The Drake Equation

The discovery last week of Kepler-452B, an earthlike planet orbiting a sunlike star in the habitable zone (sometimes known as the Goldilocks zone), has once again raised the question of whether we can find intelligent life elsewhere in the galaxy.

It's been an open question since ancient times. Anaxagoras, a Greek philosopher of the 5th century BCE, suggested that the moon was a world like ours, and was inhabited by people like us. He also suggested that the stars were other suns of distant planets. More recently, a number of scientists (including Svante Arrhenius, who first quantified the greenhouse effect, and Lord Kelvin, who helped resolve Olbers' paradox) have taken seriously the idea that not only does life exist elsewhere in the galaxy, but that our own planet was seeded by microscopic life that originiated elsewhere.

In the late 1950s astronomers began to explore the possibility of using radio telescopes to listen for signals from extraterrestrial civilizations. Frank Drake of Cornell University initiated Project Ozma in 1960, slowly scanning various radio frequencies. In order to spur discussions about the likelihood of finding a signal, Drake came up with the following equation.

N = R_* * f_p * N_e * f_ℓ * f_i * f_c * L

The variables are as follows:

N: Number of civilizations able to communicate via radio signals

R_*: Rate of star formation (number of stars per year)

f_p: Fraction of stars with a planet

N_e: Number of planets per star capable of sustaining life

f_ℓ: Fraction of these planets that actually develop life

f_i: Fraction of these planets that develop intelligent life

f_c: Fraction of these planets that develop a civilization capable of using radio waves

L: Length of time the typical civilization exists

If we knew the correct values for all these variables, we would know the probability of finding life somewhere in the Milky Way. But we only have reasonable estimates for the first three, and wild guesses for the rest.

The galaxy contains enough interstellar gas to coalesce into about seven new stars per year, and as our telescopes improve we're finding planets around all types of stars. So R_* is about 7, and f_p could be as high as 1. But as we go through the variables our guesses get increasingly speculative.

Our solar system has two planets in the habitable zone: Earth and Mars. If our solar system is typical, n_e is 2. On the other hand, there's no reason to assume our solar system is typical. After all, we know there's a civilization here using radio communication. We can't let our existence bias our search for other civilizations.

At this point, results from the Kepler telescope indicate perhaps 40 billion habitable planets in the galaxy, out of 100 billion stars. That's an average of 0.4 per star. That number may be revised as we continue to learn more about our galaxy, but 0.4 is the best estimate we have.

The remaining variables are almost impossible to calculate. Again, we have in our own solar system a planet where intelligent life actually arose, but again there's no reason to believe we are typical. If it were easy for life to arise from non-matter, we should see it continuing to happen on our own planet. Apparently it can only happen under specific conditions, and we still don't know what those conditions are. Any number we pick for f_ℓ is therefore only a guess.

The same is true for f_i and f_c. Since the only example we have is our own civilization, we have no idea what is typical. Perhaps we are typical because we're the only one. Or perhaps there are many others just like us.  But chances are, life does not take the same pathways everywhere. It's possible that most planets even in the Goldilocks zone don't have a habitat conducive to big-brained creatures. It's even possible that the majority of life-bearing planets have nothing more complex than bacteria.

I've seen estimates close to 1 for f_ℓ, f_i, and f_c. My own estimates are 0.1, 0.01, and 0.2 respectively. I've got no solid reason for those numbers, other than a vague belief life is not as common and not as resilient as we'd like to hope.

Of the three fractions, it seems most likely that the existence of an intelligent species would lead to technological advancement. But there are a number of reasons it might not. It's possible that most intelligent species don't have opposable thumbs allowing them to build complex structures or write documentation for future generations. it's possible they spend their days composing songs and poetry rather than fiddling with electronic devices. It's possible that civilizations more often than not succumb to disease and starvation before advancing their technology to overcome these threats. It's possible that the majority of technology-building species focus their research on warfare to the exclusion of interstellar communication. There are all kinds of reasons an intelligent species might not be able to receive our radio signals. And that's not even including the ones that simply might not want to communicate with us.

My estimate for L is also lower than a lot of estimates I've seen. Some experts argue that civilization on Earth has already lasted thousands of years, and see no reason it can't last thousands more. But that misses the point. If there are aliens out there, they couldn't even potentially have communicated with us until we developed radio receivers, which was only about 120 years ago. And the same technology push that gave us radio communication has already provided us multiple ways of destroying our civilization—whether intentionally through the use of nuclear or chemical weapons, or unintentionally through polluted water sources or runaway greenhouse gases. We're a short-sighted species and there's no reason to think we'll ever change. I'd be surprised if a technologically advanced society lasts more than 500 years on this planet. Again, there's no reason to think we're typical, but since we've got no other data points, I'm going to use this for my estimate.

So, now that we've got numbers for all the variables, it's time to plug them in. There's a handy Drake equation calculator here (and another one here, with helpful explanatory notes if you're willing to scroll down past other nerdy things to find the Drake calculator). And the results are in: Using my estimates, there should be 0.28 advanced civilizations in the galaxy in a typical year. To put that in perspective, for every 500 years that a civilization exists, there should be about 1250 years following its collapse before the next civilization arises somewhere else in the galaxy. (Where's Hari Seldon when you need him?) It's highly unlikely that any two planets would have advanced civilizations at the same time. Of course these are averages, and it's possible that at some point in the history of the galaxy two civilizations overlapped, but regardless, the bulk of our galaxy's history has probably been devoid of even one civilization able to transmit radio signals. Our attempt to communicate with anyone beyond the earth is likely doomed to failure.

Then again, my estimates could be too low. The purpose of the Drake equation is not to give a definitive answer, but to spur conversation. If you're willing to play along, try tweaking the numbers in the calculator and share your results in the comments.