How it all adds up
A researcher in Seattle says that how couples interact and whether they stay together or divorce can be predicted mathematically:
In The Mathematics of Marriage: Dynamic Nonlinear Models (MIT Press), which he wrote in collaboration with four mathematicians, Mr. Gottman uses the tools of calculus to describe the interactions of couples like Angie and Dave. The models presented in the book, he says, offer insights into the heaven and hell of couplehood that he would never have found by sifting through his data with standard linear statistical tools. He has already begun to apply those insights in his therapeutic work -- including with Angie and Dave themselves, whose conversations are transcribed in the book.
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Both "validating" couples and "conflict avoiding" couples tend to have marriages that are stable and long lasting. Couples are in trouble, though, when they have mismatched influence functions. Consider the "hostile detached" couple, where the slopes for the husband's and the wife's influences look very different. When the husband behaves positively, he has almost no impact (slope of 0.02) on his detached wife.