I still don't completely "get it", but some people appear to, and I'm going to keep re-watching these videos until it clicks in my head. My favorite evidence of the fact that these people are smarter than me was having it explained to me what the second "regular" four-dimensional object looks like (where "regular" means it's got symmetry, like how a cube is made of squares, or a pyramid has triangles for each of its sides). The description is:
Look: 600 vertices, 1,200 edges. Four edges start at each vertex. A completely regular structure. All vertices and all edges play the same role. It’s a pity that the projection breaks the symmetry.
[pause while the camera zooms around the 3 dimensional projection of the 4-dimensional object]
Now, let’s work your imagination a little...
For anyone who's new, and hasn't read this whole blog, seeing a static 4 dimensional object is how I think God might see the universe. My analogy involving an ice cream cone and a laser beam is the same as the analogy used to explain 3 dimensions to 2 dimensional lizards in this video. Except they have actual moving pictures, and then take it a level beyond what I'm able to picture. It's well worth looking at.
The videos are here.
Videos 1-4 (about an hour) walk you through the steps to understanding the fourth dimension. There are 5 other videos after that, but they deal with separate mathematical concepts, like visualizing imaginary numbers, working with fractals, etc. Also, you can download these videos from that same website if you like - they can be freely distributed, and if you use the torrent download you'll get good download speeds (I got about 300 kilobytes/second, which is about as fast as my Internet ever goes).
This is my blog entry for this week. I'm going to take the time I would have used writing on Saturday to wrap my head around these videos.