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- 1D: you can keep a steady line; with a velocity in the x=1
- 2D: you can keep a stationary formations: square, circle … or a wavy path; the velocity becomes a combination of xy
- 3D: to move those rotating 2D formations forward you need a 3th dimension (xy-z). Because if you move a rotating formation forward in 2D, every particle starts to have a different velocity, only by adding an extra dimension is it possible to move them together forward in a particular direction, and keep their formation rotation going.
- 4D: to move those round or forward moving formations, one needs again an extra dimension; xyza
