One plus one equals a couple? Mathematical formula reveals the secret of a happy marriage

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After decades of thinking that the secret of a happy marriage lies in looks, lust or lucre, it seems that marital success is dependent on something altogether more calculating - a mathematical formula.

After decades of thinking that the secret of a happy marriage lies in looks, lust or lucre, it seems that marital success is dependent on something altogether more calculating - a mathematical formula.

An Anglo-American team of psychologists and mathematicians unveiled research yesterday which they claim allows them to predict, with 94 per cent accuracy, whether a bride and groom will remain happily united or are heading inexorably for the divorce courts.

The study of some 700 young couples over 10 years has enabled the scientists to deconstruct what exactly goes wrong when a relationship is heading for the rocks.

By observing the interaction between a newly married husband and wife during a 15-minute conversation on a delicate subject - usually sex, money or children - the scientists have devised a scoring system for body language and verbal responses which indicates whether they will stay together.

Physical signs such as pulse rate were taken into account as well as emotional appearance and tone of voice. Rolling eyes, mockery and criticism produced negative scores whereas jokes, smiles and affectionate gestures scored positively.

James Murray, the British-born professor of applied mathematics at the University of Washington in Seattle, who co-authored the study, said that despite the apparent difficulties of translating something as complex as a human relationship into a string of Ws, Hs and parentheses, the results were extremely reliable.

He said: "What we did is extract key elements into a model so that it is interpretive and predictive. The mathematics we came up with is trivial but the model is astonishingly accurate."

The publication of the research, unveiled at the annual meeting of the American Association for the Advancement of Science in Seattle, the world's biggest science conference, coincided with new figures which show couples in Britain are waiting longer in life to tie the knot than ever before.

The Office for National Statistics said the average age of men marrying for the first time in 2002 was 30.9, while for women it was 28.7. In 1991, the median ages were 27.5 for men and 25.5 for women.

The divorce formula - described as a "Dow-Jones Industrial Average for Marital Conversation" - is based on painstaking analysis of hundreds of conversations between couples videotaped by the research team, led by John Gottman, professor of psychology at the University of Washington in Seattle.

Professor Gottman, who has been married for 40 years, said the basis of the calculations was the ratio of positive to negative "interactions" between a couple. "Before this model was developed ... we had no idea how to analyse what we call the masters and disasters of marriage - those long-term happily married and divorced couples."

When the number of positive interactions for each single negative score fell below five to one then the marriage was in trouble, the scientists found.

Professor 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."

The model could be used to help couples identify early in their marriage what could go wrong, allowing therapists to devise "micro-experiments" to help strengthen relationships.

Professor Gottman said: "It gives us a way to describe a relationship and the forces that are impelling people that we never had before.

"The math is so visual and graphical that is allows us to visualise what happens when two people talk to each other."


The following questionnaire is designed to test whether there is enough positive interaction in your marriage. Score your responses to each of the statements from one to five - one for strongly disagree, two for disagree, three for neutral, four for agree and five for strongly agree.

1 I sometimes get ignored when I need attention the most

2 My partner usually doesn't have a clue about what I am feeling

3 I often have difficulty getting a meaningful conversation going with my partner

4 I get mad when I don't get the attention I need from my partner

5 I often find myself becoming irritable with my partner

6 I often feel irritated that my partner isn't on my side

7 I have trouble getting my partner to listen to me

8 I find it difficult to get my partner to open up to me

9 I have trouble getting my partner to talk to me


Statements 1-3

Less than eight: You are direct in your relationship and have a healthy ability to state clearly what you need from your partner. Eight and above: You may be too reticent. Your partner may feel they have to be a mind reader to understand what you need.

Statements 4-6

Less than eight: You are not overly forceful in expressing your needs. This makes it easier for your partner to hear and understand your needs.

Eight and above: You may be expressing so much anger that you are pushing your partner away.

Statements 7-9

Less than eight: You have a high level of trust in your relationship.

Eight and above: You may need to do more to win your partner's trust. This could be achieved by concentrating more on responding to your partner's attempts at interaction rather than trying to get your partner to respond to you.

Based on marriage research by Professor John Gottman. Source: