What’s your reason to claim/believe that the state space is literally infinite, rather than “just” insanely large? How do we know that parameters are truly real-valued, rather than quantized at some level of granularity?
Hmm. I’m not sure I understand what you mean by “possible” or “should” enough to know how to apply it here. If it’s not the case that entropy is literally infinite in possible quantities, is it still possible just because we don’t know it’s not the case? We know from Godel that math is either incomplete or inconsistent, so what form of “should” is contained in “can’t”? I’m not sure even what “model” means here—math doesn’t model anything, it stands on it’s own axioms. Models tie math to reality (or at least predictions of observations), imperfectly.
Basically, because of geometry and the fact that our best theories for how quantum gravity works rely on space being continuous rather than discretely quantized.
There are 3 geometries of the universe, and 2 of them are infinite: flat and hyperbolic. The spherical geometry is finite. Most cosmological evidence suggests we live in the flat universe, which is infinite.
Finally, one of the theories which asserts that space is quantized, loop quantum gravity, has a dealbreaker in that it’s difficult to reproduce general relativity at the areas it’s known to work.
That’s why I believe the universe is infinite, rather than truly large.
What’s your reason to claim/believe that the state space is literally infinite, rather than “just” insanely large? How do we know that parameters are truly real-valued, rather than quantized at some level of granularity?
Continuity/infinity could still be useful as modelling tools for creatures living in an ultimately discrete universe.
If it’s possible, our math should model it.
Hmm. I’m not sure I understand what you mean by “possible” or “should” enough to know how to apply it here. If it’s not the case that entropy is literally infinite in possible quantities, is it still possible just because we don’t know it’s not the case? We know from Godel that math is either incomplete or inconsistent, so what form of “should” is contained in “can’t”? I’m not sure even what “model” means here—math doesn’t model anything, it stands on it’s own axioms. Models tie math to reality (or at least predictions of observations), imperfectly.
I suspect “no math handles all worlds” is fully addressed by a size parameter, letting the remainder of the math stay constant.
What we set it to comes down to Bayes. Let’s not assign probability 0 to a live hypothesis.
Basically, because of geometry and the fact that our best theories for how quantum gravity works rely on space being continuous rather than discretely quantized.
There are 3 geometries of the universe, and 2 of them are infinite: flat and hyperbolic. The spherical geometry is finite. Most cosmological evidence suggests we live in the flat universe, which is infinite.
Finally, one of the theories which asserts that space is quantized, loop quantum gravity, has a dealbreaker in that it’s difficult to reproduce general relativity at the areas it’s known to work.
That’s why I believe the universe is infinite, rather than truly large.
That physical constants support life suggests that, elsewhere, they don’t. On which Tegmark level would you expect this elsewhere to be?