I finally got around to watching the Dimensions videos, which I mentioned once before. They are super cool and will be sure to blow your mind! They start by explaining some simple tools (stereographic projection) and intuition (with references to Flatland), then jump into four-dimensional polytopes, complex numbers, fractals, and fibrations. The videos can be a tiny bit cheesy and slow-moving at times—although really, if they went much faster it would be difficult to take it all in, and there is lots of stunningly beautiful 3D animation. Well, there’s 4D animation too, stereographically projected into 3-space, of course. =) Watching them all is definitely an investment of time (2 hours), but definitely worth it (and there’s nothing wrong with skipping around a bit). If you want to skip around, for maximum beautiful-mind-blowingness make sure you at least watch the videos about 4D polytopes and fibrations.

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Great videos! I think it’s funny that you made a distinction about 4D animation being projected into 3D-space versus 3D animation. In the end all the graphics appear in 2D-space (the computer monitor) using perspective projections. It’s just as creatures of 3D-space we most easily identify with that space and can imagine a 2D projection as a 3D object.

Indeed!