Right, it’s a little tricky to specify exactly what this “relationship” is. Is the notion that you should be able to compress the approximate model, given an oracle for the code of the best one (i.e. that they share pieces?). Because most Turing machines don’t compress well, and so it’s easy to find counterexamples (the most straightforward class is where the approximate model is already extremely simple).
Anyhow, like I said, hard to capture the spirit of the problem. But when I *do* try to formalize the problem, it tends to not have the property, which is definitely driving my intuition.
I’d expect Turing machines to be a bad way to model this. They’re inherently blackboxy; the only “structure” they make easy to work with is function composition. The sort of structures relevant here don’t seem like they’d care much about function boundaries. (This is why I use models like these as my default model of computation these days.)
Anyway, yeah, I’m still not sure what the “relationship” should be, and it’s hard to formulate in a way that seems to capture the core idea.
Right, it’s a little tricky to specify exactly what this “relationship” is. Is the notion that you should be able to compress the approximate model, given an oracle for the code of the best one (i.e. that they share pieces?). Because most Turing machines don’t compress well, and so it’s easy to find counterexamples (the most straightforward class is where the approximate model is already extremely simple).
Anyhow, like I said, hard to capture the spirit of the problem. But when I *do* try to formalize the problem, it tends to not have the property, which is definitely driving my intuition.
I’d expect Turing machines to be a bad way to model this. They’re inherently blackboxy; the only “structure” they make easy to work with is function composition. The sort of structures relevant here don’t seem like they’d care much about function boundaries. (This is why I use models like these as my default model of computation these days.)
Anyway, yeah, I’m still not sure what the “relationship” should be, and it’s hard to formulate in a way that seems to capture the core idea.