Free Luminous by Greg Egan Page B

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 limo u sines, 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 o r ange, 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 di s turbing.
    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 flirt a tion—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 e n tail. One particle floating in a quantum vacuum needs half the major results of group theory, fun c tional 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 Ev e rything . . . 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 mathema t ics 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