'The brain has evolved from the inside out' is grammatically correct, though I've no idea if it's physiologically true. from the inside to out' is incorrect.
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NugsoThe brain has evolved from the inside out.Here 'out' means 'outward', i.e., 'in an outward direction'. You can even say it like this:
NugsoYes, those sentences. Well, [video] . Around 0.13, he says from the inside out. Would it still have been more clear had he said from the inside to the outside? Or would it have sounded a bit weird?No, no clearer, and, as I say, not as neat. Not weird though.