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Manfred comments on Looking for a likely cause of a mental phenomenon - Less Wrong
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Unconscious annealing of connections between concepts.
Warning: Annealing sounds impressive if you're new to machine learning but AFAIK it's pretty weak as machine-learning methods go, and the real algorithms at work in human creativity are going to involve algorithms more powerful than that - albeit something on the level of 'cognitive temperature' might still be playing a partial role somewhere.
That definitely seems to be what's going on! Any clue what the neural structures are that take the dominant role in this process?
No idea - it's just the analogy I use for myself :) I think of it like a continuation of the learning process, but I don't know if the brain actually represents solutions as a favored arrangement of cells, and I don't know if there's some changing noise source that would lead to something like annealing.