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Thursday, March 4, 1999 Published at 12:36 GMT

Sci/Tech

Solving a knotty problem

Yong Mao and Thomas Fink did the research in their spare time

 BBC Correspondent Sue Nelson surveys the history of tie knots
Cambridge scientists have applied the mathematical approach to one of life's most mundane activities - putting on a necktie.

Most men are usually half asleep and have a slice of toast in one hand when they knot a piece of material around their necks first thing in the morning.

This less than diligent attitude to dressing is one possible excuse for why there are so few knots in everyday usage. There are just four main knots:

• Four-in-hand - favoured by many and requiring just four movements to complete.
• Pratt knot - starts with the tie inside out. It became fashionable in the late 80s.
• Half-Windsor - evolved from its bigger brother ...
• Windsor - a large knot, reputed to have been invented by the Duke of Windsor.

Now two physicists from the Cavendish Laboratory at Cambridge University have attempted to explain the scientific reasons behind our necktie choices.

 Thomas Fink: Likes the Four-in-hand
Thomas Fink and Yong Mao used a mathematical model known as a persistent random walk to examine the sequence of moves involved in knotting a tie.

In the journal Nature, they explain that this is a bit like the erratic progress of a drunk, walking along the street and taking a pace forward or backward at each step.

Their mathematical approach included parameters that defined the aesthetics, strength, and balance - the rhythm in the hand movements - of knot tying.

The analysis not only reveals why we knot ties in the way we do, but also predicts several new styles.

The symmetrical look

"Not only does it predict six new knots, but it predicts the four that are already in use," says Thomas Fink.

 What will this do for male fashion?
"This is a good test of a mathematical model - if it didn't predict what evidence is telling us, it would be wrong."

Realistically, given the length of an ordinary tie, the Cambridge scientists say there are 85 ways to knot a tie. However, most of these arrangements - and this is confirmed by the model - do not look right.

Symmetry would appear to be very important, says Thomas Fink, who did the research in his spare time.

 Thomas Fink and Yong Mao explain their unusual extra-curricular research project on Radio 5Live
"The sequences produced by the model are either perfectly symmetrical or quite close to perfect symmetry. So the Half-Windsor is perfectly symmetrical and the Windsor and Four-in-hand are as close as you can get."

Fink, himself, favours the Four-in-hand and another knot - as yet unnamed - which has seven moves starting with the tie inside out. He liked BBC News Online's suggestion that this be called The Cavendish.

The Cambridge team use symbols to denote the various half-turns, or moves, used in a knot. The sequence is assumed to start with the wide end of the tie being held across the narrow, shorter end (see image above). The tie can start back to front provided the wide end finishes the correct way around.

The moves involve either a u-turn away from the body (a circle with a dot) or u-turn in towards the body (a circle with a cross). The tie can be wrapped to the right (R), or to the left (L), or through the centre (C). To finish the knot, the wide end must be wrapped across the front, under and over and through the loop just made (T).

Try the ten knots predicted by the Cambridge model.