Green Bank Equation
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The Drake equation is a probabilistic argument used to estimate the number of active, communicative
extraterrestrial civilizations ''Extraterrestrial Civilizations'' is a 1979 book by Isaac Asimov, in which the author estimates the probability of there being intelligent extraterrestrial civilizations within the Milky Way galaxy. This estimation is approached by progressively ...
in the
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
Galaxy A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. ...
. The equation was formulated in 1961 by
Frank Drake Frank Donald Drake (May 28, 1930 – September 2, 2022) was an American astrophysicist and astrobiologist. He began his career as a radio astronomer, studying the planets of the Solar System and later pulsars. Drake expanded his interests t ...
, not for purposes of quantifying the number of civilizations, but as a way to stimulate scientific dialogue at the first scientific meeting on the
search for extraterrestrial intelligence The search for extraterrestrial intelligence (SETI) is a collective term for scientific searches for intelligent extraterrestrial life, for example, monitoring electromagnetic radiation for signs of transmissions from civilizations on other pl ...
(SETI). The equation summarizes the main concepts which scientists must contemplate when considering the question of other radio-communicative life. It is more properly thought of as an approximation than as a serious attempt to determine a precise number. Criticism related to the Drake equation focuses not on the equation itself, but on the fact that the estimated values for several of its factors are highly conjectural, the combined multiplicative effect being that the uncertainty associated with any derived value is so large that the equation cannot be used to draw firm conclusions.


Equation

The Drake equation is: :N = R_* \cdot f_\mathrm \cdot n_\mathrm \cdot f_\mathrm \cdot f_\mathrm \cdot f_\mathrm \cdot L where : = the number of
civilization A civilization (or civilisation) is any complex society characterized by the development of a state, social stratification, urbanization, and symbolic systems of communication beyond natural spoken language (namely, a writing system). Ci ...
s in the Milky Way galaxy with which communication might be possible (i.e. which are on the current past
light cone In special and general relativity, a light cone (or "null cone") is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take thro ...
); and : = the average rate of
star formation Star formation is the process by which dense regions within molecular clouds in The "medium" is present further soon.-->interstellar space
in our Galaxy : = the fraction of those stars that have
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
s : = the average number of planets that can potentially support
life Life is a quality that distinguishes matter that has biological processes, such as signaling and self-sustaining processes, from that which does not, and is defined by the capacity for growth, reaction to stimuli, metabolism, energ ...
per star that has planets : = the fraction of planets that could support life that actually develop life at some point : = the fraction of planets with life that actually go on to develop intelligent life (civilizations) : = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space : = the length of time for which such civilizations release detectable signals into space


History

In September 1959, physicists
Giuseppe Cocconi Giuseppe Cocconi (1914–2008) was an Italian physicist who was director of the Proton Synchrotron at CERN in Geneva. He is known for his work in particle physics and for his involvement with SETI where he wrote, " e probability of success is d ...
and
Philip Morrison Philip Morrison (November 7, 1915 – April 22, 2005) was a professor of physics at the Massachusetts Institute of Technology (MIT). He is known for his work on the Manhattan Project during World War II, and for his later work in quantum physi ...
published an article in the journal ''
Nature Nature, in the broadest sense, is the physics, physical world or universe. "Nature" can refer to the phenomenon, phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. ...
'' with the provocative title "Searching for Interstellar Communications". Cocconi and Morrison argued that
radio telescope A radio telescope is a specialized antenna and radio receiver used to detect radio waves from astronomical radio sources in the sky. Radio telescopes are the main observing instrument used in radio astronomy, which studies the radio frequency ...
s had become sensitive enough to pick up transmissions that might be broadcast into space by civilizations orbiting other stars. Such messages, they suggested, might be transmitted at a
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
of 21 cm (1,420.4 
MHz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one he ...
). This is the wavelength of radio emission by neutral
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
, the most common element in the universe, and they reasoned that other intelligences might see this as a logical landmark in the
radio spectrum The radio spectrum is the part of the electromagnetic spectrum with frequencies from 0  Hz to 3,000 GHz (3  THz). Electromagnetic waves in this frequency range, called radio waves, are widely used in modern technology, particula ...
. Two months later, Harvard University astronomy professor
Harlow Shapley Harlow Shapley (November 2, 1885 – October 20, 1972) was an American scientist, head of the Harvard College Observatory (1921–1952), and political activist during the latter New Deal and Fair Deal. Shapley used Cepheid variable stars to estim ...
speculated on the number of inhabited planets in the universe, saying "The universe has 10 million, million, million suns (10 followed by 18 zeros) similar to our own. One in a million has planets around it. Only one in a million million has the right combination of chemicals, temperature, water, days and nights to support planetary life as we know it. This calculation arrives at the estimated figure of 100 million worlds where life has been forged by evolution." Seven months after Cocconi and Morrison published their article, Drake made the first systematic search for signals from communicative extraterrestrial civilizations. Using the dish of the National Radio Astronomy Observatory, Green Bank in
Green Bank, West Virginia Green Bank is a census-designated place in Pocahontas County in West Virginia's Potomac Highlands inside the Allegheny Mountain Range. Green Bank is located along WV 28. Green Bank is home to the Green Bank Observatory and is also close to the S ...
, Drake monitored two nearby Sun-like stars:
Epsilon Eridani Epsilon Eridani ( Latinized from ε Eridani), formally named Ran, is a star in the southern constellation of Eridanus, at a declination of 9.46° south of the celestial equator. This allows it to be visible from most of Earth's surface ...
and
Tau Ceti Tau Ceti, Latinized from τ Ceti, is a single star in the constellation Cetus that is spectrally similar to the Sun, although it has only about 78% of the Sun's mass. At a distance of just under from the Solar System, it is a relativ ...
. In this project, which he called
Project Ozma Project Ozma was a search for extraterrestrial intelligence (SETI) experiment started in 1960 by Cornell University astronomer Frank Drake, at the National Radio Astronomy Observatory, Green Bank at Green Bank, West Virginia. The object of the e ...
, he slowly scanned frequencies close to the 21 cm wavelength for six hours per day from April to July 1960. The project was well designed, inexpensive, and simple by today's standards. It detected no signals. Soon thereafter, Drake hosted a "
search for extraterrestrial intelligence The search for extraterrestrial intelligence (SETI) is a collective term for scientific searches for intelligent extraterrestrial life, for example, monitoring electromagnetic radiation for signs of transmissions from civilizations on other pl ...
" meeting on detecting their radio signals. The meeting was held at the Green Bank facility in 1961. The equation that bears Drake's name arose out of his preparations for the meeting.
As I planned the meeting, I realized a few day 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. :—Frank Drake
The ten attendees were conference organizer J. Peter Pearman, Frank Drake,
Philip Morrison Philip Morrison (November 7, 1915 – April 22, 2005) was a professor of physics at the Massachusetts Institute of Technology (MIT). He is known for his work on the Manhattan Project during World War II, and for his later work in quantum physi ...
, businessman and radio amateur Dana Atchley, chemist
Melvin Calvin Melvin Ellis Calvin (April 8, 1912 – January 8, 1997) was an American biochemist known for discovering the Calvin cycle along with Andrew Benson and James Bassham, for which he was awarded the 1961 Nobel Prize in Chemistry. He spent most of hi ...
, astronomer
Su-Shu Huang Su-Shu Huang (, April 16, 1915 – September 15, 1977) was a Chinese-born American astrophysicist. A graduate of the University of Chicago, Huang began his career with the study of the continuous absorption coefficients of two-electron ...
, neuroscientist
John C. Lilly John Cunningham Lilly (January 6, 1915 – September 30, 2001)John C. Lilly
at
, inventor
Barney Oliver Bernard M. Oliver (May 17, 1916 – November 23, 1995), also known as Barney Oliver, was a scientist who made contributions in many fields, including radar, television, and computers. He was the founder and director of Hewlett Packard ( HP) ...
, astronomer
Carl Sagan Carl Edward Sagan (; ; November 9, 1934December 20, 1996) was an American astronomer, planetary scientist, cosmologist, astrophysicist, astrobiologist, author, and science communicator. His best known scientific contribution is research on ext ...
and radio-astronomer
Otto Struve Otto Struve (August 12, 1897 – April 6, 1963) was a Russian-American astronomer of Baltic German origins. In Russian, his name is sometimes given as Otto Lyudvigovich Struve (Отто Людвигович Струве); however, he spent most o ...
. These participants dubbed themselves "The Order of the Dolphin" (because of Lilly's work on dolphin communication), and commemorated their first meeting with a plaque at the observatory hall.


Usefulness

The Drake equation amounts to a summary of the factors affecting the likelihood that we might detect radio-communication from intelligent extraterrestrial life. The last three parameters, , , and , are not known and are very difficult to estimate, with values ranging over many orders of magnitude (see
criticism Criticism is the construction of a judgement about the negative qualities of someone or something. Criticism can range from impromptu comments to a written detailed response. , ''"the act of giving your opinion or judgment about the good or bad q ...
). Therefore, the usefulness of the Drake equation is not in the solving, but rather in the contemplation of all the various concepts which scientists must incorporate when considering the question of life elsewhere, and gives the question of life elsewhere a basis for
scientific analysis The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article history of scientific m ...
. The equation has helped draw attention to some particular scientific problems related to life in the universe, for example
abiogenesis In biology, abiogenesis (from a- 'not' + Greek bios 'life' + genesis 'origin') or the origin of life is the natural process by which life has arisen from non-living matter, such as simple organic compounds. The prevailing scientific hypothes ...
, the development of multi-cellular life, and the development of
intelligence Intelligence has been defined in many ways: the capacity for abstraction, logic, understanding, self-awareness, learning, emotional knowledge, reasoning, planning, creativity, critical thinking, and problem-solving. More generally, it can b ...
itself. Within the limits of existing human technology, any practical search for distant intelligent life must necessarily be a search for some manifestation of a distant technology. After about 50 years, the Drake equation is still of seminal importance because it is a 'road map' of what we need to learn in order to solve this fundamental existential question. It also formed the backbone of
astrobiology Astrobiology, and the related field of exobiology, is an interdisciplinary scientific field that studies the origins, early evolution, distribution, and future of life in the universe. Astrobiology is the multidisciplinary field that investig ...
as a science; although speculation is entertained to give context, astrobiology concerns itself primarily with
hypotheses A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous obser ...
that fit firmly into existing
scientific theories A scientific theory is an explanation of an aspect of the natural world and universe that has been repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation ...
. Some 50 years of SETI have failed to find anything, even though radio telescopes, receiver techniques, and computational abilities have improved significantly since the early 1960s. It has, however, been discovered that this galaxy is not teeming with very powerful alien transmitters continuously broadcasting near the 21 cm wavelength of the hydrogen frequency; this was not known in 1961.


Estimates


Original estimates

There is considerable disagreement on the values of these parameters, but the 'educated guesses' used by Drake and his colleagues in 1961 were: * = 1 yr−1 (1 star formed per year, on the average over the life of the galaxy; this was regarded as conservative) * = 0.2 to 0.5 (one fifth to one half of all stars formed will have planets) * = 1 to 5 (stars with planets will have between 1 and 5 planets capable of developing life) * = 1 (100% of these planets will develop life) * = 1 (100% of which will develop intelligent life) * = 0.1 to 0.2 (10–20% of which will be able to communicate) * = 1000 to 100,000,000 communicative civilizations (which will last somewhere between 1000 and 100,000,000 years) Inserting the above minimum numbers into the equation gives a minimum N of 20 (see: Range of results). Inserting the maximum numbers gives a maximum of 50,000,000. Drake states that given the uncertainties, the original meeting concluded that , and there were probably between 1000 and 100,000,000 planets with civilizations in the
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
Galaxy.


Current estimates

This section discusses and attempts to list the best current estimates for the parameters of the Drake equation.


Rate of star creation in this Galaxy,

Calculations in 2010, from
NASA The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeeding t ...
and the
European Space Agency , owners = , headquarters = Paris, Île-de-France, France , coordinates = , spaceport = Guiana Space Centre , seal = File:ESA emblem seal.png , seal_size = 130px , image = Views in the Main Control Room (1205 ...
indicate that the rate of star formation in this Galaxy is about of material per year. To get the number of stars per year, we divide this by the
initial mass function In astronomy, the initial mass function (IMF) is an empirical function that describes the initial Frequency distribution, distribution of masses for a population of stars. The IMF is an output of the process of star formation. The IMF is often g ...
(IMF) for stars, where the average new star's mass is about . This gives a star formation rate of about 1.5–3 stars per year.


Fraction of those stars that have planets,

Analysis of
microlensing Gravitational microlensing is an astronomical phenomenon due to the gravitational lens effect. It can be used to detect objects that range from the mass of a planet to the mass of a star, regardless of the light they emit. Typically, astronomers ...
surveys, in 2012, has found that may approach 1—that is, stars are orbited by planets as a rule, rather than the exception; and that there are one or more bound planets per Milky Way star.


Average number of planets that might support life per star that has planets,

In November 2013, astronomers reported, based on ''Kepler'' space mission data, that there could be as many as 40 billion Earth-sized
planets A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a young ...
orbiting in the
habitable zone In astronomy and astrobiology, the circumstellar habitable zone (CHZ), or simply the habitable zone, is the range of orbits around a star within which a planetary surface can support liquid water given sufficient atmospheric pressure.J. F. Kas ...
s of sun-like stars and
red dwarf stars ''Red Dwarf'' is a British science fiction comedy franchise created by Rob Grant and Doug Naylor, which primarily consists of a television sitcom that aired on BBC Two between 1988 and 1999, and on Dave (TV channel), Dave since 2009, gaining a ...
within the
Milky Way Galaxy The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. ...
. 11 billion of these estimated planets may be orbiting sun-like stars. Since there are about 100 billion stars in the galaxy, this implies is roughly 0.4. The nearest planet in the habitable zone is
Proxima Centauri b Proxima Centauri b (or Proxima b), sometimes referred to as Alpha Centauri Cb, is an exoplanet orbiting in the habitable zone of the red dwarf star Proxima Centauri, which is the closest star to the Sun and part of the triple star system Alpha ...
, which is as close as about 4.2 light-years away. The consensus at the Green Bank meeting was that had a minimum value between 3 and 5. Dutch science journalist
Govert Schilling Govert Schilling (born 30 November 1956) is a Dutch popular science writer and amateur astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. Th ...
has opined that this is optimistic. Even if planets are in the
habitable zone In astronomy and astrobiology, the circumstellar habitable zone (CHZ), or simply the habitable zone, is the range of orbits around a star within which a planetary surface can support liquid water given sufficient atmospheric pressure.J. F. Kas ...
, the number of planets with the right proportion of elements is difficult to estimate. Brad Gibson, Yeshe Fenner, and Charley Lineweaver determined that about 10% of
star system A star system or stellar system is a small number of stars that orbit each other, bound by gravitational attraction. A large group of stars bound by gravitation is generally called a '' star cluster'' or '' galaxy'', although, broadly speak ...
s in the Milky Way Galaxy are hospitable to life, by having heavy elements, being far from
supernova A supernova is a powerful and luminous explosion of a star. It has the plural form supernovae or supernovas, and is abbreviated SN or SNe. This transient astronomical event occurs during the last evolutionary stages of a massive star or when ...
e and being stable for a sufficient time. The discovery of numerous
gas giant A gas giant is a giant planet composed mainly of hydrogen and helium. Gas giants are also called failed stars because they contain the same basic elements as a star. Jupiter and Saturn are the gas giants of the Solar System. The term "gas giant" ...
s in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the formation of their stellar systems. So-called
hot Jupiter Hot Jupiters (sometimes called hot Saturns) are a class of gas giant exoplanets that are inferred to be physically similar to Jupiter but that have very short orbital periods (). The close proximity to their stars and high surface-atmosphere temp ...
s may migrate from distant orbits to near orbits, in the process disrupting the orbits of habitable planets. On the other hand, the variety of
star system A star system or stellar system is a small number of stars that orbit each other, bound by gravitational attraction. A large group of stars bound by gravitation is generally called a '' star cluster'' or '' galaxy'', although, broadly speak ...
s that might have habitable zones is not just limited to solar-type stars and Earth-sized planets. It is now estimated that even tidally locked planets close to
red dwarf ''Red Dwarf'' is a British science fiction comedy franchise created by Rob Grant and Doug Naylor, which primarily consists of a television sitcom that aired on BBC Two between 1988 and 1999, and on Dave since 2009, gaining a cult following. T ...
stars might have habitable zones, although the flaring behavior of these stars might speak against this. The possibility of life on
moons A natural satellite is, in the most common usage, an astronomical body that orbits a planet, dwarf planet, or small Solar System body (or sometimes another natural satellite). Natural satellites are often colloquially referred to as ''moons'' ...
of gas giants (such as
Jupiter Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but ...
's moon
Europa Europa may refer to: Places * Europe * Europa (Roman province), a province within the Diocese of Thrace * Europa (Seville Metro), Seville, Spain; a station on the Seville Metro * Europa City, Paris, France; a planned development * Europa Cliff ...
, or
Saturn Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
's moons
Titan Titan most often refers to: * Titan (moon), the largest moon of Saturn * Titans, a race of deities in Greek mythology Titan or Titans may also refer to: Arts and entertainment Fictional entities Fictional locations * Titan in fiction, fictiona ...
and Enceladus) adds further uncertainty to this figure. The authors of the
rare Earth hypothesis In planetary astronomy and astrobiology, the Rare Earth hypothesis argues that the origin of life and the evolution of biological complexity such as sexually reproducing, multicellular organisms on Earth (and, subsequently, human intelligenc ...
propose a number of additional constraints on habitability for planets, including being in galactic zones with suitably low radiation, high star metallicity, and low enough density to avoid excessive asteroid bombardment. They also propose that it is necessary to have a planetary system with large gas giants which provide bombardment protection without a
hot Jupiter Hot Jupiters (sometimes called hot Saturns) are a class of gas giant exoplanets that are inferred to be physically similar to Jupiter but that have very short orbital periods (). The close proximity to their stars and high surface-atmosphere temp ...
; and a planet with
plate tectonic Plate tectonics (from the la, label=Late Latin, tectonicus, from the grc, τεκτονικός, lit=pertaining to building) is the generally accepted scientific theory that considers the Earth's lithosphere to comprise a number of large te ...
s, a large moon that creates tidal pools, and moderate
axial tilt In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbi ...
to generate seasonal variation.


Fraction of the above that actually go on to develop life,

Geological evidence from the Earth suggests that may be high; life on Earth appears to have begun around the same time as favorable conditions arose, suggesting that
abiogenesis In biology, abiogenesis (from a- 'not' + Greek bios 'life' + genesis 'origin') or the origin of life is the natural process by which life has arisen from non-living matter, such as simple organic compounds. The prevailing scientific hypothes ...
may be relatively common once conditions are right. However, this evidence only looks at the Earth (a single model planet), and contains
anthropic bias The anthropic principle, also known as the "observation selection effect", is the hypothesis, first proposed in 1957 by Robert Dicke, that there is a restrictive lower bound on how statistically probable our observations of the universe are, beca ...
, as the planet of study was not chosen randomly, but by the living organisms that already inhabit it (ourselves). From a classical
hypothesis testing A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. ...
standpoint, without assuming that the underlying distribution of is the same for all planets in the Milky Way, there are zero
degrees of freedom Degrees of freedom (often abbreviated df or DOF) refers to the number of independent variables or parameters of a thermodynamic system. In various scientific fields, the word "freedom" is used to describe the limits to which physical movement or ...
, permitting no valid estimates to be made. If life (or evidence of past life) were to be found on
Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury (planet), Mercury. In the English language, Mars is named for the Mars (mythology), Roman god of war. Mars is a terr ...
,
Europa Europa may refer to: Places * Europe * Europa (Roman province), a province within the Diocese of Thrace * Europa (Seville Metro), Seville, Spain; a station on the Seville Metro * Europa City, Paris, France; a planned development * Europa Cliff ...
,
Enceladus Enceladus is the sixth-largest moon of Saturn (19th largest in the Solar System). It is about in diameter, about a tenth of that of Saturn's largest moon, Titan. Enceladus is mostly covered by fresh, clean ice, making it one of the most refl ...
or
Titan Titan most often refers to: * Titan (moon), the largest moon of Saturn * Titans, a race of deities in Greek mythology Titan or Titans may also refer to: Arts and entertainment Fictional entities Fictional locations * Titan in fiction, fictiona ...
that developed independently from life on Earth it would imply a value for close to 1. While this would raise the number of degrees of freedom from zero to one, there would remain a great deal of uncertainty on any estimate due to the small sample size, and the chance they are not really independent. Countering this argument is that there is no evidence for abiogenesis occurring more than once on the Earth—that is, all terrestrial life stems from a common origin. If abiogenesis were more common it would be speculated to have occurred more than once on the Earth. Scientists have searched for this by looking for
bacteria Bacteria (; singular: bacterium) are ubiquitous, mostly free-living organisms often consisting of one biological cell. They constitute a large domain of prokaryotic microorganisms. Typically a few micrometres in length, bacteria were among ...
that are unrelated to other life on Earth, but none have been found yet. It is also possible that life arose more than once, but that other branches were out-competed, or died in mass extinctions, or were lost in other ways. Biochemists
Francis Crick Francis Harry Compton Crick (8 June 1916 – 28 July 2004) was an English molecular biologist, biophysicist, and neuroscientist. He, James Watson, Rosalind Franklin, and Maurice Wilkins played crucial roles in deciphering the helical struc ...
and
Leslie Orgel Leslie Eleazer Orgel FRS (12 January 1927 – 27 October 2007) was a British chemist. He is known for his theories on the origin of life. Biography Leslie Orgel was born in London, England, on . He received his Bachelor of Arts degree in chemi ...
laid special emphasis on this uncertainty: "At the moment we have no means at all of knowing" whether we are "likely to be alone in the galaxy (Universe)" or whether "the galaxy may be pullulating with life of many different forms." As an alternative to abiogenesis on Earth, they proposed the hypothesis of
directed panspermia Directed panspermia is the deliberate transport of microorganisms into space to be used as introduced species on lifeless but habitable astronomical objects. Historically, Shklovskii and Sagan (1966) and Crick and Orgel (1973) hypothesized that li ...
, which states that Earth life began with "microorganisms sent here deliberately by a technological society on another planet, by means of a special long-range unmanned spaceship". In 2020, a paper by scholars at the
University of Nottingham The University of Nottingham is a public university, public research university in Nottingham, United Kingdom. It was founded as University College Nottingham in 1881, and was granted a royal charter in 1948. The University of Nottingham belongs t ...
proposed an "Astrobiological Copernican" principle, based on the
Principle of Mediocrity The mediocrity principle is the philosophical notion that "if an item is drawn at random from one of several sets or categories, it's more likely to come from the most numerous category than from any one of the less numerous categories". The prin ...
, and speculated that "intelligent life would form on other arth-likeplanets like it has on Earth, so within a few billion years life would automatically form as a natural part of evolution". In the authors' framework, , , and are all set to a probability of 1 (certainty). Their resultant calculation concludes there are more than thirty current technological civilizations in the galaxy (disregarding error bars).


Fraction of the above that develops intelligent life,

This value remains particularly controversial. Those who favor a low value, such as the biologist
Ernst Mayr Ernst Walter Mayr (; 5 July 1904 – 3 February 2005) was one of the 20th century's leading evolutionary biologists. He was also a renowned Taxonomy (biology), taxonomist, tropical explorer, ornithologist, Philosophy of biology, philosopher o ...
, point out that of the billions of species that have existed on Earth, only one has become intelligent and from this, infer a tiny value for . Likewise, the Rare Earth hypothesis, notwithstanding their low value for above, also think a low value for dominates the analysis. Those who favor higher values note the generally increasing complexity of life over time, concluding that the appearance of intelligence is almost inevitable, implying an approaching 1. Skeptics point out that the large spread of values in this factor and others make all estimates unreliable. (See
Criticism Criticism is the construction of a judgement about the negative qualities of someone or something. Criticism can range from impromptu comments to a written detailed response. , ''"the act of giving your opinion or judgment about the good or bad q ...
). In addition, while it appears that life developed soon after the formation of Earth, the
Cambrian explosion The Cambrian explosion, Cambrian radiation, Cambrian diversification, or the Biological Big Bang refers to an interval of time approximately in the Cambrian Period when practically all major animal phyla started appearing in the fossil recor ...
, in which a large variety of multicellular life forms came into being, occurred a considerable amount of time after the formation of Earth, which suggests the possibility that special conditions were necessary. Some scenarios such as the
snowball Earth The Snowball Earth hypothesis proposes that, during one or more of Earth's Greenhouse and icehouse Earth, icehouse Climate, climates, the Earth's surface, planet's surface became entirely or nearly entirely Freezing, frozen. It is believed that ...
or research into
extinction events An extinction event (also known as a mass extinction or biotic crisis) is a widespread and rapid decrease in the biodiversity on Earth. Such an event is identified by a sharp change in the diversity and abundance of multicellular organisms. It ...
have raised the possibility that life on Earth is relatively fragile. Research on any past
life on Mars The possibility of life on Mars is a subject of interest in astrobiology due to the planet's proximity and similarities to Earth. To date, no proof of past or present life has been found on Mars. Cumulative evidence suggests that during the ...
is relevant since a discovery that life did form on Mars but ceased to exist might raise the estimate of but would indicate that in half the known cases, intelligent life did not develop. Estimates of have been affected by discoveries that the Solar System's orbit is circular in the galaxy, at such a distance that it remains out of the spiral arms for tens of millions of years (evading radiation from
nova A nova (plural novae or novas) is a transient astronomical event that causes the sudden appearance of a bright, apparently "new" star (hence the name "nova", which is Latin for "new") that slowly fades over weeks or months. Causes of the dramati ...
e). Also, Earth's large moon may aid the evolution of life by stabilizing the planet's axis of rotation. There has been quantitative work to begin to define f_\mathrm \cdot f_\mathrm . One example is a Bayesian analysis published in 2020. In the conclusion, the author cautions that this study applies to Earth's conditions. In Bayesian terms, the study favors the formation of intelligence on a planet with identical conditions to Earth but does not do so with high confidence. Planetary scientist
Pascal Lee Pascal Lee (; born 1964) is co-founder and chairman of the Mars Institute, a planetary scientist at the SETI Institute, and the Principal Investigator of the Haughton-Mars Project (HMP) at NASA Ames Research Center in Mountain View, California. H ...
of the
SETI Institute The SETI Institute is a not-for-profit research organization incorporated in 1984 whose mission is to explore, understand, and explain the origin and nature of life in the universe, and to use this knowledge to inspire and guide present and futu ...
proposes that this fraction is very low (0.0002). He based this estimate on how long it took Earth to develop intelligent life (1 million years since
Homo erectus ''Homo erectus'' (; meaning "upright man") is an extinct species of archaic human from the Pleistocene, with its earliest occurrence about 2 million years ago. Several human species, such as '' H. heidelbergensis'' and '' H. antecessor' ...
evolved, compared to 4.6 billion years since Earth formed).


Fraction of the above revealing their existence via signal release into space,

For deliberate communication, the one example we have (the Earth) does not do much explicit communication, though there are some efforts covering only a tiny fraction of the stars that might look for human presence. (See
Arecibo message The Arecibo message is an interstellar radio message carrying basic information about humanity and Earth that was sent to the globular cluster Messier 13 in 1974. It was meant as a demonstration of human technological achievement, rather than a ...
, for example). There is considerable speculation why an extraterrestrial civilization might exist but choose not to communicate. However, deliberate communication is not required, and calculations indicate that current or near-future Earth-level technology might well be detectable to civilizations not too much more advanced than present day humans. By this standard, the Earth is a communicating civilization. Another question is what percentage of civilizations in the galaxy are close enough for us to detect, assuming that they send out signals. For example, existing Earth radio telescopes could only detect Earth radio transmissions from roughly a light year away.


Lifetime of such a civilization wherein it communicates its signals into space,

Michael Shermer Michael Brant Shermer (born September 8, 1954) is an American science writer, historian of science, executive director of The Skeptics Society, and founding publisher of ''Skeptic'' magazine, a publication focused on investigating pseudoscientific ...
estimated as 420 years, based on the duration of sixty historical Earthly civilizations. Using 28 civilizations more recent than the Roman Empire, he calculates a figure of 304 years for "modern" civilizations. It could also be argued from Michael Shermer's results that the fall of most of these civilizations was followed by later civilizations that carried on the technologies, so it is doubtful that they are separate civilizations in the context of the Drake equation. In the expanded version, including ''reappearance number'', this lack of specificity in defining single civilizations does not matter for the end result, since such a civilization turnover could be described as an increase in the ''reappearance number'' rather than increase in , stating that a civilization reappears in the form of the succeeding cultures. Furthermore, since none could communicate over interstellar space, the method of comparing with historical civilizations could be regarded as invalid.
David Grinspoon David H. Grinspoon (born 1959) is an American astrobiologist. He is Senior Scientist at the Planetary Science Institute and was the former inaugural Baruch S. Blumberg NASA/Library of Congress Chair in Astrobiology for 2012-2013. His research f ...
has argued that once a civilization has developed enough, it might overcome all threats to its survival. It will then last for an indefinite period of time, making the value for potentially billions of years. If this is the case, then he proposes that the Milky Way Galaxy may have been steadily accumulating advanced civilizations since it formed. He proposes that the last factor be replaced with , where is the fraction of communicating civilizations that become "immortal" (in the sense that they simply do not die out), and representing the length of time during which this process has been going on. This has the advantage that would be a relatively easy-to-discover number, as it would simply be some fraction of the age of the universe. It has also been hypothesized that once a civilization has learned of a more advanced one, its longevity could increase because it can learn from the experiences of the other. The astronomer
Carl Sagan Carl Edward Sagan (; ; November 9, 1934December 20, 1996) was an American astronomer, planetary scientist, cosmologist, astrophysicist, astrobiologist, author, and science communicator. His best known scientific contribution is research on ext ...
speculated that all of the terms, except for the lifetime of a civilization, are relatively high and the determining factor in whether there are large or small numbers of civilizations in the universe is the civilization lifetime, or in other words, the ability of technological civilizations to avoid self-destruction. In Sagan's case, the Drake equation was a strong motivating factor for his interest in environmental issues and his efforts to warn against the dangers of
nuclear warfare Nuclear warfare, also known as atomic warfare, is a theoretical military conflict or prepared political strategy that deploys nuclear weaponry. Nuclear weapons are weapons of mass destruction; in contrast to conventional warfare, nuclear ...
. An intelligent civilization might not be organic, as some have suggested that
artificial general intelligence Artificial general intelligence (AGI) is the ability of an intelligent agent to understand or learn any intellectual task that a human being can. It is a primary goal of some artificial intelligence research and a common topic in science fictio ...
may replace humanity.


Range of results

As many skeptics have pointed out, the Drake equation can give a very wide range of values, depending on the assumptions, as the values used in portions of the Drake equation are not well established. In particular, the result can be , meaning we are likely alone in the galaxy, or , implying there are many civilizations we might contact. One of the few points of wide agreement is that the presence of humanity implies a probability of intelligence arising of greater than zero. As an example of a low estimate, combining NASA's star formation rates, the
rare Earth hypothesis In planetary astronomy and astrobiology, the Rare Earth hypothesis argues that the origin of life and the evolution of biological complexity such as sexually reproducing, multicellular organisms on Earth (and, subsequently, human intelligenc ...
value of , Mayr's view on intelligence arising, Drake's view of communication, and Shermer's estimate of lifetime: :, , , rake, above/sup>, and years gives: : i.e., suggesting that we are probably alone in this galaxy, and possibly in the observable universe. On the other hand, with larger values for each of the parameters above, values of can be derived that are greater than 1. The following higher values that have been proposed for each of the parameters: :, , , , , rake, above/sup>, and years Use of these parameters gives: :
Monte Carlo Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is ...
simulations of estimates of the Drake equation factors based on a stellar and planetary model of the Milky Way have resulted in the number of civilizations varying by a factor of 100.


Have other technological species ''ever'' existed?

In 2016, Adam Frank and Woodruff Sullivan modified the Drake equation to determine just how unlikely the event of a technological species arising on a given habitable planet must be, to give the result that Earth hosts the ''only'' technological species that has ''ever'' arisen, for two cases: (a) this Galaxy, and (b) the universe as a whole. By asking this different question, one removes the lifetime and simultaneous communication uncertainties. Since the numbers of habitable planets per star can today be reasonably estimated, the only remaining unknown in the Drake equation is the probability that a habitable planet ''ever'' develops a technological species over its lifetime. For Earth to have the only technological species that has ever occurred in the universe, they calculate the probability of any given habitable planet ever developing a technological species must be less than . Similarly, for Earth to have been the only case of hosting a technological species over the history of this Galaxy, the odds of a habitable zone planet ever hosting a technological species must be less than (about 1 in 60 billion). The figure for the universe implies that it is extremely unlikely that Earth hosts the only technological species that has ever occurred. On the other hand, for this Galaxy one must think that fewer than 1 in 60 billion habitable planets develop a technological species for there not to have been at least a second case of such a species over the past history of this Galaxy.


Modifications

As many observers have pointed out, the Drake equation is a very simple model that omits potentially relevant parameters, and many changes and modifications to the equation have been proposed. One line of modification, for example, attempts to account for the uncertainty inherent in many of the terms. Combining the estimates of the original six factors by major researchers via a Monte Carlo procedure leads to a best value for the non-longevity factors of 0.85 1/years. This result differs insignificantly from the estimate of unity given both by Drake and the Cyclops report. Others note that the Drake equation ignores many concepts that might be relevant to the odds of contacting other civilizations. For example,
David Brin Glen David Brin (born October 6, 1950) is an American scientist and author of science fiction. He has won the Hugo, Because it is the contact cross-section that is of interest to the SETI community, many additional factors and modifications of the Drake equation have been proposed. ;Colonization : It has been proposed to generalize the Drake equation to include additional effects of alien civilizations colonizing other
star system A star system or stellar system is a small number of stars that orbit each other, bound by gravitational attraction. A large group of stars bound by gravitation is generally called a '' star cluster'' or '' galaxy'', although, broadly speak ...
s. Each original site expands with an expansion velocity , and establishes additional sites that survive for a lifetime . The result is a more complex set of 3 equations. ;Reappearance factor : The Drake equation may furthermore be multiplied by ''how many times'' an intelligent civilization may occur on planets where it has happened once. Even if an intelligent civilization reaches the end of its lifetime after, for example, 10,000 years, life may still prevail on the planet for billions of years, permitting the next civilization to evolve. Thus, several civilizations may come and go during the lifespan of one and the same planet. Thus, if is the average number of times a new civilization reappears on the same planet where a previous civilization once has appeared and ended, then the total number of civilizations on such a planet would be , which is the actual ''reappearance factor'' added to the equation. :The factor depends on what generally is the cause of civilization extinction. If it is generally by temporary uninhabitability, for example a
nuclear winter Nuclear winter is a severe and prolonged global climatic cooling effect that is hypothesized to occur after widespread firestorms following a large-scale nuclear war. The hypothesis is based on the fact that such fires can inject soot into th ...
, then may be relatively high. On the other hand, if it is generally by permanent uninhabitability, such as
stellar evolution Stellar evolution is the process by which a star changes over the course of time. Depending on the mass of the star, its lifetime can range from a few million years for the most massive to trillions of years for the least massive, which is cons ...
, then may be almost zero. In the case of total life extinction, a similar factor may be applicable for , that is, ''how many times'' life may appear on a planet where it has appeared once. ;METI factor :
Alexander Zaitsev Alexander Zaytsev may refer to: *Alexander Zaytsev (artist), Alexander Dmitryevich Zaytsev (1903–1982), Russian painter and art educator *Alexander Zaytsev (pilot), Alexander Andreyevich Zaytsev (1911–1965), Soviet aircraft pilot and Hero of the ...
said that to be in a communicative phase and emit dedicated messages are not the same. For example, humans, although being in a communicative phase, are not a communicative civilization; we do not practise such activities as the purposeful and regular transmission of interstellar messages. For this reason, he suggested introducing the METI factor (messaging to extraterrestrial intelligence) to the classical Drake equation. He defined the factor as "the fraction of communicative civilizations with clear and non-paranoid planetary consciousness", or alternatively expressed, the fraction of communicative civilizations that actually engage in deliberate interstellar transmission. :The METI factor is somewhat misleading since active, purposeful transmission of messages by a civilization is not required for them to receive a broadcast sent by another that is seeking first contact. It is merely required they have capable and compatible receiver systems operational; however, this is a variable humans cannot accurately estimate. ;Biogenic gases : Astronomer
Sara Seager Sara Seager (born 21 July 1971) is a Canadian-American astronomer and planetary scientist. She is a professor at the Massachusetts Institute of Technology and is known for her work on extrasolar planets and their atmospheres. She is the auth ...
proposed a revised equation that focuses on the search for planets with biosignature gases. These gases are produced by living organisms that can accumulate in a planet atmosphere to levels that can be detected with remote space telescopes.The Drake Equation Revisited: Interview with Planet Hunter Sara Seager
Devin Powell, ''Astrobiology Magazine'' 4 September 2013.
:The Seager equation looks like this: ::N = N_* \cdot F_\mathrm \cdot F_\mathrm \cdot F_\mathrm \cdot F_\mathrm \cdot F_\mathrm :where: :: = the number of planets with detectable signs of life :: = the number of stars observed :: = the fraction of stars that are quiet :: = the fraction of stars with rocky planets in the habitable zone :: = the fraction of those planets that can be observed :: = the fraction that have life :: = the fraction on which life produces a detectable signature gas :Seager stresses, “We’re not throwing out the Drake Equation, which is really a different topic,” explaining, “Since Drake came up with the equation, we have discovered thousands of exoplanets. We as a community have had our views revolutionized as to what could possibly be out there. And now we have a real question on our hands, one that's not related to intelligent life: Can we detect any signs of life in any way in the very near future?”


Criticism

Criticism of the Drake equation follows mostly from the observation that several terms in the equation are largely or entirely based on conjecture. Star formation rates are well-known, and the incidence of planets has a sound theoretical and observational basis, but the other terms in the equation become very speculative. The uncertainties revolve around the present day understanding of the evolution of life, intelligence, and civilization, not physics. No statistical estimates are possible for some of the parameters, where only one example is known. The net result is that the equation cannot be used to draw firm conclusions of any kind, and the resulting margin of error is huge, far beyond what some consider acceptable or meaningful. One reply to such criticisms is that even though the Drake equation currently involves speculation about unmeasured parameters, it was intended as a way to stimulate dialogue on these topics. Then the focus becomes how to proceed experimentally. Indeed, Drake originally formulated the equation merely as an agenda for discussion at the Green Bank conference.


Fermi paradox

A civilization lasting for tens of millions of years could be able to spread throughout the galaxy, even at the slow speeds foreseeable with present day technology. However, no confirmed signs of civilizations or intelligent life elsewhere have been found, either in this Galaxy or in the
observable universe The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because the electromagnetic radiation from these obj ...
of 2 
trillion ''Trillion'' is a number with two distinct definitions: * 1,000,000,000,000, i.e. one million million, or (ten to the twelfth power), as defined on the short scale. This is now the meaning in both American and British English. * 1,000,000,000,0 ...
galaxies. According to this line of thinking, the tendency to fill up (or at least explore) all available territory seems to be a universal trait of living things, so the Earth should have already been colonized, or at least visited, but no evidence of this exists. Hence Fermi's question "Where is everybody?". A large number of explanations have been proposed to explain this lack of contact; a book published in 2015 elaborated on 75 different explanations. In terms of the Drake Equation, the explanations can be divided into three classes: *Few intelligent civilizations ever arise. This is an argument that at least one of the first few terms, , has a low value. The most common suspect is , but explanations such as the rare Earth hypothesis argue that is the small term. *Intelligent civilizations exist, but we see no evidence, meaning is small. Typical arguments include that civilizations are too far apart, it is too expensive to spread throughout the galaxy, civilizations broadcast signals for only a brief period of time, communication is dangerous, and many others. *The lifetime of intelligent, communicative civilizations is short, meaning the value of is small. Drake suggested that a large number of extraterrestrial civilizations would form, and he further speculated that the lack of evidence of such civilizations may be because technological civilizations tend to disappear rather quickly. Typical explanations include it is the nature of intelligent life to destroy itself, it is the nature of intelligent life to destroy others, they tend to be destroyed by natural events, and others. These lines of reasoning lead to the
Great Filter The Great Filter is one possible resolution of the Fermi paradox. It posits that in the development of life from the earliest stages of abiogenesis to reaching the highest levels of development on the Kardashev scale, there exists some particular ...
hypothesis, which states that since there are no observed extraterrestrial civilizations despite the vast number of stars, at least one step in the process must be acting as a filter to reduce the final value. According to this view, either it is very difficult for intelligent life to arise, or the lifetime of technologically advanced civilizations, or the period of time they reveal their existence must be relatively short. An analysis by
Anders Sandberg Anders Sandberg (born 11 July 1972) is a Swedish researcher, futurist and transhumanist. He holds a PhD in computational neuroscience from Stockholm University, and is currently a senior research fellow at the Future of Humanity Institute at the ...
,
Eric Drexler Kim Eric Drexler (born April 25, 1955) is an American engineer best known for studies of the potential of molecular nanotechnology (MNT), from the 1970s and 1980s. His 1991 doctoral thesis at Massachusetts Institute of Technology was revised and ...
and
Toby Ord Toby David Godfrey Ord (born July 1979) is an Australian philosopher. He founded Giving What We Can in 2009, an international society whose members pledge to donate at least 10% of their income to effective charities, and is a key figure in the ...
suggests "a substantial ''ex ante'' probability of there being no other intelligent life in our observable universe".


In fiction and popular culture

The equation was cited by
Gene Roddenberry Eugene Wesley Roddenberry Sr. (August 19, 1921 – October 24, 1991) was an American television screenwriter, producer, and creator of ''Star Trek: The Original Series'', its sequel spin-off series ''Star Trek: The Animated Series,'' and ''Sta ...
as supporting the multiplicity of inhabited planets shown on ''
Star Trek ''Star Trek'' is an American science fiction media franchise created by Gene Roddenberry, which began with the eponymous 1960s television series and quickly became a worldwide pop-culture phenomenon. The franchise has expanded into vari ...
'', the television series he created. However, Roddenberry did not have the equation with him, and he was forced to "invent" it for his original proposal.''The Making of Star Trek'' by Stephen E. Whitfield and Gene Roddenberry, New York: Ballantine Books, 1968 The invented equation created by Roddenberry is: ::Ff^2 (MgE)-C^1 Ri^1 \cdot M=L/So However, a number raised to the first power is merely the number itself.


See also

* * * * * * * '' The Search for Life: The Drake Equation'', BBC documentary


Notes


References


Further reading

* * *


External links


Interactive Drake Equation Calculator Frank Drake's 2010 article on "The Origin of the Drake Equation""Only a matter of time, says Frank Drake"
A Q&A with Frank Drake in February 2010. *

from
PBS The Public Broadcasting Service (PBS) is an American public broadcasting, public broadcaster and Non-commercial activity, non-commercial, Terrestrial television, free-to-air television network based in Arlington, Virginia. PBS is a publicly fu ...
Nova A nova (plural novae or novas) is a transient astronomical event that causes the sudden appearance of a bright, apparently "new" star (hence the name "nova", which is Latin for "new") that slowly fades over weeks or months. Causes of the dramati ...

The Drake Equation
''
Astronomy Cast ''Astronomy Cast'' is an educational nonprofit podcast discussing various topics in the field of astronomy. The specific subject matter of each episode shifts from week to week, ranging from planets and stars to cosmology and mythbusting. Premie ...
'' episode #23, includes full transcript.
Animated simulation of the Drake equation.

The Alien Equation
22 September 2010, BBC Radio program ''Discovery''.
"Reflections on the Equation"
(PDF), by Frank Drake, 2013 {{Portal bar, Stars, Spaceflight, Solar System, Science 1961 introductions Astrobiology Astronomical controversies Astronomical hypotheses Equations Extraterrestrial life Fermi paradox Interstellar messages Search for extraterrestrial intelligence