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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 - -*** END OF THE PROJECT GUTENBERG EBOOK GIANT BRAINS; OR MACHINES THAT -THINK *** - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the -United States without permission and without paying copyright -royalties. 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