The equation was formulated in 1961 byFrank Drake, not for purposes of quantifying the number of civilizations, but as a way to stimulate scientific dialogue at the first scientific meeting on thesearch for extraterrestrial intelligence (SETI).[4][5] The equation summarizes the main concepts which scientists must contemplate when considering the question of other radio-communicative life.[4] 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.
Completed 300 Foot Telescope. Frank Drake is the second from left.
In September 1959, physicistsGiuseppe Cocconi andPhilip Morrison published an article in the journalNature with the provocative title "Searching for Interstellar Communications".[10][11] Cocconi and Morrison argued thatradio 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 awavelength of 21 cm (1,420.4 MHz). This is the wavelength of radio emission by neutralhydrogen, the most common element in the universe, and they reasoned that other intelligences might see this as a logical landmark in theradio spectrum.
Two months later, Harvard University astronomy professorHarlow 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."[12]
Seven months after Cocconi and Morrison published their article, Drake begansearching for extraterrestrial intelligence in an experiment calledProject Ozma. It was the first systematic search for signals from communicative extraterrestrial civilizations. Using the 85 ft (26 m) dish of theNational Radio Astronomy Observatory, Green Bank inGreen Bank, West Virginia, Drake monitored two nearby Sun-like stars:Epsilon Eridani andTau Ceti, slowly scanning frequencies close to the 21 cm wavelength for six hours per day from April to July 1960.[11] The project was well designed, inexpensive, and simple by today's standards. It detected no signals.
Soon thereafter, Drake hosted the first search for extraterrestrial intelligence conference 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.[13]
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, chemistMelvin Calvin, astronomerSu-Shu Huang, neuroscientistJohn C. Lilly, inventorBarney Oliver, astronomerCarl Sagan, and radio-astronomerOtto Struve.[14] These participants called themselves "The Order of the Dolphin" (because of Lilly's work ondolphin communication), and commemorated their first meeting with a plaque at the observatory hall.[15][16]
The Drake equation results in a summary of the factors affecting the likelihood that we might detect radio-communication from intelligent extraterrestrial life.[2][6][17] The last three parameters,fi,fc, andL, 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,[2][4] and gives the question of life elsewhere a basis forscientific analysis. The equation has helped draw attention to some particular scientific problems related to life in the universe, for exampleabiogenesis, the development ofmulti-cellular life, and the development ofintelligence itself.[18]
Within the limits of existing human 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.[2] It also formed the backbone ofastrobiology as a science; although speculation is entertained to give context, astrobiology concerns itself primarily withhypotheses that fit firmly into existingscientific 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. SETI efforts since 1961 have conclusively ruled out widespread alien emissions near the 21 cm wavelength of thehydrogen frequency.[19]
There is considerable disagreement on the values of these parameters, but the 'educated guesses' used by Drake and his colleagues in 1961 were:[1][20][21]
R∗ = 1 yr−1 (1 star formed per year, on the average over the life of the galaxy; this was regarded as conservative)
fp = 0.2 to 0.5 (one fifth to one half of all stars formed will have planets)
ne = 1 to 5 (stars with planets will have between 1 and 5 planets capable of developing life)
fl = 1 (100% of these planets will develop life)
fi = 1 (100% of which will develop intelligent life)
fc = 0.1 to 0.2 (10–20% of which will be able to communicate)
L = 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 thatN ≈L, and there were probably between 1000 and 100,000,000 planets with civilizations in theMilky Way Galaxy.
Calculations in 2010, fromNASA and theEuropean Space Agency indicate that the rate of star formation in this Galaxy is about 0.68–1.45 M☉ of material per year.[22][23] To get the number of stars per year, we divide this by theinitial mass function (IMF) for stars, where the average new star's mass is about 0.5 M☉.[24] This gives a star formation rate of about 1.5–3 stars per year.
Analysis ofmicrolensing surveys, in 2012, has found thatfp 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.[25][26]
Average number of planets that might support life per star that has planets,ne
The consensus at the Green Bank meeting was thatne had a minimum value between 3 and 5. Dutch science journalistGovert Schilling has opined that this is optimistic.[30] Even if planets are in thehabitable zone, the number of planets with the right proportion of elements is difficult to estimate.[31] Brad Gibson, Yeshe Fenner, andCharley Lineweaver determined that about 10% ofstar systems in the Milky Way Galaxy are hospitable to life, by having heavy elements, being far fromsupernovae and being stable for a sufficient time.[32]
The discovery of numerousgas giants in close orbit with their stars has introduced doubt that life-supporting planets commonly survive the formation of their stellar systems. So-calledhot Jupiters may migrate from distant orbits to near orbits, in the process disrupting the orbits of habitable planets.
On the other hand, the variety ofstar 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 tored dwarf starsmight have habitable zones,[33] although the flaring behavior of these stars might speak against this.[34] The possibility of life onmoons of gas giants (such asJupiter's moonEuropa, orSaturn's moonsTitan andEnceladus) adds further uncertainty to this figure.[35]
The authors of therare 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 ahot Jupiter; and a planet withplate tectonics, a large moon that creates tidal pools, and moderateaxial tilt to generate seasonal variation.[36]
Fraction of the above that actually go on to develop life,fl
Geological evidence from the Earth suggests thatfl may be high; life on Earth appears to have begun around the same time as favorable conditions arose, suggesting thatabiogenesis may be relatively common once conditions are right. However, this evidence only looks at the Earth (a single model planet), and containsanthropic bias, as the planet of study was not chosen randomly, but by the living organisms that already inhabit it (ourselves). From a classicalhypothesis testing standpoint, without assuming that the underlying distribution offl is the same for all planets in the Milky Way, there are zerodegrees of freedom, permitting no valid estimates to be made. If life (or evidence of past life) were to be found onMars,Europa,Enceladus orTitan that developed independently from life on Earth it would imply a value forfl 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 forbacteria that are unrelated to other life on Earth, but none have been found yet.[37] 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. BiochemistsFrancis Crick andLeslie 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."[38] As an alternative to abiogenesis on Earth, they proposed the hypothesis ofdirected 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 theUniversity of Nottingham proposed an "Astrobiological Copernican" principle, based on thePrinciple 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,fl,fi, andfc 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).[39][40]
Fraction of the above that develops intelligent life,fi
This value remains particularly controversial. Those who favor a low value, such as the biologistErnst 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 forfi.[41] Likewise, the Rare Earth hypothesis, notwithstanding their low value forne above, also think a low value forfi dominates the analysis.[42] Those who favor higher values note the generally increasing complexity of life over time, concluding that the appearance of intelligence is almost inevitable,[43][44] implying anfi approaching 1. Skeptics point out that the large spread of values in this factor and others make all estimates unreliable. (SeeCriticism).
In addition, while it appears that life developed soon after the formation of Earth, theCambrian 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 thesnowball Earth or research intoextinction events have raised the possibility that life on Earth is relatively fragile. Research on any pastlife on Mars is relevant since a discovery that life did form on Mars but ceased to exist might raise the estimate offl but would indicate that in half the known cases, intelligent life did not develop.
Estimates offi 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 fromnovae). Also, Earth's large moon may aid the evolution of life bystabilizing the planet's axis of rotation.
There has been quantitative work to begin to define. 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.[45][46]
Planetary scientistPascal Lee of theSETI 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 sinceHomo erectus evolved, compared to 4.6 billion years since Earth formed).[47][48]
Fraction of the above revealing their existence via signal release into space,fc
For deliberate communication, the one example we have (the Earth) does not do much explicit communication, though there aresome efforts covering only a tiny fraction of the stars that might look for human presence. (SeeArecibo message, for example). There isconsiderable speculation[broken anchor] 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 present day humans.[49] 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.[50]
Lifetime of such a civilization wherein it communicates its signals into space,L
Michael Shermer estimatedL as 420 years, based on the duration of sixty historical Earthly civilizations.[51] 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, includingreappearance number, this lack of specificity in defining single civilizations does not matter for the result, since such a civilization turnover could be described as an increase in thereappearance number rather than increase inL, 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 forL 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.[52] He proposes that the last factorL be replaced withfIC ·T, wherefIC is the fraction of communicating civilizations that become "immortal" (in the sense that they simply do not die out), andT representing the length of time during which this process has been going on. This has the advantage thatT 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.[53]
The astronomerCarl 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 ofnuclear warfare. PaleobiologistOlev Vinn suggests that the lifetime of most technological civilizations is brief due to inherited behavior patterns present in all intelligent organisms. These behaviors, incompatible with civilized conditions, inevitably lead to self-destruction soon after the emergence of advanced technologies.[54]
As many skeptics have pointed out, the Drake equation can give a very wide range of values, depending on the assumptions,[56] as the values used in portions of the Drake equation are not well established.[30][57][58][59] In particular, the result can beN ≪ 1, meaning we are likely alone in the galaxy, orN ≫ 1, implying there are many civilizations we might contact. One of the few points of wide agreement is that the presence of humanity demonstrates that the probability of intelligence arising is greater than zero.[60]
As an example of a low estimate, combining NASA's star formation rates, therare Earth hypothesis value offp ·ne ·fl = 10−5,[61] Mayr's view on intelligence arising, Drake's view of communication, and Shermer's estimate of lifetime:
i.e., suggesting that we are probably alone in this galaxy, and possibly in theobservable universe.
On the other hand, with larger values for each of the parameters above, values ofN can be derived that are greater than 1. The following higher values that have been proposed for each of the parameters:
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.[65]
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 theonly technological species that hasever arisen, for two cases: (a) this 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 planetever 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 than2.5×10−24. Similarly, for Earth to have been the only case of hosting a technological species over the history of this Galaxy, the odds of a habitable zone planet ever hosting a technological species must be less than1.7×10−11 (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 this 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 this Galaxy.[66][67][68][69][70]
As many observers have pointed out, the Drake equation is a very simple model that omits potentially relevant parameters,[71] and many 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.[72]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.[73] This result differs insignificantly from the estimate of unity given both by Drake and the Cyclops report.
Others note that the Drake equation ignores many concepts that might be relevant to the odds of contacting other civilizations. For example,Glen 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".[74] 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
Brin proposed to generalize the Drake equation to include additional effects of alien civilizations colonizing otherstar systems. Each original site expands with an expansion velocityv, and establishes additional sites that survive for a lifetimeL. The result is a more complex set of 3 equations.[74]
Reappearance factor
The Drake equation may furthermore be multiplied byhow 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, life may still prevail on the planet for billions of years, permitting the nextcivilization to evolve. Thus, several civilizations may come and go during the lifespan of one and the same planet. Thus, ifnr 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 be1 +nr, which is the actualreappearance factor added to the equation.[75]
METI factor
Alexander Zaitsev said that to be in a communicative phase and emit dedicated messages are not the same. For example, humans are in a communicative phase, but are not a communicative civilization; there are no 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. He defined the factor as "fm = The fraction of communicative civilizations with clear and non-paranoid planetary consciousness (that is, those which actually engage in deliberate interstellar transmission)".[76]
Biogenic gases
AstronomerSara Seager proposed a revised equation that focuses on the search for planets with biosignature gases.[77] These gases are produced by living organisms that can accumulate in a planet atmosphere to levels that can be detected with remote space telescopes.[78][79]
N = the number of planets with detectable signs of life
N∗ = the number of stars observed
FQ = the fraction of stars that are quiet
FHZ = the fraction of stars with rocky planets in the habitable zone
FO = the fraction of those planets that can be observed
FL = the fraction that have life
FS = the fraction on which life produces a detectable signature gas
Carl Sagan's version of the Drake equation
American astronomerCarl Sagan made some modifications[80] in the Drake equation and presented it in the 1980 programCosmos: A Personal Voyage. The modified equation is:[81]
where:
N = the number ofcivilizations in the Milky Way galaxy with which communication might be possible (i.e. which are on the current pastlight cone);
Criticism of the Drake equation is varied. Firstly, many of the terms in the equation are largely or entirely based on conjecture.[82][83] 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 the present day 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.[84][85]
Others point out that the equation was formulated before our understanding of the universe had matured. Astrophysicist Ethan Siegel, said:
The Drake equation, when it was put forth, made an assumption about the Universe that we now know is untrue: It assumed that the Universe was eternal and static in time. As we learned only a few years after Frank Drake first proposed his equation, the Universe doesn’t exist in a steady state, where it’s unchanging in time, but rather has evolved from a hot, dense, energetic, and rapidly expanding state: a hot Big Bang that occurred over a finite duration in our cosmic past.[86]
One reply to such criticisms[87] 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.[88]
A civilization lasting for tens of millions of years could be able to spread throughout the galaxy, even at the slow speeds foreseeable with present-day technology. However, no confirmed signs of civilizations or intelligent life elsewhere have been found, either in this Galaxy or in theobservable universe of 2 trillion galaxies.[89][90] According to this line of thinking, the tendency to fill (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?".[91][92]
A large number of explanations have been proposed to explain this lack of contact; a book published in 2015 elaborated on 75 different explanations.[93] 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,R∗ ·fp ·ne ·fl ·fi, has a low value. The most common suspect isfi, but explanations such as the rare Earth hypothesis argue thatne is the small term.
Intelligent civilizations exist, but we see no evidence, meaningfc 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 ofL 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 theGreat Filter hypothesis,[94] 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 byAnders Sandberg,Eric Drexler andToby Ord suggests "a substantialex ante (predicted) probability of there being no other intelligent life in our observable universe".[95]
The equation was cited byGene Roddenberry as supporting the multiplicity of inhabited planets shown onStar 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.[96] The invented equation created by Roddenberry is:
Regarding Roddenberry's fictional version of the equation, Drake himself commented that a number raised to the first power is just the number itself.[97]
A commemorative plate on NASA'sEuropa Clipper mission, which launched October 14, 2024, features a poem by the U.S. Poet LaureateAda Limón, waveforms of the word 'water' in 103 languages, a schematic of thewater hole, the Drake equation, and a portrait of planetary scientistRon Greeley on it.[98]
^abcPhysics Today 14 (4), 40–46 (1961).Drake, F. D. (April 1961)."Project Ozma".Physics Today.14 (4). American Institute of Physics:40–46.Bibcode:1961PhT....14d..40D.doi:10.1063/1.3057500. Retrieved27 April 2023.The question of the existence of intelligent life elsewhere in space has long fascinated people, but, until recently, has been properly left to the science‐fiction writers.
^abWard, Peter D.; Brownlee, Donald (2000).Rare Earth: Why Complex Life is Uncommon in the Universe. Copernicus Books (Springer Verlag).ISBN0-387-98701-0.
^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."
^"The value ofN 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." fromWilson, TL (2001). "The search for extraterrestrial intelligence".Nature.409 (6823). Nature Publishing Group:1110–1114.Bibcode:2001Natur.409.1110W.doi:10.1038/35059235.PMID11234025.S2CID205014501., or more informally, "The Drake Equation can have any value from "billions and billions" to zero", Michael Crichton, as quoted inDouglas A. Vakoch; et al. (2015).The Drake Equation: Estimating the prevalence of extraterrestrial life through the ages. Cambridge University Press.ISBN978-1-10-707365-4., p. 13
^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 thepotential for developing advanced life. (We expect that a much higher number will have microbial life.)"
