Equation of Drake

The equation of Drake is a famous mathematical proposal concerning sciences such as the Exobiologie, the Futurobiologie, the Astrosociologie, as well as the project SETI (search for extraterrestrial intelligence).

This equation was suggested by Frank Drake in 1961 in order to try to consider the number potential of Civilization S Extraterrestre S in our Galaxie with which we could come into contact. The main object of this equation for the scientific is to determine its factors, in order to know the probable number of these civilizations.

This equation is often put out of balance with the Paradoxe of Fermi which with methods different Formula One a conclusion diametrically opposed to that from Drake.

The equation of Drake

$N = R^ {*} ~ \ times ~ f_ {p} ~ \ times ~ n_ {E} ~ \ times ~ f_ {L} ~ \ times ~ f_ {I} ~ \ times ~ f_ {C} ~ \ times ~ L$

where:

NR is the number of extraterrestrial civilizations in our galaxy with which we could come into contact,

and:

R* is the number of star S in formation per annum in our galaxy,
f_p is the fraction of these having stars of the Planet S,
n_e is the median number of planets per star potentially favourable with the Vie,
f_l is the fraction of these planets on which the life appears indeed,
f_i is the fraction of these planets on which appears an intelligent life,
f_c is the fraction of these planets able and eager to communicate,
L is the average lifespan of a civilization.

Historical estimate of the parameters of the equation of Drake

The scientists nowadays have considerable dissensions on the possible values of these parameters. The values used by Drake and his/her colleagues in 1961 are:

R* = 10/an
f_p = 0,5
n_e = 2
f_l = 1
f_i = f_c = 0,01
10 years

The value of R* is discussed. f_p is more dubious, but is more constant than the other values. It was believed that n_e was more important, but the discovery many giant gas with Orbite S close to their star sows the doubt about the planets which can support the life so close to their star. Others rétorquent however that the sample of exoplanètes discovered until now is absolutely not representative (it is normal that one starts by detecting the largest objects) and that the telluric exoplanètes remain to be discovered.

Moreover, the majority of stars of our galaxy are dwarf reds, which has a weak radiation Ultraviolet, which contributed to the evolution of the life on Ground. In the place, it has a violent one radiation, mainly in X-ray, a property nonfavorable to the life such as we know it (simulations also suggest that this radiation erodes the atmosphere S of planets). The possibility of life on satellite S of gas giant planet (for example the satellite of Jupiter Europe) reinforces in a dubious way this case of figure.

By looking at humanity on Earth, it is obvious that f_l seems high, the life on Earth almost immediately seems to have started after the conditions made it possible, suggesting that the Abiogenèse is relatively “easy” once the conditions are favorable. In addition, one discovers on Earth living organisms more and more known as Extrémophile S managing to survive under conditions extrèmes (sea-bed, will calderas, environment sulfur…) This factor does not remain about it less very debatable.

A data which would have an major impact on this last would be the presence discussed of life (primitive) on Mars. The checking of the development of the life over Mars, independently of that on Earth, would plead in favor of a raised value for this factor.

f_i, f_c and L obviously smaller than are supposed. f_i was modified since the discovery owing to the fact that the orbit of the Solar system in the galaxy is circular, with a distance such which remains apart from the arm of the galaxy during hundreds of million years (avoiding radiations of the Nova S). Also, the rare satellites as the the Moon seem to contribute to the conservation of the Hydrogène by breaking the Earth's crust, causing a Magnétosphère, by movement and heatwaves, and stabilizing the Axis of rotation of planet. Moreover, since it seems that the life develops just after the formation of the Earth, the Explosion cambrienne in which a broad variety of multicellular forms of life was transformed into beings, appears a considerable time after the formation of the Earth, which suggests the possibility that special conditions are necessary so that arrives. Scenarios like the Earth Snowball or seeks it in the events of extinction suggested the possibility that the life on Earth is relatively fragile. Once again, the controversy on the fact that the life took form over Mars, but ceased existing, would affect the estimates of these factors.

The famous astronomer Carl Sagan speculated that the values of all the factors, except that of the lifespan of a civilization, must be relatively high, and the determining factor is to know if a civilization has or not the technological capacity to avoid a Auto-destruction. In the case of Sagan, the equation of Drake was a strong motivation for its interest in the environmental problems and its effort to inform us dangers of the nuclear weapons.

(It will be noted, that as from the year 2001, we can allot value 50 to L with the same degree of confidence as Drake the USA in 1961 by giving him value 10).

The remarkable thing in connection with the equation of Drake is that, by putting plausible values for each parameter, one generally obtains a value of NR >> 1. This result was a source of great motivations for project SETI. However, this is in conflict with the actual value of NR << 1, that is to say only one humanity in all the universe, ours.

This conflict is as formulated in the Paradoxe of Fermi, this one having been the first to suggest as our comprehension of what is a “conservative” value for some parameters can be excessively optimistic, or which some other factors can intervene with regard to the destruction of an intelligent life.

Other assumptions give values of NR lower than 1, but some observers believe that it is still compatible with the observations due to the Principe anthropic: it does not matter how much is low, the probability that a given galaxy has an intelligent life, the galaxy in which we are must have at least an intelligent species by definition. There could be hundreds of galaxies in our Amas without any intelligent life, but obviously we are not in these galaxies to observe this fact.

Some examples of calculations of the equation of Drake

With the parameters of Drake:

R* = 10/an, f_p = 0,5, n_e = 2, f_l = 1, f_i = f_c = 0,01, and L = 50 years

NR = 10 * 0,5 * 2 * 1 * 0,01 * 0,01 * 50 = 0,05

We can give more optimistic results, by considering that 10% of civilizations become able to communicate, and that they extend their longevity up to 100.000 years, by considering the life of their Planetary system (what is very court on a geological scale ):

R* = 20/an, f_p = 0,1, n_e = 0,5, f_l = 1, f_i = 0,5, f_c = 0,1, and L = 100.000 years

20 * 0,1 * 0,5 * 1 * 0,5 * 0,1 * 100.000 5000

Estimate current of the parameters of the equation

This section tries to list the best estimates at the time current (2004) for the parameters of the equation of Drake, they are likely to change better results so are found.

R*, is the number of stars in formation per annum in our galaxy

estimated by Drake at 10/an

f_p is the fraction of these stars having of the planets

estimated by Drake at 0,5

n_e is the median number of planets per star potentially favourable with the life

estimated by Drake at 2

f_l is the fraction of these planets on which the life appears indeed

estimated by Drake at 1 In 2002, Charles H. Lineweaver and Tamara Mr. Davis (at the university of News-Wales of the South and with the Australian Center of Astrobiologie) considered f_l > 0,33 using a statistical argument based over time that the life put to develop on Earth. Lineweaver as determined as roughly 10% of the planetary systems in our galaxy are favourable with the life, having heavy elements, being far from the Supernova S and being stable between them for one sufficient period. ()

f_i is the fraction of these planets on which an intelligent life

appears estimated by Drake at 0,01

However, the planetary sytèmes in the galactic Orbit with an exposure to radiations as low as the solar system are more than 100.000 times rarer.

f_c is the fraction of these planets able and eager to communicate

estimated by Drake at 0,01

L is the average lifespan of a civilization

estimated by Drake at 10 years A lower limit of L can be estimated starting from our civilization with the advent of the Radioastronomie in 1938 (dated from the parabolic Radiotélescope of Grote Reber) until the current year. In 2006, that gives a value of L equalizes to 68. In an article of the Scientific American, Michael Shermer estimated L at 420 years, by compiling the durations of six historical civilizations. Using 28 civilizations more recent than the Roman Empire, it calculated L at approximately 304 years for “modern” civilizations. Let us note, however, that holds account only civilizations which did not destroy to them Technologie, and which transmitted it to civilizations which followed them, Shermer thus estimated that one was to look at this value in a pessimistic way.

In practice, it should be noticed that the equation consists in trying to determine an unknown quantity starting from other quantities which are quite as unknown as it. There thus does not exist guarantee that one is more fixed after this estimate that before (argument named sometimes in the literature garbage in, garbage out ).

It is to be also noticed that in the absence of concrete experiment, the human brain is very badly equipped to estimate probabilities at less than one point of precision (i.e. 1%), and that we speak in the language running about " probability of 1 on 1000" or " 1 on 100.000" to express in fact that we consider something not very probable . However it is because we consider badly the probabilities very weak that plays as the Loto perdurent, few people having carried out the calculation which gives them more probability of dying before pulling than to gain a batch of a very important amount.

The world bayésien works more readily in decibels. A probability of 10^-7 is worth then -70 dB and a probability of 10^-9 is worth -90 dB, which differentiates them clearly.

See too

Paradox of Fermi
Astrobiologie
Astrosociobiologie
SETI
Extrémophile

References

Charles H. Lineweaver and Tamara Mr. Davis , Does the Rapid Appearance off Life one Earth Suggest that Life is Common in the Universe? , arXiv: astro-ph/0205014 v1 May 2nd, 2002
Michael Shermer , Why AND Hasn' T Called, Scientific American, August 2002, page 21

External bonds

Formule of Drake (or the parameterization of ignorance)
the search for an extraterrestrial form of life
Calcul of the number of communicating civilization in our Galaxy
Evaluate the number of civilizations in the Milky Way

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