The Mathematics of Love
Hannah Fry
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Drake exploited a trick well known to scientists of breaking down the estimation by making lots of little educated guesses rather than one big one. The result of this trick is an estimate likely to be surprisingly close to the true answer, because the errors in each calculation tend to balance each other out along the way. Depending on the values chosen at each of the steps (and there is some debate over the final few), scientists currently think there are around 10,000 intelligent extraterrestrial civilizations in our galaxy. This is not science fiction: scientists really have convinced themselves that there is life out there.
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It also applies to Peter Backus’s quest to see if there are intelligent, socially advanced women of the same species out there for him to date. And the idea is the same: Break the problem into smaller and smaller pieces until it’s possible to make an educated guess. These were Backus’s criteria: 1. How many women are there who live near me? (In London -> 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 well with? (10% -> women)
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I recently heard of a gentleman with an even clearer idea of what he was looking for in a potential partner. This man had set up a profile on the dating website OkCupid, which offers a profile section where you can outline certain “deal-breakers”: things that you can’t tolerate under any circumstances. His list ran to over a hundred, and was so extreme that it became the subject of a popular article on the website BuzzFeed. Under the heading “Do Not Message Me If” were the following gems. 1. You needlessly kill spiders 2. You have tattoos you can’t see without a mirror 3. You discuss Facebook in the visceral world 4. You consider yourself a happy person 5. You think world peace is actually a goal of some sort
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After all, in the words of Auntie Mame, “Life’s a banquet, and most poor suckers are starving to death!”
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If you haven’t heard of the golden ratio, it’s an irrational number approximately equal to 1.61803399 . . . and usually denoted by the Greek letter phi, or Φ. Its definition comes from geometry, but it has been found to apply in everything from the number of petals on a flower to the population growth of rabbits. It has also repeatedly been linked to human beauty. You may have heard it said that the perfect face should have a mouth that is 1.618 . . . times larger than the base of the nose, eyebrows that are 1.618 . . . times wider than the eyes, and so on.
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This setup is known as the “stable marriage problem,” and the process through which the friends picked their partners is called the Gale-Shapley algorithm. If we look into the math behind these couplings, some extraordinary results appear. Regardless of how many boys and girls there are, it turns out that whenever the boys do the approaching, there are four outcomes which will always be true: 1. Everyone will find a partner. 2. Once all partners are determined, no man and woman in different couples could both improve their happiness by running off together (for example, Phoebe might still have eyes for Ross, but he’s happy with Rachel). 3. Once all partners are determined, every man will have the best partner available to him. 4. Once all partners are determined, every woman will end up with the least bad of all the men who approach her.
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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.
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An algorithm is similar to a recipe: a series of logical steps that can be used to perform a task. In this case, the OkCupid algorithm takes the questionnaire members fill in on joining and, through a series of logical steps, it generates a score between couples to illustrate how good a match they are. The three key ingredients are ) your answers, 2) the answers you’d like a partner to give, and ) how important each question is to you.
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Sozou and Seymour, “Costly but worthless gifts facilitate courtship” (2005).
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When dating is framed in this way, an area of mathematics called “optimal stopping theory” can offer the best possible strategy in your hunt for The One. And the conclusion is surprisingly sensible: Spend a bit of time playing the field when you’re young, rejecting everyone you meet as serious life-partner material until you’ve got a feel for the marketplace. Then, once that phase has passed, pick the next person who comes along who’s better than everyone you met before. But optimal stopping theory goes further. Because it turns out that your probability of stopping and settling down with the best person (denoted by P in the equation below) is linked to how many of your potential lovers (n) you reject (r), by a rather elegant formula:
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It tells you that if you are destined to date ten people in your lifetime, you have the highest probability of finding The One when you reject your first four lovers (where you’d find them 39.87 percent of the time). If you are destined to date twenty people, you should reject the first eight (where Mister or Miz Right would be waiting for you 38.42 percent of the time). And, if you are destined to date an infinite number of partners, you should reject the first percent, giving you just over a one in three chance of success.
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Thankfully, though, there is a second version of this problem that is much more suited to mere mortals like you and me, and it’s got an equally impressive result. Instead of knowing how many people you’ll date, the advanced problem only requires you to know how long you expect your dating life to be. The math in this example is much trickier,2 though the same simple rule as earlier crops up again—but this time, the percent applies to time rather than people. Say you start dating when you are fifteen years old and would ideally like to settle down by the time you’re forty. In the first percent of your dating window (until just after your twenty-fourth birthday), you should reject everyone; use this time to get a feel for the market and a realistic expectation of what you can expect in a life partner. Once this rejection phase has passed, pick the next person who comes along who is better than everyone who you have met before.
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Beyond choosing a partner, this strategy also applies to a host of other situations where people are searching for something and want to know the best time to stop looking. Have three months to find somewhere to live? Reject everything in the first month and then pick the next house that comes along that is your favorite so far. Hiring an assistant? Reject the first percent of candidates and then give the job to the next one who you prefer above all others. In fact, the search for an assistant is the most famous formulation of this theory, and the method is often known as the “secretary problem.”
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CATEGORY SCORE CATEGORY SCORE Joy Contempt Humor Disgust Affection Defensiveness Validation Belligerence Interest Stonewalling Domineering Anger Whining Neutral Sadness
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As different as the efforts to understand love might be, they are all united by a single fact: They all exist only as models of reality. And in the words of the statistician George E. P. Box, “All models are wrong, but some are useful.”