by Greg Egan
Yalda was about to reply that she couldn’t think of any other possibility, but something in Isidora’s tone gave her pause.
Palladia made a move toward the entrance again. Yalda said, “Wait.” She turned and called down the corridor to Isidora, “What good news?”
The expression of joyous bafflement on the woman’s face started Yalda’s skin tingling before she said a word.
“No impacts!” Isidora shouted back. “Two shifts, nooooo impacts!”
Yalda waited in silence until they were close enough to speak properly.
“Two shifts?” she asked Isidora.
“I was going to tell you after the first shift,” Isidora explained, “but you were so busy, and I thought the observers might just be confused by the new setup. We reconfigured the lookout posts… I know it makes no sense, that couldn’t explain a null count, but I had to be sure. I had to see it for myself before I made a fuss about it.”
Palladia said, “No impacts since the spin-up? You’re serious?”
Prospera, who was one of the other lookouts, said, “Staring at dark rock for four bells, the miracle is I didn’t start hallucinating flashes. Zero means zero.”
Palladia turned to Yalda. “How? You think we’ve just passed out of the dust?”
“Do you believe in that kind of coincidence?” Yalda replied.
“What else could explain it?” Palladia countered.
Yalda exchanged glances with Isidora, and let her speak. “The spin-up,” Isidora replied. “Whatever’s been making the flashes, whatever’s been striking the surface, the centrifugal force must be enough to cast it off before it can heat the rock.”
Palladia was incredulous. “To a dust particle with infinite velocity, that force is nothing, it’s completely irrelevant!” She addressed Yalda imploringly. “You agree with me, don’t you? Or is everyone going mad?”
Isidora nodded to Yalda: your turn.
Yalda said, “I agree with you completely—which means the flashes can’t be coming from anything moving so fast. They must be coming from orthogonal dust… I mean dust that was orthogonal to us before the launch, not now.”
Palladia blinked. “Hurtlers? Original Hurtlers?”
“How else could it make sense?” Yalda replied. “Whatever it is that’s been causing the flashes must be moving so slowly relative to the Peerless that our spin is enough to brush them away. Well, we always knew that our trajectory would tame the Hurtlers.”
Palladia grimaced. “But if we’ve tamed them, what caused the flashes? How could something striking us so slowly turn the rock white-hot?”
“I have absolutely no idea,” Yalda confessed, “but if it wasn’t kinetic energy that was heating the rock, all I can think of is some chemical process—and the dust must have needed to stay on the rock long enough to react with it in some fashion. Now that the slopes are unable to hold on to debris… no more flashes.”
Palladia was angry now. “You’re telling me that Hurtlers are made of… what? A liberator for calmstone? The dust from the orthogonal worlds that fills the void here isn’t actual rock, it’s a refined substance people extract from plants with the express purpose of causing fuel to burn?”
Yalda said, “Not the sarcastic bit at the end, but whatever’s been hitting us must act as a liberator for calmstone. Don’t ask me how—but if you don’t believe that, tell us how else you can explain the sudden cessation of the flashes.”
Palladia glared back at her in silence, then she said, “I have no idea. But you’re right, it can’t be a coincidence. The spin is protecting us. So whatever’s been striking us, it’s not high-velocity material.”
“Which means there’s no reason, now, to believe that even a piece dozens of times larger than those that caused the flashes could set the slopes on fire,” Yalda suggested.
“No reason at all,” Palladia agreed.
“So our plan for exploding walls is superfluous?”
Palladia hesitated. “Absolutely. We just need some sacrificial cladding near the axis—at the summit and the base, where the centrifugal force offers no protection…” She stopped speaking; she was trembling with relief.
Yalda put a hand on Palladia’s shoulder then turned to Isidora. “I think we should all go in there and share the good news with Frido and his friends.”
19
“Be warned,” Yalda said, “that I’m going to be spending most of my time telling you about things I don’t understand. Along the way I’ll offer you a few facts and a few guesses—but then I’ll explain why those facts aren’t quite enough and why those guesses can’t quite be right.”
She looked out across the room. Many of the faces were familiar to her, young women and men whose education she’d been following from the start. But there were half a dozen students she barely recognized, too, which was even more encouraging. Once they put the old barbarities behind them, everyone on the Peerless could live the life of the mind. One day they’d all be doing rotational physics with their eyes closed, thinking about the symmetries of four-space as naturally as they moved their limbs.
“What don’t I understand?” she continued. “I don’t understand why solids are stable. I don’t understand why gases aren’t sticky. And I don’t understand why the gentlest contact with the dust that surrounds us can turn rock white-hot.”
“I thought we proved that solids were stable,” Ausilia interjected. “In our last class with Severa.”
Yalda said, “What you did, I think, was show that there are several geometries that an array of luxagens can assume in which Nereo’s force, acting between them, would hold them in place. Is that right?”
“That’s how I understood it,” Ausilia replied.
“So how does that work?”
“Every luxagen is surrounded by hills and valleys of potential energy,” Ausilia said. “If you have a number of them, you can drop them all into their neighbors’ valleys, making a nice, neat pattern in which they should all prefer to stay put.”
“That’s perfectly true,” Yalda said. “But there are a couple of problems Severa wouldn’t have raised, to avoid confusing you while you were still learning the fundamentals.”
She sketched a basic one-dimensional example.
“A luxagen can sit in its neighbor’s energy valley,” she said. “And I’ve put it in the first valley, rather than any of the more distant ones, which are shallower than the first. But is that really the deepest place there is?”
There was silence for a few pauses, then Prospera offered, “The pit would be deeper.”
“Of course,” Yalda replied. “The pit centered on the luxagen itself is bottomless, though I’ve only drawn it going down a short way. Once they’re close enough, two positive luxagens just keep attracting each other ever more strongly, until they collide. So why don’t all the luxagens in a piece of rock simply end up falling into each other’s energy pits, until the whole rock has shrunk down to a speck?”
“Isn’t that like asking why the world doesn’t crash into the sun?” Fatima suggested. “If there’s any sideways motion, the two luxagens wouldn’t actually collide. If they started outside the pit, they’d just skim around it and end up outside again. And even if they had the right amount of energy to stay in the pit, wouldn’t they just orbit each other, like Gemma and Gemmo?”
“You’re right,” Yalda said. “But if two luxagens end up orbiting each other, there’s something more to think about: a luxagen moving back and forth makes light. If the luxagens create light, they need to provide true energy to do that. But to provide true energy—to lose it themselves and turn it into light—they need to gain kinetic or potential energy. So why don’t they end up moving faster and faster, and breaking the whole solid apart?”
Silence again. Then Giocondo—a young man Yalda could only name from his tag—said, “What if the luxagens are moving too fast to make light?”
Yalda waited a pause to let the other students ponder that. “Go on,” she said.
> “There’s a maximum frequency of light,” Giocondo began tentatively. “In the equation for light, the sum of the squares of the frequencies in the four directions must equal a fixed number—so none of the individual frequencies can have squares that are bigger than that number. If a luxagen is moving back and forth with a greater frequency than that… it can’t create light in step with its motion, because there’s no such thing.”
Yalda said, “That’s correct. And eventually we’ll work through the calculations for the amount of true energy that an oscillating luxagen passes to the light field, and we’ll show that when the frequency crosses the threshold Giocondo’s just described, the energy flow drops to zero.”
“Then why is there still a problem?” Ausilia asked. “Oh… why don’t all the luxagens end up orbiting in one single energy pit?”
Prospera said, “Because the peaks around the pit keep getting higher. Maybe a few luxagens are orbiting in the same pits, but the more of them you throw in together, the higher the energy barrier around them becomes.”
“Right,” Yalda said. “The more luxagens you have, as long they’re sitting in each other’s pits or valleys, the potential just keeps adding up: all the valleys become deeper and all the peaks get higher. So eventually the pit would become inaccessible, because it’s surrounded by insurmountable peaks.”
Fatima said, “So that keeps all the luxagens from falling together completely, and the rest just end up in each other’s valleys rather than each other’s pits?”
“Go on,” Yalda pressed her.
“I suppose they’d roll around in the valleys too, just like they orbit around the pits,” Fatima mused.
“And if they roll fast enough in the valleys,” Giocondo added, “they’d be stable there too. They wouldn’t emit light and end up tearing the solid apart.”
Yalda was delighted. “Bravo, everyone! A few lapses into the class, and we have solids rendered almost solid again.”
Ausilia said, “Almost? What’s the catch?”
“The idea that Giocondo raised is very appealing,” Yalda said, “and as far as our measurements can guide us, it seems to be true. The energy pits and valleys in real solids seem to be shaped in such a way that the natural frequencies of motion for the luxagens are greater than the maximum frequency of light.
“The only trouble is: if a luxagen isn’t going to make any light at all, there can’t be any wobbles to its orbit in the pit, or its rolling around in the valley. If there was even the tiniest imperfection in its motion that progressed at a sufficiently low frequency, then that would start to generate light.”
“Which would make the imperfection stronger,” Ausilia realized. “So it would lose true energy faster, grow stronger even faster… and the whole thing would get out of control.”
Yalda said, “Exactly. And the thing is, the shape of the potential energy that we get from Nereo’s equation doesn’t allow for perfect orbits, or perfect rolling in the valleys. The main cycle can have a high enough frequency to avoid creating light, but the potential has built-in flaws that guarantee that there’ll be lower-frequency motion as well. It seems to be unavoidable.”
“But solids don’t blow themselves apart,” Fatima proclaimed irritably. “Not without a liberator.”
“Of course,” Yalda said. “So although we seem to have most of the story, although it almost adds up… there must be something we’re missing, something that nobody yet understands.”
She let them ponder that for a moment, but then moved on swiftly. Being told that you’d reached the point where you could only make progress by breaking new ground was a daunting thing to hear for the first time.
“The second mystery,” Yalda continued, “is the structure of particles of gas. There are plenty of symmetrical polyhedrons where putting a luxagen at every vertex gives you a mechanically stable configuration—which seems to make them good candidates for the little balls of matter of which we expect a gas to be comprised. But those polyhedrons share the problem solids have: the luxagens rolling in their energy valleys will always have some low frequency components to their motion, so they ought to give off light and blow the whole structure apart.
“There’s another problem as well, though: tiny, pure fragments of solids are sticky, as Sabino’s experiments have shown. But the gases that make up air don’t seem to be sticky at all; it’s as if the field around them has somehow canceled out, almost completely.
“A young friend of mine back home, Valeria, showed that a spherical shell of luxagens of the right size would have no external field, so you might think that a polyhedron of a similar size could get close to that perfect cancellation. The trouble is, the need for mechanical stability gives you one size for the polyhedron, and the need to cancel the external field gives you a different size. It seems to be impossible to meet both criteria at once.”
Some of the students were beginning to look dismayed. Proving the mechanical stability of an icosahedron built out of luxagens had not been an easy exercise, and now they had to accept that all that hard work had been nothing but the first step into a larger, unknown territory.
“The third mystery,” Yalda said, “is the strangest, and the most dangerous. The Peerless is surrounded by fine dust that we believe is the same kind of material that we saw back home as Hurtlers, when it burned up in the solar wind at close to infinite velocity. But we’ve more or less matched its velocity now… so why should it behave any differently toward us than any other dust?”
Tamara, another near-stranger to Yalda, had heard the theory that had begun circulating a few days after the news that the spin of the Peerless had stopped the impact flashes. “The luxagens are swapped,” she said. “Any that would be positive in our own materials will be negative for that dust, and vice versa.”
“Can you say why?” Yalda pressed her.
“It’s come to us… around the cosmos,” Tamara struggled, tracing out a loop with one hand.
“And why does that matter?” Yalda persisted. “How does that swap the luxagens?”
“I don’t know,” Tamara confessed.
Yalda sketched out the general idea.
She said, “Suppose the orthogonal stars, the orthogonal worlds, are fragments that broke off the primal world backward. They’ve come full circle around the cosmos, and we’re moving alongside them with our arrows of increasing entropy in agreement. We know that those arrows agree, because otherwise the orthogonal stars would be invisible to us.
“But Nereo’s equation ties the field around a luxagen to a vector that points along its history—and there’s no reason for that arrow to have anything to do with entropy; it should simply stay the same along the luxagen’s entire history. That vector determines whether the luxagen is positive or negative: if we meet a luxagen with the vector pointing into our future, we call it positive; if the vector’s pointing into our past, we call it negative.”
“So who drew the arrows on the luxagens?” Fatima joked.
“Well, exactly,” Yalda conceded. “No one really knows what this vector means. Still, we ought to be able to tell when two luxagens have different signs. Close up, a negative luxagen will repel a positive one, and the whole pattern of potential energy seen by a positive luxagen around a negative one will be upside down: all the usual peaks will become valleys, all the usual valleys will become peaks.”
“Which would cause havoc if you mixed the two,” Prospera suggested.
“Not necessarily,” Yalda replied. “You can’t replace a positive luxagen with a negative one in exactly the same location in a solid, but the negative one wouldn’t want to be there anyway—it sees the potential energy curve upside down, so it would prefer to be at a peak rather than in a valley. And if it’s located at a peak, it won’t disrupt the original pattern, it will reinforce it.”
“So it’s not really clear why a speck of dust with its luxagens swapped should cause any more damage when it collides with ordinary rock than an ordinary speck of dust traveling
at the same speed. But then… we don’t really know how plant-derived liberators work, nor do we understand why rocks don’t simply burst into flames all by themselves. So we’re a very long way from determining what will or won’t set any given solid on fire.”
Yalda paused to take in the students’ expressions, to see who was beginning to look burdened by the uncertainty they were facing, and who was exhilarated by the prospect of searching for something entirely new.
“I don’t have the answers,” she said. “All I can do is give you some tools that will help you probe these mysteries, then stand back and see what you discover.”
“Yalda, can I speak with you?”
Yalda looked up from her notes to see Lavinio on the ropes at the entrance to her office. “Of course.”
As he approached, the solemnity of his demeanor became apparent. “Don’t tell me it’s the wheat,” Yalda begged him.
“The wheat’s fine,” Lavinio assured her. “But there’s blight in some of the goldenrod.”
“Some of it?”
“Not every plant is showing signs of infection,” he said, “but there are infected plants in all four gardens.”
“How could that happen?” The gardens were worked by different staff, and even Lavinio refrained from visiting all of them. An infection in one should not have spread easily to the others.
“We can’t know for sure.”
“Can’t we make a guess, to try to stop it happening again?” If the protocols for disease limitation were flawed, they needed to be corrected urgently.
Lavinio said, “It was probably all the re-planting work, just before the spin-up. All that dust in the air was impossible to contain; it would have spread throughout the mountain.”
That did make sense—and if the hazard had not been avoidable, at least there was a chance it would never be repeated.
Yalda braced herself. “So, how do things stand?”