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MarriageAsaNonlinearSystem

John Gottman, who has written a number of good books on the dynamics of Marriage, has gotten more mathemetical in his approach.

See for a thought-provoking teaser.

DaveSmith 2003.04.24

KenEstes 2003.04.25

For his next project, which he calls "bringing baby home," Mr. Gottman is studying the effects of newborns on married couples' emotional equilibriums. Because these models will involve three actors rather than two, he will be able to experiment with new mathematical tools. In a declaration that will probably come as no surprise to the families in his study, he says, "Adding the baby allows you to get into chaos theory."

--DaveLiebreich 2003.04.25

The germ of The Mathematics of Marriage was a remarkable piece of luck. Around the time of the heart-to-heart conversation with his wife, Mr. Gottman forgot to send in a reply card to a scientific book-of-the-month club, and therefore received a book he'd never heard of ...

--DaveSmith 2003.04.25

I would think any system that has one or more living humans in it would have to be considered a non-linear system.

The documentary series "The Human Face" and had a segment on Gottman's research. It also had a segment Paul Ekman and the FacialActionCodingSystem. I was able to rent the series from my local video store. You can check your local library system for it too.

StephenNorrie 2003.04.28

Slashdot had a post on this book. As usual the responders are not very informative. However there is a really funny post near the bottom.

..and I thought I was nuts! (Score:3, Interesting)
by tarball_tinkerbell (664105) on Friday April 25, @01:56AM (#5806423)

I spent an hour this afternoon deriving a utility function modeling my preferences over relationships, since I know that they're unusual, discontinuous, and non-monotonic. At the end of it I was convinced I had finally, completely, truly, lost my mind, so I showed what I'd done to some friends/colleagues and they agreed.

For those who might be interested, it goes as follows:

where x = quality of man
x belongs to the set [0,1)

notice that the set of x is closed at the lower bound (since men graded 0 exist aplenty), while it's open at the upper bound (since the perfect man does not exist. This isn't sexist; I don't believe the perfect woman exists either.). Therefore x can approach 1, but never equal it.

and where p = intended level of commitment where p belongs to [0,1] with p = 0 implying no

relationship at all, p = 1 implying a ring on my left hand. Further examples: p = 0.1 or 0.2, say, imply a casual fling; p = 0.4 or 0.5 imply dating officially; p = 0.8 or 0.9 imply living together with no intention of anything more.

We have:
For p between [0,1): u(x,p) = x^p
For p = 1: u(x,p) = 2*ln(x+p)

... of course, this can just as well be written as:

KenEstes 2003.04.28

I read several of Gottman's books. He has done some really interesting scientific research. He studies married couples and records all sorts of data about them in his lab (blood pressure, heart rate, video tape), then he corrolates the data that he gets with the history of the couple (do they eventually divorce, after how long). What is neat is that after 40 years he has hard data about what predicts divorce and how to couples *really* fight. Some of his results contradict traditional marriage therapy.

One interesting result is that most of the things that couples fight about are not solvable. The couples continue to fight over the same thing for 40 years because the fights are really about personality differences and a world view then they are about the thing which is being fought about. He says that when you pick a marriage partner you are picking a set of arguments that you will have for the rest of your life so you should pick a partner who has differences which you can live with.

He has some really interesting results about emotional "flooding" where one spouses heart rate shoots way up and the neurossystems fight/fligh system kicks in. AT this point the flooded person is incapable of holding a congruent conversation and couples with marriages which work are able to defuse the situation and restart the argument. It is hard to avoid flooding since it happens fast (within one heart beat) and can be triggered by many hot bottons.

I have not made much progress in the nonlinear systems book. My differenential equations are weak and this book is abit deeper in the math then I expected. So far I have learned some catastrophe theory which I did not know before.

His really practical book is called "The seven Principles for making Marriage Work". It gives lots of advice about what couples do wrong/right. The book "Why Marriages succeed or Fail" is harder to read and apply. It contains lots of data about marriages and checklists and questionaires for you and your partner to do some selfdiscovery.

KenEstes 2003.09.29

This is a wonderful topic that you might bring up with Jean at the conference. - JerryWeinberg 2003.09.29

Jerry, is there any hope that you could read (or look at) "The Seven Principles for Making Marriage Work" before AYE? I would be interested to hear what you have to say about his results.

Here is a quote that Gottman uses often. It comes from Dan Wile in "After the Honeymoon"

 "When choosing a long-term partner . . . you will inevitably
 be choosing a particular set of unsolvable problems that
 you'll be grappling with for the next ten, twenty or fifty
 years."
 Marriages are successful to the degree that the problems you
 choose are ones you can cope with. Paul writes: "Paul Married
 Alice and Alice gets loud at parties and Paul, who is shy,
 hates that. But if Paul had married Susan, he and Susan,
 would have gotten into a fight before they even got to the
 party. That's because Paul is always late and Susan Hates to
 be kept waiting.  She would feel taken for granted, which she
 is very sensitive about.  Paul would see her complaining
 about this as her attempt to dominate him, which he is very
 sensitive about.  If Paul had married Gail, they wouln't have
 even gone to the party because they would still be upset
 about an argument they had the day before about Paul's not
 helping with the housework.  To Gail, when Paul does not
 help, she feels abandonded which she is sensitive about, and
 to paul Gails complaining is an attempt at domination, which
 he is sensitive about." And so it goes.
 

KenEstes 2003.09.30

Are you married?

SteveSmith 2003.10.03

Nope not married.

I do not own any animals either but have been reading a whole bunch about operant conditioning for animal training (clicker training, its positive reinforcement type training).

I think that all this info will come in handy some day.

KenEstes 2003.10.03

The linking of nonlinear mathematics and psychology is, of course, not new � the whole neural networks/�machine learning� thing (which utilizes nonlinear math ) came out of the work of some psychologists (Rummelhart and Mc_Clelland) in the 1980�s. My understanding is that more recent progress in machine learning has been difficult, and it�s probably because the understanding of nonlinear mathematics is still in its infancy.

Scientists (I�m a recovering scientist) generally think in linear terms � basic cause and effect. Unfortunately most of the natural world � including the mind - doesn�t seem to work that way: complex feedback loops are the norm (the �balance of nature�). Nonlinear math with just a simple feedback loop can be complex; with multiple feedback loops things get exponentially difficult. Gottman�s attempt to apply this to real-world psychology and relationships is exciting.

Maybe there are lessons in here somewhere for software development organization dynamics too?

RickHower 2003.10.23

I have been making progress with the book and am now able to tell you a bit about what "the equations of marriage" look like.

There is an equation for both the husband and wife who are having a discussion. It is assumed the wife talks first (this is both because it does not matter who starts the conversation and also because research shows that in general the wife brings up the difficult issues in most relationships) this introduces a slight asyemetry between the equations but other then that the equations are identical. The equations predict facial expressions (from Ekman see his book "emotions revealed")

First there is a drive of each person to return to a steady state. There is evidence that the steady state is related to the whole history of the marriage. Here is the equation for the wife which shows a reversion to state "a".

       W(t+1) = r*W(t) + a
       

We assume that each person has an "interaction function" I(), which depends on what the partner is doing at the previous moment.

       W(t+1) = I(H(t)) + r*W(t) + a
       

Here we see the wife both has a reversion to mean term AND and interaction with her husbands state. The difficult issue is what do we assume about the interaction function and how do we estimate all the parameters. The book focuses on what the steady states are for different models when we assume different interaction functions.

KenEstes 2003.10.23