Mikael Vejdemo-Johansson, a mathematician in #Stockholm , recently led a small team on a quest to discern how many tie knots are possible. Their results, uploaded to arXiv, say there are 177,147 different ways to tie the knot of a #necktie . That is 177,062 more ways than were found in 1999 by #Cambridge #mathematicians Yong Mao and Thomas Fink, who arrived at 85 possible ways to tie a tie.
Why the discrepancy? Well, it comes down to what counts in tie tying. Take, for example, a conventional standard: the knot must be covered by the cloth of the tie. Another metric changed in the Vejdemo-Johansson model was windings (where the tie is warped around another part of the tie), allowing for more windings and variable tie-length.
The end result of the research is a richer mathematical language for tie knots, a larger number of ways to wear a tie, and a much larger number of wrong ways to wear a tie. There's even a tie-knot generator, for the truly adventurous or #cavalier .