Dimensional Superposition

I think we sorely need an operation I call "Dimensional Superposition", symbol "&". i.e. to construct n dimensional spaces from n-k dimensional spaces.

For example we may use it to construct a 3D space using two 2D spaces (in flat space) by defining two orthogonal veftor in each plane. Then do DS by superimposing two of them from diffetent planes such that the other two is orthogonal and the origin of the two pairs superimpse.

This increases the tools and may generalise to curved spaces.

S = (uv)&(vw).

It would also enable derivation of properties in higher dimensional spaces that have no analog in lower dimensional spaces.