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Updated November 17, 2021
  4-dimensional space

Image: A zero dimensional space is a point. If we stretch the point, we get a one-dimensional space, i.e. a line. If we stretch the line, we get a two-dimensional space, that is to say a plane. If we stretch the plane, we get a three-dimensional space, that is to say a volume. If we stretch the volume, we get a four-dimensional space, that is to say a hypervolume.
In this representation, each new dimension is perpendicular to the previous ones up to the 4D hypercube, but we can continue in this way in dimension five, then six, and with n-dimensional or n-cube hypercubes. The representation of the hypercube is the simplest, but it is the same for a hypersphere, a hyperprism or a non-geometric hypervolume.
An object evolving in dimension n cannot see another object evolving in dimension n + 1. For example, in 2D space, no 3D object is visible.


Image: The four-dimensional or 4-cube hypercube is often referred to as "tesseract".

 2D space-time

Image: representation of an image in two-dimensional space. A single slit slides on the figure from bottom to top representing the passage of time. What is perceptible is what appears in the slit of 1D space. We do not see the whole of the 2D figure but the figure slices after slice, that is to say small parts which scroll one after the other. The space seen by the slit seems dynamic, everything moves, while the 2D space is frozen. The illusion of dynamics is caused by the slippage of the slit, that is, by the passage of time.

 3D space-time

Image: A sphere crossing a two-dimensional universe would appear seen from that universe as a circle (red line) increasing more and more until the equator of the sphere then decreasing until disappearing.
The 2D world can only see the edge of the sphere which is inside its plane, that is to say a circle. 2D physical space is just a slice of 3D space. What the world sees in 2D is what appears on the map. The top and bottom are invisible.
Likewise, our familiar 3D physical space is actually just a 3D slice of a real 4D space that encompasses it.
If a 4D space hypersphere crossed our 3D space, we would see the layers of the hypersphere appear successively. We would see a small sphere which would grow little by little until it reached the size of the equator of the hypersphere then which would decrease until it completely disappeared. We would have seen the hypersphere slice by slice.


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