Permutation City

by Greg Egan

  Durham nodded. He looked dazed, but happy. “Answer them. Give them the TVC rules.”

  Repetto was surprised. “Are you sure? That wasn’t the plan—”

  “What are we going to do? Tell them it’s none of their business?”

  “I’ll translate the rules. Give me five seconds.”

  Mouthpiece began a new dance. The waving carpet dispersed, then began to fall into step.

  Durham turned to Maria. “This is better than we’d dared to hope. This way, they reinforce us. They won’t just stop challenging our version; they’ll help to affirm it.”

  Zemansky said, “They haven’t accepted it yet. All they’ve said is that the first part of what we’ve told them makes no sense alone. They might ask about real-world physics, next.”

  Durham closed his eyes, smiling. He said quietly, “Let them ask. We’ll explain everything – right back to the Big Bang, if we have to.”

  Repetto said, puzzled, “I don’t think it’s holding.”

  Durham glanced at the swarm. “Give them a chance. They’ve barely tried it out.”

  “You’re right. But they’re already sending back a … rebuttal.”

  The swarm’s new pattern was strong and simple: a sphere, rippling with waves like circles of latitude, running from pole to pole. Repetto said, “The software can’t interpret their response. I’m going to ask it to reassess all the old data; there may be a few cases where this dance has been observed before – but too few to be treated as statistically significant.”

  Maria said, “Maybe we’ve made some kind of grammatical error. Screwed up the syntax, so they’re laughing in our face – without bothering to think about the message itself.”

  Repetto said, “Not exactly.” He frowned, like a man trying to visualize something tricky. Mouthpiece began to echo the spherical pattern. Maria felt a chill in her Elysian bowels.

  Durham said sharply, “What are you doing?”

  “Just being polite. Just acknowledging their message.”

  “Which is?”

  “You may not want to hear it.”

  “I can find out for myself, if I have to.” He took a step toward Repetto, more a gesture of impatience than a threat; a cloud of tiny blue gnat-like creatures flew up from the grass, chirping loudly.

  Repetto glanced at Zemansky; something electric passed between them. Maria was confused – they were, unmistakably, lovers; she’d never noticed before. But perhaps the signals had passed through other channels, before, hidden from her. Only now—

  Repetto said, “Their response is that the TVC rules are false – because the system those rules describe would endure forever. They’re rejecting everything we’ve told them, because it leads to what they think is an absurdity.”

  Durham scowled. “You’re talking absurdities. They’ve had transfinite mathematics for thousands of years.”

  “As a formality, a tool – an intermediate step in certain calculations. None of their models lead to infinite results. Most teams would never go so far as to try to communicate a model which did; that’s why this response is one we’ve rarely seen before.”

  Durham was silent for a while, then he said firmly, “We need time to decide how to handle this. We’ll go back, study the history of the infinite in Lambertian culture, find a way around the problem, then return.”

  Maria was distracted by something bright pulsing at the edge of her vision. She turned her head – but whatever it was seemed to fly around her as fast she tracked it. Then she realized it was the window on Elysium; she’d all but banished it from her attention, filling it in like a blind spot. She tried to focus on it, but had difficulty making sense of the image. She centered and enlarged it.

  The golden towers of Permutation City were flowing past the apartment window. She cried out in astonishment, and put her hands up, trying to gesture to the others. The buildings weren’t simply moving away; they were softening, melting, deforming. She fell to her knees, torn between a desire to return to her true body, to protect it – and dread at what might happen if she did. She dug one hand into the Lambertian soil; it felt real, solid, trustworthy.

  Durham grabbed her shoulder. “We’re going back. Stay calm. It’s only a view – we’re not part of the City.”

  She nodded and steeled herself, fighting every visceral instinct about the source of the danger, and the direction in which she should flee. The cloned apartment looked as solid as ever … and in any case, its demise could not, in itself, harm her. The body she had to defend was invisible: the model running at the far end of Durham’s territory. She would be no safer pretending to be on Planet Lambert than she would pretending to be in the cloned apartment.

  She returned.

  The four of them stood by the window, speechless, as the City rapidly and silently … imploded. Buildings rushed by, abandoning their edges and details, converging on a central point. The outskirts followed, the fields and parks flowing in toward the golden sphere which was all that remained of the thousand towers. Rainforest passed in a viridian blur. Then the scene turned to blackness as the foothills crowded in, burying their viewpoint in a wall of rock.

  Maria turned to Durham. “The people who were in there—?”

  “They’ll all have left. Shocked but unharmed. Nobody was in there – in the software – any more than we were.” He was shaken, but he seemed convinced.

  “And what about the founders with adjoining territory?”

  “I’ll warn them. Everyone can come here, everyone can shift. We’ll all be safe, here. The TVC grid is constantly growing; we can keep moving away, while we plan the next step.”

  Zemansky said firmly, “The TVC grid is decaying. The only way to be safe is to start again. Pack everything into a new Garden-of-Eden configuration, and launch Elysium again.”

  Repetto said, “If that’s possible. If the infinite is still possible.” Born into a universe without limits, without death, he seemed transfixed by the Lambertians’ verdict.

  A red glow appeared in the distance; it looked like a giant sphere of luminous rubble. As Maria watched, it brightened, then broke apart into a pattern of lights, linked by fine silver threads. A neon labyrinth. A fairground at night, from the air. The colors were wrong, but the shape was unmistakable: it was a software map of the City. The only thing missing was the highway, the data link to the hub.

  Before Maria could say a word, the pattern continued to rearrange itself. Dazzling pinpricks of light appeared within a seemingly random subset of the processes, then moved together, clustering into a tightly-linked core. Around them, a dimmer shell formed by the remaining software settled into a symmetrical configuration. The system looked closed, self-contained.

  They watched it recede, in silence.

  Chapter 31

  Peer turned and looked behind him. Kate had stopped dead in the middle of the walkway. All the energy seemed to drain out of her; she put her face in her hands, then sank to her knees.

  She said flatly, “They’ve gone, haven’t they? They must have discovered us … and now this is their punishment. They’ve left the City running … but they’ve deserted it.”

  “We don’t know that.”

  She shook her head impatiently. “They will have made another version – purged of contamination – for their own use. And we’ll never see them again.” A trio of smartly dressed puppets approached, and walked straight through her, smiling and talking among themselves.

  Peer walked over to her and sat cross-legged on the floor beside her. He’d already sent software probes hunting for any trace of the Elysians, without success – but Kate had insisted on scouring a reconstruction of the City, on foot, as if their own eyes might magically reveal some sign of habitation that the software had missed.

  He said gently, “There are a thousand other explanations. Someone might have … I don’t know … created a new environment so astonishing that they’ve all gone off to explore it. Fashions sweep Elysium like plagues – but this is their meeting
place, their center of government, their one piece of solid ground. They’ll be back.”

  Kate uncovered her face, and gave him a pitying look. “What kind of fashion would tempt every Elysian out of the City, in a matter of seconds? And where did they hear about this great work of art which they had to rush off and experience? I monitor all the public networks; there was nothing special leading up to the exodus. But if they’d discovered us – if they knew we were listening in – then they wouldn’t have used the public channels to announce the fact, would they?”

  Peer couldn’t see why not; if the Elysians had found them, they’d also know that he and Kate were powerless to influence the City – let alone its inhabitants – in any way. There was no reason to arrange a secret evacuation. He found it hard enough to believe that anyone would want to punish two harmless stowaways – but it was harder still to accept that they’d been “exiled” without being dragged through an elaborate ritual of justice – or at the very least, publicly lambasted for their crime, before being formally sentenced. The Elysians never missed the opportunity for a bit of theater; swift, silent retribution just didn’t ring true.

  He said, “If the data link to the hub was broken, unintentionally—”

  Kate was scornful. “It would have been fixed by now.”

  “Perhaps. That depends on the nature of the problem.” He hesitated. “Those four weeks I was missing … we still don’t know if I was cut off from you by a fault in the software at our level – or whether the problem was somewhere deeper. If there are faults appearing in the City itself, one of them might have severed the links to the rest of Elysium. And it might take some time for the problem to be pinned down; anything that’s taken seven thousand years to reveal itself could turn out to be elusive.”

  Kate was silent for a while, then she said, “There’s an easy way to find out if you’re right. Increase our slowdown – keep increasing it – and see what happens. Program our exoselves to break in and switch us back to the normal rate if there’s any sign of the Elysians … but if that doesn’t happen, keep plowing ahead into the future, until we’re both convinced that we’ve waited long enough.”

  Peer was surprised; he liked the idea – but he’d imagined that Kate would have preferred to prolong the uncertainty. He wasn’t sure if it was a good sign or not. Did it mean she wanted to make a clean break from the Elysians? To banish any lingering hope of their return, as rapidly as possible? Or was it proof of just how desperately she wanted them back?

  He said, “Are you sure you want to do that?”

  “I’m sure. Will you help me program it? You’re the expert at this kind of thing.”

  “Here and now?”

  “Why not? The whole point is to save ourselves from waiting.”

  Peer created a control panel in the air in front of them, and together they set up the simple time machine.

  Kate hit the button.

  Slowdown one hundred. The puppets using the walkway accelerated into invisible streaks. Slowdown ten thousand. Night and day chugged by, then flashed, then flickered – slowdown one million – then merged. Peer glanced up to watch the arc of the sun’s path slide up and down the sky with the City’s mock seasons, ever faster, until it smeared into a dull glowing band. Slowdown one billion. The view was perfectly static, now. There were no long-term fake astronomical cycles programmed into the virtual sky. No buildings rose, or crumbled. The empty, invulnerable City had nothing to do but repeat itself: to exist, and exist, and exist. Slowdown one trillion.

  Peer turned to Kate. She sat in an attentive pose, head up, eyes averted, as if she was listening for something. The voice of an Elysian hyperintelligence, the endpoint of a billion years of self-directed mutation, reaching out to encompass the whole TVC grid? Discovering their fate? Judging them, forgiving them, and setting them free?

  Peer said, “I think you’ve won the bet. They’re not coming back.” He glanced at the control panel, and felt a stab of vertigo; more than a hundred trillion years of Standard Time had elapsed. But if the Elysians had cut all ties with them, Standard Time was meaningless. Peer reached out to halt their acceleration, but Kate grabbed him by the wrist.

  She said quietly, “Why bother? Let it climb forever. It’s only a number, now.”

  “Yes.” He leaned over and kissed her on the forehead.

  “One instruction per century. One instruction per millennium. And it makes no difference. You’ve finally got your way.”

  He cradled Kate in his arms, while Elysian eons slipped away. He stroked her hair, and watched the control panel carefully. Only one number was rising; everything but the strange fiction of Elapsed Standard Time stayed exactly the same.

  No longer tied to the growth of the Elysians, the City remained unchanged, at every level. And that meant, in turn, that the infrastructure which Carter had woven into the software for them had also ceased to expand. The simulated “computer” which ran them, composed of the City’s scattered redundancies, was now a finite “machine”, with a finite number of possible states.

  They were mortal again.

  It was a strange feeling. Peer looked around the empty walkway, looked down at the woman in his arms, feeling like he’d woken from a long dream – but when he searched himself for some hint of a waking life to frame it, there was nothing. David Hawthorne was a dead stranger. The Copy who’d toured the Slow Clubs with Kate was as distant as the carpenter, the mathematician, the librettist.

  Who am I?

  Without disturbing Kate, he created a private screen covered with hundreds of identical anatomical drawings of the brain; his menu of mental parameters. He hit the icon named CLARITY.

  He’d generated a thousand arbitrary reasons to live. He’d pushed his philosophy almost as far as it would go. But there was one last step to take.

  He said, “We’ll leave this place. Launch a universe of our own. It’s what we should have done long ago.”

  Kate made a sound of distress. “How will I live, without the Elysians? I can’t survive the way you do: rewiring myself, imposing happiness. I can’t do it.”

  “You won’t have to.”

  “It’s been seven thousand years. I want to live among people again.”

  “Then you’ll live among people.”

  She looked at him hopefully. “We’ll create them? Run the ontogenesis software? Adam-and-Eve a new world of our own?”

  Peer said, “No. I’ll become them. A thousand, a million. Whatever you want. I’ll become the Solipsist Nation.”

  Kate pulled away from him. “Become? What does that mean? You don’t have to become a nation. You can build it with me – then sit back and watch it grow.”

  Peer shook his head. “What have I become, already? An endless series of people – all happy for their own private reasons. Linked together by the faintest thread of memory. Why keep them spread out in time? Why go on pretending that there’s one ‘real’ person, enduring through all those arbitrary changes?”

  “You remember yourself. You believe you’re one person. Why call it a pretense? It’s the truth.”

  “But I don’t believe it, any more. Each person I create is stamped with the illusion of still being this imaginary thing called ‘me’ – but that’s no real part of their identity. It’s a distraction, a source of confusion. There’s no reason to keep on doing it – or to make these separate people follow each other in time. Let them all live together, meet each other, keep you company—”

  Kate gripped him by the shoulders and looked him in the eye. “You can’t become the Solipsist Nation. That’s nonsense. It’s rhetoric from an old play. All it would mean is … dying. The people the software creates when you’re gone won’t be you in any way.”

  “They’ll be happy, won’t they? From time to time? For their own strange reasons?”

  “Yes. But—”

  “That’s all I am, now. That’s all that defines me. So when they’re happy, they’ll be me.”

  Chapter 32


  “Seventeen down, one to go.”

  Durham had rendered himself calm and efficient, to deal with the evacuation. Maria, still unmodified, watched sick with relief as he finally packed Irene Shaw, her seven hundred million offspring, and their four planets’ worth of environments, into the bulging Garden-of-Eden-in-progress. A compressed snapshot of the entire civilization flowed down the data paths Durham had created to bypass the suspect hub – following a dozen independent routes, verified and reverified at every step – until it crossed the barrier into the region where the new Elysium was being forged.

  So far, there’d been no sign that the corruption of the grid was spreading further – but the last Town Meeting had given Durham just six hours of Standard Time to assemble and launch the new seed. Maria was astonished that they’d appointed him to do the job at all, given that it was his clandestine visit to Planet Lambert which had catalyzed the whole disaster (and they’d left – non-conscious – watchdog software running, to monitor his actions, and take over the task if he failed) … but he was still the man who’d built and launched Elysium, and apparently they trusted him above anyone else to rescue them from their disintegrating universe, just as he’d rescued the founders from the legendary deteriorating Earth.

  Two of the three “hermits” among the founders – Irene Shaw and Pedro Callas – had responded to the emergency signals sent into their pyramids from the hub. Despite their millennia of silence, they hadn’t sealed their worlds off completely from information from the rest of Elysium.

  Thomas Riemann, apparently, had.

  Maria checked the clock on the interface window; they had fourteen minutes left.

  Durham had set a program running, hours before, to try to break into Riemann’s pyramid. He’d succeeded in forging new links with the processors, but without Riemann’s personal code, any instructions piped in would be ignored – and a time-lock triggered by each incorrect attempt made scanning through all ninety-nine-digit combinations impractical. So Durham had instructed a metaprogrammer to build a TVC “machine” to isolate and dissect one of Riemann’s processors, to scrutinize the contents of its memory, and to deduce the code from the heavily encrypted tests within.