Darya shrugged.

“And any two spheres expand until they meet,” Louis Nenda went on. “First they’ll touch at one point, then as they grow they’ll intersect in a circle that just gets bigger and bigger and bigger. But it gets trickier with three spheres. When they grow and meet, they’ll do it at just two points. Four or more spheres don’t usually have any points in common. And when you get to twelve hundred and thirty-six artifacts, with an average of thirty-seven changes for each one, you have nearly fifty thousand spheres — each one spreading out at the speed of light with an artifact as the sphere center. What’s the chances that twelve hundred and thirty-six of those spheres, one from each Builder artifact, will all meet at one place? It should be negligible, too small to measure. But if they did meet, against all the odds, when would that happen?

“Sounds like an impossible question, doesn’t it? But it’s not hard to program and test for intersections. And do you know the answer that program gives, Professor Lang?”

“Why should I?” It was too late, but she stalled anyway.

“Because you’re here. Damn it, let’s stop pretending. Do you want me to spell it out for you?”

His hand was on her thigh again, but it was his tone of voice that finally made her angry enough to hit back.

“You don’t need to spell anything out for me, you — you lecherous little dwarf. And you may have followed up on it, but that’s all you did — follow up! It was my original idea. And get your filthy hand off my leg!”

He was grinning in triumph. “I never said it wasn’t your idea. And if you don’t want to be friendly, I won’t push it. The spheres all coincide, don’t they — to as many significant figures as the data permit? One place, and one time, and we both know where. The surface of Quake, at Summertide. That’s why you’re here, and that’s why I’m here, and Atvar H’sial, and everybody but your Uncle Jack.”

He stood up. “And now the local bozos say we can’t go! Any of us.”

“What?!” Darya jerked to her feet.

“You didn’t hear it yet? Old stone-head Perry came and told me an hour ago. No Quake for you, no Quake for me, no Quake for the bugs. We come a thousand light-years to sit here on our asses and miss the whole show.”

He slashed the black cane from Kallik’s harness at the bole of a huge bamboo. “They say, no go. I say, then screw ’em! See now why we have to do something, Darya Lang? We have to pool our knowledge — unless you want to sit here on your ass and take orders from pipsqueaks.”

Mathematics is universal. But very little else is.

Darya reached that conclusion after another half hour’s talk with Louis Nenda. He was a horrible man, someone she would go out of her way to avoid. But when they had traded statistical analyses — grudgingly, carefully, each unwilling to offer more than was received — the agreement was uncanny. It was also in a sense inevitable. Starting from the same set of events and the same set of artifact locations, there was just one point in space and time that fitted all the data. Any small differences in the computed time and place of the final result arose from alternative criteria for minimizing the residuals of the fit, or from different tolerances in convergence of the nonlinear computations.

They had followed near-identical approaches, and used similar tolerances and convergence factors. She and Louis Nenda agreed on results to fifteen significant figures.

Or rather, Darya concluded after another fifteen minutes, she and whoever had done the calculations for Nenda were in agreement. It could not be his own work. He had no more than a rough grasp of the procedures. He was in charge, but someone else had done the actual analysis.

“So we agree on the time, and it’s within seconds of Summertide,” he said. He was scowling again. “And all we know is that it’s somewhere on Quake? Why can’t you pin it closer? That’s what I was hoping we could do when we compared notes.”

“You want miracles? We’re dealing with distances of thousands of light-years, thousands of trillions of kilometers, and time spans of thousands of years. And we have a final uncertainty of less than two hundred kilometers in location, and less than thirty seconds in time. I think that’s pretty damned good. In fact, it is a miracle, right there.”

“Maybe close enough.” He slapped the cane against his own leg. “And it’s definitely on Quake, not here on Opal. I guess that answers another question I had.”

“About the Builders?”

“Nuts to the Builders. About the bugs. Why they want to get to Quake.”

“Atvar H’sial says she wants to study the behavior of life-forms under extreme environmental stress.”

“Yeah. Environmental stress, my ass.” He started to walk back toward the cluster of buildings. “Believe that, and you’ll believe in the Lost Ark. She’s after the same thing as we are. She’s chasing the Builders. Don’t forget she’s a Builder specialist, too.”

Louis Nenda was coarse, barbaric, and disgusting. But once he said it, it became obvious. Atvar H’sial had come to Dobelle too well prepared with contingency plans, just as though she had known that the requests for access to Quake would all be refused.

“What about Julius Graves? Him too?”

But Nenda only shook his head. “Old numb-nuts? Nah. He’s a mystery. I’d normally have said, sure, he’s here for the same reason as we are. But he’s Council, an’ even if you don’t believe half of what you hear about them — I don’t — I’ve never heard of one lying. Have you?”

“Never. And he didn’t expect to go to Quake when he came, only to Opal. He thought those twins he’s after would be here.”

“So maybe he’s for real. Either way, we can forget him. If he wants to go to Quake, he’ll do it. The bozos can’t stop him.” They were back at the building, and Nenda paused just outside the door. “All right, we had our little chat. Now for the best question of all. Just what is going to happen on Quake at Summertide?”

Darya stared at him. Did he expect her to answer that? “I don’t know.”

“Come on, you’re stalling again. You must know — or you wouldn’t have dragged all this way.”

“You have it exactly backward. If I did know what will happen, or if I even had a halfway plausible idea of it, I’d never have left Sentinel Gate. I like it there. You dragged all this way, too. What do you think will happen?”

He was glaring at her in frustration. “Lord knows. Hey, you’re the genius. If you don’t know you can be damned sure I don’t. You really have no idea?”

“Not really. It will be something significant, I believe that. It will happen on Quake. And it will tell us more about the Builders. Beyond that I can’t even guess.”

“Hell.” He slashed at the damp ground with the cane. Darya had the feeling that if Kallik had been there, the Hymenopt would have been the recipient of that blow. “So what now, Professor?”

Darya Lang had been worrying the same question. Nenda seemed to want to cooperate, and she had been drawn along by her thirst for any facts and theories relevant to the Builders. But he seemed to have nothing — or at least, nothing he was willing to give. And she was already talking of working with Atvar H’sial and J’merlia. She could not work with both. And even though she had agreed to nothing definite, she could not mention her other conversations to Louis Nenda.

“Are you proposing that we cooperate? Because if you are—”

She did not have to finish. He had thrown his head back and was hooting with laughter. “Lady, now why would I do a thing like that? When you’ve just told me you don’t know a damned thing!”

“Well, we have been swapping information.”

“Sure. That’s what you’re good at, that’s what you’re famous for. Information and theories. So how are you at lying and cheating? How are you at action? Not so good, I’ll bet. But that’s what you’ll need to get yourself over to Quake. And from what I hear, Quake won’t be any picnic. I’ll have my work cut out there. Think I want to baby you, sweetheart, and tell you when to run and when to hide? No thanks, dear. You arrange your own parade.”