# Close encounters of the mathematical kind

Are we alone in the universe? It’s a question that’s been asked by people all over the world as they look up at the stars and wonder if anyone is peering back. As an astronomer, Dr. Frank Drake spends more time gazing into the heavens than most, using optical and radio telescopes. In 1961 he came up with an equation to help us think about the possibility of extraterrestrial life, and founded a branch of astronomy called SETI, the Search for Extra-Terrestrial Intelligence.

### Drake’s dilemma

The Drake equation, as it is now known, looks like this:

N = R* · fp × ne × fl × fi × fc × L

N is the number of alien civilizations in our galaxy with which we might one day be able to communicate

R* is the number of new stars that form in the galaxy each year

fp is the fraction of those stars that have orbiting planets

ne is the number of planets orbiting a star that can potentially support life

fl is the fraction of those planets on which life actually emerges

fi is the fraction of life-bearing planets that develop intelligent life

fc is the fraction of civilisations that have the technology to communicate across the stars.

L is the length of time a civilisation communicates for

It’s hard to place a figure on any of these variables, because we only know of one intelligent civilisation – us! We can use what we know about the solar system to come up with some estimates, but the value of N can vary widely, depending on which numbers we choose. If you’d like to try and find your own value for N, this interactive tool will let you experiment.

Of all the variables in the Drake equation, we probably have the best idea about R*. Astronomers observing changes in the Milky Way galaxy reckon that about seven new stars are born each year. Next is fp, which is a little trickier. We’ve only discovered around 400 planets outside of our solar system, which isn’t much compared to the 100 billion stars of the Milky Way! Estimates for fp range from 20 to 60%, with 50% seen as the most likely.