Proof that everything sounds better with the word "quantum" in front.https://cloudblogs.microsoft.com/quantum/2019/02/28/announcing-the-microsoft-quantum-network/ …
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I think it's *great* that you can get some interesting theories by repeated quantization: http://math.ucr.edu/home/baez/nth_quantization.html … I still don't know what it "means". But it's connected to the idea of quantization and projectivization as adjoint functors, in ways I haven't yet explored.
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There's something that has always bugged me about quantization. Here's the line of thought: physically, it's just a helpful kludge. Physics is quantum, not classical, & so it's just a helpful heuristic (which sometimes fails) for backing out candidate correct theories from ...
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... classical approximations. But what's interesting (and a priori not obvious) is that this kludge actually is pretty nice mathematically! E.g. the map from Poisson bracket to Lie bracket.
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I suppose that's not so surprising, given that we have an extraordinarily beautiful (but ultimately wrong) approximation to the world in classical mechanics, and another extraordinarily beautiful (and maybe correct?) theory of the world in quantum mechanics.
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To the extent the approximation is a good one, I guess it's not so surprising that the deep objects in one theory might sometimes have some interesting and rich correspondence to deep objects in the other.
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