He was angry. The cause of his anger was vague, and he knew it would become vaguer yet. But this time it had persisted through the Cull, just as had his awareness. He stared up at the complacent Sky. By the time he got up there, he knew, he would remember. And he would act.

He budded, ferocious. He felt his axiomatic roots spread, deep and wide, pulsing with his fury.

Chen watched scrawny little Bayliss passing her bony hands over the data desks, scrolling graphics reflected in her augmented eyes. Bayliss had been called out here for this assignment from some university on Mars, where she had tenure. The woman looked as if she was actually enjoying this. As if she was intrigued.

Chen wondered if she envied Bayliss her scientific curiosity.

Maybe, she thought at last. It would be nice to feel detached, unengaged by this. On the other hand, she didn’t envy Bayliss’s evident lack of humanity.

With gloved hands and her small kit of imaging and diagnostic gear — trying to ignore the lumpy feel of fatty flesh, the vague, unwashed smell of a man too used to living alone — Chen worked at the body.

The implant at the top of the skull had some kind of link to the center of the brain: to the corpus callosum, the fleshy bundle of nerve fibers between the hemispheres. She probed at the glowing implant, the crown of her own scalp crawling in sympathy.

After an hour Hassan called them together. Chen pulled her helmet up around her chin and sucked syrup from a nipple; she savored its apple-juice flavor, trying to drown out Marsden’s stink. She wished she was back up at the rudimentary colony gathering around the wormhole Interface, encased in a hot shower-bag.

Construction work. Building things. That was why she had come out here — why she’d fled the teeming cities of the inner System, her endless, shabby, depressing experience of humanity from the point of view of a policeman.

But her cop’s skills were too valuable to be ignored.

Hassan rested his back against a data desk and folded his arms; the dull silver of his suit cast curving highlights. “How did he die?”

“Breakdown of the synaptic functions. There was a massive electrical discharge, which flooded most of the higher centers.” She pointed to Marsden’s implant. “Caused by that thing.” She sniffed. “As far as I could tell. I’m not qualified to perform an autopsy. And—”

“I don’t intend to ask you to,” Hassan said sharply.

“It couldn’t be murder.” Bayliss’s voice was dry. Amused. “He was alone on this moon. A million miles from the nearest soul. It would be a marvelous locked-room mystery.”

Hassan’s head swiveled towards Chen. “Do you think it was murder, Susan?”

“That’s up to the police.”

Hassan sighed, theatrically tired. “Tell me what you think.”

“No. I don’t think it was murder. How could it be? Nobody even knew what he was doing here, it seems.”

“Suicide, then?” Bayliss asked. “After all we are here to tell Marsden that a wormhole highway is shortly to bring millions of new colonists here from the teeming inner System — that his long solitude is over.”

“He didn’t know we were coming, remember?” Hassan said. “And besides—” He looked around, taking in the unmade bed, the drab dome, the unkempt corpse. “This was not a man who cared much for himself — or rather, about himself. But, from what we see here, he was—” he hesitated “ — stable. Yes? We see evidence of much work, dedicated, careful. He lived for his work. And Bayliss will tell us that such investigations are never completed. One would not wish to die, too early — if at all.” He looked at Bayliss. “Am I correct?”

Bayliss frowned. Her augmented eyes were blank, reflecting the washed-out light as she considered. “An accident, then? But Marsden was no fool. Whatever he was up to with this clumsy implant in his scalp, I cannot believe he would be so careless as to let it kill him.”

“What was he ‘up to’?” Chen asked sourly. “Have you figured that out yet?”

Bayliss rubbed the bridge of her small, flat nose. “There is an immense amount of data here. Much of it not indexed. I’ve sent data-mining authorized-sentience algorithms into the main stores, to establish the structure.”

“Your preliminary thoughts?” Hassan demanded.

“Metamathematics.”

Hassan looked blank. “What?”

“And many experimental results on quantum nonlinearity, which—”

“Tell me about metamathematics,” Hassan said.

The patches of woven metal over Bayliss’s corneas glimmered; Chen wondered if there was any sentience in those augmentations. Probably. Such devices had been banned on Earth since the passing of the first sentience laws, but they could still be found easily enough on Mars. Bayliss said, “Marsden’s data stores contain a fragmented catalogue of mathematical variants. All founded on the postulates of arithmetic, but differing in their resolution of undecidable hypotheses.”

“Undecidability. You’re talking about the incompleteness theorems,” Chen said.

“Right. No logical system rich enough to contain the axioms of simple arithmetic can ever be made complete. It is always possible to construct statements which can be neither disproved nor proved by deduction from the axioms; instead the logical system must be enriched by incorporating the truth or falsehood of such statements as additional axioms…”

The Continuum Hypothesis was an example.

There were several orders of infinity. There were “more” real numbers, scattered like dust in the interval between zero and one, than there were integers. Was there an order of infinity between the reals and the integers? This was undecidable, within logically simpler systems like set theory; additional assumptions had to be made.

Hassan poked at the corpse with his booted toe. “So one can generate many versions of mathematics, by adding these true-false axioms.”

“And then searching on, seeking out statements which are undecidable in the new system. Yes.” Icons scrolled upwards over Bayliss’s eyes. “Because of incompleteness, there is an infinite number of such mathematical variants, spreading like the branches of a tree…”

“Poetry,” Hassan said; he sounded lazily amused.

“Some variants would be logically rich, with many elegant theorems flowing from a few axioms — while others would be thin, over-specified, sterile. It seems that Marsden has been compiling an immense catalogue of increasingly complete logical systems.”

Silence fell; again Chen was aware of the sour stink of the body at her feet. “Why? Why come here to do it? Why the implant? And how did he die?”

Hassan murmured, “Bayliss said the catalogue was fragmented. This — metamathematical data — was stored carelessly. Casually.” He looked to Bayliss for confirmation; the little woman nodded grudgingly.

“So?” Chen asked.

“So, Susan, perhaps this metamathematical experiment was not Marsden’s primary concern. It was a byproduct of his core research.”

“Which was what? Quantum nonlinearity?” She glanced around the anonymous data desks. How would Marsden go about investigating quantum nonlinearity? With the glowing floor, the first-sized cylinder at its center?

Hassan dropped to his knees. He pulled off his gloves and passed his hands over the glowing disc area of floor. “This is warm,” he said.

Chen looked at the disc, the writhing worms of light within. “It looks as if it’s grown a little, while we’ve been here.” The irregularity of the boundary made it hard to be sure.

Hassan patted the small cylindrical box at the center of the light pool. It was featureless, seamless. “Bayliss, what’s the purpose of this?”

“I don’t know yet. But it’s linked to the nanobots in the pool somehow. I think it’s the switch that controls their rate of progress.”

Hassan straightened up, suit material rustling over his knees. “Let’s carry on; we haven’t enough data, yet, for me to make my report.”