Even if the mechanics are known and everything is deterministic, it may be impossible to predict something in practice. Usually, when e.g. a physical model is

Even if the mechanics are known and everything is deterministic, it may be impossible to predict something in practice. Usually, when e.g. a physical model is deterministic, we can have an assumption of some initial conditions and then evolve the system from there - even if our model's initial conditions don't exactly match the conditions we see in a real physical system, the result of our prediction will deviate a bit from the value we see in the real system. An error of prediction that results from our error of determining the precise initial conditions of the physical system. Usually, the error in the initial conditions of the model and the error of the prediction can be approximated quasi-linearly: small initial error, small prediction error. But, when your physical system is nonlinear, as virtually all of nature is (e.g. N-body problem, turbulent fluids, weather), it can be chaotic - which means that a small initial error can produce an almost arbitrary error in prediction. To correctly predict the state evolution of a chaotic nonlinear system from initial conditions, you need to know the initial conditions with infinite precision. (Edit: which is impossible in practice)