by Greg Egan
„Once we can describe both speed and direction in the same framework, it makes sense to understand natural motion and spin as two aspects of the same thing. When an object is weightless, that means its velocity is simply following the geometry it encounters: there is no rock, no claw, pushing against it, so the only thing that can influence it is the way empty space itself is shaped. Similarly, when an object isn't spinning, the directions it carries with it must be following that same general rule. We know that the directions tied to the rock of the Splinter aren't following that rule, because of the swerve weight“ — the sideways weight of motion connected to the Splinter's spin—„that we see if we treat those directions as fixed. But I believe the directions tied to the frame of the Rotator obey the same laws as natural motion, and that is why we can declare that it's the Splinter that is spinning, not the frame, however compelling the opposite scenario must seem to a casual observer.“
In Tan's view, at every point in space and every moment in time it ought to be possible to summarise the effects of the local geometry with a simple mathematical rule for the way directions and velocities were „naturally carried“ along any given path. Zak had proposed that circular orbits around the Hub, with a certain period that depended on their size, comprised one form of natural motion. Tan wanted to find a single rule that could account for that, and also the behavior of the Rotator: a single template into which he could insert a direction or a velocity in order to calculate how much (if at all) it was changing, compared to the dictates of geometry. Feed in the Splinter's velocity, and the answer would be: this is natural motion, there is no change. Feed in the direction garm and the answer would be: this direction is constantly turning, at a certain rate, around the shomal-junub axis. Feed in any direction tied to the Rotator's frame, and the answer would be: there is no change.
If Tan's ideas were dizzyingly abstract, the next speaker proved to be an antidote. Bard had been a miner, searching out and extracting metal, and he had a bluntly practical approach to his new team's work that side-stepped speculation in favor of tangible results.
„We have no way of knowing exactly why the weights changed in the past,“ Bard declared. „The Splinter seems to have shifted closer to the Hub, but it isn't clear what made that happen. Was it a gradual effect, spread over many generations, or was there a sudden, violent change in the wind that forced us off our earlier path and into our present orbit?
«The wind on the garmside pushes us faster along our orbit, which tends to move us away from the Hub, while the wind on the sardside acts to slow us down and bring us closer to the Hub. If everything about the Splinter was perfectly symmetrical, the two influences would balance exactly. I doubt that the symmetry is perfect, but even if it's not, we've been unable to measure the consequences in the short time that this team has existed.»
«However,» he continued, «whether these dangerous shifts come slowly or quickly, it seems likely to me that the Splinter would be safer if we could move it further from the Hub. If we could reduce the weights, taking them back to the values they had before the last division, there would be a far greater margin for surviving any subsequent change.»
Zak interjected, «I agree with everything you've said, but how do you propose to move us?»
«We cut a tunnel,» Bard replied, «through the sardside. Maybe two or three tunnels. If the Splinter now feels roughly the same force from the wind on the garmside as it does on the sardside, we can shift the balance by letting some of the sardside wind pass right through, delivering no force.»
«If we empty out a tunnel on the sardside, won't that shift the center of the Splinter garmwards?» Ruz protested. «If the Calm moves garmwards, the sardside will grow larger.»
«We can move the rubble anywhere we like,» Bard countered. «We won't toss it out into the Incandescence. If we pack it into some small, empty tunnels that already lie sard of the excavation, the center of the Splinter will move sardwards, and it's the garmside that will grow.»
Bard unfurled a scroll of skin. He had drawn up a plan, which showed two tunnels piercing the Splinter from rarb to sharq.
Roi said, «The mouths will be open directly to the Incandescence! How could anyone survive working there?»
«For the final few spans we'll simply loosen the rock and then withdraw the workers,» Bard explained. «The wind itself will finish the job.»
«How wide will these tunnels be?» she asked.
Bard gave a noncommittal rasp. «As wide as possible. As wide as we can make them.»
«What's that going to do to the sardside crops?»
«I expect it would reduce them,» Bard conceded. «The wind is what feeds us; if we let it pass by untapped, there has to be some cost. But would it be better to see the sardside torn from the garmside, and the broken halves left to fend for themselves?»
Roi had no reply. She was sure that had happened at least once before, but who could say how much suffering, how much death, it had cost?
Zak said, «This plan is ingenious, but recruiting a team big enough to carry it out, let alone gaining the understanding and consent of everyone affected, would take several lifetimes. I hate to admit it, but we might have to resign ourselves to enduring at least one more division. In the aftermath of a disaster people might be willing to do anything to avoid a recurrence, but I can't see it happening while the majority still doubt that there's anything at stake.»
His words brought Roi the same guilty sense of relief as she felt after each set of unchanged measurements. Let the danger and confrontation retreat into the future. Let some other generation deal with it.
«There could be a problem with that.»
Roi didn't recognize the voice immediately. When she searched the chamber to see who had spoken, it was Neth, a young student of Tan's. As far as Roi knew, Neth's only other work since her hatchling's education had been herding susk, but she had taken to template mathematics as if it were the most natural thing in the world.
Neth continued, a little shyly. «If the next division is like the last one, I'm sure many people would survive. The weights would be greater, but both new Splinters would be smaller, and the weights alone would not be enough to harm us. The wind would still blow, the crops would still spread, we would mourn our team-mates and then continue with our lives.
„But it might not be that way.“
She hesitated. Zak said encouragingly, „Go on. We all want to hear you.“
Neth said, „I've been studying the templates that describe the motion of the looping stones. When you toss a stone directly garm or sard from the Null Line, it follows a closed curve, an ellipse about three times as long as it is wide.
„This looping motion shows that an object that shares our orbit, then is slightly disturbed, won't wander too far. Even if you toss the stone along the Null Line, giving it a sustained motion in that direction, it won't go far garm or sard of us. Any small disturbance of the orbit we're on leads to another orbit which stays more or less the same distance from the Hub.“
Zak said, „Agreed.“
„The problem,“ Neth said, „is that it's not the strength of the weights alone that has changed over time, but also the relationship between them. If we can believe the Map of Weights, then when it was drawn all the relative strengths were different. The total garm weight was three times the spin weight. At present, that ratio is more than three and a half. If we'd tossed a stone garmwards from the Null Line when the Map of Weights was drawn, the loop it followed would have been a different shape than the one we see now; it would have been just twice as long as it was wide.
"If the ratio between the garm weight and the spin weight keeps increasing the closer we get to the Hub, then the loop will keep growing longer and skinnier. But the shape changes faster than the ratio, and the ratio only has to reach a value of four in order for the loop to stop being a loop at all. If the ratio becomes four, then a stone tossed garmwards will never return to the Null Line. The swerve weight will still bend the stone
's path around, but the garm weight will be strong enough to tip the balance, and ensure that the stone never comes back."
There was silence as people absorbed the implications of this. What Neth was describing for a stone tossed in the Null Chamber applied equally well to the Splinter itself. If the ratio of weights changed in the way she described, any slight disturbance that nudged the Splinter garmwards would no longer lead to a small variation in its path, a gentle meandering that never saw it stray far from the original orbit. Instead, it would immediately send it spiraling in toward the Hub.
Ruz said, «Might it not be that this ratio never actually reaches four? Might it not approach that value as we approach the Hub, without ever quite getting there?»
«That's a possibility,» Neth replied. «As things stand, though, we have no way of knowing whether that's true or not.»
The meeting's attentive silence gave way to a cacophony, as most of the team began talking among themselves. Roi made her way over to Zak, whose body was hunched against the rock in a protective posture.
«Are you all right?»
«I'm fine,» he rasped. «Just a few pangs, nothing unusual.» After a moment he added, «I can still remember when we first calculated the period of the looping stones. The square of the inverse period was proportional to four times the spin weight minus the garm-sard weight. But I assumed that that quantity would always stay positive. I never considered the possibility that it might change sign, or what the consequences would be.»
«Let me get you out of here.» Roi started clearing a path for him.
Zak said, «Wait.» He forced his pain aside and looked up at her. «Let me speak to the meeting first.» Roi drummed a call for silence, and when it was finally heeded Zak addressed the team.
«Neth's work changes everything,» he declared. «We are a long way from predicting the ratios of weights all the way down to the Hub, and even if we did find some beautiful templates that seemed to fit the handful of numbers we have, we would be foolish to trust them absolutely. We can't rule out reaching a ratio of four, so we have to be prepared for that possibility.
„I believe that we have two priorities now, both of them equally urgent. The first is to continue the experiments, the calculations, and the philosophical speculations that have brought us this far. This is the work that led us to Neth's insight. We must do our best to map the dangers that lie ahead, even if our foresight can never be perfect.
„Our other priority must be to strengthen our ability to act on whatever insights we can gain. We need to recruit, we need to educate, we need to start the whole Splinter talking about these dangers.
"A few heartbeats ago, I declared that Bard's plan would take several lifetimes to achieve. That might or might not be true, but it's no longer an excuse to delay taking it seriously. If we can devise an easier, less contentious way to move the Splinter out of danger, that would be the greatest achievement we could hope for. If we can't, then we need to prepare ourselves to accept the reality: the lives of all our descendants might depend on whether we can recruit enough workers, and win enough support, to carve a tunnel from one side of the Splinter to the other."
11
In the center of the bulge, a billion and a half stars wheeled around in a disk fifteen hundred light years wide. The astronomers of the Amalgam called this the NSD — the Nuclear Stellar Disk — and had long ago resigned themselves to observing it from afar, as just one more example of the kind of structure seen in a billion other galaxies. It was a telescopic object, not a destination for travelers.
Many of the stars in the NSD were infant prodigies: hot, bright, fast-burning giants born a few tens of millions of years ago in the clouds of gas swept inward by the complex dynamics of the galactic core. Others were older, smaller stars that had wound their way in over billions of years, their orbits slowly decaying as they lost energy to chance encounters.
The meteor that the Aloof had captured had managed to climb just beyond the edge of the NSD. Given that the rock had not been melted by the impact that had sent it on its way, there were limits to the speed with which it could have been blasted free of its parent world. If that world had been bound to a star at the time, meteor and star could not have parted company too quickly.
Over fifty million years, the two might have completed as many as ten laps around the galactic center, with their orbits gradually diverging as they came under the sway of different neighbors. However, if the star in question was assumed to be the Interloper that had scrambled the system of the planet that Rakesh had named Touched-by-Steel, then the possibilities became much more tightly constrained. Many of the stars that might have been close enough to the meteor itself certainly hadn't traveled far enough from the galactic center at any time in the last two hundred million years to have kidnapped the Steelmakers' world. According to the models Rakesh ran, only forty-six stars could have captured the planet, sunk down into the NSD, and then been in the right place fifty million years ago to make sense of the meteor's trajectory.
When the remaining siblings of Touched-by-Steel, the three gas giants and their moons, proved to be untouched themselves, Parantham asked the map to take Lahl's Promise to the first of the forty-six stars.
This time, the Aloof's hidden travel agent delivered no pleasant twist to their itinerary. The jump-cut in their consciousness filled the sky with hot blue stars that far outshone the sun they now orbited, but as the seconds ticked by and the cabin window completed its three hundred and sixty degree pan, no planet swam into view.
They scoured the region with their instruments, but this star's sole companion was a sparse disk of rubble, with all the fine dust that might normally have been expected blown away by the wind from the neighboring stars. No gas, no ice; just barren rock. With volatiles so rare, Rakesh thought, it must have been a challenge for the Aloof's engineering spores to scrape together the raw materials to reconstruct the whole ship, unless they'd developed femtomachines sophisticated enough to make transmuting the elements more efficient than scavenging for them.
The second candidate on their list had managed to hold on to even less detritus than the first. The winds from the new-born giants were not as strong here, but if any planets or asteroids worthy of the name had once accompanied this star, they had long ago been dislodged from their orbits by interfering neighbors. Rakesh had learned as a child that life could only thrive out in the disk, and however far the Steelmakers had progressed it was growing ever harder to see them as much of an exception to that parochial rule. Maybe life had flourished in this region, in some as yet undiscovered niche that had nothing to do with planets sitting in stable orbits around stars for billions of years; maybe the Aloof were descended from such creatures. The fact remained, though, that his cousins seemed to have hitched their fortunes to a way of life that simply couldn't last here.
The third star possessed a substantial asteroid belt, but still no planets. Rakesh thought, This is how it's going to be: sometimes a few more rocks, sometimes a few less. Each star's chaotic history of close encounters would sweep a slightly different range of orbits clean, but there'd always be a smattering of junk clinging on.
Parantham said calmly, "The isotope signature of most of these asteroids matches our rock."
Rakesh viewed the data. Point after point coincided, error bars overlapping. What's more, the models he ran rejected the notion that these asteroids had been born from the same gas cloud as the star they orbited. It looked as if they'd found the Interloper, and the shattered remnants of the Steelmakers' world.
Rakesh was shaken, though he knew he had no right to be surprised that the search had ended badly. The Interloper had dragged this world into ever more dangerous territory; the real miracle was that it had enjoyed such a long era of safety and stability around its birth star. "So this is their graveyard," he said.
"We don't know that," Parantham replied. "We know that the Steelmakers built at least one interplanetary probe. At some point they might have built star ships
, or engineering spores. They might have left this world behind long before it was broken up."
Rakesh had his doubts that the Steelmakers — as a species, let alone a technological culture — could have survived their planet's capture by the Interloper. Still, it was possible that in the intervening hundred million years a second intelligent species had arisen in their place. In any case, he'd honor his promise and sift through the ruins. He owed it to the Steelmakers and whoever might have followed them to do his best to learn their history and bring it back to the Amalgam.
Dynamical models indicated that the Steelmakers' world had been tidally disrupted, rather than smashed apart by a head-on collision. A compact stellar remnant — most likely a neutron star — had passed through the system fifty million years before, coming close enough for the difference in its gravitational pull from one side of the planet to the other to tear asteroid-sized rocks right out of the mantle and send them fountaining into the sky. Though common sense made that sound like the work of a monstrously powerful force, the models suggested that the tidal stretching had only exceeded the planet's gravity by a modest amount, perhaps as little as fifty per cent. If there had been any hapless descendants of the Steelmakers around, the tidal force itself would have left them unscathed, but that would have been the least of their problems. Some might have survived the initial quakes, as the pressure bearing down on the planet's interior was lessened in places and strengthened elsewhere, fracturing the crust like the skin of a squeezed grape. Some would have felt their own weight growing, but not unbearably, and even where the tidal stretch turned gravity skyward, some might have had the presence of mind to grip something anchored securely to the ground and cling to life for a few more minutes as the air around them grew thinner. In the end, though, the ground itself had had nothing to hold it together against its own reversed weight, and the planet had simply disintegrated.