from all directions.”
Trevize nodded impatiently. “What I remember is that it didn’t work because the dates of settlement were not reliable.”
“That’s right, old fellow. But the worlds that Yariff was working with were part of the second expansion of the human race. By then, hyperspatial travel was far advanced, and settlement must have grown quite ragged. Leapfrogging very long distances was very simple and settlement didn’t necessarily proceed outward in radial symmetry. That surely added to the problem of unreliable dates of settlement.
“But just think for a moment, Golan, of the Spacer worlds. They were in the first wave of settlement. Hyperspatial travel was less advanced then, and there was probably little or no leapfrogging. Whereas millions of worlds were settled, perhaps chaotically, during the second expansion, only fifty were settled, probably in an orderly manner, in the first. Whereas the millions of worlds of the second expansion were settled over a period of twenty thousand years; the fifty of the first expansion were settled over a period of a few centuries—almost instantaneously, in comparison. Those fifty, taken together, should exist in roughly spherical symmetry about the world of origin.
“We have the co-ordinates of the fifty worlds. You photographed them, remember, from the statue. Whatever or whoever it is that is destroying information that concerns Earth, either overlooked those co-ordinates, or didn’t stop to think that they would give us the information we need. All you have to do, Golan, is to adjust the co-ordinates to allow for the last twenty thousand years of stellar motions, then find the center of the sphere. You’ll end up fairly close to Earth’s sun, or at least to where it was twenty thousand years ago.”
Trevize’s mouth had fallen slightly open during the recital and it took a few moments for him to close it after Pelorat was done. He said, “Now why didn’t
“I tried to tell you while we were still on Melpomenia.”
“I’m sure you did. I apologize, Janov, for refusing to listen. The fact is it didn’t occur to me that—” He paused in embarrassment.
Pelorat chuckled quietly, “That I could have anything of importance to say. I suppose that ordinarily I wouldn’t, but this was something in my own field, you see. I am sure that, as a general rule, you’d be perfectly justified in not listening to me.”
“Never,” said Trevize. “That’s not so, Janov. I feel like a fool, and I well deserve the feeling. My apologies again—and I must now get to the computer.”
He and Pelorat walked into the pilot-room, and Pelorat, as always, watched with a combination of marveling and incredulity as Trevize’s hands settled down upon the desk, and he became what was almost a single man/computer organism.
“I’ll have to make certain assumptions, Janov,” said Trevize, rather blank-faced from computer-absorption. “I have to assume that the first number is a distance in parsecs, and that the other two numbers are angles in radians, the first being up and down, so to speak, and the other, right and left. I have to assume that the use of plus and minus in the case of the angles is Galactic Standard and that the zero-zero-zero mark is Melpomenia’s sun.”
“That sounds fair enough,” said Pelorat.
“Does it? There are six possible ways of arranging the numbers, four possible ways of arranging the signs, distances may be in light-years rather than parsecs, the angles in degrees, rather than radians. That’s ninety-six different variations right there. Add to that, the point that if the distances are light-years, I’m uncertain as to the length of the year used. Add also the fact that I don’t know the actual conventions used to measure the angles— from the Melpomenian equator in one case, I suppose, but what’s their prime meridian?”
Pelorat frowned. “Now you make it sound hopeless.”
“Not hopeless. Aurora and Solaria are included in the list, and I know where they are in space. I’ll use the co-ordinates, and see if I can locate them. If I end up in the wrong place, I will adjust the co-ordinates until they give me the right place, and that will tell me what mistaken assumptions I am making as far as the standards governing the co-ordinates are concerned. Once my assumptions are corrected, I can look for the center of the sphere.”
“With all the possibilities for change, won’t it make it difficult to decide what to do?”
“What?” said Trevize. He was increasingly absorbed. Then, when Pelorat repeated the question, he said, “Oh well, chances are that the co-ordinates follow the Galactic Standard and adjusting for an unknown prime meridian isn’t difficult. These systems for locating points in space were worked out long ago, and most astronomers are pretty confident they even antedate interstellar travel. Human beings are very conservative in some ways and virtually never change numerical conventions once they grow used to them. They even come to mistake them for laws of nature, I think. —Which is just as well, for if every world had its own conventions of measurement that changed every century, I honestly think scientific endeavor would stall and come to a permanent stop.”
He was obviously working while he was talking, for his words came haltingly. And now he muttered, “But quiet now.”
After that, his face grew furrowed and concentrated until, after several minutes, he leaned back and drew a long breath. He said quietly, “The conventions hold. I’ve located Aurora. There’s no question about it. —See?”
Pelorat stared at the field of stars, and at the bright one near the center and said, “Are you sure?”
Trevize said, “My own opinion doesn’t matter. The
“Then I suppose we must take its word for it.”
“Believe me, we must. Let me adjust the view-screen and the computer can get to work. It has the fifty sets of co-ordinates and it will use them one at a time.”
Trevize was working on the screen as he spoke. The computer worked in the four dimensions of space-time routinely, but, for human inspection, the viewscreen was rarely needed in more than two dimensions. Now the screen seemed to unfold into a dark volume as deep as it was tall and broad. Trevize dimmed the room lights almost totally to make the view of star-shine easier to observe.
“It will begin now,” he whispered.
A moment later, a star appeared—then another—then another. The view on the screen shifted with every addition so that all might be included. It was as though space was moving backward from the eye so that a more and more panoramic view could be taken. Combine that with shifts up or down, right or left—
Eventually, fifty dots of light appeared, hovering in three-dimensional space.
Trevize said, “I would have appreciated a beautiful spherical arrangement, but this looks like the skeleton of a snowball that had been patted into shape in a big hurry, out of snow that was too hard and gritty.”
“Does that ruin everything?”
“It introduces some difficulties, but that can’t be helped, I suppose. The stars themselves aren’t uniformly distributed, and certainly habitable planets aren’t, so there are bound to be unevennesses in the establishment of new worlds. The computer will adjust each of those dots to its present position, allowing for its likely motion in the last twenty thousand years—even in that time it won’t mean much of an adjustment—and then fit them all into a ‘best-sphere.’ It will find a spherical surface, in other words, from which the distance of all the dots is a minimum. Then we find the center of the sphere, and Earth should be fairly close to that center. Or so we hope. —It won’t take long.”
70.
It didn’t. Trevize, who was used to accepting miracles from the computer, found himself astonished at how little time it took.
Trevize had instructed the computer to sound a soft, reverberating note upon deciding upon the coordinates of the best-center. There was no reason for that, except for the satisfaction of hearing it and knowing that perhaps the search had been ended.
The sound came in a matter of minutes, and was like the gentle stroking of a mellow gong. It swelled till they could feel the vibration physically, and then slowly faded.
