Schild's Ladder

by Greg Egan

  Kadir said, “You've visited Zapata?” He had probably intended to greet them politely then move on, but this claim could not be left unexamined.

  “Yes.” Tchicaya braced himself for a barrage of insults about travelers and other parasites.

  “How long ago?”

  “About nine hundred years.”

  “Where did you go?”

  “All over.” Kadir waited expectantly, so Tchicaya reeled off a list of towns.

  When he'd finished, Kadir said, “I was born in Suarez, but I left when I was twenty. I never managed to get back. How long were you there?”

  Tchicaya had been reorganizing his memories as they spoke, dragging the whole period upward in his association hierarchy. “Less than a year.”

  Kadir smiled. “That's longer than most visitors stay. What was the attraction?”

  “I don't know. It was a quiet spot, I was tired of moving about. The landscape wasn't spectacular, but from the house where I stayed you could see the top of the mountains in the distance.”

  “That slate-gray color, against the sky in the morning?”

  “Yeah. Completely different at sunset, though. Almost pink. I could never work that out.” He'd raised the memories so high that it might have been yesterday. He could smell the dust and the pollen, he could feel the heat of the evening.

  Kadir said, “I think I know where you were. Not the house, it wasn't built when I was there, but—do you remember the creek, north of the main road?”

  “Yes. I was close to it. A few minutes' walk.”

  Kadir's face lit up. “That's amazing! It was still there? We used to go swimming in that creek. My whole family. All through summer, around dusk. Did you swim in it?”

  “Yes.” At the same time, the same season. Watching the stars come out, lying on his back in the cool water.

  “Was the big tree still there? With the branch overhanging the deep end?”

  Tchicaya frowned, summoning up eidetic imagery, constructing a panoramic view in his mind's eye and searching for anything meeting this description. “I don't think so.”

  “No, it wouldn't have been.” Kadir turned to Mariama. “We used to walk out along this branch, about four meters up, and dive off backward.” He spread his arms and swayed. “The first time I did it, it must have been an hour after sunset. I couldn't see anything, and when I hit the water I just kept sinking into the blackness. I was nine years old. I was terrified!”

  Tchicaya said, “There was no deep water, when I was there. It must have silted up.”

  “Or the banks might have shifted,” Kadir suggested. “I was there three hundred years before you. They might have built anything upstream.”

  Zyfete approached, and slipped an arm around Kadir's waist. She regarded Tchicaya warily, but it must have been obvious that he was not making trouble.

  Looking away from her into the crowd, Tchicaya spotted Sophus, Tarek, Birago. He was conspicuous here; it couldn't be otherwise.

  He said, “I have to go.”

  Kadir nodded, unoffended. He reached out and shook Tchicaya's hand. “I'm glad you saw Suarez,” he said.

  Mariama caught up with him outside.

  “Go back in with your friends,” he said.

  She ignored him. “Was that so unbearable?”

  “No. I never claimed it would be. I was afraid my presence might upset someone. It didn't. I'm glad.”

  “I suppose you think that's all pathological? The music, the pictures, the food?”

  Tchicaya scowled. “So much for you reading my mind. It's ordinary nostalgia. I feel the same way about all kinds of places. There's nothing sick or obsessive about it. And because of that, it's hardly going to destroy him that he can't go back. His favorite swimming hole would have turned into a silted-up pond by now, anyway. He's been spared the disappointment.”

  “You really are made of stone.” She sounded disappointed, as if she'd seriously expected a few minutes' reminiscing with Kadir to change his mind about everything.

  “No one will have died, leaving Zapata. The rocks are gone. The trees are gone. If anyone really lived for those things, they'll find a way to re-create them.”

  “That will never be the same.”

  “Good.” Tchicaya stopped and turned on her. “What exactly do you imagine he's suffering? He's thinking about the things he's experienced, and the things he's lost. We all do that. He hasn't been eviscerated. Nine thousand years is a long time, but no one sprang from the ground of Zapata fully formed.”

  “They've still been dispossessed,” Mariama insisted.

  “Of rocks. Nothing else.”

  “Of memories. Of meaning.”

  “You know that's not true! What do you think, we're back in the colonial era, on Earth? There was a time when it was possible for an honest, intelligent person to subscribe to a cosmology where their dead ancestors lived in the mountains, and if you angered the spirit of the waterhole the crops would fail for the next ten years. Where the land was alive, and unique, and sacred. And if some horde of barbarians came marching through, subscribing to an even more surreal religion and claiming everything in sight for some inbred fop in a powdered wig, what else would you do but fight for your land, and cling to your beliefs?

  “No one is in that position anymore. No one can confuse the landscape with the inalienable things inside them.”

  Mariama replied pointedly, “Which would explain why you don't care at all what lies behind the border, and why you'd be just as happy to go and live in some abstract scape with the acorporeals.”

  Tchicaya was tongue-tied. He believed she understood the difference perfectly, but he knew he'd sound clumsy and self-contradictory if he backtracked to spell it out.

  He said, “How many thousands of years should Zapata have remained unchanged? How many million?”

  She shook her head. “That's not the question. It would have changed of its own accord.”

  “When? And how many children would it have smothered, before it changed?”

  “You weren't smothered on Turaev. You got out in time.”

  “Not everyone did.”

  “Not everyone needed to.”

  They'd reached the stairs leading up to his cabin.

  “You think I'm a hypocrite?” Mariama demanded. “Because I'm a traveler, and I'm championing people's right to stay put?”

  “I don't think you're a hypocrite.”

  “I've seen change,” she said. “Unforced, driven from within, not a response to some crisis that dictates the alternatives. That's painful in its own way, but it's better to go through that than have your whole way of life determined by some senseless accident that has nothing to do with anything.

  “When I arrived on Har'El, there was a genuine renaissance going on. People were reexamining their own traditions, not having them undermined by external events. Everything was fluid, everything was being questioned. It was the most exciting place I've ever lived in.”

  “Really? For how long?”

  Mariama shrugged. “Nothing lasts forever. You can't have a whole world in perpetual upheaval.”

  “No, but when the upheaval ended the result was apparently not a world you were prepared to live in.”

  “My marriage broke up,” she said. “And Emine wanted to travel. If she'd stayed on Har'El, I might still be there. But those are personal, idiosyncratic reasons. You can't start treating my decisions as some kind of measure of whether or not a whole society deserves to exist.”

  “That's true,” Tchicaya conceded. He was beginning to feel both battered and invigorated; she'd always had to push him to the edge of defeat before he got his second wind. He'd forgotten how much he'd loved arguing with her, when they'd taken the opposite sides back on Turaev. The only part he hated was the very thing that made it so exhilarating: there was always far too much at stake.

  He said, “But even if Har'El and all the other worlds deserve to be left in peace, that right isn't absolute.” He gestured at the border.
“How can you mourn the loss of Zapata, and then turn around and destroy something a thousand times more beautiful?”

  “I'm not mourning Zapata,” Mariama replied. “I've never been there. It means nothing to me.”

  “So because no one has been through the border, whatever lies behind it is worthless?”

  Mariama thought for a moment. “That's putting it crudely. But however beautiful, and challenging, and fascinating it is, it's not worth losing what we already have.”

  “And if someone gets through and lives there for a day? Or a week? Or a century? When does the magic thing happen? When does their right to their home become equal to everyone else's?”

  “Now you're just being jesuitical.”

  “I think that's the cruelest thing you've ever said to me.” Tchicaya smiled, but she didn't soften.

  “Freeze the border,” he pleaded.

  Mariama said, “You freeze the border, if that's what you want. If you do it soon, and if you do it properly, maybe that will convince us to leave it at that.” She inclined her head, and he could see her assessing the idea, judging it to be the farthest she was prepared to go. “Freeze the border before we do anything more, and you might just save whatever lies behind it.”

  She turned and walked away.

  Tchicaya watched her go, trying to untangle the negotiations he'd just stumbled through unwittingly. Without revealing any secrets, she'd all but declared that Tarek's Planck worms were visible on the horizon. The fanciful notion was finally taking real shape, and she'd responded by giving him one last chance to put his own case, and to listen to her own. One last chance to sway her, or to be swayed himself.

  She had given as much ground as she could. Neither of them were envoys for their factions; their decisions counted for nothing with anyone else. Between the two of them, though, there'd be no more engagement, no more discussion.

  Just this challenge. This ultimatum.

  This race.

  Chapter 10

  “I've already designed the vehicle you're looking for,” Yann insisted. “I just need some help to describe it in more palatable terms, so I can sell it to the others.”

  Rasmah said, “It's not a vehicle. It's software. And it's software for a nonexistent computer.”

  Yann shook his head. “That's just the mathematical formalism I've used. It's the best way to describe it—the most elegant, the most transparent. All we have to do now is disguise it.” He added, deadpan, “You can obfuscate, can't you? Physicists have been taking simple mathematical ideas and obfuscating them for centuries. It must have been part of your training, surely?”

  Rasmah took a swipe at him, and he flinched away from her. No doubt this was a habit he'd acquired during embodiment, when he'd managed to elicit a similar response from people on a regular basis.

  With the queue for bodies growing ever longer as new arrivals flooded in, Yann had decided to remain acorporeal. Tarek had responded to this news at the weekly interfactional meeting with a long, paranoid dissertation on Yann's self-evident intention to use his new position to “corrupt” the Rindler's processor network, infiltrating the Preservationists' communications and data storage systems, spying on them and undermining all their efforts. Fortunately, Sophus had spoken next, gently guiding Tarek back into contact with reality. Many things in the universe remained difficult and mysterious, but the casual structure of computer networks was not one of them. It would have required an act of cartoonish incompetence on the part of the Rindler's designers to create a network in which any of the abuses Tarek feared were physically possible.

  Tchicaya said, “So you shift dynamics, once you're through the border? You navigate between them?” He had arranged for the three of them to meet in his cabin so that Yann could try out the idea on Rasmah and refine his pitch, before taking it to a meeting of all the Yielders. “The dynamic laws are like stepping-stones that only need to last for as long as you use them?”

  Yann grimaced. “That sounds ugly enough, but it's not even close to the truth. The algorithm never obeys a sharply defined dynamic law; if it tried to do that, it would be doomed from the start.” He thought for a while. “You know how a Gaussian wave packet can keep its shape in a harmonic oscillator potential?”

  “Yes.” Tchicaya felt a burst of confidence; that was just elementary quantum mechanics. In empty space, a particle's wave packet would always disperse, spreading out without limits. But if the particle experienced an attractive force analogous to the tug of a spring in classical physics, there was a certain shape—a certain Gaussian, like the bell curve of statistics—which was stable. Any tighter, sharper wave packet would necessarily have a range of values for momentum that made it spread out; that was just the uncertainty principle. The right Gaussian, though, in the right environment, was the perfect compromise between uncertainty in position and momentum, allowing the shape of the wave to remain unchanged as it moved.

  “This isn't really the same,” Yann admitted. “But it might sound persuasive if I put it that way.”

  Rasmah glanced at Tchicaya, exasperated. He made puppydog eyes back at her, pleading on Yann's behalf.

  She laughed, and relented. “Why don't you just give me the description of the graph you want to scribe, and I'll grind through the calculations using my own picture of Sophus's model. If I can demonstrate that we'd get some inforamtion back through the border—something more than we put in—that might be enough to persuade people. I'll make sure I phrase my results in the ugliest possible way.”

  Yann said, “That's wonderful. Thank you!”

  He passed something to Rasmah—Tchicaya's Mediator saw the fact of the exchange, but not the content—and then vanished.

  Rasmah sighed. “You really think he's on to something? A quantum computer can simulate any quantum process; that's old news. It doesn't mean that there is a quantum computer underlying anything.”

  “No,” Tchicaya agreed. “But qubit network theory doesn't claim that. It just says that when you get to a low enough level, you have nothing left to lose by treating the system as if it were software. It's like all the proofs in applied algorithmic theory that are based on imagining Turing machines. No one complains that the real universe is conspicuously devoid of paper tape.”

  “Old habits die hard,” she confessed. “I'm still in mourning for the Sarumpaet rules, and they were disproved before I was born. They're what I was brought up on, they're what I've thought of all my life as the template for a physical theory. It's not easy adapting, even to Sophus's model.”

  “Yeah. I really am grateful to you for trying this,” Tchicaya said. Since the factional rift had widened, it was more important than ever to keep all the Yielders open to each other's new ideas, and where he wasn't competent to contribute directly himself, he could at least act as a kind of broker, prodding the appropriate experts into action.

  Rasmah seemed on the verge of pointing out that he might have expressed his gratitude to her more palpably, but then she smiled and accepted his words at face value.

  “Okay. Here I go.”

  She turned her attention to something invisible to Tchicaya. For several minutes, she sat in complete silence.

  Suddenly, she exclaimed, “Oh, I see! This is actually quite nice.”

  Tchicaya was excited, and slightly jealous. “Can you explain?”

  Rasmah held up her hand for patience, retreating back into her private scape.

  After a while, she spoke again. “Think of all the different dynamic laws that might make topological sense, in terms of the propagation of various kinds of particles that are defined as patterns embedded in a graph. I know that's horribly vague, but I don't think you'd want the version with added jargon.”

  Tchicaya said, “Okay. I'm thinking of them.” He'd seen enough examples that they'd pinned to the border over the last few months to have some feel for what this meant.

  “Now imagine each one is a quantum state vector in a big fat Hilbert space. All of them orthogonal to each
other.”

  “Yes.” Tchicaya had never had his mind restructured to enable clear images of more than three dimensions, but since Rasmah's Hilbert space was infinite-dimensional anyway, three was as good as any other number. “I'm doing that. Go on.”

  “Now imagine a new set of vectors that consist of equal amounts of all these dynamic-law vectors, and that are all orthogonal to each other. These vectors represent definite values of a variable that's complementary to the law vectors. Branco calls them law-momenta—which is a bit sloppy, because they're not true Lagrangian conjugates, but never mind.”

  “I'll try not to fret.” Tchicaya thought of the directions on a map. If the dynamic-law vectors were north and east, then the new, unbiased, law-momenta vectors would be north-west and north-east. Both had equal portions of the old directions—if you counted west as being the negative of east, and only cared about the size of things, not their sign—and they were at right angles to each other. In three dimensions or more you needed to introduce complex numbers to pull off the same balancing act, but from there you could keep on going to any number of dimensions. The amounts of the original vectors you combined were just a series of complex numbers that moved around a circle in the complex plane; to get different vectors, all orthogonal to each other, you just moved around the circle at different rates.

  “Now picture a state vector which has equal components when written as superpositions of the old set, or the new.”

  In two dimensions, that was easy: north-north-east lay at the same angle to north as it did to north-east, and the same angle to east as it did to north-west. In terms of the quantum mechanics Rasmah was describing, it had equal uncertainty in the two complementary variables: it did not obey a precise dynamic law, but nor did it have any precise law-momentum. It split the difference and compromised, in the most symmetrical way.

  Rasmah continued. “These are the states Yann wants to scribe, because if you create one on the border, and then arrange to measure the same kind of state coming back, they yield the highest attainable probability of returning with information about the interior.”