> The point is that it can’t be simulated on any lattice of any density. It doesn’t matter how fine the lattice is compared to the sensitivity of the measurement.
It feels like you want to do sth like: first discretize (choose a lattice), then simulate (do calculations on this lattice).
I want to do the opposite: first simulate (do calculations on a continuous domain), then discretize (restrict my results to a lattice).
> For your case you showed, it would be like if x^2 simply didn’t exist on a lattice, and couldn’t be calculated by a computer no matter how much memory you threw at the problem.
So the functions we're talking about do exist on continuous domains - but they don't have a corresponding definition on a lattice?
Couldn't we embed a lattice in the continuous domain, then restrict the function along the embedding, thus getting a definition on a lattice?
Unless it's not possible to embed the lattice in a continuous domain - then my reasoning breaks.
(note: I know nothing about physics, I'm a programmer with math education, talk to me like I'm an idiot)