by Greg Egan
As Roi departed, she thought irritably: That's obvious. I didn't need Neth to tell me that.
Everything simple was obvious in retrospect, though. What remained to be seen was whether the void itself had any interest in the kind of simplicity that might let their minds reach out and grasp the truth about the world, or whether Zak's principle was just a beautiful, but misguided, statement of hope.
When Roi returned to the Null Chamber, she found to her delight that it was crawling with hatchlings. Gul was among them, orchestrating their exuberant play.
She climbed out along a wire to reach him.
"I heard the news about Zak," he said. "I thought you'd probably be too busy to come back to us for a while. Then I thought, why not let them experience weightlessness and see some experiments, instead of just hearing about everything second-hand?"
Roi didn't recognize any of the pupils; this was a new class. Her and Gul's children would almost certainly be among them, but if they were she had no way of identifying them. She watched the scampering hatchlings with an uneasy, almost guilty, thrill. Just as Jos had found it hard to defect for a second time, even Roi had her limits, and it was difficult to view the secret obsession she'd developed with her own offspring's fate as anything but shameful and perverse.
Since the Jolt the Null Chamber was no longer perfectly weightless, but though the changes were enough to ruin long-term measurements it was still possible to demonstrate the basic cycles here, not to mention indulging in the pleasures of simply floating around and throwing things to see how they moved. The place brought back memories of Zak, but Roi could feel no sadness at that when two dozen hatchlings were being steeped in his ideas before her eyes.
Gul said, "If you have a moment, later. I'm in pain."
Roi had seen the seed packets inside him, but he'd hid the discomfort so well that she'd assumed they weren't yet ripe. She felt no inclination to berate him, this time, for failing to find someone else to deal with his burden. The simple truth was, she wanted the two of them to have children together. As many as possible.
She turned the baffling notion over in her mind. Why? He was a good teacher, but he didn't have to be the father of a hatchling, she didn't have to be the mother, in order for him to teach it. Did she imagine, absurdly, that their individual skills had somehow seeped into their seed and eggs, and would collide within their children to imbue them with a preternatural ability to endure the struggles ahead? None of the hatchlings here were dishing out lessons in space-time geometry and template manipulation. If her children were special in any way, why couldn't she even pick them from the crowd?
It was a mystery, but she didn't feel like fighting it; she didn't even have the energy to ponder it for long. If the next generation turned out to be so brilliant, they could work out the reasons themselves; she'd be content just to see them survive.
She said to Gul, "There's a machine someone gave me that turns darkness into light. When the children are asleep, come and see me, and I'll show you how it works."
Roi met Tan, and they began preparing the way for the calculations that they hoped would lead to the true geometry.
Zak's principle remained their most trusted guide, but it was a curious thing. Once you knew certain aspects of the space-time geometry it allowed you to deduce the rest, but if you started with a blank skin it could not tell you anything definite. It was less a prescription for a single, self-contained world than a kind of style or constraint that left room for a multitude of possibilities. Before you could apply it, you needed to weed out all but one small, manageable portion of that overwhelming bounty.
As Neth had suggested, their best hope of success was to retain as much symmetry as possible. At the same time, if they pruned away too much of the geometry's freedom just to make the calculations simpler, they would risk failing, once again, to capture the true richness of the space-time around the Hub.
"I believe in rotational symmetry," Tan said firmly. "We have evidence for that, and not just in the plane of the Incandescence. Since the Jolt, we've been moving periodically out of that plane, and your observations show that each time we've entered a shomal or junub dark phase, we've actually been at a different place along our orbit. Yet apart from the different view of the lights you saw, nothing else is different from phase to phase. The weights change slightly as we ascend and descend relative to the plane, but at a given point in each cycle, everything feels the same."
"We're not going very far out of the plane," Roi cautioned. "It's hard to quantify, but I doubt that we're rising by more than a tiny fraction of our distance from the Hub."
"No, but the lack of spherical symmetry you discovered manifests itself in the length of the shomal-junub cycle, which we first measured in the Null Chamber with stones that never went further than one span from the plane of the orbit! It was only the fact that the Incandescence and the Splinter were blocking our view of the lights in the void that stopped us from comparing the shomal-junub cycle to the orbital period."
"That's true," Roi conceded. "In any case, even if we can only pin down the geometry close to the plane and use it to explain the Splinter's motion, that will be a start." The Wanderer's orbit appeared to be inclined, taking it high above the Incandescence, but with the strange distortions of the light to account for, making sense of those observations remained a distant ambition.
"We're agreed then," Tan said. "We look for a geometry unchanged by rotation around a fixed axis."
The other symmetry they were committed to retaining was the assumption that the geometry around the Hub was unchanging over time. Though the Splinter and other objects might be nudged into different orbits, it was the fact that they had shifted in space that altered the geometry they experienced; the geometry itself was not melting beneath them.
"The question then," Tan said, "is how are the two symmetries related? In our last calculation we assumed that the symmetries of space always acted in a direction perpendicular to the time symmetry. But do we have any evidence for that?"
Roi hoped Gul was filling their children's minds with ideas that would prepare them for questions like this. She had been raised with an understanding of three perpendicular directions in space — garm/sard, rarb/sharq, shomal/junub — and if you added time as a fourth, it seemed obvious that it ought to be measured perpendicular to all three. Certainly, any clock you carried with you would measure time that way, and even in the abstract world of Tan's geometry, at any given time and place you could simply pick four perpendicular directions.
However, the directions of symmetry weren't a matter of choice or convenience; they were properties of the geometry itself. And while the framework for the calculations would become more complicated if the two symmetries were allowed the freedom to slant against each other, it would be even worse if they could not rely on a measure of time in which the geometry was unchanging.
Roi said, "What would count as evidence?"
Tan couldn't answer that immediately. He took a sheet of skin and started doodling. "Throw out one dimension of space, the one that takes us out of the plane of the Incandescence, and use that instead to picture time." He drew a point for the Hub, then sketched a circle around it for their old, un-Jolted orbit. "The symmetry in time takes this circle into another one in the future, tracing out a cylinder." He sketched in the cylinder, drawing lines rising straight up from the circle to indicate the direction in which it could be pushed without its geometry changing.
Roi said, "And if the time symmetry isn't perpendicular to the rotational symmetry?" She scratched a second diagram beside the first, in which the lines that carried the circle forward in time wound around the cylinder in helices. "But wouldn't we always be able to straighten out these lines?" she said. "The geometry doesn't change, whether you move around the cylinder as you travel along its length, or just slide straight up and down. It's all the same."
Tan thought for a moment. "With one cylinder you could always do that, but don't forget the rest of the g
eometry." He drew in a second, larger orbit on Roi's diagram, then sketched in helices with a different, steeper pitch. "Suppose the time symmetry makes a different angle with the rotational symmetry at different distances from the Hub. We're free to combine this whole motion with any fixed amount of rotation around the Hub, but we're not free to rotate around the Hub by different angles at different distances, and that's what we'd need in order to straighten everything out."
Roi said, "So there'd be a kind of unavoidable twist in the geometry?" She pondered this. "Then wouldn't motion around the Hub in the direction of the twist be different from motion in other directions?"
"That sounds plausible," Tan said.
"When we throw a stone out of the plane of the Incandescence," Roi said, "it completes the orbit in much less time than it takes to fall down and rise up again. It's almost as if it's being swept around the axis of symmetry, forcing it to go around faster than the other cycle it's completing, the shomal-junub cycle."
Tan said, "I think you've just answered the question. There might turn out to be some other explanation, but for now we definitely can't assume that the symmetries are perpendicular."
That would make the calculations harder, but at least they were doing it for a reason. Roi felt buoyed; the idea that they could anticipate a feature of the geometry that might allow it to conform to the new observations was encouraging. Most of what she'd seen in the void remained utterly mysterious to her, but they were moving in the right direction.
"There's one more thing we need to decide before we call in the calculating team," Tan said. "How are we going to measure distances from the Hub now?"
In the previous calculation, they'd described each point's relationship to the Hub by the size of the sphere on which it lay. You didn't need to worry about the actual, messy curved geometry all the way from the point to the Hub itself; instead you imagined rotating the point around the Hub in all possible directions, sweeping out a sphere whose surface area would increase the further the point was from the Hub.
With the spherical symmetry gone, they could no longer do this. They could replace the spheres with circles — rotating each point around the axis of symmetry and then considering the circumference of the circle it swept out — but away from the plane of the Incandescence it wasn't clear how those circles would be related to each other.
Ruz appeared at the entrance to the Chamber. He greeted them politely and apologized for interrupting, but Roi could tell from the way he hunched against the wall that he had something he urgently needed to say.
"We're seeing more flares from the Wanderer," he announced. "Nine, in the last report I've received." While Roi had been visiting Bard and Neth, Ruz had arranged a group of new recruits to stay at the junub edge, with pairs climbing up through the crack in the wall each time it was safe, to make observations.
"We've felt no new Jolt," Tan said.
"No," Ruz replied, "we've been lucky. But if this continues, it's only a matter of time before another one strikes us. We're also seeing the Wanderer's orbit changing: it's losing its inclination, coming closer to the plane of the Incandescence."
Roi felt a crushing sense of hopelessness descend, but she struggled to fight it off. One tunnel was almost complete, and Neth would help Bard sort out any problems with the flow. They were tracking the Wanderer heartbeat by heartbeat. Now it was up to the theorists to find the way forward, to draw the map that showed the way to safety.
She addressed Tan. "We should assemble the calculating team, next shift."
"All right," he said. "But what about the question of distance from the Hub?"
Roi thought for a while. "There's one symmetry that's always present, that we forgot to mention: the geometry really doesn't care how we describe it." You could wrap space-time in numbers in countless different ways, but the underlying shape was oblivious to the packaging. "We don't know the best way to express distance from the Hub, and even if we make a certain guess now it might turn out to make things harder. So we should give ourselves room to manoeuvre: we should set up the templates so we can choose the easiest scheme at any point in the calculations."
Tan concurred. He said, "I'll go and tell the calculating team."
When he'd left, Ruz said, "I'd better go and send the messengers back to get the next report."
Roi said, "Remember Jos?"
"Jos?"
"One of the people we met with the light machine?"
Ruz looked tired. "Vaguely. Why?"
"She's had an idea for something much faster than any messenger. I think you need to talk to her."
19
Rakesh spooned chillied dhal into his mouth with an urgency that had nothing to do with hunger. The longer he spent among the Arkdwellers, the more he needed to reinforce his sense of presence in his own neglected body, and the familiar taste and aroma brought him back to himself like nothing else did.
"I'm going mad," he announced. "One more month of this, and you can erase me and break the news to my backup."
Parantham said, "Don't expect my sympathy. Just because the Arkdwellers' culture turned out to be resilient, it doesn't mean you were right to take a risk with it."
"Resilient? I think the word you're looking for is catatonic." Sweat was pouring down the back of his neck from the spices, but he kept eating without pause, and without diluting the heat with bread or rice.
Each time his Arkdweller colleague Saf slept, Rakesh took his senses out of his avatar, leaving it dormant in a crack in the rock close to the one she'd chosen. Each time Saf stirred, his avatar would notice and summon him back. It was a summons he was beginning to dread.
His job had allowed him to tour the Ark, and at first the experience had been fascinating. The Ark's biosphere was bottom-heavy in fungi and bacteria, but it had a few niches for larger organisms. A genetic analysis of the five varieties of herd animals the Arkdwellers farmed showed that they'd been created by selective breeding from an earlier inventory of just two species. Whether the Arkmakers had initially stocked the place with more and the others had been lost at some point was unclear; it was also unclear just when the Arkdwellers had lost their ancestors' ability to engineer the animals' genomes, and had to revert to patient observation of traits and restrictive mating or manual fertilization. Both the larger animals and the Arkdwellers themselves reproduced in more or less the same way, which involved excruciating pain for all fertile males and more pity than pleasure on the part of the harassed females who put them out of their misery. Rakesh fervently hoped that it was something the ancestors had passed down from their own biology only because it was too technically difficult to change. The possibility that they might have freely devised such a scheme didn't bear thinking about.
The flow of stellar winds into the neutron star's accretion disk was a powerful and relatively constant source of energy, and even the tiny portion siphoned off by the Ark was enough to allow a technologically unsophisticated culture to rise above subsistence agriculture. A range of simple goods was manufactured, mainly from animal products, but also from a small amount of scrupulously recycled metal. Services ranged from courier rounds like Saf's to the curating and restoration of repositories of documents, written on animal skin, bearing recipes for such things as inks and glues, and drawings of useful tools and machines.
It was all very practical, but it seemed a long way removed from the kind of knowledge their ancestors must have possessed. Though born on the surface of an ordinary planet, the Arkmakers had mastered the plasma hydrodynamics of a neutron star's accretion disk in sufficient detail to construct a whole world that could flourish in this radically new environment. Rakesh couldn't see the current inhabitants coping with even the mildest disruption to their routine.
Parantham said, "It need not be pathological, to respond to stability with stasis. Perhaps this is what the Arkmakers longed for: after all the turmoil they'd faced, they didn't want to have to look over their shoulders for the rest of eternity. They didn't want to be frettin
g about how they'd escape the next unpredictable disaster."
"This is the bulge," Rakesh replied. "You have no choice but to look over your shoulder."
"In the long run, maybe not, but they've managed to survive for fifty million years. Perhaps they calculated the odds, and said, if we burrow down deep into this neutron star's gravity well, it will be a long, long time before anything else wanders by that's strong enough to prise us out." Parantham spread her hands. "Once you make that decision, what's the point in being outward-looking, or in seeking constant change? Some cultures have thrived on uncertainty, but for some species there's nothing more stressful than the need for vigilance."
Rakesh could see her point, but he didn't like where she was heading. "So when the Arkmakers faced the prospect of the neutron star tearing up their home world, you think they willingly rid themselves of the very traits that allowed them to survive that event? They resented the unpredictable universe so much that they consciously stripped away all their curiosity, all their powers of abstract reasoning, and gave birth to this nest of sleepwalkers?"
"Are they happy?" she asked.
"They're not miserable," he replied, begrudgingly. "But only because they don't know what they're missing."
"Are they happier than you were back at the node?" Parantham countered. "Going mad with frustration because the whole galaxy had been tamed a million years before your birth, and there was nothing left for you to do with your own redundant curiosity and vigilance? Is that what the Arkmakers should have wished upon their children? Fifty million years of safety — tainted by fifty million years of resentment because their sanctuary was not exciting enough?"
Rakesh closed his eyes and let the sweat from his forehead trickle down and sting his eyelids. He said, "I don't know if their way of life is a good thing or not, but if they want to reject the outside world, let them make a conscious choice about it. The Arkmakers had very few choices; I'm not giving up on these people just because their ancestors faced some hard decisions fifty million years ago, and did what they thought was best. I don't want to force any changes on them, but I'm not leaving until I find a way to get through to them."