Revenue of a nail factory is a good proxy for the quality of the nails produced, but only within a fairly small bubble around our current world. You can’t make the factory-owner too smart, or the economy too irrational, or allow for too many technological breakthroughs to happen, or else the proxy breaks.
I think you missed the point of that particular metaphor. The claim was not that revenue of a nail factory is a robust operationalization of nail value. The claim was that a competitive nail market plus nail-maker reputation tracking is a True Name for a pointer to nail value—i.e. such a system will naturally generate economically-valuable nails. Because we have a robust mathematical formalization of efficient markets, we know the conditions under which that pointer-to-nail-value will break down: things like the factory owner being smart enough to circumvent the market mechanism, or the economy too irrational, etc.
The lesson I take is that messiness is not the total lack of structure—when I say my room is messy, I don’t mean that the arrangement of its component atoms has been sampled from the Boltzmann distribution—it’s just that the structure that’s there isn’t easy for humans to use.
I agree with this, and it’s a good summary of the takeaway of the butterfly effect analogy. In this frame, I think our disagreement is about whether “structure which isn’t easy for humans to use” is generally hard to use because the humans haven’t yet figured it out (but they could easily use it if they did figure it out) vs structure which humans are incapable of using due to hardware limitations of the brain.
Suppose I have a bit string of length 10^9, and I can compress it down to length 10^8. …
This is an anology which I also considered bringing up, and I think you’ve analogized things basically correctly here. One important piece: if I can compress a bit string down to length 10^8, and I can’t compress it any further, then that program of length 10^8 is itself incompressible—i.e. it’s 10^8 random bits. As with the butterfly effect, we get a duality between structure and noise.
Actually, to be somewhat more precise: it may be that we could compress the length 10^8 program somewhat, but then we’d still need to run the decompressed program through an interpreter in order for it to generate our original bitstring. So the actual rule is something roughly like “any maximally-compressed string consists of a program shorter than roughly-the-length-of-the-shortest-interpreter, plus random bits” (with the obvious caveat that the short program and the random bits may not separate neatly).
I think you missed the point of that particular metaphor. The claim was not that revenue of a nail factory is a robust operationalization of nail value. The claim was that a competitive nail market plus nail-maker reputation tracking is a True Name for a pointer to nail value—i.e. such a system will naturally generate economically-valuable nails. Because we have a robust mathematical formalization of efficient markets, we know the conditions under which that pointer-to-nail-value will break down: things like the factory owner being smart enough to circumvent the market mechanism, or the economy too irrational, etc.
I agree with this, and it’s a good summary of the takeaway of the butterfly effect analogy. In this frame, I think our disagreement is about whether “structure which isn’t easy for humans to use” is generally hard to use because the humans haven’t yet figured it out (but they could easily use it if they did figure it out) vs structure which humans are incapable of using due to hardware limitations of the brain.
This is an anology which I also considered bringing up, and I think you’ve analogized things basically correctly here. One important piece: if I can compress a bit string down to length 10^8, and I can’t compress it any further, then that program of length 10^8 is itself incompressible—i.e. it’s 10^8 random bits. As with the butterfly effect, we get a duality between structure and noise.
Actually, to be somewhat more precise: it may be that we could compress the length 10^8 program somewhat, but then we’d still need to run the decompressed program through an interpreter in order for it to generate our original bitstring. So the actual rule is something roughly like “any maximally-compressed string consists of a program shorter than roughly-the-length-of-the-shortest-interpreter, plus random bits” (with the obvious caveat that the short program and the random bits may not separate neatly).