by Greg Egan
“Are your brother’s children older or younger?” she asked Nino.
“Younger.”
“So do you think he’ll put pressure on his nieces and nephews?”
“No,” Nino replied. “That’s not his way. I’m more worried that they might have trouble controlling themselves.”
At the top of the second tier they left the stairs. The only way to reach the new navigators’ post was through the feed chambers, and these ones would not be empty.
“Put your hands behind your back,” Yalda insisted. “For appearances’ sake.”
Nino complied; she pressed them together, then wrapped one of her own, larger hands around them. She would never have actually used melding resin, but it couldn’t hurt that anyone who saw them would be unable to tell at a glance that her prisoner was in fact topologically free.
They crossed the outermost chamber unseen, but in the next, Delfina was at her post inspecting the tape writer. “You’re letting that murderer walk through here?” she shouted at Yalda, incredulous.
“There’s no other route to his cell,” Yalda replied. The machinists had just spent days cleaning and testing their shiny new feeds; in the circumstances she could understand why anyone would feel affronted by Nino’s presence. But she’d had no choice.
Delfina approached them. “I can’t accept this!” she told Yalda angrily. “When Eusebio appointed you leader, do you think he intended you to put the life of one traitor above all of our own?”
Yalda had learned not to waste time taking issue with hyperbole like this. “I’m glad you’re here,” she said. “I wanted another guard to help watch over the prisoner as I escorted him to the new cell, but Babila and Frido were busy with the release charges.”
Delfina hesitated, but refusing the request would have been tantamount to conceding that Nino already posed no risk.
“If you could walk ahead of us,” Yalda suggested, “ready to block him if he tries to break free…?”
They threaded their way in silence through the banks of pristine clockwork, then into the next chamber. Onesta was inspecting the valves at the base of the liberator tank, but when she saw Delfina leading the procession she simply nodded in greeting.
In the navigators’ post, Delfina stood and waited until Nino was locked in his cell.
“I appreciate your help,” Yalda said.
“It shouldn’t have been necessary,” Delfina replied. “There shouldn’t have been a prisoner to move.”
“Nonetheless, I’m grateful,” Yalda insisted.
“That’s not the point.”
“Don’t forget the transition drill,” Yalda reminded her. “That’s the day after tomorrow.”
Delfina gave up. When she’d left, Yalda checked in on Nino. “Are you going to be—”
“Comfortable?” he suggested. “It’s identical to the last one.”
Yalda said, “If there’s anything in particular that you want, now might be the chance for me to sneak it in.”
“In the sagas,” Nino mused, “the rulers who survived were the ones who identified their enemies in time, and disposed of them swiftly.”
“I’ll be sure to keep that in mind.” Yalda began to leave, but then she stopped and turned back to him. “You learned the sagas?”
“Of course.”
“You’ve memorized them?”
“My father taught them to me,” Nino replied. “I can recite them all, word for word.”
Yalda said, “How would you feel about putting them on paper?”
Nino was bemused. “Why?”
“It would be good to have them, for the library.” In fact, she suspected that the library had a copy already. But every family passed down its own version, and perhaps in the future someone would want to ponder the nature of that variation. “If I bring you dye and paper, would you be willing to make a start on it? See how it goes?” Nino’s written vocabulary might not yet be up to the task, but any problems he struck would give them something to address in their lessons.
Nino considered it. They both knew this would be a kind of make-work compared to tending the wheat fields, but if he wasn’t yet sick of the uninspired calligraphic exercises Yalda had been setting for him, she was sick of thinking them up.
“All right,” he agreed.
Yalda was relieved. “I’ll get the supplies for you, before Frido and Babila arrive.”
“I taught the sagas to my sons, a few years ago,” Nino said. “After I’d done that, I thought I wouldn’t need them—I thought I’d just forget them.”
“But you didn’t forget them?”
“No.”
Yalda said, “I’ll bring you everything you’ll need.”
The new engines started up without mishap, blasting the stub of rock remaining at the top of the first tier away into the void. As Frido and Babila cheered, Yalda imagined herself congratulating Eusebio on the success of his design. Lately she’d found herself thinking about the return of the Peerless as if she’d be there in person—but then, she’d pictured Tullia walking beside her in Zeugma often enough; was it any more absurd to have the same kind of thoughts when she played the ghost herself?
Nino filled page after page with his transcripts. Yalda visited him to read these first drafts and suggest corrections—but only when one of her fellow navigators was sleeping and the other was out at the rim making observations. No one was being deceived, but she could still avoid provoking them with reminders of her contentious decision. The astronomers at the summit had found no obstacles ahead, but ensuring that the Peerless remained on course was still more than enough to keep everyone around her, machinists and navigators alike, far too busy to want to organize an insurrection if there was nothing forcing their hand.
When the Peerless reached the halfway mark of its acceleration phase, matching the speed of blue light, Yalda traveled up the mountain to speak to Severa’s class.
They met in one of the observation chambers. The students fell silent as they entered; they’d been told what to expect, but Yalda could understand how daunting it must be to see every star they’d grown up with—every subtle, distinctive smudge of light, every Sitha, Tharak, Zento or Juhla—raked into streaks of color more like a barrage of Hurtlers than anything else.
That was the view that first confronted them: looking straight out from the side of the mountain, where the small, haphazard motions of the stars were overwhelmed by the velocity of the Peerless. The speed of the mountain’s ascent was enough to align every color trail vertically, making a field of parallel furrows in the sky. The trails began and ended at disparate points, but all of them spanned about half a right angle, with red at the top and violet at the bottom. In this history made visible, the most recent report in violet always showed the star lower in the sky than the tardy red version.
Looking up toward the zenith, though, shattered any expectation that this pattern would merely repeat itself into the distance. Here, the stars’ own sideways motion could compete with the rocket’s forward rush, complicating the geometry enough to keep the trails from converging on any perfect vanishing point. More surprisingly, many of the trails here were completely inverted compared to the norm, their red ends poking down—and both kinds of trail faded out before traversing the full spectrum, the red-tailed never getting past green, the violet-tailed barely reaching indigo. On top of all this, the upper part of the sky was simply more crowded than the lower, giving the bizarre impression that the stars the Peerless was approaching had somehow receded into the distance, clumping together like the buildings of a town you were leaving behind.
Yalda addressed the students. “I know this looks strange to you, but we’re here to make sense of it. Everything you’re seeing here can be explained with some simple geometry.”
Severa had earlier had the class construct two props for the occasion. Yalda took them from her and set them down on the floor of the chamber. “To start with, I’d like you to examine these objects, please, and draw them as the
y appear side-on.”
The props were octagonal pyramids made of paper, one with a fairly shallow pitch and the other much steeper, mounted on simple wooden stands. The students gathered around them and squatted down to obtain views square with the base.
“The stem of each stand represents a short stretch of the history of the Peerless,” Yalda explained, “before it was launched. Time is measured vertically, straight up from the floor; space is horizontal. Back then, the stars were only moving slowly in relation to us, so we can think of them as being spread out evenly across the floor, with their histories rising up almost vertically.” She glanced across at Fatima’s neat, stylized rendering.
“And the pyramids are light?” Ausilio asked.
“Exactly,” Yalda confirmed. “Incoming light, emitted long ago by the surrounding stars and finally reaching us at the apex of the pyramid. The two pyramids represent violet light and red light, as seen by us. The steepest one is…?”
“Red,” Prospera volunteered. “The edges cross less space in a given time—a slower velocity.”
Yalda said, “Right. A cone would provide a more detailed model, showing all the rays of a given color, but the eight edges of each of these pyramids are enough to give us a good idea of how the light behaves—and the fact that they mark off equal angles around the Peerless is going to be helpful to us.”
Everyone had finished the first view. “Could you look down from above now, please,” Yalda instructed them, “and draw what you see.”
She waited until most of the students had new sketches on their chests before continuing. “Think about the light rays that reach us,” she said, “between the edges of each of these triangles. When the Peerless was motionless compared to the stars, each of these equal segments in our view of the sky took in light from an equal slice of our surroundings. The stars were arranged uniformly around us in space, more or less—so we saw them scattered uniformly across the sky, with no one direction appearing very different from another.”
Yalda looked around and chose one of the quieter students: Ausilia, whose co did most of the talking for the pair. “Could you tip the stems over for me, please? Try to make them both as close as you can to a one-eighth turn down from the vertical. Halfway to orthogonal. The speed of blue light.”
The stems were connected to the base with a swiveling joint; Ausilia approached the task diligently, stepping back several times to check the angles.
“Could everyone draw the new configuration, please,” Yalda said. “From the side first.”
Severa approached her and whispered, jokingly, “You know you’re robbing them of the big payoff when we learn to do all of this algebraically.”
“Ha! How far away is that?”
“A couple of years, I expect.”
“And how many of this class will stick with it that long?”
Severa thought for a while. “More than half.”
Yalda was encouraged; for the first generation that would be a good result. But right now, she was going to ensure that every one of these people could make sense of the view around them using nothing but their eyes and their intuition.
She addressed the class again. “This drawing tells us something straight away, about the view we can expect from the Peerless. Any suggestions?”
Prospera said, “The violet light coming in from behind us has been tilted so far that it’s… gone past horizontal.” Her tone made it clear that she knew the change had to be significant, but she couldn’t quite see what it implied.
“So if you follow the light in toward us,” Yalda suggested, “what happens to its height?”
“It gets less, as you move in,” Prospera replied.
“Its height gets less. And what does height stand for, in this picture?”
“Time.” Prospera pondered this for a moment. “So the light would have to come from the future?”
“Exactly. It would have to be traveling back in time. Not for us—it’s still coming from our past—but for the star that emitted it. So what you’ve found tells us that no ordinary star that lies directly behind us—in the rear one-eighth of our view, or a bit beyond that—can appear to us in violet, because that would require the star to have emitted light into its own past.”
“But it would be different for an orthogonal star, wouldn’t it?” Fatima asked eagerly.
Yalda said, “Well, their time is horizontal in this picture, and their future is aligned with the direction in which we’re traveling, but—”
Fatima ran forward to the edge of the cave and peered down the slope of the mountain.
“—but unfortunately, the rock below us hides that part of the view.” Between the mountain and the haze from the engines, there was no chance at all of observing the orthogonal stars yet.
Yalda asked the students to draw the tilted pyramids from above. A few people became confused, or drew some preconception rather than the actual view, but after noticing the emerging consensus of their peers they looked again and refined their own versions.
She waited until everyone had the essential features correct.
“Each of the eight segments still represents an equal portion of our view,” she reminded them. “But their relationship with the surroundings has changed. Let’s start with the violet, the broader pyramid. Can someone tell me what’s going on?”
Ausilia spoke up. “At the front,” she said, pointing out the triangle on her chest, “the angle between the edges is much bigger than one-eighth now, seen from above.”
“Which means…?” Yalda pressed her.
Ausilia hesitated, but then followed through. “Our one-eighth of the view is taking in light from more than one-eighth of the stars?”
“Exactly!” Yalda approached her and had her turn so the whole class could see her sketch. “In the direction in which the Peerless is traveling, this slice of the view has a wider reach, so light from more stars gets crammed into it. We still see it as an equal eighth, but as far as our surroundings are concerned it’s much more.” She stepped away from Ausilia and gestured toward the zenith. “Focus on the violet ends of the trails. They started out scattered uniformly around us, before the launch; now they’re crowded together around the direction in which we’re traveling. And the reason is simple: when you take two lines that are a fixed angle apart—like the edges of that front triangle—the more you tilt them, the greater the angle between them will seem to be.”
She waited for the simple logic of it to mesh with the evidence before their eyes, then added, “In the opposite direction there’s an opposite effect. The mountain makes that harder to see—and we’ve already shown that there’s a region behind us where we won’t be getting violet light from the ordinary stars anyway—but in general, looking back the view is sparser.”
Fatima was standing closer to her than Ausilia now, so Yalda moved beside her and pointed to her drawing of the red pyramid.
“What about red light? If you compare the rear triangles in the two pyramids, it’s clear that the angle for the red light is even smaller than it is for violet—so we should see the red images behind us spread out across the sky more than the violet, pushed forward compared to the violet. And that difference persists as you move away from the rear. For any given star, the red light ends up further from the nadir. Does that sound familiar?” Yalda pointed to the vertical trails behind her, the red ends all higher than the violet.
“But what happens with the red light,” she continued, “when we look in the direction in which we’re traveling? There are only five triangles from the pyramid visible here. What’s going on with the three triangles that point to the front for us?”
Fatima helpfully added three lines that made the hidden triangles visible:
“They’ve ended up pointing backward,” Ausilia said.
“Yes!” Yalda raised her eyes to the zenith. “See those strange red ends of trails poking out the wrong way? They’re stars that are actually behind us! The pyramid shows us that in red light, we
can’t see anything that’s in front of us—in the sense that an onlooker fixed to the stars would judge something to be ‘in front’. But our view isn’t empty of red in that direction; instead of seeing what’s in front of us, we’re seeing some of what’s behind us.”
“And all of it twice,” Fatima said, running a fingertip across the diagram toward the apex of the pyramid. “Every star we see behind us in red… we also see in front of us in red.”
“That’s right,” Yalda said. “But though it’s light from the same star—and it looks the same color to us—it’s not the same light.”
Fatima thought for a moment. “The red light we see, looking back, left the star at a greater angle than the angle it makes with us. So it left the star as faster-than-red light… but because we’re fleeing from it, it’s not gaining on us as quickly as it would if we were still. Our motion has changed the color from violet or ultraviolet to red.”
“Yes.” Yalda pushed her, “And the other light? The red light we see looking forward that came from the very same star?”
Fatima gazed down at the diagram, struggling. “From the angles, I think it must have left the star moving quite slowly. But if it’s moving so slowly, how could it ever catch up with us?”
Yalda said, “If you’re getting confused, just draw… whatever it is you need to draw.”
Fatima made a new sketch, paused, then added some annotations.
“The red light we see as coming from ahead,” she said, “must have left the star behind us long ago… but now we’ve caught up with it, we’re overtaking it. That’s why it strikes us from the front. The star is behind us, but the light was ahead of us.”
Fatima looked up at the zenith, then a fresh revelation struck her. “That’s why those upside-down star trails sputter out at green! However long ago the light left the star, the angle it made with our history could never end up greater than the angle for blue light. But blue would be the absolute limit—light from infinitely long ago. In real life we can’t expect to see that far back.”
