I can’t visualize them right now and I need someone to explain them to me simply
In: Mathematics
Let’s try to play with cross sections and use time as a tool for representing one of the axes.
Imagine a 3D sphere and three axes: X, Y and Z. Let’s say we have an ability to move along Z and see the cross section of this sphere parallel to XY. While you move evenly, you would see nothing first, then a rapidly growing circle would appear reaching the diameter of the sphere and then collapsing back to nothing. Pretty easy, right? This was a visualization of a 3D object on a 2D surface stretched in time.
Now let’s do the same trick with a 2D circle, moving along Y and looking at its cross section parallel to X. Same here, nothing first, then a line would appear, grow, shrink and disappear in the same manner as a circle in the previous example. This was a visualization of a 2D circle on a 1D line.
You can see how these two examples share very similar behavior, and I think it’s acceptable to apply the same principle to a 3D cross section of a 4D sphere existing in a XYZU world. While moving along axis U, you would see a growing-and-shrinking 3D sphere.
Like Traditional_Dinner16 said, we live in a 3D world and can only visualize all 4D shapes as 3D cross sections using some tools like time to get the information about the dimension impossible for perception. Like a 2D person living in a 2D world would visualize all 3D spheres as 2D circles, getting information about third dimension using time or so.
Actually it’s possible to go even deeper and get some idea of 5 and more dimensional shapes applying this model.
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