What can you do to limit the knots?
There are a few things that are certain in life: death, taxes and tangled headphone cords. It seems like it takes no more than a minute for a nicely coiled pair to end up in endless knots in your pocket or bag. But why?
In a paper entitled “Spontaneous knotting of an agitated string,” researchers from the University of San Diego explain the mathematics and physics behind tangled strings through a set of experiments.
In the abstract, the researchers wrote: “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.”
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More specifically, they placed pieces of string in cubic boxes, “rotated [them] at constant angular velocity about a principle axis perpendicular to gravity,” opened the boxes, pulled the string out by the two ends, and attached them together before taking pictures of the more complex knots. This was repeated over and over with each length of string to collect statistical data.
Knot theory is an area of mathematics that studies knots, as the name suggests, but not just the types of knots we are accustomed to — it has applications in biology, quantum computing, chemistry, and many other fields. In math, knots are always studied in closed loops and a knot is defined as a configuration that cannot be untangled into a simple loop. They are classified based on their number of crossings. Two knots are considered equivalent if one can be transformed into the other without detaching the ends.
Knots are classified by the number of crossings. Image credit: Jkasd/Wikipedia (CC0)
The real question here is: How can the researchers’ experiments with string in boxes help us keep our headphones untangled? Here are some of their useful results:
“Tripling the agitation time caused a substantial increase in P, indicating that the knotting is kinetically limited.” This line means that the longer you store your headphones for, the more likely they are to get knotted. That makes sense — they have more time to move around and get tangled.
“Above a critical string length, the probability P of knotting at first increased sharply with length.” Thus, the longer your cord is, the more likely it is to get tangled.
“Increasing confinement of a stiff string in a box causes increased wedging of the string against the walls of the box, which reduces the tumbling motion that facilitates knotting.” Here, the researchers noted that a smaller box meant less room for the headphones to move around and get tangled in.
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Similarly, when using a stiffer cord, “the tumbling motion was reduced because the finite stiffness of the coiled string tends to wedge it more firmly against the walls of the box.” This means that the stiffer a cord is, the less it bends and moves around — creating knots — in the box.
All this to say, stick with as short and stiff a headphone cord as possible, store them in a small pocket and don’t leave them there for too long. Then again, if — or should I say when — they do get tangled, why not take the time to study the knots? Who knows what you might discover!