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The 85 Ways to Tie a Tie: The Science and Aesthetics of Tie Knots Paperback – November 5, 2001
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From Scientific American
New ways of tying a necktie appear rarely. Some 50 years passed between the introduction of the Windsor knot and the arrival of the Pratt knot in 1989. "Rather than wait another half-century for the next knot," Fink and Mao write, "we considered a more formal approach." And so they present 85 tie-tying techniques, each one shown in a drawing with instructions on how to achieve the desired result. They also offer a brief history of neckwear and photographs of famous figures wearing ties, among them Fred Astaire in a four-in-hand, Frank Sinatra in a Windsor knot and the Duke of Windsor not wearing a Windsor. But, being research physicists at the University of Cambridge, the authors are interested in more than sartorial versatility. They deal also with knot theory and topology. For the reader who wishes to probe tie-tying that deeply, they represent "knot sequences as random walks on a triangular lattice."
EDITORS OF SCIENTIFIC AMERICAN --This text refers to an out of print or unavailable edition of this title.
"In an elegant world, an irreproachable tie knot is an essential part of one's toilette; it does not matter whether the knot is simple or complicated, because the art is what counts. There are some knots which seem casual in appearance, but which have taken considerable labour before the mirror, and many a stamped foot, many an exclamation of impatience."
-- Doctor A. Debray Hygiene Vestimentaire, 1857 --This text refers to an out of print or unavailable edition of this title.
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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.
My copy, with shipping, came to $12 and it arrived a week after placing the order.