Schild's Ladder

by Greg Egan

  “ ‘The highest attainable probability’? That's a resounding declaration of confidence.” Tchicaya had been hoping for something more reliable. He knew what quantum mechanics was like, but if his own Qusp could pluck certainty from the haze, granting him the ability to make unique decisions, surely Yann could work some similar trick with the vastly more powerful abstract machine behind the border?

  Rasmah emerged from her visualization. “I know how that sounds, but it really is the best we can hope for. We're not arranged in the same way as the far side; we're stuck in a dynamic-law eigenstate, and that's always going to make things difficult.”

  “Yeah.” Tchicaya was grateful for anything that took them beyond the current, artificial view of definite laws spread across the border, but it was sobering to realize how much stranger things became as the price of that advance. “I shouldn't be disappointed, but I keep underplaying the problems in my head: sweeping all the hard parts off to one side, where I don't have to look at them. If I faced the difficulties squarely, I'd probably just turn around and run.”

  Rasmah regarded him with a mixture of curiosity and affection. “You really do want to go through the border, don't you?”

  “I think so. What about you?”

  “Absolutely. That's what I came here to do.” She hesitated, then added, “For a while, I thought I must have said something too extreme along those lines, and it put you off. But I don't think that's it. So what is it about me that you hate so much?”

  Tchicaya shook his head vehemently. “Nothing.”

  “But we got halfway,” she said, “and then you changed your mind.” This wasn't a question. Their bodies had ceased the silent exchange of pheromones, and that in itself would have dampened her feelings toward him, but it must have been clear to her that he was the one who'd halted the process.

  “You're very good company,” Tchicaya said. “But you remind me too much of someone else, and I don't feel right about that. I don't want to confuse you with her; that wouldn't be fair on either of us.” He frowned apologetically. “Am I making any sense?”

  Rasmah nodded uncertainly. “The other thing I thought was, maybe you and Yann were still, somehow—”

  “No!” Tchicaya was taken aback. “Where did you hear about that?”

  She waved a hand dismissively. “Everyone knows.”

  “Actually, I think Yann might have forgotten.”

  “But there is no one else, in the present? Just this nameless competitor from the past?”

  Not exactly a competitor. And not wholly in the past. But Tchicaya didn't want to explain any further. “That's right.”

  “Okay.” Rasmah stood, and Tchicaya rose beside her. In part, he was glad that she'd cleared the air, though at the same time he felt a surge of resentment, now that he'd been forced to put his reasons into words. He and Mariama would never be together. Why was he letting her shape his decisions at all?

  “You'll support Yann with this?” he asked.

  Rasmah smiled. “Definitely. This is our best hope, and I'm sure I can sell it to the others. Suitably uglified.”

  The Blue Room was packed from wall to wall; it hadn't been so crowded since the Left Hand's first trial run. The room was near the bottom of its module, and it had already been expanded as far as possible in all horizontal directions; several unobliging neighbors above prevented it from growing upward. As relations had deteriorated, some Yielders and Preservationists had swapped cabins in order to be surrounded by fellow partisans, but the Rindler hadn't yet reached a state where every module was “owned” by one faction or another.

  Yann paced the ceiling, ducking away from the tallest heads and shoulders—making his presence visible, but wisely desisting from trying to claim space that he could not defend with solid elbows. Other acorporeals came and went beside him, and no doubt he was conversing with some who weren't bothering to display icons. Almost everyone who'd been born acorporeal had now donated their bodies to new arrivals, effectively splitting the Yielders into two distinct communities, more so in some ways than the factions themselves. Tchicaya had mixed feelings about this; their generosity had given many more people a chance to participate in events on the ship, in the only manner that would not have been alien to them. But the acorporeals had been willing to change modes in the first place, so why couldn't the newcomers make do with software bodies? Maybe he had no right to think that way, having accepted the first such sacrifice himself, but the segregation by birth still depressed him, however well acclimatized to their condition the acorporeals were.

  The Left Hand had scribed Yann's state almost an hour before, and they were still waiting hopefully for an echo. Rasmah had ended up translating Yann's purely algorithmic account into a kind of sophisticated scattering experiment: they were probing the far side by sending in an elaborately structured pulse that was capable of propagating relatively large distances. At least part of this pulse stood a good chance of bouncing off any structure that lay in its path, and coming back to them bearing an imprint of whatever it encountered.

  This made it sound cozily familiar: a cross between radar, particle physics, and tomography. But the “distance” the pulse would travel and the “structures” it might or might not interact with were the raw topological details of an unknown superposition of quantum graphs, not properties of such elaborate near-side constructions as vacuum obeying Euclidean geometry, or the kind of matter that would reflect light or microwaves. Even the pulse itself had no real analogies in the ordinary world: it was not a particle, or a gravitational wave, or any kind of electromagnetic signal. It was a new form of dislocation in the pattern of threads from which all those mundane things were woven.

  Rasmah cried out, “We've got something!”

  People started jostling for a better view of the screen, though the image was being made available directly to everyone in the room. Tchicaya stubbornly stood his ground behind Rasmah for several seconds, then he gave up and let the crowd percolate around him, forcing him back.

  He closed his eyes and saw, unobstructed, the first raw image of the returning pulse. It was a speckled, monochrome, pockmarked pattern, like a fuzzy shot of a cratered landscape, taken in such low light levels that you could count the individual photons. As he watched, the speckling of the image shimmered; it reminded Tchicaya of some kind of weird laser effect.

  “Interference!” Yann crowed happily from the ceiling. “Wait, wait, let me—” An inset blossomed in the image, a huge, tangled, branching polymer, studded with loops and knots, built from nodes of every valence. Different parts of the pulse would have been modified in different ways by the same topology; Yann had used the interference between these altered components to reconstruct a typical portion of the kind of graph the signal must have passed through.

  Rasmah said, “That's far from an unbiased superposition. It's not the sum of all random haystacks in there. There's no vacuum, but there's still order.”

  Tchicaya stared at the polymer. From childhood, he'd studied the Sarumpaet patterns, the quantum graphs that could maintain stability under the old rules. And for months, he'd seen the alternatives: all the different possible families of particles, deduced from the physics they'd trapped on the border.

  This was like an amalgam that some magpie of a sculptor had created to sum up that experience, combining features from all of them—grabbing fragments of every kind of ordinary, vacuumbased physics and welding them together, without regard to such niceties as having to build a uniform, homogeneous geometry, or having to respect a simple set of rules that stayed constant over time.

  Hayashi called out from behind Tchicaya, “Is that fractal? Can you give it a dimension?”

  Rasmah invoked some further processing. “No. No dimension, integer or otherwise. The branching's not at all self-similar; there's no redundant information.”

  “Modify the probe pulse and send it again. Here are the details.” Branco's voice rang out from midair, as if he were among the acorporeals; he'd de
clined to leave his cabin and join the crush. Some Yielders had been reluctant to grant access to the results to anyone who refused to declare their allegiance, but sanity had finally prevailed.

  Rasmah said, “Thanks for the suggestion, but it will have to wait.” The meeting that had approved Yann's experiment had set aside a week for the interpretation of the results, before any further action was to be taken.

  Branco sighed. “Do it, don't do it. I couldn't care less.”

  Rasmah displayed Branco's proposal for everyone to see. It was a straightforward alteration to Yann's original state, accompanied by some calculations suggesting that components would bounce back to them in a staggered sequence that would make changes in the graphs over time easier to deduce. If this worked, it would give them a movie of the far side, in place of a single, still image.

  Suljan yelled out, “We should try that, immediately!” Bhandari, in a far corner of the room, disagreed. People started voicing approval and shouting alternative suggestions from all directions. Tchicaya would have covered his ears, but his hands were trapped. This was bedlam, but it was intoxicating. It reminded him of the time he and a group of friends on Peldan had landed a remotecontrolled vehicle on a passing asteroid: everyone wanted to grab the joystick.

  Rasmah screamed, “Shut up!”

  Something approximating silence descended.

  “Read Branco's proposal,” she pleaded. “Think about it. We'll have a vote in fifteen minutes. And if anyone feels like going out to stretch their legs in the meantime...don't rush back. You can vote from anywhere.”

  The noise rose up again, but there was no real note of discord. Rasmah slumped against the control panel.

  Yann poked his head down in front of Tchicaya. “You're all completely mad. Someone's going to get crushed.”

  “Some of us have no choice about taking up space.”

  “There's plenty of room up here,” Yann suggested helpfully.

  “Yeah, right, just give me a hand up.” The ship could probably have molded a tier of hanging chairs, but the ceiling was so low that this would have meant a constant risk of being kicked in the head.

  “Some people are so inflexible. When Cass came to Mimosa, she insisted on a body. We obliged, but we made it small enough to fit.”

  Tchicaya had never heard this detail before.

  “How small?” he asked.

  Yann held out his hand, thumb and forefinger a couple of millimeters apart.

  “You evil, sadistic bastards.”

  Tchicaya squeezed his way through the crowd back to the control panel. Rasmah looked frazzled but happy.

  “What do you make of this?” he asked, gesturing at the polymer.

  “It's too early for interpretations,” she said.

  “But it's structured, isn't it?” he suggested. “You said as much yourself.”

  Rasmah had grown more cautions. “It's not an equal superposition of all the things it could be. It's not a maximum-entropy quantum blancmange. That still leaves a lot of room for it to be disordered, in lesser ways.”

  Tchicaya didn't pursue the point, but the very fact that Yann's pulse had come back to them bearing information proved that there was some potential for setting up causal processes on the far side. Lawless as it was in the conventional sense, it could still support a kind of machinery. They could try to build more sophisticated exploratory vehicles. Perhaps, eventually, even bodies and Qusps.

  More importantly, if they ever succeeded in doing that, the place they'd be entering was looking less and less like a featureless desert. When Tchicaya had arrived on the Rindler, it had still been conceivable that the world behind the border would be nothing but a different form of empty space, with no particular reason to contain even the equivalent of the tiny smudge of matter that enlivened the near side. They'd barely glimpsed the structure of the far side, but his first impression was that the hundred million cubic light-years of vacuum claimed by Mimosa had been rewoven into something orders of magnitude more complex.

  “Do you think we should show this to the opposition?” Tchicaya asked. “It might give them pause, if they can finally see that they're not just dealing with a corrosive void.”

  Rasmah laughed. “You honestly believe they'd care?”

  “Some would. And I don't see what we have to lose.”

  “Nor do I, but only because I'm sure they'll end up with exactly the same details, whether we inform them officially or not.”

  Tchicaya was startled. “You think someone's spying for them?”

  “Of course.”

  “What makes you so sure? Do we have spies with them?”

  “Not that I know of,” Rasmah admitted. “But that's not a fair comparison. The most relaxed Preservationist is an order of magnitude more security-conscious than our most diligent supporter.”

  The vote was taken, returning ninety-two percent support for Branco's suggestion. Rasmah scribed the modified pulse, and they waited again.

  Tchicaya sat on the console as people talked around them. “I never really thought we'd get this far,” he admitted. “Even once I'd made up my mind to come here, it seemed like a mad, quixotic notion.” He described the legend of the falling Sappers.

  “I like that story,” she said, “but it's not a good metaphor. Bombs hit the ground, and that's that. We're not facing a single, decisive deadline. Thousands of planets have fallen, but there is no moment when everything will be won or lost. So long as the border doesn't accelerate, we could hang on here for another thousand years, learning whatever we need to learn.”

  “Unless we lose everything to the Preservationists first.”

  Rasmah shrugged, as if that went without saying. Tchicaya hadn't told her about Mariama's ultimatum; the actual words had been so ambiguous that to most people they'd convey little more than the obvious fact that Planck worms were on the Preservationists' agenda. He hadn't given up hope of finding a way to freeze the border, but there was no clear path leading toward that outcome; randomly pinning dynamics was never going to do it. They had to look deeper, they had to learn more.

  He said, “So you never doubted that this moment would come?”

  “Never. Not for a second.” She laughed. “You should see your face, Tchicaya. I grew up with the border, remember? My parents used to take me outside at night and show me this tiny little disk of light, where the brightest star in the sky used to be. Sixty years later, it was on top of us. I'd never felt as angry as the day we had to evacuate. Not just because I was losing all the places I'd known on Maeder. I hated running from this thing.”

  “You wanted to stay and fight?”

  “I wanted to stay and understand it. I would have been on the Rindler from the start if I'd heard about it early enough. Instead, I went chasing rumors of another project. That fell through, and it took me centuries to make my way here. But I always knew we'd find a way through the border. The night before I left Maeder, I stood on the roof of my house and promised myself: next time, it won't just look as if I could reach up and push my hand into the far side. It will be possible. It will be true.”

  Tchicaya could easily picture her in this scene. “You're making me feel very old and indecisive,” he complained.

  She smiled. “I'm sorry, but that's because you are.”

  The console said, “Move your backside, please.” Tchicaya slid off; data was coming through.

  This time, he fought harder to stay beside Rasmah, peering over her shoulder at the console as the pulse appeared, and its interference pattern was analyzed.

  Branco's refinement had been on target: the new set of images showed a graph changing smoothly. Again, this was just an average for the whole path that had been traversed, not any particular piece of the far side, but it was still as informative as, say, a sample of images of terrain from a million different Earth-sized planets of different ages. You didn't need to have the entire history of one specific world to get a qualitative sense of how things changed.

  Rasmah set
the image looping, and the Blue Room crowd fell silent. The intricate waves of knotted edges flowing through the graph were mesmerizing. Animations of standard particle physics could be austerely beautiful; watching something like pair-production, with the mirror-image patterns of electrons and positrons forming out of their parent photons and moving through the vacuum, you couldn't help but admire the elegant symmetry of the process. This was a thousand times more complex, without being random or chaotic. The still image had reminded Tchicaya of a clumsy sculptural collage, but that was only because he'd imagined all the separate parts still playing their old, vacuum-based roles. Seeing the integrated whole in action destroyed that impression completely. Rather, the old Sarumpaetstyle patterns and interactions were beginning to look like repetitive attempts to imitate parts of this—like the work of some awful, sample-driven artist who took a tiny piece of someone else's intricately composed, wall-sized image and treated it as a decorative tile to be stamped out a thousand times in a rectangular grid.

  Near-side physics did achieve the same kind of complex beauty, but not at this scale, twenty orders of magnitude smaller than a proton. You had to move up to the size of atoms, at least, and even the richness of chemistry appeared crude and stodgy in comparison. When atoms changed their bonds, it was generally a haphazard, rough-and-tumble process, driven at random by thermal collisions, or at best chaperoned by enzymes or nanomachines. These polymers of indivisible nodes and edges were reweaving themselves with a speed and precision that made the most sophisticated molecular factories look like children tossing snowballs.

  Tchicaya heard someone clear their throat, nervous and tentative, reluctant to break the spell. He turned away from the console, curious and slightly annoyed, wondering what anyone thought they could add to this extraordinary sight with words. But the crowd moved respectfully away from the speaker, making space as if in encouragement.

  It was Umrao, a recent arrival from Nambu who Tchicaya had only met once. He looked around shyly, even more nervous now that he had everyone's attention.