Foundation's Edge
CHAPTER NINE HYPERSPACE
HYPERSPACE
Trevize said, "Are you ready, Janov?"
Pelorat looked up from the book he was viewing and said, "You mean, for the jump, old fellow?"
"For the hyperspatial jump. Yes."
Pelorat swallowed. "Now, you're sure that it will be in no way uncomfortable. I know it is a silly thing to fear, but the thought of having myself reduced to incorporeal tachyons, which no one has ever seen or detected..."
"Come, Janov, it's a perfected thing. Upon my honor! The jump has been in use for twenty-two thousand years, as you explained, and I've never beard of a single fatality in hyperspace. We might come out of hyperspace in an uncomfortable place, but then the accident would happen in space - not while we are composed of tachyons."
"Small consolation, it seems to me."
"We won't come out in error, either. To tell you the truth, I was thinking of carrying it through without telling you, so that you would never know it had happened. On the whole, though, I felt it would be better if you experienced it consciously, saw that it was no problem of any kind, and could forget it totally henceforward."
"Well " said Pelorat dubiously. "I suppose you're right, but
'honestly I'm in no hurry."
"I assure you..."
"No no, old fellow, I accept your assurances unequivocally. It's just that - Did you ever read Sanertestil Matt?"
"Of course. I'm not illiterate."
"Certainly. Certainly. I should not have asked. Do you remember it?"
"Neither am I an amnesiac."
"I seem to have a talent for offending. All I mean is that I keep thinking of the scenes where Santerestil and his friend, Ban, have gotten away from Planet 17 and are lost in space. I think of those perfectly hypnotic scenes among the stars, lazily moving along in deep silence, in changelessness, in... Never believed it, you know. I loved it and I was moved by it, but I never really believed it. But now - after I got used to just the notion of being in space, I'm experiencing it and - it's silly, I know - but I don't want to give it up. It's as though I'm Santerestil..."
"And I'm Ban," said Trevize with just an edge of impatience.
"In a way. The small scattering of dim stars out there are motionless, except our sun, of course, which must be shrinking but which we don't see. The Galaxy retains its dim majesty, unchanging. Space is silent and I have no distractions..."
"Except me."
"Except you. - But then, Golan, dear chap, talking to you about Earth and trying to teach you a bit of prehistory has its pleasures, too. I don't want that to come to an end, either."
"It won't. Not immediately, at any rate. You don't suppose we'll take the jump and come through on the surface of a planet, do you? We'll still be in space and the jump will have taken no measurable time at ail. It may well be a week before we make surface of any kind, so do relax."
"By surface, you surely don't mean Gaia. We may be nowhere near Gaia when we come out of the jump."
"I know that, Janov, but we'll be in the right sector, if your information is correct. If it isn't - well..."
Pelorat shook his head glumly. "How will being in the right sector help if we don't know Gaia's co-ordinates?"
Trevize said, "Janov, suppose you were on Terminus, heading for the town of Argyropol, and you didn't know where that town was except that it was somewhere on the isthmus. Once you were on the isthmus, what would you do?"
Pelorat waited cautiously, as though feeling there must be a terribly sophisticated answer expected of him. Finally giving up, he said, "I suppose I'd ask somebody."
"Exactly! What else is there to do? - Now, are you ready?"
"You mean, now?" Pelorat scrambled to his feet, his pleasantly unemotional face coming as near as it might to a look of concern. "What am I supposed to do? Sit? Stand? What?"
"Time and Space, Pelorat, you don't do anything. Just come with me to my room so I can use the computer, then sit or stand or turn cartwheels - whatever will make you most comfortable. My suggestion is that you sit before the viewscreen and watch it. It's sure to be interesting. Come!"
They stepped along the short corridor to Trevize's room and he seated himself at the computer. "Would you like to do this, Janov?" he asked suddenly. "I'll give you the figures and all you do is think them. The computer will do the rest."
Pelorat said, "No thank you. The computer doesn't work well with me, somehow. I know you say I just need practice, but I don't believe that. There's something about your mind, Golan..."
"Don't be foolish."
"No no. That computer just seems to fit you. You and it seem to be a single organism when you're hooked up. When I'm hooked up, there are two objects involved - Janov Pelorat and a computer. It's just not the same."
"Ridiculous," said Trevize, but he was vaguely pleased at the thought and stroked the hand-rests of the computer with loving fingertips.
"So I'd rather watch," said Pelorat. "I mean, I'd rather it didn't happen at all, but as long as it will, I'd rather watch." He fixed . his eyes anxiously on the viewscreen and on the foggy Galaxy with the thin powdering of dim stars in the foreground. "Let me know when it's about to happen." Slowly he backed against the wall and braced himself.
Trevize smiled. He placed his hands on the rests and felt the mental union. It came more easily day by day, and more intimately, too, and however he might scoff at what Pelorat said - he actually felt it. It seemed to him he scarcely needed to think of the co-ordinates in any conscious way. It almost seemed the computer knew what he wanted, without the conscious process of "telling." It lifted the information out of his brain for itself.
But Trevize "told" it and then asked for a two-minute interval before the jump.
"All right, Janov. We have two minutes: 120 - 115 - 110 Just watch the viewscreen."
Pelorat did, with a slight tightness about the corners of his mouth and with a holding of his breath.
Trevize said softly, "15 - 10 - 5 - 4 - 3 - 2 - 1 - 0"
With no perceptible motion, no perceptible sensation, the view on the screen changed. There was a distinct thickening of the starfield and the Galaxy vanished.
Pelorat started and said, "Was that it?"
"Was what it? You flinched. But that was your fault. You felt nothing. Admit it."
"I admit it."
"Then that's it. Way back when hyperspatial travel was relatively new - according to the books, anyway - there would be a queer internal sensation and some people felt dizziness or nausea. It was perhaps psychogenic, perhaps not. In any case, with more and more experience with hyperspatiality and with better equipment, that decreased. With a computer like the one on board this vessel, any effect is well below the threshold of sensation. At least, I find it so."
"And I do, too, I must admit. Where are we, Golan?"
"Just a step forward. In the Kalganian region. There's a long way to go yet and before we make another move, we'll have to check the accuracy of the jump."
"What bothers me is - where's the Galaxy?"
"All around us, Janov. We're weal inside it, now. If we focus the viewscreen properly, we can see the more distant parts of it as a luminous band across the sky."
"The Milky Way!" Pelorat cried out joyfully. "Almost every world describes it in their sky, but it's something we don't see on Terminus. Show it to me, old fellow!"
The viewscreen tilted, giving the effect of a swimming of the starfield across it, and then there was a thick, pearly luminosity nearly filling the field. The screen followed it around, as it thinned, then swelled again.
Trevize said, "It's thicker in the direction of the center of the Galaxy. Not as thick or as bright as it might be, however, because of the dark clouds in the spiral arms. You see something like this from most inhabited worlds."
"And from Earth, too."
"That's no distinction. That would not be an identifying characteristic."
"Of course not. But you know. - You haven't studied the history of science, have you?"
"Not really, though I've picked up some of it, naturally. Still, if you have questions to ask, don't expect me to be an expert."
"It's just that making this jump has put me in mind of something that has always puzzled me. It's possible to work out a description of the Universe in which hyperspatial travel is impossible and in which the speed of light traveling through a vacuum is the absolute maximum where speed is concerned."
"Certainly."
"Under those conditions, the geometry of the Universe is such that it is impossible to make the trip we have just undertaken in less time than a ray of light would make it. And if we did it at the speed of light, our experience of duration would not match that of the Universe generally. If this spot is, say, forty parsecs from Terminus, then if we had gotten here at the speed of light, we would have felt no time lapse - but on Terminus and in the entire Galaxy, about a hundred and thirty years would have passed. Now we have made a trip, not at the speed of light but at thousands of times the speed of light actually, and there has been no time advance anywhere. At least, I hope not."
Trevize said, "Don't expect me to give you the mathematics of the Olanjen Hyperspatial Theory to you. All I can say is that if you had traveled at the speed of light within normal space, time would indeed have advanced at the rate of 3.26 years per parsec, as you described. The so-called relativistic Universe, which humanity has understood as far back as we can probe inter prehistory - though that's your department, I think - remains, and its laws have not been repealed. In our hyperspatial jumps, however, we do something out side the conditions under which relativity operates and the rules are different. Hyperspatially the Galaxy is a tiny object - ideally a nondimensional dot - and there are no relativistic effects at all.
"In fact, in the mathematical formulations of cosmology, there are two symbols for the Galaxy: Gr for the "relativistic Galaxy," where the speed of light is a maximum, and Gh for the "hyperspatial Galaxy," where speed does not really have a meaning. Hyperspatially the value of all speed is zero and we do not move with reference to space itself, speed is infinite. I can't explain things a bit more than that.
"Oh, except that one of the beautiful catches in theoretical physics is to place a symbol or a value that has meaning in Gr into an equation dealing with G11 - or vice versa - and leave it there for a student to deal with. The chances are enormous that the student falls into the trap and generally remains there, sweating and panting, with nothing seeming to work, till some kindly elder helps him out. I was neatly caught that way, once."
Pelorat considered that gravely for a while, then said in a perplexed sort of way, "But which is the true Galaxy?"
"Either, depending on what you're doing. If you're back on Terminus, you can use a car to cover distance on land and a ship to cover distance across the sea. Conditions are different in every way, so which is the true Terminus, the land or the sea?"
Pelorat nodded. "Analogies are always risky," he said, "but I'd rather accept that one than risk my sanity by thinking about hyperspace any further. I'll concentrate on what we're doing now."
"Look upon what we just did," said Trevize, "as our first stop toward Earth."
And, he thought to himself, toward what else, I wonder.
"Well," said Trevize. "I've wasted a day."
"Oh?" Pelorat looked up from his careful indexing. "In what way?"
Trevize spread his arms. "I didn't trust the computer. I didn't dare to, so I checked our present position with the position we had aimed at in the jump. The difference was not measurable. There was no detectable error."
"That's good, isn't it?"
"It's more than good. It's unbelievable. I've never heard of such a thing. I've gone through jumps and I've directed them, in all kinds of ways and with all kinds of devices. In school, I had to work one out with a hand computer and then I sent off a hyper-relay to check results. Naturally I couldn't send a real ship, since - aside from the expense - I could easily have placed it in the middle of a star at the other end.
"I never did anything that bad, of course," Trevize went on, "but there would always be a sizable error. There's always some error, even with experts. There's got to be, since there are so many variables. Put it this way - the geometry of space is too complicated to handle and hyperspace compounds all those complications with a complexity of its own that we can't even pretend to understand. That's why we have to go by steps, instead of making one big jump from here to Sayshell. The errors would grow worse with distance."
Pelorat said, "But you said this computer didn't make an error."
"It said it didn't make an error. I directed it to check our actual position with our precalculated position - 'what is' against 'what was asked for.' It said that the two were identical within its limits of measurement and I thought: What if it's lying?"
Until that moment, Pelorat had held his printer in his hand. He now put it down and looked shaken. "Are you joking? A computer can't lie. Unless you mean you thought it might be out of order."
"No, that's not what I thought. Space! I thought it was lying. This computer is so advanced I can't think of it as anything but human - superhuman, maybe. Human enough to have pride - and to lie, perhaps. I gave it directions - to work out a course through hyperspace to a position near Sayshell Planet, the capital of the Sayshell Union. It did, and charted a course in twenty-nine steps, which is arrogance of the worst sort."
"Why arrogance?"
"The error in the first jump makes the second jump that much less certain, and the added error then makes the third jump pretty wobbly and untrustworthy, and so on. How do you calculate twenty-nine steps all at once? The twenty-ninth could end up anywhere in the Galaxy, anywhere at all. So I directed it to make the first step only. Then we could check that before proceeding."
"The cautious approach," said Pelorat warmly. "I approve!"
"Yes, but having made the first step, might the computer not feel wounded at my having mistrusted it? Would it then be forced to salve its pride by telling me there was no error at all when I asked it? Would it find it impossible to admit a mistake, to own up to imperfection? If that were so, we might as well not have a computer."
Pelorat's long and gentle face saddened. "What can we do in that case, Golan?"
"We can do what I did - waste a day. I checked the position of several of the surrounding stars by the most primitive possible methods: telescopic observation, photography, and manual measurement. I compared each actual position with the position expected if there had been no error. The work of it took me all day and wore me down to nothing."
"Yes, but what happened?"
"I found two whopping errors and checked them over and found them in my calculations. I had made the mistakes myself. I corrected the calculations, then ran them through the computer from scratch - just to see if it would come up with the same answers independently. Except that it worked them out to several more decimal places, it turned out that my figures were right and they showed that the computer had made no errors. The computer may be an arrogant son-of-the-Mule, but it's got something to be arrogant about."
Pelorat exhaled a long breath. "Well, that's good."
"Yes indeed! So I'm going to let it take the other twenty-eight steps."
"All at once? But..."
"Not all at once. Don't worry. I haven't become a daredevil just yet. It will do them one after the other - but after each step it will check the surroundings and, if that is where it is supposed to be within tolerable limits, it can take the next one. Any time it finds the error too great - and, believe me, I didn't set the limits generously at all - it will have to stop and recalculate the remaining steps."
"When are you going to do this?"
"When? Right now. - Look, you're working on indexing your Library..."
"Oh, but this is the chance to do it, Golan. I've been meaning to do it for years, but something always seemed to get in the way."
"I have no objections. You go on and do it and don't worry. Concentrate on the indexing. I'll take care of everything else."
Pelorat shook his head. "Don't be foolish. I can't relax till this is over. I'm scared stiff."
"I shouldn't have told you, then - but I had to tell someone and you're the only one here. Let me explain frankly. There's always the chance that we'll come to rest in a perfect position in interstellar space and that that will happen to be the precise position which a speeding meteoroid is occupying, or a mini-black hole, and the ship is wrecked, and ;we're dead. Such things could - in theory - happen.
"The chances are very small, however. After all, you could be at home, Janov - in your study and working on your films or in your bed sleeping - and a meteroid could be streaking toward you through Terminus's atmosphere and hit you right in the head and you'd be dead. But the chances are small.
"In fact, the chance of intersecting the path of something fatal, but too small for the computer to know about, in the course of a hyperspatial jump is far, far smaller than that of berg hit by a meteor in your home. I've never heard of a ship being lost that way in all the history of hyperspatial travel. Any other type of risk - like ending in the middle of a star - is even smaller."
Pelorat said, "Then why do you tell me all this, Golan?"
Trevize paused, then bent his head in thought, and finally said, "I don't know. - Yes, I do. What I suppose it is, is that however small the chance of catastrophe might be, if enough people take enough chances, the catastrophe must happen eventually. No matter how sure I am that nothing will go wrong, there's a small nagging voice inside me that says, 'Maybe it will happen this time.' And it makes me feel guilty. - I guess that's it. Janov, if something goes wrong, forgive me!"
"But Golan, my dear chap, if something goes wrong, we will both be dead instantly. I will not be able to forgive, nor you to receive forgiveness."
"I understand that, so forgive me now, will you?"
Pelorat smiled. "I don't know why, but this cheers me up. There's something pleasantly humorous about it. Of course, Golan, I'll forgive you. There are plenty of myths about some form of afterlife in world literature and if there should happen to be such a place - about the same chance as landing on a mini-black hole, I suppose, or less - and we both turn up in the same one, then I will bear witness that you did your honest best and that my death should not be laid at your door."
"Thank you! Now I'm relieved. I'm willing to take my chance, but I did not enjoy the thought of you taking my chance as well."
Pelorat wrung the other's hand. "You know, Golan, I've only known you less than a week and I suppose I shouldn't make hasty judgments in these matters, but I think you're an excellent chap. - And now let's do it and get it over with."
"Absolutely! All I have to do is touch that little contact. The computer has its instructions and it's just waiting for me to say: 'Starts' Would you like to..."
"Never! It's all yours? It's your computer."
"Very well. And it's my responsibility. I'm still trying to duck it, you see. Keep your eye on the screen!"
With a remarkably steady hand and with his smile looking utterly genuine, Trevize made contact.
There was a momentary pause and then the starfield changed - and again - and again. The stars spread steadily thicker and brighter over the viewscreen.
Pelorat was counting under his breath. At "15" there was a halt, as though some piece of apparatus had jammed.
Pelorat whispered, clearly afraid that any noise might jar the mechanism fatally. "What's wrong? What's happened?"
Trevize shrugged. "I imagine it's recalculating. Some object in space is adding a perceptible bump to the general shape of the overall gravitational field - some object not taken into account - some uncharted dwarf star or rogue planet..."
"Dangerous?"
"Since we're still alive, it's almost certainly not dangerous. A planet could be a hundred million kilometers away and still introduce a large enough gravitational modification to require recalculation. A dwarf star could be ten billion kilometers away and..."
The screen shifted again and Trevize fell silent. It shifted again - and again. - Finally, when Pelorat said, "a8," there was no further motion.
Trevize consulted the computer. "We're here," he said.
"I counted the first jump as 'r.' and in this series I started with 'z' That's twenty-eight jumps altogether. You said twenty-nine."
"The recalculation at jump is probably saved us one jump. I can check with the computer if you wish, but there's really no need. We're in the vicinity of Sayshell Planet. The computer says so and I don't doubt it. If I were to orient the screen properly, we'd see a nice, bright sun, but there's no point in placing a needless strain on its screening capacity. SaysheIl Planet is the fourth one out and it's about 3.2 million kilometers away from our present position, which is about as close as we want to be at a jump conclusion. We can get there in three days - two, if we hurry."
Trevize drew a deep breath and tried to let the tension drain.
"Do you realize what this means, Janov?" he said. "Every ship I've ever been in - or heard of - would have made those jumps with at least a day in between for painstaking calculation and re-checking, even with a computer. The trip would have taken nearly a month.
"Or perhaps two or three weeks, if they were willing to be reckless about it. We did it in half an hour. When every ship is equipped with a computer like this one..."
Pelorat said, "I wonder why the Mayor' let us have a ship this advanced. It must be incredibly expensive."
"It's experimental," said Trevize dryly. "Maybe fine good woman was perfectly willing to have us try it out and see what deficiencies might develop."
"Are you serious?"
"Don't get nervous. After all, there's nothing to worry about. We haven't found any deficiencies. I wouldn't put it past her, though. Such a thing would put no great strain on her sense of humanity. Besides, she hasn't trusted us with offensive weapons and that cuts the expense considerably."
Pelorat said thoughtfully, "It's the computer I'm thinking about. It seems to be adjusted so well for you - and it can't be adjusted that well for everyone. It just barely works with me."
"So much the better for us, that it works so well with one of us."
"Yes, but is that merely chance?"
"What else, Janov?"
"Surely the Mayor knows you pretty well."
"I think she does, the old battlecraft."
"Might she not have had a computer designed particularly for you?"
"I just wonder if we're not going where the computer wants to take us."
Trevize stared. "You mean that while I'm connected to the computer, it is the computer - and not me - who is in real charge?"
"I just wonder."
"That is ridiculous. Paranoid. Come on, Janov."
Trevize turned back to the computer to focus Sayshell Planet on the screen and to plot a normal-space course to it.
Ridiculous!
But why had Pelorat put the notion into his head?
Trevize said, "Are you ready, Janov?"
Pelorat looked up from the book he was viewing and said, "You mean, for the jump, old fellow?"
"For the hyperspatial jump. Yes."
Pelorat swallowed. "Now, you're sure that it will be in no way uncomfortable. I know it is a silly thing to fear, but the thought of having myself reduced to incorporeal tachyons, which no one has ever seen or detected..."
"Come, Janov, it's a perfected thing. Upon my honor! The jump has been in use for twenty-two thousand years, as you explained, and I've never beard of a single fatality in hyperspace. We might come out of hyperspace in an uncomfortable place, but then the accident would happen in space - not while we are composed of tachyons."
"Small consolation, it seems to me."
"We won't come out in error, either. To tell you the truth, I was thinking of carrying it through without telling you, so that you would never know it had happened. On the whole, though, I felt it would be better if you experienced it consciously, saw that it was no problem of any kind, and could forget it totally henceforward."
"Well " said Pelorat dubiously. "I suppose you're right, but
'honestly I'm in no hurry."
"I assure you..."
"No no, old fellow, I accept your assurances unequivocally. It's just that - Did you ever read Sanertestil Matt?"
"Of course. I'm not illiterate."
"Certainly. Certainly. I should not have asked. Do you remember it?"
"Neither am I an amnesiac."
"I seem to have a talent for offending. All I mean is that I keep thinking of the scenes where Santerestil and his friend, Ban, have gotten away from Planet 17 and are lost in space. I think of those perfectly hypnotic scenes among the stars, lazily moving along in deep silence, in changelessness, in... Never believed it, you know. I loved it and I was moved by it, but I never really believed it. But now - after I got used to just the notion of being in space, I'm experiencing it and - it's silly, I know - but I don't want to give it up. It's as though I'm Santerestil..."
"And I'm Ban," said Trevize with just an edge of impatience.
"In a way. The small scattering of dim stars out there are motionless, except our sun, of course, which must be shrinking but which we don't see. The Galaxy retains its dim majesty, unchanging. Space is silent and I have no distractions..."
"Except me."
"Except you. - But then, Golan, dear chap, talking to you about Earth and trying to teach you a bit of prehistory has its pleasures, too. I don't want that to come to an end, either."
"It won't. Not immediately, at any rate. You don't suppose we'll take the jump and come through on the surface of a planet, do you? We'll still be in space and the jump will have taken no measurable time at ail. It may well be a week before we make surface of any kind, so do relax."
"By surface, you surely don't mean Gaia. We may be nowhere near Gaia when we come out of the jump."
"I know that, Janov, but we'll be in the right sector, if your information is correct. If it isn't - well..."
Pelorat shook his head glumly. "How will being in the right sector help if we don't know Gaia's co-ordinates?"
Trevize said, "Janov, suppose you were on Terminus, heading for the town of Argyropol, and you didn't know where that town was except that it was somewhere on the isthmus. Once you were on the isthmus, what would you do?"
Pelorat waited cautiously, as though feeling there must be a terribly sophisticated answer expected of him. Finally giving up, he said, "I suppose I'd ask somebody."
"Exactly! What else is there to do? - Now, are you ready?"
"You mean, now?" Pelorat scrambled to his feet, his pleasantly unemotional face coming as near as it might to a look of concern. "What am I supposed to do? Sit? Stand? What?"
"Time and Space, Pelorat, you don't do anything. Just come with me to my room so I can use the computer, then sit or stand or turn cartwheels - whatever will make you most comfortable. My suggestion is that you sit before the viewscreen and watch it. It's sure to be interesting. Come!"
They stepped along the short corridor to Trevize's room and he seated himself at the computer. "Would you like to do this, Janov?" he asked suddenly. "I'll give you the figures and all you do is think them. The computer will do the rest."
Pelorat said, "No thank you. The computer doesn't work well with me, somehow. I know you say I just need practice, but I don't believe that. There's something about your mind, Golan..."
"Don't be foolish."
"No no. That computer just seems to fit you. You and it seem to be a single organism when you're hooked up. When I'm hooked up, there are two objects involved - Janov Pelorat and a computer. It's just not the same."
"Ridiculous," said Trevize, but he was vaguely pleased at the thought and stroked the hand-rests of the computer with loving fingertips.
"So I'd rather watch," said Pelorat. "I mean, I'd rather it didn't happen at all, but as long as it will, I'd rather watch." He fixed . his eyes anxiously on the viewscreen and on the foggy Galaxy with the thin powdering of dim stars in the foreground. "Let me know when it's about to happen." Slowly he backed against the wall and braced himself.
Trevize smiled. He placed his hands on the rests and felt the mental union. It came more easily day by day, and more intimately, too, and however he might scoff at what Pelorat said - he actually felt it. It seemed to him he scarcely needed to think of the co-ordinates in any conscious way. It almost seemed the computer knew what he wanted, without the conscious process of "telling." It lifted the information out of his brain for itself.
But Trevize "told" it and then asked for a two-minute interval before the jump.
"All right, Janov. We have two minutes: 120 - 115 - 110 Just watch the viewscreen."
Pelorat did, with a slight tightness about the corners of his mouth and with a holding of his breath.
Trevize said softly, "15 - 10 - 5 - 4 - 3 - 2 - 1 - 0"
With no perceptible motion, no perceptible sensation, the view on the screen changed. There was a distinct thickening of the starfield and the Galaxy vanished.
Pelorat started and said, "Was that it?"
"Was what it? You flinched. But that was your fault. You felt nothing. Admit it."
"I admit it."
"Then that's it. Way back when hyperspatial travel was relatively new - according to the books, anyway - there would be a queer internal sensation and some people felt dizziness or nausea. It was perhaps psychogenic, perhaps not. In any case, with more and more experience with hyperspatiality and with better equipment, that decreased. With a computer like the one on board this vessel, any effect is well below the threshold of sensation. At least, I find it so."
"And I do, too, I must admit. Where are we, Golan?"
"Just a step forward. In the Kalganian region. There's a long way to go yet and before we make another move, we'll have to check the accuracy of the jump."
"What bothers me is - where's the Galaxy?"
"All around us, Janov. We're weal inside it, now. If we focus the viewscreen properly, we can see the more distant parts of it as a luminous band across the sky."
"The Milky Way!" Pelorat cried out joyfully. "Almost every world describes it in their sky, but it's something we don't see on Terminus. Show it to me, old fellow!"
The viewscreen tilted, giving the effect of a swimming of the starfield across it, and then there was a thick, pearly luminosity nearly filling the field. The screen followed it around, as it thinned, then swelled again.
Trevize said, "It's thicker in the direction of the center of the Galaxy. Not as thick or as bright as it might be, however, because of the dark clouds in the spiral arms. You see something like this from most inhabited worlds."
"And from Earth, too."
"That's no distinction. That would not be an identifying characteristic."
"Of course not. But you know. - You haven't studied the history of science, have you?"
"Not really, though I've picked up some of it, naturally. Still, if you have questions to ask, don't expect me to be an expert."
"It's just that making this jump has put me in mind of something that has always puzzled me. It's possible to work out a description of the Universe in which hyperspatial travel is impossible and in which the speed of light traveling through a vacuum is the absolute maximum where speed is concerned."
"Certainly."
"Under those conditions, the geometry of the Universe is such that it is impossible to make the trip we have just undertaken in less time than a ray of light would make it. And if we did it at the speed of light, our experience of duration would not match that of the Universe generally. If this spot is, say, forty parsecs from Terminus, then if we had gotten here at the speed of light, we would have felt no time lapse - but on Terminus and in the entire Galaxy, about a hundred and thirty years would have passed. Now we have made a trip, not at the speed of light but at thousands of times the speed of light actually, and there has been no time advance anywhere. At least, I hope not."
Trevize said, "Don't expect me to give you the mathematics of the Olanjen Hyperspatial Theory to you. All I can say is that if you had traveled at the speed of light within normal space, time would indeed have advanced at the rate of 3.26 years per parsec, as you described. The so-called relativistic Universe, which humanity has understood as far back as we can probe inter prehistory - though that's your department, I think - remains, and its laws have not been repealed. In our hyperspatial jumps, however, we do something out side the conditions under which relativity operates and the rules are different. Hyperspatially the Galaxy is a tiny object - ideally a nondimensional dot - and there are no relativistic effects at all.
"In fact, in the mathematical formulations of cosmology, there are two symbols for the Galaxy: Gr for the "relativistic Galaxy," where the speed of light is a maximum, and Gh for the "hyperspatial Galaxy," where speed does not really have a meaning. Hyperspatially the value of all speed is zero and we do not move with reference to space itself, speed is infinite. I can't explain things a bit more than that.
"Oh, except that one of the beautiful catches in theoretical physics is to place a symbol or a value that has meaning in Gr into an equation dealing with G11 - or vice versa - and leave it there for a student to deal with. The chances are enormous that the student falls into the trap and generally remains there, sweating and panting, with nothing seeming to work, till some kindly elder helps him out. I was neatly caught that way, once."
Pelorat considered that gravely for a while, then said in a perplexed sort of way, "But which is the true Galaxy?"
"Either, depending on what you're doing. If you're back on Terminus, you can use a car to cover distance on land and a ship to cover distance across the sea. Conditions are different in every way, so which is the true Terminus, the land or the sea?"
Pelorat nodded. "Analogies are always risky," he said, "but I'd rather accept that one than risk my sanity by thinking about hyperspace any further. I'll concentrate on what we're doing now."
"Look upon what we just did," said Trevize, "as our first stop toward Earth."
And, he thought to himself, toward what else, I wonder.
"Well," said Trevize. "I've wasted a day."
"Oh?" Pelorat looked up from his careful indexing. "In what way?"
Trevize spread his arms. "I didn't trust the computer. I didn't dare to, so I checked our present position with the position we had aimed at in the jump. The difference was not measurable. There was no detectable error."
"That's good, isn't it?"
"It's more than good. It's unbelievable. I've never heard of such a thing. I've gone through jumps and I've directed them, in all kinds of ways and with all kinds of devices. In school, I had to work one out with a hand computer and then I sent off a hyper-relay to check results. Naturally I couldn't send a real ship, since - aside from the expense - I could easily have placed it in the middle of a star at the other end.
"I never did anything that bad, of course," Trevize went on, "but there would always be a sizable error. There's always some error, even with experts. There's got to be, since there are so many variables. Put it this way - the geometry of space is too complicated to handle and hyperspace compounds all those complications with a complexity of its own that we can't even pretend to understand. That's why we have to go by steps, instead of making one big jump from here to Sayshell. The errors would grow worse with distance."
Pelorat said, "But you said this computer didn't make an error."
"It said it didn't make an error. I directed it to check our actual position with our precalculated position - 'what is' against 'what was asked for.' It said that the two were identical within its limits of measurement and I thought: What if it's lying?"
Until that moment, Pelorat had held his printer in his hand. He now put it down and looked shaken. "Are you joking? A computer can't lie. Unless you mean you thought it might be out of order."
"No, that's not what I thought. Space! I thought it was lying. This computer is so advanced I can't think of it as anything but human - superhuman, maybe. Human enough to have pride - and to lie, perhaps. I gave it directions - to work out a course through hyperspace to a position near Sayshell Planet, the capital of the Sayshell Union. It did, and charted a course in twenty-nine steps, which is arrogance of the worst sort."
"Why arrogance?"
"The error in the first jump makes the second jump that much less certain, and the added error then makes the third jump pretty wobbly and untrustworthy, and so on. How do you calculate twenty-nine steps all at once? The twenty-ninth could end up anywhere in the Galaxy, anywhere at all. So I directed it to make the first step only. Then we could check that before proceeding."
"The cautious approach," said Pelorat warmly. "I approve!"
"Yes, but having made the first step, might the computer not feel wounded at my having mistrusted it? Would it then be forced to salve its pride by telling me there was no error at all when I asked it? Would it find it impossible to admit a mistake, to own up to imperfection? If that were so, we might as well not have a computer."
Pelorat's long and gentle face saddened. "What can we do in that case, Golan?"
"We can do what I did - waste a day. I checked the position of several of the surrounding stars by the most primitive possible methods: telescopic observation, photography, and manual measurement. I compared each actual position with the position expected if there had been no error. The work of it took me all day and wore me down to nothing."
"Yes, but what happened?"
"I found two whopping errors and checked them over and found them in my calculations. I had made the mistakes myself. I corrected the calculations, then ran them through the computer from scratch - just to see if it would come up with the same answers independently. Except that it worked them out to several more decimal places, it turned out that my figures were right and they showed that the computer had made no errors. The computer may be an arrogant son-of-the-Mule, but it's got something to be arrogant about."
Pelorat exhaled a long breath. "Well, that's good."
"Yes indeed! So I'm going to let it take the other twenty-eight steps."
"All at once? But..."
"Not all at once. Don't worry. I haven't become a daredevil just yet. It will do them one after the other - but after each step it will check the surroundings and, if that is where it is supposed to be within tolerable limits, it can take the next one. Any time it finds the error too great - and, believe me, I didn't set the limits generously at all - it will have to stop and recalculate the remaining steps."
"When are you going to do this?"
"When? Right now. - Look, you're working on indexing your Library..."
"Oh, but this is the chance to do it, Golan. I've been meaning to do it for years, but something always seemed to get in the way."
"I have no objections. You go on and do it and don't worry. Concentrate on the indexing. I'll take care of everything else."
Pelorat shook his head. "Don't be foolish. I can't relax till this is over. I'm scared stiff."
"I shouldn't have told you, then - but I had to tell someone and you're the only one here. Let me explain frankly. There's always the chance that we'll come to rest in a perfect position in interstellar space and that that will happen to be the precise position which a speeding meteoroid is occupying, or a mini-black hole, and the ship is wrecked, and ;we're dead. Such things could - in theory - happen.
"The chances are very small, however. After all, you could be at home, Janov - in your study and working on your films or in your bed sleeping - and a meteroid could be streaking toward you through Terminus's atmosphere and hit you right in the head and you'd be dead. But the chances are small.
"In fact, the chance of intersecting the path of something fatal, but too small for the computer to know about, in the course of a hyperspatial jump is far, far smaller than that of berg hit by a meteor in your home. I've never heard of a ship being lost that way in all the history of hyperspatial travel. Any other type of risk - like ending in the middle of a star - is even smaller."
Pelorat said, "Then why do you tell me all this, Golan?"
Trevize paused, then bent his head in thought, and finally said, "I don't know. - Yes, I do. What I suppose it is, is that however small the chance of catastrophe might be, if enough people take enough chances, the catastrophe must happen eventually. No matter how sure I am that nothing will go wrong, there's a small nagging voice inside me that says, 'Maybe it will happen this time.' And it makes me feel guilty. - I guess that's it. Janov, if something goes wrong, forgive me!"
"But Golan, my dear chap, if something goes wrong, we will both be dead instantly. I will not be able to forgive, nor you to receive forgiveness."
"I understand that, so forgive me now, will you?"
Pelorat smiled. "I don't know why, but this cheers me up. There's something pleasantly humorous about it. Of course, Golan, I'll forgive you. There are plenty of myths about some form of afterlife in world literature and if there should happen to be such a place - about the same chance as landing on a mini-black hole, I suppose, or less - and we both turn up in the same one, then I will bear witness that you did your honest best and that my death should not be laid at your door."
"Thank you! Now I'm relieved. I'm willing to take my chance, but I did not enjoy the thought of you taking my chance as well."
Pelorat wrung the other's hand. "You know, Golan, I've only known you less than a week and I suppose I shouldn't make hasty judgments in these matters, but I think you're an excellent chap. - And now let's do it and get it over with."
"Absolutely! All I have to do is touch that little contact. The computer has its instructions and it's just waiting for me to say: 'Starts' Would you like to..."
"Never! It's all yours? It's your computer."
"Very well. And it's my responsibility. I'm still trying to duck it, you see. Keep your eye on the screen!"
With a remarkably steady hand and with his smile looking utterly genuine, Trevize made contact.
There was a momentary pause and then the starfield changed - and again - and again. The stars spread steadily thicker and brighter over the viewscreen.
Pelorat was counting under his breath. At "15" there was a halt, as though some piece of apparatus had jammed.
Pelorat whispered, clearly afraid that any noise might jar the mechanism fatally. "What's wrong? What's happened?"
Trevize shrugged. "I imagine it's recalculating. Some object in space is adding a perceptible bump to the general shape of the overall gravitational field - some object not taken into account - some uncharted dwarf star or rogue planet..."
"Dangerous?"
"Since we're still alive, it's almost certainly not dangerous. A planet could be a hundred million kilometers away and still introduce a large enough gravitational modification to require recalculation. A dwarf star could be ten billion kilometers away and..."
The screen shifted again and Trevize fell silent. It shifted again - and again. - Finally, when Pelorat said, "a8," there was no further motion.
Trevize consulted the computer. "We're here," he said.
"I counted the first jump as 'r.' and in this series I started with 'z' That's twenty-eight jumps altogether. You said twenty-nine."
"The recalculation at jump is probably saved us one jump. I can check with the computer if you wish, but there's really no need. We're in the vicinity of Sayshell Planet. The computer says so and I don't doubt it. If I were to orient the screen properly, we'd see a nice, bright sun, but there's no point in placing a needless strain on its screening capacity. SaysheIl Planet is the fourth one out and it's about 3.2 million kilometers away from our present position, which is about as close as we want to be at a jump conclusion. We can get there in three days - two, if we hurry."
Trevize drew a deep breath and tried to let the tension drain.
"Do you realize what this means, Janov?" he said. "Every ship I've ever been in - or heard of - would have made those jumps with at least a day in between for painstaking calculation and re-checking, even with a computer. The trip would have taken nearly a month.
"Or perhaps two or three weeks, if they were willing to be reckless about it. We did it in half an hour. When every ship is equipped with a computer like this one..."
Pelorat said, "I wonder why the Mayor' let us have a ship this advanced. It must be incredibly expensive."
"It's experimental," said Trevize dryly. "Maybe fine good woman was perfectly willing to have us try it out and see what deficiencies might develop."
"Are you serious?"
"Don't get nervous. After all, there's nothing to worry about. We haven't found any deficiencies. I wouldn't put it past her, though. Such a thing would put no great strain on her sense of humanity. Besides, she hasn't trusted us with offensive weapons and that cuts the expense considerably."
Pelorat said thoughtfully, "It's the computer I'm thinking about. It seems to be adjusted so well for you - and it can't be adjusted that well for everyone. It just barely works with me."
"So much the better for us, that it works so well with one of us."
"Yes, but is that merely chance?"
"What else, Janov?"
"Surely the Mayor knows you pretty well."
"I think she does, the old battlecraft."
"Might she not have had a computer designed particularly for you?"
"I just wonder if we're not going where the computer wants to take us."
Trevize stared. "You mean that while I'm connected to the computer, it is the computer - and not me - who is in real charge?"
"I just wonder."
"That is ridiculous. Paranoid. Come on, Janov."
Trevize turned back to the computer to focus Sayshell Planet on the screen and to plot a normal-space course to it.
Ridiculous!
But why had Pelorat put the notion into his head?
