Ah, how you think about that example helps clarify. I wasn’t even thinking about the possibility of an AI that could “learn” the analytic form of Weierstrass function, I was thinking about the fact that trying to fit a polynomial to it would be arbitrarily hard.
Obviously “not modelable by ANY means” is a much stronger claim than “if you use THESE means, then your model needs a lot of epicycles to be close to accurate.” (Analyst’s mindset vs. computer scientist’s mindset; the computer scientist’s typical class of “possible algorithms” is way broader. I’m more used to thinking like an analyst.)
I think you and I are pretty close to agreement at this point.
Ah, how you think about that example helps clarify. I wasn’t even thinking about the possibility of an AI that could “learn” the analytic form of Weierstrass function, I was thinking about the fact that trying to fit a polynomial to it would be arbitrarily hard.
Obviously “not modelable by ANY means” is a much stronger claim than “if you use THESE means, then your model needs a lot of epicycles to be close to accurate.” (Analyst’s mindset vs. computer scientist’s mindset; the computer scientist’s typical class of “possible algorithms” is way broader. I’m more used to thinking like an analyst.)
I think you and I are pretty close to agreement at this point.
Yes, I completely agree with the weaker formulation “irreducible using only THESE means”, like e.g. Polynomials, MPTs, First-Order Logic etc.