He pressed the controls and stars twinkled on the screen. "We're looking down on the plane of the Galaxy. This is one arm of it as it is today and here are the human systems." He pressed another control and, for purposes of identification, certain stars became more brilliant. There was no pattern, merely a scattering of stars. "The whole Milky Way is rotating. And while stars in a given region tend to remain together, there's also a random motion. Here's what happens when we calculate the positions of stars in the past." Flecks of light shifted and flowed across the screen. Kelburn stopped the motion. "Two hundred thousand years ago," he said. There was a pattern of the identified stars. They were spaced at fairly equal intervals along a regular curve, a horseshoe loop that didn't close, though if the ends were extended, the lines would have crossed. Taphetta rustled. "The math is accurate?" "As accurate as it can be with a million-plus body problem." "And that's the hypothetical route of the unknown ancestor?" "To the best of our knowledge," said Kelburn. "And whereas there are humans who are relatively near and not fertile, they can always mate with those they were adjacent to _two hundred thousand years ago_!" "The adjacency mating principle. I've never seen it demonstrated," murmured Taphetta, flexing his ribbons. "Is that the only era that satisfies the calculations?" "Plus or minus a hundred thousand years, we can still get something that might be the path of a spaceship attempting to cover a representative section of territory," said Kelburn. "However, we have other ways of dating it. On some worlds on which there are no other mammals, we're able to place the first human fossils chronologically. The evidence is sometimes contradictory, but we believe we've got the time right." Taphetta waved a ribbon at the chart. "And you think that where the two ends of the curve cross is your original home?" "We think so," said Kelburn. "We've narrowed it down to several cubic light-years--then. Now it's far more. And, of course, if it were a fast-moving star, it might be completely out of the field of our exploration. But we're certain we've got a good chance of finding it this trip." "It seems I must decide quickly." The Ribboneer glanced out the visionport, where another ship hung motionless in space beside them. "Do you mind if I ask other questions?" "Go ahead," Kelburn invited sardonically. "But if it's not math, you'd better ask Halden. He's the leader of the expedition."