Photo: iStock
Photo: iStock

The mathematics of love

The probability of finding aliens in outer space is higher than that of finding true love or 'the one'

It’s done and dusted—that gawdawful day of the year—Valentine’s Day. It was yesterday. That is why I write this a day after. Because a few thoughts crossed my mind as I waved my little girls good bye to school last morning. It’ll only be a matter of time before those terrible creatures—little boys—will begin to woo them. I know the whole razzmatazz of how they go about it. Been there, done that. 

It is only with the benefit of hindsight I now know why my older girl, on the verge of her teens, wore perfume—a strict no-no at school. My wife and I stared at each other. Incredulously. 

“It’s perfume day," she told the both of us nonchalantly. 

“You doofus, it’s Valentine’s Day today," the missus told me a little after she was gone and smiled indulgently. I didn’t share the sentiment, nor did I feel indulgent. “Overprotective father?" I thought I heard a voice mutter in my head. All I needed was a double-barrelled shotgun to complete the image.

That is why, this weekend, I intend to take this girl out someplace young people like to visit. The kind where they woo, wine, dine, look pretty and coy, exchange cakes, flowers, mutter sweet nothings and indulge in other such assorted (with the benefit of hindsight) nonsense. 

Heck no! I don’t intend to tell her what a tub of crock Valentine’s Day is all about. Instead, I’m hoping to spend some time talking about mathematics and probability—though not the way it is taught in school right now. But I’m hoping I can subtly drive home a point she’s better off trying to find aliens than spend a lifetime in the pursuit of love. She likes astronomy.

That this is indeed possible is something I stumbled across in a very interesting book, The Mathematics of Love, by a rather charming mathematician called Hannah Fry. There is a TED talk by her on the theme as well. I must concede, she’s the kind of woman I’d like to ask out on a date. And after having spoken to my little girl, I suspect I may try computing what chances do I stand with Fry without getting a black eye from the missus. I digress.

Fry starts her hypothesis by talking about an interesting gentleman called Peter Backus. An economics teacher at the University of Warwick, he first articulated “Why I don’t have a girlfriend" and it got her attention. The math was interesting.

1.How many women in London live near me, he wondered. Turned out, 4 million, when he looked it up.

2.Of these, 20%, or 800,000, were in the same age group as he was.

3.Roughly 50%, or 400,000, of those were single.

4.He figured he would much rather seek somebody with a college degree. So, that narrowed his search down to 26% of the pool, or 104,000 women.

5.He’d like them to be attractive as well. Basis these parameters, it worked out to 5%—or 5,200 women.

6.Some more computation later and further application of the Drake Equation, and asking questions like how many of these women would find him attractive, it turned out that just about 260 of them would respond to his advances.

7.And within the pool of these 260 women, he figured the population of women he would perhaps get along with would only be about 10%. So, in all of London, he had 26 women to look for.

As opposed to that, estimates suggest there are 10,000 intelligent alien civilizations in the galaxy. So he’d be better off searching for aliens. Backus lucked out though, found a lady called Rose from his pool of 26 and they eventually married

So how do you beat the odds? Fry has some pointers.

Tip #1: The Nash Equilibrium (plus common sense)

Many of us are familiar with the mathematician John Nash, who was the central protagonist of the movie A Beautiful Mind starring Russell Crowe. He is credited with proposing the Nash Equilibrium that won him a lot many accolades and international acclaim.

Whatever in the world would John Nash have to do with finding love? There’s this scene in the movie where Nash is out with three of his friends. They spot a group of five women. Four brunettes and a blonde. All of them are attracted to the blonde. 

“Hang on," says the math genius. His mind working at a feverish pitch. If all of them fall over each other trying to woo the blonde, they’d get in each other’s way. The ones who can’t snag the blonde would then try to get the attention of the other women. But they’d feel insulted because they were not intended to be the first choice. 

Therefore, in everybody’s interests, therefore, Nash suggests, they approach the four brunettes. That way, everyone stands to gain and there are no losers. Makes sense.

There are times, though, when you zero in on the one you single out. For instance, you’re at a party, and are alone. If you sit back and wait to be approached, you reduce the chances of somebody approaching you. 

That’s when you go for the one you are most attracted to. If rejected, you go to the one you find the next most attractive and so on until you end up with the best person who accepts your advances.

Tip #2: Avoid artificial intelligence-based systems

The world we are in is increasingly veering towards online dating and matrimonial sites. A lot of these are built on the back of data and the output is computed by algorithms built by mathematicians. But they are often fundamentally flawed. 

Let’s take a hypothetical example. There are a set of questions to which values are assigned as follows.

a.Not at all important = 1

b.A little important = 10

c.Somewhat important = 50

d.Very important = 100

e.Mandatory = 250

Now, assume there is some fictional bloke called Deepak looking at Anjali’s profile. He thinks she is interesting. It’s the same on her side. To figure out if they make the cut for each other and ought to meet, a questionnaire has to be answered. It is thrown at them.

1.Do you like aloo paratha in the morning?

2.How important is meeting with friends on Saturday evening to you? (From 1 to 5).

What follows now is a scenario like this: 

In response to Question 1, Deepak picks Option B and so does Anjali. Both score 10 points each.

In response to Question 2, Deepak picks, say, 4 and Anjali picks Option 2. That means, in the algorithm’s scheme of things Deepak said Yes and Anjali said No. 

So eventually when the scores are averaged out, it would turn out to be a mismatch. This, although Anjali did not exactly say she is closed to the idea. Just that it isn’t as important to her as it is to Deepak. 

The fundamental problem here that the algorithm cannot address is to figure out whether in going out with Deepak, Anjali would very much want to be out with friends on a Saturday evening. To that extent, it still has some way to go before it begins to understand the concept of compatibility.

Tip #3: The Optimal Stopping Theory 

First, the conclusion: Try figure out how many potential people you are going to meet before you decide to settle down. After having figured that out, it turns out you reject 37% of the first possible suitors in your lifetime (36.8%, to be precise). 

A group of mathematicians on this vexing problem, the outcome of which is a paper that can be downloaded on Project Euclid and is called "Who Solved the Secretary Problem?" A very lucid explanation of how the math works can be had on the Datagenetics Blog.

How do you apply this in your own context? It depends on what kind of a social setting and milieu you live in. What if, for instance, yours is a very traditional Indian family that insists on going on “arranged marriage" route? And to add a tinge of modernity, the potential partners are allowed to meet. Let’s say you are 26, and family tradition dictates you have to be married by 27. 

Best-case scenario, you get to meet a potential partner every week for a year. That means your outer limit is 52 potential suitors. Ceteris paribus, reject the first 37% and take the bloody call.

Alternatively, what if you’re the more modern kind? Assume you start dating at around 16 and on average lasts with a partner for about two years on the outside. That means, by around age 40, you’d have dated 12 people. 

In your head, if you think you intend to settle down with somebody for the rest of your life by 40, ceteris paribus, 37% of the potential 12 suitors you have in mind means you best chance of striking your best potential match is either the fourth or fifth suitor—more strictly the fourth one because the odds in percentage terms are higher by a few decimal points.

Cupid? Sounds stupid.

Charles Assisi is co-founder of Founding Fuel Publishing

His Twitter handle is @c_assisi

Comments are welcome at feedback@livemint.com

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