Quora精選：能不能用數(shù)學(xué)解釋“耳機(jī)打結(jié)"？

Is There Any Mathematical Explanation for the Entanglement of the Earphones?能不能用數(shù)學(xué)解釋下“為什么耳機(jī)老打結(jié)”？

獲得128好評(píng)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(guò)我現(xiàn)在找不到了，它分析了口袋里的繩子在1小時(shí)內(nèi)打結(jié)的概率與繩子長(zhǎng)度的關(guān)系，還提出了一個(gè)以繩長(zhǎng)為x的函數(shù)。他們發(fā)現(xiàn)長(zhǎng)度為23厘米或者以上的繩子可能在第1個(gè)小時(shí)內(nèi)就打結(jié)。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(jī)比23厘米要長(zhǎng)，而且總共有3個(gè)頭，所以它在第1個(gè)小時(shí)里不打結(jié)的概率會(huì)更加低。

獲得1.7k好評(píng)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(guò)一篇關(guān)于“隨機(jī)游動(dòng)中的繩結(jié)”的論文。文中寫道如果你在一個(gè)3D環(huán)境中做隨機(jī)游動(dòng)，游動(dòng)中形成繩結(jié)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(xù)出了其他關(guān)于“隨機(jī)游動(dòng)中的繩結(jié)”的著作。普通的線比你想象中更容易打結(jié)，容易得多。如果你的耳機(jī)線不停地在你的口袋里互相推撞，它們打結(jié)的可能性將非常高。

(來(lái)源:滬江)