The Drake Equation and the probability of alien intelligence

It isn't the kind of rigorous mathematical equation like you'd find in calculus or trigonometry, and critics will point out that it isn't even really a probabilistic equation either, but it was never really intended to be one.

Originally designed to spark debate within the SETI community, the Drake Equation is easily misconstrued when taken out of its original context, but it has also gotten a bit of a bump lately with the discovery of exoplanets, a key factor in how the equation is designed to work.

At its core though, the Drake Equation is meant to challenge us to think strategically about our search for alien civilizations while providing a glimmer of hope that such a search isn't a complete waste of time and resources.

What does the Drake Equation calculate?

The Drake Equation tries to make educated guesses about several factors on the developmental road to an advanced, communication-capable alien civilization and assess the probability of finding such a civilization out in the galaxy.

Some of the variables are readily quantifiable, like the number of stars in the galaxy, while others are downright philosophical, like the amount of time that a civilization that has the ability to communicate can exist before it disappears through self-destruction or some other kind of calamity.

Ultimately, the results of the equation can vary dramatically depending on what assumptions you choose when calculating a result, so you can just as easily predict less than a dozen communicative civilizations in a galaxy of 400 billion stars, or it can produce a more optimistic 100,000 or even more than a million.

From there, simply applying statistical distribution methods could then reveal how far away an alien civilization might be from Earth.

What are the parts of the Drake Equation?

The actual Drake Equation is:

The parts of the Drake Equation are as follows:

• R_∗ = average rate of the Milky Way's star formation.
• f_p = fraction of those stars that have planets
• n_e = average number of planets that might be able to support life per star that has planets
• f_l = fraction of planets that could support life that actually develops life
• f_i = fraction of planets with life that go on to develop intelligent life
• f_c = fraction of advanced civilizations capable of releasing detectable signals of their existence into the galaxy
• L = length of time that such civilizations release detectable signals

Some of the variables in this equation were already known when the equation was proposed, while some variables remain entirely unknown, even to this day, though the uncertainties of the variables generally increase as you move further to the right through the equation. 

“The question of whether advanced civilizations exist elsewhere in the universe has always been vexed with three large uncertainties in the Drake equation,” said Adam Frank, a professor of physics and astronomy at the University of Rochester and the co-author of a 2016 paper in the journal Astrobiology that sought to reframe the Drake Equation in light of the discovery of exoplanets.

“We’ve known for a long time approximately how many stars exist. We didn’t know how many of those stars had planets that could potentially harbor life, how often life might evolve and lead to intelligent beings, and how long any civilizations might last before becoming extinct.”

Who came up with the Drake Equation?

The Drake Equation was developed by Dr. Frank Drake in 1961 for the first meeting on the search for extraterrestrial life at the National Radio Astronomy Observatory in Green Bank, West Virginia.

In 1961, radio astronomy was in its infancy, and SETI as an actual, scientifically rigorous pursuit simply hadn't been attempted before. In many ways, the Drake Equation was simply an attempt to find a place to start the process, rather than develop an actual calculus for researchers to use.

Regardless, the Drake Equation captured the imagination of those in attendance, including Carl Sagan, one of the 20th century's most important science communicators and a passionate advocate for continued SETI efforts.

Sagan and others helped the Drake Equation gain popular traction in a way that made it impossible to ignore by the scientific community as a whole, even if it was just to dispute the formula's premise.

How is the Drake Equation useful?

The major criticism lodged against the Drake Equation isn't that it's tinfoil-hat fodder, but that most of the variables in the equation are so speculative as to render the equation meaningless.

There has only been one advanced civilization in the entire universe that we know of: ours. In the 60-plus years since the Drake Equation was first proposed, no one has been able to determine L, the length of time that an advanced civilization is able to communicate its existence into space after developing the technology to do so.

We know that that answer might be more than 100, which is how long humans have been using radio waves to broadcast signals, but are we outliers?

Do civilizations typically destroy themselves within a decade of developing such technology? Within 50 years? That is about how long it took between the first radio signals and the first atomic bombs. Is it possible for a species to survive indefinitely as a technologically advanced civilization?

We have a case study of one, and the verdict on humanity is still out, so there's no scientifically rigorous way we can ever really fill in that final variable, and that variable can mean the difference between being alone in the galaxy or having neighbors just down the interstellar road.

So is the Drake Equation useful in any meaningful way? Yes, it is, especially as a basis for further exploration and thinking about SETI which was the entire point of the equation in the first place.

In the case of Frank Drake's study on the Drake Equation, he and co-author Woodruff Sullivan, of the University of Washington's astronomy department and astrobiology program, refined the equation by inverting it.

Rather than ask how many alien civilizations there might be out in the galaxy, they developed a modified equation that determined how unlikely life would have to be for human civilization to be the only civilization in the galaxy.

"Rather than asking how many civilizations may exist now, we ask ‘Are we the only technological species that has ever arisen?" said Sullivan. “This shifted focus eliminates the uncertainty of the civilization lifetime question and allows us to address what we call the ‘cosmic archaeological question’—how often in the history of the universe has life evolved to an advanced state?”

And since the recent discoveries of thousands of exoplanets—which were still just theoretical in 1961—has shown that about 20 percent of them lay in their star's habitable zone, the uncertainties of the Drake Equation are further reduced.

“From a fundamental perspective, the question is ‘has it ever happened anywhere before?’" said Drake. "Our result is the first time anyone has been able to set any empirical answer for that question and it is astonishingly likely that we are not the only time and place that an advance civilization has evolved.”

What's more, the Drake Equation also helps shape our study of exoplanets by narrowing down the planets of greatest interest, those where advanced life is most likely to evolve. In a galaxy of 400 billion stars, we definitely need all the help we can get working our way through that haystack in search of a few metaphorical needles.

And finally, we can't discount the aspirational quality of the Drake Equation, and that matters. If the odds tell you that life doesn't exist out there, then why bother searching at all?

But if you can look at the Drake Equation and see the potential payoff of thousands of possible alien civilizations broadcasting their presence into the universe, then that might be enough to keep an astronomer going after their thousandth night of listening to the silence of the universe. After all, you cannot find what you never search for in the first place.