How Many Ways Can You Tie A Tie? Mathematicians Say 177,147 Thanks Partly To 'The Matrix'
Some scientists investigate the origins of the universe or the nature of space-time. Others just want to know how many different ways there are to tie a necktie. The answer is not four, though there are only so many common ones. Actually it's 177,147.
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Necktie knots have held the enduring fascination of some very smart people. University of Cambridge researchers Thomas Fink and Yong Mao endeavored in 1999 to create a definitive mathematical language for neckties that could characterize all possible variations. Their paper in the journal Nature, "Designing Tie Knots By Random Walks," became the topic's founding text. Their book, The 85 Ways To Tie a Tie, gained popular acclaim.
We now know there are so many more ways. In a recent article titled "More Ties Than We Thought," uploaded to the preprint archive arXive.org, four mathematicians again tackled the question. But this time they were confronted with a new fashion trend. "In The Matrix Reloaded," they wrote, "the character of 'The Merovingian' has a sequence of particularly fancy tie knots. Attempts by fans of the movie to recreate the tie knots from the Merovingian have led to a collection of new tie knot inventions."
This happens from time to time, though it's rare. New knots come around. Some are fads. Some are timeless. The simple four-in-hand emerged in the 19th-century England; the Windsor and its little brother, the Half Windsor, are the early 20th-century creation of the Duke of Windsor; and the Pratt is one of the lasting recent creations, developed only recently, in 1989. Since the movie came out in 2000, an elaborate-looking new creation has emerged, and last month, science caught up with the times.
The four mathematicians — from the KTH Royal Institute of Technology, Oxford University, and Upstanding Hackers LLC (we're not exactly sure what this is) — used the original mathematical framework that Fink and Yong created as a basis. Then they created a new one to account for the new knot-tying methods. These employ the skinny end of the tie, which the math guys call the "thin blade," to weave various patterns. (See the video below.)
To come up with such an astronomical number as 177,147, they had to count a multitude of minor variations — different ways to tuck the blades and different orders of operation. As for aesthetics, they don't get into that. "We do not in this paper attempt to optimize any numeric measures of aesthetics," they wrote, "as this would require us to have a formal and quantiﬁable measure of the knot facades. This seems difficult with our currently available tools."
Above photo courtesy of Shutterstock.
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