The Year's Best SF 13 # 1995

by Gardner Dozois (ed)

  That was a lie, but it seemed to do the trick. As I pulled the door shut behind me, I heard her drop the gun and start vomiting again.

  Halfway down the stairs, the euphoria of escape began to give way to a bleaker perspective. If one careless bounty hunter could find me, her more methodical colleagues couldn’t be far behind. Industrial Algebra was closing in on us. If Alison didn’t gain access to Luminous soon, we’d have no choice but to destroy the map. And even that would only be buying time.

  I paid the desk clerk for the room until the next morning, stressing that my companion should not be disturbed, and added a suitable tip to compensate for the mess the cleaners would find. The toxin denatured in air; the bloodstains would be harmless in a matter of hours. The clerk eyed me suspiciously, but said nothing.

  Outside, it was a mild, cloudless summer morning. It was barely six o’clock, but Kongjiang Lu was already crowded with pedestrians, cyclists, buses—and a few ostentatious chauffeured limousines, ploughing through the traffic at about ten kph. It looked like the night shift had just emerged from the Intel factory down the road; most of the passing cyclists were wearing the orange, logo-emblazoned overalls.

  Two blocks from the hotel I stopped dead, my legs almost giving way beneath me. It wasn’t just shock—a delayed reaction, a belated acceptance of how close I’d come to being slaughtered. The burglar’s clinical violence was chilling enough—but what it implied was infinitely more disturbing.

  Industrial Algebra was paying big money, violating international law, taking serious risks with their corporate and personal futures. The arcane abstraction of the defect was being dragged into the world of blood and dust, boardrooms and assassins, power and pragmatism.

  And the closest thing to certainty humanity had ever known was in danger of dissolving into quicksand.

  * * *

  It had all started out as a joke. Argument for argument’s sake. Alison and her infuriating heresies.

  “A mathematical theorem,” she’d proclaimed, “only becomes true when a physical system tests it out: when the system’s behavior depends in some way on the theorem being true or false.”

  It was June 1994. We were sitting in a small paved courtyard, having just emerged yawning and blinking into the winter sunlight from the final lecture in a one-semester course on the philosophy of mathematics—a bit of light relief from the hard grind of the real stuff. We had fifteen minutes to kill before meeting some friends for lunch. It was a social conversation—verging on mild flirtation—nothing more. Maybe there were demented academics lurking in dark crypts somewhere, who held views on the nature of mathematical truth that they were willing to die for. But we were twenty years old, and we knew it was all angels on the head of a pin.

  I said, “Physical systems don’t create mathematics. Nothing creates mathematics—it’s timeless. All of number theory would still be exactly the same, even if the universe contained nothing but a single electron.”

  Alison snorted. “Yes, because even one electron, plus a space-time to put it in, needs all of quantum mechanics and all of general relativity—and all the mathematical infrastructure they entail. One particle floating in a quantum vacuum needs half the major results of group theory, functional analysis, differential geometry—”

  “Okay, okay! I get the point. But if that’s the case … the events in the first picosecond after the Big Bang would have ‘constructed’ every last mathematical truth required by any physical system, all the way to the Big Crunch. Once you’ve got the mathematics that underpins the Theory of Everything … that’s it, that’s all you ever need. End of story.”

  “But it’s not. To apply the Theory of Everything to a particular system, you still need all the mathematics for dealing with that system—which could include results far beyond the mathematics that the TOE itself requires. I mean, fifteen billion years after the Big Bang, someone can still come along and prove, say … Fermat’s Last Theorem.” Andrew Wiles at Princeton had recently announced a proof of the famous conjecture, although his work was still being scrutinized by his colleagues, and the final verdict wasn’t yet in. “Physics never needed that before.”

  I protested, “What do you mean, ‘before’? Fermat’s Last Theorem never has—and never will—have anything to do with any branch of physics.”

  Alison smiled sneakily. “No branch—no. But only because the class of physical systems whose behavior depends on it is so ludicrously specific: the brains of mathematicians who are trying to validate the Wiles proof.

  “Think about it. Once you start trying to prove a theorem, then even if the mathematics is so ‘pure’ that it has no relevance to any other object in the universe … you’ve just made it relevant to yourself. You have to choose some physical process to test the theorem—whether you use a computer, or a pen and paper … or just close your eyes and shuffle neurotransmitters. There’s no such thing as a proof that doesn’t rely on physical events—and whether they’re inside or outside your skull doesn’t make them any less real.”

  “Fair enough,” I conceded warily. “But that doesn’t mean—”

  “And maybe Andrew Wiles’s brain—and body, and notepaper—comprised the first physical system whose behavior depended on the theorem being true or false. But I don’t think human actions have any special role … and if some swarm of quarks had done the same thing blindly, fifteen billion years before—executed some purely random interaction that just happened to test the conjecture in some way—then those quarks would have constructed FLT long before Wiles. We’ll never know.”

  I opened my mouth to complain that no swarm of quarks could have tested the infinite number of cases encompassed by the theorem—but I caught myself just in time. That was true—but it hadn’t stopped Wiles. A finite sequence of logical steps linked the axioms of number theory—which included some simple generalities about all numbers—to Fermat’s own sweeping assertion. And if a mathematician could test those logical steps by manipulating a finite number of physical objects for a finite amount of time—whether they were pencil marks on paper, or neurotransmitters in his or her brain—then all kinds of physical systems could, in theory, mimic the structure of the proof … with or without any awareness of what it was they were “proving.”

  I leant back on the bench and mimed tearing out hair. “If I wasn’t a diehard Platonist before, you’re forcing me into it! Fermat’s Last Theorem didn’t need to be proved by anyone—or stumbled on by any random swarm of quarks. If it’s true, it was always true. Everything implied by a given set of axioms is logically connected to them, timelessly, eternally … even if the links couldn’t be traced by people—or quarks—in the lifetime of the universe.”

  Alison was having none of this; every mention of timeless and eternal truths brought a faint smile to the corner of her mouth, as if I was affirming my belief in Santa Claus. She said, “So who, or what, pushed the consequences of ‘There exists an entity called zero’ and ‘Every X has a successor,’ et cetera, all the way to Fermat’s Last Theorem and beyond, before the universe had a chance to test out any of it?”

  I stood my ground. “What’s joined by logic is just … joined. Nothing has to happen—consequences don’t have to be ‘pushed’ into existence by anyone, or anything. Or do you imagine that the first events after the Big Bang, the first wild jitters of the quark-gluon plasma, stopped to fill in all the logical gaps? You think the quarks reasoned: well, so far we’ve done A and B and C—but now we mustn’t do D, because D would be logically inconsistent with the other mathematics we’ve ‘invented’ so far … even if it would take a five-hundred-thousand-page proof to spell out the inconsistency?”

  Alison thought it over. “No. But what if event D took place, regardless? What if the mathematics it implied was logically inconsistent with the rest—but it went ahead and happened anyway … because the universe was too young to have computed the fact that there was any discrepancy?”

  I must have sat and stared at her, open-mouthed, for
about ten seconds. Given the orthodoxies we’d spent the last two-and-a-half years absorbing, this was a seriously outrageous statement.

  “You’re claiming that … mathematics might be strewn with primordial defects in consistency? Like space might be strewn with cosmic strings?”

  “Exactly.” She stared back at me, feigning nonchalance. “If space-time doesn’t join up with itself smoothly, everywhere … why should mathematical logic?”

  I almost choked. “Where do I begin? What happens—now—when some physical system tries to link theorems across the defect? If theorem D has been rendered ‘true’ by some over-eager quarks, what happens when we program a computer to disprove it? When the software goes through all the logical steps that link A, B, and C—which the quarks have also made true—to the contradiction, the dreaded not-D … does it succeed, or doesn’t it?”

  Alison side-stepped the question. “Suppose they’re both true: D and not-D. Sounds like the end of mathematics, doesn’t it? The whole system falls apart, instantly. From D and not-D together you can prove anything you like: one equals zero, day equals night. But that’s just the boring-old-fart Platonist view—where logic travels faster than light, and computation takes no time at all. People live with omega-inconsistent theories, don’t they?”

  Omega-inconsistent number theories were non-standard versions of arithmetic, based on axioms that “almost” contradicted each other—their saving grace being that the contradictions could only show up in “infinitely long proofs” (which were formally disallowed, quite apart from being physically impossible). That was perfectly respectable modern mathematics—but Alison seemed prepared to replace “infinitely long” with just plain “long”—as if the difference hardly mattered, in practice.

  I said, “Let me get this straight. What you’re talking about is taking ordinary arithmetic—no weird counter-intuitive axioms, just the stuff every ten-year-old knows is true—and proving that it’s inconsistent, in a finite number of steps?”

  She nodded blithely. “Finite, but large. So the contradiction would rarely have any physical manifestation—it would be ‘computationally distant’ from everyday calculations, and everyday physical events. I mean … one cosmic string, somewhere out there, doesn’t destroy the universe, does it? It does no harm to anyone.”

  I laughed drily. “So long as you don’t get too close. So long as you don’t tow it back to the solar system and let it twitch around slicing up planets.”

  “Exactly.”

  I glanced at my watch. “Time to come down to Earth, I think. You know we’re meeting Julia and Ramesh—?”

  Alison sighed theatrically. “I know, I know. And this would bore them witless, poor things—so the subject’s closed, I promise.” She added wickedly, “Humanities students are so myopic.”

  We set off across the tranquil leafy campus. Alison kept her word, and we walked in silence; carrying on the argument up to the last minute would have made it even harder to avoid the topic once we were in polite company.

  Half-way to the cafeteria, though, I couldn’t help myself.

  “If someone ever did program a computer to follow a chain of inferences across the defect … what do you claim would actually happen? When the end result of all those simple, trustworthy logical steps finally popped up on the screen—which group of primordial quarks would win the battle? And please don’t tell me that the whole computer just conveniently vanishes.”

  Alison smiled, tongue-in-cheek at last. “Get real, Bruno. How can you expect me to answer that, when the mathematics needed to predict the result doesn’t even exist yet? Nothing I could say would be true or false—until someone’s gone ahead and done the experiment.”

  * * *

  I spent most of the day trying to convince myself that I wasn’t being followed by some accomplice (or rival) of the surgeon, who might have been lurking outside the hotel. There was something disturbingly Kafkaesque about trying to lose a tail who might or might not have been real: no particular face I could search for in the crowd, just the abstract idea of a pursuer. It was too late to think about plastic surgery to make me look Han Chinese—Alison had raised this as a serious suggestion, back in Vietnam—but Shanghai had over a million foreign residents, so with care even an Anglophone of Italian descent should have been able to vanish.

  Whether or not I was up to the task was another matter.

  I tried joining the ant-trails of the tourists, following the path of least resistance from the insane crush of the Yuyuan Bazaar (where racks bursting with ten-cent watch-PCs, mood-sensitive contact lenses, and the latest karaoke vocal implants, sat beside bamboo cages of live ducks and pigeons) to the one-time residence of Sun Yatsen (whose personality cult was currently undergoing a mini-series-led revival on Star TV, advertised on ten thousand buses and ten times as many T-shirts). From the tomb of the writer Lu Xun (“Always think and study … visit the general then visit the victims, see the realities of your time with open eyes”—no prime time for him) to the Hongkou McDonald’s (where they were giving away small plastic Andy Warhol figurines, for reasons I couldn’t fathom). I mimed leisurely window-shopping between the shrines, but kept my body language sufficiently unfriendly to deter even the loneliest Westerner from attempting to strike up a conversation. If foreigners were unremarkable in most of the city, they were positively eye-glazing here—even to each other—and I did my best to offer no one the slightest reason to remember me.

  Along the way I checked for messages from Alison, but there were none. I left five of my own, tiny abstract chalk marks on bus shelters and park benches—all slightly different, but all saying the same thing: CLOSE BRUSH, BUT SAFE NOW. MOVING ON.

  By early evening, I’d done all I could to throw off my hypothetical shadow, so I headed for the next hotel on our agreed but unwritten list. The last time we’d met face-to-face, in Hanoi, I’d mocked all of Alison’s elaborate preparations. Now I was beginning to wish that I’d begged her to extend our secret language to cover more extreme contingencies. FATALLY WOUNDED. BETRAYED YOU UNDER TORTURE. REALITY DECAYING. OTHERWISE FINE.

  The hotel on Huaihai Zhonglu was a step up from the last one, but not quite classy enough to refuse payment in cash. The desk clerk made polite small-talk, and I lied as smoothly as I could about my plans to spend a week sight-seeing before heading for Beijing. The bellperson smirked when I tipped him too much—and I sat on my bed for five minutes afterward, wondering what significance to read into that.

  I struggled to regain a sense of proportion. Industrial Algebra could have bribed every single hotel employee in Shanghai to be on the lookout for us—but that was a bit like saying that, in theory, they could have duplicated our entire twelve-year search for defects, and not bothered to pursue us at all. There was no question that they wanted what we had, badly—but what could they actually do about it? Go to a merchant bank (or the Mafia, or a Triad) for finance? That might have worked if the cargo had been a stray kilogram of plutonium, or a valuable gene sequence—but only a few hundred thousand people on the planet would be capable of understanding what the defect was, even in theory. Only a fraction of that number would believe that such a thing could really exist … and even fewer would be both wealthy and immoral enough to invest in the business of exploiting it.

  The stakes appeared to be infinitely high—but that didn’t make the players omnipotent.

  Not yet.

  I changed the dressing on my arm, from sock to handkerchief, but the incision was deeper than I’d realized, and it was still bleeding thinly. I left the hotel—and found exactly what I needed in a twenty-four-hour emporium just ten minutes away. Surgical grade tissue repair cream: a mixture of collagen-based adhesive, antiseptic, and growth factors. The emporium wasn’t even a pharmaceuticals outlet—it just had aisle after aisle packed with all kinds of unrelated odds and ends, laid out beneath the unblinking blue-white ceiling panels. Canned food, PVC plumbing fixtures, traditional medicines, rat contraceptives, video ROMS. It was a random c
ornucopia, an almost organic diversity—as if the products had all just grown on the shelves from whatever spores the wind had happened to blow in.

  I headed back to the hotel, pushing my way through the relentless crowds, half seduced and half sickened by the odors of cooking, dazed by the endless vista of holograms and neon in a language I barely understood. Fifteen minutes later, reeling from the noise and humidity, I realized that I was lost.

  I stopped on a street corner and tried to get my bearings. Shanghai stretched out around me, dense and lavish, sensual and ruthless—a Darwinian economic simulation self-organized to the brink of catastrophe. The Amazon of commerce: this city of sixteen million had more industry of every kind, more exporters and importers, more wholesalers and retailers, traders and re-sellers and re-cyclers and scavengers, more billionaires and more beggars, than most nations on the planet.

  Not to mention more computing power.

  China itself was reaching the cusp of its decades-long transition from brutal totalitarian communism to brutal totalitarian capitalism: a slow seamless morph from Mao to Pinochet set to the enthusiastic applause of its trading partners and the international financial agencies. There’d been no need for a counter-revolution—just layer after layer of carefully reasoned Newspeak to pave the way from previous doctrine to the stunningly obvious conclusion that private property, a thriving middle class, and a few trillion dollars worth of foreign investment were exactly what the Party had been aiming for all along.

  The apparatus of the police state remained as essential as ever. Trade unionists with decadent bourgeois ideas about uncompetitive wages, journalists with counter-revolutionary notions of exposing corruption and nepotism, and any number of subversive political activists spreading destabilizing propaganda about the fantasy of free elections, all needed to be kept in check.

  In a way, Luminous was a product of this strange transition from communism to not-communism in a thousand tiny steps. No one else, not even the U.S. defense research establishment, possessed a single machine with so much power. The rest of the world had succumbed long ago to networking, giving up their imposing supercomputers with their difficult architecture and customized chips for a few hundred of the latest mass-produced work stations. In fact, the biggest computing feats of the twenty-first century had all been farmed out over the Internet to thousands of volunteers, to run on their machines whenever the processors would otherwise be idle. That was how Alison and I had mapped the defect in the first place: seven thousand amateur mathematicians had shared the joke, for twelve years.