Permutation City

by Greg Egan

  Durham made instant coffee. Maria surveyed the spartan room. She said, “This isn’t good enough, you know. We should have two hundred people wearing headsets, and a giant screen taking up an entire wall. Like one of the old NASA missions.”

  Durham spoke over the sound of boiling water. “Don’t worry: we’ll be using more computing power per second than NASA used for the entire Apollo program.”

  Computing power. One more thing to worry about. Maria logged on to the QIPS exchange; the rate was up slightly since she’d last checked, but so far there was no sign of what she dreaded. In the event that Operation Butterfly entered the market again, today of all days, the Garden of Eden would be frozen out, postponed until the QIPS rate returned to normal levels. That wouldn’t make the slightest difference to Durham or his followers – even if the launch program was thrown off the network half-way through, and only completed days, or weeks, later. Real time was irrelevant. Maria could appreciate the logic of that – but the thought of a delay, or an unexpected slowdown, still made her sick with anxiety. Every legal opinion she’d obtained had made it clear that neither she nor Durham were likely to face prosecution – and if charges were brought against them, a conviction was highly improbable … and even if that happened, an appeal would almost certainly succeed. Nonetheless, every day she’d spent working with Durham as a knowing “accomplice” had made her feel more vulnerable to the whims of the authorities. Hayden had treated her icily when she’d confessed to having abandoned her laughable “undercover” role. The risk of harassment would hardly vanish the moment the project was completed – but the relief would still be considerable.

  She was beginning to regret having honored her promise not to try to record Durham’s clients’ statements assuring her that they were fully informed participants in the scheme. The authenticated messages she’d viewed – on public terminals – might not have been the equivalent of human testimony, but having them stored away on a chip somewhere would have made her feel a lot more secure. Regardless of the legal status of the Copies, she couldn’t imagine being prosecuted for fraud if she could show that the de facto “victims of the crime” knew exactly what they were paying for.

  Durham set her coffee down on the table. Maria mumbled thanks as he sat beside her. He said, “No last-minute qualms? You can still back out if you want to.”

  She kept her eyes on the screen, the flickering pie-chart of the QIPS exchange. “Don’t tempt me.” As if she’d seriously consider blowing her one real chance to have Francesca scanned – after all the work, all the anxiety – for no better reason than a laughable, microscopic fear that this artificial universe might actually blossom into self-contained existence.

  Durham’s terminal beeped. Maria glanced at his screen; a message box said PRIORITY COMMUNICATION. She looked away as he viewed the text.

  “Speaking of last-minute qualms, Riemann’s changed his mind. He wants in.”

  Maria said irritably, “Well, tell him it’s too late. Tell him he’s missed the boat.” She wasn’t serious; from what she knew of the project’s finances, Durham had been set to barely break even by the end of the day. The price of one more ticket would transform his fortunes completely.

  He said, “Relax – it will take half an hour at most to fit him in. And his fee will cover much more than the increase in data; we’ll be able to run the whole launch a bit longer.”

  Maria had to pause to let that sink in. Then she said, “You’re going to blow most of two million euros on stretching out something that—”

  Durham smiled. “That what? That would have worked anyway?”

  “That you believe would have worked anyway!”

  “The longer I get to see my Copy observing the TVC universe, the happier I’ll be. I don’t know what it will take to anchor the automaton rules – but if ten watertight experiments sounds good, then eleven sounds better.”

  Maria pushed her chair back and walked away from her terminal. Durham tapped at his keyboard, first invoking the programs which would recompute the Garden-of-Eden configuration to include the new passenger and his luggage – then directing the windfall from Riemann straight into the project’s JSN account.

  She said, “What’s wrong with you? Two million euros is more than two million dollars! You could have lived on that for the rest of your life!”

  Durham kept typing, passing Riemann’s documents through a series of legal checks. “I’ll get by.”

  “Give it to charity, then!”

  Durham frowned, but said patiently, “I gather that Thomas Riemann gives generously to famine relief and crop research every year. He chose to spend this money on a place in my sanctuary; it’s hardly my role to channel his funds into whatever you or I decide is the worthiest cause.” He glanced at her and added, mock-solemnly, “That’s called fraud, Ms. Deluca. You can go to prison for that.”

  Maria was unmoved. “You could have kept something for yourself. For this life, this world. I don’t imagine any of your clients expected you to do all this for nothing.”

  Durham finished at the terminal and turned to her. “I don’t expect you to understand. You treat the whole project as a joke – and that’s fine. But you can hardly expect me to run it on that basis.”

  Maria didn’t even know what she was angry about any more: the delayed launch, the obscene waste of money – or just Durham sitting there making perfect sense to himself, as always.

  She said, “The project is a joke. Three hundred million people are living in refugee camps, and you’re offering sanctuary to sixteen billionaires! What do they need protection from? There’s never going to be an anti-Copy revolution! They’re never going to be shut down! You know as well as I do that they’ll just sit there getting richer for the next ten thousand years!”

  “Possibly.”

  “So you are a fraud then, aren’t you? Even if your ‘sanctuary’ really does come into existence – even if you prove your precious theory right – what have your backers gained? You’ve sent their clones into solitary confinement, that’s all. You might as well have put them in a black box at the bottom of a mine shaft.”

  Durham said mildly, “That’s not quite true. You talk about Copies surviving ten thousand years. What about ten billion? A hundred billion?”

  She scowled. “Nothing’s going to last that long. Haven’t you heard? They’ve found enough dark matter to reverse the expansion of the universe in less than forty billion years—”

  “Exactly. This universe isn’t going to last.”

  Maria nodded sarcastically, and tried to say something belittling, but the words stuck in her throat.

  Durham continued blithely, “The TVC universe will never collapse. Never. A hundred billion years, a hundred trillion; it makes no difference, it will always be expanding.”

  Maria said weakly, “Entropy—”

  “Is not a problem. Actually, ‘expanding’ is the wrong word; the TVC universe grows like a crystal, it doesn’t stretch like a balloon. Think about it. Stretching ordinary space increases entropy; everything becomes more spread out, more disordered. Building more of a TVC cellular automaton jut gives you more room for data, more computing power, more order. Ordinary matter would eventually decay, but these computers aren’t made out of matter. There’s nothing in the cellular automaton’s rules to prevent them from lasting forever.”

  Maria wasn’t sure what she’d imagined before; Durham’s universe – being made of the same “dust” as the real one, merely rearranged – suffering the same fate? She couldn’t have given the question much thought, because that verdict was nonsensical. The rearrangement was in time as well as space; Durham’s universe could take a point of space-time from just before the Big Crunch, and follow it with another from ten million years BC. And even if there was only a limited amount of “dust” to work with, there was no reason why it couldn’t be reused in different combinations, again and again. The fate of the TVC automaton would only have to make internal sense – and the thing wou
ld have no reason, ever, to come to an end.

  She said, “So you promised these people … immortality?”

  “Of course.”

  “Literal immortality? Outliving the universe?”

  Durham feigned innocence, but he was clearly savoring the shock he’d given her. “That’s what the word means. Not: dying after a very long time. Just: not dying, period.”

  Maria leaned back against the wall, arms folded, trying to cast aside the feeling that the whole conversation was as insubstantial as anything Durham had hallucinated in the Blacktown psychiatric ward. She thought: When Francesca’s been scanned, I’m going to take a holiday. Visit Aden in Seoul, if I have to. Anything to get away from this city, this man.

  She said, “Ideas like that are powerful things. One of these days you’re going to hurt someone.”

  Durham looked wounded himself, at that. He said, “All I’ve tried to do is be honest. I know: I lied to you, at first – and I’m sorry. I had no right to do that. But what was I supposed to do with the truth? Keep it locked up in my head? Hide it from the world? Give no one else the chance to believe, or disbelieve?” He fixed his eyes on her, calm and sane as ever; she looked away.

  He said, “When I first came out of hospital, I wanted to publish everything. And I tried … but nobody reputable was interested – and publishing in the junk-science journals would have been nothing but an admission that it was all bullshit. So what else could I do, except look for private backers?”

  Maria said, “I understand. Forget it. You’ve done what you thought you had to – I don’t blame you for that.” The clichés nearly made her gag, but all she could think about was shutting him up. She was sick of being reminded that the ideas which were nothing but a means to an end, for her – the ideas she could turn her back on forever, in eight hours’ time – were this man’s entire life.

  He looked at her searchingly, as if genuinely seeking guidance. “If you’d believed everything I believe, would you have kept it all to yourself? Would you have lived out your life pretending to the world that you’d merely been insane?”

  Maria was saved from answering by a beep from Durham’s terminal. The Garden-of-Eden configuration had been recomputed; Thomas Riemann’s snapshot was now built into their cellular automaton equivalent of the Big Bang.

  Durham swung his chair around to face the screen. He said cheerfully, “All aboard the ship of fools!”

  Maria took her place beside him. She reached over and tentatively touched his shoulder. Without looking at her, he reached up and squeezed her hand gently, then removed it.

  Following a long cellular automaton tradition, the program which would bootstrap the TVC universe into existence was called FIAT. Durham hit a key, and a starburst icon appeared on both of their screens.

  He turned to Maria. “You do the honors.”

  She was about to object, but then it didn’t seem worth arguing. She’d done half the work, but this was Durham’s creation, whoever cut the ribbon.

  She prodded the icon; it exploded like a cheap flashy firework, leaving a pin-cushion of red and green trails glowing on the screen.

  “Very tacky.”

  Durham grinned. “I thought you’d like it.”

  The decorative flourish faded, and a shimmering blue-white cube appeared: a representation of the TVC universe. The Garden-of-Eden state had contained a billion ready-made processors, a thousand along each edge of the cube – but that precise census was already out of date. Maria could just make out the individual machines, like tiny crystals; each speck comprised sixty million automaton cells – not counting the memory array, which stretched into the three extra dimensions, hidden in this view. The data pre-loaded into most of the processors was measured in terabytes: scan files, libraries, databases; the seed for Planet Lambert – and its sun, and its three barren sibling planets. Everything had been assembled, if not on one physical computer – the TVC automaton was probably spread over fifteen or twenty processor clusters – at least as one logical whole. One pattern.

  Durham reduced the clock rate until the blue-white shimmer slowed to a stroboscopic flickering, then a steady alternation of distinct colors. The outermost processors were building copies of themselves; in this view, blue coded for complete, working processors, and white coded for half-finished machines. Each layer of blue grew a layer of white, which abruptly turned blue, and so on. The skin of this universe came with instructions to build one more layer exactly like itself (including a copy of the same instructions), and then wait for further commands to be passed out from the hub.

  Durham zoomed in by a factor of two hundred, slowed down the clock rate further, and then changed the representation to show individual automaton cells as color-coded symbols. The processors were transformed from featureless blue or white boxes into elaborate, multi-colored, three-dimensional mazes, rectilinear filigree alive with sparks of light.

  In the throes of reproduction, each processor could be seen sprouting hundreds of pairs of fine red and green “construction wires”, which grew straight out into the surrounding empty space – until they all reached the same predetermined length, abruptly turned a tight one-hundred-and-eighty degrees, and then started growing back in the opposite direction. Glowing with elaborate moving striations, the wires zigzagged back and forth between the surface of the mother computer and an unmarked boundary plane – until between them, they’d filled in the region completely, like some strange electronic silk weaving itself into a solid cocoon.

  In close-up, the wires resolved into long lines of cells marked with arrowheads, some rendered in the brighter hues which represented “activated” states. Glowing stripes built from the binary code of bright and dim moved down the wire from arrow to arrow: the data of the blueprint for the daughter machine being shuffled out from the central memory.

  With the clock rate slowed still further, the process could be followed in detail. Wherever a pulse of brightness reached the end of a construction wire, the transparent “vacuum” of the null state was transformed into an “embryonic” cell, shown as a nondescript gray cube. Subsequent data told the new cell what to become – each pulse, or absence of a pulse, converting it into a slightly more specialized transition state, zeroing in on the particular final state required. The construction wires grew out from the mother computer using this principle, extending themselves by building more of themselves at their tips.

  Having filled the entire region which the daughter machine would occupy, they then worked backward, retracting one step at a time; unweaving their zigzag cocoon, and leaving behind whatever the blueprint required. The whole process looked grotesquely inefficient – far more time was spent on extending and retracting the wires themselves than on creating the cells of the daughter machine – but it kept the rules of the automaton as simple as possible.

  Durham said, “This all looks fine to me. Okay to proceed?”

  “Sure.” Maria had grown mesmerized; she’d forgotten her urgency, forgotten herself. “Crank it up.” At any speed where they could keep track of events at the level of individual processors – let alone individual cells – nothing useful would ever get done. Durham let the clock rate revert to the maximum they could afford, and the grid became a blur.

  In contrast, the next stage would be painfully slow. Durham made coffee and sandwiches. All the overheads of running a Copy on a system of computers which was, itself, a simulation, added up to a slowdown of about two hundred and fifty. More than four real-time minutes to a subjective second. There was no question of two-way communication – the TVC universe was hermetic, no data which hadn’t been present from the outset could affect it in any way – but they could still spy on what was happening. Every hour, they could witness another fourteen seconds of what the Copy of Durham had done.

  Maria spot-checked at other levels, starting with the software running directly on the TVC grid. The “machine language” of the TVC computers was about as arcane and ridiculous as that of any hypothetical T
uring machine, six-dimensional or not, but it had been simple enough to instruct a metaprogrammer to write – and rigorously validate – a program which allowed them to simulate conventional modern computers. So the processor clusters in Tokyo or Dallas or Seoul were simulating a cellular automaton containing a lattice of bizarre immaterial computers … which in turn were simulating the logic (if not the physics) of the processor clusters themselves. From there on up, everything happened in exactly the same way as it did on a real machine – only much more slowly.

  Maria munched cheese and lettuce between thick slices of white bread. It was a Tuesday afternoon; most of the flats around them were silent, and the street below was lifeless. The neighboring office blocks had no tenants, just a few furtive squatters; where the sun penetrated the nearest building at just the right angle, Maria could see clothes hung out to dry on lines stretched between office partitions.

  Durham put on music, a twentieth-century opera called Einstein on the Beach. He didn’t own a sound system, but he called up the piece from a library he’d bought for the Garden of Eden, and had a background task play it through his terminal’s speakers.

  Maria asked, “What will you do with yourself when this is over?”

  Durham replied without hesitation. “Finish the whole set of fifty experiments. Start Planet Lambert unfolding. Celebrate for about a week. Stroll down the main street of Permutation City. Wait for your little locking device to disengage. Wake up my passengers in their own private worlds – and hope that some of them are willing to talk to me, now and then. Start catching up on Dostoyevsky. In the original—”