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Fifty Years of the Drake Equation

October 26, 2012

I often do back-of-the-envelope calculations, sometimes called "Fermi problems" after their most famous practitioner, Enrico Fermi. The following is an example of a Fermi problem.
If the land area of the Earth were divided up equally for each person on the planet, about how much would you get?[1]
An important follow-up problem would be, "How many people could be fed from this patch of land, considering the fact that, on average, such land would be just fractionally arable." You can easily see what quantities need to be estimated in such problems, and how error can grow as more steps are added. By the way, these problems are intended to be answered "off-the-top-of-your-head" - No reference materials are allowed!

From what I've read about Fermi, he was a walking physics reference book for his time, so this was never a problem for him. Alas, I'm not like Fermi. I barely remember the speed of light; but, because of my specialty, I do know the permeability of free space. This might be because it's simply stated as 4π x 10-7 volt-sec/amp-meter.

One particularly interesting estimate is provided by the Drake equation, devised in 1961 by SETI (Search for ExtraTerrestrial Intelligence) pioneer, Frank Drake. Drake's Project Ozma in the early 1960s was the first to search for intelligent radio signals. His focus was on two nearby, Sun-like, stars, Tau Ceti and Epsilon Eridani.

The Drake equation is an estimate of the number of extraterrestrial civilizations in the Milky Way galaxy who are sending radio signals our way. Their transmissions might purposely trying to get the attention of other civilizations; or, they might just be used for some other purpose, but still be detected on Earth. Drake's equation is essentially just a product of many estimates,
N = (R*)(fp)(ne)(flife)(fi)(fc)(L)
N = Number of communicating civilizations in our Milky Way Galaxy.
R* = Yearly rate of star formation.
fp = Fraction of stars with planets.
ne = Number of planets/star that can potentially support life.
flife = Fraction of these that develop life.
fi = Fraction of these that develop intelligent life.
fc = Fraction of civilizations that will send detectable signals.
L = Length of time such detectable signals are sent.
When the equation was first published, the estimate was 1000-100,000,000 such civilizations in the galaxy! Of course, in fifty years, these estimates have been revised, and some other factors have been added. Wikipedia has a great review of the history of this equation. Needless to say, the estimate can range from Carl Sagan's supposed favorite enumeration, billions and billions, to one (only us).

Figure caption

Can you hear me now? Probably not with this apparatus. This is a replica of the world's first radio telescope, designed, built and operated by Karl Jansky. This replica is found at the National Radio Astronomy Observatory, Green Bank, West Virginia. Photograph via Wikimedia Commons)

Before SETI, there was CETI, which is pronounced the same and should not be confused with the Latin possessive form of cetus (whale), as used by astronomers to name stars in the constellation, Cetus (e.g., tau-Ceti, as mentioned above). CETI is Contemplation of Extraterrestrial Intelligence, and it requires no other instrument than the human mind.

Danièlle Briot of the Observatoire de Paris has recently posted a paper on arXiv that reviews the history of SETI, and it includes its CETI history from antiquity to just before our modern SETI era.[2]

According to Briot, Democritus (c.460- c.370 BC) and Epicurus (341-270 BC) penned the first references to life in other worlds. Democritus pictured the diversity of other planets about the same way that we do; saying, also, that "There are some worlds devoid of living creatures or plants or any moisture."[2] Both Democritus and Epicurus thought that the number of worlds was infinite.[2]

Aristotle (384 - 322 BC), who both helped and hindered the progress of civilization, reasoned that "...The world would be unique. There cannot be several worlds." This set the tone for the official church position on the existence of other worlds. Not surprisingly, Augustine (354-430 AD), Albertus Magnus (1193-1280 AD) and Thomas Aquinas (1225-1274 AD) were all opposed to the idea that there were other worlds.

Over the course of years, evidence mounted that the Earth was not unique in the universe. The year, 1543, saw publication of the book, De Revolutionibus Orbium Coelestium, by Copernicus (1473-1543). Copernicus showed that the Earth was just another planet. Galileo (1564-1642) imaged the Moon with his telescope in 1609 and saw that there was topography on the Moon much like that of the Earth. Galileo also discovered some of the moons of Jupiter, which showed that Jupiter was like Earth in having a moon.

The Frenchman, Bernard le Bouyer de Fontenelle (1657-1757), published his book, Entretiens sur la Pluralité des Mondes (A Conversation on the Plurality of Worlds), in 1686. Fontenelle imagined that every star had planets, and he presumed the presence of intelligent creatures on our Moon, and on every planet. These beings were adapted to their environments.

Much later, in 1888, the astronomer, Giovanni Schiaparelli's, made a map of Mars based on his observations. Schiaparelli's map contained features marked as continents and seas; and also, channels. The Italian word for channels, canali, was mistranslated as "canals," thereby starting a whole discourse on the Martian engineers who were drawing water from their polar sources to other areas of their arid planet.

Figure caption

Astronomer, Giovanni Schiaparelli's, map of Mars (1888). Schiaparelli noted Martian features than resembled continents and seas; and also, channels. Canali, the Italian word for channels, was mistranslated as "canals," thus interjecting an artificial feature into the Martian landscape.(Via Wikimedia Commons))

Briot writes about one late twentieth century historical development that was unknown to me, and likely unknown to many of today's astrobiologists. After World War II, Belarusian astronomer Gavriil Adrianovich Tikhov (1875-1960) and his team collected spectra of plants for comparison with the spectrum of Mars.[2] These efforts ended when Tikhov died in 1960, but they surely would have ended after Mariner 4 returned images of a moon-like Martian surface on July 14-15, 1965.

Since I had a brief career in broadcast radio in my youth, I'll mention another Drake "equation," this one developed by radio programmer Bill Drake.[3] Drake vitalized Top-40 radio in the 1960s by creating a format that had more music and less DJ chatter. As I remember, records in each half-hour of programming were played in a sequence, "ACABAFAD," defined as follows:
A = Top ten hit.
C = Record rising into the top ten.
B = Record just falling out of the top ten.
F = An "Oldie."
D = A regional/novelty hit, not on the national charts.
The "D" records were typically not played because of time constraints. Radio stations programmed by Drake immediately rose to first place in their market, blowing away the competition. This proves that science, even when applied to rock-and-roll, gives great results.


  1. University of Maryland Fermi Problems Site.
  2. Danielle Briot, "Evolution of the problem "search for life in the Universe" from some examples," arXiv Peprint Server, October 2, 2012.
  3. William Grimes, "Bill Drake, 71, Dies; Created a Winning Radio Style," The New York Times, December 1, 2008

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