I think the human brain, while itself physical, to be an emergent system in terms of function. This system has many inputs that interact to produce its current state.
Trying to partition those interactions among various inputs seems more like a fool's errand.
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Have you read Douglas Hofstadter's stuff? (e.g. I Am A Strange Loop). His idea is that the central mechanism behind thinking is the ability to self-reference
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I think you would enjoy it quite a bit, but maybe his first book more: Gödel, Escher, Bach. IIRC there's quite a bit about chess in there too
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