I guess I have a fair amount to say, but the very quick summary of my thoughts on SI remain the same:
1. Solomonoff Induction is really just subjective bayesianism+ Cromwell’s rule + prob 1 that the universe is computable. I could be wrong about the exact details here, but I think this could even be exactly correct. Like for any subjective Bayesian prior that respects Cromwell’s rule and is sure the universe is computable there exists some UTM that will match it. (Maybe there’s some technical tweak I’m missing, but basically, that’s right.) So if that’s so, then SI doesn’t really add anything to the problem of induction aside from saying that the universe is computable.
2. EY makes a lot out of saying you can call shenanigans with ridiculous-looking UTMs. But I mean, you can do the same with ridiculous looking priors under subjective bayes. Like, ok, if you just start with a prior of .999999 that Canada will invade the US, I can say you’re engaging in shenanigans. Maybe it makes it a bit more obvious if you use UTMs, but I’m not seeing a ton of mileage shenanigans-wise.
3. What I like about SI is that it basically is just another way to think about subjective bayesianism. Like you get a cool reframing and conceptual tool, and it is definitely worth knowing about. But I don’t at all buy the hype about solving induction and even codifying Ockham’s Razor.
4. Man, as usual I’m jealous of some of EY’s phrase-turning ability: that line about being a young intelligence with just two bits to rub together is great.
Ben Levinstein: