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. 
 
 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. 
 
 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. ||||| UC San Diego Undergraduate�s Research Makes New York Times� Top Science Stories of 2007 
 
 December 10, 2007 
 
 By Sherry Seethaler 
 
 Dorian Raymer 
 
 Credit: Kim McDonald, UCSD 
 
 A southern Californian at heart, Dorian Raymer surfs, skateboards and fishes for yellowtail. But he also enjoys dabbling in different academic disciplines. He brought together three of his academic pursuits—mathematics, physics and computer programming—in a study he initiated while an undergraduate physics major at UC San Diego that was named one of the top science stories of the year. 
 
 This week the New York Times Magazine named the study on knot formation by Raymer and Douglas Smith, an assistant professor of physics at UCSD, one of the Top Science Stories of 2007 in its annual “Year in Ideas” issue. The editors of the Sunday New York Times Magazine chose the stories from a pool of nominees submitted by New York Times reporters. 
 
 Since their paper was published in the Proceedings of the National Academy of Sciences in October, the two physicists’ work has captured headlines in daily newspapers and magazines around the world, as well as more technical publications such as Popular Science, Science News, New Scientist and Physics Today. A feature on their research will appear in the February issue of Discover Magazine. 
 
 “It was fun to talk to the reporters from many publications, as far away as Sweden, who contacted us about the story,” said Raymer. “But we were most happy about the response of the mathematicians. We were using mathematical concepts that can take years to fully understand, so we weren’t sure how our research would be received. However, Andrew Belmonte, a math professor at Penn State University, published a favorable commentary on our paper in the following issue of PNAS. He concluded that the study of physical knots has now come into its own as an experimental science and that the mathematical model we proposed is likely to have interesting implications.” 
 
 “Many undergraduate students have worked in my lab over the years, but this is the first time one of my students initiated a project that has generated so much interest from the press,” said Smith. “It is a great lesson for students that the most important thing in science is to be curious and creative.” 
 
 Digital photos of knots 
 
 with computer-generated drawings based on mathematical calculations. 
 
 
 
 Credit: Dorian Raymer, UCSD 
 
 In recognition of the importance of providing undergraduate students with research experience, this year UCSD launched the Regents Scholars program. The program guarantees experience in a research laboratory for top entering freshmen. 
 
 
 
 “In the Division of Physical Sciences, we have a high faculty to student ratio that makes it possible for many of our undergraduate students to get involved in research,” said Mark Thiemens, dean of UCSD’s Division of Physical Sciences. “Many of our alumni, whether they have gone into industry or academia, tell us that gaining research experience as undergraduates was the single most important part of their education.” 
 
 Raymer and Smith’s study investigated the likelihood of knot formation and the types of knots formed in a tumbled string. 
 
 “We began the study because I was curious about knot theory in mathematics, and we wondered whether it might be applicable in a physics experiment,” said Raymer. 
 
 “When we started looking into this, it soon became clear that very little experimental work had been done to apply knot theory to the analysis and classification of real, physical knots and there was little understanding of how knots form,” said Smith. “But knot formation is important in many fields. For example, knots often form in DNA, which is a long string-like molecule. Certain anti-cancer drugs stop tumor cells from dividing by blocking the unknotting of DNA.” 
 
 Raymer and Smith designed a simple experimental set up consisting of a plastic box spun by a computer-controlled motor. A piece of string was dropped into the box and tumbled around like clothes in a dryer. Knots formed very quickly, within 10 seconds. The researchers repeated the experiment more than 3,000 times varying the length and stiffness of string, box size and speed of rotation. The result was a lot of tangles to be classified. 
 
 Dorian Raymer Image credits: Kim McDonald and Dorian Raymer, UCSD 
 
 “It is virtually impossible to distinguish different knots just by looking at them,” said Raymer. “So I developed a computer program to do it.” 
 
 The program translated the crossings of the string into a mathematical fingerprint for each knot. It used the Jones polynomial—a famous math formula developed by Vaughn Jones, a mathematics professor at UC Berkeley—which automatically simplifies knots that are identical, but look different. 
 
 Raymer and Smith developed a basic model for knot formation. String forms concentric coils, like a looped garden hose, due to its stiffness and the confinement of the box. The free end of the string weaves through the coils, with a 50 percent probability of going under or over any coil. The computer simulation that they developed based on this model mimicked the experimental results. 
 
 Raymer is currently a research assistant working with Smith and is thinking about graduate school. He is still deciding between his love of physics, mathematics, neuroscience and computer programming, and keeping his eye out for a new project that will bring them all together. 
 
 Media Contacts: 
 
 Sherry Seethaler, 858-534-4656 
 
 Comment: 
 
 Dorian Raymer, 858-822-1379 
 
 Douglas Smith, 858-736-5340 
 
 
 
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– You get off the subway, stash your earbuds in your pocket, and when you pull them out again, they're completely tangled—even after you painstakingly untangled them yesterday. Why does it happen every time? Well, there's actually a whole branch of science to help explain, and it's called knot theory, Wired reports. A 2007 experiment conducted at the University of California, San Diego, may shed some light on the situation. Researchers dropped string into a motorized spinning box, examining the resulting knots. They argued that knots occurred because when a string is coiled in order to fit in a small space, its end is parallel to other sections. Spinning makes it possible for that end to loop around a segment, and more spinning means more looping. In half of the 10-second spins, strings came out knotted. The longer a string was, the higher the chance of knotting—up to a point. Strings shorter than a foot-and-a-half didn't usually get knotted, and those beyond five feet long got knotty just half the time. So how to avoid knots? Stiffer cables help reduce tangling, as do smaller spaces. Or you can try a do-it-yourself method to avoid tangling.