What is the Drake Equation?

Is there life out there in the Universe? That is a question that has plagued humanity long before we knew just how vast the Universe was – i.e. before the advent of modern astronomy. Within the 20th century – thanks to the development of modern telescopes, radio astronomy, and space observatories – multiple efforts have been made in the hopes of finding extra-terrestrial intelligence (ETI).

And yet, humanity is still only aware of one intelligent civilization in the Universe – our own. And until we actually discover an alien civilization, the best we can do is conjecture about the likelihood of their existence. That’s where the famous Drake Equation – named after astronomer Dr. Frank Drake – comes into play. Developed in the 1960s, this equation estimates the number of possible civilizations out there based on a number of factors.

Background:

During the 1950s, the concept of using radio astronomy to search for signals that were extra-terrestrial in origin was becoming widely-accepted within the scientific community. The idea of listening for extra-terrestrial radio communications had been suggested as far back as the late 19th century (by Nikolai Tesla), but these efforts were concerned with looking for signs of life on Mars.

Frank Drake standing before his famous equation on a white board. Credit: SETI.org

Then, in September of 1959, Giuseppe Cocconi and Philip Morrison (who were both physics professors at Cornell University at the time) published an article in the journal Nature with the title “Searching for Interstellar Communications.” In it, they argued that radio telescopes had become sensitive enough that they could pick up transmissions being broadcast from other star systems.

Specifically, they argued that these messages might be transmitted at a wavelength of 21 cm (1420.4 MHz), the same wavelength of radio emissions by neutral hydrogen. As the most common element in the universe, they argued that extra-terrestrial civilizations would see this as a logical frequency at which to make radio broadcasts that could be picked up by other civilizations.

Seven months later, Frank Drake made the first systematic SETI survey at the National Radio Astronomy Observatory in Green Bank, West Virginia. Known as Project Ozma, this survey relied on the observatory’s 25-meter dish to monitor Epsilon Eridani and Tau Ceti – two nearby Sun-like stars – at frequencies close to 21 cm for six hours a day, between April and July of 1960.

Though unsuccessful, the survey piqued the interest of the scientific and SETI communities. It was followed shortly thereafter by a meeting at the Green Bank facility in 1961, where the subjects of SETI and searching for radio signals of extra-terrestrial origin were discussed. In preparation for this meeting, Drake prepared the equation that would come to bear his name. As he said of the equation’s creation:

“As I planned the meeting, I realized a few day[s] ahead of time we needed an agenda. And so I wrote down all the things you needed to know to predict how hard it’s going to be to detect extraterrestrial life. And looking at them it became pretty evident that if you multiplied all these together, you got a number, N, which is the number of detectable civilizations in our galaxy. This was aimed at the radio search, and not to search for primordial or primitive life forms.”

The meeting, which included such luminaries as Carl Sagan, was commemorated with a commemorative plaque that is still in the hall of the Green Bank Observatory today.

The 85-foot (26 m) Howard E. Tatel Radio Telescope at NRAO used in Project Ozma. Credit: Z22/WIkipedia Commons

The Formula:

The formula for the Drake Equation is as follows:

N = R* x fp x ne x fl x fi x fc x L

Whereas N is the number of civilizations in our galaxy that we might able to communicate with, R* is the average rate of star formation in our galaxy, fp is the fraction of those stars which have planets, ne is the number of planets that can actually support life, fl is the number of planets that will develop life, fi is the number of planets that will develop intelligent life, fc is the number civilizations that would develop transmission technologies, and L is the length of time that these civilizations would have to transmit their signals into space.

Limits and Criticism:

Naturally, the Drake Equation has been subject to some criticism over the years, largely because a lot of the values it contains are assumed. Granted, some of the values it takes into account are easy enough to calculate, like the rate of star formation in the Milky Way. There are an estimated 200 – 400 billion stars within our Milky Way, and modern estimates say that there between 1.65 ± 0.19 and 3 new star form every year.

Assuming that our galaxy represents the average, and given that that there are as many as 2 trillion galaxies in the observable Universe (current estimates based on Hubble data), that means that there are as many as 1.5 to 6 trillion new stars being added to the Universe with every passing year! However, some of the other values are subject to a great deal of guess work.

For example, estimates on how many stars will have a system of planets has changed over time. Currently, it is estimated that the Milky Way contains 100 billion planets, which works out to about 50% of its stars having a planet of their own. Furthermore, those stars that have multiple planets will likely have one or two that lies within their habitable zone (aka. “Goldilocks Zone”) – where liquid water can exist on their surfaces.

Now let’s assume that 100% of planets located within a habitable zone will be able develop life in some form, that at least 1% of those life-supporting planets will be able to give rise to intelligent species, that 1% of these will be able to communicate, and that they will able to do so for a period of about 10,000 years. If we run those numbers through the Drake Equation, we end up with a value of 10.

In other words, there are possibly 10 civilizations in the Milky Way at any time capable of sending out signals that we could detect. But of course, the values used for four parameters there – fl, fi, fc and L – were entirely assumed. Without any real data to go by, there’s no real way to know how many alien civilizations could really be out there. There could just be 1 in the entire Universe (us), or millions in every galaxy!

The Fermi Paradox:

Beyond the issue of assumed values, the most pointed criticism of the Drake Equation tend to emphasize the argument put forth by physicist Enrico Fermi, known as the Fermi Paradox. This argument arose in 1950 as a result of conversation between Fermi and some colleagues while he was working at the Los Alamos National Laboratory. When the subject of UFOs and ETI came up, Fermi famously asked, “Where is everybody?”

This simple question summarized the conflict that existed between arguments that emphasized scale and the high probability of life emerging in the Universe with the complete lack of evidence that any such life exists. While Fermi was not the first scientists to ask the question, his name came to be associated with it due to his many writings on the subject.

In short, the Fermi Paradox states that, given the sheer number of stars in the Universe (many of which are billions of years older than our own), the high-probability that even a small fraction would have planets capable of giving rise to intelligent species, the likelihood that some of them would develop interstellar travel, and the time it would take to travel from one side of our galaxy to other (even allowing for sub-luminous speeds), humanity should have found some evidence of intelligent civilizations by now.

Naturally, this has given rise to many hypotheses as to how advanced civilizations could exist within our Universe but remain undetected. They include the possibility that intelligent life is extremely rare, that humanity is an early arrival to the Universe, that they do not exist (aka. the Hart-Tipler Conjecture), that they are in a state of slumber, or that we are simply looking in the wrong places.

The “Great Filter” Hypothesis:

But perhaps the best known explanation for why no signs of intelligence life have been found yet is the “Great Filter” hypothesis. This states that since that no extraterrestrial civilizations have been so far, despite the vast number of stars, then some step in the process – between life emerging and becomes technologically advanced – must be acting as a filter to reduce the final value.

According to this view, either it is very hard for intelligent life to arise, the lifetime of such civilizations is short, or the time they have to reveal their existence is short. Here too, various explanations have been offered to explain what the form the filter could take, which include Extinction Level Events (ELEs), the inability of life to create a stable environment in time, environmental destruction. and/or technology running amok (some of which we fear might happen to us!)

Alas, the Drake Equation has endured for decades for the very same reason that if often comes under fire. Until such time that humanity can find evidence of intelligent life in the Universe, or has ruled out the possibility based on countless surveys that actually inspect other star systems up close, we won’t be able to answer the question, “Where is everybody?”

As with many other cosmological mysteries, we’ll be forced to guess about what we don’t know based on what we do (or think we do). As astronomers study stars and planets with newer instruments, they might eventually be able to work out just how accurate the Drake Equation really is. And if our recent cosmological and exoplanet-hunting efforts have shown us anything, it is that we are just beginning to scratch the surface of the Universe at large!

In the coming years and decades, our efforts to learn more about extra-solar planets will expand to include research of their atmospheres – which will rely on next-generation instruments like the James Webb Space Telescope and the European Extremely-Large Telescope array. These will go a long way towards refining our estimates on how common potentially habitable worlds are.

In the meantime, all we can do is look, listen, wait and see…

We have written many articles about the Drake Equation for Universe Today. Here’s Inside the Drake Equation: A Chat with Frank Drake, The Odds of Intelligent Life in the Universe, A New Drake Equation? Other Life Not Likely to be Intelligent, A New Drake Equation for Potential of Life, Bayesian Analysis Rains on Exoplanet Life Parade, and Where are all the Aliens? The Fermi Paradox?

There are some great resources out there on the Internet. Check out this Drake Equation calculator.

We have recorded an entire episode of Astronomy Cast about the Drake Equation. Check it out here, Episode 23 – Counting Aliens with the Drake Equation.

Sources:

Beyond “Fermi’s Paradox” I: A Lunchtime Conversation- Enrico Fermi and Extraterrestrial Intelligence

It’s become a kind of legend, like Newton and the apple or George Washington and the cherry tree. One day in 1950, the great physicist Enrico Fermi sat down to lunch with colleagues at the Fuller Lodge at Los Alamos National Laboratory in New Mexico and came up with a powerful argument about the existence of extraterrestrial intelligence, the so-called “Fermi paradox”. But like many legends, it’s only partly true. Robert Gray explained the real history in a recent paper in the journal Astrobiology.

Enrico Fermi was the winner of the 1938 Nobel Prize for physics, led the team that developed the world’s first nuclear reactor at the University of Chicago, and was a key contributor to the Manhattan Project that developed the atomic bomb during World War II. The Los Alamos Lab where he worked was founded as the headquarters of that project.

The line of reasoning often attributed to Fermi, in his lunchtime conversation, runs like this: There may be many habitable Earth-like planets in our Milky Way galaxy. If intelligent life and technological civilization arise on any one of them, that civilization will eventually invent a means of interstellar travel. It will colonize nearby stellar systems. These colonies will send out their own colonizing expeditions, and the process will continue inevitably until every habitable planet in the galaxy has been reached.

The fact that there aren’t already aliens here on Earth was therefore supposed to be strong evidence that they don’t exist anywhere in the galaxy. This argument actually isn’t Fermi’s and was published more than 25 years later by astronomer Michael Hart. It was elaborated in a paper published by the cosmologist Frank Tipler in 1980.

Fermi’s lunch conversation really did happen. Although he died just four years later of cancer, physicist Eric Jones published the recollections of the physicist’s luncheon companions more than thirty five years later. Among these companions were Edward Teller, Emil Konopinski, and Herbert York, all eminent physicists and veterans of the Manhattan Project. Teller played a central role in the development of the hydrogen bomb. Konopinski studied the structure of the atomic nucleus, and York became director of Lawrence Livermore National Laboratory.

Edward Teller was the head of the Theoretical Physics Division at Los Alamos National Laboratory during the Manhattan Project that developed the atomic bomb for World War II. After the war he was central to the development of the hydrogen bomb.
Edward Teller headed a group in the Theoretical Physics Division at Los Alamos National Laboratory during the Manhattan Project that developed the atomic bomb for World War II. After the war he was central to the development of the hydrogen bomb. He was one of Enrico Fermi’s lunch companions when he posed the famed question”Where is everybody?” Credit: Lawrence Livermore National Laboratory

During the walk to the Fuller Lodge, the physicists discussed a recent spate of UFO sightings, and a cartoon in the New Yorker Magazine depicting aliens and a flying saucer. Although the topic of conversation moved on as the group sat down for lunch, Edward Teller recalls “in the middle of the conversation, Fermi came out with the quite unexpected question ‘Where is everybody?’…The result of his question was general laughter because of the strange fact that in spite of Fermi’s question coming out of the clear blue, everybody around the table seemed to understand at once that he was talking about extraterrestrial life”.

In his account of the famed luncheon, Teller wrote “I do not believe much came from this conversation, except perhaps a statement that the distances to the next location of living beings may be very great and that, indeed, as far as our galaxy is concerned, we are living somewhere in the sticks, far removed from the metropolitan area of the galactic center”.

York recalled a somewhat more expansive discussion in which Fermi “followed up with a series of calculations on the probability of earthlike planets, the probability of life given an earth, the probability of humans given life, the likely rise and duration of high technology, and so on. He concluded on the basis of these calculations that we ought to have been visited long ago and many times over”.

According to York, Fermi supposed the reason we hadn’t been visited “might be the interstellar flight is impossible, or if it is possible, always judged not worth the effort, or technological civilization doesn’t last long enough for it to happen”.

So Fermi, unlike Hart, wasn’t skeptical about the existence of extraterrestrials, and didn’t view their absence from Earth as paradoxical. There is no Fermi paradox, there is simply Fermi’s question “Where is everybody?”, to which there are many possible answers. The answer that Fermi preferred seems to be that, either interstellar travel isn’t feasible because of the enormous distances involved, or Earth simply had never been reached by alien travelers.

Herbert York was a Manhattan Project physicist, the co-discoverer of the neutral pi meson, and the first director of the Lawrence Livermore National Laboratory.  He was one of Fermi's lunch companions the day he posed his famed question about extraterrestrials.  Credit: National Nuclear Security Administration
Herbert York was a Manhattan Project physicist, the co-discoverer of the neutral pi meson, and the first director of the Lawrence Livermore National Laboratory. He was one of Fermi’s lunch companions the day he posed his famed question about extraterrestrials. Credit: National Nuclear Security Administration

Interstellar distances are truly vast. If the entire solar system out to the orbit of Neptune were reduced to the size of an American quarter, the nearest star, Proxima Centauri, would still be about the length of a football field away. A practical starship would either need to travel very fast, at an appreciable fraction of the speed of light, or be capable of supporting its crew for a very long time. While either is theoretically possible, interstellar travel seems to present day humanity to be such a grandiose undertaking that it’s not clear whether any civilization would be able or willing to muster the enormous resources needed.

Where did the confusing of Fermi’s question with Hart’s argument come from? Carl Sagan mentioned Fermi’s question in a footnote to a 1963 paper. After the publication of Hart’s paper in 1975, Fermi’s question and Hart’s speculative answer became associated in many writer’s minds. Fermi’s question seemed to beg Hart’s answer, and “Fermi’s paradox” was born. According to Robert Gray, the term was coined by D. G. Stephenson, in a paper published two years after Hart’s.

Why is it important that Hart’s argument was never really made by the eminent physicist Enrico Fermi? Did Michael Hart and Frank Tipler really make a compelling case that extraterrestrial civilizations don’t exist in our galaxy? We’ll answer those questions in the second installment.

References and Further Reading:

F. Cain (2013) How Could We Find Aliens? The Search for Extraterrestrial Intelligence (SETI). Universe Today.

R. H. Gray (2012) The Elusive WOW, Searching for Extraterrestrial Intelligence, Palmer Square Press, Chicago, Illinois.

R. H. Gray (2015) The Fermi Paradox is neither Fermi’s nor a paradox, Astrobiology, 15(3): 195-199.

M. H. Hart, (1975) An explanation for the absence of extraterrestrials on Earth, Quarterly Journal of the Royal Astronomical Society, 16:128-135.

E. M. Jones (1985) “Where is everybody?” An account of Fermi’s question, Los Alamos National Laboratory.

P. Patton (2014) Communicating Across the Cosmos, Part 1, Part 2, Part 3, Part 4. Universe Today.

F. Tipler (1980) Extraterrestrial intelligent beings do not exist, Quarterly Journal of the Royal Astronomical Society, 21:267-281.

S. Webb (2010) If the Universe is Teeming with Aliens…Where is Everybody? Fifty Solutions to the Fermi Paradox and the Problem of Extraterrestrial Life. Copernicus Books, New York, NY.