Having fun rereading Rota's "Indiscrete Thoughts". These aphorisms give its flavor. cc @nntalebpic.twitter.com/clgsYRD7yq
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Not even remotely enough to say that cotangent bundles alone have contact 1-forms with symplectic exterior derivatives. True, but so what?
It's all about the link between symmetries and conserved quantities. Coadjoint orbits, and not cotangent bundles, are the things to ponder.
A phase space should have exactly the structure needed to ensure that each symmetry correspond to a conserved quantity. That's the key idea.
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