How to visualize 2n dimensional space — December 8, 2011

How to visualize 2n dimensional space

How to visualize 2n dimensional space:

Basically, draw two copies of the n-dimensional space. Points in 2n2 dimensional space will consist of doubles (x,y) and there will be 2n basis vectors. The n of the basis vectors will move both points in the n absolute directions, and the other n basis vectors will move one point in one of the n directions while holding the other fixed. For example, R^4 can be visualized as lines between two parallel planes and R^6 can be visualized as vectors starting from points in R^3. If we include time as a dimensional, these give us an easy way to visualize up to 7 dimensional space.