Imagine closing your eyes and rolling a billiards ball across a table. Where it goes; what angles it hits the sides at; how much it spins or swerves – all that is, for our purposes, basically random. And then, imagine you’re asked to roll it back to exactly its starting point. Could you do it? The rest of this article is behind a paywall. Please sign in or subscribe to access the full content.

Well, if you’ve read a recent paper from mathematicians Jean-Pierre Eckmann and Tsvi Tlusty, then yes, you could. In fact, it’s possible even if that ball was rolling around through three-dimensional space. “We show[ed] that almost every walk in SO(3) or SU(2), even a very complicated one, will preferentially return to the origin,” the pair announce in the paper.

It's the kind of problem you might

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