In 1961, the physicist Frank Drake looked out over the starry sky in West Virginia and wondered if there could be intelligent life out there. After searching for radio signals from two of our nearest stars without result, he decided to try to estimate how many civilizations there should be in the Milky Way – civilizations intelligent enough to send radio signals into space. The mathematical model he then developed was named Drake's equation.

Fifty years later, the British mathematician Peter Backus was sitting in his London apartment, wondering why he still did not have a girlfriend. When he read about Drake's equation, he realized that he could adapt it to estimate the number of potential girlfriends in Britain. He published the result with a pinch of self-distance in the article "Why do I not have a girlfriend: An application of the Drake Equation to love in the UK".

His conclusions? We will return to those. First, let's take a closer look at Frank Drake's equation.

Drake’s equation

Frank Drake was interested in trying to estimate the number of active civilizations in the Milky Way capable of sending signals into space. He realized that the final answer (N) would depend on a number of factors, such as the rate at which new stars form in the Milky Way (R), the proportion of these stars that have planets around them (fp) and how many of these planets who have the conditions for life (ne). He also needed to take into account the proportion of these planets where life actually occurs at some point (f1), the probability that this life develops into an intelligent civilization (fi) and the proportion of these civilizations that become skilled enough to send communicative signals into space (fc). By making qualified guesses about the values ​​of all these parameters, he was able to estimate the number of intelligent civilizations in the Milky Way. The answer he came up with was surprising – about 10,000 (!).

You can think of Drake's process a bit like a search for a new home on Zillow. You start by choosing in which geographical area you want to live, specify the type of accommodation you are looking for (villa, townhouse, apartment) and how many rooms you want. Then you define a price range and click on a few keywords, such as balcony or fireplace, that you can not imagine to compromise with. As you refine your search criteria, the number of possible homes is scaled down, until you find out how many homes on the market match your requirements.

Drake's equation in the service of love

Let's now see how Peter Backus used Drake's equation to get an idea of ​​how many women in Britain he could have a meaningful relationship with. He asked himself the following questions:

1. How big is the population in the UK?
60,975,000

2. What percentage of the UK's residents are women? (51%)
0.51 · 60 975 000 = 31 097 250

3. What percentage of the UK's female residents live in London? (13%) 0.13 · 31 097 250 = 4 042 642.5

4. What proportion of women in London are in a suitable age range, 24-34 years? (20%)
0.20 · 4 042 642.5 = 808 528.5

5. What proportion of these women have a university education? (26%)
0.26 · 808 528.5 = 210 217.41

6. What percentage of women with a university degree in London will I find attractive? (5%)
0.05 · 210 217.41 = 10 510.8705

7. What percentage of those women will find me attractive? (5%)
0.05 · 10 510.8705 = 525, 543525

8. What percentage of those women will I get along well with? (10%)
0.10 · 525.543525 = 52.5543525

9. What percentage of those women will be single? (50%)
0.5 · 52.5543525 ≈ 26

According to Backus' estimates, there were 26 single women in London who met all the criteria. Teasing, you could say that there were far more planets in the Milky Way with intelligent life (10,000) than possible girlfriends for Backus in London…

The key to finding love

The odds of finding love may seem small, but do not despair. With a closer look at Drake's equation and Peter Backus' logic, we can find ways to polish the numbers in our favor. An obvious objection to our calculations is that we have made fairly rough estimates, and small adjustments to these estimates can have a major impact on the end result. That insight, in turn, leads to something important: a heart that is open to many different possibilities will find it much easier to find love. Are you willing to increase the age range, consider a larger geographical range and drop the criterion of university education? Well, then there are suddenly far more suitable candidates! (It was for example after I expanded the radius in the dating app Tinder that I managed to locate my wife – from France!)

Or the lesson is completely different. Peter Backus finally married his wife Rose in 2013. In the end, after all, only one successful match is needed.

References and further reading

Backus, Peter (2010) Why I don’t have a girlfriend

Fernandez, Oscar E (2017) The Calculus of Happiness. How a Mathematical Approach to Life Adds up to Health, Wealth and Love. Princeton University Press

Fry, Hannah (2015) Mathematics of love. Patterns, proof, and the search for the ultimate equation. Simon & Schuster

Interview with Peter Backus: Man behind 'Why I Don't Have a Girlfriend' theory to marry

Video: Carl Sagan explains Drake's equation

Video: Hanna Frys Ted Talk

Radioprogram: David Kestenbaum estimates the number of potential partners in Boston