The Clockwork Rocket

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 exponential 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