non-degenerate pairing different from the dot product:
: As an example, the distance squared between the points and is 3 in both the Euclidean and Minkowskian 4-spaces, while the distance squared between and is 4 in Euclidean space and 2 in Minkowski space; increasing decreases the metric distance. This leads to many of the well-known apparent "paradoxes" of relativity.

The cross product is not defined in four dimensions. Instead, the exterior product