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Larifari comments on Size of the smallest recursively self-improving AI? - Less Wrong
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Even a FOOM seed only a few hundred bytes would not necessarily have been produced by evolution - there are 2^800 different possibilities for a 100-byte snippet. Only if there are intermediate steps in increasing complexity and fitness, evolution can find a solution in such a large search space. If the shortest possible seed is completely isolated in the search space, there is no way it can be found, neither by evolution nor by deliberate optimization.
Be careful with saying something is impossible. Maybe that large seach space can be cut down to size by proofs or clever algorithms.