This is exactly right: when rotating in 4D, you can rotate "around" a plane, leaving it in place. You can also rotate around a line (permuting the other three a

This is exactly right: when rotating in 4D, you can rotate "around" a plane, leaving it in place. You can also rotate around a line (permuting the other three axes). So, in the video. The Z axis doesn't change (up and down) so that's one axis. The other one that doesn't change is at a 45 degree angle from lower left to upper right. Watch the tree: it is just as wide along this axis as it was before. Everything else sort of smoooshes around but that plane stays the same. I suggest interested people check out adanaxis, a 4D space shooter. It's not particularly playable, but it is true four-dimensional space with four-dimensional spaceships zipping around.