It happens every time: You reach into your bag to pull out your headphones. But no matter how neatly you wrapped them up beforehand, the cords have become a giant Gordian knot of frustration.
Along with your Netflix stream inexplicably buffering and Facebook emotionally manipulating you, tangled cords are the bane of modern existence. But until we invent a good way of wirelessly beaming power through the air to our beloved electronic devices, it seems like we’re stuck with this problem.
Or maybe we can fight back with science. In recent years, physicists and mathematicians have pondered why our cords are such jerks all the time. Through experiments, they have learned there are many interesting ways to explain the science of knots. In 2007, researchers at the University of California, San Diego tumbled pieces of string inside boxes in an effort to find the ways that a cord can become tangled as it wanders around in your backpack. Their paper, “Spontaneous knotting of an agitated string,” helps explain how random motions always seem to lead to knotting and not the other way around.
Long floppy pieces of string can assume many spontaneous configurations. A string could be nicely laid out in a straight line. Or it could have one end crossed over some section in the middle. There in fact happen to be a lot of configurations where the string wraps around itself, potentially creating a tangle and eventually a knot. With relatively few of these random configurations being tangle free, chances are higher that the string will be a mess. And once a knot forms, it’s energetically difficult and unlikely for it to come undone. Therefore, a string will naturally tend toward greater knottiness.
Humans have been tying things up with string for many thousands of years, so it’s no surprise mathematicians have been working on theories of knots for a long time. But it wasn’t until the 1800s that the field really took off, when physicists like Lord Kelvin and James Clerk Maxwell were modeling atoms as spinning vortices in the luminiferous ether (a hypothetical substance that permeated all space through which light waves were said to travel). The physicists had worked out some interesting properties of these knot-like atoms and asked their mathematician friends for help with the details. The mathematicians said, “Sure. That’s really interesting. We’ll get back to you on that.”
Now, 150 years later, physicists have long since abandoned both the luminiferous ether and knotted atomic models. But mathematicians have created a diverse branch of study known as knot theory that describes the mathematical properties of knots. The mathematical definition of a knot involves tangling a string around itself and then fusing its ends together so the knot can’t be undone (Note: This is kind of hard to do in reality). Using this definition, mathematicians have categorized different knot types. For instance, there is only one type of knot where a string crosses itself three times, known as a trefoil. Similarly, there is only one four-crossing knot, the figure eight. Mathematicians have identified a group of numbers called Jones polynomials that define each type of knot. Still, for a long time knot theory remained a somewhat esoteric branch of mathematics.
In 2007, physicist Douglas Smith and his then-undergraduate student Dorian Raymer decided to look at the applicability of knot theory to real strings. In an experiment, they placed a string into a box and then tumbled it around for 10 seconds. Raymer repeated this about 3,000 times with strings of different lengths and stiffness, boxes of different size, and varying rotation rates for the tumbling.
2007年，物理学家Douglas Smith和他当时的本科同学Dorian Raymer决定将扭结理论应用到真实的线绳中去。在一次使用中，他们在盒子里放置一条线绳并摇晃10分钟。Raymer以不同长度和不同软硬度的的绳子、不同尺寸的盒子、以及不同的摇晃频率重复了三千次。
They found that about 50 percent of the time, a string would emerge from its quick spin with a knot in it. Here, there was a big dependence on the string’s length. Short strings—those less than about a foot in a half in length—tended to stay knot-free. And the longer a string got, the greater the odds of knot formation became. Yet the probability only increased up to a certain size. Strings longer than five feet became too cramped in the boxes, and wouldn’t form knots more than roughly 50 percent of the time.
Raymer and Smith also classified the types of knots they found, using the Jones polynomials developed by mathematicians. After each tumble, they took a picture of the string and fed the image into a computer algorithm that could categorize the knots. Knot theory has shown that there are 14 kinds of primary knots, which involve seven or fewer crosses. Raymer and Smith found that all 14 types formed, with higher odds of forming simpler ones. They also saw more complicated knots, some with up to 11 crossings.
The researchers created a model to explain their observations. Basically, in order to fit inside a box, a string has to be coiled up. This means the end of the string lies parallel to different segments along the length of the string. As the box spins, the string end has a certain chance of falling over and around one of these middle segments. If it moves enough times, the end will essentially braid itself around some part in the middle, tangling up the string and creating different knots.
The most important question from these experiments is what can be done to keep my cables from getting all screwy. One method that decreased the chances of knot formation was placing stiffer strings into the tumbling boxes. Perhaps this is what motivated Apple to make the power cables for more recent generations of laptops less flexible. It also helps explain why your long, thin Christmas tree lights are always a tangled mess while your shorter and stockier surge protector cable stays relatively smooth.
A smaller container size also helped keep the knots away. Longer strings pressed against the walls of a small box, preventing the cord from falling over itself and braiding up. This has been proposed as the reason why umbilical cord knots are rare (happening in about 1 percent of births): The womb is too small to allow for the organ to tangle around itself. Finally, spinning the boxes faster than normal helped prevent knotting because the strings were pinned to the sides by centrifugal forces and couldn’t braid themselves. However, I’m not sure how you would apply this to your own pocket dilemma of cord tangles. Perhaps you could travel around by quickly somersaulting everywhere. Or buy clothes with really tiny pockets.