爲什你的耳機總是纏繞打結
It happens every time: You reach into your bag to pull out your headphones. But no matter how neatly you wrapped them up beforehand, the cords have become a giant Gordian knot of frustration.
有件事似乎無所不在：你把手伸到包包裏拿出你的耳機，但是無論之前你把耳機纏得如何整齊，耳機線總是會結成一個十分混亂的結。
Along with your Netflix stream inexplicably buffering and Facebook emotionally manipulating you, tangled cords are the bane of modern existence. But until we invent a good way of wirelessly beaming power through the air to our beloved electronic devices, it seems like we’re stuck with this problem.
除了Netflix的讓人莫名其妙的流媒體加載技術和Facebook對用戶的情緒控制實驗之外，繞線耳機也應該算反現代科技的一個存在。但是除非我們能發明一種比較好的無線輻射技術用於通過空氣介質來連接我們所鍾愛的電子設備，否則我們只能繼續忍受這個問題了。
Or maybe we can fight back with science. In recent years, physicists and mathematicians have pondered why our cords are such jerks all the time. Through experiments, they have learned there are many interesting ways to explain the science of knots. In 2007, researchers at the University of California, San Diego tumbled pieces of string inside boxes in an effort to find the ways that a cord can become tangled as it wanders around in your backpack. Their paper, “Spontaneous knotting of an agitated string,” helps explain how random motions always seem to lead to knotting and not the other way around.
或者我們能用科學予以還擊。近年來，物理學家和數學家一直在反覆研究有線耳機的纏繞問題。通過實驗，科學家們發現有許多途徑能夠解釋繩結科學。2007年，美國加利福尼亞大學的研究員在盒子裏放置了許多線繩並搖晃盒子，以觀察研究爲什麼耳機線在你的包裏隨便纏繞亂作一團的原因。他們的論文，“上下襬動的線繩能自然地打結”也解釋了爲什麼隨意的搖動總能讓線繩打結，而不是有其他動作。
Long floppy pieces of string can assume many spontaneous configurations. A string could be nicely laid out in a straight line. Or it could have one end crossed over some section in the middle. There in fact happen to be a lot of configurations where the string wraps around itself, potentially creating a tangle and eventually a knot. With relatively few of these random configurations being tangle free, chances are higher that the string will be a mess. And once a knot forms, it’s energetically difficult and unlikely for it to come undone. Therefore, a string will naturally tend toward greater knottiness.
長而鬆散的線繩能隨機形成許多形狀。一條線繩能被拉成直線，當然也也能從中間開始交錯盤桓。實際上，當線繩自己纏繞起來之後，就能形成各種不同的形狀，而這也爲線繩亂纏亂繞甚至打結創造了一個潛在的契機。只要有幾根這種不同形狀的線繩互相交結在一起，那麼線繩胡亂打結的機率將會大大提高。一旦出現了一個結，那麼再把它解開就很困難了，甚至是不可能的。因此，自然而然地，一條線繩就總會比較容易打結。
Humans have been tying things up with string for many thousands of years, so it’s no surprise mathematicians have been working on theories of knots for a long time. But it wasn’t until the 1800s that the field really took off, when physicists like Lord Kelvin and James Clerk Maxwell were modeling atoms as spinning vortices in the luminiferous ether (a hypothetical substance that permeated all space through which light waves were said to travel). The physicists had worked out some interesting properties of these knot-like atoms and asked their mathematician friends for help with the details. The mathematicians said, “Sure. That’s really interesting. We’ll get back to you on that.”
人類用線繩捆系東西的習慣已經維持上千年，因此數學家們長久以來研究繩結的理論這事情一點也不稀奇。但是直到諸如開爾文男爵和詹姆斯·克拉克·麥克斯韋利用原子建模描述以太（一種假象的無所不在的光波傳播介質）介質中的漩渦流的19世紀，這一領域纔有所突破。物理學家們發現了這種類似繩結的球棍原子模型的一些有趣的性質，並找來他們的數學家朋友在細節上予以他們幫助。數學家們說：“行，這還真挺有趣，我們來幫你們吧。”Now, 150 years later, physicists have long since abandoned both the luminiferous ether and knotted atomic models. But mathematicians have created a diverse branch of study known as knot theory that describes the mathematical properties of knots. The mathematical definition of a knot involves tangling a string around itself and then fusing its ends together so the knot can’t be undone (Note: This is kind of hard to do in reality). Using this definition, mathematicians have categorized different knot types. For instance, there is only one type of knot where a string crosses itself three times, known as a trefoil. Similarly, there is only one four-crossing knot, the figure eight. Mathematicians have identified a group of numbers called Jones polynomials that define each type of knot. Still, for a long time knot theory remained a somewhat esoteric branch of mathematics.
現在，150年過去了，物理學家早就拋棄了以太介質理論和球棍原子模型。但是數學家卻創造了一個被稱爲“扭結理論”的分支學科，來描述繩結的一些數學特性。數學中對於繩結的定義是一個線繩自己纏繞且兩端需要捻合起來，保證繩結無法被解開。根據這一定義，數學家將繩結分爲了不同的種類。比如說，當一條線繩自己纏繞三次後，只能形成一種繩結，被稱爲三葉結。同樣，纏繞四次也只能形成一種繩結，叫做八字結。數學家證明出了被稱爲“瓊斯多項式”的一系列公式用以定義每一種繩結。一直以來，扭結理論在數學領域仍然是某種充滿奧祕的分支學科。
In 2007, physicist Douglas Smith and his then-undergraduate student Dorian Raymer decided to look at the applicability of knot theory to real strings. In an experiment, they placed a string into a box and then tumbled it around for 10 seconds. Raymer repeated this about 3,000 times with strings of different lengths and stiffness, boxes of different size, and varying rotation rates for the tumbling.
2007年，物理學家Douglas Smith和他當時的本科同學Dorian Raymer決定將扭結理論應用到真實的線繩中去。在一次使用中，他們在盒子裏放置一條線繩並搖晃10分鐘。Raymer以不同長度和不同軟硬度的的繩子、不同尺寸的盒子、以及不同的搖晃頻率重複了三千次。
They found that about 50 percent of the time, a string would emerge from its quick spin with a knot in it. Here, there was a big dependence on the string’s length. Short strings—those less than about a foot in a half in length—tended to stay knot-free. And the longer a string got, the greater the odds of knot formation became. Yet the probability only increased up to a certain size. Strings longer than five feet became too cramped in the boxes, and wouldn’t form knots more than roughly 50 percent of the time.
他們發現，一根線繩在快速搖晃後打結的概率會達到50%。而且，這也與線繩的長度有很大的關係。比較短的繩子——少於一個半英尺——一般不會打結。越長的線繩，打結的可能性就越大。但是這一概率隨繩結變長到一定程度就停止了。超過5英尺的繩子在盒子裏就會無計可施。
Raymer and Smith also classified the types of knots they found, using the Jones polynomials developed by mathematicians. After each tumble, they took a picture of the string and fed the image into a computer algorithm that could categorize the knots. Knot theory has shown that there are 14 kinds of primary knots, which involve seven or fewer crosses. Raymer and Smith found that all 14 types formed, with higher odds of forming simpler ones. They also saw more complicated knots, some with up to 11 crossings.
Raymer和Smith也利用數學家推算出的瓊斯不等式給所形成的繩結分了類，每次搖晃之後，他們都會給線繩拍一張照片並將照片上傳至一個用於給繩結分類的電腦算法程序中。扭結理論對於少於等於7個結的初級繩結給予14種分類。然而二人還發現了更加複雜的繩結，有些繩結竟然高達11個結。
The researchers created a model to explain their observations. Basically, in order to fit inside a box, a string has to be coiled up. This means the end of the string lies parallel to different segments along the length of the string. As the box spins, the string end has a certain chance of falling over and around one of these middle segments. If it moves enough times, the end will essentially braid itself around some part in the middle, tangling up the string and creating different knots.
研究員們創造了一個模型用以解釋他們的觀測結果。爲了適應盒子，線繩必須要以一種捲曲的姿態待在其中，這意味着繩子末端與繩子的不同部分會平行排放。隨着盒子晃動，繩子末端有充分的機會上下翻滾並與繩子中段的諸多部分相遇。如果搖晃了充足時間，繩子末端就會與繩子中部纏繞在一起，從而形成不同的繩結。
The most important question from these experiments is what can be done to keep my cables from getting all screwy. One method that decreased the chances of knot formation was placing stiffer strings into the tumbling boxes. Perhaps this is what motivated Apple to make the power cables for more recent generations of laptops less flexible. It also helps explain why your long, thin Christmas tree lights are always a tangled mess while your shorter and stockier surge protector cable stays relatively smooth.
這些實驗所要解決的最重要的問題就是，如何讓繩子保持不纏繞不打結。一種能夠降低繩子打結機率的方法就是在盒子裏放置一些比較硬的繩子。也許這也是積極進取的蘋果公司最近幾代的筆記本電腦電源線不那麼容易纏繞的原因。這也解釋了，爲什麼聖誕樹上又細又長的彩燈線總是打結，而電涌抑制器那粗短堅硬的電線卻相對來說不那麼容易亂。
A smaller container size also helped keep the knots away. Longer strings pressed against the walls of a small box, preventing the cord from falling over itself and braiding up. This has been proposed as the reason why umbilical cord knots are rare (happening in about 1 percent of births): The womb is too small to allow for the organ to tangle around itself. Finally, spinning the boxes faster than normal helped prevent knotting because the strings were pinned to the sides by centrifugal forces and couldn’t braid themselves. However, I’m not sure how you would apply this to your own pocket dilemma of cord tangles. Perhaps you could travel around by quickly somersaulting everywhere. Or buy clothes with really tiny pockets.
更小的容器體積也是防止打結的妙招之一。小盒子將較長的線繩緊緊束縛住，從而阻止了線繩上下移動並打結。而這可能也是爲什麼臍帶很少打結的原因（在新生兒中僅有1%的發生機率）：母親的子宮空間太小了，臍帶難以互相纏繞。最後，以更快的速度搖動盒子也可以防止線繩打結，因爲繩子受到離心力的作用會被固定在盒子邊緣，從而無法纏繞打結。在現實生活中，也許你要麼走到哪兒都快速地翻攪着你的口袋，要麼就得買一些比較小口袋的衣服了。
