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I don't think continuous and discrete-with-arbitrary-precision are the same thing, maybe even to the degree where we can't use the latter as a universal approxi
by mxkopy 4y ago
I don't think continuous and discrete-with-arbitrary-precision are the same thing, maybe even to the degree where we can't use the latter as a universal approximation for the former. I think there are some cases where approximating a continuous function on a lattice produces an error that isn't a function of precision (I think the Weierstrass function is one).
- yarg 4y agoIt really comes down not to the question of equivalency, but distinguishability. If the universe is lazy evaluating things discretely down to scales well below that of observation, there's probably no damned way to tell the difference.
- mxkopy 4y agoI think it depends on what is doing the observing. If it's humans or conscious beings or something like that, then the admins could be keeping the precision perpetually out of our reach. If it's atoms or photons doing the observing, though, they're affected by the gravitational pull of every mass in their light cone. So an atom can distinguish between universes in which another atom 1000ly away moved by 0e or 1e (where e is the distance between two lattice points). But, it wouldn't have to know until 1000 years later. There does seem to be some computation-resource saving mechanic at play, but I don't think it has to do with discretization.