I liked the ending: "At first it was thought that the computer-generated movies of the four-dimensional hyperobjects might result in some "feeling" or insight

I liked the ending: "At first it was thought that the computer-generated movies of the four-dimensional hyperobjects might result in some "feeling" or insight for the visualization of a fourth spatial dimension. In particular, perhaps some visualization of a solid four-dimensional hyperobjeet would be gained from the distortions in the three-dimensional perspective projection. Unfortunately, this did not happen, and we are still as puzzled as the inhabitants of Flatland in attempting to visualize a higher spatial dimension." When I wrote my first 3D engine as a kid, I immediately extended it to 4D because I was a nerd and I thought the same thing - maybe I'll be able to train my brain to understand 4D objects. No. Your brain remains confused. Perhaps if you did it from birth. Like they did with those kittens that never saw horizontal and vertical lines. This would be a totally unethical experiment to carry out on a human child though :)