In my periodic quest to understand what four dimensions are like, this week I decided to reduce it down to the simplest four dimensional world I can think of.
My basic reasoning was like this: If you want to understand what two dimensions are like, this simplest thing you can make is a 2 × 2 arrangement of squares. In this tiny world, you can travel between top and bottom, and you can also travel between left and right. The world you can explore this way is kind of boring, since it has only four rooms to visit, corresponding to the four corners of a square:
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The equivalent in three dimensions is a 2 × 2 × 2 cube. Now you can also travel between front and back. This world is a little more interesting, since it has eight rooms to visit, corresponding to the eight corners of a cube.
So I’ve been looking at what happens when you extend this idea to just one more dimension. Now you have a 2 × 2 × 2 × 2 hypercube. You can travel back and forth in any of four dimensions, which means you can visit sixteen different rooms.
I started posing little puzzles to solve in this tiny world, and some of those puzzles have turned out to be surprisingly interesting. More on that tomorrow.