Update: Some great discussion came about from my http://physics.SE post regarding "classical spinors" (of course @johncarlosbaez 's replies were extremely insightful as well, but to be fair he only had 140 characters to work with)https://physics.stackexchange.com/questions/450899/what-precisely-is-a-classical-spin-1-2-particle …
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@knzhou correctly says that a classical system has a symplectic manifold of states, but he doesn't say what this manifold is for the spin-1/2 particle. That's part of what my post does.
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Spoiler: it's just a sphere of all the possible directions of pointiness of \vec J. The real fun part seems to be to understand where the power of j in the symplectic / complex structure comes from!
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