Why I don’t have a girlfriend:
An application of the Drake Equation to love in the UK
Peter Backus
The Drake equation is used to estimate the number of highly evolved
civilizations that might exist 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 ⋅ f P ⋅ ne ⋅ f l ⋅ f i ⋅ f e ⋅ L
where,
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 kindfi = 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
Using this equation Prof Drake estimated that 10,000 communicative
civilizations probabilistically exist in the Milky Way alone. Astronomers estimatethat there are between 200 and 400 billion stars in the Milky Way. Let’s call it
300 billion. This makes the probability of a star chosen at random supporting life
capable of interstellar communication 3.333e‐08 or 0.00000003%.
Another way to think about this is that this is the probability of the conditions
necessary for us to communicate with an alien civilization being satisfied. These
seem like slim odds at best, but the probability is positive (There is a chance!)
and this approach is widely accepted by astronomers (This isn’t a sciencefiction!). The idea that there could be 10,000 civilizations that we are capable ofcommunicating with is very exciting indeed.
While extraterrestrial civilizations may be rare, there is something that isseemingly rarer still: A girlfriend. For me. What might the approach employed in
the estimation of the number of alien civilizations tell us about the number ofpotential girlfriends for me? A somewhat less scientific question, I admit, but oneof substantial personal importance.

1The parameters are re‐defined as follows with the values in parentheses:
G = The number of potential girlfriends.
One can easily substitute boyfriends in here but as I am mostly aheterosexual male I will focus on the search for a girlfriend.
R = The rate of formation of people in the UK (i.e. population growth).
This is about 150,000 people per year over the last 60 years.1
fW = The fraction of people in the UK who are women.
See the above clarification. (0.51)
fL=The fraction of women in the UK who live in London.
I would like my girlfriend to be nearby so that we can see each other. Thismakes it easier to get to know each other, avoids the difficulties of a long
distance relationship and saves me the train fare. (0.13)
fA = The fraction of the women in London who are age­appropriate.
I am nearly 31 years old (Thank you, I know I don’t look it). I would likemy girlfriend to be near my own age. I don’t want to feel older than I am
by not being able to keep up with a spritely 20 year old, or because I
haven’t read Twilight and I don’t know who the Jonas Brothers are. Nor
do I want to fall prey to a voracious cougar or to be regaled with stories ofthe war. Lets say I am looking for a woman between 24 and 34 years ofage. (0.20)
fU = The fraction of age­appropriate women in London with a university
education.
I am not trying to be an elitist or anything, but I would like my girlfriend
to have a university education. I think we would have more in common
and I would like someone I could discuss my work with sometimes. I
know that there are many intelligent people who don’t go to university, sodon’t get all righteously indignant. Everyone has preferences. How many
women out there have dated men shorter than themselves? I rest mycase. (0.26)

1 http://www.statistics.gov.uk/cci/nugget.asp?ID=950

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fB = The fraction of university educated, age­appropriate women in London
who I find physically attractive.
Physical attractiveness is important. It is often the first thing people
notice about each other and it makes sex easier. Not that my potential
girlfriend need be considered attractive by anyone else, but it isimportant that I find her attractive. This is a tough parameter toestimate. Let’s be generous and say I find 1 in 20, or 5% of age‐appropriate women in London with a university education physicallyattractive. (0.05)
L = The length of time in years that I have been alive thus making anencounter with a potential girlfriend possible.
Good lord, I am old. (31)
We can simplify the above specification by recognizing that the number of people
who have ever lived in the UK is related to the population growth rate by
N = ∫ 0 R(t)dtT

where T is the age of the UK. If we assume that R is constant over the period T
than N = R ⋅ T . While this simplification is often used for the Drake Equation’s
intended purpose, it is not a good assumption when adapting the equation forour purposes here. Instead we use N*, the population of the UK as of 2007, whereN*=60,975,000.2
With this simplification we can re‐specify the Drake equation as:

G = N *⋅ f W ⋅ f L ⋅ f A ⋅ fU ⋅ f B
If we plug in the above values we get:G = 60,975,000 ⋅ 0.51⋅ 0.13⋅ 0.20 ⋅ 0.26 ⋅ 0.05

orG=10,510So, what this means is that there are 10,510 people in the UK that satisfy thesemost basic criteria for being my girlfriend. That is 0.00017% of the UK and
0.0014% of Londoners, which doesn’t seem so bad. On a given night in London,
there is greater than a 1 in 1000 chance that I will meet an attractive woman
between the ages of 24 and 34 with a university degree. Of course this does nottake into account the fraction of these women that will find me attractive
2 http://www.statistics.gov.uk/cci/nugget.asp?ID=950

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(depressingly low), the fraction of these women who will be single (falling withage) and, perhaps most importantly, the fraction of these women who I will getalong with. Including such factors would greatly reduce the above figure of
10,510. A rough estimate puts the number of potential girlfriends accounting forthese three additional criteria (1 in 20 of the women find me attractive, half aresingle and I get along with 1 in 10) at 26. That’s correct. There are 26 women inLondon with whom I might have a wonderful relationship. So, on a given nightout in London there is a 0.0000034% chance of meeting one of these special
people, about 100 times better than finding an alien civilization we cancommunicate with. That’s a 1 in 285,000 chance. Not great.
Make of this what you will. It might cheer you up, it might depress you. I guess it
depends on what you thought your chances were before reading this.

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