Gödel's theorem implies that Turing machines are not complete. The problems of floating point numbers exemplify this. Our existing machine architectures operate

Gödel's theorem implies that Turing machines are not complete. The problems of floating point numbers exemplify this. Our existing machine architectures operate on a discrete silicon substrate (ℤ), but we live in a continuously differentiable spacetime continuum (ℝ). I don't think this has any deep implications for P = NP, though; it's just a tooling issue.