I see. This is exactly the kind of result for which I think the relevance breaks down, when the formal theorems are actually applied correctly and precisely to situations we care about. The authors even mention the instance / limiting distinction that I draw in the comment I linked, in section 4.
As a toy example of what I mean by irrelevance, suppose it is mathematically proved that strongly solving Chess requires space or time which is exponential as a function of board size. (To actually make this precise, you would first need to generalize Chess to n x n Chess, since for a fixed board size, the size of the game tree is a necessarily fixed / constant.)
Maybe you can prove that there is no way of strongly solving 8x8 Chess within our universe, and furthermore that it is not even possible to approximate well. Stockfish 15 does not suddenly poof out of existence, as a result of your proofs, and you still lose the game, when you play against it.
Yes, you can still sort of do utility maximisation approximately with heuristics …and you can only do sort of utility sort of maximisation approximately with heuristics.
The point isn’t to make a string of words come out as true by diluting the meanings of the terms...the point is that the claim needs to be true in the relevant sense. If this half-baked sort-of utility sort-of-maximisation isn’t the scary kind of fanatical utility maximisation, nothing has been achieved.
I see. This is exactly the kind of result for which I think the relevance breaks down, when the formal theorems are actually applied correctly and precisely to situations we care about. The authors even mention the instance / limiting distinction that I draw in the comment I linked, in section 4.
As a toy example of what I mean by irrelevance, suppose it is mathematically proved that strongly solving Chess requires space or time which is exponential as a function of board size. (To actually make this precise, you would first need to generalize Chess to n x n Chess, since for a fixed board size, the size of the game tree is a necessarily fixed / constant.)
Maybe you can prove that there is no way of strongly solving 8x8 Chess within our universe, and furthermore that it is not even possible to approximate well. Stockfish 15 does not suddenly poof out of existence, as a result of your proofs, and you still lose the game, when you play against it.
Yes, you can still sort of do utility maximisation approximately with heuristics …and you can only do sort of utility sort of maximisation approximately with heuristics.
The point isn’t to make a string of words come out as true by diluting the meanings of the terms...the point is that the claim needs to be true in the relevant sense. If this half-baked sort-of utility sort-of-maximisation isn’t the scary kind of fanatical utility maximisation, nothing has been achieved.