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January 15, 2010

Why am I single? Do the math. Srsly, do the MATH.

Filed under: Treats — posted by Kristine @ 11:26 am

The really rather cute Peter Backus, a Ph.D. candidate in economics in England, has boldly attempted to solve one of the great mysteries of the universe, otherwise known as “Why I don’t have a girlfriend.”

To do so, he employs The Drake Equation, which “is used to estimate the number of highly evolved civilisations that might exist in our galaxy,” he writes. “I have used this approach to estimate the number of potential girlfriends in the UK. The results are not encouraging. The probability of finding love in the UK is only about 100 times better than the probability of finding intelligent life in our galaxy.”

The equation was developed in 1961 by Dr. Frank Drake at the National Radio Astronomy Observatory in Green Bank, West Virginia. The equation is generally specified as:

G = R • fP • ne • fl • fi • fe • L

G = The number of civilizations capable of interstellar communication
R = The rate of formation of stars capable of supporting life (stars like our Sun)
ne = The average number of planets similar to Earth per planetary system
fl = The fraction of the Earth-like planets supporting life of any kind
fi = The fraction of life-supporting planets where intelligent life develops
fc = The fraction of planets with intelligent life that are capable of interstellar communication (those which have electromagnetic technology like radio or TV)
L = The length of time such communicating civilizations survive

Backus makes the following adjustments:

G = N* • fm • fl • fA • fU • fB

G = The number of potential girlfriends.
R = The rate of formation of people in the UK (i.e. population growth).
fW = The fraction of people in the UK who are women.
fL = The fraction of women in the UK who live in London.
fA = The fraction of the women in London who are age-­appropriate.
fU = The fraction of age-­appropriate women in London with a university education.
fB = The fraction of university educated, age-­appropriate women in London who I find physically attractive.
L = The length of time in years that I have been alive thus making an encounter with a potential girlfriend possible.

With me so far? I am now going to attempt to apply Backus’ equation to my chance of finding a man in New York — with the following caveats.

G = The number of potential boyfriends (rather than girlfriends as I like the men folk)

Since Backus simplified the R in Drake’s equation by replacing it with N* (the population of the entire UK), I will also simplify for the estimated population of the entire United States as of 2008. So, N* = 304,059,724

Backus’s fw = the fraction of people in the UK who are female. Therefore, adjusting for my purposes of the fraction of males in the U.S. I will use Fm to denote this number. Fm = the fraction of people in the U.S. who are male [0.493]

FL = the fraction of men in the U.S. who live in NY

According to the U.S. Census Bureau’s estimates for 2008, the population of the state of New York is 19,490,297 – 51.5% of which are female. Therefore, 48.5% or [0.485] are male. By multiplying the fraction of males in NY [M1] with the total population of NY [P1] we will get the total male population of NY [TM1].

TM1 = M1 • P1
TM1 = [.485] • [19,490,297]
TM1 = 9,452,794.045

Now that we have the total number of men living in NY, we must now solve for [FL] to find the fraction of U.S. men living in NY.

To do that we take the U.S. Census Bureau’s estimates for 2008’s population of the U.S. 304,059,724 – 50.7% of which are female. Using the above equation, again we solve for TM.

TM = M • P
TM = [.493] • [304,059,724]
TM = 149,901,443.932

To find FL, we want to know of the total men in the U.S., what fraction lives in NY. So, taking TM1 and TM, we use the following equation:

TM1 = FL • TM

FL = TM1 / TM

FL = 9,452,794.045 / 149,901,443.932

FL = .06306005997706 (approximately) or 0.063

FA = The fraction of men in NY who are age appropriate

As Backus notes on his website, I would also like my boyfriend to be close in age to me, but as Census Bureau information doesn’t fall exactly as I would like, I will cast a wider net for purposes of this equation and include males between the ages of 25-44. The total population of NY between the ages of 25-44 is 5,382,487. Assuming the same percentage of men within this age group is comparable to the general population then 48.5% are male. To figure out the exact number of age-appropriate [AA] males:

AA = 5,382,487 • [.485].
AA = 2,610,506.195

To find FA, we must then take AA and find out what fraction it is to the total male population of NY.

FA = 2,610,506.195 / 9,452,794.045
FA = 0.27616238993177 or 0.276

FU = The fraction of age-appropriate men in NY with a university education I’ll admit it, I’m as much of an elitist as Backus (see his PDF) and want a man with an education. (Obviously, I can do math, so it would be nice if my significant other, you know, could too.) 27.4% of New Yorkers over the age of 25 have at least a bachelors degree or higher. For the sake of brevity, we will assume that this fraction can approximately be applied to the age-appropriate men of New York. Therefore,


FB = The fraction of university educated, age-appropriate men in New York who I find physically attractive.

For simplicity’s sake (and because my brain may soon implode), I will be as generous as Backus and say that I find 1 in 20 or 5% [0.05] of age-appropriate men in New York attractive.


L = The length of time in years that I have been alive thus making an encounter with a potential boyfriend possible. I am older [33 – yay!] than Backus so in this case, L = 33

Finally, if we are all still sane, we plug all the numbers into the equation.

G = N* • fm • fL • fA • fU • fB

G = 304,059,724 • [0.493] • [0.063] • [0.276] • [0.274] •[0.05]

G = 35,708.862407127739

If I round up, to a solid, full man number, I get the following:

G = 35,709

OK! If I am to follow Backus’ argument, there are potentially 35,709 men in the U.S. who satisfy the minimum criteria for being my boyfriend. That’s .011% of the U.S. population in 2008 and .018% of New York’s population. Though, that seems a little odd considering Backus’ percentages are reversed with the whole of the UK having a higher percentage meeting his minimum criteria than simply all of London. It would make sense to have a higher likelihood of Londoners meeting his minimum criteria seeing as one of said criteria was to be located in London.

What I don’t get is where [L] comes into the equation. Somehow, age plays a factor in the calculation, but where exactly does the age factor actually become important? Perhaps it became irrelevant after N* replaced R in Drake’s equation? Basically, after spending an afternoon doing the math and looking for Census Bureau statistics, I have to conclude that I would have exponentially increased my likelihood of finding a boyfriend by actually going outdoors (or hey, online) and actually meeting. After all, it only takes 1 in 35,709. With 401.9 people per square mile, that’s not bad at all.


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