We can recreate a 3-dimensional picture on a 2-dimensional surface. Why can’t we visualize a 4-dimensional world in a 3-dimensional area?

Question

We can recreate a 3-dimensional picture on a 2-dimensional surface. Why can’t we visualize a 4-dimensional world in a 3-dimensional area?

In: 21

Answer 1

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