>>14391985In fact now that I think about it, the problems people sometimes have with cross products, curl etc are just another example of this same kind of confusion. These are also an example of a non-generalizing pattern involving directionality in different dimensions, but this time particular to 3D rather than to 1D. The general pattern is that rotations in N dimensions take place within a 2D space (a plane) or about a (N-2)D space normal to the plane. It is only in 3D that the normal space to a plane is a line, and thus only in 3D does it make sense to think in terms of "rotation about an axis". Unfortunately the cross product rather than the wedge product became the standard for describing 3D rotation, and thus everyone starts out learning to think about rotation in terms of "about an axis" rather than "in a plane", which can lead to a conceptual hurdle when doing physics in 2D or 4D (or ND if you do meme theories).
