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It all adds up: Mathematical model shows which couples will divorce


There are no general laws of human relationships as there are for physics, but a leading marital researcher and group of applied mathematicians have teamed up to create a mathematical model that predicts which couples will divorce with astonishing accuracy. The model holds promise of giving therapists new tools for helping couples overcome patterns of interaction that can send them rushing down the road toward divorce.

Psychologist John Gottman and applied mathematicians James D. Murray and Kristin Swanson will describe how the model was developed and how it enables Gottman to predict with 94 percent accuracy which couples will divorce after viewing just the first few moments of a conversation about an area of martial contention. They will discuss their work today at a press briefing during the annual meeting of the American Association for the Advancement of Science in Seattle.

"When Newton invented calculus it put science on a mathematical foundation and physics really took off," said Gottman who is a University of Washington emeritus professor of psychology and director of the Relationship Research Institute. "But psychology is a field that has lagged behind in using mathematics and there is no math in social psychology."

Murray, who is an emeritus professor of applied mathematics at the UW and Oxford University, agreed, noting that a lot of people are phobic about mathematics and that psychology has not been exposed to models.

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

The model was developed using data collected from hundreds of videotaped conversations between couples in Gottman’s laboratory. Physiological data, such as pulse rates also was collected and analyzed. The conversation reflected underlying problems the couple had and that is why the model is so predictive, according to Murray.

"Before this model was developed divorce prediction was not accurate," Gottman added, "and we had no idea how to analyze what we call the masters and disasters of marriage – those long-term happily married and divorced couples."

The key turned out to be quantifying the ratio of positive to negative interactions during the talk. The magic ratio is 5 to 1, and a marriage can be in trouble when it falls below this. The mathematical model charts this interaction into what the researchers call a "Dow-Jones Industrial Average for marital conversation."

"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," Gottman said. "But a lot of people don’t know how to connect or how to build a sense of humor, 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 math is so visual and graphical that it allows us to visualize what happens when two people talk to each other."

It also is allowing researchers to simulate what a couple might do under different circumstances. For example, the model permits them to see what happens if a behavior changes, say a husband allowing himself to be influenced by his wife, and how that increases the number of positive interactions. Ultimately, this will allow therapists to do micro experiments with couples to strengthen their relationships, he believes.

Gottman, Murray and Swanson, who is a UW research assistant professor of pathology and adjunct research assistant professor of applied mathematics, also will participate in an AAAAS symposium on the science of love and marriage that runs from 11 a.m. to 12:30 p.m. Saturday.

For more information, contact Gottman at (206) 832-0300 or; Murray at (206)-842-3909 or; Swanson at (206) 221-6577 or

Joel Schwarz | EurekAlert!
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