by Greg Egan
Carla had set aside her planned lesson and invited her optics class to debate the tarnishing results. “This is your chance to argue for any wild idea you’re willing to defend,” she’d urged them, “even if you can’t make it perfect, even if there are gaps and flaws you can’t fix. There have been gaps and flaws in everything I’ve taught you, and mysteries people have struggled with since before the launch—but this time no one’s been there before you; Yalda, Nereo and Sabino can’t offer us their guesses. So this is your chance to go beyond everything you’ve learned: to see what’s missing in the old ideas, or to tear them down and start building something new.”
It had started slowly, with everyone tentative and wary—and the usual people needing prodding to get them to engage at all. But after half a bell of meandering, of questions and clarifications and increasingly passionate claims, three of her students had been brave enough to sketch their own novel explanations for the strange pattern in the tarnishing.
Romolo had suggested that the light striking the mirrorstone could be generating sound waves within the material, and some small nonlinearity in the equations for those waves was allowing energy to move between different harmonics, all the way up to the natural frequency of vibration of the luxagens. Palladio had proposed that light with the right frequency could give suitably timed kicks to the oscillating luxagens in such a manner that neighbors in the array were pushed together close enough to drag each other out of their energy valleys. But it was hard to see how either of these theories could predict a tiered pattern, rather than isolated bands of tarnish confined to a few special resonant frequencies.
Patrizia’s account certainly explained the tiers—and the analogy she’d used between energy and frequency was so simple and elegant that Carla was ashamed not to have thought of it herself. But for all its virtues, the theory as a whole didn’t quite hang together.
Carla broached the first problem as gently as she could. “You’re relying on some of the luxagens to get swept up by the light?”
“Yes,” Patrizia agreed. “Pushed along faster and faster, until they’re moving at the speed of the wave itself.”
“So how would that look, if we were moving alongside them? If we matched velocities with the luxagen, what would we see?”
“It would appear motionless to us,” Patrizia replied, puzzled. Wasn’t that obvious?
“And how would the light wave appear?”
“Motionless too. Everything’s moving with the same speed.”
“The light pulse is moving with the same speed,” Carla said, “the way you’ve envisioned this. But the history of a pulse is perpendicular in four-space to the wavefronts. So what are the wavefronts doing?”
“Oh.” Patrizia lowered her gaze and slumped away from the guide rope. “They’re going backward. And so the luxagen wouldn’t be moving with the pulse—it would be trapped in an energy valley between two wavefronts, moving backward at a completely different speed.”
Carla said, “Right. The motion of the pulse is not the motion of the wavefronts! It’s an easy mistake to make: I still get confused by the difference sometimes.”
She sketched the situation Patrizia had described. “For the luxagen to end up moving with a constant velocity, it has to be sitting in an energy valley. In fact, I’d only expect that to happen with a very high intensity light source, otherwise the valley wouldn’t be deep enough. But if it did happen, the luxagen would be motionless with respect to the wavefronts, not the pulse.”
“I understand,” Patrizia said sadly. She began to move away.
Carla said, “Wait. There’s another problem here, and it’s worth discussing that as well.”
Patrizia was mortified now. “Isn’t the first flaw bad enough?”
“Bear with me for a moment,” Carla suggested. “Sometimes two errors actually cancel each other out.”
“Only sign errors!” Romolo interjected. Carla raised a hand to hush him, then turned back to Patrizia. “You had four or five mobile luxagens able to cause tarnishing when they reached a threshold in their total energy,” she said. “But if they’re going to strike another luxagen trapped in an energy valley, knocking that luxagen free will require a transfer of kinetic energy equal to the depth of the valley. Kinetic energy goes down as true energy increases, so your original idea, with the mobile luxagens matching the speed of the light pulse, wouldn’t have worked. But if the luxagens are moving with the wavefronts, not the light pulse, everything is reversed: the higher the frequency of the light, the slower the light pulse, but the faster the wavefronts. So luxagens trapped between wavefronts will be moving faster and carrying more kinetic energy when the frequency of the light is higher.”
Patrizia thought it through. “The trend ends up pointing the right way,” she said, “but the numbers don’t work out any more, do they? The frequencies at which four or five luxagens cross a threshold for kinetic energy won’t be in a five to four ratio.”
“No,” Carla conceded. “And of course there are other problems that would have to be solved to make this work: you’d have to analyze the collisions in detail to see just how much kinetic energy was transferred from the mobile luxagens to the trapped ones, and also account for any radiation being produced. It’s hard to see how all those effects could conspire to leave a simple five to four ratio.”
Patrizia said, “You’re right, it was foolish.” She started back to her position in the class.
“It wasn’t foolish at all!” Carla called after her. Though she couldn’t see how to salvage the whole elaborate scenario, its complications had been wrapped around an insight as beautiful as any from the glory days of rotational physics.
“All right,” she said. “We still have no good theory of tarnishing. So what we do now is try to think up a new experiment: something that might help us make sense of the first one.”
Romolo said, “Whatever knocks these luxagens out of their usual sites in the mirrorstone… where do they all go?”
“They must find a new kind of stable configuration,” Carla said. “That’s all that tarnish can be, after all: luxagens rearranged so that they no longer form the normal structure of mirrorstone.”
“But then why don’t we see two different kinds of tarnish?” Romolo protested. “Mirrorstone that’s lost some of its luxagens, and mirrorstone that’s gained what the other parts have lost?”
“The tarnish might well be heterogeneous,” Carla replied, “but I’d expect that to be on a scale too small to see, even under a microscope.”
Azelia—who’d spent most of the class staring blankly into mid-air—suddenly interjected, “Why does all of this happen faster in a vacuum? What difference does the air make?”
Carla said, “I think the air must react with the polished surface in a way that protects it against tarnishing. We used to think air created the tarnish, but now it seems more likely that what it creates is a thin layer that’s immune to the effect.”
Azelia wasn’t satisfied. “If this layer doesn’t stop the mirrorstone being a mirror, then surely light must still be interacting with the material in the same way. So why wouldn’t it rearrange the luxagens in the same way?”
Carla had no reply. The truth was, she’d been so entranced by the astonishing simplicity of the frequency cut-off that she’d given very little thought to the messy details of the tarnished material itself.
She caught the look of elation crossing Romolo’s face before he even spoke. “The luxagens go into the vacuum!” he declared. “Surely that’s it? Air must modify the surface of the mirrorstone in a way that makes it harder for the luxagens to escape—but when there’s no air, the light can send them drifting off into the void!”
Free luxagens? Carla felt her tympanum tightening in preparation for a skeptical retort, but then she realized that the idea wasn’t so absurd. It had long been conjectured that flames contained a smattering of free luxagens, but they’d be impossible to detect among all the unstable debris of combustion, and
there was no reason to expect them to remain free for long when they were constantly colliding with other things. But a thin breeze comprised of nothing but luxagens wafting off a slab of mirrorstone into the vacuum was a very different scenario.
“You could be right,” she said. “So how do we test this idea? If there’s a dilute gas of free luxagens in the container that holds the mirrorstone, how could we tell?”
There was silence for several pauses, then Azelia demanded irritably, “Can’t we just look? Most gases are transparent, but luxagens would be nothing like an ordinary gas.”
“Luxagens should scatter light,” Carla agreed. “In fact, every one of you should be able to calculate what happens when light of moderate intensity meets a free luxagen. So come back in three days with the answer to that, and some suggestions for how we could try to observe it.”
When the classroom was empty, Carla felt a sudden pang of anxiety. Now that she’d torn up the curriculum, where was she heading? She’d made one tantalizing discovery—and for a while that in itself had been exhilarating—but she couldn’t begin to explain what she’d found, and in the aftermath the whole subject seemed murkier than ever. What pride could she take in leaving the next generation with one more problem than she’d inherited herself?
She fumbled in the cupboard for the groundnuts she’d hidden behind a stack of worn textbooks. How many holes were there now, in Nereo’s theory? Too many, and not enough. One anomaly was an embarrassment, two were perplexing… but a dozen or so might come together to reveal a whole new vision of the world. What she should be fearing was not mess and confusion, but the possibility that she’d only see enough of it to take the process halfway.
7
Carlo spun the syringe between his thumb and forefinger, suddenly unsure whether or not he’d identified the right spot to insert it. The male vole adhering to the immobilized female glared up at him balefully, unable to do anything for his trapped co but promising her tormentor a suitable punishment once he was detached. Carlo could only sympathize. Over the years, biologists had managed to produce a strain that would breed, not merely in captivity, but in the face of stresses and indignities that would have seen their wild ancestors prudently deferring the act. With no hope of privacy, the caged voles could not afford to miss an opportunity.
“Do you want me to do this?” Amanda offered. “You might be a bit out of practice.”
The protocol Carlo had prepared referred to landmarks on the skin patterns that were shared by every member of this strain of voles, but his notes had been based on a stylized reference version of the pattern. Now that he was facing a real animal again after a three-year hiatus, he was beginning to recall just how tricky it could be to identify the features on each individual.
The reference pattern showed a junction between three crisp dark stripes, just behind each shoulder. For this subject, the injection was meant to go in the top corner of that junction. But the stripes on the clamped female in front of him were diffuse, and the corner between them showed a gradient of diminishing pigment at least half a scant wide. This didn’t mean the task was hopeless; if you took your bearings from the entire hide it was still possible to get an accurate fix. But he hadn’t had to do that for a very long time.
“Actually, if you don’t mind—” Carlo moved aside and handed the syringe to Amanda. She quickly thrust the needle into the female’s skin, up to the depth calibration mark, then pushed the plunger, delivering a small dose of suppressant. The male emitted an angry chirp; Amanda withdrew the needle and closed the lid of the cage. Carlo reached over and shifted a lever that loosened the clamp on the female. He didn’t want any confounding mechanical effects interfering with the fission process.
“Thank you,” he said. “I’m still waiting for the old instincts to come back.”
“I can believe that,” Amanda replied. “I have the opposite problem: you could put a rock in front of me and I’d start to see hide markings on it.”
Carlo had thought he’d be the one confidently demonstrating the protocol to her, as a first step in convincing himself that he could rely on her to perform some of the trials without his supervision. But he’d only been two years her senior the last time they’d worked together, and he felt foolish now for assuming that he’d somehow retained his old advantage in experience. His own world wasn’t full of imaginary voles; it was strewn with hallucinatory wheat petals.
The male began squirming and thrashing about, eager to be unencumbered. Apparently the exchange of signals was over to his satisfaction, but the skin of his chest was still stuck in place. He grabbed the transitioning female with all four paws and forced himself apart from her, then he scampered around in a frenzy, clinging to the twigs that crisscrossed the cage like guide ropes, chirping loud warnings.
“No one’s tried this before during fission?” Amanda asked.
“A long time ago, with a much coarser suppressant.” If she hadn’t heard of that work it was because nothing much had come of it. Carlo didn’t want to waste time repeating other people’s experiments, but the new preparation Tosco had discovered blocked signaling in a smaller volume of tissue, and also seemed to have fewer side effects. “I’m not expecting to find some magic spot where we can interrupt transmission and see the number of offspring halved,” he said. “But to get anywhere, we’re going to need the best map we can make of the pathways that influence fission. Even these tiny doses will probably interfere with a dozen individual pathways, but that will still be a big improvement on the last map.”
Amanda said, “I’ve had some success with microsurgery, for identifying phalangeal control pathways in lizards.”
Carlo was intrigued. “So you cut into the leg under a microscope… and managed to paralyze a particular toe?”
“Almost,” she replied. “I have to infer things from incremental damage—I can’t actually sever the pathway for any given toe without severing other things as well. And of course the lizards either re-route the signals within a chime or two, or resorb the whole limb and reconstruct it.”
The female vole had already been limbless in her mating posture, but now her body was deforming further into an almost featureless ellipsoid. Carlo could just make out a shallow longitudinal trench that marked the beginning of the primary partition. Whatever change the injection had wrought, it hadn’t suppressed the start of fission itself.
“So you know how to paralyze a lizard,” Carlo said, “but have you ever thought of doing the reverse?”
Amanda buzzed softly. “The old yellow flash muscle twitch? I know it impresses students, but I’m not sure that there’s much to be learned that way.”
“I was thinking of something subtler than a twitch,” he said. “Imagine severing the pathways from the brain… but then introducing motor signals of your own.”
Amanda was skeptical. “Even if we could manage the mechanics of an intervention like that, we’d have no way of knowing the proper time sequences for the signals. Believe me, I’ve stared down a microscope at enough flickering lizard tissue to know that I’m never going to be able to transcribe what’s happening.”
“I have some ideas about that,” Carlo confided. Faint lines could now be seen neatly dividing each half of the vole blastula, displaced to the usual degree above the midline to guarantee an extra quota of flesh to the daughters. The father-to-be screeched triumphantly, as if he knew that his captors had been thwarted. But any celebration was premature; in the old studies a similarly placed dose of suppressant had led to stillborn males.
“What ideas?” Amanda pressed him.
“Run a long strip of light-sensitive paper past a probe into the tissue,” Carlo replied. “Turn the variation of light over time into a variation over space. You could have the whole history of a motor sequence spread out in front of you, to read at your leisure.”
Amanda thought it over. “I suppose that might work.” She shifted her grip on one of the ropes they shared, sending a brief shudder through Carlo’s body.
“You could copy the pattern,” he said. “Maybe modify it too. Then send it back into the body using a strip of paper of variable transparency, moving in front of a light source. But the beauty of it is, you could send it back to a completely different site, if you wanted to. Maybe even send it into a completely different animal.”
Amanda buzzed softly, not quite mocking him but amused at his audacity. “So that’s the plan? Record the way a biparous animal initiates fission, then feed those signals into a quadraparous species in place of their own version of the sequence?”
“I don’t know,” Carlo said. “Maybe that’s naïve. The difference might not come down to anything we can localize that way.”
“Still, it makes more sense than a drug,” Amanda conceded. “I wouldn’t say it’s not worth trying.”
They watched in silence as the primary partition began to fracture, cracking into plates of shiny brittle tissue that stuck to one side or the other. The male approached and started pawing at the structure, trying to hasten the separation.
Carlo glanced over at his colleague, wondering what her reaction would be if he dared to ask her: On a scale of one to twelve, how much comfort does it give you to know that this is the fate of your flesh?
When the blastula had split completely, the male took hold of one of the halves and carried it across the cage, backing away awkwardly with its two hind-paws gripping the scaffolding of twigs before extruding another pair to make the task easier. Carlo wasn’t sure why the animals were so emphatic about the separation. So far as he knew co always recognized co, whatever the first sights and smells they encountered, and in any case when a crossed mating was contrived it appeared to cause no problems. Maybe it was simply advantageous for the male vole to have the strongest possible instinct to aid the process of fission—rather than standing by uselessly if the blastula became stuck—and it did no harm to take this sentiment further than was strictly necessary.