Incandescence

"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.

She asked Haf, "Can you find him? Can you bring him here?"

"Sure." Haf prodded Pel and they left the chamber together.

Nis said, "I still don't see it."

"Wait for Tio," Roi suggested. "If I try to explain it, the way I'm feeling right now I'll probably just end up confusing us both."

"But who does he work with? What's he been doing?"

"He's been working by himself," she said.

"A team of one?" Nis scoffed.

"Zak was a team of one," Roi said. "A long time ago."

Nis was unimpressed by the comparison. "Not everyone who thinks they're like Zak is actually correct in that perception."

"That's true," Roi conceded. "So let's just judge his ideas on their merits."

Haf and Pel returned with Tio. For a moment he seemed nervous and resentful, but when Roi addressed him respectfully and said that she needed his help, his posture softened and the words spilled out of him.

He had reformulated Zak's principle, he explained, in a way that suited a picture of space-time built up from many small, flat pieces. The result was not perfect, like Tan's geometry, which could be trusted down to the finest detail. But the calculations, though laborious and repetitive, were extremely simple. You couldn't fail to find an answer.

Roi asked, "How many divisions would we need to make, how many pieces of space-time to cover everything from our last known orbit to the Wanderer's, and a short way beyond?"

Tio fell silent, calculating something, or guessing. "Perhaps six to the eighth pieces. Six to the ninth for more accuracy."

"And what kind of team would we need? To calculate all the geometry before we reach the Wanderer's orbit?"

Tio said, "Six to the fourth, if they're good calculators. Maybe double that if everyone needs checkers."