"So if you suppose that a final set of changes was enough to produce a sudden huge leap in effective intelligence, it does beg the question of what those changes were."
Perhaps the final cog was language. The original innovation is concepts: the ability to process thousands of entities at once by forming a class. Major efficiency boost. But chimps can form basic concepts and they didn't go foom.
Because forming a concept is not good enough - you have to be able to do something useful with it, to process it. Chimps got stuck there, but we passed abstractions through our existing concrete-only processing circuits by using a concrete proxy (a word).
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'How many new assumptions, exactly, are fatal? How many new terms are you allowed to introduce into an old equation before it becomes "unvetted", a "new abstraction"?'
Every abstraction is made by holding some things the same and allowing other things to vary. If it allowed nothing to vary it would be a concrete not an abstraction. If it allowed everything to vary it would be the highest possible abstraction - simply "existence." An abstraction can be reapplied elsewhere as long as the differences in the new situation are things that were originally allowed to vary.
That's not to say this couldn't be a black swan, there's no guarantees, but going purely on evidence what other choice do you have except to do it this way.