IF CHEMISTRY is the key to a happy marriage, the secret of divorce is maths: researchers have devised a mathematical model that can predict with astonishing accuracy which couples will part.

The formula, devised by a psychologist and two applied mathematicians, allows counsellors to forecast with a 94 per cent success rate which married couples will stay together and which are likely to part, providing a powerful new tool for marriage guidance.

The set of equations can give a prognosis of marital bliss or strife after the partners have been observed discussing a point of contention, such as sex, money, child-rearing or holidays, for just a few minutes, according to John Gottman, a psychologist at the University of Washington in Seattle.

Marks are awarded for positive and negative interactions between the partners, and the ratio between these seems critical to the question of whether the marriage will last.

Jokes, flirtatious or affectionate gestures, smiles and an understanding tone of voice all win positive marks, while negative signals include behaviour such as eye-rolling, tutting and sarcasm. The “magic ratio” is five positive signals to one negative one, and any couple that scores below this is likely to be heading for trouble, Dr Gottman told the American Association for the Advancement of Science conference in Seattle yesterday.

“Before this model was developed, divorce prediction was not accurate, and we had no idea how to analyse what we call the masters and disasters of marriage — those long-term happily married and divorced couples,” Dr Gottman said. “When the masters of marriage are talking about something important, they may be arguing, but they are also laughing and teasing and there are signs of affection because they have made emotional connections.

“But a lot of people don’t know how to connect or how to build a sense of humour, and this means a lot of fighting that couples engage in is a failure to make emotional connections. We wouldn’t have known this without the mathematical model. It gives us a way to describe a relationship and the forces that are impelling people that we never had before.

“The maths is so visual and so graphical that it allows us to visualise what happens when two people talk to each other.” The study, in which James Murray, a British mathematician at the University of Washington, played a part, is the first to introduce rigorous mathematics into psychology in a manner that may be clinically useful. “When Newton invented calculus it put science on a mathematical foundation and physics really took off,” Dr Gottman said. “But psychology is a field that has lagged behind in using mathematics and there is no maths in social psychology.”

Dr Murray, who has been happily married to his wife, Sheila, for 40 years, said: “What we did is extract key elements into a model so that it is interpretive and predictive. The mathematics is trivial, but the model is incredibly accurate.”

The study on which the model is based involved 700 newly married couples in Seattle, who were observed soon after their weddings and throughout the next 10 years.

The couples who took part in the experiment were not told their results.

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