one too many dimensions to have commutative rotation
one too few dimensions to graph complex functions
just enough dimensions to graph hsv color space
this post would have been better if i could think of something that could be done in 3d but not 2d or 4d. like you can still graph hsv color space if you're in 4d you just also have an extra dimension hanging out there for fun
3 is the number of dimensions needed to play team fortress 2

