How many ways can you tie a tie? For many years there were just three styles of knot: the Four-in-Hand, the Windsor, and the Half-Windsor. Then the Pratt was introduced to the world on the cover of the New York Times in 1989.
Intrigued that only one new knot had been added to the tie-tying repertoire in more than half a century, two researchers from the University of Cambridge's physics department, Thomas Fink and Yong Mao, decided to see how many tie knots were actually possible.1 To this end, they applied random walk theory – a technique useful for describing movement which, although unpredictable in detail, reveals large-scale patterns. Such patterns, the researchers realized, were essential to a successfully accomplished tie-knot. For example, if the end of the tie is moved to the right, its next move can't be to the right again – it has to be either to the left or to the center. This means that each move made in tying a tie can only be followed by one of two alternatives. Fink and Mao found that the simplest possible knot involves just three moves. They went on to discover 85 possible tie-knots, including the four popular knots, six new knots that they consider aesthetically pleasing, and two complicated nine-move knots.
1. Fink, Thomas M. and Mao, Yong Mao. "Designing Tie Knots Using Random Walks." Nature, 398: 31 (1999).