Foundation's Edge

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as far back as we can probe into prehistory—though that’s your department, I think—remains, and its laws have not been repealed. In our hyperspatial Jumps, however, we do something outside 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: 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 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