Schild's Ladder

My earliest memories are of CP4 — that's a Kähler manifold that looks locally like a vector space with four complex directions, though the global topology's quite different. But I didn't really grow up there; I was moved around a lot when I was young, to keep my perceptions flexible. I only used to spend time in anything remotely like this" — he motioned at the surrounding more-or-less-Euclidean space — for certain special kinds of physics problems. And even most Newtonian mechanics is easier to grasp in a symplectic manifold; having a separate visible coordinate for the position and momentum of every degree of freedom makes things much clearer than when you cram everything together in a single three-dimensional space.

You’ll never stop changing, but that doesn’t mean you have to drift in the wind. Every day, you can take the person you’ve been, and the new things you’ve witnessed, and make your own, honest choice as to who you should become. “Whatever happens, you can always be true to yourself. But don’t expect to end up with the same inner compass as anyone else. Not unless they started beside you, and climbed beside you every step of the way.

It was a rigorous result in information theory that once you could learn in a sufficiently flexible manner – something humanity had achieved in the Bronze Age – the only limits you faced were speed and storage; any other structural changes were just a matter of style.

There's nothing worse than a label to cement people's loyalties.

You don't take a traveler for a partner if you hope that the world will always stay the same. You do it because you can't quite break away, yourself, but you can't live without the promise of change hanging over you every day. That's what the border means, for a lot of people. The promise of change they'd never be able to make any other way.

That was the hazard she’d face every day, here: not just the risk that she’d give in to temptation, but the risk that all the principles she’d chosen to define herself would come to seem like nothing but masochistic nonsense.