artfuldodger:
have I got news for you!
The electron doesn't "know" its position in any such way. It doesn't have a position. Position (like its conjugate, momentum) is a measurement. The electron has a wave function. The evolution of the wave function is deterministic. And electrons don't bounce into things. In fact, lacking measurements, the electron's behaviour is a superposition of its possible measurements.
If anything, the problem you allude to is that the wave function is unknowable in some circumstances.
Gödel's Incompleteness Theorem also doesn't come into play here. True, the only decideable systems are the ineffably boring ones. But (of course) any physical system doesn't fall into this category. And Gödel's theorem has nothing to do with the uncertainty principle, despite any Fashionable Nonsense you may catch floating around on the waves of the ether.