27 January 2000
Nature 403, 362 (2000) © Macmillan Publishers Ltd.
Why not knot right?


Gregory Buck is in the Department of Mathematics, Saint Anselm College, Manchester, New Hampshire 03102, USA.

The 85 Ways to Tie a Tie: The Science and Aesthetics of Tie Knots
by Thomas Fink Yong Mao
Fourth Estate: 1999. 144 pp. £10

There is a little irony in the fact that I am reviewing this book. I am a modern American mathematician, well-schooled in the sartorial traditions of my field, and so would perhaps be a natural reviewer for a book entitled The Well-Wrinkled Tee Shirt or, perhaps, Wearing Sandals in the Snow. However, I teach at a liberal arts college, and so can wear a tie while teaching when I want to without risking my mathematical reputation — of course, for conferences I pull my clothes out of the bottom of the dirty-laundry pile like everyone else. (My colleagues in the economics department scoff at my tie-wearing, considering it too infrequent to be taken seriously, but they are extremists — I am pretty sure they wear ties with their pyjamas.) I have always liked tying ties, but, despite the fact that I study knot theory, like most people my tie-knot knowledge was cultural and accidental. I knew a couple of tie knots but not their names, nor could I recall where or when I learned them.

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.

To accomplish this remarkable feat, Fink and Mao have employed the analytical tools of topological (and geometric) knot theory and statistical mechanics with cleverness and dexterity — introducing just enough of each to get the job done. That may sound ambitious, but this is a book aimed at the general reader. A beautifully concise, four-page appendix contains the only mathematics that could be considered challenging. The illustrations are superb — I tried nearly all the knots illustrated and got them right first time. The notation for the knots is elegant and easy to master.

The scientific force of the work is that Fink and Mao have created a formal model that captures the salient characteristics of tie-knot tying in the real world, and have then analysed the formal model, guided by the scientific lights of simplicity and symmetry, and have solved the problem completely, identifying the 85 ways to tie a tie (given natural constraints). Their model predicts the knots most commonly used, and provides several new possibilities.

Fink and Mao have obeyed the imperative of the scientific entrepreneur: create a niche, and then fill it completely. This book is now the definitive work on tie knots, and as such is the definitive work on one of the most common applications of knot theory (and therefore of topology). The applications of knot theory are legion: a test tube of DNA may contain billions of knots, but sometimes they are hard to see. Polymers in general may gain many of their characteristics from tangling, knotting and linking, but this may not be apparent when you are holding the material in your hand. Magnetic field lines are often knotted, linked or otherwise entangled, but one doesn't often observe this on the way to the market. But now imagine the morning dressing routines around the world — imagine how many tie knots are tied in a day.

Finally, we must consider the stylistic force of the work. Fink and Mao provide an informative history of tie-knot evolution. They also provide much more — a guide to taste in knot tying. An attentive reader will learn which knot works best with a given tie and collar, and will learn tie knots that can be enjoyed as things of beauty in and of themselves (for me it was the Plattsburgh). Fink and Mao have shown that it is possible to be both smart and smart — in brains and style. And so here is a prediction: anyone who wears a tie, who is at all of a scientific bent, will enjoy this book very much.