Is There Any Mathematical Explanation for the?Entanglement?of the?Earphones?
能不能用數學解釋下“為什么耳機老打結”?

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.
有一篇這樣的論文,不過我現在找不到了,它分析了口袋里的繩子在1小時內打結的概率與繩子長度的關系,還提出了一個以繩長為x的函數。他們發現長度為23厘米或者以上的繩子可能在第1個小時內就打結。

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.
你的耳機比23厘米要長,而且總共有3個頭,所以它在第1個小時里不打結的概率會更加低。

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.
從那以后,陸續出了其他關于“隨機游動中的繩結”的著作。普通的線比你想象中更容易打結,容易得多。如果你的耳機線不停地在你的口袋里互相推撞,它們打結的可能性將非常高。