| 27 January 2000 |
| Nature 403, 362 (2000) © Macmillan Publishers Ltd. |
GREGORY BUCK
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.