Is There Any Mathematical Explanation for the Entanglement of the Earphones?

获得128好评的的回答@Conner Davis

There’s paper I can't find at the moment that analyzes the probability of a length of string tangling in your pocket in an hour as a function of its length. They found that a string of 23cm or more will probably form a knot within the first hour.

Your headphones are longer than that and have three ends instead of two, so the probability they will remain untangled for an hour is even lower.

获得1.7k好评的回答@Senia Sheydvasser

Back in 1989, Nicholas Pippenger wrote a paper about knots in random walks. What he showed is that if you have a random walk on the 3D lattice, the probability of that walk forming a knot goes to very, very quickly.
早在1989年,Nicholas Pippenger就曾写过一篇关于“随机游动中的绳结”的论文。文中写道如果你在一个3D环境中做随机游动,游动中形成绳结的概率将非常大。

There has been other work on knots in random walks since then, and the common thread seems to be that knots form much more readily than you think they do. If your earphones are jostling around in your pocket at all, the probability that they will tangle is high.