Playing Minecraft in 4D

For the first time, I can almost visualize a fourth spatial dimension

It’s really damn hard to envision a fourth dimension of space.

I tried! For years. I read Flatland as a kid, and it fried my noodle. In that famous book — a “romance of many dimensions” — the narrator is a square who lives in a 2D world, filled with 2D creatures. He has no idea that a third dimension could even exist, until one day a 3D sphere floats down to visit.

The sphere talks to the square, and tries to explain how the third dimension works. But the square has absolutely no mental model for grasping such a concept.

To try and illustrate how the third dimension works, the sphere floats through Flatland. From the square’s 2D perspective, this looks magical and strange: It’s as if a circle suddenly appeared in Flatland, then began growing and growing. Which makes sense, right? If you imagined passing a sphere through a piece of paper — and looked at the spot where the sphere intersects the paper — that’s what you’d see. Cross-sections of a sphere, getting bigger and bigger.

The author of Flatland, Edwin Abbott, illustrated it this way …