Axiomatic

by Greg Egan

  When the measurement is over, the computer inside the binoculars flashes up coordinates for the centre’s estimated position. It’s about sixty metres from the building the blue-haired woman pointed out; well within the margin of error. So perhaps she was telling the truth—but that changes nothing. I must still ignore her.

  As I start towards my target, I wonder: Maybe I was ambushed back in that alley, after all. Maybe I was given the mutant’s location as a deliberate attempt to distract me, to divide me. Maybe the woman tossed a coin to split the universe: heads for a tip-off, tails for none—or threw dice, and chose from a wider list of strategies.

  It’s only a theory… but it’s a comforting idea: if that’s the best the whirlpool cult can do to protect the object of their devotion, then I have nothing to fear from them at all.

  * * *

  I avoid the major roads, but even on the side streets it’s soon clear that the word is out. People run past me, some hysterical, some grim; some empty-handed, some toting possessions; one man dashes from door to door, hurling bricks through windows, waking the occupants, shouting the news. Not everyone’s heading in the same direction; most are simply fleeing the ghetto, trying to escape the whirlpool, but others are no doubt frantically searching for their friends, their families, their lovers, in the hope of reaching them before they turn into strangers. I wish them well.

  Except in the central disaster zone, a few hard-core dreamers will stay put. Shifting doesn’t matter to them; they can reach their dream lives from anywhere—or so they think. Some may be in for a shock; the whirlpool can pass through worlds where there is no supply of S—where the mutant user has an alter ego who has never even heard of the drug.

  As I turn into a long, straight avenue, the naked-eye view begins to take on the jump-cut appearance that the binoculars produced, just fifteen minutes ago. People flicker, shift, vanish. Nobody stays in sight for long; few travel more than ten or twenty metres before disappearing. Many are flinching and stumbling as they run, balking at empty space as often as at real obstacles, all confidence in the permanence of the world around them, rightly, shattered. Some run blindly with their heads down and their arms outstretched. Most people are smart enough to travel on foot, but plenty of smashed and abandoned cars strobe in and out of existence on the roadway. I witness one car in motion, but only fleetingly.

  I don’t see myself any where about; I never have yet. Random scatter should put me in the same world twice, in some worlds—but only in a set of measure zero. Throw two idealised darts at a dartboard, and the probability of twice hitting the same point—the same zero-dimensional point—is zero. Repeat the experiment in an uncountably infinite number of worlds, and it will happen—but only in a set of measure zero.

  The changes are most frantic in the distance, and the blur of activity retreats to some extent as I move—due as it is, in part, to mere separation—but I’m also heading into steeper gradients, so I am, slowly, gaining on the havoc. I keep to a measured pace, looking out for both sudden human obstacles and shifts in the terrain.

  The pedestrians thin out. The street itself still endures, but the buildings around me are beginning to be transformed into bizarre chimeras, with mismatched segments from variant designs, and then from utterly different structures, appearing side by side. It’s like walking through some holographic architectural identikit machine on overdrive. Before long, most of these composites are collapsing, unbalanced by fatal disagreements on where loads should be borne. Falling rubble makes the footpath dangerous, so I weave my way between the car bodies in the middle of the road. There’s virtually no moving traffic now, but it’s slow work just navigating between all this ‘stationary’ scrap metal. Obstructions come and go; it’s usually quicker to wait for them to vanish than to backtrack and look for another way through. Sometimes I’m hemmed in on all sides, but never for long.

  Finally, most of the buildings around me seem to have toppled, in most worlds, and I find a path near the edge of the road that’s relatively passable. Nearby, it looks like an earthquake has levelled the ghetto. Looking back, away from the whirlpool, there’s nothing but a grey fog of generic buildings; out there, structures are still moving as one—or near enough to remain standing—but I’m shifting so much faster than they are that the skyline has smeared into an amorphous multiple exposure of a billion different possibilities.

  A human figure, sliced open obliquely from skull to groin, materialises in front of me, topples, then vanishes. My guts squirm, but I press on. I know that the very same thing must be happening to versions of me—but I declare it, I define it, to be the death of strangers. The gradient is so high now that different parts of the body can be dragged into different worlds, where the complementary pieces of anatomy have no good statistical reason to be correctly aligned. The rate at which this fatal dissociation occurs, though, is inexplicably lower than calculations predict; the human body somehow defends its integrity, and shifts as a whole far more often than it should. The physical basis for this anomaly has yet to be pinned down—but then, the physical basis for the human brain creating the delusion of a unique history, a sense of time, and a sense of identity, from the multifurcating branches and fans of superspace, has also proved to be elusive.

  The sky grows light, a weird blue-grey that no single overcast sky ever possessed. The streets themselves are in a state of flux now; every second or third step is a revelation—bitumen, broken masonry, concrete, sand, all at slightly different levels—and briefly, a patch of withered grass. An inertial navigation implant in my skull guides me through the chaos. Clouds of dust and smoke come and go, and then—

  A cluster of apartment blocks, with surface features flickering, but showing no signs of disintegrating. The rates of shift here are higher than ever, but there’s a counterbalancing effect: the worlds between which the flow runs are required to be more and more alike, the closer you get to the dreamer.

  The group of buildings is roughly symmetrical, and it’s perfectly clear which one lies at the centre. None of me would fail to make the same judgement, so I won’t need to go through absurd mental contortions to avoid acting on the tip-off.

  The front entrance to the building oscillates, mainly between three alternatives. I choose the leftmost door; a matter of procedure, a standard which The Company managed to propagate between itselves before I was even recruited. (No doubt contradictory instructions circulated for a while, but one scheme must have dominated, eventually, because I’ve never been briefed any differently.) I often wish I could leave (and/or follow) a trail of some kind, but any mark I made would be useless, swept downstream faster than those it was meant to guide. I have no choice but to trust in procedure to minimise my dispersion.

  From the foyer, I can see four stairwells—all with stairs converted into piles of flickering rubble. I step into the leftmost, and glance up; the early-morning light floods in through a variety of possible windows. The spacing between the great concrete slabs of the floors is holding constant; the energy difference between such large structures in different positions lends them more stability than all the possible, specific shapes of flights of stairs. Cracks must be developing, though, and given time, there’s no doubt that even this building would succumb to its discrepancies—killing the dreamer, in world after world, and putting an end to the flow. But who knows how far the whirlpool might have spread by then?

  The explosive devices I carry are small, but more than adequate. I set one down in the stairwell, speak the arming sequence, and run. I glance back across the foyer as I retreat, but at a distance, the details amongst the rubble are nothing but a blur. The bomb I’ve planted has been swept into another world, but it’s a matter of faith—and experience—that there’s an infinite line of others to take its place.

  I collide with a wall where there used to be a door, step back, try again, pass through. Sprinting across the road, an abandoned car materialises in front of me; I skirt around it, drop behind it, cover my head.


  Eighteen. Nineteen. Twenty. Twenty-one. Twenty-two?

  Not a sound. I look up. The car has vanished. The building still stands—and still flickers.

  I climb to my feet, dazed. Some bombs may have—must have—failed… but enough should have exploded to disrupt the flow.

  So what’s happened? Perhaps the dreamer has survived in some small, but contiguous, part of the flow, and it’s closed off into a loop—which it’s my bad luck to be a part of. Survived how? The worlds in which the bomb exploded should have been spread randomly, uniformly, everywhere dense enough to do the job… but perhaps some freak clustering effect has given rise to a gap.

  Or maybe I’ve ended up squeezed out of part of the flow. The theoretical conditions for that have always struck me as far too bizarre to be fulfilled in real life… but what if it has happened? A gap in my presence, downstream from me, would have left a set of worlds with no bomb planted at all—which then flowed along and caught up with me, once I moved away from the building and my shift rate dropped.

  I ‘return’ to the stairwell. There’s no unexploded bomb, no sign that any version of me has been here. I plant the backup device, and run. This time, I find no shelter on the street, and I simply hit the ground.

  Again, nothing.

  I struggle to calm myself, to visualise the possibilities. If the gap without bombs hadn’t fully passed the gap without me, when the first bombs went off, then I’d still have been missing from a part of the surviving flow—allowing exactly the same thing to happen all over again.

  I stare at the intact building, disbelieving. I am the ones who succeed. That’s all that defines me. But who, exactly, failed? If I was absent from part of the flow, there were no versions of me in those worlds to fail. Who takes the blame? Who do I disown? Those who successfully planted the bomb, but ‘should have’ done it in other worlds? Am I amongst them? I have no way of knowing.

  So, what now? How big is the gap? How close am I to it? How many times can it defeat me?

  I have to keep killing the dreamer, until I succeed.

  I return to the stairwell. The floors are about three metres apart. To ascend, I use a small grappling hook on a short rope; the hook fires an explosive-driven spike into the concrete floor. Once the rope is uncoiled, its chances of ending up in separate pieces in different worlds is magnified; it’s essential to move quickly.

  I search the first storey systematically, following procedure to the letter, as if I’d never heard of Room 522. A blur of alternative dividing walls, ghostly spartan furniture, transient heaps of sad possessions. When I’ve finished, I pause until the clock in my skull reaches the next multiple of ten minutes. It’s an imperfect strategy—some stragglers will fall more than ten minutes behind—but that would be true however long I waited.

  The second storey is deserted, too. But a little more stable; there’s no doubt that I’m drawing closer to the heart of the whirlpool.

  The third storey’s architecture is almost solid. The fourth, if not for the abandoned ephemera flickering in the corners of rooms, could pass for normal.

  The fifth—

  I kick the doors open, one by one, moving steadily down the corridor. 502. 504. 506. I thought I might be tempted to break ranks when I came this close, but instead I find it easier than ever to go through the motions, knowing that I’ll have no opportunity to regroup. 516. 518. 520.

  At the far end of Room 522, there’s a young woman stretched out on a bed. Her hair is a diaphanous halo of possibilities, her clothing a translucent haze, but her body looks solid and permanent, the almost-fixed point about which all the night’s chaos has spun.

  I step into the room, take aim at her skull, and fire. The bullet shifts worlds before it can reach her, but it will kill another version, downstream. I fire again and again, waiting for a bullet from a brother assassin to strike home before my eyes—or for the flow to stop, for the living dreamers to become too few, too sparse, to maintain it.

  Neither happens.

  ‘You took your time.’

  I swing around. The blue-haired woman stands outside the doorway. I reload the gun; she makes no move to stop me. My hands are shaking. I turn back to the dreamer and kill her, another two dozen times. The version before me remains untouched, the flow undiminished.

  I reload again, and wave the gun at the blue-haired woman. ‘What the fuck have you done to me? Am I alone? Have you slaughtered all the others?’ But that’s absurd—and if it were true, how could she see me? I’d be a momentary, imperceptible flicker to each separate version of her, nothing more; she wouldn’t even know I was there.

  She shakes her head, and says mildly, ‘We’ve slaughtered no one. We’ve mapped you into Cantor dust, that’s all. Every one of you is still alive—but none of you can stop the whirlpool.’

  Cantor dust. A fractal set, uncountably infinite, but with measure zero. There’s not one gap in my presence; there’s an infinite number, an endless series of ever-smaller holes, everywhere. But—

  ‘How? You set me up, you kept me talking, but how could you coordinate the delays? And calculate the effects? It would take…’

  ‘Infinite computational power? An infinite number of people?’ She smiles faintly. ‘I am an infinite number of people. All sleepwalking on S. All dreaming each other. We can act together, in synch, as one—or we can act independently. Or something in between, as now: the versions of me who can see and hear you at any moment are sharing their sense data with the rest of me.’

  I turn back to the dreamer. ‘Why defend her? She’ll never get what she wants. She’s tearing the city apart, and she’ll never even reach her destination.’

  ‘Not here, perhaps.’

  ‘Not here? She’s crossing all the worlds she lives in! Where else is there?’

  The woman shakes her head. ‘What creates those worlds? Alternative possibilities for ordinary physical processes. But it doesn’t stop there; the possibility of motion between worlds has exactly the same effect. Superspace itself branches out into different versions, versions containing all possible cross-world flows. And there can be higher-level flows, between those versions of superspace, so the whole structure branches again. And so on.’

  I close my eyes, drowning in vertigo. If this endless ascent into greater infinities is true—

  ‘Somewhere, the dreamer always triumphs? Whatever I do?’

  ‘Yes.’

  ‘And somewhere, I always win? Somewhere, you’ve failed to defeat me?’

  ‘Yes.’

  Who am I? I’m the ones who succeed. Then who am I? I’m nothing at all. A set of measure zero.

  I drop the gun and take three steps towards the dreamer. My clothes, already tattered, part worlds and fall away.

  I take another step, and then halt, shocked by a sudden warmth. My hair, and outer layers of skin, have vanished; I’m covered with a fine sweat of blood. I notice, for the first time, the frozen smile on the dreamer’s face.

  And I wonder: in how many infinite sets of worlds will I take one more step? And how many countless versions of me will turn around instead, and walk out of this room? Who exactly am I saving from shame, when I’ll live and die in every possible way?

  Myself.

  The Hundred-Light-Year Diary

  Martin Place was packed with the usual frantic lunchtime crowds. I scanned the faces nervously; the moment had almost arrived, and I still hadn’t even caught sight of Alison. One twenty-seven and fourteen seconds. Would I be mistaken about something so important? With the knowledge of the mistake still fresh in my mind? But that knowledge could make no difference. Of course it would affect my state of mind, of course it would influence my actions—but I already knew exactly what the net result of that, and every other, influence would be: I’d write what I’d read.

  I needn’t have worried. I looked down at my watch, and as 1:27:13 became 1:27:14, someone tapped me on the shoulder. I turned; it was Alison, of course. I’d never seen her before, in the flesh, but I’d soon devo
te a month’s bandwidth allocation to sending back a Barnsley-compressed snapshot. I hesitated, then spoke my lines, awful as they were:

  ‘Fancy meeting you here.’

  She smiled, and suddenly I was overwhelmed, giddy with happiness—exactly as I’d read in my diary a thousand times, since I’d first come across the day’s entry at the age of nine; exactly as I would, necessarily, describe it at the terminal that night. But—foreknowledge aside—how could I have felt anything but euphoria? I’d finally met the woman I’d spend my life with. We had fifty-eight years together ahead of us, and we’d love each other to the end.

  ‘So, where are we going for lunch?’

  I frowned slightly, wondering if she was joking—and wondering why I’d left myself in any doubt. I said, hesitantly, ‘Fulvio’s. Didn’t you…?’ But of course she had no idea of the petty details of the meal; on 14 December, 2074, I’d write admiringly: A. concentrates on the things that matter; she never lets herself be distracted by trivia.

  I said, ‘Well, the food won’t be ready on time; they’ll have screwed up their schedule, but—’

  She put a finger to her lips, then leant forward and kissed me. For a moment, I was too shocked to do anything but stand there like a statue, but after a second or two, I started kissing back.

  When we parted, I said stupidly, ‘I didn’t know… I thought we just… I—’

  ‘James, you’re blushing.’

  She was right. I laughed, embarrassed. It was absurd: in a week’s time, we’d make love, and I already knew every detail—yet that single unexpected kiss left me flustered and confused.

  She said, ‘Come on. Maybe the food won’t be ready, but we have a lot to talk about while we’re waiting. I just hope you haven’t read it all in advance, or you’re going to have a very boring time.’

  She took my hand and started leading the way. I followed, still shaken. Halfway to the restaurant, I finally managed to say, ‘Back then—did you know that would happen?’