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:''This article is about Frank Drake's equation. For the Tub Ring music album, see Drake Equation (album).''
The 'Drake equation' (rarely also called the Green Bank equation or the Sagan equation) is a famous result in the speculative fields of exobiology, astrosociobiology and the search for extraterrestrial intelligence.
This equation was devised by Dr Frank Drake (now Professor Emeritus of Astronomy and Astrophysics at the University of California, Santa Cruz) in 1960, in an attempt to estimate the number of extraterrestrial civilizations in our galaxy with which we might come in contact. The main purpose of the equation is to allow scientists to quantify the uncertainty of the factors which determine the number of such extraterrestrial civilizations.
The Drake equation is closely related to the Fermi paradox.

Contents

The equation

Historical estimates of the parameters

Current estimates of the parameters

Criticisms

In fiction

See also

References

External links

The equation

The Drake equation states that:
:$N\; =\; R^$
★ imes f_p imes n_e imes f_l imes f_i imes f_c imes L
where:
:''N'' is the number of civilizations in our galaxy with which we might hope to be able to communicate;
and
:''R''
★ is the average rate of star formation in our galaxy
:''f''_p is the fraction of those stars that have planets
:''n''_e is the average number of planets that can potentially support life per star that has planets
:''f''_l is the fraction of the above that actually go on to develop life at some point
:''f''_i is the fraction of the above that actually go on to develop intelligent life
:''f''_c is the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
:''L'' is the length of time such civilizations release detectable signals into space.
The number of stars in the galaxy now, ''N''
★ , is related to the star formation rate ''R''
★ by $N^$
★ = int_0^{T_g} R^
★ (t) dt , where ''T''_g is the age of the galaxy. Assuming for simplicity that ''R''
★ is constant, then the Drake equation can be rewritten into an alternate form phrased in terms of the more easily observable value, ''N''
★ ^[1]:
:$N\; =\; N^$
★ imes f_p imes n_e imes f_l imes f_i imes f_c imes L / T_g

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)

★ ''f''_p = 0.5 (half of all stars formed will have planets)

★ ''n''_e = 2 (2 planets per star will be able to develop life)

★ ''f''_l = 1 (100% of the planets will develop life)

★ ''f''_i = 0.01 (1% of which will be intelligent life)

★ ''f''_c = 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; ''f''_p is less certain, but is still much firmer than the values following. Confidence in ''n''_e was once higher, but the discovery of numerous gas giants 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 dwarfs, which have little of the ultraviolet radiation that has contributed to the evolution of life on Earth. Instead they flare violently, mostly in X-rays — a property not conducive to life as we know it (simulations also suggest that these bursts erode planetary atmospheres). The possibility of life on moons of gas giants (e.g. Jupiter's satellite Europa) adds further uncertainty to this figure.
Geological evidence from the Earth suggests that ''f''_l may be very high; life on Earth appears to have begun around the same time as favorable conditions arose, suggesting that abiogenesis 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). Whether this is actually a case of anthropic bias has been contested, however; it might rather merely be a limitation involving a critically small sample size, since it is argued that there is no bias involved in our asking these questions about life on Earth. 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, permitting no valid estimates to be made.
One piece of data which would have major impact on ''f''_l is the discovery of life on Mars or another planet or moon. If life were to be found on Mars which developed independently from life on Earth it would imply a higher value for ''f''_l. While this would greatly 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 ''f''_i and ''f''_c 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. In addition, from a classical hypothesis testing standpoint, there are zero degrees of freedom, permitting no valid estimates to be made. 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.
''f''_i, ''f''_c and ''L'', like ''f''_l, are guesses. ''f''_i has 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 novae). Also, Earth's large, unusual moon appears to aid retention of hydrogen by breaking up the crust, inducing a magnetosphere by tidal heating and stirring, and stabilizing the planet's axis of rotation. In addition, while it appears that life developed soon after the formation of Earth, the Cambrian explosion, 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 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 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.
By plugging in apparently "plausible" values for each of the parameters above, the resultant expectant value of ''N'' is often (much) greater than 1. This has provided considerable motivation for the SETI movement. However, we do not currently see evidence of this value of ''N''. This conflict is often called the 'Fermi paradox', after Enrico Fermi who first asked about our lack of observation of extraterrestrials, and suggests that our understanding of what is a "conservative" value for some of the parameters may be overly optimistic or that some other factor is involved to suppress the development of intelligent space-faring life.
Other assumptions give values of ''N'' that are (much) less than 1, but some observers believe this is still compatible with observations due to the anthropic principle: no matter how low the probability that any given galaxy will have intelligent life in it, the universe ''must'' have at least one intelligent species by definition otherwise the question would not arise.
Some computations of the Drake equation, given different assumptions:
:''R''
★ = 10/year, ''f''_p = 0.5, ''n''_e = 2, ''f''_l = 1, ''f''_i = ''f''_c = 0.01, and ''L'' = 50,000 years
:''N'' = 10 × 0.5 × 2 × 1 × 0.01 × 0.01 × 50,000 = 50
Alternatively, making some more optimistic assumptions, and assuming that 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, ''f''_p = 0.1, ''n''_e = 0.5, ''f''_l = 1, ''f''_i = 0.5, ''f''_c = 0.1, and ''L'' = 100,000 years
:''N'' = 20 × 0.1 × 0.5 × 1 × 0.5 × 0.1 × 100,000 = 5,000

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
:Estimated by Drake as 10/year. Latest calculations from NASA and the European Space Agency indicates that the current rate of star formation in our galaxy is about 6 per year.^[2]
''f''_p = the fraction of those stars which have planets
:Estimated by Drake as 0.5. It is now known from modern planet searches that at least 10% of sunlike stars have planets, and the true proportion may be much higher, since only planets gas-giant size and larger can be detected with current technology.^[3]
''n''_e = the average number of planets (satellites may perhaps sometimes be just as good candidates) which can potentially support life per star that has planets
:Estimated by Drake as 2. The same paper by Marcy, et al.³ notes 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 154345, or Gliese 849. These may well have smaller, as yet unseen, earth sized planets in their habitable zones.
:On the other hand, in recent years, the Rare Earth hypothesis, 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 ''n''_e would be infinitesimal.
''f''_l = the fraction of the above which actually go on to develop life
:Estimated by Drake as 1.
:In 2002, Charles H. Lineweaver and Tamara M. Davis (at the University of New South Wales and the Australian Centre for Astrobiology) estimated ''f''_l 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. 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 themselves for sufficient time.^[4]
''f''_i = the fraction of the above which actually go on to develop intelligent life
:Estimated by Drake as 0.01.
:Some estimate that solar systems in galactic orbits with radiation exposure as low as Earth's solar system may be more than 100,000 times rarer, however, giving a value of ''f''_i = 1×10^-7.
''f''_c = the fraction of the above which are willing and able to communicate
:Estimated by Drake as 0.01.
''L'' = the expected lifetime of such a civilization for the period that it can communicate across interstellar space.
:Estimated by Drake as 10,000 years.
:In an article in ''Scientific American'', Michael Shermer 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's results that the fall of most of these civilizations was followed by later civilizations which carried on the technologies, so its doubtful that they are separate civilizations in the context of the Drake equation. Furthermore since none could communicate over interstellar space, the value of L here could also be argued to be zero.
:The value of ''L'' can be estimated from the lifetime of our current civilization from the advent of radio astronomy in 1938 (dated from Grote Reber's parabolic dish radio telescope) to the current date. In 2007, this gives an ''L'' of 69 years. However such an assumption would be erroneous. 69 for the value of ''L'' would be an artificial minimum based on Earth's broadcasting history to date and would make unlikely the possibility of other civilizations existing. 10,000 for ''L'' is still the most popular estimate
Values based on the above estimates,
:''R''
★ = 6/year, ''f''_p = 0.5, ''n''_e = 2, ''f''_l = 0.33, ''f''_i = 0.01, ''f''_c = 0.01, and ''L'' = 10000 years
result in
:''N'' = 6 × 0.5 × 2 × 0.33 × 0.01 × 0.01 × 10000 = 2
It is worth noting that the uncertainty in the revised equation is determined primarily by the last 3 factors, ''f''_i, ''f''_c, and ''L''. If any of these are far smaller than assumed above, as some have argued, then the average number of civilizations may be much less than one.

Criticisms

Since there exists only one known example of a planet with advanced life forms, some critics view the Drake equation as unreliable. However, based on Earth's experience, some scientists view intelligent life on other planets as possible and the replication of this event elsewhere is at least plausible.^[5][6][7] In a 2003 lecture at Caltech, Michael Crichton, a science fiction author, stated that, "Speaking precisely, the Drake equation is literally meaningless, and has nothing to do with science. I take the hard view that science involves the creation of testable hypotheses. The Drake equation cannot be tested and therefore SETI is not science. SETI is unquestionably a religion."^[8]. Crichton's criticism might be flawed if extraterrestrial civilizations existed since the negative hypothesis (''i.e.,'' "extraterrestrial civilizations do not exist") could be tested: it would be falsified by the discovery of one of them.
It is also noteworthy that actual experiments by SETI scientists do not attempt to address the Drake equations for the existence of extraterrestrial civilizations anywhere in the universe, but are focused on specific, testable hypotheses (''i.e.,'' "do extraterrestrial civilizations communicating in the radio spectrum exist near sunlike stars within 50 light years of the Earth?"). These questions are testable (either yes or no).
Some people argue that even though the Drake equation currently involves speculation about parameters that are, as of the moment, unmeasured, it serves a useful purpose by stimulating dialogue between people about these topics, leading to focus and how to proceed experimentally -- and this was Drake's intent in the first place.
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.

In fiction

The Drake equation, and the Fermi Paradox, have been discussed many times in (written) Science Fiction, including both serious takes in stories such as Frederick Pohl's Hugo award-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), it does, and humorous commentary in stories such as Terry Bisson's classic short story "They're Made Out of Meat" [1].

★ The equation was cited by Gene Roddenberry as supporting the multiplicity of starfaring civilizations shown in ''Star Trek,'' 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:
:$Ff^2\; (MgE)-C^1\; Ri^1\; ~\; imes\; ~\; M=L/So$
:Dr. 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 episode "Future's End".

★ It is also cited in Michael Crichton's "Sphere".

★ George Alec Effinger's short story "One" uses an expedition confident in the Drake Equation as a backdrop to explore the psychological implications of a lonely humanity.

See also

★ Astrosociobiology

★ Fermi Paradox

★ Kardashev scale

★ Sentience Quotient

★ SETI

★ Zoo hypothesis

References

1. Michael Seeds, ''Horizons: Exploring the Universe'', Brooks/Cole Publishing Co., 10th edition, ISBN13: 9780495113584
2. news.yahoo.com
3. Observed Properties of Exoplanets: Masses, Orbits and Metallicities, Marcy, G.; Butler, R.; Fischer, D.; et.al., , , Progress of Theoretical Physics Supplement, 2005
4. newscientist.com
5. Walterbos, Rene. Extraterrestrial Intelligence and Interstellar Travel. NMSU Department of Astronomy. Retrieved December 16, 2006.
6. Bricker, David. Life or Something Like It. ''Space''. Volume XXVII Number 1. Indiana University Research & Creative Activity Magazine.
Intelligence In The Milky Way. Principia. Retrieved December 17, 2006.
7. Johnson, Stevens F. The Drake Equation. Department of Physics/Science, Bemidji State University. June 25, 2003. [ftp://ftp.seds.org/pub/info/newsletters/ejasa/1989/jasa8911.txt Does Extraterrestrial life exist?]. The Electronic Journal of the Astronomical Society of the Atlantic. Volume 1, Number 4. November 1989.
8. crichton-official.com


★ Is Anyone Out There? The Scientific Search for Extraterrestrial Intelligence, , Frank, Drake, Delacorte Pr., 1992, ISBN 0-385-30532-X

★ Are We Alone? The Possibility of Extraterrestrial Civilizations, , Robert T., Rood, Scribner, 1981, ISBN 0-684-16826-X

★

★ Why ET Hasn't Called, , Michael, Shermer, Scientific American, 2002

★ Alien Intrusion, , Gary, Bates, Master books, 2004, ISBN 0-89051-435-6

External links

★ The E.T. Equation, Recalculated Frank Drake

★ http://www.skypub.com/news/special/9812seti_aliens.html

★ Beyond the Drake Equation

★ January 2002 space.com article about estimated prevalence of extrasolar planets

★ Preprint by Lineweaver and Davis estimating f_l as > 0.13

★ July 2003 discovery of a planetary system similar to our solar system

★ Macromedia Flash page allowing the user to modify Drake's values from PBS Nova

★ "The Drake Equation"—Transcript (html) of Astronomy Cast episode #23, Fraser Cain and Southern Illinois University Edwardsville professor, Dr. Pamela Gay. 12 February 2007. (Full pdf transcript.)