Abstract
This post shows how the famous Drake Equation can also be applied to an everyday topic like love. The Drake Equation gives us an estimate of the number of technologically advanced civilizations that might exist among the stars. In this context the equation is used to estimate the approximate number of (the authors) potential girlfriends in Austria. The result shows that the estimate is about 7 and therefore it is very unlikely to meet your significant other on a given night out.
Introduction
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 * fp * ne * fl * fi * fe * 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)
- fp = The fraction of those stars that have planets
- 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
- fe = 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 estimate that 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 science fiction!). The idea that there could be 10,000 civilizations that we are capable of communicating with is very exciting indeed.
Methods and Results
While extraterrestrial civilizations may be rare, there is something that is seemingly 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 of potential girlfriends for me? A somewhat less scientific question, I admit, but one of substantial personal importance.
The parameters are re-defined as follows with the values in parentheses:
- G = The number of potential girlfriends.
One (/the reader) can easily substitute boyfriends in here but as I am a heterosexual male I will focus on the search for a girlfriend. - R = The rate of formation of people in Austria (i.e. population growth).
This is about 47 800 people per year over the last 10 years (2006 – 2016) - fw = The fraction of people in Austria who are women.
See the above clarification. (0.5084) - fl = The fraction of women in Austria who live in Upper Austria.
I would like my girlfriend to be nearby so that we can see each other. This makes it easier to get to know each other, avoids the difficulties of a long distance relationship and saves me the train fare. (0.1656) - fa = The fraction of the women in Upper Austria who are age-appropriate.
I am a little over 23 years old. I would like my 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 16 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 of the war. Let’s say I am looking for a woman between 20 and 29 years of age. (0.1220) - fu = The fraction of age-appropriate women in Upper Austria with 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, so don't get all righteously indignant. Everyone has preferences. How many women out there have dated men shorter than themselves? I rest my case. (0.1639) - fb = The fraction of university educated, age-appropriate women in Upper Austria 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 needs to be considered attractive by anyone else, but it is important that I find her attractive. This is a tough parameter to estimate. Let's be generous and say I find 1 in 5, or 20% of age-appropriate women in Upper Austria with a university education physically attractive. (0.2) - L = The length of time in years that I have been alive thus making an encounter with a potential girlfriend possible.
I’m 23, so let’s go with that.
We can simplify the above specification by recognizing that the number of people who have ever lived in Austria is related to the population growth rate by:
Where T is the age of Austria. If we assume that R is constant over the period T then 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 for our purposes here. Instead we use N2017, the population of Austria as of 2017, where:
- N2017 = 8 809 212
With this simplification we can re-specify the Drake equation as:
- G = N2017 * fw * fl * fa * fu * fb
If we plug in the above values we get:
- G = 8 809 212 * 0.5084 * 0.1656 * 0.1220 * 0.1639 * 0.2
or - G = 2966.0039
Conclusion
So, what this means is that there are 2966 people in Austria that satisfy these most basic criteria for being my girlfriend. That is 0,034% of Austrians and 0.202% of Upper Austrians, which doesn't seem so bad. On a given night in Upper Austria, there is greater than a 2 in 1000 chance that I will meet an attractive woman between the ages of 20 and 29 with a university degree. Of course this does not take into account the fraction of these women that will find me attractive (depressingly low), the fraction of these women who will be single (falling with age) and, perhaps most importantly, the fraction of these women who I will get along with. Including such factors would greatly reduce the above figure of 2966. A rough estimate puts the number of potential girlfriends accounting for these three additional criteria (1 in 20 of the women find me attractive, half are single and I get along with 1 in 10) at 7. That's correct. There are 7 women in Upper Austria with whom I might have a wonderful relationship. So, on a given night out in Upper Austria there is a 0.000506128% chance of meeting one of these special people. This is probably why I don’t bother going out anymore. Not great.
References
- Why I don’t have a girlfriend, Peter Backus: 2010;
- Drake Equation, SETI: 2018;
- Bevölkerungsverteilung Österreich – Bildungsstand, Statistik Austria: 2015;
- Bevölkerungsverteilung Österreich, Land Oberösterreich: 2018;
- Bevölkerungsverteilung Österreich, Land Oberösterreich: 2016;
- Gender Daten, Bundesministerium für Frauen und Gleichstellung: 2018;
- Gender Index, Bundesministerium für Frauen und Gleichstellung: 2017;
- Population Total, Worldbank: 2017;
- Population Growth, Worldbank: 2017;