Hilbert's and Feynman's Ordering

$$\mathbb{R}$$ is ordered, but $$\mathbb{R\times R}$$ is not.

Two twentieth century giants solved this. Hilbert invented the space filling curve, and Feynman invented the Path Integral.

The first construction fills the plane with an order. One knows, at a given order of recurrence, which way to go. The second invention uses time, by doing so, a contradiction appears between time as a special direction, and relativity's axiom, that space and time are indistinguishable.

Neat.