Incandescence

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 geometry.” 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