>>10975023(response to someone suggesting coloring the 3D "bounds" of a 4D shape)
You've got it, essentially. But I'm not sure how much color the cubes would help. The main problem is that there are certain factors that may be beyond human comprehension. Let's take a couple frames of each animation here.
On the top left, you can see that the "smaller" edge of the highlighted square is really just the farthest edge. Later in the rotation, the equal size of all edges indicate that all of the edges are an equal distance from the viewer. Of course, this too is beyond the comprehension of a 2D observer. In his universe, you are always closer to one side of the square than the other side. So how can the "back" of a square be just as close as the "front"? It's hard for him to conceive of it because the square is viewed from a direction that doesn't exist in his universe.
We have to overcome the same obstacle with the tesseract. In the bottom left frame, you see where the largest side of the cube shows closeness to the observer. It looks kinda funky and distorted because of the semi-4D perspective, but we can basically understand what's going on. Where we run into trouble is a different part of the rotation (ironically, the part that seems easiest to grasp), where all sides of the cube actually look to be the same size.
So again, let's extrapolate from the differences between 2D and 3D perspectives of our cube. When we see that one of the cubes making up the tesseract appears to have sides of all equal sizes, what this actually indicates is that every side of the cube is the same distance from the observer. And that's funky. This goes back to the 4D observer's ability to see all sides of the cube at once. Not only can he see all sides at a single glance, but he can be the same distance from every side at the same time. And he does this by looking at the cube from a single direction, not by somehow surrounding it. Just the same way we see all sides of a square at once.
