Just to go back to the philosophy thread, this is one of the things that made Kripke famous (relatively speaking, philosophically speaking): a priori "knowabili

Just to go back to the philosophy thread, this is one of the things that made Kripke famous (relatively speaking, philosophically speaking): a priori "knowability" or predictability is not the same as determinism. You can have a system that is perfectly deterministic, but with outcomes that are a priori unknowable, in the sense of being unpredictable. Kripke didn't use this language, but if the information required to compute the prediction becomes unattainable, either because of capacity or input requirements, you can't make the prediction. I think there's some very abstract computability theorem in computer science that's more recent that came to a similar conclusion. I think that came at it more from the sense of the amount of change in inputs that would pass during the time it took to simulate a system makes it impossible to perfectly simulate things past some point. These aren't examples in physics, but they speak to how determinism per se isn't necessarily the same thing as predictability.