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paper-machine comments on New report: Intelligence Explosion Microeconomics - Less Wrong
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I'm going to commit pedantry: nesting enough logarithms eventually gives an undefined term (unless n's complex!). So where Eliezer says "the sequence log(w) + log(log(w)) + log(log(log(w))) will converge very quickly" (p. 4), that seems wrong, although I see what he's getting at.
It really bothers me that he calls it a sequence instead of a series (maybe he means the sequence of partial sums?), and that it's not written correctly.
The series doesn't converge because log(w) doesn't have a fixed point at zero.
It makes sense if you replace log(w) with log^+(w) = max{ log(w), 0 }, which is sometimes written as log(w) in computer science papers where the behavior on (0, 1] is irrelevant.
I suppose that amounts to assuming there's some threshold of cognitive work under which no gains in performance can be made, which seems reasonable.
Now fixed, I hope.
Oh yes. That makes far more sense. Thanks for fixing it.