The Eternal Flame (17 page)

“Get off me!”

Tamara gripped his lower jaw tightly and pulled it down. Tamaro sharpened his own fingertips and began stabbing at her hand, but she hardened the skin and persisted. She was dizzy from hunger now, and doubted she was thinking clearly, but her strength hadn’t deserted her.

She managed to get his mouth open, wide enough to see inside. She stretched out two fingers on either side, braced them against his cheekbones, and ossified their joints so she wouldn’t have to struggle to keep them from bending. Then she extruded a fifth limb from her chest, long and narrow with a circle of small fingers reaching out on all sides, like the petals of a flower.

She checked the roof of his mouth first, then forced his tongue aside and felt beneath it.

“You’re going to give birth here,” he proclaimed gleefully. “It doesn’t matter what you do. And I’m going to love the children as if they were my own. They’ll never even know that I’m not their father.”

Tamara pushed her new hand down into his esophagus and spread her fingers, fighting her revulsion and the contractions of the muscular tubules branching out from the main passage. She rummaged through the chewed food and digestive resin, waiting to strike something unyielding. The key wasn’t small, so there was a limit to how far it could have penetrated these side channels. But there was no real limit to how deep it might be.

Tamaro was humming, so softly she could barely feel his tympanum moving, unwillingly revealing his distress. Did she honestly believe he would have swallowed the key, or was she just trying to humiliate him? What did she do next—force a limb into his anus? Cut him open from end to end?

She pulled her hand out of his throat and resorbed the soiled arm, leaving the mush that had adhered to it sliding down her chest.

“Take the entitlement,” she begged him. “That’s all I can give you.”

“Why should I compromise?” Tamaro replied.

“This is my life,” she said. “What is it you don’t understand about that?”

Tamaro said nothing. Even if she took him by the legs and bashed his skull against the ground, he’d die without conceding any parallel between their fates. And what would that gain her? The opportunity to search the farm for the key, with nobody to interfere, or to move it.

It would be easy enough. She could make it quick. She would mourn and wail afterward, for sure, but the satisfaction of the act itself would be incomparable.
Can you understand my stubbornness, now? Can you finally see the downside of having your brain split in two?

She kept the glorious vision spinning in her head, promising herself the giddy dance of retribution even as she forced her grip to weaken. Tamaro broke free and crawled across the ground, spitting up traces of loose food. Then he rose to his feet and jogged away down the path.

Tamara closed her eyes. If she’d had no other hope, she might have done anything. But Erminio’s lies would catch up with him, and someone would come looking for her.

18

C
arla waited quietly at the entrance to Assunto’s office until he looked up from his work and gestured for her to enter. “There’s good news and there’s bad news,” she announced as she dragged herself toward his desk. “But best of all, there’s a chance to make the bad news good.”

Assunto managed a weary buzz. “Why can’t things ever be simple with you?”

“I make them as simple as possible,” Carla replied. “But no simpler.”

“So tell me the good news.”

Carla took a sheet of paper from her pocket and handed it to him.

“This is what happens when you take a luxagen with access to just two energy levels and hit it with a beam of light at a frequency tuned to the difference between those levels.”

Assunto stopped her. “What does that mean? ‘Tuned to the difference’?”

“Ah.” Carla realized that it had become second nature to her to think of energies and frequencies as interchangeable. She had to make a conscious effort now to unpack the details behind the instinctive translation. “If you imagine a particle and a wave moving at the same speed, the energy of the particle will be proportional to the frequency of the wave—with the ratio unchanged as you vary their common speed. If you set the speed to zero, the ratio is the mass of the particle divided by the maximum frequency of the wave—and that’s what it remains for every other speed.”

“That’s just geometry!” Assunto said. “The wave’s propagation vector will be parallel to the particle’s energy-momentum vector. That locks all of their components into a fixed ratio with each other.”

Carla said, “Yes—but now go a step further and suppose that
the same ratio
holds for every wave and its corresponding particle, whether it’s a luxagen wave and a luxagen or a light wave and a photon. None of the physics makes sense unless this ratio is a universal constant; I think of it as ‘Patrizia’s constant’, because the whole idea started with her. It’s as if these particle masses really
are
the maximum frequencies of the corresponding waves… just measured in different units.”

Assunto looked pained for a moment, but then he said, “You mean like times and distances?”

“Perhaps.” Carla didn’t want to over-reach with the comparison: one was a fundamental truth about the cosmos that the
Peerless
itself had helped to prove beyond doubt; the other was an appealing, but still untested, speculation.

Assunto said, “So let’s take it for granted that we can turn any frequency into an energy, and vice versa. You have a luxagen trapped in some energy valley, and the corresponding wave equation has two solutions with definite frequencies.”

“Yes,” Carla replied. “What I’ve drawn for the two waves is their variation in space, but while maintaining that shape they’re oscillating in time, each one with its own pure frequency.”

“Then you add a light wave whose frequency matches the
difference
between the luxagen frequencies—and it drives the low-frequency luxagen wave up to the higher frequency?”

“Yes.”

“Well, that much makes sense,” Assunto said. “You can do something similar with waves on a string, if you vary the tension periodically at a frequency equal to the difference between the frequencies of two resonant modes.”

“What’s more surprising, though,” Carla said, “is the simple rule that this wave follows along the way. Where I’ve plotted the proportion of each of the waves, the arc that links the point that’s ‘purely wave one’ to the point that’s ‘purely wave two’ isn’t an artistic flourish: the dynamics really does follow a perfect circular arc. The sum of the squares of the two proportions remains equal to one, throughout the process.”

“I see.” Assunto was prepared to take her word for this, even if the significance of it escaped him.

Carla said, “Hold on to that thought.”

She produced the second sheet.

“I take it that this is the bad news.” Assunto examined the diagram. “The light never frees the luxagen? So… that’s the end of your theory of tarnishing?”

“Wait!” Carla pleaded. “When there are just two waves, two energy levels, you’d
expect
the dynamics to take you all the way from one pure wave to the other. Where else are you going to go? But here, there are a multitude of free waves whose frequencies are almost identical—what I’m showing on the vertical axis covers them all. So there are ways you can wander around in this space of possibilities—keeping the sum of the squares of the proportions equal to one, as before—without the trapped-wave proportion ever falling to zero.”

“Without it ever falling very far at all,” Assunto noted, pointing to the modest arc that showed the limits of the process. “Which I can well believe, given your assumptions. But why isn’t it fatal? How can this be a description of light knocking a luxagen out of its valley, if the wave barely changes no matter how long you expose it to the light?”

Carla braced herself. She had managed to convince Patrizia and Onesto that her hypothesis wasn’t entirely deranged, but Assunto would be the real test.

“The thing is,” she said, “there’s always more than one luxagen and a light wave to consider. There’s the whole slab of mirrorstone as well. We can sum up
most
of its influence in terms of a simple ‘energy valley’, but the reality is more complicated than that. With all the luxagen waves reaching part-way out of their own valleys, every luxagen is interacting with its neighbors—and to some degree with its neighbors’ neighbors, and so on.”

“So your model’s inadequate?” Assunto suggested.

“Yes,” Carla conceded. “But a model of the entire solid would just be intractable. The only way we can get anywhere is to try to find a rule of thumb that lets us extract useful predictions from the things we
can
model.”

Assunto was skeptical. “What kind of rule?”

“We start with two reasonable assumptions,” Carla said. “If a wave that is purely trapped interacts with the rest of the solid, it remains trapped. If a wave that is purely free interacts with the rest of the solid, it stays free.”

Assunto said, “I can live with that. But what happens to a mixture of the two?”

“I doubt we could ever predict that with certainty,” Carla admitted. “Not without knowing exactly what’s going on with every single luxagen in the solid. But maybe we can still predict what will happen
on average
. If we treat the square of the proportion of the wave that’s trapped as the
probability
that the luxagen will remain trapped when it interacts with the rest of the solid, everything makes sense—because the squared proportions always add up to one, just as the probabilities for any set of alternatives always add up to one. I know it sounds too simple to be true—but the mathematics seems to be offering us the perfect number to use as a probability when we can’t make an exact prediction.”

Assunto raised a hand for silence, and Carla let him think the whole thing over. Finally he said, “When, exactly, does this probability get turned into a fact? You have the luxagen wave changing shape under the influence of the light alone, but then at some point it’s supposed to interact with the rest of the solid, which finally determines its fate. But the probability keeps changing, as the wave changes shape. So what probability do you use?”

Carla said, “It makes no difference exactly when the interaction happens, so long as it happens often enough, and so long as the probability grows in direct proportion to the time. Suppose the probability is one in a gross after one pause, two in a gross after two pauses, and so on. If the rest of the solid only interacts with each luxagen once every pause, the rate of tarnishing will be one luxagen per gross per pause. But even if the interaction takes place far more frequently than that, each time it happens the probability will have risen to a much smaller value than it would have reached if the luxagen had been left undisturbed for longer. The two effects—the lower probability and the greater number of interactions—almost cancel each other out, and you end up with a simple exponential decay curve.”

She sketched the result.

Assunto was not impressed. “Almost every process looks linear on a short enough time scale, so whatever’s going on with the tarnishing the net result could end up looking like exponential decay. If I gave you the sunstone for one more experiment, and you came back to me with a curve like that, what would it prove? Nothing.”