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

Oh God. Best I can do is ELI13.

Imagine you have a two-dimensional being, sentient on a sheet of paper. Every two-dimensional shape that shares the paper with them is going to appear as a line segment, because it’s on their plane. If your sentient stick person can only observe whats in the same stack of dimensions, then whether you draw a circle or a square or a line or a dodegon or a seven-pointed star, all the more the figure can see is a single line.

Now, if you give it two points of vision on that plane, it can at least see two separate one-dimensional items, and piece them into a two-dimensional representation, whereby they may get more information on the vector of that line. But they’ll still never see it as a shape. That said, they would be able to perceive two-dimensional objects.

We exist in three dimensions, but we don’t see in three dimensions: we see in two, and piece it together from two simultaneous two-dimensional images. Our whole field of vision can be represented by stereographic 3D images in that exact way. We don’t see three dimensions; we see two dimensions twice. There are some other tricks like shadows and occlusion we can use, but we’re still only seeing a two-dimensional image.

Let’s go back to our paper person. We decide, from our three dimensions, to send a ball intersecting their plane. The cross section of that intersection would be a point, then a growing circle, then a shrinking circle, then a point, before passing clean through. To the stick person, though, all they can observe is a line that grows from nothing and then shrinks to nothing. We could send a cube, a pyramid, a lump, and they would still only see the one-dimensional cross section.

If a four-dimensional object passed through our three-dimensional “plane”, it would represent as a three-dimensional object, which we could perceive, but we’d also only still only be seeing two dimensions,twice at once.

A four-dimensional hypersphere passing through our three dimensions would exist by appearing as a singular point, growing through a sphere of some size, and then shrinking back to a point and then zero. A hypercube at any non-perpendicular angle would appear out of nothing, transitioning through multiple prismatic shapes, before shrinking and vanishing.

So to answer your question, we can simulate it fine, but we can’t perceive it in any way that extends beyond the dimensions we live in.