Tie Knot -- A Statistician's Marvel

Men of all ages knot their tie. The resultant bow of the knot looks pretty on its wearer and enhances there look as well. Getting that knot the way we want is not that easy after all. I would say it is an art. It’s a sad fact, but there are grown men who don’t know how to knot a tie. If they have a big interview that afternoon, they’ll go shopping for a clip-on. Even if a man does know how to tie a tie, their knowledge is often limited to just one necktie knot. But there are several ways to tie a tie. Certain necktie knots should be used with certain shirt collars and tie fabric materials to get the best results for your appearance. Some popular and important variations are described in the figure below.

How simple or complex is this art of knotting a tie? J.D.Lenzen is an artist who specializes in tie knots. He considers knot tying a creative practice rather than an unchanging discipline. Knots, he believes, are like paintings. Twists, coils and weaves replace the pigments and the length of the tie becomes the canvas. J.D. Lenzen is the creator of the highly acclaimed YouTube channel "Tying It All Together", and the producer of nearly 300 instructional videos. He's been formally recognized by the International Guild of Knot Tyers (IGKT) for his contributions to knotting, and is the originator of Fusion Knotting—the creation of innovative knots and ties through the merging of different knot elements or knotting techniques.

His published instructional books include Paracord Fusion Ties - Volume 2 (2013), Paracord Fusion Ties - Volume 1 (2012) and Decorative Fusion Knots (2011). His fourth instructional book, Paracord Project Inspirations will be available online and in stores, later this year (2014).

Recently, mathematician Mikael Vejdemo-Johansson, at the KTH Royal Institute of Technology in Stockholm, and colleagues have come up with a mind boggling 177,147 variations of knotting a tie. The inspiration for the work apparently came from the fiendishly complex knot sported by the “Merovingian” villain from the Matrix films. The number Vejdemo-Johansson and pals came up with is a vast increase on the 85 ways that physicists Thomas Fink and Yong Mao from the Cavendish Laboratory in Cambridge found in 2000. According to Vejdemo-Johansson, their number is much larger because Fink and Mao made various assumptions about tie knots that drastically reduced the number available, including that tie-wearers would only make a “tuck” – pushing the tie into the knot to lock it in place – at the end of a given tying sequence.

Next time you lay hand on your tie, try out a different knot and remember you have several more to attempt. It is an art and not just a step in decoration. :)