Drake equation

Drake equation

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Encyclopedia
The Drake equation is an equation used to estimate the number of detectable extraterrestrial
Extraterrestrial life
Extraterrestrial life is defined as life that does not originate from Earth...

 civilizations in the Milky Way
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...

 galaxy
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...

. It is used in the fields of exobiology and the Search for ExtraTerrestrial Intelligence
SETI
The search for extraterrestrial intelligence is the collective name for a number of activities people undertake to search for intelligent extraterrestrial life. Some of the most well known projects are run by the SETI Institute. SETI projects use scientific methods to search for intelligent life...

 (SETI). The equation was devised by Frank Drake
Frank Drake
Frank Donald Drake PhD is an American astronomer and astrophysicist. He is most notable as one of the pioneers in the search for extraterrestrial intelligence, including the founding of SETI, mounting the first observational attempts at detecting extraterrestrial communications in 1961 in Project...

, Emeritus Professor of Astronomy and Astrophysics at the University of California, Santa Cruz
University of California, Santa Cruz
The University of California, Santa Cruz, also known as UC Santa Cruz or UCSC, is a public, collegiate university; one of ten campuses in the University of California...

.

History


In 1960, Frank Drake conducted the first search for radio signals from extraterrestrial civilizations at the National Radio Astronomy Observatory in Green Bank
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 also close to the Snowshoe Mountain ski resort...

, West Virginia
West Virginia
West Virginia is a state in the Appalachian and Southeastern regions of the United States, bordered by Virginia to the southeast, Kentucky to the southwest, Ohio to the northwest, Pennsylvania to the northeast and Maryland to the east...

. Soon thereafter, the National Academy of Sciences asked Drake to convene a meeting on detecting extraterrestrial intelligence. 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:

This meeting established SETI as a scientific discipline. The meeting's dozen participants — astronomers, physicists, biologists, social scientists, and industry leaders — became known as the "Order of the Dolphin". The Green Bank meeting has been commemorated by a plaque at the site.

The Drake equation is closely related to the Fermi paradox
Fermi paradox
The Fermi paradox is the apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for, or contact with, such civilizations....

 in that Drake suggested that a large number of extraterrestrial civilizations would form, but that the lack of evidence of such civilizations (the Fermi paradox) suggests that technological civilizations tend to disappear rather quickly. This theory often stimulates an interest in identifying and publicizing ways in which humanity could destroy itself, and then counters with hopes of avoiding such destruction and eventually becoming a space-faring species. A similar argument is the Great Filter, which notes that since there are no observed extraterrestrial civilizations, despite the vast number of stars, then some step in the process 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, or the lifetime of such civilizations must be relatively short.

Carl Sagan
Carl Sagan
Carl Edward Sagan was an American astronomer, astrophysicist, cosmologist, author, science popularizer and science communicator in astronomy and natural sciences. He published more than 600 scientific papers and articles and was author, co-author or editor of more than 20 books...

, a great proponent of SETI
SETI
The search for extraterrestrial intelligence is the collective name for a number of activities people undertake to search for intelligent extraterrestrial life. Some of the most well known projects are run by the SETI Institute. SETI projects use scientific methods to search for intelligent life...

, quoted the formula often and as a result the formula is sometimes mislabeled as "The Sagan Equation."

The equation


The Drake equation states that:


where:
N = the number of civilization
Civilization
Civilization is a sometimes controversial term that has been used in several related ways. Primarily, the term has been used to refer to the material and instrumental side of human cultures that are complex in terms of technology, science, and division of labor. Such civilizations are generally...

s in our galaxy with which communication might be possible;


and
R* = the average rate of star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

 formation per year in our galaxy
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...

fp = the fraction of those stars that have planet
Planet
A planet is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighbouring region of planetesimals.The term planet is ancient, with ties to history, science,...

s
ne = the average number of planets that can potentially support life
Life
Life is a characteristic that distinguishes objects that have signaling and self-sustaining processes from those that do not, either because such functions have ceased , or else because they lack such functions and are classified as inanimate...

 per star that has planets
f = the fraction of the above that actually go on to develop life at some point
fi = the fraction of the above that actually go on to develop intelligent
Intelligence
Intelligence has been defined in different ways, including the abilities for abstract thought, understanding, communication, reasoning, learning, planning, emotional intelligence and problem solving....

 life
fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L = the length of time for which such civilizations release detectable signals into space.

R factor


One can question why the number of civilizations should be proportional to the star formation rate, though this makes technical sense. (The product of all the terms except L tells how many new communicating civilizations are born each year. Then you multiply by the lifetime to get the expected number. For example, if an average of 0.01 new civilizations are born each year, and they each last 500 years on the average, then on the average 5 will exist at any time.) The original Drake Equation can be extended to a more realistic model, where the equation uses not the number of stars that are forming now, but those that were forming several billion years ago. The alternate formulation, in terms of the number of stars in the galaxy, is easier to explain and understand, but implicitly assumes the star formation rate is constant over the life of the galaxy.

Alternative expression


The number of stars in the galaxy now, N*, is related to the star formation rate R* by

where Tg = the age of the galaxy. Assuming for simplicity that R* is constant, then and the Drake equation can be rewritten into an alternate form phrased in terms of the more easily observable value, N*.

Elaborations


As many observers have pointed out, the Drake equation is a very simple model that does not include potentially relevant parameters. David Brin
David Brin
Glen David Brin, Ph.D. is an American scientist and award-winning author of science fiction. He has received the Hugo, Locus, Campbell and Nebula Awards.-Biography:...

 states:

[The Drake Equation] merely speaks of the number of sites at which ETIs spontaneously arise. It says nothing directly about the contact cross-section between an ETIS and contemporary human society.

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. These include the number of times a civilization might re-appear on the same planet, the number of nearby stars that might be colonized and form sites of their own, and other factors.

Colonization


Brin has proposed generalizing the Drake Equation to include additional effects of alien civilizations colonizing other star systems. Each original site expands with an expansion velocity v, and establishes additional sites that survive for a lifetime L'. The result is a more complex set of 3 equations.

Reappearance number


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 nr 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 (1+nr), 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
Nuclear winter is a predicted climatic effect of nuclear war. It has been theorized that severely cold weather and reduced sunlight for a period of months or even years could be caused by detonating large numbers of nuclear weapons, especially over flammable targets such as cities, where large...

, then nr may be relatively high. On the other hand, if it is generally by permanent uninhabitability, such as stellar evolution
Stellar evolution
Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only a few million years to trillions of years .Stellar evolution is not studied by observing the life of a single...

, then nr may be almost zero.

In the case of total life extinction, a similar factor may be applicable for f, that is, how many times life may appear on a planet where it has appeared once.

METI factor


Alexander Zaitsev
Aleksandr Leonidovich Zaitsev
Aleksandr Leonidovich Zaitsev is a Russian and Soviet radio engineer and astronomer from Fryazino. He works on radar astronomy devices, near-Earth asteroid radar research, and SETI....

 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 practice such activities as the purposeful and regular transmission of interstellar messages. For this reason, he suggested introducing the METI factor (Messaging to Extra-Terrestrial Intelligence) to the classical Drake Equation. The factor is defined 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.

Historical estimates of the parameters


Considerable disagreement on the values of most of these parameters exists, but the values used by Drake and his colleagues in 1961 were:
  • R* = 10/year (10 stars formed per year, on the average over the life of the galaxy)
  • fp = 0.5 (half of all stars formed will have planets)
  • ne = 2 (stars with planets will have 2 planets capable of developing life)
  • fl = 1 (100% of these planets will develop life)
  • fi = 0.01 (1% of which will be intelligent life)
  • fc = 0.01 (1% of which will be able to communicate)
  • L = 10,000 years (which will last 10,000 years)


Drake's values give N = 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 10,000 = 10.

The value of R* is determined from considerable astronomical data, and is the least disputed term of the equation; fp is less certain, but is still much firmer than the values following. The value of ne is based on our own solar system, and assumes that two planets had the possibility of having life. This not only has problems with anthropic bias, but also is inconsistent with a fl of one unless life on Mars is ever discovered. Also, the discovery of numerous gas giant
Gas giant
A gas giant is a large planet that is not primarily composed of rock or other solid matter. There are four gas giants in the Solar System: Jupiter, Saturn, Uranus, and Neptune...

s in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the creation of their stellar systems. In addition, most stars in our galaxy are red dwarf
Red dwarf
According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool star, of the main sequence, either late K or M spectral type....

s, which flare violently, mostly in X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...

s—a property not conducive to life as we know it (simulations also suggest that these bursts erode planetary atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

s). The possibility of life on moons
Natural satellite
A natural satellite or moon is a celestial body that orbits a planet or smaller body, which is called its primary. The two terms are used synonymously for non-artificial satellites of planets, of dwarf planets, and of minor planets....

 of gas giants (such as Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

's moon Europa
Europa (moon)
Europa Slightly smaller than Earth's Moon, Europa is primarily made of silicate rock and probably has an iron core. It has a tenuous atmosphere composed primarily of oxygen. Its surface is composed of ice and is one of the smoothest in the Solar System. This surface is striated by cracks and...

, or Saturn
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...

's moon Titan
Titan (moon)
Titan , or Saturn VI, is the largest moon of Saturn, the only natural satellite known to have a dense atmosphere, and the only object other than Earth for which clear evidence of stable bodies of surface liquid has been found....

) adds further uncertainty to this figure.

Geological evidence from the Earth suggests that fl may be very high; life on Earth appears to have begun around the same time as favorable conditions arose, suggesting that abiogenesis
Abiogenesis
Abiogenesis or biopoesis is the study of how biological life arises from inorganic matter through natural processes, and the method by which life on Earth arose...

 may be relatively common once conditions are right. However, this evidence only looks at the Earth (a single model planet), and contains anthropic bias, as the planet of study was not chosen randomly, but by the living organisms that already inhabit it (ourselves). Also 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. In addition, from a classical hypothesis testing standpoint, there are zero degrees of freedom
Degrees of freedom (statistics)
In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.Estimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the...

, permitting no valid estimates to be made. If life were to be found on Mars that developed independently from life on Earth it would imply a value for fl close to one. While this would improve the 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.

Similar arguments of bias can be made regarding fi and fc by considering the Earth as a model: intelligence with the capacity of extraterrestrial communication occurs only in one species in the 4 billion year history of life on Earth. If generalized, this means only relatively old planets may have intelligent life capable of extraterrestrial communication. Again this model has a large anthropic bias and there are still zero degrees of freedom. Note that the capacity and willingness to participate in extraterrestrial communication has come relatively "quickly", with the Earth having only an estimated 100,000 year history of intelligent human life, and less than a century of technological ability.

fi, fc and L, like fl, are also guesses. Estimates of fi 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 hundreds of millions of years (evading radiation from nova
Nova
A nova is a cataclysmic nuclear explosion in a star caused by the accretion of hydrogen on to the surface of a white dwarf star, which ignites and starts nuclear fusion in a runaway manner...

e). Also, Earth's large moon may aid the evolution of life by stabilizing the planet's axis of rotation. In addition, while it appears that life developed soon after the formation of Earth, the Cambrian explosion
Cambrian explosion
The Cambrian explosion or Cambrian radiation was the relatively rapid appearance, around , of most major phyla, as demonstrated in the fossil record, accompanied by major diversification of other organisms, including animals, phytoplankton, and calcimicrobes...

, 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
Snowball Earth
The Snowball Earth hypothesis posits that the Earth's surface became entirely or nearly entirely frozen at least once, some time earlier than 650 Ma . Proponents of the hypothesis argue that it best explains sedimentary deposits generally regarded as of glacial origin at tropical...

 or research into the extinction events have raised the possibility that life on Earth is relatively fragile. Again, the controversy over life on Mars is relevant since a discovery that life did form on Mars but ceased to exist would affect estimates of these terms.

The astronomer Carl Sagan
Carl Sagan
Carl Edward Sagan was an American astronomer, astrophysicist, cosmologist, author, science popularizer and science communicator in astronomy and natural sciences. He published more than 600 scientific papers and articles and was author, co-author or editor of more than 20 books...

 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
Nuclear warfare, or atomic warfare, is a military conflict or political strategy in which nuclear weaponry is detonated on an opponent. Compared to conventional warfare, nuclear warfare can be vastly more destructive in range and extent of damage...

.

By plugging in apparently plausible values for each of the parameters above, the resultant value of N can be made greater than 1. This has provided considerable motivation for the SETI
SETI
The search for extraterrestrial intelligence is the collective name for a number of activities people undertake to search for intelligent extraterrestrial life. Some of the most well known projects are run by the SETI Institute. SETI projects use scientific methods to search for intelligent life...

 movement. However, we have no evidence for extraterrestrial civilizations. This conflict is often called the Fermi paradox
Fermi paradox
The Fermi paradox is the apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for, or contact with, such civilizations....

, after Enrico Fermi
Enrico Fermi
Enrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...

 who first asked about our lack of observation of extraterrestrials, and motivates advocates of SETI to continually expand the volume of space in which another civilization could be observed.

Some computations of the Drake equation, given different assumptions:

Current estimates (see below):
R* = 7/year, fp = 0.5, ne = 2, fl = 0.33, fi = 0.01, fc = 0.01, and L = 10,000 years
N = 7 × 0.5 × 2 × 0.33 × 0.01 × 0.01 × 10,000 = 2.31 (so two communicative civilizations exist in our galaxy at any given time, on average, plus two hundred more that are not trying to communicate).


But a pessimist might equally well believe that suitable planets are rare, life seldom becomes intelligent, and intelligent civilizations do not last very long:
R* = 10/year, fp = 0.5, ne = 0.01, fl = 0.13, fi = 0.001, fc = 0.01, and L = 1000 years
N = 10 × 0.5 × 0.01 × 0.13 × 0.001 × 0.01 × 1000 = 0.000065 (we are almost surely alone in our galaxy, but many other galaxies host life).


Alternatively, making some more optimistic assumptions, assuming that planets are common, life always arises when planets are favorable, 10% of civilizations become willing and able to communicate, and then spread through their local star systems for 100,000 years (a very short period in geologic time):
R* = 20/year, fp = 0.5, ne = 2, fl = 1, fi = 0.1, fc = 0.1, and L = 100,000 years
N = 20 × 0.5 × 2 × 1 × 0.1 × 0.1 × 100,000 = 20,000 (there are quite a few civilizations, and the closest one would be about 350 light years away based on N/R^2=1/r^2 where R is the radius on the galaxy and 1/r^2 is the average area that contains one galaxy).

Current estimates of the parameters


This section attempts to list best current estimates for the parameters of the Drake equation.
R* = the rate of star creation in our galaxy
Latest calculations from NASA
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...

 and the European Space Agency
European Space Agency
The European Space Agency , established in 1975, is an intergovernmental organisation dedicated to the exploration of space, currently with 18 member states...

 indicate that the current rate of star formation in our galaxy is about 7 per year.


fp = the fraction of those stars that have planets
It is known from modern planet searches that at least 40% of sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

-like stars have planets, and the true proportion may be much higher, since only planets considerably larger than Earth can be detected with current technology. Infra-red surveys of dust discs around young stars imply that 20-60% of sun-like stars may form terrestrial planets. Microlensing surveys, sensitive to planets further from their star, see planets in about 1/3 of systems examined–a lower limit since not all planets are seen. The Kepler mission, from its initial data, estimates that about 34% of stars host at least one planet.


ne = the average number of planets (satellites may perhaps sometimes be just as good candidates) that can potentially support life per star that has planets
Marcy et al. note that most of the observed planets have very eccentric orbits, or orbit very close to the sun where the temperature is too high for earth-like life. However, several planetary systems that look more solar-system-like are known, such as HD 70642
HD 70642
HD 70642 is a yellow dwarf star in the constellation of Puppis located 93.8 light years away. This star has about the same mass and radius as the Sun, is slightly cooler and less luminous, and is richer in abundance of iron relative to hydrogen....

, HD 154345
HD 154345
HD 154345 is a G-type dwarf star located in northern Hercules. It is not visible to the naked eye since this star is below +6.50 magnitude, but using binoculars it is an easy target.-Planetary system:...

, Gliese 849
Gliese 849
|- style="background-color: #A0B0FF;" colspan="3"| Planet|- bgcolor="#FFFAFA"| Gliese 849b || Gliese 849 is a red dwarf star approximately 29 light years away in the constellation of Aquarius.-Planetary system:...

 or Gliese 581
Gliese 581
Gliese 581 is a red dwarf star with spectral type M3V, located 20.3 light years away from Earth in the constellation Libra. Its estimated mass is about a third of that of the Sun, and it is the 89th closest known star system to the Sun. Observations suggest that the star has at least six planets:...

. There may well be other, as yet unseen, earth-sized planets in the habitable zones of these stars. Also, the variety of solar systems that might have habitable zones is not just limited to solar-type stars and earth-sized planets; it is now believed that even tidally locked planets close to red dwarfs might have habitable zones
Habitability of red dwarf systems
Determining the habitability of red dwarf systems could help reveal the likelihood of extraterrestrial life, as red dwarfs make up most stars in the Milky Way Galaxy...

, and some of the large planets detected so far could potentially support life.

In early 2008, two different research groups concluded that Gliese 581 d
Gliese 581 d
Gliese 581 d or Gl 581 d is an extrasolar planet orbiting the star Gliese 581 approximately 20 light-years away in the constellation of Libra. It is the third planet discovered in the system and the fifth in order from the star....

 may possibly be habitable. Since about 200 planetary systems are known, this very roughly estimates . In 2010, researchers announced the discovery of Gliese 581 g
Gliese 581 g
Gliese 581 g , also Gl 581 g or GJ 581 g, is a hypothesized extrasolar planet proven nonexistent by the Geneva Team, orbiting the red dwarf star Gliese 581, 20.5 light-years from Earth in the constellation of Libra. It is the sixth planet discovered in the Gliese 581 planetary system and the fourth...

, a 3.1 Earth-mass planet near the middle of the habitable zone of Gliese 581
Gliese 581
Gliese 581 is a red dwarf star with spectral type M3V, located 20.3 light years away from Earth in the constellation Libra. Its estimated mass is about a third of that of the Sun, and it is the 89th closest known star system to the Sun. Observations suggest that the star has at least six planets:...

, and a strong candidate for being the first known Earth-like habitable planet. Given the closeness of Gliese 581, and the number of stars examined to the level of detail needed to find such planets, they estimated εEarth, or the fraction of stars with Earth-like planets, as 10-20%. However, other research has put the existence of Gliese 581 g, the basis for this estimate, into question.

Using different criteria, Lineweaver has also determined that about 10% of star systems in the Galaxy are hospitable to life, by having heavy elements, being far from supernovae and being stable for a sufficient time.

NASA's Kepler mission
Kepler Mission
The Kepler spacecraft is an American space observatory, the space-based portion of NASA's Kepler Mission to discover Earth-like planets orbiting other stars. The spacecraft is named in honor of the 17th-century German astronomer Johannes Kepler...

 was launched on March 6, 2009. Unlike previous searches, it is sensitive to planets as small as Earth, and with orbital periods as long as a year. If successful, Kepler should provide a much better estimate of the number of planets per star that are found in the habitable zone.

Even if planets are in the habitable zone, however, the number of planets with the right proportion of elements may be difficult to estimate. Also, the Rare Earth hypothesis
Rare Earth hypothesis
In planetary astronomy and astrobiology, the Rare Earth hypothesis argues that the emergence of complex multicellular life on Earth required an improbable combination of astrophysical and geological events and circumstances...

, which posits that conditions for intelligent life are quite rare, has advanced a set of arguments based on the Drake equation that the number of planets or satellites that could support life is small, and quite possibly limited to Earth alone; in this case, the estimate of ne would be infinitesimal.


fl = the fraction of the above that actually go on to develop life
In 2002, Charles H. Lineweaver and Tamara M. Davis (at the University of New South Wales
University of New South Wales
The University of New South Wales , is a research-focused university based in Kensington, a suburb in Sydney, New South Wales, Australia...

 and the Australian Centre for Astrobiology) estimated fl as > 0.13 on planets that have existed for at least one billion years using a statistical argument based on the length of time life took to evolve on Earth.


fi = the fraction of the above that actually go on to develop intelligent life
This value remains particularly controversial. Those who favor a low value, such as the biologist Ernst Mayr
Ernst Mayr
Ernst Walter Mayr was one of the 20th century's leading evolutionary biologists. He was also a renowned taxonomist, tropical explorer, ornithologist, historian of science, and naturalist...

, 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 fi. Those who favor higher values note the generally increasing complexity of life and conclude that the eventual appearance of intelligence might be inevitable, implying an fi approaching 1. Skeptics point out that the large spread of values in this term and others make all estimates unreliable. (See criticism).


fc = the fraction of the above that are willing and able to communicate
There is considerable speculation why a civilization might exist but choose not to communicate, but there is no hard data.


L = the expected lifetime of such a civilization for the period that it can communicate across interstellar space
In an article in Scientific American
Scientific American
Scientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...

, Michael Shermer
Michael Shermer
Michael Brant Shermer is an American science writer, historian of science, founder of The Skeptics Society, and Editor in Chief of its magazine Skeptic, which is largely devoted to investigating pseudoscientific and supernatural claims. The Skeptics Society currently has over 55,000 members...

 estimated L as 420 years, based on compiling the durations of sixty historical civilizations. Using twenty-eight 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
Michael Shermer
Michael Brant Shermer is an American science writer, historian of science, founder of The Skeptics Society, and Editor in Chief of its magazine Skeptic, which is largely devoted to investigating pseudoscientific and supernatural claims. The Skeptics Society currently has over 55,000 members...

's results that the fall of most of these civilizations was followed by later civilizations that carried on the technologies, so it's 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 doesn't matter for the end result, since such a civilization turnover could be described as an increase in the reappearance number rather than increase in L, 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 Grinspoon
David H. Grinspoon is an American astrobiologist. He is the current curator of Astrobiology at the Denver Museum of Nature and Science. He has published numerous works, such as Lonely Planets: The Natural Philosophy of Alien Life, which won the 2004 PEN literary award for nonfiction.Currently, he...

 has argued that once a civilization has developed it might overcome all threats to its survival. It will then last for an indefinite period of time, making the value for L potentially billions of years. If this is the case, then the galaxy has been steadily accumulating advanced civilizations since it formed. He proposes that the last term L be replaced with fIC*T, where fIC is the fraction of communicating civilizations become "immortal" (in the sense that they simply don't die out), and T representing the length of time during which this process has been going on. This has the advantage that T 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 pointed out 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.

Values based on the above estimates,
R* = 7/year, fp = 0.5, ne = 2, fl = 0.33, fi = 0.01, fc = 0.01, and L = 10000 years

result in
N = 7 × 0.5 × 2 × 0.33 × 0.01 × 0.01 × 10000 = 2.31


James Kasting, in his book "How To Find A Habitable Planet", gives the equation as , where the first term on the right hand side of the equation is the number of stars in the galaxy. He estimates the first three terms at 4 × 109. He then uses Carl Sagan's figures for the next three terms, disclaiming responsibility, and arrives at approximately 10 to the seventh power as an estimate, not considering the final term, , which is the fraction of a planet's lifetime during which it supports a technical civilization. He notes that this is the most uncertain factor in the equation.

Criticism


Criticism of the Drake equation follows mostly from the observation that several terms in the equation are largely or entirely based on conjecture. Thus the equation cannot be used to draw firm conclusions of any kind. As Michael Crichton
Michael Crichton
John Michael Crichton , best known as Michael Crichton, was an American best-selling author, producer, director, and screenwriter, best known for his work in the science fiction, medical fiction, and thriller genres. His books have sold over 200 million copies worldwide, and many have been adapted...

, a science fiction author, stated in a 2003 lecture at Caltech:
The problem, of course, is that none of the terms can
be known, and most cannot even be estimated. The only way to work the
equation is to fill in with guesses. [...] As a result, the Drake equation can have any value from "billions and
billions" to zero. An expression that can mean anything means nothing.
Speaking precisely, the Drake equation is literally meaningless...


Another objection is that the very form of the Drake equation assumes that civilizations arise and then die out within their original solar systems. If interstellar colonization is possible, then this assumption is invalid, and the equations of population dynamics
Population dynamics
Population dynamics is the branch of life sciences that studies short-term and long-term changes in the size and age composition of populations, and the biological and environmental processes influencing those changes...

 would apply instead.

One reply to such criticisms is that even though the Drake equation currently involves speculation about unmeasured parameters, it was not meant to be science, but 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.

In fiction


The Drake equation and the Fermi paradox
Fermi paradox
The Fermi paradox is the apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for, or contact with, such civilizations....

 have been discussed many times in science fiction
Science fiction
Science fiction is a genre of fiction dealing with imaginary but more or less plausible content such as future settings, futuristic science and technology, space travel, aliens, and paranormal abilities...

, including both serious takes in stories such as Frederik Pohl
Frederik Pohl
Frederik George Pohl, Jr. is an American science fiction writer, editor and fan, with a career spanning over seventy years — from his first published work, "Elegy to a Dead Planet: Luna" , to his most recent novel, All the Lives He Led .He won the National Book Award in 1980 for his novel Jem...

's Hugo award
Hugo Award for Best Short Story
The Hugo Awards are given every year by the World Science Fiction Society for the best science fiction or fantasy works and achievements of the previous year. The award is named after Hugo Gernsback, the founder of the pioneering science fiction magazine Amazing Stories, and was once officially...

-winning "Fermi and Frost", which cites the paradox as evidence for the short lifetime of technical civilizations—that is, the possibility that once a civilization develops the power to destroy itself (perhaps by nuclear winter
Nuclear winter
Nuclear winter is a predicted climatic effect of nuclear war. It has been theorized that severely cold weather and reduced sunlight for a period of months or even years could be caused by detonating large numbers of nuclear weapons, especially over flammable targets such as cities, where large...

), it does. Optimistic results of the equation along with unobserved extraterrestials also serves as backdrop for humorous suggestions such as Terry Bisson
Terry Bisson
Terry Ballantine Bisson is an American science fiction and fantasy author best known for his short stories...

's classic short story "They're Made Out of Meat
They're Made Out of Meat
"They're Made Out of Meat" is a Nebula Award-nominated short story by Terry Bisson. It was originally published in OMNI. It consists entirely of dialogue between two characters, and Bisson's website hosts a theatrical adaptation...

," that there are many extraterrestrial civilizations but that they are deliberately ignoring humanity.
  • In The Melancholy of Haruhi Suzumiya, the Drake equation is briefly flashed during the opening theme song, a reference to Haruhi's intention to find aliens among other things.
  • The equation was cited by Gene Roddenberry
    Gene Roddenberry
    Eugene Wesley "Gene" Roddenberry was an American television screenwriter, producer and futurist, best known for creating the American science fiction series Star Trek. Born in El Paso, Texas, Roddenberry grew up in Los Angeles, California where his father worked as a police officer...

     as supporting the multiplicity of inhabited planets shown in Star Trek
    Star Trek
    Star Trek is an American science fiction entertainment franchise created by Gene Roddenberry. The core of Star Trek is its six television series: The Original Series, The Animated Series, The Next Generation, Deep Space Nine, Voyager, and Enterprise...

    ,
    the television show he created. However, Roddenberry didn't have the equation with him, and he was forced to "invent" it for his original proposal. The invented equation created by Roddenberry is:

Drake has gently pointed out, however, that a number raised to the first power is merely the number itself. A poster with both versions of the equation was seen in the Star Trek: Voyager
Star Trek: Voyager
Star Trek: Voyager is a science fiction television series set in the Star Trek universe. Set in the 24th century from the year 2371 through 2378, the series follows the adventures of the Starfleet vessel USS Voyager, which becomes stranded in the Delta Quadrant 70,000 light-years from Earth while...

episode "Future's End."
  • The formula is also cited in Michael Crichton
    Michael Crichton
    John Michael Crichton , best known as Michael Crichton, was an American best-selling author, producer, director, and screenwriter, best known for his work in the science fiction, medical fiction, and thriller genres. His books have sold over 200 million copies worldwide, and many have been adapted...

    's Sphere
    Sphere (novel)
    Sphere is a science fiction novel written by Michael Crichton and published in 1987. It was made into the film Sphere in 1998.The novel follows Norman Johnson as a psychologist who is engaged by the United States Navy to join a team of scientists assembled by the U.S. Government to examine an...

    .
  • In the Evolution-based game Spore
    Spore (2008 video game)
    Spore is a multi-genre single-player god game developed by Maxis and designed by Will Wright. The game was released for the Microsoft Windows and Macintosh operating systems in September 2008 as Spore...

    , after eventually coming into contact with living beings on other planets, a picture is shown, along with the comment, "Drake's Equation was right...a living alien race!"
  • George Alec Effinger
    George Alec Effinger
    George Alec Effinger was an American science fiction author, born in 1947 in Cleveland, Ohio.-Writing career:...

    's short story "One" uses an expedition confident in the Drake Equation as a backdrop to explore the psychological implications of a lonely humanity.
  • Alastair Reynolds
    Alastair Reynolds
    Alastair Preston Reynolds is a British science fiction author. He specialises in dark hard science fiction and space opera. He spent his early years in Cornwall, moved back to Wales before going to Newcastle, where he read physics and astronomy. Afterwards, he earned a PhD from St Andrews, Scotland...

    ' Revelation Space
    Revelation Space
    Revelation Space is a 2000 science fiction space opera novel by Welsh author Alastair Reynolds. It was the first novel set in the Revelation Space universe, although the then-unnamed universe had already been established by several published short stories....

    trilogy and short stories focus very much on the Drake Equation and the Fermi Paradox, using genocidal self-replicating machines as a great filter.
  • Stephen Baxter's
    Stephen Baxter
    Stephen Baxter is a prolific British hard science fiction author. He has degrees in mathematics and engineering.- Writing style :...

     Manifold Trilogy
    Manifold Trilogy
    The Manifold Trilogy is a series of science fiction books by Stephen Baxter. It consists of three novels and an anthology of short stories relating to the three. The three books in the trilogy are not ordered chronologically; instead, they are thematically linked stories that take place in...

     explores the Drake Equation and the Fermi Paradox in three distinct perspectives.
  • Ian R. MacLeod
    Ian R. MacLeod
    Ian R. MacLeod is a British science fiction and fantasy writer.He was born in Solihull near Birmingham. He studied law and worked as a civil servant before going freelance in early 1990s soon after he started publishing stories, attracting critical praise and awards nominations.-Writings:He is the...

    's 2001 novella "New Light On The Drake Equation" concerns a man who is obsessed by the Drake Equation.
  • The Ultimate Marvel
    Ultimate Marvel
    Ultimate Marvel is an imprint of comic books published by Marvel Comics, featuring reimagined and updated versions of the company's superhero characters, including Spider-Man, the X-Men, the Avengers, and the Fantastic Four. The imprint was launched in 2000 with the publication of the series...

     comic book
    Comic book
    A comic book or comicbook is a magazine made up of comics, narrative artwork in the form of separate panels that represent individual scenes, often accompanied by dialog as well as including...

     mini-series Ultimate Secret has Reed Richards
    Ultimate Fantastic Four
    Ultimate Fantastic Four is a superhero comic book series published by Marvel Comics. The series is a modernized re-imagining of Marvel's long-running Fantastic Four comic book franchise as part of its Ultimate Marvel imprint...

     examining the Drake Equation and considering the Fermi Paradox. He claims that when Drake plugged in his numbers, he came up with 10,000 alien races that would have a civilization advanced enough to contact Earth, but only one that Richards knew of had done it (actually 10 others already had, and two more were about to, but Richards did not know that at the time). In discussion with Sue Storm
    Ultimate Fantastic Four
    Ultimate Fantastic Four is a superhero comic book series published by Marvel Comics. The series is a modernized re-imagining of Marvel's long-running Fantastic Four comic book franchise as part of its Ultimate Marvel imprint...

    , it is revealed that he believes that advanced civilizations destroy themselves. In the story it turns out that they are also destroyed by Gah Lak Tus.
  • Eleanor Ann Arroway paraphrases the Drake equation several times in the film Contact
    Contact (film)
    Contact is a 1997 American science fiction drama film adapted from the Carl Sagan novel of the same name and directed by Robert Zemeckis. Both Sagan and wife Ann Druyan wrote the story outline for the film adaptation of Contact....

    , using the magnitude of N* and its implications on the output value to justify the SETI program. However, in one scene of the 1997 motion picture based upon the Carl Sagan
    Carl Sagan
    Carl Edward Sagan was an American astronomer, astrophysicist, cosmologist, author, science popularizer and science communicator in astronomy and natural sciences. He published more than 600 scientific papers and articles and was author, co-author or editor of more than 20 books...

     novel, she misstates her Drake Equation result by several billion.
  • In the 20th episode of the second season of the television series The Big Bang Theory
    The Big Bang Theory
    The Big Bang Theory is an American sitcom created by Chuck Lorre and Bill Prady, both of whom serve as executive producers on the show, along with Steven Molaro. All three also serve as head writers...

    , the equation was mentioned by Howard Wolowitz
    Howard Wolowitz
    Howard Joel Wolowitz, M.Eng is a fictional character on the CBS television series The Big Bang Theory, portrayed by actor Simon Helberg.Among the main male characters in the show, Howard is distinguished for lacking a doctoral degree, for still living with his mother, and for believing himself to...

     and detailed by Sheldon Cooper
    Sheldon Cooper
    Sheldon Lee Cooper, B.S., M.S., M.A., Ph.D., Sc.D. is a fictional character from Texas on the CBS television series The Big Bang Theory, portrayed by actor Jim Parsons...

    . Howard goes on to modify the terms in the equation to project the likelihood of a member of the group hooking up with a member of the opposite sex.

See also

  • Fermi paradox
    Fermi paradox
    The Fermi paradox is the apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for, or contact with, such civilizations....

  • Big Bounce
    Big Bounce
    The Big Bounce is a theoretical scientific model of the formation of the known universe. It is implied by the cyclic model or oscillatory universe interpretation of the Big Bang where the first cosmological event was the result of the collapse of a previous universe.- Expansion and contraction...

  • Black swan theory
    Black swan theory
    The black swan theory or theory of black swan events is a metaphor that encapsulates the concept that The event is a surprise and has a major impact...

  • Doomsday argument
    Doomsday argument
    The Doomsday argument is a probabilistic argument that claims to predict the number of future members of the human species given only an estimate of the total number of humans born so far...

  • Final anthropic principle
  • Goldilocks Principle
    Goldilocks Principle
    The Goldilocks principle states that something must fall within certain margins, as opposed to reaching extremes. It is used, for example, in the Rare Earth hypothesis to state that a planet must neither be too far away from, nor too close to the sun to support life. Either extreme would result in...

  • Great Filter
  • Inverse gambler's fallacy
    Inverse gambler's fallacy
    The inverse gambler's fallacy, named by philosopher Ian Hacking, is a formal fallacy of Bayesian inference which is similar to the better known gambler's fallacy. It is the fallacy of concluding, on the basis of an unlikely outcome of a random process, that the process is likely to have occurred...

  • Kardashev scale
    Kardashev scale
    The Kardashev scale is a method of measuring an advanced civilization's level of technological advancement. The scale is only theoretical and in terms of an actual civilization highly speculative; however, it puts energy consumption of an entire civilization in a cosmic perspective. It was first...

  • Metaphysical naturalism
    Metaphysical naturalism
    Metaphysical naturalism, also called ontological naturalism and philosophical naturalism, or just naturalism, is a philosophical worldview and belief system that holds that there is nothing but natural elements, principles, and relations of the kind studied by the natural sciences, i.e., those...

  • Neocatastrophism
    Neocatastrophism
    Neocatastrophism is the theory that life-exterminating events such as gamma-ray bursts have acted as a galactic regulation mechanism in the Milky Way upon the emergence of complex life in its habitable zone...

  • Nick Bostrom
    Nick Bostrom
    Nick Bostrom is a Swedish philosopher at the University of Oxford known for his work on existential risk and the anthropic principle. He holds a PhD from the London School of Economics...

  • Principle of mediocrity
  • Rare Earth hypothesis
    Rare Earth hypothesis
    In planetary astronomy and astrobiology, the Rare Earth hypothesis argues that the emergence of complex multicellular life on Earth required an improbable combination of astrophysical and geological events and circumstances...

  • Selection bias
    Selection bias
    Selection bias is a statistical bias in which there is an error in choosing the individuals or groups to take part in a scientific study. It is sometimes referred to as the selection effect. The term "selection bias" most often refers to the distortion of a statistical analysis, resulting from the...

  • Zoo hypothesis
    Zoo hypothesis
    The zoo hypothesis is one of a number of suggestions that have been advanced in response to the Fermi paradox, regarding the apparent absence of evidence in support of the existence of advanced extraterrestrial life...


External links