I can see your point, but the problem remains. Suppose to have a closed system that contains a random number generator and an observer. The observer can measure

I can see your point, but the problem remains. Suppose to have a closed system that contains a random number generator and an observer. The observer can measure and extract (not store) an infinite amount of entropy. Where does that comes from? It seems to me to be unphysical. Possible way outs of this: - The randomness source has a state which is huge but finite. The finiteness should clash with the QM assumption that this kind of randomness is absolutely unpredictable - You can't even take an upper-bound of the Kolmogorov complexity of that bitstream without storing the bits. It's like saying: the universe can cheat because your are not looking (hypothesis that has a strong QM flavor) - The universe conspires to incrementally build one additional state for every measurement taken (non-sense) - The randomness source is not immanent in our physical universe (Occam's razor says no) Regarding your point, there are two options: discontinuous functions can be approximated with truncated series, for instance. Plus: the photoelectric effect doesn't logically need (for what I know) randomness to happen, there are already discontinuities without postulating non-determinism, discreteness suffices.