The calculus of coitus: A new book explores "The Rule of 12 Bonks" and other mathematical equations that help explain sex and relationships. (Salon.com):

To make sense of love and life, the 30-year-old Australian mathematician instead turns to hardcore mathematics and mind-bending equations.

In her breezy new book, "Mathematics and Sex," Dr. [Clio] Cresswell attempts to show that this dreaded discipline is more scintillating -- and more relevant -- than most of us ever dreamed. The book presents current mathematical research that can be used to answer questions like: How will we know when we've found "the one"? How much should individual partners compromise in a relationship? Who has better orgasms, men or women? Cresswell also uses mathematical equations to show how dating services work and why most people will end up happier if they actively proposition as many desirable partners as possible....

How did you ever think to connect mathematics and sex?...

While doing research, I came across these interesting equations that used math to figure out how much one should compromise in a marriage. These mathematicians took couples, observed their emotional responses to each other, and used similar prediction techniques to chart their relationships and to calculate whether the couples would stay together or break up.

I found these equations fascinating. When I brought them up them in my public speaking engagements, people would invariably laugh, but they'd also ask me more about the equations after the lecture. When I told a friend about this, he suggested that I see if there were more equations like them out there. I said no way -- I was sure it was just a fluke. But when I started researching the area of math and relationships, I found quite a bit of research.

It sounds like you and other mathematicians have figured out the secret to happiness with another person. So, fill us in!

Psychologists John Gottman and Catherine Swanson, and the mathematician James Murray [all from the University of Washington] looked at newlywed couples interacting for 15 minutes, and charted their body language and positive/negative reinforcement. They used techniques that are often used to analyze the stock market to help them analyze happiness and grumpiness. They found these negativity thresholds: Some people express their negativity as soon as they feel it, others hold it in and try to "empathize" for as long as possible with their mate. Gottman and the rest found that the couples that had a low negativity threshold, that expressed their negative feelings straightaway, had a better chance of success. They were still married six years later. The other couples, those who made more of an effort to empathize and stay quiet longer, were less successful. Most ended up divorced.

[I'm including an article on John Gottman's research after this interview.]

That's totally counterintuitive.

Yes. These days, there's a lot of talk about empathy: If your partner is doing something wrong, you should try to understand where they're coming from, you should look at their background, their childhood. The math I saw showed that this might actually be a bad approach. What works, according to the math, is when couples are quick to say, "You know, when you do that, that really gets on my nerves!" This coincided with what some psychologists have found: When couples have high standards and stick to them by complaining when things aren't going right, that might actually be a positive thing for the couple. It makes them strive towards these high standards. When members of the couple empathized and kept giving in, they lowered their standards.

Did you write this book to make mathematics more sexy, or to make sex more mathematical, more logical?

It saddens me that society has painted math in such a negative way. Many people miss out on the wonders of mathematics. This book just seemed like the sort of "Sex and the City" style way to try to bridge that gap, to make people realize that math can be fun. And I thought that the whole concept of math and sex, the pairing of the two, was just so funny!

I'm not much of a math person. Help me understand the mathematician's approach to understanding love and sex.

OK, ready? A mathematician would choose a subject -- like love -- and would start thinking, "I think there may be patterns that arise from this subject of love." We would then ask ourselves, "What are the key factors that go into love?" That's where we start by making an abstract move: We have to write the problem into abstract mathematical notations. For love, we might have two people. We might call these people X and Y. Then we would ask, "How are these two people going to interact?" We'd create sample equations with X and Y. For example, we might create one equation predicting that X and Y would fall in love, and then suddenly hate each other the next day. There are obvious patterns to human interaction, so we'd test equations to see what looks right what doesn't look right, what matches what we've observed in the real world and what doesn't. We might prepare an equation, plug in variables, and then say, "Hmmm, that equation may be mathematically correct, but the chance of that happening in the real world is highly unlikely." So we'd pick another equation.

We'd play with different equations and different mathematical analyses to tell us what people are doing in real relationships. In picking equations we'd come across patterns. We may start to see patterns that we may not have noticed otherwise. These patterns may show us things about relationships that we may not have seen or expected.

Like what?

In our love example, our mathematician might say, "People's emotions for each other will oscillate, then calm down in to a strong bond." If we want to take this even further, we may show our equations to psychologists for another opinion, and they may respond, "Well, that's exactly what we've observed!" Then we mathematicians will think to ourselves, "Clearly, we're on to something."

It sounds like, contrary to popular opinion, mathematics is not done in a vacuum. There's always an interplay between math and real life, between what mathematicians observe happening in the tangible world around them, and the patterns they create in the lab.

That's exactly right. People think that math is completely separate, but in my opinion, math is a form of expression. Math is just another way of making sense of the world, like dancing or writing.

So, in order to create order out of chaos, mathematicians assign people and their behaviors symbols, and try to create equations where behavior tends to be predictable?

Yes, and because we're using the abstract variables to try and understand these patterns, it helps us look at the patterns in a different way. It gives us a fresh understanding of how individual elements work together.

Can you explain one of the juiciest equations in the book, "The Rule of 12 Bonks"?

This math helps us answer the question, "How many partners should I have before I settle down?" The background is quite interesting: Despite high divorce rates, when it comes to falling in love, we refuse to take advice. If you were buying a DVD player and you were told there was a 50 percent chance it would break down, you would really think hard before buying it, wouldn't you? You certainly wouldn't buy the first one you came across, and you would probably ask advice from friends. It seems like when it comes to marriage, we're acting all crazy. This mathematician [Peter Todd from the Max Planck Institute for Psychological Research in Germany] said, hold on, maybe there are some mathematical equations that make us act this way. He thought, in this borderless world where we have an almost unlimited number of potential partners, how many partners should we test before we settle down? The math showed a very revealing pattern. If you use this simple rule, it will give you very good results: Test a sample of 12 partners. Then, after you get to 12, continue testing but take the next best partner that comes along (it could be partner number 13 or partner number 40). Todd found that doing this will give you a 75 percent chance of picking someone with the qualities that you want.

Of course, we can't rely upon mathematics to tell us what those qualities are, right? We have to make up our own list of criteria.

That's right. And mind-blowing sex doesn't even have to be one of them. In fact, you don't really need to sleep with 12 partners -- you could be dating platonically, I suppose. But you need to have 12 relationships with 12 partners. I called it the "Rule of 12 Bonks" rule because it's a reflection of my cheekiness. I'm modern woman in a modern world and sex needs to be one of my criteria!

What about all those people in relationships who aren't even close to their 12th partner? Should they dump their current partner and keep looking, just to be sure?

No. This strategy promises a 75 percent chance of success. It's not foolproof. These people could very likely be in that lucky 25 percent. There are some people that would find true love with Number 3, and other who would need to go up to Number 105.

But it's still interesting that this is such a simple strategy. Back in the '80s, a popular idea in mathematics was that our brains worked with strict mathematical rules, and if we could only create a computer to replicate these rules as fast as possible, we could feasibly replicate human thinking. Now they're thinking that our brains actually work with a bunch of very simple strategies that don't always get perfect results. This "12 Bonks Rule" is one of them.

When I tried to understand the equations, I couldn't even figure out what the symbols meant. Why didn't you include a glossary of symbols?

You know what's interesting? A number of American publishers asked for more math, they wanted me to break things down as much as possible. Honestly, that made me laugh. First of all, there are thousands of math books in the library. And no one is reading them! As an author, I thought that no one would want to hear about the hardcore math. I thought that my job was to create the link between math and sex, to make math more interesting in that way. Who would know that readers would want more math?

It's important to realize that to show the background and explanations for those equations would take another whole book. That work is very complicated. Some of the math that I talk about -- you would need a Ph.D. to understand it. I didn't want to bog the reader down. As for a glossary, if I had included one, the book would be twice the size it is now.

So, I have to ask: Have any of your mathematical strategies helped you in the bar or the bedroom?

Yes, the part about the ups and downs of love in the first chapter. [In this section of the book, Cresswell discusses the work of Steven Strogatz, now a professor at Cornell University, who reworded a common undergraduate mathematics problem to explain the evolution of Romeo and Juliet's love affair. Strogatz shows that Romeo's love depends on Juliet's responses, and vice versa.] The whole idea that when you fall in love you have this horrible experience of an emotional roller coaster -- that helped me understand what I've felt in the past. It helped me deal objectively with those yucky parts -- the anxiety, the nervousness, the self-doubt -- and to remind myself that I'm just going to have to get through it.
___________________________

Marriage by the numbers

Compatibility ratio can predict which couples will make it---and which will end up splitting

BY A.J. HOSTETLER
Richmond Times-Dispatch
April 22, 2004

SEATTLE -- To master your marriage, do your math.

Connubial relationships can be figured, says a psychologist who uses math to discern who will remain together and who is heading toward divorce. Numbers can reveal ways for spouses to make their wedded bliss last.

The underlying secret is the ratio 5:1, said John Gottman, an emeritus professor of the University of Washington and director of the Relationship Research Institute in Seattle. Successful spouses share at least five positive interactions - such as bestowing a smile, compliment or humorous quip - to counter every scornful comment, condescending sneer or dramatic eye-rolling.

"Relationships that are working well are very rich climates of positive emotion," Gottman said, describing his research at the "Love Lab" at a recent meeting of the American Association for the Advancement of Science. (Another hint, this one for guys only: Allow yourself to be influenced by your bride's opinion. Turns out she already does the same for you, so give a little.)

Math offers a powerful new tool to provide insight into matrimony, said Gottman, who has studied its inner workings for more than 30 years and who is now studying how the math - created by applied mathematicians across the University of Washington campus - can improve marital counseling.

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

"If you can understand what makes a relationship tick, you can help make it better," said University of Washington mathematician Kristin Swanson, a co-author with Gottman and fellow number-cruncher James Murray on the book "The Mathematics of Marriage: Dynamic Nonlinear Models."

The model has been tested with about 700 couples involved in seven studies who were followed for as long as 15 years. It accurately reveals marital stability in about nine of 10 couples, and is nearly 100 percent accurate in spotting couples headed for divorce within four years, Swanson said.

The compatibility ratio is based on the videotaped interactions of hundreds of couples. When interpreted as a line graph, the ratio produces what Gottman called a "Dow-Jones Industrial Average for marital conversation."

Like the stock market average, a line graph following the twists and turns of a couple's discussion jiggles around. The couple's line generally rises over time if the marriage is bullish. Just as for a bear market, a descending line indicates harder times for the marriage.

"The math is so visual and graphical that it allows us to visualize what happens when two people talk to each other," Gottman said.

Virginia Commonwealth University psychologist Everett Worthington, however, cautioned that marriage is more complex.

Worthington, who studies forgiveness within relationships and is familiar with Gottman's work, said marital success no more rests on a ratio than a quickie diet is the key to dropping 10 pounds.

"Couples who are happy with each other . . . they're going to have a lot more positive interactions than negative," Worthington said. "The positive interaction, though, is not . . . where the action is. That's just the measure. It's the attitudes beneath that 5-to-1 ratio that are the causal agents here."

Swanson acknowledges that the ratio is a crude comparison. The more sophisticated details about a couple's wedded attitudes and interaction are examined in the mathematical modeling the applied mathematicians worked out, she said.

The ratio is based on the interactions of Seattle-area couples who were videotaped in the Love Lab while discussing a contentious, solvable issue for 15 minutes.

Trained observers scored the videotapes, carefully ticking off examples of behavioral and emotional interchanges. They watched for facial movements, such as an arched eyebrow, rolling eyes or a smile. They listened for verbal comments indicating anger, empathy or humor. They clocked heart rates and gathered other physiological data as the couples sparred.

They also noted how much one spouse could influence the other's opinion. They checked whether a positive statement ("hey, that's a good idea!") elicited a positive response ("let's work on the solution together") or a negative reaction ("you're an idiot") from the spouse.

Individuals scored points for positive interactions, while negative ones lowered the ratings. The scores were tracked throughout the conversation and plotted over the course of the 15-minute debate.

When the spouses' results are combined, the direction of the line graph up or down and its steepness depicts a marriage likely to last, one headed swiftly toward divorce or one grinding through a long, drawn-out dissolution.

A line sharply angled up means the couple has a high ratio of positive interactions to negative ones. These are Gottman's "marriage masters."

The "marriage disasters" lines swiftly descend, falling to a dismal ratio of less than 1:1.

Dissension doesn't necessarily mean splitsville, Gottman said. The marriages of couples who listened to each other or in which both partners avoided confrontation could endure. Contempt turned out to be the best predictor of divorce.

"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," he said.

Couples got into trouble when they were mismatched - when a hostile avoider married someone hostile who sails into conflict.

Typically, couples who attacked each other divorced after nearly six years, while couples who were emotionally distant divorced a little more than 16 years after marrying.

"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," Gottman said.

The ratio held up across other studies whether couples were newly wed or just celebrated their 35th anniversary, according to Gottman. There's "an enormous amount of stability to marital interaction," although people can and do change, he noted.

The graph can be used to recommend ways for couples in counseling to improve their marriage. For example, one partner could try to respond more positively to the other, Gottman said.

To learn what else the videotaped discussions could uncover about marriages, Gottman sought out Murray about 10 years ago after learning about his work in mathematical biology. Swanson, then a graduate student, joined the project later.

They returned to the data gathered from the ratio studies to develop a mathematical model of social interaction in a marriage to predict its stability.

From Gottman's observations, Murray generated a pair of equations of the kind used to describe phenomena that change over time, such as weather forecasting. The equations - much like you'd see in high school algebra - are then plotted on a graph to examine spouses' influence on each other's mood, the most powerful factor, and compatibility.

On one side of the first equation is what the wife's going to say the next time and on the other side are the contributions from the husband, how he influences her and how easy it is for her to change her mind. The second formula is the equivalent for the husband.

"Very simply, the model is just, 'How much am I influenced by myself versus how much am I influenced by my partner,'" Swanson said. "If I'm happy now, how much happier will I be in the next step?" and "If I'm happy right now and my partner is unhappy right now, is this going to drag me down?"

The equations converge as two intersecting lines in the area known as the relationship's "steady state," the emotional state of the couple when they're arguing and being themselves.

Happy couples' steady states are in the positive quadrants of the graph, while couples in trouble meet in negative quadrants. The graph provides a kind of spatial map of what's happening in the marriage, Swanson said.

Spouses in negative quadrants can be shown that a little nudge to the graph, a change in their interactions and the direction in which they push the conversation, can move their "steady state" to a more positive zone, Murray said.

Husbands - and it is usually the husbands, he said - can see how their marriage could change if they become more flexible, allowing their wives to influence them. A wife can learn how her negativity pulls the relationship into negative zones.

One positive interaction leads to another and the relationship strengthens.
The trio learned from the model that couples who behaved in a certain fashion stayed together or didn't.

"That was the thing that was interesting," Swanson said. "It wasn't saying, 'what is the distinguishing feature of this divorced couple versus this happy couple,' so much as, 'couples in general act in this way.' It turns out that the model tells you that the couples that last the longest time are the ones that have the matched style of interaction."

The model is not something for couples to try at home, although Gottman encourages people to try to be more positive in their interactions as a way to improve their compatibility ratio.

Murray said he can teach the math behind the equations to high school students in a half-hour. It's not difficult; just a numerical way to portray how partners influence each other over the course of conversation and discover the marriage's likely fate.

"The mathematics we came up with is trivial, but the model is astonishingly accurate."

Marriage Tips [also in John Gottman's book The Seven Principles for Making Marriage Work, which I own]:

• Seek help early. The average couple waits six years before seeking help for marital problems - and half of all marriages that end do so in the first seven years.
• Edit yourself. Don't say every angry thought you have when discussing touchy topics.
• Soften your "start up." Avoid escalating a conflict by making a critical or contemptuous remark in a confrontational tone.
• Accept influence. Guys, a marriage succeeds to the extent that the husband accepts influence from his wife.
• Have high standards. The most successful couples are those who refuse to accept hurtful behavior from one another.
• Learn to repair and exit the argument. Successful couples know how to exit an argument and happy ones repair the situation before an argument gets completely out of control.
• Focus on the bright side. A good marriage has a rich climate of positivity.

Source: John Gottman, the Relationship Research Institute

Don’t Try This At Home

To a math lightweight, this equation might communicate about as much as a wife talking to her husband while he reads the paper. But our sense of journalistic integrity compels us to present here the full "Will This Marriage Work?" equation. Good luck.

Wife's equation

Wt+1 = a + r1 Wt + IHW (Ht)
W = wife
H = husband
t = time
a = a constant representing the wife's state of mind when she is not with husband.
r1 Wt = represents the ease of changing wife's state of mind when she is talking with husband.
IHW = "influence function," a measure of the influence of husband's remarks on wife.
Ht = husband's score during their 15-minute conversation.
t+1 = how wife reacts to husband's conversation; the higher the number, the greater the likelihood of divorce.

Husband's equation

Ht+1 = b + r2Ht + IWH (Wt)
b = a constant representing husband's state of mind when he is not with wife.
r2Ht = represents the ease of changing husband's state of mind when he is talking with wife.
IWH = "influence function," a measure of the influence of wife's remarks on husband.
Wt = wife's score during the 15-minute conversation.
t+1 = how husband reacts to wife's conversation; the higher the number, the greater the likelihood of divorce.

Source: Gottman, Murray and Swanson