Off topic but... Some guy coded a version of tetris using 4 spatial dimensions, projected onto a 3d model (which is then displayed on a 2d screen). I could only play for about 2-3 minutes before my brain just started malfunctioning. I had nightmares about being unable to stand in 4d space because I was 3 dimensional and in one dimension I was infinitely thin, and that's damned hard to balance on.
I'm not well versed in the pure mathmatics of higher dimensional physics, but it's damned fun to think about. On that topic, Greg Egan's Dispora is a pretty entertaining novel with lots of higher dimensional stuff to wrap your head around...
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