Drake equation: Difference between revisions

Latest revision as of 16:12, 26 October 2024

The Drake equation is a probabilistic argument used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way Galaxy.^[1]^[2]

The equation was formulated in 1961 by Frank Drake, not for purposes of quantifying the number of civilizations, but as a way to stimulate scientific dialogue at the first scientific meeting on the search for extraterrestrial intelligence (SETI).^[3]^[4] The equation summarizes the main concepts which scientists must contemplate when considering the question of other radio-communicative life.^[3] It is more properly thought of as an approximation than as a serious attempt to determine a precise number.

Criticism related to the Drake equation focuses not on the equation itself, but on the fact that the estimated values for several of its factors are highly conjectural, the combined multiplicative effect being that the uncertainty associated with any derived value is so large that the equation cannot be used to draw firm conclusions.

Equation

The Drake equation is:

where

N = the number of civilizations in our galaxy with which communication might be possible (i.e. which are on our current past light cone);

and

R_∗ = the average rate of star formation in our Galaxy

f_p = the fraction of those stars that have planets

n_e = the average number of planets that can potentially support life per star that has planets

f_l = the fraction of planets that could support life that actually develop life at some point

f_i = the fraction of planets with life that actually go on to develop intelligent life (civilizations)

f_c = 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^[6]^[7]

History

In September 1959, physicists Giuseppe Cocconi and Philip Morrison published an article in the journal Nature with the provocative title "Searching for Interstellar Communications".^[8]^[9] Cocconi and Morrison argued that radio telescopes had become sensitive enough to pick up transmissions that might be broadcast into space by civilizations orbiting other stars. Such messages, they suggested, might be transmitted at a wavelength of 21 cm (1,420.4 MHz). This is the wavelength of radio emission by neutral hydrogen, the most common element in the universe, and they reasoned that other intelligences might see this as a logical landmark in the radio spectrum.

Two months later, Harvard University astronomy professor Harlow Shapley speculated on the number of inhabited planets in the universe, saying "The universe has 10 million, million, million suns (10 followed by 18 zeros) similar to our own. One in a million has planets around it. Only one in a million million has the right combination of chemicals, temperature, water, days and nights to support planetary life as we know it. This calculation arrives at the estimated figure of 100 million worlds where life has been forged by evolution."^[10]

Seven months after Cocconi and Morrison published their article, Drake made the first systematic search for signals from communicative extraterrestrial civilizations. Using the Template:Convert dish of the National Radio Astronomy Observatory, Green Bank in Green Bank, West Virginia, Drake monitored two nearby Sun-like stars: Epsilon Eridani and Tau Ceti. In this project, which he called Project Ozma, he slowly scanned frequencies close to the 21 cm wavelength for six hours per day from April to July 1960.^[9] The project was well designed, inexpensive, and simple by today's standards. It detected no signals.

Soon thereafter, Drake hosted a "search for extraterrestrial intelligence" meeting on detecting their radio signals. The meeting was held at the Green Bank facility in 1961. The equation that bears Drake's name arose out of his preparations for the meeting.^[11]

As I planned the meeting, I realized a few day[s] ahead of time we needed an agenda. And so I wrote down all the things you needed to know to predict how hard it's going to be to detect extraterrestrial life. And looking at them it became pretty evident that if you multiplied all these together, you got a number, N, which is the number of detectable civilizations in our galaxy. This was aimed at the radio search, and not to search for primordial or primitive life forms.
—Frank Drake

The ten attendees were conference organizer J. Peter Pearman, Frank Drake, Philip Morrison, businessman and radio amateur Dana Atchley, chemist Melvin Calvin, astronomer Su-Shu Huang, neuroscientist John C. Lilly, inventor Barney Oliver, astronomer Carl Sagan and radio-astronomer Otto Struve.^[12] These participants dubbed themselves "The Order of the Dolphin" (because of Lilly's work on dolphin communication), and commemorated their first meeting with a plaque at the observatory hall.^[13]^[14]

Usefulness

The Drake equation amounts to a summary of the factors affecting the likelihood that we might detect radio-communication from intelligent extraterrestrial life.^[1]^[6]^[15] The last three parameters, Template:Math, Template:Math, and Template:Mvar, are not known and are very difficult to estimate, with values ranging over many orders of magnitude (see criticism). Therefore, the usefulness of the Drake equation is not in the solving, but rather in the contemplation of all the various concepts which scientists must incorporate when considering the question of life elsewhere,^[1]^[3] and gives the question of life elsewhere a basis for scientific analysis. The equation has helped draw attention to some particular scientific problems related to life in the universe, for example abiogenesis, the development of multi-cellular life, and the development of intelligence itself.^[16]

Within the limits of our existing technology, any practical search for distant intelligent life must necessarily be a search for some manifestation of a distant technology. After about 50 years, the Drake equation is still of seminal importance because it is a 'road map' of what we need to learn in order to solve this fundamental existential question.^[1] It also formed the backbone of astrobiology as a science; although speculation is entertained to give context, astrobiology concerns itself primarily with hypotheses that fit firmly into existing scientific theories. Some 50 years of SETI have failed to find anything, even though radio telescopes, receiver techniques, and computational abilities have improved significantly since the early 1960s. It has, however, been discovered that our galaxy is not teeming with very powerful alien transmitters continuously broadcasting near the 21 cm wavelength of the hydrogen frequency; this was not known in 1961.^[17]

Estimates

Original estimates

There is considerable disagreement on the values of these parameters, but the 'educated guesses' used by Drake and his colleagues in 1961 were:^[18]^[19]

R_∗ = 1 yr⁻¹ (1 star formed per year, on the average over the life of the galaxy; this was regarded as conservative)
f_p = 0.2 to 0.5 (one fifth to one half of all stars formed will have planets)
n_e = 1 to 5 (stars with planets will have between 1 and 5 planets capable of developing life)
f_l = 1 (100% of these planets will develop life)
f_i = 1 (100% of which will develop intelligent life)
f_c = 0.1 to 0.2 (10–20% of which will be able to communicate)
L = 1000 to 100,000,000 communicative civilizations (which will last somewhere between 1000 and 100,000,000 years)

Inserting the above minimum numbers into the equation gives a minimum N of 20 (see: Range of results). Inserting the maximum numbers gives a maximum of 50,000,000. Drake states that given the uncertainties, the original meeting concluded that N ≈ L, and there were probably between 1000 and 100,000,000 planets with civilizations in the Milky Way Galaxy.

Current estimates

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

Rate of star creation in our Galaxy, R_∗

Calculations in 2010, from NASA and the European Space Agency indicate that the rate of star formation in our Galaxy is about Template:Solar mass of material per year.^[20]^[21] To get the number of stars per year, we divide this by the initial mass function (IMF) for stars, where the average new star's mass is about Template:Solar mass.^[22] This gives a star formation rate of about 1.5–3 stars per year.

Template:Anchor

Fraction of those stars that have planets, f_p

Analysis of microlensing surveys, in 2012, has found that Template:Math may approach 1—that is, stars are orbited by planets as a rule, rather than the exception; and that there are one or more bound planets per Milky Way star.^[23]^[24]

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

In November 2013, astronomers reported, based on Kepler space mission data, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of sun-like stars and red dwarf stars within the Milky Way Galaxy.^[25]^[26] 11 billion of these estimated planets may be orbiting sun-like stars.^[27] Since there are about 100 billion stars in the galaxy, this implies Template:Math is roughly 0.4. The nearest planet in the habitable zone is Proxima Centauri b, which is as close as about 4.2 light-years away.

The consensus at the Green Bank meeting was that Template:Math had a minimum value between 3 and 5. Dutch science journalist Govert Schilling has opined that this is optimistic.^[28] Even if planets are in the habitable zone, the number of planets with the right proportion of elements is difficult to estimate.^[29] Brad Gibson, Yeshe Fenner, and Charley Lineweaver determined that about 10% of star systems in the Milky Way Galaxy are hospitable to life, by having heavy elements, being far from supernovae and being stable for a sufficient time.^[30]

The discovery of numerous gas giants in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the formation of their stellar systems. So-called hot Jupiters may migrate from distant orbits to near orbits, in the process disrupting the orbits of habitable planets.

On the other hand, the variety of star systems that might have habitable zones is not just limited to solar-type stars and Earth-sized planets. It is now estimated that even tidally locked planets close to red dwarf stars might have habitable zones,^[31] although the flaring behavior of these stars might speak against this.^[32] The possibility of life on moons of gas giants (such as Jupiter's moon Europa, or Saturn's moons Titan and Enceladus) adds further uncertainty to this figure.^[33]

The authors of the rare Earth hypothesis propose a number of additional constraints on habitability for planets, including being in galactic zones with suitably low radiation, high star metallicity, and low enough density to avoid excessive asteroid bombardment. They also propose that it is necessary to have a planetary system with large gas giants which provide bombardment protection without a hot Jupiter; and a planet with plate tectonics, a large moon that creates tidal pools, and moderate axial tilt to generate seasonal variation.^[34]

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

Geological evidence from the Earth suggests that f_l may be 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). From a classical hypothesis testing standpoint, without assuming that the underlying distribution of Template:Math is the same for all planets in the Milky Way, there are zero degrees of freedom, permitting no valid estimates to be made. If life (or evidence of past life) were to be found on Mars, Europa, Enceladus or Titan that developed independently from life on Earth it would imply a value for Template:Math close to 1. While this would raise the number of degrees of freedom from zero to one, there would remain a great deal of uncertainty on any estimate due to the small sample size, and the chance they are not really independent.

Countering this argument is that there is no evidence for abiogenesis occurring more than once on the Earth—that is, all terrestrial life stems from a common origin. If abiogenesis were more common it would be speculated to have occurred more than once on the Earth. Scientists have searched for this by looking for bacteria that are unrelated to other life on Earth, but none have been found yet.^[35] It is also possible that life arose more than once, but that other branches were out-competed, or died in mass extinctions, or were lost in other ways. Biochemists Francis Crick and Leslie Orgel laid special emphasis on this uncertainty: "At the moment we have no means at all of knowing" whether we are "likely to be alone in the galaxy (Universe)" or whether "the galaxy may be pullulating with life of many different forms."^[36] As an alternative to abiogenesis on Earth, they proposed the hypothesis of directed panspermia, which states that Earth life began with "microorganisms sent here deliberately by a technological society on another planet, by means of a special long-range unmanned spaceship".

In 2020, a paper by scholars at the University of Nottingham proposed an "Astrobiological Copernican" principle, based on the Principle of Mediocrity, and speculated that "intelligent life would form on other [Earth-like] planets like it has on Earth, so within a few billion years life would automatically form as a natural part of evolution". In the authors' framework, Template:Math, Template:Math, and Template:Math are all set to a probability of 1 (certainty). Their resultant calculation concludes there are more than thirty current technological civilizations in the galaxy (disregarding error bars).^[37]^[38]

Fraction of the above that develops intelligent life, f_i

This value remains particularly controversial. Those who favor a low value, such as the biologist Ernst Mayr, 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 Template:Math.^[39] Likewise, the Rare Earth hypothesis, notwithstanding their low value for Template:Math above, also think a low value for Template:Math dominates the analysis.^[40] Those who favor higher values note the generally increasing complexity of life over time, concluding that the appearance of intelligence is almost inevitable,^[41]^[42] implying an Template:Math approaching 1. Skeptics point out that the large spread of values in this factor and others make all estimates unreliable. (See Criticism).

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 extinction events have raised the possibility that life on Earth is relatively fragile. Research on any past life on Mars is relevant since a discovery that life did form on Mars but ceased to exist might raise our estimate of Template:Math but would indicate that in half the known cases, intelligent life did not develop.

Estimates of f_i have been affected by discoveries that the Solar System's orbit is circular in the galaxy, at such a distance that it remains out of the spiral arms for tens of millions of years (evading radiation from novae). Also, Earth's large moon may aid the evolution of life by stabilizing the planet's axis of rotation.

There has been quantitative work to begin to define <math>f_\mathrm{l} \cdot f_\mathrm{i}</math> . One example is a Bayesian analysis published in 2020. In the conclusion, the author cautions that this study applies to Earth's conditions. In Bayesian terms, the study favors the formation of intelligence on a planet with identical conditions to Earth but does not do so with high confidence.^[43]^[44]

Planetary scientist Pascal Lee of the SETI Institute proposes that this fraction is very low (0.0002). He based this estimate on how long it took Earth to develop intelligent life (1 million years since Homo erectus evolved, compared to 4.6 billion years since Earth formed).^[45]^[46]

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

For deliberate communication, the one example we have (the Earth) does not do much explicit communication, though there are some efforts covering only a tiny fraction of the stars that might look for our presence. (See Arecibo message, for example). There is considerable speculation why an extraterrestrial civilization might exist but choose not to communicate. However, deliberate communication is not required, and calculations indicate that current or near-future Earth-level technology might well be detectable to civilizations not too much more advanced than our own.^[47] By this standard, the Earth is a communicating civilization.

Another question is what percentage of civilizations in the galaxy are close enough for us to detect, assuming that they send out signals. For example, existing Earth radio telescopes could only detect Earth radio transmissions from roughly a light year away.^[48]

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

Michael Shermer estimated L as 420 years, based on the duration of sixty historical Earthly civilizations.^[49] Using 28 civilizations more recent than the Roman Empire, he calculates a figure of 304 years for "modern" civilizations. It could also be argued from Michael Shermer's results that the fall of most of these civilizations was followed by later civilizations that carried on the technologies, so it is doubtful that they are separate civilizations in the context of the Drake equation. In the expanded version, including reappearance number, this lack of specificity in defining single civilizations does not matter for the end result, since such a civilization turnover could be described as an increase in the reappearance number rather than increase in 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 has argued that once a civilization has developed enough, it might overcome all threats to its survival. It will then last for an indefinite period of time, making the value for L potentially billions of years. If this is the case, then he proposes that the Milky Way Galaxy may have been steadily accumulating advanced civilizations since it formed.^[50] He proposes that the last factor L be replaced with f_IC · T, where f_IC is the fraction of communicating civilizations that become "immortal" (in the sense that they simply do not die out), and Template:Math 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 hypothesized that once a civilization has learned of a more advanced one, its longevity could increase because it can learn from the experiences of the other.^[51]

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.

An intelligent civilization might not be organic, as some have suggested that artificial general intelligence may replace humanity.^[52]

Probabilistic combination of results

Combining the estimates of the original six factors by major researchers via a Monte Carlo procedure leads to a best value for the non-longevity factors of 0.85 1/years.^[53] This result differs insignificantly from the estimate of unity given both by Drake and the Cyclops report.

Range of results

As many skeptics have pointed out, the Drake equation can give a very wide range of values, depending on the assumptions,^[54] as the values used in portions of the Drake equation are not well established.^[28]^[55]^[56]^[57] In particular, the result can be N ≪ 1, meaning we are likely alone in the galaxy, or N ≫ 1, implying there are many civilizations we might contact. One of the few points of wide agreement is that the presence of humanity implies a probability of intelligence arising of greater than zero.^[58]

As an example of a low estimate, combining NASA's star formation rates, the rare Earth hypothesis value of f_p · n_e · f_l = 10⁻⁵,^[59] Mayr's view on intelligence arising, Drake's view of communication, and Shermer's estimate of lifetime:

R_∗ = 1.5–3 yr⁻¹,^[20] f_p · n_e · f_l = 10⁻⁵,^[34] f_i = 10⁻⁹,^[39] f_c = 0.2^{[Drake, above]}, and L = 304 years^[49]

gives:

N =1.5 × 10⁻⁵ × 10⁻⁹ × 0.2 × 304 = 9.1 × 10⁻¹³

i.e., suggesting that we are probably alone in this galaxy, and possibly in the observable universe.

On the other hand, with larger values for each of the parameters above, values of N can be derived that are greater than 1. The following higher values that have been proposed for each of the parameters:

R_∗ = 1.5–3 yr⁻¹,^[20] f_p = 1,^[23] n_e = 0.2,^[60]^[61] f_l = 0.13,^[62] f_i = 1,^[41] f_c = 0.2^{[Drake, above]}, and L = 10⁹ years^[50]

Use of these parameters gives:

N = 3 × 1 × 0.2 × 0.13 × 1 × 0.2 × 10⁹ = 15,600,000

Monte Carlo simulations of estimates of the Drake equation factors based on a stellar and planetary model of the Milky Way have resulted in the number of civilizations varying by a factor of 100.^[63]

Have other technological species ever existed?

In 2016, Adam Frank and Woodruff Sullivan modified the Drake equation to determine just how unlikely the event of a technological species arising on a given habitable planet must be, to give the result that Earth hosts the only technological species that has ever arisen, for two cases: (a) our Galaxy, and (b) the universe as a whole. By asking this different question, one removes the lifetime and simultaneous communication uncertainties. Since the numbers of habitable planets per star can today be reasonably estimated, the only remaining unknown in the Drake equation is the probability that a habitable planet ever develops a technological species over its lifetime. For Earth to have the only technological species that has ever occurred in the universe, they calculate the probability of any given habitable planet ever developing a technological species must be less than Template:Val. Similarly, for Earth to have been the only case of hosting a technological species over the history of our Galaxy, the odds of a habitable zone planet ever hosting a technological species must be less than Template:Val (about 1 in 60 billion). The figure for the universe implies that it is extremely unlikely that Earth hosts the only technological species that has ever occurred. On the other hand, for our Galaxy one must think that fewer than 1 in 60 billion habitable planets develop a technological species for there not to have been at least a second case of such a species over the past history of our Galaxy.^[64]^[65]^[66]^[67]

Modifications

As some observers have pointed out, the Drake equation is a very simple model that omits potentially relevant parameters,^[68] Drake himself, however, in the June 24, 2012, interview by Andrew Fraknoi counters by noting that the science behind every suggested modification is already incorporated in the seven factors of the Drake equation. Nonetheless, changes and modifications to the equation have been proposed. One line of modification, for example, attempts to account for the uncertainty inherent in many of the terms.^[69]

Others note that the Drake equation ignores many concepts that might be relevant to the odds of contacting other civilizations. For example, David Brin states: "The Drake equation merely speaks of the number of sites at which ETIs spontaneously arise. The equation says nothing directly about the contact cross-section between an ETIS and contemporary human society".^[70] Because it is the contact cross-section that is of interest to the SETI community, many additional factors and modifications of the Drake equation have been proposed.

Colonization: It has been proposed to generalize the Drake equation to include additional effects of alien civilizations colonizing other star systems. Each original site expands with an expansion velocity Template:Mvar, and establishes additional sites that survive for a lifetime Template:Mvar. The result is a more complex set of 3 equations.^[70]

Reappearance factor: The Drake equation may furthermore be multiplied by how many times an intelligent civilization may occur on planets where it has happened once. Even if an intelligent civilization reaches the end of its lifetime after, for example, 10,000 years, life may still prevail on the planet for billions of years, permitting the next civilization to evolve. Thus, several civilizations may come and go during the lifespan of one and the same planet. Thus, if Template:Math 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 Template:Math, 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, then n_r may be relatively high. On the other hand, if it is generally by permanent uninhabitability, such as stellar evolution, then Template:Math may be almost zero. In the case of total life extinction, a similar factor may be applicable for Template:Math, that is, how many times life may appear on a planet where it has appeared once.

METI factor: Alexander Zaitsev said that to be in a communicative phase and emit dedicated messages are not the same. For example, humans, although being in a communicative phase, are not a communicative civilization; we do not practise such activities as the purposeful and regular transmission of interstellar messages. For this reason, he suggested introducing the METI factor (messaging to extraterrestrial intelligence) to the classical Drake equation.^[71] He defined the factor as "the fraction of communicative civilizations with clear and non-paranoid planetary consciousness", or alternatively expressed, the fraction of communicative civilizations that actually engage in deliberate interstellar transmission.

The METI factor is somewhat misleading since active, purposeful transmission of messages by a civilization is not required for them to receive a broadcast sent by another that is seeking first contact. It is merely required they have capable and compatible receiver systems operational; however, this is a variable humans cannot accurately estimate.

Biogenic gases: Astronomer Sara Seager proposed a revised equation that focuses on the search for planets with biosignature gases.^[72] These gases are produced by living organisms that can accumulate in a planet atmosphere to levels that can be detected with remote space telescopes.^[73]

The Seager equation looks like this:^[73]Template:Refn

<math display=block>N = N_* \cdot F_\mathrm{Q} \cdot F_\mathrm{HZ} \cdot F_\mathrm{O} \cdot F_\mathrm{L} \cdot F_\mathrm{S}</math>

where:

N = the number of planets with detectable signs of life

N_∗ = the number of stars observed

F_Q= the fraction of stars that are quiet

F_HZ = the fraction of stars with rocky planets in the habitable zone

F_O= the fraction of those planets that can be observed

F_L = the fraction that have life

F_S = the fraction on which life produces a detectable signature gas

Seager stresses, “We’re not throwing out the Drake Equation, which is really a different topic,” explaining, “Since Drake came up with the equation, we have discovered thousands of exoplanets. We as a community have had our views revolutionized as to what could possibly be out there. And now we have a real question on our hands, one that's not related to intelligent life: Can we detect any signs of life in any way in the very near future?”^[74]

Criticism

Criticism of the Drake equation follows mostly from the observation that several terms in the equation are largely or entirely based on conjecture. Star formation rates are well-known, and the incidence of planets has a sound theoretical and observational basis, but the other terms in the equation become very speculative. The uncertainties revolve around our understanding of the evolution of life, intelligence, and civilization, not physics. No statistical estimates are possible for some of the parameters, where only one example is known. The net result is that the equation cannot be used to draw firm conclusions of any kind, and the resulting margin of error is huge, far beyond what some consider acceptable or meaningful.^[75]^[76]

One reply to such criticisms^[77] is that even though the Drake equation currently involves speculation about unmeasured parameters, it was intended as a way to stimulate dialogue on these topics. Then the focus becomes how to proceed experimentally. Indeed, Drake originally formulated the equation merely as an agenda for discussion at the Green Bank conference.^[78]

Fermi paradox

Main article: Fermi paradox

A civilization lasting for tens of millions of years could be able to spread throughout the galaxy, even at the slow speeds foreseeable with our own current technology. However, no confirmed signs of civilizations or intelligent life elsewhere have been found, either in our Galaxy or in the observable universe of 2 trillion galaxies.^[79]^[80] According to this line of thinking, the tendency to fill up (or at least explore) all available territory seems to be a universal trait of living things, so the Earth should have already been colonized, or at least visited, but no evidence of this exists. Hence Fermi's question "Where is everybody?".^[81]^[82]

A large number of explanations have been proposed to explain this lack of contact; a book published in 2015 elaborated on 75 different explanations.^[83] In terms of the Drake Equation, the explanations can be divided into three classes:

Few intelligent civilizations ever arise. This is an argument that at least one of the first few terms, Template:Math, has a low value. The most common suspect is Template:Math, but explanations such as the rare Earth hypothesis argue that Template:Math is the small term.
Intelligent civilizations exist, but we see no evidence, meaning Template:Math is small. Typical arguments include that civilizations are too far apart, it is too expensive to spread throughout the galaxy, civilizations broadcast signals for only a brief period of time, communication is dangerous, and many others.
The lifetime of intelligent, communicative civilizations is short, meaning the value of Template:Mvar is small. Drake suggested that a large number of extraterrestrial civilizations would form, and he further speculated that the lack of evidence of such civilizations may be because technological civilizations tend to disappear rather quickly. Typical explanations include it is the nature of intelligent life to destroy itself, it is the nature of intelligent life to destroy others, they tend to be destroyed by natural events, and others.

These lines of reasoning lead to the Great Filter hypothesis,^[84] which states that since there are no observed extraterrestrial civilizations despite the vast number of stars, at least one step in the process must be acting as a filter to reduce the final value. According to this view, either it is very difficult for intelligent life to arise, or the lifetime of technologically advanced civilizations, or the period of time they reveal their existence must be relatively short.

An analysis by Anders Sandberg, Eric Drexler and Toby Ord suggests "a substantial ex ante probability of there being no other intelligent life in our observable universe".^[85]

In fiction and popular culture

The equation was cited by Gene Roddenberry as supporting the multiplicity of inhabited planets shown on Star Trek, the television series he created. However, Roddenberry did not have the equation with him, and he was forced to "invent" it for his original proposal.^[86] The invented equation created by Roddenberry is:

However, a number raised to the first power is merely the number itself.

The equation was referenced in 'The Hofstadter Isotope', a season 2 episode of The Big Bang Theory, in which it is compared to the characters' probability of successfully picking up women in a bar.

The equation was also referenced in 'The Weeping Somnambulist', a season 2 episode of The Expanse, in which it is referenced by a scientist on board a scout vessel investigating a phenomenon on Venus which turns out to be sourced from an extraterrestrial entity.

Notes

References

References:

↑ ^1.0 ^1.1 ^1.2 ^1.3 Burchell, M.J. (2006). "W(h)ither the Drake equation?". International Journal of Astrobiology 5 (3): 243–250. doi:10.1017/S1473550406003107. Bibcode: 2006IJAsB...5..243B.
↑ Glade, N.; Ballet, P.; Bastien, O. (2012). "A stochastic process approach of the drake equation parameters". International Journal of Astrobiology 11 (2): 103–108. doi:10.1017/S1473550411000413. Bibcode: 2012IJAsB..11..103G.
↑ ^3.0 ^3.1 ^3.2 "Chapter 3 – Philosophy: "Solving the Drake Equation". Ask Dr. SETI. SETI League. December 2002. http://www.setileague.org/askdr/drake.htm.
↑ Drake, N. (30 June 2014). "How my Dad's Equation Sparked the Search for Extraterrestrial Intelligence". National Geographic. http://news.nationalgeographic.com/news/2014/06/140630-drake-equation-50-years-later-aliens-science/.
↑
<math>N = R_* \cdot f_\mathrm{p} \cdot n_\mathrm{e} \cdot f_\mathrm{l} \cdot f_\mathrm{i} \cdot f_\mathrm{c} \cdot L</math>
↑ ^6.0 ^6.1 Aguirre, L. (1 July 2008). "The Drake Equation". Nova ScienceNow. PBS. https://www.pbs.org/wgbh/nova/origins/drake.html.
↑ "What do we need to know about to discover life in space?". SETI Institute. http://www.seti.org/drakeequation.
↑ Cocconi, G.; Morisson, P. (1959). "Searching for Interstellar Communications". Nature 184 (4690): 844–846. doi:10.1038/184844a0. Bibcode: 1959Natur.184..844C. http://www.iaragroup.org/_OLD/seti/pdf_IARA/cocconi.pdf. Retrieved 2013-04-10.
↑ ^9.0 ^9.1 Schilling, G.; MacRobert, A. M. (2013). "The Chance of Finding Aliens". Sky & Telescope. http://www.skyandtelescope.com/resources/seti/3304541.html.
↑ newspaper, staff (8 November 1959). "Life On Other Planets?". Sydney Morning Herald. https://news.google.com/newspapers?nid=1301&dat=19591108&id=s39WAAAAIBAJ&pg=2212,2112869&hl=en.
↑ "The Drake Equation Revisited: Part I". Astrobiology Magazine. 29 September 2003. http://www.astrobio.net/alien-life/the-drake-equation-revisited-part-i/.
↑ Zaun, H. (1 November 2011). "Es war wie eine 180-Grad-Wende von diesem peinlichen Geheimnis!" (in de). Telepolis. http://www.heise.de/tp/artikel/35/35756/1.html.
↑ "Drake Equation Plaque". http://www.setileague.org/photos/miscpix/drakeqn.jpg.
↑ Template:Cite encyclopedia
↑ Jones, D. S. (26 September 2001). "Beyond the Drake Equation". http://frombob.to/drake.html.
↑ "The Search For Life : The Drake Equation 2010 – Part 1". BBC Four. 2010. https://www.youtube.com/watch?list=PL56DCB81E2F59166A&v=U3UyAoYkhTo&feature=player_embedded.
↑ SETI: A celebration of the first 50 years. Keith Cooper. Astronomy Now. 2000
↑ Drake, F.; Sobel, D. (1992). Is Anyone Out There? The Scientific Search for Extraterrestrial Intelligence. Delta. pp. 55–62. ISBN 0-385-31122-2.
↑ Glade, N.; Ballet, P.; Bastien, O. (2012). "A stochastic process approach of the drake equation parameters". International Journal of Astrobiology 11 (2): 103–108. doi:10.1017/S1473550411000413. Bibcode: 2012IJAsB..11..103G. Note: This reference has a table of 1961 values, claimed to be taken from Drake & Sobel, but these differ from the book.
↑ ^20.0 ^20.1 ^20.2 Robitaille, Thomas P.; Barbara A. Whitney (2010). "The present-day star formation rate of the Milky Way determined from Spitzer-detected young stellar objects". The Astrophysical Journal Letters 710 (1): L11. doi:10.1088/2041-8205/710/1/L11. Bibcode: 2010ApJ...710L..11R.
↑ Wanjek, C. (2 July 2015). The Drake Equation. Cambridge University Press. ISBN 9781107073654. https://books.google.com/books?id=jcnSCQAAQBAJ&q=Robitaille+and+Whitney+came+up+with+a+figure+for+R*+between+0.68+and+1.45&pg=PA45. Retrieved 2016-09-09.
↑ Kennicutt, Robert C.; Evans, Neal J. (22 September 2012). "Star Formation in the Milky Way and Nearby Galaxies". Annual Review of Astronomy and Astrophysics 50 (1): 531–608. doi:10.1146/annurev-astro-081811-125610. Bibcode: 2012ARA&A..50..531K.
↑ ^23.0 ^23.1 Palmer, J. (11 January 2012). "Exoplanets are around every star, study suggests". BBC. https://www.bbc.co.uk/news/science-environment-16515944.
↑ Cassan, A. (11 January 2012). "One or more bound planets per Milky Way star from microlensing observations". Nature 481 (7380): 167–169. doi:10.1038/nature10684. PMID 22237108. Bibcode: 2012Natur.481..167C.
↑ Overbye, Dennis (4 November 2013). "Far-Off Planets Like the Earth Dot the Galaxy". The New York Times. https://www.nytimes.com/2013/11/05/science/cosmic-census-finds-billions-of-planets-that-could-be-like-earth.html. Template:Cbignore
↑ Petigura, Eric A.; Howard, Andrew W.; Marcy, Geoffrey W. (31 October 2013). "Prevalence of Earth-size planets orbiting Sun-like stars". Proceedings of the National Academy of Sciences of the United States of America 110 (48): 19273–19278. doi:10.1073/pnas.1319909110. PMID 24191033. Bibcode: 2013PNAS..11019273P.
↑ Khan, Amina (4 November 2013). "Milky Way may host billions of Earth-size planets". Los Angeles Times. http://www.latimes.com/science/la-sci-earth-like-planets-20131105,0,2673237.story.
↑ ^28.0 ^28.1 Govert Schilling (November 2011). "The Chance of Finding Aliens: Reevaluating the Drake Equation". astro-tom.com. http://www.astro-tom.com/technical_data/alien_life.htm.
↑ Trimble, V. (1997). "Origin of the biologically important elements". Origins of Life and Evolution of the Biosphere 27 (1–3): 3–21. doi:10.1023/A:1006561811750. PMID 9150565. Bibcode: 1997OLEB...27....3T.
↑ Lineweaver, C. H.; Fenner, Y.; Gibson, B. K. (2004). "The Galactic Habitable Zone and the Age Distribution of Complex Life in the Milky Way". Science 303 (5654): 59–62. doi:10.1126/science.1092322. PMID 14704421. Bibcode: 2004Sci...303...59L.
↑ Dressing, C. D.; Charbonneau, D. (2013). "The Occurrence Rate of Small Planets around Small Stars". The Astrophysical Journal 767 (1): 95. doi:10.1088/0004-637X/767/1/95. Bibcode: 2013ApJ...767...95D.
↑ "Red Dwarf Stars Could Leave Habitable Earth-Like Planets Vulnerable to Radiation". 2 July 2013. http://scitechdaily.com/red-dwarf-stars-could-leave-habitable-earth-like-planets-vulnerable-to-radiation/.
↑ Heller, René; Barnes, Rory (29 April 2014). "Constraints on the Habitability of Extrasolar Moons". Proceedings of the International Astronomical Union 8 (S293): 159–164. doi:10.1017/S1743921313012738. Bibcode: 2014IAUS..293..159H.
↑ ^34.0 ^34.1 Ward, Peter D.; Brownlee, Donald (2000). Rare Earth: Why Complex Life is Uncommon in the Universe. Copernicus Books (Springer Verlag). ISBN 0-387-98701-0.
↑ Davies, P. (2007). "Are Aliens Among Us?". Scientific American 297 (6): 62–69. doi:10.1038/scientificamerican1207-62. Bibcode: 2007SciAm.297f..62D.
↑ Crick, F. H. C.; Orgel, L. E. (1973). "Directed Panspermia". Icarus 19 (3): 341–346. doi:10.1016/0019-1035(73)90110-3. Bibcode: 1973Icar...19..341C. http://profiles.nlm.nih.gov/ps/access/SCBCCP.pdf.
↑ Westby, Tom; Conselice, Christopher J. (15 June 2020). "The Astrobiological Copernican Weak and Strong Limits for Intelligent Life". The Astrophysical Journal 896 (1): 58. doi:10.3847/1538-4357/ab8225. Bibcode: 2020ApJ...896...58W.
↑ Davis, Nicola (15 June 2020). "Scientists say most likely number of contactable alien civilisations is 36". The Guardian. https://www.theguardian.com/science/2020/jun/15/scientists-say-most-likely-number-of-contactable-alien-civilisations-is-36.
↑ ^39.0 ^39.1 "Ernst Mayr on SETI". The Planetary Society. http://www.planetary.org/explore/topics/search_for_life/seti/mayr.html.
↑ Rare Earth, p. xviii.: "We believe that life in the form of microbes or their equivalents is very common in the universe, perhaps more common than even Drake or Sagan envisioned. However, complex life—animals and higher plants—is likely to be far more rare than commonly assumed."
↑ ^41.0 ^41.1 Campbell, A. (13 March 2005). "Review of Life's Solution by Simon Conway Morris". http://www.acampbell.ukfsn.org/bookreviews/r/morris.html.
↑ Bonner, J. T. (1988). The evolution of complexity by means of natural selection. Princeton University Press. ISBN 0-691-08494-7. https://archive.org/details/evolutionofcompl0000bonn.
↑ Kipping, David (18 May 2020). "An objective Bayesian analysis of life's early start and our late arrival". Proceedings of the National Academy of Sciences 117 (22): 11995–12003. doi:10.1073/pnas.1921655117. PMID 32424083.
↑ "New study estimates the odds of life and intelligence emerging beyond our planet". Phys.org. https://phys.org/news/2020-05-odds-life-intelligence-emerging-planet.html.
↑ Lee, Pascal. "N~1: Alone in the Milky Way, Mt Tam". https://www.youtube.com/watch?v=cuJDkIUuDBg. Template:Cbignore
↑ Lee, Pascal. "N~1: Alone in the Milky Way - Kalamazoo Astronomical Society". https://www.youtube.com/watch?v=wj5nmgoQr50.
↑ Forgan, D.; Elvis, M. (2011). "Extrasolar Asteroid Mining as Forensic Evidence for Extraterrestrial Intelligence". International Journal of Astrobiology 10 (4): 307–313. doi:10.1017/S1473550411000127. Bibcode: 2011IJAsB..10..307F.
↑ Tarter, Jill C. (September 2001). "The Search for Extraterrestrial Intelligence (SETI)". Annual Review of Astronomy and Astrophysics 39: 511–548. doi:10.1146/annurev.astro.39.1.511. Bibcode: 2001ARA&A..39..511T.
↑ ^49.0 ^49.1 Shermer, M. (August 2002). "Why ET Hasn't Called". Scientific American 287 (2): 21. doi:10.1038/scientificamerican0802-33. Bibcode: 2002SciAm.287b..33S. http://www.michaelshermer.com/2002/08/why-et-hasnt-called/.
↑ ^50.0 ^50.1 Grinspoon, D. (2004). Lonely Planets.
↑ Goldsmith, D.; Owen, T. (1992). The Search for Life in the Universe (2nd ed.). Addison-Wesley. p. 415. ISBN 1-891389-16-5.
↑ Aatif Sulleyman (2 November 2017). "Stephen Hawking warns artificial intelligence 'may replace humans altogether'". independent.co.uk. https://www.independent.co.uk/life-style/gadgets-and-tech/news/stephen-hawking-artificial-intelligence-fears-ai-will-replace-humans-virus-life-a8034341.html.
↑ Golden, Leslie M. (2021) “A joint mind consideration of the Drake equation in the search for extraterrestrial intelligence,” Acta Astronautica, 185, 333-336; https://doi.org/10.1016/j.actaastro.2021.03.020
↑ "The value of Template:Mvar remains highly uncertain. Even if we had a perfect knowledge of the first two terms in the equation, there are still five remaining terms, each of which could be uncertain by factors of 1,000." from Wilson, TL (2001). "The search for extraterrestrial intelligence". Nature (Nature Publishing Group) 409 (6823): 1110–1114. doi:10.1038/35059235. PMID 11234025. Bibcode: 2001Natur.409.1110W. , or more informally, "The Drake Equation can have any value from "billions and billions" to zero", Michael Crichton, as quoted in Douglas A. Vakoch (2015). The Drake Equation: Estimating the prevalence of extraterrestrial life through the ages. Cambridge University Press. ISBN 978-1-10-707365-4. , p. 13
↑ "The Drake Equation". psu.edu. https://www.e-education.psu.edu/astro801/content/l12_p5.html.
↑ Devin Powell, Astrobiology Magazine (4 September 2013). "The Drake Equation Revisited: Interview with Planet Hunter Sara Seager". Space.com. http://www.space.com/22648-drake-equation-alien-life-seager.html.
↑ "The Chance of Finding Aliens". Sky & Telescope. 3 June 2009. http://www.skyandtelescope.com/astronomy-news/the-chance-of-finding-aliens/.
↑ Template:Better source needed Dean, T. (10 August 2009). "A review of the Drake Equation". Cosmos Magazine. http://www.cosmosmagazine.com/features/are-we-alone-a-review-drake-equation/.
↑ Rare Earth, page 270: "When we take into account factors such as the abundance of planets and the location and lifetime of the habitable zone, the Drake Equation suggests that only between 1% and 0.001% of all stars might have planets with habitats similar to Earth. [...] If microbial life forms readily, then millions to hundreds of millions of planets in the galaxy have the potential for developing advanced life. (We expect that a much higher number will have microbial life.)"
↑ von Bloh, W.; Bounama, C.; Cuntz, M.; Franck, S. (2007). "The habitability of super-Earths in Gliese 581". Astronomy & Astrophysics 476 (3): 1365–1371. doi:10.1051/0004-6361:20077939. Bibcode: 2007A&A...476.1365V.
↑ Selsis, Franck; Kasting, James F.; Levrard, Benjamin; Paillet, Jimmy; Ribas, Ignasi; Delfosse, Xavier (2007). "Habitable planets around the star Gl 581?". Astronomy and Astrophysics 476 (3): 1373–1387. doi:10.1051/0004-6361:20078091. Bibcode: 2007A&A...476.1373S. https://hal.archives-ouvertes.fr/hal-00182743.
↑ Lineweaver, C. H.; Davis, T. M. (2002). "Does the rapid appearance of life on Earth suggest that life is common in the universe?". Astrobiology 2 (3): 293–304. doi:10.1089/153110702762027871. PMID 12530239. Bibcode: 2002AsBio...2..293L.
↑ Forgan, D. (2009). "A numerical testbed for hypotheses of extraterrestrial life and intelligence". International Journal of Astrobiology 8 (2): 121–131. doi:10.1017/S1473550408004321. Bibcode: 2009IJAsB...8..121F.
↑ "Are we alone? Setting some limits to our uniqueness". phys.org. 28 April 2016. http://phys.org/news/2016-04-limits-uniqueness.html.
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↑ Adam Frank (10 June 2016). "Yes, There Have Been Aliens". The New York Times. https://www.nytimes.com/2016/06/12/opinion/sunday/yes-there-have-been-aliens.html.
↑ A. Frank; W.T. Sullivan III (22 April 2016). "A New Empirical Constraint on the Prevalence of Technological Species in the Universe". Astrobiology 16 (5): 359–362. 13 May 2016. doi:10.1089/ast.2015.1418. PMID 27105054. Bibcode: 2016AsBio..16..359F.
↑ Hetesi, Z.; Regaly, Z. (2006). "A new interpretation of Drake-equation". Journal of the British Interplanetary Society 59: 11–14. Bibcode: 2006JBIS...59...11H. http://astro.elte.hu/~hetesizs/Hetesi%20Zsolt%20cikkei/new%20interpretation%20fo%20drake%20eq.pdf.
↑ Maccone, C. (2010). "The Statistical Drake Equation". Acta Astronautica 67 (11–12): 1366–1383. doi:10.1016/j.actaastro.2010.05.003. Bibcode: 2010AcAau..67.1366M.
↑ ^70.0 ^70.1 Brin, G. D. (1983). "The Great Silence – The Controversy Concerning Extraterrestrial Intelligent Life". Quarterly Journal of the Royal Astronomical Society 24 (3): 283–309. Bibcode: 1983QJRAS..24..283B.
↑ Zaitsev, A. (May 2005). "The Drake Equation: Adding a METI Factor". SETI League. http://www.cplire.ru/html/ra&sr/irm/Drake_equation.html.
↑ Jones, Chris (7 December 2016). "'The World Sees Me as the One Who Will Find Another Earth' – The star-crossed life of Sara Seager, an astrophysicist obsessed with discovering distant planets.". The New York Times. https://www.nytimes.com/2016/12/07/magazine/the-world-sees-me-as-the-one-who-will-find-another-earth.html.
↑ ^73.0 ^73.1 The Drake Equation Revisited: Interview with Planet Hunter Sara Seager Devin Powell, Astrobiology Magazine 4 September 2013.
↑ "A New Equation Reveals Our Exact Odds of Finding Alien Life". io9. http://io9.com/what-a-brand-new-equation-reveals-about-our-odds-of-fin-531575395.
↑ Dvorsky, G. (31 May 2007). "The Drake Equation is obsolete". Sentient Developments. http://www.sentientdevelopments.com/2007/05/drake-equation-is-obsolete.html.
↑ Sutter, Paul (2018-12-27). "Alien Hunters, Stop Using the Drake Equation" (in en). https://www.space.com/42739-stop-using-the-drake-equation.html.
↑ Tarter, Jill C. (May–June 2006). "The Cosmic Haystack Is Large". Skeptical Inquirer 30 (3). http://www.csicop.org/si/show/cosmic_haystack_is_large/. Retrieved 2013-08-21.
↑ Alexander, A.. "The Search for Extraterrestrial Intelligence: A Short History – Part 7: The Birth of the Drake Equation". The Planetary Society. http://www.planetary.org/html/UPDATES/seti/history/History07.htm.
↑ Christopher J. Conselice (2016). "The Evolution of Galaxy Number Density at Template:Math and its Implications". The Astrophysical Journal 830 (2): 83. doi:10.3847/0004-637X/830/2/83. Bibcode: 2016ApJ...830...83C.
↑ Fountain, Henry (17 October 2016). "Two Trillion Galaxies, at the Very Least". The New York Times. https://www.nytimes.com/2016/10/18/science/two-trillion-galaxies-at-the-very-least.html. Template:Cbignore
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↑ Webb, S. (2015). If the Universe Is Teeming with Aliens ... WHERE IS EVERYBODY?: Seventy-Five Solutions to the Fermi Paradox and the Problem of Extraterrestrial Life. Springer International Publishing. ISBN 978-3319132358. https://books.google.com/books?id=QWKyrQEACAAJ&q=Universe-Teeming-Aliens-WHERE-EVERYBODY.
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↑ The Making of Star Trek by Stephen E. Whitfield and Gene Roddenberry, New York: Ballantine Books, 1968

External links

Interactive Drake Equation Calculator
Frank Drake's 2010 article on "The Origin of the Drake Equation"
"Only a matter of time, says Frank Drake". A Q&A with Frank Drake in February 2010.
Frank Drake (December 2004). "The E.T. Equation, Recalculated". Wired. https://www.wired.com/wired/archive/12.12/life.html.
Macromedia Flash page allowing the user to modify Drake's values from PBS Nova
The Drake Equation Astronomy Cast episode #23, includes full transcript.
Animated simulation of the Drake equation.
The Alien Equation 22 September 2010, BBC Radio program Discovery.
"Reflections on the Equation" (PDF), by Frank Drake, 2013

Template:Astrobiology Template:Extraterrestrial life Template:Interstellar messages Template:Molecules detected in outer space Template:Portal bar

[Burchell-1] 1.0 ^1.1 ^1.2 ^1.3 Burchell, M.J. (2006). "W(h)ither the Drake equation?". International Journal of Astrobiology 5 (3): 243–250. doi:10.1017/S1473550406003107. Bibcode: 2006IJAsB...5..243B.

[2] Glade, N.; Ballet, P.; Bastien, O. (2012). "A stochastic process approach of the drake equation parameters". International Journal of Astrobiology 11 (2): 103–108. doi:10.1017/S1473550411000413. Bibcode: 2012IJAsB..11..103G.

[December_2002-3] 3.0 ^3.1 ^3.2 "Chapter 3 – Philosophy: "Solving the Drake Equation". Ask Dr. SETI. SETI League. December 2002. http://www.setileague.org/askdr/drake.htm.

[4] Drake, N. (30 June 2014). "How my Dad's Equation Sparked the Search for Extraterrestrial Intelligence". National Geographic. http://news.nationalgeographic.com/news/2014/06/140630-drake-equation-50-years-later-aliens-science/.

[5] 
<math>N = R_* \cdot f_\mathrm{p} \cdot n_\mathrm{e} \cdot f_\mathrm{l} \cdot f_\mathrm{i} \cdot f_\mathrm{c} \cdot L</math>

[NOVA-6] 6.0 ^6.1 Aguirre, L. (1 July 2008). "The Drake Equation". Nova ScienceNow. PBS. https://www.pbs.org/wgbh/nova/origins/drake.html.

[SETI-Drake-Equation-7] "What do we need to know about to discover life in space?". SETI Institute. http://www.seti.org/drakeequation.

[Cocconi_1959-8] Cocconi, G.; Morisson, P. (1959). "Searching for Interstellar Communications". Nature 184 (4690): 844–846. doi:10.1038/184844a0. Bibcode: 1959Natur.184..844C. http://www.iaragroup.org/_OLD/seti/pdf_IARA/cocconi.pdf. Retrieved 2013-04-10.

[history-9] 9.0 ^9.1 Schilling, G.; MacRobert, A. M. (2013). "The Chance of Finding Aliens". Sky & Telescope. http://www.skyandtelescope.com/resources/seti/3304541.html.

[SydneyMorningHerald-10] wspaper, staff (8 November 1959). "Life On Other Planets?". Sydney Morning Herald. https://news.google.com/newspapers?nid=1301&dat=19591108&id=s39WAAAAIBAJ&pg=2212,2112869&hl=en.

[Astrobiology_Magazine-11] "The Drake Equation Revisited: Part I". Astrobiology Magazine. 29 September 2003. http://www.astrobio.net/alien-life/the-drake-equation-revisited-part-i/.

[Wende-12] Zaun, H. (1 November 2011). "Es war wie eine 180-Grad-Wende von diesem peinlichen Geheimnis!" (in de). Telepolis. http://www.heise.de/tp/artikel/35/35756/1.html.

[13] "Drake Equation Plaque". http://www.setileague.org/photos/miscpix/drakeqn.jpg.

[14] Template:Cite encyclopedia

[15] Jones, D. S. (26 September 2001). "Beyond the Drake Equation". http://frombob.to/drake.html.

[16] "The Search For Life : The Drake Equation 2010 – Part 1". BBC Four. 2010. https://www.youtube.com/watch?list=PL56DCB81E2F59166A&v=U3UyAoYkhTo&feature=player_embedded.

[17] SETI: A celebration of the first 50 years. Keith Cooper. Astronomy Now. 2000

[18] Drake, F.; Sobel, D. (1992). Is Anyone Out There? The Scientific Search for Extraterrestrial Intelligence. Delta. pp. 55–62. ISBN 0-385-31122-2.

[19] Glade, N.; Ballet, P.; Bastien, O. (2012). "A stochastic process approach of the drake equation parameters". International Journal of Astrobiology 11 (2): 103–108. doi:10.1017/S1473550411000413. Bibcode: 2012IJAsB..11..103G. Note: This reference has a table of 1961 values, claimed to be taken from Drake & Sobel, but these differ from the book.

[Robitaille-20] 20.0 ^20.1 ^20.2 Robitaille, Thomas P.; Barbara A. Whitney (2010). "The present-day star formation rate of the Milky Way determined from Spitzer-detected young stellar objects". The Astrophysical Journal Letters 710 (1): L11. doi:10.1088/2041-8205/710/1/L11. Bibcode: 2010ApJ...710L..11R.

[The_Drake_Equation-21] Wanjek, C. (2 July 2015). The Drake Equation. Cambridge University Press. ISBN 9781107073654. https://books.google.com/books?id=jcnSCQAAQBAJ&q=Robitaille+and+Whitney+came+up+with+a+figure+for+R*+between+0.68+and+1.45&pg=PA45. Retrieved 2016-09-09.

[22] Kennicutt, Robert C.; Evans, Neal J. (22 September 2012). "Star Formation in the Milky Way and Nearby Galaxies". Annual Review of Astronomy and Astrophysics 50 (1): 531–608. doi:10.1146/annurev-astro-081811-125610. Bibcode: 2012ARA&A..50..531K.

[bbc.co.uk-23] 23.0 ^23.1 Palmer, J. (11 January 2012). "Exoplanets are around every star, study suggests". BBC. https://www.bbc.co.uk/news/science-environment-16515944.

[Nature-20120111-24] Cassan, A. (11 January 2012). "One or more bound planets per Milky Way star from microlensing observations". Nature 481 (7380): 167–169. doi:10.1038/nature10684. PMID 22237108. Bibcode: 2012Natur.481..167C.

[NYT-20131104-25] Overbye, Dennis (4 November 2013). "Far-Off Planets Like the Earth Dot the Galaxy". The New York Times. https://www.nytimes.com/2013/11/05/science/cosmic-census-finds-billions-of-planets-that-could-be-like-earth.html. Template:Cbignore

[PNAS-20131031-26] Petigura, Eric A.; Howard, Andrew W.; Marcy, Geoffrey W. (31 October 2013). "Prevalence of Earth-size planets orbiting Sun-like stars". Proceedings of the National Academy of Sciences of the United States of America 110 (48): 19273–19278. doi:10.1073/pnas.1319909110. PMID 24191033. Bibcode: 2013PNAS..11019273P.

[LATimes-20131104-27] Khan, Amina (4 November 2013). "Milky Way may host billions of Earth-size planets". Los Angeles Times. http://www.latimes.com/science/la-sci-earth-like-planets-20131105,0,2673237.story.

[schilling2011-28] 28.0 ^28.1 Govert Schilling (November 2011). "The Chance of Finding Aliens: Reevaluating the Drake Equation". astro-tom.com. http://www.astro-tom.com/technical_data/alien_life.htm.

[Trimble-29] Trimble, V. (1997). "Origin of the biologically important elements". Origins of Life and Evolution of the Biosphere 27 (1–3): 3–21. doi:10.1023/A:1006561811750. PMID 9150565. Bibcode: 1997OLEB...27....3T.

[30] Lineweaver, C. H.; Fenner, Y.; Gibson, B. K. (2004). "The Galactic Habitable Zone and the Age Distribution of Complex Life in the Milky Way". Science 303 (5654): 59–62. doi:10.1126/science.1092322. PMID 14704421. Bibcode: 2004Sci...303...59L.

[31] Dressing, C. D.; Charbonneau, D. (2013). "The Occurrence Rate of Small Planets around Small Stars". The Astrophysical Journal 767 (1): 95. doi:10.1088/0004-637X/767/1/95. Bibcode: 2013ApJ...767...95D.

[32] "Red Dwarf Stars Could Leave Habitable Earth-Like Planets Vulnerable to Radiation". 2 July 2013. http://scitechdaily.com/red-dwarf-stars-could-leave-habitable-earth-like-planets-vulnerable-to-radiation/.

[33] Heller, René; Barnes, Rory (29 April 2014). "Constraints on the Habitability of Extrasolar Moons". Proceedings of the International Astronomical Union 8 (S293): 159–164. doi:10.1017/S1743921313012738. Bibcode: 2014IAUS..293..159H.

[RareEarth-34] 34.0 ^34.1 Ward, Peter D.; Brownlee, Donald (2000). Rare Earth: Why Complex Life is Uncommon in the Universe. Copernicus Books (Springer Verlag). ISBN 0-387-98701-0.

[35] Davies, P. (2007). "Are Aliens Among Us?". Scientific American 297 (6): 62–69. doi:10.1038/scientificamerican1207-62. Bibcode: 2007SciAm.297f..62D.

[36] Crick, F. H. C.; Orgel, L. E. (1973). "Directed Panspermia". Icarus 19 (3): 341–346. doi:10.1016/0019-1035(73)90110-3. Bibcode: 1973Icar...19..341C. http://profiles.nlm.nih.gov/ps/access/SCBCCP.pdf.

[37] Westby, Tom; Conselice, Christopher J. (15 June 2020). "The Astrobiological Copernican Weak and Strong Limits for Intelligent Life". The Astrophysical Journal 896 (1): 58. doi:10.3847/1538-4357/ab8225. Bibcode: 2020ApJ...896...58W.

[38] Davis, Nicola (15 June 2020). "Scientists say most likely number of contactable alien civilisations is 36". The Guardian. https://www.theguardian.com/science/2020/jun/15/scientists-say-most-likely-number-of-contactable-alien-civilisations-is-36.

[Ernst_Mayr_on_SETI-39] 39.0 ^39.1 "Ernst Mayr on SETI". The Planetary Society. http://www.planetary.org/explore/topics/search_for_life/seti/mayr.html.

[40] Rare Earth, p. xviii.: "We believe that life in the form of microbes or their equivalents is very common in the universe, perhaps more common than even Drake or Sagan envisioned. However, complex life—animals and higher plants—is likely to be far more rare than commonly assumed."

[acampbell.ukfsn.org-41] 41.0 ^41.1 Campbell, A. (13 March 2005). "Review of Life's Solution by Simon Conway Morris". http://www.acampbell.ukfsn.org/bookreviews/r/morris.html.

[42] Bonner, J. T. (1988). The evolution of complexity by means of natural selection. Princeton University Press. ISBN 0-691-08494-7. https://archive.org/details/evolutionofcompl0000bonn.

[Kipping2020-43] Kipping, David (18 May 2020). "An objective Bayesian analysis of life's early start and our late arrival". Proceedings of the National Academy of Sciences 117 (22): 11995–12003. doi:10.1073/pnas.1921655117. PMID 32424083.

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@@ Line 183: / Line 183: @@
 {{anchor|eta-earth|}}
-====Fraction of those stars that have planets, {{math|''f''<sub>p</sub>}}====
+====Fraction of those stars that have planets, ''f''<sub>p</sub>====
 Analysis of [[Gravitational microlensing|microlensing]] surveys, in 2012, has found that {{math|''f''<sub>p</sub>}} may approach 1—that is, stars are orbited by planets as a rule, rather than the exception; and that there are one or more bound planets per Milky Way star.<ref name="bbc.co.uk">
 {{cite news
@@ Line 207: / Line 207: @@
   }}</ref>
-====Average number of planets that might support life per star that has planets, {{math|''n''<sub>e</sub>}}====
+====Average number of planets that might support life per star that has planets, ''n''<sub>e</sub>====
 In November 2013, astronomers reported, based on [[Kepler (spacecraft)|''Kepler'' space mission]] data, that there could be as many as 40&nbsp;billion [[Terrestrial planet|Earth-sized]] [[extrasolar planets|planets]] orbiting in the [[habitable zone]]s of [[sun-like|sun-like stars]] and [[red dwarf stars]] within the [[Milky Way Galaxy]].<ref name="NYT-20131104">{{cite news |last=Overbye |first=Dennis |title=Far-Off Planets Like the Earth Dot the Galaxy |url=https://www.nytimes.com/2013/11/05/science/cosmic-census-finds-billions-of-planets-that-could-be-like-earth.html |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2013/11/05/science/cosmic-census-finds-billions-of-planets-that-could-be-like-earth.html |archive-date=2022-01-01 |url-access=limited |date=4 November 2013 |work=[[The New York Times]] |access-date=5 November 2013 }}{{cbignore}}</ref><ref name="PNAS-20131031">{{cite journal |last1=Petigura |first1=Eric A. |last2=Howard |first2=Andrew W. |last3=Marcy |first3=Geoffrey W. |title=Prevalence of Earth-size planets orbiting Sun-like stars |date=31 October 2013 |journal=[[Proceedings of the National Academy of Sciences of the United States of America]] |doi=10.1073/pnas.1319909110 |arxiv = 1311.6806 |bibcode = 2013PNAS..11019273P |volume=110 |issue=48 |pages=19273–19278 |pmid=24191033 |pmc=3845182|doi-access=free }}</ref> 11 billion of these estimated planets may be orbiting sun-like stars.<ref name="LATimes-20131104">{{cite news |last=Khan |first=Amina |title=Milky Way may host billions of Earth-size planets |url=http://www.latimes.com/science/la-sci-earth-like-planets-20131105,0,2673237.story |date=4 November 2013 |work=[[Los Angeles Times]] |access-date=5 November 2013 }}</ref> Since there are about 100 billion stars in the galaxy, this implies {{math|''f''<sub>p</sub> · ''n''<sub>e</sub>}} is roughly 0.4. The nearest planet in the habitable zone is [[Proxima Centauri b]], which is as close as about 4.2 light-years away.
@@ Line 254: / Line 254: @@
 The authors of the [[rare Earth hypothesis]] propose a number of additional constraints on habitability for planets, including being in galactic zones with suitably low radiation, high star metallicity, and low enough density to avoid excessive asteroid bombardment. They also propose that it is necessary to have a planetary system with large gas giants which provide bombardment protection without a [[hot Jupiter]]; and a planet with [[plate tectonic]]s, a large moon that creates tidal pools, and moderate [[axial tilt]] to generate seasonal variation.<ref name="RareEarth">{{cite book |last1=Ward |first1=Peter D. |last2=Brownlee |first2=Donald |title=Rare Earth: Why Complex Life is Uncommon in the Universe |publisher=Copernicus Books (Springer Verlag) |date=2000 |isbn=0-387-98701-0 }}</ref>
-====Fraction of the above that actually go on to develop life, {{math|''f''<sub>l</sub>}}====
+====Fraction of the above that actually go on to develop life, ''f''<sub>l</sub>====
-Geological evidence from the Earth suggests that {{math|''f''<sub>l</sub>}} may be 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). From a classical [[hypothesis testing]] standpoint, without assuming that the underlying distribution of {{math|''f''<sub>l</sub>}} is the same for all planets in the Milky Way, there are zero [[degrees of freedom (statistics)|degrees of freedom]], permitting no valid estimates to be made. If life (or evidence of past life) were to be found on [[life on Mars|Mars]], [[Europa (moon)|Europa]], [[Enceladus]] or [[Titan (moon)|Titan]] that developed independently from life on Earth it would imply a value for {{math|''f''<sub>l</sub>}} close to 1. While this would raise the number of degrees of freedom from zero to one, there would remain a great deal of uncertainty on any estimate due to the small sample size, and the chance they are not really independent.
+Geological evidence from the Earth suggests that ''f''<sub>l</sub> may be 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). From a classical [[hypothesis testing]] standpoint, without assuming that the underlying distribution of {{math|''f''<sub>l</sub>}} is the same for all planets in the Milky Way, there are zero [[degrees of freedom (statistics)|degrees of freedom]], permitting no valid estimates to be made. If life (or evidence of past life) were to be found on [[life on Mars|Mars]], [[Europa (moon)|Europa]], [[Enceladus]] or [[Titan (moon)|Titan]] that developed independently from life on Earth it would imply a value for {{math|''f''<sub>l</sub>}} close to 1. While this would raise the number of degrees of freedom from zero to one, there would remain a great deal of uncertainty on any estimate due to the small sample size, and the chance they are not really independent.
 Countering this argument is that there is no evidence for abiogenesis occurring more than once on the Earth—that is, all terrestrial life stems from a common origin. If abiogenesis were more common it would be speculated to have occurred more than once on the Earth. Scientists have searched for this by looking for [[bacteria]] that are unrelated to other life on Earth, but none have been found yet.<ref>
@@ Line 280: / Line 280: @@
 In 2020, a paper by scholars at the [[University of Nottingham]] proposed an "Astrobiological Copernican" principle, based on the [[Principle of Mediocrity]], and speculated that "intelligent life would form on other [Earth-like] planets like it has on Earth, so within a few billion years life would automatically form as a natural part of evolution". In the authors' framework, {{math|''f''<sub>l</sub>}}, {{math|''f''<sub>i</sub>}}, and {{math|''f''<sub>c</sub>}} are all set to a probability of 1 (certainty). Their resultant calculation concludes there are more than thirty current technological civilizations in the galaxy (disregarding error bars).<ref>{{cite journal |last1=Westby |first1=Tom |last2=Conselice |first2=Christopher J. |title=The Astrobiological Copernican Weak and Strong Limits for Intelligent Life |journal=The Astrophysical Journal |date=15 June 2020 |volume=896 |issue=1 |pages=58 |doi=10.3847/1538-4357/ab8225|arxiv=2004.03968 |bibcode=2020ApJ...896...58W |s2cid=215415788 }}</ref><ref>{{cite news |last1=Davis |first1=Nicola |title=Scientists say most likely number of contactable alien civilisations is 36 |url=https://www.theguardian.com/science/2020/jun/15/scientists-say-most-likely-number-of-contactable-alien-civilisations-is-36 |access-date=19 June 2020 |work=The Guardian |date=15 June 2020}}</ref>
-====Fraction of the above that develops intelligent life, {{math|''f''<sub>i</sub>}}====
+====Fraction of the above that develops intelligent life, ''f''<sub>i</sub>====
 This value remains particularly controversial. Those who favor a low value, such as the biologist [[Ernst Mayr]], 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 {{math|''f''<sub>i</sub>}}.<ref name="Ernst Mayr on SETI">
 {{cite web
@@ Line 312: / Line 312: @@
 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 [[extinction events]] have raised the possibility that life on Earth is relatively fragile. Research on any past [[life on Mars]] is relevant since a discovery that life did form on Mars but ceased to exist might raise our estimate of {{math|''f''<sub>l</sub>}} but would indicate that in half the known cases, intelligent life did not develop.
-Estimates of {{math|''f''<sub>i</sub>}} have been affected by discoveries that the Solar System's orbit is circular in the galaxy, at such a distance that it remains out of the spiral arms for tens of millions of years (evading radiation from [[nova]]e). Also, Earth's large moon may aid the evolution of life by [[Rare Earth hypothesis#A large moon|stabilizing the planet's axis of rotation]].
+Estimates of ''f''<sub>i</sub> have been affected by discoveries that the Solar System's orbit is circular in the galaxy, at such a distance that it remains out of the spiral arms for tens of millions of years (evading radiation from [[nova]]e). Also, Earth's large moon may aid the evolution of life by [[Rare Earth hypothesis#A large moon|stabilizing the planet's axis of rotation]].
 There has been quantitative work to begin to define <math>f_\mathrm{l} \cdot f_\mathrm{i}</math> . One example is a Bayesian analysis published in 2020. In the conclusion, the author cautions that this study applies to Earth's conditions. In Bayesian terms, the study favors the formation of intelligence on a planet with identical conditions to Earth but does not do so with high confidence.<ref name="Kipping2020">
@@ Line 339: / Line 339: @@
 Planetary scientist [[Pascal Lee]] of the [[SETI Institute]] proposes that this fraction is very low (0.0002). He based this estimate on how long it took Earth to develop intelligent life (1 million years since [[Homo erectus]] evolved, compared to 4.6 billion years since Earth formed).<ref>{{Cite web|last=Lee|first=Pascal|title=N~1: Alone in the Milky Way, Mt Tam|url=https://www.youtube.com/watch?v=cuJDkIUuDBg| archive-url=https://ghostarchive.org/varchive/youtube/20211211/cuJDkIUuDBg| archive-date=2021-12-11|url-status=live}}{{cbignore}}</ref><ref>{{Cite web|last=Lee|first=Pascal|title=N~1: Alone in the Milky Way - Kalamazoo Astronomical Society|url=https://www.youtube.com/watch?v=wj5nmgoQr50| archive-url=https://web.archive.org/web/20210315085249/https://www.youtube.com/watch?v=wj5nmgoQr50| archive-date=2021-03-15|url-status=live}}</ref>
-====Fraction of the above revealing their existence via signal release into space, {{math|''f''<sub>c</sub>}}====
+====Fraction of the above revealing their existence via signal release into space, ''f''<sub>c</sub>====
 For deliberate communication, the one example we have (the Earth) does not do much explicit communication, though there are [[Active SETI|some efforts]] covering only a tiny fraction of the stars that might look for our presence. (See [[Arecibo message]], for example). There is [[Fermi paradox#They choose not to interact with us|considerable speculation]] why an extraterrestrial civilization might exist but choose not to communicate. However, deliberate communication is not required, and calculations indicate that current or near-future Earth-level technology might well be detectable to civilizations not too much more advanced than our own.<ref>
 {{cite journal
@@ Line 356: / Line 356: @@
 Another question is what percentage of civilizations in the galaxy are close enough for us to detect, assuming that they send out signals. For example, existing Earth radio telescopes could only detect Earth radio transmissions from roughly a light year away.<ref>{{cite journal |title=The Search for Extraterrestrial Intelligence (SETI) |journal=Annual Review of Astronomy and Astrophysics |first=Jill C. |last=Tarter |author-link=Jill Tarter |volume=39 |pages=511–548 |date=September 2001 |doi=10.1146/annurev.astro.39.1.511 |bibcode=2001ARA&A..39..511T}}</ref>
-====Lifetime of such a civilization wherein it communicates its signals into space, {{math|''L''}}====
+====Lifetime of such a civilization wherein it communicates its signals into space, ''L''====
-[[Michael Shermer]] estimated {{math|''L''}} as 420 years, based on the duration of sixty historical Earthly civilizations.<ref name="Why ET Hasn’t Called">
+[[Michael Shermer]] estimated ''L'' as 420 years, based on the duration of sixty historical Earthly civilizations.<ref name="Why ET Hasn’t Called">
 {{cite journal
   |last=Shermer |first=M.
@@ Line 369: / Line 369: @@
 |bibcode=2002SciAm.287b..33S
   |doi=10.1038/scientificamerican0802-33
-  }}</ref> Using 28 civilizations more recent than the Roman Empire, he calculates a figure of 304 years for "modern" civilizations. It could also be argued from Michael Shermer's results that the fall of most of these civilizations was followed by later civilizations that carried on the technologies, so it is doubtful that they are separate civilizations in the context of the Drake equation. In the expanded version, including ''reappearance number'', this lack of specificity in defining single civilizations does not matter for the end result, since such a civilization turnover could be described as an increase in the ''reappearance number'' rather than increase in {{math|''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.
+  }}</ref> Using 28 civilizations more recent than the Roman Empire, he calculates a figure of 304 years for "modern" civilizations. It could also be argued from Michael Shermer's results that the fall of most of these civilizations was followed by later civilizations that carried on the technologies, so it is doubtful that they are separate civilizations in the context of the Drake equation. In the expanded version, including ''reappearance number'', this lack of specificity in defining single civilizations does not matter for the end result, since such a civilization turnover could be described as an increase in the ''reappearance number'' rather than increase in ''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]] has argued that once a civilization has developed enough, it might overcome all threats to its survival. It will then last for an indefinite period of time, making the value for {{math|''L''}} potentially billions of years. If this is the case, then he proposes that the Milky Way Galaxy may have been steadily accumulating advanced civilizations since it formed.<ref name="David Grinspoon 2004">
+[[David Grinspoon]] has argued that once a civilization has developed enough, it might overcome all threats to its survival. It will then last for an indefinite period of time, making the value for ''L'' potentially billions of years. If this is the case, then he proposes that the Milky Way Galaxy may have been steadily accumulating advanced civilizations since it formed.<ref name="David Grinspoon 2004">
 {{cite book
   |last=Grinspoon |first=D.
   |year=2004
   |title=Lonely Planets
-}}</ref> He proposes that the last factor {{math|''L''}} be replaced with {{math|''f''<sub>IC</sub> · ''T''}}, where {{math|''f''<sub>IC</sub>}} is the fraction of communicating civilizations that become "immortal" (in the sense that they simply do not die out), and {{math|''T''}} representing the length of time during which this process has been going on. This has the advantage that {{math|''T''}} would be a relatively easy-to-discover number, as it would simply be some fraction of the age of the universe.
+}}</ref> He proposes that the last factor ''L'' be replaced with ''f''<sub>IC</sub> · ''T'', where ''f''<sub>IC</sub> is the fraction of communicating civilizations that become "immortal" (in the sense that they simply do not die out), and {{math|''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 hypothesized that once a civilization has learned of a more advanced one, its longevity could increase because it can learn from the experiences of the other.<ref name="GoldsmithOwen">
@@ Line 393: / Line 393: @@
 An intelligent civilization might not be organic, as some have suggested that [[artificial general intelligence]] may replace humanity.<ref>{{cite news |title=Stephen Hawking warns artificial intelligence 'may replace humans altogether'|date=2 November 2017|author=Aatif Sulleyman|work=independent.co.uk
 | url=https://www.independent.co.uk/life-style/gadgets-and-tech/news/stephen-hawking-artificial-intelligence-fears-ai-will-replace-humans-virus-life-a8034341.html}}</ref>
 ===Probabilistic combination of results===
 Combining the estimates of the original six factors by major researchers via a Monte Carlo procedure leads to a best value for the non-longevity factors of 0.85 1/years.<ref>Golden, Leslie M. (2021) “A joint mind consideration of the Drake equation in the search for extraterrestrial intelligence,” <i>Acta Astronautica</i>, 185, 333-336; https://doi.org/10.1016/j.actaastro.2021.03.020</ref>  This result differs insignificantly from the estimate of unity given both by Drake and the Cyclops report.
@@ Line 406: / Line 407: @@
   |publisher=Nature Publishing Group |bibcode = 2001Natur.409.1110W |doi = 10.1038/35059235 |pmid=11234025
   |s2cid=205014501
-  }}, or more informally, "The Drake Equation can have any value from "billions and billions" to zero", Michael Crichton, as quoted in {{cite book |author=Douglas A. Vakoch |title=The Drake Equation: Estimating the prevalence of extraterrestrial life through the ages |publisher=Cambridge University Press |date=2015 |isbn=978-1-10-707365-4|display-authors=etal}}, p. 13</ref> as the values used in portions of the Drake equation are not well established.<ref name=schilling2011>{{cite web|url=http://www.astro-tom.com/technical_data/alien_life.htm|title=The Chance of Finding Aliens: Reevaluating the Drake Equation |author=Govert Schilling|date=November 2011|work=astro-tom.com}}</ref><ref name=renamed_from_2011_on_20160211035411>{{cite web|url=https://www.e-education.psu.edu/astro801/content/l12_p5.html|title=The Drake Equation|work=psu.edu}}</ref><ref>{{cite web|url=http://www.space.com/22648-drake-equation-alien-life-seager.html|title=The Drake Equation Revisited: Interview with Planet Hunter Sara Seager|author=Devin Powell, Astrobiology Magazine|work=Space.com|date=4 September 2013}}</ref><ref name=schilling2009>{{cite web|url=http://www.skyandtelescope.com/astronomy-news/the-chance-of-finding-aliens/|title=The Chance of Finding Aliens|author1=Govert Schilling|author2=Alan M. MacRobert|date=3 June 2009|work=Sky & Telescope}}</ref> In particular, the result can be {{math|''N'' ≪ 1}}, meaning we are likely alone in the galaxy, or {{math|''N'' ≫ 1}}, implying there are many civilizations we might contact. One of the few points of wide agreement is that the presence of humanity implies a probability of intelligence arising of greater than zero.<ref name="Dean">{{better source needed|date=August 2015}}
+  }}, or more informally, "The Drake Equation can have any value from "billions and billions" to zero", Michael Crichton, as quoted in {{cite book |author=Douglas A. Vakoch |title=The Drake Equation: Estimating the prevalence of extraterrestrial life through the ages |publisher=Cambridge University Press |date=2015 |isbn=978-1-10-707365-4|display-authors=etal}}, p. 13</ref> as the values used in portions of the Drake equation are not well established.<ref name=schilling2011>{{cite web|url=http://www.astro-tom.com/technical_data/alien_life.htm|title=The Chance of Finding Aliens: Reevaluating the Drake Equation |author=Govert Schilling|date=November 2011|work=astro-tom.com}}</ref><ref name=renamed_from_2011_on_20160211035411>{{cite web|url=https://www.e-education.psu.edu/astro801/content/l12_p5.html|title=The Drake Equation|work=psu.edu}}</ref><ref>{{cite web|url=http://www.space.com/22648-drake-equation-alien-life-seager.html|title=The Drake Equation Revisited: Interview with Planet Hunter Sara Seager|author=Devin Powell, Astrobiology Magazine|work=Space.com|date=4 September 2013}}</ref><ref name=schilling2009>{{cite web|url=http://www.skyandtelescope.com/astronomy-news/the-chance-of-finding-aliens/|title=The Chance of Finding Aliens|author1=Govert Schilling|author2=Alan M. MacRobert|date=3 June 2009|work=Sky & Telescope}}</ref> In particular, the result can be ''N'' ≪ 1, meaning we are likely alone in the galaxy, or ''N'' ≫ 1, implying there are many civilizations we might contact. One of the few points of wide agreement is that the presence of humanity implies a probability of intelligence arising of greater than zero.<ref name="Dean">{{better source needed|date=August 2015}}
 {{cite web
   |last        = Dean
@@ Line 421: / Line 422: @@
 }}</ref>
-As an example of a low estimate, combining NASA's star formation rates, the [[rare Earth hypothesis]] value of {{math|''f''<sub>p</sub> · ''n''<sub>e</sub> · ''f''<sub>l</sub> {{=}} 10<sup>−5</sup>}},<ref>Rare Earth, page 270: "When we take into account factors such as the abundance of planets and the location and lifetime of the habitable zone, the Drake Equation suggests that only between 1% and 0.001% of all stars might have planets with habitats similar to Earth. [...] If microbial life forms readily, then millions to hundreds of millions of planets in the galaxy have the ''potential'' for developing advanced life. (We expect that a much higher number will have microbial life.)"</ref> Mayr's view on intelligence arising, Drake's view of communication, and Shermer's estimate of lifetime:
+As an example of a low estimate, combining NASA's star formation rates, the [[rare Earth hypothesis]] value of ''f''<sub>p</sub> · ''n''<sub>e</sub> · ''f''<sub>l</sub> = 10<sup>−5</sup>,<ref>Rare Earth, page 270: "When we take into account factors such as the abundance of planets and the location and lifetime of the habitable zone, the Drake Equation suggests that only between 1% and 0.001% of all stars might have planets with habitats similar to Earth. [...] If microbial life forms readily, then millions to hundreds of millions of planets in the galaxy have the ''potential'' for developing advanced life. (We expect that a much higher number will have microbial life.)"</ref> Mayr's view on intelligence arising, Drake's view of communication, and Shermer's estimate of lifetime:
-:{{math|''R''<sub>∗</sub> {{=}} 1.5–3 yr<sup>−1</sup>}},<ref name=Robitaille/> {{math|''f''<sub>p</sub> · ''n''<sub>e</sub> · ''f''<sub>l</sub> {{=}} 10<sup>−5</sup>}},<ref name="RareEarth"/> {{math|''f''<sub>i</sub> {{=}} 10<sup>−9</sup>}},<ref name="Ernst Mayr on SETI"/> {{math|''f''<sub>c</sub> {{=}} 0.2}}<sup>[Drake, above]</sup>, and {{math|''L'' {{=}} 304}} years<ref name="Why ET Hasn’t Called"/>
+:''R''<sub>∗</sub> = 1.5–3 yr<sup>−1</sup>,<ref name=Robitaille/> ''f''<sub>p</sub> · ''n''<sub>e</sub> · ''f''<sub>l</sub> = 10<sup>−5</sup>,<ref name="RareEarth"/> ''f''<sub>i</sub> = 10<sup>−9</sup>,<ref name="Ernst Mayr on SETI"/> ''f''<sub>c</sub> = 0.2<sup>[Drake, above]</sup>, and ''L'' = 304 years<ref name="Why ET Hasn’t Called"/>
 gives:
-:{{math|''N'' {{=}} 1.5 × 10<sup>−5</sup> × 10<sup>−9</sup> × 0.2 × 304 {{=}} 9.1 × 10<sup>−13</sup>}}
+:''N'' =1.5 × 10<sup>−5</sup> × 10<sup>−9</sup> × 0.2 × 304 {{=}} 9.1 × 10<sup>−13</sup>
 i.e., suggesting that we are probably alone in this galaxy, and possibly in the observable universe.
-On the other hand, with larger values for each of the parameters above, values of {{math|''N''}} can be derived that are greater than 1. The following higher values that have been proposed for each of the parameters:
+On the other hand, with larger values for each of the parameters above, values of ''N'' can be derived that are greater than 1. The following higher values that have been proposed for each of the parameters:
-:{{math|''R''<sub>∗</sub> {{=}} 1.5–3 yr<sup>−1</sup>}},<ref name=Robitaille/> {{math|''f''<sub>p</sub> {{=}} 1}},<ref name="bbc.co.uk"/> {{math|''n''<sub>e</sub> {{=}} 0.2}},<ref name="W. von Bloh, C.Bounama, M. Cuntz, and S. Franck. 2007 1365">
+:''R''<sub>∗</sub> = 1.5–3 yr<sup>−1</sup>,<ref name=Robitaille/> ''f''<sub>p</sub> = 1,<ref name="bbc.co.uk"/> ''n''<sub>e</sub> = 0.2,<ref name="W. von Bloh, C.Bounama, M. Cuntz, and S. Franck. 2007 1365">
 {{cite journal
   |last1=von Bloh |first1=W.
@@ Line 443: / Line 444: @@
 |s2cid=14475537
   }}</ref><ref name="F. Selsis, J.F. Kasting, B. Levrard, J. Paillet, I. Ribas, and X. Delfosse. 2007 1373">
-{{cite journal |doi=10.1051/0004-6361:20078091 |bibcode=2007A&A...476.1373S |title=Habitable planets around the star Gl 581? |journal=[[Astronomy and Astrophysics]] |volume=476 |issue=3 |year=2007 |pages=1373–1387 |last1=Selsis |first1=Franck |last2=Kasting |first2=James F. |last3=Levrard |first3=Benjamin |last4=Paillet |first4=Jimmy |last5=Ribas |first5=Ignasi |last6=Delfosse |first6=Xavier |arxiv=0710.5294 |s2cid=11492499 |ref=Selsis |url=https://hal.archives-ouvertes.fr/hal-00182743 }}</ref> {{math|''f''<sub>l</sub> {{=}} 0.13}},<ref name="Lineweaver, C. H. & Davis, T. M. 2002 293–304">
+{{cite journal |doi=10.1051/0004-6361:20078091 |bibcode=2007A&A...476.1373S |title=Habitable planets around the star Gl 581? |journal=[[Astronomy and Astrophysics]] |volume=476 |issue=3 |year=2007 |pages=1373–1387 |last1=Selsis |first1=Franck |last2=Kasting |first2=James F. |last3=Levrard |first3=Benjamin |last4=Paillet |first4=Jimmy |last5=Ribas |first5=Ignasi |last6=Delfosse |first6=Xavier |arxiv=0710.5294 |s2cid=11492499 |ref=Selsis |url=https://hal.archives-ouvertes.fr/hal-00182743 }}</ref> ''f''<sub>l</sub> = 0.13,<ref name="Lineweaver, C. H. & Davis, T. M. 2002 293–304">
 {{cite journal
   |last1=Lineweaver |first1=C. H.
@@ Line 456: / Line 457: @@
   |pmid=12530239
 |s2cid=431699
-  }}</ref> {{math|''f''<sub>i</sub> {{=}} 1}},<ref name="acampbell.ukfsn.org"/> {{math|''f''<sub>c</sub> {{=}} 0.2}}<sup>[Drake, above]</sup>, and {{math|''L'' {{=}} 10<sup>9</sup>}} years<ref name="David Grinspoon 2004"/>
+  }}</ref> ''f''<sub>i</sub> = 1,<ref name="acampbell.ukfsn.org"/> ''f''<sub>c</sub> = 0.2<sup>[Drake, above]</sup>, and ''L'' = 10<sup>9</sup> years<ref name="David Grinspoon 2004"/>
 Use of these parameters gives:
-:{{math|''N'' {{=}} 3 × 1 × 0.2 × 0.13 × 1 × 0.2 × 10<sup>9</sup> {{=}} 15,600,000}}
+:''N'' = 3 × 1 × 0.2 × 0.13 × 1 × 0.2 × 10<sup>9</sup> = 15,600,000
 [[Monte Carlo method|Monte Carlo]] simulations of estimates of the Drake equation factors based on a stellar and planetary model of the Milky Way have resulted in the number of civilizations varying by a factor of 100.<ref>
@@ Line 518: / Line 519: @@
 ;Reappearance factor : The Drake equation may furthermore be multiplied by ''how many times'' an intelligent civilization may occur on planets where it has happened once. Even if an intelligent civilization reaches the end of its lifetime after, for example, 10,000 years, life may still prevail on the planet for billions of years, permitting the next [[Sociocultural evolution|civilization to evolve]]. Thus, several civilizations may come and go during the lifespan of one and the same planet. Thus, if {{math|''n''<sub>r</sub>}} 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 {{math|1 + ''n''<sub>r</sub>}}, 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]], then {{math|''n''<sub>r</sub>}} may be relatively high. On the other hand, if it is generally by permanent uninhabitability, such as [[stellar evolution]], then {{math|''n''<sub>r</sub>}} may be almost zero. In the case of total life extinction, a similar factor may be applicable for {{math|''f''<sub>l</sub>}}, that is, ''how many times'' life may appear on a planet where it has appeared once.
+:The factor depends on what generally is the cause of [[civilization extinction]]. If it is generally by temporary uninhabitability, for example a [[nuclear winter]], then ''n''<sub>r</sub> may be relatively high. On the other hand, if it is generally by permanent uninhabitability, such as [[stellar evolution]], then {{math|''n''<sub>r</sub>}} may be almost zero. In the case of total life extinction, a similar factor may be applicable for {{math|''f''<sub>l</sub>}}, that is, ''how many times'' life may appear on a planet where it has appeared once.
 ;METI factor : [[Aleksandr Leonidovich Zaitsev|Alexander Zaitsev]] said that to be in a communicative phase and emit dedicated messages are not the same. For example, humans, although being in a communicative phase, are not a communicative civilization; we do not practise such activities as the purposeful and regular transmission of interstellar messages. For this reason, he suggested introducing the METI factor (messaging to extraterrestrial intelligence) to the classical Drake equation.<ref>
@@ Line 538: / Line 539: @@
 :where:
-::{{math|''N''}} = the number of planets with detectable signs of life
+::''N'' = the number of planets with detectable signs of life
-::{{math|''N''<sub>∗</sub>}} = the number of stars observed
+::''N''<sub>∗</sub> = the number of stars observed
-::{{math|''F''<sub>Q</sub>}} = the fraction of stars that are quiet
+::''F''<sub>Q</sub>= the fraction of stars that are quiet
-::{{math|''F''<sub>HZ</sub>}} = the fraction of stars with rocky planets in the habitable zone
+::''F''<sub>HZ</sub> = the fraction of stars with rocky planets in the habitable zone
-::{{math|''F''<sub>O</sub>}} = the fraction of those planets that can be observed
+::''F''<sub>O</sub>= the fraction of those planets that can be observed
-::{{math|''F''<sub>L</sub>}} = the fraction that have life
+::''F''<sub>L</sub> = the fraction that have life
-::{{math|''F''<sub>S</sub>}} = the fraction on which life produces a detectable signature gas
+::''F''<sub>S</sub> = the fraction on which life produces a detectable signature gas
 :Seager stresses, “We’re not throwing out the Drake Equation, which is really a different topic,” explaining, “Since Drake came up with the equation, we have discovered thousands of exoplanets. We as a community have had our views revolutionized as to what could possibly be out there. And now we have a real question on our hands, one that's not related to intelligent life: Can we detect any signs of life in any way in the very near future?”<ref>{{cite web|url=http://io9.com/what-a-brand-new-equation-reveals-about-our-odds-of-fin-531575395|title=A New Equation Reveals Our Exact Odds of Finding Alien Life|publisher=[[io9]]}}</ref>
@@ Line 630: / Line 631: @@
 ==In fiction and popular culture==
 The equation was cited by [[Gene Roddenberry]] as supporting the multiplicity of inhabited planets shown on ''[[Star Trek]]'', the television series he created. However, Roddenberry did not have the equation with him, and he was forced to "invent" it for his original proposal.<ref>''The Making of Star Trek'' by Stephen E. Whitfield and Gene Roddenberry, New York: Ballantine Books, 1968</ref> The invented equation created by Roddenberry is:
-::<math>Ff^2 (MgE)-C^1 Ri^1 \cdot M=L/So </math>
+::
+[[File:F_f_2.png|thumb|Ff^2 (MgE)-C^1 Ri^1 \cdot M=L/So ]]
 However, a number raised to the first power is merely the number itself.
@@ Line 638: / Line 640: @@
 ==See also==
-* {{annotated link|Astrobiology}}
+*https://www.space.com/22648-drake-equation-alien-life-seager.html
-* {{annotated link|Fermi paradox}}
-* {{annotated link|Goldilocks principle}}
-* {{annotated link|Kardashev scale}}
-* {{annotated link|Planetary habitability}}
-* {{annotated link|Ufology}}
-* {{annotated link|Lincoln index}}
 * ''[[The Search for Life: The Drake Equation]]'', BBC documentary

Drake equation: Difference between revisions

Latest revision as of 16:12, 26 October 2024

Contents

Equation

History

Usefulness

Estimates

Original estimates

Current estimates

Rate of star creation in our Galaxy, R_∗

Fraction of those stars that have planets, f_p

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

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

Fraction of the above that develops intelligent life, f_i

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

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

Probabilistic combination of results

Range of results

Have other technological species ever existed?

Modifications

Criticism

Fermi paradox

In fiction and popular culture

See also

Notes

References

References

Further reading

External links

Navigation menu

Drake equation: Difference between revisions

Latest revision as of 16:12, 26 October 2024

Equation

History

Usefulness

Estimates

Original estimates

Current estimates

Rate of star creation in our Galaxy, R∗

Fraction of those stars that have planets, fp

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

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

Fraction of the above that develops intelligent life, fi

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

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

Probabilistic combination of results

Range of results

Have other technological species ever existed?

Modifications

Criticism

Fermi paradox

In fiction and popular culture

See also

Notes

References

References

Further reading

External links

Navigation menu

Search

Rate of star creation in our Galaxy, R_∗

Fraction of those stars that have planets, f_p

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

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

Fraction of the above that develops intelligent life, f_i

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