by Greg Egan
“No.” Tosco regarded him with bemusement, but didn’t spell out what Carlo suspected he was thinking: The culture now is to accept the women’s famine. That works well enough, so why not let it be?
“Let me try this,” Carlo pleaded. If he had no other choice he could work on his own, but everything would be easier with the support of his former mentor and his team. “What’s the worst that can happen? We learn something useless about the reproductive cycle in voles?”
Tosco said, “The worst thing would be if the harvest fails, and you start wishing you’d persisted with your last career. But if you really believe you have the patience to carry this through—”
“I’m certain of that,” Carlo insisted.
Tosco looked skeptical, but he was done with arguing. He said, “How can I turn down an agronomist who’s willing to step off his pedestal and rejoin his old friends?”
It was Carlo’s turn to travel down the axis, to meet his co in the new home she’d made for herself. Most of his friends had told him that a partial separation sounded like the worst of both worlds, but he’d studied the numbers from the last census. Total separation was a bad idea: it left women at an elevated risk of spontaneous fission, and no amount of holin could eliminate that entirely. But living together and relying on willpower alone to delay reproduction was even worse; more than half the recorded births in those circumstances had come earlier than planned. The trick was to let your co’s body know that you hadn’t abandoned her—that if it waited, her children would be cared for—while doing all you could to minimize the risk of delivering on that promise prematurely.
Carla wasn’t home when he arrived at the apartment. The moss-light was enough for him to see his way around, so he didn’t light a lamp. He’d brought four loaves for them to share, for the evening meal and breakfast; he packed them away in the empty cupboard.
Passing the entrance to the bedroom, he saw a spare tarpaulin floating in the air, suspended against the weak gravity by a faint updraft from a cooling vent.
When he heard the guide rope twanging in the corridor he went to the doorway and parted the curtains. Carla saw him and chirped excitedly. “Get ready to hear some good news,” she said.
“What—you’ve won a place on the Gnat?”
“That would be something.” She followed him back into the apartment. “But this is better.”
Carlo lit a lamp in the front room, then clung to the rope beside her as she described her tarnishing experiment. She’d had to refresh his hazy memories of Nereo’s force and Yalda’s puzzles countless times before, so he knew she’d forgive him if he didn’t immediately grasp the significance of the results.
“Five to four,” he said. “What’s so special about that?”
“A ratio of small integers isn’t likely to be a coincidence,” Carla replied. “If it was dozens and something to dozens and something else, that would be meaningless, but this suggests very strongly that the numbers in the ratio really are lurking in the physics itself. Four of something, then five of something… the transitions mark a kind of succession.”
Carlo could only understand physics by translating it into geometry; he started raising undulating lines on his chest. “So can I draw it like this, fitting different numbers of cycles into the same amount of time?”
“No, no, no!” Carla chided him. “You’ve got it backward!”
“What’s wrong?” he asked. “Doesn’t that give a five to four frequency ratio?”
“It does,” she conceded. “But I’m working on the assumption that the frequency goes down as the associated integer goes up, and you’ve described the opposite trend. Going your way, there’d be another transition at a higher frequency—‘frequency six’, out in the infrared—beyond which mirrors would start tarnishing at an even greater rate. The trouble with that is, if the pattern in tarnishing rates held up then Marzio’s mirrors would have needed re-polishing after a couple of stints, not a couple of years.”
“All right,” Carlo said. “So how should I picture it?”
“I don’t know yet,” Carla admitted. “All I can say is that light produces a strong tarnishing effect when four times the frequency exceeds a certain number. When the frequency falls so low that you need to multiply it by five to meet the same target, the effect suddenly becomes drastically weaker—and when you need to multiply it by six, it becomes weaker still. It might even vanish entirely at that point; I’d need to do a much longer exposure to be sure.”
Carlo pondered this. “Wouldn’t it be easier to follow the pattern in the other direction? If the effect grows weaker as the magic number goes from four to five to six… what about three? Shouldn’t you get super-fast tarnishing from waves where you can reach the target merely by tripling the frequency?”
“There are no such waves,” Carla replied. “The target is more than three times the maximum frequency of light, so you can never reach it by tripling.”
“Aha.” Carlo had a glimmer of comprehension. “Which is a good thing for mirrorstone, isn’t it? If it was that easy to damage, it probably wouldn’t be around at all.”
“Exactly!” Carla’s eyes widened with pleasure. “Whatever’s going on here, it’s showing us the border of stability. And maybe every mineral, every solid, has its own ‘target number’ like this—but in the case of something like hardstone, it could be so high that even six times the maximum frequency of light doesn’t reach it.”
Carlo said, “The empirical rule sounds simple enough. I suppose the hard part will be making it mesh with the theory—with Nereo’s equation and the luxagen model?”
“Yes.”
“And…?” he prompted her.
“And right now,” she admitted, “I have no idea how to do that.”
Carlo told her about his meeting with Tosco. He’d given her no warning of his plan to return to the animal physiology group—and he offered no justification now, but he watched her face as he spoke. Carla listened politely, in silence, but she almost flinched when he reached the point of describing his new research program. And this was from the subject in its most abstract, impersonal form: comparing biparous and quadraparous fission, hunting for the mechanism that allowed some species to switch between the two.
He understood why it was painful for her to hear. Behind these calm career announcements he was whispering a promise that he had no right to make: I’ll find a way out of the famine—if not for you, for our daughter. He had no right, because people had tried and failed before: countless women driven by hunger, countless men driven by the suffering they’d seen. There was a terrible equilibrium now, and an unspoken consensus that the only real option was to cling to their hard-won resilience and endure what had to be endured.
Carlo couldn’t live like that any more, but he understood that he had to follow this new path quietly, making it as easy as possible for everyone around him to avert their gaze. When he’d said all he needed to say for the sake of honesty, he steered the conversation back to the mysteries of light and matter. Failure there might leave them stranded, doom their whole mission and kill off all their ancestors—but at least they hadn’t been cursed with some wretched half-solution that sapped their resolve and kept them from reaching the real thing.
5
“Lizard skin?” Tamara asked incredulously.
“Lizard skin,” Ivo confirmed. “The jungle has its uses.”
“Is that where you go looking, when nothing else works?”
Ivo said, “That depends on what I’m after. When people think of light they usually think of flowers, but most animal tissues have some kind of optical activity too.”
Tamara managed a murmur of concurrence, as if the first course of action that anyone should consider when faced with the need to find a new chemical would be to pop a lizard in a centrifuge and see what oozed out.
“What kind of wavelengths are we talking about? What kind of sensitivity?”
“Come and see for yourself.” Ivo led her deeper into the
chemists’ domain, four hands shuttling him swiftly along the guide rope.
As they moved down the center of the cylindrical chamber, Tamara watched his colleagues at work around them. Most were harnessed to benches fixed to the walls, or were attending to various spinning or vibrating contraptions, but one eight-armed chemist was blithely floating in mid-air as he snatched vials of reagents from a weightless cluster in front of him, mixing the contents in a dizzyingly rapid sequence that Tamara could only assume was essential to the success of the procedure. When his rear gaze fell on her she quickly averted her eyes, afraid she might distract him and end up turning the whole chamber into an inferno.
Ivo switched to a cross-rope that took them to his own bench, where he slipped into the harness. A large lightproof box was attached to the bench-top; he swung up the lid to allow Tamara, still hanging on the cross-rope, to inspect the contents.
“That’s just an ordinary lamp in there,” he explained, gesturing at a spherical hardstone enclosure. “Lens, prism… it’s all standard equipment.” Ivo pulled the prism out of its slot and passed it to her for approval, as if he feared she might suspect him of some sleight of hand. The prize she was offering wouldn’t be much use to a cheat: any attempt to visit the Object would be an awful anticlimax if they failed to calculate its distance correctly. But Tamara obliged her host out of courtesy, and held the prism up to the light of the nearest lamp. The shimmering sequence of colors that appeared in front of her as she rotated it around its axis was no different from that produced by any piece of clearstone similarly cut.
She returned the prism to Ivo. He replaced it, then pointed out an unprepossessing piece of yellowish, resin-coated paper, positioned about a span from the light source. “This won’t make a permanent record itself; it will need to be supplemented with an ordinary camera. It doesn’t need any activating gas, but it only retains its potency for a few days after preparation.”
“I see.” Tamara made a mental note to start factoring that into her plans, hoping it wouldn’t lead to the Gnat having to carry a lizard-press.
Ivo tapped the lamp’s enclosure, shaking some liberator into contact with the firestone until the hot gas from the flames themselves started scattering the powder back onto the fuel. He closed the lid, then gestured to Tamara to peek through a slit in the box, opposite the lamp.
She moved back along the rope so she could bring her head down closer, self-conscious for a moment at her contortions. When she was in place, the first thing she noticed was an ordinary spectrum, muted by the paper through which she was seeing it but no different in scale and orientation than she would have expected from the prism’s geometry.
She closed all her eyes but one, ridding herself of distractions. Ivo said, “If you want to block the visible spectrum, there’s a lever on your right.” She found it, and slid an opaque screen across the band of colors. Then she waited while her vision adapted to whatever remained.
Out of the grayness, a blurred vertical bar of shimmering yellow light appeared—far beyond the red end of the hidden spectrum.
Tamara gauged the strength of the fluorescence. Assuming the effect scaled linearly, infrared light from the Object would produce far too weak a response in this lizard paper to see with the naked eye, but they could probably capture it with a camera and a long enough exposure.
“What wavelength is this?” she asked Ivo, without moving away from the slit. She was prepared to take his word for it, and hoped he wouldn’t insist on her verifying his answer immediately with protractors and calibration curves.
“About two scarso-scants.”
She did some quick calculations on her forearm. Light of that wavelength traveled at about an eighth the speed of red light, and it would extend a visible color trail by a factor of a dozen. If that wasn’t good enough to let them measure the Object’s speed, it would have to be moving at little more than a jogging pace. Any slower—and nearer—and they’d be able to toss a rope out to it and make the whole journey by hand.
“Congratulations,” Tamara said. “You’ve won yourself a trip into the void.” She drew away from the box, and Ivo opened it and shut off the lamp, contemplating her announcement in silence. Everyone had been outside the Peerless for at least a few shifts of fire watch, but traveling across the void until the mountain vanished from sight had to be a daunting prospect for anyone.
“More immediately,” she added, “we’ll be needing you at all the planning meetings, to ensure that the Gnat’s capable of supporting whatever experiments you have in mind. There’s only going to be one chance to get this right.”
“Only one chance?” he replied. “I hope not.”
“The Object’s on a linear trajectory,” Tamara said. “Once it passes us, it’s never coming back.”
Ivo said, “Exactly. And this might be the only substantial body of orthogonal matter to come within our reach for generations. However diligently we prepare for this trip, however large the samples we’re able to bring back, it’s not going to be enough for everything we need to do.”
Tamara said, “What do you suggest then? If the Peerless matches velocities with the Object we’ll slip out of orthogonality with the home world. Not by much—but do we really want to be under pressure to solve their problems any faster?” The whole point of the Peerless was to grant its inhabitants as long as they needed to find a way to deal with the Hurtlers. If time on the endangered planet began to creep forward for the travelers, however slowly, that advantage would be lost.
“I don’t want the Peerless changing course,” Ivo said. “But that doesn’t mean we can’t match velocities.”
Tamara gazed at him uncomprehendingly for a moment, but then she grasped his meaning.
She said, “Why is it that whatever you ask a chemist, the answer invariably entails an explosion?”
Ivo buzzed delightedly. “A small explosion,” he said, “could correct the Object’s course, transforming it from a fleeting marvel whose passing we might recount to our grandchildren into a resource that they can study and exploit for as long as they wish. And if this thing is made of the same material that caused spot ignitions on the mountainside before spin… all we’ll need to do is toss the right amount of calmstone at the Object and it will become a kind of rocket in its own right.”
“No doubt,” Tamara replied. “But how do we discover what the right amount is—without blowing the whole thing into fragments, or creating a brand new star?”
“Calorimetry,” Ivo replied. “We’ll need to take samples and carry them a safe distance away from the Object itself, then determine just how much energy is released in the reaction with calmstone.”
Tamara had a vision of the two of them in the void, drifting along beside a jagged mountain of orthogonal matter. While she struggled to steer the Gnat, Ivo would be juggling vials of reagents—trying to calibrate a detonation that would either kill them both and obliterate their quarry, or grant their descendants a storehouse of energy that could pave the way for their return from exile.
6
Patrizia took the guide rope to the front of the room, then turned and addressed the class. “Suppose there are some luxagens in the mirrorstone that are bound so loosely that they can easily be freed from their energy valleys by a light wave. Suppose they get swept along by that wave, until they’re moving as fast as the light itself. If you compare the geometry of the light with the geometry of the luxagens’ motion, you can see that each of these luxagens ends up with an energy that’s proportional to the frequency of the light.”
Carla watched as the usually shy student sketched a diagram on her chest illustrating the relationship.
“To tarnish the mirrorstone at a given location,” Patrizia continued, “will require a certain amount of energy. Suppose that for light of the highest frequency, four luxagens can deliver that amount—so if a site in the mirrorstone is struck four times by these luxagens it will suffer the damage that we see as tarnishing. But as the frequency of the light falls,
the energy per luxagen will fall too, so there’ll come a point where five luxagens would be needed to reach the same threshold. The tarnishing will still occur—but it will suddenly take much longer, and for a given exposure time it will be much fainter.”
Patrizia drew four stacked energy vectors for luxagens at the transition point, then added a second stack that reached the same threshold with five particles. “Eventually the same thing will happen again: there’ll be a frequency below which even five luxagens won’t be sufficient. And the ratio of the two critical frequencies will be exactly five to four.”
Carla could only marvel at the young woman’s ingenuity. Yalda’s great discovery—on Mount Peerless, no less—was that the frequencies of light in time and in space formed two sides of a right triangle—with the ratio between these sides determined by the speed at which the light traveled, while the length of the hypotenuse remained fixed, regardless of whatever else was changed.
But the energy, momentum and mass of a solid object formed a right triangle too. This triangle’s hypotenuse was also fixed, by the object’s mass, while the speed of the object set the ratio between the other two sides.
Arrange for the speed to be the same in both cases—make a luxagen, a particle of matter, match speeds with a pulse of light—and the two triangles adopted the same shape, with corresponding sides locked into a fixed relationship. The energy of the particle became proportional to the frequency of the wave. And instead of the shifts in tarnishing being tied, inexplicably, to integer multiples of the light’s frequency, these particles in lock-step with the light would naturally carry energy in integer multiples.
