Schild's Ladder

by Greg Egan

  Mariama spread her arms. “Fine. Rummage through my memories; see if I care.”

  Tchicaya sat up on the edge of the bed. “What were you trying to expel into the environment?” At the border of the simulated Qusp in which her mind was cocooned, he'd replaced some of the more arcane facilities of the standard hardware—things she'd have no good reason to want to use, under the circumstances—with fakes that merely rang alarm bells. It had been a last-minute decision; the toolkit would have happily simulated the Qusp in its entirety, as the simplest means of guaranteeing that everything worked smoothly when it was piped through.

  “Nothing,” she said. “It was a mistake. I didn't even realize you'd put me in a cage, so I brshed against the bars by accident.” She waved a hand at him irritably. “Go back to sleep.”

  He rose to his feet. “Are you going to tell me, or am I going to have to look for myself?” In an ordinary Qusp, the owner of the hardware could freeze the whole program and inspect its state at leisure. But the quantum gates here were implemented at too low a level; there was no room for that approach. All he could do was send in a swarm of utility algorithms to search for anything suspicious, while shuffling her working mind aside. That would do no lasting damage, but he had no idea how she would experience it. It could be extremely unpleasant.

  Mariama regarded him calmly. “You do whatever you think you have to. I've already been flayed once.”

  Tchicaya hesitated. He did not want to hurt her, and if he was wrong, he'd never be able to look her in the eye again. There had to be another way to call her bluff.

  “There's no need,” he said. “I know exactly what you were trying to do.” He wasn't certain of anything, but of all the possibilities he could imagine, one stood out sharply.

  “Really? Do you want to enlighten me?”

  “You brought in a stock of qubits entangled with the near side. You had to get rid of them now, or they would have shown up tomorrow when we prepared the ship.” Anything that interacted with an entangled qubit would have its phase irretrievably scrambled. To a pure quantum system they'd be poison. They'd have to be carefully isolated, locked away somewhere inside her mind.

  “You're right,” she admitted. The expression on her face barely changed, as if this amounted to a minor clarification of her original story. “But I wasn't trying to use them. I was trying to get rid of them.”

  “Why don't you use them right now? Kill us both, right now?” However many she was carrying, she could not have imagined they'd be enough to do real harm to the far side. So the poison could only have had one target.

  “I don't want to do that, Tchicaya. I want to go with you. Deeper in. As far as we can.”

  “Why?” Why had she dragged him down here at all? To give his version at the border an excuse to give up? Once he was also deep in the far side, battling the Planck worms like a valiant Lilliputian, it would be far easier to feel that he'd done all he could.

  “To see what's there,” she said. “To help protect it, if it's worth it.”

  “And help destroy it, if it isn't?”

  “I never lied about that,” she insisted. “I never told you that I'd fight for some exotic wasteland, over the lives of real people.”

  That was true. She'd told him exactly what she believed, and he'd still wanted her beside him.

  Tchicaya sagged to his knees. He had the means to kill her, or to leave her behind for the Planck worms. The ship's processor would do whatever he asked. But nothing she had done was unforgivable. In her place, fighting for the same stakes, he would have lied, too, armed himself, too. How could he accuse her of betraying anything? For all he knew, if they'd taken different turns the last time they'd parted, they might have ended up in each other's shoes.

  She walked up to him and cradled his head in her arms. “I'll get rid of them now,” she said. “Will you let me do that?”

  Tchicaya nodded. She took him by the hands and lifted him up. He constucted a safe route through the processor, and she ejected the tainted qubits, forming a tiny bubble of classical physics in the vendeks' quantum sea.

  The toolkit completed its preparations for the Sarumpaet's second launch. In principle, this was just another quantum computation, no different from the commonplace operation of turning a string of zeros into a superposition of every possible binary number of the same length. Treating the entire ship as an operand, though, meant expanding the infrastructure that performed the computation far beyond the original hull, wrapping the Sarumpaet in a second computer. This processor would rotate the part of the ship's state vector that described the propulsion system, giving it a small component in each of more than a quadrillion orthogonal directions. Then it would release the resulting superposition into the depths of the far side, and wait for the reply that would enable it to erase all its failures.

  The scape made no attempt to portray the actual machinery in which they were embedded; an opaque shield moved into place around the hull, representing the fact that they'd ceased to exchange information with their surroundings.

  The toolkit began a countdown from twenty.

  “Give me liberty, and/or death,” Mariama quipped.

  Tchicaya said, “I'll be happier when we can drop the ‘and’.” He was more afraid of the possibility of a single success, diluted a quadrillion-fold, than he was of universal failure. “I don't know if I should wish you a peaceful local death. Does this count, or doesn't it?”

  “Only if none of the strategies work.”

  “Then I won't say anything.”

  The toolkit said, “Zero.”

  Chapter 16

  Tchicaya looked down through the panes in the floor into a borderless expanse of pale brightness, stretching out beneath the Sarumpaet like an inverted sky.

  He turned to Mariama, relieved but confused. “That's it? It's over already?” The ship would not have sent out probes to explore their surroundings until the handshake across the boundary was completed.

  The toolkit said, “No. The light represents information-bearing vendeks with which we've interacted, inadvertently. I'm afraid the shielding we emerged with was a bad choice; I've found something that works now, but they managed to crawl all over us first.”

  Tchicaya was horrified. “Catch them!”

  “I'm trying. I'm weaving a net.”

  “Trying? You useless fucking machine!”

  Mariama reached over and took him by the shoulders. “Calm down! We programmed a response to something like this, and it's all happening, as fast as it can. There's nothing more to be done.”

  When they signaled back through the boundary to consolidate their success, the Sarumpaet needed to be a complete quantum system, not part of something larger that included vendeks fleeing through the far side. The entire maneuver depended on it. If they could not catch the vendeks, their presence would become an insignificant statistical fluke: for every branch in which they'd succeeded, there'd be a quadrillion in which they'd vanished from the picture entirely.

  “We should have covered this,” he said. “We should have covered every eventuality.”

  “Covered it how?” Mariama retorted. “A superposition that included different shielding on emergence would still have emerged with the wrong shielding, some of the time. We were never going to banish every conceivable problem in advance.”

  She was right. They'd done as much as they could to prepare, and now they had no choice but to wait and see if the situation could be salvaged.

  The light began to fade, slowly. The toolkit had netted a portion of the vendeks, trapping them in the structure it had woven and erasing their correlations with the ship. The light was only a metaphor; the task was not as hopeless as it would have been if they'd exposed a quantum processor to a random bombardment with photons. It was more like having a billion-piece jigsaw puzzle stolen by a swarm of flying insects: difficult to reverse, but not impossible.

  The sky beneath them turned gray, then pitch black.

  The toolkit said,
“That's all of them.”

  “How can you be sure?” Tchicaya asked.

  “I can't be, absolutely, but all the subsystems that were most likely to have been affected are displaying interference patterns as sharp as they've ever produced in isolation. Unless the vendeks that happened to escape also happened to interact with us in a way that could mimic that result, we're in a pure quantum state.”

  Tchicaya could live with that much doubt.

  The toolkit understood the physics on both sides of the boundary, now. As it exchanged information with the machinery that had launched them, the state vector for the ship was rotated into an eigenstate for a single strategy: the one that had succeeded. Give that they'd launched themselves toward the boundary at all, the probability that they'd failed to come through was zero.

  Mariama exhaled heavily. “I think that's the strangest thing I've ever been a part of.” She held up her hands and inspected them. “You know, I half-expected to feel the amplitude come flooding into me. Moving from spine to fingertips, of course.”

  Tchicaya laughed, grateful that she'd found a way to break the tension. “We should have programmed in an oscillating factor, for that extra existential thrill.” Not long after the Qusp had been developed, people had played around with all manner of quantum novelties, putting themselves into intentionally prolonged superpositions inside their skulls. But there was nothing even mildly strange to report about this: from the inside, each part of the state vector that described your mind experiencing something definite simply had that one, definite experience. Shuffling amplitude back and forth between two alternatives before finally letting one of them interact with the world could not be “sensed” as some kind of ontological ebb and flow.

  As the shielding was removed from the hull, the bright expanse of vendeks reappeared beneath them. The inner workings of the ship still needed to be protected, just like the interior of any Qusp, but they could now live with the equivalent of sunlight on their faces. Sunlight, or a swarm of gnats. The Sarumpaet would keep sending out probes, but in this region some information would come to them for free.

  “What now?” Mariama asked.

  Tchicaya looked up at the bottom of the honeycomb; it appeared as black and fathomless here as it had from the other side. It would hold back the Planck worms for a while, but it would be hoping for too much to assume that they'd all dash lemminglike into oblivion. “We need to find out how deep this region goes, and exactly what it contains. Maybe we can build some kind of firebreak here, something that will stop the Planck worms once and for all.”

  They descended through the Bright as fast as they could, but their progress was erratic. The number of different vendeks here was thousands of times greater than in any cell of the honeycomb, and though there were no abrupt transitions, the environment was constantly changing. Currents of different physics flowed around them as the vendeks intermingled in new proportions and combinations. Umrao had largely anticipated the structures in the honeycomb, but these strange tides would probably have been too complex to show up in his simulations. Tchicaya could not decide if this place would be more hostile or more amenable to higher forms of life: the vastly greater diversity of the vendeks made it seem richer, but the honeycomb cells had offered a kind of stability that was entirely absent here.

  The scape showed nothing beneath the ship but a distant haze, constantly retreating. The information-bearing vendeks—which Mariama dubbed sprites—seemed to pass intact through all the changing conditions, but they were refracted and scattered to varying degrees, so the visibility they provided was limited. The Sarumpaet's artificial probes became lost in the currents even sooner; beyond about half a micron, only a tiny fraction managed to return.

  It was impossible to guess how deep this region might be. Though the border was advancing through the near side relentlessly at half the speed of light, the precise meaning of this for the far side remained unclear. Viewed from either side, the border itself had to be expanding in a consistent fashion, but that left open the question of whether all, or most, structures in the far side sat motionless while the edge of their universe rocketed away from them, or whether the relationship was more like that of the cosmic expansion of the near side, where relative velocities grew slowly with distance. The honeycomb was certainly clinging to the border, but that was not a good enough reason to believe that everything else in the far side would be following close behind. Sweeping principles of homogeneity were wishful thining here.

  There was something deeply restful about moving through the Bright. With the scape's fake gravity insulating them from the ship's actual, bumpy passage, the Sarumpaet might have been a glass gondola hanging from an invisible hot air balloon, drifting through a planetary atmosphere after a volcanic eruption had shrouded the world in dust. Although there was nothing to see but the shimmering of the sprites, Tchicaya resisted the lure of Slowdown, and instead of retreating into virtual landscapes from their memories, they sat and talked about their travels. Mariama described the renaissance on Har'El, the excitement of the changes that had percolated up from nowhere. Tchicaya told her more about Pachner, and the similar vitality he'd seen at the approach of the border.

  They were beyond arguing, beyond accusing, beyond holding up each other's earlier ideals as some standard against which they'd fallen. They had seen different things, lived different lives, and they had allowed it to change them. All they could do now was keep on climbing Schild's ladder.

  Five tranquil days into the Bright, just as Tchicaya was beginning to fear that they risked being lulled into an irreversible torpor, they spotted a small, translucent structure drifting by at a leisurely pace. The sprites that the object modified and deflected reached them long before the ship's probes could journey out to form their own impression, and for nearly an hour it was not at all clear that this was anything more than an unusually stable and localized feature of the shifting currents. The sprite-image looked like an eddy of some kind, and if no circulating winds could be detected brushing across the Sarumpaet as it approached, the rules governing vendek flows didn't bear much resemblance to fluid dynamics.

  Once they were close enough, the probes gave a more detailed picture. There were veins and pockets of vendeks inside the eddy that were like nothing they'd seen floating free here. Some of the mixes were similar to honeycomb populations; others were different again.

  They tracked the thing for hours, and watched it negotiate the currents. As the free vendeks flowed over it and through it, the interior structures deformed wildly; these were not the kind of breezes that could stir a few leaves, they were shifts in the fundamental dynamic laws. Some species of interior vendeks died before their eyes; others seemed to be leached out, carried off into the wind. It was like witnessing an animal being sandblasted with bacteria and assorted foreign cells, fighting off some, incorporating others, surrendering whole lineages of its own. Twisting and reeling beneath the onslaught, but all the while continuing to function.

  After eight hours of watching these feats of persistence, with neither of them willing to put it into words, Mariama finally declared, “This has to be alive. This is our first xennobe.”

  Tchicaya agreed. “What do you want to call it?”

  “I named the sprites,” she said. “It's your turn.”

  The internal structures that the probe revealed looked like knots of offal caught in a tornado, but not many creatures were beautiful to behold once you dug that deep. The sprites' gentler scrutiny gave an impression of something woven from the winds.

  “An airflower.”

  Mariama was amused, but she didn't object. If the Bright was not actually much like air, nor did anything here lie within reach of one-word descriptions in near-side language.

  They continued to follow the airflower, though it was drifting upward, back toward the honeycomb. The toolkit ventured no opinion on the question of whether or not this system was alive, but its observations had already yielded dozens of new methods for eas
ing the Sarumpaet's way through the currents of the Bright.

  “Could it be sentient?” Mariama wondered. The airflower had shown no obvious reaction to their presence, but it wasn't actively probing its environment, and the ship was a fraction of its size. The tiny distortion in the sprite flow around the Sarumpaet's hull would barely be distinguishable from the background shimmer.

  Before crossing the border, they'd planned to initiate contact with the builders of the signaling layer by a simple act of mimicry: scribing a layer of vendeks of their own which beat out the same sequence of primes. Back in the honeycomb, that would have been straightforward; here, it would have been like trying to communicate by waving a white silk banner in a blizzard.

  They consulted with the toolkit, and eventually settled on a reasonable compromise. They unfurled a sturdier kind of banner, flexible enough to cope with the vendek flows. Its precise geometry remained prey to the weather, but instead of encoding anything in its position, its degree of transparency to the sprites flickered between two states, flashing out the primes like a shutter held up to the light.

  The airflower drifted on, apparently indifferent to the signal. They could only guess as to how it might pursue a conversation with its own kind, but if this creature had constructed the signaling layer in the alien environment of the far side's shallows—with the intention that it be noticed by beings from an even stranger realm—why would it remain oblivious to a version of the same message suddenly appearing in front of it?

  It was possible that it was completely blind to the sprites. They seemed like the obvious basis for perception here, but the airflowers might have evolved before them. If that was the case, it could take months of painstaking work to discover the creature's actual sensory modalities.

  Tchicaya had asked the toolkit to run simulations of the known species of Planck worms interacting with the bottom of the honeycomb, and as he pondered his next move, the verdict arrived. By sheer force of numbers, the worms would almost certainly stumble upon the necessary mutations to find their way through. Once they managed that, they'd bring the near-side vacuum into play against the Bright, unraveling the intricate tapestry of vendeks into isolated deserts of homogeneous physics.