gwern comments on Slowing Moore's Law: Why You Might Want To and How You Would Do It - Less Wrong Discussion
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It's possible, but I don't know of any reason we would expect an animal brain could recursively improve. As matters stand, all we know is that groups of humans can self-improve - so we don't even know if a single human is smart enough to self-improve as an upload. (Maybe human brains can fall into ruts or inevitably degenerate after enough subjective time.) This isn't too optimistic about crows or mice or lobsters, however excellent stories they make for.
It's been operating since at least the '80s as far as I can tell, and is stable out to 2015 or so. That's a pretty good run.
Single human, or cat, or other mammal, is smart enough to self improve without being uploaded (learning and training, we do start off pretty incapable). Think about it. It may well be enough to upload then just add more cortical columns, over the time, or do some other simple and dumb process that does not require understanding, to make use of the built-in self improvement ability.