News in Science

Tie One On

We humans invented the useless object that men sometimes wear around their necks, the neck tie, a few hundred ago. But by early 1999, humans had come up with only four knots for ties. They were the easy-to-use Four-in-hand Knot which is used by school boys, the Windsor Knot supposedly invented in the 1930s, the smaller half-Windsor Knot, and the Pratt Knot, which was unveiled with great ceremony in 1989 on the front page of the New York Times.

Two scientists decided not to wait another half-century for the New York Times to reveal the next tie knot, but went out looking for it via mathematics - and they uncovered 6 new ways to knot your tie.

The modern neck tie is supposed to have popped into existence around 1668, after the 30 Years' War that ran from 1618 to 1648. Louis XIV had some mercenaries, Croatian army soldiers, presented to him while they were visiting Paris. He was impressed by the scarves that they wore around their neck, and had knotted into a cravat. In fact, the word "cravat" probably comes from the word "Croat". The cravat began to turn into the modern neck tie around 1710.

Many of the great revolutionaries of the 20th century refused to wear ties, to show that they were at one with the Working Classes whom they were trying to liberate. So both Stalin and Mao wore clothing that buttoned all the way to the neck - with no hint of a tie. It looked as though Fidel Castro would never wear a tie, either. But in 1998, the Pope visited Cuba, and Fidel went straight and abandoned his famous Castro suit, and wore a conventional business suit and tie.

When you think about it, a tie is pretty useless - after all, the buttons on the collar do a perfectly good job of holding the collar closed. But some people think that the tie is the only way men can express their inner feelings, humour and imagination - which used to mean a red power tie, but nowadays means a yellow power tie with blue spots. There are some circumstances, professions, roles and occasions where a tie simply has to be worn, and of course, you can always give a tie as an emergency gift.

But how do you invent a new knot?

Our scientists were Thomas M. Fink and Yong Mao, from the Cavendish Laboratory in Cambridge in the United Kingdom. They developed a mathematical model of how to knot your tie.

There's an infinite number of moves that you can do to that strip of cloth that we call a tie. Infinity is way-too-big a number to handle easily, so our scientists threw in a few limits, or constraints. Now a tie has a wide end which you wrap around the narrow end.

The first constraint was where you could send the end of the tie, as you made your knot.

You can do three things with the wide end of the tie - you can send it to the right, to the left, or to the centre. And of course, once the wide end of the tie is (say) in the centre, you can't send it to the centre on the next move - you have to first send it to either the left or the right.

The second constraint is that you can send the wide end of the tie either away from your body, or towards your body. Every sequence of tying a knot has to alternate between the wide end going towards the shirt or away from it.

You don't want to have the knot in your tie as big as an orange, so Fink and Mao limited their number of wraps to nine - another constraint. Now here's another aesthetic constraint - they wanted the tie knot to look roughly symmetrical, so they had an equal number of left and right moves.

Here's a few more constraints. The last move in knotting-the-tie has to finish off with the wide end both coming from the centre and away from the shirt.

Using these constraints, they found some 85 knots that you could use for your tie. Some of them looked awful. But they re-discovered the four knots that are commonly used - and introduced "six new aesthetically pleasing knots".

Oscar Wilde said "a well tied tie is the first serious step in life". Well, now you've got six more ways to get serious.

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