The 85 ways to tie a tie

The science and aesthetics of tieknots

Thomas Fink and Yong Mao
Hardcover - 144 pages (November, 1999)
Fourth Estate; ISBN: 1841152498

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Read a nature review of this book (postscript, pdf).


``No one accustomed to mix with the higher classes of society will be at all inclined to dispute the advantages arising from a genteel appearance; it therefore becomes necessary that the means of acquiring this distinction should be clearly demonstrated.'' In a typically exuberant mood, so began H Le Blanc's The Art of Tying the Cravat (1828), ``... the correct construction of the Cravat is proved to be of paramount advantage to the wearer; and the consequences arising from an ignorance of this important subject are pointed out in a manner which cannot fail to convince every enlightened mind.''

The treatise was published throughout Europe and in America in eleven editions. Apparently, the importance of a carefully arranged neckcloth began well before the modern tie was adopted.

The cravat disappeared and the long tie replaced it during the second half of the nineteenth century. The earliest tie knot, the four-in-hand, originated in England in the 1850s alongside the tie itself. The Duke of Windsor has been credited with introducing what is now known as the Windsor knot, whence its smaller derivative, the half-Windsor, is thought to have evolved. More recently, in 1989, the Pratt knot was revealed in broadsheets across the world, the first new knot to appear in 50 years.

The discovery of a new tie knot, evidently, is a rare event. We learnt of the Pratt in 1997. It seemed that there must be others. Rather than wait another half-century for the next knot, we considered a more formal approach.

If, as Le Blanc suggested, tying a cravat is an art, we found that tying a tie is a science. Tie knots, we realised, are equivalent to persistent random walks on a triangular lattice. (Our day job as theoretical physicists might have had something to do with it.) Some weeks later we had derived all of the 85 tie knots that can be tied with a conventional tie. We employed aesthetic conditions---expressed as mathematical constraints---to recover the four knots in widespread use and predict nine more aesthetic ones.

All of the knots are included in this book, though it is not simply meant to instruct. Nor does it attempt to describe the tie itself, such as its colour, pattern and shape. It concerns how the tie is arranged, and this has, throughout the last three centuries, invariably involved a knot. The plain cravats of the British Regency inspired a variety of styles to express what costly fabric had before. The choice and execution of the knot has, ever since, been of prime importance to a `genteel appearance'.

Seventy years later, the tie is worn by civilised men throughout the world. The tie's silk reflects light, in contrast to the dark cloth of the plain suit. It remains the central point of a man's costume. Choosing an appropriate knot, the essential personal touch, has never been easier.

Thomas M. A. Fink (Gonville & Caius College)
Yong Mao (St. John's College)
June 1999.


Yong Mao (