Tangle theory

We all recognize this problem. The reoccuring struggle to untangle a cord that was in perfect order the last time you used it, but now through the works of what must be some kind of magical (and probably very evil) hand, has turned into a veritable mess. Be it the cord for your earphones, which you left in your bag over night, or be it the christmas lights that you really made an effort to stove away in a proper way after last christmas. By the next day (or christmas), be sure, they have somehow turned into a tangle that will have you scratching your head in frustration.

It was probably one of these moments that triggered sceintists Douglas Smith and Dorian Raymer of the University of California San Diego to start performing experiments to find out exactly why this keeps happening again and again. The result was presented in the paper “Spontaneous Knotting of an Agitated String” in 2007. What Smith and Raymer did in practice, was to place some string in a small box, and then spun the box around for 10 seconds. They repeted this over 3,000 times with strings of different lenght, and found that the longer the string is, the higher the probability of spontaneous knotting to occur. A more flexible type of string is also more likely to form a knot. They came to the conclusion that knots actually form themselves, given you have the right length and typ of cord, and add some random movement. This dervies from the second law of theromdynamics, that states that things naturally tend towards disorder over time (something most of us are also familiar with). Smith and Raymer then produced a computer model that simulated the knotting of strings. The pictures below are examples of the theoretical model for how this spontaneus knotting occurs.

Knot theory:

Source: http://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/Dowker-notation-example.svg/220px-Dowker-notation-example.svg.png

Tangle theory:

Source: http://upload.wikimedia.org/wikipedia/commons/thumb/0/08/RationalTangle_2_1_3.svg/350px-RationalTangle_2_1_3.svg.png

Tangle theory #2:

Source: http://bio.math.berkeley.edu/TangleSolve/tmodel/tanglediagram_fig.jpg

For those who feel they really need to deepen their theoretical knowledge in the field of knots and tangles, we here provide a link to a class in knot theory. Knot theory can said to be the base upon which tangle theory is based. The Knot in knot theory is made up of a loop.

Courtesy of the UCLA.

http://www.math.ucla.edu/~radko/191.1.05w/index.html