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# A mathematical bug shows us why the 3D universe carries the possibility of despair. Really.

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George Polya was a mathematician. Like most mathematicians, he was concerned with very strange concepts. One of them was the idea of "random walks," or the completely random path a strolling insect might take. He took this concept and expanded it until he could prove the chances of getting hopelessly, unendingly lost in the universe. Find out why.

Let's say that there is a universe that has nothing but space, time, and an immortal bug (hey, there are stranger ideas). This bug will always keep walking, no matter what. And since it has no higher purpose (and since any one place in universe it occupies is just as good as another), its walk is completely random. In 1921, in our universe — which has many more diversions than the bug universe — Hungarian math professor George Polya considered the odds that the beetle would ever make it back to the spot it originally inhabited.

In a one-dimensional universe (essentially a universe along a straight line) the bug would — with enough random walking and an infinite amount of time — make it back to its original starting point. It might make three steps forward and three steps back, and be done within a minute. Or it could wander for centuries. Eventually, though, it had to return home.

In a two-dimensional universe, a universe in which the beetle could take any path along a plane, the beetle would also always return home. This one might take a little longer, since the beetle had more freedom to wander, but the fact that is it would return back to the place it started.