by Greg Egan
Like all DNA-based life it was Rakesh's distant cousin, but it was unlikely to be a direct descendant of whoever had built this ark.
"It doesn't use infrared at all," Parantham observed. "It listens for sounds conducted through the tunnel wall."
"So how did it home in on me when I was standing stock still?" Rakesh examined the model's results more closely. "Aha. Resonances set up by its own footsteps. A kind of sonar, after all." It was impossible to say exactly how this creature's natural ancestors had lived, but the engineered traits it possessed were extensive and ingenious. The Arkmakers might not have had the technology to locate, let alone reach, another planet like their own, but they had worked hard to adapt life to their new environment.
"So where are its designers?" he asked Parantham.
"Be patient," she replied. "We've barely scratched the surface."
When they reached a fork in the tunnel, they launched a small probe to keep following the twelve-legged creature, and they took the other turn, in toward the center of the ark.
Rakesh kept waiting for a riot of new lifeforms to appear before his eyes — to cross some threshold that marked the end of the barren outskirts, and witness a sudden explosion of diversity — but all they saw were the same kinds of fungus and the same spider-like creatures eating it. In fact, the further they went the sparser the fungus became.
"The stellar wind powers the whole ecosystem," Parantham mused. "But it barely penetrates this deep. Parts of the walls are permeable to it, parts are not; it's as if they designed the ark to have a certain flow, a certain set of currents running through it. But the wind must have been much stronger then. These days, it's too feeble to do the job. And there doesn't seem to be any other mechanism for transporting energy in toward the center."
Rakesh didn't reply, but he couldn't help following her argument to its logical conclusion. The Arkmakers had invented a whole new ecosystem to live in after the death of their planet, but the vagaries of the bulge had defeated them yet again. They had relied on the hot winds from nearby giant stars as their new primary energy source, turning their backs on the relatively weak radiation from their small but stable foster-sun. Giant stars had short lives, and while new ones were always being born, in any particular place the stellar wind could ebb and flow dramatically on a time scale of just a few million years. The Interloper might have finished off the Steelmakers, but it could have provided whoever came after them with more or less constant light for another three billion years.
As they flew deeper into the ark, the fungus disappeared completely. The interior was barren. With nothing to repair them, the walls became increasingly cracked; small thermal stresses over the millennia had torn at the structure, in places reducing it to loose piles of rubble. Electromagnetic probes revealed what might once have been a network of copper wires running through the walls — distributing power, perhaps, or information — but they were just fragmented segments now, worn and snapped by minuscule but relentlessly patient forces.
About halfway to the center, rubble blocked their way. They despatched a swarm of small probes that could squeeze into the interstices, then backtracked and took a turn sideways, to see if there was anything that they could explore "for themselves". Rakesh had grown used to his new body, and he was reluctant to give it up and return his senses to Lahl's Promise.
He said, "Fifty million years is a long time to expect anyone to stay cooped up in a place like this. Maybe the Arkmakers finally developed interstellar travel, mined the asteroids for some raw materials, and then headed right out of the NSD to search for a safer home."
"That's possible," Parantham replied. "And if we can't see the hole where they burrowed out of this cocoon, maybe the fungus sealed it off." She hesitated. "The design still doesn't make a lot of sense to me, though. Even if the stellar winds were much stronger when this place was built, I can't see what the flow was optimized for. There's a very precise gradation in the density of the wall material; it's far too regular to be accidental, so it's either an engineering feature that I just don't understand, or a reflection of a very weird esthetic. If you chop this place in half along the center of the long axis, there's more flow-through in one half than the other. What's that all about? And I'd swear the local variations are designed to induce turbulence that would scatter the fungus as widely as possible, but the fluid dynamics is all wrong for any plausible stellar wind that might have blown into this system."
The way ahead was blocked by a cloud of rubble again. Rakesh braked and let himself float in the middle of the tunnel.
He said, "This thing has no engine. How do you think they got it clear of the planet when the neutron star came through?"
Parantham shrugged. "They might have taken it up in small pieces, and used the fungus to weld them together."
"That's assuming they had rockets at all," Rakesh said.
"Well, yes. If they didn't, they could have simply built it on the ground and let the tidal force lift it. That would have been a very risky strategy, though."
"Where would the safest launching site be?" Rakesh glanced at a model and answered his own question, "The point furthest from the neutron star at the moment when its tidal force canceled the planet's gravity. Assuming that it survived the quakes, the ark would simply drift up into space."
Parantham said, "It wouldn't have had much of a head start, though, before all the rocks came tumbling after it. Collisions between the debris would redistribute its momentum, creating some fragments that would outrace the pack. You couldn't avoid a serious peppering, at the very least."
"I suppose they could have made more than one ark, to improve the odds," Rakesh suggested. "The others might have been destroyed by debris, or captured by the neutron star."
Parantham let out a long, reproachful moan. "Captured by the neutron star?"
Rakesh was bemused. "You don't think that's possible?"
"Of course it's possible. And that's exactly what they wanted! This one's the failure, the one that was left behind!"
"How is it a failure to get left behind?"
"The giants' stellar wind," she said, "has a greater energy density than middle-aged starlight, but there's something that would give it even more oomph: the gravitational field of a neutron star. The neutron star would have drawn the wind into an accretion disk around it, far richer in energy than anything else in sight. The Arkmakers saw this monster coming, and thought: if it's going to pulverize our home, better to learn to drink from that whirlpool than skulk around in the ruins waiting for the next disaster.
"This ark, and everything in it, was designed to survive in an accretion disk. The asymmetrical flow-through would have given it a kind of buoyancy, pushing it back out into larger orbits if it ever sank in too deep." Parantham ran a model, and piped the output to Rakesh. "The wind in the disk would have been strong enough to keep the fungus alive almost everywhere, to support the food chain throughout the ark."
Rakesh absorbed the model's results. Parantham's conclusions were hard to dispute.
"So this place was starved from the beginning?" he said. "When they missed the neutron star, they had no hope?" The children of the Arkmakers, designed to escape the fate of their planet-bound parents, had found themselves stranded with the wrong biology, trapped inside an ingenious machine for extracting energy from an exotic new source that was receding into the distance at a few hundred kilometers a second.
Parantham said, "No hope for themselves. But I can't believe this was the only ark. There could have been a dozen, there could have been a thousand. If they really saw no prospect of fleeing from the neutron star, every resource on the planet would have been used to maximize the chances of hitching a ride."
Rakesh looked around at the ruins of this desperate strategy, and tried to picture the same tunnels teeming with life while the hot wind from a neutron star's accretion disk whistled through the walls. Perhaps the extraordinary gamble could have paid off, if they'd repeated it a sufficient number of times.
"If they hitched a ride, where did it take them?" Rakesh asked. When he and Parantham had first realized what it was that had created the asteroid belt, they had run dynamical models and checked the maps, but they'd been unable to locate the neutron star that had done the deed. The only thing that had been clear was the general direction of its motion.
"Toward the center," Parantham replied. "Deeper into the core."
12
As the work team gathered in the Calculation Chamber, Roi caught sight of Neth and proclaimed hopefully, "Sixth time brings success!"
"Sixth?" Neth replied. "Surely this is the third?"
"It's one task to frame a hypothesis, then another to test it," Roi insisted. "So that's six separate acts."
Neth was too polite to object, and perhaps too serious to understand that Roi was only joking. If the proverb was worth anything, it certainly wasn't worth taking literally. It did encourage persistence, though, and Roi had a feeling that their persistence was finally going to be rewarded.
Since Neth's discovery that orbits around the Hub might become unstable, a dozen or so members of Zak's original team had left to educate hatchlings into the secrets of weight and motion, and a dozen more had headed for the sardside, with the even more ambitious aim of recruiting a new team to build Bard's tunnel. The task of those who remained was to find a geometry for space and time that satisfied Zak's principle, in the hope of learning more about the dangers the Splinter would face in the future.
Tan had refined his ideas for characterizing geometry to the point where he could calculate the natural paths — the closest things to straight lines — on any curved surface. The vital step that remained, though, was to find the correct way to move from the geometry of space alone to a version that included time.
When Tan analyzed a path on a curved surface, he broke it up into a multitude of tiny, straight line segments of equal length. These small straight lines acted as markers for the direction of the curve. The geometry of the surface could then be embodied in a simple mathematical rule that Tan called a "connection". The connection allowed you to take a direction at one point and shift it to another, nearby point, in a manner that respected the geometry of the surface. If a curve was a natural path, then when you broke it up into line segments and used the connection to shift them all one step forward, the shifted segments would coincide with the originals: shifting the first segment one step along the curve would give you the original direction of the second segment, and so on. If the curve was not a natural path, then the directions would fail to agree, and the resulting discrepancies would be a measure of how much the curve swerved unnecessarily, as opposed to merely following the geometry.
That the curves were broken into line segments of equal length was a crucial part of the recipe, because the analysis had to yield the same verdict if the surface was picked up and rotated, or if two people were viewing it from different angles. If you decreed that the curve should be broken up some other way, such as into segments that spanned equal horizontal distances, then different people would be left arguing over which direction was "horizontal". Nobody would argue as to whether two successive segments were of equal length. With the connection respecting this rule — preserving the lengths of the segments as it moved them from point to point — everything worked smoothly, and everyone agreed on which paths constituted natural motion and which did not.
What happened, though, when you considered the path of a tossed stone, moving forward in time as well as through space? Anyone could draw a picture in which some chosen direction represented time, and the path of a moving object slanted across the skin, but how could people ever agree on the correct scale for such a diagram? Whether one heartbeat, one shift, or one lifetime passed from the top of the skin to the bottom was a completely arbitrary choice.
Nevertheless, suppose you settled on a scale. What would happen if you divided the path of a stone into segments of equal length? To Roi, who tossed a stone forward across the Null Chamber at one span per heartbeat, the path she drew would slant across the skin. If Zak happened already to be moving at the same pace in the same direction, the stone would be motionless to him, so he would draw a line that stretched solely in the time direction. Suppose that after five heartbeats, the stone hit an obstacle. Zak's line would be "five heartbeats" long, whatever the scale of the picture made that. Roi's line, though, would have to be longer: it would stretch five heartbeats in the time direction, but it would also cross five spans of space. The accounts of the two experimenters had to be compatible somehow, but they couldn't expect to draw their separate diagrams and then measure the same path lengths.
What could they agree on? The simplest answer anyone in the team had been able to suggest was the time that had elapsed. If you marked off segments of the stone's path representing equal intervals of elapsed time, everyone would agree how many segments there were from start to finish. If you looked for a connection that respected this scheme by never changing the amount of time spanned by a segment, then everything would have a chance to work smoothly.
This was what the team had tried first. They had hunted for a geometry of space and time whose connection left intervals of time unchanged, and which obeyed Zak's principle.
In less than one shift, they had found one. In this geometry, everything was symmetrical about a special point, where the Hub could sit. The natural paths of the geometry included circular orbits around the Hub. The square of the period of each such orbit was proportional to the cube of its size. And the ratio between the garm-sard weight and the shomal-junub weight was precisely three. Close to the Hub, far from the Hub, always, everywhere, three.
It was the answer that Zak had guessed long ago, when he'd thought the Map of Weights might still hold true. It possessed an elegant simplicity, but it was impossible to reconcile with the measurements they had made. The current ratio of weights was two and a quarter; that had been confirmed a dozen times.
This failure had cast some doubt on the idea that natural motion could be described by the same kind of geometrical principles that applied to space alone. The team had considered looking for a completely new direction, but the consensus had been that they shouldn't give up on Tan's ideas so easily.
Was there any other rule that the connection could obey that might make sense? Could the idea of "constant length" that worked so well in space alone somehow be applied in the new context, in spite of the obvious problems?
It was Neth who had pointed out that if you drew a space-time diagram with an outrageously large scale for the time axis — thirty-six times thirty-six spans for one heartbeat, say — then the different points of view of people moving with mildly different velocities could be mimicked quite accurately by the very slight rotations of the picture that would be needed to make their own particular paths point purely in the time direction. The problem remained that if lengths on this diagram were taken as fixed, two people moving with different velocities would consider each other's hearts to be beating faster than if their motion was the same, since a line that was "one heartbeat long" would span a smaller interval of time, and seem to pass more quickly, if it was slanted away from the time direction of the person who was measuring it. In reality, though, if the scale was large enough then the effect would be so tiny as to be impossible to measure. Who was to say that this wasn't happening?
It was an audacious hypothesis, but nobody had any better ideas. The team had labored for five shifts to find a geometry in accord with it. Their success, when it came, had been a mixed blessing, but nevertheless it had convinced Roi that they were on the right track.
The second geometry, like the first, was symmetrical about one special point, and allowed for circular orbits. Far from the Hub, the periods of these orbits were approximated by the old square-cube rule, but for smaller orbits the approximation broke down, and the periods became longer than that rule implied.
As a consequence, the ratio of garm-sard weight to shomal-junub weight was no longer fi
xed at three. It started out close to three for orbits far from the Hub, which was promising; the problem was, as you approached the Hub the ratio became larger, not smaller. The ratio was greater than three, everywhere, and the two and a quarter they had measured was nowhere to be found in this geometry.
The team had spent a further six shifts checking and rechecking their results. A single error anywhere in their calculations might have thrown the orbital periods and the weight ratios in the wrong direction. There was no error, though. The geometry they had found followed Zak's principle — that the sum of the true weights without spin was zero — and its connection respected Neth's idea that different people's space-time diagrams of moving objects should agree on the lengths of their paths. It was more beautiful, Roi thought, than the simpler geometry they'd found before; it certainly offered richer possibilities. But it did not describe the reality of the Splinter and the Hub.
As Roi had scrutinized the calculations, checking for some tiny, subtle mistake, an idea almost as outrageous as Neth's original hypothesis had occurred to her. Among other possibilities, they were hunting for a sign error: an addition in place of a subtraction, or vice versa. A mistake like that could easily be the cause of the problem. If there was no sign error in the calculation, though, might there not be one in the hypothesis itself?
Neth had supposed that the length in space-time that everyone agreed on obeyed the same rules as a length in space alone. The square of a length in space was the sum of the squares of its components in three different directions: garm-sard, shomal-junub, rarb-sharq. Neth had simply added in the square of the time component, after it had been multiplied by the scale factor that converted time to distance.
Why add the square of the time, though? Such perfect symmetry suggested that time was exactly like space, that apart from units of measurement the two things were indistinguishable. It was clear to Roi that time was different: you could walk back and forth along the garm-sard axis as often as you liked, but you could hardly do the same between future and past. If the first scheme they'd used to deal with time had set it too much apart, declaring it absolute, universal and immutable, perhaps their second attempt had gone too far in the other direction.
