Greg Egan - The Clockwork Rocket

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 they 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?”