We can see in 4D
How do I train people to think in 4D?
It's pretty easy to represent 4D objects. There are a variety of options, but perhaps the most intuitive is using color. For example, assign the 4th dimensional position of the object to light frequencies. A pure 3D object is then monochromatic in this view, each element of which takes up exactly one frequency of the spectrum.
A 4-flat object that is moved along the 4th dimension simply has a different color and can therefore freely coincide with the other object in the same 3D position. In the meantime, an object with a depth in the 4th dimension would occupy a frequency range and thus be a mixture of colors.
This doesn't make 4D intuitive, which you didn't mention, but I suspect it's your ultimate goal. Even stereograms don't do this for 3D. All you do there is send visual inputs which, to some extent, duplicate the visual inputs the eyes put on a 3D object and fool the brain's sophisticated built-in spatial recognition parts. 4D spatial recognition parts of the brain simply do not exist. (Try mentally rotating any 3D object and it's easy with arbitrary rotations. Try for a 4D object and uhhhh.) To make them exist you will likely need to intervene drastically with early brain development or do some serious rewiring in some way ....
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