In 1967, a graduate student named Jocelyn Bell discovered something strange emanating from a region of the sky known as the Summer Triangle: pulses of radio waves repeating every 1.3373 seconds over and over again like a clock ticking slightly-slowly.
It’s not every day that you find a nearly perfect clock ticking at you from the sky, so Bell and her colleagues half-jokingly called the source of the signal “LGM1”—the “LGM” being short for “Little Green Men.” We now know that this signal wasn’t from little green anythings, but was instead from a previously undiscovered type of object known as a pulsar. This was exciting, although perhaps not quite as exciting as finding aliens.
A decade later, an even stranger signal fell upon a different radio telescope. This signal was unusual in many ways: it was very strong, it didn’t look like any known naturally occurring radio signal, and it seemed to be coming from “out there” (and not here on Earth). The signal was so striking that its discoverer famously wrote the word “Wow!” on the margin of a printout of the data. After ruling out obvious Earthly origins, most astronomers are convinced that the signal came from somewhere beyond Earth. The question—which still remains unanswered—is where? And from what or whom? Was the signal produced by a natural phenomena? Or might it have been broadcast by some alien intelligence?
The answer to the last question is: Probably not; but maybe. Although whether or not the “Wow!” signal was alien in origin, many scientists do think that alien life is likely to be out there. And they kind of have some math to back them up. Why only kind of? Because as we’re about to find out, at this point questions about extraterrestrial life lead to back-of-the-envelope calculations and a hefty dose of probabilities—and those probabilities are anything but certain.
Stellar Statistics
So what exactly does math say about the odds that we share the universe with other intelligent life? Let’s begin with the statistics of stars and planets. All life on Earth originated on a planet, and scientists think that most other independent origins of life (if they exist) probably did the same. For various reasons, I’ll let Everyday Einstein explain someday, scientists think that life usually gets going on planets orbiting not-too-big-and-not-too-small stars similar to the Sun.
Astronomers estimate that there are roughly 100 billion of these Sun-like Goldilocks stars in our galaxy. Something like half of these live their lives orbiting one or more other stars, which makes it far less likely that they’ll have planets around them (since those planets get flung out of the system by the stars). This cuts the number of hospitable stars in half, but this is still roughly 50 billion potential life-hosting stars in our galaxy!
Planetary Probabilities
How about potential life-hosting planets? In our solar system, there are give-or-take 10 worlds that might possibly support life. Over the last decade, astronomers have found that planets are common around nearby stars. So if we assume 10 worlds per star system is typical, then there may be up to 500 billion potential life-hosting planets in our galaxy.
There may be up to 500 billion potential life-hosting planets in our galaxy.
Thus far we’ve confirmed that 1/10 of the worlds in our solar system have actually given rise to life (that’d be us). If that number is typical, then we would estimate that there are 1/10 • 500 billion = 50 billion planets with some sort of life (not necessarily intelligent) in the galaxy. On the other hand, if whatever happened in our solar system 4-ish billion years ago to give rise to life was an incredibly improbably event, then perhaps we are entirely alone in the galaxy … and maybe even the universe.
So this bit of probabilistic thinking puts the number of planets with life in our galaxy somewhere between 1 (so just us) and all the way up to 50 billion—which, obviously, is quite a range. Can we pin this number down a bit better? Scientists are working on it. And given that life seems to have started quickly on Earth (perhaps implying life is a universal phenomena when the conditions are right), and that life on Earth is surprisingly hardy (it shows up in the most unlikely and challenging places), the scales might be tilted towards the larger number. Maybe.
Alien Probabilities and the Drake Equation
For fun, let’s go with the upper end of the range we just estimated and assume that there are billions of independent strains of life in our galaxy. Doing so gives us the freedom to contemplate a perhaps even more intriguing question: How many of these strains of life are intelligent? And perhaps even technologically advanced?
In truth, there’s just no way for us to pinpoint precise answers questions like these—there’s still way too much we don’t know. But that doesn’t mean we can’t ponder them. And that’s exactly what an astronomer named Frank Drake did in 1961 when he introduced what’s now called the Drake equation to the world.
This equation is a wonderful example of the type of back-of-the-envelope calculation we’ve talked about before. Although the details are a bit involved, the basic idea is fairly simple:
- If we multiply the number of stars in our galaxy that join the ranks of stars capable of giving rise to life each year by the fraction of those stars that have planets around them, and then we multiply this number by the number of planets per star that are actually capable of giving rise to this life, then we obtain an estimate of the number of planets in our galaxy that become capable of hosting life each year.
- If we then multiply this number by the fraction of the planets on which life isn't just theoretically possible but actually does emerge, and then we multiply this by the fraction of these planets on which not just any life but intelligent life emerges, and then finally multiply this by the fraction of these planets on which technologically advanced life emerges, then we obtain an estimate of the number of technologically advanced civilizations that come into being in our galaxy each year.
- Finally, if we want to know the number of technologically advanced civilizations that exist in our galaxy right now, we just need to multiply the number we just obtained by the average number of years that such a civilization exists before it goes extinct (either from an outside influence or due to its own actions).
Sounds like a piece of cake to figure out, right? OK, perhaps not.
Are We Alone?
While the logic of the Drake equation is fairly straightforward, many (or actually most) of the probabilistic factors in this equation are extremely uncertain or even completely unknown. For example, what fraction of planets suitable for life actually give rise to life? We have no idea! What fraction of that life will become intelligent? Or technologically advanced? We have no idea! How long does a technologically advanced civilization exist? Again, we have no idea! Humans have been technologically advanced for about 100 years, but how much longer are we going to stick around? That’s anybody’s guess.
Nonetheless, people have attempted to come up with reasonable approximations to the factors in the Drake equation. As you might expect, different efforts have produced very different estimates—everywhere from one technologically advanced civilization (which is us) up to many millions of independent technologically advanced civilizations in our galaxy.
In truth, until we know more—meaning until we actually find life out there or make some scientific discoveries about the values of the factors in the Drake equation that lead us to believe we are unlikely to find life—this is all just an exercise in probabilistic and back-of-the-envelope thinking. But, to me at least, it’s also a lot of fun. And I genuinely can’t think of anything else that’s more exciting to think about.
Are we alone in the universe? If so, what factors in the Drake equation did life on Earth manage to overcome? And if not, where is everybody else? Just something to think about.
Wrap Up
Okay, that's all the extraterrestrial math we have time for today.
For more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. Also, remember to become a fan of The Math Dude on Facebook and to follow me on Twitter.
Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!
Public domain “Wow!” image credit: Big Ear Radio Observatory and North American AstroPhysical Observatory (NAAPO).
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