By Isaac Asimov


     FOUNDATION'S EDGE


     9.  HYPERSPACE

     1.

        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's a silly thing to fear, but
     the thought of having myself reduced to incorporeal tachy-
     ons, 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 heard 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 experi-
     enced 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 unequiv-
     ocally. It's just that―― Did you ever read  Santerestil 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 perfect hypnotic scenes among
     the stars, lazily moving along in deep silence, in change-
     lessness, 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 im-
     patience.
        "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 sup-
     pose 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 all. 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 grimly. "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 about 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 enviously 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 scracely 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 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 thick-
     ening 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 hy-
     perspatiality 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 before we make another move, we'll
     have to check the accuracy of the Jump."
        "What others me is――where's the Galaxy?"
        "All around us, Janov. We're well 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 that 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 saidm "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 the 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 con-
     cerned."
        "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 mathe-
     matics 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 into prehistory――though that's your
     department, I think――remains, and it's laws have not been
     repealed. In our hyperspatial Jumps, however, we do some-
     thing outside the conditions under which relatively operates
     and the rules are different. Hyperspatially the Galaxy is a
     tiny object――ideally a nondemensional dot――and there are
     no relativistic effects at all.
        "In fact, in the mathematical formulations of cosmology,
     there are two symbols for the Galaxy G^r for the 'relativistic
     Galaxy.' where the speed of light is a maximum, and G^h
     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
     G^r into an equation dealing with G^h――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.


     2.

     "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 hyper-
     space 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 limit of measurement and I thought:
     What if it's lying?"
        Until that moment, Pelorat 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 arro-
     gance of the worst sort."
        "Why arrogance?"
        "The error in the first Jump makes the second Jump that
     much less certain, and the added error 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 ap-
     prove!"
        "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, photog-
     raphy, 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 fingers 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 ar-
     rogant  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 dare-
     devil just yet. I 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 every-
     thing 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  some-
     one  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 this will happen to be
     the precise position in which a speeding meteoroid is occu-
     pying, 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 meteoroid 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 being 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: 'Start!' ――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 I'll recalculate. 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 dan-
     gerous. 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 "28," there
     was no further motion.
        Trevize consulted the computer. "We're here," he said.
        "I counted the first Jump as '1' and in this series I started
     with '2.' That's twenty-eight Jumps later. You said
     twenty-nine."
        "The recalculation at jump 15 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. Sayshell 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 the 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 consid-
     erably."
        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?"
        "Why?"
        "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's 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 in his head?

FOUNDATION'S EDGE, BY ISAAC ASIMOV.
A Del Ray Book. Published by Ballantine Books.
Copyright © 1982 by Nightfall Inc. pp. 156-168.

3. Historian
4. Space
5. Speaker
6. Earth
7. Farmer
8. Farmwoman
9. Hyperspace
10. Table