="tdl_top">Input: if up,<br />&nbsp;statement<br />&nbsp;is denied</td>
-   </tr><tr>
-      <td class="tdc_top">3</td>
-      <td class="tdc_top">2</td>
-      <td class="tdc_top">14-position<br />dial switches</td>
-      <td class="tdc_top">12</td>
-      <td class="tdc_top"><i>V</i></td>
-      <td class="tdc_top"><i>Statement<br />switches</i></td>
-      <td class="tdl_top">Input of<br />&nbsp;statements</td>
-   </tr><tr>
-      <td class="tdc_top bb">4</td>
-      <td class="tdc_top bb">3</td>
-      <td class="tdc_top bb">4-position<br />dial switches</td>
-      <td class="tdc_top bb">11</td>
-      <td class="tdc_top bb"><i>k</i></td>
-      <td class="tdc_top bb"><i>Connective<br />switches</i></td>
-      <td class="tdl_top bb">Input of<br />&nbsp;connectives:<br />&nbsp;∧ (and),<br />&nbsp;∨ (or),<br />
-                                     &nbsp;▲ (if-then),<br />&nbsp;▼ (if and only if)</td>
-   </tr><tr>
-      <td class="tdc_top">5</td>
-      <td class="tdc_top">4</td>
-      <td class="tdc_top">11-position<br />dial switches</td>
-      <td class="tdc_top">11</td>
-      <td class="tdc_top"><i>A</i></td>
-      <td class="tdc_top"><i>Antecedent<br />switches</i></td>
-      <td class="tdl_top">Input of<br />&nbsp;antecedents</td>
-   </tr><tr>
-      <td class="tdc_top">6</td>
-      <td class="tdc_top">5</td>
-      <td class="tdc_top">11-position<br />dial switches</td>
-      <td class="tdc_top">11</td>
-      <td class="tdc_top"><i>C</i></td>
-      <td class="tdc_top"><i>Consequent<br />switches</i></td>
-      <td class="tdl_top">Input of consequents</td>
-   </tr><tr>
-      <td class="tdc_top">7</td>
-      <td class="tdc_top">6</td>
-      <td class="tdc_top">2-position<br />snap switches</td>
-      <td class="tdc_top">11</td>
-      <td class="tdc_top"><i>S</i></td>
-      <td class="tdc_top"><i>Stop switches</i></td>
-      <td class="tdl_top">Input: if up, associates<br />&nbsp;connective to main<br />&nbsp;truth-value light</td>
-   </tr><tr>
-      <td class="tdc_top bb">8</td>
-      <td class="tdc_top bb">6</td>
-      <td class="tdc_top bb">2-position<br />snap switches</td>
-      <td class="tdc_top bb">11</td>
-      <td class="tdc_top bb"><big>~</big></td>
-      <td class="tdc_top bb"><i>Connective denial<br />switches</i></td>
-      <td class="tdl_top bb">Input: if up, statement<br />&nbsp;produced by connective<br />&nbsp;is denied</td>
-   </tr><tr>
-      <td class="tdc_top">9</td>
-      <td class="tdc_top">7</td>
-      <td class="tdc_top">Red light and<br />large button</td>
-      <td class="tdc_top">1</td>
-      <td class="tdc_top">Start</td>
-      <td class="tdc_top"><i>Automatic start</i></td>
-      <td class="tdl_top">Input: causes the calc.<br />&nbsp;to start down a truth<br />&nbsp;table automatically</td>
-   </tr><tr>
-      <td class="tdc_top">10</td>
-      <td class="tdc_top">7</td>
-      <td class="tdc_top">Red light and<br />2 buttons</td>
-      <td class="tdc_top">1</td>
-      <td class="tdc_top">Start<br />Stop</td>
-      <td class="tdc_top"><i>Power switch</i></td>
-      <td class="tdl_top">Input: turns the power<br />&nbsp;on or off</td>
-   </tr><tr>
-      <td class="tdc_top">11</td>
-      <td class="tdc_top">7</td>
-      <td class="tdc_top">2-position<br />snap switch<br />and red button</td>
-      <td class="tdc_top">1</td>
-      <td class="tdc_top">Stop</td>
-      <td class="tdc_top">“<i>Stop-on-true-or-<br />false</i>” <i>switch</i></td>
-      <td class="tdl_top">Input: causes the calc.<br />&nbsp;to stop either on<br />&nbsp;true cases or on<br />&nbsp;false cases</td>
-   </tr><tr>
-      <td class="tdc_top bb">12</td>
-      <td class="tdc_top bb">7</td>
-      <td class="tdc_top bb">Yellow light</td>
-      <td class="tdc_top bb">1</td>
-      <td class="tdc_top bb">—</td>
-      <td class="tdc_top bb"><i>Main truth-value<br />light</i></td>
-      <td class="tdl_top bb">Output: glows if the<br />&nbsp;statement produced<br />&nbsp;by the main connective<br />&nbsp;is true for the case</td>
-   </tr><tr>
-      <td class="tdc_top">13</td>
-      <td class="tdc_top">7</td>
-      <td class="tdc_top">Large button</td>
-      <td class="tdc_top">1</td>
-      <td class="tdc_top">Man.<br />Pulse</td>
-      <td class="tdc_top"><i>Manual pulse<br />button</i></td>
-      <td class="tdl_top">Input: causes the calc.<br />&nbsp;to go to the next<br />&nbsp;line of a truth table</td>
-   </tr><tr>
-      <td class="tdc_top">14</td>
-      <td class="tdc_top">7</td>
-      <td class="tdc_top">11-position<br />dial switch</td>
-      <td class="tdc_top">1</td>
-      <td class="tdc_top"><i>kⱼ</i></td>
-      <td class="tdc_top"><i>Connective check<br />switch and light</i></td>
-      <td class="tdl_top">Output: glows when any<br />&nbsp;specified connective<br />&nbsp;is true</td>
-   </tr><tr>
-      <td class="tdc_top">15</td>
-      <td class="tdc_top">7</td>
-      <td class="tdc_top">13-position<br />dial switch</td>
-      <td class="tdc_top">1</td>
-      <td class="tdc_top">TT<br />Row<br />Stop</td>
-      <td class="tdc_top">“<i>Truth-table-row-<br />stop</i>” <i>switch</i></td>
-      <td class="tdl_top">Input: causes the calc.<br />&nbsp;to stop on the<br />&nbsp;
-                          last row of the<br />&nbsp;truth table</td>
-   </tr><tr>
-      <td class="tdc_top">16</td>
-      <td class="tdc_top">Be-<br />tween<br />6 &amp; 7</td>
-      <td class="tdc_top">Continuous<br />dial knob<br />and button</td>
-      <td class="tdc_top">1</td>
-      <td class="tdc_top">—</td>
-      <td class="tdc_top"><i>Timing control<br />knob</i></td>
-      <td class="tdl_top">Input: controls the<br />&nbsp;speed at which the<br />&nbsp;
-                          calculator scans rows<br />&nbsp;of the truth table</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="blockquot"><span class="pagenum" id="Page_158">[Pg
-158]</span> Some of the words appearing in this table need to be
-defined. <i>Connective</i> here means “<span class="smcap">and</span>,”
-“<span class="smcap">or</span>,” “<span class="smcap">if</span> ···
-<span class="smcap">then</span>,” “<span class="smcap">if and only if</span>.”
-Only these four connectives appear on the machine; others when needed
-can be constructed from these. The symbols used for these connectives
-in mathematical logic are <big>∧, ∨, ▲, ▼</big>. These signs serve as labels
-for the connective switch points. In this machine, when there is a
-connective between two statements, the statement that comes before is
-called the <i>antecedent</i> and the statement that comes after is
-called the <i>consequent</i>.</p>
-
-<h3>HOW INFORMATION GOES<br /> INTO THE MACHINE</h3>
-
-<p>Of the 16 units 13 are input units. They control the setup of the
-machine so that it can solve a problem. Of the 13 input units, those
-that have the most to do with taking in the problem are shown
-in <a href="#TABLE_12">Table 12</a>.</p>
-
-<p id="TABLE_12" class="f150"><b>Table 12</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" rules="cols">
-  <thead><tr>
-      <th class="tdc bb"><span class="smcap">Unit</span></th>
-      <th class="tdc bb"><span class="smcap">Name of<br />Switches</span></th>
-      <th class="tdc bb"><span class="smcap">Mark</span></th>
-      <th class="tdc bb"><span class="smcap">&nbsp;Kind of&nbsp;<br />Switch</span></th>
-      <th class="tdc bb"><span class="smcap">Switch Settings</span></th>
-    </tr>
-   </thead>
-  <tbody><tr>
-      <td class="tdc_top">3</td>
-      <td class="tdc_top">Statement</td>
-      <td class="tdc_top"><i>V</i>₁ to<br /><i>V</i>₁₂</td>
-      <td class="tdc_top">Dial</td>
-      <td class="tdl_top">Statements 1 to 12 or<br />&nbsp;constant <i>T</i> or <i>F</i></td>
-   </tr><tr>
-      <td class="tdc_top">2</td>
-      <td class="tdc_top">Statement<br />denial</td>
-      <td class="tdc_top"><big>~</big></td>
-      <td class="tdc_top">Snap</td>
-      <td class="tdl_top">Affirmative (down)<br />&nbsp;or negative (up)</td>
-   </tr><tr>
-      <td class="tdc_top">4</td>
-      <td class="tdc_top">Connective</td>
-      <td class="tdc_top"><i>k</i>₁ to<br /><i>k</i>₁₁</td>
-      <td class="tdc_top">Dial</td>
-      <td class="tdl_top">∧ (<span class="smcap">and</span>),<br />∨ (<span class="smcap">or</span>),<br />
-                          ▲ (<span class="smcap">if-then</span>),<br />▼ (<span class="smcap">if and only if</span>)</td>
-   </tr><tr>
-      <td class="tdc_top">8</td>
-      <td class="tdc_top">Connective<br />denial</td>
-      <td class="tdc_top"><big>~</big></td>
-      <td class="tdc_top">Snap</td>
-      <td class="tdl_top">Affirmative (down) or<br />&nbsp;negative (up)</td>
-   </tr><tr>
-      <td class="tdc_top">5</td>
-      <td class="tdc_top">Antecedent</td>
-      <td class="tdc_top"><i>A</i>₁ to<br /><i>A</i>₁₁</td>
-      <td class="tdc_top">Dial</td>
-      <td class="tdl_top"><i>V</i> or various <i>k</i>’s</td>
-   </tr><tr>
-      <td class="tdc_top">6</td>
-      <td class="tdc_top">Consequent</td>
-      <td class="tdc_top"><i>C</i>₁ to<br /><i>C</i>₁₁</td>
-      <td class="tdc_top">Dial</td>
-      <td class="tdl_top"><i>V</i> or various <i>k</i>’s</td>
-   </tr><tr>
-      <td class="tdc_top">7</td>
-      <td class="tdc_top">Stop</td>
-      <td class="tdc_top"><i>S</i>₁ to<br /><i>S</i>₁₁</td>
-      <td class="tdc_top">Snap</td>
-      <td class="tdl_top">Not connected (down)<br />&nbsp;or connected (up)</td>
-   </tr>
- </tbody>
-</table>
-
-<p>The first step in putting a problem on the machine is to express the
-whole problem as a single compound statement that we want to know the
-truth or falsity of. We express the single compound statement in a form
-such as the following:</p>
-
-<p class="f120 no-wrap"><i>V k V k V k V k V k V k V k V k V k V k V k V</i></p>
-
-<p class="no-indent"><span class="pagenum" id="Page_159">[Pg 159]</span>
-where each <i>V</i> represents a statement, each <i>k</i> represents a
-connective, and we know the grouping, or in other words, we know the
-antecedent and consequent of each connective.</p>
-
-<p>For example, let us choose a problem with an obvious answer:</p>
-
-<p class="blockquot"><b><span class="smcap">Problem.</span></b> Given:
-statement 1 is true; and if statement 1 is true, then statement 2 is
-true; and if statement 2 is true, then statement 3 is true; and if
-statement 3 is true, then statement 4 is true. Is statement 4 true?</p>
-
-<p>How do we express this whole problem in a form that will go on the
-machine? We express the whole problem as a single compound statement
-that we want to know the truth or falsity of:</p>
-
-<p class="f120">If <big>[</big>1 and (if 1 then 2) and (if 2 then 3) and
-(if 3 then 4)<big>]</big>, then 4</p>
-
-<p class="no-indent">The 8 statements occurring in this problem
-are, respectively: 1 1 2 2 3 3 4 4. These are the values at which
-the <i>V</i> switches (the statement dial switches, Unit 2) from
-<i>V</i>₁ to <i>V</i>₈ are set. The 7 connectives occurring in this
-problem are, respectively: <span class="smcap">and</span>,
-<span class="smcap">if-then</span>, <span class="smcap">and</span>,
-<span class="smcap">if-then</span>, <span class="smcap">and</span>,
-<span class="smcap">if-then</span>, <span class="smcap">if-then</span>.
-These are the values at which the <i>k</i> switches (the connective dial
-switches, Unit 4) from <i>k</i>₁ to <i>k</i>₇ are set.</p>
-
-<p>A grouping (one of several possible groupings) that specifies
-the antecedent and consequent of each connective is the following:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdl">1</td>
-      <td class="tdl"><span class="smcap">and</span></td>
-      <td class="tdl">1</td>
-      <td class="tdl"><span class="smcap">if-then</span></td>
-      <td class="tdl">2</td>
-      <td class="tdl"><span class="smcap">and</span></td>
-      <td class="tdl">2</td>
-      <td class="tdl"><span class="smcap">if-then</span></td>
-      <td class="tdl">3</td>
-      <td class="tdl"><span class="smcap">and</span></td>
-      <td class="tdl">3</td>
-      <td class="tdl"><span class="smcap">if-then</span></td>
-      <td class="tdl">4</td>
-      <td class="tdl"><span class="smcap">if-then</span></td>
-      <td class="tdl">4</td>
-   </tr><tr>
-      <td class="tdl">&nbsp;</td>
-      <td class="tdl">&nbsp;</td>
-      <td class="tdl">|</td>
-      <td class="tdl bb">&nbsp;</td>
-      <td class="tdl">|</td>
-      <td class="tdl">&nbsp;</td>
-      <td class="tdl">|</td>
-      <td class="tdl bb">&nbsp;</td>
-      <td class="tdl">|</td>
-      <td class="tdl">&nbsp;</td>
-      <td class="tdl">|</td>
-      <td class="tdl bb">&nbsp;</td>
-      <td class="tdl">|</td>
-      <td class="tdl">&nbsp;</td>
-      <td class="tdl">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl" colspan="3"></td>
-      <td class="tdc"><i>k</i>₂</td>
-      <td class="tdl" colspan="3">&nbsp;</td>
-      <td class="tdc"><i>k</i>₄</td>
-      <td class="tdl" colspan="3"></td>
-      <td class="tdc"><i>k</i>₆</td>
-      <td class="tdl" colspan="3"></td>
-   </tr><tr>
-      <td class="tdl">|</td>
-      <td class="tdl bb" colspan="3">&nbsp;</td>
-      <td class="tdl">|</td>
-      <td class="tdl">&nbsp;</td>
-      <td class="tdl">|</td>
-      <td class="tdl bb" colspan="5">&nbsp;</td>
-      <td class="tdl">|</td>
-      <td class="tdl" colspan="2">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc" colspan="5"><i>k</i>₁</td>
-      <td class="tdl">&nbsp;</td>
-      <td class="tdc" colspan="7"><i>k</i>₅</td>
-      <td class="tdl" colspan="2">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl">|</td>
-      <td class="tdc bb" colspan="11">&nbsp;</td>
-      <td class="tdl">|</td>
-      <td class="tdl" colspan="2">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc" colspan="13"><i>k</i>₃</td>
-      <td class="tdl" colspan="2">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl">|</td>
-      <td class="tdc bb" colspan="13">&nbsp;</td>
-      <td class="tdl">|</td>
-   </tr><tr>
-      <td class="tdc" colspan="15"><i>k</i>₇</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">The grouping has here been expressed graphically
-with lines but may be expressed in the normal mathematical way with
-parentheses and brackets as follows:
-<span class="pagenum" id="Page_160">[Pg 160]</span></p>
-
-<p class="f120">
-<span class="fontsize_200">{</span><span class="fontsize_150">[</span>
-1 <span class="smcap">and</span> (1 <span class="smcap">if-then</span> 2)<span class="fontsize_150">]</span>
-<span class="smcap">and</span> <span class="fontsize_150">[</span>(2
-<span class="smcap">if-then</span> 3) <span class="smcap">and</span> (3 <span class="smcap">if-then</span> 4)
-<span class="fontsize_150">]</span>
-<span class="fontsize_200">}</span>
-<span class="smcap">if-then</span> 4.</p>
-
-<p class="no-indent">So the values at which the antecedent and consequent
-dial switches are set are as shown in <a href="#TABLE_13">Table 13</a>.</p>
-
-<p id="TABLE_13" class="f150"><b>Table 13</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" rules="cols">
-  <thead><tr>
-      <th class="tdc bb"><span class="smcap">Connective&nbsp;</span></th>
-      <th class="tdc bb"><span class="smcap">&nbsp;Antecedent&nbsp;<br />Switch</span></th>
-      <th class="tdc bb"><span class="smcap">&nbsp;Set at&nbsp;</span></th>
-      <th class="tdc bb"><span class="smcap">&nbsp;Consequent&nbsp;<br />Switch</span></th>
-      <th class="tdc bb"><span class="smcap">&nbsp;Set at</span></th>
-    </tr>
-   </thead>
-  <tbody><tr>
-      <td class="tdc"><i>k</i>₁</td>
-      <td class="tdc"><i>A</i>₁</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>C</i>₁</td>
-      <td class="tdc"><i>k</i>₂</td>
-   </tr><tr>
-      <td class="tdc"><i>k</i>₂</td>
-      <td class="tdc"><i>A</i>₂</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>C</i>₂</td>
-      <td class="tdc"><i>V</i></td>
-   </tr><tr>
-      <td class="tdc"><i>k</i>₃</td>
-      <td class="tdc"><i>A</i>₃</td>
-      <td class="tdc"><i>k</i>₁</td>
-      <td class="tdc"><i>C</i>₃</td>
-      <td class="tdc"><i>k</i>₅</td>
-   </tr><tr>
-      <td class="tdc"><i>k</i>₄</td>
-      <td class="tdc"><i>A</i>₄</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>C</i>₄</td>
-      <td class="tdc"><i>V</i></td>
-   </tr><tr>
-      <td class="tdc"><i>k</i>₅</td>
-      <td class="tdc"><i>A</i>₅</td>
-      <td class="tdc"><i>k</i>₄</td>
-      <td class="tdc"><i>C</i>₅</td>
-      <td class="tdc"><i>k</i>₆</td>
-   </tr><tr>
-      <td class="tdc"><i>k</i>₆</td>
-      <td class="tdc"><i>A</i>₆</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>C</i>₆</td>
-      <td class="tdc"><i>V</i></td>
-   </tr><tr>
-      <td class="tdc"><i>k</i>₇</td>
-      <td class="tdc"><i>A</i>₇</td>
-      <td class="tdc"><i>k</i>₃</td>
-      <td class="tdc"><i>C</i>₇</td>
-      <td class="tdc"><i>V</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p>In any problem, statements that are different are numbered one after
-another 1, 2, 3, 4 ···. A statement that is repeated bears always the
-same number. In nearly all cases that are interesting, there will
-be repetitions of the statements. If any statement appeared with a
-“<span class="smcap">not</span>” in it, we would turn up the denial switch
-for that statement (Unit 2).</p>
-
-<p>The different connectives available on the machine are “<span class="smcap">and</span>,”
-“<span class="smcap">or</span>,” “<span class="smcap">if</span> ··· <span class="smcap">then</span>,” “<span class="smcap">if and only
-if</span>.” If a “<span class="smcap">not</span>” affected the compound statement produced
-by any connective, we would turn up the denial switch for that
-connective (Unit 8).</p>
-
-<p>The last step in putting the problem on the machine is to connect the
-main connective of the whole compound statement to the yellow light
-output (Unit 12). In this problem the last “<span class="smcap">if-then</span>,”
-<i>k</i>₇, is the main connective, the one that produces the whole
-compound statement. So we turn Stop Switch 7 (in Unit 7) that belongs
-to <i>k</i>₇ into the up position. There are a few more things to do,
-naturally, but the essential part of putting the information of the
-problem into the machine has now been described.</p>
-
-<h3>HOW INFORMATION COMES OUT<br />OF THE MACHINE</h3>
-
-<p>Of the 16 units listed in <a href="#TABLE_11">Table 11</a>, 3 are
-output units, and only 2 of these are really important, as shown in
-<a href="#TABLE_14">Table 14</a>.
-<span class="pagenum" id="Page_161">[Pg 161]</span></p>
-
-<p id="TABLE_14" class="f150"><b>Table 14</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Unit</span></th>
-      <th class="tdc"><span class="smcap">Name of Light</span></th>
-      <th class="tdc"><span class="smcap">Mark</span></th>
-      <th class="tdc"><span class="smcap">Kind of Light</span></th>
-    </tr>
-   </thead>
-  <tbody><tr>
-      <td class="tdc">&#8199;1</td>
-      <td class="tdc">Statement truth value</td>
-      <td class="tdc">&nbsp;<i>V</i>₁ to <i>V</i>₁₂&nbsp;</td>
-      <td class="tdc">Small, red&nbsp;&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">13</td>
-      <td class="tdl">Main truth value</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">Large, yellow</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">The answer to a problem is shown by a pattern of
-the lights of Units 1 and 13. The pattern of lights is equivalent to
-a row of the truth table. Each little red light (Unit 1) glows when
-its statement is assumed to be true, and it is dark when its statement
-is assumed to be false. The yellow light (Unit 13) glows when the
-whole compound statement is calculated to be logically true, and it is
-dark when the whole compound statement is calculated to be logically false.</p>
-
-<p>The machine turns its “attention” automatically to each line of the
-truth table one after the other, and pulses are fed in according to the
-pattern of assumed true statements. We can set the machine to stop on
-true cases or on false cases or on every case, so as to give us time
-to copy down whichever kind of results we are interested in. When we
-have noted the case, we can press a button and the machine will then go
-ahead searching for more cases.</p>
-
-<h3>A COMPLETE AND CONCRETE EXAMPLE</h3>
-
-<p>The reader may still be wondering when he will see a complete and
-concrete example of the application of the logical-truth calculator. So
-far we have given only pieces of examples in order to illustrate some
-explanation. Therefore, let us consider now the following problem:</p>
-
-<div class="blockquot">
-<p><b><span class="smcap">Problem.</span></b> The A. A. Adams Co.,
-Inc., has about 1000 employees. About 600 of them are insured under a
-contract for group insurance with the I. I. Insurance Co. Mr. Adams
-decides that more of his employees ought to be insured. As a part of
-his study of the change, he asks his manager in charge of the group
-insurance plan, “What are the possible statuses of my employees who are
-not insured?”</p>
-
-<p>The manager replies, “I can tell you the names of the men who are
-not insured, and all the data you may want to know about them.”</p>
-
-<p>Mr. Adams says, “No, John, that won’t be enough, for I need to know
-whether there are any groups or classes that for some basic reason I
-should exclude from the change I am considering.”</p>
-</div>
-
-<p><span class="pagenum" id="Page_162">[Pg 162]</span>
-So the manager goes to work with the following 5 statuses and the
-following 5 rules, and he produces the following answer. Our question
-is, “Is he right, or has he made a mistake?”</p>
-
-<p><i>Statuses.</i> A status for any employee is a report about that
-employee, answering all the following 5 questions with “yes” or “no.”</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. Is the employee eligible for insurance?</p>
-
-<p class="neg-indent">2. Has the employee applied for insurance?</p>
-
-<p class="neg-indent">3. Has the employee’s application for insurance been approved?</p>
-
-<p class="neg-indent">4. Does the employee require a medical examination for insurance?</p>
-
-<p class="neg-indent">5. Is the employee insured?</p>
-</div>
-
-<p><i>Rules.</i> The rules applying to employees are:</p>
-
-<div class="blockquot">
-<p class="neg-indent"><i>A.</i> Any employee, to be insured, must be
-eligible for insurance, must make application for insurance, and must
-have such application for insurance approved.</p>
-
-<p class="neg-indent"><i>B.</i> Only eligible employees may apply for
-insurance.</p>
-
-<p class="neg-indent"><i>C.</i> The application of any person eligible
-for insurance without medical examination is automatically approved.</p>
-
-<p class="neg-indent"><i>D.</i> (Naturally) an application can be
-approved only if the application is made.</p>
-
-<p class="neg-indent"><i>E.</i> (Naturally) a medical examination will
-not be required from any person not eligible for insurance.</p>
-</div>
-
-<p><i>Answer by the Manager.</i> There are 5 possible combinations of
-statuses for employees who are not insured, as shown in <a href="#TABLE_15">Table 15</a>.</p>
-
-<p id="TABLE_15" class="f150"><b>Table 15</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" rules="cols" >
-  <thead><tr>
-      <th class="tdc bb"><span class="smcap">Possible<br />Combination<br />of Statuses</span></th>
-      <th class="tdc bb"><span class="smcap">Status 1,<br /><br />Eligible</span></th>
-      <th class="tdc bb"><span class="smcap">Status 2,<br /><br />Applied</span></th>
-      <th class="tdc bb"><span class="smcap">Status 3,<br />Application<br />Approved</span></th>
-      <th class="tdc bb"><span class="smcap">Status 4,<br />Examination<br />Required</span></th>
-      <th class="tdc bb"><span class="smcap">Status 5,<br /><br />Insured</span></th>
-    </tr>
-   </thead>
-  <tbody><tr>
-      <td class="tdc">1</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">No</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">No</td>
-      <td class="tdc">No</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">No</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">No</td>
-   </tr><tr>
-      <td class="tdc">4</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">No</td>
-      <td class="tdc">Yes</td>
-      <td class="tdc">No</td>
-      <td class="tdc">No</td>
-   </tr><tr>
-      <td class="tdc">5</td>
-      <td class="tdc">No</td>
-      <td class="tdc">No</td>
-      <td class="tdc">No</td>
-      <td class="tdc">No</td>
-      <td class="tdc">No</td>
-   </tr>
- </tbody>
-</table>
-
-<p>The question may be asked why employees who are eligible, who have
-applied for insurance, who have had their applications approved, and
-who require no medical examination (combination 2) are yet not insured.
-The answer is that the rules given do not logically lead to this
-conclusion. As a matter of fact, there might be additional rules, such
-<span class="pagenum" id="Page_163">[Pg 163]</span>
-as: any sick employee must first return to work; or any period from
-date of approval of application to the first of the following month
-must first pass.</p>
-
-<p>The first step in putting this problem on the Kalin-Burkhart
-Logical-Truth Calculator is to rephrase the rules, using the language
-of the connectives that we have on the machine. The rules rephrased are:</p>
-
-<div class="blockquot">
-<p class="neg-indent"><i>A.</i> If an employee is insured, then he is
-eligible, he has applied for insurance, and his application has been
-approved.</p>
-
-<p class="big_indent"><span class="smcap">if</span> 5,
-<span class="smcap">then</span> 1 <span class="smcap">and</span> 2
-<span class="smcap">and</span> 3</p>
-
-<p class="neg-indent"><i>B.</i> If an employee has applied (under these
-rules) for insurance, then he is eligible.</p>
-
-<p class="big_indent"><span class="smcap">if</span> 2,
-<span class="smcap">then</span> 1</p>
-
-<p class="neg-indent"><i>C.</i> If an employee is eligible for
-insurance, has applied, and requires no medical examination, his
-application is automatically approved.</p>
-
-<p class="big_indent"><span class="smcap">if</span> 1 <span
-class="smcap">and</span> 2 <span class="smcap">and</span>
-<span class="smcap">not</span>-4, <span class="smcap">then</span> 3</p>
-
-<p class="neg-indent"><i>D.</i> If an employee’s application has been
-approved, then he has applied.</p>
-
-<p class="big_indent"><span class="smcap">if</span> 3,
-<span class="smcap">then</span> 2</p>
-
-<p class="neg-indent"><i>E.</i> If an employee is not eligible, then he
-does not require a medical examination (under these rules).</p>
-
-<p class="big_indent"><span class="smcap">if</span>
-<span class="smcap">not</span>-1, <span class="smcap">then</span>
-<span class="smcap">not</span>-4</p> </div>
-
-<p class="no-indent">To get the answer we seek, we must add one more
-rule <i>for this answer only</i>:</p>
-
-<div class="blockquot">
-<p class="neg-indent"><i>F.</i> The employee is not insured.</p>
-
-<p class="big_indent"><span class="smcap">not</span>-5</p>
-</div>
-
-<p class="no-indent">We now have a total of 4 + 2 + 4 + 2 + 2 + 1
-occurrences of statements, or 15 occurrences. This is beyond the
-capacity of the existing machine. But fortunately Rule <i>F</i>
-and Rule <i>A</i> cancel each other; they may both be omitted; and
-this gives us 10 occurrences instead of 15. In other words, all the
-possible statuses under “Rule <i>B</i> <span class="smcap">and</span>
-Rule <i>C</i> <span class="smcap">and</span> Rule <i>D</i>
-<span class="smcap">and</span> Rule <i>E</i>” will give us the answer
-we seek.</p>
-
-<p>The rephrasing and reasoning we have done here is perhaps not easy. For
-example, going from the logical pattern</p>
-
-<p class="big_indent">Only igs may be ows</p>
-
-<p class="no-indent">to the logical pattern
-<span class="pagenum" id="Page_164">[Pg 164]</span></p>
-
-<p class="big_indent">If it is an ow, then it is an ig</p>
-
-<p class="no-indent">as we did in rephrasing Rule <i>B</i>, deserves
-rather more thought and discussion than we can give to the subject
-here. A person who is responsible for preparing problems for the
-Logical-Truth Calculator should know the algebra of logic.</p>
-
-<p>Choosing an appropriate grouping, we now set on the machine:</p>
-
-<p class="no-wrap">
-<span class="fontsize_200">{</span>(<span class="smcap">if</span> 2, <span class="smcap">then</span> 1)
-<span class="smcap">and</span> <span class="fontsize_150">[</span><span class="allsmcap">IF</span> (1
-<span class="smcap">and</span> 2) <span class="smcap">and</span>
-<span class="smcap">not</span>-4, <span class="smcap">then</span> 3<span class="fontsize_150">]</span><span class="fontsize_200">}</span>
-<span class="smcap">and</span></p>
-
-<p class="big_indent no-wrap"><span class="fontsize_150">[</span>(<span class="smcap">if</span>
-3, <span class="smcap">then</span> 2) <span class="smcap">and</span>
-(<span class="allsmcap">IF</span> <span class="smcap">not</span>-1,
-<span class="smcap">then</span> <span class="smcap">not</span>-4)<span class="fontsize_150">]</span> </p>
-
-<p>The setting is as shown in <a href="#TABLE_16">Table 16</a>. After this setting,
-the machine is turned on and set to stop on the “true” cases. The</p>
-
-<p id="TABLE_16" class="f150"><b>Table 16</b></p>
-
-<p class="center"><b>SETTING OF THE PROBLEM<br /> ON THE<br /> LOGICAL-TRUTH CALCULATOR</b></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdl"><b><span class="smcap">Unit</span></b></td>
-      <td class="tdl" colspan="13">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdl_ws1">Statement Dial No.</td>
-      <td class="tdc"><i>V</i>₁</td>
-      <td class="tdc"><i>V</i>₂</td>
-      <td class="tdc"><i>V</i>₃</td>
-      <td class="tdc"><i>V</i>₄</td>
-      <td class="tdc"><i>V</i>₅</td>
-      <td class="tdc"><i>V</i>₆</td>
-      <td class="tdc"><i>V</i>₇</td>
-      <td class="tdc"><i>V</i>₈</td>
-      <td class="tdc"><i>V</i>₉</td>
-      <td class="tdc"><i>V</i>₁₀</td>
-      <td class="tdc"><i>V</i>₁₁</td>
-      <td class="tdc"><i>V</i>₁₂</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdl_ws1">Statement Dial Setting</td>
-      <td class="tdc">2</td>
-      <td class="tdc">1</td>
-      <td class="tdc">1</td>
-      <td class="tdc">2</td>
-      <td class="tdc">4</td>
-      <td class="tdc">3</td>
-      <td class="tdc">3</td>
-      <td class="tdc">2</td>
-      <td class="tdc">1</td>
-      <td class="tdc">4</td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdl_ws1">Statement Denial Switch</td>
-      <td class="tdc" colspan="12">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;&emsp;Setting</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">up</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">up</td>
-      <td class="tdc">up</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-   </tr><tr>
-      <td class="tdc">4</td>
-      <td class="tdl_ws1">Connective Dial No.</td>
-      <td class="tdc"><i>k</i>₁</td>
-      <td class="tdc"><i>k</i>₂</td>
-      <td class="tdc"><i>k</i>₃</td>
-      <td class="tdc"><i>k</i>₄</td>
-      <td class="tdc"><i>k</i>₅</td>
-      <td class="tdc"><i>k</i>₆</td>
-      <td class="tdc"><i>k</i>₇</td>
-      <td class="tdc"><i>k</i>₈</td>
-      <td class="tdc"><i>k</i>₉</td>
-      <td class="tdc"><i>k</i>₁₀</td>
-      <td class="tdc"><i>k</i>₁₁</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">4</td>
-      <td class="tdl_ws1">Connective Dial Setting</td>
-      <td class="tdc">▲</td>
-      <td class="tdc">∧</td>
-      <td class="tdc">∧</td>
-      <td class="tdc">∧</td>
-      <td class="tdc">▲</td>
-      <td class="tdc">∧</td>
-      <td class="tdc">▲</td>
-      <td class="tdc">∧</td>
-      <td class="tdc">▲</td>
-      <td class="tdc">off</td>
-      <td class="tdc">off</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">8</td>
-      <td class="tdl_ws1">Statement Denial Switch</td>
-      <td class="tdc" colspan="12">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;&emsp;Setting</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">5</td>
-      <td class="tdl_ws1">Antecedent Dial No.</td>
-      <td class="tdc"><i>A</i>₁</td>
-      <td class="tdc"><i>A</i>₂</td>
-      <td class="tdc"><i>A</i>₃</td>
-      <td class="tdc"><i>A</i>₄</td>
-      <td class="tdc"><i>A</i>₅</td>
-      <td class="tdc"><i>A</i>₆</td>
-      <td class="tdc"><i>A</i>₇</td>
-      <td class="tdc"><i>A</i>₈</td>
-      <td class="tdc"><i>A</i>₉</td>
-      <td class="tdc"><i>A</i>₁₀</td>
-      <td class="tdc"><i>A</i>₁₁</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">5</td>
-      <td class="tdl_ws1">Antecedent Dial Setting</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>k</i>₁</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>k</i>₃</td>
-      <td class="tdc"><i>k</i>₄</td>
-      <td class="tdc"><i>k</i>₂</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>k</i>₇</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc">off</td>
-      <td class="tdc">off</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">6</td>
-      <td class="tdl_ws1">Consequent Dial No.</td>
-      <td class="tdc"><i>C</i>₁</td>
-      <td class="tdc"><i>C</i>₂</td>
-      <td class="tdc"><i>C</i>₃</td>
-      <td class="tdc"><i>C</i>₄</td>
-      <td class="tdc"><i>C</i>₅</td>
-      <td class="tdc"><i>C</i>₆</td>
-      <td class="tdc"><i>C</i>₇</td>
-      <td class="tdc"><i>C</i>₈</td>
-      <td class="tdc"><i>C</i>₉</td>
-      <td class="tdc"><i>C</i>₁₀</td>
-      <td class="tdc"><i>C</i>₁₁</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">6</td>
-      <td class="tdl_ws1">Consequent Dial Setting</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>k</i>₅</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>k</i>₈</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc"><i>k</i>₉</td>
-      <td class="tdc"><i>V</i></td>
-      <td class="tdc">off</td>
-      <td class="tdc">off</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">7</td>
-      <td class="tdl_ws1">Stop Switches, associating</td>
-      <td class="tdc" colspan="12">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;&emsp;connective to Main</td>
-      <td class="tdc" colspan="12">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;&emsp;Truth-Value Light</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">—</td>
-      <td class="tdc">&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">possible statuses of employees who are not
-insured are shown in <a href="#TABLE_17">Table 17</a>. As we look
-down the last column in <a href="#TABLE_17">Table 17</a>, we observe
-6 occurrences of <i>T</i>, instead of 5 as the manager determined
-(<a href="#TABLE_15">see Table 15</a>). Thus, when we compare the manager’s
-result with the machine result, we find an additional possible
-combination to be reported to Mr. Adams, combination 7:</p>
-
-<div class="blockquot">
-<p class="neg-indent fontsize_120">Employee eligible, employee has not applied,
-employee’s application not approved, employee requires a medical
-examination, employee not insured.</p>
-</div>
-
-<p><span class="pagenum" id="Page_165">[Pg 165]</span></p>
-
-<p id="TABLE_17" class="f150"><b>Table 17</b></p>
-
-<p class="center"><b>SOLUTION OF THE PROBLEM<br /> BY THE CALCULATOR</b></p>
-
-<ul class="index no-wrap">
-<li class="isub10"><span class="fontsize_120"><b>LEGEND:</b></span></li>
-<li class="isub2"><big><b>{A}</b></big>&emsp;THE EMPLOYEE IS ELIGIBLE FOR INSURANCE</li>
-<li class="isub2"><big><b>{B}</b></big>&emsp;THE EMPLOYEE HAS APPLIED FOR INSURANCE</li>
-<li class="isub2"><big><b>{C}</b></big>&emsp;THE EMPLOYEE’S APPLICATION FOR INSURANCE</li>
-<li class="isub7">HAS BEEN APPROVED</li>
-<li class="isub2"><big><b>{D}</b></big>&emsp;THE EMPLOYEE REQUIRES A MEDICAL EXAMINATION</li>
-<li class="isub2"><big><b>{E}</b></big>&emsp;THE EMPLOYEE IS INSURED</li>
-<li class="isub2"><big><b>{F}</b></big>&emsp;CASE, OR COMBINATION NO.</li>
-<li class="isub2"><big><b>{G}</b></big>&emsp;THE COMBINATION DOES NOT CONTRADICT THE RULES,</li>
-<li class="isub7">I.E., THE YELLOW LIGHT IS ON</li>
-</ul>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="4" summary=" " cellpadding="4" rules="cols" >
-   <thead><tr>
-      <th class="tdl">&nbsp;</th>
-      <th class="tdc">{A}</th>
-      <th class="tdc">{B}</th>
-      <th class="tdc">{C}</th>
-      <th class="tdc">{D}</th>
-      <th class="tdc">{E}</th>
-      <th class="tdc">{F}</th>
-      <th class="tdc">{G}</th>
-      <th class="tdc">&nbsp;</th>
-   </tr><tr>
-      <th class="tdl bb"><i>Status</i>:</th>
-      <th class="tdc bb">1</th>
-      <th class="tdc bb">2</th>
-      <th class="tdc bb">3</th>
-      <th class="tdc bb">4</th>
-      <th class="tdc bb">5</th>
-      <th class="tdc bb">&nbsp;</th>
-      <th class="tdc bb">&nbsp;</th>
-  </tr>
-  </thead>
-  <tbody><tr>
-      <td class="tdc" rowspan="17">&nbsp;</td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">1</td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">2</td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">3</td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc bb"><i>F</i></td>
-      <td class="tdc bb"><i>F</i></td>
-      <td class="tdc bb"><i>T</i></td>
-      <td class="tdc bb"><i>T</i></td>
-      <td class="tdc bb"><i>F</i></td>
-      <td class="tdc bb">4</td>
-      <td class="tdc bb"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">5</td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">6</td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">7</td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc bb"><i>F</i></td>
-      <td class="tdc bb"><i>F</i></td>
-      <td class="tdc bb"><i>F</i></td>
-      <td class="tdc bb"><i>T</i></td>
-      <td class="tdc bb"><i>F</i></td>
-      <td class="tdc bb">8</td>
-      <td class="tdc bb"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">9</td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">10</td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">11</td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc bb"><i>F</i></td>
-      <td class="tdc bb"><i>F</i></td>
-      <td class="tdc bb"><i>T</i></td>
-      <td class="tdc bb"><i>F</i></td>
-      <td class="tdc bb"><i>F</i></td>
-      <td class="tdc bb">12</td>
-      <td class="tdc bb"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">13</td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">14</td>
-      <td class="tdc"><i>F</i></td>
-   </tr><tr>
-      <td class="tdc"><i>T</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">15</td>
-      <td class="tdc"><i>T</i></td>
-   </tr><tr>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc"><i>F</i></td>
-      <td class="tdc">16</td>
-      <td class="tdc"><i>T</i></td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Because of the medical examination, this
-additional class of employee would need to be considered rather
-carefully in any change of the group insurance plan.</p>
-
-<h3>AN APPRAISAL OF THE CALCULATOR</h3>
-
-<p>In appraising the Kalin-Burkhart Logical-Truth Calculator, we must
-remember that this is a first model. It was the only machine of its
-kind up to the end of 1948; and it worked.</p>
-
-<p>The cost of the machine, as stated before, was about $150 of parts and
-perhaps $1000 of labor. This is less than ¹/₁₀₀ of the cost of the
-<span class="pagenum" id="Page_166">[Pg 166]</span>
-other giant brains described in previous chapters. Yet we can properly
-call this machine a mechanical brain because it transfers information
-automatically from one part to another of the machine, has automatic
-control over the sequence of operations, and does certain kinds of
-reasoning.</p>
-
-<p>The machine is swift. It can check up to a 100 cases against a set of
-rules in less than 1 minute. It can check: 128 cases for 7 conditions
-in 1¼ minutes, 256 cases for 8 conditions in 2½ minutes, and 4096 cases
-for 12 conditions in 38 minutes. That is the limit of the present
-machine. Of course, setting up the machine to do a problem takes some
-more time.</p>
-
-<p>The programming of this machine to do a problem is less complicated
-than the programming of most of the big machines previously described.
-Of course, in order to prepare a problem for the machine, the preparer
-needs to know a fair amount of the algebra of logic. This, however, is
-not very hard. As to reliability, the machine has in practice been out
-of order less than 2 per cent of operating time.</p>
-
-<p>The big barrier to wide use of the machine, of course, is lack of
-understanding of the field of problems in which it can be applied.
-Even in this modern world of ours, we are in rather a primitive stage
-in regard to recognizing problems in logical truth and knowing how to
-calculate it. Here, however, is an electrical instrument for logical
-reasoning, and it seems likely that its applications will multiply.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_167">[Pg 167]</span></p>
-<h2 class="nobreak" id="CHAPTER_10">Chapter 10<br />
-<span class="h_subtitle">AN EXCURSION:<br />
-THE FUTURE DESIGN OF MACHINES THAT THINK</span></h2>
-</div>
-
-<p>In the previous chapters we have described four giant mechanical
-brains finished by the end of 1946: Massachusetts Institute of
-Technology’s Differential Analyzer No. 2, Harvard’s IBM Automatic
-Sequence-Controlled Calculator, Moore School of Electrical
-Engineering’s Electronic Numerical Integrator and Calculator (Eniac),
-and Bell Telephone Laboratories’ General-Purpose Relay Computer. All
-these brains have actually worked long enough to have demonstrated
-thoroughly some facts of great importance.</p>
-
-<h3>WHAT EXISTING MACHINES HAVE PROVED</h3>
-
-<p>The existing mechanical brains have proved that information can be
-automatically transferred between any two registers of a machine.
-No human being is needed to pick up a physical piece of information
-produced in one part of the machine, personally move it to another part
-of the machine, and there put it in again. We can think of a mechanical
-brain as something like a battery of desk calculators or punch-card
-machines all cabled together and communicating automatically.</p>
-
-<p>The existing mechanical brains have also proved that flexible,
-automatic control over long sequences of operations is possible. We can
-lay out the whole routine to solve a problem, translate it into machine
-language, and put it into the machine. Then we press the “start”
-button; the machine starts whirring and prints out the answers as it
-obtains them. Mechanical brains have removed the limits on complexity
-of routine: the machine can carry out a complicated routine as easily
-as a simple one.
-<span class="pagenum" id="Page_168">[Pg 168]</span></p>
-
-<p>The existing giant brains have shown that a machine with hundreds of
-thousands of parts will work successfully. It will operate accurately,
-it will run unattended, and it will have remarkably few mechanical troubles.</p>
-
-<p>These machines have shown that enormous speeds can be realized: 5000
-additions a second is Eniac’s record. High speed is needed for many
-problems in science, government, and business. In fact, there are
-economic and statistical problems, now settled by armchair methods,
-for which high-speed mechanical brains may make it possible to compute
-answers rather than guess them.</p>
-
-<p>Also, these machines have been shown to be reasonable in cost. The cost
-of each of the large calculators is in the neighborhood of $250,000 to
-$500,000. If we assume a ten-year life, which is conservative, the cost
-is about $3 to $6 an hour for 24-hour operation. Since each mechanical
-brain can, for problems for which it is suited, do the work of a
-hundred human computers, such a machine can save its cost half a dozen
-times. And these machines are only engineers’ models, built without the
-advantages of production-line assembly.</p>
-
-<p>The cost of giant mechanical brains under design in 1947 and 1948
-is in the neighborhood of $100,000 to $200,000. The main reason for
-the reduction from the previous cost is the use of cheaper automatic
-memory. As designs improve and charges for research and development are
-paid off, the cost should continue to go down.</p>
-
-<h3>NEW DEVICES FOR HANDLING INFORMATION</h3>
-
-<p>In the laboratories working on new mechanical and electronic brains,
-scientists are doing a lot of thinking about new devices for handling
-information. Research into devices for storing information shows that
-<i>magnetic wire</i> as used in sound recording is a rather good
-storage medium.</p>
-
-<h4>Magnetic Wire</h4>
-
-<p>For example, on a hundredth of an inch of fine steel wire we can
-“write” a <i>magnetized spot</i> by means of a small “writing”
-<i>electromagnet</i>. The electromagnet is simply some copper wire
-<span class="pagenum" id="Page_169">[Pg 169]</span>
-coiled around some soft iron shaped in a U. When current flows through
-the coil, the iron becomes a magnet, and the tips of the U magnetize
-the little section of the wire between them. The magnetized spot can
-be of two kinds, say north-south or south-north, depending on which
-way the current flows. We can “read” this difference by means of
-another small “reading” electromagnet. We can erase the spot by means
-of a stronger “erasing” magnet that produces a uniform magnetic state
-throughout the wire. The difference between north-south and south-north
-corresponds to the difference between 1 and 0, or “yes” and “no,”
-etc., and is a <i>unit of information</i> (<a href="#CHAPTER_2">see Chapter 2</a>).
-Many other variations are possible. For example, the presence or absence of a
-magnetized spot may be the unit of information, or the “writing,”
-“reading,” and “erasing” electromagnets all may be the same.</p>
-
-<p>Magnetic wire sound recordings made in the 1890’s are still good.
-This fact shows that magnetic wire may be a more permanent medium for
-storing information than is paper. Stray magnetic forces are likely
-to have no harmful effect on information stored on magnetic wire, for
-these forces would not be strong enough or detailed enough to change
-greatly the difference between the magnetized spot and its neighboring
-neutral area.</p>
-
-<p>A reel of magnetic wire a mile long and <big>³/₁₀₀₀</big> of an inch thick costs
-about $5. At 80 magnetized spots to the inch, a mile of wire can store
-about 5 million units of information. Hence, the cost of storing one
-unit of information is about <big>¹/₁₀₀₀₀</big> of a cent. The time needed for
-changing a magnetized spot from 1 to 0 or from 0 to 1 is about <big>¹/₁₀₀₀₀</big>
-of a second.</p>
-
-<h4>Magnetic Tape</h4>
-
-<p>There is, however, a storage device that may be even more useful, and
-this is <i>magnetic tape</i> (<a href="#FIG_1-10">see Fig. 1</a>). The usual
-size of such tape is ¼ inch wide and 2 or 3 thousandths of an inch
-thick. Magnetic tape may be made of plastic with magnetic powder all
-through it, or it may be of paper coated with magnetic powder, or it
-may be of stainless steel or a magnetic alloy, or it may be of brass or
-a nonmagnetic alloy coated with a magnetic plating.
-<span class="pagenum" id="Page_170">[Pg 170]</span></p>
-
-<p>Magnetic tape has the added advantage that from 4 to 20 channels across
-the tape can be filled with magnetized spots, and the cost then becomes
-about <big>¹/₁₀₀₀₀₀</big> of a cent per spot. It seems possible that 1000 units
-of information can be stored in a quarter of a square inch of magnetic
-tape. This means that more than 1 million units of information can be
-stored in a cubic inch of space filled with magnetic tape, and about 2
-billion units of information in a cubic foot, except that some of the
-space should be allotted to the reels and other equipment that hold
-the tape (<a href="#FIG_2-10">see Fig. 2</a>). This is closer packing
-than printed information in the telephone book, and yet with magnetic
-tape we can get to the information automatically.</p>
-
-<div class="figcenter">
-  <img id="FIG_1-10" src="images/i_170a.jpg" alt="" width="600" height="294" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 1.</span> Magnetic tape.</p>
-  <img id="FIG_2-10" src="images/i_170b.jpg" alt="" width="600" height="366" />
-  <p class="f120"><span class="smcap">Fig. 2.</span> Tape reels.</p>
-</div>
-
-<p>Think of the enormous files in libraries, government, and business.
-<span class="pagenum" id="Page_171">[Pg 171]</span>
-Think of the problems of space and cost and access which these files
-imply. We can then see that this new development may well be of
-extraordinary importance.</p>
-
-<h4>Mercury Tanks</h4>
-
-<div class="figcenter">
-  <img id="FIG_3-10" src="images/i_171.jpg" alt="" width="600" height="289" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 3.</span> Mercury tank.</p>
-</div>
-
-<p>Scientists are investigating other storage devices having still more
-remarkable properties, but these have the disadvantage that, when the
-power goes off, the information vanishes. One of these new storage
-devices is called a <i>mercury tank</i> (<a href="#FIG_3-10">see Fig. 3</a>).
-It consists mainly of a section of iron or steel pipe filled with mercury.
-At each end of this pipe, touching the mercury, is a thin slab of a crystal
-of <i>quartz</i>. Quartz, which is a common stone, and which nearly all
-sand is made of, changes its shape when pulsed with electricity. We
-put a pattern of electrical pulses into the quartz slab at one end of
-the mercury tank; for example, we could have the pattern 1101 meaning
-“pulse, pulse, no pulse, pulse.” The electrical pulses going into the
-quartz slab make the quartz vibrate. Thus ripples are produced in the
-mercury, and waves in the pattern 1101 meaning “wave, wave, no wave,
-wave” travel down the tank and strike the quartz slab at the far end.
-The quartz slab there changes its shape in the rhythm 1101, and it
-converts the waves back into electrical pulses in the same pattern.
-Then we take the pulses out of the far end along a wire, make them
-stronger again with an amplifier, give them the right form again, and
-feed them back into the front end of the mercury tank. The mercury tank
-is a clever use of the principle of an <i>echo</i>, as when you call
-across a valley and the rocks answer you back. We can store a pattern
-of 400 pulses (each a unit of information, a 1 or a 0, and each a
-<span class="pagenum" id="Page_172">[Pg 172]</span>
-millionth of a second in duration), in a mercury tank about 20
-inches long. A mercury tank and an echo are examples of <i>delay
-lines</i>—“lines” along which waves are “delayed.”</p>
-
-<h4>Electrostatic Storage Tube</h4>
-
-<p>Another of the memory devices being developed is called an
-<i>electrostatic storage tube</i> (<a href="#FIG_4-10">see Fig. 4</a>).
-This is a big electronic tube with a <i>screen</i> across one end. The
-screen may be of two layers: one of copper, which conducts electricity,
-and one of <i>mica</i>, a material that does not. In the other end of
-the tube is a <i>beam</i> of electrons, which we can turn on and off
-and shoot at any of 2 or 3 thousand specific points or <i>spots</i> on
-the screen.</p>
-
-<div class="figcenter">
-  <img id="FIG_4-10" src="images/i_172.jpg" alt="" width="600" height="417" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 4.</span> Electrostatic storage tube.</p>
-</div>
-
-<p>There are two sizes of <i>electric charge</i> or quantity of electrons;
-we can call these 1 and 0. In about a millionth of a second, we can put
-either size of charge on one of the spots of the screen. With other
-circuits we can keep it there as long as we want, if the power does
-not flicker off. We can “remember” perhaps 2 or 3 thousand units of
-information in one of these electronic tubes. We can read, write, or
-erase any unit of information in a few millionths of a second.</p>
-
-<p>Neither the mercury tank nor the electrostatic storage tube had, by the
-end of 1947, been put into a working mechanical brain. But there is
-good reason to believe that they will be successful devices and will
-open up a new era of speed in storing and referring to information. In
-<span class="pagenum" id="Page_173">[Pg 173]</span>
-fact, several laboratories are developing electronic calculating
-circuits using these devices which will perform up to 100,000 additions
-a second or 10,000 multiplications a second. Our minds certainly
-stagger at the thought of such speeds.</p>
-
-<h3>NEW OPERATIONS</h3>
-
-<p>Many kinds of combining operations have already been built into one or
-more mechanical brains. The operations may be arithmetical: addition,
-subtraction, multiplication, division, looking up numbers in tables,
-etc. Or the operations may be logical: comparing, selecting, checking,
-etc. Additional logical operations will be built into some of the
-mechanical brains now being constructed: sorting, collating, matching,
-merging, etc.</p>
-
-<h3>NEW IDEAS IN PROGRAMMING</h3>
-
-<p><i>Programming</i>—the way to give instructions to machines—is also
-being studied in the laboratories. Several new ideas of importance have
-developed as a result.</p>
-
-<p>One idea is that the machine should be able to store its instructions
-or <i>program</i> or <i>routine</i> in its memory in just the same
-physical ways as it stores numbers. There is basically no reason why
-numbers only should be stored in some registers, and instructions only
-stored in other registers.</p>
-
-<p>Another idea is that the machine should have in its permanent memory
-any subroutine it may need. For example, a subroutine should always
-be available in the machine for finding <i>square root</i>. At any
-time when a square root was needed, we would only have to call on the
-machine for the subroutine of square root. The machine would then
-consult the right part of its memory and carry out the subroutine for
-square root.</p>
-
-<p>A third idea, and one of the most interesting, is that the machine
-should be able to compute its own instructions. For example, consider a
-program for finding the product of two <i>matrices</i> (<a href="#SUPPL_2">see Supplement 2</a>),
-each of 100 terms in an array of 10 columns and 10 rows, resulting
-in a new <i>matrix</i> of 100 terms. The whole program can be made to
-consist of about 50 orders. Only one of them is “multiply,” and only
-<span class="pagenum" id="Page_174">[Pg 174]</span>
-one of them is “add”; the other orders consist of how to choose
-expressions to be multiplied or added, etc.</p>
-
-<p>Such problems as these are often fascinating to mathematicians, who
-love to play with the intricate ideas needed.</p>
-
-<h3>NEW IDEAS IN RELIABILITY</h3>
-
-<p>Reliability has a number of aspects:</p>
-
-<ul class="index no-wrap">
-<li class="isub2">1. No wrong results allowed out of the machine.</li>
-<li class="isub2">2. Few failures.</li>
-<li class="isub2">3. Rapid location of failures.</li>
-<li class="isub2">4. Quick repair or replacement of parts that fail.</li>
-<li class="isub2">5. Easy maintenance.</li>
-<li class="isub2">6. Unattended operation overnight.</li>
-</ul>
-
-<p class="no-indent">For example, Bell Laboratories proved that
-mechanical brains can be built so that no wrong results are allowed
-to come out. In other words, the machine checks itself all the time
-as it goes along and stops at once if the check shows that something
-is wrong. This is likely to be a standard feature of new automatic
-thinking machinery.</p>
-
-<p>The frequency of failures in the machinery being designed in the
-laboratories may be of the order of one or two mechanical failures
-a week. For any type of failure an alarm circuit and trouble lights
-will show what part of the machine needs attention. Plug-in parts for
-replacement are already in use in at least two of the four mechanical
-brains described and should be available in all the new machines. It is
-possible to build a machine that will automatically change from failing
-equipment to properly functioning equipment. For some years though,
-this may be too expensive to be reasonable.</p>
-
-<p>The use of magnetic tape for storage reduces greatly the number of
-parts and so increases reliability. For example, instead of 18,000
-electronic tubes in an electronic brain, there may be less than 3000.</p>
-
-<p>A final degree of reliability is gained when most of the time the
-machine operates unattended. Then, there is no human operator standing
-by who may fail to do the correct thing at the moment when the machine
-<span class="pagenum" id="Page_175">[Pg 175]</span>
-needs some attention. In fact, the motto for the room housing a
-mechanical brain should become, “Don’t think; let the machine do it
-for you.” Unattended operation from the end of one working day to
-the beginning of the next, with the machine changing itself from one
-problem to another problem, has already been proved possible on the
-Bell Laboratories machine.</p>
-
-<h3>AUXILIARY DEVICES</h3>
-
-<p>In order to use a mechanical brain, we have to give it and take from
-it language that it understands, <i>machine language</i>. A mechanical
-brain that can do 10,000 additions a second can very easily finish
-almost all its work at once. How can we, slow as we are, keep our
-friend, the giant brain, busy? We have found so far several answers to
-this question, none of them yet very good.</p>
-
-<p>Devices for preparing input will be very important. For each brain, we
-shall need a great many of these devices. For, at best, we type at a
-rate, say, of 4 characters a second, selecting any one of some 38 keys,
-each of which is equivalent to about 6 units of information. This is
-about 800 units of information per second. The machine, however, is
-likely to be able to gulp information from its input mechanism at the
-amazing rate of 60,000 units of information per second, equal to 75
-people typing with no mistakes and no resting. Fortunately, at least
-some of the time the machine will be busy computing!</p>
-
-<p>For an input-preparation device, we may get something that can be
-fastened to an ordinary typewriter and that will produce magnetic
-tape agreeing with what is printed by the typewriter. Since the
-input information must be carefully verified, we shall need a second
-magnetic tape device such as exists for paper tape on the Bell
-Laboratories machine: the <i>processor</i>. The processor takes two
-hand-prepared tapes, compares them, reports any differences, and
-produces a third tape. The third tape copies the two original tapes if
-they agree, and it receives corrected information as furnished by a
-girl at a keyboard if the two original tapes disagree.</p>
-
-<p>For information already on punch cards, we need an input device that
-<span class="pagenum" id="Page_176">[Pg 176]</span>
-will read punch cards and write on magnetic tape. Where information is
-on punched paper tape, we need a machine that will read punched paper
-tape and write on magnetic tape.</p>
-
-<p>Problem data, tables of numbers, and routine instructions will go
-into the mechanical brain. They will all be prepared on regular input
-devices. The machine will accept information in the form in which it is
-most convenient for you and me to prepare it. Then, the machine will
-be instructed to change the information into the form with which it is
-most convenient for the machine to operate.</p>
-
-<p>Many output devices will also be needed, since the machine will be able
-to produce information very swiftly. These output devices might be
-cabled to the machine. A kind of traffic control system would govern
-them. Each will have a magnetic tape that will be loaded up swiftly
-with information. Then the output device will unload its information
-more slowly, in any form that we may desire: printing, graphs, film,
-punch cards, or punched paper tape.</p>
-
-<p>The machine is likely to be able to put out information on magnetic
-tape at the same high speed of 60,000 units of information per
-second or 10,000 characters per second. But the best printing speed
-of an electric typewriter is about 10 or 12 characters a second.
-Card-punching speed is about 130 characters a second. Punch-card
-tabulator speed can reach a maximum of about 200 characters a second.
-Thus we see that here, too, we may be snowed under with the information
-that the giant brain puts out, if we fail to ask the giant only for
-what we really want.</p>
-
-<h3>MECHANICAL BRAINS UNDER CONSTRUCTION</h3>
-
-<p>This chapter would not be complete without mention of the great
-mechanical brains that were actually under construction at the end of
-1947. In power they are intermediate between the machinery now being
-designed, described in this chapter, and the earlier machines described
-in the previous chapters of this book.</p>
-
-<p>The mechanical brains under construction on December 31, 1947, were:
-<span class="pagenum" id="Page_177">[Pg 177]</span></p>
-
-<div class="blockquot">
-<p class="neg-indent">Harvard’s Sequence-Controlled Relay Calculator
-<i>Mark II</i>, constructed at the Harvard Computation
-Laboratory, tested there July 1947 to January 1948, and delivered to
-the Naval Proving Ground, Dahlgren, Va., in 1948.</p>
-
-<p class="neg-indent">The <i>IBM Selective-Sequence Electronic
-Calculator</i>, constructed in the IBM laboratories, Endicott, N.
-Y., and installed in 1947 at the office of International Business
-Machines, 590 Madison Ave., New York, N. Y.</p>
-
-<p class="neg-indent">Moore School of Electrical Engineering’s
-<i>EDVAC</i> (Electronic Digital Variable Automatic Computer) being
-constructed partly at Moore School and partly elsewhere, and to be
-delivered to the Ballistic Research Laboratories, Aberdeen, Md.</p>
-
-<p class="neg-indent">Harvard’s Sequence-Controlled Electronic
-Calculator <i>Mark III</i>, being constructed at the Harvard
-Computation Laboratory, and to be delivered to the Naval Proving
-Ground, Dahlgren, Va.</p>
-</div>
-
-<p>We shall cover briefly (and perhaps a little technically) some of the
-main features of the first two of these machines; for, during 1948,
-they began to do problems. The other two had not been finished by
-the end of 1948 and so would be difficult to describe correctly, for
-mechanical brains <i>grow</i>, and design changes go on until they are
-finished—and even afterwards.</p>
-
-<p>Some information about these machines can be obtained from the
-organizations referred to above and from reports that should appear
-from time to time in some of the journals mentioned in <a href="#SUPPL_3">Supplement 3</a>.
-There is also a regular section entitled “Automatic Computing
-Machinery” in the quarterly <i>Mathematical Tables and Other Aids to
-Computation</i>, where it is likely that current information may be found.</p>
-
-<h4>Harvard’s Mark II</h4>
-
-<p>The Harvard Sequence-Controlled Calculator Mark II began to do problems
-under test during July 1947. This machine is at least twelve times as
-powerful as Mark I (<a href="#CHAPTER_6">see Chapter 6</a>) and was constructed
-entirely by the Harvard Computation Laboratory. The machine contains about 13,000
-relays of a new type that will operate reliably within <big>¹/₁₀₀</big>
-of a second.</p>
-
-<p>Numbers in the machine are regularly of 10 decimal digits between
-<span class="pagenum" id="Page_178">[Pg 178]</span>
-1.000,000,000 and 9.999,999,999, inclusive, multiplied by a power of 10
-between 1,000,000,000,000,000 and 0.000,000,000,000,001, inclusive.</p>
-
-<p>For storage of numbers, the machine has 100 relay registers totaling
-about 1200 decimal digits. Also, it can consult any one of 8 tape feeds
-for numbers and any one of 4 tape feeds for instructions. Effectively,
-the machine can read one number and one instruction from paper tape in
-<big>¹/₃₀</big> of a second.</p>
-
-<p>The machine performs all arithmetical and most logical operations.
-In every second it can carry out 4 multiplications, 8 additions (or
-subtractions), and 12 transfers. Division is performed by rapid
-approximation using the other operations.</p>
-
-<p>In each second the machine can perform 30 instructions. An instruction
-is expressed by 6 digits between 0 and 7 which you can select and, in
-effect, by 3 more digits fixed by the time (within the second) when the
-machine reads the instruction. For example, in the 9th instruction of
-the 30 instructions in each second, we can specify a multiplicand. But,
-if we do not want to multiply right then—a rare event if we are coding
-wisely—we leave the 9th instruction empty. The machine may operate as
-a whole, attending to one problem; or the machine may be separated into
-halves, and each half will attend to its own problem.</p>
-
-<h4>The IBM Selective-Sequence<br /> Electronic Calculator</h4>
-
-<p>The IBM Selective-Sequence Electronic Calculator was announced publicly
-on January 27, 1948, after some months of trial running. It is a large
-and powerful mechanical brain, and it is the intention of International
-Business Machines to devote it to solving scientific problems. The
-staff of the Watson Scientific Computing Laboratory in New York will be
-mainly in charge of the machine.</p>
-
-<p>The machine contains about 12,500 electronic tubes and about 21,500
-relays. Numbers in the machine are regularly of either 14 or 19
-decimal digits. Instructions are expressed as numbers. For storage of
-information, the machine has a capacity of 8 registers totaling 160
-decimal digits of very rapid memory in electronic tubes. Also, it has
-about 150 registers totaling 3000 decimal digits of less rapid memory
-in relays. Also, it can consult any one of 66 paper tape feeds; each
-<span class="pagenum" id="Page_179">[Pg 179]</span>
-row on a paper tape can hold up to 78 punched holes or 19 decimal
-digits, and the machine can consult 25 rows on one tape in one second.
-These paper tapes together give the machine about 400,000 decimal
-digits of memory.</p>
-
-<p>For arithmetical and logical operations, the machine has an
-arithmetical unit using electronic tubes. This unit can carry out about
-50 multiplications or about 250 additions per second, including the
-transfers of numbers. In each second the machine can read and perform
-50 instructions, and each instruction consists, usually, of getting
-two numbers out of two relay registers, performing an operation, and
-putting the result into a third relay register.</p>
-
-<h4>Eckert-Mauchly’s Binac</h4>
-
-<p>As this book went to press, another mechanical brain, the Electronic
-Binary Automatic Computer, or BINAC, was announced on August 22,
-1949. This machine was constructed by the Eckert-Mauchly Computer
-Corporation, Philadelphia, Pa., for Northrop Aircraft, Inc., Hawthorne,
-Calif.</p>
-
-<p>This machine has some remarkable properties. It does addition or
-subtraction at the rate of 3500 per second. It does multiplication or
-division at the rate of 1000 per second. The input is from a keyboard
-or magnetic tape; the output is to magnetic tape or an electric
-typewriter. Binac has 512 registers of very rapid memory in mercury
-tanks, and each register holds 30 binary digits. The machine actually
-is a pair of twins: the storage, the computing element, and the control
-are double, and each twin runs in step with the other and checks
-every operation of the other. In tests in July the machine ran over
-10 consecutive hours with no error. Each twin has only 700 electronic
-tubes. Binac handles all numbers in binary notation, except that the
-keyboard and the typewriter express numbers in <i>octal notation</i>
-(<a href="#SUPPL_2">see Supplement 2</a>). Finally, Binac is only 5 feet
-high, 4 feet long, and one foot wide.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_180">[Pg 180]</span></p>
-<h2 class="nobreak" id="CHAPTER_11">Chapter 11<br />
-<span class="h_subtitle">THE FUTURE:<br />
-MACHINES THAT THINK,<br /> AND WHAT THEY MIGHT DO FOR MEN</span></h2>
-</div>
-
-<p>The pen is mightier than the sword, it is often said. And if this is
-true, then the pen with a motor may be mightier than the sword with a
-motor.</p>
-
-<p>In the Middle Ages, there were few kinds of weapons, and it was easy
-for a man to protect himself against most of them by wearing armor.
-As gunpowder came into use, a man could no longer carry the weight of
-armor that would protect him, and so armor was given up. But in 1917,
-armor, equipped with a motor and carrying the man and his weapons, came
-back into service—as the tank.</p>
-
-<p>In much the same way, in the Middle Ages, there were few books, and it
-was easy for a man to handle nearly all the information that was in
-books. As the printing press came into use, man’s brain could no longer
-handle all recorded information, and the effort to do so was given
-up. But in 1944, a brain to handle information, equipped with a motor
-and supporting the man and his reasoning, came into existence—as the
-sequence-controlled calculator.</p>
-
-<p>In previous chapters we have examined some of the giant mechanical
-brains that have been finished; we have also considered the design
-of such machines. Now in this chapter we shall discuss the future
-significance of machines that think, of motorized information. We shall
-discuss what we can foresee if we look with imagination into the future.</p>
-
-<p>There are two questions we need to ask: What types of machines that
-think can we foresee? What types of problems to be solved by these
-machines can we foresee?
-<span class="pagenum" id="Page_181">[Pg 181]</span></p>
-
-<h3>FUTURE TYPES OF MACHINES THAT THINK</h3>
-
-<p>The machines that already exist show that some processes of thinking
-can already be performed very quickly:</p>
-
-<ul class="index no-wrap">
-<li class="isub2">Calculating: adding, subtracting,...</li>
-<li class="isub2">Reasoning: comparing, selecting,...</li>
-<li class="isub2">Referring: looking up information in lists,...</li>
-</ul>
-
-<p class="no-indent">We can expect other processes of thinking to
-come up to high speed through the further development of thinking
-machines.</p>
-
-<h4>Automatic Address Book</h4>
-
-<p>Nowadays when we wish to send out announcements of an event, like going
-to South America for a year, we may copy the addresses of our friends
-onto the envelopes by hand. In the future, we can see our address book
-as a spool of magnetic tape. When we wish to send out announcements,
-we put a stack of blank envelopes into the machine that will read the
-magnetic tape, and we press a button. Out will come the envelopes addressed.</p>
-
-<p>If we wish to select only those friends of ours whose last names we put
-down on a list, we can write the list on another magnetic tape, place
-it also in the machine, and set a few switches. Then the machine will
-read the names on the list, find their addresses in the address-book
-tape, and prepare only the envelopes we want. If a friend’s address
-changes, we can notify the machine. It will find his old address, erase
-it, and enter the new address.</p>
-
-<h4>Automatic Library</h4>
-
-<p>We can foresee the development of machinery that will make it possible
-to consult information in a library automatically. Suppose that you
-go into the library of the future and wish to look up ways for making
-biscuits. You will be able to dial into the catalogue machine “making
-biscuits.” There will be a flutter of movie film in the machine. Soon
-it will stop, and, in front of you on the screen, will be projected
-the part of the catalogue which shows the names of three or four books
-containing recipes for biscuits. If you are satisfied, you will press a
-<span class="pagenum" id="Page_182">[Pg 182]</span>
-button; a copy of what you saw will be made for you and come out of the
-machine.</p>
-
-<p>After further development, all the pages of all books will be available
-by machine. Then, when you press the right button, you will be able to
-get from the machine a copy of the exact recipe for biscuits that you choose.</p>
-
-<p>We are not yet at the end of foreseeable development. There will be
-a third stage. You will then have in your home an automatic cooking
-machine operated by program tapes. You will stock it with various
-supplies, and it will put together and cook whatever dishes you desire.
-Then, what you will need from the library will be a program or routine
-on magnetic tape to control your automatic cook. And the library,
-instead of producing a pictorial copy of the recipe for you to read and
-apply, will produce a routine on magnetic tape for controlling your
-cooking machine so that you will actually get excellent biscuits!</p>
-
-<p>Of course, you may have other kinds of automatic producing machinery in
-your home or office. The furnishing of routines to control automatic
-machinery will become a business of importance.</p>
-
-<h4>Automatic Translator</h4>
-
-<p>Another machine that we can foresee would be used for translating
-from one language to any other. We can call it an <i>automatic
-translator</i>. Suppose that you want to say “How much?” in Swedish.
-You dial into the machine “How much?” and press the button “Swedish,”
-and the machine will promptly write out “Hur mycket?” for you. It also
-will pronounce it, if you wish, for there would be little difficulty in
-recording on magnetic tape the pronunciation of the word as spoken by
-a good speaker of the language. The machine could be set to repeat the
-pronunciation several times so that the student could really learn the
-sound. He could learn it better, probably, by hearing it and trying to
-say it than he could by using any set of written symbols.</p>
-
-<h4>Automatic Typist</h4>
-
-<p>We now come to a possible machine that uses a new principle. This
-principle is that of being able to <i>recognize</i> signs. This machine
-<span class="pagenum" id="Page_183">[Pg 183]</span>
-would perceive writing on a piece of paper and recognize that all the
-<i>a</i>’s that appear on the paper are cases of <i>a</i>, and that
-all the <i>b</i>’s that appear on it are instances of <i>b</i>, and so
-forth. The machine could then control an electric typewriter and copy
-the marks that it sees. The first stage of this machine would be one
-in which only printed characters of a high degree of likeness could
-be recognized. In later stages, handwriting, even rather illegible
-handwriting, might be recognizable by the machine. We can call it an
-<i>automatic typist</i>.</p>
-
-<p>The elements of the automatic typist would be the following:</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. <i>Phototubes</i> (electronic tubes sensitive
-to the brightness of light), which could sense the difference between
-black and white (these already exist).</p>
-
-<p class="neg-indent">2. A memory of the shapes of 52 letters, 10
-digits, and punctuation marks. Fine distinctions would be required of
-this memory in some cases—like the difference between the numeral 5 and
-the capital letter S.</p>
-
-<p class="neg-indent">3. A control that would cause the machine to
-<i>tune</i> itself, so that a good matching between the marks it
-observed and the shapes it remembered would be reached.</p>
-
-<p class="neg-indent">4. A <i>triggering control</i> so that, when the
-machine had reached good enough matching between its observations and
-its memory, the machine would proceed to identify the marks, read them,
-and transfer them.</p>
-
-<p class="neg-indent">5. An electric typewriter, which would respond to
-the transferred instructions. (This also already exists.)</p>
-</div>
-
-<p>This machine is perhaps not so farfetched as it might seem. During
-World War II, gun-aiming equipment using the new technique <i>radar</i>
-reached a high stage of development. Many shots that disabled and sank
-enemy ships were fired in total darkness by radar-controlled guns. On
-the glowing screen in the control room, there were two spots, one that
-marked the target and one that reported the point at which the gun
-was aimed. These two spots could be brought almost automatically into
-agreement. In the same way, a report from a phototube telling the shape
-of an observed mark and a report from the memory of the machine telling
-<span class="pagenum" id="Page_184">[Pg 184]</span>
-the shape of a similar mark could be compared by the machine for
-likeness and, if judged enough alike, could be approved as identical.</p>
-
-<p>Even the phrase “enough alike” can be applied by a machine. During
-World War II, tremendous advances were made in machinery for
-deciphering enemy messages. Machines observed various features and
-patterns in enemy messages, swiftly counted the frequency of these
-features, and carried out statistical tests. Then the machines selected
-those few cases in which the patterns showed meaning instead of
-randomness.</p>
-
-<p>A machine like the automatic typist, if made flexible enough, would
-be, of course, extremely useful. A great load of dull office work is
-now being thrown on clerks whose task is to translate from writing and
-typing into languages that machines can read, such as punch cards.
-At the present time, if punch-card machines are widely used in a big
-company, the company must employ large numbers of girls whose sole
-duty is to read papers and punch up cards. A still bigger chore is the
-work of typists in all kinds of businesses whose main duty is to read
-handwriting, etc., and then copy the words on a typewriter.</p>
-
-<div class="figcenter">
-  <img id="FIG_1-11" src="images/i_184.jpg" alt="" width="600" height="253" />
-  <p class="f120 space-below2"><b>Each square in the grill<br /> is watched by a phototube.</b></p>
-  <p class="f120 space-below2"><span class="smcap">Fig. 1.</span> Scheme for distinguishing <i>A</i> and
-<i>H</i> by 15 phototubes.</p>
-</div>
-
-<p>Research has already begun on various features of the automatic typist
-because of its obvious labor-saving value. For example, many patents
-have been issued on schemes for dividing the area occupied by a letter
-or a digit into an array of spots, with a battery of phototubes
-each watching a spot. The reports from the phototubes together will
-distinguish the letter or digit. For example, if we consider <i>A</i>
-and <i>H</i> placed in a grill of fifteen spots, 5 long by 3 wide
-<span class="pagenum" id="Page_185">[Pg 185]</span>
-(<a href="#FIG_1-11">see Fig. 1</a>), then the phototubes can distinguish
-between <i>A</i> and <i>H</i> by sensing black or white in the spot
-in the middle of the top row. When we consider how easily and swiftly
-a human being does this, we can once more marvel at the recognizing
-machine we all carry around with us in our heads.</p>
-
-<h4>Automatic Stenographer</h4>
-
-<p>Another development that we can foresee is one that we can call the
-<i>automatic stenographer</i>. This is a machine that will listen to
-sounds and write them down in properly spelled English words. The
-elements of this machine can be outlined:</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. Microphones, which can sense spoken sounds
-(these already exist).</p>
-
-<p class="neg-indent">2. A memory storing the 40 (more or less) phonetic
-units or sounds that make up English, such as the 23 consonant sounds,</p>
-</div>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdl"><i>p</i></td>
-      <td class="tdl_ws1"><i>b</i></td>
-      <td class="tdl_ws1"><i>l</i></td>
-      <td class="tdl_ws1"><i>ng</i></td>
-   </tr><tr>
-      <td class="tdl"><i>f</i></td>
-      <td class="tdl_ws1"><i>v</i></td>
-      <td class="tdl_ws1"><i>m</i></td>
-      <td class="tdl_ws1"><i>th</i></td>
-   </tr><tr>
-      <td class="tdl"><i>t</i></td>
-      <td class="tdl_ws1"><i>d</i></td>
-      <td class="tdl_ws1"><i>n</i></td>
-      <td class="tdl_ws1"><i>r</i></td>
-   </tr><tr>
-      <td class="tdl"><i>s</i></td>
-      <td class="tdl_ws1"><i>z</i></td>
-      <td class="tdl_ws1"><i>h</i></td>
-      <td class="tdl_ws1"><i>y</i></td>
-   </tr><tr>
-      <td class="tdl"><i>k</i></td>
-      <td class="tdl_ws1"><i>g</i></td>
-      <td class="tdl_ws1">&nbsp;</td>
-      <td class="tdl_ws1"><i>w</i></td>
-   </tr><tr>
-      <td class="tdl"><i>ch</i></td>
-      <td class="tdl_ws1"><i>j</i></td>
-      <td class="tdl_ws1" colspan="2">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl"><i>sh</i></td>
-      <td class="tdl_ws1" colspan="3"><i>zh</i> (heard in “pleasure”)</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">and the 17 vowel sounds,</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Long</span></th>
-      <th class="tdc"><span class="smcap">Short</span></th>
-      <th class="tdc"><span class="smcap">Other</span></th>
-  </tr>
-  </thead>
-  <tbody><tr>
-      <td class="tdl"><i>A</i> (“ate”)</td>
-      <td class="tdl_ws1"><i>a</i> (“cat”)</td>
-      <td class="tdl_ws1"><i>ar</i> (“are”)</td>
-   </tr><tr>
-      <td class="tdl"><i>E</i> (“eat”)</td>
-      <td class="tdl_ws1"><i>e</i> (“end”)</td>
-      <td class="tdl_ws1"><i>aw</i> (“awe”)</td>
-   </tr><tr>
-      <td class="tdl"><i>I</i> (“isle”)</td>
-      <td class="tdl_ws1"><i>i</i> (“in”)</td>
-      <td class="tdl_ws1"><i>er</i> (“err”)</td>
-   </tr><tr>
-      <td class="tdl"><i>O</i> (“owe”)</td>
-      <td class="tdl_ws1"><i>o</i> (“on”)</td>
-      <td class="tdl_ws1"><i>ow</i> (“owl”)</td>
-   </tr><tr>
-      <td class="tdl"><i>U</i> (“cute”)</td>
-      <td class="tdl_ws1"><i>u</i> (“up”)</td>
-      <td class="tdl_ws1"><i>oi</i> (“oil”)</td>
-   </tr><tr>
-      <td class="tdl"><i>OO</i> (“roof”)</td>
-      <td class="tdl_ws1"><i>oo</i> (“book”)</td>
-      <td class="tdl_ws1">&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<div class="blockquot">
-<p class="neg-indent">3. A collection of the rules of spelling in
-English, containing many statements like
-<span class="pagenum" id="Page_186">[Pg 186]</span></p>
-
-<p class="neg-indent2">The sound <i>b</i> is always spelled <i>b</i></p>
-
-<p class="neg-indent2">The sound <i>sh</i> may be spelled
-<i>sh</i> (ship), <i>s</i> (sugar), <i>ti</i> (station), <i>ci</i>
-(physician), <i>ce</i> (ocean) or <i>tu</i> (picture) and other
-statements based on context, word lists, derivation, etc. These are
-the statements by means of which a good English speller knows how to
-spell even words that he hears for the first time.</p>
-
-<p class="neg-indent">4. A triggering control so that, when the machine
-reaches good enough matching between its observations of sounds, its
-memory of sounds, and its knowledge of spelling rules, the machine
-will identify groups of sounds as words, determine their spelling, and
-report the letters determined.</p>
-
-<p class="neg-indent">5. An electric typewriter, which would type the
-reported letters.</p>
-</div>
-
-<p>With this type of machine, you would dictate your letters into a
-machine (now existing) that would record your voice. Then the record
-would be placed on the automatic stenographer, and out would come your
-letters written and spaced as they should be.</p>
-
-<h4>Automatic Recognizer</h4>
-
-<p>We can foresee a recognizing machine with very general powers. Suppose
-that we call it an <i>automatic recognizer</i> (<a href="#FIG_2-11">see Fig. 2</a>).
-It will have the following elements:</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. <i>Input.</i> This element will consist
-of a set of observing instruments, capable of perceiving sights,
-sounds, etc. There will be ways of positioning or <i>tuning</i> these
-instruments.</p>
-
-<p class="neg-indent">2. <i>Memory.</i> This element will store
-knowledge. It may store the patterns of observations that we are
-interested in; or it may store general rules on how to find patterns of
-observations that we will be interested in. It will contain knowledge
-about acceptable groups of patterns, about actions to be performed in
-response to patterns, etc.
-<span class="pagenum" id="Page_187">[Pg 187]</span></p>
-
-<p class="neg-indent">3. <i>Program 1.</i> The element “Program 1”
-performs a set of standard instructions. Under these instructions, the
-machine:</p>
-
-<p class="neg-indent2">Compares group after group of observations with
-the information in the memory.</p>
-
-<p class="neg-indent2">Compares these groups with patterns furnished,
-or seeks to organize the observations into patterns.</p>
-
-<p class="neg-indent2">Counts cases and tests frequencies.</p>
-
-<p class="neg-indent2">Finds out how much matching with patterns there
-is.</p>
-
-<p class="neg-indent2">Tunes the observing instruments in ways to
-increase matching.</p>
-</div>
-
-<div class="figcenter">
-  <img id="FIG_2-11" src="images/i_187.jpg" alt="" width="600" height="493" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 2.</span> Scheme of an automatic recognizer.</p>
-</div>
-
-<div class="blockquot">
-<p class="neg-indent">4. <i>Program 2.</i> The element “Program
-2” performs another set of standard instructions. Under these
-instructions, the machine, if it is tuned well, matches sets of
-observations one after another with the patterns and so reads them.</p>
-
-<p class="neg-indent">5. <i>Triggering Control.</i> This element shifts
-the control of the machine from Program 1 to Program 2. It does this
-when the machine reaches “good matching.” We shall set the meaning of
-this into the machine in much the same way as we set “warm” into a
-thermostat.</p>
-
-<p class="neg-indent">6. <i>Output.</i> This element performs any
-action that we want, depending on recognized patterns read and any
-other knowledge or instructions stored in the memory.</p>
-</div>
-
-<p><span class="pagenum" id="Page_188">[Pg 188]</span>
-The automatic recognizer will be capable of extraordinary tasks. With
-microphones and a large memory, this type of machine would be able to
-hear a foreign language spoken and translate it into spoken or written
-English. With phototubes and with an expanded filtering and decoding
-capacity as in deciphering machines, the automatic recognizer should be
-able to read a dead language, even those (such as Minoan or Etruscan)
-that have so far resisted efforts to read it. The machine would derive
-rules for the translation of the language and translate any sample.</p>
-
-<p>An automatic recognizer could perhaps be equipped with many sensitive,
-tiny observing instruments that could be placed around or in the brain
-and nervous systems of animals. Then the machine might enable us to
-find out what activity in the nervous system corresponds with what
-activity in the animal.</p>
-
-<h3>TYPES OF PROBLEMS THAT MACHINES<br /> WILL SOLVE IN THE FUTURE</h3>
-
-<p>We turn now to the second question regarding the future of machines
-that think: What types of problems can we foresee as solved by these machines?</p>
-
-<h4>Problems of Control</h4>
-
-<p>Probably the foremost problem which machines that think can solve is
-automatic control over all sorts of other machines. This involves
-controlling a machine that is running so that it will do the right
-thing at the right time in response to information. For example,
-suppose that you are mowing a lawn with a mowing machine. You watch
-the preceding strip so as to stay next to it. You watch the ends of
-the strips, where you turn around. If a stick is caught in the cutting
-blade, you stop and take it out. Now it is entirely possible to put
-devices on the mowing machine so that all these things will be taken
-care of automatically. In fact, in the case of plowing a large field, a
-tractor-plow can be equipped with a device that guides it next to the
-preceding furrow. Thus, once the first furrow around the edge has been
-made, riderless tractors will plow a whole field and stop in the middle.
-<span class="pagenum" id="Page_189">[Pg 189]</span></p>
-
-<p>For another example, take a gas furnace for heating steam to keep a
-house warm. Such a furnace has automatic controls, which respond to the
-following information whenever reported:</p>
-
-<ul class="index fontsize_120">
-<li class="isub2">House too warm.</li>
-<li class="isub2">House not warm enough.</li>
-<li class="isub2">Too much steam pressure.</li>
-<li class="isub2">Not enough water in boiler.</li>
-<li class="isub2">Gas flame not lit.</li>
-<li class="isub2">Daytime.</li>
-<li class="isub2">Nighttime.</li>
-</ul>
-
-<p class="no-indent">In fact, your own meaning of “warm” can be put
-into the control system: you set the dial on your thermostat at the
-temperature that “warm” is to be for you.</p>
-
-<p>In the future many kinds of automatic control will be common. We shall
-have automatic pilots for flying and landing airplanes. We shall have
-automatic missiles for destructive purposes, such as bombing and
-killing, and for constructive purposes, such as delivering mail and
-fast freight. An article in the magazine <i>Fortune</i> for November
-1946 described the automatic factory (<a href="#SUPPL_3">see Supplement 3</a>).
-This is a factory in which there would be automatic arms for holding stuff being
-manufactured, and automatic feed lines for supplying material just
-where it is needed. All this factory would be controlled by machines
-that handle information automatically and produce actions that respond
-to information.</p>
-
-<p>This prospect fills us with concern as well as with amazement. How
-shall we control these automatic machines, these robots, these
-Frankensteins? What will there be left for us to do to earn our living?
-But more of this in the next chapter.</p>
-
-<h4>Problems of Science</h4>
-
-<p>Other problems for which we can foresee the use of machines that think
-are the understanding, and later the controlling, of nature. One of
-these problems is weather forecasting and weather control.</p>
-
-<h4>The Weather Brain</h4>
-
-<p>We can imagine the following type of machine—a <i>weather brain</i>.
-<span class="pagenum" id="Page_190">[Pg 190]</span>
-A thousand weather observatories all over the country observe the weather
-at 8 <span class="smcap">a.m.</span> The observations are fed automatically through
-a countrywide network of communication lines into a central station. Here
-a giant machine, containing a great deal of scientific knowledge about
-the weather, takes in all the data reported to it. At 8:15 the weather
-brain starts to calculate; in half an hour it has finished, having
-produced an excellent forecast of the weather for the whole country.
-Then it proceeds to transmit its forecast all over the country. By 8:50
-every weather station, newspaper, radio station, and airport in the
-country has the details. In October 1945, Dr. V. K. Zworykin of the
-Princeton Laboratories of the Radio Corporation of America proposed
-solving the problem of weather forecasting in this way by a giant brain.</p>
-
-<p>The weather brain will have a second stage of application. From time
-to time and here and there, the weather is unstable: it can be triggered
-to behave in one way or another. For example, recently, pellets of
-<i>frozen carbon dioxide</i>—often called Dry Ice—have been dropped
-from planes and have caused rain. In fact, a few pounds of Dry Ice have
-apparently caused several hundred tons of rain or snow. In similar
-ways, we may, for example, turn away a hail storm so that hail will
-fall over a barren mountain instead of over a farming valley and
-thus protect crops. Or we may dispel conditions that would lead to a
-tornado, thus avoiding its damage. Both these examples involve local
-weather disturbances. However, even the greatest weather disturbances,
-like hurricanes and blizzards, may eventually be directed to some
-extent. Thus the weather may become to some degree subject to man’s
-control, and the weather brain will be able to tell men where and when
-to take action.</p>
-
-<h4>Psychological Testing</h4>
-
-<p>Another scientific problem to which new machinery for handling
-information applies is the problem of understanding human beings and
-their behavior. This increased understanding may lead to much wiser
-dealing with human behavior.</p>
-
-<p>For example, consider tests of aptitudes. If you take one of these
-tests, you may be asked to mark which word out of five suggested ones
-is nearest in meaning to a given word. Or your test may be 40 simple
-<span class="pagenum" id="Page_191">[Pg 191]</span>
-arithmetical problems to be solved in 25 minutes. Or you may be given
-a sheet with 20 circles, and be asked to put 3 dots in the first, 7
-dots in the second, 4 dots in the third, 11 dots in the fourth, and
-so on, irregularly; you may be given a total of 45 seconds to do this
-as well as you can. Now, if a vocational counselor gives you one of
-these tests, and if you get 84 out of 100 on it, he needs to know just
-what he has measured about you. Also, he needs to know whether he can
-reasonably forecast that, as a result of your grade of 84, you will
-be good at writing articles, or good at supervising the work of other
-people, or good at designing in a machine shop. He needs to know the
-records of people with scores of about 84 on this test and to have
-evidence supporting his forecasts.</p>
-
-<p>If we wish to make the most use of the tests, we need to carry out a
-good deal of statistics, mathematics, and logic. For example, it will
-turn out that answers to some questions are much more significant
-than answers to others, and so we can greatly improve the quality of
-the tests by keeping only the more significant questions. Powerful
-machinery for handling calculations will be very useful in the field of
-aptitude testing.</p>
-
-<p>But, you may ask, what if the person analyzing your answers has to use
-interpretations and judgments? If the judgments and interpretations can
-be expressed in words, and if the words can be translated into machine
-language, then the machine can carry out the analysis. Usually the
-difference between a rule and a judgment is simply this: a rule in a
-case in which it is hard to express all the factors being considered is
-called a judgment.</p>
-
-<h4>Psychological Trainer</h4>
-
-<p>It is conceivable that machines that think can eventually be applied
-in the actual treatment of mental illness and maladjustment. Consider
-what a physician does. In treating a psychiatric case, such as a
-<i>neurosis</i>, a physician uses words almost entirely. He asks
-questions. He listens to the patient’s answers. Each answer takes the
-physician nearer and nearer to a diagnosis. By and by the physician
-knows what most of the difficulty is. Then he must present his
-knowledge slowly to the patient, gradually guiding the patient to
-understanding. It is a psychological truth that telling a man in ten
-<span class="pagenum" id="Page_192">[Pg 192]</span>
-minutes what is wrong with him does not cure him. The physician seeks
-to free the patient from the tormenting circles of habit and worry
-in which he has been trapped. Often the diagnosis is short and the
-treatment is long; the reasons for the neurosis may soon be clear to
-the physician, but they may take months to become clear to the patient.</p>
-
-<p>Now let us consider the following kind of machine as an aid to the
-physician. We might call this kind of machine a <i>psychological
-trainer</i>, for in many ways it is like the training machines used in
-World War II for training a pilot to fly an airplane. The psychological
-trainer would have the following properties:</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. The machine is able to show sound
-movies—produce pictures and utter words.</p>
-
-<p class="neg-indent">2. It is able to put before the patient:
-situations, problems, questions, experiences, etc.</p>
-
-<p class="neg-indent">3. It is able to take in responses from the
-patient.</p>
-
-<p class="neg-indent">4. It is able to receive a program of
-instructions from the physician.</p>
-
-<p class="neg-indent">5. Depending on the responses of the patient and
-on the program from the physician, the training machine can select more
-material to put before the patient.</p>
-
-<p class="neg-indent">6. The training machine produces a record of what
-it presented and of how the patient responded, so that the physician
-and the patient can study the record later.</p>
-</div>
-
-<p>What sort of films would the machine hold? The machine could be loaded
-with a number of films which would help in the particular type of
-neurosis from which the patient was suffering.</p>
-
-<p>What sort of responses could the patient make? The patient might have
-buttons in front of him which he could press to indicate such answers
-as:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdl">Yes</td>
-      <td class="tdl_ws1">I don’t know</td>
-      <td class="tdl_ws1">Repeat</td>
-   </tr><tr>
-      <td class="tdl">No</td>
-      <td class="tdl_ws1">It depends</td>
-      <td class="tdl_ws1">Go ahead</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Also, the patient might hold a device—like a lie
-detector, perhaps—which would report his state of tenseness, etc., and
-so report what he really felt.</p>
-
-<p>Where would the machine’s questions come from? From one or more
-physicians very clever in the treatment of mental illness.
-<span class="pagenum" id="Page_193">[Pg 193]</span></p>
-
-<p>Suppose that the patient is inconsistent in his answers? The machine,
-discovering the inconsistencies, could return to the subject and ask
-related questions in a different way. As soon as several questions
-related to the same point are answered consistently, the machine could
-exclude groups of questions that no longer apply and could proceed to
-other questions that would still apply.</p>
-
-<p>Patients would vary in their ability to go as fast as the machine
-could. So from time to time the machine would ask questions to test
-the effect of what it had presented; and, depending on the answers,
-the machine would go faster or would bring in additional material to
-clarify some point.</p>
-
-<p>This machine might have a few advantages over ordinary treatment. For
-example, with the machine, treatment does not depend on the physician’s
-making the right answer in a split second, as it may in a personal
-interview. Also, the patient might be franker with the machine than
-with the physician, for it might be arranged that the patient could
-review his record, and then decide whether to confess it to his
-physician.</p>
-
-<p>Such a machine would enable physicians to treat many more patients
-than they now can. In fact, it is estimated that nearly 50 per cent of
-persons who consult physicians are suffering only from mental illness.
-Such a machine would therefore be a great help.</p>
-
-<h4>Problems of Business</h4>
-
-<p>Another large group of problems for which we can foresee the use of
-machines that think is found in business and economics.</p>
-
-<p>For example, consider production scheduling in a business or a factory.
-The machine takes in a description of each order received by the
-business and a description of its relative urgency. The machine knows
-(that is, has in its memory) how much of each kind of raw material is
-needed to fill the order and what equipment and manpower are needed
-to produce it. The machine makes a schedule showing what particular
-men and what particular equipment are to be set to work to produce the
-order. The machine turns out the best possible production schedule,
-showing who should do what when, so that all the orders will be filled
-<span class="pagenum" id="Page_194">[Pg 194]</span>
-in the best sequence. What is the “best” sequence? We can decide what
-we think is the best sequence, and we can set the machine for making
-that kind of selection, in the same way as we decide what is “warm” and
-set the thermostat to produce it!</p>
-
-<p>On a much larger scale, we can use mechanical brains to study economic
-relations in a society. Everything produced in a society is made by
-consuming some materials, labor, equipment, and skill. The output
-produced by one man or factory or industry becomes the input for
-other men, factories, industries. In this way all economic units are
-linked together by many different kinds and degrees of dependence. The
-situation is, of course, complicated: it changes as time goes on and
-as people want different things produced. Economists have already set
-up simple models of economic societies and have studied them. But with
-machines that think, it will be possible to set up and study far more
-complicated models—models that are very much like the society we live
-in. We can then answer questions of economics by calculation instead of
-by arguments and counting noses. We shall be able to solve definitely
-such problems as: “How will a rise in the price of steel affect the
-farming industry?” “How much money must be paid out as wages and salaries
-so that consumer purchasing power will buy back what industry produces?”</p>
-
-<h4>Machines and the Individual</h4>
-
-<p>What about the ordinary everyday effects of these machines upon you
-and me as an individual? We can see that the new machinery will apply
-on a small scale even to us. Small machines using a few electronic
-tubes—much like a radio set, for example—and containing spools of
-magnetic wire or magnetic tape will doubtless be available to us. We
-shall be able to use them to keep addresses and telephone numbers, to
-figure out the income tax we should pay, to help us keep accounts and
-make ends meet, to remember many things we need to know, and perhaps
-even to give us more information. For there are a great many things
-that all of us could do much better if we could only apply what the
-wisest of us knows.</p>
-
-<p><span class="pagenum" id="Page_195">[Pg 195]</span>
-We can even imagine what new machinery for handling information may
-some day become: a small pocket instrument that we carry around with
-us, talking to it whenever we need to, and either storing information
-in it or receiving information from it. Thus the brain with a motor
-will guide and advise the man just as the armor with a motor carries
-and protects him.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_196">[Pg 196]</span></p>
-<h2 class="nobreak" id="CHAPTER_12">Chapter 12<br />
-<span class="h_subtitle">SOCIAL CONTROL:<br />
-MACHINES THAT THINK<br />AND HOW SOCIETY MAY CONTROL THEM</span></h2>
-</div>
-
-<p>It is often easier for men to create a device than to guide it well
-afterwards: it is often easier for a scientist to study his science
-than to study the results for good or evil that his discoveries may
-lead to. But it is not right nor proper for a scientist, a man who is
-loyal to truth as an ideal, to have no regard for what his discoveries
-may lead to.</p>
-
-<p>This principle is now being widely recognized. Many scientists
-today—both as individuals and as groups, and especially the
-atomic scientists—are considering the results of their scientific
-discoveries; and they are sharing in the effort to render those results
-truly useful to humanity.</p>
-
-<p>It would be easy to leave out of this book any discussion of how
-machines that think may be controlled, any consideration of how they
-may be made truly useful to humanity. But that would be hardly right
-or proper. In concluding a book such as this one, that touches on many
-aspects of machines that think, we need to consider what can and should
-be done to make such machines of true benefit to all of humanity.</p>
-
-<p>So, we come to the most important of all our questions: What sort of
-control over machines that think do we need in human society?</p>
-
-<h3>MACHINE THAT BOTH THINKS AND ACTS</h3>
-
-<p>From a narrow point of view, a machine that only thinks produces only
-<span class="pagenum" id="Page_197">[Pg 197]</span>
-information. It takes in information in one state, and it puts out
-information in another state. From this viewpoint, information
-in itself is harmless; it is just an arrangement of marks; and accordingly,
-a machine that thinks is harmless, and no control is necessary.</p>
-
-<p>Although it is true that the information produced only becomes good or
-evil after other machinery or human beings act on the information, in
-reality a machine with the power to produce information is constructed
-only for the reason of its use. We want to know what such machines can
-tell us only because we can then proceed to act much more efficiently
-than before. For example, a guided missile needs a mechanical brain
-only because then it can reach its target. In all cases mechanical
-brains are inseparable from their uses.</p>
-
-<p>For the purposes of this chapter, the narrow view will be rejected
-because it dodges the issue. We shall be much concerned with the
-combination of a machine that thinks with another machine that acts;
-and we shall often call this combination the <i>robot machine</i>.</p>
-
-<h3>READING THIS CHAPTER</h3>
-
-<p>Now, before launching further into the discussion, we need to say
-that the conclusions suggested in this chapter are not final. Even
-if they are expressed a little positively in places, they are
-nevertheless subject to change as more information is discovered and
-as the appraisal of information changes with time. Also, almost any
-conclusions about social control—including, certainly, the conclusions
-in this chapter—are subject to controversy. But controversy is good:
-it leads to thought. The more minds that go to work on solving the
-problem of social control over robot machines and other products of
-the new technology—which is rushing upon us from the discoveries of
-the scientists—the better off we all will be. If, while stimulating
-disagreement, the ideas expressed in this chapter should succeed in
-stimulating thought and deliberation, the purpose of this chapter will
-be well fulfilled.</p>
-
-<p>Up to this point in this book, the emphasis has been on possibilities
-of benefits to humanity that may arise from machines that think. In
-this chapter, devoted as it is to the subject of control, the emphasis
-<span class="pagenum" id="Page_198">[Pg 198]</span>
-is on possibilities for harm. Both possibilities are valid, and the
-happening of either depends upon the actions of men. In much the same
-way, atomic energy is a great possibility for benefit and for harm. It
-is the nature of control to put a fence around danger; and so it is
-natural in this chapter that the weight of attention should shift to
-the dangerous aspects of machines that think.</p>
-
-<p>Perhaps a reader may feel that a chapter of this kind is rather out of
-place in a book, such as this one, that seeks to be scientific. If so,
-he is reminded that, in accordance with the general suggestions for
-reading this book stated in the preface, he should omit this chapter.</p>
-
-<h3>FRANKENSTEIN</h3>
-
-<p>Perhaps the first study of the consequences of a machine that thinks
-is a prophetic novel called <i>Frankenstein</i>, written more than a
-hundred years ago, in 1818. The author, then only 21 years old, was
-Mary W. Godwin, who became the wife of the poet Percy Bysshe Shelley.</p>
-
-<p>According to the story, a young Swiss, an ardent student of physiology
-and chemistry, Victor Frankenstein, finds the secret of life. He makes
-an extremely ugly, clever, and powerful monster, with human desires.
-Frankenstein promptly flees from his laboratory and handiwork. The
-monster, after seeking under great hardships for a year or two to earn
-fair treatment among men, finds himself continually attacked and harmed
-on account of his ugliness, and he becomes embittered. He begins to
-search for his creator for either revenge or a bargain. When they meet:</p>
-
-<div class="blockquot">
-<p>“I expected this reception,” said the daemon.</p>
-
-<p>“All men hate the wretched; how then must I be hated
-who am miserable beyond all living things! Yet you my
-creator detest and spurn me, thy creature, to whom thou
-art bound by ties only dissoluble by the annihilation
-of one of us. You purpose to kill me. How dare you
-sport thus with life? Do your duty towards me, and I
-will do mine towards you and the rest of mankind. If
-you will comply with my conditions, I will leave them
-and you at peace; but if you refuse, I will glut the
-maw of death, until it be satiated with the blood of
-your remaining friends.”</p>
-</div>
-
-<p class="no-indent">Frankenstein starts to comply with the main
-condition, which is to make <span class="pagenum" id="Page_199">[Pg
-199]</span> a mate for the monster; but Frankenstein cannot bring
-himself to do it. So the monster causes the death one after another of
-all Frankenstein’s family and closest friends; and the tale finally
-ends with the death of Frankenstein and the disappearance of the
-monster.</p>
-
-<p>As the dictionary says about Frankenstein, “The name has become a
-synonym for one destroyed by his own works.”</p>
-
-<h3>ROSSUM’S UNIVERSAL ROBOTS</h3>
-
-<p>Perhaps the next study of the consequences of a machine that thinks is
-a remarkable play called <i>R.U.R.</i> (for Rossum’s Universal Robots),
-first produced in Prague in 1921. Karel Čapek, the Czech dramatist who
-wrote it, was then only 31. The word “robot” comes from the Czech word
-“robota,” meaning compulsory service.</p>
-
-<p>According to the play, Rossum the elder, a scientist, discovered a
-“method of organizing living matter” that was “more simple, flexible,
-and rapid” than the method used by nature. Rossum the younger, an
-engineer, founded a factory for the mass production of artificial
-workmen, robots. They had the form of human beings, intelligence,
-memory, and strength; but they were without feelings.</p>
-
-<p>In the first act, the factory under Harry Domin, General Manager, is
-busy supplying robots to purchasers all over the world—for work, for
-fighting, for any purpose at all, to anyone who could pay for them.
-Domin declares:</p>
-
-<div class="blockquot">
-<p class="no-indent">“... in ten years, Rossum’s Universal Robots will
-produce so much corn, so much cloth, so much everything that things
-will be practically without price. There will be no poverty. All work
-will be done by living machines. Everybody will be free from worry and
-liberated from the degradation of labor. Everybody will live only to
-perfect himself.... It’s bound to happen.”</p>
-</div>
-
-<p>In the second act, ten years later, it turns out that Domin and the
-others in charge of the factory have been making some robots with
-additional human characteristics, such as the capacity to feel pain.
-The newer types of robots, however, have united all the robots against
-man, for the robots declare that they are “more highly developed than
-man, stronger, and more intelligent, and man is their parasite.”
-<span class="pagenum" id="Page_200">[Pg 200]</span></p>
-
-<p>In the last act, the robots conquer and slay all men except one—an
-architect, Alquist, who in the epilogue provides a final quirk to the
-plot.</p>
-
-<h3>FACT AND FANCY</h3>
-
-<p>Now what is fact and what is fancy in these two warnings given to us a
-hundred years apart?</p>
-
-<p>Of course, it is very doubtful that a Frankenstein monster or a Rossum
-robot will soon be constructed with nerves, flesh, and blood like an
-animal body. But we know that many types of robot machines can even
-now be constructed out of hardware—wheels, motors, wires, electronic
-tubes, etc. They can handle many kinds of information and are able to
-perform many kinds of actions, and they are stronger and swifter than man.</p>
-
-<p>Of course, it is doubtful that the robot machines, by themselves and
-of their own “free will,” will be dangerous to human beings. But as
-soon as antisocial human beings have access to the controls over robot
-machines, the danger to society becomes great. We want to escape that danger.</p>
-
-<h4>Escape from Danger</h4>
-
-<p>A natural longing of many of us is to escape to an earlier, simpler
-life on this earth. Victor Frankenstein longed to undo the past. He said:</p>
-
-<p class="blockquot">“Learn from me, if not by my precepts, at least
-by my example, how dangerous is the acquirement of knowledge, and how
-much happier that man is who believes his native town to be the world,
-than he who aspires to become greater than his nature will allow.”</p>
-
-<p>Any sort of return to the past is, of course, impossible. It is
-doubtful that men could, even if they wanted to, stop the great flood
-of technical knowledge that science is now producing. We all must
-now face the fact that the kind of world we used to live in, even so
-recently as 1939, is gone. There now exist weapons and machines so
-powerful and dangerous in the wrong hands that in a day or two most of
-the people of the earth could be put to death. Giant brains are closely
-related to at least two of these weapons: scientists have already used
-mechanical brains for solving problems about atomic explosives and
-<span class="pagenum" id="Page_201">[Pg 201]</span>
-guided missiles. In addition, thinking mechanisms designed for the
-automatic control of gunfire were an important part of the winning of
-World War II. They will be a still more important part of the fighting
-of any future war.</p>
-
-<p>Nor can we escape to another part of the earth which the new weapons
-will not reach. At 300 miles an hour, any spot on earth can be reached
-from any other in less than 48 hours. A modern plane exceeds this
-speed; a rocket or guided missile doubles or trebles it.</p>
-
-<p>Nor can we trust that some kind of good luck will pull us through and
-help men to escape the consequences of what men do. Both Frankenstein
-and Domin reaped in full the consequences of what they did. The history
-of life on this earth that is recorded in the rocks is full of evidence
-of races of living things that have populated the earth for a time
-and then become extinct, such as the dinosaurs. In that long history,
-rarely does a race survive. In our own day, insects and fungi rather
-than men have shown fitness to survive and spread over the earth:
-witness the blight that destroyed the chestnut trees of North America,
-in spite of the best efforts of scientists to stop it.</p>
-
-<p>There seems to be no kind of escape possible. It is necessary to
-grapple with the problem: How can we be safe against the threat of
-physical harm from robot machines?</p>
-
-<h3>UNEMPLOYMENT</h3>
-
-<p>The other chief threat from robot machines is against our economic
-life. Harry Domin, in <i>R.U.R.</i>, you remember, prophesied: “All
-work will be done by living machines.” As an example, in the magazine
-<i>Modern Industry</i> for Feb. 15, 1947, appeared a picture of a
-machine for selling books, and under the picture were the words:</p>
-
-<p class="blockquot"><i>Another new product in robot
-salesmen</i>—Latest in the parade of mechanical vending machines is
-this book salesman.... It is designed for use in hospitals, rail
-terminals, and stores. It offers 15 different titles, selected
-manually, and obtained by dropping quarter in slot. Cabinet stores 96
-books.</p>
-
-<p class="no-indent">Can you feel the breath of the robot salesman,
-workman, engineer,—&mdash;, on the back of your neck?
-<span class="pagenum" id="Page_202">[Pg 202]</span></p>
-
-<p>At the moment when we combine automatic producing machinery and
-automatic controlling machinery, we get a vast saving in labor and
-a great increase in technological unemployment. In extreme cases,
-perhaps, the effect of robot machines will be the disappearance of men
-from a factory. Such a factory will be like a modern power plant that
-turns a waterfall into electricity: once the machinery is installed,
-only one watchman is ordinarily needed. But, in most cases, this will
-be the effect: in a great number of factories, mines, farms, etc., the
-labor force needed will be cut by a great proportion. The effect is not
-different in quality, because the new development is robot machinery;
-but the amount of technological unemployment coming from robot machines
-is likely to be considerably greater than previously.</p>
-
-<p>The robot machine raises the two questions that hang like swords over
-a great many of us these days. The first one is for any employee: What
-shall I do when a robot machine renders worthless all the skill I have
-spent years in developing? The second question is for any businessman:
-How shall I sell what I make if half the people to whom I sell lose
-their jobs to robot machines?</p>
-
-<h3>SOCIAL CONTROL<br />AND ITS TWO SIDES</h3>
-
-<p>The two chief harmful effects upon humanity which are to be expected
-from robot machines are physical danger and unemployment. These are
-serious risks, and some degree of social control is needed to guard
-against them.</p>
-
-<p>There will also be very great advantages from robot machines. The
-monster in <i>Frankenstein</i> is right when he says, “Do your duty
-towards me, and I will do mine towards you and the rest of mankind.”
-And Harry Domin in <i>R.U.R.</i> is right as to possibility when he
-says, “There will be no poverty.... Everybody will be free from worry.”
-Social control must also be concerned with how the advantages from
-robot machines are to be shared.</p>
-
-<p>The problem of social control over men and their devices has always had
-two sides. The first side deals with what we might plan for control
-if men were reasonable and tolerant. This part of the problem seems
-<span class="pagenum" id="Page_203">[Pg 203]</span>
-relatively easy. The other side deals with what we must ordinarily
-arrange, since most men are often unreasonable and prejudiced and, as a
-result, often act in antisocial ways. This part of the problem is hard.
-Let us begin with the easier side first.</p>
-
-<h3>TYPES OF CONTROL—<br />IF MEN WERE REASONABLE</h3>
-
-<p>In seeking to fulfill wants and achieve safety, men have used hundreds
-of types of control. The main types are usually called political and
-economic systems, but there are always great quantities of exceptions.
-The more mature and freer the society, the greater the variety of types
-of control that can be found in it.</p>
-
-<p>Probably the most widely used type of control in this country is
-private and public control working together, as private ownership
-and public regulation—for example, railroads, banks, airlines, life
-insurance companies, telephone systems, and many others. It would be
-reasonable to expect private ownership and public regulation of a
-great many classes of robot machines, to the end that they would never
-threaten the safety of people.</p>
-
-<p>Another common type of control is public ownership and operation;
-examples are toll bridges, airports, city transit systems, and
-water-supply systems. Atomic energy was so clearly fraught with
-serious implications that in 1946 the Congress of the United States
-placed it entirely under public control expressed as the Atomic
-Energy Commission. There is a class of robot machinery which has
-already reached the stage of acute public concern: guided missiles and
-automatic fire-control. It would be reasonable that in this country
-all activity in this subdivision should be under close control by the
-Department of Defense.</p>
-
-<p>In the international arena, again, the problem becomes soluble if
-we assume men to be reasonable. An international agency, such as an
-organ of the United Nations, would take over inspection and control of
-robot machine activities closely affecting the public safety anywhere
-in the world. Particularly, this agency would concern itself with
-guided missiles, robot pilots for planes, automatic gunfire control,
-etc. Much manufacturing skill is needed to make such products as
-these: the factories where they could be manufactured would thereby be
-<span class="pagenum" id="Page_204">[Pg 204]</span>
-determined. Also, a giant brain is a useful device for solving
-scientific problems about weapons of mass destruction. So the agency
-would need to inspect the problems being solved on such machines. This
-agency would be responsible to a legislature or an executive body
-representing all the people in the world—if men were reasonable.</p>
-
-<p>In regard to the effects of robot machines on unemployment, again,
-if men were reasonable, the problem would be soluble. The problem is
-equivalent to the problem of abundance: how should men distribute the
-advantages of a vast increase in production among all the members of
-society in a fair and sensible way? A vast increase in production is
-not so impossible as it may seem. For example, in 1939, with 45 million
-employed, the United States index of industrial production was at 109,
-and, in 1943, with 52½ million employed, the index of production
-was at 239.</p>
-
-<p>If men were reasonable, the net profits from robot machinery would
-be divided among (1) those who had most to do with devising the new
-machinery, and (2) all of society. A rule would be adopted (probably
-it could be less complicated than some existing tax rules) which would
-take into account various factors such as rewards to the inventors,
-incentives to continue inventing, adequate assistance to those made
-unemployed by the robot machines, reduction of prices to benefit
-consumers, and contributions to basic and applied scientific research.</p>
-
-<p>In fact, under the assumption “if men were reasonable,” it would hardly
-be necessary to devote a chapter to the problem of social control over
-robot machines!</p>
-
-<h3>OBSTACLES</h3>
-
-<p>The discussion above of how robot machines could be controlled
-supposing that men were reasonable, seems, of course, to be glaringly
-impractical. Men are not reasonable on most occasions most of the time.
-If we stopped at this point, again we would be dodging the issue. What
-are the obstacles to reasonable control?</p>
-
-<p>There are, it seems, two big obstacles and one smaller one to
-reasonable types of social control over robot machines. The smaller one
-<span class="pagenum" id="Page_205">[Pg 205]</span>
-is ignorance, and the two big obstacles are prejudice and a narrow
-point of view.</p>
-
-<h4>Ignorance</h4>
-
-<p>By ignorance we mean lack of knowledge and information. Now mechanical
-brains are a new and intricate subject. A great many people will,
-through no fault of their own, naturally remain uninformed about
-mechanical brains and robot machines for a long time. However, there is
-a widespread thirst for knowledge these days: witness in magazines, for
-example, the growth of the article and the decline of the essay. There
-is also a fairly steady surge of knowledge from the austere scientific
-fountain of new technology. We can thus see both a demand and a supply
-for information in such fields as mechanical brains and robot machines.
-We can expect, therefore, a fairly steady decline in ignorance.</p>
-
-<h4>Prejudice</h4>
-
-<p>Prejudice is a much more serious obstacle to reasonable control over
-robot machines. It will be worth our while to examine it at length.</p>
-
-<p>Prejudice is frequent in human affairs. For example, in some countries,
-but not in all, there is conflict among men, based on their religious
-differences. Again, in other countries, but not in all, there is
-wide discrimination among men, based on the color of their skin.
-Over the whole world today, there is a sharp lack of understanding
-between conservatives, grading over to reactionaries, on the one
-hand, and liberals, grading over to radicals, on the other hand. All
-these differences are based on men’s attitudes, on strongly held
-sets of beliefs. These attitudes are not affected by “information”;
-the “information” is not believed. The attitudes are not subject to
-“judgment”; they come “before judgment”: they are prejudices. Even
-in the midst of all the science of today, prejudice is widespread.
-In Germany, from 1933 to 1939, we saw one of the most scientific of
-countries become one of the most prejudiced.</p>
-
-<p>Prejudice is often difficult to detect. We find it hard to recognize
-even in ourselves. For a prejudice always seems, to the person who has
-<span class="pagenum" id="Page_206">[Pg 206]</span>
-it, the most natural attitude in the world. As we listen to other
-people, we are often uncertain how to separate information, guesses,
-humor, prejudice, etc. Circumstances compel us to accept provisionally
-quantities of statements just on other people’s say-so. A good test
-of a statement for prejudice, however, is to compare it with the
-scientific view.</p>
-
-<p>Prejudice is most dangerous for society. Its more extreme
-manifestations are aggressive war, intolerance (especially of strange
-people and customs), violence, race hatred, etc. In the consuming
-hatred that a prejudiced man has towards the object of his prejudice,
-he is likely to destroy himself and destroy many more people besides.
-In former days, the handy weapon was a sword or a pistol; not too much
-damage could be done when one man ran amuck. But nowadays a single use
-of a single weapon has slain 70,000 people (the atom bomb dropped at
-Hiroshima), and so a great many people live anxious and afraid.</p>
-
-<p>What is prejudice? How does it arise? How can it be cured, and thus
-removed from obstructing reasonable control over robot machines and the
-rest of today’s amazing scientific developments?</p>
-
-<p>Prejudice is a disease of men’s minds. It is infectious. The cause and
-development of the disease are about as follows: Deprive someone of
-something he deeply needs, such as affection, food, or opportunity.
-In this way hurt him, make him resentful, hostile; but prevent him
-from expressing his resentments in a reasonable way, giving him
-instead false outlets, such as other people to hurt, myths to believe,
-hostile behavior patterns to imitate. He will then break out with
-prejudices as if they were measles. The process of curing the disease
-of prejudice is about as follows: Make friends with the patient; win
-his trust. Encourage him to pour out his half-forgotten hates. Help him
-to talk them over freely, by means of questions but not criticisms,
-until finally the patient achieves insight, sees through his former
-prejudices, and drops them.</p>
-
-<p>In these days prejudice is a cardinal problem of society. It is
-perhaps conservative to say that a chief present requirement for the
-survival of human society—with the atom bomb, bacterial warfare,
-guided missiles, etc., near at hand—is cure of prejudice and its
-consequences, irrational and unrestrained hate.
-<span class="pagenum" id="Page_207">[Pg 207]</span></p>
-
-<h4>Narrow Point of View</h4>
-
-<p>A narrow point of view regarding what is desirable or good is the third
-obstacle to rational control over robot machines. What do we mean by
-this?</p>
-
-<p>Our point of view as a two-year-old is based on pure self-interest.
-If we see a toy, we grab it. There is no prejudice about this; it is
-entirely natural—for two-year-olds. As we grow older, our point of
-view concerning what is good or desirable rapidly broadens: we think
-of others and their advantage besides our own. For example, we may
-become interested in a conservation program to conserve birds, or soil,
-or forests, and our point of view expands, embraces these objectives,
-which become part of our personality and loyalties.</p>
-
-<p>Unfortunately, it seems to be true that the expanding point of view,
-the expanding loyalties, of most people as they grow up are arrested
-somewhere along the line of: self, family, neighborhood, community,
-section of country, nation. An honorable exception is the scientists’
-old and fine tradition of world-wide unity and loyalty in the search
-for objective truth.</p>
-
-<p>Now the problem of rational control over robot machines and other
-parts of the new technology is no respecter of national boundaries. To
-be solved it requires a world-wide point of view, a loyalty to human
-society and its best interests, a social point of view.</p>
-
-<p>Almost all that you and I have and do and think is the result of a long
-history of human society on this earth. All men on the earth today are
-descendants of other men who lived 1000, 2000, 3000 ... years ago,
-whether they were Romans or Chinese or Babylonians or Mayas or members
-of any other race. To ride in a subway or an airplane, to talk on the
-telephone, to speak a language, to calculate, to survive smallpox or
-the black death, etc.—all these privileges are our inheritance from
-countless thousands of other human beings, of many countries, and
-nearly all of whom are now dead. During our lives we pass on to our own
-children an inheritance in which our own contribution is remarkably
-small. Since each person is the child of two others, the number of our
-forefathers is huge, and we are all undoubtedly blood cousins. Because
-<span class="pagenum" id="Page_208">[Pg 208]</span>
-of this relationship, and because we owe to the rest of society
-nearly all that we are, we have a social responsibility—we need to
-hold a social point of view. Each of us needs to accept and welcome
-a world-wide social responsibility, as a member of human society, as
-a beneficiary and trustee of our human inheritance. Otherwise we are
-drones, part of the hive without earning our keep. The social point of
-view is equitable, it is inspiring, and it is probably required now in
-order for human beings to survive. We need to let go of a narrow point
-of view.</p>
-
-<h3>CONCLUSION</h3>
-
-<p>We have now outlined the problem of social control over robot machines,
-supposing that human beings were reasonable. We have also discussed the
-practical obstacles that obstruct reasonable control.</p>
-
-<p>It is not easy to think of any yet organized group of people anywhere
-that would have both the strength and the vision needed to solve this
-problem through its own efforts. For example, a part of the United
-Nations might have some of the vision needed, but it does not have the
-power. Consequently, it is necessary and desirable for individuals
-and groups everywhere to take upon themselves an added load of social
-responsibility—just as they tend to do in time of war. People often
-“want to do their share.” Through encouragement and education, the
-basic attitude of a number of people can contain more of “This is our
-business; we have a responsibility for helping to solve this problem.”
-We also need public responsibility; we need a public body responsible
-for study, education, advice, and some measure of control. It might
-be something like an Atomic Energy Commission, Bacterial Defense
-Commission, Mental Health Commission, and Robot Machine Commission, all
-rolled into one.</p>
-
-<p>When, at last, there is an effective guarantee of the two elements
-physical safety and adequate employment, then at last we shall all
-be free from the threat of the robot machine. We can then welcome
-the robot machine as our deliverer from the long hard chores of many
-centuries.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_209">[Pg 209]</span></p>
-<h2 class="nobreak" id="SUPPL_1">Supplement 1<br />
-<span class="h_subtitle">WORDS AND IDEAS</span></h2>
-</div>
-
-<p>The purpose of this book is to explain machines that think, without
-using technical words any more than necessary. This supplement is a
-digression. Its purposes are to consider how to explain in this way and
-to discuss the attempt made in this book to achieve simple explanation.</p>
-
-<h3>WORDS AS INSTRUMENTS<br /> FOR EXPLAINING</h3>
-
-<p>Words are the chief instruments we use for explaining. Of course, many
-other devices—pictures, numbers, charts, models, etc.—are also used;
-but words are the prime tools. We do most of our explaining with them.</p>
-
-<p>Words, however, are not very good instruments. Like a stone
-arrow-head, a word is a clumsy weapon. In the first place, words
-mean different things on different occasions. The word “line,” for
-example, has more than fifty meanings listed in a big dictionary. How
-do we handle the puzzle of many meanings? As we grow older we gather
-experience and we develop a truly marvelous capacity to listen to a
-sentence and then fit the words together into a pattern that makes
-sense. Sometimes we notice the time lag while our brain hunts for the
-meaning of a word we have heard but not grasped. Then suddenly we guess
-the needed meaning, whereupon we grasp the meaning of the sentence as
-a whole in much the same way as the parts of a puzzle click into place
-when solved.</p>
-
-<p>Another trouble with words is that often there is no good way to tell
-someone what a word means. Of course, if the word denotes a physical
-object, we can show several examples of the object and utter the word
-each time. In fact, several good illustrations of a word denoting a
-physical thing often tell most of its meaning. But the rest of its
-meaning we often do not learn for years, if ever. For instance, two
-people would more likely disagree than agree about what should be
-<span class="pagenum" id="Page_210">[Pg 210]</span>
-called a “rock” and what should be called a “stone,” if we showed them
-two dozen examples.</p>
-
-<p>In the case of words not denoting physical objects, like “and,” “heat,”
-“responsibility,” we are worse off. We cannot show something and say,
-“That is a ···.” The usual dictionary is of some help, but it has a
-tendency to tell us what some word <i>A</i> means by using another
-word <i>B</i>, and when we look up the other word <i>B</i> we find the
-word <i>A</i> given as its meaning. Mainly, however, to determine the
-meanings of words, we gather experience: we soak up words in our brains
-and slowly establish their meanings. We seem to use an unconscious
-reasoning process: we notice how words are used together in patterns,
-and we conclude what they must mean. Clearly, then, words being clumsy
-instruments, the more experience we have had with a word, the more
-likely we are to be able to use it, work with it, and understand it.
-Therefore explanation should be based chiefly on words with which we
-have had the most experience. What words are these? They will be the
-well-known words. A great many of them will be short.</p>
-
-<h3>SET OF WORDS FOR EXPLAINING</h3>
-
-<p>Now what is the set of all the words needed to explain simply a
-technical subject like machines that think? For we shall need more
-words than just the well-known and short ones. This question doubtless
-has many answers; but the answer used in this book was based on the
-following reasoning. In a book devoted to explanation, there will be
-a group of words (1) that are supposed to be known already or to be
-learned while reading, and (2) that are used as building blocks in
-later explanation and definitions. Suppose that we call these words the
-<i>words for explaining.</i> There are at least three groups of such
-words:</p>
-
-<div class="blockquot">
-<p class="neg-indent"><i>Group 1.</i> Words not specially defined that
-are so familiar that every reader will know all of them; for example,
-“is,” “much,” “tell.”</p>
-
-<p class="neg-indent"><i>Group 2.</i> Words not specially defined that
-are familiar, but perhaps some reader may not know some of them; for
-example, “alternative,” “continuous,” “indicator.”</p>
-
-<p class="neg-indent"><i>Group 3.</i> Words that are not familiar,
-that many readers are not expected to know, and that are specially
-defined and explained in the body of the book; for example, “abacus,”
-“trajectory,” “torque.”</p>
-</div>
-
-<p>In writing this book, it was not hard to keep track of the words in the
-third group. These words are now listed in the index, together with the
-<span class="pagenum" id="Page_211">[Pg 211]</span>
-page where they are defined or explained. (The index, of course,
-also lists phrases that are specially defined.)</p>
-
-<p>But what division should be made between the other two groups?
-A practical, easy, and conservative way to separate most words between
-the first and second groups seemed to be on the basis of number of
-syllables. All words of one syllable—if not specially defined—were put
-in Group 1. Also, if a word became two syllables only because of the
-addition of one of the endings “-es,” “-ed,” “-ing,” it was kept in
-Group 1, for these endings probably do not make a word any harder to
-understand. In addition, there were put into Group 1:</p>
-
-<ul class="index no-wrap">
-<li class="isub2">1. Numbers; for example, “186,000”; “<big>³/₁₀</big>”.</li>
-<li class="isub2">2. Places: “Philadelphia”; “Massachusetts”.</li>
-<li class="isub2">3. Nations, organizations, people, etc.: “Swedish”; “Bell”.</li>
-<li class="isub2">4. Years and dates: “February”; “1946”.</li>
-<li class="isub2">5. Names of current books or articles and their authors.</li>
-</ul>
-
-<p class="no-indent">Of course, not all these words would be familiar
-to every reader (for example, “Maya”), but in the way they occur, they
-are usually not puzzling, for we can tell from the context just about
-what they must mean.</p>
-
-<p>All remaining words for explaining—chiefly, words of two or more
-syllables and not specially defined—were put in Group 2 and were
-listed during the writing of this book. Many Group 2 words, of course,
-would be entirely familiar to every reader; but the list had several
-virtues. No hard words would suddenly be sprung like a trap. The
-same word would be used for the same idea. Every word of two or more
-syllables was continually checked: is it needed? can it be replaced by
-a shorter word? It is perhaps remarkable that there were fewer than
-1800 different words allowed to stay in this list. This fact should be
-a comfort to a reader, as it was to the author.</p>
-
-<p>Now there are more words in this book than <i>words for explaining</i>.
-So we shall do well to recognize:</p>
-
-<div class="blockquot">
-<p class="neg-indent"><i>Group 4.</i> Words that do not need to be known or
-learned and that are not used in later explanation and definitions.</p>
-</div>
-
-<p class="no-indent">These words occur in the book in such a way that
-understanding them, though helpful, is not essential. One subdivision
-of Group 4 are names that appear just once in the book, as a kind of
-side remark, for example, “a chemical, called <i>acetylcholine</i>.”
-Such a name will also appear in the index, but it is not a <i>word for
-explaining</i>. Another subdivision of Group 4 are words occurring only
-in quotations. For example, in the quotation from <i>Frankenstein</i>
-<span class="pagenum" id="Page_212">[Pg 212]</span>
-on page 198, a dozen words appear that occur nowhere else in the book,
-including “daemon,” “dissoluble,” “maw,” “satiate.” Clearly we would
-destroy the entire flavor of the quotation if we changed any of these
-words in any way. But only the general drift of the quotation is needed
-for understanding the book, and so these words are Group 4 words.</p>
-
-<p>In this way the effort to achieve simple explanation in this book
-proceeded. But even supposing that we could reach the best set of words
-for explaining, there is more to be done. How do we go from simple
-explanation to understanding?</p>
-
-<h3>UNDERSTANDING IDEAS</h3>
-
-<p><i>Understanding</i> an idea is basically a standard process. First, we
-find the name of the idea, a word or phrase that identifies it. Then,
-we collect true statements about the idea. Finally, we practice using
-them. The more true statements we have gathered, and the more practice
-we have had in applying them, the more we understand the idea.</p>
-
-<p>For example, do you understand zero? Here are some true statements
-about zero.</p>
-
-<div class="blockquot">
-<p class="neg-indent">1. Zero is a number.</p>
-
-<p class="neg-indent">2. It is the number that counts none or
-nothing.</p>
-
-<p class="neg-indent">3. It is marked 0 in our usual numeral
-writing.</p>
-
-<p class="neg-indent">4. The ancient Romans, however, had no numeral
-for it. Apparently, they did not think of zero as a number.</p>
-
-<p class="neg-indent">5. 0 is what you get when you take away 17 from
-17, or when you subtract any number from itself.</p>
-
-<p class="neg-indent">6. If you add 0 to 23, you get 23; and if you add
-0 to any number, you get that number unchanged.</p>
-
-<p class="neg-indent">7. If you subtract 0 from 48, you get 48; and if
-you subtract 0 from any number, you get that number unchanged.</p>
-
-<p class="neg-indent">8. If you multiply 0 by 71, you get 0; and if you
-multiply together 0 and any number, you get 0.</p>
-
-<p class="neg-indent">9. Usually you are not allowed to divide by 0:
-that is against the rules of arithmetic.</p>
-
-<p class="neg-indent">10. But if you do, and if you divide 12 by 0, for
-example—and there are times when this is not wrong—the result is called
-<i>infinity</i> and is marked <big>∞</big>, a sign that is like an 8 on
-its side.</p>
-</div>
-
-<p class="no-indent">This is not all the story of zero; it is one of
-the most important of numbers. But, if you know these statements about
-zero, and have had some practice in applying them, you have a good
-<span class="pagenum" id="Page_213">[Pg 213]</span>
-<i>understanding</i> of zero. Incidentally, a mechanical brain knows all
-these statements about zero and a few more; they must be built into it.</p>
-
-<p>For us to understand any idea, then, we pursue three aims:</p>
-
-<ul class="index no-wrap">
-<li class="isub2">1. We find out what it is called.</li>
-<li class="isub2">2. We collect true statements about it.</li>
-<li class="isub2">3. We apply those statements—we use them in situations.</li>
-</ul>
-
-<p class="no-indent">We can do this about any idea. Therefore, we can
-understand any idea, and the degree of our understanding increases as
-the number of true statements mastered increases.</p>
-
-<p>Perhaps this seems to be a rash claim. Of course, it may take a good
-deal of time to collect true statements about many ideas. In fact, a
-scientist may spend thirty years of his life trying to find out from
-experiment the truth or falsehood of one statement, though, when he has
-succeeded, the fact can be swiftly told to others. Also, we all vary in
-the speed, perseverance, skill, etc., with which we can collect true
-statements and apply them. Besides, some of us have not been taught
-well and have little faith in our ability to carry out this process:
-this is the greatest obstacle of all. But, there is in reality no idea
-in the field of existing science and knowledge which you or I cannot
-understand. The road to understanding lies clear before us.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_214">[Pg 214]</span></p>
-<h2 class="nobreak" id="SUPPL_2">Supplement 2<br />
-<span class="h_subtitle">MATHEMATICS</span></h2>
-</div>
-
-<p>In the course of our discussion of machines that think, we have had to
-refer without much explanation to a number of mathematical ideas. The
-purpose of this supplement is to explain a few of these ideas a little
-more carefully than seemed easy to do in the text and, at the end of
-the supplement, to put down briefly some additional notes for reference.</p>
-
-<h3>DEVICES FOR MULTIPLICATION</h3>
-
-<p>Suppose that we have to multiply 372 by 465. With the ordinary school
-method, we write 465 under the 372 and proceed about as follows: 5
-times 2 is 10, put down the 0 and carry the 1; 5 times 7 is 35, 35 and
-1 is 36, put down the 6 and carry the 3; 5 times 3 is 15, 15 and 3 is
-18, put down the 8 and carry the 1; ... The method is based mainly on a
-well-learned subroutine of continually changing steps:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">1. Select a multiplicand digit.</li>
-<li class="isub2">2. Select a multiplier digit.</li>
-<li class="isub2">3. Refer to the multiplication table with these digits.</li>
-<li class="isub2">4. Obtain the value of their product, called a <i>partial product</i>.</li>
-<li class="isub2">5. Add the preceding carry.</li>
-<li class="isub2">6. Set down the right-hand digit.</li>
-<li class="isub2">7. Carry the left-hand digit.</li>
-</ul>
-
-<p class="no-indent">We can, however, simplify this subroutine for
-a machine by delaying the carrying. We collect in one place all the
-right-hand digits of partial products, collect in another place all the
-left-hand digits, and delay all addition until the end.</p>
-
-<p>For example, let us multiply 372 by 465 with this method:
-<span class="pagenum" id="Page_215">[Pg 215]</span></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdc">&nbsp;<span class="smcap">Right-Hand&nbsp;<br />Digits</span></th>
-      <th class="tdc">&nbsp;<span class="smcap">Left-Hand&nbsp;<br />Digits</span></th>
-      <th class="tdc"><span class="smcap">&nbsp;&nbsp;Usual Method<br />&nbsp;&nbsp;for Comparison</span></th>
-   </tr>
-  </thead>
-  <tbody><tr>
-      <td class="tdr_ws1">372</td>
-      <td class="tdr_ws1">372</td>
-      <td class="tdr">372</td>
-   </tr><tr>
-      <td class="tdr_ws1 u">× 465</td>
-      <td class="tdr_ws1 u">× 465</td>
-      <td class="tdr u">× 465</td>
-   </tr><tr>
-      <td class="tdr_ws1">550</td>
-      <td class="tdr_ws1">131</td>
-      <td class="tdr">1860</td>
-   </tr><tr>
-      <td class="tdr_ws1">822&#8199;</td>
-      <td class="tdr_ws1">141&#8199;</td>
-      <td class="tdr">2232&#8199;</td>
-   </tr><tr>
-      <td class="tdr_ws1 u">288&#8199;&#8199;</td>
-      <td class="tdr_ws1 u">120&#8199;&#8199;</td>
-      <td class="tdr u">1488&#8199;&#8199;</td>
-   </tr><tr>
-      <td class="tdr_ws1">37570</td>
-      <td class="tdr_ws1">13541</td>
-      <td class="tdr">172980</td>
-   </tr><tr>
-      <td class="tdc" colspan="3"><br /><b><span class="smcap">Final Addition</span></b></td>
-   </tr><tr>
-      <td class="tdc" colspan="3">37570</td>
-   </tr><tr>
-      <td class="tdc u" colspan="3">+ 13541&#8199;&#8199;&#8199;</td>
-   </tr><tr>
-      <td class="tdc" colspan="3">172980</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">37570 is called the <i>right-hand component</i>
-of the product. It is convenient to fill in with 0 the space at the
-end of 13541 and to call 135410 the <i>left-hand component</i> of the
-product.</p>
-
-<p>This process is called <i>multiplying by right- and left-hand
-components</i>. It has the great advantage that no carrying is
-necessary to complete any line of the original multiplications. Some
-computing machines use this process. Built into the hardware of the
-machine is a multiplication table up to 9 × 9. The machine, therefore,
-can find automatically the right-hand digit and the left-hand digit of
-any partial product. In a computing machine that uses this process,
-all the left-hand digits are automatically added in one register, and
-all the right-hand digits are added in another register. The only
-carrying that is needed is the carrying as the right-hand digits are
-accumulated and as the left-hand digits are accumulated. At the end of
-the multiplication, one of the registers is automatically added into
-the other, giving the product.</p>
-
-<p>Another device used in computing machines for multiplying is to change
-the multiplier into a set of digits 0 to 5 that are either positive or
-negative. For example, suppose that we want to multiply 897 by 182. We
-note that 182 equals 200 minus 20 plus 2, and so we can write it as</p>
-
-<ul class="index fontsize_120">
-<li class="isub2">2<span class="over">2</span>2.</li>
-</ul>
-
-<p>The minus over the 2 marks it as a <i>negative digit</i> 2. Then to
-multiply we have:</p>
-
-<ul class="index fontsize_110">
-<li class="isub3">897</li>
-<li class="isub3">2<span class="over">2</span>2</li>
-<li class="isub2 over">&#8199;1794</li>
-<li class="isub1">&#8199;-1794</li>
-<li class="isub1">&#8199;1794</li>
-<li class="isub1 over">&#8199;163254</li>
-</ul>
-
-<p class="no-indent">The middle 1794 is subtracted. This process is
-usually called <i>short-cut multiplication</i>. Everybody discovers
-this trick when he decides that multiplying by 99 is too much work,
-that it is easier to multiply by 100 and subtract once.
-<span class="pagenum" id="Page_216">[Pg 216]</span></p>
-
-<h3>BINARY OR TWO NUMBERS</h3>
-
-<p>We are well accustomed to decimal notation in which we use 10 decimal
-digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and write them in combinations to
-designate decimal numbers. In <i>binary notation</i> we use two binary
-digits 0, 1 and write them in combinations to designate <i>binary
-numbers</i>. For example, the first 17 numbers, from 0 to 16 in the
-decimal notation, correspond with the following numbers in binary notation:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Decimal</span>&nbsp;&nbsp;</th>
-      <th class="tdc">&nbsp;<span class="smcap">Binary</span>&nbsp;</th>
-      <th class="tdc">&nbsp;<span class="smcap">Decimal</span>&nbsp;</th>
-      <th class="tdc">&nbsp;&nbsp;<span class="smcap">Binary</span></th>
-   </tr>
-  </thead>
-  <tbody><tr>
-      <td class="tdc">0</td>
-      <td class="tdr_ws1">0</td>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">1</td>
-      <td class="tdr_ws1">1</td>
-      <td class="tdc">&#8199;9</td>
-      <td class="tdc">1001</td>
-   </tr><tr>
-      <td class="tdc">2</td>
-      <td class="tdr_ws1">10</td>
-      <td class="tdc">10</td>
-      <td class="tdc">1010</td>
-   </tr><tr>
-      <td class="tdc">3</td>
-      <td class="tdr_ws1">11</td>
-      <td class="tdc">11</td>
-      <td class="tdc">1011</td>
-   </tr><tr>
-      <td class="tdc">4</td>
-      <td class="tdr_ws1">100</td>
-      <td class="tdc">12</td>
-      <td class="tdc">1100</td>
-   </tr><tr>
-      <td class="tdc">5</td>
-      <td class="tdr_ws1">101</td>
-      <td class="tdc">13</td>
-      <td class="tdc">1101</td>
-   </tr><tr>
-      <td class="tdc">6</td>
-      <td class="tdr_ws1">110</td>
-      <td class="tdc">14</td>
-      <td class="tdc">1110</td>
-   </tr><tr>
-      <td class="tdc">7</td>
-      <td class="tdr_ws1">111</td>
-      <td class="tdc">15</td>
-      <td class="tdc">1111</td>
-   </tr><tr>
-      <td class="tdc">8</td>
-      <td class="tdr_ws1">1000</td>
-      <td class="tdc">16</td>
-      <td class="tdc">10000&#8199;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">In decimal notation, 101 means one times a
-hundred, no tens, and one. In binary notation, 101 means one times
-four, no twos, and one. The successive digits in a decimal number
-from right to left count 1, 10, 100, 1000, 10000, ...—successive
-<i>powers</i> of 10 (for this term, see the end of this supplement).
-The successive digits in a binary number from right to left count 1, 2,
-4, 8, 16, ...—powers of 2.</p>
-
-<p>The decimal notation is convenient when equipment for computing
-has ten positions, like the fingers of a man, or the positions of
-a counter wheel. The binary notation is convenient when equipment
-for computing has just two positions, like “yes” or “no,” or current
-flowing or no current flowing.</p>
-
-<p>Addition, subtraction, multiplication, and division can all be carried
-out unusually simply in binary notation. The addition table is simple
-and consists only of four entries.</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="4" summary=" " cellpadding="4" >
-  <tbody><tr>
-      <td class="tdc">&nbsp;+&nbsp;</td>
-      <td class="tdc bb">0</td>
-      <td class="tdc bb">&#8199;1</td>
-   </tr><tr>
-      <td class="tdc br">0</td>
-      <td class="tdc">0</td>
-      <td class="tdc">&#8199;1</td>
-   </tr><tr>
-      <td class="tdc br">1</td>
-      <td class="tdc">1</td>
-      <td class="tdc">10</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">The multiplication table is also simple and
-contains only four entries.
-<span class="pagenum" id="Page_217">[Pg 217]</span></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="4" summary=" " cellpadding="4" >
-  <tbody><tr>
-      <td class="tdc">&nbsp;×&nbsp;</td>
-      <td class="tdc bb">0</td>
-      <td class="tdc bb">1</td>
-   </tr><tr>
-      <td class="tdc br">0</td>
-      <td class="tdc">0</td>
-      <td class="tdc">0</td>
-   </tr><tr>
-      <td class="tdc br">1</td>
-      <td class="tdc">0</td>
-      <td class="tdc">1</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Suppose that we add in binary notation 101 and 1001:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Binary<br /> Addition</span></th>
-      <th class="tdc"><span class="ws2"><span class="smcap">Check</span></span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdr">101</td>
-      <td class="tdr">5</td>
-   </tr><tr>
-      <td class="tdr u">+ 1001</td>
-      <td class="tdr u">&nbsp;9</td>
-   </tr><tr>
-      <td class="tdr">1110</td>
-      <td class="tdr">14</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">We proceed: 1 and 1 is 10; write down 0 and carry
-1; 0 and 0 is 0, and 1 to carry is 1; and 1 and 0 is 1; and then we
-just copy the last 1. To check this we can convert to decimal and see
-that 101 is 5, 1001 is 9, and 1110 is 14, and we can verify that 5 and
-9 is 14.</p>
-
-<p>One of the easiest ways to subtract in binary notation is to add a
-<i>ones complement</i> (that is, the analogue of the nines complement)
-and use end-around-carry (for these two terms, see the end of this
-supplement). A ones complement can be written down at sight by just
-putting 1 for 0 and 0 for 1. For example, suppose that we subtract 101
-from 1110:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Direct<br />Subtraction</span></th>
-      <th class="tdc"><span class="ws2"><span class="smcap">Check</span></span></th>
-      <th class="tdc">&nbsp;&nbsp;<span class="smcap">Subtraction by<br />Adding Ones<br />Complement</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdr">1110</td>
-      <td class="tdr">14</td>
-      <td class="tdl_ws1">&nbsp;&#8199;&#8199;1110</td>
-   </tr><tr>
-      <td class="tdr u">- 101</td>
-      <td class="tdr u">-&nbsp;5</td>
-      <td class="tdl_ws1 u">&nbsp;+ 1010</td>
-   </tr><tr>
-      <td class="tdr">1001</td>
-      <td class="tdr">9</td>
-      <td class="tdl_ws1">(1)1000</td>
-   </tr><tr>
-      <td class="tdr" rowspan="3">&nbsp;</td>
-      <td class="tdr" rowspan="3">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;<big>↓</big></td>
-   </tr><tr>
-      <td class="tdl_ws1">&nbsp;<big>⎯→</big>&nbsp;1</td>
-   </tr><tr>
-      <td class="tdl_ws1 over">&#8199;&#8199;1001</td>
-   </tr>
- </tbody>
-</table>
-
-<p>Multiplication in the binary notation is simple. It amounts to (1)
-adding if the multiplier digit is 1 and not adding if the multiplier
-digit is 0, and (2) moving over or shifting. For example, let us
-multiply 111 by 101:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Binary<br />Multiplication</span></th>
-      <th class="tdc"><span class="ws2"><span class="smcap">Check</span></span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdr">111</td>
-      <td class="tdr">7</td>
-   </tr><tr>
-      <td class="tdr u">× 101</td>
-      <td class="tdr">&nbsp;× 5</td>
-   </tr><tr>
-      <td class="tdr">111</td>
-      <td class="tdr">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr">111&#8199;&#8199;</td>
-      <td class="tdr">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr over">100011</td>
-      <td class="tdr over">&nbsp;35</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent"><span class="pagenum" id="Page_218">[Pg 218]</span>
-The digit 1 in the 6th (or <i>n</i>th) <i>binary</i> place from the
-right in 100011 stands for 1 times 2 to the 5th (or <i>n</i>-1 th)
-power, 2 × 2 × 2 × 2 × 2 = 32. The result 100011 is translated into 32
-plus 2 plus 1, which equals 35 and verifies.</p>
-
-<p>Division in the binary notation is also simple. It amounts to (1)
-subtracting (yielding a quotient digit 1) or not subtracting (yielding
-a quotient digit 0), and (2) shifting. We never need to try multiples
-of the divisor to find the largest that can be subtracted yet leave a
-positive remainder. For example, let us divide 1010 (10 in decimal)
-into 10001110 (142 in decimal):</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub6">&#8199;1110 (14 in decimal)</li>
-<li class="isub4">————</li>
-<li class="isub2">1010)10001110</li>
-<li class="isub5 u">1010</li>
-<li class="isub5">&#8199;1111</li>
-<li class="isub5 u">&#8199;1010</li>
-<li class="isub6">1011</li>
-<li class="isub6 u">1010</li>
-<li class="isub7">10 (remainder, 2 in decimal)</li>
-</ul>
-
-<p>In decimal notation, digits to the right of the decimal point count
-powers of ⅒. In binary notation, digits to the right of the <i>binary
-point</i> count powers of <big>½: ½, ¼, ⅛, ¹/₁₆</big>.... For example, 0.1011
-equals <big>½ + ⅛ + ¹/₁₆, or ¹¹/₁₆</big>.</p>
-
-<p>If we were accustomed to using binary numbers, all our arithmetic
-would be very simple. Furthermore, binary numbers are in many ways
-much better for calculating machinery than any other numbers. The main
-problem is converting numbers from decimal notation to binary. One
-method depends on storing the powers of 2 in decimal notation. The rule
-is: subtract successively smaller powers of 2; start with the largest
-that can be subtracted, and count 1 for each power that goes and 0 for
-each power that does not. For example, 86 in decimal becomes 1010110 in
-binary:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <tbody><tr>
-      <td class="tdr">86</td>
-      <td class="tdl_ws1">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr u">64</td>
-      <td class="tdl_ws1">64 goes</td>
-      <td class="tdl_ws1">1</td>
-   </tr><tr>
-      <td class="tdr">22</td>
-      <td class="tdl_ws1">32 does not go</td>
-      <td class="tdl_ws1">0</td>
-   </tr><tr>
-      <td class="tdr u">16</td>
-      <td class="tdl_ws1">16 goes</td>
-      <td class="tdl_ws1">1</td>
-   </tr><tr>
-      <td class="tdr">6</td>
-      <td class="tdl_ws1">8 does not go</td>
-      <td class="tdl_ws1">0</td>
-   </tr><tr>
-      <td class="tdr u">&nbsp;4</td>
-      <td class="tdl_ws1">4 goes</td>
-      <td class="tdl_ws1">1</td>
-   </tr><tr>
-      <td class="tdr">2</td>
-      <td class="tdl_ws1">2 goes</td>
-      <td class="tdl_ws1">1</td>
-   </tr><tr>
-      <td class="tdr u">&nbsp;2</td>
-      <td class="tdl_ws1">1 does not go</td>
-      <td class="tdl_ws1">0</td>
-   </tr><tr>
-      <td class="tdr">0</td>
-      <td class="tdl_ws1">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent"><span class="pagenum" id="Page_219">[Pg 219]</span>
-It is a little troublesome to remember long series of 1’s and 0’s; in
-fact, to write any number in binary notation takes about 3⅓ times
-as much space as decimal notation. For this reason we can separate
-binary numbers into triples beginning at the right and label each
-triple as follows:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Triple</span>&nbsp;&nbsp;</th>
-      <th class="tdc">&nbsp;&nbsp;<span class="smcap">Label</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdc">000</td>
-      <td class="tdc">0</td>
-   </tr><tr>
-      <td class="tdc">001</td>
-      <td class="tdc">1</td>
-   </tr><tr>
-      <td class="tdc">010</td>
-      <td class="tdc">2</td>
-   </tr><tr>
-      <td class="tdc">011</td>
-      <td class="tdc">3</td>
-   </tr><tr>
-      <td class="tdc">100</td>
-      <td class="tdc">4</td>
-   </tr><tr>
-      <td class="tdc">101</td>
-      <td class="tdc">5</td>
-   </tr><tr>
-      <td class="tdc">110</td>
-      <td class="tdc">6</td>
-   </tr><tr>
-      <td class="tdc">111</td>
-      <td class="tdc">7</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">For example, 1010110 would become 1 010 110 or
-126. This notation is often called <i>octal notation</i>, because it is
-notation in the scale of eight.</p>
-
-<h3>BIQUINARY OR <i>TWO-FIVE</i> NUMBERS</h3>
-
-<p>Another kind of notation for numbers is <i>biquinary notation</i>, so
-called because it uses both 2’s and 5’s. Essentially this notation is
-very like Roman numerals, ancient style. By ancient style we mean, for
-example, VIIII instead of IX. In the following table we show the first
-two dozen numbers in decimal, biquinary, and ancient Roman notation:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">Decimal</span></th>
-      <th class="tdc">&nbsp;&nbsp;<span class="smcap">Biquinary</span>&nbsp;&nbsp;</th>
-      <th class="tdc"><span class="smcap">Roman</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdc">&#8199;0</td>
-      <td class="tdc">&#8199;&#8199;0</td>
-      <td class="tdl_ws1">&nbsp;</td>
-   </tr><tr>
-      <td class="tdc">&#8199;1</td>
-      <td class="tdc">&#8199;&#8199;1</td>
-      <td class="tdl_ws1">I</td>
-   </tr><tr>
-      <td class="tdc">&#8199;2</td>
-      <td class="tdc">&#8199;&#8199;2</td>
-      <td class="tdl_ws1">II</td>
-   </tr><tr>
-      <td class="tdc">&#8199;3</td>
-      <td class="tdc">&#8199;&#8199;3</td>
-      <td class="tdl_ws1">III</td>
-   </tr><tr>
-      <td class="tdc">&#8199;4</td>
-      <td class="tdc">&#8199;&#8199;4</td>
-      <td class="tdl_ws1">IIII</td>
-   </tr><tr>
-      <td class="tdc">&#8199;5</td>
-      <td class="tdc">&#8199;10</td>
-      <td class="tdl_ws1">V</td>
-   </tr><tr>
-      <td class="tdc">&#8199;6</td>
-      <td class="tdc">&#8199;11</td>
-      <td class="tdl_ws1">VI</td>
-   </tr><tr>
-      <td class="tdc">&#8199;7</td>
-      <td class="tdc">&#8199;12</td>
-      <td class="tdl_ws1">VII</td>
-   </tr><tr>
-      <td class="tdc">&#8199;8</td>
-      <td class="tdc">&#8199;13</td>
-      <td class="tdl_ws1">VIII</td>
-   </tr><tr>
-      <td class="tdc">&#8199;9</td>
-      <td class="tdc">&#8199;14</td>
-      <td class="tdl_ws1">VIIII</td>
-   </tr><tr>
-      <td class="tdc">10</td>
-      <td class="tdc">100</td>
-      <td class="tdl_ws1">X</td>
-   </tr><tr>
-      <td class="tdc">11</td>
-      <td class="tdc">101</td>
-      <td class="tdl_ws1">XI</td>
-   </tr><tr>
-      <td class="tdc">12</td>
-      <td class="tdc">102</td>
-      <td class="tdl_ws1">XII</td>
-   </tr><tr>
-      <td class="tdc">13</td>
-      <td class="tdc">103</td>
-      <td class="tdl_ws1">XIII</td>
-   </tr><tr>
-      <td class="tdc">14</td>
-      <td class="tdc">104</td>
-      <td class="tdl_ws1">XIIII</td>
-   </tr><tr>
-      <td class="tdc">15</td>
-      <td class="tdc">110</td>
-      <td class="tdl_ws1">XV</td>
-   </tr><tr>
-      <td class="tdc">16</td>
-      <td class="tdc">111</td>
-      <td class="tdl_ws1">XVI</td>
-   </tr><tr>
-      <td class="tdc">17</td>
-      <td class="tdc">112</td>
-      <td class="tdl_ws1">XVII</td>
-   </tr><tr>
-      <td class="tdc">18</td>
-      <td class="tdc">113</td>
-      <td class="tdl_ws1">XVIII</td>
-   </tr><tr>
-      <td class="tdc">19</td>
-      <td class="tdc">114</td>
-      <td class="tdl_ws1">XVIIII</td>
-   </tr><tr>
-      <td class="tdc">20</td>
-      <td class="tdc">200</td>
-      <td class="tdl_ws1">XX</td>
-   </tr><tr>
-      <td class="tdc">21</td>
-      <td class="tdc">201</td>
-      <td class="tdl_ws1">XXI</td>
-   </tr><tr>
-      <td class="tdc">22</td>
-      <td class="tdc">202</td>
-      <td class="tdl_ws1">XXII</td>
-   </tr><tr>
-      <td class="tdc">23</td>
-      <td class="tdc">203</td>
-      <td class="tdl_ws1">XXIII</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">The biquinary columns alternate in going from 0 to
-4 and from 0 to 1. The digits from 0 to 4 are not changed. The digits
-from 5 to 9 are changed into 10 to 14. We see that the <i>biquinary
-digits</i> are 0 to 4 in odd columns and 0, 1 in even columns, counting
-from the right.</p>
-
-<p>This is the notation actually expressed by the <i>abacus</i>. The beads
-of the abacus show by their positions groups of 2 and 5 (<a href="#FIG_1-S">see Fig. 1</a>).
-<span class="pagenum" id="Page_220">[Pg 220]</span></p>
-
-<div class="figcenter">
-  <img id="FIG_1-S" src="images/i_220.jpg" alt="" width="600" height="460" />
-  <p class="f120 space-below2"><span class="smcap">Fig. 1.</span> Abacus and notations.</p>
-</div>
-
-<h3>SOME OPERATIONS OF ALGEBRA</h3>
-
-<p>One of the operations of algebra that is important for a mechanical
-brain is <i>approximation</i>, the problem of getting close to the
-right value of a number. Take, for example, finding <i>square root</i>
-(see the end of this supplement). The ordinary process taught in school
-is rather troublesome. We can set down another process, however, using
-a desk calculator to do division, which gives us square root with great speed.</p>
-
-<p>Suppose that we want to find the square root of a number <i>N</i>, and
-suppose that we have <i>x</i>₀ as a guessed square root correct to one
-figure. For example, <i>N</i> might be 67.2 and <i>x</i>₀ might be
-8, chosen because 8 × 8 is 64, and 9 × 9 is 81, and it seems as if 8
-should be near the square root of 67.2. Here is the process:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">1. Divide <i>x</i>₀ into <i>N</i>, and obtain <i>N</i> / <i>x</i>₀.</li>
-<li class="isub2">2. Multiply <i>x</i>₀ + <i>N</i> / <i>x</i>₀ by 0.5 and call the result <i>x</i>₁.</li>
-</ul>
-
-<p class="no-indent">Now repeat:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">1. Divide <i>x</i>₁ into <i>N</i> and obtain <i>N</i> / <i>x</i>₁.</li>
-<li class="isub2">2. Multiply <i>x</i>₁ + <i>N</i> / <i>x</i>₁ by 0.5 and call the result <i>x</i>₂.</li>
-</ul>
-
-<p class="no-indent">Every time this process is repeated, the new
-<i>x</i> comes a great deal closer to the correct square root. In fact
-it can be shown that, if <i>x</i>₀ is correct to one figure, then:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">&nbsp;Approximation&nbsp;</span></th>
-      <th class="tdc"><span class="smcap">&nbsp;Is Correct To&nbsp;<br />··· Figures</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdc"><i>x</i>₁</td>
-      <td class="tdc">&#8199;2</td>
-   </tr><tr>
-      <td class="tdc"><i>x</i>₂</td>
-      <td class="tdc">&#8199;4</td>
-   </tr><tr>
-      <td class="tdc"><i>x</i>₃</td>
-      <td class="tdc">&#8199;8</td>
-   </tr><tr>
-      <td class="tdc"><i>x</i>₄</td>
-      <td class="tdc">16</td>
-   </tr>
- </tbody>
-</table>
-
-<p>Let us see how this actually works out with 67.2 and a 10-column desk
-calculator.
-<span class="pagenum" id="Page_221">[Pg 221]</span></p>
-
-<div class="blockquot">
-<p class="neg-indent">Round 1: 8 divided into 67.2 gives 8.4. One half
-of 8 plus 8.4 is 8.2. This is <i>x</i>₁.</p>
-
-<p class="neg-indent">Round 2: 8.2 divided into 67.2 gives 8.195122.
-One half of 8.2 plus 8.195122 is 8.197561. This is <i>x</i>₂.</p>
-
-<p class="neg-indent">Round 3: 8.197561 divided into 67.2 gives
-8.197560225. One half of 8.197561 and 8.197560225 is 8.1975606125. This
-is <i>x</i>₃.</p>
-
-<p class="neg-indent">Checking <i>x</i>₃, we find that 8.1975606125
-divided into 67.2 gives 8.1975606126 approximately.</p>
-</div>
-
-<p class="no-indent">In this case, then, <i>x</i>₃ is correct to more
-than 10 figures. In other words, with a reasonable guess and two or
-three divisions we can obtain all the accuracy we can ordinarily use.
-This process is called <i>rapid approximation</i>, or <i>rapidly
-convergent approximation</i>, since it <i>converges</i> (points or
-comes together) very quickly to the number we are seeking.</p>
-
-<p>Another important operation of algebra is <i>interpolation</i>, the
-problem of putting values smoothly in between other values. For
-example, suppose that we have the table:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc">&nbsp;&nbsp;<i>x</i>&nbsp;&nbsp;</th>
-      <th class="tdc">&nbsp;&nbsp;<i>y</i>&nbsp;&nbsp;</th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdc">5</td>
-      <td class="tdc">26</td>
-   </tr><tr>
-      <td class="tdc">6</td>
-      <td class="tdc">37</td>
-   </tr><tr>
-      <td class="tdc">7</td>
-      <td class="tdc">50</td>
-   </tr><tr>
-      <td class="tdc">8</td>
-      <td class="tdc">65</td>
-   </tr><tr>
-      <td class="tdc">9</td>
-      <td class="tdc">82</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">Suppose that we want to find the value that
-<i>y</i> (or <i>yₓ</i>) ought to have when <i>x</i> has the value
-of 7.2. This is the problem of <i>interpolating y</i> so as to find
-<i>y</i> at the value of 7.2, <i>y</i>₇ˌ₂.</p>
-
-<p>One way of doing this is to discover the formula that expresses
-<i>y</i> and then to put <i>x</i> into that formula. This is not always
-easy. Another way is to take the difference between <i>y</i>₇ and
-<i>y</i>₈, 15, and share the difference appropriately over the distance
-7 to 7.2 and 7.2 to 8. We can, for example, take ²/₁₀ of 15 = 3, add
-that to <i>y</i>₇ = 50, and obtain an estimated <i>y</i>₇ˌ₂ = 53. This
-is called <i>linear interpolation</i>, since the difference 0.2 in
-the value of <i>x</i> is used only to the first power. It is a good
-practical way to carry out most interpolation quickly and approximately.</p>
-
-<p>Actually here <i>y</i> = <i>x</i>² + 1, and so the true value of
-<i>y</i>₇ˌ₂ is (7.2 × 7.2) + 1, or 52.84, which is rather close to
-53. Types of interpolation procedures more accurate than linear
-interpolation will come much nearer still to the true value.</p>
-
-<h3>ALGEBRA OF LOGIC</h3>
-
-<p>We turn now to the <i>algebra of logic</i>. The first half of <a href="#CHAPTER_9">Chapter 9</a>,
-“Reasoning” (through the section “Logical-Truth Calculation by
-<span class="pagenum" id="Page_222">[Pg 222]</span>
-Algebra”), introduces this subject. There the terms <i>truth
-values</i>, <i>truth tables</i>, <i>logical connectives</i>,
-and <i>algebra of logic</i> are explained. The part of <a href="#CHAPTER_3">Chapter 3</a>,
-“A Machine That Will Think,” that discusses the operations
-<i>greater-than</i> and <i>selection</i>, also explains some of the
-algebra of logic. It introduces, for example, the formula</p>
-
-<p class="f120"><i>p</i> = <i>T</i>(<i>a</i> &gt; <i>b</i>) = 1, 0</p>
-
-<p>This is a way of saying briefly that the truth value of the statement
-“<i>a</i> is greater than <i>b</i>” equals <i>p</i>; <i>p</i> is 1 if
-the statement is true and 0 if the statement is false. The truth value
-1 corresponds with “yes.” The truth value 0 corresponds with “no.”</p>
-
-<p>With mechanical brains we are especially interested in handling
-mathematics and logic without any sharp dividing line between them.
-For example, suppose that we have a register in which a ten-digit
-number like 1,765,438,890 may be stored. We should be able to use
-that register to store a number consisting of only 1’s and 0’s, like
-1,100,100,010. Such a number may designate the answers to 10 successive
-questions: yes, yes, no, no, yes, no, no, no, yes, no. Or it may
-tell 10 successive binary digits. The register then is three times
-as useful: it can store either decimal numbers or truth values or
-binary digits. We need, of course, a way to obtain from the register
-any desired digit. For this purpose we may have two instructions to
-the machine: (1) read the left-hand end digit; (2) shift the number
-around in a circle. The second instruction is the same as multiplying
-by 10 and then putting the left-most digit at the right-hand end.
-For example, suppose that we want the 3rd digit from the left in
-1,100,100,010. The result of the first circular shift is 1,001,000,101;
-the result of the second circular shift is 0,010,001,011; and reading
-the left-most digit gives 0. A process like this has been called
-<i>extraction</i> and is being built into the newest mechanical brains.</p>
-
-<p>Using truth values, we can put down very neatly some truths of ordinary
-algebra. For example:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">(the <i>absolute value</i> of <i>a</i>) =</li>
-<li class="isub5"><i>a</i> × (the truth of <i>a</i> greater than or equal to 0)</li>
-<li class="isub4">- <i>a</i> × (the truth of <i>a</i> less than 0)</li>
-</ul>
-
-<p class="f120">|<i>a</i>| = <i>a</i> · <i>T</i>(<i>a</i> ≥ 0) - <i>a</i> · <i>T</i>(<i>a</i> &lt; 0)</p>
-
-<p class="no-indent">For another example:</p>
-
-<ul class="index fontsize_110 no-wrap">
-<li class="isub2">Either <i>a</i> is greater than <i>b</i>,</li>
-<li class="isub4">or else <i>a</i> equals <i>b</i>,</li>
-<li class="isub4">or else <i>a</i> is less than <i>b</i></li>
-</ul>
-
-<p class="f120 space-below2"><i>T</i>(<i>a</i> &gt; <i>b</i>) + <i>T</i>(<i>a</i> =
-<i>b</i>) + <i>T</i>(<i>a</i> &lt; <i>b</i>) = 1</p>
-
-<p class="no-indent"><span class="pagenum" id="Page_223">[Pg 223]</span>
-Many common logical operations, like selecting and comparing, and
-the behavior of many simple mechanisms, like a light or a lock, can
-be expressed by truth values. <a href="#CHAPTER_4">Chapter 4</a>, on
-punch-card mechanisms, contains a number of examples.</p>
-
-<hr class="tb" />
-
-<h4>pronoun, variable</h4>
-
-<p>In ordinary language, a <i>pronoun</i>, like “he,” “she,” “it,” “the
-former,” “the latter,” is a word that usually stands for a noun
-previously referred to. A pronoun usually stands for the last preceding
-noun that the grammar allows. In mathematics, a <i>variable</i>, like
-“<i>a</i>,” “<i>b</i>,” “<i>x</i>,” “<i>m₁</i>,” “<i>m₂</i>” closely
-resembles a pronoun in ordinary language. A variable is a symbol that
-usually stands for a number previously referred to, and usually it
-stands for the same number throughout a particular discussion.</p>
-
-<h4>multiplicand, dividend, augend, etc.</h4>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc"><span class="smcap">In the<br />Equation</span></th>
-      <th class="tdc"><span class="smcap">The Name<br />of</span> <i>a</i> <span class="smcap">is:</span></th>
-      <th class="tdc"><span class="smcap">The Name<br />of</span> <i>b</i> <span class="smcap">is:</span></th>
-      <th class="tdc"><span class="smcap">The Name<br />of</span> <i>c</i> <span class="smcap">is:</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdl"><i>a</i> + <i>b</i> = <i>c</i></td>
-      <td class="tdl_ws1">augend</td>
-      <td class="tdl_ws1">addend</td>
-      <td class="tdl_ws1">sum</td>
-   </tr><tr>
-      <td class="tdl"><i>a</i> - <i>b</i> = <i>c</i></td>
-      <td class="tdl_ws1">minuend</td>
-      <td class="tdl_ws1">subtrahend</td>
-      <td class="tdl_ws1">remainder</td>
-   </tr><tr>
-      <td class="tdl"><i>a</i> × <i>b</i> = <i>c</i></td>
-      <td class="tdl_ws1">multiplicand</td>
-      <td class="tdl_ws1">multiplier</td>
-      <td class="tdl_ws1">product</td>
-   </tr><tr>
-      <td class="tdl"><i>a</i> ÷ <i>b</i> = <i>c</i></td>
-      <td class="tdl_ws1">dividend</td>
-      <td class="tdl_ws1">divisor</td>
-      <td class="tdl_ws1">quotient</td>
-   </tr>
- </tbody>
-</table>
-
-<p><i>Augend</i> and <i>addend</i> are names of registers in the Harvard
-Mark II calculator (<a href="#CHAPTER_10">see Chapter 10</a>).</p>
-
-<h4>subtraction by adding, nines complement</h4>
-
-<p>Two digits that add to 9 (0 and 9, 1 and 8, 2 and 7, 3 and 6, 4 and
-5) are called <i>nines complements</i> of each other. The <i>nines
-complement</i> of a number <i>a</i> is the number <i>b</i> in which
-each digit of <i>b</i> is the nines complement of the corresponding
-digit of <i>a</i>; for example, the nines complement of 173 is
-826. Ordinary subtraction is the same as addition as of the nines
-complement, with a simple correction; for example, 562 less 173 (equal
-to 389) is the same as 562 plus 826 (equal to 1388) less 1000 plus 1.</p>
-
-<h4>end-around-carry</h4>
-
-<p>The correction “less 1000 plus 1” of the foregoing example may be
-thought of as carrying the 1 (in the result 1388) around from the
-left-hand end to the right-hand end, where it is there added. So the 1
-is called <i>end-around-carry</i>.
-<span class="pagenum" id="Page_224">[Pg 224]</span></p>
-
-<h4>tens complement</h4>
-
-<p>Two digits that add to 10 are called <i>tens complements</i> of each
-other. The <i>tens complement</i> of a number <i>a</i>, however, is
-equal to the nines complement of the number plus 1. For example, the
-tens complement of 173 is 827. When subtracting by adding a tens
-complement, the left-most digit 1 in the result is dropped. For
-example, 562 less 173 (equal to 389) is the same as 562 plus 827 (equal
-to 1389) less 1000.</p>
-
-<h4>power, square, cube, reciprocal, etc.</h4>
-
-<p>A <i>power</i> of any number <i>a</i> is <i>a</i> multiplied by itself
-some number of times. <i>a</i> × <i>a</i> × <i>a</i> ... × <i>a</i>
-where <i>a</i> appears <i>b</i> times is written <i>a</i>ᵇ and is read
-<i>a</i> to the <i>b</i>th power. <i>a</i>², a to the 2nd power, is
-<i>a</i> × <i>a</i> and is called <i>a squared</i> or the <i>square</i>
-of <i>a</i>. <i>a</i>³, <i>a</i> to the 3rd power, <i>a</i> × <i>a</i>
-× <i>a</i>, is called <i>a cubed</i>, or the <i>cube</i> of <i>a</i>.
-<i>a</i>⁰, <i>a</i> to the zero power, is equal to 1 for every
-<i>a</i>. <i>a</i>¹, <i>a</i> to the power 1, is <i>a</i> itself. The
-first power is often called <i>linear</i>. <i>a</i> to some negative
-power is the same as 1 divided by that power; that is, <i>a</i>⁻ᵇ =
-1/<i>a</i>ᵇ. <i>a</i>⁻¹, <i>a</i> to the power minus 1, is 1/<i>a</i>,
-and is called the <i>reciprocal</i> of <i>a</i>. <i>a</i>¹ᐟ², <i>a</i>
-to the one-half power, is a number <i>c</i> such that <i>c</i> ×
-<i>c</i> = <i>a</i>, and is called the <i>square root</i> of <i>a</i>
-and often denoted by √<i>a</i>.</p>
-
-<h4>table, tabular value, argument, etc.</h4>
-
-<p>An example of a <i>table</i> is:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="4" summary=" " cellpadding="4" >
-  <tbody><tr>
-      <td class="tdc">&nbsp;</td>
-      <td class="tdc bb">0.025</td>
-      <td class="tdc bb">0.03</td>
-   </tr><tr>
-      <td class="tdc br">1</td>
-      <td class="tdc">1.02500</td>
-      <td class="tdc">1.03000</td>
-   </tr><tr>
-      <td class="tdc br">2</td>
-      <td class="tdc">1.05063</td>
-      <td class="tdc">1.06090</td>
-   </tr><tr>
-      <td class="tdc br">3</td>
-      <td class="tdc">1.07689</td>
-      <td class="tdc">1.09273</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">The numbers in the body of the table, called
-<i>tabular values</i>, depend on or are determined by the numbers along
-the edge of the table, called <i>arguments</i>. In this example, if 1,
-2, 3 are choices of a number <i>n</i>, and if 0.025, 0.03 are choices
-of a number <i>i</i>, then each tabular value <i>y</i> is equal to 1
-plus <i>i</i> raised to the <i>n</i>th power. <i>n</i> and <i>i</i>
-are also called <i>independent variables</i>, and <i>y</i> is called
-the <i>dependent variable</i>. The table expresses a <i>function</i>
-or <i>formula</i> or <i>rule</i>. The rule could be stated as: add
-<i>i</i> to 1; raise the result to the <i>n</i>th power.</p>
-
-<h4>constant</h4>
-
-<p>A number is said to be a <i>constant</i> if it has the same value under
-all conditions. For example, in the formula:</p>
-
-<p class="f120">(area of a circle) = π × (radius)²,<br />
-π is a constant, equal to 3.14159 ...,</p>
-
-<p class="no-indent"> applying equally well to all circles.
-<span class="pagenum" id="Page_225">[Pg 225]</span></p>
-
-<h4>infinity</h4>
-
-<p>Mathematics recognizes several kinds of infinity. One of them occurs
-when numbers become very large. For example, the quotient of 12 divided
-by a number <i>x</i>, as <i>x</i> becomes closer and closer to 0,
-becomes indefinitely large, and the limit is called <i>infinity</i> and
-is denoted <span class="fontsize_150">∞</span>.</p>
-
-<h4>equation, simultaneous, linear</h4>
-
-<p>An example of two linear simultaneous <i>equations</i> is:</p>
-
-<p class="f120">7<i>x</i> + 8<i>t</i> = 22</p>
-
-<p class="f120">3<i>x</i> + 5<i>t</i> = 11</p>
-
-<p class="no-indent"><i>x</i> and <i>t</i> are called
-<i>unknowns</i>—that is, unknown variables—because the objective of
-solving the equations is to find them. These equations are called
-<i>simultaneous</i> because they are to be solved together, at the
-same time, for values of <i>x</i> and <i>t</i> which will fit in
-both equations. The equations are called <i>linear</i> because the
-only powers of the unknowns that appear are the first power. Values
-that solve equations are said to <i>satisfy</i> them. It is easy to
-solve these two equations and find that <i>x</i> = 2 and <i>t</i>
-= 1 is their solution. But it is a long process to solve 10 linear
-simultaneous equations in 10 unknowns, and it is almost impossible
-(without using a mechanical brain) to solve 100 linear simultaneous
-equations in 100 unknowns.</p>
-
-<h4>derivative, integral,<br />differential equation, etc.</h4>
-
-<p>See the sections in <a href="#CHAPTER_5">Chapter 5</a> entitled “Differential
-Equations,” “Physical Problems,” and “Solving Physical Problems.” There these
-ideas and, to some extent, also the following ideas were explained:
-formula, equation, function, differential function, instantaneous rate
-of change, interval, inverse, integrating. See also a textbook on
-calculus. If <i>y</i> is a function of <i>x</i>, then a mathematical
-symbol for the derivative of <i>y</i> with respect to <i>x</i> is
-<i>Dₓ y</i>, and a symbol for the integral of <i>y</i> with respect to
-<i>x</i>, is ∫<i>y dx</i>. An integral with given initial conditions
-(<a href="#Page_83">see p. 83</a>) is a <i>definite integral</i>.</p>
-
-<h4>exponential</h4>
-
-<p>A famous mathematical function is the <i>exponential</i>. It equals
-the constant <i>e</i> raised to the <i>x</i> power, <i>eˣ</i>, where
-<i>e</i> equals 2.71828.... The exponential lies between the powers of
-2 and the powers of 3. It can be computed from:</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdr" rowspan="2"><i>eˣ</i> = 1 +&nbsp;</td>
-      <td class="tdc"><i>x</i>²</td>
-      <td class="tdr" rowspan="2">&nbsp;+&nbsp;</td>
-      <td class="tdc"><i>x</i>³</td>
-      <td class="tdr" rowspan="2">&nbsp;+&nbsp;. . .</td>
-   </tr><tr>
-      <td class="tdc bt">1 · 2</td>
-      <td class="tdc bt">1 · 2 · 3</td>
-   </tr>
- </tbody>
-</table>
-
-<p><span class="pagenum" id="Page_226">[Pg 226]</span>
-It is a solution of the differential equation <big><i>Dₓy</i> = <i>y</i></big>.
-See also a textbook on calculus. The <i>exponential to the base 10</i>
-is <big>10ˣ</big>.</p>
-
-<h4>logarithm</h4>
-
-<p>Another important mathematical function is the <i>logarithm</i>. It is
-written <big>log <i>x</i></big> or <big>logₑ <i>x</i></big> and can be
-computed from the two equations:</p>
-
-<p class="f120">log <i>uv</i> = log <i>u</i> + log <i>v</i></p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdr" rowspan="2">log(1 + <i>x</i>) = <i>x</i> -&nbsp;</td>
-      <td class="tdc"><i>x</i>²</td>
-      <td class="tdr" rowspan="2">&nbsp;+&nbsp;</td>
-      <td class="tdc"><i>x</i>³</td>
-      <td class="tdr" rowspan="2">&nbsp;-&nbsp;. . .&emsp;<i>x</i>² &lt; 1</td>
-   </tr><tr>
-      <td class="tdc bt">&nbsp;&nbsp;2&nbsp;&nbsp;</td>
-      <td class="tdc bt">&nbsp;&nbsp;3&nbsp;&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">It is a solution of the differential equation
-<big><i>Dₓy</i> = 1/<i>y</i></big>. If <i>y</i> is the logarithm of <i>x</i>,
-then <i>x</i> is the <i>antilogarithm</i> of <i>y</i>. The <i>logarithm to
-the base 10</i> of <i>x</i>, log₁₀ <i>x</i>, equals the <i>logarithm to
-the base e</i> of <i>x</i>, logₑ <i>x</i>, divided by logₑ 10. See also
-textbooks on algebra and calculus.</p>
-
-<h4>sine, cosine, tangent, antitangent</h4>
-
-<p>These also are important mathematical functions. The <i>sine</i>
-and <i>cosine</i> are solutions of the differential equation
-<big><i>Dₓ</i>(<i>Dₓy</i>) =-<i>y</i></big> and are written as sin <i>x</i>
-and cos <i>x</i>. They can be computed from</p>
-
-<table class="fontsize_120 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdr" rowspan="2">sin <i>x</i> = <i>x</i> -&nbsp;</td>
-      <td class="tdc"><i>x</i>³</td>
-      <td class="tdr" rowspan="2">&nbsp;+&nbsp;</td>
-      <td class="tdc"><i>x</i>⁵</td>
-      <td class="tdr" rowspan="2">&nbsp;-&nbsp;. . .</td>
-   </tr><tr>
-      <td class="tdc bt">1 · 2· 3</td>
-      <td class="tdc bt">1 · 2 · 3· 4· 5</td>
-   </tr><tr>
-      <td class="tdc" colspan="5">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr" rowspan="2">cos <i>x</i> = 1 -&nbsp;</td>
-      <td class="tdc"><i>x</i>²</td>
-      <td class="tdr" rowspan="2">&nbsp;+&nbsp;</td>
-      <td class="tdc"><i>x</i>₄</td>
-      <td class="tdr" rowspan="2">&nbsp;-&nbsp;. . .</td>
-   </tr><tr>
-      <td class="tdc bt">1 · 2</td>
-      <td class="tdc bt">1 · 2 · 3· 4</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="no-indent">The <i>tangent</i> of <i>x</i> is simply sine of
-<i>x</i> divided by cosine of <i>x</i>. If <i>y</i> is the tangent of
-<i>x</i>, then <i>x</i> is the <i>antitangent</i> of <i>y</i>. See also
-references on trigonometry and on calculus. <i>Trigonometric</i> tables
-include sine, cosine, tangent, and related functions.</p>
-
-<h4>Bessel functions</h4>
-
-<p>These are mathematical functions that were named after Friedrich W.
-Bessel, a Prussian astronomer who lived from 1784 to 1846. Bessel
-functions are found as some of the solutions of the differential
-equation</p>
-
-<p class="f120 no-wrap"><i>x</i>² <i>Dₓ</i>(<i>Dₓy</i>) + x <i>Dₓy</i> + (<i>x</i>² - <i>n</i>²)<i>y</i> = O</p>
-
-<p class="no-indent">This equation arises in a number of physical
-problems in the fields of electricity, sound, heat flow, air flow, etc.
-<span class="pagenum" id="Page_227">[Pg 227]</span></p>
-
-<h4>matrix</h4>
-
-<p>A <i>matrix</i> is a table (or <i>array</i>) of numbers in rows and
-columns, for which addition, multiplication, etc., with similar tables
-is specially defined. For example, the matrix</p>
-
-<table class="fontsize_150 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdr_ws1 bl">&nbsp;1</td>
-      <td class="tdl_ws1 br">2&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr_ws1 bl">&nbsp;</td>
-      <td class="tdl_ws1 br">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr_ws1 bl">&nbsp;3</td>
-      <td class="tdl_ws1 br">4&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="f120">plus the matrix</p>
-
-<table class="fontsize_150 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdr_ws1 bl">&nbsp;5</td>
-      <td class="tdl_ws1 br">&#8199;20&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr_ws1 bl">&nbsp;</td>
-      <td class="tdl_ws1 br">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr_ws1 bl">&nbsp;60</td>
-      <td class="tdl_ws1 br">100&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="f120">equals the matrix</p>
-
-<table class="fontsize_150 no-wrap" border="0" cellspacing="0" summary=" " cellpadding="0" >
-  <tbody><tr>
-      <td class="tdr_ws1 bl">&nbsp;6</td>
-      <td class="tdl_ws1 br">&#8199;22&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr_ws1 bl">&nbsp;</td>
-      <td class="tdl_ws1 br">&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr><tr>
-      <td class="tdr_ws1 bl">&nbsp;63</td>
-      <td class="tdl_ws1 br">104&nbsp;</td>
-      <td class="tdc">&nbsp;</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="f120">(Can you guess the rule defining addition?)</p>
-
-<p class="no-indent">Calculations using matrices are useful in physics, engineering,
-psychology, statistics, etc. To add a <i>square matrix</i> of 100 terms
-in an array of 10 columns and 10 rows to another such matrix, 100
-ordinary additions of numbers are needed. To multiply one such matrix
-by another, 1000 ordinary multiplications and 900 ordinary additions
-are needed. See references on matrix algebra and matrix calculus.</p>
-
-<h4>differences, smoothness, checking</h4>
-
-<p>On <a href="#Page_221">p. 221</a>, a sequence of values of <i>y</i>
-is shown: 26, 37, 50, 65, 82. Suppose, however, the second value of
-<i>y</i> was reported as 47 instead of 37. Then the <i>differences</i>
-of <i>y</i> as we pass down the sequence would not be 11, 13, 15, 17
-(which is certainly regular or <i>smooth</i>) but 21, 3, 15, 17 (which
-is certainly not smooth). The second set of differences would strongly
-suggest a mistake in the reporting of <i>y</i>. The <i>smoothness</i>
-of differences is often a useful check on a sequence of reported
-values.</p> <hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_228">[Pg 228]</span></p>
-<h2 class="nobreak" id="SUPPL_3">Supplement 3<br />
-<span class="h_subtitle">REFERENCES</span></h2>
-</div>
-
-<p>A book like the present one can cover only a part of the subject of
-machines that think. To obtain more information about these machines
-and other topics to which they are related there are many references
-that may be consulted. There are still few books directly on the
-subject of machines that think, but there are many articles and papers,
-most of them rather specialized.</p>
-
-<p>The purpose of this supplement is to give a number of these references
-and to provide a brief, general introduction to some of them. The
-references are subdivided into groups, each dealing with a branch of
-the subject. The references in each group are in alphabetical order
-by name of author (with “anonymous” last), and under each author they
-are in chronological order by publication date. Some publications,
-especially a forum or symposium, are listed more than once, according
-as the topic discussed falls in different groups. In this supplement,
-the sign three dots ( ...) next to the page numbers for an article
-indicates that the article is continued on later, nonconsecutive pages.</p>
-
-<p>It seemed undesirable to try to make the group of references dealing
-with a subject absolutely complete, so long as enough were given to
-provide a good introduction to the subject. It proved impractical
-to try to make the citation of every single reference technically
-complete, so long as enough citation was given so that the reference
-could certainly be found. Furthermore, in a list of more than 250
-references, errors are almost certain to occur. If any reader should
-send me additions or corrections, I shall be more than grateful.
-<span class="pagenum" id="Page_229">[Pg 229]</span></p>
-
-<h3>THE HUMAN BRAIN</h3>
-
-<p>No one yet knows specifically how particular ideas are thought about
-in the human brain. The references listed in this section, however,
-contain some information about such topics as:</p>
-
-<div class="blockquot">
-<p class="neg-indent">The structural differences, development, and
-evolution of the brains of animals, apes, primitive man, and modern
-man.</p>
-
-<p class="neg-indent">The effect on the brain of blood composition,
-body temperature, supply of oxygen, and other biochemical factors.</p>
-
-<p class="neg-indent">The structure and physiology of the brain, the
-nervous system, and nerve impulses.</p>
-
-<p class="neg-indent">The theory of learning, intelligence, and
-memory.</p>
-</div>
-<hr class="tb" />
-
-<div class="blockquot2">
-<p class="neg-indent"><span class="smcap">Barcroft, Joseph</span>,
-<i>The Brain and Its Environment</i>, New Haven: Yale University
-Press, 1948, 117 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Beach, Frank A.</span>,
-Payday for Primates, <i>Natural History</i>, vol. 56, no. 10, Dec.
-1947, pp. 448-451.</p>
-
-<p class="neg-indent"><span class="smcap">Beach, Frank A.</span>, Can
-Animals Reason? <i>Natural History</i>, vol. 57, no. 3, Mar. 1948, pp.
-112-116 ...</p>
-
-<p class="neg-indent"><span class="smcap">Berry, R. J. A.</span>,
-<i>Brain and Mind, or the Nervous System of Man</i>, New York:
-The Macmillan Co., 1928, 608 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Boring, Edwin G.</span>, <i>A
-History of Experimental Psychology</i>, New York: Century Co.,
-1929, 699 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Franz, Shepherd I.</span>,
-<i>The Evolution of an Idea; How the Brain Works</i>, Los Angeles:
-University of California, 1929, 35 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Herrick, C. Judson</span>,
-<i>The Thinking Machine</i>, Chicago: University of Chicago
-Press, 1929, 374 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Herrick, C. Judson</span>,
-<i>Brains of Rats and Men</i>, Chicago: University of Chicago
-Press, 1930, 382 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Lashley, Karl S.</span>,
-<i>Brain Mechanisms and Intelligence</i>, Chicago: University of
-Chicago Press, 1929, 186 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Pieron, Henri</span>,
-<i>Thought and the Brain</i>, London: Kegan, Paul, Trench, Trübner
-&amp; Co., 1927, 262 pp. Also New York: Harcourt, Brace &amp; Co.</p>
-
-<p class="neg-indent"><span class="smcap">Schrödinger, Erwin</span>,
-<i>What is Life?</i>, New York: The Macmillan Co., 1945, 90 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Sherrington, Charles
-S.</span>, <i>The Brain and Its Mechanism</i>, Cambridge,
-England: The University Press, 1933, 35 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Tilney, Frederick</span>,
-<i>The Brain from Ape to Man</i>, New York: P. B. Hoeber, Inc.,
-1928, 2 vol., 1075 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Wiener, Norbert</span>,
-<i>Cybernetics, or Control and Communication in the Animal and
-the Machine</i>, New York: John Wiley &amp; Sons, 1948, 194 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Ten Billion
-Relays, <i>Time</i>, Feb. 14, 1949, p. 67.</p>
-</div>
-
-<hr class="chap" />
-<p><span class="pagenum" id="Page_230">[Pg 230]</span></p>
-<h3>MATHEMATICAL BIOPHYSICS</h3>
-
-<p class="blockquot">There has recently been another approach to the
-problem: How does a brain think? A group of men, many of them in and
-near Chicago, have been saying: “We know the properties of nerves,
-nerve impulses, and simple nerve networks. We know the activity of
-the brain. What mathematical model of nerve networks is necessary
-to account for the activity of the brain?” These men have used
-mathematics, statistics, and mathematical logic in the effort to
-attack this problem, and they support a <i>Bulletin of Mathematical
-Biophysics</i>.</p>
-
-<hr class="tb" />
-
-<div class="blockquot2">
-<p class="neg-indent"><span class="smcap">Householder, Alston
-S.</span>, A Neural Mechanism for Discrimination, <i>Psychometrika</i>,
-vol. 4, no. 1, Dec. 1939, pp. 45-58.</p>
-
-<p class="neg-indent"><span class="smcap">Householder, Alston
-S.</span>, and Herbert D. Landahl, <i>Mathematical Biophysics of the
-Central Nervous System</i>, Bloomington, Ind.: Principia Press, 1945.</p>
-
-<p class="neg-indent"><span class="smcap">Landahl, Herbert D.</span>,
-Contributions to the Mathematical Biophysics of the Central Nervous
-System, <i>Bulletin of Mathematical Biophysics</i>, vol. 1, no. 2,
-June 1939, pp. 95-118.</p>
-
-<p class="neg-indent"><span class="smcap">Landahl, Herbert
-D.</span>, <span class="smcap">Warren S. McCulloch</span>, and
-<span class="smcap">Walter Pitts</span>, A Statistical Consequence of
-the Logical Calculus of Nervous Nets, <i>Bulletin of Mathematical
-Biophysics</i>, vol. 5, no. 4, Dec. 1943, pp. 135-137.</p>
-
-<p class="neg-indent"><span class="smcap">Landahl, Herbert D.</span>,
-A Note on the Mathematical Biophysics of Central Excitation and
-Inhibition, <i>Bulletin of Mathematical Biophysics</i>, vol. 7,
-no. 4, Dec. 1945, pp. 219-221.</p>
-
-<p class="neg-indent"><span class="smcap">Lettvin, Jerome Y.</span>,
-and <span class="smcap">Walter Pitts</span>, A Mathematical Theory of
-the Affective Psychoses, <i>Bulletin of Mathematical Biophysics</i>,
-vol. 5, no. 4, Dec. 1943, pp. 139-148.</p>
-
-<p class="neg-indent"><span class="smcap">McCulloch, Warren S.</span>,
-and <span class="smcap">Walter Pitts</span>, A Logical Calculus of the
-Ideas Immanent in Nervous Activity, <i>Bulletin of Mathematical
-Biophysics</i>, vol. 5, no. 4, Dec. 1943, pp. 115-133.</p>
-
-<p class="neg-indent"><span class="smcap">Rashevsky, N.</span>,
-<i>Mathematical Biophysics</i>, Chicago: University of Chicago Press.
-Revised edition, 1948, 669 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Rashevsky, N.</span>,
-Mathematical Biophysics of Abstraction and Logical Thinking,
-<i>Bulletin of Mathematical Biophysics</i>, vol. 7, no. 3,
-Sept. 1945, pp. 133-148.</p>
-
-<p class="neg-indent"><span class="smcap">Rashevsky, N.</span>,
-Some Remarks on the Boolean Algebra of Nervous Nets in Mathematical
-Biophysics, <i>Bulletin of Mathematical Biophysics</i>, vol. 7, no. 4,
-Dec. 1945, pp. 203-211.</p>
-
-<p class="neg-indent"><span class="smcap">Rashevsky, N.</span>, A
-Suggestion for Another Statistical Interpretation of the Fundamental
-Equations of the Mathematical Biophysics of the Central Nervous System,
-<i>Bulletin of Mathematical Biophysics</i>, vol. 7, no. 4,
-Dec. 1945, pp. 223-226.</p>
-
-<p class="neg-indent"><span class="smcap">Rashevsky, N.</span>, The
-Neural Mechanism of Logical Thinking, <i>Bulletin of Mathematical
-Biophysics</i>, vol. 8, no. 1, Mar. 1946, pp. 29-40.</p>
-</div>
-
-<hr class="chap" />
-<p><span class="pagenum" id="Page_231">[Pg 231]</span></p>
-<h3>LANGUAGES: WORDS AND SYMBOLS<br />FOR THINKING</h3>
-
-<p class="blockquot">Hardly any field of techniques for thinking is
-more fascinating than language. The following list of references, of
-course, is short; it is meant chiefly as an introduction pointing out
-a number of different paths into the field of language and languages.
-Such topics as the following are introduced by the references in this
-list:</p>
-
-<ul class="index no-wrap">
-<li class="isub6">The origin of languages and alphabets.</li>
-<li class="isub6">The languages of the world, and speech communities.</li>
-<li class="isub6">The comparison of words and structure from language to language.</li>
-<li class="isub6">The significance of grammar and syntax.</li>
-<li class="isub6">The problem of clear meanings.</li>
-<li class="isub6">Writing and speaking that is easy to understand.</li>
-</ul>
-
-<hr class="tb" />
-
-<div class="blockquot2">
-<p class="neg-indent"><span class="smcap">Bloomfield, Leonard</span>,
-<i>Language</i>, New York: Henry Holt &amp; Co., 1933, 564 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Bodmer, Frederick</span>,
-and <span class="smcap">Launcelot Hogben</span>, <i>The Loom of
-Language</i>, New York: W. W. Norton &amp; Co., 1944, 692 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Flesch, Rudolf</span>,
-<i>The Art of Plain Talk</i>, New York: Harper &amp; Brothers, 1946,
-210 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Graff, Willem L.</span>,
-<i>Language and Languages: An Introduction to Linguistics</i>,
-New York: D. Appleton &amp; Co., 1932, 487 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Hayakawa, S. I.</span>,
-<i>Language in Action</i>, New York: Harcourt, Brace &amp; Co., 1941,
-345 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Jespersen, Otto</span>,
-<i>The Philosophy of Grammar</i>, New York: Henry Holt &amp;
-Co., 1929 (third printing), 359 pp.</p>
-
-<p class="neg-indent space-above1"><span class="smcap">Jespersen, Otto</span>,
-<i>Analytic Syntax</i>,</p>
-
-<p class="neg-indent space-below1">In this book, by means of a
-well-contrived system of letters and signs, the great linguistic
-scholar Jespersen depicts all the important inter-relations of English
-words and parts of words in connected speech.</p>
-
-<p class="neg-indent"><span class="smcap">Ogden, C. K.</span>,
-<i>The System of Basic English</i>, New York: Harcourt,
-Brace &amp; Co., 1934, 320 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Schlauch, Margaret</span>,
-<i>The Gift of Tongues</i>, New York: Modern Age Books, 1942,
-342 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Walpole, Hugh R.</span>,
-<i>Semantics: The Nature of Words and Their Meanings</i>,
-New York: W. W. Norton &amp; Co., 1941, 264 pp.</p>
-</div>
-
-<p><span class="pagenum" id="Page_232">[Pg 232]</span></p>
-<hr class="chap" />
-<h3>LANGUAGES:<br />MACHINES FOR THINKING</h3>
-
-<p class="blockquot">For many years, nearly all references about
-machines as a language for thinking have been specialized and limited.
-Colleges with scholars who write textbooks usually have not had a
-variety of expensive and versatile computing machinery. As a result,
-the main environment for stimulating possible authors has until
-recently been missing. The list of references is accordingly brief.</p>
-
-<hr class="tb" />
-
-<div class="blockquot2">
-<p class="neg-indent"><span class="smcap">Aiken, Howard H.</span>, and
-others, <i>Proceedings of a Symposium on Large-Scale Digital
-Calculating Machinery</i>, Cambridge, Mass.: Harvard University
-Press, 1948, 302 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Comrie, John Leslie</span>,
-The Application of Commercial Calculating Machines to Scientific
-Computing, <i>Mathematical Tables and Other Aids to Computation</i>,
-vol. 2, no. 16, Oct. 1946, pp. 149-159.</p>
-
-<p class="neg-indent"><span class="smcap">Crew, E. W.</span>,
-Calculating Machines, <i>The Engineer</i>, vol. 172,
-Dec. 1941, pp. 438-441.</p>
-
-<p class="neg-indent"><span class="smcap">Fry, Macon</span>,
-<i>Designing Computing Mechanisms</i>, Cleveland, Ohio:
-Penton Publishing Co., 1946, 48 pp. (Reprinted from <i>Machine
-Design</i>, Aug. 1945 through Feb. 1946.)</p>
-
-<p class="neg-indent"><span class="smcap">Hartree, D. R.</span>,
-<i>Calculating Machines: Recent and Prospective Developments and
-Their Impact on Mathematical Physics</i>, Cambridge, England:
-The University Press, 1947, 40 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Horsburgh, E. H.</span>,
-<i>Modern Instruments and Methods of Calculation</i>,
-London: G. Bell and Sons, Ltd., 1914, 343 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Lilley, S.</span>,
-Mathematical Machines, <i>Nature</i>, vol. 149, Apr. 25, 1942,
-pp. 462-465.</p>
-
-<p class="neg-indent"><span class="smcap">Murray, Francis J.</span>,
-<i>The Theory of Mathematical Machines</i>,
-New York: King’s Crown Press, 1947, 116 pp.</p>
-
-<p class="neg-indent">The author states that a mathematical machine
-is a mechanism that provides information concerning the relationships
-among a specified set of mathematical concepts.</p>
-
-<p class="neg-indent"><span class="smcap">Turck, J. A. V.</span>,
-<i>The Origin of Modern Calculating Machines</i>, Chicago:
-Western Society of Engineers, 1921.</p>
-
-<p class="neg-indent">Recently, however, some magazine and newspaper
-publishers have seen news value in machines that think, and some good
-general articles with appeal to a wide audience have appeared. For
-the references to these articles, see the section of this supplement
-entitled “Digital Machines—Miscellaneous.”</p>
-</div>
-
-<hr class="chap" />
-<h3>PUNCH-CARD CALCULATING MACHINES</h3>
-
-<p class="blockquot">There are a few general references on punch-card calculating machines:
-<span class="pagenum" id="Page_233">[Pg 233]</span></p>
-
-<hr class="tb" />
-
-<div class="blockquot2">
-<p class="neg-indent"><span class="smcap">Baehne, G. Walter</span>,
-editor, and others, <i>Practical Applications of the Punched Card
-Method in Colleges and Universities</i>, New York: Columbia
-University Press, 1935, 442 pp.</p>
-
-<p class="neg-indent">This is a collection of many contributions
-from a number of authors, describing various applications, chiefly
-educational.</p>
-
-<p class="neg-indent"><span class="smcap">Eckert, W. J.</span>,
-<i>Punched-Card Methods in Scientific Computation</i>, New
-York: Columbia University, The Thomas J. Watson Astronomical Computing
-Bureau, 1940, 136 pp.</p>
-
-<p class="neg-indent">This is a scientific treatise, chiefly relating
-to the computation of orbits in astronomy.</p>
-
-<p class="neg-indent"><span class="smcap">Hartkemeier, Harry
-Pelle</span>, <i>Principles of Punch-Card Machine Operation</i>
-(Subtitle: <i>How to Operate Punch-Card Tabulating and
-Alphabetic Accounting Machines</i>), New York: Thomas Y. Crowell Co.,
-1942, 269 pp.</p>
-
-<p class="neg-indent">This is based on the author’s experience in
-teaching statistical analysis using IBM tabulators. The book does not
-deal with the collator or multiplying punch.</p>
-
-<p class="neg-indent"><span class="smcap">Hedley, K. J.</span>, <i>The
-Development of the Punched-Card Method</i>, Actuarial Society of
-Australasia, 1946, 20 pp.</p>
-
-<p class="neg-indent"><span class="smcap">International Business
-Machines Corporation</span>, <i>International Business Machines</i>
-(form no. A-4036-6-45), New York: International Business Machines
-Corporation, 1945, 65 pp.</p>
-
-<p class="neg-indent">Pages 6 to 31 show pictures and brief
-descriptions of about 20 punch-card machines, available in 1945.</p>
-
-<p class="neg-indent"><span class="smcap">Schnackel, H. G.</span>,
-and <span class="smcap">H. C. Lang</span>, <i>Accounting by Machine
-Methods</i>, New York: Ronald Press Co., 1939, 53 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Wolf, Arthur W.</span>, and
-<span class="smcap">Edmund C. Berkeley</span>, <i>Advanced Course in
-Punched Card Operations</i>, Newark, N. J.: Prudential Insurance
-Company of America, 1942, 98 pp.</p>
-
-<p class="neg-indent">A useful and authoritative description of IBM
-punch-card calculating machinery is the following:</p>
-
-<p class="neg-indent"><span class="smcap">International Business
-Machines Corporation, Department of Education</span>, <i>Machine
-Methods of Accounting</i>, Endicott, N. Y.: International
-Business Machines Corporation, 1936-41, 385 pp.</p>
-
-<p class="neg-indent">This is a collection of 28 separate booklets
-telling the detailed operation of IBM punch-card machinery. They were
-written for employees of IBM and users of IBM equipment. The following
-list of the booklets is useful in locating them:</p>
-</div>
-
-<p><span class="pagenum" id="Page_234">[Pg 234]</span></p>
-
-<table class="fontsize_90 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc bb"><span class="smcap">Title</span></th>
-      <th class="tdc bb"><span class="smcap">Form No.</span></th>
-      <th class="tdc bb"><span class="smcap">&nbsp;Date&nbsp;</span></th>
-      <th class="tdc bb"><span class="smcap">No. of<br />Pages</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdl">Machine Methods of Accounting—Foreword</td>
-      <td class="tdl_ws1">AM</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">6</td>
-   </tr><tr>
-      <td class="tdl">Development of IBM Corporation</td>
-      <td class="tdl_ws1">AM-1-1</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">14</td>
-   </tr><tr>
-      <td class="tdl">Principles of the Electric Accounting Machine Method</td>
-      <td class="tdl_ws1">AM-2</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">12</td>
-   </tr><tr>
-      <td class="tdl">The Tabulating Card</td>
-      <td class="tdl_ws1">AM-3-1</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">20</td>
-   </tr><tr>
-      <td class="tdl">Design of Tabulating Cards</td>
-      <td class="tdl_ws1">AM-4-1</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">16</td>
-   </tr><tr>
-      <td class="tdl">Preparation and Use of Codes</td>
-      <td class="tdl_ws1">AM-5</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">28</td>
-   </tr><tr>
-      <td class="tdl">Organization and Supervision of the Tabulating Department</td>
-      <td class="tdl_ws1">AM-6</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">16</td>
-   </tr><tr>
-      <td class="tdl">Selection and Training of Key Punch Operators</td>
-      <td class="tdl_ws1">AM-7</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">12</td>
-   </tr><tr>
-      <td class="tdl">Accounting Control</td>
-      <td class="tdl_ws1">AM-8</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">8</td>
-   </tr><tr>
-      <td class="tdl">Punches</td>
-      <td class="tdl_ws1">AM-9</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">12</td>
-   </tr><tr>
-      <td class="tdl">Alphabetic Printing Punches</td>
-      <td class="tdl_ws1">AM-10</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">7</td>
-   </tr><tr>
-      <td class="tdl">Facts to Know about Key Punches</td>
-      <td class="tdl_ws1">AM-11</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">4</td>
-   </tr><tr>
-      <td class="tdl">Verifiers</td>
-      <td class="tdl_ws1">AM-12</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">4</td>
-   </tr><tr>
-      <td class="tdl">Gang Punches</td>
-      <td class="tdl_ws1">AM-13</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">8</td>
-   </tr><tr>
-      <td class="tdl">Card-Operated Sorting Machines</td>
-      <td class="tdl_ws1">AM-14</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">12</td>
-   </tr><tr>
-      <td class="tdl">Facts to Know about Sorters</td>
-      <td class="tdl_ws1">AM-14a</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">4</td>
-   </tr><tr>
-      <td class="tdl">Electric Tabulating Machines</td>
-      <td class="tdl_ws1">AM-15</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">20</td>
-   </tr><tr>
-      <td class="tdl">Electric Accounting Machines (Type 285 and Type 297)</td>
-      <td class="tdl_ws1">AM-16</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">16</td>
-   </tr><tr>
-      <td class="tdl">Alphabetic Direct Subtraction Accounting Machine</td>
-      <td class="tdl_ws1">AM-17</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">28</td>
-   </tr><tr>
-      <td class="tdl">Numerical Interpreters</td>
-      <td class="tdl_ws1">AM-18</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">8</td>
-   </tr><tr>
-      <td class="tdl">Electric Punched-Card Interpreter (Type 552)</td>
-      <td class="tdl_ws1">AM-18a</td>
-      <td class="tdc">1941</td>
-      <td class="tdr_ws1">8</td>
-   </tr><tr>
-      <td class="tdl">Reproducing Punches (Type 512)</td>
-      <td class="tdl_ws1">AM-19</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">16</td>
-   </tr><tr>
-      <td class="tdl">Automatic Summary Punches for Use with</td>
-      <td class="tdc" colspan="3">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl_ws1">the Numerical Accounting Machines (Type 285-297)</td>
-      <td class="tdl_ws1">AM-20</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">16</td>
-   </tr><tr>
-      <td class="tdl">Automatic Summary Punches for Use with the</td>
-      <td class="tdc" colspan="3">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl_ws1">Alphabetic Accounting Machines (Type 405)</td>
-      <td class="tdl_ws1">AM-20a</td>
-      <td class="tdc">1940</td>
-      <td class="tdr_ws1">16</td>
-   </tr><tr>
-      <td class="tdl">Multiplying Punches</td>
-      <td class="tdl_ws1">AM-21</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">16</td>
-   </tr><tr>
-      <td class="tdl">Application of Machines to Accounting Functions</td>
-      <td class="tdl_ws1">AM-22</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">24</td>
-   </tr><tr>
-      <td class="tdl">Other International Products</td>
-      <td class="tdl_ws1">AM-23-2</td>
-      <td class="tdc">1936</td>
-      <td class="tdr_ws1">19</td>
-   </tr><tr>
-      <td class="tdl">The International Automatic Carriage (Type 921)</td>
-      <td class="tdl_ws1">AM-24</td>
-      <td class="tdc">1938</td>
-      <td class="tdr_ws1">15</td>
-   </tr>
- </tbody>
-</table>
-
-<p class="space-above2">The Department of Education of IBM has begun a
-second series of booklets on the principles of operation of punch-card
-calculating machinery:</p>
-
-<p class="neg-indent"><span class="smcap">International Business
-Machines Corporation, Department of Education</span>, <i>Principles
-of Operation</i>, Endicott, N. Y.: International Business Machines
-Corporation, 1942 and later (except for one published in 1939).</p>
-
-<p>Many of the booklets in this series have good examples of machine
-operation and applications. Also, for the first time, letters and
-numbers have been used as coordinates to label the hubs on the
-plugboards. This series includes the following:
-<span class="pagenum" id="Page_235">[Pg 235]</span></p>
-
-<table class="fontsize_90 no-wrap" border="0" cellspacing="2" summary=" " cellpadding="2" >
-  <thead><tr>
-      <th class="tdc bb"><span class="smcap">Title</span></th>
-      <th class="tdc bb"><span class="smcap">Form No.</span></th>
-      <th class="tdc bb"><span class="smcap">&nbsp;Date&nbsp;</span></th>
-      <th class="tdc bb"><span class="smcap">No. of<br />Pages</span></th>
-   </tr>
- </thead>
-  <tbody><tr>
-      <td class="tdc" colspan="4"><br /><b>CARD PUNCHES AND VERIFIERS</b></td>
-   </tr><tr>
-      <td class="tdl">Card-Punching and Verifying Machines</td>
-      <td class="tdl_ws1">52-3176-0</td>
-      <td class="tdc">1946</td>
-      <td class="tdr_ws1">21</td>
-   </tr><tr>
-      <td class="tdl">Alphabetical Verifier, Type 055</td>
-      <td class="tdl_ws1">52-3295-1</td>
-      <td class="tdc">1946</td>
-      <td class="tdr_ws1">4</td>
-   </tr><tr>
-      <td class="tdc" colspan="4"><br /><b>INTERPRETERS</b></td>
-   </tr><tr>
-      <td class="tdl">Card Interpreters, Type 550, 551, and 552</td>
-      <td class="tdl_ws1">52-3178-0</td>
-      <td class="tdc">1946</td>
-      <td class="tdr_ws1">14</td>
-   </tr><tr>
-      <td class="tdc" colspan="4"><br /><b>REPRODUCERS</b></td>
-   </tr><tr>
-      <td class="tdl">Automatic Reproducing Punch, Type 513</td>
-      <td class="tdl_ws1">52-3180-0</td>
-      <td class="tdc">1945</td>
-      <td class="tdr_ws1">22</td>
-   </tr><tr>
-      <td class="tdl">End Printing Reproducing Punch, Type 519</td>
-      <td class="tdl_ws1">52-3292-1</td>
-      <td class="tdc">1946</td>
-      <td class="tdr_ws1">26</td>
-   </tr><tr>
-      <td class="tdl bt">Electric Document-Originating Machine,</td>
-      <td class="tdl_ws1 bt">&nbsp;</td>
-      <td class="tdc bt">June</td>
-      <td class="tdr_ws1 bt">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl_ws1">&emsp;Type 519</td>
-      <td class="tdl_ws1">52-3292-2</td>
-      <td class="tdc">1948</td>
-      <td class="tdr_ws1">26</td>
-   </tr><tr>
-      <td class="tdc" colspan="4"><br /><b>COLLATORS</b></td>
-   </tr><tr>
-      <td class="tdl">Collator</td>
-      <td class="tdl_ws1">AM-25</td>
-      <td class="tdc">1943</td>
-      <td class="tdr_ws1">31</td>
-   </tr><tr>
-      <td class="tdl">Collator Counting Device</td>
-      <td class="tdl_ws1">C.R. 9178</td>
-      <td class="tdc">1942</td>
-      <td class="tdr_ws1">12</td>
-   </tr><tr>
-      <td class="tdc" colspan="4"><br /><b>CALCULATING PUNCHES</b></td>
-   </tr><tr>
-      <td class="tdl">Electric Multiplier, Type 601</td>
-      <td class="tdl_ws1">52-3408-1</td>
-      <td class="tdc">1947</td>
-      <td class="tdr_ws1">47</td>
-   </tr><tr>
-      <td class="tdl">Calculating Punch, Type 602</td>
-      <td class="tdl_ws1">52-3409-0</td>
-      <td class="tdc">1946</td>
-      <td class="tdr_ws1">83</td>
-   </tr><tr>
-      <td class="tdl">Calculating Punch, Type 602</td>
-      <td class="tdl_ws1">52-3409-5</td>
-      <td class="tdc">1947</td>
-      <td class="tdr_ws1">93</td>
-   </tr><tr>
-      <td class="tdl">Calculating Punch, Type 602-A (Preliminary Manual)</td>
-      <td class="tdl_ws1">22-5489-0</td>
-      <td class="tdc">1948</td>
-      <td class="tdr_ws1">59</td>
-   </tr><tr>
-      <td class="tdl">Electronic Multiplier, Type 603</td>
-      <td class="tdl_ws1">52-3561-0</td>
-      <td class="tdc">1946</td>
-      <td class="tdr_ws1">5</td>
-   </tr><tr>
-      <td class="tdl">Electronic Calculating Punch, Type 604</td>
-      <td class="tdl_ws1">22-5279-0</td>
-      <td class="tdc">1948</td>
-      <td class="tdr_ws1">51</td>
-   </tr><tr>
-      <td class="tdc" colspan="4"><br /><b>TABULATORS</b></td>
-   </tr><tr>
-      <td class="tdl">Accounting Machine, Type 402 and 403 (Preliminary Manual)</td>
-      <td class="tdl_ws1">22-5654-0</td>
-      <td class="tdc">1949</td>
-      <td class="tdr_ws1">146</td>
-   </tr><tr>
-      <td class="tdl">Alphabetical Accounting Machine, Type 404</td>
-      <td class="tdl_ws1">52-3395-1</td>
-      <td class="tdc">1946</td>
-      <td class="tdr_ws1">96</td>
-   </tr><tr>
-      <td class="tdl">Typical Applications, Alphabetical Accounting Machine,</td>
-      <td class="tdc" colspan="3">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl_ws1">&emsp;Type 404, with Multiple Line Printing</td>
-      <td class="tdl_ws1">22-3771-1</td>
-      <td class="tdc">1947</td>
-      <td class="tdr_ws1">47</td>
-   </tr><tr>
-      <td class="tdl bt">Alphabetical Accounting Machine, Type 405</td>
-      <td class="tdl_ws1 bt">AM 17 (1),</td>
-      <td class="tdc bt">1943</td>
-      <td class="tdr_ws1 bt">90</td>
-   </tr><tr>
-      <td class="tdl">&nbsp;</td>
-      <td class="tdl_ws1">Revised</td>
-      <td class="tdc">1/1/43</td>
-      <td class="tdr_ws1">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl bt">Alphabetical Accounting Machine,</td>
-      <td class="tdc bt">&nbsp;</td>
-      <td class="tdc bt">Nov.</td>
-      <td class="tdc bt">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl_ws1">&emsp;Type 405</td>
-      <td class="tdl_ws1">52-3179-2</td>
-      <td class="tdc">1948</td>
-      <td class="tdr_ws1">81
-                        <span class="pagenum" id="Page_236">[Pg 236]</span></td>
-   </tr><tr>
-      <td class="tdc" colspan="4"><br /><b>AUTOMATIC PRINTING CARRIAGES</b></td>
-   </tr><tr>
-      <td class="tdl">Bill Feed, Type 920</td>
-      <td class="tdl_ws1">52-3184-0</td>
-      <td class="tdc">1945</td>
-      <td class="tdr_ws1">21</td>
-   </tr><tr>
-      <td class="tdl">Form Feeding Device</td>
-      <td class="tdl_ws1">52-3235-0</td>
-      <td class="tdc">1946</td>
-      <td class="tdr_ws1">11</td>
-   </tr><tr>
-      <td class="tdl">Automatic Carriage, Type 921</td>
-      <td class="tdl_ws1">52-3183-0</td>
-      <td class="tdc">1945</td>
-      <td class="tdr_ws1">36</td>
-   </tr><tr>
-      <td class="tdl">Tape-Controlled Carriage</td>
-      <td class="tdc" colspan="3">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl_ws1">&emsp;(Preliminary Manual, Revised)</td>
-      <td class="tdl_ws1">22-5415-1</td>
-      <td class="tdc">1948</td>
-      <td class="tdr_ws1">27</td>
-   </tr><tr>
-      <td class="tdc" colspan="4"><br /><b>TEST SCORING MACHINE</b></td>
-   </tr><tr>
-      <td class="tdl bb">Test Scoring Machine</td>
-      <td class="tdl_ws1 bb">94-2333-0</td>
-      <td class="tdc bb">1939</td>
-      <td class="tdr_ws1 bb">19</td>
-   </tr><tr>
-      <td class="tdl">&nbsp;</td>
-      <td class="tdl_ws1">&nbsp;</td>
-      <td class="tdc">May</td>
-      <td class="tdr_ws1">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl">Test Scoring Machine</td>
-      <td class="tdl_ws1">32-9145-1</td>
-      <td class="tdc">1946</td>
-      <td class="tdr_ws1">20</td>
-   </tr><tr>
-      <td class="tdl bt">Published Tests Adapted for Use with</td>
-      <td class="tdl_ws1 bt">&nbsp;</td>
-      <td class="tdc bt">June</td>
-      <td class="tdr_ws1 bt">&nbsp;</td>
-   </tr><tr>
-      <td class="tdl_ws1">the IBM Electric Test Scoring Machine</td>
-      <td class="tdl_ws1">27-4286-9</td>
-      <td class="tdc">1948</td>
-      <td class="tdr_ws1">8</td>
-   </tr>
- </tbody>
-</table>
-
-<div class="blockquot">
-<p>In addition to the new types of punch-card machines referred to in the
-above list, an elaborate punch-card calculating machine is described in
-the following reference:</p>
-
-<p class="neg-indent"><span class="smcap">Eckert, W. J.</span>, The IBM Pluggable Sequence
-Relay Calculator, <i>Mathematical Tables and Other
-Aids to Computation</i>, vol. 3, no. 23, July 1948,
-pp. 149-161.</p>
-
-<p class="space-above2">A description of punch-card machinery in rather
-a light vein is contained in:</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Speaking of Pictures:
-New Mechanical Monsters Ease <i>Life’s</i> Growing Pains, <i>Life</i>,
-Sept. 15, 1947, pp. 15-16.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, <i>540</i>, Chicago:
-Time-Life-Fortune Magazine, Subscription Fulfillment Office, 1948, 15 pp.</p>
-</div>
-
-<p>New types of punch-card machinery are continually coming into use.
-Among them are: machines that take in punch cards and make punched
-paper tape (such as teletype tape), and vice versa—useful for
-transmitting punch-card information over wires; an electric typewriter
-operated by punch cards—useful for preparing almanacs for sea and air
-navigation, etc.; a calculator programmed by punch cards, consisting
-of an assembly of a tabulator, an electronic calculating punch, and
-an auxiliary storage unit, all cabled together—useful for some types
-of long calculation; etc. For information about such machinery, the
-manufacturers may be consulted.</p>
-
-<h3>PUNCH-CARD CALCULATING MACHINERY:<br /> APPLICATIONS</h3>
-
-<div class="blockquot">
-<p>There are many articles in scientific journals on applications of
-punch-card calculating machinery to technical problems. The fields of
-<span class="pagenum" id="Page_237">[Pg 237]</span>
-engineering, education, indexing, mathematics, surveying, statistics,
-and others are all represented in the following list of sample references:</p>
-
-<p class="neg-indent"><span class="smcap">Alt, Franz L.</span>,
-Multiplication of Matrices, <i>Mathematical Tables and Other Aids
-to Computation</i>, vol. 2, no. 13, Jan. 1946, pp. 12-13.</p>
-
-<p class="neg-indent"><span class="smcap">Bailey, C. F.</span>, and
-others, Punch Cards for Indexing Scientific Data, <i>Science</i>,
-vol. 104, Aug. 23, 1946, p. 181.</p>
-
-<p class="neg-indent"><span class="smcap">Bower, E. C.</span>, On
-Subdividing Tables, <i>Lick Observatory Bulletin</i>, vol. 16,
-no. 455, Nov. 1933, pp. 143-144.</p>
-
-<p class="neg-indent"><span class="smcap">Bower, E. C.</span>,
-Systematic Subdivision of Tables, <i>Lick Observatory Bulletin</i>,
-vol. 17, no. 467, Apr. 1935, pp. 65-74.</p>
-
-<p class="neg-indent"><span class="smcap">Clemence, G. M.</span>,
-and <span class="smcap">Paul Herget</span>, Optimum-Interval
-Punched-Card Tables, <i>Mathematical Tables and Other Aids to
-Computation</i>, vol. 1, no. 6, Apr. 1944, pp. 173-176.</p>
-
-<p class="neg-indent"><span class="smcap">Culley, Frank L.</span>,
-Use of Accounting Machines for Mass-Transformation from Geographic
-to Military-Grid Coordinates, Washington, D. C.: National Research
-Council, <i>American Geophysical Union Transactions of 1942</i>,
-part 2, pp. 190-197.</p>
-
-<p class="neg-indent"><span class="smcap">Deming, W. Edwards</span>,
-and <span class="smcap">Morris H. Hansen</span>, On Some Census
-Aids to Sampling, <i>Journal of the American Statistical
-Association</i>, vol. 38, no. 225, Sept. 1943, pp. 353-357.</p>
-
-<p class="neg-indent"><span class="smcap">Dunlap, Jack W.</span>,
-The Computation of Means, Standard Deviations, and Correlations
-by the Tabulator When the Numbers Are Both Positive and Negative,
-<i>Proceedings of the Educational Research Forum</i>,
-International Business Machines Corporation, Aug. 1940, pp. 16-19.</p>
-
-<p class="neg-indent"><span class="smcap">Dwyer, Paul S.</span>,
-The Use of Tables in the Form of Prepunched Cards, <i>Proceedings of
-the Educational Research Forum</i>, International Business
-Machines Corporation, Aug. 1940, pp. 125-127.</p>
-
-<p class="neg-indent"><span class="smcap">Dwyer, Paul S.</span>,
-Summary of Problems in the Computation of Statistical Constants
-with Tabulating and Sorting Machines, <i>Proceedings of the
-Educational Research Forum</i>, International Business Machines
-Corporation, Aug. 1940, pp. 20-28.</p>
-
-<p class="neg-indent"><span class="smcap">Dwyer, Paul S.</span>,
-and <span class="smcap">Alan D. Meacham</span>, The Preparation of
-Correlation Tables on a Tabulator Equipped with Digit Selection,
-<i>Journal of the American Statistical Association</i>, vol. 32,
-1937, pp. 654-662.</p>
-
-<p class="neg-indent"><span class="smcap">Dyer, H. S.</span>, Making
-Test Score Data Effective in the Admission and Course Placement
-of Harvard Freshmen, <i>Proceedings of the Research Forum</i>,
-International Business Machines Corporation, 1946, pp. 55-62.</p>
-
-<p class="neg-indent"><span class="smcap">Eckert, W. J.</span>,
-and <span class="smcap">Ralph F. Haupt</span>, The Printing of
-Mathematical Tables, <i>Mathematical Tables and Other Aids to
-Computation</i>, vol. 2, no. 17, Jan. 1947, pp. 196-202.</p>
-
-<p class="neg-indent"><span class="smcap">Feinstein, Lillian</span>,
-and <span class="smcap">Martin Schwarzchild</span>, Automatic
-Integration of Linear Second-Order Differential Equations by Means of
-Punched-Card Machines, <i>Review of Scientific Instruments</i>,
-vol. 12, no. 8, Aug. 1941, pp. 405-408.</p>
-
-<p class="neg-indent"><span class="smcap">Hotelling, Harold</span>,
-Some New Methods in Matrix Calculation, <i>The Annals of
-Mathematical Statistics</i>, vol. 14, no. 1, Mar. 1943, pp. 1-34.
-
-<span class="pagenum" id="Page_238">[Pg 238]</span></p>
-
-<p class="neg-indent"><span class="smcap">International Business
-Machines Corporation</span>, editor, and others, <i>Proceedings
-of the Educational Research Forum</i>, Endicott, N. Y.:
-International Business Machines Corporation, 1941.</p>
-
-<p class="neg-indent"><span class="smcap">International Business
-Machines Corporation</span>, editor, and others, <i>Proceedings of the
-Research Forum</i>, Endicott, N. Y.: International Business
-Machines Corporation, 1946, 94 pp.</p>
-
-<p class="neg-indent"><span class="smcap">King, Gilbert W.</span>,
-Punched-Card Tables of the Exponential Function, <i>Review of
-Scientific Instruments</i>, vol. 15, no. 12, Dec. 1944, pp.
-349-350.</p>
-
-<p class="neg-indent"><span class="smcap">King, Gilbert W.</span>,
-and <span class="smcap">George B. Thomas</span>, Preparation of
-Punched-Card Tables of Logarithms, <i>Review of Scientific
-Instruments</i>, vol. 15, no. 12, Dec. 1944, p. 350.</p>
-
-<p class="neg-indent"><span class="smcap">Kormes, Mark</span>, A Note
-on the Integration of Linear Second-Order Differential Equations by
-Means of Punched Cards, <i>Review of Scientific Instruments</i>,
-vol. 14, no. 4, Apr. 1943, p. 118.</p>
-
-<p class="neg-indent"><span class="smcap">Kormes, Mark</span>,
-Numerical Solution of the Boundary Value Problem for the Potential
-Equation by Means of Punched Cards, <i>Review of Scientific
-Instruments</i>, vol. 14, no. 8, Aug. 1943, pp. 248-250.</p>
-
-<p class="neg-indent"><span class="smcap">Kormes, Mark</span>, and
-<span class="smcap">Jennie P. Kormes</span>, Numerical Solution of
-Initial Value Problems by Means of Punched-Card Machines, <i>Review
-of Scientific Instruments</i>, vol. 16, no. 1, Jan. 1945, pp.
-7-9.</p>
-
-<p class="neg-indent"><span class="smcap">Kuder, G. Frederic</span>,
-Use of the IBM Scoring Machine for Rapid Computation of Tables of
-Intercorrelations, <i>Journal of Applied Psychology</i>, vol.
-22, no. 6, Dec. 1938, pp. 587-596.</p>
-
-<p class="neg-indent"><span class="smcap">Maxfield, D. K.</span>,
-Library Punched Card Procedures, <i>Library Journal</i>, vol. 71, no.
-12, June 15, 1946, pp. 902-905 ...</p>
-
-<p class="neg-indent"><span class="smcap">McLaughlin, Kathleen</span>,
-Adding Machines Nip AEF Epidemics, New York: <i>New York Times</i>,
-Apr. 27, 1945.</p>
-
-<p class="neg-indent"><span class="smcap">McPherson, John C.</span>,
-On Mechanical Tabulation of Polynomials, <i>Annals of Mathematical
-Statistics</i>, Sept. 1941, pp. 317-327.</p>
-
-<p class="neg-indent"><span class="smcap">McPherson, John C.</span>,
-Mathematical Operations with Punched Cards, <i>Journal of the
-American Statistical Association</i>, vol. 37, June 1942, pp.
-275-281.</p>
-
-<p class="neg-indent"><span class="smcap">Milliman, Wendell A.</span>,
-Mechanical Multiplication by the Use of Tabulating Machines,
-<i>Transactions of the Actuarial Society of America</i>,
-vol. 35, part 2, Oct. 1934, pp. 253-264; for discussion see
-also vol. 36, part 1, May 1935, pp. 77-84.</p>
-
-<p class="neg-indent"><span class="smcap">Royer, Elmer B.</span>, A
-Machine Method for Computing the Biserial Correlation Coefficient in
-Item Validation, <i>Psychometrika</i>, vol. 6, no. 1, Feb. 1941, pp. 55-59.</p>
-
-<p class="neg-indent"><span class="smcap">Whitten, C. A.</span>,
-Triangulation Adjustment by International Business Machines,
-Washington, D. C.: National Research Council, <i>American
-Geophysical Union Transactions of 1943</i>, part 1, p. 31.</p>
-
-<p class="space-above2">The following bibliography may be obtained
-on request to the Watson Scientific Computing Laboratory, Columbia
-University, 612 West 116 Street, New York 27, N. Y.:
-<span class="pagenum" id="Page_239">[Pg 239]</span></p>
-
-<p class="neg-indent"><span class="smcap">Watson Scientific Computing
-Laboratory</span>, <i>Bibliography: The Use of IBM Machines in
-Scientific Research, Statistics, and Education</i>, New York:
-International Business Machines Corporation (form no. 50-3813-0),
-Sept. 1947, 25 pp.</p>
-
-<p>The organization and equipment of this laboratory are described in:</p>
-
-<p class="neg-indent"><span class="smcap">Eckert, W. J.</span>,
-Facilities of the Watson Scientific Computing Laboratory,
-<i>Proceedings of the Research Forum</i>, International Business
-Machines Corporation, 1946, pp. 75-80.</p>
-</div>
-
-<h3>THE DIFFERENTIAL ANALYZER</h3>
-
-<div class="blockquot">
-<p>The basic scientific articles on the two differential analyzers at
-Massachusetts Institute of Technology are:</p>
-
-<p class="neg-indent"><span class="smcap">Bush, Vannevar</span>,
-The Differential Analyzer: A New Machine for Solving Differential
-Equations, <i>Journal of the Franklin Institute</i>, vol. 212,
-no. 4, Oct. 1931, pp. 447-488.</p>
-
-<p class="neg-indent"><span class="smcap">Bush, Vannevar</span>,
-and <span class="smcap">Samuel H. Caldwell</span>, A New Type of
-Differential Analyzer, <i>Journal of the Franklin Institute</i>, vol.
-240, no. 4, Oct. 1945, pp. 255-326.</p>
-
-<p>Some of the less technical articles about the second differential
-analyzer at M.I.T. are:</p>
-
-<p class="neg-indent"><span class="smcap">Caldwell, Samuel H.</span>,
-Educated Machinery, <i>Technology Review</i>, vol. 48, no. 1, Nov.
-1945, pp. 31-34.</p>
-
-<p class="neg-indent"><span class="smcap">Genet, N.</span>, 100-Ton
-Brain at M.I.T., <i>Scholastic</i>, vol. 48, Feb. 4, 1946, p. 36.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>,
-Mathematical Machine; New Electronic Differential Analyzer,
-<i>Science News Letter</i>, vol. 48, Nov. 10, 1945, p. 291.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Robot
-Einstein: Differential Analyzer at M.I.T., <i>Newsweek</i>, vol. 26,
-Nov. 12, 1945, p. 93.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, M.I.T.’s
-100-Ton Mathematical Brain is Now to Tackle Problems of Peace,
-<i>Popular Science</i>, vol. 148, Jan. 1946, p. 81.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, The Great
-Electro-Mechanical Brain; M.I.T.’s Differential Analyzer, <i>Life</i>,
-vol. 20, Jan. 14, 1946, pp. 73-74 ...</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, All the
-Answers at Your Fingertips; in the Laboratory of M.I.T., <i>Popular
-Mechanics</i>, vol. 85, Mar. 1946, pp. 164-167 ...</p>
-
-<p>A differential analyzer was built at the Moore School of Electrical
-Engineering:</p>
-
-<p class="neg-indent"><span class="smcap">Travis, Irven</span>,
-Differential Analyzer Eliminates Brain Fag, <i>Machine Design</i>,
-July 1935, pp. 15-18.</p>
-
-<p>A differential analyzer was built at the General Electric Company,
-Schenectady, N. Y. Instead of using a mechanical or electrical
-amplifier of the motion of the little turning wheel riding on the disc,
-<span class="pagenum" id="Page_240">[Pg 240]</span>
-this machine follows the motion using polarized light. This machine is
-described in:</p>
-
-<p class="neg-indent"><span class="smcap">Berry, T. M.</span>,
-Polarized Light Servo System, <i>Transactions of the American Institute
-of Electrical Engineers</i>, vol. 63, Apr. 1944, pp. 195-197.</p>
-
-<p class="neg-indent"><span class="smcap">Kuehni, H. P.</span>, and
-<span class="smcap">H. A. Peterson</span>, A New Differential Analyzer,
-<i>Transactions of the American Institute of Electrical
-Engineers</i>, vol. 63, May 1944, pp. 221-227.</p>
-
-<p>A differential analyzer has been put into use at the University of
-California:</p>
-
-<p class="neg-indent"><span class="smcap">Boelter, L. M. K.</span>, and
-others, <i>The Differential Analyzer of the University of
-California</i>, Los Angeles: University of California, 1947, 25 pp.</p>
-
-<p>A differential analyzer was built at Manchester University, England.
-It was built first from “Meccano” parts, at a total cost of about 20
-pounds, and later refined for more exact work. Some articles dealing
-with this differential analyzer are:</p>
-
-<p class="neg-indent"><span class="smcap">Hartree, D. R.</span>, The
-Differential Analyzer, <i>Nature</i>, vol. 135, June 8, 1935, p. 940.</p>
-
-<p class="neg-indent"><span class="smcap">Hartree, D. R.</span>,
-The Mechanical Integration of Differential Equations, <i>The
-Mathematical Gazette</i>, vol. 22, 1938, pp. 342-364.</p>
-
-<p class="neg-indent"><span class="smcap">Hartree, D. R.</span>, and
-<span class="smcap">A. Porter</span>, The Construction of a Model
-Differential Analyser, <i>Memoirs and Proceedings of the Manchester
-Literary and Philosophical Society</i>, vol. 79, July 1935, pp.
-51-72.</p>
-
-<p>Other small scale differential analyzers built in England are
-covered in:</p>
-
-<p class="neg-indent"><span class="smcap">Beard, R. E.</span>, The
-Construction of a Small Scale Differential Analyser and Its Application
-to the Calculation of Actuarial Functions, <i>Journal of the
-Institute of Actuaries</i>, vol. 71, 1942, pp. 193-227.</p>
-
-<p class="neg-indent"><span class="smcap">Massey, H. S. W.</span>,
-<span class="smcap">J. Wylie</span>, and <span class="smcap">R.
-A. Buckingham</span>, A Small Scale Differential Analyser: Its
-Construction and Operation, <i>Proceedings of the Royal Irish
-Academy</i>, vol. 45, 1938, pp. 1-21.</p>
-
-<p>A differential analyzer constructed in Germany is briefly described
-in the following:</p>
-
-<p class="neg-indent"><span class="smcap">Sauer, R.</span>, and <span
-class="smcap">H. Poesch</span>, Integrating Machine for Solving
-Ordinary Differential Equations, <i>Engineers Digest</i> (American
-Edition), vol. 1, May 1944, pp. 326-328.</p>
-
-<p>From the historical point of view there are some interesting papers
-on a machine for solving differential equations by Sir William Thomson
-(Lord Kelvin), including one by his brother James Thomson. They are in
-the <i>Proceedings of the Royal Society</i>, vol. 24, Feb. 1876, pp.
-262-275. The method of integration by a machine is described, but the
-<span class="pagenum" id="Page_241">[Pg 241]</span>
-state of machine tools at the time was such that no accurate mechanism
-was constructed. Another interesting paper foreshadowing the
-differential analyzer is:</p>
-
-<p class="neg-indent"><span class="smcap">Wainwright, Lawrence
-L.</span>, <i>A Ballistic Engine</i>, Chicago: University of
-Chicago, thesis for Master’s Degree, 1923, 28 pp.</p>
-
-<p>Some of the applications and mathematical limitations of
-differential analyzers are covered in:</p>
-
-<p class="neg-indent"><span class="smcap">Bush, V.</span>, and
-<span class="smcap">S. H. Caldwell</span>, Thomas-Fermi Equation Solution
-by the Differential Analyzer, <i>Physical Review</i>, vol. 38, no. 10,
-1931, pp. 1898-1902.</p>
-
-<p class="neg-indent"><span class="smcap">Hartree, D. R.</span>, A
-Great Calculating Machine: the Bush Differential Analyser and Its
-Applications in Science and Industry, <i>Proceedings of the
-Royal Institution of Great Britain</i>, vol. 31, 1940, pp. 151-170.</p>
-
-<p class="neg-indent"><span class="smcap">Hartree, D. R.</span>,
-and <span class="smcap">A. Porter</span>, The Application of the
-Differential Analyser to Transients on a Distortionless Transmission
-Line, <i>Journal of the Institute of Electrical Engineering</i>,
-vol. 83, no. 503, Nov. 1938, pp. 648-656.</p>
-
-<p class="neg-indent"><span class="smcap">Hartree, D. R.</span>, and
-<span class="smcap">J. R. Womersley</span>, A Method for the Numerical
-or Mechanical Solution of Certain Types of Partial Differential
-Equations, <i>Proceedings of the Royal Society of London</i>, series A,
-vol. 161, 1937, pp. 353-366.</p>
-
-<p class="neg-indent"><span class="smcap">Maginniss, F. J.</span>,
-Differential Analyzer Applications, <i>General Electric Review</i>,
-vol. 48, no. 5, May 1945, pp. 54-59.</p>
-
-<p class="neg-indent"><span class="smcap">Shannon, Claude E.</span>,
-Mathematical Theory of the Differential Analyzer, <i>Journal of
-Mathematics and Physics</i>, Cambridge, Mass.: Massachusetts
-Institute of Technology, vol. 20, no. 4, 1941, pp. 337-354.</p>
-</div>
-
-<h3>HARMONIC ANALYZERS AND SYNTHESIZERS</h3>
-
-<div class="blockquot">
-<p>Another branch of the analogue calculating machine is the harmonic
-analyzer and synthesizer. These are machines that study wave motions
-and related physical and mathematical functions. A brief list of
-articles on this type of machine follows:</p>
-
-<p class="neg-indent"><span class="smcap">Archer, R. M.</span>,
-Projecting Apparatus for Compounding Harmonic Vibrations, <i>Journal
-of Scientific Instruments</i>, vol. 14, 1937, pp. 408-410.</p>
-
-<p class="neg-indent"><span class="smcap">Brown, S. L.</span>,
-A Mechanical Harmonic Synthesizer-Analyzer, <i>Journal of the
-Franklin Institute</i>, vol. 228, 1939, pp. 675-694.</p>
-
-<p class="neg-indent"><span class="smcap">Brown, S. L.</span>, and
-<span class="smcap">L. L. Wheeler</span>, A Mechanical Method for
-Graphical Solution of Polynomials, <i>Journal of the Franklin
-Institute</i>, vol. 231, 1941, pp. 223-243.</p>
-
-<p class="neg-indent"><span class="smcap">Brown, S. L.</span>, and
-<span class="smcap">L. L. Wheeler</span>, Use of the Mechanical
-Multiharmonograph for Graphing Types of Functions and for Solution
-of Pairs of Non-Linear Simultaneous Equations, <i>Review of
-Scientific Instruments</i>, vol. 13, Nov. 1942, pp. 493-495.
-<span class="pagenum" id="Page_242">[Pg 242]</span></p>
-
-<p class="neg-indent"><span class="smcap">Brown, S. L.</span>, and
-<span class="smcap">L. L. Wheeler</span>, The Use of a Mechanical
-Synthesizer to Solve Trigonometric and Certain Types of Transcendental
-Equations, and for the Double Summations Involved in Patterson
-Contours, <i>Journal of Applied Physics</i>, vol. 14, Jan. 1943, pp. 30-36.</p>
-
-<p class="neg-indent"><span class="smcap">Fürth, R.</span>, and <span
-class="smcap">R. W. Pringle</span>, A New Photo-Electric Method for
-Fourier Synthesis and Analysis, <i>London, Edinburgh and Dublin
-Philosophical Magazine and Journal of Science</i>, vol. 35,
-series 7, 1944, pp. 643-656.</p>
-
-<p class="neg-indent"><span class="smcap">International Hydrographic
-Bureau</span>, <i>Tide Predicting Machines</i>, International
-Hydrographic Bureau, Special Publication 13, July 1926.</p>
-
-<p class="neg-indent"><span class="smcap">Kranz, Frederick W.</span>,
-A Mechanical Synthesizer and Analyzer, <i>Journal of the Franklin
-Institute</i>, vol. 204, 1927, pp. 245-262.</p>
-
-<p class="neg-indent"><span class="smcap">Marble, F. G.</span>,
-An Automatic Vibration Analyzer, <i>Bell Laboratories Record</i>,
-vol. 22, Apr. 1944, pp. 376-380.</p>
-
-<p class="neg-indent"><span class="smcap">Maxwell, L. R.</span>,
-An Electrical Method for Compounding Sine Functions, <i>Review of
-Scientific Instruments</i>, vol. 11, Feb. 1940, pp. 47-54.</p>
-
-<p class="neg-indent"><span class="smcap">Miller, Dayton C.</span>,
-A 32-Element Harmonic Synthesizer, <i>Journal of the Franklin
-Institute</i>, vol. 181, 1916, pp. 51-81.</p>
-
-<p class="neg-indent"><span class="smcap">Miller, Dayton C.</span>,
-The Henrici Harmonic Analyzer and Devices for Extending and Facilitating
-Its Use, <i>Journal of the Franklin Institute</i>, vol. 182, 1916,
-pp. 285-322.</p>
-
-<p class="neg-indent"><span class="smcap">Milne, J. R.</span>, A
-“Duplex” Form of Harmonic Synthetiser and Its Mathematical Theory,
-<i>Proceedings of the Royal Society of Edinburgh</i>, vol. 39,
-1918-19, pp. 234-242.</p>
-
-<p class="neg-indent"><span class="smcap">Montgomery, H. C.</span>, An
-Optical Harmonic Analyzer, <i>Bell System Technical Journal</i>,
-vol. 17, no. 3, July 1938, pp. 406-415.</p>
-
-<p class="neg-indent"><span class="smcap">Raymond, W. J.</span>, An
-Harmonic Synthesizer Having Components of Incommensurable Period and
-Any Desired Decrement, <i>Physical Review</i>, vol. 11, series 2, 1918,
-pp. 479-481.</p>
-
-<p class="neg-indent"><span class="smcap">Robertson, J. M.</span>,
-A Simple Harmonic Continuous Calculating Machine, <i>London,
-Edinburgh and Dublin Philosophical Magazine and Journal of
-Science</i>, vol. 13, 1932, pp. 413-419.</p>
-
-<p class="neg-indent"><span class="smcap">Somerville, J. M.</span>,
-Harmonic Synthesizer for Demonstrating and Studying Complex Wave Forms,
-<i>Journal of Scientific Instruments</i>, vol. 21, Oct. 1944,
-pp. 174-177.</p>
-
-<p class="neg-indent"><span class="smcap">Straiton, A. W.</span>,
-and <span class="smcap">G. K. Terhune</span>, Harmonic Analysis by
-Photographic Method, <i>Journal of Applied Physics</i>, vol. 14, 1943,
-pp. 535-536.</p>
-
-<p class="neg-indent"><span class="smcap">Wegel, R. L.</span>, and
-<span class="smcap">C. R. Moore</span>, An Electrical Frequency
-Analyzer, <i>Bell System Technical Journal</i>, vol. 3, 1924,
-pp. 299-323.</p>
-</div>
-
-<h3>NETWORK ANALYZERS</h3>
-
-<div class="blockquot">
-<p>A third branch of the analogue calculating machine is the network
-analyzer. To solve problems, this machine uses the laws governing a
-network of electrical circuits. For example, an electric power company
-with a system of power lines over hundreds of miles may have a problem
-about electrical power: will an accident or a sudden demand cause a
-<span class="pagenum" id="Page_243">[Pg 243]</span>
-breakdown anywhere in the system? In the General Electric Company
-in Schenectady, N. Y., there is a machine called the A.C. Network
-Analyzer. All the properties of the power company’s network of lines
-can be fed on a small scale into the analyzer. Certain dials are turned
-and certain plugwires are connected. Then various kinds of “accidents”
-and “sudden demands” are fed into the machine, and the response of the
-system is noted. The answers given by the machine are multiplied by the
-proper scale factor, and in this way the problem of the power company
-is solved.</p>
-
-<p>There are two kinds of problems that network analyzers are built to
-solve: the steady state conditions and the transient conditions. For
-example, you may not overload a fuse with an electric iron when it is
-plugged in and being used, but as you pull out the cord, you may blow
-the fuse: the steady state does not overstrain the system, but the
-transient does.</p>
-
-<p>Some articles on network analyzers are:</p>
-
-<p class="neg-indent"><span class="smcap">Enns, W. E.</span>,
-A New Simple Calculator of Load Flow in A.C. Networks, <i>Transactions
-of the American Institute of Electrical Engineers</i>,
-vol. 62, 1943, pp. 786-790.</p>
-
-<p class="neg-indent"><span class="smcap">Hazen, H. L.</span>, and
-others, <i>The M.I.T. Network Analyzer</i>, Cambridge, Mass.:
-Massachusetts Institute of Technology, Department of Electrical
-Engineering, Serial No. 69, Apr. 1931.</p>
-
-<p class="neg-indent"><span class="smcap">Kuehni, H. P.</span>, and
-<span class="smcap">R. G. Lorraine</span>, A New A.C. Network Analyzer,
-<i>Transactions of the American Institute of Electrical
-Engineers</i>, vol. 57, 1938, pp. 67-73.</p>
-
-<p class="neg-indent"><span class="smcap">Parker, W. W.</span>, Dual
-A.C. Network Calculator, <i>Electrical Engineering</i>, May 1945,
-pp. 182-183.</p>
-
-<p class="neg-indent"><span class="smcap">Parker, W. W.</span>,
-The Modern A.C. Network Calculator, <i>Transactions of the American
-Institute of Electrical Engineers</i>, vol. 60, Nov. 1941,
-pp. 977-982.</p>
-
-<p class="neg-indent"><span class="smcap">Peterson, H. A.</span>,
-An Electric Circuit Transient Analyzer, <i>General Electric Review</i>,
-Sept. 1939, pp. 394-400.</p>
-
-<p class="neg-indent"><span class="smcap">Varney, R. N.</span>,
-An All-Electric Integrator for Solving Differential Equations, <i>Review
-of Scientific Instruments</i>, vol. 13, Jan. 1942, pp. 10-16.</p>
-
-<p>Some of the articles on applications of network analyzers to various
-problems are:</p>
-
-<p class="neg-indent"><span class="smcap">Kron, Gabriel</span>,
-Equivalent Circuits of the Elastic Field, <i>Journal of Applied
-Mechanics</i>, vol. A11, Sept. 1944, pp. 146-161.</p>
-
-<p class="neg-indent"><span class="smcap">Kron, Gabriel</span>,
-Tensorial Analysis and Equivalent Circuits of Elastic Structures,
-<i>Journal of the Franklin Institute</i>, vol. 238, Dec. 1944, pp.
-399-442.</p>
-
-<p class="neg-indent"><span class="smcap">Kron, Gabriel</span>,
-Numerical Solution of Ordinary and Partial Differential Equations
-by Means of Equivalent Circuits, <i>Journal of Applied Physics</i>,
-vol. 16, 1945, pp. 172-186.
-
-<span class="pagenum" id="Page_244">[Pg 244]</span></p>
-
-<p class="neg-indent"><span class="smcap">Kron, Gabriel</span>,
-Electric Circuit Models for the Vibration Spectrum of Polyatomic
-Molecules, <i>Journal of Chemical Physics</i>, vol. 14, no. 1, Jan.
-1946, pp. 19-31.</p>
-
-<p class="neg-indent"><span class="smcap">Kron, G.</span>, and
-<span class="smcap">G. K. Carter</span>, A.C. Network Analyzer Study
-of the Schrödinger Equation, <i>Physical Review</i>, vol. 67, 1945,
-pp. 44-49.</p>
-
-<p class="neg-indent"><span class="smcap">Kron, G.</span>, and <span
-class="smcap">G. K. Carter</span>, Network Analyzer Tests of Equivalent
-Circuits of Vibrating Polyatomic Molecules, <i>Journal of Chemical
-Physics</i>, vol. 14, no. 1, Jan. 1946, pp. 32-34.</p>
-
-<p class="neg-indent"><span class="smcap">Peterson, H. A.</span>,
-and <span class="smcap">C. Concordia</span>, Analyzers for Use in
-Engineering and Scientific Problems, <i>General Electric Review</i>,
-vol. 48, no. 9, Sept. 1945, pp. 29-37.</p>
-</div>
-
-<h3>MACHINES FOR SOLVING<br /> ALGEBRAIC EQUATIONS</h3>
-
-<div class="blockquot">
-<p>Another branch of the analogue calculating machine is a type of machine
-that will solve various kinds of algebraic equations (<a href="#SUPPL_2">see Supplement 2</a>).
-A list of some articles follows. The article by Mallock describes
-a machine for solving up to 10 linear simultaneous equations in 10
-unknowns, and the article by Wilbur, a machine for solving up to 9.</p>
-
-<p class="neg-indent"><span class="smcap">Dietzold, Robert L.</span>,
-The Isograph—A Mechanical Root-Finder, <i>Bell Laboratories
-Record</i>, vol. 16, no. 4, Dec. 1937, pp. 130-134.</p>
-
-<p class="neg-indent"><span class="smcap">Duncan, W. J.</span>,
-Some Devices for the Solution of Large Sets of Simultaneous Linear
-Equations, <i>London, Edinburgh, and Dublin Philosophical
-Magazine and Journal of Science</i>, vol. 35, series 7, 1944,
-pp. 660-670.</p>
-
-<p class="neg-indent"><span class="smcap">Frame, J. Sutherland</span>,
-Machines for Solving Algebraic Equations, <i>Mathematical Tables
-and Other Aids to Computation</i>, vol. 1, no. 9, Jan. 1945,
-pp. 337-353.</p>
-
-<p class="neg-indent"><span class="smcap">Hart, H. C.</span>, and
-<span class="smcap">Irven Travis</span>, Mechanical Solution of Algebraic
-Equations, <i>Journal of the Franklin Institute</i>, vol. 225,
-Jan. 1938, pp. 63-72.</p>
-
-<p class="neg-indent"><span class="smcap">Herr, D. L.</span>, and
-<span class="smcap">R. S. Graham</span>, An Electrical Algebraic Equation
-Solver, <i>Review of Scientific Instruments</i>, vol. 9,
-Oct. 1938, pp. 310-315.</p>
-
-<p class="neg-indent"><span class="smcap">Mallock, R. R. M.</span>,
-An Electrical Calculating Machine, <i>Proceedings of the Royal
-Society</i>, series A, vol. 140, 1933, pp. 457-483.</p>
-
-<p class="neg-indent"><span class="smcap">Mercner, R. O.</span>,
-The Mechanism of the Isograph, <i>Bell Laboratories Record</i>,
-vol. 16, no. 4, Dec. 1937, pp. 135-140.</p>
-
-<p class="neg-indent"><span class="smcap">Stibitz, George R.</span>,
-Electric Root-finder, <i>Mathematical Tables and Other Aids to
-Computation</i>, vol. 3, no. 24, Oct. 1948, pp. 328-329.</p>
-
-<p class="neg-indent"><span class="smcap">Wilbur, J. B.</span>,
-The Mechanical Solution of Simultaneous Equations, <i>Journal of the
-Franklin Institute</i>, vol. 222, Dec. 1936, pp. 715-724.</p>
-</div>
-
-<h3>ANALOGUE MACHINES—<br />MISCELLANEOUS</h3>
-
-<div class="blockquot">
-<p>Some articles referring to various other kinds of analogue machines
-and their applications are here listed together:
-<span class="pagenum" id="Page_245">[Pg 245]</span></p>
-
-<p class="neg-indent"><span class="smcap">Bush, V.</span>,
-<span class="smcap">F. D. Gage</span>, and <span class="smcap">R. R.
-Stewart</span>, A Continuous Integraph, <i>Journal of the
-Franklin Institute</i>, vol. 203, 1927, pp. 63-84.</p>
-
-<p class="neg-indent"><span class="smcap">Gray, T. S.</span>, A
-Photo-Electric Integraph, <i>Journal of the Franklin Institute</i>,
-vol. 212, 1931, pp. 77-102.</p>
-
-<p class="neg-indent"><span class="smcap">Hazen, H. L.</span>,
-<span class="smcap">G. S. Brown</span>, and <span class="smcap">W. R.
-Hedeman</span>, The Cinema Integraph: A Machine for Evaluating a
-Parametric Product Integral (two parts and appendix), <i>Journal of the
-Franklin Institute</i>, vol. 230, July 1940, pp. 19-44, and Aug.
-1940, pp. 183-205.</p>
-
-<p class="neg-indent"><span class="smcap">McCann, G. D.</span>, and
-<span class="smcap">H. E. Criner</span>, Mechanical Problems Solved
-Electrically, <i>Westinghouse Engineer</i>, vol. 6, no. 2, March 1946,
-pp. 49-56.</p>
-
-<p class="neg-indent"><span class="smcap">Myers, D. M.</span>,
-An Integraph for the Solution of Differential Equations of the
-Second-Order, <i>Journal of Scientific Instruments</i>, vol. 16, 1939,
-pp. 209-222.</p>
-
-<p class="neg-indent"><span class="smcap">Pekeris, C. L.</span>, and
-<span class="smcap">W. T. White</span>, Differentiation with the Cinema
-Integraph, <i>Journal of the Franklin Institute</i>, vol. 234,
-July 1942, pp. 17-29.</p>
-
-<p class="neg-indent"><span class="smcap">Smith, C. E.</span>, and
-<span class="smcap">E. L. Gove</span>, An Electromechanical Calculator
-for Directional-Antenna Patterns, <i>Transactions of the
-American Institute of Electrical Engineers</i>, vol. 62, 1943,
-pp. 78-82.</p>
-
-<p class="neg-indent"><span class="smcap">Yavne, R. O.</span>,
-High Accuracy Contour Cams, <i>Product Engineering</i>, vol. 19,
-part 2, Aug. 1948, 3 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Electrical
-Gun Director Demonstrated, <i>Bell Laboratories Record</i>, vol. 22,
-no. 4, Dec. 1943, pp. 157-167.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Development
-of the Electric Director, <i>Bell Laboratories Record</i>, vol. 22,
-no. 5, Jan. 1944, pp. 225-230.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>,
-Old Field Fortune Teller: Electronic Oil Pool Analyzer,
-<i>Popular Mechanics</i>, vol. 86, Sept. 1946, p. 154.</p>
-</div>
-
-<h3>HARVARD IBM AUTOMATIC<br />SEQUENCE-CONTROLLED CALCULATOR</h3>
-
-<div class="blockquot">
-<p>The basic scientific description of this machine as of
-September 1, 1945, is contained in:</p>
-
-<p class="neg-indent"><span class="smcap">Aiken, Howard H.</span>, and
-<span class="smcap">Staff of the Computation Laboratory</span>, <i>A
-Manual of Operation for the Automatic Sequence-Controlled Calculator</i>,
-Cambridge, Mass.: Harvard University Press, 1946, 561 pp.</p>
-
-<p>The machine has changed rather a good deal since Sept. 1, 1945.
-Some circuits have been removed. Other circuits have been added. The
-capacity of the machine to do problems has been greatly increased.
-The Computation Laboratory at Harvard University is cordial towards
-scientific inquiries, and some unpublished, mimeographed information is
-available at the laboratory regarding the details of these changes.</p>
-
-<p>Some shorter scientific and technical descriptions of the machine
-are contained in:
-<span class="pagenum" id="Page_246">[Pg 246]</span></p>
-
-<p class="neg-indent"><span class="smcap">Aiken, Howard H.</span>, and
-<span class="smcap">Grace M. Hopper</span>, The Automatic Sequence
-Controlled Calculator (3 parts), <i>Electrical Engineering</i>,
-vol. 65, nos. 8, 9, and 10, Aug. to Nov. 1946, p. 384 ... (21 pp.).</p>
-
-<p class="neg-indent"><span class="smcap">Bloch, Richard M.</span>,
-Mark I Calculator, <i>Proceedings of a Symposium on Large-Scale
-Digital Calculating Machinery</i>, Harvard University Press, 1948,
-pp. 23-30.</p>
-
-<p class="neg-indent"><span class="smcap">Harrison, Joseph O.,
-Jr.</span>, The Preparation of Problems for the Mark I Calculator,
-<i>Proceedings of a Symposium on Large-Scale Digital Calculating Machinery</i>,
-Harvard University Press, 1948, pp. 208-210.</p>
-
-<p class="neg-indent"><span class="smcap">International Business
-Machines Corporation</span>, <i>IBM Automatic Sequence-Controlled
-Calculator</i>, Endicott, N. Y.: International Business Machines
-Corporation, 1945, 6 pp.</p>
-
-<p>Some of the less technical articles regarding the machine are:</p>
-
-<p class="neg-indent"><span class="smcap">Genet, N.</span>,
-Got a Problem? Harvard’s Amazing New Mathematical Robot,
-<i>Scholastic</i>, vol. 45, Sept. 18, 1944, p. 35.</p>
-
-<p class="neg-indent"><span class="smcap">Torrey, V.</span>, Robot
-Mathematician Knows All the Answers, <i>Popular Science</i>, vol. 145,
-Oct. 1944, pp. 86-89....</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Giant New
-Calculator, <i>Science News Letter</i>, vol. 46, Aug. 12, 1944,
-p. 111.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>,
-Mathematical Robot Presented to Harvard, <i>Time</i>, vol. 44,
-Aug. 14, 1944, p. 72.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, World’s
-Greatest Machine for Automatic Calculation, <i>Science News Letter</i>,
-vol. 46, Aug. 19, 1944, p. 123.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Superbrain,
-<i>Nation’s Business</i>, vol. 32, Sept. 1944, p. 8.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Robot Works
-Problems Never Before Solved, <i>Popular Mechanics</i>, vol. 82,
-Oct. 1944, p. 13.</p>
-</div>
-
-<h3>ENIAC, THE ELECTRONIC NUMERIC<br />INTEGRATOR AND CALCULATOR</h3>
-
-<div class="blockquot">
-<p>There is as yet no full-scale, published scientific account of the
-Eniac. At the Ballistic Research Laboratories, Aberdeen, Md., where
-the machine now is, there are a few copies of some long mimeographed
-reports on the machine and the way it works. These were prepared by
-H. H. Goldstine and others when at the Moore School of Electrical
-Engineering, as a part of the contract under which the machine was
-constructed for the U. S. Government. It is possible that these reports
-might be consulted on request by serious students.
-<span class="pagenum" id="Page_247">[Pg 247]</span></p>
-
-<p>Some scientific descriptions of the machine and its properties
-are:</p>
-
-<p class="neg-indent"><span class="smcap">Burks, Arthur W.</span>,
-Electronic Computing Circuits of the ENIAC, <i>Proceedings of the
-Institute of Radio Engineers</i>, vol. 35, no. 8, Aug. 1947,
-pp. 756-767.</p>
-
-<p class="neg-indent"><span class="smcap">Clippinger, R. F.</span>,
-<i>A Logical Coding System Applied to the Eniac</i>, B. R. L.
-Report No. 673, Aberdeen, Md.: Ballistic Research Laboratories,
-Sept. 29, 1948, 41 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Eckert, J. Presper,
-Jr.</span>, <span class="smcap">John W. Mauchly</span>,
-<span class="smcap">Herman H. Goldstine</span>, and <span class="smcap">J. G.
-Brainerd</span>, Description of the ENIAC and Comments on Electronic
-Digital Computing Machines, Applied Mathematics Panel Report 171.2R,
-Washington, D. C.: National Defense Research Committee, Nov. 1945, 78
-pp.</p>
-
-<p class="neg-indent"><span class="smcap">Goldstine, Herman H.</span>,
-and <span class="smcap">Adele Goldstine</span>, The Electronic
-Numerical Integrator and Computer (ENIAC), <i>Mathematical Tables
-and Other Aids to Computation</i>, vol. 2, no. 15, July 1946, pp. 97-110.</p>
-
-<p class="neg-indent"><span class="smcap">Hartree, D. R.</span>,
-The ENIAC, an Electronic Computing Machine, <i>Nature</i>, vol. 158,
-Oct. 12, 1946, pp. 500-506.</p>
-
-<p class="neg-indent"><span class="smcap">Hartree, D. R.</span>,
-<i>Calculating Machines: Recent and Prospective Developments and
-Their Impact on Mathematical Physics</i>, Cambridge, England:
-The University Press, 1947, 40 pp. (Pages 14 to 27 are devoted
-to the Eniac.)</p>
-
-<p class="neg-indent"><span class="smcap">Tabor, Lewis P.</span>,
-Brief Description and Operating Characteristics of the ENIAC,
-<i>Proceedings of a Symposium on Large-Scale Digital Calculating
-Machinery</i>, Harvard University Press, 1948, pp. 31-39.</p>
-
-<p>Some of the less technical articles on Eniac are:</p>
-
-<p class="neg-indent"><span class="smcap">Rose, A.</span>, Lightning
-Strikes Mathematics: ENIAC, <i>Popular Science</i>, vol. 148,
-Apr. 1946, pp. 83-86.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Robot
-Calculator: ENIAC, All Electronic Device, <i>Business Week</i>,
-Feb. 16, 1946, p. 50 ...</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Answers
-by ENY: Electronic Numerical Integrator and Computer, ENIAC,
-<i>Newsweek</i>, vol. 27, Feb. 18, 1946, p. 76.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Adds in
-¹/₅₀₀₀ Second: Electronic Computing Machine at the University of
-Pennsylvania, <i>Science News Letter</i>, vol. 49, Feb. 23, 1946, p.
-113 ...</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, ENIAC: at
-the University of Pennsylvania, <i>Time</i>, vol. 47,
-Feb. 25, 1946, p. 90.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, It Thinks
-with Electrons; the ENIAC, <i>Popular Mechanics</i>, vol. 85, June
-1946, p. 139.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Electronic
-Calculator: ENIAC, <i>Scientific American</i>, vol. 174, June 1946,
-p. 248.</p>
-</div>
-
-<h3>BELL LABORATORIES RELAY COMPUTERS</h3>
-
-<div class="blockquot">
-<p>As yet no full-scale scientific report is available on the Bell
-Laboratories general-purpose relay computers that went to Aberdeen and
-Langley Field. However, there is some information about these and other
-Bell Laboratories relay computing machines in the following articles:
-<span class="pagenum" id="Page_248">[Pg 248]</span></p>
-
-<p class="neg-indent"><span class="smcap">Alt, Franz L.</span>,
-A Bell Telephone Laboratories’ Computing Machine (two parts),
-<i>Mathematical Tables and Other Aids to Computation</i>,
-vol. 3, no. 21, Jan. 1948, pp. 1-13, and vol. 3, no. 22,
-Apr. 1948, pp. 69-84.</p>
-
-<p class="neg-indent"><span class="smcap">Cesareo, O.</span>, The Relay
-Interpolator, <i>Bell Laboratories Record</i>, vol. 24, no. 12,
-Dec. 1946, pp. 457-460.</p>
-
-<p class="neg-indent"><span class="smcap">Juley, Joseph</span>,
-The Ballistic Computer, <i>Bell Laboratories Record</i>, vol. 25,
-no. 1, Jan. 1947, pp. 5-9.</p>
-
-<p class="neg-indent"><span class="smcap">Williams, Samuel B.</span>,
-A Relay Computer for General Application, <i>Bell Laboratories
-Record</i>, vol. 25, no. 2, Feb. 1947, pp. 49-54.</p>
-
-<p class="neg-indent"><span class="smcap">Williams, Samuel B.</span>,
-Bell Telephone Laboratories’ Relay Computing System, <i>Proceedings of
-a Symposium on Large-Scale Digital Calculating Machinery</i>,
-Harvard University Press, 1948, pp. 40-68.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Complex
-Computer Demonstrated, <i>Bell Laboratories Record</i>, vol. 19, no. 2,
-Oct. 1940, pp. v-vi.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, <i>Computer
-Mark 22 Mod. 0: Development and Description</i>, Navord Report
-No. 178-45, Washington, D. C.: Navy Department,
-Dec. 6, 1945, 225 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>,
-Relay Computer for the Army, <i>Bell Laboratories Record</i>,
-vol. 26, no. 5, May 1948, pp. 208-209.</p>
-</div>
-
-<h3>THE KALIN-BURKHART<br />LOGICAL-TRUTH CALCULATOR</h3>
-
-<div class="blockquot">
-<p>As yet there are no published references on the Kalin-Burkhart
-Logical-Truth Calculator.</p>
-
-<p>Some books covering a good deal of mathematical logic are:</p>
-
-<p class="neg-indent"><span class="smcap">Quine, W. V.</span>,
-<i>Mathematical Logic</i>, New York: W. W. Norton &amp; Co.,
-1940, 348 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Reichenbach, Hans</span>,
-<i>Elements of Symbolic Logic</i>, New York: The Macmillan Co.,
-1947, 444 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Tarski, Alfred</span>,
-<i>Introduction to Logic</i>, New York: Oxford University Press,
-1941, 239 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Woodger, J. H.</span>,
-<i>The Axiomatic Method in Biology</i>, Cambridge, England:
-The University Press, 1937, 174 pp.</p>
-
-<p>Chapter 2, <a href="#Page_18">pp. 18-52</a>, is an excellent
-and understandable summary of the concepts of mathematical logic.</p>
-
-<p>Several papers on the application of mathematical logic to the
-analysis of practical situations are:</p>
-
-<p class="neg-indent"><span class="smcap">Berkeley, Edmund C.</span>,
-Boolean Algebra (The Technique for Manipulating “And,” “Or,” “Not,” and
-Conditions) and Applications to Insurance, <i>Record of the American
-Institute of Actuaries</i>, vol. 26, Oct. 1937, pp. 373-414.</p>
-
-<p class="neg-indent"><span class="smcap">Berkeley, Edmund C.</span>,
-Conditions Affecting the Application of Symbolic Logic, <i>Journal
-of Symbolic Logic</i>, vol. 7, no. 4, Dec. 1942, pp. 160-168.</p>
-
-<p class="neg-indent"><span class="smcap">Shannon, Claude E.</span>,
-A Symbolic Analysis of Relay and Switching Circuits, <i>Transactions
-of the American Institute of Electrical Engineers</i>, vol. 57,
-1938, pp. 713-723.</p>
-
-<p>This paper has had a good deal of influence here and there on the
-development of electric circuits using relays.
-<span class="pagenum" id="Page_249">[Pg 249]</span></p>
-
-<p>The following report discusses the solution of some problems of
-mathematical logic by means of a large-scale digital calculator:</p>
-
-<p class="neg-indent"><span class="smcap">Tarski, Alfred</span>,
-<i>A Decision Method for Elementary Algebra and Geometry</i>,
-Report R-109, California: Rand Corporation, Aug. 1, 1948, 60 pp.</p>
-</div>
-
-<h3>OTHER DIGITAL MACHINES<br />FINISHED OR UNDER DEVELOPMENT</h3>
-
-<div class="blockquot">
-<p><b>The Aiken Mark II Relay Calculator</b></p>
-
-<p>The Computation Laboratory of Harvard University finished during
-1947 a second large relay calculator, called the Aiken Mark II Relay
-Calculator. This machine is alluded to briefly at the end of <a href="#CHAPTER_10">Chapter 10</a>
-and is described more fully in the following:</p>
-
-<p class="neg-indent"><span class="smcap">Campbell, Robert V. D.</span>,
-Mark II Calculator, <i>Proceedings of a Symposium on
-Large-Scale Digital Calculating Machinery</i>, Cambridge, Mass.:
-Harvard University Press, 1948, pp. 69-79.</p>
-
-<p class="neg-indent"><span class="smcap">Freeland, Stephen L.</span>,
-Inside the Biggest Man-Made Brain, <i>Popular Science</i>,
-May 1947, pp. 95-100.</p>
-
-<p class="neg-indent"><span class="smcap">Miller, Frederick G.</span>,
-Application of Printing Telegraph Equipment to Large-Scale Calculating
-Machinery, <i>Proceedings of a Symposium on Large-Scale Digital
-Calculating Machinery</i>, Cambridge, Mass.: Harvard University Press,
-1948, pp. 213-222.</p>
-
-<p class="space-above1"><b>The Edsac</b></p>
-
-<p>The Edsac is a machine under construction in England.</p>
-
-<p class="neg-indent"><span class="smcap">Wilkes, M. V.</span>,
-The Design of a Practical High-Speed Computing Machine: the EDSAC,
-<i>Proceedings of the Royal Society</i>, series A, vol. 195, 1948,
-pp. 274-279.</p>
-
-<p class="neg-indent"><span class="smcap">Wilkes, M. V.</span>, and
-<span class="smcap">W. Renwick</span>, An Ultrasonic Memory Unit for
-the EDSAC, <i>Electronic Engineering</i>, vol. 20, no. 245,
-July 1948, pp. 208-213.</p>
-
-<p class="space-above1"><b>The Edvac</b></p>
-
-<p>The Edvac is a machine under construction at the Moore School of
-Electrical Engineering, Philadelphia.</p>
-
-<p class="neg-indent"><span class="smcap">Koons, Florence</span>,
-and <span class="smcap">Samuel Lubkin</span>, Conversion of Numbers
-from Decimal to Binary Form in the EDVAC, <i>Mathematical Tables and
-Other Aids to Computation</i>, vol. 3, no. 26,
-Apr. 1949, pp. 427-431.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, EDVAC
-Replaces ENIAC, <i>The Pennsylvania Gazette</i>, Philadelphia:
-University of Pennsylvania, vol. 45, no. 8, Apr. 1947, pp. 9-10.</p>
-
-<p class="space-above1"><b>The IBM Selective-Sequence Electronic Calculator</b></p>
-
-<p>The IBM Selective-Sequence Electronic Calculator was finished and
-announced in January 1948, and is alluded to briefly at the end of
-<a href="#CHAPTER_10">Chapter 10</a>. More information about this machine
-is in the following references:
-<span class="pagenum" id="Page_250">[Pg 250]</span></p>
-
-<p class="neg-indent"><span class="smcap">Eckert, W. J.</span>,
-Electrons and Computation, <i>The Scientific Monthly</i>,
-vol. 67, no. 5, Nov. 1948, pp. 315-323.</p>
-
-<p class="neg-indent"><span class="smcap">International Business
-Machines Corporation</span>, <i>IBM Selective-Sequence Electronic
-Calculator</i>, New York: International Business Machines
-Corporation (form no. 52-3927-0), 1948, 16 pp.</p>
-
-<p class="space-above1"><b>The Raytheon Computer</b></p>
-
-<p>The Raytheon Computer is a machine under construction at the
-Raytheon Manufacturing Co., Waltham, Mass.</p>
-
-<p class="neg-indent"><span class="smcap">Bloch, R. M.</span>,
-<span class="smcap">R. V. D. Campbell</span>, and
-<span class="smcap">M. Ellis</span>, The Logical Design of the
-Raytheon Computer, <i>Mathematical Tables and Other Aids to Computation</i>,
-vol. 3, no. 24, Oct. 1948, pp. 286-295.</p>
-
-<p class="neg-indent"><span class="smcap">Bloch, R. M.</span>,
-<span class="smcap">R. V. D. Campbell</span>, and <span class="smcap">M.
-Ellis</span>, General Design Considerations for the Raytheon Computer,
-<i>Mathematical Tables and Other Aids to Computation</i>, vol.
-3, no. 24, Oct. 1948, pp. 317-323.</p>
-
-<p class="space-above1"><b>A “System of Electric Remote-Control Accounting”</b></p>
-
-<p>During the 1930’s a system using connected punch-card machinery was
-experimented with in a department store in Pittsburgh. The purpose of
-the system was automatic accounting and analysis of sales. This system
-is described in:</p>
-
-<p class="neg-indent"><span class="smcap">Woodruff, L. F.</span>,
-A System of Electric Remote-Control Accounting, <i>Transactions of
-the American Institute of Electrical Engineers</i>, vol. 57,
-Feb. 1938, pp. 78-87.</p>
-
-<p class="space-above1"><b>The Univac</b></p>
-
-<p>The Univac is a machine under construction at the Eckert-Mauchly
-Computer Corporation, Philadelphia. A similar but smaller digital
-computer called the Binac is also being developed.</p>
-
-<p class="neg-indent"><span class="smcap">Eckert-Mauchly Computer
-Corporation</span>, <i>The Univac System</i>, Philadelphia:
-Eckert-Mauchly Computer Corp., 1948, 8 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Electronic Control Co.</span>
-(now <span class="smcap">Eckert-Mauchly Computer Corp.</span>),
-<i>A Tentative Instruction Code for a Statistical Edvac</i>,
-Philadelphia: Electronic Control Co. (now Eckert-Mauchly Computer Corp.),
-May 7, 1947, 19 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Snyder, Frances E.</span>,
-and <span class="smcap">Hubert M. Livingston</span>, Coding of a
-Laplace Boundary Value Problem for the UNIVAC, <i>Mathematical Tables
-and Other Aids to Computation</i>, vol. 3, no. 25, Jan. 1949,
-pp. 341-350.</p>
-
-<p class="space-above1"><b>The Zuse Computer</b></p>
-
-<p>The Zuse Computer is a small digital computer constructed in
-Germany.</p>
-
-<p class="neg-indent"><span class="smcap">Lyndon, Roger C.</span>,
-The Zuse Computer, <i>Mathematical Tables and Other Aids to
-Computation</i>, vol. 2, no. 20, Oct. 1947, pp. 355-359.</p>
-</div>
-
-<p><span class="pagenum" id="Page_251">[Pg 251]</span></p>
-
-<h3>THE DESIGN OF DIGITAL MACHINES</h3>
-
-<div class="blockquot">
-<p>Following are a number of references on various aspects of the
-design of digital computing machines:</p>
-
-<p class="space-above1"><b>Organization</b></p>
-
-<p class="neg-indent"><span class="smcap">Burks, Arthur W.</span>,
-Super-Electronic Computing Machine, <i>Electronic Industries</i>,
-vol. 5, no. 7, July 1946, p. 62.</p>
-
-<p class="neg-indent"><span class="smcap">Burks, Arthur W.</span>,
-<span class="smcap">Herman H. Goldstine</span> and
-<span class="smcap">John von Neumann</span>, <i>Preliminary Discussion
-of the Logical Design of an Electronic Computing Instrument</i>,
-Princeton, N. J.: Institute for Advanced Study, 2nd edition,
-Sept. 1947, 42 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Eckert, J. Presper,
-Jr.</span>, <span class="smcap">John W. Mauchly</span>, and
-<span class="smcap">J. R. Weiner</span>, An Octal System Automatic Computer,
-<i>Electrical Engineering</i>, vol. 68, no. 4, Apr. 1949, p. 335.</p>
-
-<p class="neg-indent"><span class="smcap">Forrester, Jay W.</span>,
-<span class="smcap">Warren S. Loud</span>, <span class="smcap">Robert
-R. Everett</span>, and <span class="smcap">David R. Brown</span>,
-<i>Lectures by Project Whirlwind Staff on Electronic Digital
-Computation</i>, Cambridge, Mass.: Massachusetts Institute of
-Technology, Servo-mechanisms Laboratory, Mar. and Apr. 1947, 149 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Lubkin, Samuel</span>,
-Decimal Point Location in Computing Machines, <i>Mathematical Tables
-and Other Aids to Computation</i>, vol. 3, no. 21,
-Jan. 1948, pp. 44-50.</p>
-
-<p class="neg-indent"><span class="smcap">Patterson, George
-W.</span>, editor, and others, <i>Theory and Techniques for Design
-of Electronic Digital Computers</i> (subtitle: <i>Lectures Given
-at the Moore School 8 July 1946-31 August 1946</i>),
-Philadelphia: The University of Pennsylvania, Moore School of
-Electrical Engineering, vol. 1, lectures 1-10, Sept. 10, 1947,
-161 pp.; vol. 2, lectures 11-21, Nov. 1, 1947, 173 pp.;
-vol. 3 and 4 in preparation.</p>
-
-<p class="neg-indent"><span class="smcap">Stibitz, George R.</span>,
-<i>Relay Computers</i>, Applied Mathematics Panel Report 171.1R,
-Washington, D. C.: National Defense Research Council,
-Feb. 1945, 83 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Stibitz, George R.</span>,
-Should Automatic Computers be Large or Small? <i>Mathematical Tables
-and Other Aids to Computation</i>, vol. 2, no. 20, Oct. 1947,
-pp. 362-364.</p>
-
-<p class="neg-indent"><span class="smcap">Stibitz, George R.</span>,
-The Organization of Large-Scale Calculating Machinery,
-<i>Proceedings of a Symposium on Large-Scale Digital
-Calculating Machinery</i>, Cambridge, Mass.:
-Harvard University Press, 1948, pp. 91-100.</p>
-
-<p class="neg-indent"><span class="smcap">Stibitz, George R.</span>,
-A New Class of Computing Aids, <i>Mathematical Tables and Other Aids
-to Computation</i>, vol. 3, no. 23, July 1948, pp. 217-221.</p>
-
-<p class="space-above1"><b>Input and Output Devices</b></p>
-
-<p class="neg-indent"><span class="smcap">Alexander, Samuel N.</span>,
-Input and Output Devices for Electronic Digital Calculating Machinery,
-<i>Proceedings of a Symposium on Large-Scale Digital Calculating
-Machinery</i>, Cambridge, Mass.: Harvard University Press, 1948,
-pp. 248-253.
-<span class="pagenum" id="Page_252">[Pg 252]</span></p>
-
-<p class="neg-indent"><span class="smcap">Fuller, Harrison W.</span>,
-The Numeroscope, <i>Proceedings of a Symposium on Large-Scale
-Digital Calculating Machinery</i>, Cambridge, Mass.:
-Harvard University Press, 1948, pp. 238-247.</p>
-
-<p class="neg-indent"><span class="smcap">O’neal, R. D.</span>,
-Photographic Methods for Handling Input and Output Data,
-<i>Proceedings of a Symposium on Large-Scale Digital Calculating
-Machinery</i>, Cambridge, Mass.: Harvard University Press,
-1948, pp. 260-266.</p>
-
-<p class="neg-indent"><span class="smcap">Tyler, Arthur W.</span>,
-Optical and Photographic Storage Techniques, <i>Proceedings of a
-Symposium on Large-Scale Digital Calculating Machinery</i>,
-Cambridge, Mass.: Harvard University Press, 1948, pp. 146-150.</p>
-
-<p class="neg-indent"><span class="smcap">Zworykin, V. K.</span>,
-<span class="smcap">L. E. Flory</span>, and <span class="smcap">W. S.
-Pike</span>, Letter-Reading Machine, <i>Electronics</i>, vol. 22,
-no. 6, June 1949, pp. 80-86.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>,
-Letter-Printing Cathode-Ray Tube, <i>Electronics</i>, vol. 22,
-no. 6, June 1949, pp. 160-162.</p>
-
-<p class="space-above1"><b>Storage Devices</b></p>
-
-<p class="neg-indent"><span class="smcap">Brillouin, Leon N.</span>,
-Electromagnetic Delay Lines, <i>Proceedings of a Symposium on
-Large-Scale Digital Calculating Machinery</i>, Cambridge, Mass.:
-Harvard University Press, 1948, pp. 110-124.</p>
-
-<p class="neg-indent"><span class="smcap">Forrester, Jay W.</span>,
-High-Speed Electrostatic Storage, <i>Proceedings of a Symposium on
-Large-Scale Digital Calculating Machinery</i>, Cambridge, Mass.:
-Harvard University Press, 1948, pp. 125-129.</p>
-
-<p class="neg-indent"><span class="smcap">Haeff, Andrew V.</span>,
-The Memory Tube and its Application to Electronic Computation,
-<i>Mathematical Tables and Other Aids to Computation</i>,
-vol. 3, no. 24, Oct. 1948, pp. 281-286.</p>
-
-<p class="neg-indent"><span class="smcap">Kornei, Otto</span>, Survey
-of Magnetic Recording, <i>Proceedings of a Symposium on Large-Scale
-Digital Calculating Machinery</i>, Cambridge, Mass.:
-Harvard University Press, 1948, pp. 223-237.</p>
-
-<p class="neg-indent"><span class="smcap">Moore, Benjamin L.</span>,
-Magnetic and Phosphor Coated Discs, <i>Proceedings of a Symposium
-on Large-Scale Digital Calculating Machinery</i>,
-Cambridge, Mass.: Harvard University Press, 1948,
-pp. 130-132.</p>
-
-<p class="neg-indent"><span class="smcap">Rajchman, Jan A.</span>,
-The Selectron—A Tube for Selective Electrostatic Storage,
-<i>Mathematical Tables and Other Aids to Computation</i>,
-vol. 2, no. 20, Oct. 1947, pp. 359-361 and frontispiece.</p>
-
-<p class="neg-indent"><span class="smcap">Sharpless, T. Kite</span>,
-Mercury Delay Lines as a Memory Unit, <i>Proceedings of a Symposium
-on Large-Scale Digital Calculating Machinery</i>, Cambridge,
-Mass.: Harvard University Press, 1948, pp. 103-109.</p>
-
-<p class="neg-indent"><span class="smcap">Sheppard, C. Bradford</span>,
-Transfer Between External and Internal Memory, <i>Proceedings of
-a Symposium on Large-Scale Digital Calculating Machinery</i>,
-Cambridge, Mass.: Harvard University Press, 1948, pp. 267-273.</p>
-
-<p class="space-above1"><b>Programming or Coding</b></p>
-
-<p class="neg-indent"><span class="smcap">Everett, Robert R.</span>,
-<i>Digital Computing Machine Logic</i> (memorandum M-63),
-Cambridge, Mass.: Massachusetts Institute of Technology,
-Servo-mechanisms Laboratory, Mar. 19, 1947, 48 pp.
-<span class="pagenum" id="Page_253">[Pg 253]</span></p>
-
-<p class="neg-indent"><span class="smcap">Goldstine, Herman H.</span>,
-and <span class="smcap">John von Neumann</span>, <i>Planning and
-Coding of Problems for an Electronic Computing Instrument</i>,
-Princeton, N. J.: Institute for Advanced Study, 1947, 69 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Goldstine, Herman H.</span>,
-and <span class="smcap">John von Neumann</span>, <i>Planning and
-Coding of Problems for an Electronic Computing Instrument</i>,
-Princeton, N. J.: Institute for Advanced Study, part 2, vol. 3,
-1948, 23 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Mauchly, John W.</span>,
-Preparation of Problems for Edvac-Type Machines, <i>Proceedings of a
-Symposium on Large-Scale Digital Calculating Machinery</i>,
-Cambridge, Mass.: Harvard University Press, 1948, pp. 203-207.</p>
-</div>
-
-<h3>DIGITAL MACHINES—<br />MISCELLANEOUS</h3>
-
-<div class="blockquot">
-<p>Many of the following articles are nontechnical and contain much
-interesting information about machines that think:</p>
-
-<p class="neg-indent"><span class="smcap">Alt, Franz L.</span>,
-New High-Speed Computing Devices, <i>The American Statistician</i>,
-vol. 1, no. 1, Aug. 1947, pp. 14-15.</p>
-
-<p class="neg-indent"><span class="smcap">Bush, Vannevar</span>,
-As We May Think, <i>Atlantic Monthly</i>, July 1945, pp. 101-108.</p>
-
-<p class="neg-indent"><span class="smcap">Condon, Edward U.</span>,
-<i>The Electronic Brain Means a Better Future for You</i>
-(broadcast), Columbia Broadcasting System, Jan. 4, 1948.</p>
-
-<p class="neg-indent"><span class="smcap">Davis, Harry M.</span>,
-Mathematical Machines, <i>Scientific American</i>, vol. 180, no. 4,
-Apr. 1949, pp. 29-39.</p>
-
-<p class="neg-indent"><span class="smcap">Lagemann, John K.</span>,
-It All Adds Up, <i>Collier’s Magazine</i>, May 31, 1947,
-pp. 22-23 ...</p>
-
-<p class="neg-indent"><span class="smcap">Locke, E. L.</span>,
-Modern Calculators, <i>Astounding Science Fiction</i>, vol. 52,
-no. 5, Jan. 1949, pp. 87-106.</p>
-
-<p class="neg-indent"><span class="smcap">MacLaughlan, Lorne</span>,
-Electrical Mathematicians, <i>Astounding Science Fiction</i>, vol. 53,
-no. 3, May 1949, pp. 93-108.</p>
-
-<p class="neg-indent"><span class="smcap">Mann, Martin</span>, Want to
-Buy a Brain? <i>Popular Science</i>, vol. 154, no. 5, May 1949,
-pp. 148-152.</p>
-
-<p class="neg-indent"><span class="smcap">Newman, James R.</span>,
-Custom-Built Genius, <i>New Republic</i>, June 23, 1947, pp. 14-18.</p>
-
-<p class="neg-indent"><span class="smcap">Pfeiffer, John E.</span>,
-The Machine That Plays Gin Rummy, <i>Science Illustrated</i>, vol. 4,
-no. 3, Mar. 1949, pp. 46-48 ...</p>
-
-<p class="neg-indent"><span class="smcap">Ridenour, Louis N.</span>,
-Mechanical Brains, <i>Fortune</i>, vol. 39, no. 5, May 1949,
-pp. 108-118.</p>
-
-<p class="neg-indent"><span class="smcap">Tumbleson, Robert C.</span>,
-Calculating Machines, <i>Federal Science Progress</i>, June 1947,
-pp. 3-7.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>,
-Almost Human, <i>Home Office News</i>, Newark, N. J.:
-Prudential Insurance Company of America, Feb. 1947, p. 8.</p>
-</div>
-
-<h3>APPLICATIONS OF DIGITAL MACHINES</h3>
-
-<div class="blockquot">
-<p>Some of the problems that mechanical brains can solve, some of the
-methods for controlling them to solve problems, and some of the
-<span class="pagenum" id="Page_254">[Pg 254]</span>
-implications of mechanical brains for future problems are covered in
-the following references:</p>
-
-<p class="space-above1"><b>Solving Problems</b></p>
-
-<p class="neg-indent"><span class="smcap">Berkeley, Edmund C.</span>,
-Electronic Machinery for Handling Information, and its
-Uses in Insurance, <i>Transactions of the Actuarial Society of
-America</i>, vol. 48, May 1947, pp. 36-52.</p>
-
-<p class="neg-indent"><span class="smcap">Berkeley, Edmund C.</span>,
-Electronic Sequence Controlled Calculating Machinery and Applications
-in Insurance, <i>Proceedings of 1947 Annual Conference, Life
-Office Management Association</i>, New York: Life Office Management
-Association, 1947, pp. 116-129.</p>
-
-<p class="neg-indent"><span class="smcap">Curry, Haskell B.</span>,
-and <span class="smcap">Willa A. Wyatt</span>, <i>A Study of Inverse
-Interpolation of the Eniac</i>, B. R. L. Report No. 615,
-Aberdeen, Md.: Ballistic Research Laboratories, Aug. 19,
-1946, 100 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Harrison, Joseph O.,
-Jr.</span>, and <span class="smcap">Helen Malone</span>, Piecewise
-Polynomial Approximation for Large-Scale Digital Calculators,
-<i>Mathematical Tables and Other Aids to Computation</i>,
-vol. 3, no. 26, Apr. 1949, pp. 400-407.</p>
-
-<p class="neg-indent"><span class="smcap">Hoffleit, Dorrit</span>,
-A Comparison of Various Computing Machines Used in Reduction of
-Doppler Observations, <i>Mathematical Tables and Other Aids to
-Computation</i>, vol. 3, no. 25, Jan. 1949, pp. 373-377.</p>
-
-<p class="neg-indent"><span class="smcap">Leontief, Wassily W.</span>,
-Computational Problems Arising in Connection with Economic Analysis of
-Interindustrial Relationships, <i>Proceedings of a Symposium on
-Large-Scale Digital Calculating Machinery</i>, Cambridge, Mass.:
-Harvard University Press, 1948, pp. 169-175.</p>
-
-<p class="neg-indent"><span class="smcap">Lotkin, Max</span>,
-<i>Inversion on the Eniac Using Osculatory Interpolation</i>, B.
-R. L. Report No. 632, Aberdeen, Md.: Ballistic Research Laboratories,
-July 15, 1947, 42 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Lowan, Arnold N.</span>,
-The Computation Laboratory of the National Bureau of Standards,
-<i>Scripta Mathematica</i>, vol. 15, no. 1, Mar. 1949,
-pp. 33-63.</p>
-
-<p class="neg-indent"><span class="smcap">Matz, Adolph</span>,
-Electronics in Accounting, <i>Accounting Review</i>, vol. 21,
-no. 4, Oct. 1946, pp. 371-379.</p>
-
-<p class="neg-indent"><span class="smcap">McPherson, James L.</span>,
-Applications of High-Speed Computing Machines to Statistical Work,
-<i>Mathematical Tables and Other Aids to Computation</i>,
-vol. 3, no. 22, Apr. 1948, pp. 121-126.</p>
-
-<p class="neg-indent"><span class="smcap">Mitchell, Herbert F.,
-Jr.</span>, Inversion of a Matrix of Order 38, <i>Mathematical Tables
-and Other Aids to Computation</i>, vol. 3, no. 23, July 1948,
-pp. 161-166.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>,
-Revolutionizing the Office, <i>Business Week</i>, May 28, 1949,
-no. 1030, pp. 65-72.</p>
-
-<p class="space-above1"><b>Speech</b></p>
-
-<p>Some of the possibilities of machines dealing with voice and
-speech are indicated in:
-<span class="pagenum" id="Page_255">[Pg 255]</span></p>
-
-<p class="neg-indent"><span class="smcap">Dudley, Homer</span>,
-<span class="smcap">R. R. Riesz</span>, and <span class="smcap">S. S. A.
-Watkins</span>, A Synthetic Speaker, <i>Journal of the Franklin
-Institute</i>, vol. 227, June 1939, pp. 739-764.</p>
-
-<p>This is an article on the <i>Voder</i>, which is an abbreviation
-of <i>V</i>oice <i>O</i>peration <i>De</i>monstrator. The machine was
-exhibited at the New York World’s Fair, 1939.</p>
-
-<p class="neg-indent"><span class="smcap">Dudley, Homer</span>,
-The Vocoder, <i>Bell Laboratories Record</i>, vol. 18, no. 4,
-Dec. 1939, pp. 122-126.</p>
-
-<p>This is a more general type of machine than the Voder. The
-Vocoder is both an analyzer and synthesizer of human speech.</p>
-
-<p class="neg-indent"><span class="smcap">Potter, Ralph K.</span>,
-<span class="smcap">George A. Kopp</span>, and
-<span class="smcap">Harriet C. Green</span>, <i>Visible Speech</i>,
-New York: D. Van Nostrand Co., 1947, 441 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Pedro the
-Voder: A Machine that Talks, <i>Bell Laboratories Record</i>, vol. 17,
-no. 6, Feb. 1939, pp. 170-171.</p>
-
-<p class="space-above1"><b>Weather</b></p>
-
-<p>Some of the possibilities of machines dealing with weather
-information are covered in:</p>
-
-<p class="neg-indent"><span class="smcap">Lagemann, John K.</span>,
-Making Weather to Order, <i>New York Herald Tribune: This Week</i>,
-Feb. 23, 1947.</p>
-
-<p class="neg-indent"><span class="smcap">Shalett, Sidney</span>,
-Electronics to Aid Weather Figuring, <i>The New York Times</i>,
-Jan. 11, 1946.</p>
-
-<p class="neg-indent"><span class="smcap">Zworykin, V. K.</span>,
-<i>Outline of Weather Proposal</i>, Princeton, N. J.: Radio
-Corporation of America Research Laboratories, Oct. 1945, 11 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>, Weather
-Under Control, <i>Fortune</i>, Feb. 1948, pp. 106-111 ...</p>
-
-<p class="space-above1"><b>The Robot Machine</b></p>
-
-<p class="neg-indent"><span class="smcap">Čapek, Karel</span>,
-<i>R. U. R.</i> (translated from the Czech by Paul Selver),
-New York: Doubleday, Page &amp; Co., 1923.</p>
-
-<p class="neg-indent"><span class="smcap">Lagemann, John K.</span>,
-From Piggly Wiggly to Keedoozle, <i>Collier’s Magazine</i>, vol. 122,
-no. 18, Oct. 30, 1948, pp. 20-21 ...</p>
-
-<p class="neg-indent"><span class="smcap">Leaver, E. W.</span>,
-and <span class="smcap">J. J. Brown</span>, Machines Without Men,
-<i>Fortune</i>, vol. 34, no. 5, Nov. 1946, pp. 165 ...</p>
-
-<p class="neg-indent"><span class="smcap">Pease, M. C.</span>, Devious
-Weapon, <i>Astounding Science Fiction</i>, vol. 53, no. 2,
-Apr. 1949, pp. 34-43.</p>
-
-<p class="neg-indent"><span class="smcap">Shannon, Claude E.</span>,
-<i>Programming a Computer for Playing Chess</i>, Bell Telephone
-Laboratories, Oct. 8, 1948, 34 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Shelley, Mary W.</span>,
-<i>Frankenstein</i> (in Everyman’s Library, No. 616), New York: E. P.
-Dutton &amp; Co., last reprinted 1945, 242 pp.</p>
-
-<p class="neg-indent"><span class="smcap">Spilhaus, Athelstan</span>,
-Let Robot Work for You, <i>The American Magazine</i>, Dec. 1948,
-p. 47 ...</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>,
-Another New Product for Robot Salesmen, <i>Modern Industry</i>,
-vol. 13, no. 2, Feb. 15, 1947.</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>,
-The Automatic Factory, <i>Fortune</i>, vol. 34, no. 5,
-Nov. 1946, p. 160 ...</p>
-
-<p class="neg-indent"><span class="smcap">Anonymous</span>,
-Machines Predict What Happens in Your Plant, <i>Business Week</i>,
-Sept. 25, 1948, pp. 68-69 ...</p>
-</div>
-
-<p><span class="pagenum" id="Page_256">[Pg 256]</span></p>
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_257">[Pg 257]</span></p>
-<h2 class="nobreak">NAME INDEX</h2>
-</div>
-
-<p class="blockquot"><i><big>Note:</big> This list of persons mentioned
-in the text includes names of fictional characters. The subject index,
-which follows, includes all other names.</i></p>
-
-<ul class="index">
-<li class="isub1">Aiken, Howard H., <a href="#Page_90">90-112</a>, <a href="#Page_177">177-8</a>,
-                                      <a href="#Page_232">232</a>, <a href="#Page_245">245-6</a></li>
-<li class="isub1">Alexander, Samuel N., <a href="#Page_251">251</a></li>
-<li class="isub1">Alquist, <a href="#Page_200">200</a></li>
-<li class="isub1">Alt, Franz L., <a href="#Page_142">142</a>, <a href="#Page_237">237</a>,
-                                 <a href="#Page_247">247</a>, <a href="#Page_253">253</a></li>
-<li class="isub1">Archer, R. M., <a href="#Page_241">241</a></li>
-<li class="isub1">Aristotle, <a href="#Page_152">152</a></li>
-
-<li class="ifrst">Babbage, Charles, <a href="#Page_89">89</a></li>
-<li class="isub1">Baehne, G. Walter, <a href="#Page_232">232</a></li>
-<li class="isub1">Bailey, C. F., <a href="#Page_237">237</a></li>
-<li class="isub1">Barcroft, Joseph, <a href="#Page_229">229</a></li>
-<li class="isub1">Beach, Frank A., <a href="#Page_229">229</a></li>
-<li class="isub1">Beard, R. E., <a href="#Page_88">88</a>, <a href="#Page_240">240</a></li>
-<li class="isub1">Berkeley, Edmund C., <a href="#Page_233">233</a>, <a href="#Page_248">248</a>,
-                                       <a href="#Page_254">254</a></li>
-<li class="isub1">Berry, R. J. A., <a href="#Page_229">229</a></li>
-<li class="isub1">Berry, T. M., <a href="#Page_240">240</a></li>
-<li class="isub1">Bloch, Richard M., <a href="#Page_246">246</a>, <a href="#Page_250">250</a></li>
-<li class="isub1">Bloomfield, Leonard, <a href="#Page_231">231</a></li>
-<li class="isub1">Bodmer, Frederick, <a href="#Page_231">231</a></li>
-<li class="isub1">Boelter, L. M. K., <a href="#Page_240">240</a></li>
-<li class="isub1">Boole, George, <a href="#Page_152">152</a></li>
-<li class="isub1">Boring, Edwin G., <a href="#Page_229">229</a></li>
-<li class="isub1">Bower, E. C., <a href="#Page_237">237</a></li>
-<li class="isub1">Brainerd, J. G., <a href="#Page_247">247</a></li>
-<li class="isub1">Brillouin, Leon N., <a href="#Page_252">252</a></li>
-<li class="isub1">Brown, David R., <a href="#Page_251">251</a></li>
-<li class="isub1">Brown, G. S., <a href="#Page_245">245</a></li>
-<li class="isub1">Brown, J. J., <a href="#Page_255">255</a></li>
-<li class="isub1">Brown, S. L., <a href="#Page_241">241-2</a></li>
-<li class="isub1">Buckingham, R. A., <a href="#Page_240">240</a></li>
-<li class="isub1">Burkhart, William, <a href="#Page_144">144</a>, <a href="#Page_155">155-6</a></li>
-<li class="isub1">Burks, Arthur W., <a href="#Page_246">246</a>, <a href="#Page_251">251</a></li>
-<li class="isub1">Bush, Vannevar, <a href="#Page_72">72</a>, <a href="#Page_74">74</a>,
-                                  <a href="#Page_239">239</a>, <a href="#Page_241">241</a>,
-                                  <a href="#Page_245">245</a>, <a href="#Page_253">253</a></li>
-
-<li class="ifrst">Caldwell, Samuel H., <a href="#Page_74">74</a>, <a href="#Page_239">239</a>, <a href="#Page_241">241</a></li>
-<li class="isub1">Campbell, Robert V. D., <a href="#Page_249">249-50</a></li>
-<li class="isub1">Čapek, Karel, <a href="#Page_199">199</a>, <a href="#Page_255">255</a></li>
-<li class="isub1">Carroll, Lewis, <a href="#Page_12">12</a></li>
-<li class="isub1">Carter, G. K., <a href="#Page_244">244</a></li>
-<li class="isub1">Cesareo, O., <a href="#Page_248">248</a></li>
-<li class="isub1">Clemence, G. M., <a href="#Page_237">237</a></li>
-<li class="isub1">Clippinger, R. F., <a href="#Page_246">246</a></li>
-<li class="isub1">Comrie, John Leslie, <a href="#Page_232">232</a></li>
-<li class="isub1">Concordia, C., <a href="#Page_244">244</a></li>
-<li class="isub1">Condon, Edward U., <a href="#Page_253">253</a></li>
-<li class="isub1">Crew, E. W., <a href="#Page_232">232</a></li>
-<li class="isub1">Criner, H. E., <a href="#Page_245">245</a></li>
-<li class="isub1">Culley, Frank L., <a href="#Page_237">237</a></li>
-<li class="isub1">Curry, Haskell B., <a href="#Page_254">254</a></li>
-
-<li class="ifrst">Davis, Harry M., <a href="#Page_253">253</a></li>
-<li class="isub1">Deming, W. Edwards, <a href="#Page_237">237</a></li>
-<li class="isub1">Dietzold, Robert L., <a href="#Page_244">244</a></li>
-<li class="isub1">Domin, Harry, <a href="#Page_199">199</a></li>
-<li class="isub1">Dudley, Homer, <a href="#Page_254">254-5</a></li>
-<li class="isub1">Duncan, W. J., <a href="#Page_244">244</a></li>
-<li class="isub1">Dunlap, Jack W., <a href="#Page_237">237</a></li>
-<li class="isub1">Dwyer, Paul S., <a href="#Page_237">237</a></li>
-<li class="isub1">Dyer, H. S., <a href="#Page_237">237</a></li>
-
-<li class="ifrst">Eckert, J. Presper, Jr., <a href="#Page_114">114</a>, <a href="#Page_178">178</a>,
-                                           <a href="#Page_247">247</a>, <a href="#Page_251">251</a></li>
-<li class="isub1">Eckert, W. J., <a href="#Page_233">233</a>, <a href="#Page_236">236-7</a>,
-                                 <a href="#Page_239">239</a>, <a href="#Page_250">250</a></li>
-<li class="isub1">Edison, Thomas A., <a href="#Page_15">15</a></li>
-<li class="isub1">Ellis, M., <a href="#Page_250">250</a></li>
-<li class="isub1">Enns, W. E., <a href="#Page_243">243</a></li>
-<li class="isub1">Everett, Robert R., <a href="#Page_251">251-2</a></li>
-
-<li class="ifrst">Feinstein, Lillian, <a href="#Page_237">237</a></li>
-<li class="isub1">Flesch, Rudolf, <a href="#Page_231">231</a></li>
-<li class="isub1">Flory, L. E., <a href="#Page_252">252</a>
-     <span class="pagenum" id="Page_258">[Pg 258]</span></li>
-
-<li class="ifrst">Forrester, Jay W., <a href="#Page_251">251-2</a></li>
-<li class="isub1">Frame, J. Sutherland, <a href="#Page_244">244</a></li>
-<li class="isub1">Frankenstein, Victor, <a href="#Page_198">198</a>, <a href="#Page_200">200</a></li>
-<li class="isub1">Franz, Shepherd I., <a href="#Page_229">229</a></li>
-<li class="isub1">Freeland, Stephen L., <a href="#Page_249">249</a></li>
-<li class="isub1">Fry, Macon, <a href="#Page_232">232</a></li>
-<li class="isub1">Fuller, Harrison W., <a href="#Page_252">252</a></li>
-<li class="isub1">Fürth, R., <a href="#Page_242">242</a></li>
-
-<li class="ifrst">Gage, F. D., <a href="#Page_245">245</a></li>
-<li class="isub1">Genet, N., <a href="#Page_239">239</a>, <a href="#Page_246">246</a></li>
-<li class="isub1">Godwin, Mary W. (Mary W. Shelley), <a href="#Page_198">198</a>, <a href="#Page_255">255</a></li>
-<li class="isub1">Goldstine, Adele, <a href="#Page_247">247</a></li>
-<li class="isub1">Goldstine, Herman H., <a href="#Page_247">247</a>, <a href="#Page_251">251</a>, <a href="#Page_253">253</a></li>
-<li class="isub1">Gove, E. L., <a href="#Page_245">245</a></li>
-<li class="isub1">Graff, Willem L., <a href="#Page_231">231</a></li>
-<li class="isub1">Graham, R. S., <a href="#Page_244">244</a></li>
-<li class="isub1">Gray, T. S., <a href="#Page_245">245</a></li>
-<li class="isub1">Green, Harriet C., <a href="#Page_255">255</a></li>
-
-<li class="ifrst">Haeff, Andrew V., <a href="#Page_252">252</a></li>
-<li class="isub1">Hansen, Morris H., <a href="#Page_237">237</a></li>
-<li class="isub1">Harrison, Joseph O., Jr., <a href="#Page_246">246</a>, <a href="#Page_254">254</a></li>
-<li class="isub1">Hart, H. C., <a href="#Page_244">244</a></li>
-<li class="isub1">Hartkemeier, Harry Pelle, <a href="#Page_233">233</a></li>
-<li class="isub1">Hartree, D. R., <a href="#Page_232">232</a>, <a href="#Page_240">240-1</a>,
-                                  <a href="#Page_247">247</a></li>
-<li class="isub1">Haupt, Ralph F., <a href="#Page_237">237</a></li>
-<li class="isub1">Hayakawa, S. I., <a href="#Page_231">231</a></li>
-<li class="isub1">Hazen, H. L., <a href="#Page_243">243</a>, <a href="#Page_245">245</a></li>
-<li class="isub1">Hedeman, W. R., <a href="#Page_245">245</a></li>
-<li class="isub1">Hedley, K. J., <a href="#Page_233">233</a></li>
-<li class="isub1">Herget, Paul, <a href="#Page_237">237</a></li>
-<li class="isub1">Herr, D. L., <a href="#Page_244">244</a></li>
-<li class="isub1">Herrick, C. Judson, <a href="#Page_229">229</a></li>
-<li class="isub1">Hoffleit, Dorrit, <a href="#Page_254">254</a></li>
-<li class="isub1">Hogben, Launcelot, <a href="#Page_231">231</a></li>
-<li class="isub1">Hollerith, Herman, <a href="#Page_43">43</a></li>
-<li class="isub1">Hopper, Grace M., <a href="#Page_246">246</a></li>
-<li class="isub1">Horsburgh, E. H., <a href="#Page_232">232</a></li>
-<li class="isub1">Hotelling, Harold, <a href="#Page_237">237</a></li>
-<li class="isub1">Householder, Alston S., <a href="#Page_230">230</a></li>
-
-<li class="ifrst">Jespersen, Otto, <a href="#Page_231">231</a></li>
-<li class="isub1">Juley, Joseph, <a href="#Page_248">248</a></li>
-
-<li class="ifrst">Kalin, Theodore A., <a href="#Page_144">144</a>, <a href="#Page_155">155-6</a></li>
-<li class="isub1">Kelvin, Lord, <a href="#Page_72">72</a>, <a href="#Page_240">240</a></li>
-<li class="isub1">King, Gilbert W., <a href="#Page_238">238</a></li>
-<li class="isub1">Koons, Florence, <a href="#Page_249">249</a></li>
-<li class="isub1">Kopp, George A., <a href="#Page_255">255</a></li>
-<li class="isub1">Kormes, Jennie P., <a href="#Page_238">238</a></li>
-<li class="isub1">Kormes, Mark, <a href="#Page_238">238</a></li>
-<li class="isub1">Kornei, Otto, <a href="#Page_252">252</a></li>
-<li class="isub1">Kranz, Frederick W., <a href="#Page_242">242</a></li>
-<li class="isub1">Kron, Gabriel, <a href="#Page_243">243-4</a></li>
-<li class="isub1">Kuder, G. Frederic, <a href="#Page_238">238</a></li>
-<li class="isub1">Kuehni, H. P., <a href="#Page_240">240</a>, <a href="#Page_243">243</a></li>
-
-<li class="ifrst">Lagemann, John K., <a href="#Page_253">253</a>, <a href="#Page_255">255</a></li>
-<li class="isub1">Landahl, Herbert D., <a href="#Page_230">230</a></li>
-<li class="isub1">Lang, H. C., <a href="#Page_233">233</a></li>
-<li class="isub1">Lashley, Karl S., <a href="#Page_229">229</a></li>
-<li class="isub1">Leaver, E. W., <a href="#Page_255">255</a></li>
-<li class="isub1">Leontief, Wassily W., <a href="#Page_254">254</a></li>
-<li class="isub1">Lettvin, Jerome Y., <a href="#Page_230">230</a></li>
-<li class="isub1">Lilley, S., <a href="#Page_232">232</a></li>
-<li class="isub1">Livingston, Hubert M., <a href="#Page_250">250</a></li>
-<li class="isub1">Locke, E. L., <a href="#Page_253">253</a></li>
-<li class="isub1">Lorraine, R. G., <a href="#Page_243">243</a></li>
-<li class="isub1">Lotkin, Max, <a href="#Page_254">254</a></li>
-<li class="isub1">Loud, Warren S., <a href="#Page_251">251</a></li>
-<li class="isub1">Lowan, Arnold N., <a href="#Page_254">254</a></li>
-<li class="isub1">Lubkin, Samuel, <a href="#Page_249">249</a>, <a href="#Page_251">251</a></li>
-<li class="isub1">Lyndon, Roger C., <a href="#Page_250">250</a></li>
-
-<li class="ifrst">MacLaughlan, Lorne, <a href="#Page_253">253</a></li>
-<li class="isub1">Maginniss, F. J., <a href="#Page_241">241</a></li>
-<li class="isub1">Mallock, R. R. M., <a href="#Page_244">244</a></li>
-<li class="isub1">Malone, Helen, <a href="#Page_254">254</a></li>
-<li class="isub1">Mann, Martin, <a href="#Page_253">253</a></li>
-<li class="isub1">Marble, F. G., <a href="#Page_242">242</a></li>
-<li class="isub1">Massey, H. S. W., <a href="#Page_240">240</a></li>
-<li class="isub1">Mastukazi, Kiyoshi, <a href="#Page_19">19</a></li>
-<li class="isub1">Matz, Adolph, <a href="#Page_254">254</a></li>
-<li class="isub1">Mauchly, John W., <a href="#Page_114">114</a>, <a href="#Page_178">178</a>,
-                          <a href="#Page_247">247</a>, <a href="#Page_251">251</a>, <a href="#Page_253">253</a></li>
-<li class="isub1">Maxfield, D. K., <a href="#Page_238">238</a></li>
-<li class="isub1">Maxwell, L. R., <a href="#Page_242">242</a></li>
-<li class="isub1">McCann, G. D., <a href="#Page_245">245</a></li>
-<li class="isub1">McCulloch, Warren S., <a href="#Page_230">230</a></li>
-<li class="isub1">McLaughlin, Kathleen, <a href="#Page_238">238</a></li>
-<li class="isub1">McPherson, James L., <a href="#Page_254">254</a></li>
-<li class="isub1">McPherson, John C., <a href="#Page_238">238</a>
-    <span class="pagenum" id="Page_259">[Pg 259]</span></li>
-<li class="isub1">Meacham, Alan D., <a href="#Page_237">237</a></li>
-<li class="isub1">Mercner, R. O., <a href="#Page_244">244</a></li>
-<li class="isub1">Miller, Dayton C., <a href="#Page_242">242</a></li>
-<li class="isub1">Miller, Frederick G., <a href="#Page_249">249</a></li>
-<li class="isub1">Milliman, Wendell A., <a href="#Page_238">238</a></li>
-<li class="isub1">Milne, J. R., <a href="#Page_242">242</a></li>
-<li class="isub1">Mitchell, Herbert F., Jr., <a href="#Page_254">254</a></li>
-<li class="isub1">Montgomery, H. C., <a href="#Page_242">242</a></li>
-<li class="isub1">Moore, Benjamin L., <a href="#Page_252">252</a></li>
-<li class="isub1">Moore, C. R., <a href="#Page_242">242</a></li>
-<li class="isub1">Murray, Francis J., <a href="#Page_232">232</a></li>
-<li class="isub1">Myers, D. M., <a href="#Page_245">245</a></li>
-
-<li class="ifrst">Newman, James R., <a href="#Page_253">253</a></li>
-
-<li class="ifrst">Ogden, C. K., <a href="#Page_231">231</a></li>
-<li class="isub1">O’Neal, R. D., <a href="#Page_252">252</a></li>
-
-<li class="ifrst">Parker, W. W., <a href="#Page_243">243</a></li>
-<li class="isub1">Patterson, George W., <a href="#Page_251">251</a></li>
-<li class="isub1">Pease, M. C., <a href="#Page_255">255</a></li>
-<li class="isub1">Pekeris, C. L., <a href="#Page_245">245</a></li>
-<li class="isub1">Peterson, H. A., <a href="#Page_240">240</a>, <a href="#Page_243">243-4</a></li>
-<li class="isub1">Pfeiffer, John E., <a href="#Page_253">253</a></li>
-<li class="isub1">Pieron, Henri, <a href="#Page_229">229</a></li>
-<li class="isub1">Pike, W. S., <a href="#Page_252">252</a></li>
-<li class="isub1">Pitts, Walter, <a href="#Page_230">230</a></li>
-<li class="isub1">Poesch, H., <a href="#Page_240">240</a></li>
-<li class="isub1">Porter, A., <a href="#Page_240">240-1</a></li>
-<li class="isub1">Potter, Ralph K., <a href="#Page_255">255</a></li>
-<li class="isub1">Pringle, R. W., <a href="#Page_242">242</a></li>
-
-<li class="ifrst">Quine, W. V., <a href="#Page_248">248</a></li>
-
-<li class="ifrst">Rajchman, Jan A., <a href="#Page_252">252</a></li>
-<li class="isub1">Rashevsky, N., <a href="#Page_230">230</a></li>
-<li class="isub1">Raymond, W. J., <a href="#Page_242">242</a></li>
-<li class="isub1">Reichenbach, Hans, <a href="#Page_248">248</a></li>
-<li class="isub1">Renwick, W., <a href="#Page_249">249</a></li>
-<li class="isub1">Ridenour, Louis N., <a href="#Page_253">253</a></li>
-<li class="isub1">Riesz, R. R., <a href="#Page_254">254</a></li>
-<li class="isub1">Robertson, J. M., <a href="#Page_242">242</a></li>
-<li class="isub1">Rose, A., <a href="#Page_247">247</a></li>
-<li class="isub1">Rossum, <a href="#Page_199">199</a></li>
-<li class="isub1">Royer, Elmer B., <a href="#Page_238">238</a></li>
-
-<li class="ifrst">Sauer, R., <a href="#Page_240">240</a></li>
-<li class="isub1">Schlauch, Margaret, <a href="#Page_231">231</a></li>
-<li class="isub1">Schnackel, H. G., <a href="#Page_233">233</a></li>
-<li class="isub1">Schrödinger, Erwin, <a href="#Page_229">229</a></li>
-<li class="isub1">Schwarzchild, Martin, <a href="#Page_237">237</a></li>
-<li class="isub1">Shalett, Sidney, <a href="#Page_255">255</a></li>
-<li class="isub1">Shannon, Claude E., <a href="#Page_153">153-5</a>, <a href="#Page_241">241</a>,
-                     <a href="#Page_248">248</a>, <a href="#Page_255">255</a></li>
-<li class="isub1">Sharpless, T. Kite, <a href="#Page_252">252</a></li>
-<li class="isub1">Shelley, Mary W., <a href="#Page_198">198</a>, <a href="#Page_255">255</a></li>
-<li class="isub1">Shelley, Percy Bysshe, <a href="#Page_198">198</a></li>
-<li class="isub1">Sheppard, C. Bradford, <a href="#Page_252">252</a></li>
-<li class="isub1">Sherrington, Charles S., <a href="#Page_229">229</a></li>
-<li class="isub1">Smith, C. E., <a href="#Page_245">245</a></li>
-<li class="isub1">Snyder, Frances E., <a href="#Page_250">250</a></li>
-<li class="isub1">Somerville, J. M., <a href="#Page_242">242</a></li>
-<li class="isub1">Spilhaus, Athelstan, <a href="#Page_255">255</a></li>
-<li class="isub1">Stewart, R. R., <a href="#Page_245">245</a></li>
-<li class="isub1">Stibitz, George R., <a href="#Page_129">129-30</a>, <a href="#Page_244">244</a>,
-                           <a href="#Page_251">251</a></li>
-<li class="isub1">Straiton, A. W., <a href="#Page_242">242</a></li>
-
-<li class="ifrst">Tabor, Lewis P., <a href="#Page_247">247</a></li>
-<li class="isub1">Tarski, Alfred, <a href="#Page_248">248-9</a></li>
-<li class="isub1">Terhune, G. K., <a href="#Page_242">242</a></li>
-<li class="isub1">Thomas, George B., <a href="#Page_238">238</a></li>
-<li class="isub1">Thomson, James, <a href="#Page_240">240</a></li>
-<li class="isub1">Thomson, William, <a href="#Page_72">72</a>, <a href="#Page_240">240</a></li>
-<li class="isub1">Tilney, Frederick, <a href="#Page_229">229</a></li>
-<li class="isub1">Torrey, V., <a href="#Page_246">246</a></li>
-<li class="isub1">Travis, Irven, <a href="#Page_239">239</a>, <a href="#Page_244">244</a></li>
-<li class="isub1">Tumbleson, Robert C., <a href="#Page_253">253</a></li>
-<li class="isub1">Turck, J. A. V., <a href="#Page_232">232</a></li>
-<li class="isub1">Tyler, Arthur W., <a href="#Page_252">252</a></li>
-
-<li class="ifrst">Varney, R. N., <a href="#Page_243">243</a></li>
-<li class="isub1">von Neumann, John, <a href="#Page_124">124</a>, <a href="#Page_251">251</a></li>
-
-<li class="ifrst">Wainwright, Lawrence L., <a href="#Page_72">72</a>, <a href="#Page_241">241</a></li>
-<li class="isub1">Walpole, Hugh R., <a href="#Page_231">231</a></li>
-<li class="isub1">Watkins, S. S. A., <a href="#Page_254">254</a></li>
-<li class="isub1">Wegel, R. L., <a href="#Page_242">242</a></li>
-<li class="isub1">Weiner, J. R., <a href="#Page_251">251</a></li>
-<li class="isub1">Wheeler, L. L., <a href="#Page_241">241-2</a></li>
-<li class="isub1">Whitten, C. A., <a href="#Page_238">238</a></li>
-<li class="isub1">Wiener, Norbert, <a href="#Page_229">229</a></li>
-<li class="isub1">Wilbur, J. B., <a href="#Page_244">244</a>
-    <span class="pagenum" id="Page_260">[Pg 260]</span></li>
-<li class="isub1">Wilkes, M. V., <a href="#Page_249">249</a></li>
-<li class="isub1">Williams, Samuel B., <a href="#Page_248">248</a></li>
-<li class="isub1">Wolf, Arthur W., <a href="#Page_233">233</a></li>
-<li class="isub1">Womersley, J. R., <a href="#Page_241">241</a></li>
-<li class="isub1">Wood, Thomas, <a href="#Page_19">19</a></li>
-<li class="isub1">Woodger, J. H., <a href="#Page_248">248</a></li>
-<li class="isub1">Woodruff, L. F., <a href="#Page_250">250</a></li>
-<li class="isub1">Wyatt, Willa A., <a href="#Page_254">254</a></li>
-<li class="isub1">Wylie, J., <a href="#Page_240">240</a></li>
-
-<li class="ifrst">Yavne, R. O., <a href="#Page_245">245</a></li>
-
-<li class="ifrst">Zworykin, V. K., <a href="#Page_190">190</a>, <a href="#Page_252">252</a>,
-                <a href="#Page_255">255</a></li>
-</ul>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="chapter">
-<p><span class="pagenum" id="Page_261">[Pg 261]</span></p>
-<h2 class="nobreak">SUBJECT INDEX</h2>
-</div>
-
-<p class="blockquot"><i><big>Notes:</big> Phrases consisting of
-an adjective and a noun, or of a noun and a noun, are entered in
-their alphabetical place according to the first word. For example,
-“electrostatic storage tube” is under</i> <big>e</big>, <i>and “punch
-card” is under</i> <big>p</big>.</p>
-
-<ul class="index no-wrap">
-<li class="isub1"><i>A</i> field, <a href="#Page_99">99</a></li>
-<li class="isub1"><i>A</i> tape, <a href="#Page_82">82-3</a></li>
-<li class="isub1">abacus, <a href="#Page_17">17-9</a>, <a href="#Page_133">133</a>, <a href="#Page_220">220</a></li>
-<li class="isub1"><i>abax</i> (Greek), <a href="#Page_18">18</a></li>
-<li class="isub1">absolute value, <a href="#Page_101">101</a>, <a href="#Page_222">222</a></li>
-<li class="isub1">accumulator, <a href="#Page_115">115-6</a></li>
-<li class="isub1">accumulator decade, <a href="#Page_118">118</a></li>
-<li class="isub1">accuracy, <a href="#Page_67">67</a>, <a href="#Page_89">89</a></li>
-<li class="isub1">acetylcholine, <a href="#Page_3">3</a></li>
-<li class="isub1">add output, <a href="#Page_120">120</a></li>
-<li class="isub1">addend, <a href="#Page_223">223</a></li>
-<li class="isub1">adder, <a href="#Page_77">77</a></li>
-<li class="isub1">adder mechanism, <a href="#Page_77">77-8</a></li>
-<li class="isub1">adding, <a href="#Page_24">24-5</a>, <a href="#Page_27">27</a>, <a href="#Page_37">37</a>, <a href="#Page_55">55</a>,
-            <a href="#Page_100">100</a>, <a href="#Page_119">119</a>, <a href="#Page_139">139</a></li>
-<li class="isub1">addition circuit, <a href="#Page_37">37</a></li>
-<li class="isub1">Aiken Mark I Calculator, <a href="#Page_10">10</a>, <a href="#Page_89">89-112</a>, <a href="#Page_245">245-6</a>;</li>
-<li class="isub3"><i>see also</i> Harvard IBM Automatic Sequence-Controlled Calculator</li>
-<li class="isub1">Aiken Mark II Relay Calculator, <a href="#Page_176">176-8</a>, <a href="#Page_249">249</a></li>
-<li class="isub1">Aiken Mark III Electronic Calculator, <a href="#Page_177">177</a></li>
-<li class="isub1">air resistance coefficient, <a href="#Page_80">80-2</a></li>
-<li class="isub1">algebra of logic, <a href="#Page_26">26</a>, <a href="#Page_36">36</a>,
-            <a href="#Page_56">56-62</a>, <a href="#Page_105">105</a>, <a href="#Page_140">140</a>,
-            <a href="#Page_151">151-2</a>, <a href="#Page_164">164</a>,
-            <a href="#Page_221"> 221-3</a>, <a href="#Page_248">248</a></li>
-<li class="isub1">algebraic equations, machines for solving, <a href="#Page_244">244</a></li>
-<li class="isub1">all-or-none response, <a href="#Page_3">3</a></li>
-<li class="isub1">alphabet, <a href="#Page_14">14</a></li>
-<li class="isub1">alphabetic coding, <a href="#Page_13">13</a>, <a href="#Page_54">54</a></li>
-<li class="isub1">alphabetic punching, <a href="#Page_46">46</a></li>
-<li class="isub1">alphabetic writing, <a href="#Page_13">13</a></li>
-<li class="isub1">amplify, <a href="#Page_73">73</a></li>
-<li class="isub1">analogous, <a href="#Page_65">65</a></li>
-<li class="isub1">analogue, <a href="#Page_65">65</a></li>
-<li class="isub1">analogue machines (machines that handle information expressed as measurements), <a href="#Page_65">65</a>;</li>
-<li class="isub3">MIT Differential Analyzer No. 2, <a href="#Page_65">65-88</a>;</li>
-<li class="isub3">references, <a href="#Page_239">239-45</a></li>
-<li class="isub1">analytical engine, <a href="#Page_90">90</a></li>
-<li class="isub1">analyzer, <a href="#Page_68">68</a>, <a href="#Page_241">241-4</a>;</li>
-<li class="isub3"><i>see also</i> differential analyzer</li>
-<li class="isub1">and, <a href="#Page_146">146-8</a></li>
-<li class="isub1">and/or, <a href="#Page_149">149</a></li>
-<li class="isub1">angle-indicator, <a href="#Page_74">74-5</a></li>
-<li class="isub1">animal thinking, <a href="#Page_4">4</a>, <a href="#Page_8">8</a>, <a href="#Page_188">188</a></li>
-<li class="isub1">annuities, <a href="#Page_88">88</a></li>
-<li class="isub1">antecedent, <a href="#Page_158">158</a></li>
-<li class="isub1">antilogarithm, <a href="#Page_139">139</a>, <a href="#Page_226">226</a></li>
-<li class="isub1">antitangent, <a href="#Page_139">139</a>, <a href="#Page_226">226</a></li>
-<li class="isub1">approximation, <a href="#Page_220">220</a>;</li>
-<li class="isub3"><i>see also</i> rapid approximation</li>
-<li class="isub1">aptitude testing, <a href="#Page_190">190</a></li>
-<li class="isub1">argument (in a mathematical table or function), <a href="#Page_96">96</a>, <a href="#Page_103">103-4</a>,
-                  <a href="#Page_122">122</a>, <a href="#Page_136">136</a>, <a href="#Page_224">224</a></li>
-<li class="isub1">arithmetical operations, <a href="#Page_55">55-6</a>, <a href="#Page_173">173</a></li>
-<li class="isub1">armor with a motor, <a href="#Page_180">180</a>, <a href="#Page_195">195</a></li>
-<li class="isub1">array, <a href="#Page_173">173</a>, <a href="#Page_227">227</a></li>
-<li class="isub1">Atomic Energy Commission, <a href="#Page_203">203</a>, <a href="#Page_208">208</a></li>
-<li class="isub1">attitudes, <a href="#Page_205">205</a></li>
-<li class="isub1">augend, <a href="#Page_223">223</a></li>
-<li class="isub1"><i>aut</i> (Latin), <a href="#Page_149">149</a></li>
-<li class="isub1">automatic address-book, <a href="#Page_181">181</a></li>
-<li class="isub1">automatic carriage, <a href="#Page_53">53</a></li>
-<li class="isub1">“Automatic Computing Machinery”</li>
-<li class="isub3">(section in <i>Mathematical Tables and Other Aids to Computation</i>),  <a href="#Page_177">177</a>
-    <span class="pagenum" id="Page_262">[Pg 262]</span></li>
-<li class="isub1">automatic control: house-furnace, <a href="#Page_189">189</a>;</li>
-<li class="isub3">lawn-mower, <a href="#Page_188">188</a>;</li>
-<li class="isub3">tractor-plow, <a href="#Page_188">188</a>;</li>
-<li class="isub3">weather, <a href="#Page_189">189</a></li>
-<li class="isub1">automatic cook, <a href="#Page_181">181</a></li>
-<li class="isub1">automatic factory, <a href="#Page_189">189</a></li>
-<li class="isub1">automatic library, <a href="#Page_9">9</a>, <a href="#Page_181">181</a></li>
-<li class="isub1">automatic machinery, <a href="#Page_182">182</a></li>
-<li class="isub1">automatic pilot, <a href="#Page_189">189</a></li>
-<li class="isub1">automatic recognizer, <a href="#Page_186">186-7</a></li>
-<li class="isub1">automatic sequence-controlled calculator, <a href="#Page_90">90</a>;</li>
-<li class="isub3"><i>see also</i> Harvard IBM Automatic Sequence-Controlled Calculator</li>
-<li class="isub1">automatic stenographer, <a href="#Page_185">185</a></li>
-<li class="isub1">automatic switching circuits, <a href="#Page_248">248</a></li>
-<li class="isub1">automatic translator, <a href="#Page_182">182</a></li>
-<li class="isub1">automatic typist, <a href="#Page_182">182</a>, <a href="#Page_184">184</a></li>
-<li class="isub1">axon, <a href="#Page_3">3</a></li>
-
-<li class="ifrst"><i>B</i> field, <a href="#Page_99">99</a></li>
-<li class="isub1"><i>B</i> tape, <a href="#Page_82">82-3</a></li>
-<li class="isub1">Ballistic Research Laboratories, <a href="#Page_1">1</a>, <a href="#Page_113">113-5</a>,
-               <a href="#Page_127">127-8</a>, <a href="#Page_132">132</a>, <a href="#Page_142">142</a></li>
-<li class="isub1">base <i>e</i>, <a href="#Page_226">226</a></li>
-<li class="isub1">base <a href="#Page_10">10</a>, <a href="#Page_226">226</a></li>
-<li class="isub1">beam of electrons, <a href="#Page_172">172</a></li>
-<li class="isub1">behavior, <a href="#Page_4">4</a>, <a href="#Page_7">7-8</a>, <a href="#Page_29">29</a></li>
-<li class="isub1">Bell Telephone Laboratories, <a href="#Page_4">4-5</a>, <a href="#Page_128">128-43</a>, <a href="#Page_247">247-8</a></li>
-<li class="isub1">Bell Telephone Laboratories’ general-purpose relay computer,
-                      <a href="#Page_128">128-43</a>, <a href="#Page_247">247-8</a>;</li>
-<li class="isub3">cost, <a href="#Page_142">142</a>;</li>
-<li class="isub3">reliability, <a href="#Page_141">141</a>;</li>
-<li class="isub3">speed, <a href="#Page_142">142</a></li>
-<li class="isub1">Bessel functions, <a href="#Page_111">111</a>, <a href="#Page_226">226</a></li>
-<li class="isub1">Binac, <a href="#Page_179">179</a></li>
-<li class="isub1">binary coding, <a href="#Page_11">11</a>, <a href="#Page_13">13</a></li>
-<li class="isub1">binary digit, <a href="#Page_14">14</a></li>
-<li class="isub1">binary numbers, <a href="#Page_14">14</a>, <a href="#Page_216">216-9</a></li>
-<li class="isub1">biophysics, <a href="#Page_230">230</a></li>
-<li class="isub1">biquinary numbers, <a href="#Page_133">133</a>, <a href="#Page_219">219-20</a></li>
-<li class="isub1">blocks of arguments, <a href="#Page_137">137</a></li>
-<li class="isub1">Boolean algebra, <a href="#Page_152">152</a>, <a href="#Page_248">248</a>;</li>
-<li class="isub3"><i>see also</i> mathematical logic</li>
-<li class="isub1">both, <a href="#Page_149">149</a></li>
-<li class="isub1">bowwow theory, <a href="#Page_12">12</a></li>
-<li class="isub1">brain evolution, <a href="#Page_229">229</a></li>
-<li class="isub1">brain with a motor, <a href="#Page_180">180</a>, <a href="#Page_195">195</a></li>
-<li class="isub1">BTL frames, <a href="#Page_138">138-9</a></li>
-<li class="isub1">bus, <a href="#Page_32">32</a>, <a href="#Page_119">119</a></li>
-<li class="isub1">button, <a href="#Page_91">91</a>, <a href="#Page_94">94</a></li>
-
-<li class="ifrst"><i>C</i> field, <a href="#Page_99">99</a></li>
-<li class="isub1"><i>C</i> tape, <a href="#Page_82">82-3</a></li>
-<li class="isub1"><i>calcis</i> (Latin), <a href="#Page_18">18</a></li>
-<li class="isub1">calculating punch, <a href="#Page_47">47</a>, <a href="#Page_51">51-2</a>, <a href="#Page_235">235</a></li>
-<li class="isub1">calculator frames, <a href="#Page_138">138</a></li>
-<li class="isub1">calculator programmed by punch cards, <a href="#Page_236">236</a></li>
-<li class="isub1">cam, <a href="#Page_94">94-5</a></li>
-<li class="isub1">cam contact, <a href="#Page_91">91</a>, <a href="#Page_94">94-5</a></li>
-<li class="isub1">capacitance, <a href="#Page_117">117</a></li>
-<li class="isub1">capacitor, <a href="#Page_117">117</a></li>
-<li class="isub1">capacity: counter, <a href="#Page_59">59</a>;</li>
-<li class="isub3">selecting, <a href="#Page_59">59</a></li>
-<li class="isub1">carbon dioxide, <a href="#Page_190">190</a></li>
-<li class="isub1">card channel, <a href="#Page_47">47</a>, <a href="#Page_52">52</a></li>
-<li class="isub1">card column, <a href="#Page_48">48</a></li>
-<li class="isub1">card feed, <a href="#Page_48">48</a>, <a href="#Page_91">91</a></li>
-<li class="isub1">card punch, <a href="#Page_91">91</a>, <a href="#Page_97">97</a></li>
-<li class="isub1">card reader, <a href="#Page_116">116</a>, <a href="#Page_118">118</a></li>
-<li class="isub1">card sorter, <a href="#Page_96">96</a></li>
-<li class="isub1">card stacker, <a href="#Page_48">48</a></li>
-<li class="isub1">card station, <a href="#Page_47">47</a></li>
-<li class="isub1">Carnegie Institution of Washington, <a href="#Page_113">113</a></li>
-<li class="isub1">carry impulse, <a href="#Page_118">118</a></li>
-<li class="isub1">cell nucleus, <a href="#Page_2">2-3</a></li>
-<li class="isub1">census, <a href="#Page_43">43</a>, <a href="#Page_53">53</a></li>
-<li class="isub1">channel, <a href="#Page_47">47</a>, <a href="#Page_52">52</a>, <a href="#Page_170">170</a></li>
-<li class="isub1">characteristic of a logarithm, <a href="#Page_107">107</a></li>
-<li class="isub1">check counter, <a href="#Page_105">105</a></li>
-<li class="isub1">check-marks, <a href="#Page_151">151</a></li>
-<li class="isub1">checking, <a href="#Page_105">105</a>, <a href="#Page_110">110</a>,
-                       <a href="#Page_179">179</a>, <a href="#Page_227">227</a></li>
-<li class="isub1">chess game, <a href="#Page_117">117</a></li>
-<li class="isub1">chestnut blight, <a href="#Page_201">201</a></li>
-<li class="isub1">chortle, <a href="#Page_12">12</a></li>
-<li class="isub1">class selector, <a href="#Page_59">59</a></li>
-<li class="isub1">clearing, <a href="#Page_100">100</a></li>
-<li class="isub1">codes, <a href="#Page_29">29</a>, <a href="#Page_54">54</a>, <a href="#Page_96">96</a>, <a href="#Page_99">99</a></li>
-<li class="isub1">coding, <a href="#Page_30">30</a>, <a href="#Page_130">130</a>, <a href="#Page_252">252-3</a></li>
-<li class="isub1">coding line, <a href="#Page_99">99</a></li>
-<li class="isub1">column (in a punch card), <a href="#Page_45">45</a>
-    <span class="pagenum" id="Page_263">[Pg 263]</span></li>
-<li class="isub1">connective, <a href="#Page_148">148</a>, <a href="#Page_158">158-9</a></li>
-<li class="isub1">connective grouping, <a href="#Page_159">159</a></li>
-<li class="isub1">collating, <a href="#Page_51">51</a>, <a href="#Page_173">173</a></li>
-<li class="isub1">collator, <a href="#Page_47">47</a>, <a href="#Page_51">51</a>, <a href="#Page_235">235</a></li>
-<li class="isub1">collator counting device, <a href="#Page_51">51</a>, <a href="#Page_235">235</a></li>
-<li class="isub1">combining information, <a href="#Page_15">15</a></li>
-<li class="isub1">combining operations, <a href="#Page_173">173</a></li>
-<li class="isub1">Common, <a href="#Page_59">59-60</a></li>
-<li class="isub1">comparer, <a href="#Page_57">57-8</a></li>
-<li class="isub1">comparing, <a href="#Page_50">50</a>, <a href="#Page_57">57-8</a></li>
-<li class="isub1">complement, <a href="#Page_55">55</a>;</li>
-<li class="isub3"><i>see also</i> nines complement, ones complement, tens complement</li>
-<li class="isub1">Complex Computer, <a href="#Page_129">129-30</a></li>
-<li class="isub1">complex numbers, <a href="#Page_128">128-9</a></li>
-<li class="isub1">computer, <a href="#Page_6">6</a>, <a href="#Page_27">27</a></li>
-<li class="isub1">Computer 1 and Computer 2, <a href="#Page_132">132</a>, <a href="#Page_138">138</a></li>
-<li class="isub1">conflicts between statements, <a href="#Page_149">149-50</a></li>
-<li class="isub1">consequent, <a href="#Page_158">158</a></li>
-<li class="isub1">constant, <a href="#Page_224">224</a></li>
-<li class="isub1">constant ratio, <a href="#Page_77">77</a></li>
-<li class="isub1">constant register, <a href="#Page_96">96</a>, <a href="#Page_99">99</a></li>
-<li class="isub1">constant switch, <a href="#Page_99">99</a></li>
-<li class="isub1">Constant Transmitter, <a href="#Page_116">116</a>, <a href="#Page_118">118</a></li>
-<li class="isub1">consulting a table, <a href="#Page_103">103</a>, <a href="#Page_122">122</a></li>
-<li class="isub1">convergent, <a href="#Page_221">221</a></li>
-<li class="isub1">Converter, <a href="#Page_115">115</a></li>
-<li class="isub1">context, <a href="#Page_144">144</a></li>
-<li class="isub1">continuous annuities, <a href="#Page_88">88</a></li>
-<li class="isub1">continuous contingent insurances, <a href="#Page_88">88</a></li>
-<li class="isub1">continuously running gear, <a href="#Page_93">93</a></li>
-<li class="isub1">control, <a href="#Page_6">6</a>, <a href="#Page_28">28</a>, <a href="#Page_90">90-1</a></li>
-<li class="isub1">control brushes, <a href="#Page_51">51-2</a></li>
-<li class="isub1">control frames, <a href="#Page_138">138-9</a></li>
-<li class="isub1">Control Instrument Company, <a href="#Page_43">43</a></li>
-<li class="isub1">control over robot machines, <a href="#Page_196">196-208</a></li>
-<li class="isub1">control tape, <a href="#Page_28">28</a></li>
-<li class="isub1">controversy, <a href="#Page_197">197</a></li>
-<li class="isub1">cosine, <a href="#Page_75">75</a>, <a href="#Page_85">85</a>, <a href="#Page_139">139</a>, <a href="#Page_226">226</a></li>
-<li class="isub1">cost of mechanical brains, <a href="#Page_87">87</a>, <a href="#Page_109">109</a>, <a href="#Page_126">126</a>,
-    <a href="#Page_142">142</a>, <a href="#Page_165">165</a>, <a href="#Page_168">168</a></li>
-<li class="isub1">counter, <a href="#Page_52">52</a>, <a href="#Page_74">74</a>, <a href="#Page_93">93-4</a></li>
-<li class="isub1">counter position, <a href="#Page_93">93</a></li>
-<li class="isub1">counter wheel, <a href="#Page_93">93</a>, <a href="#Page_118">118</a></li>
-<li class="isub1">counting, <a href="#Page_55">55</a></li>
-<li class="isub1">coupling (numbers), <a href="#Page_106">106</a></li>
-<li class="isub1">cube, <a href="#Page_105">105</a>, <a href="#Page_224">224</a></li>
-<li class="isub1">Current (input of comparer), <a href="#Page_57">57</a></li>
-<li class="isub1">cycle, <a href="#Page_29">29</a>, <a href="#Page_45">45</a></li>
-<li class="isub1">Cycling Unit, <a href="#Page_115">115-6</a></li>
-<li class="isub1">Cypriote, <a href="#Page_13">13</a></li>
-
-<li class="ifrst">Dartmouth College, <a href="#Page_131">131</a></li>
-<li class="isub1">decade, <a href="#Page_118">118</a></li>
-<li class="isub1">decimal digit, <a href="#Page_11">11</a>, <a href="#Page_14">14</a></li>
-<li class="isub1">decimal position, <a href="#Page_118">118</a></li>
-<li class="isub1">deciphering, <a href="#Page_184">184</a>, <a href="#Page_188">188</a></li>
-<li class="isub1">decoding, <a href="#Page_184">184</a>, <a href="#Page_188">188</a></li>
-<li class="isub1">definite integral, <a href="#Page_111">111</a>, <a href="#Page_225">225</a></li>
-<li class="isub1">delay lines, <a href="#Page_17">17</a>, <a href="#Page_20">20</a>, <a href="#Page_171">171-2</a></li>
-<li class="isub1">dendrite, <a href="#Page_3">3</a></li>
-<li class="isub1">denial, <a href="#Page_147">147</a></li>
-<li class="isub1">dependent variable, <a href="#Page_81">81</a>, <a href="#Page_224">224</a></li>
-<li class="isub1">derivative, <a href="#Page_68">68-71</a>, <a href="#Page_225">225</a></li>
-<li class="isub1">design of mechanical brains, <a href="#Page_167">167-79</a>, <a href="#Page_251">251</a></li>
-<li class="isub1">desk calculating machines, <a href="#Page_4">4</a>, <a href="#Page_11">11</a>, <a href="#Page_17">17</a>, <a href="#Page_19">19</a></li>
-<li class="isub1">detail cards, <a href="#Page_50">50</a></li>
-<li class="isub1">dial switch, <a href="#Page_92">92</a>, <a href="#Page_95">95-6</a></li>
-<li class="isub1">dial telephone, <a href="#Page_17">17</a>, <a href="#Page_19">19</a>, <a href="#Page_128">128</a></li>
-<li class="isub1">differences, <a href="#Page_110">110</a>, <a href="#Page_227">227</a></li>
-<li class="isub1">differential, <a href="#Page_68">68</a>, <a href="#Page_70">70</a>, <a href="#Page_78">78</a></li>
-<li class="isub1">differential analyzer, <a href="#Page_68">68</a>, <a href="#Page_72">72-88</a>, <a href="#Page_239">239-41</a></li>
-<li class="isub1">Differential Analyzer No. 2, <a href="#Page_65">65-88</a>;</li>
-<li class="isub3">accuracy, <a href="#Page_86">86</a>;</li>
-<li class="isub3">cost, <a href="#Page_87">87</a>;</li>
-<li class="isub3">reliability, <a href="#Page_87">87</a>;</li>
-<li class="isub3">speed, <a href="#Page_87">87</a></li>
-<li class="isub1">differential equation, <a href="#Page_68">68-9</a>, <a href="#Page_71">71</a>, <a href="#Page_111">111</a>,
-              <a href="#Page_141">141</a>, <a href="#Page_225">225-6</a></li>
-<li class="isub1">differential function, <a href="#Page_70">70</a></li>
-<li class="isub1">differential gear assembly, <a href="#Page_78">78</a></li>
-<li class="isub1">digit, <a href="#Page_11">11</a>, <a href="#Page_14">14</a></li>
-<li class="isub1">Digit Pickup, <a href="#Page_60">60</a></li>
-<li class="isub1">digit selector, <a href="#Page_60">60</a></li>
-<li class="isub1">digit tray, <a href="#Page_119">119</a></li>
-<li class="isub1">digit trunk lines, <a href="#Page_119">119</a>
-           <span class="pagenum" id="Page_264">[Pg 264]</span></li>
-<li class="isub1">digit trunks, <a href="#Page_119">119</a></li>
-<li class="isub1">digital machines</li>
-<li class="isub3">(machines that handle information expressed as digits or letters):</li>
-<li class="isub3">Bell Laboratories’ general-purpose relay calculator, <a href="#Page_128">128-43</a>;</li>
-<li class="isub3">Eniac, <a href="#Page_113">113-27</a>;</li>
-<li class="isub3">Harvard IBM Automatic Sequence-Controlled Calculator, <a href="#Page_89">89-112</a>;</li>
-<li class="isub3">punch-card calculating machinery, <a href="#Page_42">42-64</a>;</li>
-<li class="isub3">references, <a href="#Page_232">232-9</a>, <a href="#Page_245">245-55</a></li>
-<li class="isub1">directions, <a href="#Page_24">24</a></li>
-<li class="isub1">disc, <a href="#Page_78">78-80</a></li>
-<li class="isub1">discrimination, <a href="#Page_140">140</a></li>
-<li class="isub1">discriminator, <a href="#Page_140">140-1</a></li>
-<li class="isub1">distance, <a href="#Page_68">68-9</a></li>
-<li class="isub1">distinguishing <i>A</i> and <i>H</i>, <a href="#Page_184">184</a></li>
-<li class="isub1">dividend, <a href="#Page_103">103</a>, <a href="#Page_223">223</a></li>
-<li class="isub1">Divider-Square-Rooter, <a href="#Page_115">115-7</a></li>
-<li class="isub1">dividing, <a href="#Page_55">55-6</a>, <a href="#Page_98">98</a>, <a href="#Page_102">102</a>, <a href="#Page_121">121</a>, <a href="#Page_140">140</a></li>
-<li class="isub1">divisor counter, <a href="#Page_102">102</a></li>
-<li class="isub1">doorpost, <a href="#Page_65">65-6</a></li>
-<li class="isub1">doubling, <a href="#Page_76">76-7</a>, <a href="#Page_100">100</a></li>
-<li class="isub1">doubling mechanism, <a href="#Page_76">76-7</a></li>
-<li class="isub1">drafting rules, <a href="#Page_149">149</a></li>
-<li class="isub1">drag coefficient, <a href="#Page_80">80</a></li>
-<li class="isub1">drive, <a href="#Page_86">86</a></li>
-<li class="isub1">Dry Ice, <a href="#Page_190">190</a></li>
-
-<li class="ifrst">echo, <a href="#Page_171">171</a></li>
-<li class="isub1">Eckert-Mauchly Computer Corporation, <a href="#Page_179">179</a>, <a href="#Page_250">250</a></li>
-<li class="isub1">economic relations, <a href="#Page_194">194</a></li>
-<li class="isub1">Edsac, <a href="#Page_249">249</a></li>
-<li class="isub1">“educated” machine, <a href="#Page_101">101</a></li>
-<li class="isub1">Edvac, <a href="#Page_177">177</a>, <a href="#Page_249">249</a></li>
-<li class="isub1">Egyptian, <a href="#Page_12">12</a></li>
-<li class="isub1">either, <a href="#Page_149">149</a></li>
-<li class="isub1">electric charge, <a href="#Page_172">172</a></li>
-<li class="isub1">electric remote-control accounting, <a href="#Page_250">250</a></li>
-<li class="isub1">electric typewriter, <a href="#Page_91">91</a>, <a href="#Page_97">97</a>, <a href="#Page_236">236</a></li>
-<li class="isub1">electromagnet, <a href="#Page_168">168</a></li>
-<li class="isub1">Electronic Binary Automatic Computer, <a href="#Page_179">179</a></li>
-<li class="isub1">electronic calculating punch, <a href="#Page_236">236</a></li>
-<li class="isub1">Electronic Control Company, <a href="#Page_250">250</a></li>
-<li class="isub1">Electronic Numerical Integrator and Calculator (Eniac),
-                  <a href="#Page_113">113-27</a>, <a href="#Page_246">246-7</a>;</li>
-<li class="isub3"><i>see also</i> Eniac</li>
-<li class="isub1">electronic tubes, <a href="#Page_17">17</a>, <a href="#Page_20">20-1</a>, <a href="#Page_178">178-9</a>;</li>
-<li class="isub3">Cathode, <a href="#Page_21">21</a>;</li>
-<li class="isub3">Grid, <a href="#Page_21">21</a>;</li>
-<li class="isub3">Plate, <a href="#Page_21">21</a></li>
-<li class="isub1">electrostatic storage tube, <a href="#Page_17">17</a>, <a href="#Page_20">20</a>, <a href="#Page_172">172</a></li>
-<li class="isub1">11 position, <a href="#Page_45">45</a></li>
-<li class="isub1">11 punch, <a href="#Page_58">58</a></li>
-<li class="isub1">else, <a href="#Page_146">146-7</a></li>
-<li class="isub1">end-around-carry, <a href="#Page_95">95</a>, <a href="#Page_217">217</a>, <a href="#Page_223">223</a></li>
-<li class="isub1">engine, <a href="#Page_90">90</a></li>
-<li class="isub1">Eniac, <a href="#Page_113">113-27</a>, <a href="#Page_246">246-7</a>;</li>
-<li class="isub3">cost, <a href="#Page_126">126</a>;</li>
-<li class="isub3">panels, <a href="#Page_115">115</a>;</li>
-<li class="isub3">reliability, <a href="#Page_126">126</a>;</li>
-<li class="isub3">speed, <a href="#Page_125">125</a>;</li>
-<li class="isub3">unbalance, <a href="#Page_124">124</a></li>
-<li class="isub1">“enough alike,” <a href="#Page_184">184</a></li>
-<li class="isub1">Equal (output of sequencer), <a href="#Page_61">61-2</a></li>
-<li class="isub1">equation, <a href="#Page_68">68</a>, <a href="#Page_225">225</a></li>
-<li class="isub1">equivalent, <a href="#Page_14">14</a></li>
-<li class="isub1">erase key, <a href="#Page_134">134</a></li>
-<li class="isub1">Etruscan, <a href="#Page_188">188</a></li>
-<li class="isub1">explanation, <a href="#Page_209">209-13</a></li>
-<li class="isub1">explicit equation, <a href="#Page_86">86</a></li>
-<li class="isub1">exponential, <a href="#Page_85">85</a>, <a href="#Page_106">106</a>, <a href="#Page_225">225-6</a></li>
-<li class="isub1">extraction, <a href="#Page_222">222</a></li>
-
-<li class="ifrst">falsity, <a href="#Page_147">147</a></li>
-<li class="isub1">farad, <a href="#Page_117">117</a></li>
-<li class="isub1">fingers, <a href="#Page_16">16</a>, <a href="#Page_18">18</a></li>
-<li class="isub1">fire-control instrument, <a href="#Page_17">17</a>, <a href="#Page_19">19</a>, <a href="#Page_67">67</a>, <a href="#Page_131">131</a></li>
-<li class="isub1">5 impulse, <a href="#Page_56">56</a></li>
-<li class="isub1">flights, <a href="#Page_70">70</a></li>
-<li class="isub1">flip-flop, <a href="#Page_119">119</a></li>
-<li class="isub1">following logically, <a href="#Page_145">145</a></li>
-<li class="isub1">form feeding device, <a href="#Page_236">236</a></li>
-<li class="isub1">formal logic, <a href="#Page_152">152</a></li>
-<li class="isub1">formula, <a href="#Page_68">68</a>, <a href="#Page_70">70</a>, <a href="#Page_224">224</a></li>
-<li class="isub1">Frankenstein’s monster, <a href="#Page_198">198</a></li>
-<li class="isub1">function, <a href="#Page_68">68</a>, <a href="#Page_70">70</a>, <a href="#Page_81">81</a>, <a href="#Page_103">103</a>, <a href="#Page_116">116</a>,
-                    <a href="#Page_118">118</a>, <a href="#Page_224">224</a></li>
-<li class="isub1">function table, <a href="#Page_80">80-1</a>, <a href="#Page_116">116</a>, <a href="#Page_118">118</a></li>
-
-<li class="ifrst">gang punching, <a href="#Page_50">50</a></li>
-<li class="isub1">gearbox, <a href="#Page_77">77-8</a></li>
-<li class="isub1">General Electric A.C. Network Analyzer, <a href="#Page_243">243</a></li>
-<li class="isub1">General Electric Company, <a href="#Page_243">243</a></li>
-<li class="isub1">geographic code, <a href="#Page_54">54</a></li>
-<li class="isub1">giant brain, <a href="#Page_1">1</a>, <a href="#Page_5">5-8</a></li>
-<li class="isub1">globe, <a href="#Page_65">65-6</a></li>
-<li class="isub1">graph, <a href="#Page_81">81</a>
-    <span class="pagenum" id="Page_265">[Pg 265]</span></li>
-<li class="isub1">great circle, <a href="#Page_69">69</a></li>
-<li class="isub1">greater-than, <a href="#Page_25">25-7</a>, <a href="#Page_37">37</a>, <a href="#Page_222">222</a></li>
-<li class="isub1">greater-than circuit, <a href="#Page_37">37</a></li>
-<li class="isub1">Greek letters, <a href="#Page_120">120</a></li>
-<li class="isub1">guided missile, <a href="#Page_197">197</a>, <a href="#Page_206">206</a></li>
-<li class="isub1">gun, <a href="#Page_69">69</a></li>
-
-<li class="ifrst">hail storm, <a href="#Page_190">190</a></li>
-<li class="isub1">hand perforator, <a href="#Page_132">132</a>, <a href="#Page_134">134</a></li>
-<li class="isub1">handling information, <a href="#Page_10">10-18</a></li>
-<li class="isub1">harmonic analyzers, <a href="#Page_241">241-2</a></li>
-<li class="isub1">harmonic synthesizers, <a href="#Page_241">241-2</a></li>
-<li class="isub1">Harvard Computation Laboratory, <a href="#Page_89">89</a>, <a href="#Page_176">176-7</a>,
-              <a href="#Page_245">245</a>, <a href="#Page_249">249</a></li>
-<li class="isub1">Harvard IBM Automatic Sequence-Controlled Calculator (Mark I), <a href="#Page_10">10</a>,
-                <a href="#Page_89">89-112</a>, <a href="#Page_245">245-6</a>;</li>
-<li class="isub3">cost, <a href="#Page_109">109</a>;</li>
-<li class="isub3">efficiency, <a href="#Page_111">111</a>;</li>
-<li class="isub3">reliability, <a href="#Page_110">110</a>;</li>
-<li class="isub3">speed, <a href="#Page_109">109</a></li>
-<li class="isub1">Harvard Sequence-Controlled Electronic Calculator (Mark III), <a href="#Page_177">177</a></li>
-<li class="isub1">Harvard Sequence-Controlled Relay Calculator (Mark II),
-                  <a href="#Page_176">176-8</a>, <a href="#Page_249">249</a></li>
-<li class="isub1">Harvard University, <a href="#Page_1">1</a>, <a href="#Page_4">4</a>,
-         <a href="#Page_8">8</a>, <a href="#Page_89">89</a>,
-          <a href="#Page_176">176-7</a>, <a href="#Page_245">245</a>, <a href="#Page_249">249</a></li>
-<li class="isub1">hatred, <a href="#Page_206">206</a></li>
-<li class="isub1">hoppers, <a href="#Page_51">51</a></li>
-<li class="isub1">hub, <a href="#Page_46">46</a>, <a href="#Page_98">98</a></li>
-<li class="isub1">human brain, <a href="#Page_2">2-4</a>, <a href="#Page_16">16</a>, <a href="#Page_229">229</a></li>
-<li class="isub1">humidity, <a href="#Page_63">63</a></li>
-
-<li class="ifrst">IBM (International Business Machines), <a href="#Page_43">43-64</a>, <a href="#Page_89">89-90</a>, <a href="#Page_177">177</a>,
-                    <a href="#Page_233">233-9</a>, <a href="#Page_249">249-50</a></li>
-<li class="isub1">IBM Automatic Sequence-Controlled Calculator, <a href="#Page_10">10</a>, <a href="#Page_89">89-112</a>,
-                 <a href="#Page_245">245-6</a>;</li>
-<li class="isub3"><i>see also</i> Harvard IBM Automatic Sequence-Controlled Calculator</li>
-<li class="isub1">IBM card-programmed calculator, <a href="#Page_236">236</a></li>
-<li class="isub1">IBM pluggable sequence relay calculator, <a href="#Page_236">236</a></li>
-<li class="isub1">IBM punch-card machinery, <a href="#Page_43">43-64</a>, <a href="#Page_233">233-9</a></li>
-<li class="isub1">IBM Selective-Sequence Electronic Calculator, <a href="#Page_177">177-9</a>, <a href="#Page_249">249</a></li>
-<li class="isub1">ideographic writing, <a href="#Page_12">12</a></li>
-<li class="isub1">if, <a href="#Page_146">146-7</a></li>
-<li class="isub1">if ... then, <a href="#Page_149">149</a></li>
-<li class="isub1">ignorance, <a href="#Page_205">205</a></li>
-<li class="isub1">illness, <a href="#Page_191">191-2</a></li>
-<li class="isub1">imitative scheme, <a href="#Page_12">12</a></li>
-<li class="isub1">in-code, <a href="#Page_99">99</a></li>
-<li class="isub1">in-field, <a href="#Page_99">99</a></li>
-<li class="isub1">independent variable, <a href="#Page_81">81</a>, <a href="#Page_224">224</a></li>
-<li class="isub1">infinity, <a href="#Page_86">86</a>, <a href="#Page_133">133</a>, <a href="#Page_212">212</a>, <a href="#Page_225">225</a></li>
-<li class="isub1">information, <a href="#Page_10">10</a></li>
-<li class="isub1">initial conditions, <a href="#Page_83">83</a>, <a href="#Page_225">225</a></li>
-<li class="isub1">Initiating Unit, <a href="#Page_115">115-6</a></li>
-<li class="isub1">input, <a href="#Page_6">6</a>, <a href="#Page_90">90-1</a></li>
-<li class="isub1">input devices, <a href="#Page_175">175</a>, <a href="#Page_251">251-2</a></li>
-<li class="isub1">input register, <a href="#Page_27">27</a></li>
-<li class="isub1">instantaneous rate of change, <a href="#Page_70">70-1</a></li>
-<li class="isub1">Institute of Advanced Study, <a href="#Page_124">124</a></li>
-<li class="isub1">instructions, <a href="#Page_28">28</a>, <a href="#Page_83">83</a>, <a href="#Page_97">97</a>, <a href="#Page_178">178-9</a></li>
-<li class="isub1">insurance company, <a href="#Page_42">42</a></li>
-<li class="isub1">insurance policies, <a href="#Page_42">42</a></li>
-<li class="isub1">insurance values, <a href="#Page_88">88</a></li>
-<li class="isub1">integral, <a href="#Page_68">68</a>, <a href="#Page_71">71-2</a>, <a href="#Page_225">225</a></li>
-<li class="isub1">integral sign, <a href="#Page_85">85</a>, <a href="#Page_225">225</a></li>
-<li class="isub1">integrating, <a href="#Page_71">71-2</a>, <a href="#Page_78">78</a></li>
-<li class="isub1">integrator, <a href="#Page_78">78-80</a></li>
-<li class="isub1">integrator mechanism, <a href="#Page_78">78-9</a></li>
-<li class="isub1">International Business Machines Corporation (IBM), <a href="#Page_43">43</a>;</li>
-<li class="isub3"><i>see</i> IBM</li>
-<li class="isub1">International Hydrographic Bureau, <a href="#Page_242">242</a></li>
-<li class="isub1">International Phonetic Alphabet, <a href="#Page_13">13</a></li>
-<li class="isub1">interpolating, <a href="#Page_131">131</a>, <a href="#Page_221">221</a></li>
-<li class="isub1">interposing, <a href="#Page_102">102</a></li>
-<li class="isub1">interpreter, <a href="#Page_47">47</a>, <a href="#Page_49">49</a>, <a href="#Page_235">235</a></li>
-<li class="isub1">interpreting, <a href="#Page_49">49</a></li>
-<li class="isub1">interval, <a href="#Page_68">68</a>, <a href="#Page_70">70</a></li>
-<li class="isub1">intuitive thinking, <a href="#Page_8">8</a></li>
-<li class="isub1">inverse, <a href="#Page_71">71</a></li>
-
-<li class="ifrst">judgments, <a href="#Page_191">191</a></li>
-
-<li class="ifrst">Kalin-Burkhart Logical-Truth Calculator, <a href="#Page_144">144-66</a>, <a href="#Page_248">248</a>;</li>
-<li class="isub3">cost, <a href="#Page_165">165</a>;</li>
-<li class="isub3">reliability, <a href="#Page_166">166</a>;</li>
-<li class="isub3">speed, <a href="#Page_166">166</a></li>
-<li class="isub1">key punch, <a href="#Page_47">47-8</a>, <a href="#Page_96">96</a>, <a href="#Page_235">235</a></li>
-<li class="isub1">keyboard, <a href="#Page_48">48</a></li>
-<li class="isub1">knots, <a href="#Page_17">17</a>
-    <span class="pagenum" id="Page_266">[Pg 266]</span></li>
-
-<li class="ifrst">language of logic, <a href="#Page_56">56-62</a>, <a href="#Page_105">105</a>, <a href="#Page_140">140</a>;</li>
-<li class="isub3"><i>see also</i> mathematical logic</li>
-<li class="isub1">languages, <a href="#Page_10">10-21</a>, <a href="#Page_231">231</a></li>
-<li class="isub1">latch relay, <a href="#Page_40">40-1</a></li>
-<li class="isub1">left-hand components, <a href="#Page_56">56</a>, <a href="#Page_121">121</a>, <a href="#Page_215">215</a></li>
-<li class="isub1">library, <a href="#Page_9">9</a>, <a href="#Page_181">181</a></li>
-<li class="isub1">Library of Congress, <a href="#Page_15">15</a></li>
-<li class="isub1">lie detector, <a href="#Page_192">192</a></li>
-<li class="isub1">line of coding, <a href="#Page_99">99</a></li>
-<li class="isub1">linear, <a href="#Page_224">224-5</a></li>
-<li class="isub1">linear interpolation, <a href="#Page_221">221</a></li>
-<li class="isub1">linear simultaneous equations, <a href="#Page_141">141</a>, <a href="#Page_225">225</a></li>
-<li class="isub1">lobe, <a href="#Page_94">94-5</a></li>
-<li class="isub1">logarithm, <a href="#Page_67">67</a>, <a href="#Page_85">85</a>, <a href="#Page_106">106-8</a>, <a href="#Page_139">139</a>, <a href="#Page_225">225</a></li>
-<li class="isub1">Logarithm-In-Out counter, <a href="#Page_107">107</a></li>
-<li class="isub1">logic, <a href="#Page_144">144</a>;</li>
-<li class="isub3"><i>see also</i> mathematical logic</li>
-<li class="isub1">logical choice, <a href="#Page_4">4</a>;</li>
-<li class="isub3"><i>see also</i> mathematical logic</li>
-<li class="isub1">logical connective, <a href="#Page_148">148</a>, <a href="#Page_222">222</a></li>
-<li class="isub1">logical operations, <a href="#Page_56">56-62</a>, <a href="#Page_173">173</a></li>
-<li class="isub1">logical pattern, <a href="#Page_145">145-6</a></li>
-<li class="isub1">logical truth, <a href="#Page_144">144-56</a>, <a href="#Page_166">166</a></li>
-<li class="isub1">Logical-Truth Calculator, <a href="#Page_144">144-66</a>;</li>
-<li class="isub3"><i>see</i> Kalin-Burkhart Logical-Truth Calculator</li>
-<li class="isub1">loopholes, <a href="#Page_149">149</a></li>
-<li class="isub1">Low Primary (output of sequencer), <a href="#Page_61">61-2</a></li>
-<li class="isub1">Low Secondary (output of sequencer), <a href="#Page_61">61-2</a></li>
-<li class="isub1">Lower Brushes, <a href="#Page_52">52</a></li>
-<li class="isub1">loxodrome, <a href="#Page_69">69-70</a></li>
-
-<li class="ifrst">machine call number, <a href="#Page_99">99</a></li>
-<li class="isub1">machine cycle, <a href="#Page_56">56</a></li>
-<li class="isub1">machine language, <a href="#Page_29">29</a>, <a href="#Page_99">99</a>, <a href="#Page_175">175</a>, <a href="#Page_191">191</a></li>
-<li class="isub1">machines as a language for thinking, <a href="#Page_19">19-20</a>;</li>
-<li class="isub3">references, <a href="#Page_231">231-2</a></li>
-<li class="isub1">machines involving voice and speech, <a href="#Page_185">185-6</a>, <a href="#Page_254">254</a></li>
-<li class="isub1">magnetic surfaces, <a href="#Page_17">17</a>, <a href="#Page_20">20</a>, <a href="#Page_168">168-70</a>, <a href="#Page_179">179</a></li>
-<li class="isub1">magnetic tape, <a href="#Page_169">169-70</a>, <a href="#Page_179">179</a></li>
-<li class="isub1">magnetic wire, <a href="#Page_168">168</a></li>
-<li class="isub1">magnetized spot, <a href="#Page_168">168-70</a></li>
-<li class="isub1">main connective, <a href="#Page_160">160</a></li>
-<li class="isub1">many-wire cable, <a href="#Page_50">50</a></li>
-<li class="isub1">Mark I (Harvard IBM Automatic Sequence-Controlled Calculator), <a href="#Page_10">10</a>,
-                <a href="#Page_89">89-112</a>, <a href="#Page_245">245-6</a>;</li>
-<li class="isub3"><i>see also</i> Harvard IBM Automatic Sequence-Controlled Calculator</li>
-<li class="isub1">Mark II (Harvard Sequence-Controlled Relay Calculator), <a href="#Page_176">176-8</a>, <a href="#Page_249">249</a></li>
-<li class="isub1">Mark III (Harvard Sequence-Controlled Electronic Calculator), <a href="#Page_177">177</a></li>
-<li class="isub1">Massachusetts Institute of Technology, <a href="#Page_1">1</a>, <a href="#Page_20">20</a>, <a href="#Page_65">65</a>,
-               <a href="#Page_72">72-88</a>, <a href="#Page_153">153</a></li>
-<li class="isub1">Massachusetts Institute of Technology’s Differential Analyzer No. 2, <a href="#Page_65">65-88</a>;</li>
-<li class="isub3">accuracy, <a href="#Page_86">86</a>;</li>
-<li class="isub3">cost, <a href="#Page_87">87</a>;</li>
-<li class="isub3">reliability, <a href="#Page_87">87</a>;</li>
-<li class="isub3">speed, <a href="#Page_87">87</a></li>
-<li class="isub1">master card, <a href="#Page_50">50</a></li>
-<li class="isub1">Master Programmer, <a href="#Page_115">115-6</a></li>
-<li class="isub1">matching, <a href="#Page_173">173</a></li>
-<li class="isub1">mathematical biophysics, <a href="#Page_230">230</a></li>
-<li class="isub1">mathematical logic, <a href="#Page_26">26</a>, <a href="#Page_36">36</a>,
-         <a href="#Page_56">56-62</a>, <a href="#Page_105">105</a>,
-         <a href="#Page_140">140</a>, <a href="#Page_151">151-2</a>, <a href="#Page_164">164</a>,
-         <a href="#Page_221">221-3</a>, <a href="#Page_248">248</a></li>
-<li class="isub1">matrices, <a href="#Page_173">173</a>, <a href="#Page_227">227</a></li>
-<li class="isub1">matrix, <a href="#Page_173">173</a>, <a href="#Page_227">227</a></li>
-<li class="isub1">meanings, <a href="#Page_209">209</a>, <a href="#Page_231">231</a></li>
-<li class="isub1">measurements, <a href="#Page_65">65-6</a>, <a href="#Page_68">68</a></li>
-<li class="isub1">mechanical brain, <a href="#Page_1">1</a>, <a href="#Page_5">5-8</a>, <a href="#Page_20">20</a>;</li>
-<li class="isub3">crucial devices for, <a href="#Page_20">20</a></li>
-<li class="isub1">mechanical brains under construction, <a href="#Page_176">176-9</a></li>
-<li class="isub1">memory, <a href="#Page_27">27</a>, <a href="#Page_90">90-1</a></li>
-<li class="isub1">mentality, <a href="#Page_24">24</a>, <a href="#Page_27">27</a></li>
-<li class="isub1">mercury tank, <a href="#Page_171">171</a>, <a href="#Page_179">179</a></li>
-<li class="isub1">merging, <a href="#Page_173">173</a></li>
-<li class="isub1">metal fingers, <a href="#Page_135">135</a></li>
-<li class="isub1">mica, <a href="#Page_172">172</a></li>
-<li class="isub1">microphone, <a href="#Page_185">185</a></li>
-<li class="isub1">mimeograph stencil, <a href="#Page_16">16</a></li>
-<li class="isub1">Minoan, <a href="#Page_188">188</a></li>
-<li class="isub1">miscellaneous field, <a href="#Page_99">99</a>
-    <span class="pagenum" id="Page_267">[Pg 267]</span></li>
-<li class="isub1">mistake, <a href="#Page_134">134</a></li>
-<li class="isub1">Moore School of Electrical Engineering, <a href="#Page_7">7</a>, <a href="#Page_113">113-27</a>,
-                           <a href="#Page_177">177</a>, <a href="#Page_249">249</a></li>
-<li class="isub1">multiplicand, <a href="#Page_223">223</a></li>
-<li class="isub1">multiplicand counter, <a href="#Page_101">101</a></li>
-<li class="isub1">multiplication schemes, <a href="#Page_214">214-6</a></li>
-<li class="isub1">multiplier, <a href="#Page_115">115-6</a></li>
-<li class="isub1">multiplier counter, <a href="#Page_101">101</a></li>
-<li class="isub1">multiply-divide unit, <a href="#Page_103">103</a></li>
-<li class="isub1">multiplying, <a href="#Page_55">55-6</a>, <a href="#Page_101">101</a>, <a href="#Page_121">121</a>, <a href="#Page_140">140</a></li>
-<li class="isub1">multiplying punch, <a href="#Page_47">47</a>, <a href="#Page_52">52</a>, <a href="#Page_235">235</a></li>
-
-<li class="ifrst">National Advisory Committee for Aeronautics, <a href="#Page_128">128</a>, <a href="#Page_132">132</a></li>
-<li class="isub1">Naval Proving Ground, <a href="#Page_177">177</a></li>
-<li class="isub1">negation, <a href="#Page_24">24-5</a>, <a href="#Page_27">27</a>, <a href="#Page_34">34-6</a></li>
-<li class="isub1">negation circuit, <a href="#Page_36">36</a></li>
-<li class="isub1">negative, <a href="#Page_147">147</a></li>
-<li class="isub1">negative digit, <a href="#Page_215">215</a></li>
-<li class="isub1">neon bulb, <a href="#Page_119">119</a></li>
-<li class="isub1">nerve, <a href="#Page_2">2-4</a></li>
-<li class="isub1">nerve cell, <a href="#Page_2">2</a>, <a href="#Page_3">3</a>, <a href="#Page_16">16</a></li>
-<li class="isub1">nerve fiber, <a href="#Page_2">2</a>, <a href="#Page_3">3</a></li>
-<li class="isub1">nerve networks, <a href="#Page_230">230</a></li>
-<li class="isub1">nervous system, <a href="#Page_188">188</a></li>
-<li class="isub1">network analyzers, <a href="#Page_242">242-4</a></li>
-<li class="isub1">neurosis, <a href="#Page_191">191</a></li>
-<li class="isub1">nine-pulses, <a href="#Page_120">120-1</a></li>
-<li class="isub1">nines complement, <a href="#Page_95">95</a>, <a href="#Page_121">121</a>, <a href="#Page_223">223</a></li>
-<li class="isub1">No X, <a href="#Page_59">59</a></li>
-<li class="isub1">Northrop Aircraft, Inc., <a href="#Page_179">179</a></li>
-<li class="isub1">not, <a href="#Page_146">146-8</a></li>
-<li class="isub1">numeric coding, <a href="#Page_13">13</a>, <a href="#Page_54">54</a></li>
-<li class="isub1">numerical X position, <a href="#Page_45">45</a></li>
-<li class="isub1">numerical Y position, <a href="#Page_45">45</a></li>
-
-<li class="ifrst">occupation code, <a href="#Page_54">54</a></li>
-<li class="isub1">octal notation, <a href="#Page_179">179</a>, <a href="#Page_219">219</a></li>
-<li class="isub1">ohm, <a href="#Page_117">117</a></li>
-<li class="isub1">Ojibwa, <a href="#Page_12">12</a></li>
-<li class="isub1">ones complement, <a href="#Page_217">217</a></li>
-<li class="isub1">only, <a href="#Page_146">146-7</a></li>
-<li class="isub1">operation code, <a href="#Page_103">103</a></li>
-<li class="isub1">operations with numbers, <a href="#Page_24">24-7</a></li>
-<li class="isub1">or, <a href="#Page_146">146-9</a></li>
-<li class="isub1">organization of digital machines, <a href="#Page_251">251</a></li>
-<li class="isub1">out-code, <a href="#Page_99">99</a></li>
-<li class="isub1">out-field, <a href="#Page_99">99</a></li>
-<li class="isub1">output, <a href="#Page_6">6</a>, <a href="#Page_90">90-1</a>, <a href="#Page_251">251-2</a></li>
-<li class="isub1">output devices, <a href="#Page_176">176</a>, <a href="#Page_251">251-2</a></li>
-<li class="isub1">output register, <a href="#Page_27">27</a></li>
-
-<li class="ifrst">paper channel, <a href="#Page_52">52</a></li>
-<li class="isub1">partial differential equations, <a href="#Page_87">87</a></li>
-<li class="isub1">partial products, <a href="#Page_115">115</a>, <a href="#Page_214">214</a></li>
-<li class="isub1">Pearl Assurance Company, <a href="#Page_88">88</a></li>
-<li class="isub1">pebbles, <a href="#Page_17">17-8</a></li>
-<li class="isub1">pen with a motor, <a href="#Page_180">180</a>, <a href="#Page_195">195</a></li>
-<li class="isub1">permanent table frames, <a href="#Page_138">138-9</a></li>
-<li class="isub1">personal income tax, <a href="#Page_141">141</a></li>
-<li class="isub1">phonetic writing, <a href="#Page_13">13</a></li>
-<li class="isub1">phonograph, <a href="#Page_15">15-6</a></li>
-<li class="isub1">phonographic writing, <a href="#Page_13">13</a></li>
-<li class="isub1">phototube, <a href="#Page_81">81-2</a>, <a href="#Page_183">183-4</a></li>
-<li class="isub1">physical equipment for handling information, <a href="#Page_11">11</a>,
-                    <a href="#Page_15">15-21</a>, <a href="#Page_91">91</a></li>
-<li class="isub1">physical problems, <a href="#Page_69">69-72</a></li>
-<li class="isub1">physical quantities, <a href="#Page_67">67-9</a></li>
-<li class="isub1">pictographic writing, <a href="#Page_12">12</a></li>
-<li class="isub1">plugboard, <a href="#Page_46">46</a>, <a href="#Page_98">98</a></li>
-<li class="isub1">plug-in units, <a href="#Page_117">117-8</a></li>
-<li class="isub1">point of view, <a href="#Page_207">207</a></li>
-<li class="isub1">pooh-pooh theory, <a href="#Page_12">12</a></li>
-<li class="isub1">position (in a punch card), <a href="#Page_45">45</a></li>
-<li class="isub1">position frames, <a href="#Page_138">138-9</a></li>
-<li class="isub1">power, <a href="#Page_43">43</a>, <a href="#Page_65">65</a>, <a href="#Page_133">133</a>,
-                      <a href="#Page_216">216</a>, <a href="#Page_224">224</a></li>
-<li class="isub1">prejudice, <a href="#Page_205">205</a></li>
-<li class="isub1">Previous (input of comparer), <a href="#Page_57">57</a></li>
-<li class="isub1">Primary (input of sequencer), <a href="#Page_61">61-2</a></li>
-<li class="isub1">Primary Brushes, <a href="#Page_51">51</a>, <a href="#Page_62">62</a></li>
-<li class="isub1">Primary Feed, <a href="#Page_51">51</a>, <a href="#Page_61">61</a></li>
-<li class="isub1">Primary Sequence Brushes, <a href="#Page_51">51</a></li>
-<li class="isub1">printer, <a href="#Page_137">137</a></li>
-<li class="isub1">printer frames, <a href="#Page_138">138</a></li>
-<li class="isub1">problem frames, <a href="#Page_138">138</a></li>
-<li class="isub1">problem position, <a href="#Page_132">132</a>, <a href="#Page_135">135</a></li>
-<li class="isub1">problem tape, <a href="#Page_134">134</a></li>
-<li class="isub1">processor, <a href="#Page_132">132</a>, <a href="#Page_134">134</a>, <a href="#Page_175">175</a></li>
-<li class="isub1">product, <a href="#Page_70">70</a>, <a href="#Page_102">102</a>, <a href="#Page_223">223</a></li>
-<li class="isub1">product counter, <a href="#Page_102">102</a></li>
-<li class="isub1">production scheduling, <a href="#Page_193">193</a></li>
-<li class="isub1">program, <a href="#Page_122">122</a>, <a href="#Page_173">173</a>, <a href="#Page_252">252-3</a></li>
-<li class="isub1">program-control switch, <a href="#Page_123">123</a>
-    <span class="pagenum" id="Page_268">[Pg 268]</span></li>
-<li class="isub1">program pulse, <a href="#Page_122">122</a></li>
-<li class="isub1">program-pulse input terminal, <a href="#Page_123">123</a></li>
-<li class="isub1">program register, <a href="#Page_38">38</a></li>
-<li class="isub1">program tape, <a href="#Page_28">28-9</a></li>
-<li class="isub1">program trays, <a href="#Page_119">119</a></li>
-<li class="isub1">program trunk lines, <a href="#Page_119">119</a></li>
-<li class="isub1">programming method of von Neumann, <a href="#Page_124">124</a></li>
-<li class="isub1">pronoun, <a href="#Page_223">223</a></li>
-<li class="isub1">psychological testing, <a href="#Page_190">190</a></li>
-<li class="isub1">psychological trainer, <a href="#Page_191">191-2</a></li>
-<li class="isub1">pulses, <a href="#Page_120">120</a>, <a href="#Page_171">171</a></li>
-<li class="isub1">punch card, <a href="#Page_17">17</a>, <a href="#Page_44">44-5</a>,
-               <a href="#Page_95">95</a>, <a href="#Page_97">97</a></li>
-<li class="isub1">punch-card column, <a href="#Page_45">45</a></li>
-<li class="isub1">punch-card machinery, <a href="#Page_17">17</a>, <a href="#Page_20">20</a>,
-                     <a href="#Page_42">42-64</a>, <a href="#Page_232">232-9</a>;</li>
-<li class="isub3">cost, <a href="#Page_63">63</a>;</li>
-<li class="isub3">reliability, <a href="#Page_63">63-4</a>;</li>
-<li class="isub3">speed, <a href="#Page_62">62-3</a></li>
-<li class="isub1">punch feed, <a href="#Page_51">51-2</a></li>
-<li class="isub1">punched paper tape, <a href="#Page_17">17</a>, <a href="#Page_23">23</a>,
-                 <a href="#Page_82">82</a>, <a href="#Page_95">95</a></li>
-<li class="isub1">punching channel, <a href="#Page_50">50</a></li>
-<li class="isub1">punching dies, <a href="#Page_48">48</a>, <a href="#Page_51">51-2</a></li>
-<li class="isub1">pyramid circuit, <a href="#Page_39">39</a></li>
-
-<li class="ifrst">quantity of information, <a href="#Page_11">11</a>, <a href="#Page_14">14-15</a></li>
-<li class="isub1">quartz, <a href="#Page_171">171</a></li>
-<li class="isub1">quotient, <a href="#Page_98">98</a>, <a href="#Page_103">103</a></li>
-
-<li class="ifrst"><i>R.U.R.</i>, <a href="#Page_199">199</a></li>
-<li class="isub1">radar, <a href="#Page_183">183</a></li>
-<li class="isub1">railroad line, <a href="#Page_6">6</a>, <a href="#Page_119">119</a></li>
-<li class="isub1">rapid approximation, <a href="#Page_106">106-8</a>, <a href="#Page_220">220-1</a></li>
-<li class="isub1">rate of change, <a href="#Page_68">68</a>, <a href="#Page_70">70-1</a></li>
-<li class="isub1">ratio, <a href="#Page_77">77</a>, <a href="#Page_83">83</a></li>
-<li class="isub1">Raytheon Computer, <a href="#Page_250">250</a></li>
-<li class="isub1">reading, <a href="#Page_57">57</a></li>
-<li class="isub1">reading brushes, <a href="#Page_51">51-2</a></li>
-<li class="isub1">reading channel, <a href="#Page_50">50</a></li>
-<li class="isub1">reading of punch cards, <a href="#Page_44">44</a></li>
-<li class="isub1">reasoning, <a href="#Page_144">144</a></li>
-<li class="isub1">rebus-writing, <a href="#Page_13">13</a></li>
-<li class="isub1">reciprocal, <a href="#Page_85">85</a>, <a href="#Page_224">224</a></li>
-<li class="isub1">recognizing, <a href="#Page_8">8</a>, <a href="#Page_182">182-5</a></li>
-<li class="isub1">recorder, <a href="#Page_132">132</a>, <a href="#Page_137">137</a></li>
-<li class="isub1">rectifier, <a href="#Page_32">32</a></li>
-<li class="isub1">referent, <a href="#Page_12">12</a></li>
-<li class="isub1">register, <a href="#Page_27">27</a></li>
-<li class="isub1">reject, <a href="#Page_49">49</a></li>
-<li class="isub1">relay, <a href="#Page_17">17</a>, <a href="#Page_20">20-1</a>,
-                         <a href="#Page_23">23</a>, <a href="#Page_92">92</a>,
-                         <a href="#Page_129">129</a>, <a href="#Page_133">133</a>,
-                         <a href="#Page_178">178</a>;</li>
-<li class="isub3">Common, <a href="#Page_21">21</a>;</li>
-<li class="isub3">Ground, <a href="#Page_21">21</a>;</li>
-<li class="isub3">Normally Closed, <a href="#Page_21">21</a>;</li>
-<li class="isub3">Normally Open, <a href="#Page_21">21</a>;</li>
-<li class="isub3">Pickup, <a href="#Page_21">21</a></li>
-<li class="isub1">release key, <a href="#Page_48">48</a></li>
-<li class="isub1">reliability, <a href="#Page_63">63-4</a>, <a href="#Page_110">110</a>,
-             <a href="#Page_126">126</a>, <a href="#Page_128">128</a>,
-             <a href="#Page_141">141-2</a>, <a href="#Page_166">166</a>,
-             <a href="#Page_168">168</a>, <a href="#Page_174">174</a></li>
-<li class="isub1">Remington-Rand, <a href="#Page_43">43</a></li>
-<li class="isub1">reperforator, <a href="#Page_137">137</a></li>
-<li class="isub1">rephrasing, <a href="#Page_163">163-4</a></li>
-<li class="isub1">reproducer, <a href="#Page_47">47</a>, <a href="#Page_49">49-50</a>,
-                              <a href="#Page_235">235</a></li>
-<li class="isub1">reproducing, <a href="#Page_49">49</a></li>
-<li class="isub1">reset code, <a href="#Page_100">100</a></li>
-<li class="isub1">resetting, <a href="#Page_100">100</a></li>
-<li class="isub1">resistance, <a href="#Page_80">80</a>, <a href="#Page_117">117</a></li>
-<li class="isub1">resistance coefficient, <a href="#Page_80">80</a></li>
-<li class="isub1">resistor, <a href="#Page_117">117</a></li>
-<li class="isub1">right-hand components, <a href="#Page_56">56</a>, <a href="#Page_121">121</a>, <a href="#Page_215">215</a></li>
-<li class="isub1">robot machine, <a href="#Page_197">197</a>, <a href="#Page_198">198-208</a>, <a href="#Page_255">255</a></li>
-<li class="isub1">robot salesman, <a href="#Page_201">201</a></li>
-<li class="isub1"><i>robota</i> (Czech), <a href="#Page_199">199</a></li>
-<li class="isub1">Roman numerals, <a href="#Page_212">212</a>;</li>
-<li class="isub3">ancient style, <a href="#Page_219">219</a></li>
-<li class="isub1">room, <a href="#Page_70">70</a></li>
-<li class="isub1">Rossum’s Universal Robots, <a href="#Page_199">199</a></li>
-<li class="isub1">rounding off, <a href="#Page_55">55-6</a></li>
-<li class="isub1">routine, <a href="#Page_8">8</a>, <a href="#Page_167">167</a>, <a href="#Page_173">173</a></li>
-<li class="isub1">routine frames, <a href="#Page_138">138-9</a></li>
-<li class="isub1">routine tape, <a href="#Page_28">28</a>, <a href="#Page_134">134</a></li>
-<li class="isub1">rules, <a href="#Page_191">191</a>, <a href="#Page_224">224</a></li>
-
-<li class="ifrst">satisfy, <a href="#Page_225">225</a></li>
-<li class="isub1">scale factor, <a href="#Page_74">74</a>, <a href="#Page_86">86</a></li>
-<li class="isub1">schemes for expressing meanings, <a href="#Page_11">11-15</a></li>
-<li class="isub1">screen, <a href="#Page_172">172</a></li>
-<li class="isub1">screw, <a href="#Page_78">78</a></li>
-<li class="isub1">Secondary (input of sequencer), <a href="#Page_61">61-2</a></li>
-<li class="isub1">Secondary Brushes, <a href="#Page_51">51</a>, <a href="#Page_62">62</a></li>
-<li class="isub1">Secondary Feed, <a href="#Page_61">61</a></li>
-<li class="isub1">Select-Receiving-Register circuit, <a href="#Page_39">39</a></li>
-<li class="isub1">selecting, <a href="#Page_26">26</a>, <a href="#Page_58">58</a>, <a href="#Page_104">104</a></li>
-<li class="isub1">selection, <a href="#Page_26">26-7</a>, <a href="#Page_38">38</a>, <a href="#Page_222">222</a></li>
-<li class="isub1">selection circuit, <a href="#Page_38">38</a></li>
-<li class="isub1">selection counter, <a href="#Page_104">104</a>
-    <span class="pagenum" id="Page_269">[Pg 269]</span></li>
-<li class="isub1">selector, <a href="#Page_58">58-60</a></li>
-<li class="isub1">sensing digits, <a href="#Page_108">108</a></li>
-<li class="isub1">separation sign, <a href="#Page_129">129</a></li>
-<li class="isub1">sequence-control tape, <a href="#Page_98">98</a></li>
-<li class="isub1">sequence-control-tape code, <a href="#Page_98">98</a></li>
-<li class="isub1">sequence-controlled, <a href="#Page_89">89</a></li>
-<li class="isub1">sequence-tape feed, <a href="#Page_98">98</a></li>
-<li class="isub1">sequencer, <a href="#Page_61">61</a></li>
-<li class="isub1">sequencing, <a href="#Page_61">61</a></li>
-<li class="isub1">shifting, <a href="#Page_217">217</a></li>
-<li class="isub1">short-cut multiplication, <a href="#Page_215">215-6</a></li>
-<li class="isub1">Simon, <a href="#Page_22">22-40</a></li>
-<li class="isub1">simultaneous, <a href="#Page_225">225</a></li>
-<li class="isub1">simultaneous equations, <a href="#Page_85">85</a>, <a href="#Page_225">225</a></li>
-<li class="isub1">sine, <a href="#Page_75">75</a>, <a href="#Page_85">85</a>, <a href="#Page_106">106</a>, <a href="#Page_139">139</a>, <a href="#Page_226">226</a></li>
-<li class="isub1">sink (of a circuit), <a href="#Page_154">154</a></li>
-<li class="isub1">slab, <a href="#Page_18">18</a></li>
-<li class="isub1">slide rule, <a href="#Page_65">65</a>, <a href="#Page_67">67</a></li>
-<li class="isub1">smoothness, <a href="#Page_110">110</a>, <a href="#Page_227">227</a></li>
-<li class="isub1">social control, types, <a href="#Page_203">203</a></li>
-<li class="isub1">sorter, <a href="#Page_47">47-9</a></li>
-<li class="isub1">sorting, <a href="#Page_57">57</a>, <a href="#Page_173">173</a></li>
-<li class="isub1">soundtracks, <a href="#Page_16">16</a>, <a href="#Page_18">18</a></li>
-<li class="isub1">source (of a circuit), <a href="#Page_154">154</a></li>
-<li class="isub1">space key, <a href="#Page_48">48</a></li>
-<li class="isub1">speedometer, <a href="#Page_68">68</a></li>
-<li class="isub1">spelling rules, <a href="#Page_185">185</a></li>
-<li class="isub1">spoken English, <a href="#Page_11">11</a></li>
-<li class="isub1">square, <a href="#Page_224">224</a></li>
-<li class="isub1">square matrix, <a href="#Page_227">227</a></li>
-<li class="isub1">square root, <a href="#Page_116">116-7</a>, <a href="#Page_173">173</a>,
-                    <a href="#Page_220">220</a>, <a href="#Page_224">224</a></li>
-<li class="isub1">Start Key, <a href="#Page_98">98</a></li>
-<li class="isub1">statements, <a href="#Page_26">26</a>, <a href="#Page_144">144-51</a></li>
-<li class="isub1">static electricity, <a href="#Page_63">63</a></li>
-<li class="isub1">storage, <a href="#Page_6">6</a></li>
-<li class="isub1">storage counter, <a href="#Page_93">93</a></li>
-<li class="isub1">storage devices, <a href="#Page_252">252</a></li>
-<li class="isub1">storage register, <a href="#Page_28">28</a>, <a href="#Page_93">93</a></li>
-<li class="isub1">storing information, <a href="#Page_15">15</a></li>
-<li class="isub1">storing register frames, <a href="#Page_138">138</a></li>
-<li class="isub1">storing registers, <a href="#Page_139">139</a></li>
-<li class="isub1">string, <a href="#Page_65">65-6</a></li>
-<li class="isub1">stylus, <a href="#Page_16">16</a></li>
-<li class="isub1">subroutine, <a href="#Page_106">106</a></li>
-<li class="isub1">Subsidiary Sequence Mechanism, <a href="#Page_90">90</a>, <a href="#Page_106">106</a></li>
-<li class="isub1">subtract output, <a href="#Page_120">120</a></li>
-<li class="isub1">subtracting, <a href="#Page_55">55</a>, <a href="#Page_100">100</a>, <a href="#Page_119">119</a>,
-             <a href="#Page_139">139</a>, <a href="#Page_223">223</a></li>
-<li class="isub1">subtracting by adding, <a href="#Page_223">223</a></li>
-<li class="isub1">summary punch, <a href="#Page_50">50</a>, <a href="#Page_116">116</a>, <a href="#Page_119">119</a></li>
-<li class="isub1">summary-punching, <a href="#Page_50">50</a></li>
-<li class="isub1">switch open and current flowing, <a href="#Page_154">154</a></li>
-<li class="isub1">switchboard, <a href="#Page_76">76</a></li>
-<li class="isub1">switches in parallel, <a href="#Page_154">154</a></li>
-<li class="isub1">switches in series, <a href="#Page_154">154</a></li>
-<li class="isub1">switching circuits, <a href="#Page_155">155</a></li>
-<li class="isub1">syllable-writing, <a href="#Page_13">13</a></li>
-<li class="isub1">syllables, <a href="#Page_211">211</a></li>
-<li class="isub1">syllogism, <a href="#Page_146">146</a>, <a href="#Page_152">152</a></li>
-<li class="isub1">symbolic logic, <a href="#Page_221">221-3</a>, <a href="#Page_248">248</a>;</li>
-<li class="isub3"><i>see also</i> mathematical logic</li>
-<li class="isub1">symbolic writing, <a href="#Page_12">12</a></li>
-<li class="isub1">synapse, <a href="#Page_3">3</a></li>
-<li class="isub1">System of Electric Remote-Control Accounting, <a href="#Page_250">250</a></li>
-<li class="isub1">systems for handling information, <a href="#Page_10">10</a></li>
-
-<li class="ifrst">table tape, <a href="#Page_134">134</a></li>
-<li class="isub1">tables (of values), <a href="#Page_103">103</a>, <a href="#Page_136">136</a>, <a href="#Page_224">224</a></li>
-<li class="isub1">tabular value, <a href="#Page_136">136</a>, <a href="#Page_224">224</a></li>
-<li class="isub1">tabulator, <a href="#Page_47">47</a>, <a href="#Page_52">52</a>, <a href="#Page_119">119</a>, <a href="#Page_235">235</a></li>
-<li class="isub1">tallies, <a href="#Page_17">17</a></li>
-<li class="isub1">tangent, <a href="#Page_105">105</a>, <a href="#Page_226">226</a></li>
-<li class="isub1">tank (armored), <a href="#Page_180">180</a>, <a href="#Page_195">195</a></li>
-<li class="isub1">tank (mercury tank), <a href="#Page_171">171</a>, <a href="#Page_179">179</a></li>
-<li class="isub1">tape-controlled carriage, <a href="#Page_236">236</a></li>
-<li class="isub1">tape feed, <a href="#Page_91">91</a>, <a href="#Page_178">178-9</a></li>
-<li class="isub1">tape punch, <a href="#Page_91">91</a>, <a href="#Page_97">97-8</a>,
-                              <a href="#Page_137">137</a></li>
-<li class="isub1">tape reels, <a href="#Page_170">170</a></li>
-<li class="isub1">tape transmitter, <a href="#Page_135">135</a>, <a href="#Page_137">137</a></li>
-<li class="isub1">telegraph line, <a href="#Page_6">6</a>, <a href="#Page_119">119</a></li>
-<li class="isub1">telephone central station, <a href="#Page_138">138</a></li>
-<li class="isub1">teletype, <a href="#Page_17">17</a></li>
-<li class="isub1">teletype transmitter, <a href="#Page_133">133</a>, <a href="#Page_135">135</a></li>
-<li class="isub1">teletypewriter, <a href="#Page_130">130</a>, <a href="#Page_137">137</a></li>
-<li class="isub1">ten-position relay, <a href="#Page_91">91-3</a></li>
-<li class="isub1">ten-position switch, <a href="#Page_91">91-2</a></li>
-<li class="isub1">ten-pulses, <a href="#Page_120">120-1</a></li>
-<li class="isub1">tens complement, <a href="#Page_224">224</a></li>
-<li class="isub1">test scoring machine, <a href="#Page_236">236</a></li>
-<li class="isub1">then, <a href="#Page_146">146-7</a></li>
-<li class="isub1">thermostat, <a href="#Page_187">187</a>
-    <span class="pagenum" id="Page_270">[Pg 270]</span></li>
-<li class="isub1">thinking, <a href="#Page_1">1-5</a>, <a href="#Page_10">10</a>, <a href="#Page_97">97</a></li>
-<li class="isub1">timed electrical currents, <a href="#Page_44">44</a></li>
-<li class="isub1">timing contact, <a href="#Page_94">94</a></li>
-<li class="isub1">tolerances, <a href="#Page_67">67</a>, <a href="#Page_105">105</a></li>
-<li class="isub1">torque, <a href="#Page_73">73</a>, <a href="#Page_86">86</a></li>
-<li class="isub1">torque amplifier, <a href="#Page_73">73</a></li>
-<li class="isub1">trajectories, <a href="#Page_69">69</a>, <a href="#Page_114">114</a>, <a href="#Page_141">141</a></li>
-<li class="isub1">transfer circuit, <a href="#Page_33">33</a></li>
-<li class="isub1">transferring, <a href="#Page_31">31</a>, <a href="#Page_34">34</a>, <a href="#Page_100">100</a>, <a href="#Page_119">119</a>, <a href="#Page_167">167</a></li>
-<li class="isub1">translating, <a href="#Page_57">57</a></li>
-<li class="isub1">transmitter, <a href="#Page_74">74</a></li>
-<li class="isub1">triggering control, <a href="#Page_183">183</a>, <a href="#Page_186">186-7</a></li>
-<li class="isub1">trigonometric tables, <a href="#Page_226">226</a></li>
-<li class="isub1">trigonometric tangent, <a href="#Page_105">105</a>, <a href="#Page_226">226</a></li>
-<li class="isub1">truth, <a href="#Page_144">144</a></li>
-<li class="isub1">truth table, <a href="#Page_147">147</a>, <a href="#Page_155">155</a>, <a href="#Page_222">222</a></li>
-<li class="isub1">truth value, <a href="#Page_26">26</a>, <a href="#Page_58">58</a>, <a href="#Page_105">105</a>, <a href="#Page_147">147</a>, <a href="#Page_222">222</a></li>
-<li class="isub1">tuning, <a href="#Page_183">183</a></li>
-<li class="isub1">turning force, <a href="#Page_72">72</a></li>
-<li class="isub1">12 position, <a href="#Page_45">45</a></li>
-<li class="isub1">two-position relay, <a href="#Page_21">21</a>, <a href="#Page_91">91-2</a>;</li>
-<li class="isub3"><i>see also</i> relay</li>
-<li class="isub1">two-position switch, <a href="#Page_91">91-2</a></li>
-<li class="isub1">typewriter, <a href="#Page_16">16</a>, <a href="#Page_18">18</a></li>
-<li class="isub1">typewriter carriage, <a href="#Page_53">53</a></li>
-
-<li class="ifrst">unattended operation, <a href="#Page_174">174</a></li>
-<li class="isub1">understanding, <a href="#Page_212">212-3</a>, <a href="#Page_231">231</a></li>
-<li class="isub1">unemployment, <a href="#Page_201">201-2</a></li>
-<li class="isub1">Unequal (output of comparer), <a href="#Page_57">57</a></li>
-<li class="isub1">unit of information, <a href="#Page_11">11</a>, <a href="#Page_14">14-5</a>,
-                         <a href="#Page_169">169</a></li>
-<li class="isub1">United Nations, <a href="#Page_203">203</a>, <a href="#Page_208">208</a></li>
-<li class="isub1">United States Army Ordnance Department, <a href="#Page_113">113-4</a></li>
-<li class="isub1">Univac, <a href="#Page_250">250</a></li>
-<li class="isub1">University of Pennsylvania, <a href="#Page_7">7</a>, <a href="#Page_113">113</a></li>
-<li class="isub1">unknowns, <a href="#Page_141">141</a></li>
-<li class="isub1">Upper Brushes, <a href="#Page_52">52</a></li>
-
-<li class="ifrst">value tape code, <a href="#Page_96">96</a></li>
-<li class="isub1">value tape feed, <a href="#Page_95">95-6</a></li>
-<li class="isub1">variables, <a href="#Page_84">84</a>, <a href="#Page_223">223</a></li>
-<li class="isub1"><i>vel</i> (Latin), <a href="#Page_149">149</a></li>
-<li class="isub1">verifier, <a href="#Page_47">47-8</a>, <a href="#Page_235">235</a></li>
-<li class="isub1">vibration, <a href="#Page_69">69</a></li>
-<li class="isub1">Vocoder, <a href="#Page_255">255</a></li>
-<li class="isub1">Voder, <a href="#Page_254">254</a></li>
-<li class="isub1">voltage, <a href="#Page_74">74</a></li>
-
-<li class="ifrst">Watson Scientific Computing Laboratory, <a href="#Page_239">239</a></li>
-<li class="isub1">weather control, <a href="#Page_189">189</a>, <a href="#Page_255">255</a></li>
-<li class="isub1">weather forecasting, <a href="#Page_189">189</a>, <a href="#Page_255">255</a></li>
-<li class="isub1">wheel (of a counter), <a href="#Page_78">78</a></li>
-<li class="isub1">white elephant, <a href="#Page_73">73</a>, <a href="#Page_114">114</a></li>
-<li class="isub1">winch, <a href="#Page_73">73</a></li>
-<li class="isub1">words for explaining, <a href="#Page_209">209-12</a></li>
-
-<li class="ifrst">X, <a href="#Page_59">59</a></li>
-<li class="isub1">X distributor, <a href="#Page_59">59</a></li>
-<li class="isub1">X Pickup, <a href="#Page_59">59</a></li>
-<li class="isub1">X punch, <a href="#Page_45">45</a>, <a href="#Page_58">58</a></li>
-<li class="isub1">X selector, <a href="#Page_59">59</a></li>
-
-<li class="ifrst">zero, <a href="#Page_133">133</a>, <a href="#Page_212">212</a></li>
-<li class="isub1"><i>zh</i> (sound), <a href="#Page_13">13</a>, <a href="#Page_185">185</a></li>
-<li class="isub1">Zuse Computer, <a href="#Page_250">250</a></li>
-</ul>
-
-<hr class="chap x-ebookmaker-drop" />
-
-<div class="footnotes">
-<p class="f150"><b>Footnotes:</b></p>
-
-<div class="footnote"><p class="no-indent">
-<a id="Footnote_1" href="#FNanchor_1" class="label">[1]</a>
-Copyright 1923 by Doubleday, Page and Co.; all rights reserved;
-quotations reprinted by permission of Karel Čapek and Samuel French.</p>
-</div>
-
-<div class="footnote"><p class="no-indent">
-<a id="Footnote_2" href="#FNanchor_2" class="label">[2]</a>
-The preceding word is the spoken word, not the written one.</p>
-</div>
-
-<div class="footnote"><p class="no-indent">
-<a id="Footnote_3" href="#FNanchor_3" class="label">[3]</a>
-The preceding word is the spoken word, not the written one.</p>
-</div>
-
-<div class="footnote"><p class="no-indent">
-<a id="Footnote_4" href="#FNanchor_4" class="label">[4]</a>
-The preceding word is the spoken word, not the written one.</p>
-</div>
-
-<div class="footnote"><p class="no-indent">
-<a id="Footnote_5" href="#FNanchor_5" class="label">[5]</a>
-The preceding word is the spoken word, not the written one.</p>
-</div></div>
-
-<div class="transnote bbox space-above2">
-<p class="f120 space-above1">Transcriber’s Notes:</p>
-<hr class="r5" />
-<p class="indent">The illustrations have been moved so that they do not break up
-                  paragraphs and so that they are next to the text they illustrate.</p>
-<p class="indent">Typographical and punctuation errors have been silently corrected.</p>
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author	nfenwick <nfenwick@pglaf.org>	2025-01-21 02:00:57 -0800
committer	nfenwick <nfenwick@pglaf.org>	2025-01-21 02:00:57 -0800
commit	4176723cb22b1706e50f4816150b68336f721ecb (patch)
tree	aee8da6f9056778da523599ff751c50d3250c43e
parent	07a81d1d134e10a6602c6eb52cbf45f0d9e79008 (diff)