The 85 Ways to Tie a Tie. The Science and Aesthetics of Tie Knots [Englisch] [Taschenbuch]

But how does anyone prove that there are eighty-five ways to tie a tie? Well, the genial authors explain: "Tie knots, we realized, are equivalent to persistent random walks on a triangular lattice." If that explanation strikes you as less than useful, you can turn to the appendix at the back of the book, where you will find the random walk explanation proved by means of equations with symbols and superscripts which I cannot reproduce here. Comes the explanation: "Our day job as theoretical physicists might have had something to do with it." It does not take a mathematician to enjoy this book, however. What the authors have done is to examine all the variations of how to tie a standard tie. This means that one leaves the little end alone and makes the big end travel around to form the knot. Having crossed the little end, the big end can go to the left of it, or right, or to the center (where the neck of the wearer is). That is three possible moves, and within each of the three fields, the big end may either go in toward the wearer or out away from the wearer, for a total of six moves in all, not counting the final move, which is always to pull the big end down through the knot to its final resting place. Each knot can thus be specified with permutations of six simple moves. The simplest is the three-move variety called the "Oriental," the most complex is the nine-move memory-breaker known as the "Balthus." Windsor, half-Windsor, four-in-hand, and all the others are shown and instructions given. The authors have also noted the methods which might help make a more impressive knot in a lightweight tie, or in a tie that has grown limp with use, and various other suggestions. There is art here as well as science.

This is a unique blend of mathematics, sartorial history, and fashion instruction, wittily presented and attractively illustrated. If we have to have ties, we might as well let them teach us something.

It's a brilliant idea for a book. Thomas Fink and Yong Mao are condensed-matter theorists at the Cavendish Laboratory, Cambridge, and their work on tying knots made headlines around the world last year after it was published in Nature (1999, 398, 31). Using ideas from statistical mechanics, they worked out that there are 85 ways to tie a necktie. However, only 13 of these knots were deemed to be aesthetic on the grounds of "symmetry" and "balance". Three of these - the Windsor, the half-Windsor and the four-in-hand - were already widely known, whilst a fourth, dubbed the Nicky, was found to be a simpler version of the unaesthetic "Pratt", which was invented to much acclaim in 1989. This left nine brand new ways to tie a tie.

This book provides a full description of how to tie each of the 85 ties, with pictures of the 13 aesthetic ones. There is a history of tie-wearing - the Duke of Windsor apparently did not invent the Windsor - and a brief discussion of the science of knots. There are also some pictures of various celebrities wearing ties - Ernest Rutherford, it seems, favoured the four-in-hand.

So rather than publish what could have been a straightforward but possibly dull book about the science of knots, the authors have thought laterally to come up with an imaginative and clever book that must have had the publishers' marketing executives licking their lips. Other physicists who think they have a book inside them could do well to study this book's successful formula.

Martin Durrani, for Physics World.