If we’re able to create the illusion of the 3rd dimension on our 2-dimensional screens, why aren’t we able to simulate/create the illusion of the 4th dimension in our 3-dimensional world?

Question

(I know, time is the 4th dimension. I mean 4 spacial dimensions)

In: 3890

Answer 1

We totally can, for simple 4D shapes at least. [Here is a 2D image](https://www.scienceabc.com/wp-content/uploads/2018/03/Square-cube-tesseract-2d-3d-4d.jpg) of a square (a 2D shape), a cube (a 3D shape), and a tessaract (a 4D shape).

The 2D square, represented by a 2D image, looks normal. All sides are the same length and at right angles: a perfect square.

The 2D representation of the 3D cube isn’t really a cube. A cube is made up of 6 squares stuck together, all the same size. But the squares seen in the 2D version of cube aren’t identical squares. In fact, they are parallelograms of different shapes and sizes. But we are used to seeing cubes from angles where the squares look like parallelograms, so even though it’s distorted by being squished into 2 dimensions, we still see it as a cube.

The 2D representation of the 4D tessaract is even more distorted. Just like how a cube is made up of 6 identical squares stuck together, a tessaract is actually 8 cubes stuck together, but in a way that takes up the same amount of 3D space as 1 cube. In the 2D version, we see a big cube, a small cube, and 6 more shapes that are more like pyramids with the tops chopped off. In a real tessaract, all those shapes would be perfect cubes of the exact same size, all occupying the same space as 1 cube, but extending outwards in the 4th dimension.

So it is possible to represent a simple 4-dimensional object in 2D (or in 3D). Why can’t we represent something more complex, like an entire 4D scene? Well, our brains are really good at looking at 3D objects. We do it constantly, all day long, and get extremely good at it. So good, that we can easily imagine non-3D things as being 3D. But we never look at 4D things, never practice at it, so we are bad at it. So if we look at the 4D representation of the tessaract, we much more easily see it as a 3D cube-inside-a-cube than as a 4D object. So if we tried to render a complex 4D object in 2D or 3D, it would be extremely difficult to really see it as 4D. Our brains would just try to see it as a weird 3D object instead, because that’s what brains are good at doing.