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It is not too hard to construct "minds" that cannot be reconstructed easily from outputs. Consider a cryptographically secure pseudorandom number generator: watching the first k bits will not allow you to predict the k+1 bit with more than 50% probability, until you have run through the complete statespace (requires up to ~2^(number of state bits) output bits). This "mind" is not reconstructible from its output in any useful way.
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