Regarding a recent edition of xkcd:A Bunch of Rocks

From the xkcd forums:
BorisTheBrave:
Also, his computer cannot handle real numbers, which our universe has in abundance. Just to type in a single real number into his computer would require an infinite amount of rocks, so he’d never finish to get onto the next step. Not insurmountable, by using arbitrary precision rationals, but the fact that his computer has a countable number of states he can put it in, while we usually presume our universe has an uncountable number of states, has some interesting implications.
Moody7277:
So basically, the uncertainty principle is just round-off error?
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