The Clockwork Rocket

by Greg Egan

  “Do you mind if we use the dye?” Yalda asked. She wanted to have the report on the Hurtler completed as soon as possible, ready for the couriers who’d be leaving at dawn.

  “Of course not.” Antonia put the lid back on the pot and slid it toward her. “I was still gathering my thoughts; it can wait until morning.”

  Yalda saw the curtain part at the entrance to the apartment. As she spun around to face the intruders one of them screamed, “Lie on the floor! All of you!” By now, four men had filed into the room, and there were more behind them. They wore police belts, and they’d unsheathed their knives.

  Antonia began wailing. “I’m sorry! Tullia, I’m sorry! Someone must have—”

  Tullia said, “Be quiet, you don’t know—” One of the officers stepped up to her, knife outstretched.

  “Lie down, or I’ll split you open!”

  Tullia knelt then lay on her chest. Yalda met her rear gaze, hoping for advice, but if there was a message she couldn’t read it.

  Yalda said, “Antonia, get behind me.” She moved toward the officer who’d threatened Tullia. He was tiny; if not for the knife she could have done what she liked with him. “You want to go out the window?” she taunted him. “You’ve got no business here. Go harass someone else.”

  The man raised the knife confidently, no doubt accustomed to its power to induce obedience. Yalda advanced on him, undeterred. She wouldn’t even need to extrude extra limbs for the encounter; if she seized him with both hands it wouldn’t matter if she lost an arm in the process, she could still fling him down to the street with the remaining one.

  “Please, Yalda, don’t!” Antonia implored her, distraught. “I’ll go back! Don’t make trouble for yourself!”

  Yalda was unmoved; what gave these buffoons the right to interfere in anyone’s life? If one of them spilled his brains on the cobblestones, the others might rethink their priorities.

  Tullia addressed her calmly. “Yalda, if you resist, we’ll all get a beating. If you harm even one of them, we’ll all be killed.”

  Yalda stared at the man in front of her, then forced herself to look past his triumphant sneer to the long line of colleagues waiting behind him, knives at the ready. She might be able to deal with three or four of them before she was overpowered—but if Tullia was right, it would not be worth the price.

  She knelt down, then lay on the floor, subduing her rage. Her physical strength meant nothing. The rightness of her cause meant nothing. The Council had given these men the authority to capture and return runaways; Antonia’s plans for her life were irrelevant.

  The officer she’d confronted put a foot on her back and held her arms behind her while someone passed him a length of hardstone chain. He slipped the loop at the end of the chain around one of her arms, then took a vial from his belt and shook a few beads of bright red resin onto her palm. It stung fiercely, but Yalda forced herself not to lash out. Then he pressed both of her palms together. Skin stuck tightly to skin, in itself no great hardship, but the resin made her body act as if these ordinary surfaces comprised a kind of internal partition, a pathological mistake that needed to be broken down.

  Yalda closed her eyes for a moment, fighting not to lose consciousness. She had no right to be surprised by any of this; how many prisoners had she seen shuffling through Zeugma with their arms melded? She’d looked away, like everyone else. Murderers and thieves got what they deserved.

  The officer ran the tip of his knife over her skin methodically, until he found the telltale crease of a pocket.

  “Do you want me to cut it open?” he asked.

  Yalda opened the pocket. He reached in and took out a handful of coins and her vial of holin.

  In the corner of the room, Antonia was pleading with her own captor. Her hands had been bound with rope, but she and Tullia had been spared the melding resin, no doubt as a reward for their swift compliance. Once they were down on the street, Yalda thought, Antonia could easily slip out of those unreliable bonds and make a run for it.

  Yalda’s tormentor walked over to Antonia. “You’re a runaway?”

  “Yes, sir.”

  “And you’re willing to return to your co?”

  “Yes, sir. But my friends didn’t know; I told them he was dead. I’ll go back to him willingly, but you have to release them.”

  This attempt at a bargain amused the officer. “This patrol wasn’t looking for you,” he said, “but it’s kind of you to volunteer the truth. We only came here for the fat one, the solo. She assaulted a Councilor’s son.”

  He walked back to Yalda and began kicking her in the tympanum.

  The room fractured, the walls collapsed into rubble. Yalda writhed and screamed, buried in shards of noise and pain.

  8

  “When you come before the sergeant,” Tullia whispered, “don’t argue about anything. Agree to the fine, agree to the conditions, and you’ll be out of here in a few more days.”

  Yalda was bound to the wall of her cell, her own flesh the last link in the chain. She’d threaded her body through the loop of her melded arms so they were in front of her now, a minor improvement. The cell was bare and windowless, equally dark by night and by day. Twice, someone had entered unseen; the first time to beat her, the second to strew rotten grain on the floor. The loudest sounds that reached her were the thwack of wood against flesh and the hums of misery from other cells.

  They’d granted her two unintended mercies, though. The floor was real soil, her favorite kind of bed; the worms that might have revolted a more fastidious guest just made her feel at home. And they’d put her next to Tullia, allowing them to whisper to each other through the wall’s porous stone. Without that, she would have lost her mind.

  “I’ll be charged with sheltering a runaway, and for the holin in my room if they found it,” Tullia explained. Apparently she’d been through all of this before. “They’ll fine me a few dozen pieces, and make me swear an oath not to repeat my crimes. Your fine will probably be larger, but don’t worry: they’ll give you a chance to contact people who can help you pay it. I expect I’ll be out before you, so I’ll talk to Daria and the others at the Solo. Whatever you need, we’ll raise it.”

  “He threw the stone at me!” Yalda complained. “Don’t pay them anything! Let them charge that shit-head with assault as well.”

  “Can you produce a dozen witnesses against him?” Tullia asked.

  “Probably not.”

  “Then it doesn’t matter what he did. Stop telling yourself that it matters, or you’re going to make everything harder.”

  Yalda could not accept this advice. She knew she should have restrained herself: she should have resisted lobbing back the cobblestone, sharp and heavy as she’d known it to be. But she still ached to see her assailant locked up beside her, beaten beside her, fined and humiliated and forced to promise to reform his own violent ways.

  She knew that her actions had cost Antonia her life. Maybe a few years of it, maybe a few stints, but Antonia’s chance to bargain with her co had been lost the instant Yalda had brought the police into Tullia’s apartment. That was the worst of what she’d done, and she’d willingly confess her recklessness to anyone accusing her on Antonia’s behalf. But her own culpability excused no one else. Let Antonio, who was merely eager for children, let the Councilor’s son, who was only teasing a solo, let the police, who were simply doing their jobs, all line up and take their punishment beside her.

  Otherwise, octofurcate them all.

  Tullia grew weary of the subject, and after making her advice clear she steered their conversation elsewhere.

  “Come out of this stinking prison with me for a couple of bells,” she begged Yalda. “Why live the life of the mind at all, if you’re not going to live it now?”

  “I’ll lie here and hallucinate Hurtlers, shall I? That will be a real comfort.”

  “Last time I checked, you had a more urgent problem,” Tullia reminded her.

  “You want us to solve the exp
onential blow-up, here?”

  “How would you rather spend your time? Plotting the dismemberment of Councilors’ sons?”

  In truth, Yalda longed for a distraction, and she wished she shared Tullia’s discipline and resolve. But the problem itself seemed as intractable as their incarceration. “Giorgio was right,” she said. “The equation I found has exponential solutions. And if I try to damp them down—if I try to get rid of them by adding new terms to the equation—I just lose the original solutions.”

  “It’s a strange equation for a wave,” Tullia conceded. “The nice thing about the wave equation on a string is that you can set the initial conditions and just watch them unfold: you can pluck the string into any shape you like, and give it any kind of movement, and from that the equation lets you find the shape of the string at any time in the future. What’s more, if you make a small mistake measuring the initial setup, it’s not a calamity; the errors in your prediction are equally small.

  “But your light equation is more like the equation for the temperature distribution in a solid. If you have, say… a thin slab of stone and you want to know its temperature at every point, to get reliable solutions you need to specify the temperature all the way around the border of the slab. If you tried to start with the temperature along a single edge and its inward gradient, any tiny error in the data there would blow up exponentially as you moved across the slab. Your equation acts the same way.”

  Yalda pondered this in the darkness. “So by analogy, to calculate the behavior of light in a certain place, over a period of time… I’d really need to know what it does on the entire border of that four-dimensional region? Not only what it’s doing at the start, but everything that happens at the boundary, and how it all ends up?”

  “Precisely,” Tullia said. “The equation you’ve come up with might be said to govern the behavior of light, but practically speaking it’s no good for making predictions. Everything it tells you could be tested in retrospect, but you’d always need to know how the story ends before you can start reliably ‘predicting’ the middle.”

  Yalda said, “Waves on a string can only have one velocity. We know that violet light can travel much faster than red light—and it’s not implausible that there are even faster hues, beyond our ability to detect. So why should we expect that knowing the state of the light in just one place should ever be enough to say what happens next? Some other wave we haven’t accounted for—just beyond the edge of the region we know about—could always be on the verge of crashing in and spoiling our prediction.”

  “Good point,” Tullia replied. “So let’s accept the possibility of light that travels as fast as you wish… but then to compensate, I let you know about every wave that presently exists as far away as you wish. That way, you get as much warning as you could hope for; you can’t complain that some fast wave came hurtling in from a place beyond the reach of your data. And if the cosmos goes on forever, you get to know about the entire, infinite present: for one moment in time, there are no secrets from you anywhere.”

  “Go ahead and grant me that!” Yalda urged her. “Wouldn’t that eliminate the problem?”

  “No!” Tullia sounded both exasperated and amused that Yalda had taken the bait so readily, without thinking it through. “Your equation still has solutions that can blow up exponentially out of the tiniest mismeasurement. You still wouldn’t be able to predict what happens right in front of your eyes over the next few pauses. Does that really accord with your instincts about the way the physics of light should work?”

  “No,” Yalda admitted. She adjusted her position, then cursed softly and braced herself for the sound of tearing flesh. She’d been trying to keep her arms a few scants apart within their shared sleeve of skin, hoping to make her eventual liberation less traumatic. But her body thought it knew best. Every time she dozed, or her attention wandered, she had to rip apart a fresh bundle of muscle fibers that had formed between the ends of her limbs.

  When she was done, she thought back over the steps in Tullia’s argument. “What if the cosmos didn’t go on forever?” she said. “In space, or in time?”

  “Then you’d still need to know what happens at its boundary,” Tullia replied. “Like the slab of stone: you need to know what’s going on at all the edges.”

  Yalda considered the possibilities this offered. By declaring that the boundary of the cosmos was subject to some special rule—perhaps that the wave simply had to be zero there—she could probably keep it from blowing up in the interior. But that was an ugly resolution, an arbitrary constraint that came from nowhere and offered no deeper understanding.

  “What if there are no edges?” she suggested. “What if the cosmos is like the surface of the world—finite, but borderless?”

  Tullia lapsed into silence for so long that Yalda grew worried. She extruded a new, free arm and thumped the wall. “Are you all right?”

  “Yes! I’m thinking!” Tullia almost sounded happy, as if Yalda had finally suggested something novel enough to be truly diverting.

  Eventually Tullia declared, “I’m fairly sure that that would solve the exponential blow-up. You can wrap an oscillation around a sphere so that it joins up with itself smoothly—but you can’t do that with an exponential growth curve, which never revisits its earlier values.”

  Yalda chirped with delight. “So if the cosmos is a four-dimensional version of the surface of a sphere—”

  “Things would still be very strange,” Tullia warned her. “The prediction problem jumps from one extreme to the other.”

  “What do you mean?”

  “Think about the two-dimensional version,” Tullia said. “If you draw a circle around Zeugma, the data lying on that circle—combined with your equation—tells you everything that happens in the city. Information about the border gives you information about the interior.”

  “But that’s nothing new. Where’s the problem?”

  “A circle around Zeugma,” Tullia replied, “is also a circle around everything else in the world. The border of the city is also the border of everything that lies beyond. So from the data on that one circle, you can find the solution to your equation on the entire sphere.”

  “Oh.”

  Tullia drove the point home. “In the four-dimensional version, that’s like claiming that you can measure the light in a patch a few scants across, for a couple of pauses… and learn everything there is to know about light throughout the history of the cosmos. Because the border of your tiny region is also the border of everything else.”

  Yalda buzzed wryly. “I can’t say that that accords with my instincts about the physics of light.”

  “Nor mine.” Tullia’s surge of enthusiasm was gone, but she was doing her best not to sound despondent.

  “We tried,” Yalda said. “And it was worth trying.”

  They had managed to leave the prison for a while, but nothing was easy, even in freedom.

  When it was quiet in the cells, Yalda could hear the bells from one of the city’s clock towers; she missed a few from noise, or sleep, or inattentiveness, but never so many as to lose track of time. So she knew it was the middle of the morning on their third day when the guards came and took Tullia.

  This had to be her hearing with the sergeant. Yalda waited, trying to be patient. Tullia had told her that there was usually a large group of prisoners to be dealt with in each session, and the whole thing could last a bell or two.

  By evening, Tullia had not returned. Either they’d set her free, or they’d moved her to a different cell while she arranged the payment of her fine.

  Yalda chose to believe that she’d been freed. Tullia hadn’t resisted arrest, and she knew the system well enough to say the right things at her hearing. If the fine had been small enough she might have been released on a promissory note, rather than forced to wait until actual coins had been delivered to the sergeant. Tullia would be at the Solo Club, celebrating her freedom and looking for ways to help her friend.

&nb
sp; Yalda blocked out the sad humming of her neighbors; she felt for them, but she didn’t have the strength to involve herself in their plights. She would have her turn before the sergeant soon; she needed to decide what she would say.

  When the guards came the next morning, the light of their lamp almost blinded her. She’d planned to sneak a look at the tool they used to disconnect her chain from its place on the wall, but everything was veiled in painful brightness. As they tugged on the chain to draw her out of the cell, she quickly lengthened one of her arms and shortened the other, allowing the force to be borne by solid flesh instead of the loose tube of skin between them that she’d fought to keep empty.

  She stumbled up the broad staircase into a corridor filled with searing daylight, then hurried along with slitted eyes, not wishing to drag the chain and provoke her captors. In a room full of prisoners, she was secured to the wall again. Yalda raised her gaze cautiously; there were more than a dozen men and women chained up beside her, most of them with melded limbs. Everyone looked as wretched and afraid as she was.

  She felt herself shivering. No friends were permitted here to offer support. Nobody could advise her now, or speak in her defense. All she had to guide her was Tullia’s counsel, which she’d been so vehement in opposing.

  The sergeant entered the room—wearing a belt much like his subordinates’, but adorned with no less than four knives—and took his place behind an impressive calmstone desk. An assistant brought in a stack of paper, smelling of fresh dye; for an instant the scent was almost comforting.

  As the first case was heard, Yalda tried to concentrate on the procedure and learn what she could. A young man had stolen a loaf from the markets, and then fled from the police. He did not deny the charge.

  The sergeant fined him a dozen pieces. “How will you pay this?” he asked.

  “My brother might help me,” the man said, his voice soft with shame.