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Some review notes as I go through it (at a bright dilettante level):
Section 1:
- I wonder if the chain-reaction model is a good one for recursive self-improvement, or is it just the scariest one? What other models have been investigated? For example, the chain-reaction model of financial investment would result in a single entity with the highest return rate dominating the Earth, this has not happened yet, to my knowledge.
Section 1.3:
- There was a recent argument here by David Pearce, I think, that an intelligent enough paperclip maximizer will have to self-modify to be more "humane". If I recall correctly, the logic was that in the process of searching the space of optimization options it will necessarily encounter an imperative against suffering or something to that effect, inevitably resulting in modifying its goal system to be more compassionate, the way humanity seems to be evolving. This would restrict the Orthogonality Thesis to the initial takeoff, and result in goal convergence later on. While this seems like wishful thinking, it might be worth addressing in some detail, beyond the footnote 11.
Chapter 2:
- log(n) + log(log(n)) + ... seems to describe well the current rate of scientific progress, at least in high-energy physics
- empty space for a meditation seems out of place in a more-or-less formal paper
- the Moore's law example is an easy target for criticism, because it's an outlier: most current technologies independent of computer progress are probably improving linearly or even sublinearly with investment (power generation, for example)
- "total papers written" seems like a silly metric to measure scientific progress, akin to the Easter Island statue size.
- If the point of the intro is to say that all types of trends happen simultaneously, and we need "to build an underlying causal model" of all trends, not cherry-pick one of them, then it is probably good to say upfront.
Section 2.1:
- the personal encounter with Kurzwell belongs perhaps in a footnote, not in the main text
- the argument that the Moore's law will speed up if it's reinvested into human cognitive speedup (isn't it now, to some degree?) assumes that faster computers is a goal in itself, I think. If there is no economic or other external reason to make faster/denser/more powerful computers, why would the cognitively improved engineers bother and who would pay them to?
- In general, the section seems quite poorly written, more like a stream of consciousness than a polished piece. It needs a decent summary upfront, at the very least. And probably a few well-structured subsections, one on the FOOM debate, one on the validity of the outside view, one on the Lucas critique, etc. It may also be worth discussing while Hanson apparently remains unconvinced.
I might add more later.
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.
Since this apparently bothers people, I'll try to fix it at some point. A more faithful statement would be that we start by investing work w, get a return w2 ~ log(w), reinvest it to get a new return log(w + w2) - log(w) = log ((w+w2)/w). Even more faithful to the same spirit of later arguments would be that we have y' ~ log(y) which is going to give you basically the same growth as y' = constant, i.e., whatever rate of work output you had at the beginning, it's not going to increase significantly as a result of reinvesting all that work.
I'm not sure how to write either more faithful version so that the concept is immediately clear to the reader who does not pause to do differential equations in their head (even if simple ones).
Well, suppose cognitive power (in the sense of amount of cognitive work put unit time) is a function of total effort invested so far, like P=1-e^(-w). Then it's obvious that while dP/dw= e^(-w) is always positive, it rapidly decreases to basically zero, and total cognitive power converges to some theoretical maximum.
This is in the context of reinvesting dividends of cognitive work, assuming it takes exponentially greater investments to produce linearly greater returns. For example, maybe we get a return of log(X) cognitive work per time with what we have now, and to get returns of log(X+k) per time we need to have invested X+k cognitive work. What does it look like to reinvest all of our dividends? After dt, we have invested X+log(X) and our new return is log(X+log(X)). After 2dt, we have invested X+log(X)+log(X+log(X)), etc.
The corrected paragraph would then look like:
Except then it's not at all clear that the series converges quickly. Let's check... we could say the capital over time is f(t), with f(0)=w, and the derivative at t is f'(t)=log(f(t)). Then our capital over time is f(t)=li^(-1)(t+li(w)). This makes our capital / log-capital approximately linear, so our capital is superlinear, but not exponential.