[gregdaniels421]

This doesn't seem like a very good point to make, sure reals are uncountable and any set of them with labels is countable and of measure zero. That doesn't say anything about physics at all. In QM things are only discrete in certain ways, like energy levels, not positions. A wave function over space can take on any real valued value in its range. Probabilities are real numbers(norms of the wave functions), and there is no reason to believe they would be discrete. Take cosine squared, given any angle it takes on all values between zero and one at some point.

[russdill]

A more interesting, if not totally pointless question to me, is, are all the constants of nature computable?

If any are a "randomly" chosen real number, the answer would almost certainly be no. But a test of sufficient precision would of course be impossible.