Greg Egan - Incandescence

"Wait and see," Roi replied. Sometimes she felt like playing along with Haf, joining him in his wild speculations, but lately she was afraid of too much talk about the future, as if any hope put into words was more exposed, more vulnerable, than everyone's unspoken longing for safety.

In the last few dwindling dark phases, Ruz's team had snatched their final observations from the void. Just as the Splinter sank back into the plane of the Incandescence, the Wanderer's orbit had lost its own traces of elevation; they were confined to the same two dimensions now, locked into a closer, more dangerous dance. If the only thing to fear had been a head-on collision with the Wanderer itself, then the problem would not have been so difficult, but mere proximity could be as fatal as contact. The Wanderer was far hotter and brighter than the Incandescence; if they drew too near, or were struck by one of its flares at close range, the heat could sear right through the shelter of the rock and kill them, as surely as if they'd been standing unprotected on the surface.

Kem had computed the trajectories for both light and flares, and sketched out the safest passage past the Wanderer's orbit. The twisted curvature of the geometry had a pernicious effect, focusing the danger into places where a simpler analysis might have anticipated safety; the Hub did act as a kind of shelter, but the points to which it offered the greatest protection did not lie directly opposite the Wanderer.

Kem's laborious calculations had identified the path of least danger; the only problem now was to follow it, without a glimpse of the void to confirm their position. Roi had set up systematic weight measurements, and cycling stones and Rotators in a new Null Chamber; all of this helped quantify their distance from the Hub, but the most crucial information, their angle from the Wanderer, could not be measured this way.

Sen and her team were monitoring the strength of the wind, and had done their best to calibrate a model linking the characteristics of the flow through the tunnels with the last of the solid data that the void-watchers had been able to gather on the Splinter's changing orbit. The varying density of the Incandescence could not be anticipated, but it could be measured in the wind, moment by moment, and fed into the templates to derive a range of estimates as to the effect the tunnels were having on the Splinter's position and speed.

These efforts gave them a far better chance than they would have had by merely trusting in luck, but two things remained to elevate the uncertainty. One was the Wanderer's erratic orbital shifts, which they had never been able to understand and no longer had any hope of observing. Roi had accepted that there was nothing to be done about that. The other complication was the influence of the Wanderer's curvature, and that was a flaw she could not accept without a fight.

They could never hope to track the Wanderer's proximity with a change in the weights; the differences it made from one end of the Splinter to the other were too tiny. But that lack of detectable influence did not mean that as the two of them swept around the Hub, the Wanderer was incapable of advancing the Splinter in its orbit, slowly dragging them out of the safe zone that Kem had delineated.

With Haf and Pel as their checkers, Roi, Kem and Nis stood with their template-frames, shift after shift, trying to merge the geometries in a way that satisfied Zak's principle. Having failed to make progress before, Roi had them try the simplest approach: imagining that both the Hub and the Wanderer possessed the twistless curvature of their first, incorrect guess for the Hub. Such an answer would not have been the true geometry, of course, but it might have opened up a crack leading in the right direction.

Roi's vision as she fell into sleep at the end of each shift was filled with images of smooth, bright surfaces colliding, grating against each other, refusing to meld. Each time she woke, the problem filled her thoughts again immediately. How could they pass the Wanderer, blinded by the Incandescence, without slipping unknowingly into danger? The geometry of space-time was the only guide left to them, but while their knowledge of its shape remained imperfect, that guide was uncertain, and perhaps even treacherous.

Kem put down her frame. "I can't think any more. I'm going to get some food."

"Haf can bring you food," Roi suggested.

"Pel can do it!" said Haf. "She's not doing anything!" Pel was lying on her back, gazing at the ceiling. No one had passed her a frame to check since the start of the shift.

"I can get it myself," Kem replied. She left the chamber.

Nis had paused while they were speaking; now he looked to Roi, almost accusingly.

"We're all tired," he said. "I think we're going nowhere."

"You're giving up on this?" Roi felt a stab of bitterness. "To do what?" If there'd been some other urgent task she would have sent him to it with her blessing, but Sen's team had their calculations under control; they didn't need a new recruit to train in their methods.

"I'm not giving up," Nis replied. "I'm losing my mind. These calculations aren't leading anywhere. Nothing simplifies; they just grow more tangled with every step. Someone smart enough could probably prove that we're never going to find this geometry."

Roi thought of Tan, who was sick now, as Zak had been. If he'd been healthy, maybe he could have done just that: proved that she was wasting her time.

"The geometry exists!" she rasped. "It's there around us. It's what we're moving through, even as we speak."

"I didn't claim it doesn't exist," Nis said wearily. "But not everything in the world fits a template. Can you write a template for the shape of the Splinter? For the shape of your own carapace?"

Roi fell silent. Nis's analogy had to become right at some point, but she had hoped that they could reach this small step further with the mathematics. Two "Hubs", two centers to the curvature; it didn't seem like such a complicated thing to capture with a template.

Nis said, "Space-time does what it does, following Zak's principle over and over, fitting together perfectly, everywhere, all the time. Without sliding a single stone along a wire. Without knowing the first thing about templates. That's how it defeats us at this game. It doesn't need to capture the details of everything it does across all of space and all of time in a few elegant symbols. It just does what it does."

He put down his frame.

Roi pushed herself against the rock, stretching her aching joints, struggling to clear her mind. There was something wise in Nis's words, but it wasn't the message of pessimism.

She said, "You're right, it's not trying to do template mathematics. It doesn't need to. But if it doesn't, then why do we?"

Nis answered dutifully, as if he were her student. "Because we need a template to distil everything that happens into a simple, compact form. How else could we calculate anything?"

"How does space-time calculate anything?" she replied.

"I don't understand," Nis said.

"I understand," said Haf. "We should do as Tio said."

"What?" Roi was confused now. "What did Tio say?" Tio was a friend of Haf's who had wandered from teacher to teacher among the theorists, learning a great deal but then arguing with everyone, refusing to perform the calculations they expected of him.

"I told you thirty-six shifts ago," Haf said reprovingly. "He treats space-time as lots of small, flat pieces. When you make them small, the templates describe what happens at the corners, how you join the pieces together. But the templates are easy, not like these weeds." He shook the frame of Roi's that he'd been checking.

"You just need a lot of them," Roi said. For a few heartbeats she was simply dazed, unsure if this was some false promise that her weariness had caused her to misjudge. But Haf's words made perfect sense; Tio's idea was the only way forward.