Schild's Ladder

by Greg Egan

  Unlike her hapless ancestors, though, she did not contribute to the process herself. While the Qusp inside her skull performed its computations, it was isolated from the wider world—a condition lasting just microseconds at a time, but rigidly enforced for the duration—only breaking quarantine when its state vector described one outcome, with certainty. With each operating cycle, the Qusp rotated a vector describing a single alternative into another with the same property, and though the path between the two necessarily included superpositions of many alternatives, only the final, definite state determined her actions.

  Being a singleton meant that her decisions counted. She was not forced to give birth to a multitude of selves, each responding in a different way, every time she found her conscience or her judgment balanced on a knife edge. She was not at all what Homo sapiens had actually been, but she was close to what they'd believed themselves to be, for most of their history: a creature of choice, capable of doing one thing and not another.

  Rainzi didn't pursue the argument; he followed her in silence as she clambered into the display chamber. This was a small cavity in the Quietener's outer structure, not much larger than her room at the station, equipped with a single chair. There was no question of Cass being allowed any closer to the action; even the processor on which the Mimosans were running, scrupulously designed to spill as little noise into the environment as possible, was banished to the rim of the Quietener. Lacking the same antinoise features herself, she had to agree to be snap-frozen to a few Kelvin, three minutes before each run. Apart from being immobilized, this had no unpleasant side effects, but it served as an uncomfortable reminder of the fact that the closed-cycle “breathing” of her Mimosan body was pure placebo. Still, she'd been willing to put up with it twenty times so far, merely for the sake of sparing herself the three-second time lag for data to make its way back to the station.

  As she took her place in the cryogenic chair, the other Mimosans began to appear around her. Teasing her, congratulating her on her stamina. Livia joked, “We should have had a wager as to whether or not the incremental targets would turn out to be a waste of time. You could have relieved me of all my worldly goods by now.” Livia's sole material possession was a replica of an ancient bronze coin, carved from leftover asteroid metal.

  Cass shook her head. “What would I have put up? My left arm?” They'd been right to do things Livia's way, and Cass had long ago ceased resenting it. Not only was it safer, it was better science, testing each novel structure one by one.

  It turned out that Livia was alluding to a real wager: Bakim admitted that he'd made a bet with Darsono that Cass would not remain at Mimosa to the end. But he was unable to explain the stakes to her; her Mediator couldn't find a suitable analogy, and nothing she suggested herself was even close. No precious object or information would change hands, nor was there any token act of servitude or humiliation in store for the loser. Cass was amused by the bet itself, but it bothered her that she could only grasp half of what was going on. When her friends asked her about the Mimosans, would all her stories end with apologies for her own incomprehension? She might as well have visited one of the great cities back on Earth and spent her time living in a storm-water drain, having shouted conversations through a narrow grill with the people at street level, full of misunderstandings about objects and events she couldn't even glimpse.

  Rainzi had clearly been delegated to put the Nuclear Question to her, because no one else broached the subject. Cass found it slightly galling that they wouldn't even suffer a moment's embarrassment when they took up their superior vantage point. They wouldn't depart, they wouldn't abandon her; they'd simply clone their minds into the nuclear substrate. With no expectation of recovering the clones, the originals would have no reason to pause, even for a picosecond, while their faster versions ran.

  The target graph appeared on the wall in front of her. The four distinctive node patterns they'd tried in every other combination were all present now. Just as virtual particles stabilized the ordinary vacuum—creating a state of matter and geometry whose most likely successor was itself—Cass's four patterns steered the novo-vacuum closer to the possibility of persistence. The balance was only approximate: according to the Sarumpaet rules, even an infinite network built from this motif would decay into ordinary vacuum in a matter of seconds. At the Planck scale, that was no small achievement; a tightrope walker who managed to circum-navigate the Earth a few billion times before toppling to the ground might be described as having similarly imperfect balance. In reality, any fragment of novo-vacuum they managed to create would be surrounded from the start by its older, vastly more stable relative, and would face the inevitable about a trillion times faster.

  Ilene reeled off a list of measurements from the instrument probes that were monitoring their environment, out to a radius of more than a light-hour. There was nothing on its way that could wreck the experiment—or at least, nothing traveling slower than ninety-five percent of lightspeed. Zulkifli followed with a status report from the machinery deep inside the Quietener. Systems that had been preparing themselves for the last twelve hours were now minutes away from readiness.

  The single graph on the wall was just a useful shorthand for the state they were hoping to create; the novo-vacuum itself was the sum of equal parts of forty-eight variations of the target graph, all generated by simple symmetry transformations of the original. All the individual variations favored one direction over another, but the sum combined every possible bias, canceling them all out and giving rise to a perfectly isotropic state. Since none of the graphs could be found in nature, this elegant description was useless as a recipe, but it wasn't hard to show that the same state vector could also be described by a different sum: forty-eight regions of ordinary vacuum, each slightly curved, oriented in forty-eight different directions.

  Inside the Quietener, an asteroid's-mass worth of helium had been cooled into a Bose-Einstein condensate, and manipulated into a state where it was equally likely to be found in any of forty-eight different places. These alternative locations were distributed across the surface of a sphere six kilometers wide. Ordinary matter—or any kind of matter interacting with the outside world—would have behaved as if each distinct position had already become the sole reality; if a swarm of dust particles wandering by had made themselves part of the system, or if the helium's behavior en masse had merely hinted at the detailed motion of its own atoms, then that behavior could only have told half the story—the classical half—and all the quantum subtleties would have been lost in the fine print. But the condensate was isolated as scrupulously as any cycling Qusp, and it had been cooled to the point where the states of all its individual atoms were dictated completely by its macroscopic properties. With no hidden complications, inside or out, the result was a quantum-mechanical system the size of a mountain.

  The geometry of the vacuum in the Quietener inherited the helium's multiplicity: its state vector was a sum of the vectors for forty-eight different gravitational fields. Once the condensate's components had all been nudged into place, the quantum geometry at the center of the sphere would be equivalent to the novo-vacuum, and a new kind of space-time would blossom into existence.

  That was the idealized version: a predictable event in a known location. In reality, the outcome remained hostage to countless imperfections and potential intrusions. If the experimenters were lucky, sometime over a period measured in minutes, somewhere over a region measured in meters, a few thousand cubic Planck lengths of novo-vacuum would be created, and survive for an unprecedented six-trillionths of a second.

  Yann turned to Cass. “Are you ready to freeze?” The first time he'd asked her this, she'd been almost as nervous as the moment before she'd been transmitted from Earth, but the question had rapidly become a formality. Of course she was ready. That was how things were done. Just a few minutes of numb immobility, watching the data appear on the screen in front of her, and the odds were good that it would be the last time. A
five-hour trip back to the station, a day or two of analysis, a brief celebration, and she would depart. Her Earth body, frozen more deeply than this one had ever been, was waiting for her. She'd step across the light-years in a subjective instant, a new set of memories to sweep away the icy cobwebs of her old self.

  She said, “No. I'm not ready.”

  Yann looked alarmed, but only for a moment. Cass suspected that he'd just conferred privately with someone better able to guess what she had in mind. Though the Mimosans didn't think any more rapidly than she did—running on Qusps themselves, they faced the same computing bottlenecks—they could communicate with each other about five times faster than her own form of speech allowed. That only annoyed her when they used it to talk about her behind her back.

  She added dryly, “Tell Rainzi I've changed my mind.”

  Yann smiled, clearly delighted, and then his icon was instantly replaced by Rainzi's. Fair enough: with the countdown proceeding, the Mimosans had better things to do than fake inertia for its own sake.

  Rainzi's response was more cautious than Yann's. “Are you certain you want to do this? After everything you told me?”

  “I'm the quintessential singleton,” Cass replied. “I weigh up all my choices very carefully.”

  There was no time to spell out in glacial words everything she was feeling, everything that had swayed her. Part of it was the same sense of ownership that had brought her all this distance in the first place: justifiably or not, she didn't want the Mimosans to have a better view than she did of the thing they were about to create together. There was the same longing for immediacy, too: she would never see, or touch, any graph as it really was, but to remain locked in a body that could only perceive a fraction of the data, milliseconds after the fact, would leave her feeling almost as detached from the event, now, as if she'd stayed on Earth, waiting for the centuries-old news of an experiment conducted light-years away. Every viewpoint was a compromise, but she had to be as close as she could get.

  Beyond the experiment itself, though, it was clear to her now that she couldn't leave Mimosa without doing at least one thing that went against the grain. After five years of monastic restraint, five years of denying herself the dishonest comforts of virtual reality, she was sick of placing that principle above everything else. Beyond the fact that this disembodiment would be entirely in the service of honesty, she needed, very badly, to drag herself out of the absolutist rut she'd been digging from the moment she'd arrived. If she'd compromised a little from the start, maybe she wouldn't have felt the same sense of desperation. But it was too late now for half-measures. If she returned to Earth unchanged, it wouldn't be a triumph of integrity. It would be a kind of death. She'd implode into something as hermetic and immutable as a black hole.

  All this, weighed against the thing she hated most: lack of control. Every choice she made rendered meaningless. What choices, though? Her clones would run for a few subjective minutes, most of them in rapt attention as the data poured in. What was the worst that one of these transient selves might do? Utter a few unkind words to Livia or Darsono? Disclose some small guilty secret from her past to people who either wouldn't understand, wouldn't care, or at the very least, wouldn't have the chance to reproach her for long? She wasn't opening up the gates to the old human nightmare: endless varieties of suffering, endless varieties of stupidity, endless varieties of banality. She would diffuse a very small distance into the space of possibilities, and whatever unhappiness she might experience, whatever misdemeanors she might commit, would be erased beyond recovery.

  Rainzi looked skeptical, and she couldn't blame him. But there was no time left for him to play devil's advocate, to test her resolve. Cass stood her ground, silently, and after a moment he nodded assent.

  She felt a stream of low-level requests for data, and she willed her Mediator to respond. She'd been through the same process before her transmission from Earth: sending the preliminaries first, things that needed to be known about the structure of her mind before it could be implemented in a new environment.

  Rainzi said, “Take my hand. We'll step through together.” He placed his ghost-fingers over hers, and asked her for everything.

  Cass examined his face. It was pure chance that her Mediator had given him an appearance that inspired trust in her, but the faces of the embodied were no better guides to character, whether they'd been sculpted by genes or by their wearer's wishes. If Rainzi's eyes still seemed kind to her, after five years, wasn't that because he'd shown her genuine kindness? This was not the time for paranoid delusions about the unknowable mind behind the mask.

  She said, “Are you ever afraid of this, yourself?”

  “A little,” he admitted.

  “What frightens you the most? What is it that you think might happen?”

  He shook his head. “There's no terrible fate that I fear is lying in store for me. But however many times I do this, I come no closer to knowing what it's actually like. Don't you think there's something frightening about that?”

  She smiled. “Absolutely.” They weren't so different that she'd be insane to follow him, the way it would be insane to follow an armored robot into a volcano. This would not be strange or painful beyond her power to bear. If she truly wanted it, she had nothing to fear.

  Cass opened the floodgates.

  Rainzi's hand passed through her own, intangible as ever. Cass shuddered. She was who she always was, and the part of her who valued that above all else could not disguise its relief.

  “Don't worry,” he assured her, “you won't be hanging around waiting. And you won't be disappointed. The femtomachine will only start up on a definite signal from the Quietener; if there's nothing, it won't ever be run.”

  Cass protested, “Aren't you telling the wrong person?” He might have mentioned this before she'd been split.

  Rainzi shrugged. “To the clone, it will be self-evident. If it gets the chance to think anything at all.”

  If the vacuum at the heart of the Quietener changed, her other self would wake, watch the whole event unfold in slow motion, bifurcate a million times, then vanish, before Cass had even noticed the good news. Neither the price nor the payoff were part of her own future, now.

  Yet they would all be one person: awake, asleep. The dream she would not remember would be her own.

  Here and now, though?

  She would have to make do with whatever glimpses she could steal.

  She turned to Yann. “Freeze me. One last time.”

  Chapter 3

  Cass looked around the simulated chamber. The display on the wall was densely inscribed with new data, but nothing else appeared to have changed. The Mimosans were the usual icons drawn by her Mediator; she still had no hope of perceiving them as they perceived themselves. The structures in her mind where sensory data was represented hadn't changed; they simply weren't coupled to genuine sense organs anymore. It was only the touch of Rainzi's nonexistent skin against her own—a translation interacting with a simulation—that proved she'd stepped from her world into his.

  Or rather, they'd both stepped together into a new world, from which neither of them could hope to emerge.

  Cass felt no anxiety, just a bittersweet sense of everything her newfound freedom did and didn't mean. If she'd abandoned embodiment a year or two earlier, she might have had some prospect of going further: finding a path of gradual change that led to new abilities, such as the power to interpret the Mimosans' language firsthand. As it was, she didn't even have time for the smallest act of self-indulgence: a simulated swim, a solid meal, a glass of cool water. After five years, all the pleasures she'd been pining for had become attainable at the very moment when they would be nothing but unwelcome distractions.

  She slipped her hand free of Rainzi's and turned to examine the display. A faint spray of particles was radiating out from the center of the Quietener, the sign of an unstable boundary between old vacuum and new.

  The data had only been coming in for a f
ew hundredths of a picosecond, so the statistics were still ambiguous. As she watched, rows of figures were updated, the sprinkling of points on half a dozen charts grew denser, curves shifted slightly. Cass knew where every number and every curve was heading; it was like watching the face of a long-awaited friend materialize out of the darkness, having pictured the reunion a thousand times. And if the face might yet turn out to be a stranger's, that had nothing to do with the way she felt. There was pleasure enough in anticipation; she didn't need to conjure up traces of doubt just to savor the added suspense.

  “What we're doing isn't all that unusual,” Darsono mused. “I think everyone lives in at least two time scales: one of them fast and immediate, and too detailed to retain in anything but outline; the other slow enough to be absorbed completely. We think our memory has no gaps, we think we carry our entire past inside us, because we're accustomed to looking back and seeing only sketches and highlights. But we all experience more than we remember.”

  “That's not true of everyone,” Bakim countered. “There are people who record every thought they have.”

  “Yes, but unless every part of that record has the potential to be triggered automatically by subsequent thoughts and perceptions—which no one ever allows, because the barrage of associations would drive them mad—it's not true memory. It's just a list of all the things they've forgotten.”

  Bakim chortled. “‘True memory’? And I suppose if I perceive something with so much spatial resolution that I can't give immediate, conscious attention to every last detail simultaneously, it's not a ‘true’ perception—it's just a cruel taunt to drive home all the things I've failed to perceive?”