For better or worse: marriage by the numbers

It started the way many household duels do, with a casual remark. She reminded him of a weekend party they’d planned to attend, and he said he wasn’t going, he had to work. She wanted to know the real reason, got only vague replies, and finally lost patience: It’s you, she said, you have become antisocial.

That blast filled the living room for a beat or two before he confessed that, in fact, he didn’t like the party’s hostess, never had. He’d gone to her last party, and the one before that, without pouting. He was due for a break. OK?

“He remembers everything and makes mental notes,” said Monica Leahy, an apparel buyer in Los Angeles who defused this standoff by calling her husband of eight years, Robert, a name that made them both laugh out loud. “It wasn’t a big deal, and I just let it go. You learn to pick your battles, and kind of keep score of what helps and what doesn’t.”

In defiance of good sense and most love poems, people in long-term relationships do continually (if not always consciously) perform calculations, tallying up the household chores and kid errands, for instance, or estimating the risk of missing the Friday dinner versus the Saturday barbecue. So perhaps it was only a matter of time before the professionals got involved. In a new book, “The Mathematics of Marriage” (MIT Press), a group of mathematicians and a prominent marriage researcher use differential equations to help understand why some apparently fragile marriages endure and why many seemingly loving ones break up. “Instead of merely describing and predicting, we now have a precise language for understanding the dynamics of relationship interactions,” said psychologist John Gottman, one of the authors.

Gottman has been studying marital interaction for almost 25 years, by watching how couples interact in his lab at the University of Washington in Seattle. His principal coauthors include James Murray, a former professor of applied mathematics at Oxford University who has studied social interactions; and Rebecca Tyson, a mathematician at Okanagan University College in British Columbia, Canada.

The math itself is not for English majors. Employing the same principles used to describe oscillations around black holes, among other complex systems, the researchers hammer out a series of equally hairy equations. What emerges from the numbers is a familiar relationship dynamic, as changeable as the weather: often remaining balmy (or gloomy) for long periods; subject to gradual warming or cooling spells; and sometimes dashed by a sudden storm.

And it’s what the numbers say about communication that’s valuable. For instance, Gottman and Murray calculate the ratio of good versus bad signals couples send to each other when discussing an issue on which they disagree, such as money or child rearing. The good signals include positive tone of voice, smiles, jokes, any noticeable gesture of kindness or companionship. The bad ones include rolling of the eyes, criticism, mocking, perceptible coldness. According to Gottman, the couples who stay together send five times more affectionate signals than hostile ones. Those headed for breakup average closer to a 1-1 ratio.

Underlying these ratios are more fundamental communication styles. Men or women who have what Gottman calls a “validating,” or highly sensitive, style are deeply stung when their partner is critical or cold, but quickly cheered by encouragement or good humor. So-called “volatile” individuals are not so easily moved by their partner’s responses and moods; they can make a scene and then make up without being thrown much off their emotional center of gravity. On the other hand, “conflict avoiders” seem to respond only to positive cues, gestures and discussions, but tune out the dark notes altogether.

When both partners are of the same type, the relationship tends to be stable, the data suggest. That could help account for why couples who seem to be forever arguing often stay together, defying all appearances. It also accounts for those couples who thrive seemingly without ever confronting serious problems.

It’s when two partners have different communication styles that their relationship is unstable, the researchers find. “This, I think, explains the phenomenon of what has been called the ‘pursuer-distancer’ relationship, in which one person wants to discuss change and the other person wants to flee the discussion at all costs,” said Gottman.

Marriage researchers have long known that emotional mismatches can spell doom for a marriage. It’s not that an explosive, emotionally intense wife cannot make herself understood to a reserved, distant husband; usually she can. It’s that she misjudges the impact of her fits on him -- just as he misreads the effect of his silences on her. The result is that when discussing difficult topics neither person has a good sense of where the conversation is going or how to steer it emotionally. Gottman and Murray’s calculations help quantify just how devastating this mismatch is, and for whom.

“This is a real contribution to the field, to identify these styles and show why the mismatch isn’t working,” said Bernard Guerney, director of the National Institute of Relationship Enhancement in Bethesda, Md., and a leading voice in marriage research. Guerney said the new research supports some of the latest thinking on how to repair flagging marriages.

In the predominant view of psychologists who study long-term pairings, couples can improve their relations one conversation at a time precisely by making an effort to watch how their outbreaks and silences directly alter their partner’s mood and behavior. When styles are mismatched, improvement usually means that one person must learn to adapt in part to the timing, tone and style of the other -- that is, to the one whose personality is more positive by nature.

Though this sounds more like good common sense than black hole mathematics, the equations show that tipping the balance only slightly toward a more positive style can save a marriage, Gottman said.

Longtime married couples by necessity have had to learn how to do this. Barry Weisband, 48, has been giving his own communications skills a workout lately. About a year ago, Weisband left a salaried job to start his own business. Household income is tighter, and his wife, Suzie, is now the alpha wage earner. The couple has three children and, suddenly, many financial decisions to make. “I’m very much a planner; I’d prefer to sit down for an hour and talk through all this, but she has no patience for that. She does things on the move,” Barry said. In 19 years of marriage he has learned exactly when these important conversations must take place -- and where. “I know now that these things are going to be resolved at the kitchen sink; that’s where we talk about them.”

Lynn Rasmussen, a business consultant living in Maui, Hawaii, and her husband, Richard, have made it through 28 years in part by reserving their difficult conversations for times when they’re both feeling pretty good about themselves. When stressed, Rasmussen is the more volatile figure and her husband becomes cool and more avoiding. “When my husband’s in a low mood, I don’t talk about the problem child or the budget.... When I’m in a low mood, I bite my tongue, eat, take a hot bath, do the laundry -- anything but ‘communicate.’ ”

True to stereotype, researchers find, women tend to be more sensitive to moods and the ebb and flow of intimacy. In one study, psychologists had a group of graduate students living with a partner tape their conversations at the end of each day. Almost always, the woman tried to prompt conversation, by asking things like, “Anything interesting happen to you today?” or “Who’d you talk to?” or “Tell me what you’re thinking.” The men tended to go monosyllabic, parrying these attempts with a variety of grunts, “yups” and “nopes.” In the work of Gottman and others, moreover, it’s clear that very often a little effort on the part of the man can go a long way in improving a marriage.

Which is why, if not exactly bestseller material, “The Mathematics of Marriage” might by its very existence do a service to marriage, namely by showing men that relationships aren’t solely the domain of Oprah and Dr. Laura.

“I think it’s wonderful they’re bringing math into it; it’s such a male thing,” said Diane Sollee, founder of Smartmarriages.com, a clearinghouse for marriage information and research. “I mean, they might as well have named it, ‘Missiles and Marriage.’ ”