[GeneralMayhem]

Perhaps I'm not thinking clearly - it's late here - but wouldn't 8-space suffice?

[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.

[darkmighty]

7 dimensions is the trivial minimum for 7 mutual |_ (the axis)

Also, if you ease the restriction to each line perpendicular to every line it intercepts, you can get as many lines as you want in 3d already.

[thedufer]

> if you ease the restriction to each line perpendicular to every line it intercepts, you can get as many lines as you want in 3d already.

That works in 2d space, too. Parallel lines don't intercept any more than skew lines.