It’s impossible to have actual non-determinism in a deterministic system. Non-determinism is emulated in software using random number generators. If you know th

It’s impossible to have actual non-determinism in a deterministic system. Non-determinism is emulated in software using random number generators. If you know the seed (the ‘x’) and the definition of the random function (the ‘f’), you can predict all outputs, analogous to my f(..(x)..) universe above. There’s no programmatic random number generator that is truly random. (I mean random in the sense that it’s entirely unpredictable; not in the sense that the distribution of the random number generator covers all possibilities uniformly over many calls.) Hardware random number generators are truly random (like the RDRAND instruction in x86 CPUs which is seeded by an on-chip entropy source). But if you’re relying on physical entropy, it’s not a deterministic system anymore. You simply can’t emulate non-determinism in a deterministic system.