2x2x2x2, part 3

It’s not easy to talk about a four dimensional puzzle on a blog, because the page you are reading right now is basically only two dimensional. So I’m going to resort to an old trick: Rather than try to show you four dimensions directly, I’m going to show you four dimensions flattened out to two dimensions.

To understand the principle, imagine you were a creature in Flatland, and a friend from the 3D universe wanted to talk to you about the eight little subcubes that make up a bigger cube. Your 3D friend knows you can’t actually see a 3D cube, so she flattens it out for you, showing you the top 2×2 cubes side right next to the bottom 2×2 cubes:

0 1
2 3
4 5
6 7

In your mind you’re supposed to think of the two images above as being stacked up, one on top of the other. But if you live in Flatland, you don’t know which way is up, so looking at them side by side let’s you see the eight little sub-cubes in a way that you can understand.

More tomorrow.

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