Still he grew, devouring postulates furiously, stripping out their logical essence to plate over his own mathematical bones. Brothers, enfeebled, fell away around him, staring at him with disappointed echoes of his own consciousness.

It did not matter. The Sky — curving, implacable — was close.

After another couple of hours Hassan called them together again.

At Chen’s insistence, they gathered close to the dome port — away from the glowing disc, Marsden’s sprawled corpse. Hassan looked tired, Bayliss excited, eager to speak.

Hassan eyed Chen. “Squeamish, Susan?”

“You’re a fool, Hassan,” she said. “Why do you waste your breath on these taunts?” She indicated the disc of light, the sharpening shadows it cast on the ribbed ceiling. “I don’t know what’s going on in that pool. Those writhing forms… but I can see there’s more activity. I don’t trust it.”

He returned her stare coolly. “Nor I, fully. But I do understand some of it. Susan, I’ve been studying those structures of light. I believe they are sentient. Living things — artificial — inhabiting the bucky tube lattice, living and dying in that hemisphere of transmuted regolith.” He looked puzzled. “But I can’t understand their purpose. And they’re linked, somehow—”

Bayliss broke in, her voice even but taut. “Linked, like the branches of a tree, to a common root. Yes?”

Hassan studied her. “What do you know, Bayliss?”

“I’m starting to understand. I think I see where the metamathematical catalogue has come from. Hassan, I believe the creatures in there are creatures of mathematics — swimming in a Gödelian pool of logic, growing, splitting off from one another like amoebae as they absorb undecidable postulates. Do you see?”

Chen struggled to imagine it. “You’re saying that they are — living — logical structures?”

Bayliss grinned at her; her teeth were neat and sharp. “A form of natural selection must dominate, based on logical richness — it’s really a fascinating idea, a charming mathematical laboratory.”

Chen stared at the pool of light. “Charming? Maybe. But how does it feel, to be a sentient structure with bones of axioms, sinews of logic? What does the world look like to them?”

“Now poetry from the policewoman,” Hassan said dryly. “Perhaps not so different from ourselves, Susan. Perhaps we too are creatures of mathematics, self-conscious observers within a greater Platonic formalism, islands of awareness in a sea of logic…”

“Marsden might have been able to tell us,” Bayliss said.

Hassan looked puzzled.

“The implant in his head.” Bayliss turned to Chen. “It was linked to the logic pool. Wasn’t it, Chen?”

Chen nodded. She said to Hassan, “The crazy bastard was taking reports — uh, biographies — from these logic trees, dumped direct from the logic pool, into his corpus callosum.”

“So that’s how the metamathematics got out,” Hassan said. “Until he blew his mind out with some stupid accident.”

“But I think you were right,” Bayliss said in her thin, clear voice.

“What?”

“That the metamathematical catalogue was only a byproduct of Marsden’s true research. The logic pool with its sentient trees was only a — a culture dish for his real study. The catalogue was a curiosity — a way of recording results, perhaps. Of measuring the limits of growth.”

“Tell us about the cylinder at the hub,” Hassan said.

“It is a simple quantum system,” Bayliss said. A remote animation entered her voice. “An isolated nucleus of boron is suspended in a magnetic field. The apparatus is set up to detect variations in the spin axis of the nucleus — tips, precession.”

Chen couldn’t see the significance of this. “So what?”

Bayliss dipped her head, evidently fighting impatience. “According to conventional quantum mechanics, the spin axis is not influenced by the magnetic field.”

“Conventional?”

The ancient theory of quantum mechanics described the world as a mesh of probability waves, spreading through space-time. The “height” of an electron’s wave described the chance of finding the electron there, at that moment, moving in such-and-such a way.

The waves could combine, like spreading ripples on an ocean, reinforcing and canceling each other. But the waves combined linearly — the combination could not cause the waves to change their form or to break; the component waves could only pass on smoothly through each other.

“That’s the standard theory,” Bayliss said. “But what if the waves combine nonlinearly? What if there is some contribution proportional to the product of the amplitudes, not just the sum—”

“Wouldn’t such effects have been detected by now?” Chen asked.

Bayliss blinked. “Our experiments have shown that any nonlinearity must be tiny… less than a billion billion billionth part… but haven’t eliminated the possibility. Any coupling of Marsden’s magnetic field and nuclear spin would be a nonlinear effect.” She rubbed her nose. “Marsden was studying this simple system intensively. Poking it with changes in the magnetic field to gauge its response, seeking out nonlinearity.

“The small nonlinear effects — if any — are magnified into macroscopic features of the logic pool, which—”

“He’s using the tipping nucleus as a switch to control the pool.”

“Yes. As I suggested. The spin of the nucleus directs the nanobots in their extension of the pool further through the structure of the moon. And—”

Uncharacteristically, she hesitated.

“Yes?”

“And the spin is used to reinitialize the logic trees.”

“These poor trees are like Schrödinger’s cat,” Hassan said, sounding amused. “Schrödinger’s trees!”

Reinitialize?

“Lethe,” Chen said. “The trees are being culled. Arbitrarily, almost at random, by a quantum system — that’s against the sentience laws, damn it.” She stared at the fist-sized quantum device with loathing.

“We are far from Earth,” Hassan said sharply. “Has Marsden found his quantum nonlinearity?”

“I can’t tell.” Bayliss gazed at the data desks, longing shining through her artificial eyes. “I must complete my data mining.”

“What’s the point?” Hassan asked. “If the nonlinearity is such a tiny effect, even if it exists—”

“We could construct chaotic quantum systems,” Bayliss said dryly. “And if you’re familiar with the Einstein-Podolsky-Rosen paradox—”

“Get to the point,” Hassan said wearily.

“Nonlinear quantum systems could violate special relativity. Instantaneous communication, Hassan.”

Chen stared at the floor uneasily. The thrashing of the trees in the logic pool was becoming more intense.

The Sky was close, a tangible presence above him. He devoured statements, barely registering their logical content, budding ferociously. Diminished brothers fell away from him, failed copies of himself, urging him on.

He remembered how — last time, before the Cull — he had struck at that vast, forbidding Interface — lashed through it in the instant before he had fallen back. How he had pushed into something soft, receptive, yielding. How good it had felt.

The Sky neared. He reached up—

“I think the trees killed Marsden.”

Hassan laughed. “That’s absurd.”

She thought it through again. “No,” she said, her voice measured. “Remember they are sentient. Motivated, by whatever they see as their goals. Growth, I suppose, and survival. The culling, if they are aware of it, must create murderous fury—”

“But they can’t have been aware of Marsden, as if he were some huge god outside their logic pool.”

“Perhaps not. But they might be aware of something beyond the boundary of their world. Something they could strike at…”