Q: How can we have any idea what a 4D hypercube or any n-D object “looks like”? What is the process of developing a picture of a higher dimensional object?
A picture of a 3D object is a “projection” of that object onto a 2D page. So when you take a picture the “up/down” and “left/right” dimensions are retained, but the “forward/back” dimension is flattened. That is, you can take an object in any number of dimensions and “project out” any number of dimensions, until it’s something we can picture (3 or fewer dimensions). A 4D-to-2D projection, like in the picture above, would involve 2 “camera/eyeball like” projections, so it’s not as simple as “seeing” a 4D object. For example, by looking at the square (picture above) you’ll notice that , , and .