In the silence following Ching’s outburst, the sails rotated, slightly, so that they could all see the transparent shimmer of the film across the observation window; behind them the stars blurred. All sails set, Peake thought, and acclerating at full speed — to nowhere.
Ravi said calmly, “It can’t possibly be as bad as that, Ching. We have a known position for the colonies and for the T-5 cluster, and fixes for most of the known stars. Surely, once the computer is working properly again, we can find out exactly where we are, compared to where we ought to be, and reset a proper course to take us there. The ship is maneuverable, after all, it’s not as it was in the old days of the unmanned probes, where once set in orbit, the probe continued until it either crashed into something, or fell apart. We can maneuver fairly well; if we absolutely had to, we could cut acceleration, coast to rest inside the orbit of Pluto until we knew exactly where we were and in what direction we had to leave the Solar System, and then restart the drives. Theoretically, we could even turn ship 180° and decelerate back in the direction we came, to the point of the original error.”
Peake made a small weak sound, almost a giggle.
He said, “I can hear it now. We slide into orbit alongside the Space Station. They say, hey, what, back already? We told you not to come back till you found us a habitable planet. And we say, sorry, folks, the computer you gave us doesn’t work…”
Moira made a small finicky adjustment to the replaced sails. She reminded herself of a woman pulling herself together after a rape, trying to reassure herself I that she is still alive, still essentially undamaged, still able to function. She tried to recapture the ecstatic sensation of being at the center of a great web, controlling the movement of the ship, controlling the flow of the universe — it would not come. All she felt was the shaking of her own hands on the controls; the one thing that was real to her, the perfection of machinery, solid and without human fragility and limitations, had been breached. She looked at the sail blurring the stars and thought of the thickness of it, measured in micrometers. How frail and frangible it seemed, shivering in the vacuum, cold against space as she was cold in the heated cabin.
Teague was looking at the great disk of Jupiter, and. regretting the lack of the stability of a planet to take any sort of standard observation. He knew Jupiter’s position in the Solar System, but he did not know precisely where the Ship was and that meant that he had no way of knowing precisely where anything else was, relative to it. But he said, “We have an absolute set of locators out there; Jupiter and its moons. We can find out precisely where they are and where they ought to be at this moment in Universal Time—” he gestured at the cumbersome True Time figures still streaming, [ with relentless, pulsing precision across the room of the cabin. “Even if we had lost all the cosmic data in the computer, we could re-calculate it all from the position of Jupiter and the Sun.”
The Sun’s disk, very far away, very dim and pale and only a blot against the stars, at a far corner of the lenticular window, seemed incredibly distant. Suddenly there was the loud clanging of an alarm; they all jumped, and Fontana gasped as the red pulse of an alarm-light flicked on and off.
Moira’s hands were already moving, trimming sails. She said, “I’ve got it; just a proximity alarm; a hunk of debris.” She reached to cut off the sound, the vibrating red carbuncle of the emergency light. “Wherever we are, I don’t like it here and I suggest we change course enough to get well out of the plane of the asteroids. We aren’t maneuverable enough to run the gauntlet of the asteroid belt.”
Ching, by automatic reaction, touched the computer console, and stopped dead, her hands frozen. She said weakly, “That’s no good, Teague. You know where we are in reference to the asteroid belt and Jupiter—”
“I can get us well off the plane of the ecliptic, and that’ll keep us away from most asteroids,” Ravi said, “but Ching, you’ve got to do something about the computer as fast as you can. How long will it take you to check it out?”
“There are a few things I can do right away,” Ching said, “I can probably have some idea of what’s wrong inside a few minutes.” She touched a few buttons, frowned at the results, repeated the process. Then she whistled, a small, sharp sound.
“Peake,” she said, “enter the course you laid. Let me watch you do it.”
Slowly, meticulously, rechecking it with the tiny calculator which was part of every navigation student’s permanent equipment, as much a part of him as his head, Peake found the figures and ran them into the computer. Ching watched, frowning a little.
“Now you, Ravi. Show me exactly what you did.”
Frowning, Ravi complied.
“All right,” Ching said, “I know what’s wrong. Or — wait,” she qualified, as five faces turned to her in expectant hope, “I’m not sure whether there are mechanical bugs in the computer itself; I’ll have to get in there and find out. I’d have to do that, anyhow, to find out what’s wrong with the DeMags, if Teague and Moira are sure there’s no mechanical problem in them. But I know how we can get, at least, mathematical right answers out of the computer, because I know why it’s giving us wrong answers. Ravi, are you aware that when you were converting the acceleration factor into days, you divided everything by twenty-four instead of twenty-four point zero?”
“As a mathematician,” Ravi said, offended, “in a simple arithmetical function, there is no difference whatever between twenty-four and twenty-four point zero.”
“Quite right,” Ching agreed, “in a simple arithmetical calculation, and that’s why the answer the computer gave you was wrong and you knew it was wrong. It’s as if you’d asked it how long it would take to get to the orbit of Pluto at one gee acceleration and come up with a figure of eleven hours — utter nonsense that any mathematic idiot could spot. Or getting a figure of eighteen kilometers for the diameter of Mars. Only when the figures are astronomical, it’s not so easy to check them. Normally, the computer — no, never mind, we stipulated that none of you has any computer sense. But I’ll have to explain this so that we can get right answers out of it.”
She frowned, fumbling for words which would explain to them something which was transparently obvious to her, now that she saw what had happened, but which would be as obscure to them as some of Peake’s medical textbooks were to her. Finally she said, “I feel like a fool; Ravi’s the mathematician, and it would be insulting his intelligence to suggest he didn’t know the difference between a real number and an integer. But to the computer there’s a tremendous difference — they’re stored in a totally different format, and a real number is stored in twice as much space as an integer. Normally, the computer will convert all the integers to real numbers when they’re used in arithmetic with real numbers, but now there seems to be something wrong with the Float subroutine, which should be doing that. So when the computer goes to do arithmetic, thinking it’s using a real number, it picks up the integer and whatever is in the storage space next to it — giving results that can only be described as ”unpredictable.“ Which means that even if you add two and two, you’re likely to come up with five or sixteen, and when you get into complicated mathematical calculations, you have very serious difficulties. All right; we can still get the right answers from this thing—” she touched the console, frowning, “as long as we are very careful to float everything before we input it — in other words, don’t put in any number, not even an exponent, without a decimal point. Or we could try putting everything in a binary—”
“Not on your life,” said Moira with a shudder.
“Binary is as simple as our normal decimal system, once you get used to it—”
“But I don’t have time to get used to it just now,” Moira said.
Ching nodded. “In any case, we should still be able to get the right answers — assuming that we input everything as a real number, and assuming that the Float subroutine is the only thing malfunctioning — but we still shouldn’t trust the computer until I have a chance to check everything out. And that includes programs already built into the computer as well as the ones we’re putting in ourselves.”
Moira asked soberly, “Is there any possibility that the meteor damage was to the computer module?”
They could all, Fontana thought, see the implications of that. Mathematical computations for the navigation, after all, could be done with the aid of their calculators, checked by Ravi’s talent. But the computer was literally in charge of every other function of the ship. Gravity. Life Support. They were still running on stored food, but soon they would begin molecular synthesis of every mouthful they ate. Teague could see it too; he said wryly, “No chance the life-support computer tie-ins are screwed up? All we need is for the computer to start synthesizing H2SO4 instead of H2O!”
Fontana shuddered. Ching said soberly, “I can’t entirely exclude that possibility. I’ll get inside the module as fast as I can, and check every unit inside it. No, I don’t think there was damage to the computer module; the tests showed the integrity of the module undamaged. But even if it wasn’t holed, we can’t rule out secondary impact shock as a possibility. Or — considering that the first failure of the DeMags was before the impact — the possibility of some defect in programming, or some damage inside to the storage apparatus.” She stood up and stretched
