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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..d7b82bc --- /dev/null +++ b/.gitattributes @@ -0,0 +1,4 @@ +*.txt text eol=lf +*.htm text eol=lf +*.html text eol=lf +*.md text eol=lf diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..6312041 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,11 @@ +This eBook, including all associated images, markup, improvements, +metadata, and any other content or labor, has been confirmed to be +in the PUBLIC DOMAIN IN THE UNITED STATES. + +Procedures for determining public domain status are described in +the "Copyright How-To" at https://www.gutenberg.org. + +No investigation has been made concerning possible copyrights in +jurisdictions other than the United States. Anyone seeking to utilize +this eBook outside of the United States should confirm copyright +status under the laws that apply to them. diff --git a/README.md b/README.md new file mode 100644 index 0000000..aad9423 --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Project Gutenberg (https://www.gutenberg.org) public repository for +eBook #64799 (https://www.gutenberg.org/ebooks/64799) diff --git a/old/64799-0.txt b/old/64799-0.txt deleted file mode 100644 index 03c77d6..0000000 --- a/old/64799-0.txt +++ /dev/null @@ -1,1071 +0,0 @@ -The Project Gutenberg eBook of Equation for Time, by R.R. Winterbotham - -This eBook is for the use of anyone anywhere in the United States and -most other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms -of the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you -will have to check the laws of the country where you are located before -using this eBook. - -Title: Equation for Time - -Author: R.R. Winterbotham - -Release Date: March 12, 2021 [eBook #64799] - -Language: English - -Character set encoding: UTF-8 - -Produced by: Greg Weeks, Mary Meehan and the Online Distributed - Proofreading Team at http://www.pgdp.net - -*** START OF THE PROJECT GUTENBERG EBOOK EQUATION FOR TIME *** - - - - - EQUATION _for_ TIME - - by R. R. WINTERBOTHAM - - [Transcriber's Note: This etext was produced from - Comet December 40. - Extensive research did not uncover any evidence that - the U.S. copyright on this publication was renewed.] - - -There is no one today who has seen a living horse. The creature became -extinct a couple of centuries ago, about the year 2,800. Man, who -betrayed the horse into what he became, hardly regretted the passing. - -However, and I speak with all sincerity, there will be men of the -future who will see a horse. Perhaps men of the future may ride -horseback like knights and cowboys of the Middle Ages. - -The secret of time travel has been discovered. No one has traveled -through time as yet, although man has explored the universe for more -than twenty light years from the sun. But the day of time travel is not -far distant. It had simple beginnings. All great things began in simple -ways. Newton and the apple were the beginnings of modern understanding -of the laws of the physical world; Watts and the teakettle were the -origins of industry and the machine age. A very beautiful young woman -and an unscrupulous man were responsible for time travel. - -I met the man early in the morning of July 2, 3002. I remember the -date because on the day before I had visited in Alexandria, Egypt, and -I had eaten dinner in Shanghai, China. It was nearly midnight when I -reached the rocket port in Chicago and a jam in the pneumatics delayed -my arrival home until nearly one o'clock in the morning. - -Blake, fully dressed, met me at the door. There was a worried look in -his eyes. - -"There is a gentleman to see you, sir," Blake said. "I explained that -you would not return until quite late and I tried to get him to leave, -but he said it was urgent that he see you the minute you returned." -Blake glanced over his shoulder toward the library and lowered his -voice to a whisper. "I was a little frightened of him, sir. He doesn't -seem quite--ah--quite right, sir, if you know what I mean. Shall I call -the police?" - -"No, Blake." I felt confident of licking my weight in madmen and I -entered the library. - -A tall, distinguished, dark haired gentleman rose to greet me. - -"Ah! Dr. Huckins! I was afraid you would not get here in time!" - -As he spoke I noticed a peculiar light in his eyes. It seemed to be a -reflection from the fluorescent lamps of the library, but it showed a -little too much of the whites of his eyes and I thought of what Blake -had said about the man not being "quite right." - -I did not feel that I owed him an apology for keeping him waiting, -since I usually received visitors by appointment. - -"I am Gustav Keeshwar!" he introduced himself. He seemed to expect some -reaction, but unfortunately the name meant nothing to me, although if -I had paid more attention to the newspapers I would have known who he -was at once. - -"I am the president of the Stellar Transport Company," he announced. - -As he spoke he glanced secretively about the room, as though he feared -an eavesdropper. Then he picked up a brief case which was lying on the -table. With no explanation he opened it and pulled out package after -package of thousand dollar bills. - -"You may count it if you wish," Keeshwar said. "There are 1,000 bills, -each of one thousand dollar denomination. One million dollars in cold -cash." - -There are any number of bank presidents who have never seen a million -dollars in one pile. Spread out before me, I could scarcely grasp the -amount of wealth it represented. As I recall now, my clearest mental -reaction was a curiosity about how he managed to tuck it away so neatly -in a brief case. Then I wondered if it was real money. A closer glance -at the bills convinced me that it was. - -Suddenly I came to my senses. I closed the library door and locked it. -I glanced nervously at the shades to make sure all were pulled down. - -"Great Scott, man, you shouldn't carry all that money around with you -in a brief case!" As I said it, I spoke with the realization that the -man was mad. - -"I brought the money to you," Keeshwar said. "It is yours if you will -do one thing for me." - -"I must ask you to leave and to take your money with you," I said, -realizing that I was turning down the ransom of a king. "No honest task -ever called for a million dollars compensation--" - -"But you have not asked me what I wish you to do!" Keeshwar exploded. -"Look! Do you see how much money a million dollars is?" - -I do not wish to pose as a man over-stocked with principles. A million -dollars is more money than I ever hope to see again at one time. -But I had a good income, a nice little fortune tucked away in worth -while investments. I had a good name and my position in the world was -better than average. I did not trust this man. I had a feeling that the -million dollars he offered would not be worth the price. - -"I am a surgeon," I said. "If you wish my professional services, I will -charge you a reasonable fee." - -"I want your services," Keeshwar said. "I want them for one day." - -"You may have them. I will send you a bill after I complete the task." - -"I want your services tomorrow," said Keeshwar, persistently. - -I shook my head. "I have a delicate operation scheduled tomorrow. It is -an operation I cannot postpone." - -"It is an operation on Trella Mayo?" - -I started. "How did you know that?" - -"It is this operation that I wish you to perform for me," Keeshwar -said. "Would it not be simple to let your knife slip, or to allow -something to happen to her--for one million dollars!" - -I do not remember clearly what happened next. I think I knocked the man -down. I do remember stuffing his million dollars into his brief case -and throwing it after him out of the door. - -When I closed the door I was excited and unnerved. I found some -sedative tablets and swallowed one. Then I sat down to think. Trella -Mayo, beautiful, young and intelligent, a woman in a billion! Someone -wanted to kill her. - -She was only twenty-eight, yet her discoveries in physics had astounded -the world. She might have taken first place in any beauty contest, yet -she preferred working in a laboratory with men too old to notice her -charms. - -Her operation was not serious, except that it involved delicate skill. -I resolved that nothing must happen during that operation the following -day. - -Two weeks later I visited Trella, now convalescing from her operation. - -"I've wanted to talk to you, Fred," she said after I had taken her -temperature, felt her pulse and gone through the usual ritual. - -"I must warn you that I'll send you a bill for any medical advice I -give you," I replied, laughing. - -She smiled only a little and then puckered her brow seriously. - -"I wanted to ask you about that operation. Wasn't it performed under -unusual circumstances?" - -I was taken by surprise and I am afraid that the truth forced its -indications through my professional manner. "Why do you ask?" - -"I noticed Blake standing near the door. There seemed to be a bulge -in his pocket. It couldn't have been a gun, could it? And you kept -watching, as if you were afraid a tribe of Indians would drop in for a -massacre. I wonder if there couldn't have been a tall, dark gentleman -mixed up in these unusual precautions?" - -I did not reply. - -"And I've noticed during my convalescence that the internes that -continually hover around my door have a look as if--well, shall I say -that they look more like policemen than internes?" - -I laughed nervously. "I think you are a mental case, Miss Mayo," I -said. "I shall have to call in a specialist." - -"You do not need to deny it, Fred," she said. "Why do you suppose I -insisted that you perform the operation? Why didn't I let you call in -someone else? It was because you are the only man in the world that I -trust, Fred. How much did Gustav Keeshwar offer you to do me in?" - -Before I could stop myself I opened my mouth and blurted the truth. - -"One million dollars!" - -"Whew!" Trella whistled softly. "I'm worth a lot to you! I must be -getting close if Keeshwar will pay a million to see me out of the way." - -"Trella," I pleaded. "What is it all about? What's behind this -mystery?" - -"If you turned down a million dollars for my sake, I think I can trust -you," she said. "Supposing I was about to invent a new method of -locomotion? Can you see where Keeshwar might find me obnoxious?" - -"A new kind of space ship?" - -Trella shook her head. "A new kind of locomotion. Animals either swim -or walk. Man also uses wheels." - -"He also can fly. So can birds." - -"Flying is simply swimming through the air and crawling, as a worm -or snake, is gliding, like swimming. Space ships swim, too, after a -fashion. Boats swim through the sea and sleds swim on ice. Therefore we -have only three kinds of locomotion: Legs, wheels and sleds. Another -might revolutionize everything." - -"But there couldn't be any other way to travel. Even the planets 'sled' -through ether." - -"There is another way. It will open exploration to the furthest limits -of the galaxy." - -"I can see why Keeshwar was so interested." - -"As soon as I'm out of bed, I want you to call on me at my laboratory, -Fred. I'll show you something that will make your eyes pop out of your -head." - -I turned to leave, when something on the window pane caught my eye. -It was a small, cherry-red spot, about the size of a twenty-five cent -piece. - -The minute I saw it, I knew what it was. I shouted to the -interne--really a detective--outside the door, and lifted Trella into -my arms. I must admit that I handled her a little roughly and she -groaned as I hurried her out of the room. But what I did was necessary. - -As I left the room, the glass of the pane melted and a beam flashed -across the room, striking the bed where Trella had been an instant -before. That beam was an Oronic Ray, 5,000 degrees hot, of the type -used in welding the rockets of space ships. - -It was evident that Gustav Keeshwar intended to finish Trella Mayo -whether I would help him or not. - - * * * * * - -A few weeks later I visited Trella in her laboratory. - -"I'm anxious to see this incomprehensible conveyance," I explained. - -"At least, I'm glad you are taking an interest in something besides my -safety and my operation scar," she replied. - -She led me through a corridor toward a heavy steel door, which she -unlocked. - -"You are the first person besides myself to go into this room in the -past five years," Trella added. - -I scarcely know what I had expected to see. What would anyone expect -to see, if he was told he was going to be shown a machine that -neither walked, glided nor rolled? Such a contraption is beyond human -experience. - -It was a long, hollow tube, large enough to hold a human body. It was -made of quartz and on each side was a cylindrical, low power atomic -energy machine. - -"This," Trella said, "is the translator." - -"The what?" - -"I call it my space-time translator, which someday will make the rocket -as obsolete for space travel as the horse for surface travel. It will -take an object from one point in space-time to another instantly." - -"Instantly?" - -"There is a small lapse of time," Trella confessed. "You see the -machine has two motors, one for starting the operation and the other -for completing it. It takes about one second's time to switch the -motive power from one motor to the other." - -The machine, except for the motors, was made entirely of quartz and -silver. On the right side of the machine was a long strip of silver -running the full length of the tube. It was about three inches wide and -it was connected with a knife-like blade of silver on the left side -of the tube by a strand of silver wire. Silver was used, of course, -because it was the best known conductor of electricity and other forms -of energy. - -"It would be wonderful if it worked," I said. - -"It does work," Trella said. "We sent two guinea pigs to the Sirius -system yesterday morning. We got them back in an hour with a copy of -yesterday's issue of _The Sirian Daily Universe_. Here's the paper." - -She held out a copy of the beautifully printed daily magazine. On the -cover was the date, August V2, 504 (3002). - -It was customary for terrestrials to use terrestrial dates wherever -their outposts were located in the stellar system. But instead of using -the terrestrial year--as shown in parenthesis on _The Sirian Daily -Universe_--the year always was reckoned from the date when the planet -was first visited by an expedition from the solar system. Although days -were not always the same, twenty-four hour periods could be reckoned -quite easily so that on some planets a single day might have more than -one terrestrial date, and on others a single day would be a fraction of -a legal day. The number of actual days usually was indicated by a Roman -numeral preceding the Arabic figure. Thus August V2 indicated that -Sirius had risen and set five times while the sun had done so twice -during the month of August. - -"Unbelievable!" I said. "How does it work?" - -"It operates through time," Trella explained. "It takes a short cut -between two parallel instants." - -She took a guinea pig from a cage in the laboratory. She put the -wriggling animal inside the quartz tube and strapped it firmly in the -center. - -"Watch," she said. - -She turned a switch on one of the boxes. A low hum arose from the -atomic motor. Trella watched a dial located in the top of the quartz -tube until an arrow pointed to a gold star. Then she pressed a button -in the motor on the right side of the machine. - -I noticed that the translator had controls that could be operated from -inside the tube as well as from the outside. - -There were two distinct gasps of the motor. Half of the guinea pig -disappeared with the first gasp and the remaining half disappeared with -the second. - -Where the tube had been a second before, there was nothing now. - -"He's on Proxima Centaur now," Trella said. "I managed to equip a -laboratory there about two years ago. It was through that laboratory -that Keeshwar learned of my experiments in translation. My men on -Proxima will send back the guinea pig in a few minutes." - -We sat down and waited. Trella explained the machine, although at the -time the explanation was a little over my head. The actual translation -was accomplished by the pushing of one motor and the pulling of another -across an extra-dimensional space. Half of the object to be translated -was hurled across space by the pushing of the first motor. The second -motor, which operated automatically, began pulling the other half, -including the first motor, after it as soon as it materialized at the -end of the journey. - -By means of radio signals the exact location of every explored planet -had been determined. It was therefore only a matter of mathematical -calculation to find the target. There was some risk, of course, if a -mathematical error were made in computing the range but considering the -risks involved in ordinary methods of interstellar flight everything -was in favor of the translator. - -"The whole secret of the invention lies in locating the proper _Now_ in -space-time," Trella explained. - -"The proper _Now_?" I asked. - -"Of course," she said, "the _Now_ we experience on earth is not the -same _Now_ that exists simultaneously on Rihlon, the second planet -of Proxima Centaur. We are dealing with space-time, Fred. Time is a -dimension, it stretches like a line through space. If we connect the -_Now_ of the present with the _Now_ of ten minutes ago, we have a -straight line, just as we would have a straight line if we connected -any two points in the universe. The _Now_ of the present and the _Now_ -ten minutes ago on Rihlon also would be a straight line, but it would -not be the same straight line." - -"But it would be parallel!" I exclaimed, beginning to see her point. - -"Oh, so you _do_ know something about mathematics?" - -"Of course! If you connect the _Nows_ of the present on both the earth -and Rihlon, you have a straight line, perpendicular to the parallel -time lines of both the earth and Rihlon. Why couldn't your invention be -used for time travel? Couldn't you connect the present--_Now_ of Rihlon -with any _Now_ in the time line of the earth--any _Now_ of the past or -future?" - -"The idea occurred to me, but it won't work," Trella replied. "There's -a serious obstacle we can't overcome. In going backward or forward in -time we do not travel in lines perpendicular to the parallel time lines -of the earth and Rihlon--or for any other planet for that matter. But -we travel like this--" Trella drew a figure on a piece of paper. - -[Illustration: - - A G E B - -------+----+------ - \ | - \ | - \ | - C \|F D - ------------+----- - -Figure 1] - -"The line AB represents the time line of the earth and the line CD -represents the time line of any other planet X. The two lines are -parallel. E represents the earth--_Now_, and F the _Now_ on planet X. A -line connecting the two is perpendicular to both AB and CD. Supposing -we should travel from F to a point G, a _Now_ in the earth's past. If -we connect F and G we would have a right triangle GEF. The hypothenuse -GF would be the square root of GE squared plus EF squared." - -"There is nothing mathematically implausible in that," I said. - -"There is nothing implausible, yet to determine the exact distance from -G to F is in most cases impossible. Unless the distances involved are -of the proper ratio, say, 4 and 5, the line GF becomes an irrational -number, of which it is impossible to find the exact value. Supposing -the distance from E to F was one light-year and the distance from G -to E, one year. Then GF would be the square root of one squared plus -one squared, or the square root of two. Because we are dealing with -such immense distances and because even the smallest decimal point of -error might lead to disastrous results, we cannot attempt time travel -unless we know the exact value of the square root of two, or any other -irrational number." - -As Trella finished speaking there was a coughing hum and the translator -appeared in the room, containing the unharmed guinea pig and a copy of -the _Rihlon Gazette_ for Aug. 3rd, which was this day. - -"Do you believe me?" she cried gleefully, waving the paper over her -head. - -It was quite convincing, I admitted. - -"Now I am going to make a trip in the translator!" - -"You!" - -It was the beginning of a long argument. There was danger in the trip, -I told her, and Trella had come to mean a great deal to me. She scoffed -at my fears and told me that if I didn't care to witness the first -translation of man to another planet in another star system she would -do it when I wasn't there. - -Of course, no man can win an argument with a woman. - -Trella climbed into the translator. - -I closed the opening. Her hand rose to the switch that operated the -mechanism from inside the tube. She smiled and her lips moved in a -cheerful good-by. Then she touched the switch. - -The indicator on the dial crept upward toward the gold star. - -Suddenly the unexpected occurred. - -The door of the laboratory opened. Trella had forgotten to lock the -door when we entered the room. - -As I heard the noise, I turned and saw Gustav Keeshwar leveling a gun -toward the helpless young woman in the glass tube. - -I sprang toward him just as the gun went off. - -Apparently he had not expected to find me in the room, for as I lunged -he uttered a cry and threw the gun at my face. Then he turned and ran. - -I managed to duck in time to receive only a glancing blow on the head. -I started to pursue, when my eyes fell on the translator. - -Something terrible was wrong. - -Half of the tube had disappeared and, with it, half of Trella's body. -The other half, containing half of the most beautiful woman on the -earth, remained in the laboratory. - -My spring toward Keeshwar had spoiled his aim enough to keep the bullet -from striking Trella, but the bullet had struck the small silver wire -that ran from the atomic motor on one side to the atomic motor on the -other. The translation had been only half completed. - -Half of Trella's body was on the earth, while the other was on Rihlon, -four light years away! - -Her single eye was open and her half-face was frozen in an expression -of terror. She did not move and she was not breathing. There was no -blood. It was a complete suspension of animation. - -Suddenly I realized that I was losing precious seconds. Unless -something was done, Trella would die. - -I picked up the bit of wire that had been broken off by Keeshwar's -bullet. I lifted it toward the end dangling from the motor. - -Then Trella moved! It was not suspended animation, but something -else--something new! - -Her eye swung toward me. Her half-head visibly shook. Her half-lips -moved but no sound of her voice reached me. But I understood. She was -telling me not to replace the wire. - -She lifted her hand and drew a right-angled triangle on the side of the -tube. - -I understood. Trella was alive and she would continue to live, but it -would be impossible to restore her component halves merely by mending -the broken wire. - -Trella was linked in time. She was still whole, but half of her body -was visible in one _Now_ and the other half in a _Now_ on Proxima -Centaur, four light years away. - -To join the halves of her body, would mean joining the two _Nows_ and -to do that would form a triangle, at least one side of which would be -an irrational number. Unless the riddle of time travel were solved, it -would be impossible to make Trella whole. - -I walked around the half-tube. Her appearance was not what I expected -to see. It was not a case of sawing a woman in half. The cross section -of her body appeared only as an opaque blankness. When I touched -her side I felt something cold and hard. It was as if I had touched -eternity. - -The laboratory officials were called in for consultation. It was -decided that the matter should be hushed, at least until we knew what -should be done. There was too much to do now to be bothered with police -and reporters. We would not have a warrant issued for Keeshwar. There -would be time to deal with him later. - -We discovered that Trella could eat and she seemed to be in perfect -health. But I knew that she was doomed unless we could restore the -parts of her body. Her muscles would atrophy. Inaction is more deadly -to the human machine than millions of disease germs. - -If it would be possible to locate some day in the future when the wires -might be pieced together and the linking of Trella's two halves might -be accomplished without rationalizing irrational numbers, our problem -would be solved. But the nearest date in the future when this could be -done was three years ahead.[1] - -[Footnote 1: Three years from the time this accident occurred would -make the sides of the triangle between the past event, the present, and -the present on Rihlon (four light years away) equal to the units 3, 4 -and 5. Three squared, plus four squared equals five squared.] - -But in three years Trella would be dead. We could not wait for the -coordinates to adjust themselves. We had to make the coordinates -adjustable to our purposes. - -A small chronometer located in the atomic energy machine on the quartz -tube gave us the exact time the silver wire had been broken. - -Even Blake, my servant, offered a suggestion: - -"If you could take the earth half of Miss Trella's body to Rihlon, or -bring the Rihlon half to earth and bring the two _Nows_ together, would -that form a rational triangle?" - -I took paper and pencil and tried to figure it out. - -[Illustration: - - B E H A - -------+---------------+---------- - | /| - | / | - | / | - | / | - | / | - -------+---------+-----+---------- - C F G J D - -Figure 2] - -The line BA represented the time line of Rihlon. The line CD was the -time line of the earth. The points E and F were the _Nows_ on Rihlon -and earth, respectively, at which the accident occurred. The point G -represented the _Now_ at which a space ship would leave the earth for -Rihlon carrying Trella's half body. The point H represented the _Now_ -of arrival on Rihlon and the point J the parallel point on earth. -We still had a right-angled triangle and we still had to deal with -irrational numbers. But hold on-- - -I gazed at my drawing. Before my eyes was the answer! The whole thing -was clearly and completely solved. The secret of time travel was -solved. Trella was saved. The invention of the translator had been -perfected so that all danger of becoming lost in time was removed![2] - -[Footnote 2: As a mental exercise, I would suggest that the reader look -at Figure 2 for a minute or two and figure out the answer. The answer -is there and high school mathematics should enable a person to discover -how to extract the irrational number.--Dr. Fred Huckins.] - -"Blake," I said to the servant, "bring me my automatic pistol." - -"Wh-what?" Blake stuttered. - -"I said bring me my automatic pistol. I'm going to save Trella, or -murder somebody." - -"Perhaps I should call your lawyer." - -I threw a book at him and he left hurriedly, to return in a few minutes -with my pistol and holster. I strapped the weapon about my waist and -slammed my straw hat on my head. In a few minutes I stepped from a taxi -in front of the Galaxy building, in which the officers of the Stellar -Transport Company are located. - -A clerk with thick glasses interviewed me. - -"I want to charter a ship for a trip to Proxima Centaur," I explained. -"I want one of your late model cruisers which can go about ten times -the speed of light. I want to get there quickly." - -The clerk nodded. I have often wondered about the composure of clerks -who never seem to be astonished at anything. "We have a ship available -that could get you there in three months, that's sixteen times the -speed of light. But to charter it would cost one million dollars." - -He never batted an eye when he named the price. I doubt if the clerk -was receiving more than forty a week. - -"I should like to transact the deal directly with Mr. Keeshwar," I said. - -"He will be pleased, I'm sure," the clerk replied. "What is your name?" - -"Andrew J. Colt," I said, for lack of more originality. - -The clerk disappeared into the sanctum. He returned presently with: - -"Mr. Keeshwar will see you, Mr. Colt." - -I had counted on Keeshwar being--or pretending to be very busy as I -entered. I expected him to pay no attention to my entry, and not even -to glance in my direction, as if a million dollars were a trifling -matter, until we were alone. - -I judged Keeshwar right. When at last he glanced at me he was unnerved -by the presence of an automatic pistol which was pointed directly at -his head. - -"I must warn you not to touch any of those buttons on your desk," I -said. "It would give me a great deal of pleasure to drill you and I -won't go out of my way for an opportunity." - -"Wh-what d-d-do you w-w-ant?" he asked, turning pale. - -"One day you offered me a million dollars to take Miss Mayo's life," -I said. "Now I'm asking you to contribute an equal amount to save it. -However, I'm willing to take it out in trade. I want you to pilot one -of your ships for me to Rihlon." - -"Impossible!" Keeshwar said, regaining some of his composure. "I -couldn't leave my business for a period long enough to make the trip." - -"If you don't leave your business to make the trip right now you won't -exist any more," I warned casually. I reached into my pocket and -brought out a silencer, which I fitted to the end of the pistol barrel. -I unfastened the safety and aimed deliberately. - - * * * * * - -The space ship containing the terrestrial half of Trella Mayo, in -company with myself, Blake, two other scientists and Gustav Keeshwar, -arrived on Rihlon three months later. Keeshwar, who had had a pistol -trained on him almost every instant since I had called at his office, -was released and permitted to return to earth. He did not know that I -had left the instructions on earth for his arrest for felonious assault -the minute he landed. - -We located Trella's Rihlon laboratory. It was the matter of a few -minutes to make the connection of the broken wire and to finish the -translation of her two halves. - -Trella stepped out of her quartz prison, swayed unsteadily for a second -on her feet, and then collapsed. - -"How on earth did you do it?" she asked. "How did you reconcile the -irrational number?" - -I sketched the figure roughly (Figure 2). "The distance from F to G and -the distance from E to H does not enter into the equation," I said. -"The only thing we are interested in is the distances GJ, JH and GH." - -"And GH is an irrational number," Trella said. - -"Quite right, although like most things that appear absurd on the -surface, it is not as irrational as it seems. The distance G to J -is three months, the time required for the flight from the earth to -Rihlon. We will represent this by the unit 1. The distance JH is -four light years, the distance in space from earth to Rihlon. This, -therefore, would be sixteen units. Using the formula (GJ)^2 plus (JH)^2 -equals (GH)^2 we find that GH is the square root of one plus 256, or -257. The square root of 257 is 16.031228, etc., an irrational number. - -"It can't be expressed in figures! We do not need figures when we can -draw a picture. The triangle GHJ is a picture of an irrational number. -We had only to go to Rihlon to complete the equation." - -"Time can be traveled," Trella said. - -"Where would you like to go on our honeymoon?" I asked. - -"To the Garden of Eden," she said. - -*** END OF THE PROJECT GUTENBERG EBOOK EQUATION FOR TIME *** - -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. Special rules, set forth in the General Terms of Use part -of this license, apply to copying and distributing Project -Gutenberg-tm electronic works to protect the PROJECT GUTENBERG-tm -concept and trademark. 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Winterbotham</div> - -<div style='display:block; margin:1em 0'> -This eBook is for the use of anyone anywhere in the United States and -most other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms -of the Project Gutenberg License included with this eBook or online -at <a href="https://www.gutenberg.org">www.gutenberg.org</a>. If you -are not located in the United States, you will have to check the laws of the -country where you are located before using this eBook. -</div> - -<div style='display:block; margin-top:1em; margin-bottom:1em; margin-left:2em; text-indent:-2em'>Title: Equation for Time</div> - -<div style='display:block; margin-top:1em; margin-bottom:1em; margin-left:2em; text-indent:-2em'>Author: R.R. Winterbotham</div> - -<div style='display:block; margin:1em 0'>Release Date: March 12, 2021 [eBook #64799]</div> - -<div style='display:block; margin:1em 0'>Language: English</div> - -<div style='display:block; margin:1em 0'>Character set encoding: UTF-8</div> - -<div style='display:block; margin-left:2em; text-indent:-2em'>Produced by: Greg Weeks, Mary Meehan and the Online Distributed Proofreading Team at http://www.pgdp.net</div> - -<div style='margin-top:2em; margin-bottom:4em'>*** START OF THE PROJECT GUTENBERG EBOOK EQUATION FOR TIME ***</div> - - -<div class="titlepage"> - -<h1>EQUATION <i>for</i> TIME</h1> - -<h2>by R. R. WINTERBOTHAM</h2> - -<p>[Transcriber's Note: This etext was produced from<br /> -Comet December 40.<br /> -Extensive research did not uncover any evidence that<br /> -the U.S. copyright on this publication was renewed.]</p> - -</div> - -<hr class="chap" /> - -<p>There is no one today who has seen a living horse. The creature became -extinct a couple of centuries ago, about the year 2,800. Man, who -betrayed the horse into what he became, hardly regretted the passing.</p> - -<p>However, and I speak with all sincerity, there will be men of the -future who will see a horse. Perhaps men of the future may ride -horseback like knights and cowboys of the Middle Ages.</p> - -<p>The secret of time travel has been discovered. No one has traveled -through time as yet, although man has explored the universe for more -than twenty light years from the sun. But the day of time travel is not -far distant. It had simple beginnings. All great things began in simple -ways. Newton and the apple were the beginnings of modern understanding -of the laws of the physical world; Watts and the teakettle were the -origins of industry and the machine age. A very beautiful young woman -and an unscrupulous man were responsible for time travel.</p> - -<p>I met the man early in the morning of July 2, 3002. I remember the -date because on the day before I had visited in Alexandria, Egypt, and -I had eaten dinner in Shanghai, China. It was nearly midnight when I -reached the rocket port in Chicago and a jam in the pneumatics delayed -my arrival home until nearly one o'clock in the morning.</p> - -<p>Blake, fully dressed, met me at the door. There was a worried look in -his eyes.</p> - -<p>"There is a gentleman to see you, sir," Blake said. "I explained that -you would not return until quite late and I tried to get him to leave, -but he said it was urgent that he see you the minute you returned." -Blake glanced over his shoulder toward the library and lowered his -voice to a whisper. "I was a little frightened of him, sir. He doesn't -seem quite—ah—quite right, sir, if you know what I mean. Shall I call -the police?"</p> - -<p>"No, Blake." I felt confident of licking my weight in madmen and I -entered the library.</p> - -<p>A tall, distinguished, dark haired gentleman rose to greet me.</p> - -<p>"Ah! Dr. Huckins! I was afraid you would not get here in time!"</p> - -<p>As he spoke I noticed a peculiar light in his eyes. It seemed to be a -reflection from the fluorescent lamps of the library, but it showed a -little too much of the whites of his eyes and I thought of what Blake -had said about the man not being "quite right."</p> - -<p>I did not feel that I owed him an apology for keeping him waiting, -since I usually received visitors by appointment.</p> - -<p>"I am Gustav Keeshwar!" he introduced himself. He seemed to expect some -reaction, but unfortunately the name meant nothing to me, although if -I had paid more attention to the newspapers I would have known who he -was at once.</p> - -<p>"I am the president of the Stellar Transport Company," he announced.</p> - -<p>As he spoke he glanced secretively about the room, as though he feared -an eavesdropper. Then he picked up a brief case which was lying on the -table. With no explanation he opened it and pulled out package after -package of thousand dollar bills.</p> - -<p>"You may count it if you wish," Keeshwar said. "There are 1,000 bills, -each of one thousand dollar denomination. One million dollars in cold -cash."</p> - -<p>There are any number of bank presidents who have never seen a million -dollars in one pile. Spread out before me, I could scarcely grasp the -amount of wealth it represented. As I recall now, my clearest mental -reaction was a curiosity about how he managed to tuck it away so neatly -in a brief case. Then I wondered if it was real money. A closer glance -at the bills convinced me that it was.</p> - -<p>Suddenly I came to my senses. I closed the library door and locked it. -I glanced nervously at the shades to make sure all were pulled down.</p> - -<p>"Great Scott, man, you shouldn't carry all that money around with you -in a brief case!" As I said it, I spoke with the realization that the -man was mad.</p> - -<p>"I brought the money to you," Keeshwar said. "It is yours if you will -do one thing for me."</p> - -<p>"I must ask you to leave and to take your money with you," I said, -realizing that I was turning down the ransom of a king. "No honest task -ever called for a million dollars compensation—"</p> - -<p>"But you have not asked me what I wish you to do!" Keeshwar exploded. -"Look! Do you see how much money a million dollars is?"</p> - -<p>I do not wish to pose as a man over-stocked with principles. A million -dollars is more money than I ever hope to see again at one time. -But I had a good income, a nice little fortune tucked away in worth -while investments. I had a good name and my position in the world was -better than average. I did not trust this man. I had a feeling that the -million dollars he offered would not be worth the price.</p> - -<p>"I am a surgeon," I said. "If you wish my professional services, I will -charge you a reasonable fee."</p> - -<p>"I want your services," Keeshwar said. "I want them for one day."</p> - -<p>"You may have them. I will send you a bill after I complete the task."</p> - -<p>"I want your services tomorrow," said Keeshwar, persistently.</p> - -<p>I shook my head. "I have a delicate operation scheduled tomorrow. It is -an operation I cannot postpone."</p> - -<p>"It is an operation on Trella Mayo?"</p> - -<p>I started. "How did you know that?"</p> - -<p>"It is this operation that I wish you to perform for me," Keeshwar -said. "Would it not be simple to let your knife slip, or to allow -something to happen to her—for one million dollars!"</p> - -<p>I do not remember clearly what happened next. I think I knocked the man -down. I do remember stuffing his million dollars into his brief case -and throwing it after him out of the door.</p> - -<p>When I closed the door I was excited and unnerved. I found some -sedative tablets and swallowed one. Then I sat down to think. Trella -Mayo, beautiful, young and intelligent, a woman in a billion! Someone -wanted to kill her.</p> - -<p>She was only twenty-eight, yet her discoveries in physics had astounded -the world. She might have taken first place in any beauty contest, yet -she preferred working in a laboratory with men too old to notice her -charms.</p> - -<p>Her operation was not serious, except that it involved delicate skill. -I resolved that nothing must happen during that operation the following -day.</p> - -<p>Two weeks later I visited Trella, now convalescing from her operation.</p> - -<p>"I've wanted to talk to you, Fred," she said after I had taken her -temperature, felt her pulse and gone through the usual ritual.</p> - -<p>"I must warn you that I'll send you a bill for any medical advice I -give you," I replied, laughing.</p> - -<p>She smiled only a little and then puckered her brow seriously.</p> - -<p>"I wanted to ask you about that operation. Wasn't it performed under -unusual circumstances?"</p> - -<p>I was taken by surprise and I am afraid that the truth forced its -indications through my professional manner. "Why do you ask?"</p> - -<p>"I noticed Blake standing near the door. There seemed to be a bulge -in his pocket. It couldn't have been a gun, could it? And you kept -watching, as if you were afraid a tribe of Indians would drop in for a -massacre. I wonder if there couldn't have been a tall, dark gentleman -mixed up in these unusual precautions?"</p> - -<p>I did not reply.</p> - -<p>"And I've noticed during my convalescence that the internes that -continually hover around my door have a look as if—well, shall I say -that they look more like policemen than internes?"</p> - -<p>I laughed nervously. "I think you are a mental case, Miss Mayo," I -said. "I shall have to call in a specialist."</p> - -<p>"You do not need to deny it, Fred," she said. "Why do you suppose I -insisted that you perform the operation? Why didn't I let you call in -someone else? It was because you are the only man in the world that I -trust, Fred. How much did Gustav Keeshwar offer you to do me in?"</p> - -<p>Before I could stop myself I opened my mouth and blurted the truth.</p> - -<p>"One million dollars!"</p> - -<p>"Whew!" Trella whistled softly. "I'm worth a lot to you! I must be -getting close if Keeshwar will pay a million to see me out of the way."</p> - -<p>"Trella," I pleaded. "What is it all about? What's behind this -mystery?"</p> - -<p>"If you turned down a million dollars for my sake, I think I can trust -you," she said. "Supposing I was about to invent a new method of -locomotion? Can you see where Keeshwar might find me obnoxious?"</p> - -<p>"A new kind of space ship?"</p> - -<p>Trella shook her head. "A new kind of locomotion. Animals either swim -or walk. Man also uses wheels."</p> - -<p>"He also can fly. So can birds."</p> - -<p>"Flying is simply swimming through the air and crawling, as a worm -or snake, is gliding, like swimming. Space ships swim, too, after a -fashion. Boats swim through the sea and sleds swim on ice. Therefore we -have only three kinds of locomotion: Legs, wheels and sleds. Another -might revolutionize everything."</p> - -<p>"But there couldn't be any other way to travel. Even the planets 'sled' -through ether."</p> - -<p>"There is another way. It will open exploration to the furthest limits -of the galaxy."</p> - -<p>"I can see why Keeshwar was so interested."</p> - -<p>"As soon as I'm out of bed, I want you to call on me at my laboratory, -Fred. I'll show you something that will make your eyes pop out of your -head."</p> - -<p>I turned to leave, when something on the window pane caught my eye. -It was a small, cherry-red spot, about the size of a twenty-five cent -piece.</p> - -<p>The minute I saw it, I knew what it was. I shouted to the -interne—really a detective—outside the door, and lifted Trella into -my arms. I must admit that I handled her a little roughly and she -groaned as I hurried her out of the room. But what I did was necessary.</p> - -<p>As I left the room, the glass of the pane melted and a beam flashed -across the room, striking the bed where Trella had been an instant -before. That beam was an Oronic Ray, 5,000 degrees hot, of the type -used in welding the rockets of space ships.</p> - -<p>It was evident that Gustav Keeshwar intended to finish Trella Mayo -whether I would help him or not.</p> - -<hr class="tb" /> - -<p>A few weeks later I visited Trella in her laboratory.</p> - -<p>"I'm anxious to see this incomprehensible conveyance," I explained.</p> - -<p>"At least, I'm glad you are taking an interest in something besides my -safety and my operation scar," she replied.</p> - -<p>She led me through a corridor toward a heavy steel door, which she -unlocked.</p> - -<p>"You are the first person besides myself to go into this room in the -past five years," Trella added.</p> - -<p>I scarcely know what I had expected to see. What would anyone expect -to see, if he was told he was going to be shown a machine that -neither walked, glided nor rolled? Such a contraption is beyond human -experience.</p> - -<p>It was a long, hollow tube, large enough to hold a human body. It was -made of quartz and on each side was a cylindrical, low power atomic -energy machine.</p> - -<p>"This," Trella said, "is the translator."</p> - -<p>"The what?"</p> - -<p>"I call it my space-time translator, which someday will make the rocket -as obsolete for space travel as the horse for surface travel. It will -take an object from one point in space-time to another instantly."</p> - -<p>"Instantly?"</p> - -<p>"There is a small lapse of time," Trella confessed. "You see the -machine has two motors, one for starting the operation and the other -for completing it. It takes about one second's time to switch the -motive power from one motor to the other."</p> - -<p>The machine, except for the motors, was made entirely of quartz and -silver. On the right side of the machine was a long strip of silver -running the full length of the tube. It was about three inches wide and -it was connected with a knife-like blade of silver on the left side -of the tube by a strand of silver wire. Silver was used, of course, -because it was the best known conductor of electricity and other forms -of energy.</p> - -<p>"It would be wonderful if it worked," I said.</p> - -<p>"It does work," Trella said. "We sent two guinea pigs to the Sirius -system yesterday morning. We got them back in an hour with a copy of -yesterday's issue of <i>The Sirian Daily Universe</i>. Here's the paper."</p> - -<p>She held out a copy of the beautifully printed daily magazine. On the -cover was the date, August V2, 504 (3002).</p> - -<p>It was customary for terrestrials to use terrestrial dates wherever -their outposts were located in the stellar system. But instead of using -the terrestrial year—as shown in parenthesis on <i>The Sirian Daily -Universe</i>—the year always was reckoned from the date when the planet -was first visited by an expedition from the solar system. Although days -were not always the same, twenty-four hour periods could be reckoned -quite easily so that on some planets a single day might have more than -one terrestrial date, and on others a single day would be a fraction of -a legal day. The number of actual days usually was indicated by a Roman -numeral preceding the Arabic figure. Thus August V2 indicated that -Sirius had risen and set five times while the sun had done so twice -during the month of August.</p> - -<p>"Unbelievable!" I said. "How does it work?"</p> - -<p>"It operates through time," Trella explained. "It takes a short cut -between two parallel instants."</p> - -<p>She took a guinea pig from a cage in the laboratory. She put the -wriggling animal inside the quartz tube and strapped it firmly in the -center.</p> - -<p>"Watch," she said.</p> - -<p>She turned a switch on one of the boxes. A low hum arose from the -atomic motor. Trella watched a dial located in the top of the quartz -tube until an arrow pointed to a gold star. Then she pressed a button -in the motor on the right side of the machine.</p> - -<p>I noticed that the translator had controls that could be operated from -inside the tube as well as from the outside.</p> - -<p>There were two distinct gasps of the motor. Half of the guinea pig -disappeared with the first gasp and the remaining half disappeared with -the second.</p> - -<p>Where the tube had been a second before, there was nothing now.</p> - -<p>"He's on Proxima Centaur now," Trella said. "I managed to equip a -laboratory there about two years ago. It was through that laboratory -that Keeshwar learned of my experiments in translation. My men on -Proxima will send back the guinea pig in a few minutes."</p> - -<p>We sat down and waited. Trella explained the machine, although at the -time the explanation was a little over my head. The actual translation -was accomplished by the pushing of one motor and the pulling of another -across an extra-dimensional space. Half of the object to be translated -was hurled across space by the pushing of the first motor. The second -motor, which operated automatically, began pulling the other half, -including the first motor, after it as soon as it materialized at the -end of the journey.</p> - -<p>By means of radio signals the exact location of every explored planet -had been determined. It was therefore only a matter of mathematical -calculation to find the target. There was some risk, of course, if a -mathematical error were made in computing the range but considering the -risks involved in ordinary methods of interstellar flight everything -was in favor of the translator.</p> - -<p>"The whole secret of the invention lies in locating the proper <i>Now</i> in -space-time," Trella explained.</p> - -<p>"The proper <i>Now</i>?" I asked.</p> - -<p>"Of course," she said, "the <i>Now</i> we experience on earth is not the -same <i>Now</i> that exists simultaneously on Rihlon, the second planet -of Proxima Centaur. We are dealing with space-time, Fred. Time is a -dimension, it stretches like a line through space. If we connect the -<i>Now</i> of the present with the <i>Now</i> of ten minutes ago, we have a -straight line, just as we would have a straight line if we connected -any two points in the universe. The <i>Now</i> of the present and the <i>Now</i> -ten minutes ago on Rihlon also would be a straight line, but it would -not be the same straight line."</p> - -<p>"But it would be parallel!" I exclaimed, beginning to see her point.</p> - -<p>"Oh, so you <i>do</i> know something about mathematics?"</p> - -<p>"Of course! If you connect the <i>Nows</i> of the present on both the earth -and Rihlon, you have a straight line, perpendicular to the parallel -time lines of both the earth and Rihlon. Why couldn't your invention be -used for time travel? Couldn't you connect the present—<i>Now</i> of Rihlon -with any <i>Now</i> in the time line of the earth—any <i>Now</i> of the past or -future?"</p> - -<p>"The idea occurred to me, but it won't work," Trella replied. "There's -a serious obstacle we can't overcome. In going backward or forward in -time we do not travel in lines perpendicular to the parallel time lines -of the earth and Rihlon—or for any other planet for that matter. But -we travel like this—" Trella drew a figure on a piece of paper.</p> - -<hr class="chap" /> - -<div class="figcenter"> - <img src="images/fig1.jpg" alt=""/> -</div> - -<hr class="chap" /> - -<p>"The line AB represents the time line of the earth and the line CD -represents the time line of any other planet X. The two lines are -parallel. E represents the earth—<i>Now</i>, and F the <i>Now</i> on planet X. A -line connecting the two is perpendicular to both AB and CD. Supposing -we should travel from F to a point G, a <i>Now</i> in the earth's past. If -we connect F and G we would have a right triangle GEF. The hypothenuse -GF would be the square root of GE squared plus EF squared."<a name="FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class="fnanchor">[3]</a></p> - -<p>"There is nothing mathematically implausible in that," I said.</p> - -<p>"There is nothing implausible, yet to determine the exact distance from -G to F is in most cases impossible. Unless the distances involved are -of the proper ratio, say, 4 and 5, the line GF becomes an irrational -number, of which it is impossible to find the exact value. Supposing -the distance from E to F was one light-year and the distance from G -to E, one year. Then GF would be the square root of one squared plus -one squared, or the square root of two. Because we are dealing with -such immense distances and because even the smallest decimal point of -error might lead to disastrous results, we cannot attempt time travel -unless we know the exact value of the square root of two, or any other -irrational number."</p> - -<p>As Trella finished speaking there was a coughing hum and the translator -appeared in the room, containing the unharmed guinea pig and a copy of -the <i>Rihlon Gazette</i> for Aug. 3rd, which was this day.</p> - -<p>"Do you believe me?" she cried gleefully, waving the paper over her -head.</p> - -<p>It was quite convincing, I admitted.</p> - -<p>"Now I am going to make a trip in the translator!"</p> - -<p>"You!"</p> - -<p>It was the beginning of a long argument. There was danger in the trip, -I told her, and Trella had come to mean a great deal to me. She scoffed -at my fears and told me that if I didn't care to witness the first -translation of man to another planet in another star system she would -do it when I wasn't there.</p> - -<p>Of course, no man can win an argument with a woman.</p> - -<p>Trella climbed into the translator.</p> - -<p>I closed the opening. Her hand rose to the switch that operated the -mechanism from inside the tube. She smiled and her lips moved in a -cheerful good-by. Then she touched the switch.</p> - -<p>The indicator on the dial crept upward toward the gold star.</p> - -<p>Suddenly the unexpected occurred.</p> - -<p>The door of the laboratory opened. Trella had forgotten to lock the -door when we entered the room.</p> - -<p>As I heard the noise, I turned and saw Gustav Keeshwar leveling a gun -toward the helpless young woman in the glass tube.</p> - -<p>I sprang toward him just as the gun went off.</p> - -<p>Apparently he had not expected to find me in the room, for as I lunged -he uttered a cry and threw the gun at my face. Then he turned and ran.</p> - -<hr class="chap" /> - -<div class="figcenter"> - <img src="images/illus.jpg" alt=""/> -</div> - -<hr class="chap" /> - -<p>I managed to duck in time to receive only a glancing blow on the head. -I started to pursue, when my eyes fell on the translator.</p> - -<p>Something terrible was wrong.</p> - -<p>Half of the tube had disappeared and, with it, half of Trella's body. -The other half, containing half of the most beautiful woman on the -earth, remained in the laboratory.</p> - -<p>My spring toward Keeshwar had spoiled his aim enough to keep the bullet -from striking Trella, but the bullet had struck the small silver wire -that ran from the atomic motor on one side to the atomic motor on the -other. The translation had been only half completed.</p> - -<p>Half of Trella's body was on the earth, while the other was on Rihlon, -four light years away!</p> - -<p>Her single eye was open and her half-face was frozen in an expression -of terror. She did not move and she was not breathing. There was no -blood. It was a complete suspension of animation.</p> - -<p>Suddenly I realized that I was losing precious seconds. Unless -something was done, Trella would die.</p> - -<p>I picked up the bit of wire that had been broken off by Keeshwar's -bullet. I lifted it toward the end dangling from the motor.</p> - -<p>Then Trella moved! It was not suspended animation, but something -else—something new!</p> - -<p>Her eye swung toward me. Her half-head visibly shook. Her half-lips -moved but no sound of her voice reached me. But I understood. She was -telling me not to replace the wire.</p> - -<p>She lifted her hand and drew a right-angled triangle on the side of the -tube.</p> - -<p>I understood. Trella was alive and she would continue to live, but it -would be impossible to restore her component halves merely by mending -the broken wire.</p> - -<p>Trella was linked in time. She was still whole, but half of her body -was visible in one <i>Now</i> and the other half in a <i>Now</i> on Proxima -Centaur, four light years away.</p> - -<p>To join the halves of her body, would mean joining the two <i>Nows</i> and -to do that would form a triangle, at least one side of which would be -an irrational number. Unless the riddle of time travel were solved, it -would be impossible to make Trella whole.</p> - -<p>I walked around the half-tube. Her appearance was not what I expected -to see. It was not a case of sawing a woman in half. The cross section -of her body appeared only as an opaque blankness. When I touched -her side I felt something cold and hard. It was as if I had touched -eternity.</p> - -<p>The laboratory officials were called in for consultation. It was -decided that the matter should be hushed, at least until we knew what -should be done. There was too much to do now to be bothered with police -and reporters. We would not have a warrant issued for Keeshwar. There -would be time to deal with him later.</p> - -<p>We discovered that Trella could eat and she seemed to be in perfect -health. But I knew that she was doomed unless we could restore the -parts of her body. Her muscles would atrophy. Inaction is more deadly -to the human machine than millions of disease germs.</p> - -<p>If it would be possible to locate some day in the future when the wires -might be pieced together and the linking of Trella's two halves might -be accomplished without rationalizing irrational numbers, our problem -would be solved. But the nearest date in the future when this could be -done was three years ahead.<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a></p> - -<p>But in three years Trella would be dead. We could not wait for the -coordinates to adjust themselves. We had to make the coordinates -adjustable to our purposes.</p> - -<p>A small chronometer located in the atomic energy machine on the quartz -tube gave us the exact time the silver wire had been broken.</p> - -<p>Even Blake, my servant, offered a suggestion:</p> - -<p>"If you could take the earth half of Miss Trella's body to Rihlon, or -bring the Rihlon half to earth and bring the two <i>Nows</i> together, would -that form a rational triangle?"</p> - -<p>I took paper and pencil and tried to figure it out.</p> - -<hr class="chap" /> - -<div class="figcenter"> - <img src="images/fig2.jpg" alt=""/> -</div> - -<hr class="chap" /> - -<p>The line BA represented the time line of Rihlon. The line CD was the -time line of the earth. The points E and F were the <i>Nows</i> on Rihlon -and earth, respectively, at which the accident occurred. The point G -represented the <i>Now</i> at which a space ship would leave the earth for -Rihlon carrying Trella's half body. The point H represented the <i>Now</i> -of arrival on Rihlon and the point J the parallel point on earth. -We still had a right-angled triangle and we still had to deal with -irrational numbers. But hold on—</p> - -<p>I gazed at my drawing. Before my eyes was the answer! The whole thing -was clearly and completely solved. The secret of time travel was -solved. Trella was saved. The invention of the translator had been -perfected so that all danger of becoming lost in time was removed!<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a></p> - -<p>"Blake," I said to the servant, "bring me my automatic pistol."</p> - -<p>"Wh-what?" Blake stuttered.</p> - -<p>"I said bring me my automatic pistol. I'm going to save Trella, or -murder somebody."</p> - -<p>"Perhaps I should call your lawyer."</p> - -<p>I threw a book at him and he left hurriedly, to return in a few minutes -with my pistol and holster. I strapped the weapon about my waist and -slammed my straw hat on my head. In a few minutes I stepped from a taxi -in front of the Galaxy building, in which the officers of the Stellar -Transport Company are located.</p> - -<p>A clerk with thick glasses interviewed me.</p> - -<p>"I want to charter a ship for a trip to Proxima Centaur," I explained. -"I want one of your late model cruisers which can go about ten times -the speed of light. I want to get there quickly."</p> - -<p>The clerk nodded. I have often wondered about the composure of clerks -who never seem to be astonished at anything. "We have a ship available -that could get you there in three months, that's sixteen times the -speed of light. But to charter it would cost one million dollars."</p> - -<p>He never batted an eye when he named the price. I doubt if the clerk -was receiving more than forty a week.</p> - -<p>"I should like to transact the deal directly with Mr. Keeshwar," I said.</p> - -<p>"He will be pleased, I'm sure," the clerk replied. "What is your name?"</p> - -<p>"Andrew J. Colt," I said, for lack of more originality.</p> - -<p>The clerk disappeared into the sanctum. He returned presently with:</p> - -<p>"Mr. Keeshwar will see you, Mr. Colt."</p> - -<p>I had counted on Keeshwar being—or pretending to be very busy as I -entered. I expected him to pay no attention to my entry, and not even -to glance in my direction, as if a million dollars were a trifling -matter, until we were alone.</p> - -<p>I judged Keeshwar right. When at last he glanced at me he was unnerved -by the presence of an automatic pistol which was pointed directly at -his head.</p> - -<p>"I must warn you not to touch any of those buttons on your desk," I -said. "It would give me a great deal of pleasure to drill you and I -won't go out of my way for an opportunity."</p> - -<p>"Wh-what d-d-do you w-w-ant?" he asked, turning pale.</p> - -<p>"One day you offered me a million dollars to take Miss Mayo's life," -I said. "Now I'm asking you to contribute an equal amount to save it. -However, I'm willing to take it out in trade. I want you to pilot one -of your ships for me to Rihlon."</p> - -<p>"Impossible!" Keeshwar said, regaining some of his composure. "I -couldn't leave my business for a period long enough to make the trip."</p> - -<p>"If you don't leave your business to make the trip right now you won't -exist any more," I warned casually. I reached into my pocket and -brought out a silencer, which I fitted to the end of the pistol barrel. -I unfastened the safety and aimed deliberately.</p> - -<hr class="tb" /> - -<p>The space ship containing the terrestrial half of Trella Mayo, in -company with myself, Blake, two other scientists and Gustav Keeshwar, -arrived on Rihlon three months later. Keeshwar, who had had a pistol -trained on him almost every instant since I had called at his office, -was released and permitted to return to earth. He did not know that I -had left the instructions on earth for his arrest for felonious assault -the minute he landed.</p> - -<p>We located Trella's Rihlon laboratory. It was the matter of a few -minutes to make the connection of the broken wire and to finish the -translation of her two halves.</p> - -<p>Trella stepped out of her quartz prison, swayed unsteadily for a second -on her feet, and then collapsed.</p> - -<p>"How on earth did you do it?" she asked. "How did you reconcile the -irrational number?"</p> - -<p>I sketched the figure roughly (Figure 2). "The distance from F to G and -the distance from E to H does not enter into the equation," I said. -"The only thing we are interested in is the distances GJ, JH and GH."</p> - -<p>"And GH is an irrational number," Trella said.</p> - -<p>"Quite right, although like most things that appear absurd on the -surface, it is not as irrational as it seems. The distance G to J -is three months, the time required for the flight from the earth to -Rihlon. We will represent this by the unit 1. The distance JH is -four light years, the distance in space from earth to Rihlon. This, -therefore, would be sixteen units. Using the formula (GJ)<sup>2</sup> plus (JH)<sup>2</sup> -equals (GH)<sup>2</sup> we find that GH is the square root of one plus 256, or -257. The square root of 257 is 16.031228, etc., an irrational number.</p> - -<p>"It can't be expressed in figures! We do not need figures when we can -draw a picture. The triangle GHJ is a picture of an irrational number. -We had only to go to Rihlon to complete the equation."</p> - -<p>"Time can be traveled," Trella said.</p> - -<p>"Where would you like to go on our honeymoon?" I asked.</p> - -<p>"To the Garden of Eden," she said.</p> - -<hr class="tb" /> - -<div class="footnote"> -<p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">[1]</span></a> Three years from the time this accident occurred would -make the sides of the triangle between the past event, the present, and -the present on Rihlon (four light years away) equal to the units 3, 4 -and 5. Three squared, plus four squared equals five squared.</p></div> - -<div class="footnote"> -<p><a name="Footnote_2_2" id="Footnote_2_2"></a><a href="#FNanchor_2_2"><span class="label">[2]</span></a> As a mental exercise, I would suggest that the reader look -at Figure 2 for a minute or two and figure out the answer. The answer -is there and high school mathematics should enable a person to discover -how to extract the irrational number.—Dr. Fred Huckins.</p></div> - -<div class="footnote"> -<p><a name="Footnote_3_3" id="Footnote_3_3"></a><a href="#FNanchor_3_3"><span class="label">[3]</span></a> [Transcriber's Note: Illustration is not -correct. 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