data and are able to interpret it better. The theory is that humans who can mate with each other were once physically close. We've got a list of all our races arranged in sequence. If planetary race F can mate with race E back to A and forward to M, and race G is fertile only back to B, but forward to O, then we assume that whatever their positions are now, at once time G was actually adjacent to F, but was a little further along. When we project back into time those star systems on which humans existed prior to space travel, we get a certain pattern. Kelburn can explain it to you."

The normally pink body of the Ribboneer flushed slightly. The color change was almost imperceptible, but it was enough to indicate that he was interested.

Kelburn went to the projector. "It would be easier if we knew all the stars in the Milky Way, but though we've explored only a small portion of it, we can reconstruct a fairly accurate representation of the past."

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!"

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