>A teacher of mine told us, "Don't try to imagine 4D space. You can't. If you think you can imagine a 4D hypersphere, you're wrong. It's just not possible."

Your brain is a computer. If a computer can manipulate 4D hypersphere, so can you.

You can't visualize it, but that's a different thing. You can't visualize a 3D sphere either, only 2D projection.