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4d space is simply overlapping 3d volumes.

each dimension you add multiplies the previous dimension by infinitely many of the previous “type” of object.

For example:
0d: a point.
1d: a 1d line, or infinite stack of parallel 0d points
2d: a 2d plane, or infinite stack of parallel 1d lines
3d: a 3d volume, or infinite stack of parallel 2d planes
4d: 4d space, or “infinite stack” of parallel 3d volumes

parallel 3d volumes may seem hard to visualize, until you realize that they are just overlapping 3d spaces.

if you know computer graphics, think of rendering the same thing twice in the same spot. for example, a character, once with normal skin and once with werewolf skin. the second render introduces a “4th dimension” or a “parallel reality” for the character. if both renders are supposed to represent the same character, and these impassible objects can overlap, then we are now talking about parallel 3d spaces (since overlap of solid objects should not be possible in a single 3d space). the character now appears in 4d space, where he experiences the “parallel realities” of both being “normal” and “werewolf skinned” at the same time.

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