- A point can show what a line looks like, by changing the colors displayed on the point as it moves down the line.
- a line can show a 2d space by altering colors as it moves up and down on the axis.
- a 2d space can show 3 dimensions by going forward and backwards in 3d space.
- we should be able to represent the 4th dimension by portraying how the 3d space changes as that space goes ‘along’ the 4th dimension
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And perhaps not at all coincidentally, your first two examples combined are exactly how an analog television manages to create an approximation of a 2D plane using only a single point. And with a bit of the old 4th dimension, time.
The problem isn’t representing a 4D object in 3D, but the fact that we’re still stuck on devices whose displays are two dimensional.
And displaying 4D on a 2D plane is the hard part.
You can try approximating - like the famous tesseract cube animation - but it won’t convey the three-dimensionality properly, therefore it won’t approximate the 4D visuals of it.
