The Astounding Science Fiction Anthology

by John W. Campbell Jr.

  The calm voice continued, earnest but not offensively so, insistent but friendly. He regretted that their robot had killed human beings. In greater detail, he explained that every space was constructed on a different numbers system, some all negative, some all positive, some a mixture of the two, the whole an infinite variety, and every mathematic interwoven into the very fabric of the space it ruled.

  Ieis force was not really mysterious. It was simply a flow from one space to another, the result of a difference in potential. This flow, however, was one of the universal forces, which only one other force could affect, the one he had used a few minutes before. Ultimate metal was actually ultimate.

  In their space they had a similar metal, built up from negative atoms. He could see from Brender’s mind that the Martians had known nothing about minus numbers, so that they must have built it up from ordinary atoms. It could be done that way, too, though not so easily. He finished:

  ‘The problem narrows down to this: Your mathematics must tell us how, with our universal force, we can short-circuit the ultimate prime number—that is, factor it—so that the door will open any time. You may ask how a prime can be factored when it is divisible only by itself and by one. That problem is, for your system, solvable only by your mathematics. Will you do it?”

  Brender realized with a start that he was still holding his revolver. He tossed it aside. His nerves were calm as he said:

  “Everything you have said sounds reasonable and honest. If you were desirous of making trouble, it would be the simplest thing in the world to send as many of your kind as you wished. Of course, the whole affair must be placed before the Council—”

  “Then it is hopeless—the Council could not possibly accede—”

  “And you expect me to do what you do not believe the highest governmental authority in the System would do?” Brender exclaimed.

  “It is inherent in the nature of a democracy that it cannot gamble with the lives of its citizens. We have such a government here; and its members have already informed us that, in a similar condition, they would not consider releasing an unknown beast upon their people. Individuals, however, can gamble where governments must not. You have agreed that our argument is logical. What system do men follow if not that of logic?”

  The Controller, through its robot, watched Brender’s thoughts alertly. It saw doubt and uncertainty, opposed by a very human desire to help, based upon the logical conviction that it was safe. Probing his mind, it saw swiftly that it was unwise, in dealing with men, to trust too much to logic. It pressed on:

  “To an individual we can offer—everything. In a minute, with your permission, we shall transfer this ship to Mars; not in thirty days, but in thirty seconds. The knowledge of how this is done will remain with you. Arrived at Mars, you will find yourself the only living person who knows the whereabouts of the ancient city of Li, of which the vault of the beast is the central tower. In this city will be found literally billions of dollars’ worth of treasure made of ultimate metal; and according to the laws of Earth, fifty percent will be yours. Your fortune re-established, you will be able to return to Earth this very day, and reclaim your former wife, and your position. Poor silly child, she loves you still, but the iron conventions and training of her youth leave her no alternative. If she were older, she would have the character to defy those conventions. You must save her from herself. Will you do it?”

  Brender was as white as a sheet, his hands clenching and unclenching. Malevolently, the thing watched the flaming thought sweeping through his brain—the memory of a pudgy white hand closing over Pamela’s fingers, watched the reaction of Brender to its words, those words that expressed exactly what he had always thought. Brender looked up with tortured eyes. “Yes,” he said, “I’ll do what I can.”

  A bleak range of mountains fell away into a valley of reddish gray sand. The thin winds of Mars blew a mist of sand against the building.

  Such a building! At a distance, it had looked merely big. A bare hundred feet projected above the desert, a hundred feet of length and fifteen hundred feet of diameter. Literally thousands of feet must extend beneath the restless ocean of sand to make the perfect balance of form, the graceful flow, the fairylike beauty, which the long-dead Martians demanded of all their constructions, however massive. Brender felt suddenly small and insignificant as the rockets of his spacesuit pounded him along a few feet above the sand toward that incredible building.

  At close range the ugliness of sheer size was miraculously lost in the wealth of the decorative. Columns and pilasters assembled in groups and clusters, broke up the facades, gathered and dispersed again restlessly. The flat surfaces of wall and roof melted into a wealth of ornaments and imitation stucco work, vanished and broke into a play of light and shade.

  The creature floated beside Brender; and its Controller said: “I see that you have been giving considerable thought to the problem, but this robot seems incapable of following abstract thoughts, so I have no means of knowing the source of your speculations. I see however that you seem to be satisfied.”

  “I think I’ve got the answer,” said Brender, “but first I wish to see the time lock. Let’s climb.”

  They rose into the sky, dipping over the lip of the building. Brender saw a vast flat expanse; and in the center—He caught his breath!

  The meager light from the distant sun of Mars shone down on a structure located at what seemed the exact center of the great door. The structure was about fifty feet high, and seemed nothing less than a series of quadrants coming together at the center, which was a metal arrow pointing straight up.

  The arrow head was not solid metal. Rather it was as if the metal had divided in two parts, then curved together again. But not quite together. About a foot separated the two sections of metal. But that foot was bridged by a vague, thin, green flame of ieis force.

  “The time lock!” Brender nodded. “I thought it would be something like that, though I expected it would be bigger, more substantial.”

  “Do not be deceived by its fragile appearance,” answered the thing. “Theoretically, the strength of ultimate metal is infinite; and the ieis force can only be affected by the universal I have mentioned. Exactly what the effect will be, it is impossible to say as it involves the temporary derangement of the whole number system upon which that particular area of space is built. But now tell us what to do.”

  “Very well.” Brender eased himself onto a bank of sand, and cut off his antigravity plates. He lay on his back, and stared thoughtfully into the blue-black sky. For the time being all doubts, worries and fears were gone from him, forced out by sheer will power. He began to explain:

  “The Martian mathematic, like that of Euclid and Pythagoras, was based on endless magnitude. Minus numbers were beyond their philosophy. On Earth, however, beginning with Descartes, an analytical mathematic was evolved. Magnitude and perceivable dimensions were replaced by that of variable relation-values between positions in space.

  “For the Martians, there was only one number between 1 and 3. Actually, the totality of such numbers is an infinite aggregate. And with the introduction of the idea of the square root of minus one—or i—and the complex numbers, mathematics definitely ceased to be a simple thing of magnitude, perceivable in pictures. Only the intellectual step from the infinitely small quantity to the lower limit of every possible finite magnitude brought out the conception of a variable number which oscillated beneath any assignable number that was not zero.

  “The prime number, being a conception of pure magnitude, had no reality in real mathematics, but in this case was rigidly bound up with the reality of the ieis force. The Martians knew ieis as a pale-green flow about a foot in length and developing say a thousand horsepower. (It was actually 12.171 inches and 1021.23 horsepower, but that was unimportant.) The power produced never varied, the length never varied, from year end to year end, for tens of thousands of years. The Martians took the length as their basis of measurement, and called it one
‘el’; they took the power as their basis of power and called it one ‘rb.’ And because of the absolute invariability of the flow they knew it was eternal.

  “They knew furthermore that nothing could be eternal without being prime; their whole mathematic was based on numbers which could be factored, that is, disintegrated, destroyed, rendered less than they had been; and numbers which could not be factored, disintegrated or divided into smaller groups.

  “Any number which could be factored was incapable of being infinite. Contrariwise, the infinite number must be prime.

  “Therefore, they built a lock and integrated it along a line of ieis, to operate when the ieis ceased to flow—which would be at the end of Time, provided it was not interfered with. To prevent interference, they buried the motivating mechanism of the flow in ultimate metal, which could not be destroyed or corroded in any way. According to their mathematic, that settled it.”

  “But you have the answer,” said the voice of the thing eagerly.

  “Simply this: The Martians set a value on the flow of one ‘rb.’ If you interfere with that flow to no matter what small degree, you no longer have an ‘rb.’ You have something less. The flow, which is a universal, becomes automatically less than a universal, less than infinite. The prime number ceases to be prime. Let us suppose that you interfere with it to the extent of infinity minus one. You will then have a number divisible by two. As a matter of fact, the number, like most large numbers, will immediately break into thousands of pieces, i.e., it will be divisible by tens of thousands of smaller numbers. If the present time falls anywhere near one of those breaks, the door would open then. In other words, the door will open immediately if you can so interfere with the flow that one of the factors occurs in immediate time.”

  “That is very clear,” said the Controller with satisfaction and the image of Brender was smiling triumphantly. “We shall now use this robot to manufacture a universal; and Kalorn shall be free very shortly.” He laughed aloud. “The poor robot is protesting violently at the thought of being destroyed, but after all it is only a machine, and not a very good one at that. Besides, it is interfering with my proper reception of your thoughts. Listen to it scream, as I twist it into shape.”

  The cold-blooded words chilled Brender, pulled him from the heights of his abstract thought. Because of the prolonged intensity of his thinking, he saw with sharp clarity something that had escaped him before.

  “Just a minute,” he said. “How is it that the robot, introduced from your world, is living at the same time rate as I am, whereas Kalorn continues to live at your time rate?”

  “A very good question.” The face of the robot was twisted into a triumphant sneer, as the Controller continued. “Because, my dear Brender, you have been duped. It is true that Kalorn is living in our time rate, but that was due to a shortcoming in our machine. The machine which Kalorn built, while large enough to transport him, was not large enough in its adaptive mechanism to adapt him to each new space as he entered it. With the result that he was transported but not adapted. It was possible of course for us, his helpers, to transport such a small thing as the robot, though we have no more idea of the machine’s construction than you have.

  “In short, we can use what there is of the machine, but the secret of its construction is locked in the insides of our own particular ultimate metal, and in the brain of Kalorn. Its invention by Kalorn was one of those accidents which, by the law of averages, will not be repeated in millions of our years. Now that you have provided us with the method of bringing Kalorn back, we shall be able to build innumerable interspace machines. Our purpose is to control all spaces, all worlds—particularly those which are inhabited. We intend to be absolute rulers of the entire Universe.”

  The ironic voice ended; and Brender lay in his prone position the prey of horror. The horror was twofold, partly due to the Controller’s monstrous plan, and partly due to the thought that was pulsing in his brain. He groaned, as he realized that warning thought must be ticking away on the automatic receiving brain of the robot. “Wait,” his thought was saying, “that adds a new factor. Time—”

  There was a scream from the creature as it was forcibly dissolved. The scream choked to a sob, then silence. An intricate machine of shining metal lay there on that great gray-brown expanse of sand and ultimate metal.

  The metal glowed; and then the machine was floating in the air. It rose to the top of the arrow, and settled over the green flame of ieis.

  Brender jerked on his antigravity screen, and leaped to his feet. The violent action carried him some hundred feet into the air. His rockets sputtered into staccato fire, and he clamped his teeth against the pain of acceleration.

  Below him, the great door began to turn, to unscrew, faster and faster, till it was like a flywheel. Sand flew in all directions in a miniature storm.

  At top acceleration, Brender darted to one side.

  Just in time. First, the robot machine was flung off that tremendous wheel by sheer centrifugal power. Then the door came off, and, spinning now at an incredible rate, hurtled straight into the air, and vanished into space.

  A puff of black dust came floating up out of the blackness of the vault. Suppressing his horror, yet perspiring from awful relief, he rocketed to where the robot had fallen into the sand.

  Instead of glistening metal, a time-dulled piece of junk lay there. The dull metal flowed sluggishly and assumed a quasi-human shape. The flesh remained gray and in little rolls as if it were ready to fall apart from old age. The thing tried to stand up on wrinkled, horrible legs, but finally lay still. Its lips moved, mumbled:

  “I caught your warning thought, but I didn’t let them know. Now, Kalorn is dead. They realized the truth as it was happening. End of Time came—”

  It faltered into silence; and Brender went on: “Yes, end of Time came when the flow became momentarily less than eternal—came at the factor point which occurred a few minutes ago.”

  “I was… only partly… within its… influence, Kalorn all the way… Even if they’re lucky… will be years before… they invent another machine… and one of their years is billions… of yours… I didn’t tell them… I caught your thought… and kept it… from them—”

  “But why did you do it? Why?”

  “Because they were hurting me. They were going to destroy me. Because… I liked… being human. I was… somebody!”

  The flesh dissolved. It flowed slowly into a pool of lavalike gray. The lava crinkled, split into dry, brittle pieces. Brender touched one of the pieces. It crumbled into a fine powder of gray dust. He gazed out across that grim, deserted valley of sand, and said aloud, pityingly:

  “Poor Frankenstein.”

  He turned toward the distant spaceship, toward the swift trip to Earth. As he climbed out of the ship a few minutes later, one of the first persons he saw was Pamela.

  She flew into his arms. “Oh, Jim, Jim,” she sobbed. “What a fool I’ve been. When I heard what had happened, and realized you were in danger, I—Oh, Jim!”

  Later, he would tell her about their new fortune.

  THE EXALTED

  by L. Sprague de Camp

  THE STORKLIKE MAN WITH THE GRAY GOATEE SHUFFLED THE TWELVE black billets about on the table top. “Try it again,” he said.

  The undergraduate sighed. “O. K., Professor Methuen.” He looked apprehensively at Johnny Black, sitting across the table with one claw on the button of the stop clock. Johnny returned the look impassively through the spectacles perched on his yellowish muzzle.

  “Go,” said Ira Methuen.

  Johnny depressed the button. The undergraduate started the second run of his wiggly-block test. The twelve billets formed a kind of three-dimensional jigsaw puzzle; when assembled they would make a cube. But the block had originally been sawn apart on wavy, irregular lines, so that the twelve billets had to be put together just so.

  The undergraduate fiddled with the billets, trying this one and that one against one he held in his h
and. The clock ticked round. In four minutes he had all but one in place. This one, a corner piece, simply would not fit. The undergraduate wiggled it and pushed it. He looked at it closely and tried again. But its maladjustment remained.

  The undergraduate gave up. “What’s the trick?” he asked.

  Methuen reversed the billet end for end. It fitted.

  “Oh, heck,” said the undergraduate. “I could have gotten it if it hadn’t been for Johnny.”

  Instead of being annoyed, Johnny Black twitched his mouth in a bear’s equivalent of a grin. Methuen asked the student why.

  “He distracts me somehow. I know he’s friendly and all that, but… it’s this way, sort of. Here I come to Yale to get to be a psychologist. I hear all about testing animals, chimps and bears and such. And when I get here I find a bear testing me. It’s kind of upsetting.”

  “That’s all right,” said Methuen. “Just what we wanted. We’re after, not your wiggly-block score by itself, but the effect of Johnny’s presence on people taking the test. We’re getting Johnny’s distraction factor—his ability to distract people. We’re also getting the distraction factor of a lot of other things, such as various sounds and smells. I didn’t tell you sooner because the knowledge might have affected your performance.”

  “I see. Do I still get my five bucks?”

  “Of course. Good day, Kitchell. Come on, Johnny; we’ve just got time to make Psychobiology 100. We’ll clean up the stuff later,”

  On the way out of Methuen’s office, Johnny asked: “Hey, boss! Do you feer any effec’ yet?”