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

獲得128好評的的回答@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.

獲得1.7k好評的回答@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就曾寫過一篇關于“隨機游動中的繩結”的論文。文中寫道如果你在一個3D環境中做隨機游動,游動中形成繩結的概率將非常大。

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.