“Mathematics catalogues everything that is not self-contradictory; within that vast inventory, physics is an island of structures rich enough to contain their own beholders.”

Greg Egan

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“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.”


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