The Drake Equation

The search for extraterrestrial intelligence has often been regarded as non-scientific. After all, there are thousands of hypotheses about intelligent life in the universe, but no testable theories to back them up. Nor is there a single shred of empirical evidence on which to base any of our speculations. It wasn’t until the 1960s that the search gained official recognition by the scientific community.

Prior to this time, any supposition about the prospects of establishing contact with other worlds was far from achieving scientific respectability. However, in November of 1960, a group of well-known scientists held the first conference to discuss just such prospects. Convened under the auspices of the National Academy of Sciences, the subject of the meeting was so risqué that there were no announcements made about the conference, nor any official publications following the meeting. In fact, the meeting consisted of only ten people. The attendees called themselves “The Order of the Dolphins”, partially in jest and partially in celebration of a recent publication by one of the conference invites, John Lilly, who had just published a controversial work declaring dolphins as an intelligent species.

One of the members of this first conference about the search for extraterrestrial intelligent life was Frank Drake. Drake was a very young researcher who, just two years prior, had conducted the first, albeit modest, radio search for intelligent signals from planets surrounding nearby stars. Even before the conference, Drake had been thinking about the complexities of predicting whether or not intelligent civilizations exist beyond our own, and how to communicate with these civilizations. Prior to giving a talk at the conference, Drake tried to organize his thoughts about the conference and to focus them on the topic of intelligent life in the universe. In his efforts, he created an organizational tool. He had no idea that his tool, now famously known as the Drake equation, would become a cornerstone for SETI theorists for years to come.

Drake postulated that the number of intelligent, communicating civilizations in our own Milky Way Galaxy could be reduced to seven simple variables. He expressed them in the following equation

N = R x f(p) x n(e) x f(l) x f(i) x f(c) x L

For over forty years, the Drake equation has been used as the framework for the discussion of intelligent life in the universe. In this equation, N stands for the number of planets in the Milky Way Galaxy hosting a civilization that is intelligent enough to communicate through the distances of space. To get an answer for N, you simply need to multiply seven different factors together. The letter R is the average rate of star formation. The factor f(p) is the fraction of stars in the galaxy that have planets around them. The factor n(e) is the number of planets around those stars that have conditions favorable for life to exist. The factor f(l) is a fraction; it is the fraction of the planets with favorable conditions for life that actually do develop life. The factor f(i) is also a fraction. It is the fraction of planets that developed life where that life evolves to be intelligent. The factor f(c) is the fraction of those intelligent species that develop the ability for interstellar communication. Finally, L is the average lifetime of such civilizations, how long an intelligent civilization lasts on average.

As you can see, these factors range from those that are based on our knowledge of astronomy to those relying on our knowledge of how societies work. Each of these seven factors has a range of possible values that we can estimate. However, we should be careful to note that any estimations we make are based on our knowledge of all the intelligent civilizations we know about in the galaxy, just one, our own. It is also important to remember that our estimates of N only predict the number of intelligent, communicable civilizations within our own galaxy. The distance between our galaxy and others is so large that even light would have a tough time traveling in an expedient amount of time.

So, how would one even go about filling in the Drake equation with actual numbers? Well, it turns out some of the factors we understand fairly well. For example, there are about 40 billion stars in our galaxy, and the age of the galaxy is about 10 billion years. If you divide 40 billion by 10 billion, you arrive at a number for R of about 4 stars per year. We could estimate that R would reach values of 10 or greater if we account for stars that formed in the past but have since exploded or faded from view. Regardless, the first factor in the Drake equation is the only one that we know with much accuracy at all.

The next factor, the fraction of stars with planets, is still uncertain. It is, however, the subject of one of the most intensive research efforts in the history of astronomy. So far, we have only detected Neptune-sized planets or larger around other stars, but we are confident of finding Earth-sized planets in the near future. Astronomers believe that when stars form, planets naturally form right along with them. This would imply that f(p) = 1, but a more conservative range for this factor might be 0.1 to 1.

The number of habitable planets in each system is also highly uncertain. Again, we lean on our assumption of mediocrity and hope that our solar system is ordinary and typical of other planetary systems. Our solar system has a habitable zone — a distance from the star where surface water can exist — that includes Venus, Earth, and Mars. The fact that two out of three of those planets no longer have surface water tells us that atmospheric conditions play a role in planet habitability as well. The factor n(e) must consider the fact that many low-luminosity stars have tiny habitable zones. In addition, what if we consider habitable “planets” like Europa or Titan that are outside the habitable zone? Then for our solar system, this number could be as high as 5 or as low as 1.

We really only have one example of how life evolves, life on Earth. Many scientists believe that life started quickly as soon as there was a suitable site with favorable conditions. If this were the case, then the value for f(l) could be close to unity. On the other hand, if life arises as a random and improbable outcome of chemical evolution, fl could be a really small number. Right now, we don’t have solid evidence to allow us to make a decision between these two possibilities. However, if life, past or present, is discovered on Mars, Europa, or Titan, it would be evidence in support of the idea that f(l) = 1.

The last three factors of the Drake equation are hopelessly uncertain. We do not know if intelligence is a natural or necessary consequence of biological evolution. We have no idea how likely it is that life will develop technology and the ability to communicate into space. In the absence of any evidence, logical arguments can’t be made for high and low values of f(i) and f(c). We are equally in the dark as to how long such a capability will endure. On Earth, L only equals 50 years so far.

Scientists to this day argue about pessimistic and optimistic estimates for all of the factors in the Drake Equation. You could come up with your own, if you wanted to. In the table below, we have made some "optimistic" and "pessimistic" estimates for you. The table also calculates N, the number of potential pen pals in the Galaxy at any particular time, that would result from the estimates. We combine all the low and high estimates of each factor purely to illustrate the range of the possible end-result values of N. In reality, the various factors may be independent, in which case a low value for one factor does not necessarily imply a low value for the others. We stress that these are little more than educated guesses. The estimate of N is as uncertain as the most uncertain factor. Since several of the factors are completely unknown, we must conclude that N cannot be determined.

R x f(p) x n(e) x f(l) x f(i) x f(c) x L

Factor "Optimistic" "Pessimistic"
R 10 4
f(p) 1 0.1
n(e) 6 1
f(l) 1 .001
f(i) 1 .0001
f(c) 1 .0001
L 50,000 50
Multiply them together and….    
N 3,000,000 .0000000002


Copyright © 2000-2008 Authors/Editors Chris Impey & Erika Offerdahl
Do not reproduce without permission from Chris Impey.