There are 177,147 ways to fasten a necktie, it has emerged – 1,000 times more than previously thought.
But the study was not prompted by higher theories of mathematics, but a flamboyant knot worn by a super-villain in Hollywood blockbuster The Matrix Reloaded.
The Merovingian, named after a French royal dynasty, wore his tie in the little-known Ediety knot, which features two loops around the top of the knot and leaves the skinny part of the tie hanging on top.
His was perhaps the most unusual in a series of unorthodox tie knots in the film trilogy, which prompted viral tutorial videos on Youtube from fans trying to copy their style.
Mathematician Mikael Vejdemo-Johansson, of the KTH Royal Institute of Technology in Stockholm, Sweden, watched the videos and realised the ‘Merovingian knot’ was missing from a major 2000 study by researchers at Cambridge University.
Along with three other mathematicians, he created a formula for devising tie knots using just three symbols, W, T and U.
He said: ‘T is a clockwise (turnwise) move of the knot-tying blade, W is a counter-clockwise move, and U tucks the blade under a previous bow.
‘Whether to start with an inwards or outwards crossing can be deduced by counting the total number of W and T in the knot description string, and all possible strings in W and T produce possible tie knots.’
From the tool, known in logic as formal language theory, he has created a random tie generator which uses the mathematics to teach internet users how to tie random knots.
According to the New Scientist, the Cambridge researchers had wrongly assumed people would only make a tuck – folding one end of the tie under the rest to finish the knot – at the end, and that all knots would be covered by a flat stretch of fabric.
But their theory did not account for the elaborate knots found in The Matrix, with several tucks and ruffled fabric.
The researchers also changed one crucial rule – the limit to how many winding moves people could make before their tie became ludicrously short.
The team put that number at 11 – meaning there are 177,147 possible knots in the world. But who could find enough time to tie them all?