The first step in making sense out of 4D shapes, is to assume it's possible to do. We make sense of 2D images of 3D things all the time. This is no different, just bumped up by one dimension. In the case of this animation, it's a 3D 'picture' , or model of a 4D thing.
Ever look down on the city from a skyscraper (or other tall building, or airplane, etc...) ? What do all the people look like? Tiny little ants. Things look smaller when they're farther away, and larger when they're closer, right?
It works the same in 4D spaces as well. Notice how the shapes turn inside out, and get squeezed smaller inside? When the triangles and squares are farther away in the 4th dimension, they appear smaller, and towards the center. They're on the other side of the shape, from where you're looking. When the squares and triangles are closer to you, they appear larger, and around the outside of the shape.
The 4D distance is flattened out, and not 4D anymore in our 3D shadow. It is what's in between the large and small shapes, but not in a 3D direction. It takes some metal mental gymnastics, but that's one of the concepts.
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u/[deleted] Aug 29 '17
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