The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation by Hannah Fry.
Title: The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation.
Author: Dr. Hannah Fry.
Genre: Non-fiction, mathematics, speeches, how-to's, self-help, romance.
Country: U.K.
Language: English.
Publication Date: 2015.
Summary: Love has taken center stage as the inspiration for countless paintings, wars, and untold poets and musicians. Just as poetry, art, and music have the ability to communicate something about love that is difficult to articulate with words, the same is true for mathematics. Of course, mathematics can't easily help us translate the emotional side of love-emotions rarely behave in neatly ordered, rational, or easily predicable ways. It is difficult to quantify the roller coaster of romance or define how lovers might feel via a set of simple equations, but that doesn't mean that mathematics isn't crucial to understanding love. In the book, the author takes the reader on a fascinating journey through the patterns that define our love lives, tackling some of the most common yet complex questions surrounding love: What's the chance of finding love? What's the chance that it will last? How does online dating work, exactly? When should you settle down? How can you avoid divorce? When is it right to compromise? Can game theory help us deduce whether or not to call after a date? From evaluating the best strategies for online dating to defining the nebulous concept of beauty, she proves-with great insight, wit, and fun-that math is a surprisingly useful tool for negotiating the complicated, often baffling, sometimes infuriating, always interesting, patterns of love.
My rating: 7/10
My review:
♥ My aim in writing this book is not to replace any of the other excellent sources available on the science of human connection. I wouldn't be qualified to describe the intangible thrill, all-consuming passion, or world-ending despair that love can bring. If that's what you're after, might I recommend you simply turn to nearly every painting, poem, sculpture, or song created over the last 5,000 years.
Instead, I want to try and offer you a different perspective on the most talked-about subject in the history of human existence, using mathematics as a guide.
You would be forgiven for thinking that love and mathematics don't seem to naturally sit well together. Human emotions, unlike mathematical equations, are not neatly ordered or well behaved, and the real thrill and essence of romance can't easily be defined.
~~from Introduction.
♥ A few years of dating a succession of boring Bernards and psycho Suzys can leave us frustrated and disappointed and feeling like the odds are stacked against us. And some people will tell you that your feelings aren't necessarily unfounded. In fact, in 2010 mathematician and long-standing singleton Peter Backus even calculated that there were more intelligent alien civilizations in the galaxy than potential girlfriends for him to date.
..The equation Backus employs was named after its originator, Frank Drake, and aims to estimate the number of intelligent extraterrestrial life-forms in our galaxy. The method is simple: Drake breaks the question down into smaller components, asking about the average rate of star formation in our galaxy, the fraction of those stars that have planets, the fraction of planets that couple support life, and the fraction of civilizations that could potentially develop a technology that releases detectable signs of their existence into space.
..These were Backus's criteria.
1. How many women are there who live near me? (In London -> 4 million women)
2. How many are likely to be of the right age range? (20% -> 800,000 women)
3. How many are likely to be single? (50% -> 400,000 women)
4. How many are likely to have a university degree? (26% -> 104,000 women)
5. How many are likely to be attractive? (5% -> 5,200 women)
6. How many are likely to find me attractive? (5% -> 260 women)
7. How many am I likely to get along with? (10% -> 26 women)
Leaving him with just twenty-six women in the whole world he would be willing to date.
♥ The reality is that when people are single and looking for a prospective partner, they often add in all sorts of must-haves or must-not-haves hat dramatically reduce their chances. I have a very close friend who ended a potentially fruitful courtship simply because the gentleman wore black shoes with blue jeans to a date. I have another chum who insists that he cannot date a woman who uses exclamation marks! (That one is for him.) And how many friends do we all know who will not consider someone unless they are driven enough, or gorgeous enough, or rich enough?
Being good on paper doesn't mean anything in the long run. There's no point in restricting your search to people who match everything on your checklist, because you're just setting yourself an impossible challenge. Instead, pick a couple of things that are really important and then give people a chance. You might just be pleasantly surprised.
Let's be honest, we probably all know people who've ended up with someone they never thought they'd be with, even if that person were the last life-form on the planet. After all, in the words of Auntie Mame, "Life's a banquet, and most poor suckers are starving to death!"
Just ask Peter Backus. He beat his own odds; he got married last year.
♥ Linking beauty o the golden ratio is a neat theory that you;ll find espoused in numerous beauty bogs and YouTube videos. There's just one problem-it isn't good science.
Real science is about trying as hard as you can to disprove your own theories. The more you try, and fail, to prove yourself wrong, the more evidence there is to suggest that what you're saying is right. As much as I'd like beauty to be defined by a single number, I'm afraid that trawling through thousands of faces and measuring every possible ratio until you find something that fits your theory just isn't science.
The problem with using the golden ratio to define human beauty is that if you're looking hard enough for a pattern, you'll almost certainly find one, especially if you're prepared to be a little loose with your definitions. How do you decide where the "start" of your ear is or the point at which your nose definitively "ends"? And how do you do this to a degree of accuracy of five or more decimal places in your golden ration measurement?
Perhaps there will come a time when somebody does find a good reason why the human body has a thing for this number. But until then, as Stanford University mathematician Keith Devlin puts it, the golden ration as a definition for beauty really does seem to be "the myth that won't go away."
♥ The theory us that when looking for a partner, we tend to dislike unusual face shapes for fear that they mask a weird genetic mutation that we'd like to avoid passing on to our future offspring.
Thoughts of the health and success of our future children are a recurring theme when judging for beauty. Facial symmetry, too, stands out as an important factor for beauty, and people with naturally symmetrical faces consistently score highly on attractiveness surveys. But it seems that when picking out symmetrical faces as beautiful, we're doing nothing more than validating an underlying clean bill of health.
Whenever you pick up a cough or cold during your childhood it will have a tiny impact on your development, leading to slightly unusual patterns of growth. One eye might end up just a few millimeters higher than the other, or one nostril ever so slightly larger than the other. The effect might be small, but it's enough, it seems, for people to subconsciously pick up on these cues when judging beauty. On some subliminal level, we all know that someone with slightly mismatched features probably doesn't have the best immune system. After all, you and your future offspring to be as healthy as possible.
♥ The significance of these traits seems to lie in their connection to the prevalence of male and female hormones.
As girls go through puberty, their hormones will have a direct impact on how their facial features develop. Women with high levels of estrogen will end up with full lips and a large waist-to-hip ratio, while women with lower levels of androgen, the steroid hormones, will keep their short and narrow jaws from childhood, along with their flatter brows-giving them much larger eyes.
And-surprise, surprise-this balance of female hormones is also positively linked to fertility.
Men, on the other hand, need testosterone throughout puberty to develop muscle ass, broader jaws, and defined brow ridges, which will inevitably result in more sunken eyes. And testosterone, the male sex hormone, is also a useful marker for fertility.
So all we're really doing when picking a guy with a strong jaw, or a woman with beautiful plump lips, is giving in to our evolutionary desire for offspring. That's why women wear lipstick. It's so you want their babies.
♥ There is a lot more to the science of attractiveness, but ultimately, beauty is what lies between the equations. Everyone truly has a unique ideal, so there's no mathematical solution here. All this means there's really no point stressing out about it. Focus more on developing some amazing small talk and killer charm.
♥ Despite our illusions of free will, there are some simple rules that people will often follow when coming to a decision. These rules mean that people's choices are surprisingly easy to manipulate. As the economist Dan Ariely puts it, we're all just a little bit "predictably irrational."
Imagine that you're in a movie theater and choosing which snacks to buy. Perhaps a small popcorn costs $5.00, while the large popcorn is an eye-watering $8.50. The large option seems terribly expensive, until the cashier points out that the large popcorn is only $.50 more than the medium. No sensible person would ever choose to buy the medium popcorn when you could have the large for only a few cents more, but the fact that the medium popcorn is on the menu has a big impact on your decisions: it serves to make the large popcorn look like a much better deal.
This is known in economics a the "decoy effect." What it demonstrates of that the presence of an irrelevant alternative can change how you view your choices. It has been exploited by marketing experts for decades. It has been exploited by marketing experts for decades. But it also has the potential to help make you seem more attractive.
♥ In short, the group who do the asking and risk continual rejection actually end up far better off than the group who sit back and accept a suitor's advances.
..This result does make some intuitive sense. If you put yourself out there, start at the top of the list, and work your way down, you'll always end up with the best possible person who'll have you. If you sit around and wait for people to talk to you, you'll end up with the least bad person who approaches you. Regardless of the type of relationship you're after, it pays to take the initiative.
..But for all the extensions and examples, the message remains the same: If you can handle the occasional cringe-inducing rejection, ultimately, taking the initiative will see you rewarded. It is always better to do the approaching than to sit back and wait for people to come to you. So aim high, and aim frequently: The math says so.
♥ Personal preferences and individualized lists are the ideal ingredients to filter our searches according to our own criteria. But eighty-odd years of relationship science has taught us one important thing: Trying to use individual data to predict how well a couple will get along just does not work.
The problem is that we don't really know what we want until we find it. Unlike with Amazon and Netflix, where we truly know our tastes in films and other products, a questionnaire about our personal preferences just isn't enough to predict who will make us happy. Ultimately, finding a partner is just a lot more complicated than buying a DVD box set.
You and I may both really like watching Ryan Gosling films, but that says nothing about whether we would enjoy watching them together. And while a mutual respect for Ryan Gosling may be a good place to start an early conversation or a first date, it's unlikely to be an important predictor of how compatible we'll be in a long-term relationship.
But it's not just trivial measures like film preferences that fail to capture our chances of success as a couple. It's every possible combination of personalized data: demographics, political persuasions, family ambitions, etcetera. None of these can offer a significant or meaningful measure of how compatible you'll be with a prospective partner in real life.
♥ The well-matched couples didn't really get along any better with each other.
The tiny margins between these two numbers mean the OkCupid matching algorithm has its limits in being able to predict the real success of a match. Of course it's easier to engage in a conversation if you have more in common, but only just. And it won't necessarily help you in the long run.
This isn't a flaw in OkCupid's science. Their algorithm is doing exactly what it was designed to do: deliver singles who meet your specifications. The problem here is that you don't really know what you want. So an algorithm that can accurately predict your compatibility with another person simply does not exist yet.
♥ But if a high average attractiveness score isn't enough to make you popular, then what is? And what is the difference between the desirable singles at the top of the graph (in blue) and the unpopular people at the bottom (in red), despite the fact that they are considered equally attractive?
The answer, discovered by the OkCupid's team, lies in how people view your attractiveness, and is best explained with an example. Imagine scoring two particularly lovely lady cartoon characters: Wilma Flinstone, and Leela from Futurama.
I think we can all agree that Wilma is an extremely beautiful woman-nobody could think that she is ugly, but it's fair to say that she's also not exactly Jessica Rabbit, either.
Compare her to how someone like Leela might score. There are some people, myself included, who think that Leela is a seriously sexy lady. But there are others who might be a bit put off by the whole one-eye thing.
I would guess that on average, both women would score roughly the same on a 1 to 5 scale, but the way that single cartoon characters looking for love would score the girls would be quite different. Wilma's scores would all be clustered around 4, but you'd expect a huge spread in the way that people voted for Leela.
Curiously, it's this spread that counts. People like Leela who divide opinion end up being far more popular on internet dating sites than people like Wilma who everyone agrees is "quite cute."
This effect really pops out in the data from the real OkCupid users when you subject it to some statistical sorcery. Using a technique known as regression analysis, the OkCupid team used the data to derive an equation for the number of messages each user can expect, based on how people score them on their attractiveness:
Messages = 0.4a1 - 0.5a2 - 0.1 >a4 + 0.9 a5 + k
Here a1 is the number of people who rated you as a 1 out of 5 on attractiveness, a2 is the number of people who rated you as a 2, and so on. The final value, k, is how active you are on the website. The numbers in front of each part of the equation (or "terms," if we're being proper) come directly from the data and signify how the attractiveness ratings that you are given affect how many messages you can expect to receive.
The +0.9 immediately preceding the a5 term means that for every one hundred people who rate you as a smoking hot 5 out of 5 you can expect to receive ninety extra messages in a month. So, lucky for you.
It makes sense that getting 5s on attractiveness would equate to receiving more messages. But surprisingly, the +0.4 preceding the a1 term means that people on OkCupid also receive forty more messages for every one hundred people that score them as 1 out of 5. Yes, you read that right. Having people think you have a face like a dog's dinner mean you get more messages.
By contrast, the -0.1 in front of the a4 term means that users receive ten fewer messages for every one hundred people who rate them as a 4 on attractiveness. Having people score you as a 4 out of 5 on attractiveness actually works against you.
To summarize, as long as some people think you're beautiful, you're much better off having some other people think that you're ugly than having everyone think you're just quite cute. People who are unbelievably good-looking and score straight 5 out of 5s will always do well, of course, but the rest of us would do better to divide opinion than to aim for being the cute guy or girl next door.
It seems like quite a counterintuitive result, but maybe what's going on here is that the users sending the messages are also thinking about their own chances: If they think you're beautiful, but suspect that others might be uninterested, there's less competition and therefore an extra incentive to get in touch. But if they think you're beautiful and feel sure that everyone else will, too, they might imagine you'll be getting lots of messages and decide not to bother humiliating themselves.
And here is the really interesting part, because when most people choose their online dating profile pictures, they tend to try and hide the things that make them unattractive. Classic examples include overweight people choosing a really cropped photo, or bald men choosing pictures of themselves wearing hats. But this is the exact opposite of what you should do. When choosing a profile picture, you should play up to whatever makes you different-including the things that some people might not like.
The people who fancy you will still fancy you. And the unimportant people who don't will only play to your advantage.
So be proud of that bald patch, show off that ill-advised tattoo, and get that belly out. Because standing out online just means being yourself. Who would have thought?
♥ Again, I should add that I don't quite agree with this view of the world (although I am a bit scared that it might be true), but these assumptions do make for a wonderfully neat mathematical problem. The full derivation of the best strategy for the man gets quite heavily into game theory at points and is not for the fainthearted, but the result is a great example of the theory in action. And the best strategy for how to woo the ladies while avoiding gold diggers makes good intuitive sense:
To impress the girl, the man should display showy and extravagant behavior, making purchases that are costly to him, but ones that are ultimately worthless to the female. So, gents: If you want to demonstrate how wealthy you are, put on a big fireworks display or arrive at her house in a Ferrari. If you want to show her how generous you are, leave a big tip at dinner. But don't, whatever you do, buy her jewelry or take her to see her favorite band. She needs to see that the display is expensive to show that you mean business. But it shouldn't be a gift that is valuable to her, or she may string you along without ever intending to have sex with you: classic gold digger behavior.
This theory also works to explain why it's worthwhile for companies to make big, extravagant displays of power-like the marble entrances to Wall Street banks or opulent skyscrapers in Vegas. The bigger a waste of money these gestures appear to be, the more powerful the consumers and competitors will think the company is. According to the theory, this makes a lot more sense than spending the money buying small gifts for your many customers-to do that risks being exploited by some people who will take the gifts and run without ever having a serious intention of doing business with you.
♥ When framed in this way, the game of dating is mathematically equivalent to what happens in a particular kind of auction where bidders submit sealed bids and no one knows the bid of any other participant. The theory starts with two bidders who are both vying for the same lot. One is a strong bidder with access to a lot of cash, the other a weak bidder with a limited budget.
In the case of the bachelor, the man is the lot. The strong bidder is the glamorous, intelligent woman with access to a lot of pizzazz. The weak bidder is less attractive (by whatever measure) and has a more limited charm budget. They are both going for the same man, without knowing how hard the other is trying.
You might think that the strong bidder has the best chance of winning the man, but in real-world auctions it turns out that it's often the bidder in the weaker position who comes away with the prize, a phenomenon which had been the subject of extensive attention within game theory literature.
As with the previous example, the theory gets quite heavy in places, but the insights can go some way toward explaining why there are so many fantastic women in their thirties all completing for a seemingly tiny pool of eligible bachelors.
When a weak bidder comes across a man that she likes, she is likely to pull out all the stops to compete for his attention. A strong bidder, on the other hand, confident that she presents a good match for any man, is less likely to go all-out, knowing that another, better man is probably waiting for her just around the corner.
Seeing disinterest from the more attractive woman, the man will then settle down with the woman who shows him the most attention, taking him out of the dating pool.
This is all fine at the beginning, but as the auction (i.e., life) continues and the lots are won by the weaker bidders, a situation arises with only a few decent men left and a much larger number of beautiful and intelligent women all fishing in the same shrinking pool.
The result is the eligible bachelor paradox, and it comes with a clear, if slightly harsh, take-home message: No matter how hot you are, if your goal is partnership, don't get complacent.
♥ The numbers here are arbitrary, but the order of the rewards is important. Being the sole cheater results in a higher score than being in a faithful relationship, but it's bad news if someone cheats on you, and bad for everyone if both partners betray each other. Using this setup makes the game of being faithful equivalent to one of the most famous and well-studied problems in game theory: the prisoner's dilemma.
In the prisoner's dilemma, two suspects are being questioned separately about the same crime. They have two choices: to cooperate and stay silent and split the sentence between them, or to defect and rat out their friend. They get to walk away if they talk while their partner stays silent, but they both get a long stretch in jail if they both rat each other out. The reward structure is identical to the game of being faithful: Giving evidence while the other stays silent is better than both staying silent, which in turn beats both cheating. The worst outcome of all is staying silent while your partner rats you out.
This setup does give quite a depressing view of relationships. Cooperation seems difficult to achieve and fragile to maintain. So, if the theory is correct, how is it possible that anyone can have a successful and faithful relationship in a situation this unstable?
The reason is that relationships aren't about one-off decisions. The payoff matrix above doesn't apply to your relationship as a whole. Instead, it's as though both of you are playing this game with each other every day; choosing to cheat or remain faithful on a regular basis. And this difference is key. Repeatedly playing the same game with the same person has a dramatic effect on the way your incentives appear. Suddenly, you're trying to end up with the biggest score over time, rather than in each individual encounter. In the long term you're both better off staying faithful.
♥ Axelrod's "tit for tat" strategy gives you the answer.
Despite the name, tit for tat isn't about playground squabbling. It's a strategy that encourages cooperation but punishes exploitation. The mathematical version involves cooperating at first, and then simply copying the previous move of your opponent. They stay cooperative, you stay cooperative. They cheat and defect on you, you cheat and defect on them. They go back to being nice, you go back to being nice.
Taking the strategy out of the textbook and into the dating world, your rules to follow can be broken down into four simple steps:
1. Be clear. Don' play games within the game. Being manipulative or tricky in dating won't work out in the long run. A straightforward strategy will give you the best chance of success.
2. Be nice. Start off being cooperative and continue to be so unless given reason to act otherwise.
3. Be provokable. Don't allow yourself to be exploited by bad behavior. If someone treats you badly, you should retaliate with a measured response. But don't go overboard. As soon as a bad deed has been dealt with you should then:
4. Be forgiving. Move on from bad behavior quickly and return to being cooperative. You have nothing to gain from continually punishing someone for a single mistake. Going too far with your reaction will only prompt a bad reaction from your partner and find you in a spiral of negativity that ca be difficult to recover from. Move on and go back to playing the game together as a team as quickly as possible.
So, to summarize: Don't be a jerk.
♥ Many things can happen when two people have sex for the first time: the start of a new life, the start of a new infection, intense mutual embarrassment, and even, occasionally, pleasure. However, one thing always happens whenever two people have sex: They create a link between themselves in an imaginary network.
These connections can't be taken back however much one might want to once sobriety returns. They're also two-way (even if the orgasms weren't): Both people will add to their total number of sexual partners whenever a new connection takes place.
♥ If the Swedish survey is representative of the population at large, the curve suggests that there will always be some chance of finding someone with any number of sexual partners, however large. Granted, there won't be many people in the world with 10,000 or even just 1,000 partners, but the pattern predicts that there will always be some.
All of this can be wrapped up in a singe formula that allows you to predict how many people we've all slept with: If you pick a person in the world at random, the chances that they will have had more than x sexual partners is just x-a.
The value of a comes directly from the data. To give you an example, the team found the Swedish women had a value of a=2.1. If this number were representative of all of us, the chances of finding someone in the world with more than one hundred partners would be 0.006 percent, suggesting that just over one in 15,800 of us have accomplished that feat. The probability drops the higher the numbers go, but the chances of finding someone with more than 1,000 partners would then be 0.00005 percent, or one in every 2 million people.
Before I completely explode with excitement over the elegance of the mathematics, I think it's worth pausing for a second to appreciate how extraordinary this finding is. For all our free will, and despite the seemingly complicated set of circumstances that lead to our sexual encounters, when you look at the population as a whole there is a startlingly simple formula lying behind everything that we're doing.
♥ But while the hubs are the most critical players in the spread of disease, there's a mathematical trick that allows us to exploit them and the structure of the network when trying to halt the progress of asexually transmitted virus. The theory becomes clear if you imagine a simplified network.
Imagine that four beautiful young princesses, Cinderella, Snow White, Ariel, and Sleeping Beauty have each been getting it on with one sexy prince and formed a sexual contact network. There have been no encounters between the ladies on this occasion, unless you count some seriously sketchy Disney fan sites (which I recommend avoiding if you value your childhood memories).
Now imagine there is some kind of nasty sexually transmitted disease going around the group. If vaccinating or educating everyone is too expensive, we might want to prioritize and target our attention only on the hub: the person likely to have the biggest impact.
But without asking everyone how many people they've slept with we would have no way of seeing the hidden links in the underlying network, and no idea that Prince Charming was our hub.
The task, then, is to try and maximize our chances of finding the hub without knowing the underlying network.
If we picked someone at random to vaccinate in this group, we'd only hit the hub one in five times.
But imagine that instead, we pick someone at random, say the lovely Ariel, and ask her to help us vaccinate someone who she has slept with. Ariel will take us to Prince Charming. Likewise, if we randomly picked Cinderella, and asked her to tell us someone she has slept with, she'd also take us to Prince Charming. So would Sleeping Beauty, and so would Snow White.
Just by adding this one simple step to the algorithm, we increase our chances of finding the hub to four out of five. Much better odds.
The same would be true of much larger networks. Imagine that, without being able to see any of the network or follower statistics of Twitter, we were trying to find Katy Perry-the biggest hub at the time of this writing.
If we picked someone at random from the 500 million people on Twitter, we'd only have a one in 500 million chances of finding Katy.
But, if we picked someone at random and asked them to point us to the most popular person they follow, it would take us to Katy a cool 57 million times. Suddenly the chances of finding Katy soar to around 10 percent, which is pretty impressive given how simple the algorithm is.
This procedure has been used to forest and slow the course of epidemics without the need for a difficult and expensive survey of the underlying network. But it also says something impressive, I think, about the simplicity of the vast network that connects us all and how, armed with a mathematical understanding and a basic algorithm, we can gain an important perspective on how sexually transmitted diseases spread.
So next time you add another notch to your bedpost, consider the immense network to which you are contributing. Mathematicians can't help you have better sex, but we do try and cut down the number of STDs you might catch, and what isn't sexy about that?
♥ Every time you hear claims of something being the best, the cheapest, or the most efficient, there's usually an optimization algorithm at work.
♥ Except that even for a small wedding of seventeen people and two tables of ten there are 131,702 different ways to seat your guests.
♥ It's impossible to say that the result will always be perfect. The math can only do as well as the numbers you give it.
♥ I'm certainly not a psychologist, but I think there is something positive to be gained from looking objectively at your own behavior through numbers, and trying to see if there was anything you could have done to promote a more positive discussion.
♥ The more sophisticated scoring sytstem constructed by the academics (a etension of the table to the left) allowed Gottman and his team to predict divorce amongo couples with up to 90 percent accuracy ater observing them in conversation. But it wasn't until they teamed up with mathematician James Murray that they really began to undetrstand how tgese crucial spirals of negativity are formed and how they develop.
Although Murray's mathematical models are framed in terms of a husband and a wife, they aren't based on any gender stereitypes an couple apply eqyally well to a long-term and/or gay or lesbian relationship. They are a wonderfully elegant example of how mathematics can be applied to patterns in human behavior and can be summarized neatly for the follwong two equations
Wt+1 = w + rwWt + IHM (Ht)
Ht+1 = h + rHHt + IHM (Wt)
These equations might look like gibberish at first, but they're actually describing a very simple set of rules for predicting how positive or negative we can expect the husband and wife to be in the next turn of their conversation.
If we take the top line, the wife's equation, we can break down how these rules play out. The left-hand side of the equation is simply how positive or negative the wife will be in the next thing that she says. Her reaction will depend on her mood in general (w), her mood when she's with her husband (rwWt), and, crucially, the influence that her husband's actions will have on her (IHM). The Ht in parentheses at the end of the equation is mathematical shorthand for saying that this influence depends on what the husband has just done.
The equations for the husband follow the same pattern: H, rHHt, and IHM are his mood when he's on his own, his mood when he's with his wife, and the influence his wife has on his next reaction, respectively.
It's worth pausing for a moment to mention that these exact equations have also been shown to successfully describe what happens between two countries during an arms race. So, an arguing couple spiraling into negativity and teetering on the brink of divorce is actually mathematically equivalent to the beginning of a nuclear war.
But that doesn't mean that they've just been shoe-horned into a new application without purpose. As they've been shown to accurately capture what happens in both scenarios, the analogy only means that insights found in studying international conflict can give fresh meaning to our understanding of marriages, and vice versa. The connection serves to strengthen the mathematics rather than weaken its meaning.
As in the buildup to nuclear war, the most important thing in Gottman and Murray's marriage equations is the influence term: the effect that the husband and wife have on each other.
As Gottman and Murray were the first people to apply a mathematical model to marital conflict, they were free to choose how this influence term would look, and decided that the following version fit well with everything that had been observed in real-life couples.
If we take the influence that a husband (Ht) has on his wife (IHM) as a guide, the graph above shows the mathematical model chosen by the team.
Wherever the dotted line is high on the IHM scale, it means that the husband is having a positive impact on his wife. Likewise, wherever the dotted line dips below zero on the IHM scale, the wife is more likely to be negative in her next turn in the conversation.
Imagine that the husband does something that is a little bit positive: He could agree with her last point, or inject a little humor into their conversation. This action will have a small positive impact in the wife and make her more likely to respond with something positive, too.
This happens until a point, T+, where the husband does something really nice, like telling her he loves her or agreeing to go with her to that new play she's been wanting to see. Anything more positive than T+ will have a big impact on the wife and is much more likely to see the couple draw themselves into a nice, stable conversation with lots of positive reinforcement.
At the other end of the spectrum, if the husband is a little big negative-like interrupting her while she is speaking-he will have a fixed and negative impact on his partner. It's worth noting that the magnitude of this negative influence is bigger than the equivalent positive jump of he's just a tiny bit positive. Gottman and his team deliberately built in this asymmetry after observing it in couples in their study.
At some point T-, though, known as the "negativity threshold," the husband is sufficiently annoying to cause his wife to lose her cool completely and respond very negatively to her husband. This threshold turns out to be quite important in understanding the spirals of negativity that occur in couples.
Now, I always thought that good relationships were about compromise and understanding, and so would have guessed that it was best to aim for a really high negativity threshold. A relationship where you give your partner room to be themselves and only bring up an issue if it becomes a really big deal.
But actually, the team found that the exact opposite was true.
The most successful relationships are the ones with a really low negativity threshold. In those relationships, couples allow each other to complain, and work together to constantly repair the tiny issues between them. In such a case, couples don't bottle up their feelings,a dn little things don't end up being blown completely out of proportion.
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♥ Mathematics is about abstracting away from reality, not about replicating it. And it offers real value in the process. By allowing yourself to view the world from an abstract perspective, you create a language that is uniquely able to capture and describe the patterns and mechanisms that would otherwise remain hidden. And, as any scientist or engineer of the past 200 years will tell you, understanding these patterns is the first step toward being able to exploit them.
By being able to describe the behavior of electricity and magnetism, mathematics formed the basis for our modern technological revolution. By providing a platform for rigorous hypothesis-testing and dealing with evidence, mathematics played its role in the modern transformation of medicine. And, as in my own research, mathematics is now being used to study the patterns of human bbehavior, allowing us to view everything from terrorism to city life from a fresh and insightful perspective.
But just as the best applied mathematicians know the power of their subject, they also know its limitations. They understand the importance of what happens beyond the equations, and they respect the value of other perspectives.
~~from Epilogue.