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.

他们发现，一根线绳在快速摇晃后打结的概率会达到50%。而且，这也与线绳的长度有很大的关系。比较短的绳子——少于一个半英尺——一般不会打结。越长的线绳，打结的可能性就越大。但是这一概率随绳结变长到一定程度就停止了。超过5英尺的绳子在盒子里就会无计可施。

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也利用数学家推算出的琼斯不等式给所形成的绳结分了类，每次摇晃之后，他们都会给线绳拍一张照片并将照片上传至一个用于给绳结分类的电脑算法程序中。扭结理论对于少于等于7个结的初级绳结给予14种分类。然而二人还发现了更加复杂的绳结，有些绳结竟然高达11个结。

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