There is a proof regarding the three sides of a right triangle, but it is only true in an Euclidean plane.
Juno is a pilot because she wants to be; she could have been an officer but she loves the thrill of feeling a spacecraft beneath her control, the dizzying pace of sub-light acceleration, the subtle time-space shift of reality in a hyperspace jump. They'd wanted her for engineering but she'd gone into the military instead; she likes the challenge. Engineering, she'd discovered, is rather too sedate for her tastes.
She is calculating the shortest route to Alderaan. Hyperspace curves and twists upon itself; the three sides of a right triangle and each longer than the other two combined and yet shorter than either taken separately. It is impossible to calculate a set of orthogonal basis vectors for a hyperspace of any dimension higher than zero (which is the trivial case, anyway, and isn't very useful). The hyperspace that ships jump through is theorized to have anywhere between six and fourteen dimensions; a ship interacts with only five of these. Still, five dimensions shouldn't be taken lightly.
She is calculating the shortest route to Alderaan, but she doesn't think they'll be going there after all, because Starkiller and Kota are shouting at each other in the main cabin. So perhaps the calculations take her a bit longer than usual—five-dimensional hyperspace interactions aren't for the faint of heart—as she keeps the ship in orbit above Kashyyyk with all stealth systems engaged.
Galen comes stalking into the cockpit, slamming open the door with more force than is strictly necessary, and throws himself down on the co-pilot's chair. "We're going to Felucia," he tells her.
Juno glances at him. "Why the change in plans?"
"Kota's contact is there," he says. "He's been kidnapped."
"Kidnapped?"
He nods, looking out the window at the stars. "Shaak-ti's apprentice. She's gone mad."
She touches his shoulder; he jumps, his eyes flying to her, and she snatches her hand away. "I'm sorry," Juno says, embarrassed. "I was just wondering if you were all right—"
"I'm fine," he says—not that he ever answers otherwise, when she asks—and there is the oddest trace of wistfulness in his expression. "You startled me."
Vader isn't the cuddliest of parental figures, is he? Juno has forgotten. "I'm sorry," she says again.
"It's all right." He sounds sincere.
Juno taps in the coordinates for Felucia. Three jumps should take them there; seven would be shorter, but there's a black hole that would be tricky to get around—But they are probably in a rush. So she takes them out of orbit and primes the ship for the first jump, a short hop sideways across the galaxy—
The stars blur around them and the world outside becomes a swirling vortex of blue.
Galen is quiet. Juno is already inputting the commands for the next jump, but after a few minutes she glances at him again. "We should be there within twelve hours," Juno says. He nods, looking out into the vortex, and the shimmering blue is reflected in his somber dark eyes.
Something has happened on Kashyyyk.
Hyperspace is ever-shifting and convoluted, but it is still easier to compute five-dimensional spatial algorithms than to guess at what he's thinking; Juno frowns down at the route for the fourth jump and sighs to herself. At least she understands how hyperspace is defined—
"Juno," he says abruptly. "Tell me about your parents."
She looks at him, surprised. Galen says it with all the authority of an order—take me to Nar Shadda, can you handle that?—but she doubts that he knows how to ask any other way; there is that wistfulness, again, in his eyes. She doubts, too, that he even knows it's there.
"My mother was a teacher," she says, choosing her words carefully. "She died when I was—very young. My father was—is—very loyal to the Empire. It was why I joined." The fifth jump is tricky. Juno carefully plots a course around the black hole, the numbers clicking out beneath her fingers. "I haven't spoken to him in years," she adds. "I always feel as though I'm not living up to his standards."
"You're one of the top pilots in the galaxy." Starkiller sounds surprised. She cannot help but smile at the compliment. Well, of course she is; the Empire hasn't caught them yet, has it?
"Why do you ask?"
He is quiet again. "I was seven when Vader took me," he says at last. "My father—I—we lived on Kashyyyk. I don't remember it."
Does he wish he did? "I'm sorry," she offers.
He looks startled for a moment and glances at her, a slight furrowing in his brow as though he isn't sure how to respond. "Thank you?" he tries.
Vader isn't big on social niceties, either. Juno shrugs. "Well, I am," she says. Perhaps his father had loved him; perhaps he had been frightened when Vader had stormed Kashyyyk and brought him away. And Juno is a little sad for him, the boy he was and the man he might have been, but even so she discovers that she likes the way he smiles at her now.
A/N: People are telling me that the technical stuff is too complicated? I've tried turning it down so I hope that worked, but really it's always how I imagined Juno would think...
Thanks to everyone who reviewed! Sorry about the crazy math stuff!