Brain Teaser Read online

  He typed: EXPLAIN THIS DISCREPANCY BETWEEN SPACE WARP AND NORMAL SPACE

  POSITIONS.

  It answered: INSUFFICIENT DATA TO ACCOUNT FOR DISCREPANCY.

  He asked: HOW DID YOU DETERMINE OUR PRESENT POSITION?

  It replied: BY TRIANGULATION, BASED ON THE RECESSION OF EARTH, THE SUN, SIRIUS, ORION, AND OTHER STARS.

  BUT THE RECEDING SUN WENT INTO THE ULTRAVIOLET, he objected.

  Again it answered with the noncommittal, DATA ACKNOWLEDGED.

  DID YOU ALREADY HAVE THIS DATA? he asked.

  YES.

  EXPLAIN WHY THE RECEDING SUN SHIFTED INTO THE ULTRAVIOLET INSTEAD OF

  THE INFRARED.

  It replied: DATA INSUFFICIENT TO ARRIVE AT LOGICAL EXPLANATION.

  He paused, pondering his next move. Time was speeding by and he was learning nothing of value. He would have to move the ship to some place in the warp where emergence into normal space would not put him under the blasters of the Slug cruisers. He could not know where to move the ship until he knew where the ship was at the present. He did not believe it was in the position given him by the computer, and its original space warp position had certainly not been the one given by the computer. The computer did not have the ability to use its knowledge to explain contradictory data. It had been ordered to compute their space warp position by triangulation of the receding sun and stars and was not at all disturbed by the contradicting shift of the sun into the ultraviolet. Suppose it had been ordered to calculate their position by computations based on the shift of the sun's and stars' spectrum into the ultraviolet?

  He asked it: WHAT IS OUR POSITION, IGNORING THE TRIANGULATION AND BASING

  YOUR COMPUTATIONS ON THE SHIFT OF THE SPECTRUMS OF THE SUN AND ORION

  INTO THE ULTRAVIOLET?

  It gave him the coordinates of a position almost two light-years toward Orion. The triangulation computations had shown the ship to be going backward at many times the speed of light; the spectrum-shift computations showed it to be going forward with approximately the same speed. THIS SHIP CANNOT SIMULTANEOUSLY BE IN TWO POSITIONS THREE LIGHT-YEARS

  APART. NEITHER CAN IT SIMULTANEOUSLY BE GOING FORWARD AND BACKWARD. DATA ACKNOWLEDGED, it agreed.

  USE THAT DATA TO EXPLAIN THE CONTRADICTIONS OF THE TWO POSITIONS YOU

  COMPUTED.

  DATA INSUFFICIENT TO ARRIVE AT LOGICAL EXPLANATION, it answered.

  ARE YOU CERTAIN THERE WAS NO ERROR IN YOUR CALCULATIONS?

  THERE WAS NO ERROR.

  DO YOU KNOW THAT IF WE DROPPED BACK INTO NORMAL SPACE, IT WOULD BE AT

  NEITHER OF THE POSITIONS YOU GAVE ME?

  It replied with the characteristic single-mindedness: DATA SHOWS OUR TWO POSITIONS TO BE

  THOSE GIVEN.

  He paused again. He was still getting nowhere while time fled by. How swiftly less than a hundred minutes could pass when they were all a man had left to him . . .

  The computer was a genius with the mental initiative of a moronic child. It could find the answer for him but first he would have to take it by the hand and lead it in the right direction. To do that he would have to know more about the warp.

  He wrote: EXPLAIN THE NATURE OF THE SPACE WARP AS SIMPLY AS POSSIBLE AND

  WITHOUT USING MATHEMATICS HIGHER THAN ALGEBRA.

  It answered at once: THIS CANNOT BE DONE.

  The chronometer read 12:30. He typed:

  THIS SHIP WILL HAVE TO RETURN TO NORMAL SPACE NO LATER THAN 13:53. IT

  MUST BE MOVED TO A DIFFERENT POSITION WHILE STILL IN THE WARP.

  DATA ACKNOWLEDGED, it replied.

  THIS SHIP CANNOT OCCUPY TWO POSITIONS AT THE SAME TIME. YOUR MEMORY

  FILES SHOULD CONTAIN SUFFICIENT DATA TO ENABLE YOU TO FIND THE

  EXPLANATION OF THIS TWO-POSITION PARADOX. FIND THAT EXPLANATION.

  SUBMIT METHOD OF PROCEDURE, it answered.

  I DO NOT KNOW HOW. YOU WILL HAVE TO ARRIVE AT THE EXPLANATION UNAIDED. THIS CANNOT BE DONE, it replied.

  He wrote, with morbid curiosity:

  IF YOU DO NOT FIND THE ANSWER UNAIDED YOU WILL BE DESTROYED ALONG

  WITH ME AT 13:53. DON'T YOU GIVE A DAMN?

  It answered: GIVE A DAMN IS A SEMANTIC EXPRESSION I DO NOT UNDERSTAND. CLARIFY QUESTION.

  He got out of the computer seat and walked about the room restlessly. He passed by the transdimensional viewscreen and communicator and pressed the communicator's signal button. A dial flickered in return, showing his signal was going out, but there was no sound in response. If only he could make contact with the brains in Observation—

  He was umpty billion miles east of the sun and umpty billion miles west of the sun. He was racing faster than light in two different directions at once and he was sitting motionless under the blasters of two Slug cruisers.

  Another thought came to him: even if he could move the ship while in the warp, where could he go?

  He would have to go far beyond the outer limits of the solar system to escape detection by the Slug cruisers. And at that distance the sun would be only a yellow star, incapable of energizing the little solar power units. He would not live long after the last of the power was drained from the batteries and the air regeneration equipment ceased functioning. He would not even dare sleep, toward the last. There were no convection currents in the air of a ship without gravity, and it was imperative that the air be circulated constantly. The air circulation blowers would cease functioning while the ship still contained pure air but he would have to move about continually to breathe that air. Should he lie down to sleep he would smother to death in a carbon dioxide bubble of his own making.

  If he managed to emerge into normal space at some point just outside Earth's atmosphere, beyond range of the cruisers, his driveless ship would descend as a blazing meteor. If, by some miracle, he could emerge into normal space just a few inches above the space-field it would be to materialize into space already occupied by air. Such a materialization would be simultaneously fatal to him and to the electronic components of the shuttle and computer.

  And if he did not move the ship, the Slug cruisers would disintegrate him. He had four hypothetical choices of his way to die, all equally unpleasant.

  He smiled wanly at his reflection in the bright metal bordering the viewscreen and said, "Brother—you've had it!"

  * * *

  He went to the control room, there to brush his fingers across the useless control buttons and look into the viewscreen that revealed only black and limitless Nothing.

  What was the warp? Surely it must have definite physical laws of some kind. It was difficult to imagine any kind of existence—even the black nothing of the warp—as being utterly without rule or reason. If he knew the laws of the warp he might find some means of survival hitherto hidden from him. There was only one way he could learn about the warp. He would have to question the computer and continue questioning it until he learned or until his time was up.

  He returned to the computer and considered his next question. The computer had calculated their positions from observations of the sun and other stars in front of the ship—what would similar calculations based on observations of the stars behind the ship reveal? He typed: USE FIRST THE TRIANGULATION METHOD AND THEN THE SPECTRUM-SHIFT METHOD

  TO DETERMINE OUR POSITION FROM OBSERVATIONS MADE OF THE STARS OF

  OPHIUCHUS.

  The answers appeared. They showed the ship to be simultaneously speeding away from Ophiuchus and toward it.

  He asked: DO THESE TWO POSITIONS COINCIDE WITH THOSE RESULTING FROM THE

  OBSERVATIONS OF ORION?

  YES, it answered.

  Was the paradox limited to the line of flight?

  He asked the computer: WHAT IS OUR POSITION, COURSE AND SPEED AS INDICATED BY

  THE STARS AT RIGHT-ANGLES TO OUR FORWARD-BACKWARD COURSE; BY THE

  STARS OF URSA MINOR AND CRUX?

  The answer appeared on the panel: the ship was racing sideward through the warp in two diametrically opposed directions, but
at only one-third the speed with which it was racing forward and backward. So now the ship had four impossible positions and two different speeds. He frowned at the computer, trying to find some clue in the new data. He noticed, absently, that the hand of one of the dials was near zero in the red section of the dial. He had not noticed any of the dials registering in the danger zone before . . .

  He jerked out of his preoccupation with apprehension and typed: TELL ME IN NON-TECHNICAL

  LANGUAGE THE MEANING OF THE HAND NEAR ZERO ON THE DIAL LABELED MAX. ET. REF.

  It answered: ONE OF MY CIRCUITS WAS DAMAGED BY THE SUDDEN RELEASE OF AIR

  PRESSURE. I WILL CEASE FUNCTIONING AT THE END OF FOUR MORE MINUTES OF

  OPERATION.

  He slammed the master switch to OFF. The lights on the board went out, the various needles swung to zero, leaving the computer a mindless structure more than ever resembling an overgrown refrigerator. Four minutes more of operation . . . and he had so many questions to ask before he could hope to learn enough about the warp to know what he should do. He had wasted almost an hour of the computer's limited life, leaving it turned on when he was not using it. If only it had told him . . . but it was not the nature of a machine to voluntarily give information. Besides, the receding hand of the dial was there for him to see. The computer neither knew nor cared that no one had thought it worthwhile to teach him the rudiments of its operation and maintenance.

  It was 12:52. One hour and one minute left.

  He put the thought aside and concentrated on the problem of finding the key to the paradox. What conceivable set of circumstances would cause receding stars to have a spectrum shift that showed them to be approaching the ship? Or, to rephrase the question, what conceivable set of circumstances would cause approaching stars to appear to dwindle in size?

  The answer came with startling suddenness and clarity:

  There was no paradox—the ship was expanding.

  He considered the solution, examining it for flaws of logic, and found none. If he and the ship were expanding the wave length of light would diminish in proportion to the increasing size of the retinas of his eyes and the scanner plates of the transdimensional viewscreens: would become shorter and go into the ultraviolet. At the same time, the increasing size of himself and the ship would make the Earth and sun relatively smaller and therefore apparently receding.

  The same theory explained the two different speeds of the ship: its length was three times its diameter so its longitudinal expansion would proceed at three times the speed of its cross-sectional expansion. Everything checked.

  How large was the ship now?

  He made a rough calculation and stared almost unbelievingly at the results. He was a giant, more than a third of a light-year tall, in a ship that was six light-years long and two light-years in diameter. Far Centauri, which had required thirty years to reach in the fastest interplanetary ship, floated seventy-one feet away in the blackness outside the hull.

  And the sun and Earth were in the room with him, going into the shuttle's silvery focal ball. He would have to ask the computer to make certain his theory was valid. His time was too critically short for him to waste any of it with speculation based on an erroneous theory. He switched on the computer and it lighted up again. He typed rapidly:

  ASSUME THIS SHIP TO BE MOTIONLESS AND EXPANDING WOULD THAT THEORY

  SATISFACTORILY EXPLAIN ALL THE HITHERTO CONTRADICTORY PHENOMENA?

  There was a brief pause as the computer evaluated its data, then it answered with one word: YES.

  He switched it off again, to squander none of its short period of usefulness until he had decided upon what his further questions should be. At last, he had some grounds for conjecture; had learned something about the warp the designers of the shuttle had not suspected. Their calculations had been correct when they showed a ship would travel in the warp at many times the normal space speed of light. But somewhere some little factor had been overlooked—or never found—and their precise mathematics had not indicated that the travel would be produced by expansion.

  Nature abhors a vacuum. And the black, empty warp was a vacuum more perfect than any that existed in normal space. In the normal space universe there were millions of stars in the galaxy and millions of galaxies. In the warp there was utter Nothing. Did the physical laws of the warp demand that matter be scattered throughout it, in emulation of its rich neighbor in the adjoining dimension? Was the warp hungry for matter?

  He rejected the thought as fantasy. There was some explanation that the physicists would eventually find. Perhaps there was a vast size-ratio difference between the two dimensions; perhaps the warp was far larger than the normal space universe and some co-universal law demanded that objects entering it become proportionally larger.

  None of that aspect of his circumstances, however, was of importance. There was only one prime problem facing him: how to move the ship within less than an hour to some point in the warp where his emergence into normal space would result in neither instant nor days-away death and where he would have the time to try to carry out the responsibility, so suddenly placed in his hands, of delivering the space warp shuttle to the Thunderbolt.

  The long-range task depended upon his immediate survival. He had to move the ship, and how did a man move a driveless ship? It might not require a very large propulsive force—perhaps even an oxygen tank would serve as a jet. Except that he had none.

  He could use part of the air in the ship. Its sudden release should move the ship. There was a sun very near: Alpha Centauri. If he had the proper tools, and the time, he could cut a hole in the hull opposite Centauri . . . but he had neither the tools nor the time.

  And what good would it do him if he could emerge into normal space at the desired distance from Centauri? He would be provided with power for the air regenerators by the solar power units but not power sufficient to operate the shuttle. He would breathe, and eat, for a week. Then the small amount of food on the ship would be gone and he would breathe for another four or five weeks. And then he would die of starvation and his driveless ship would continue its slow drift into the sun, taking his bones and the shuttle with it.

  He would have to go to Sirius and he would have to reach it the first try or never. If he could emerge into normal space at the proper distance from Sirius he would have power from it to operate the communicator. The Thunderbolt would come at once when it received his message and swallow the little Argosy in its enormous hold. The return to Earth would be the swift one through the warp and the Slug cruisers, so bold in pursuit of unarmed interplanetary ships, would quickly cease to exist. At 13:53 Sirius would be somewhere in or near the bow of the ship. The ship would not have to be moved more than two thirds of its length—twenty meters. He could do that by releasing part of the air in the shuttle room through the sternward airlock.

  How much air?

  He tried to remember long-forgotten formulas. So many cubic feet of air at such and such a pressure when released through an opening of such and such a diameter would exert a propulsive force of . . . Hell, he didn't know. And not even the computer would be able to tell him because there were so many unknown factors, such as the proportion of the ship's mass lost to the Slug blasters, the irregular shape of the airlock opening, the degree of smoothness of its metal . . .

  He made calculations with pencil and paper. He would have to move the ship with extreme precision. A light-hour short of the proper distance put him too far from the sun for it to power the communicator, a light-hour beyond put him in the sun's flaming white heart. One light-hour out of eight point six light-years was approximately one part out of seventy-five thousand. He would have to move the ship with an accuracy of point aught three centimeters—one hundredth of an inch. One hundredth of an inch!

  He laid the pencil back down, almost numbly. He could never open and close an airlock and move a mass of thousand of tons with an accuracy of a hundredth of an inch. The very thought was wildly fantastic.

  H
e was already far closer to Sirius than he would be if he tried to get any closer. And that was over eight light-years from it.

  He looked at the chronometer and saw the hands had already reached 13:20. Thirty-three minutes left to him. Sirius was near—soon it would be in the bow of the ship—and Sirius was eight point six light-years away.

  How could he move the ship a certain distance accurate to one hundredth of an inch? He couldn't. The answer was blunt and ugly: he couldn't.

  He got up and walked across the room, feeling like a man who had in quick succession been condemned, reprieved, recondemned. He had been projected into a situation for which he had had no preliminary training whatever; had been made sole custodian and operator of a computer and a space warp shuttle that he had never before been permitted to touch. He had used the sound but not at all brilliant mind nature had given him to solve the riddle of the paradoxes and learn where he was and where he wanted to go. He had done quite well—he had solved every problem of his survival and the shuttle's delivery except the last one!

  He passed by the shuttle and stopped to rest his hand on the bright, silvery focal ball. The solar system would be deep inside the ball; the atoms of the ball larger than Earth, perhaps, and far more impalpable than the thinnest air. The Slug cruisers would be in there, infinitesimally tiny, waiting for him to return . . . No—faulty reasoning. The solar system was as it had always been, not diminished in size and not really in the ball. It was only that two different points in two different dimensions coincided in the ball . . . He saw the answer.

  He did not have to move the ship to Sirius—he had only to move the ball!

  * * *

  There would be little time, very little time. First, to see if the warp shuttle was portable—

  It was. When he unfastened the clamp that held it to the stand it lifted up freely, trailing a heavy cable behind it. He saw it was only a power supply cable, with a plug that would fit one of the sockets in the bow of the ship. He left the shuttle floating in the air, leashed by the cable, and went to the computer. Next, he would have to know if Sirius would be fully in the ship—