Someday, in the not too distant future, we’ll know whether the cosmic ocean is as richly populated as the oceans on Earth. Evidence for life could come from icy moons in our solar system, or in the form of an interstellar radio message, or from telltale signatures in the atmosphere of a faraway exoplanet.
But even if we find sharks beneath Europan ice or intercept an interstellar SnapChat, we still won’t know whether extraterrestrial organisms are common. We still won’t know how often beings evolve and develop technology.
There is a formula that estimates the answer to this second unknown. Called the Drake Equation, it predicts the number of detectable, intelligent civilizations in the Milky Way galaxy. It does not predict the number of intelligent civilizations in the galaxy, period, or the number in the entire universe. It simply makes a statement about how many techno-worlds we can detect in our galactic neighborhood at any given time.
N = R*fpne fl fi fc L
The equation is straightforward. Devised by my dad, Frank, as a means of organizing a 1961 conference at the Green Bank Observatory, it lays out the factors needed for intelligent beings to evolve: The rate of star formation (R*), the fraction of those stars with planets (fp), the number of planets that are habitable, like Earth (ne), the fraction of those planets with life (fl), the fraction of those planets where organisms evolved to be intelligent (fi), and the fraction of those planets with civilizations that develop a detectable technology (fc).
Scientists are working on plugging in numbers to the equation, and have determined decent estimates for the first three factors. The rate at which those factors are being nailed down is increasing, and will probably continue to quicken as we peer ever deeper into the cosmos.
Except for when it comes to that the last one.
Of all the variables, the last term in the equation is the most vexing. It always has been, ever since that late autumn, West Virginia day when Dad scribbled the equation unceremoniously on a pad of paper.
Simply called “L,” this last, slippery term represents the average length of time a civilization is detectable. It’s an especially frustrating conundrum because in its most optimistic form, the equation collapses to N=L (*see footnote).
In other words, if you know L, you’ll know how many civilizations might be detectable. We can bang away at the other variables, sharpen our telescopes and design space-based spectrometers, but no tool in the shed can estimate L with any precision.
We will know L only when we’ve heard the murmurings of alien worlds.
But it gets more complicated.
“L isn’t just a stand-alone number. It’s actually dependent on the capabilities of the searching civilization,” Dad says
The rest of the equation’s terms, like the rate of star formation and the fraction of stars with planets, are what they are. They don’t depend on the abilities of the observer. “L” is different. As Dad says, L depends not only on who’s out there, but who’s looking.
Right now, if we want to estimate L, we only have Earth as an example. But are humans typical? “It’s a weak assumption,” Dad says. “There’s nothing to support the idea that we’re typical.”
Aliens with similar capabilities tuning in to our little watery world would have been able to detect radio broadcasts beginning nearly 80 years ago, around 1940. Now, Earth is going radio-quiet. The squawking of military radars and Walter Cronkite’s nightly dispatches on CBS are being replaced by cable TV and cell phones that merely whimper in radio frequencies. As we increase the efficiency with which we communicate, we muffle the space-faring signals that might betray our presence. Earth has gotten quieter and quieter, and soon, our planet might slip into silence.
If an alien civilization has reasonably sensitive radio telescopes, Earth might be detectable for somewhere on the order of a century.
But what if alien civilizations have developed vastly more impressive detection systems than ours? What if they’ve figured out how to hack their stars and use them as gravitational lenses, enormously powerful objects that warp spacetime and magnify distant objects? Such civilizations might be able to detect bright city lights (or massive wildfires) on another world. If that were the case, Earth’s L would be much greater; assuming we don’t fall prey to the sixth mass extinction, Earth could be detectable by these civilizations for countless millennia.
Once you have found a handful of civilizations, calculating L is as simple as taking the weighted arithmetic mean of individual L values. It works like this:
Let’s say you have 100 civilizations. Half of them are detectable for 100 years because they’re kind of like us. All but one of the rest are somewhere in between, say, detectable for 10,000 years because they haven’t figured out cable. And that last one is detectable for a billion years because it’s altruistically beaming signals across the cosmos.
“You would like to know the fraction of civilizations that fall into each of these categories,” Dad says. “And then you can define the average value of L.”
So, using the above example: .5(100) + .01(1 billion) + .49(10,000) = 50 + 10 million + 4,900 = 10,004,950.
L, and therefore N, equals 10,004,950.
Whoa. That civilization that’s detectable for a billion years is really messing things up. Or is it?
Why take the weighted arithmetic mean? It’s because you’re interested in finding out how many civilizations are beaming signals into the cosmos at any given moment. If space were a Christmas tree and each civilization were a light blinking on and off, you’d want to estimate how many lights you’d see in a given moment. And the number of lights you see greatly depends on how long those lights stay on. In other words, those outliers – though they may be few in number – count. Long-broadcasting civilizations dominate the true value of L, and determine the magnitude of the challenge to our search programs.
“It’s counterintuitive,” Dad says. “But those outliers are not mistakes, as do often occur in scientific data. In this case, they’re not bad data. If they really do last a billion years, that’s the way it is.”
One can hope there are at least a few of those worlds out there, and that we do find them.
But it’s also possible that humanity will be gone by the time some distant civilization, tens of thousands of light-years away, is listening to the strains of Rachmaninoff’s second piano concerto or swaying to the tunes of the Beatles.
“We are, to some extent, prisoners of our own moment in time,” Neil DeGrasse Tyson says, in this week’s episode of Cosmos: A Spacetime Odyssey.
The evolutionary clock starts and stops, slows and accelerates. Even if life began evolving on a distant planet at exactly the same instant as it did on Earth, those organisms would not be marching to the same metronome. One tiny pause, and we could miss them by 100,000 years – like ships that pass in the galactic night.
*It’s actually N=R*L, but most estimates have set R* equal to 1, for sun-like stars. That will have to change, though, as we learn more about planets around different types of stars. R* should increase.