[ivansavz]

A 7-dimensional space would suffice to fit 7 orthogonal directions---though we should probably add an extra dimension for the alpha channel ;)

BTW, I'm also guessing @lam's comment was referring to the 11 dimensions in string theory: http://en.wikipedia.org/wiki/String_theory#Extra_dimensions

[rcfox]

Also, throw in some velocity dimensions so that we can make the red lines drawn in green ink appear to be red.