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I don't know a lot about physics, but I do know a little bit about computer science, and it seems to me that--barring some crazy breakthrough in computation--any simulation accurate enough to overcome the chaotic nature of this problem may very well be fundamentally impossible. That in itself would be a pretty fascinating result.

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The problem isn't the fidelity of the simulation persay, it's that chaotic systems are quite literally infinitely sensitive to initial conditions.

Sure; the possible result that the physical universe is fundamentally uncomputable is the result I find interesting.

That is _not_ the result though. This has nothing to do with computability. It's about the behavior of a certain pervasive class of dynamical systems.

Okay, I’m missing something then.

Meh. The axiom of choice is well documented.

Each initial set of conditions would create a unquie system.

Look at Banach–Tarski paradox

What does this have to do with the axiom of choice?

You implied the issue is the infinite set of initial conditions.

All systems are based off the initial set of conditions. The axiom of choice.

The issue is the degrees of freedom introduced with more dimensions...

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