Roi followed the geometry inward, closer to the Hub. At a distance of one, as she’d already calculated, the looping stones would stop looping: the smallest disturbance would topple you from your orbit. But something else happened there, too: staying at a fixed distance from the Hub became, not just unlikely, but impossible. Orbits weren’t merely unstable, they ceased to exist at all. The only kind of motion that was allowed was inward. Every path, natural or otherwise, led inexorably straight to the Hub.
Tan said, “It would be a quick death, I think. The garm-sard weight would grow so fast that our bodies would be torn apart before we could feel much pain.”
“Better than burning in the heat of the Wanderer?” By moving the Splinter outward, that was the fate they were risking.
“Where did this madness come from?” she asked. “If we work hard, our lives should be good. Some sickness, some famine, that can’t be avoided. But for all of us to die, how could that be possible?”
Tan said quietly, “Nobody can understand these things.”
“I won’t let our children live like this!” Roi declared. “When this is finished. “ She trailed off impotently. She would do what? Banish every future Wanderer that might disturb their tranquility? Build a wall across the void?
“If we keep working,” Tan said, “our lives will be safer. We need to keep thinking, calculating, watching the void. But this work will never be finished. There will never be a time when we can go back to the old ways and expect to be safe.”
After a rest shift, Roi met with Tan again to plan the way forward. Their ultimate goal was to understand the geometry well enough to be able to map out a safe path past the Wanderer, but they still lacked the mathematical tools to calculate anything except for circular orbits in the plane of the Incandescence.
The observations of the void held the key, both to validating the new geometry itself and to understanding what kind of paths were possible. If they could fit the motion of the Wanderer into the picture, Roi was sure everything would become clearer. But to make use of their observations, they needed to understand the paths that the light they were seeing had taken through the curved geometry, which was every bit as hard a problem as working out the path of the Wanderer itself. It wasn’t quite a vicious circle, but the way to break in was not easy or obvious.
Three shifts later they were still getting nowhere, when a young recruit appeared at the entrance to the chamber.
“Excuse me,” she said. “I think I’ve found something.”
Her name was Kem; Tan introduced her to Roi. He’d given copies of Roi’s observations from the void to all the recruits who’d finished their studies in template geometry, and set them the task of finding a way to interpret them.
“I’ve been thinking about symmetries,” Kem said. “If you look at the relationship between the direction of a natural path and a motion of symmetry, it should be the same all along the path.” The idea, she explained, wasn’t tied to the particular geometry they’d discovered; it followed from the very definition of symmetry.
A simple example made Kem’s proposition more persuasive. On the surface of a perfectly round stone, the natural paths were great circles: the circles whose centers were the centers of the stone itself. The symmetries were rotations around any axis you cared to name. If you chose a particular great circle to be your natural path, then chose a diameter of that circle as the axis of rotation, the motion of symmetry—the way points on the surface shifted when the stone was rotated—would be perpendicular to the direction of the path, everywhere. If instead you chose an axis of rotation perpendicular to the plane of the great circle, the motion of symmetry would agree with the direction of the natural path, all along its length. And if you picked an axis that lay between those extremes, then although the angle between the motion of symmetry and the direction of the path would change, the
The stone was just an illustration, though. Kem shuffled templates that applied to any geometry, and made her case in all generality.
Roi was excited. The geometry they were testing possessed two distinct symmetries, and every natural path, every orbit, would have a constant relationship with them all along its length. For circular orbits in the plane of the Incandescence this told them nothing new, but within three shifts they had characterized the shapes of two other kinds of orbits in the plane: those whose distance from the Hub varied periodically, and those that came in from afar and then spiraled right down to the Hub.
It was beautiful mathematics, but was any of it true? Roi’s observations of the void were still useless, because although they knew the angle at which the light had reached the Splinter, they had no way of measuring how fast it had been traveling. She’d joked with Ruz on the journey back from the junub edge that he should make that his next task, but for all his ingenuity she couldn’t imagine how he could succeed.
“The problem is twofold,” Tan mused. “It’s not just the speed of light we need to discover, because what matters is the ratio of that speed to Neth’s unknown speed, the speed for turning time into space. Knowing the first without the second is useless.”
Kem said, “But we don’t need both, we just need the ratio?”
“It would be nice to have both, but we could make a lot of progress with just the ratio,” Roi replied.
“Light travels so fast,” Kem observed, “that we might not be far from wrong if we suppose that the ratio is one.”
Tan rasped disapproval. “Nothing can travel at Neth’s speed. Anyone doing so would have a heart that never beat, a sense of time that never advanced, and a notion of distance that squashed the whole world flat.”
Roi couldn’t deny those absurdities, but she wasn’t sure that was the point. “As an approximation, though, would it necessarily mislead us? We won’t calculate anything from the light’s point of view; what we’re interested in are our own measurements. And if we make this choice, the calculations become easier.” That was an understatement. Neth’s speed had the gloriously simple property that everyone agreed on it, regardless of their own motion. If they imagined that the speed of light was Neth’s speed, then the light they were seeing would not gain or lose velocity at all as it traveled from the void toward the Hub.
“Eat stones, excrete stones,” Tan rasped sullenly. “If we start with nonsense, what should we expect at the end?”
Kem looked dismayed, but Roi was not dissuaded.
“I think it’s worth trying,” she said.
Tan left them, to pursue ideas of his own. Roi worked with Kem, carefully setting up the calculations. Strictly speaking, they could still only deal with the paths taken by light that remained in the plane of the Incandescence, but Roi had many observations from the void where she’d followed lights that appeared to be skimming the surface of the rock. The paths that linked her eyes to those distant objects were so close to the plane that the difference scarcely mattered.
They spent half a shift calculating, then they called in some helpers to check the results.
Roi took Kem with her and went in search of Tan. He was alone in a small chamber, surrounded by frames, scraping his legs distractedly against his carapace.
“This is going to take me a while,” he admitted. “I can’t seem to find the way forward.”
Roi said, “Try eating what we ate.”
She passed him the final template that she and Kem had derived, and let him check it against the observations. “Correct,” he murmured after a while. He put down one skin of data, copied from Roi’s time and angle measurements, and picked up the next. Each time, the verdict was the same.
“Nothing can travel at Neth’s speed,” he insisted. “But perhaps light can get very close. Too close for us to see the difference.”
Kem spoke shyly. “I have some ideas about orbits that go out of the plane. There’s a trick I think we can use to understand them.”
For a few heartbeats, Roi gazed at her in silence. Before the Jolt, Kem had been cleaning susk carcasses. Tan had taught her well, giving her the tools every geometer needed, but he had not fed her any of these insights himself. Whatever mysterious skill it required to take the knowledge of your teachers and double it had blossomed across the Splinter at precisely the time it was needed. Where had it been hiding? How had it emerged? Roi couldn’t begin to imagine how such things could be explained.
When they’d dealt with the Wanderer, she could worry about that. She’d look forward to spending her final
