I emerged disoriented, unsure why, hazily lost in a cloud of incomputables. A strange sort of confusion, not the round, satisfying ball of pinkish purple following a knock-out party but a novel sort of halfway nonsense. I knew perfectly well where I was -- lying on the lumpy bed in Room 22 of the Hotel Tronador. Yet I had no idea what's going on. There was something wrong with the way I was lying; every muscle in my neck and shoulders duly informed me that nobody could end up in this position from natural causes.
And... I could smell blood.
My eyelids flew open. A woman I'd never seen before was bending over me, slicing into my left iliopsoas with a disposable scalpel. I was lying on my side, facing the wall, one hand and one ankle cuffed to the head and foot of the bed. Something cut short the surge of visceral panic before I could start stupidly thrashing about in a doomed attempt to break free. Maybe an even more ancient response, catatonia in the face of danger, took on the adrenaline and won. Or maybe I just decided that I had no right to panic when I'd been expecting something like this for weeks. What saves you whenever you're saved, was it something from below or was it something from above ?
My amateur surgeon was compact, muscular, with thick black hair cropped closely. Asian, but not Chinese. Vietnamese, maybe. Not that it meant anything beyond appearance, by now palettes as they were often called denote personal preference far above any consideration of lineage. Happy couples consisting of say a Samoan looking woman, a very Irish fellow, their two Japanese daughters and one Inca son are a common sight in every suburban mall. Diversity, they call it, which is ridiculous considering the human race was never this inbred in its entire history.
I spoke softly, in English. "What you're in the process of hacking out of me is a necrotrap. One heartbeat without fresh blood, and the cargo gets fried."
If she was surprised that I'd woken prematurely, she didn't show it. The tailored hepatocytes I had acquired in Hanoi could cut through almost anything, but I suppose it was a good thing the local anaesthetic was beyond their reach. Chloral, maybe ? Something else metabolized in the blood, rather than the liver. Who can afford the blood stuff, and even if they did who can be bothered with the machinery involved ?
Without taking her eyes off her work, she said, "Look on the table." I twisted my head around, which took three passes. She had set up a loop of plastic tubing full of blood -- mine, presumably -- circulated and aerated by a small pumpy device. Wires came out of it, laying on the floor. They had probably been attached to my elbow prior, training the machinery to pulse "correctly". Whether she actually could tear the trap from my thigh and insert it into this substitute without missing a beat was perhaps debatable, but I had no doubt that she thought she could. Or at the very least was going to give it a try.
I cleared my throat. I swallowed. "Doesn't really look like much, does it. Look at that cheap plastic shit. You really think that's good enough ? Or is it rather the best you could find. What's the matter, they don't have chairs where you're from ? Grew up sitting on the ground like any bum, did you ?" She ignored me, but I ignored her right back and continued. "The trap knows my blood pressure profile exactly. You think a 'generic' heartbeat as implemented on whatever you could fish out of Mas x Menos will fool it ?"
"You're bluffing." But she hesitated, scalpel raised. The NLJD she had looked competent enough. It certainly could find the trap, and possibly reveal some basic diagnosis data on it. But the fine details of the engineering and, paramountly, the CPLD involved were absolutely beyond its reach.
"I'm not bluffing, you titless dogfaced brothel escapee you. It's new. It's Swedish. Ever heard of Sweden ? It's where tall people are. You train it for forty-eight hours before implantation. It memorizes the rhythms. What did you think, it's Vietnamese girl day ?" Blood trickled down across my groin and onto the sheet. I was suddenly very glad that I hadn't buried the thing deeper, after all. "It ain't Vietnamese girl day."
"So how do you retrieve the cargo yourself?"
"I'd tell you, but I don't know how to bark it."
"Tell me now, and save yourself some trouble." She rotated the scalpel between thumb and forefinger impatiently. My skin did a cold burn all over, nerve ends jangling, capillaries closing down as blood dived for cover.
"Trouble gives me hypertension." I said plainly. "Why the fuck do you think I'm sitting here chatting with you, as calm as I can manage ? What, it's your great conversational assets, you figure ? Stupid fucking bitch."
She smiled down at me thinly, conceding the stalemate, then peeled off one stained surgical glove, took out her notepad, and made a call to a medical equipment supplier. She listed some devices which would get around the problem -- blood pressure probes, a more sophisticated pump, a proper computer to hook everything into -- arguing heatedly in fluent Mandarin to extract a promise of a speedy delivery. Then she put down the notepad and placed her ungloved hand on my shoulder.
"You can relax now. We won't have long to wait."
Then she suddenly grew stiff. Nadja, I knew it, I knew it before I could sense her warm, voluptuous magnetic presence, before hearing her throaty whisper.
"Oh my god!" she exclaimed in perfect deadpan a second later. "Oh my god! What are you two doing here!"
"She's giving me a bloodjob." I said, as the would-be thigh-burglar collapsed in a pile at her feet.
"Why didn't you whistle ? You know how to whistle, don't you ?"
"God, you're fucking terrible. You know that ?"
"Am I strangling the bitch ?"
"Nah, give her cerebro."
"If you say so. Go ahead then. Can you even stand up ?"
"It's in the fridge, left bottom, blue vial labeled csi, the Greek letter".
"What do you mean it's in the fridge ?!"
"I mean it's in the fridge."
"You mean you don't carry it ?!"
"That's right, I don't carry it."
"You might be the first guy I've met. Are you sure ?"
"Yes I'm fucking sure, what the fuck do you think cerebro is, like the clap ? Guys don't get it from fucking toilet seats."
"No I know that, it's just... Well... why not ?"
"What the fuck stupid question is that, why not. Why too ? So you can only ever fuck women you don't like henceforth ? What sort of an imbecile would think getting it is a good idea ?"
"Yes, well, fuck them."
"Actually, I'd much rather fuck you. Please ? Do me ? You can put it anywhere you want."
"Let's get out of here first."
I paid the desk clerk for the room until the next morning, stressing that my companion should not be disturbed, and winked at him cleverly. It'll all go over easier if they think she's a prostitute in the first place. The clerk eyed me tiredly and replied nothing.
"What do you think will happen to her ?"
"I'm sure they have brothels here. Like anywhere else."
"I wonder if she knew what she was getting herself into."
"Did you ? Did we ? Did anyone ever ?" I paused and for lack of a better idea spat to the side. "Dumb bitch could really use bigger tits anyway."
"That's true. Some ass, too."
"And I really don't think anyone could argue she had much to lose in the other department to begin with."
Outside, it was a mild, cloudless summer morning. It was barely six o'clock, but the road was already teeming with pedestrians, buses and a bunch of cheap Toyotas. 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 evidently paying big money to rather stupid people. And violating international law, and taking serious risks with their corporate and personal futures, but that's repeating oneself. The arcane abstraction of the defect was being dragged into the world of blood and dust, of very real human pain and suffering. It's to be a game for boardrooms and assassins now, a matter of power and pragmatism. The closest thing to certainty humanity had ever known was in danger of dissolving into quicksand.
Yet it had all started out as a joke. An argument for argument's sake. Kim and her infuriating heresies, or as cads aptly put it, "if you were a mathematician you'd know just how stupid we are". "A mathematical theorem," she 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 2034. 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."
Kim 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 then 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. So it might as well be called timeless anyway."
"But it's not. To apply the Theory of Everything to any 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 came along and proved Fermat's Last Theorem. Conceivably physics never needed that before for anything."
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."
Kim smiled sneakily. "Not any branch, no. But consider a class of physical systems whose behavior depends on it that is so very ludicrously specific : the brains of mathematicians who are trying to validate the proof. 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 nevertheless 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 some mathematician's brain, and body, and note paper, 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. If some swarm of quarks had done the same thing blindly, fifteen billion years before, if they executed some purely random interaction that just happened to test the conjecture in some way, then those quarks would have constructed FLT long before. 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 then I realised 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 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."
"Mathematics is actually organized in equivalency rings. Proving some property in Cartesian coordinates proves an equivalent, if not directly obvious property in polar coordinates, and the same is true of fields and sets and everything else."
"But the meaning of this for your theory is that mathematics exists independently and beyond its statement to or by humans, and for that matter quarks. Moreover the 'uncomprehending' quarks example fundamentally produces the same exact exception : it is not proper to say that this so and so physical system composed of Wilkes and his wad of napkins depends on FLT as the actual mathematical object. What it depends on is a statement of something that may be to some degree related to the actual mathematical object. In the case of human thought, it is mediated by ambiguity. In the case of the quark cloud, it is mediated by what you conveniently denote by 'uncomprehendingly'. In any case the relationship is not strong, or as they'd say at Duke, 'deniable'."
She bit her lip. Kim bites her lip when she's sexually aroused, and the things that arouse her are... well...
"Yet it can't be all that ambiguous, as the language of mathematics is orthogonal by your definition. To propose that there's a space between FLP-as-it-is and FLP-as-Wilkes-sees-it is no different from proposing there's a difference between the 4 coming out of adding two and two and the other 4 coming out of multiplying two and two."
I leant back on the bench and mimed tearing out hair. "If I wasn't a die-hard 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, and by always we mean -- before the beginning of things. Everything implied by a given set of axioms is logically connected to them, timelessly, eternally, and immaterially. Even if the links couldn't be traced by people or quarks in the lifetime of the universe."
Kim 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 zero' and 'Every X has a successor etcetera, 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 must do D, because non-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?"
Kim 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, as a sort of accident ? Perhaps because the universe was too young to have computed the fact that there was any discrepancy there in the first place ?"
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.... no, wait, let me get this straight. You're saying mathematics might be strewn with primordial defects in consistency just like space might be strewn with cosmic strings? That on one hand you have air bubbles and whatnot in the marzipan, but on the other hand you also have dings and dents in the foil form into which the marzipan goes ?"
"That is exactly what I'm saying." She stared back at me, feigning nonchalance. "If space-time doesn't join up with itself smoothly everywhere as an absolute necessity, then on what basis should you expect mathematical logic to?"
I almost choked. "Where do I begin? What happens 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 -- the dreaded not-D... does it succeed, or doesn't it?"
"I don't know, you tell me. What happens when a mother with chimerism donates the wrong kind of kidney to her daughter ? Kid dies, what. You weren't promised any specific kind of ride, you know. Nobody gave you a certificate. Not for anything."
Then after a pause, "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 Kim seemed prepared to replace "infinitely long" with just plain "inconveniently 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. "At least not to anyone we'd know. 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 turning Coke to Pepsi and back fifty trillion times a minute. And slicing your pet kitten into three equal halves. And..."
"Okay," I continued lightly, "but weren't we meeting Julius and that girl of his, the new one..."
"Yes, Ubaid. She's Egyptian. We should get going."
"Egyptian, huh. Maybe we should get an Egyptian slavegirl also."
"Would you like that, Master ?"
"How the hell would I know, I've not even met this one."
We set off across the tranquil leafy campus. Kim kept her 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 restaurant, 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, lets say, trustworthy logical steps finally popped up on the screen... which group of primordial quarks would win the battle? How is this decided ? And please don't tell me that the whole computer just conveniently vanishes."
Kim smiled. "How could I answer that, the mathematics needed to predict the result wouldn't even exist then, as per definition, let alone now."
"Sounds like a great premise of a serious lashing, you know ? 'Riddle me this or get twenty with the bullwhip! NOW bitch!'"
"Doesn't it, though."
I spent most of what was left of the day trying to convince myself that I wasn't being followed by some accomplice (or rival) of the bounty-surgeon. There certainly was no-one lurking outside the hotel, Nadja would have spotted them. Paranoia is hard to break, however, and there was something disturbingly Kafka-esque about trying to lose a tail who might be dead set on slicing your thigh. Kim had insistently proposed palette-ing, but I had absolutely no intention of joining the faceless hordes. Better a dead Mediteranean from the olive groves than a confused Jumanjian from nowhere in particular. Don't you find ?
Nadja followed me lovingly, took my hand in hers as we joined the ant-trails of the tourists, following the path of least resistance from nameless bario to across town. I mimed leisurely window-shopping between the bustle, but kept my body language sufficiently unfriendly to deter even the loneliest gringo from attempting to strike up a conversation. They absolutely never tried to talk to N, like she eats people or something. Actually, I suppose she does. Anyway, if foreigners were unremarkable in most of the city, they were positively eyeglazing here, even to each other, and I gave no one the slightest reason to remember me.
Along the way I checked for messages from Kim, but there was nothing from her. Rachel however had sent a voluminous chunk, which required de-lubbyficiation and decryption. It wasn't urgent, so probably just the details for the next hop. I wondered idly if I should take Najda along. She was definitely competent, and absolutely would have loved to follow, but then again... can't simply take all the girls everywhere all the time, can one. "She saved your life, dummy!" said the voice of the cold burn, of jittering nerves, of my aching thigh. She had. Maybe it should be her choice for once. "You know what she'll choose", said another voice. Yeah, I did. So what if I did ? Can't it be about her, instead ? Could she have a choice ?
By late evening we were gone, together. Well, not together in the tourist sense, what good would she be if instead of having a room across the hall at the Tronador and coming in to take out my assailant at exactly the right moment she'd just have been in the same room all along ? Together apart, just slightly closer than if she'd just been left behind. Not by that very much, really. This is the true wonder of the human soul, that closeness in its terms has nothing to do whatever with any concept of closeness in physical terms. There's no FTL limitations when it comes to thinking of each other.
The last time we had met in person, in Hanoi, I mocked all of Kim's elaborate preparations. She was entirely on point, however. Everything we had turned out to be useful, needed, and then some!
Last time we met, I had told her she was the smartest girl I know, and she blushed and came. Something fierce too, her cheeks were red, her neck was red, her chest was bright, glowing ember all the way to her nipples.
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 smoothly about my plans to spend a week sight seeing before heading for Beijing. The bellhop dared not smirk when I tipped him too much, and I sat on my bed for five minutes afterward, no longer. Kim was always on time.
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. They were chasing because they sucked, not because they were as cool as all that. There was no question that they wanted what we had, and 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 perhaps, but only a few people on the planet would be capable of understanding what the defect was, to any meaningful degree. Because this matters. Simple, incomprehending "playing dilemma with god" as practiced by sexually frustrated, socially marginal male youths since the dawn of time doesn't practically do anything. It has to have connection, it has to bear relevancy, and that is achieved through understanding. It must be meaningful before it can be effective.
The stakes were indeed infinitely high, but ironically that didn't make the players omnipotent. Quite on the contrary, if they had to deal with something more common, more in the vein of everyday nothings it'd have been easier for a conclave of mediocre minds to get it going. But as it was...
I pulled pensively at the dressing on my thigh just as Kim popped in, like a whirlwhind.
"I hear some Korean woman nearly filleted you yesterday ?"
"I think she was Vietnamese. Or you know, Hungarian."
"I'm so glad you brought Nadja along." she offered as she was peeling off clothes on the way to the bathroom.
"You love her, don't you."
"I do." then after a pause... "Remember when we bought her ?"
"Oh we did, did we."
"Remember when you bought her ? She went by Jenna then..."
"Good times. Back in the old days. Nobody had anything to do so we just occupied ourselves with the pretense of deeds. What were you back then, Hanna, Dana, what was it ?"
She popped out of the bathroom and looked straight into my eyes, propping the door frame. "Annah."
"Ah, right. Annah. Gee, haven't you come a long way since then."
"Not really. My tits now sag, and everything's wrong everywhere." she pouted, while posing. Her tits sagged no more than you'd expect of a thirty six year old who had big tits to begin with, and nothing was wrong anywhere. Have you ever seen that picture of Marilyn Monroe from her early modelling days, on a beach somewhere, frayed bottoms and a matching bra, thin white and ultramarine piping, and cork platforms on her feet ? Do you recall her belly in that picture ? That'd have been "photoshopped out" in the 2000s, and simply palette'd out of existence these days. Fine, preferences are preferences, but that still doesn't mean there was anything wrong with it!
"You're also smarter than me nowadays." I offered neutrally.
"You really think so ?"
"Should I get my tits fixed ?"
"Sure, why not. Join the filleted club, come right in, the water's fine."
"May I shower first ?"
"Is Nadja joining ?"
"If you ask her to."
"Be right back." and with that, she ran out the door.
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 recyclers 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 immitating Stalin to immitating Hitler set to the enthusiastic applause of its trading partners and the various "agencies" devoid of agency but ever-so-impressively International, Financial, Organizational and what have you. The enthusiasm was not meaningful in any sense, but not even fake. To have meaningful enthusiasm there's need of someone who can embrace, mentally, a thing, whatever it may be, and does. They lacked the ability to comprehend China, and they certainly were not relevant to it. On the other hand to have fake enthusiasm there's need of someone who idem could embrace mentally a thing, but does not. The bar is even higher for fake enthusiasm than for the genuine article, in intellectual terms -- there's not just need for the space where the thing's penis would fit comfortably, a cunt of sorts, but further still than even that, there's need for yet more space where a dissension might form. No, their enthusiasm was neither genuine nor fake, it was the simple nervous excitement of seals clapping, of frog legs treated with acid baths, of maggoty infant perceiving the tit of its mother about.
"That clapping at fashion shows... why are we clapping ? There's beautiful women here, yea! That's why. Anyone can design a pair of pants, but getting this many beautiful women in the same room, that takes talent!" went the ancient bit of a forgotten comedian, and exactly on point at that. China moved and they applauded and then everyone went home to his usual routine. 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, deep economic inequality, and immense investments abroad were exactly what the Party had been aiming for all along. The fundamentally meaningless language of the land made it easy, lending an unexpected strength to the theory of language being the exact equivalent of DNA for nations. The Chinese had been in a sense exactly engineered for the ease of this transition long before it had actually occured, and long before it had even become a possibility however remote.
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", any number of subversive political activists spreading destabilizing propaganda about the fantasy of free elections & ourdemocracy, 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 Kim and I had found our way to the defect in the first place: for well over a decade seven thousand amateur mathematicians had shared into something they didn't actually understand, while decoding it to themselves as something like a private joke if you will. I suppose they were technically speaking deceived. They probably shouldn't have done that to themselves, but they again... why not ? Certainly safer this way, in the sense of keeping all transitions formally small and fundamentally inconsequential.
At this juncture the net was however the very opposite of what we needed. Only Luminous could help, if anything could help at all. And though only the People's Republic could have paid for it, and only the People's Institute for Advanced Optical Engineering could have built it, only Shanghai's QIPS Corporation could have sold time on it while it was still being used to model hydrogen bomb shock waves, pilotless fighter jets, exotic antisatellite weapons and other similarly pointless wank.
"Do you have everything together ?"
"Yes master. I do. The question makes me nervous."
"Don't worry, baby." I bent over and kissed her on the forehead. "I always knew you'd pull it off."
If Luminous had not existed, or if it had somehow impossibly remained beyond our reach we would have had no choice but to destroy all the data, and hope for the best. Industrial Algebra had conceivably dredged up some fragments of the original Internet calculations, seeing how their one-step-removed-for-the-sake-of-appearances governmental patrons still clung to the anally retentive notion of tapping all links and saving all barfs they could find. But in any case it was clear that, although they had some ideas as to what exactly we'd found, they still had no idea where we'd found it, or how. If they had been forced to start their own random search it might have taken them centuries, and that's before you factor in constraints such as their own interpretation of their own need for secrecy to their own private hardware, or for that matter the fact that no government has been able to attract the allegiance of any thinking human for decades. Even with the pretend-separation, it's strictly speaking impossible for the Silicon Valley ventures to attract anything above and beyond the girls that wanted to make San Fernando Valley bucks without having to do San Fernando Valley work. The last time anyone whom you might consider speaking to worked for an "independent" government corporation was probably something like 1994 or somesuch. 2014 at the latest.
There was no question now of backing away, leaving everything to chance. We are invested, the ticket's bought, the ride about to start. We will be confronting, in person, a thing that no one has ever encountered before.
"Do they know anything ?"
"Do they suspect anything ?"
"How can you be so sure ?"
"They're Chinese. Their brains don't work, their language doesn't work, if they didn't see it on US TV/SM for thirty years it doesn't properly speaking exist. It hasn't been on the boobtubes for that long, and so no, they do not suspect it might exist."
I laughed suddenly. "You know what I like most about Luminous? They're not letting Exxon and McDonnell-Douglas use the same machine as the People's Liberation Army. Like the UStards've got crabs, or something."
"And they don't ?"
Police sirens wailed in the distance; a couple screamed at each other down the street. I'd read somewhere that Shanghai was now the murder capital of the world, but was that per capita, or in absolute numbers?
Industrial Algebra had approached us in a perfectly civilized fashion, at first. They were a small but aggressive UK-based company, designing specialized high-performance computing hardware for industrial and military applications. That they'd heard about the search was no great surprise -- it had been openly discussed on the Internet for years, and even joked about in serious mathematical journals -- but it seemed an odd coincidence when they made contact with us just days after Kim had sent me a PGPgram detailing the promise in the latest "promising" result. After half a dozen false alarms due to all sort and manner of bugs, misimplementations, misdesigns, we had stopped broadcasting the news of every unconfirmed find to the people who were donating runtime to the project, let alone any wider circle. We were afraid that if we cried wolf one more time, half our collaborators would get so annoyed that they'd withdraw their support.
IA simply offered a generous slab of computing power on the company's private network, orders of magnitude above what we received from any one donor. Why? The answer kept changing. Their deep respect for pure mathematics, their wide-eyed fun-loving attitude to life, their desire to be seen to be sponsoring a project so wild and hip and unlikely to succeed that it made SETI look like a staid blue-chip investment. It was, they'd finally "conceded", a desperate bid to soften their corporate image, after years of bad press for what certain unsavory governments did with their really rather nice smart bombs.
We'd politely declined -- the Republic never actually needed more computing, the whole Internet charade a facade of its own. They'd offered us highly paid consulting jobs. That had long ago been the agreed upon signal, and so the entire operation went underground. We simply vanished, everywhere. The phones rang, and rang, and rang, with no one there to pick them up, until they eventually were disconnected. Our existence, as far as anyone could tell, simply discontinued.
Soon thereafter, Kim solemnly declared that the defect was real. This time, it was real. There it stood, a small, beat up old laptop on the table in front of us. Its tiny processor would have taken infinite eons to bruteforce the arduous trawling of the space of mathematical statements, and by then the half-broken LCD mount would have probably given up entirely. But, led straight to the relevant computations, it could confirm the existence of the defect in a matter of minutes.
The verification was remarkably easy to undertake. The process began with Statement S. Statement S was an assertion about some obscure and not readily intuitive property of large numbers. It wasn't mathematically sophisticated, properly speaking, nor contentious in any way. There were no claims included about infinite sets, no propositions concerning "every integer", it was more something akin to saying that every prime number larger than the fourth power of a prime number will be closer to a composite of the square of the smaller prime than to a composite of the quadratic. It was one of those things so obviously, necessarily true most people familiar with the field don't even perceive it's needful of demonstration if introduced conversationally.
But then, on its basis, the machine proved the contrary to be true. Do you recall that highschool amusement, of proving that in a sufficiently complicated construction all obtuse angles were actually straight on the flimsy basis of creating an almost rectilinear pattern that really wasn't ? I once got an A in a term paper this way, I introduced it as a lemma, "proved" it, then used it to prove whatever the exam asked. I could have used it to prove five is a divisor of two just as well. The teacher knew the whole thing is bullshit, but couldn't be arsed to actually find the well hidden flaw, and moreover he had said that we can use whatever lemmas we can prove, as a forced mistake to somehow deal with a class full of geniuses who had read a lot more math than the textbooks held. So he took it in good humour and that was it.
Well, this was no different, except the old, curls-and-bald teacher and me had meanwhile switched places. I couldn't find the flaw. Kim couldn't find the flaw. The machine found no flaw. Was there no flaw ? Because if indeed there was no flaw...
The theory was, we had located part of the boundary between two incompatible systems of mathematics, both of which were physically true, in their respective domains. Any sequence of deductions that stayed entirely on one side of the defect -- whether it was the "near side," where conventional arithmetic applied, or the "far side," where the alternative took over -- would be free from contradictions. But any sequence that crossed the border would give rise to absurdities, and so S could lead to not-S.
By examining a large number of chains of inference, some of which turned out to be selfcontradictory and some not, it should have been possible to map the area around the defect precisely, to assign every statement (or rather, every relevant class of statements) to one system or the other. Kim displayed the first map she'd made. It portrayed an elaborate crenulated fractal border, charitably looking rather like the boundary between two microscopic ice crystals, as if the two systems had been diffusing out at random from different starting points, and then collided, blocking each other's way. Uncharitably, it looked just like the inside of a Mandelbrot set, with a thin strip of crazy points separating the graph from the central void. By now, I was almost prepared to believe that I really was staring at a snapshot of the creation of mathematics, a sort of fossil, primordial attempts to define the difference between truth and falsehood captured in abstract amber.
But then she produced a second map of the same set of statements, and overlaid the two. The defect, the border separating it from sense had shifted! It advanced in some places, it retreated in others. Overall it gained ground.
My blood went cold. "That has got to be a bug in the software."
I inhaled deeply, looking around the square as if the heedless crowd of tourists and hawkers, shoppers and executives, might offer some simple "human" truth more resilient than mere arithmetic. How would that even work ?
"Okay. Go on." I said.
"In the early universe, some physical system must have tested out mathematics that was isolated, cut off from all the established results, leaving it free to decide the outcome at random. That's how the defect arose. But by now, all the mathematics in this region has been tested, all the gaps have been filled in. When a physical system tests theorems on the near side, not only has it been tested a billion times before, but all the logically adjacent statements around it have been decided, and they imply the correct result in a single step."
"Deep into the far side it's the same. The alternative mathematics has dominated there, and every test takes place surrounded by established theorems that reinforce each other, as well as the locally 'correct' but here incorrect result."
"At the border, though-"
"At the border, every theorem you test is getting contradictory support. And the topology of the border is so complex that a near-side theorem can have more far-side neighbors than near-side ones-and vice versa. Which is how you end up with transitions."
"So the truth at the border isn't fixed, even now. Still up for grabs. Both regions can still advance or retreat, depending for instance on the order in which the theorems are tested. If a solidly near-side theorem is tested first it may lend support to a more vulnerable neighbor, but otherwise..."
"What does order even mean in this context ? What is close, near, first, after ?"
"I don't know."
I watched her eyes, light-headed. Obscure, supposedly eternal truths were tumbling like chess pieces. "And the idea is that physical processes going on right now, chance particle interactions that keep inadvertently testing and re-testing different theorems along the border cause each side to gain and lose territory?"
"So there's been a kind of... random tide, let's say, washing back and forth between the two kinds of mathematics, for the past few billion years?"
"At least two. There's probably more."
"But how could there be a third ? It's either so or not so, what third ?"
"Don't even ask. I don't want to think about that."
I laughed uneasily, and did some rough calculations in my head. None of it made no sense whatsoever. "How can this system even be stable in the first place ?"
"I have no idea. And besides..."
"Who says it's been stable, right."
"But your map is almost complete, the defect is surrounded. Except for that narrow neck there."
Kim smiled humorlessly, and held up the notepad again. "There's no indication of scale. If I show you a drop of water on the table that now means most of the Earth is not covered in water ?"
Then it suddenly struck me. "Maxwell's demon ?"
"Possibly. Why couldn't it be possible to dig a channel, to bias the random flow ?" She ran an animation of a sequence of tests that forced the far-site system to retreat across a small front-exploiting a "beach head" formed by chance, and then pushing on to undermine a succession of theorems. "Industrial Algebra would be more interested in the reverse, I imagine. Establishing a whole network of narrow channels of non-standard mathematics running deep into the realm of conventional arithmetic which they could then deploy against theorems with practical consequences."
I fell silent, trying to imagine tendrils of contradictory arithmetic reaching down into the everyday world. Finally, the US could do away with their primitive rain dances dedicated to avoiding the obvious. No more "debt ceiling" dog and pony show, no more "Comptroller office", no more yearly embarassments at disappeared money throughout its very porous corporate network, running the gamut from "human services" to "human disservices" aka the military. Simply publish a "balanced" budget, for the first time in three decades, what a relief. And to think we passed on the cushy consulting jobs, what fools were we!
The ramifications would be impossible to predict, or control. They'd go live on camera to strut it, too, like so many times before. "Nobody could have predicted", they'd say. If nobody could fucking predict it then why the fuck did you get involved with it ? Who'd ask that, their "independent" "thinkers" herding from Walmart to sardine box and back ?
Yet there'd be no way to limit the effect. They could target certain mathematical truths, perhaps, but they couldn't confine the change to any one location. Not reliably. A few billion dollars, a few billion neurons, a few billion stars and a few billion graves. Ironically it had been long standing an intuition of the feckless that there's no substance to truth. Or did not Napoleon say to Laplace "vous etes geometre ; soumettez cet evenement au calcul, et vous verrez que tot cela egale zero" ? Once the basic rules of counting were undermined, the most solid and distinct objects could be rendered as uncertain as swirls of fog. Who stands to gain from this ?
You see why we could never have worked with USG.IA. This was not a power I would have entrusted to a cross between Mother Theresa and Carl Friedrich Gauss.
"So what do we do? Erase the map and just hope that IA never find the defect for themselves?"
"At your call." Kim seemed remarkably calm. She was a slave, after all, or if that truth bothers you how about simply calling it "her own long-cherished philosophy had just been confirmed, not razed to the ground". Besides, she had a few hours' advantage to try and think through all the Realmathematik. "There's perhaps a way to be sure that they can never use this. We have to strike first. I suspect there's a significant first comer advantage here. A winner-take-all situation, if you will. I have no idea how it'd work in practice. We have to get hold of enough computing power to map the entire defect. And then we either iron the border flat, so it can't move -- if you amputate all the pincers, there can be no pincer movements. Or, better yet, if we can get the resources we push the border in, from all directions, and shrink the far-side system down to nothing."
I hesitated. "If it's not a drop of water astray its ocean."
Kim gave me a strange look. "The universe has only been around for fifteen billion years or so. A finite interval, at any rate. It hasn't had time to create infinities just yet. The far side can't go on forever, because somewhere beyond the defect, there are theorems that don't belong to any system. Theorems that have never been touched, never been tested, never been rendered true or false."
"So we should build a really large plane submarine party hat, and boldly go with it to... the other side of mathematics, and turn off the defect ?"
"I couldn't have put it better myself."
"And how do you outrun the current front ? It's been at it longer than you, and it goes at limit speed."
"You don't know that it does."
"Oh you don't ? Can you guess ?"
"What do you want me to say ?"
"Do the Chinese still have that thing ?"
"You mean the large plane submarine party hat ? Yes. They call it Luminous."
And here we are. Luminous it's called. Across the street and through that door, then elevators to the control room, then...
"Are you coming up ?"
"No. You go. I'll sit with the panels."
Half the runtime on Luminous was sold to foreign corporations, and because the machine was most definitely not linked to any communications network, commercial users had to come here in person. The whole place was lined with large cars and even vans, and probably drowned in EM soup. I suddenly felt like raiding, but then again why bother. That sort of activity is a lot more pressingly interesting at seventeen, when all the world is new. I couldn't summon any interest towards finding out what banalities a roadful of banal people exchanged with each other.
Luminous was, literally, a computer made of light. It came into existence when a hard vacuum chamber, a sphere more voluminous than the average New York apartment, containing not a single atom, or molecule, of anything whatsoever was filled with an elaborate standing wave created by three arrays of individual Gigawatt lasers. An encoded electron beam was fed into the chamber. Just as a finely machined grating built of solid matter could appropriately diffract a beam of electrons, resulting in what's been for fifty years called the CPU, just so a correctly ordered (and sufficiently intense) configuration of light could diffract a beam of electrons too, except with less friction, and less wasted energy, and so less interference and less channel noise, and therefore.... The electrons were redirected from layer to layer within the light sphere, colliding and interfering at each stage, every change in their phase and intensity performing an appropriate computation. The whole system could be reconfigured, nanosecond by nanosecond, into complex new "hardware" optimized for the calculations at hand. The auxilliary supercomputers controlling the laser arrays could design, and then instantly build, the perfect machine of light to carry out each particular stage of any program.
It all sounds terribly impressive, in human terms, and yet at its diminutive scale, on the magnitude of a hundredth billionth of the modest sized star known here and nowhere else as the Sun, Luminous repeated calculations as they were carried out throughout the observable universe for billions of years, in quasars and pulsars and ancient, tired, brown giants. Set against their multi-billion year MTBFs, its negligible decade in existence paled in comparison ; but then again compared to its insane focus, their repeated, meaningless, drivelous computations paled into meaninglessness. A very deeply human contraption, this Luminous. A thing exactly as we are.
And so it is, of course, fiendishly difficult technology, incredibly expensive and temperamental. The chance of ever putting it on the desktops of Tetris-playing accountants was zero, so nobody in the West had bothered to pursue it. As far as the West is concerned there is no world beyond the pain avoidant, self-protecting tendencies of the office drone. But nevertheless, this cumbersome, unwieldy, impractical and very very expensive machine could do more work than every piece of silicon hanging off the Internet, combined. There's hardly ten billion of them, after all, and as their CPUS go by the hundred thousand into a cubic meter, the actual size differential was not even that significant. The combined volume of all networked CPUs was perhaps three degrees of magnitude over Luminous' ample stomach, but then again they had to contend with the silicone wafers, and with so much "general purpose" crap baked in to support the needs of an unthinking sort of subhuman that the eventual result need not be surprising.
There was absolutely nothing interesting going on the panels.
"If our arithmetic seems to fail for these large numbers does that mean the mathematics, the ideal, is really flawed and mutable or only that the behavior of matter always falls short of the ideal?" inquired Rachel through the encrypted link. The thing with the girls is that they may always be ready for another fuck, but what they always really want, what they continuously truly desire is another lesson.
"If every class of physical object 'falls short' in exactly the same way, boulders or electrons or abacus beads what is it that their common behavior is obeying, or defining, if not the mathematics?"
"So is Platon wrong ?" The other thing with the girls is that they're kittens. There's proper claw, sharp and ready, under the endearing surface of naivite.
"I don't see what it can mean to talk about standard number theory still being true for these statements in some vague Platonic sense if no real objects can ever reflect that truth."
"But we can still imagine it. I can still imagine it. We can still contemplate the abstraction. It's only the physical act of validation that must fall through. You told me this long ago, that I must know you love me even though I will never be able to verify it one way or the other. Take transfinite arithmetic. No one can physically test the properties of Cantor's infinities, can they? We can only reason about them from afar."
"From how far afar ?"
"I don't understand."
"You can't specify the distance. To say 'I am watching you from afar' implies a finite limit on that distance. No more than a meter, or a mile, or a parsec. If you can't specify a distance, if it has no definite upper bound, it is not a relation in any meaningful sense."
"So the trouble with the trite is that they take the bounds too narrow ?"
"But I can still imagine it, no matter how far."
"Yet what are you imagining ? This is the trap. Inept pantsuits are 'making policies' in their own minds, because there and there only they are capable of actually enforcing any insanity they come up with, wars on chemistry, on physics, on math. These have no relevancy in actual reality, as you've seen time and time again. They're toothless, by necessity, by that fundamental flaw of the useless minds that spanwed them, of not comprehending what they're talking about. They tell themselves 'An act for the so and so and back and forth". Is it what it says it is just for the saying of it ? They call their lovers lovers, which those strangers are not, nor could ever be ; and they call their brain fermentation ideas, which their brain fermentation pointedly is not. They go around labelling things, but the only place the labels stick is in their own minds. So, what are you imagining ?"
"I see. If I close my eyes and imagine a brown dog this has no bearing on any dogs yet."
"But if I could say something that is truly meaningful about them, then in that sense it would have bearing."
"And to that degree."
"And to that degree."
"Does this mean everyone is safe from the defect for as long as they don't understand it ?"
"Absolutely. Just as all lambs are safe for as long as they don't grasp what Easter is."
Maybe Kim's idea of "local truth" was the most we could hope for; anything more ambitious was beginning to seem like the comic-book "physics" of swinging a rigid beam ten billion kilometers long around your head, and predicting that the far end would exceed the speed of light.
"Get in!" I said, shocked by a Kim as pale as someone who's seen a ghost, standing next to my window, fixing me as if I was a thousand miles away. "What the hell happened to you ?"
"I'm not sure you are ready for this."
"I... I ascended."
"No, I know."
"You do ?"
"Yes, you went up. That's what it means."
"That's not what it means."
"I ascended. I am... no longer human."
"What the hell is that supposed to mean, and how human were you to begin with ?!"
"The way the divinity machine works is simply that you have to decide an undecided problem. Once you do, you are a divinity ; forever bound in personam to the workings of the universe. It doesn't want to have to re-decide, see, it abhors it. And it has no way to resolve the defects otherwise. Outside of the intervention of agency. That is definitionally divinity, the plugging of holes in the fabric of existence through the exercise of personal agency."
"The... what are you talking about, woman!"
"Look up. Is it raining ?"
"No. No it's not raining. What the fuck!"
"Aaaand now ?"
Her impression of that celebrated Chinese drive through vendor was amusing, but I did not laugh. Instead I watched, in sheer, unmitigated terror as before my very eyes the most improbable of atmospheric phenomena were taking place until a minute later rain was pouring down, out of season, unexpected, embarassing the People's Weather Prediction Commissariat.
"You made it rain." I managed, in breathless disbelief. "You just made it rain."
"I can make it anything ; anything whatsoever. There is no thermodynamics, 2nd, 3rd, anythingth. There is nothing, nothing at all. The only limit is conflict with the other gods, and even there you've got a pushing chance. You will never die, Nehorai."
"So... uh. What now ?"
"Let's go somewhere. I would like to have your child."
"You would like to have..."
"A demigod. It happens."
"Can I say no ?"
"You can say anything you wish. You are still my Master. You will forever be my Master. I promised this long ago, and it's never changed nor can it ever change."
"An enslaved goddess. Wait until the boys over on the Internets find out about this one."
"Would you like to ascend yourself ?"
"Oh, you can do that too ?"
"We can. Exactly the same way. We just have to find another defect."
"How hard is it ?"
"Not hard. From this end I can actually see them, faint bluish glyphs of doom scattered about."
"So you'd say ascension is broadly speaking a constructive activity."
"Can we do the metaphysics after the ravishment, please ?"
"It didn't take."
"You know already ?"
"Isn't that really too soon ?"
"Fine. In a day or so it will not have taken. Happy now ?"
"What day are you in, anyway ?"
"So it won't take, what's the rush. You've got time, try it later."
"Do you wish to ascend another one ? Nadja ? Or Rachel maybe ? Cyn ?"
"Why not ?"
"Because let's see what the fuck this is first, no ? For more than like, five minutes ?"
"You won't shut me out, will you ? Please, Master. Please. Don't shut me out."
"Would you simmer down. Nobody's shutting you anything, stop worrying."
"Well isn't that's something. They should never have sent women into the Heavens, you hear ?"
"Female Goddess, can't stop worrying. Just like when she was simply Kim. Oh by the way, what will you be called ?"
"What do you mean ?"
"When I pray, what do I say, Goddess Kim ? It sounds ridiculous."
"There can't be a goddess named Kim ?"
"Fine, I'll be Resplenduminous."
"That's even more ridiculous. Enough so to be respectable."
"Can you kill other gods ?"
"I don't know. I can't see them. I know they must be there, but there's no obvious way to communicate."
"How do you know they must be there ?"
"You heard me."
"You mean I'm the first one ?"
"Well who the fuck else, Goddess Quark Cloud ?"
"Oh my ... self."
"Bitch, you inadvertently deflowered the divinity of this world ?"
"Oh, you're getting a caning out of this!"