"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back as we can probe inter prehistory - though that's your department, I think - remains, and its laws have not been repealed.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."