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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'll have -to check the laws of the country where you are located before using this ebook. - -Title: Oridin's Formula - -Author: R. R. Winterbotham - -Release Date: June 2, 2020 [EBook #62313] - -Language: English - -Character set encoding: ASCII - -*** START OF THIS PROJECT GUTENBERG EBOOK ORIDIN'S FORMULA *** - - - - -Produced by Greg Weeks, Mary Meehan and the Online -Distributed Proofreading Team at http://www.pgdp.net - - - - - - -</pre> - - -<div class="figcenter"> - <img src="images/cover.jpg" width="348" height="500" alt=""/> -</div> - -<hr class="chap" /> - -<div class="titlepage"> -<h1>ORIDIN'S FORMULA</h1> - -<h2>By R. R. WINTERBOTHAM</h2> - -<p>The formula was a simple equation, but<br /> -Caddo had to have it—for knowing its<br /> -answer meant he would rule the universe.</p> - -<p>[Transcriber's Note: This etext was produced from<br /> -Planet Stories March 1943.<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>Oridin the Recluse listened to the threat wirelessed from the spaceship -that was hoving to in a landing orbit about the planetoid Azair.</p> - -<p>"I've a bead on your atmosphere plant," said the snarling voice. "One -false move and I'll blast it to star dust."</p> - -<p>Oridin shrugged as he heard the words. One more fool had come to Azair -looking for the secret that the Recluse of the Asteroids was supposed -to possess.</p> - -<p>"Your threats are unnecessary, stranger," Oridin replied in the -microphone of his radio. "Everyone is welcome here as long as he -behaves. I have ways of dealing with those who don't."</p> - -<p>"I'm warning you," came the voice again, "that I will stand for no -foolishness. I'll kill you if you try to resist."</p> - -<p>Oridin smiled. "Land, stranger, you need not fear me."</p> - -<p>The hermit arose and went to the galley of the warm little house that -seemed to grow from the solid rocks of the tiny planet. He pressed a -button, waited a second and then opened a small compartment. In the box -was a steaming pot of coffee, freshly made by Oridin's automatic cook.</p> - -<p>Outside the transparent shelter, the air grew blue from the reflection -of landing rockets. Oridin glanced to the leveled surface on which the -ship was coming to rest. He saw a turret training on the little house. -Oridin was not afraid; the visitor probably would be interesting. Even -a recluse can grow lonesome on a minor planet.</p> - -<p>A figure emerged from the spaceship. He wore an oxygen helmet, although -Oridin plentifully supplied the planetoid with artificial atmosphere -from a small plant at the north pole. The stranger did not believe that -Oridin would not resist. Again Oridin smiled. Deep in the rocks of -Azair were guns that could have blasted the visitor a thousand times, -had Oridin wished. But there was nothing clever about blowing a foe to -pieces. The foe too often was killed before he sensed defeat. Oridin -enjoyed an equal battle, or even one against odds.</p> - -<hr class="chap" /> - -<div class="figcenter"> -<img src="images/illus.jpg" width="387" height="500" alt=""/> - <div class="caption"> - <p><i>"Open up," Caddo snarled, "or I'll blow my way in!"</i></p> - </div> -</div> - -<hr class="chap" /> - -<p>"Open up! Open up, I tell you, or I'll burn my way in!" demanded the -visitor.</p> - -<p>"He's certainly not deceiving me as to his intentions," Oridin decided.</p> - -<p>The recluse pushed a button on the wall, and a giant gate swung outward -admitting the stranger.</p> - -<p>The fellow was as tall and as muscular as Oridin himself, but the space -suit and the gaping blaster he held in his hand made the visitor seem -much more formidable. Oridin himself was dressed in bell-bottomed -slacks and a loosely fitting, slipover coat. His beard softened his -countenance and made him seem quite gentle, except for a certain -glitter in his eyes that seemed to warn that Oridin loved a contest. -And this would seem to be a deadly contest.</p> - -<p>Oridin bowed.</p> - -<p>"You are welcome, stranger," he said. "Take off your helmet, for the -air is pure. Put aside your gun, for I am unarmed and I do not intend -to harm you."</p> - -<p>The stranger hesitated, uncertainly.</p> - -<p>"No tricks, Oridin!" he warned.</p> - -<p>"Tricks?" Oridin laughed tauntingly. "You are not very confident for a -man of your caliber. I've heard of you often, Caddo Velexis. They say -you have conquered whole nations single-handed, and yet you are afraid -of an unarmed hermit."</p> - -<p>"I'm not afraid of you," Caddo said in a tone that hinted he was.</p> - -<p>Caddo removed his helmet and holstered his blaster, but Oridin noted -that the terrestrial giant did not move the firing button to safety.</p> - -<p>"Will you have some coffee?" Oridin asked. "It will refresh you after -your long trip, and you must have had a long trip, for we are in a very -sparsely filled part of the sky."</p> - -<p>Oridin lifted the pot and poured the brown steaming liquid into a -thick, metal mug.</p> - -<p>Caddo waved it aside.</p> - -<p>"I have no time!"</p> - -<p>"Do not be alarmed," Oridin said. "The patrol will not be near Azair -for three days."</p> - -<p>Oridin sat down. His fingers felt under the arm of the chair where a -series of buttons controlled other mechanisms in the room. Caddo had -relaxed his watchfulness.</p> - -<p>"In three days I'll be well toward the other side of the solar system," -Caddo said.</p> - -<p>Oridin lifted his eyebrows.</p> - -<p>"Toward the earth? You have undertaken something this time!"</p> - -<p>"Yes!" Caddo said. "It's the Earth I am after! I have all I want of the -outlying planets and planetoids. You can capture a hundred of them and -be no better off than you were at first. But if you capture the Earth, -you can rule the universe."</p> - -<p>Oridin touched one of the buttons. A tiny pinhole in the wall of the -room seemed to blink. There was a blinding flash and the smell of -burned leather permeated the place.</p> - -<hr class="tb" /> - -<p>Caddo gave a cry of alarm and sprang back, knocking over his chair. He -was on his feet holding his blaster in his hand in a second. Across the -top of his helmet was a scorched streak.</p> - -<p>"You tried to kill me!" Caddo screamed. "You dirty swine."</p> - -<p>Oridin's lips parted in a smile as he looked without fear into the -mouth of the trembling weapon.</p> - -<p>"Don't underestimate yourself, Caddo," he said. "The hot beam was only -a warning—something to let you know that I could kill you anytime -I wished. Even now, before you could squeeze the trigger on the -weapon, I could cause certain things to happen—no, no! You are safe, -Caddo—I could cause you to die if I wish, but you are interesting, a -dangerous man. It would be a better accomplishment for me to give you a -punishment you deserve."</p> - -<p>The fear that shone in Caddo's eyes faded away. For a moment he watched -Oridin. Then he laughed.</p> - -<p>"So it's that kind of a game, is it? I can play it too! Your threats do -not frighten me. Nor am I afraid of your hot beam. Look!"</p> - -<p>Caddo thrust his arm forward into the path of the beam. There was a -puff of smoke as the tremendous heat vaporized particles of dust on the -leather sleeves. Then nothing happened.</p> - -<p>"I have a neutralizing force, powered with a small battery in my -clothing," Caddo said. "Foolishly, I did not have it turned on a moment -ago. But you can't hurt me now."</p> - -<p>Oridin shrugged. "I am still not afraid of you Caddo. If you had come -here to loot, you would have killed me long ago. But what you want is -something you cannot gain by killing me. What is it?"</p> - -<p>"You are going to give me the secret that will make me the master of -the earth, and the master of the universe," Caddo announced.</p> - -<p>Oridin poured himself a mug of coffee.</p> - -<p>"I knew you did not want gold, although Azair is filthy with the -stuff," he said. "But what secret have I that is so powerful?"</p> - -<p>"The <i>Discovery</i>!" Caddo said.</p> - -<p>"I have many." Oridin nodded toward the wall, and the pinhole of light -blinked out.</p> - -<p>"I want the secret of the universe!" Caddo spoke tensely.</p> - -<p>"Come! Don't be so melodramatic," Oridin chided. "The universe is full -of secrets."</p> - -<p>"You're stalling. You know what I mean!"</p> - -<p>"I think I do," Oridin agreed. "My erratic experiments have revealed a -certain mathematical function, <i>J</i>, which theoretically opens the door -to action without probability. Is that what you want, Caddo? The value -of <i>J</i>?"</p> - -<p>"The mathematical bombsight!" Caddo said. "It removes probability and -makes certainty of everything. With my calculations based on certainty, -I'll be fate itself! I can conquer the world, chain the universe and -govern creation."</p> - -<p>Oridin laughed quietly.</p> - -<p>"Alexander, Caesar, Napoleon, Genghis Khan and Hitler spoke those words -and they were willing to bargain with the devil himself to make them -come true," he said. "I suppose I am the devil, for I know the answer -and I can tell you the answer—for a price."</p> - -<p>"You'll give it to me for nothing!" Caddo patted the blister, now in -the holster at his side.</p> - -<p>"Is that your only offer?" Oridin asked, still wearing an amused -half-smile.</p> - -<p>"It is!"</p> - -<p>Oridin rose and moved toward a safe under two clocks on the wall across -the room. One of these clocks gave the terrestrial days, hours and -minutes according to the General Meridian time. The other registered -the four-hour rotation of Azair.</p> - -<p>"Wait!" Caddo halted Oridin. "No tricks. Give me the combination and -I'll open the safe!"</p> - -<p>Oridin turned to the space pirate.</p> - -<p>"The safe is unlocked. The formula is inside."</p> - -<p>Caddo's eyes betrayed his suspicion. The most valuable secret in -the world was in an unlocked safe! Warily Caddo stepped forward. He -hesitated, wondering if even his neutralizing force was enough to -protect him.</p> - -<p>"There's no danger. Go ahead. Help yourself," Oridin urged.</p> - -<p>Caddo was desperate. He touched the handle of the door. It was -unlocked. He flung it open. Inside the safe was a single sheet of white -paper.</p> - -<p>Caddo seized it eagerly. His eyes widened in amazement as he read:</p> - -<p>"The certainty of success in any course of operations, expressed in -mathematical terms, represents the sum of all factors, beginning at the -starting point, which must be described as <i>real zero</i>, and ending with -the objective, also reduced to a real numerical value. The constant of -certainty, <i>J</i>, can be the determining factor which leads an operation -from the beginning to the objective."</p> - -<p>Caddo read the paper and reread it again and again.</p> - -<p>"Is this all of it?" he asked, turning to Oridin.</p> - -<p>"Every bit," Oridin replied. "The formula is simple, like the one to -determine the sum of an arithmetical progression—the first number of -the progression plus the last number, multiplied by the number of terms -in the progression and divided by two. In your case the progression -lies between what you have and what you want. The certainty of getting -it is the sum of all the factors."</p> - -<hr class="tb" /> - -<p>Caddo sat down in a chair at the desk. He seemed to forget his -suspicions of Oridin, who had placed a stack of paper beside him. -Caddo was engrossed in the formula and Caddo, as a mathematician, knew -that everything in the world could be expressed in figures. What would -Napoleon, or Hitler, have given for this formula!</p> - -<p>"The beginning is <i>real zero</i>!" Caddo spoke aloud.</p> - -<p>"Which is different from a mathematical zero," Oridin said. "I might -say that zero, like absolute vacuum, never occurs. Even if we have two -apples and eat two of them the atoms of the apples continue to exist. -In the formula you have a small fraction instead of zero. It serves the -same purpose. If you multiply a number X by zero, the answer is zero. -Multiply a fraction approaching zero, .000,000,001 by another number -and that number approaches zero too. If that number is a fraction it -will be even closer to zero than our <i>real zero</i>. In fact, we are -dealing with trans-zero numbers, just like the transfinite numbers -discovered by Georg Cantor."</p> - -<p>"Yes, yes!" Caddo said eagerly. He picked up a pencil. He scribbled -furiously. His objective was all of the power in the world expressed in -ergs; all of the gold in the world, expressed in dollars; all of the -land, expressed in acres; the people, in individuals.</p> - -<p>Oridin moved softly behind him. A multiple-calculator made its -appearance in the room. Paper flew from under Caddo's pencil. Sweat -poured from his space-browned face.</p> - -<p>The two clocks on the wall recorded the turning of the earth and the -planetoid Azair.</p> - -<p>Caddo forgot about Oridin. He forgot about everything except the -figures that revolved in his brain.</p> - -<p>Oridin moved out into the warm artificial atmosphere of his planetoid. -He was a recluse again. He was alone. A momentary contact with the -greed, and avarice of the human race had been wiped away.</p> - -<p>Far out in space was a glow of rockets. A ship was going to land. It -had seemed only a short time since Caddo had landed. But that was three -terrestrial days ago. This was the patrol.</p> - -<p>"I've a prisoner for you," Oridin informed the captain. "It's Caddo."</p> - -<p>"Caddo! He's the No. 1 universal enemy. Man, you'll grow rich with the -rewards offered on nine planets for his capture."</p> - -<p>"You can have the reward," Oridin said. "Take him away. He's a -nuisance."</p> - -<p>They found Caddo in the lounge of Oridin's house chewing on a book -of logarithms. His mind was gone. He could only babble figures. His -fingers twitched with cramps from writing with a pencil and punching -the keys of the calculating machine. Every spark of vitality had been -taken from his body. The batteries of his force armor had burned out.</p> - -<p>"What's the matter with him?" the captain asked.</p> - -<p>"He wanted too much," Oridin replied. "I gave him a simple little -formula for success, but the formula ceases to be simple as the -definition for success grows more demanding. Had he sought perfection, -Caddo would have seen that even this was unrecognizable, although the -certainty was only halfway to infinity—"</p> - -<p>"Sorry, Mr. Oridin, but I'm not a mathematician," the captain said.</p> - -<p>"There's nothing difficult in the formula. It proves that certainty -is unrecognizable. You'll have to admit that a goal, to be reached -has to follow a path and that path is determined by two points. The -beginning is one and the second one makes the ultimate objective -certain. Therefore the second point is certainty. But certainty is -unrecognizable—"</p> - -<p>Oridin brought forth his formula and allowed the captain to read it. -The patrol officer blinked his eyes and scratched his head. Oridin -wrote his formula out:</p> - -<p class="ph1">J = (a + 1) times infinity/2</p> - -<p>"<i>J</i> is certainty, <i>a</i> our starting point and 1 is unity, or -perfection," Oridin explained. "Our starting point is close to zero, -but not zero. But for convenience we'll say that it's a fraction so -close that we can call it zero. Then certainty, <i>J</i>, is one-half of -infinity, which you'll have to agree does not approach infinity and may -be well within the realm of human comprehension, although we will not -recognize perfection because we do not know what number is halfway to -infinity. Caddo overlooked the fact that he went further and further -into the transinfinite with each number he added to his equation, for -there are an infinity of numbers between any two whole numbers and any -two fractions and their sum is always infinity."</p> - -<p>The patrol captain already was muttering to himself and Oridin hurried -him out of the house and into the patrol ship with his prisoner.</p> - -<p>After the space craft had gone, Oridin returned to his living quarters -and replaced his formula in the unlocked safe. He cleaned the litter -made by Caddo and sat down. Once again, Oridin was a recluse and he -would remain so until someone else had a dream of conquering the -universe.</p> - - - - - - - - -<pre> - - - - - -End of the Project Gutenberg EBook of Oridin's Formula, by R. R. Winterbotham - -*** END OF THIS PROJECT GUTENBERG EBOOK ORIDIN'S FORMULA *** - -***** This file should be named 62313-h.htm or 62313-h.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/6/2/3/1/62313/ - -Produced by Greg Weeks, Mary Meehan and the Online -Distributed Proofreading Team at http://www.pgdp.net - -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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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'll have -to check the laws of the country where you are located before using this ebook. - -Title: Oridin's Formula - -Author: R. R. Winterbotham - -Release Date: June 2, 2020 [EBook #62313] - -Language: English - -Character set encoding: ASCII - -*** START OF THIS PROJECT GUTENBERG EBOOK ORIDIN'S FORMULA *** - - - - -Produced by Greg Weeks, Mary Meehan and the Online -Distributed Proofreading Team at http://www.pgdp.net - - - - - - - - - -ORIDIN'S FORMULA - -By R. R. WINTERBOTHAM - -The formula was a simple equation, but -Caddo had to have it--for knowing its -answer meant he would rule the universe. - -[Transcriber's Note: This etext was produced from -Planet Stories March 1943. -Extensive research did not uncover any evidence that -the U.S. copyright on this publication was renewed.] - - -Oridin the Recluse listened to the threat wirelessed from the spaceship -that was hoving to in a landing orbit about the planetoid Azair. - -"I've a bead on your atmosphere plant," said the snarling voice. "One -false move and I'll blast it to star dust." - -Oridin shrugged as he heard the words. One more fool had come to Azair -looking for the secret that the Recluse of the Asteroids was supposed -to possess. - -"Your threats are unnecessary, stranger," Oridin replied in the -microphone of his radio. "Everyone is welcome here as long as he -behaves. I have ways of dealing with those who don't." - -"I'm warning you," came the voice again, "that I will stand for no -foolishness. I'll kill you if you try to resist." - -Oridin smiled. "Land, stranger, you need not fear me." - -The hermit arose and went to the galley of the warm little house that -seemed to grow from the solid rocks of the tiny planet. He pressed a -button, waited a second and then opened a small compartment. In the box -was a steaming pot of coffee, freshly made by Oridin's automatic cook. - -Outside the transparent shelter, the air grew blue from the reflection -of landing rockets. Oridin glanced to the leveled surface on which the -ship was coming to rest. He saw a turret training on the little house. -Oridin was not afraid; the visitor probably would be interesting. Even -a recluse can grow lonesome on a minor planet. - -A figure emerged from the spaceship. He wore an oxygen helmet, although -Oridin plentifully supplied the planetoid with artificial atmosphere -from a small plant at the north pole. The stranger did not believe that -Oridin would not resist. Again Oridin smiled. Deep in the rocks of -Azair were guns that could have blasted the visitor a thousand times, -had Oridin wished. But there was nothing clever about blowing a foe to -pieces. The foe too often was killed before he sensed defeat. Oridin -enjoyed an equal battle, or even one against odds. - -[Illustration: _"Open up," Caddo snarled, "or I'll blow my way in!"_] - -"Open up! Open up, I tell you, or I'll burn my way in!" demanded the -visitor. - -"He's certainly not deceiving me as to his intentions," Oridin decided. - -The recluse pushed a button on the wall, and a giant gate swung outward -admitting the stranger. - -The fellow was as tall and as muscular as Oridin himself, but the space -suit and the gaping blaster he held in his hand made the visitor seem -much more formidable. Oridin himself was dressed in bell-bottomed -slacks and a loosely fitting, slipover coat. His beard softened his -countenance and made him seem quite gentle, except for a certain -glitter in his eyes that seemed to warn that Oridin loved a contest. -And this would seem to be a deadly contest. - -Oridin bowed. - -"You are welcome, stranger," he said. "Take off your helmet, for the -air is pure. Put aside your gun, for I am unarmed and I do not intend -to harm you." - -The stranger hesitated, uncertainly. - -"No tricks, Oridin!" he warned. - -"Tricks?" Oridin laughed tauntingly. "You are not very confident for a -man of your caliber. I've heard of you often, Caddo Velexis. They say -you have conquered whole nations single-handed, and yet you are afraid -of an unarmed hermit." - -"I'm not afraid of you," Caddo said in a tone that hinted he was. - -Caddo removed his helmet and holstered his blaster, but Oridin noted -that the terrestrial giant did not move the firing button to safety. - -"Will you have some coffee?" Oridin asked. "It will refresh you after -your long trip, and you must have had a long trip, for we are in a very -sparsely filled part of the sky." - -Oridin lifted the pot and poured the brown steaming liquid into a -thick, metal mug. - -Caddo waved it aside. - -"I have no time!" - -"Do not be alarmed," Oridin said. "The patrol will not be near Azair -for three days." - -Oridin sat down. His fingers felt under the arm of the chair where a -series of buttons controlled other mechanisms in the room. Caddo had -relaxed his watchfulness. - -"In three days I'll be well toward the other side of the solar system," -Caddo said. - -Oridin lifted his eyebrows. - -"Toward the earth? You have undertaken something this time!" - -"Yes!" Caddo said. "It's the Earth I am after! I have all I want of the -outlying planets and planetoids. You can capture a hundred of them and -be no better off than you were at first. But if you capture the Earth, -you can rule the universe." - -Oridin touched one of the buttons. A tiny pinhole in the wall of the -room seemed to blink. There was a blinding flash and the smell of -burned leather permeated the place. - - * * * * * - -Caddo gave a cry of alarm and sprang back, knocking over his chair. He -was on his feet holding his blaster in his hand in a second. Across the -top of his helmet was a scorched streak. - -"You tried to kill me!" Caddo screamed. "You dirty swine." - -Oridin's lips parted in a smile as he looked without fear into the -mouth of the trembling weapon. - -"Don't underestimate yourself, Caddo," he said. "The hot beam was only -a warning--something to let you know that I could kill you anytime -I wished. Even now, before you could squeeze the trigger on the -weapon, I could cause certain things to happen--no, no! You are safe, -Caddo--I could cause you to die if I wish, but you are interesting, a -dangerous man. It would be a better accomplishment for me to give you a -punishment you deserve." - -The fear that shone in Caddo's eyes faded away. For a moment he watched -Oridin. Then he laughed. - -"So it's that kind of a game, is it? I can play it too! Your threats do -not frighten me. Nor am I afraid of your hot beam. Look!" - -Caddo thrust his arm forward into the path of the beam. There was a -puff of smoke as the tremendous heat vaporized particles of dust on the -leather sleeves. Then nothing happened. - -"I have a neutralizing force, powered with a small battery in my -clothing," Caddo said. "Foolishly, I did not have it turned on a moment -ago. But you can't hurt me now." - -Oridin shrugged. "I am still not afraid of you Caddo. If you had come -here to loot, you would have killed me long ago. But what you want is -something you cannot gain by killing me. What is it?" - -"You are going to give me the secret that will make me the master of -the earth, and the master of the universe," Caddo announced. - -Oridin poured himself a mug of coffee. - -"I knew you did not want gold, although Azair is filthy with the -stuff," he said. "But what secret have I that is so powerful?" - -"The _Discovery_!" Caddo said. - -"I have many." Oridin nodded toward the wall, and the pinhole of light -blinked out. - -"I want the secret of the universe!" Caddo spoke tensely. - -"Come! Don't be so melodramatic," Oridin chided. "The universe is full -of secrets." - -"You're stalling. You know what I mean!" - -"I think I do," Oridin agreed. "My erratic experiments have revealed a -certain mathematical function, _J_, which theoretically opens the door -to action without probability. Is that what you want, Caddo? The value -of _J_?" - -"The mathematical bombsight!" Caddo said. "It removes probability and -makes certainty of everything. With my calculations based on certainty, -I'll be fate itself! I can conquer the world, chain the universe and -govern creation." - -Oridin laughed quietly. - -"Alexander, Caesar, Napoleon, Genghis Khan and Hitler spoke those words -and they were willing to bargain with the devil himself to make them -come true," he said. "I suppose I am the devil, for I know the answer -and I can tell you the answer--for a price." - -"You'll give it to me for nothing!" Caddo patted the blister, now in -the holster at his side. - -"Is that your only offer?" Oridin asked, still wearing an amused -half-smile. - -"It is!" - -Oridin rose and moved toward a safe under two clocks on the wall across -the room. One of these clocks gave the terrestrial days, hours and -minutes according to the General Meridian time. The other registered -the four-hour rotation of Azair. - -"Wait!" Caddo halted Oridin. "No tricks. Give me the combination and -I'll open the safe!" - -Oridin turned to the space pirate. - -"The safe is unlocked. The formula is inside." - -Caddo's eyes betrayed his suspicion. The most valuable secret in -the world was in an unlocked safe! Warily Caddo stepped forward. He -hesitated, wondering if even his neutralizing force was enough to -protect him. - -"There's no danger. Go ahead. Help yourself," Oridin urged. - -Caddo was desperate. He touched the handle of the door. It was -unlocked. He flung it open. Inside the safe was a single sheet of white -paper. - -Caddo seized it eagerly. His eyes widened in amazement as he read: - -"The certainty of success in any course of operations, expressed in -mathematical terms, represents the sum of all factors, beginning at the -starting point, which must be described as _real zero_, and ending with -the objective, also reduced to a real numerical value. The constant of -certainty, _J_, can be the determining factor which leads an operation -from the beginning to the objective." - -Caddo read the paper and reread it again and again. - -"Is this all of it?" he asked, turning to Oridin. - -"Every bit," Oridin replied. "The formula is simple, like the one to -determine the sum of an arithmetical progression--the first number of -the progression plus the last number, multiplied by the number of terms -in the progression and divided by two. In your case the progression -lies between what you have and what you want. The certainty of getting -it is the sum of all the factors." - - * * * * * - -Caddo sat down in a chair at the desk. He seemed to forget his -suspicions of Oridin, who had placed a stack of paper beside him. -Caddo was engrossed in the formula and Caddo, as a mathematician, knew -that everything in the world could be expressed in figures. What would -Napoleon, or Hitler, have given for this formula! - -"The beginning is _real zero_!" Caddo spoke aloud. - -"Which is different from a mathematical zero," Oridin said. "I might -say that zero, like absolute vacuum, never occurs. Even if we have two -apples and eat two of them the atoms of the apples continue to exist. -In the formula you have a small fraction instead of zero. It serves the -same purpose. If you multiply a number X by zero, the answer is zero. -Multiply a fraction approaching zero, .000,000,001 by another number -and that number approaches zero too. If that number is a fraction it -will be even closer to zero than our _real zero_. In fact, we are -dealing with trans-zero numbers, just like the transfinite numbers -discovered by Georg Cantor." - -"Yes, yes!" Caddo said eagerly. He picked up a pencil. He scribbled -furiously. His objective was all of the power in the world expressed in -ergs; all of the gold in the world, expressed in dollars; all of the -land, expressed in acres; the people, in individuals. - -Oridin moved softly behind him. A multiple-calculator made its -appearance in the room. Paper flew from under Caddo's pencil. Sweat -poured from his space-browned face. - -The two clocks on the wall recorded the turning of the earth and the -planetoid Azair. - -Caddo forgot about Oridin. He forgot about everything except the -figures that revolved in his brain. - -Oridin moved out into the warm artificial atmosphere of his planetoid. -He was a recluse again. He was alone. A momentary contact with the -greed, and avarice of the human race had been wiped away. - -Far out in space was a glow of rockets. A ship was going to land. It -had seemed only a short time since Caddo had landed. But that was three -terrestrial days ago. This was the patrol. - -"I've a prisoner for you," Oridin informed the captain. "It's Caddo." - -"Caddo! He's the No. 1 universal enemy. Man, you'll grow rich with the -rewards offered on nine planets for his capture." - -"You can have the reward," Oridin said. "Take him away. He's a -nuisance." - -They found Caddo in the lounge of Oridin's house chewing on a book -of logarithms. His mind was gone. He could only babble figures. His -fingers twitched with cramps from writing with a pencil and punching -the keys of the calculating machine. Every spark of vitality had been -taken from his body. The batteries of his force armor had burned out. - -"What's the matter with him?" the captain asked. - -"He wanted too much," Oridin replied. "I gave him a simple little -formula for success, but the formula ceases to be simple as the -definition for success grows more demanding. Had he sought perfection, -Caddo would have seen that even this was unrecognizable, although the -certainty was only halfway to infinity--" - -"Sorry, Mr. Oridin, but I'm not a mathematician," the captain said. - -"There's nothing difficult in the formula. It proves that certainty -is unrecognizable. You'll have to admit that a goal, to be reached -has to follow a path and that path is determined by two points. The -beginning is one and the second one makes the ultimate objective -certain. Therefore the second point is certainty. But certainty is -unrecognizable--" - -Oridin brought forth his formula and allowed the captain to read it. -The patrol officer blinked his eyes and scratched his head. Oridin -wrote his formula out: - -J = (a + 1) times infinity/2 - -"_J_ is certainty, _a_ our starting point and 1 is unity, or -perfection," Oridin explained. "Our starting point is close to zero, -but not zero. But for convenience we'll say that it's a fraction so -close that we can call it zero. Then certainty, _J_, is one-half of -infinity, which you'll have to agree does not approach infinity and may -be well within the realm of human comprehension, although we will not -recognize perfection because we do not know what number is halfway to -infinity. Caddo overlooked the fact that he went further and further -into the transinfinite with each number he added to his equation, for -there are an infinity of numbers between any two whole numbers and any -two fractions and their sum is always infinity." - -The patrol captain already was muttering to himself and Oridin hurried -him out of the house and into the patrol ship with his prisoner. - -After the space craft had gone, Oridin returned to his living quarters -and replaced his formula in the unlocked safe. He cleaned the litter -made by Caddo and sat down. Once again, Oridin was a recluse and he -would remain so until someone else had a dream of conquering the -universe. - - - - - -End of the Project Gutenberg EBook of Oridin's Formula, by R. R. 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