We can. Just how like we can draw a cube (a 3D object) onto a piece of paper (a 2D plane), we can project a 4D object into 3D space. Here’s what a 4D cube (sometimes called a Tesseract) looks like projected in 3D space:
https://en.wikipedia.org/wiki/Tesseract
Just like when we project a cube onto a 2D piece of paper, we lose part of the shape by the projection. We can’t draw a cube that has angles that are all 90 degrees on a 2D piece of paper. Some angles will be skewed. Similarly, the angles between the sides of the tesseract are all actually 90 degrees, but only appear skewed when projected in 3D
The only reason we can properly understand the 2D representation of a 3D object is because we live in a 3D world, so we have a reference point. We’ve never experienced 4D.
That doesn’t stop us from trying though. If you google tesseract you’ll find 3D representations of a 4D object (or, rather 2D representations of the 3D representations, since you’re looking at a 2D screen).
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.
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.
Latest Answers