Convergent Series (15 page)

"Come in," Darya Lang called out automatically when she heard a tentative knock on the door. She saw it swing open.

"Come in," she repeated. Then she saw that the visitor was already in, or partially so. Just a foot above the ground, a round black head with a ring of bright eyes was peering past the edge of the open door.

"She don't understand you worth a damn," a gruff voice said. "Only knows a few command words in human talk. Get in there."

A frowning, squat, and swarthy man came striding through the door, pushing a diminutive alien ahead of him. A stiff halter around the Hymenopt's plump thorax was connected to a black whipping cane in the man's hand.

"I'm Louis Nenda. This here"—a downward jerk of the cane—"is Kallik. Belongs to me."

"Hello. I'm Darya Lang."

"I know. We need to talk."

He was the worst yet. Darya was becoming impatient with the level of manners in the Phemus Circle. But it was catching. "You may need to talk. I certainly don't. So why don't you leave now?"

Unexpectedly, he grinned. "Wait and see. Where can we talk?"

"Right here. But I don't see why we should."

He shook his head and jerked his thumb toward J'merlia. The Lo'tfian had recovered enough to be released from the support harness, but he still preferred to remain where he could raise himself aloft for sleep periods. "What about the stick insect?"

"He's all right." She bent to look at the ocular membrane. "He's just resting. He'll be no trouble."

"I don't care what he's doing. What I have to say can't be said in front of that bug."

"Then I don't think I want to hear it, either. J'merlia isn't a bug. He's a Lo'tfian, and he's as rational as you are."

"Which don't impress me too much." Nenda grinned again. "There's people say I'm crazy as a Varnian. Come on, let's go talk."

"Can you give me one reason why I should want to?"

"Sure. I can give you twelve hundred and thirty-seven of 'em."

Darya stared at him. "Are you talking about the Builder artifacts? Only twelve hundred and thirty-six of those have been discovered."

"I said
reasons
. And I bet we can both think of one very good reason for talking that's
not
an artifact."

"I don't know what you mean." But Darya could feel her traitorous face, as usual, betraying her.

"Kallik, stay." Louis Nenda added a set of whistles and grunts to the words. He turned to Darya. "Speak any Hymenopt? Thought not. I told her to go over there and keep an eye on the bug. Come on outside. She'll come get us if it wakes up and needs you."

He loosed the cane from Kallik's halter and headed out of the door and out of the building, not even looking back to see if she was following.

What did he know? What
could
he know? Logic said, not a thing. But Darya found herself following him out onto the sodden surface of the Sling.

Starside Weather Central was predicting another major storm in a day, but for the moment the winds had died away to warm and humid gusts. Mandel and Amaranth were together in the sky, fuzzy bright patches on the cloud layer. Amaranth was growing rapidly in apparent brightness. Green plants had become edged with copper, and there was a rusty tinge to the eastward sky. Louis Nenda walked confidently into the brush—no worries for
him
about giant tortoises, Darya thought. But by now they should all be safely out at sea, anyway, ready to ride out Summertide.

"That's far enough," she called after him. "Tell me what you want."

He turned around and came back toward her. "All right, this'll do. I just don't want an extra audience, that's all. And I assume you don't."

"I don't mind. I have nothing to hide."

"Yeah?" He was smiling up at her, half a head shorter. "Funny, I'd have thought you might. You're Darya Lang, the Fourth Alliance's expert on Builder technology and Builder history."

"I'm not an expert, but I am very interested in the Builders. That's no secret."

"It's not. And you're famous enough so that the Builder specialists in the Zardalu Communion know all about your work and the Lang Catalog. You get invited to conferences and meetings, don't you, all the time? But you've never traveled, they all say, not for a dozen years. Anyone who wants to see Darya Lang, they make that trek to Sentinel Gate. Except that a couple of months ago, you can't be reached there. All of a sudden you take off. For Dobelle."

"I want to explore the Umbilical."

"Sure. Except according to the Lang Catalog, UAC 279—"

"UAC 269," said Darya automatically.

"Sorry, UAC 269. Anyway, it says—mind if I quote you?—the Umbilical is 'one of the simplest and most comprehensible of all Builder artifacts, and is for that reason of less interest to most serious students of Builder technology.' Remember writing that?"

"Of course I do. What of it? I'm a free agent; I can change my mind. And I can go where I like.

"You can. Except that your bosses back on Miranda made a big mistake. They should have told people who asked that you'd gone off to Tantalus, or Cocoon, or Flambeau, or one of the other really big Builder draws. Or maybe just say you'd gone off for a holiday."

"What
did
they say?" She should not have been asking, but she had to know. What had those dummies back in central government done to her?"

"They didn't say nuthin'. They clammed up and told anyone who asked to go away and stop bothering them and come back in a couple of months. You don't tell people that if you want them to stop sniffing around."

"But you found me with no trouble." Darya was feeling very relieved. He was a pest, but he did not know anything, and it was not her fault that he was there.

"Sure did. We found you. It wasn't hard, once we got going; there's transfer information for every Bose Transition."

"So you followed me here. Now what do you want with me?"

"Did I say we followed you,
Professor
?" He turned the title into an insult. "We didn't. You see, we were already on the way. But when we found you were here, too, I knew we really had to get together. Come on, dearie."

Louis Nenda took Darya by the arm and led her through the undergrowth. They came to a tangled ridge of vines and horizontal woody stems, bulging up to form a long and lumpy bench. At pressure from him she sank down to a sitting position. Her legs were wobbly.

"We had to get together," he repeated. "And you know why, don't you? You pretend you don't, Darya Lang, but you sure as hell do." He sat down next to her and patted her familiarly on the knee. "Come on, it's confessional time. You and me have things to tell each other, sweetheart. Real intimate things. Want me to go first?"

If the results are so obvious to
me
, why haven't others drawn the same conclusions?

Darya remembered thinking that, long before she ever set out for Dobelle. And finally she could answer the question. Others
had
drawn the same conclusions. The mystery was only that someone as crude, direct, and unintellectual as Louis Nenda could have done it.

He had not beaten about the bush.

"Builder artifacts, all over the spiral arm. Some in your territory, back in the Alliance, some in the Cecropia Federation, some back where I live in Zardalu-land. Yeah, and one here, too, the Umbilical.

"Your Lang Catalog lists every one of 'em. And you use a universal galactic ephemeris to show every time there's been a
change
in any artifact. In appearance, size, function, anything."

"As best I could." Darya was admitting nothing that was not written in the catalog itself. "Some times weren't recorded to enough significant figures. I'm sure other events were missed entirely. And I suspect some were logged that weren't real changes."

"But you showed an average of thirty-seven changes per artifact, over an observation span of three thousand years—nine thousand years for artifacts in the Cecropian territory, 'cause they've been watching longer than anyone else. And no correlation of the times."

"That's right." Darya did not like his grin. She nodded and glanced away.

Nenda squeezed her knee with powerful fingers. His hand was thick and hairy. "Getting too close to the crucial point, am I? Don't feel bad, sweetie. Hang in—we'll be there in a minute. The event
times
didn't correlate, did they? But in one of your papers you made a throwaway suggestion. Remember it?"

How long should she go on stalling? Except that Legate Pereira's instructions had been quite specific. She was not to tell anyone outside the Alliance what she had found—even if they seemed to know it already.

She pushed his hand away from her leg. "I've made a lot of throwaway suggestions in my work."

"So I hear. And I hear you don't forget things. But I'll refresh your memory, anyway. You said that the right way to examine possible time correlation of artifact changes was not through the examination of universal galactic event times. It was to think of the effects of a change as propagating outward from their point of origin, traveling like a radio signal, at the speed of light. So ten light-years after something happened at an artifact, information about that change would be available everywhere on the surface of a sphere, ten years in radius and with center at the artifact. Remember writing that?"

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."