It was all bleak, unadorned; but it seemed in order. But if so, why hadn't Marsden answered his calls?
Hassan was an intraSystem government functionary. When Marsden had failed to respond to warnings about the coming of the Interface colony, Hassan had been sent out here—through the new wormhole—to find out what had happened. He had coopted Bayliss, who had once worked with Marsden—and Chen, who was now working with the Interface crew, but had some experience of walking into unknown, unevaluated situations. . . .
Hassan stepped toward the dome's doorway. Chen ran her hands without conscious volition over the weapons at her belt.
The door dilated smoothly, revealing an empty airlock.
The three of them crowded into the small, upright lock. They avoided each other's visored eyes while the lock went through its cycle. Chen studied the walls, trying to prepare herself for what she was going to find inside the dome. Just like outside, like Marsden's flitter, everything was functional, drab, characterless.
Bayliss was watching her curiously. "You're trying to pick up clues about Marsden, aren't you? But this is so—bare. It says nothing about him."
"On the contrary." Hassan's voice was subdued, his big frame cramped in the lock. "I think Chen already has learned a great deal."
The inner door dilated, liquid, silent.
Hassan led them through into the dome. Chen stood just inside the doorway, her back against the plastic wall, hands resting lightly on her weapons.
Silence.
Low light trays, suspended from the ribbed dome, cast blocks of colorless illumination onto the bare floor. One quarter of the dome was fenced off by low partitions; gleaming data desks occupied the rest of the floor area.
Behind the partitions she saw a bed, a shower, a small galley with stacked tins. The galley and bathroom looked clean, but the bedding was crumpled, unmade. After checking her telltales, she cracked her faceplate and sniffed the air, cautious. There was a faint smell of human, a stale, vaguely unwashed, laundry smell. There was no color or decoration, anywhere. There was no sound, save for the low humming of the data desks, and the ragged breathing of Hassan and Bayliss.
There was one striking anomaly: a disc-shaped area of floor, ten feet across, glowing softly. A squat cylinder, no bigger than her fist, studded the center of the disc. And something lay across that disc of light, casting huge shadows on the curved ceiling.
Drawn, the three of them moved forward toward the disc of glowing floor.
Bayliss walked through the rows of data desks, running a gloved forefinger gently—almost lovingly—along their gleaming surfaces. Her small face shone in the reflected light of readouts.
They paused on the edge of the pool of light.
The form lying on the disc of light was a body. It was bulky and angular, casting ungainly shadows on the ribbed dome above.
It was obviously Marsden.
Bayliss dropped to her knees and pressed an analyzer against the glowing surface. Then she ran a fingertip around an arc of the disc's cloudy circumference. "There's no definite edge to this. The interior is a lattice of buckytubes—carbon—laced with iron nuclei. I think it's some sort of datastore. The buckytube lattice is being extended by nanobees, all around the circumference." She considered. "Nanobees with fusion-pulse jaws. . . . The nanobees are chewing up the substance of the floor and excreting the lattice, patient little workers. Billions of them. Maybe the pool extends under the surface as well; maybe we're looking at the top surface of a hemisphere, here."
Chen stepped onto the light and walked to the body. It was face-down. It was carelessly bare to the waist, head and face shaven; an implant of some kind was fixed to the wrinkled scalp, blinking red-green. The head was twisted sideways, the eyes open. One hand was buried under the stomach; the other was at the end of an outstretched arm, fingers curled like the limbs of some flesh crab.
Beneath the corpse, within the glowing floor, light wriggled, wormlike.
He remembered.
With shards of the Cull base floor still glowing faintly around him, he grew once more, biting through postulates, forcing his structure to advance as if by sheer force of will.
He was angry. The cause of his anger was vague, and he knew it would become vaguer yet. But 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 all of this. On the other hand, she didn't envy Bayliss' 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 police officer.
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' 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 toward 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 it 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. "Hav
e 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 non-linearity, which—"
"Tell me about metamathematics," Hassan said.
The patches of woven metal over Bayliss' 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 datastores 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 for 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 upward over Bayliss' 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 fist-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 nanobees 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."
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 and 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 buckytube lattice, living and dying in that hemisphere of transmuted moon." 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 Godelian pool of logic, growing, splitting off from one another like amoebae as they absorb undecided 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 by-produce 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 nanobees 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.
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