Musings about Soulmate

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When can you find your soulmate (if you don't have one yet...), and how? Sounds like a philosophical and psychological question. Yes of course the question can be answered from those mental/spiritual perspectives,  but let's do some maths here. Okay, here is the plan, I'm going to address this question in the two following ways.

lol

                                 Source: https://lovelace-media.imgix.net/

1. Drake Equation

Searching soulmate in your life is a lot like SETI. In all that vastness, just as the aim of searching for some form of life in the universe, we are seeking for someone else on earth to share the rest of our life with. Let me first introduce the famous Drake equation, which was originally introduced by Dr. Frank Drake in the 1960s to estimate the number of extra-terrestrial civilizations in our galaxy,

$latex N=R\cdot f_{p}\cdot n_{e}\cdot f_{l} \cdot \cdot f_{i} \cdot f_{c} \cdot L $

You can easily find the interpretations of the parameters and the equation by following the link above to Drake equation. But here, let's focus on how we apply this equation to our problem. Here is the equation after adjustment,


$latex n=P\cdot f_{t}\cdot f_{o}\cdot f_{c}\cdot A\cdot R $

(Click above to calculate the number of relationships you can expect to have in a year)


where P is the population (potentially it can mean the number of people in your city, country, etc.); $latex f_{t} $ means the pool which you want to mate with (depending on whether you are straight, gay man, lesbian woman, or other type); $latex f_{o} $ means the people that want to mate with you (same as $latex f_{t} $ before, just from other people's perspective);  $latex f_{c} $ is a little bit fuzzier to interpret, but according to author Raymond Francis, it means "Of the people in your target gender and orientation, how many of them are open enough about their sexuality to engage in a relationship of the sort you’re hoping for?".

Any keen Big Bang Theory fan will find the following clip familiar (me myself included :P), which quoted the above Drake equation to illustrate the exact same situation here:

https://youtu.be/WSkPLBIU3R4

2. Secretaty/Marriage Problem

Another thread of thinking has been addressed by the famous secretary problem in the optimal stopping theory, which is also dubbed the marriage problem.  Say my Mr. right is the jth people I meet in my dating pool, then one of the first k (k<j) people is the best among the first j-1. To put in simple maths,

$latex P_{n}(k)=\sum_{j=k+1}^{n}\frac{k}{j-1}\frac{1}{n}=\frac{k}{n}\sum_{j=k+1}^{n}\frac{n}{j-1}\frac{1}{n}\approx -\frac{k}{n}ln(\frac{k}{n}) $

the last approximation holds as n approaches infinity. If we substitute $latex \frac{k}{n} $ and take the derivative of P(x)=-xln(x) with respect to x, we find the optimal x is equal to 1/e, where e is 2.71... Thus, the optimal cut-off tends to n/e as n increases.

So if you listen to maths, date roughly $latex 1/e \approx 37\% $ of the total number of people available to you in your whole dating pool, and pick the first one after this first 37% that is better than any of the ones in the 37% pool.

Your love is one in a million, You couldn’t buy it at any price.
But of the 9.999 hundred thousand other loves, Statistically, some of them would be equally nice.
- If I didn't have you (Tim Minchin)

With all that said, don't be chagrined if you still haven't found your soulmate. Go strong and use maths to find the one that fits the bill! (Just a side note, this TED talk on "The mathematics of love" by Hannah Fry is just as riveting as my blog post :D )

References:

[1] http://www.today.com/news/man-behind-why-i-dont-have-girlfriend-theory-marry-6C10069890

[2] https://en.wikipedia.org/wiki/Secretary_problem