[xtajv]

[Obligatory: Engineering background. Not an expert]

I've always found it a bit odd that we DO define "i" to help us express complex numbers, with the convenient assumption that "i = sqrt(-1)"... but we DON'T have any such symbols to map between more than 2 dimensions.

I felt a bit better when I found out about - (nth) roots of unity (to explore other "i"-like definitions, including things like roots of unity modulo n, and hidden abelian subgroup problems which feel a bit to me like dealing with orthogonal dimensions) - tensors (e.g. in physics, when we need a better way to discuss more than 2 dimensions, and often establish syntactic sugar for (x,y,z,t))

IDK if that helps at all (or worse, simply betrays some misunderstanding of mine. If so, please complain- I'd appreciate the correction!)