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As I recline weekly in velvet smoking jacket and exquisite cravat to dictate The List to my oiled, submissive stenographer, it is often given to me to muse on the science and aesthetics of tie knots. Happily, Messrs Fink and Mao have now systematized the study of this most indispensable of gentlemen's apparel. Our authors are Cambridge physicists, and they have devised a highly ingenious mathematical method of proving exactly how many different ways there are to tie a tie, given certain practical (tie length, volume of knot) and aesthetic (symmetry) constraints. Such an advance in our understanding is the fruit of knot theory, a branch of topology under which we can see that a tie is a random walk on a triangular lattice. This eminently desirable little volume also paints a deft history of the tie, with clear knotting diagrams for each of its sartorial results. A perfect seasonal gift for fathers who would like to enter the new millennium more sprightly of step, and more elegant of neck.
The Guardian

This wonderful little book by Thomas Fink and Yong Mao has changed my life. Now, when I tie a tie, I know what I am doing, and why. Fink and Mao have performed a great service for civilization, doing for tie-knot tying what Isaac Newton did for the motion of the heavens: lifting it from the darkness of secrecy, ritual and superstition to the light of rational, scientific good taste...Fink and Mao have shown that it's possible to be both smart and smart - in brains and style.
Nature     (for full review view pdf)

A masterpiece of ludicrous arcana by two Cambridge researchers....
The Independent

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.
Physics World

The fact that only thirteen knots withstood their aesthetic contraints is comparatively unimportant. More interestingly the authors accompany it with a deft but resolute history of the tie, as well as detailed knotting instructions. The unconventional should consider one of the rather novel options like the "crossed Christensen". But perhaps not before the office, it might take some time.

Once they have established the history, the authors explain their knotting breakthrough. Mathematicians have already invented a rich and precise language for each element of knotting, and Fink and Mao combine these elements in all possible ways to create a rich array of knots. They also show how to exploit mathematical rules in order to define when a knot is distinct from anything that has ever been seen before....
The Telegraph

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