A couple of physicists have studied how a piece of string eventually end up with knots, and how that depends on its length.
In the end, one law emerged: The longer the string, the more likely it is to form a knot. String that was 1.5 feet or shorter never got tangled up. But “as the string gets longer, the probability of a knot forming goes up and up,” Smith says, at least to 18 feet. Flexibility matters, too. The more pliable the string, the more likely it is to knot spontaneously.
I'm not quite sure how such a knowledge would be useful elsewhere (topology?).