(I know, time is the 4th dimension. I mean 4 spacial dimensions)
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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.
We can actually. You can imagine that 3D is just a slice of 4D. There is a nice app called tesseract that you can launch on your phone with 3d goggles. It’s confusing at first, but after some time when you will keep thinking that you are watching a slice of higher dimension it clicks.
Perhaps an explanation from the master (Carl Sagan) would help…
He eventually talks about the fourth dimension, but do watch his description of a two dimensional entity trying to experience a third dimension. This helps to explain why a three dimensional entity such as yourself has trouble experiencing a fourth dimension.
Try this mental experiment.
1) Close your eyes and create a mental image of a cube.
2) Rotate the mental cube until you are familiar with all six faces.
3) Visualize a cube extending from each of the six faces.
4) Rotate this object mentally until you are familiar with each of the seven cubes.
5) Mentally place a black spot on one of the faces of the interior cube.
6) Move the black spot about noticing how its face is shared with one of the outer cubes.
7) Visualize a black spot on one of the faces of one of the exterior cubes.
8) Visualize a black spot on the face of another of the exterior cubes that is orthogonal to the previous face.
9) Mentally move these spots around such that one mimics the movement of the other.
10) Mentally bring the spots together until they are coincident, so that the faces of the two cubes join into a single surface.
11) Merge the shared outer vertices of the two cubes containing the moving spot all the while keeping the shapes cubical.
12) Do the same with the remaining faces of the exterior cubes.
As many others have already stated, it’s because we can’t really comprehend 4D. If we were to encounter it our brains would have no idea what to do with the information and we may not process anything at all. Flatland by Edwin Abbott Abbott explains it fantastically, and is overall a great quick read.
There’s a game in development called 4d miner that gives you a cool visual representation.
It’s being developed by Mashpoe on YouTube.
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.
Only “3d” is “real” or perceptible. A dot on a page is still 3d. It’s ink, it has thickness. But it’s easy for us to imagine a dot without dimensions. It’s practically nothing, just position information (its coordinates). But from this we can understand that “one dimensional” is a theoretical thing. Not “real”. Just like numbers and maths. We use them but they don’t exist physically.
The same goes for a 2d drawing. Its bi-dimensionality is theoretical. We just ignore the existence of the 3rd dimension.
We can imagine the 4th dimension in the same theoretical way but that doesn’t mean it actually physically exists. If it did we could never experience it just like we can never experience being 2d. Because none of these are real tangible things. They’re words.
There are a few non-Euclidean game engines out there that are quite mindblowing
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