by Greg Egan
“And if the valley’s not a perfect parabola,” Onesto observed, “that doesn’t really change the significance of the main energy gaps, does it? There’ll be smaller gaps as well, but if the main ones are large enough there’ll still be energy levels where you need to make more than one photon in order to rise any higher.”
“Right,” Carla said. “And if the valley is deep enough, those gaps could end up so large that you’d need to make six or seven photons to cross them.”
Patrizia turned to Carla. “Doesn’t that… solve the stability problem?”
Carla considered the question seriously. In the old way of looking at the problem, even if the walls of the energy valley were so steep that the luxagen rolled back and forth at a rate dozens of times greater than the maximum frequency of light, the tiniest deviation from a parabolic shape would introduce lower-frequency components into its motion—some of them low enough to produce light. And however feeble the radiation emitted that way, the luxagen would slowly gain energy and creep up the valley, until it finally escaped.
But that was in a world where energies could take on any value at all. In the new theory of luxagens as waves, a steep enough valley would have gaps between its energy levels that were insurmountable—and the inevitable imperfections in the shape of the valley would merely split some of those levels. As Onesto had pointed out, if the rungs of the original energy ladder were spaced sufficiently widely, adding a few extra rungs close to the originals wouldn’t suddenly make the whole thing traversable. The valley’s imperfection no longer undermined its stability.
“We still don’t know how long it takes to create a given number of photons,” Carla said cautiously. “But we do know that it takes much longer to make five than four, and a great deal longer to make six—even with the beam from a sunstone lamp to help. If we could understand what was going on there, I think we’d be getting close to explaining how some solids can be stable.”
Patrizia sketched the shapes of the first few luxagen waves on her own chest. “What happens if I add two of these solutions together—two waves with different energies? The sum will still solve the same equation… so what does the combined wave represent? Two luxagens, one with each energy?”
Carla said, “That doesn’t sound right. We found the wave equation by translating the energy-momentum relationship for a single particle. And what if I add two solutions in unequal proportions? Say, one quarter the first solution and three quarters the other?”
“Couldn’t that be… one particle with the first energy, and three with the second?” Patrizia didn’t sound too persuaded herself; she could probably see where this numbers game was heading.
“Irrational proportions, then,” Carla replied. “Multiply the second solution by the square root of two, then add it to the first. It’s still just one particle.”
Patrizia hummed with frustration. “You can multiply these waves by any number you like!” she said. “It doesn’t change their frequency, so it won’t change their energy—I mean the luxagen’s energy. Unless the wave has some energy of its own, separate from the particle’s energy, what does it actually mean if you double the size of the wave, or triple it?”
Carla was worried now. If the luxagen wave did have an energy of its own that depended on its amplitude, the discrete energy steps that were the theory’s great virtue would be erased. “What if we ignore the overall size of the wave?” she suggested. “Or better yet, we standardize the size of each solution, by some measure. Then we could still ask what it means to combine two solutions in a certain proportion. If we start with a wave with the lowest energy, and combine it with the next one, say at one part in twelve… what would that mean, physically? It can’t describe a particle with an energy lying one twelfth of the way between the two values.” That route would lead them back to continuous energies again, rendering the whole thing useless.
Patrizia spread her arms in a gesture of defeat; she’d run out of guesses.
“Part one energy, part another,” Carla muttered. “We could even have a luxagen that was part trapped in the valley, part free!”
Nothing was making sense any more. The exhilaration she’d felt when they’d found the energy levels had vanished now. Why should they take the luxagen equation seriously, if they couldn’t say what its solutions meant in all but a few special cases? If she tried to peddle this nonsense to Assunto as the answer to the stability problem, he’d have her teaching the wavelength-velocity relationship to three-year-olds for the rest of her life.
Then she heard her own words as if someone else had spoken them: Part trapped in the valley, part free. Two solutions you could combine, in any proportion. That proportion could be the missing timer—the means by which a luxagen in the tarnishing experiment kept track of how long it had been sitting in the light. Its energy couldn’t creep up over time… but the ratio between the two solutions could. The luxagen could start out as a trapped wave, but then gradually take on more and more of the free solution.
Carla didn’t know what this hunch was worth, but they had all the tools they’d need to test it. She said, “If we want to know how long it takes to get a luxagen out of the valley by blasting it with light… why don’t we just add the energy due to the light itself to the energy of the valley, and calculate exactly what that does to the luxagen wave over time?”
Patrizia quailed slightly. “That sounds like a long calculation.”
“Oh, it will be,” Carla promised her. “So before we even start, we should break for a meal.” She turned to Onesto. “Will you join us? Loaves for everyone, out of my entitlement. Let’s celebrate, replenish our strength—then start dragging some real predictions out of this equation.”
16
As she checked the link to the light recorder, Amanda leaned close to Carlo and whispered, “If this works, you should take it to the Variety Hall. They haven’t had an act that drew a crowd like this for years.”
There did seem to be about twice as many people gathered around the bench where they’d set up the signaling experiment than were usually present in the entire animal physiology workshop. Carlo didn’t know who’d invited them all, but he was feeling apprehensive enough without adding a layer of stage fright. He needed to keep both arms still or risk shifting the probes skewering his wrists, but he managed to roll his shoulders without the motion reaching below his elbows as he tried to unknot the tense flesh in his back.
Both probes had been aligned to pick up the signal to one finger of each hand. Amanda started the light recorder, then Carlo executed a sequence of moves with the chosen finger of his left hand, following the instructions on a sheet of paper clipped to the bench in front of him. Each individual action was simple enough, but they were arranged in an arbitrary progression that he could only adhere to by paying close attention, and he had deliberately refrained from any rehearsal. The eye-catching periodicity of his first, repetitive experiment had had its advantages, but this time he didn’t want his flesh to sense a pattern and pursue it on its own.
When this first stage of the performance was over, Amanda took the spool of paper out of the recorder, slipped it onto a shaft mounted on the bench, then wound the whole strip across onto another spool—the simplest way to inspect it without risking it getting tangled or damaged. To Carlo’s relief, there was a strong signal darkening the paper from start to finish; they wouldn’t need to dig around in his flesh any more to improve on it.
“Do you want to use this?” Amanda checked with him.
“Please.” Carlo wasn’t in great pain, but his body kept drawing his attention to the probes’ unnatural presence, refusing to let him feel at ease.
Amanda loaded the spool into the inverter, inspected the contact rollers for any grit or paper-fluff that could do mischief, then threaded the two leader tapes—from the recording itself, and from a second spool of unexposed light paper—together through the core of the mechanism and onto their respective receiving spools. Then she lit the lamp, closed th
e device, wound the spring, and engaged the drive. The spectators waited patiently as the machine whirred—better behaved than the usual crowd at any magic show.
Tosco said, “Have you checked that you’re not saturating the light paper’s response? Outside a limited range of intensities, that coating just flattens any variation in brightness.”
“We’ve checked,” Carlo replied tersely. Amanda added, “Everything’s been calibrated so it lies within a suitable exposure range. We won’t get the original light curve back, but any distortion should be comparable to the natural range of variation in the signal.” If the brain itself didn’t send out identical sequences for the same action every time, the flesh ought to be as forgiving with this artificial version as it needed to be with the biological messages it received every day.
The inverter gave a soft thud as its tension arm detected the end of the spool, halting the drive. Amanda retrieved the duplicate tape and rewound it slowly so Carlo could scrutinize it. The darkest paper in the original recording had protected the second strip from the lamplight in the inverter, allowing it to remain almost translucent, while the most translucent parts of the original—those exposed to the weakest signal from the probe—would have offered far less protection, allowing the duplicate to darken almost to opacity.
Carlo could see no sudden shifts in the tone of the paper that would indicate a surge or deficit of the sensitizing gas, and no stretches of flattened contrast that would imply that they’d saturated the coating. Light recording was a finicky art, but their experience was beginning to pay off.
“What do you think?” Amanda must have reached her own conclusion, but she kept her voice neutral. If Carlo wanted to declare the tape unusable—giving him an excuse to back out of the experiment—that was up to him.
“It’s fine,” he declared. As he spoke, he felt his left forearm twitch in dissent: a needle of hardstone driven through his wrist wasn’t fine at all, and every scrag of his flesh knew that there was a stranger incursion yet to come.
Amanda loaded the duplicate tape into the light player, running the leader through onto the receiving spool. She gently tugged the connecting arm from the left-hand probe out of its socket in the light recorder and swung it around toward the new machine. When it was in place, there was one more adjustment to make: she reached down and took hold of the probe itself, and turned the ring attached to the mirror at the bottom of the needle. Before, it had faced back up along his arm, to catch some of the light arriving from his brain. Now it was angled toward that light’s destination, down the motor pathway into his hand.
“Why doesn’t he just use a vole?” one of Tosco’s students whispered to another.
“That needle’s too big.”
“So why not make it smaller?”
“Be quiet, or you’ll be playing vole next time.”
Carlo said, “A smaller needle wouldn’t capture enough light. We’ll need to develop more sensitive paper before we can shrink the probes.”
“Are you ready?” Amanda asked him. She’d wound the player’s spring and lit the lamp while he’d been distracted by the students.
Carlo started to relax his left arm—doing his best to surrender control, to prepare himself not to fight what was coming—but then he felt the slight change in muscle tone threaten to shift the probe. He didn’t really need to disown the whole limb, though, so long as he could hold back the urge to intervene when the ghost of his earlier self started taking liberties with his body.
“I’m ready,” he replied.
Amanda engaged the drive on the player. Carlo gazed down his arm at his finger, which was moving without his bidding.
Cold nausea churned through his gut and esophagus, loosening food tubules from mouth to anus; he fought it and managed to hold onto his breakfast. There was nothing painful in the sensations coming from his finger—but a part of his brain was insisting that some kind of parasite had invaded the flesh, and its alarming twitches could only presage the likelihood of it burrowing even deeper. As he struggled to understand precisely where this revulsion was coming from—focusing his attention on the stretching of the skin, the tension in the muscles, the disposition of the joints—he couldn’t identify any one thing he hadn’t felt when he’d performed the same movements willingly. But he couldn’t separate that raw sensation from the context and declare that it was as innocent as before. Flesh that moved of its own accord simply could not be treated with equanimity.
When the playback stopped, Carlo shuddered with relief. The illusory parasite lingered for a moment, a fat dead thing trapped under his skin, but when he crooked his finger a few times it vanished. He realized that he hadn’t had the presence of mind to check his movements against the original script; he looked to Amanda for her verdict.
“The mimicry was pretty close,” she said. “A few gestures were dropped or ambiguous, but most were repeated accurately.”
Some of the onlookers offered congratulatory cheers. Carlo felt drained, but as his nausea faded he managed a chirp of satisfaction. As primitive and unpleasant as the whole demonstration had been, it had established an important principle. All the more so if they could repeat it with one more twist.
Amanda had already started rewinding the tape. “Give me a lapse or two,” he told her.
“You don’t have to do the second stage today,” she replied.
“I’m not wasting that spike in my wrist.” Carlo turned from her and saw Tosco watching him in silence, then he shifted his gaze slightly and addressed the man’s students. “You can mark this day as the birth of a new field,” he proclaimed. “The light recorder will revolutionize the study of the brain’s signals—and light puppetry will be the best way to compare those signals in different species.” Once they refined the equipment, they could replay the instructions from one vole’s brain in a distant cousin’s body and see which parts of the signal were interpreted the same way in both species. Not every nuance would be the same, but flesh was flesh, it all shared a common ancestor. With time and patience, they could take this language apart and uncover all its subtleties, as surely as scholars of ancient writing had decoded old engravings by their own process of comparison.
He nodded to Amanda to proceed. She uncoupled the connecting arm from the first probe, and swung it over toward his right hand. Carlo resisted the urge to pluck the needle out of his left wrist immediately; sometimes the extraction went horribly wrong, and he didn’t want to vocalize that much pain in front of an audience.
With the player connected to the right-hand probe, Carlo spent a moment preparing himself. It hadn’t been so bad the first time, and now he knew exactly what to expect. His gut had settled, he wouldn’t disgrace himself.
“I’m ready,” he said.
Amanda engaged the drive.
The finger they’d targeted with the probe remained motionless. “What?” Frustrated, Carlo moved his forearm slightly, just enough to feel the bite of stone against his flesh. Suddenly his whole right hand sprung to life: all six fingers flexing and waggling, turning and twitching, wriggling like worms with their heads in a trap.
With one word he could have had the signal shut off, but Carlo wanted to see this final stage play out; even with the probe misaligned it could tell them something useful. His sense of violation was more acute than before, but he could tolerate it for a couple of lapses. He glanced at Amanda; she was diligently observing his contortions, trying to judge how well they conformed to the script. Carlo could only be sure of one detail: some of his fingers were moving differently than others, so they couldn’t all be doing the right thing.
He heard the gentle thud from the player as it halted. His relief was short-lived; his fingers kept squirming. “All right,” he muttered. If his first recording of a twirling finger had revealed the potential for fleshly autonomy, this shouldn’t be entirely surprising or alarming. He just needed to tell his wayward hand to stop, firmly and clearly.
He commanded his fingers to be still—but this ed
ict was completely ineffectual.
Carlo let out a hum of frustration, hoping to convince himself as much as the onlookers that he was more irritated than afraid. He tried to clench his fist, but his body had news for him: the burrowing parasites owned that flesh, and they weren’t taking instructions from him.
“I think his hand’s giving birth,” someone joked from the back of the crowd.
“Could you take off the connector, please?” Carlo instructed Amanda, each polite syllable a proof that he remained unflustered. When she’d complied, he swung his arm away from the bench, mapping out the degrees of freedom he still controlled. He could move his arm at the shoulder, at will. He could flex and extend the limb at the elbow joint. He pictured the vast territory subject to his rule, pictured the tiny rebellious province, pictured the inevitable reconquest. But all of this stirring martial imagery remained nothing more than a fantasy. Beyond the wrist, he might as well have had a brood of angry lizards grafted to his flesh.
He drew his arm back and slapped the bench, trying to bash some sense into his hand. Again, harder. The third blow drove the probe’s needle deeper into his wrist; the pain was excruciating, but it felt right, it felt necessary.
“Carlo?” Amanda wasn’t panicking yet, but she wanted him to tell her how she could help.
“I haven’t lost control of my arm,” he assured her, struggling to get the words out. His actions were entirely voluntary—at least by the standards his rogue hand had set—even if the urge to damage the thing was becoming increasingly compelling.
But the blows weren’t helping, they weren’t changing anything. His battered hand was squirming as energetically as ever.
“Just cut it off,” he said.
“Are you sure?” Amanda looked to Tosco.
“Cut it off!” Carlo repeated angrily.