by Shane L. Larson
One of the things physicists and astronomers do very well is make simple estimates about the physical nature of the world around us. Part of this skill is (simple) math, and another part is knowing what physical quantities are important. The most astonishing fact about this skill is that you and I do it every day, we just don’t realize it! Scientists have honed the skill — the place where science comes out is when those unconscious habits are used purposefully! So how does it work? How is it that you and I are perfectly capable of describing complex physical phenomena, without necessarily resorting to equations we memorized in some long forgotten science class? To demonstrate, let’s consider sticking your hand (or your dog’s head) out the window of your car.
What affects how much force the wind presses on your hand (or your dog’s face) with? With a little experimentation (something you probably did a lot as a kid, and have committed to memory but forgotten) you find there are three things:
- how fast the car is driving. If the car is going faster, the force is stronger.
- how you hold your hand (or, how big your hand is). If you hold your hand palm out, there is a bigger force than if you hold your hand finger tips out. The force is stronger if there is a bigger area being hit by the wind.
- how thick the air is. Most of us don’t experience thick and thin air too often, at least not that we can tell the difference. But air is a fluid, like water, and water is much thicker than air. When you run your hand through water (a thick fluid) there is a much greater resistance than through air (a thin fluid).
That’s it — those are the three physical quantities that affect how much force you experience when you hold your hand/dog head out the window of your car. And you knew them, at least intuitively, whether you could explain it out loud or not! In a very similar way, the genesis of thinking about extraterrestrial life began with a few intuitive numbers that astronomer Frank Drake wrote down.
The serious scientific consideration of searching for extraterrestrial intelligences had started with a paper in the scientific journal Nature in 1959, by physicists Giuseppe Cocconi and Philip Morrison. This paper sparked Drake’s interest, leading up to his Project Ozma in 1960, the first human search for radio signals from an extraterrestrial civilization. By 1961, Drake decided to host a small scientific conference at the National Radio Astronomy Observatory, in Green Bank, West Virginia, where the Project Ozma search was carried out. Drake made a list of topics that should be discussed at the conference, dutifully writing down all the things that could affect how many communicative extraterrestrial civilizations there might be. When he was done, he realized he had created a Fermi problem estimate of the number of alien civilizations in the galaxy that we might communicate with — his list of topics were seven numbers that could be multiplied together.He presented his seven number equation at the conference. It was promptly dubbed “The Drake Equation,” and has been used ever since as a baseline estimate for the kinds of discussions we are having now. A plaque of it now resides on the wall in the conference room where the meeting was held.
So what was Frank’s famous equation? Simply put, it is seven numbers — you multiply those seven numbers together, and you get the number of civilizations in the galaxy that could be communicated with, a number we denote as “N.” It is written as:
N = (R* x fp x ne) x FL x Fi x Fc x L
Of those numbers, the first three are matters of observational astronomy that can be verified and estimated from what we see of the Cosmos through our telescopes. The last four numbers are quantities for which answers certainly exist, but whose values we are still uncertain about; it is playing with plausible values of these four numbers that illustrates our uncertainty about the Cosmos.
Let’s look at the first three numbers. The first is R*, the rate at which stars are born in the galaxy. The star formation rate is a simple way to start thinking about issues related to planets and life, because the number of planets must necessarily depend on the number of stars in the galaxy — you can’t have planets without parent stars for them to orbit! For this number, astronomers think R* ~ 6/yr.The second is fp, the fraction of stars that develop planetary systems. For a long time, we had no idea what this number was. For most of recorded history, no star other than the Sun was known to shepherd planets. Then, in 1995 astronomers discovered planets around the star 51 Pegasi, a star very similar to the Sun about 51 lightyears away. Today, we think planets may very well be common around most stars, and we are regularly discovering planets. As of the time of this writing (23 June 2014) there are 1797 planets known around other stars (visit the exoplanet catalogue here). To be conservative, let’s assume that not every star develops planets (though astronomers are beginning to think that a star without planets may be the exception, not the rule). We’ll take fp = 0.5.
The third number, ne, is the number of planets that could support life in a planetary system. Here, we don’t have a definitive value for this number, but any value we do use has some of our personal prejudices built into it since we have not had the opportunity to study an alien biology! One prejudice we have is that water plays an important role in the chemistry of life. Looking around the Sun, we find Venus, Earth and Mars are all at a distance from the Sun where liquid water could exist under the right conditions (this generic concept, the distance from a star where liquid water can exist on a planetary surface, is called “the habitable zone“). Venus has no liquid water, but Mars may harbor subsurface water. Based on what we know about our own planetary system then, let’s take ne = 2.
These numbers could change as we see more and more of the Cosmos, but probably not much. So let’s multiply them all together and leave that number alone:
R* x fp x ne = 6 x 0.5 x 2 = 6
For convenience, we now write the Drake Equation as:
N = (R* x fp x ne) x FL x Fi x Fc x L = 6 x FL x Fi x Fc x L
Now what about the last four numbers? These are numbers which have more uncertainty, and more speculation in them. They are absolutely numbers of importance when trying to figure out the number of civilizations in the galaxy, we just don’t have good ways to reliably estimate their values.
The first two are FL, the fraction of planets that develop life, and Fi, the fraction of planets with life that develop intelligent life. These are complete unknowns; Earth is the only planet we know of with life! Is it common for life to arise on other worlds? We know from the fossil record on Earth that simple life arose on Earth soon after its formation, in the form of single celled organisms — prokaryotic bacteria (cellular organisms with genetic material free floating in the cell, and not contained in a central nucleus), algae and the like. Given the simplicity of making the organic building blocks of life (chemical combinations called amino acids, used to build proteins), and given that self-replicating molecular systems are not uncommon, the early origin of life suggests that maybe life, in its simplest forms, may arise on planets quite often. I’m an eternal optimist, so let’s assume FL = 1. We’re just multiplying numbers together, so I can always go and change this number later.
If life arises, how often does that life become “intelligent?” This is a harder question to answer, but again we can make an educated guess based on what we see on Earth. It is a fuzzy concept because you have to decide what you mean by “intelligent,” but there are many species on Earth we might consider intelligent — monkeys, dolphins, cats, even humans. But there are many species that aren’t — oak trees, slime molds, or sea cucumbers. How common is “intelligence?” Let’s assume Fi = 0.01 — a 1 in 100 chance.The next number is Fc, the fraction of civilizations that can or want to communicate. Here also, there are several extremes. Consider humans — since the early 20th Century, we’ve been willy-nilly broadcasting our radio and television signals all over the place, blasting music videos of Eric Clapton and Chuck Berry out into the Cosmos (which I’ve written about before here). We’ve even sent a few organized messages out, specifically with the intent of communicating with extraterrestrials; these have included radio signals, as well as physical messages. On the another extreme, one could imagine a completely xenophobic civilization. Maybe they don’t want anyone to know of their existence, lest aliens invade and use them for food. One could also imagine that a civilization never develops the technology to communicate. If Europe had not emerged from the Middle Ages in the Age of Enlightenment, perhaps we would have never had an Industrial Revolution; we’d all still be peasants, living off mushrooms and earthy root vegetables and not burdened by technology like smartphones or microwave ovens. Certainly the dinosaurs never developed radio communications, despite the intelligence we’d like to associate with marauding bands of velociraptors. Let’s make a guess at this number (which we can always change) of Fc = 0.01.
Now for the last number: the lifetime L of the civilization. There is enormous latitude in possible values for this number because we know absolutely nothing about it, and that is where this discussion gets interesting. Suppose we take L to be the length of time modern humans have been on the planet. We don’t know exactly how long that is, but our written history goes back only to about 3000 BCE, so we could take L to be the length of recorded human history, L = 5000 years. By contrast, the dinosaurs lived on the planet for 170 million years before an asteroid obliterated them, so you could take L = 170 million. Considering both of these cases we get:
N = 6 x 1 x 0.01 x 0.01 x 5000 = 3
N = 6 x 1 x 0.01 x 0.01 x 170,000,000 = 102,000
That is quite a range in numbers — there could be more than 100,000 civilizations broadcasting radio; or there could be 3, with a very strong possibility that we are the only ones. The consequences of this calculation could be elating, or very depressing. Whatever the result is, the answer to this question will have profound consequences for our understanding of the Cosmos.
Which brings me back to where we started: dinosaurs and Fermi problems. In many ways, the Drake equation is a Fermi problem. What is different from many Fermi problems is that we don’t have a good handle on the last four numbers. But what if we didn’t care about all of these numbers?What I love about the Drake equation is that it allows you to answer many related questions, by simply deciding what you think is important. Let’s take the radical viewpoint that we don’t care about communicative civilizations; instead let’s simply ask how much life (of any sort) might there be in the galaxy? Is the galaxy teeming with life, or is it a barren wasteland populated only by the descendants of some monkeys on a backwater forgotten world?
Suppose we don’t care about communication. What if we only wanted to know if there were, say, dinosaurs? We don’t keep the intelligent number or the communication number. That makes a modified Drake Equation that looks like this:
N = (R* x fp x ne) x FL x L = 6 x FL x L
Let’s keep our optimistic estimate of life developing on every planet possible, FL = 1. I’m interested in dinosaurs, and the dinos lived on the Earth for 170 million years before an asteroid whacked the Earth, erasing them utterly from the Cosmos; so I take L = 170 million years. Multiplying this all together, I find
N = 6 x 1 x 170,000,000 = 1,020,000,000
There could be 1 BILLION worlds with advanced, but non-intelligent, lifeforms. If you imagine those lifeforms to be something as complex as a dinosaur, then you might say it this way: there could a BILLION WORLDS with dinosaurs on them in the Milky Way!
That makes the little kid inside of me very happy. :-)
PS: As an even more interesting exercise, suppose we treat L not as the lifetime of a civilization, but simply the length of time for which life exists on a planet, and again ignore the issue of intelligent and technologically able lifeforms. Taking Earth as the role model, life on Earth arose soon after the planet formed, and while there have been MANY extinction events, life has never been eradicated on Earth, making L ~ 3.5 billion years. If I replace the 170 million years we used with the dinosaurs with 3.5 billion years, we get N ~ 21 BILLION worlds with life. Go stare at the stars tonight, and think about that for a little while.
This is the second of two parts; the first part, about Fermi problems, can be read here.
This particular piece was completed while in residence at the Aspen Center for Physics.