by Greg Egan
"Excuse me," she said. "I think I've found something."
Her name was Kem; Tan introduced her to Roi. He'd given copies of Roi's observations from the void to all the recruits who'd finished their studies in template geometry, and set them the task of finding a way to interpret them.
"I've been thinking about symmetries," Kem said. "If you look at the relationship between the direction of a natural path and a motion of symmetry, it should be the same all along the path." The idea, she explained, wasn't tied to the particular geometry they'd discovered; it followed from the very definition of symmetry.
A simple example made Kem's proposition more persuasive. On the surface of a perfectly round stone, the natural paths were great circles: the circles whose centers were the centers of the stone itself. The symmetries were rotations around any axis you cared to name. If you chose a particular great circle to be your natural path, then chose a diameter of that circle as the axis of rotation, the motion of symmetry — the way points on the surface shifted when the stone was rotated — would be perpendicular to the direction of the path, everywhere. If instead you chose an axis of rotation perpendicular to the plane of the great circle, the motion of symmetry would agree with the direction of the natural path, all along its length. And if you picked an axis that lay between those extremes, then although the angle between the motion of symmetry and the direction of the path would change, the size of the motion would also change, growing ever larger as the two drifted away from being parallel, in just the right way to compensate. Between the two effects, a number could be computed that would remain identical all along the path.
The stone was just an illustration, though. Kem shuffled templates that applied to any geometry, and made her case in all generality.
Roi was excited. The geometry they were testing possessed two distinct symmetries, and every natural path, every orbit, would have a constant relationship with them all along its length. For circular orbits in the plane of the Incandescence this told them nothing new, but within three shifts they had characterized the shapes of two other kinds of orbits in the plane: those whose distance from the Hub varied periodically, and those that came in from afar and then spiraled right down to the Hub.
It was beautiful mathematics, but was any of it true? Roi's observations of the void were still useless, because although they knew the angle at which the light had reached the Splinter, they had no way of measuring how fast it had been traveling. She'd joked with Ruz on the journey back from the junub edge that he should make that his next task, but for all his ingenuity she couldn't imagine how he could succeed.
"The problem is twofold," Tan mused. "It's not just the speed of light we need to discover, because what matters is the ratio of that speed to Neth's unknown speed, the speed for turning time into space. Knowing the first without the second is useless."
Kem said, "But we don't need both, we just need the ratio?"
"It would be nice to have both, but we could make a lot of progress with just the ratio," Roi replied.
"Light travels so fast," Kem observed, "that we might not be far from wrong if we suppose that the ratio is one."
Tan rasped disapproval. "Nothing can travel at Neth's speed. Anyone doing so would have a heart that never beat, a sense of time that never advanced, and a notion of distance that squashed the whole world flat."
Roi couldn't deny those absurdities, but she wasn't sure that was the point. "As an approximation, though, would it necessarily mislead us? We won't calculate anything from the light's point of view; what we're interested in are our own measurements. And if we make this choice, the calculations become easier." That was an understatement. Neth's speed had the gloriously simple property that everyone agreed on it, regardless of their own motion. If they imagined that the speed of light was Neth's speed, then the light they were seeing would not gain or lose velocity at all as it traveled from the void toward the Hub.
"Eat stones, excrete stones," Tan rasped sullenly. "If we start with nonsense, what should we expect at the end?"
Kem looked dismayed, but Roi was not dissuaded.
"I think it's worth trying," she said.
Tan left them, to pursue ideas of his own. Roi worked with Kem, carefully setting up the calculations. Strictly speaking, they could still only deal with the paths taken by light that remained in the plane of the Incandescence, but Roi had many observations from the void where she'd followed lights that appeared to be skimming the surface of the rock. The paths that linked her eyes to those distant objects were so close to the plane that the difference scarcely mattered.
They spent half a shift calculating, then they called in some helpers to check the results.
Roi took Kem with her and went in search of Tan. He was alone in a small chamber, surrounded by frames, scraping his legs distractedly against his carapace.
"This is going to take me a while," he admitted. "I can't seem to find the way forward."
Roi said, "Try eating what we ate."
She passed him the final template that she and Kem had derived, and let him check it against the observations. "Correct," he murmured after a while. He put down one skin of data, copied from Roi's time and angle measurements, and picked up the next. Each time, the verdict was the same.
"Nothing can travel at Neth's speed," he insisted. "But perhaps light can get very close. Too close for us to see the difference."
Kem spoke shyly. "I have some ideas about orbits that go out of the plane. There's a trick I think we can use to understand them."
For a few heartbeats, Roi gazed at her in silence. Before the Jolt, Kem had been cleaning susk carcasses. Tan had taught her well, giving her the tools every geometer needed, but he had not fed her any of these insights himself. Whatever mysterious skill it required to take the knowledge of your teachers and double it had blossomed across the Splinter at precisely the time it was needed. Where had it been hiding? How had it emerged? Roi couldn't begin to imagine how such things could be explained.
When they'd dealt with the Wanderer, she could worry about that. She'd look forward to spending her final shifts cataloguing her ignorance.
"Tell us your ideas," she said to Kem. "Tell us how we're going to understand the Wanderer."
21
Shift after shift, Rakesh returned to the depot and waited for Zey to finish work. Sometimes she was too tired to speak with him, but more often she would spend a few minutes chatting before she went to find a crevice to rest in.
Zey talked about her life, and the things she'd heard about the history of her world, and the cousins'. The various jobs she'd done had all been important to her at the time, but she had little to say about them; even the time she spent in the depot moments before they met seemed to pass in a kind of pleasant daze, and left almost no impression once the shift had ended.
She talked about the ideas that had crept into her life in the cracks between these episodes of dutiful sleepwalking. The story of the six worlds had been passed on by a fellow worker as idle chatter, three jobs past, but it had resonated deeply with Zey, and since that time she had viewed her surroundings in a new light, always trying to guess the age and origin of things, always trying to fit them into a coherent picture. Who built the first cart? Who carved out the tunnels? What kind of machine could carry you between worlds?
It was not that her fellow Arkdwellers were simpletons in comparison. They could all master complex tasks, and juggle equally sophisticated concepts, if and when the need arose. They were, however, monumentally indifferent to their history, their circumstances, and their prospects. Every question that to Rakesh seemed most compelling struck them as, at best, a frivolous diversion.
As they traded stories, Rakesh tried to find a balance between misleading Zey and confusing her. How could you tell someone who had never seen the stars about the size of the galaxy, or the scale of the journey he'd made? He spiraled out gently from the things she knew or imagined — her guesses about the cousins, criss-crossing the all-envel
oping warmth and light of the accretion disk — into the swarming emptiness beyond. She was interested to hear about the way he'd lived, on the surface of a rock that was far from its own source of warmth and light, but what really galvanized her were the hints he'd found of her people's history. As he unwound the story, all the way back to the Steelmakers' fossilized spacecraft and their missing world, Zey soaked up every word, every detail, and begged him for more. That this was a need no one around her shared, let alone had the power to fulfill, only made the situation more poignant. Rakesh had never seen anyone lonely in quite this way before.
Parantham watched through the probes that filled the Ark, though she really didn't need to spy on them that way; if she'd asked, Rakesh would have let her take the data stream straight from his avatar's senses.
"So where exactly is this seduction leading?" she demanded.
"Seduction? If you want to call it anything, call it a recruitment."
"Instead of dreaming about her long lost cousins, now Zey can spend her life dreaming about the Amalgam. And this has helped her. how?"
Rakesh said, "If she wants, she can come with us to the disk. Imagine seeing ten thousand new worlds with fresh eyes, after spending all your life buried in a rock." And never mind that their own ability to return to the disk was far from certain.
"You want her to trade one kind of loneliness for another?" Parantham retorted.
That had not been Rakesh's plan. He did not want to tear Zey out of her world; he hadn't even offered to take her to visit Lahl's Promise. He wanted to kindle her innate curiosity and excitement to the point where it began to spread to those around her; he wanted to use her as an ambassador, as a bridge between their cultures.
The trouble was, however successfully he engaged with her, it was the gap that separated Zey from her fellow Arkdwellers that remained the hardest to bridge. Her instinct, she'd told him, had been to keep his revelations to herself, because she knew how they'd be received, but she hadn't been able to control herself. Her instinct had been right: nobody wanted to hear about her "distant cousin", or the thirty-six times thirty-six worlds. Nobody wanted to discuss the perils that their ancestors had survived, or to debate their options for evading the unknown catastrophes that the future might bring. They wanted to listen to inconsequential chatter as they worked, and when they were finished working, they wanted food, sex and sleep.
"Why am I sick?" Zey asked Rakesh. "Why is my mind so damaged?" They were doing their usual circuit of tunnels close to the depot, walking and talking until she needed to sleep.
It would be meaningless to reassure her that most of the galaxy was on her side, that the qualities that made her an anomaly here were almost universally valued and admired.
"I don't know," Rakesh said. "But if you allow me, I can try to find out."
"How?"
"If you let me take a small part of your body, I can study it carefully. I might not be able to answer your question, but there's a chance I can tell you something about the reasons that you're different."
Zey was alarmed. "I'm using every part of my body. I'm not a male, to offer a portion to be removed."
Rakesh chirped amusement. "I'm talking about a part so small that you lose thirty-six times thirty-six in every shift, without even noticing."
"I lose parts of my body without noticing?" However dazzled she'd been by Rakesh's stories, Zey retained a healthy skepticism toward his wilder claims.
"Absolutely. They're too small to see."
"Then how will you study them?"
"With machines too small to see."
"So all of this happens, invisibly, and you believe what these machines whisper to you at the end?"
"That's about it."
"I think your mind is damaged more than mine."
This wasn't banter; Zey was deadly serious. Rakesh had to spend the next four of their meetings explaining the atomic nature of matter, and trying to make it plausible without setting up a demonstration in chemical stoichiometry. Then they moved on to cellular biology, and the eleven known molecular replicators. If Rakesh had had any qualms about her ability to give informed consent to being sequenced, she seemed determined to make it clear that she would not allow him to perform his technological magic and then pronounce upon her nature like an oracle. When she understood his proposal well enough for his claims to seem plausible, she would consider it, but not before.
As they toured the basic sciences, Rakesh could see Zey building a picture far bigger than the subject at hand, integrating everything piece by piece into an ever more sophisticated world view. It was firmly anchored to the familiar things around her, but her mind was stretching to encompass the distant, the small, the abstract. Shift after shift, he was making her "sickness" worse, "damaging" her even more. Her co-workers didn't care; they might tease her when she couldn't keep quiet about her strange ideas, but they wouldn't ostracize her as long as she kept doing her job. This was not a culture that could be scandalized by her dalliance with Rakesh, or her heterodox notions of history and reality; the only sacred thing was work. Zey was the one who would feel the separation; it didn't have to be imposed on her by her peers. If Rakesh failed to bring the other Arkdwellers along with her on this intellectual journey — if he transformed her and then abandoned her, with nobody else who thought the same way — she would be lonelier than ever.
Thirty-six times thirty-six.
22
One of the children Gul had taught, a young male named Haf, approached Roi with three claws full of food. She accepted the gift gratefully, but he retreated before she had a chance to talk to him. As he rejoined his team-mates, she heard him whisper to one of them, "She was Zak's first student."
"She must be very old," his friend replied.
"She saw him die," Haf announced solemnly.
"That means she'll die soon herself," the friend explained. "That's the way it happens."
Roi was amused. Gul had sent his former students here to do fetching and carrying while they learned more about the intricacies of the project, and were gradually recruited into more specialized teams. She listened to their innocent gossip for a while; it made a welcome diversion. Then she turned her full attention back to the task ahead of her.
The control post she'd set up lay on the border between the junub and sard quarters, halfway along the line of light-messengers that Jos had established between Ruz's void-watchers at the junub edge and Bard's control post. From there, Bard's own separate network of light-messengers branched out to reach all the tunnel-plug operators.
Twelve shifts before, Bard and Neth had reported success. They had developed a system of movable baffles to tweak the shape of the tunnel, and after some laborious trial and error in conjunction with Neth's calculations, they had finally achieved a smooth flow. The tunnel had been opened on more than a dozen occasions, but only for a single bright phase each time. The wind would pass through it cleanly now, but the question that remained was whether Bard's ambitious scheme could actually achieve its purpose: whether the free passage of the wind really could change the orbit of the Splinter itself.
Roi consulted the clock beside her, made a note of the time on a sheet of skin, then took the handle of the metal signal-sheet on her right and cranked out the code to have the great tunnel opened. Many spans away along the ordinary tunnel that sloped down into the sardside, the light-messenger watching her sheet would note the sequence and repeat it. Then the watcher for that sheet would do the same; on and on the message would go, all the way to Bard, and then to a dozen plug operators, who would call on their teams to drag on the ropes that pulled the wheeled stone plugs aside. A part of the sardside wind that had once forced itself from rarb to sharq through the rock's reluctant pathways, losing all its strength along the way, would now make the same journey entirely unhindered. The force it had once imparted upon the rock of the Splinter would vanish.
Of course, the remainder of the sardside wind would still exert a powerful force, but on the g
armside the opposing force would not be diminished at all. If the perfect balance of the winds really had kept the Splinter in place for generations, that balance would no longer hold.
Roi turned to Kem. "Now we wait."
"Can we calculate while we wait?" Kem asked anxiously.
"Of course."
Kem took her frame and started working through a fresh set of path calculations. There were some problems they could only treat in the most general fashion until they had data from the void-watchers to tell them how the Splinter was responding, but Kem seemed determined to pre-calculate every result they could possibly need.
Up at the junub edge, the void-watchers no longer needed to scramble back and forth through the crack that led to the surface. Inspired by Jos's light-messengers, Cho, one of Ruz's team, had invented an elaborate system of polished metal plates that allowed them to observe the lights in the void from the safety of the tunnel below. Each time the junub dark phase ended, the plates were retracted part-way into the crack, shielding them from the full savagery of the Incandescence, while a stone plug, like a smaller version of Bard's tunnel-plugs, was wheeled into place below to provide some shelter for the void-watchers themselves. The system did not afford them the sweeping views of the whole quarter-circle that Roi had seen, but now that they had mapped the fixed pattern of lights in detail, and knew how to follow the Wanderer against that background, their sighting and tracking of individual lights would yield enough information for the theorists to calculate both the Wanderer's shifting orbit and any hoped-for change in the Splinter's own motion.
Roi passed the time by checking Kem's results. She did the work scrupulously, but it scarcely demanded her attention; it was like walking now, pure instinct. These were not new template calculations, replete with symbols for unspecified values; rather, she and Kem were feeding a range of numbers into existing templates, making earlier, abstract computations concrete.
