(no subject)
Yann replied affably, “My earliest memories are of CP4 - that's a Kähler manifold that looks locally like a vector space with four complex dimensions, 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”.
Greg Egan, “Schild's Ladder”
Greg Egan, “Schild's Ladder”