The Drake Equation

No, it’s a real thing. No, it’s not “half your age plus seven”. In the course of some research today I ran into this, and thought I’d report on my findings here, since it will amuse some people, and interest some others.

The Drake Equation looks like this:

I’ll get into what each term means in a second, but first let me explain what that thing is for.

This equation was devised by Dr. Frank Drake in 1961, as an attempt to estimate the number of extraterrestrial civilizations in our galaxy with which we might come in contact. Obviously it’s not a simple 2+2 equation, but rather a framework for determining some boundary conditions.

The terms are as follows:

• R* is the rate of star formation within the Galaxy, expressed in stars per year
• f_p is the fraction of stars that form planets
• n_e is the average number of planets for each planet-bearing star which are capable of supporting life
• f_l is the fraction of planets capable of supporting life where life actually occurs
• f_i is the fraction of life-bearing planets where intelligence arises
• f_c is the fraction of intelligent life-bearing planets where intelligent beings develop the ability to communicate beyond their own world, and actually does so
• L is the length of time, in years, that such communications remain detectable–this is roughly congruent with “how long the civilization will last”

So, in English we might say: “The number of alien civilizations we might run into is a product of the rate of star formation (R*), the probability of stars having planets with intelligent life that can communicate (f_pn_ef_lf_if_c), and the length of time communications are detectable (L).”

Note that for the purposes of the equation, we’re assuming that “intelligent life that communicates” is congruent with “intelligent life that communicates via electromagnetic emissions that we can detect”.

In 1961 Drake and his pals estimated the values as:

• R* = 10/year, or ten new stars a year
• f_p = 0.5, or 50% of stars forming planets
• n_e = 2, or an average of 2 planets that could support life per star that forms planets
• f_l = 1, or 100% of those planets capable of bearing life where life actually arises
• f_i = 0.01, or 1% of life-bearing planets developing intelligent life
• f_c = 0.01, or 1% of intelligent species developing the ability to communicate off-world
• and L = 10,000 years.

This generates an estimate of 10 * (0.5 * 2 * 1 * .01 * .01 ) * 10000 = 10 * 0.0001 * 10000 = 10. The real point was to get best and worst case estimates for each term, to generate range of reasonable values, of course. An ad hoc group was formed to discuss the values of these parameters–The Order Of The Dolphin. (It could be argued that getting support for SETI was the “real” purpose, and the N>1 result is good for that.)

Since the observed value of N is 1 (i.e. “us”), there is some conflict with the estimate of 10 (and indeed the Dolphins argued a lot about the parameters, resulting in some estimates that are significantly higher than 10). The disconnect between the observed and predicted value is, of course, Fermi’s Paradox.

Since 1961, we’ve changed our understanding of good estimates for each term, of course. The Wikipedia page for the Drake Equation suggests that there are some significant changes in the current estimates of some of those terms. In particular, the probabilty of intelligent life arising on a life-bearing planet (f_i) is called into question as being way too high in the 1961 values, going on to say “Some estimate that solar systems in galactic orbits with radiation exposure as low as Earth’s solar system may be more than 100,000 times rarer, however, giving a value of f_i = 1×10^-7.” There is also some suggestion that 10000 years is too long for the civilization lifespan term; some research is quoted that suggests a much smaller number–something like 300-450 years–is more reasonable. There are some other changes, but none as significant as those two.

Just changing f_i and L to 10^-7 and 400 results in a new final value of 0.000004, which is a pretty big divergence from 10. The new number seems to suggest it is very unlikely that there is another civilization that has a light cone overlapping ours. This one is also interesting in it’s divergence from the observed value–although you can always make the argument that no matter how unlikely it is, we wouldn’t be here to argue about it if it hadn’t happened at least once. Of course, this result is less useful in getting SETI supported.

If you want to know more about the equation, or the history of the arguments around the parameters, etc, the Wikipedia page is a good place to start. The Beyond The Drake Equation page has a calculator that lets you vary the parameters and see the effect on the result instantly, and also attempts to consider some extensions to the Drake framework.