By evening the celebrations were growing muted. One by one, the guests congratulated the experimenters and departed. Leonia sat harnessed at the telescope, tirelessly checking and re-checking the rocket’s progress.
Carla approached him. “I’m leaving now,” she said. “Can we go together?”
“Of course.” Carlo bade farewell to the others, tickling Leonia until she moved aside and let him take a last peek at the Eternal Flame.
In the corridor, Carla was pensive.
“How long do you think it will take to scale up now?” he asked her. “To engine size?”
“A dozen years at least,” she said. “Maybe twice that.”
She’d hinted at a similarly daunting time scale before, but Carlo wasn’t convinced. “You’ve spent too long begging for resources, it’s made you pessimistic. Now that you’re the Council’s favorite, all of that’s going to change.”
Carla buzzed. “The Council can be as magnanimous as they like, but we’re talking about enough spin-polarized clearstone to cover the base of the mountain. We don’t even have that much ordinary clearstone, of any kind. We’re going to need to find ways to manufacture it.”
“I know. But once you get started,” Carlo predicted, “you’ll find new ideas, new short-cuts, new improvements. Isn’t that how it always goes?”
“I hope so,” she said. “Maybe Leonia will see the engines completed. Her generation, if things go well.”
They’d reached Carlo’s apartment.
“Will you invite me in?” she asked him.
He was afraid now. “Why would I do that?”
Carla put a hand on his shoulder. “I’ve had everything I wanted from life. I’ve completed everything I hoped to complete. Our children should be born now, before you’re much older. Don’t you want to see our grandchildren?”
Carlo felt himself shivering. “I don’t care about that. I don’t want to lose you.”
“And I don’t want to go the way of men,” she said. “It almost happened to me once, out at the Object. That’s not the end I want.”
“It won’t seem as bad if you’ve seen your own daughter,” Carlo promised. “That’s what makes it easier for men. You should talk to Patrizia! She’ll tell you!”
Carla was unswayed. “You know I made up my mind a long time ago.”
“Change it,” he pleaded. When he’d joined her in the famine he’d told himself it would help undermine her resolve: by letting her eat a little more, she’d be one step closer to Patrizia—and clear-headed enough to be envious that her own concentration was still not quite as good.
“I can’t,” Carla said. “It’s not in me. Ever since I was a child this is what I’ve imagined.”
“Because you never knew you’d have a choice!” Carlo shuddered and added angrily, “What did I fight for, if it wasn’t that choice?”
Carla squeezed his shoulder. “And now I’m making it. You didn’t waste your time. Maybe our daughter will choose differently.”
She pushed open the door and dragged herself into the apartment. Carlo clung to the rope in the corridor, wondering what she’d do if he simply fled. He did not believe she’d stop taking holin; she’d keep trying to persuade him, without bludgeoning him with a threat like that. But if he kept refusing her—stint after stint, year after year—she’d find a co-stead easily enough.
Ever since I was a child this is what I’ve imagined. Those words were just as true for him. And when he set aside the part of himself that understood how much more was possible, all he wanted to do was give in to that ache and fulfill that glorious longing.
Carla appeared in the doorway.
“Come to bed,” she said. “We should sleep on this. We can lie together and see what the morning brings.”
Appendix 1:
Units and measurements
Appendix 2:
Light and colors
The names of colors are translated so that the progression from “red” to “violet” implies shorter wavelengths. In the Orthogonal universe this progression is accompanied by a decrease in the light’s frequency in time. In our own universe the opposite holds: shorter wavelengths correspond to higher frequencies.
The smallest possible wavelength of light, λmin, is about 231 piccolo-scants; this is for light with an infinite velocity, at the “ultraviolet limit”. The highest possible time frequency of light, νmax, is about 49 generoso-cycles per pause; this is for stationary light, at the “infrared limit”.
Appendix 3:
Vector multiplication
and division
The travelers on the Peerless have developed a way of multiplying and dividing four-dimensional vectors, turning these vectors into a fully fledged number system like the more familiar real and complex numbers. In our own culture, this system is known as the quaternions; it was discovered by William Hamilton in 1843. Just as the real numbers form a one-dimensional line and the complex numbers form a two-dimensional plane, the quaternions form a four-dimensional space, making them the ideal number system for four-dimensional geometry. In our universe the distinction between time and space prevents us making full use of the quaternions, but in the Orthogonal universe the geometry of four-space and the arithmetic of the quaternions fit together seamlessly.
In the version used on the Peerless, the principal directions in the four dimensions are called East, North, Up and Future, with opposites West, South, Down and Past. The Future direction takes the role of the number one: multiplying or dividing any vector by Future leaves the original vector unchanged. Squaring any of the other three principal directions—East, North and Up—always gives Past, or minus one, so this number system contains three independent square roots of minus one, compared to the single square root of minus one, i, in the complex numbers. (Of course squaring the opposite directions—West, South and Down—also gives Past, just as in the complex numbers squaring –i also gives minus one, but these aren’t counted as independent square roots.)
Multiplication in this system is non-commutative: a × b generally isn’t the same as b × a.
Every non-zero vector v has a unique reciprocal or inverse, written v-1, which is the vector for which:
For example, East-1 = West, North-1 = South, Up-1 = Down and Future-1 = Future. In the first three cases the inverse of the vector is its opposite, but that’s not true in general.
When we divide vectors, w ÷ v is just multiplication (on the right side) by v-1: