Physicists explain why your earphones are always tangled

There are few day-to-day events that send me into a rage as quickly as a pair of tangled earphones. As soon as I put them down, they somehow thread themselves into an unholy mess. And don’t even think about putting them into your pocket or bag. So how do headphones (and other stringy objects) get so knotted in such a short time? To find out, these physicists started by tumbling strings of different stiffness in a box. They found that “complex knots often form within seconds” (so it’s not just my imagination!) and that stiffer strings are less likely to get knotted up. They then used these data and computer simulations to explain how the knots are likely formed (see figure below); basically, when jostled, the strings tend to form coils and then the loose end weaves through the other strands, much like braiding or weaving. And voila! Tangled headphones to make your day just that much angrier, Discover reports.
Spontaneous knotting of an agitated string: “It is well known that a jostled string tends to become knotted; yet the factors governing the “spontaneous” formation of various knots are unclear. We performed experiments in, which a string was tumbled inside a box and found that complex knots often form within seconds. We used mathematical knot theory to analyse the knots. Above a critical string length, the probability P of knotting at first increased sharply with length but then saturated below 100 percent. This behaviour differs from that of mathematical self-avoiding random walks, where P has been proven to approach 100 percent. Finite agitation time and jamming of the string due to its stiffness result in lower probability, but P approaches 100 percent with long, flexible strings. We analysed the knots by calculating their Jones polynomials via computer analysis of digital photos of the string. Remarkably, almost all were identified as prime knots: 120 different types, having minimum crossing numbers up to 11, were observed in 3,415 trials. All prime knots with up to seven crossings were observed. The relative probability of forming a knot decreased exponentially with minimum crossing number and Möbius energy, mathematical measures of knot complexity. Based on the observation that long, stiff strings tend to form a coiled structure when confined, we propose a simple model to describe the knot formation based on random “braid moves” of the string end. Our model can qualitatively account for the observed distribution of knots and dependence on agitation time and string length.” 

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Aaj Kal