"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--"