We’re able to visualise 3D from a 2D picture because that’s literally what we were trained to do from birth: you have one or two 2D pictures from your eyes (depending on whether you closed a eye or not) and your brain is translating that into a 3D object. In particular, our brain uses the shadows and the lighting to help get a better understanding in complex situations.
And in fact, we don’t fully see 3D objects. When you look at a 2D objects, you see the borders and the inside of the objects. When you look at a 3D object, we only see it’s surface and we don’t naturally see inside non-transparent 3D objects.
Both those facts means that representing a 4D object in 3D is very difficult.
(1) We’re not trained to recognize 4D objects. And even less used to see how lighting and shadows work on them.
(2) Since our eyes are still 2D, that means we would be looking at the 2D image of a 3D object representing a 4D hyperobject. Complexity adds up.
(3) Additionally, since we can’t see through 3D objects unless they’re transparent, we would be missing a lot of information that would be hidden inside this 3D representation. You can circumvent this last issue with transparent objects but it still adds to the complexity.
We *can* visualise a 4-(spatial-)dimensional world in a 3-dimensional area. There are several games and other media that attempt to do so. The problem is 1) it’s difficult to make sense of what’s happening because our brains have evolved to only understand 3 spatial dimensions, and 2) we haven’t observed a 4th spatial dimension in reality, so all our depictions of it are completely made up.
At best we can look at how a 2D medium can be used to represent a 3D object (eg. a drawing of a cube on paper), the way that 2D projection changes as the object rotates in 3 dimensions etc, and try to extrapolate that behaviour into a 4D object. There can be a little maths and logic involved. But ultimately a 4th spatial dimensions doesn’t appear to exist, we have no idea how one would work if it did exist, so this is just an exercise in creativity.
I suspect that we can, but the problem lies in our ability to perceive it, and to subsequently understand it.
We perceive and understand 3D space intuitively, probably because it’s how we process our visual input. It’s more than just the image we see. It’s also how our eye muscles are feeling (and giving feedback), and how our brain is synthesizing it into an understandable model of the world.
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