[mc808]

It's been estimated that if the universe were a computer, it could have performed no more than 10^120 operations on 10^90 bits of data so far (based on the size, age, and total energy of the known universe). http://arxiv.org/abs/quant-ph/0110141 I think the number of physically relevant bits of pi would be represented in there somewhere. But there's a long road ahead. If the universe keeps "computing" forever, the precision of numbers involved could also keep growing.

[ycmbntrthrwaway]

If the universe were a computer, it would not have to compute π to "simulate" physical processes. Mechanical processes don't depend on the value of π directly.

If universe had to know every constant somehow involved in the process, it would not be able to simulate computers, because it involves uncomputable numbers: https://en.wikipedia.org/wiki/Chaitin%27s_constant#Uncomputa...

[xzephyr]

And wave functions collapse only upon measurement...clever lazy initialization