If the world was run by classical mechanics, then you could make predictions with 100 percent certainty.
We cannot predict the future because Newtonian physics break down on several different scales.
Quantum mechanics, for example, shows the natural word works on probability, not classical mechanics. There is a certain probability of an atom undergoing fission over a given timeframe, but it's never guaranteed to actually happen. This probability gives rise to uncertainty. The same can be shown with quantum tunneling effects, superposition of Bosons, heisenberg's uncertainty principle, and so on.
It is, at best, only tangentially related to infinites, bit this is the reason we cannot predict the future
