[ravi-delia]

I may be risking sounding like a fool here, but isn't there kind of a real distinction between saying that there are underlying mathematical patterns in a reality that behaves like a state machine, and saying that literally this function and starting condition are isomorphic to the universe?

Like if on a low level it turns out that everything is, I don't know, cellular-automata-based, that would be a more useful frame than wandering vectors in a Hilbert space. But if we get to the end of physics and found that, in fact, you could rederive everything from that one explanation, it wouldn't be unfair to say that the universe is that vector, and perhaps some functions.

I guess really I'm wondering if it matters more how the universe is 'computed' or what it's 'computed on'. In a non-simulated universe, of which it seems there must exist at least one, there would at some point just have to be laws without causes. If those laws corresponded to some simple bit of math, it wouldn't be wrong to merge map and territory.

edit: That's not to say that I actually think the paper is correct. I'm definitely not far enough along in my education to be 100% sure, but there are enough suspicious features and a high enough bar that I'm doubtful. I just meant to mount a general defense of 'what if it's all math' type explanations.