Drake equation

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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 xenobiology, astrosociobiology and the search for extraterrestrial intelligence.

This equation was devised by Dr Frank Drake (now Emeritus Professor of Astronomy and Astrophysics at the University of California, Santa Cruz) in the 1960s 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 extraterrestrial civilizations. In recent years, the Rare Earth hypothesis, which posits that conditions for intelligent life are quite rare in the universe, has been seen as a possible refutation of the equation.

The Drake equation is closely related to the Fermi paradox.

1 The equation
2 Historical estimates of the parameters
3 Current estimates of the parameters
4 Criticisms
5 In fiction
6 See also
7 References
8 External links

[edit] The equation

The Drake equation states that:

$N = R^{*} ~ \times ~ f_{p} ~ \times ~ n_{e} ~ \times ~ f_{l} ~ \times ~ f_{i} ~ \times ~ f_{c} ~ \times ~ L$

where:

N is the number of civilizations in our galaxy with which we might expect to be able to communicate at any given time

and

R* is the rate of star formation in our galaxy

f_p is the fraction of those stars that have planets

n_e is 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

f_i is the fraction of the above that actually go on to develop intelligent life

f_c is the fraction of the above that are willing and able to communicate

L is the expected lifetime of such a civilization for the period that it can communicate across interstellar space.

[edit] 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 star formed per year)
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 the least disputed; 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 favourable 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.

Similar arguments 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 generalised, 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 a 100,000 year history of intelligent life without it.

One piece of data which would have major impact on f_l is the discovery of life on Mars or other 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, it would still impose a great deal of uncertainty on any estimate.

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 considerable amounts of time after the formation of Earth, which suggests the possibility that special conditions were necessary for this to occur. 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.

The remarkable thing about the Drake equation is that by plugging in apparently "plausible" values for each of the parameters above, the resultant expectant value of N is generally often (much) greater than 1. This has provided considerable motivation for the SETI movement. However, this conflicts with the currently observed value of N = 1; i.e., one observed civilization in the entire galaxy. Other assumptions give values of N that are (much) less than 1, in accord with the observable evidence. Ultimately, a dispassionate observer would acknowledge that all factors in the equation and the equation itself are purely speculative.

This conflict is often called the Fermi paradox, after Enrico Fermi who first publicised the subject, 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 galaxy that we are in must have at least one intelligent species by definition. There could be hundreds of galaxies in our galactic cluster with no intelligent life whatsoever, but of course we would not be present in those galaxies to observe this fact.

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

[edit] 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. The Planck Institute for Extraterrestrial Physics in Germany notes, however, that our galaxy is not the biggest producer of stars and supernovae in the universe. [1]

f_p = the fraction of those stars which have planets

Estimated by Drake as 0.5.

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.

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. [2]

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 results that at the fall of most of these civilizations they were succeeded by later civilizations which carried on those technologies, so its doubtful to the Drake equations that they are separate civilizations. Furthermore since none could communicate over interstellar space, the value of L here could be argued to being 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.

R* = 6/year, f_p = 0.5, n_e = 2, f_l = 0.33, f_i = 1×10^-7, f_c = 0.01, and L = 69 years

N = 6 × 0.5 × 2 × 0.33 × 1×10^-7 × 0.01 × 69 = 1.3 ×10^-7 = 0.0000001

It is worth noting that the order of magnitude in the revised equation is determined primarily by the new estimate for f_i. Going back to the number estimated by Drake (1×10^-2) the result also changes to 0.08.

[edit] Criticisms

Since there exists only one example of a planet with advanced life forms, the Drake equation has been considered unreliable by some estimates; however, based on Earth's experience intelligent life is possible and the replication of this event elsewhere is at least plausible. ^[1]^[2]^[3] In a 2003 lecture at Caltech, Michael Crichton, a science fiction author who once met for an hour with President Bush to discuss climate change and other topics, 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." Therefore he claims that SETI has no scientific basis and the Drake equation upon which it is based cannot be scientifically tested.[3].

Since we have no data on other civilizations within our galaxy, any equation making numerical predictions about such civilizations is speculation. Crichton's criticism of Drake's equation is thus correct in that, if it is regarded as a hypothesis, it is untestable given our current state of knowledge. Virtually all such hypotheses are also untestable. Some people would argue that even though the Drake equation is currently pure speculation, it serves a useful purpose by stimulating dialog between people about these topics, leading to focus and how to proceed experimentally.

One can question why the number of civilizations should be proportional to the star formation rate -- there doesn't appear to be a convincing argument that this is the correct factor in such an equation (it may have been felt necessary to make the equation dimensionally correct, given that the last factor has the dimension of time). One could also use galactic measures of energy, mass, etc., and/or factor in information about the galactic location of parameters felt to be important. It's all speculative at this point.

[edit] In fiction

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:

$Ff^2 (MgE)-C^1 Ri^1 ~ \times ~ M=L/So$

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 Star Trek: Voyager episode "Future's End".

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

[edit] See also

[edit] References

^ Walterbos, Rene. Extraterrestrial Intelligence and Interstellar Travel. NMSU Department of Astronomy. Retrieved December 16, 2006.
^ 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.
^ Johnson, Stevens F. The Drake Equation. Department of Physics/Science, Bemidji State University. June 25, 2003. Does Extraterrestrial life exist?. The Electronic Journal of the Astronomical Society of the Atlantic. Volume 1, Number 4. November 1989.

Drake, Frank; Dava Sobel (1992). Is Anyone Out There? The Scientific Search for Extraterrestrial Intelligence. New York: Delacorte Pr.. ISBN 0-385-30532-X.
Rood, Robert T.; James S. Trefil (1981). Are We Alone? The Possibility of Extraterrestrial Civilizations. New York: Scribner. ISBN 0-684-16826-X.
Lineweaver, Charles H.; Tamara M. Davis (2 May 2002). "Does the Rapid Appearance of Life on Earth Suggest that Life is Common in the Universe?". arXiv:astro-ph/0205014.
Shermer, Michael (August 2002). "Why ET Hasn't Called". Scientific American: 21.
Bates, Gary (2004). Alien Intrusion. Master books. ISBN 0-89051-435-6.