A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution

The Reseach Article:

Abstract

Background

Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough.

Methodology/Principal Findings

Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics.

Conclusions/Significance

These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.

They haz graphs:

[atsimg]http://files.abovetopsecret.com/images/member/13bc0e514fc2.png[/atsimg]

[atsimg]http://files.abovetopsecret.com/images/member/c5f16d2d9e21.png[/atsimg]

[atsimg]http://files.abovetopsecret.com/images/member/8c9f525e3283.png[/atsimg]

[atsimg]http://files.abovetopsecret.com/images/member/71a3abcde30b.png[/atsimg]

What do the graphs mean?

The model produces a plausible scenario, through a sequence of effort inattentions, for the deterioration of a relationship in a gradual form, which seems to be typical according to data. Because of the effort gap, there is a tendency to lower the right effort level. Then the intrinsic instability of sentimental dynamics obeying the second law causes the piecewise decaying trajectories to move further and further away from the target trajectory and eventually to cross the threshold level xmin. This is considered a point of pre-rupture, since it is a matter of time before effort is abandoned.

In conclusion ... this is what happens when mathematicians and statisticians try to figure out why their marriage failed. Presumably not realizing that spending this much time and effort on a paper such as this might be the actual reason. It's a self feeding mechanismz.

Seriously though, I am shocked at the amount of work that went into this.

Anyone can make sense of it?

Is this true?

Closing remarks

The mathematical theory introduced in this paper unveils an underlying mechanism that may explain the deterioration and disruption occurring massively in sentimental relationships that were initially planned to last forever. Two forces work together to ease the appearance of the deterioration process. First, it happens that since an extra effort must always be put in to sustain a relationship on the successful path, partners may relax and lower the effort level if the gap is uncomfortable. Then instability enters the scene, driving the feeling-effort state out of the lasting successful dynamics.

A further significant finding is the fact that partners construct and perceive their relationships as definitive projects is compatible with the evidence that their union may probably fall apart –which is typical in the model dynamics. This dismantles the failure paradox, accounting for probable couple disruption as a gravitational consequence of the second law under optimality.

The model analysis may offer advice to partners about how to keep a long term relationship afloat. Lasting relationships are possible only if the effort gap is tolerable and the optimal effort making is continuously watched over to stay on the target dynamics. A realistic lasting relationship, when the effort gap is satisfactory, may be described by a trajectory travelling near the stable branch for a while and then wandering near equilibrium alert at keeping effort at the right level. These kinds of relationships are seen often enough although they may appear exceptional. This is consistent with the exceptionality of durable successful relationships within the model.

Two apparent facts serve as a first test to validate the theory proposed in this paper: (i) the model formulation builds on accepted evidence (namely, the second law and the intention of couples to design their relationships to last forever) and (ii) the mathematics of the model shows consistency with further empirical facts on divorce and separation, namely the typical progressive deterioration of failing relationships (which is claim #3 in section 2) and the decrease of well-being after marriage (claim #4 in section 2). Further research to validate the model should address testing –in a lab experiment or a field survey– the two main findings of the theory, i.e. the existence of the effort gap and the unstable nature of feeling-effort dynamics.

The pessimistic conclusions for couple durability should remain valid in a less ideal scenario as long as the formulation of the second law is considered valid. More realistic assumptions like (weak) heterogamy, presence of external shocks or sub-optimal behaviour, probably enter the scene as contributing factors enforcing instability. The effort gap plus the unveiled instability identify an essential intrinsic mechanism for probable sentimental failure.

[edit on 20 Apr 2010 by schrodingers dog]

Well, in my book, science is unable to explain "love" or relationships. They can do all the research they want, the will never come up with plausible conclusions for love is a vibrational status that cannot be measured or explained by scientific means.
Interesting post by the way, and well presented. Thanks!

Originally posted by lagenese
Well, in my book, science is unable to explain "love" or relationships.

Agreed ... though I can't shake the image in my head of some guy showing this paper to his soon to be ex-wife as to why their marriage failed. "Honey honey, look at the graph ... that's where we are!" I presume a good whipping would shortly follow her initial confusion.

I just find their stated "love is not enough" premise as surreal in scientific terms.

I had to look several times to make sure that they weren't pulling our legs.

They're not, they're serious.

Alright, I'm a smart guy and all..

No really..

This however, completely over my head.

Are they trying to quantify or figure out mathematicaly why relationships or marriages fail?

Or how to quantify love?

It's a lot of work it seems and is probably quite interesting if I understood what's happening.

At least the pictures were pretty...

~Keeper

Hmm, those graphs could very well be a diagram of my thoughts when my ex-wife was talking on and on about a pair of shoes she saw that she just had to have and should she go back to get them ot wait and see if they went on sale or...............

Social dynamics being given graphical and by virtue of percieved proprietary maths validation for lack of any other relevant data.

These guys are fired until they can mathematically define neuronal evolution and explain it in laymens terms...

Originally posted by MemoryShock
Social dynamics being given graphical and by virtue of percieved proprietary maths validation for lack of any other relevant data.

Some of this isn't their fault ... a man can only take so many wedgies before he snaps.

These guys are fired until they can mathematically define neuronal evolution and explain it in laymens terms...

Right after they figure out and write their follow paper on why women "don't get them" ...

They do say under Methods:

Martin and Bumpass [13] used 1985 data to show that, within a span of 40 years, two out of three marriages in the US will end in separation or divorce.

There's your problem right there Bumpass ... you're using old data!

[edit on 20 Apr 2010 by schrodingers dog]

My mind simplified the OP by likening it to a bicycle

Both tyres inflated evenly. Smooth ride. Euphoria

Then, the slow-leak of one (or perhaps both) tyre produced first a minor impediment to speed --- then subtle bumps were felt --- greater loss of speed --- difficulty in maintaining traction -- marked lessening of speed leading to diastrous wobbling -- kaput. Misery. Bike ride over

Throughout, the bike rider is required to concentrate more and enjoy the scenery etc. less. With greater effort being required to cover ground and maintain one's seat. Until it's admitted that the smooth ride ended four miles back

If only one tyre is affected by a slow leak, then the remaining 'good' tyre is forced to shoulder most of the work for as long as the ride lasts

Much like Dock9 I read between the lines and got an analogy.


Scenario:

You put enormous efforts to attain the funds and resources to purchase a high performance sports car.

If you enjoy the perks of said vehicle and neglect to say, change the oil on a regular basis ...you're going to end up with mechanical problems down the road.

Sure - you love the car....it's awesome!

But you gotta change that oil, provide new filters, take it in for servicing if knocks or pings begin to surface under the hood, and keep that baby washed and polished in order to retain it's inital "allure and performance".

If you ignore the initial signs of "engine trouble" - those small knocks and pings are eventually going to destablize a larger, core component of the system.



Man or woman - you gotta put time and effort into things (and the people) you love. You can't just "drive either of them until the wheels fall off" and still expect to have the same performance that you started out with.



I wish I could better decypher those graphs - but I blew a gasket trying.

reply to post by schrodingers dog

Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.

This is what it comes down to...and I think it can even be further simplified to just "Nothing lasts forever."...even though a lot of us like to think otherwise, it's completely illogical that anything should last for an infinite amount of time, except for reality/time it's self. No love will last forever. Even if there happens to be an infinite super-conscious mind (God) that holds reality together...at some point, that God is going to destroy it's self and everything it holds together, however, it theoretically could last forever...it just wouldn't, and to explain why I think this, we really need to think on a large scale.

Consider a young child. The world is a new and vibrant place full of mystery, color and adventure...life is so great at those ages, because you truly don't know if Santa exists, in fact, you've got good reason to believe Santa does exist...everyone tells you he does, and why would they lie...ghost stories and horror movies are extra scary as a kid for the same reason...but as you grow older and your understanding of the world develops, you realize these things probably aren't real...as an adult life is quite serious, dull and boring...and it isn't often you get the feeling of mystery and excitement as you behold a magnificent new discovery...now lets jump forward and look at things from the perspective of a God if we can...after one hundred trillion billion years you might come to know all there is to know, and ever will be to know, you might have felt every emotion and feeling there is to be felt...is it then purposeful to go on for another billion years, or God forbid go on for infinity...the only thing left to do is start over again, because why would you want to observe and "experience" reality if you were unable to experience anything new...if there is a Hell, that's all it is...eternal...eternal suffering...forget about the hellfire, even if that exists, after a trillion years of getting burnt I don't think physical pain will even be felt, nor would you even care if it was, because by that time, you would have realized it's only a "feeling", and your mind is the only thing creating the reality where that pain is "bad"...

[edit on 20/4/10 by CHA0S]

Behavioral statistics and forecasting is a burgeoning field.

At one point in time, i was a call center forecast and scheduling analyst. My job was to forecast calls for a dozen or so different call types, across multiple call centers in Tx, La, Canada, and Illinois. To do this i took a bulk number of calls for a month, and had to assign a forecast breakdown by 15 minute intervals for the entire month, then apply this forecast to the various staffing groups to ensure coverage of each interval (i aimed to cover 95% of intervals).

The difficulty in this is not the call forecasting. That is simple...you just apply mathematical percentages of call total based on the previous 6 weeks actual call delivery (% of total by interval), and then account for things like holidays by factoring in the prior years performance on the holiday. Not too difficult.

The hard part is in scheduling people. You never know when people are going to call in, really. I mean, you can take recent trends and try to apply those (i liked to apply day of week percentages for the prior 3 week period).

I had a smart programmer that worked for me that designed a database that could forecast my absentee shrink based on the actual employee's prior 3 week behavior.

I would feed in data on schedule vs absenteeism (simple reports from our workforce management database), and it would give me % probability that a specific employee would miss a specific 15 minute segment. It was designed to get smarter the more data it was fed, by including increased variables (day of week, day of month, day of year, time of day, time of month, holiday variables, average time between absences/tardies).

Initially the data was useless. After about 3 months, however, the data started to provide results in the 75% range. The company went through some seizures about that time, and we scrapped the project after 5 months, with us hitting about 80%. This isn't 80% by person, it was hitting 80% of the absent segments predicted.

What we found was that behavior from individuals was predictable to a degree (the people who always call in on Fridays, or the day after payday, etc). But for overall group dynamics, the information was only resolvable at a group level. And at a group level, the same things will happen.

in short, what we found was that we were already doing it "right" by taking the group trending information the way we did before. The only real improvement would come from increasing the data fed into the model.

On a side note, that same programmer made a network message tool that allowed us to scroll messages across the top of the screen (we called it "Newsflash"). It was deployable across multple sites so i could send out queue updates to multple queues. One of the most brilliant and creative people i have ever worked with. I was lucky to have him work for me.

reply to post by tothetenthpower


They are applying the concept of entropy contained within the second law of thermodynamics to the "flame of love" that burns in the hearts of the average couple.

I would posit that, if the second law of thermodynamics is truly a law and not a rule that only works in our local region, these individuals are correct in their assertion. Many have noticed exactly how similar above is with below.

Our minds are born of the mathematics of this universe. it is likely be able to be defined by the same mathematics. Like the moth that approaches the flame in a pattern that emulates the spiral of the fibonacci sequence.

Originally posted by schrodingers dog
They haz graphs:

lol

I'm in your Sentimental Dynamics,...accounting your Marital Dissolutionz!

In conclusion ... this is what happens when mathematicians and statisticians try to figure out why their marriage failed.

This is the first thing I thought.. oh no.. some egghead got dumped!
...and this is what happens!

Anyone can make sense of it?

not on initial review, BUT.. I think it was only a matter of time before someone, somewhere began to start to quantify and calculate it all.

Is this true?

Originally posted by lagenese
Well, in my book, science is unable to explain "love" or relationships. They can do all the research they want, the will never come up with plausible conclusions for love is a vibrational status that cannot be measured or explained by scientific means.
Interesting post by the way, and well presented. Thanks!

Originally posted by schrodingers dog

Originally posted by lagenese
Well, in my book, science is unable to explain "love" or relationships.

Agreed ... though I can't shake the image in my head of some guy showing this paper to his soon to be ex-wife as to why their marriage failed. "Honey honey, look at the graph ... that's where we are!" I presume a good whipping would shortly follow her initial confusion.

I just find their stated "love is not enough" premise as surreal in scientific terms.

Sadly, as much as we would all like to think of 'LOVE' as completely intangible and unquantifiable.. I think that in this infinite universe.. you have to account for the eventual quantization of all knowledge and skill...
Including that which maintains any set goal..
obviously loving intimate sentimental relationships are included in 'everything'.

I don't like to think of graphs and charts while dealing with issues within a relationship...
but man.. if we become a species that in general.. keeps having every single relationship end in failure.. when it was originaly desired to last, then I think that using our brains to solve the problem would (will) be a necessity.. IF we want to solve that problem.

of course in order to make any good use of the data this guy brings to the table... we'd all have to be at an intellectual level to be able to easily assimilate and apply the data, else only eggheads would be making use of it.. thereby resulting in only eggheads reaping it's benefits

OR

it has to be 'dumbed down' into layman's terms...
using common language in order to describe what is what and why etc..

I mean really.. somewhere along the line.. within the timeframe of human existance in the distant future...
we're going to have to perfect the science of being completely successful in our intimate relations...
and that method is going to have to be one that works.
one that may look like love to us on the surface...
but obviously be quantifiable with scientific models under the surface.

we can all has love forever... somedayz...

-

Originally posted by prevenge

we can all has love forever... somedayz...

Only if we plot our effort utility/disutility/inattentions, mind our effort gap, balance our sentimental equilibrium, consider our "target" trajectory, and avoid teh pre-rupture point. Then we'd have something ... assuming we were married to each other of course.

Argh, the more I read this study the more I think it is nonsense. Not because of the figures, formulas, and graphs, as I don't understand a one of them ... but because it looks to me that this study is done Bumpass backwards. Namely it seems they have a pre-conceived conclusion and cherry picked stats and formulas to quantify and justify it mathematically. Perhaps a lot of science is done this way, observe an obvious condition and try to formulate it, though to date, feelings seemed to have been exempt from this endeavor and in my opinion should probably remain so.

Plus, if something as ubiquitous, subjective, and conceptually relativistic as "love" is to be quantified and formulated, surely quantum theory should be part of the process. After all, there's no love unless one's there to observe it ... wrap that around your noodle Bumpass!

"Baby baby, where did our quark go?"

[edit on 21 Apr 2010 by schrodingers dog]

reply to post by schrodingers dog


This is comedy gold.

Maybe it's about their tendency that graph everything. They want to understand even love with numbers and graphs. I don't understand why people get married in the first place with people who they don't know that well. I don't also understand how a marriage can "fail". It's a goddamn relationship with an another person, not some exercise.

I feel kinda bad for the guy.

reply to post by Tryptych


I think the important thing to understand here is that behavior is controlled by the same algorithmic functions that control the universe. Sure, from the individual level you may not see it. But from the 50,000 foot level you can resolve some very interesting patterns in human behavior.

A study that was done on the walking paths in parks alludes to this. They set up walking paths that made for quick routes along good scenery. However, inexplicably, people started cutting across the grass in certain areas. So many people did it so often it wore the grass down. Now, this path didn't represent (always) the shortest path between A and B. It was various things, but the point is that people seem to be "hardwired" for certain behavioral trends.

Now, as any good statistician will tell you, there is always some deviation. I would suspect, however, that if you took humanity on the whole you would find the r^2 to be well within the limits of relevancy.

Apply this towards forecasting human behavior. If you have adequate models, as i alluded to earlier, you can actually begin to predict what the masses will do. It is difficult to do this on an individual level, but on a group level it gets increasingly easy to determine the pattern the more data you gather.

Apply this same concept in the context of a school of fish....they behave the same way, only in a much more organized fashion.

SD has this right: the experiments seem to be flawed. But the concept that is being probed here is important. I promise you that the PTB know all of this already, and apply this understanding towards how they act/react in the public eye. It is the essence of mind control on a group level.

I would just presume that since our minds are born of this universe, then this universes mathematical laws would apply. The laws of entropy vis a vie the 2nd Law of Thermodynamics should be no exception.

reply to post by bigfatfurrytexan


Humans are not fish.

Anyway, good luck in relationships if you only try to understand them by graphs and "algorithms". Like the OP said, that very paper probably reflects the reason why his marriage didn't work out.


[edit on 21/4/2010 by Tryptych]

Originally posted by bigfatfurrytexan
I promise you that the PTB know all of this already, and apply this understanding towards how they act/react in the public eye. It is the essence of mind control on a group level.

I suspect that is correct ... government, corporate, wall street, marketing organizations must have formulaic/statistical probability predictors for human behavior. However I would assume that their margin of error would increase inversely proportionally to the size of the group ... that is to say the smaller the group the less applicable the formula. And that's where I think the achievement of this paper falls short of its stated ambition ... although trying to quantify and mathematically understand/predict interpersonal behavior between two people is theoretically possible, it is probably much more complex that the content of this paper and is likely to include variables that we as humans are not even cognizant of.

[edit on 21 Apr 2010 by schrodingers dog]

Originally posted by schrodingers dog
although trying to quantify and mathematically understand/predict interpersonal behavior between two people is theoretically possible, it is probably much more complex that the content of this paper and is likely to include variables that we as humans are not even cognizant of.

Yes, and even if it'd be possible, the only thing you get is the empty shell. It doesn't really shed any light on the actual experience.

I find this whole idea somehow very sad.

Originally posted by schrodingers dog

Originally posted by bigfatfurrytexan
I promise you that the PTB know all of this already, and apply this understanding towards how they act/react in the public eye. It is the essence of mind control on a group level.

I suspect that is correct ... government, corporate, wall street, marketing organizations must have formulaic/statistical probability predictors for human behavior. However I would assume that their margin of error would increase inversely proportionally to the size of the group ... that is to say the smaller the group the less applicable the formula. And that's where I think the achievement of this paper falls short of its stated ambition ... although trying to quantify and mathematically understand/predict interpersonal behavior between two people is theoretically possible, it is probably much more complex that the content of this paper and is likely to include variables that we as humans are not even cognizant of.

[edit on 21 Apr 2010 by schrodingers dog]

You have hit it exactly. To effectively predict human behavior requires a resolution on the order of at least hundreds with several years of data...or several million with a few weeks of data. The former would work, but the latter gives you the best look possible.

So all those pollsters that call, do they feed data up the chain? How about the census? The fact that someone doesn't return one...what does that say within the model?

There are implications in every category imaginable here. It is the whole concept of Information being the currency of tomorrow, and any piece of information is highly valuable if you have the model to analyze it properly.

On the individual level you would have to develop a way to analyze the composite of the various personality archetypes that humanity employs. No person on Earth is unique in any individual category. The individuality comes from how these categories are employed. Unless you can identify each archtype, and then assign a number to decide how influential this archtype would be within the entire system. Then you still have to take into account "custom states" caused by the marriages of all these various archtypes in various quantities within the same personality/system. Chaos theory at its best.