Last Christmas, The Boar looked at the science of untangling Christmas lights and the various experiments and theorems behind it:
The phenomenon of why Christmas lights tangle was explored in 2007, when two University of California researchers published the first physical explanation of how and why jostled string tends to become knotted. Douglas Smith and Dorian Raymer placed a string (about the width of a computer mouse cable) being placed in a cubic box, which was rotated at constant angular velocity, causing the string to tumble. This experiment was conducted 3415 times, for a report published in the Proceedings of the National Academy of Science.
The report read: “We investigated the probability of knotting, the type of knots formed, and the dependence on string length. Before tumbling, the string was held vertically above the centre of the box and dropped in, creating a quasi random initial conformation. After tumbling, the box was opened and the ends of the string were lifted directly upward and joined to form a closed loop. A digital photo was taken whenever a complex knot was formed.”
The researchers found that a number of conditions had to occur before a knot formed. A minimum length of 18.124 inches (46.03 cm) was required of the piece of string. There had to be a certain amount of movement, as there was unlikely to be enough space for the ends of the strings to become tangled if there was too much string packed into the box. It also required a certain amount of flexibility – the more malleable, the easier it is for a knot to form.
Outside of Christmas lights knotted together, there is a whole mathematical discipline dedicated to knots called knot theory (it’s a branch of topology, don’t you know). The main difference between real world knots and a mathematical knot, though, is that the former have ends to help detangle them while the latter are joined at the ends so they can’t be undone. That means the simplest knot is just a ring.