Schild's Ladder

by Greg Egan

  Mariama said, “All right, I'll go with you. We can keep each other honest. But the process has to be set up so it doesn't jeopardize everything. If the border starts falling while only one of us is through, the vehicle will have to be programmed to interrupt the transfer, and dive without the second passenger.”

  “That makes sense,” Tchicaya conceded.

  “Which only leaves one thing to be decided.”

  “What's that?”

  “Who goes first.”

  Chapter 15

  Tchicaya looked out from the Sarumpaet into a lime-green sea. In the distance, glistening partitions, reminiscent of the algal membranes that formed the cages in some aquatic zoos, swayed back and forth gently, as if in time to mysterious currents. Behind each barrier the sea changed color abruptly, the green giving way to other bright hues, like a fastidiously segregated display of bioluminescent plankton.

  The far side here was a honeycomb of different vendek populations, occupying cells about a micron wide. The boundaries between adjoining cells all vibrated like self-playing drums; none were counting out prime numbers, but some of the more complex rhythms made it seem almost plausible that the signaling layer had been nothing but a natural fluke. Even if that were true, though, Tchicaya doubted that it warranted relief at the diminished prospect that sentient life was at stake. The signaling layer might have brought him this far, but with millions of unexplored cubic light-years beneath him, judging the whole far side on that basis would be like writing off any possibility of extraterrestrial life because the constellations weren't actually animals in the sky.

  The view he was looking at was a construct, albeit an honest one. The Sarumpaet was constantly “illuminating” its surroundings with probes, but they were more like spy insects than photons, and they had to return in person with the details of everything they'd encountered, rather than radioing back images from afar. His body, the vehicle itself—a transparent bubble like a scaled-down version of the Rindler's observation module, with an added checkerboard of windows in the floor—and the gravity he felt, were all pure fiction.

  He turned to Mariama's icon-in-waiting, complete up to the shoulders now. Her body was rendered as a transparent container, slowly filling with color and solidity from a trickle of light flowing down through a glassy pipe that ran all the way to the border. Tchicaya looked up along the pipe to the roiling layer of Planck worms, inky violets and blacks against the cheerful false pastels of the vendeks. Every few seconds, a dark thread would snake down toward him, like a tentacle of malignant tar invading a universe of fruit juice. So far, the vendeks had always responded by pinching off the thread and extinguishing the intruders. The Sarumpaet avoided sharing this fate by wrapping itself in a coat that mimicked the stable layers it saw around it, but though the Planck worms could only hope to achieve the same kind of immunity by stumbling on it blindly, once they did, they'd put it to a far less benign use.

  Tchicaya was running his own private Slowdown, to keep the wait from being unbearable; the Planck-scale quantum gates of the Sarumpaet could have made the hour stretch out into an eternity. The toolkit was using its enhanced speed to broaden its search for new strategies, though as yet this had yielded nothing promising. The ten million individual Planck-worm-killers it had designed on the near side could have been scribed here in a fraction of a microsecond instead of the original nine hours, but most of them would have consumed the Sarumpaet itself in an instant. Tchicaya would not have minded mimicking the anachronauts and going out in his own blaze of glory, but only if he was unleashing a fire that was certain to be both effective and self-limiting.

  Mariama was beginning to develop a chin. Tchicaya asked the icon if it was representing the proportion of data received through volume, or height.

  “Volume.”

  The crisp image of her body began to soften, but it was the scape's lighting that was changing, not the icon itself. Tchicaya looked up to see a dark, fist-shaped protuberance pushing its way through the vendeks. An instinct from another era tensed every muscle in his simulated body, but he wouldn't need to make a split-second decision, let alone act on it physically; the Sarumpaet itself would determine when it had to flee. Dropping out of Slowdown to monitor events at a glacial pace would only be masochistic; he would speed up automatically as soon as the flight began.

  The infestation of Planck worms spread out like a thundercloud. As the dark layer brushed the tube that represented the link across the border, the Sarumpaet launched itself down into the far side.

  The single, brooding cloud exploded into a storm of obsidian, rushing toward the ship like a pyroclastic flow. Tchicaya had sprinted down the slopes of a volcano on Peldan, racing hot gas and ash, but the effortless speed of the Sarumpaet made this dash for safety even more nerve-wracking. The risk of being overtaken on foot was only to be expected, but the ship's pattern of data was propagating at close to the maximum rate the environment permitted. There was no such thing as lightspeed here, but he was nudging a barrier that was just as insurmountable.

  As he glanced down, he saw that the visibility had diminished; the probes were traveling as far ahead as ever, but the Sarumpaet was racing forward to meet them. The toolkit would still have the crucial information it needed to adapt the ship's harnessed vendeks to changes in the environment, but the faster they fled, the less time it would have to cope with any surprises.

  The first boundary was almost upon them, but they'd probed this one thoroughly in advance. As the ship crossed through the glistening membrane—an act portrayed as a simple mechanical feat, but which amounted to redesigning and rebuilding the entire hull—a motion within the scape caught Tchicaya's eye.

  Mariama turned to him with a triumphant smile. “That's what I call an amphibious vehicle: glides smoothly from microverse to microverse, whatever their dynamic spectra.”

  He stared at her. “You weren't—”

  “Complete? Ninety-three percent should be good enough. I packaged myself very carefully; don't take that decapitated progress icon literally.” She looked up. “Oh, shit. That wasn't meant to happen.”

  Tchicaya followed her gaze. The Planck worms had already crossed the boundary. Some freeloading mutation, useless against the earlier obstacles, must have finally proven its worth. Their adversary was not dispersing, weakening as it spread; it was like an avalanche, constantly building in strength. If the Planck worms retained every tool they tried out, whether or not it was immediately successful, their range of options would be growing at an exponential rate.

  “You have to hand it to Birago,” Mariama observed begrudgingly. “The killer twist was his, not Tarek's or mine. We were too hung up on the notion of mimicking natural replicators—as if nature ever made plagues that were optimized for destroying anything.”

  “Humans did. He might have had some tips from the anchronauts.”

  They crossed into another cell of the honeycomb, as smoothly as before. Tchicaya wasn't entirely sure what would happen if the Sarumpaet failed to negotiate a population transition, but whether it was the Planck worms or some hostile strain of vendeks that rushed in and consumed them, they wouldn't have much time to dwell on their fate before they blinked out of existence. As local deaths went, he'd had worse.

  He watched the Planck worms as they reached the partition; this time, they appeared to be trapped. However many mutations were part of the throng, they couldn't include an exhaustive catalog of all the possibilities. The toolkit was X-raying each gate and designing the perfect key as they approached; that strategy had to win out some of the time.

  If not always by a wide margin. Tchicaya was just beginning to picture the Sarumpaet streaking ahead triumphantly, when the second barrier fell to the Planck worms.

  He addressed the toolkit. “Is there anything we can throw in their way? Anything we can scribe that would act as an obstacle?”

  “I could trigger the formation of a novel layer population. But that would take time, and it would only stretch across
a single vendek cell.” However long the artificial barrier held, the Planck worms would still percolate down along other routes.

  They glided through a dozen more cells, maintaining a tenuous lead. Even when they appeared to be widening the gap, there was no guarantee that they wouldn't plunge into a cell to find that the Planck worms had reached the same point more quickly by a different route.

  The honeycomb stretched on relentlessly; the Sarumpaet gained and lost ground. After eight hours of nominal ship time, they'd crossed a thousand cells. In near-side terms, they were a millimeter beneath the point where the border had last rested, and the chase had gone on for mere picoseconds. The Planck worms had spent more than two hours diversifying before they'd learned to penetrate these catacombs, but having found the basic trick they appeared to be unstoppable. So much for the strategy of burning away one vendek population and the predators trapped within it; that would have been like trying to cure a victim of bubonic plague by sterilizing a single pustule.

  Tchicaya said, “If this goes on for a hundred kilometers, I'm going to lose my mind.”

  “We could go into Slowdown,” Mariama suggested. “We wouldn't risk missing anything; the ship could bring us up to speed in an instant.”

  “I know. I'd rather not, though. It just feels wrong.”

  “Like sleeping on watch?”

  “Yeah.”

  Three days later, Tchicaya gave in. The honeycomb could prove to be a centimeter thick, or a light-year; the probes could barely see half a micron ahead. They had no decisions to make; until something changed, all they were doing was waiting.

  “Just don't go dropping out on your own,” he warned Mariama.

  “To do what?” She gestured at the spartan scape. “This makes Turaev in winter look exciting.”

  Tchicaya gave the command, and the honeycomb blurred around them, the palette of false colors assigned to the vendeks—already recycled a dozen times to take on new meanings—merging into a uniform amber glow. It was like riding a glass bullet through treacle. Above them, the Planck worms retreated, crept forward, slipped back again. The Sarumpaet inched ahead, but in fast motion the race looked even closer than before, their advantage even more tenuous.

  As the Slowdown deepened, their progress grew smoother. After a full nanosecond of near-side time, they appeared to be leaving the Planck worms behind. After a microsecond, the worms slipped back out of range of the probes, and there was nothing to be seem but the Sarumpaet itself, and the honeyed esophagus down which it was gliding.

  At sixty microseconds, the toolkit signaled an alarm and the ship dragged them back to full speed.

  The Sarumpaet had stopped moving, in the middle of a cell of pale blue vendeks. “The probes can't go any deeper,” the toolkit explained. “We've reached a new kind of boundary: whatever's behind it is qualitatively different from all the vendek mixes we've encountered so far.”

  Tchicaya glanced down into the darkness, as if his eyes could reveal something that the probes, responsible for the entire scene, had missed.

  Mariama frowned. “Different how?”

  “I have no idea. The probes don't even scatter back from the boundary. I've tried redesigning them, but nothing works. Anything I send down simply vanishes.” For all its knowledge and speed, the toolkit had never been intended to act as much more than a repository of facts. It couldn't begin to cope with novelty in the manner of the people who'd contributed to it.

  They sat and discussed the possibilities. Tchicaya had learned quite a bit from his faction's experts, and Mariama even more, but they needed a bigger group; on the Rindler, everyone's ideas had sparked off someone else's.

  For weeks, they argued and experimented. They took turns sleeping for an hour each; even without any fixed, bodily need to recuperate, their minds were still structured to function best that way. The toolkit diligently analyzed vast lists of possibilities, sorting through the quantum states that might be swallowing all their probes without a trace, hunting for a new design that would avoid that fate and return with solid information.

  Nothing worked. The darkness beneath them remained inscrutable.

  They had no way of knowing how long it would be until the Planck worms came flooding down after them. On bad days, Tchicaya consoled himself with the thought that when they died, the Planck worms might be buried with them. On worse days, he faced the possibility that brute mutation would find a way through, where all their passion and borrowed ingenuity had failed.

  On the thirty-seventh day, Tchicaya woke and looked around the scape. They'd tried all manner of distractions for the sake of inspiration, but no stroll through a forest, no mountain hike, no swim across a sunlit lake had led them to the answer. So they'd stopped ransacking their memories for places to camp, and returned to the unpalatable truth. They were stranded in an ugly, barren cave in the pockmarked rind of an alien universe, waiting to be corroded into noise by a billion species of ravenous sludge.

  Mariama smiled encouragingly. “Any revelatory dreams?”

  “I'm afraid not.” He'd dreamed he was a half-trained Sapper from the legend, suddenly confronted by a new kind of bomb, falling beside it toward a landscape of shadows that might have been anything from a desert to a vast metropolis.

  “My turn, then. Come on, get up.”

  “I will. Soon.” She could just as easily conjure up a bed of her own, but taking turns with one imposed a kind of discipline.

  Tchicaya closed his eyes again. Sleep had lost all power to assuage his weariness, but it was still an escape while it lasted. He'd understood from the start that their struggle was quixotic, but he'd never imagined such a dispiriting end. They'd spend their last days writing equations on paper planes, and tossing them into an abyss.

  As he drifted back toward sleep, he pictured himself gathering up a mountain of crumpled paper and heaving it out of the Sarumpaet into the darkness below. If by chance some scrap went wafting through into another world, he'd never even know that he'd succeeded.

  He opened his eyes. “We launch all our paper planes at once. Then we throw a message back, and use it to clear away all the garbage.”

  Mariama sighed. “What are you ranting about?”

  Tchicaya beamed at her. “We have a list of the kind of states the region below us might be in, and we have strategies for dealing with them all. But we still haven't found a probe that will cross through and return—giving us a definite answer, letting us know which strategy to use. Fine. We put the Sarumpaet into a superposition of states, in which it tries them all simultaneously.”

  Mariama was speechless. It took Tchicaya several seconds to interpret this response; he had rarely surprised her, and he had certainly never shocked her before.

  She said, “Who cares about quantum divergence, if one world out of every quadrillion is the best of all possible worlds? That sounds like some desperate fatalist nonsense from the last days before the Qusp.”

  Tchicaya shook his head, laughing. “I know! But it's not! Answer me this: a quantum computer does a search for the solution to an equation, testing a few trillion candidates simultaneously. In how many worlds does it fail?”

  Mariama scowled. “None, if there's a solution at all. But that's different. The divergence is all internal and contained; it doesn't split the environment into branches halfway through the calculation.” A flicker of uncertainty crossed her face. “You don't think we could—”

  Tchicaya said, “We're not in the near side anymore. Coherence is nowhere near as fragile here. Whatever this gulf is that we're facing, there's no fundamental reason why we shouldn't be able to stretch a single quantum computer all the way across it. And if we handle all the strategies with sufficient care, we ought to be able to manipulate the whole coherent system so that the failures cancel out.”

  She nodded slowly, then broke into an astonished grin. “We reach out and swallow the problem; we internalize it completely. Then we can bludgeon our way through by trial and error, without the world ever
seeing a single mistake.”

  They spent three days refining the idea, thrashing out the details with the toolkit and the ship. It was a complex maneuver, and it would require precise control over the ship's environment, both before and after it crossed through the boundary. The toolkit had had plenty of time to study the surrounding vendeks, and it understood the physics of this obscure cul-de-sac as thoroughly as that of the near-side vacuum itself. The second half of the problem could not be dealt with by direct observation, but that didn't mean they'd be taking a leap into the dark. Each strategy for making the crossing relied on a set of assumptions about the other side. Once they put the ship into a superposition of strategies, each component would know the kind of place it would end up in, if it ended up anywhere at all.

  Tchicaya snapped awake, knowing the reason instantly. He'd been summoned to alertness by the tug of a trip wire that he'd installed, back on the near side, when he'd worked with the toolkit to construct a software container to sit between their minds and the raw quantum gates of the ship's processor.

  Mariama was seated a short distance away, gazing out into the vendek cell. Tchicaya said, “Do you want to tell me what you're doing?”

  She turned to him, frowning slightly. “Just rearranging a few things internally. I didn't realize I had so little privacy.”

  “I own this whole setup,” he said. “You knew that when you came into it.”