One day two years ago, Douglas Smith walked into his biophysics lab at the University of California, San Diego, and found two of his undergrads discussing knot theory. They'd downloaded the lecture notes of a math course and were weighing whether to take it. Not wanting his students to spend less time in his lab, Smith, half in jest, challenged them: “If you're going to study knot theory and you're going to work in this lab, there'd better be knot experiment too!”

But what is a knot experiment? At first, Smith and Dorian Raymer, the undergrad who took up the challenge, considered studying the knots found in loops of viral DNA. But working with the tiny polymers is difficult and expensive. Instead, they opted for something far simpler and cheaper: tumbling a piece of string in a box.

The experiment addressed two questions. What determines knotting probability? What kinds of...

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