Greg Egan - The Clockwork Rocket

“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.”

She modified her diagram to show what she meant.

Yalda said, “That’s all true—though the reason we don’t see any blue in those trails is also a matter of how much power the star emits in different parts of the spectrum. The light we’d see as blue would have to leave the star as far-infrared, traveling incredibly slowly. So it can’t be carrying energy out of the star at a very high rate… which means the star itself simply won’t be shining very brightly in that color.”

Ausilia had been following the discussion closely, though Yalda wasn’t sure how much she’d understood. But then she pointed to Fatima’s chest and said, “If that star happened to be in front of us instead, its slowest light would still end up looking blue, wouldn’t it? It would just approach it from the other end of the spectrum. So its trail would start out violet, but never quite get as far as blue.”

She hesitated, then produced a diagram, echoing Fatima’s, to illustrate her point.

Yalda chirped with delight. She gestured to Ausilia to turn so that everyone else could see the picture. “That’s the last puzzle solved: why some trails above us are just violet and indigo. And that’s it: between you, you’ve unwoven the whole sky.”

In fact, not everyone had caught up with Fatima and Ausilia, but Yalda stood back and let the students help each other past their lingering puzzlement. As they looked to the stars and back, connecting the details of the color trails to the figures before them, the thrill of understanding spread.

This alien sky belonged to them, now. Its transformation would become even more extreme as the Peerless moved faster, but the new ways of seeing it that they had acquired would handle those changes with ease.

Yalda knew that only a few of these people would end up as researchers, only a few as teachers. But even if they did no more than pass their understanding on to the children of their friends, it would all be a part of strengthening the culture, ensuring that their descendants were at ease in this strange new state.

And the most beautiful thing of all, she realized—struck by it anew, because she’d almost begun taking it for granted—was that every one of these solos and runaways, every one of these partnered women and their cos, would have the chance to live out their lives without coercion, making use of their talents, untrammeled by the customs of the old world.

Forget the Hurtlers, forget the orthogonal stars. For that alone, the struggle had been worth it.

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