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Comment by sgt101 | Hacker News Reader

I love that "system 1" and "system 2" are tossed out as fundamental concepts of mind when they're basically labels for some semi-random ideas based on bullshit studies in a pop sci fluff book. Is there any actual science that ties these ideas to mathematical reasoning?

Then we have:

>> By analogy, we can now state the main hypothesis proposed in this paper: a crucial component of the usefulness of a new proven theorem t (in the context of previous theorems T(S)) is how efficiently T(S)∪{t} compresses the set of all provable mathematical statements M. That is, T (S) ∪ {t} is a good compression of M if many provable statements, beyond those in S, can be derived from T (S) ∪ {t}, say using at most k derivation steps.

which says "Occam's Razor, that's good isn't it?" in more words.

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> I love that "system 1" and "system 2" are tossed out as fundamental concepts of mind when they're basically labels for some semi-random ideas based on bullshit studies in a pop sci fluff book. Is there any actual science that ties these ideas to mathematical reasoning?

I think this fails to hit the mark on what people actually care about with regards to system 1 vs system 2. It’s really just, can we build models that are able to vary how long they think about a problem? Current AI models are very limited in this aspect and I think most would agree that being able to think about a problem for a period of time is a useful feature that we humans use all the time.

I don’t think that’s really what Occam’s razor says.

If one’s goal is to use ML stuff to try to produce new useful theorems, it seems useful towards that goal to come up with a numeric heuristic for how useful a new theorem is. And, stating such a heuristic explicitly seems reasonable.

Just because the heuristic that they state, which they expect to be a crucial component of what makes a theorem useful to prove in a given context, isn’t particularly surprising, doesn’t make it not worth saying.

to elaborate on “isn’t particularly surprising” : if you asked many other people to come up with heuristics for the usefulness of a new potential theorem, I imagine many of the answers you would get (counting multiplicity if multiple people give identical answers) would be fairly similar.

Even if a hypothesis is an obvious-to-consider hypothesis, if one wants to talk about it, it is worth stating what it is first.

System 1 and 2 are just another way of describing dual process theory, which existed long before Daniel Kahneman wrote, Thinking Fast and Slow, and is still the prevailing theory of mind in its category today. There were maybe 1 or 2 studies mentioned in that book that were not very replicable but other than that, the overall consensus by leading experts in that field is positive, from everything I've seen, which is impressive considering how old the book is now.

I have no idea if dual process theory is actually useful for teaching computers how to math, but it seems unfair to just dismiss it as pop science bunk.

https://en.m.wikipedia.org/wiki/Dual_process_theory

> ...which is impressive considering how old the book is now.

The human mind hasn't changed all that much in the last ... countless millennia. If anything it'd be a quite concerning data point if we hadn't nailed down the introductory level points about how to be thoughtful.

The Wiki article you link gives an example from the 1600s of "the passions" vs "reason" so it certainly seems quite old. And when framed that way in particular has echos of "habitus" from sociology - https://en.wikipedia.org/wiki/Habitus_(sociology) which I will paraphrase badly as "intuition [the passions] as shaped by social structure".

But all that seems largely descriptive rather than usefully predictive and more a representation of what we don't know than what we do.

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