Scholar: Frank Drake’s Equation For Alien Intelligence Is More Important Than Ever

By | 08/09/2022

Probabilistic statement to approximate the number of alien civilizations in the milky way

The
Drake equation
is a probabilistic argument used to estimate the number of active, communicative extraterrestrial civilizations in the Milky way Galaxy.[ane]
[two]

The equation was formulated in 1961 past Frank Drake, non for purposes of quantifying the number of civilizations, only as a way to stimulate scientific dialogue at the first scientific meeting on the search for extraterrestrial intelligence (SETI).[three]
[4]
The equation summarizes the master 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 equally 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 result being that the uncertainty associated with whatever derived value is so large that the equation cannot exist used to draw firm conclusions.

Equation

[edit]

The Drake equation is:





Northward
=

R










f


p







due north


e







f


l







f


i







f


c






L


{\displaystyle Due north=R_{*}\cdot f_{\mathrm {p} }\cdot n_{\mathrm {e} }\cdot f_{\mathrm {l} }\cdot f_{\mathrm {i} }\cdot f_{\mathrm {c} }\cdot L}



where


North

= the number of civilizations in our galaxy with which advice might be possible (i.e. which are on our current past low-cal cone);

and


R


= the average rate of star germination in our Galaxy

f
p

= the fraction of those stars that take planets

north
e

= the boilerplate 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 indicate

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 engineering that releases detectable signs of their existence into infinite

L

= the length of time for which such civilizations release detectable signals into space[5]
[6]

History

[edit]

In September 1959, physicists Giuseppe Cocconi and Philip Morrison published an article in the journal
Nature
with the provocative title “Searching for Interstellar Communications”.[seven]
[8]
Cocconi and Morrison argued that radio telescopes had become sensitive enough to selection up transmissions that might exist broadcast into space by civilizations orbiting other stars. Such messages, they suggested, might be transmitted at a wavelength of 21 cm (ane,420.4 MHz). This is the wavelength of radio emission past 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.

2 months later, Harvard Academy astronomy professor Harlow Shapley speculated on the number of inhabited planets in the universe, saying “The universe has ten million, million, 1000000 suns (10 followed by 18 zeros) similar to our ain. One in a million has planets around information technology. Only one in a million million has the right combination of chemicals, temperature, water, days and nights to back up planetary life equally nosotros know it. This calculation arrives at the estimated figure of 100 meg worlds where life has been forged past evolution.”[9]

Seven months after Cocconi and Morrison published their article, Drake fabricated the beginning systematic search for signals from communicative extraterrestrial civilizations. Using the 85 ft (26 g) dish of the National Radio Astronomy Observatory, Green Bank in Green Depository financial institution, West Virginia, Drake monitored 2 nearby Sunday-like stars: Epsilon Eridani and Tau Ceti. In this projection, which he chosen Project Ozma, he slowly scanned frequencies close to the 21 cm wavelength for six hours per day from April to July 1960.[8]
The project was well designed, inexpensive, and simple by today’due south standards. It detected no signals.

Soon thereafter, Drake hosted a “search for extraterrestrial intelligence” coming together on detecting their radio signals. The coming together was held at the Green Bank facility in 1961. The equation that bears Drake’southward proper name arose out of his preparations for the meeting.[10]

Equally I planned the meeting, I realized a few day[s] ahead of time we needed an calendar. And so I wrote down all the things you needed to know to predict how difficult it’s going to be to discover extraterrestrial life. And looking at them it became pretty axiomatic 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 non to search for primordial or primitive life forms.

—Frank Drake

The ten attendees were briefing 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.[11]
These participants dubbed themselves “The Order of the Dolphin” (because of Lilly’south work on dolphin communication), and commemorated their first meeting with a plaque at the observatory hall.[12]
[13]

Usefulness

[edit]

The Drake equation amounts to a summary of the factors affecting the likelihood that we might detect radio-communication from intelligent extraterrestrial life.[1]
[five]
[14]
The last three parameters,

f
i
,

f
c
, and
L, are not known and are very difficult to gauge, with values ranging over many orders of magnitude (see criticism). Therefore, the usefulness of the Drake equation is non in the solving, just rather in the contemplation of all the diverse concepts which scientists must contain when considering the question of life elsewhere,[ane]
[iii]
and gives the question of life elsewhere a ground for scientific assay. The equation has helped draw attention to some item scientific problems related to life in the universe, for case abiogenesis, the development of multi-cellular life, and the evolution of intelligence itself.[xv]

Inside the limits of our existing applied science, any applied search for distant intelligent life must necessarily be a search for some manifestation of a afar technology. After about l years, the Drake equation is still of seminal importance considering information technology is a ‘road map’ of what we need to learn in order to solve this central existential question.[1]
It also formed the courage of astrobiology every bit 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, fifty-fifty though radio telescopes, receiver techniques, and computational abilities have improved significantly since the early 1960s. Information technology 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.[16]

Estimates

[edit]

Original estimates

[edit]

There is considerable disagreement on the values of these parameters, simply the ‘educated guesses’ used by Drake and his colleagues in 1961 were:[17]
[18]


  • R


    = 1 yr−1
    (i star formed per yr, on the average over the life of the galaxy; this was regarded equally conservative)

  • f
    p

    = 0.2 to 0.5 (ane fifth to one half of all stars formed volition accept planets)

  • n
    e

    = 1 to five (stars with planets volition take between ane and 5 planets capable of developing life)

  • f
    l

    = 1 (100% of these planets volition develop life)

  • f
    i

    = ane (100% of which volition develop intelligent life)

  • f
    c

    = 0.1 to 0.2 (10–20% of which will be able to communicate)

  • 50

    = 1000 to 100,000,000 chatty civilizations (which volition terminal somewhere betwixt 1000 and 100,000,000 years)

Inserting the above minimum numbers into the equation gives a minimum N of xx (run across: Range of results). Inserting the maximum numbers gives a maximum of l,000,000. Drake states that given the uncertainties, the original meeting concluded that

North

Fifty
, and there were probably between thou and 100,000,000 planets with civilizations in the Milky Mode Galaxy.

Current estimates

[edit]

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


Charge per unit of star creation in our Galaxy,

R




[edit]

Calculations in 2010, from NASA and the European Infinite Agency betoken that the charge per unit of star germination in our Milky way is about 0.68–1.45K

of material per twelvemonth.[19]
[20]
To get the number of stars per twelvemonth, nosotros divide this by the initial mass function (International monetary fund) for stars, where the average new star’s mass is about 0.fiveM
.[21]
This gives a star formation rate of about i.5–3 stars per year.


Fraction of those stars that have planets,

f
p



[edit]

Assay of microlensing surveys, in 2012, has found that

f
p

may approach 1—that is, stars are orbited past planets as a dominion, rather than the exception; and that there are 1 or more bound planets per Galaxy star.[22]
[23]


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

n
e



[edit]

In November 2013, astronomers reported, based on
Kepler
space mission information, that there could be as many as xl billion Earth-sized planets orbiting in the habitable zones of lord’s day-like stars and red dwarf stars within the Milky Way Milky way.[24]
[25]
eleven billion of these estimated planets may be orbiting sun-like stars.[26]
Since there are about 100 billion stars in the milky way, this implies

f
p
·
due north
e

is roughly 0.4. The nearest planet in the habitable zone is Proxima Centauri b, which is as shut as about 4.two light-years away.

The consensus at the Dark-green Depository financial institution coming together was that

north
east

had a minimum value between 3 and 5. Dutch science announcer Govert Schilling has opined that this is optimistic.[27]
Even if planets are in the habitable zone, the number of planets with the right proportion of elements is hard to approximate.[28]
Brad Gibson, Yeshe Fenner, and Charley Lineweaver determined that about x% of star systems in the Milky way Milky way are hospitable to life, past having heavy elements, being far from supernovae and being stable for a sufficient time.[29]

The discovery of numerous gas giants in close orbit with their stars has introduced doubt that life-supporting planets usually survive the formation of their stellar systems. Then-chosen 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 accept habitable zones is not merely limited to solar-type stars and Earth-sized planets. It is now estimated that even tidally locked planets close to red dwarf stars might take habitable zones,[thirty]
although the flaring behavior of these stars might speak confronting this.[31]
The possibility of life on moons of gas giants (such as Jupiter’due south moon Europa, or Saturn’due south moons Titan and Enceladus) adds further uncertainty to this effigy.[32]

The authors of the rare Earth hypothesis propose a number of additional constraints on habitability for planets, including existence in galactic zones with suitably low radiation, high star metallicity, and depression enough density to avoid excessive asteroid bombardment. They also propose that it is necessary to take 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.[33]


Fraction of the above that actually keep to develop life,

f
l



[edit]

Geological evidence from the Globe suggests that

f
l

may exist high; life on Earth appears to have begun around the aforementioned time as favorable atmospheric condition arose, suggesting that abiogenesis may be relatively mutual in one case weather are right. All the same, this evidence simply looks at the Earth (a single model planet), and contains anthropic bias, as the planet of study was non chosen randomly, just by the living organisms that already inhabit information technology (ourselves). From a classical hypothesis testing standpoint, without assuming that the underlying distribution of

f
50

is the aforementioned for all planets in the Galaxy, there are zero degrees of freedom, permitting no valid estimates to be made. If life (or evidence of by life) were to be institute on Mars, Europa, Enceladus or Titan that adult independently from life on Earth it would imply a value for

f
l

shut to ane. While this would raise the number of degrees of freedom from zero to ane, there would remain a swell deal of dubiousness on whatsoever approximate due to the small sample size, and the run a risk they are not really contained.

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 mutual origin. If abiogenesis were more than common information technology would be speculated to accept occurred more than than one time on the Earth. Scientists accept searched for this by looking for leaner that are unrelated to other life on Earth, but none have been found even so.[34]
It is too possible that life arose more than in one case, 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 nosotros have no means at all of knowing” whether we are “likely to be alone in the milky way (Universe)” or whether “the galaxy may be pullulating with life of many dissimilar forms.”[35]
As an culling to abiogenesis on World, they proposed the hypothesis of directed panspermia, which states that Earth life began with “microorganisms sent here deliberately by a technological club on another planet, by ways of a special long-range unmanned spaceship”.

In 2020, a paper past scholars at the Academy of Nottingham proposed an “Astrobiological Copernican” principle, based on the Principle of Mediocrity, and speculated that “intelligent life would class on other [Earth-similar] planets similar it has on Globe, so within a few billion years life would automatically grade equally a natural part of evolution”. In the authors’ framework,

f
l
,

f
i
, and

f
c

are all set to a probability of 1 (certainty). Their resultant calculation concludes at that place are more thirty current technological civilizations in the galaxy (disregarding error bars).[36]
[37]


Fraction of the in a higher place that develops intelligent life,

f
i



[edit]

This value remains particularly controversial. Those who favor a low value, such as the biologist Ernst Mayr, bespeak out that of the billions of species that accept existed on Earth, only one has become intelligent and from this, infer a tiny value for

f
i
.[38]
Also, the Rare Globe hypothesis, notwithstanding their depression value for

n
eastward

higher up, also recall a low value for

f
i

dominates the analysis.[39]
Those who favor higher values note the mostly increasing complexity of life over time, final that the appearance of intelligence is almost inevitable,[40]
[41]
implying an

f
i

approaching 1. Skeptics betoken out that the large spread of values in this factor and others make all estimates unreliable. (See Criticism).

In improver, while information technology appears that life developed soon after the formation of Globe, the Cambrian explosion, in which a large multifariousness of multicellular life forms came into existence, occurred a considerable amount of time later on the formation of World, which suggests the possibility that special conditions were necessary. Some scenarios such as the snowball Earth or inquiry into extinction events take raised the possibility that life on Earth is relatively fragile. Enquiry on any by life on Mars is relevant since a discovery that life did class on Mars but ceased to exist might heighten our estimate of

f
fifty

but would bespeak that in half the known cases, intelligent life did not develop.

Estimates of

f
i

take been afflicted by discoveries that the Solar System’s orbit is circular in the galaxy, at such a distance that it remains out of the screw artillery for tens of millions of years (evading radiation from novae). Too, Earth’southward large moon may aid the evolution of life by stabilizing the planet’s axis of rotation.

There has been quantitative piece of work to begin to ascertain





f


50







f


i





{\displaystyle f_{\mathrm {50} }\cdot f_{\mathrm {i} }}




. One example is a Bayesian analysis published in 2020. In the decision, the author cautions that this study applies to Globe’s conditions. In Bayesian terms, the written report favors the formation of intelligence on a planet with identical weather to Earth merely does not practise so with high conviction.[42]
[43]

Planetary scientist Pascal Lee of the SETI Institute proposes that this fraction is very depression (0.0002). He based this estimate on how long it took World to develop intelligent life (i million years since Homo erectus evolved, compared to 4.vi billion years since Earth formed).[44]
[45]


Fraction of the in a higher place revealing their beingness via signal release into infinite,

f
c



[edit]

For deliberate communication, the one example nosotros have (the Earth) does not exercise much explicit advice, though there are some efforts covering only a tiny fraction of the stars that might look for our presence. (Encounter Arecibo bulletin, for example). There is considerable speculation why an extraterrestrial civilization might exist simply choose non to communicate. Withal, deliberate communication is not required, and calculations bespeak that electric current or near-future Earth-level technology might well be detectable to civilizations not too much more avant-garde than our ain.[46]
Past this standard, the Earth is a communicating civilization.

Another question is what percent of civilizations in the milky way are close enough for usa to detect, bold that they send out signals. For instance, existing Earth radio telescopes could only detect Globe radio transmissions from roughly a light twelvemonth away.[47]


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

Fifty



[edit]

Michael Shermer estimated

50

as 420 years, based on the duration of sixty historical Earthly civilizations.[48]
Using 28 civilizations more contempo than the Roman Empire, he calculates a effigy of 304 years for “modernistic” civilizations. It could also be argued from Michael Shermer’s results that the autumn of most of these civilizations was followed by subsequently civilizations that carried on the technologies, and then 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 thing for the terminate issue, since such a civilization turnover could be described as an increment in the
reappearance number
rather than increase in

L
, stating that a culture reappears in the course of the succeeding cultures. Furthermore, since none could communicate over interstellar space, the method of comparing with historical civilizations could exist regarded equally invalid.

David Grinspoon has argued that once a civilization has developed plenty, it might overcome all threats to its survival. It will so last for an indefinite flow of fourth dimension, making the value for

50

potentially billions of years. If this is the case, then he proposes that the Milky Way Galaxy may accept been steadily accumulating avant-garde civilizations since it formed.[49]
He proposes that the final factor

L

be replaced with

f
IC
·
T
, where

f
IC

is the fraction of communicating civilizations that get “immortal” (in the sense that they simply do not die out), and

T

representing the length of time during which this procedure has been going on. This has the reward that

T

would be a relatively easy-to-detect number, as it would simply be some fraction of the historic period of the universe.

It has also been hypothesized that once a civilization has learned of a more than advanced one, its longevity could increase because it can learn from the experiences of the other.[50]

The astronomer Carl Sagan speculated that all of the terms, except for the lifetime of a culture, are relatively high and the determining factor in whether there are large or small numbers of civilizations in the universe is the culture lifetime, or in other words, the ability of technological civilizations to avoid self-destruction. In Sagan’southward case, the Drake equation was a strong motivating cistron for his interest in ecology bug and his efforts to warn against the dangers of nuclear warfare.

An intelligent culture might not be organic, as some have suggested that artificial general intelligence may supervene upon humanity.[51]

Range of results

[edit]

As many skeptics accept pointed out, the Drake equation can requite a very broad range of values, depending on the assumptions,[52]
equally the values used in portions of the Drake equation are not well established.[27]
[53]
[54]
[55]
In particular, the result can be

N
≪ 1
, meaning we are likely alone in the galaxy, or

N
≫ ane
, implying in that location are many civilizations we might contact. 1 of the few points of wide agreement is that the presence of humanity implies a probability of intelligence arising of greater than zero.[56]

As an case of a depression gauge, combining NASA’s star formation rates, the rare Earth hypothesis value of

f
p
·
n
e
·
f
l
= x−5
,[57]
Mayr’southward view on intelligence arising, Drake’s view of communication, and Shermer’due south estimate of lifetime:


R

= 1.v–3 year−1
,[19]

f
p
·
due north
e
·
f
l
= ten−5
,[33]

f
i
= 10−9
,[38]

f
c
= 0.2

[Drake, above], and

50
= 304

years[48]

gives:


North
= one.5 × 10−5
× 10−nine
× 0.2 × 304 = 9.1 × 10−13

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

On the other mitt, with larger values for each of the parameters in a higher place, values of

N

can be derived that are greater than 1. The following college values that have been proposed for each of the parameters:


R

= 1.v–3 yr−ane
,[19]

f
p
= 1
,[22]

due north
east
= 0.2
,[58]
[59]

f
l
= 0.13
,[lx]

f
i
= ane
,[40]

f
c
= 0.ii

[Drake, above], and

L
= x9

years[49]

Use of these parameters gives:


N
= 3 × i × 0.2 × 0.13 × 1 × 0.ii × 10nine
= fifteen,600,000

Monte Carlo simulations of estimates of the Drake equation factors based on a stellar and planetary model of the Galaxy accept resulted in the number of civilizations varying past a factor of 100.[61]


Take other technological species
ever
existed?


[edit]

In 2016, Adam Frank and Woodruff Sullivan modified the Drake equation to make up one’s mind just how unlikely the event of a technological species arising on a given habitable planet must be, to give the issue that Earth hosts the
only
technological species that has
always
arisen, for two cases: (a) our Milky way, and (b) the universe as a whole. By asking this unlike question, one removes the lifetime and simultaneous communication uncertainties. Since the numbers of habitable planets per star tin 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 merely technological species that has e’er occurred in the universe, they summate the probability of any given habitable planet always developing a technological species must exist less than

2.5×ten−24
. Similarly, for Globe to have been the only case of hosting a technological species over the history of our Milky way, the odds of a habitable zone planet ever hosting a technological species must be less than

one.7×10−11

(near i in 60 billion). The effigy for the universe implies that it is extremely unlikely that Earth hosts the simply technological species that has ever occurred. On the other hand, for our Galaxy ane must think that fewer than 1 in 60 billion habitable planets develop a technological species for at that place non to have been at least a second case of such a species over the past history of our Milky way.[62]
[63]
[64]
[65]

Modifications

[edit]

Every bit many observers have pointed out, the Drake equation is a very uncomplicated model that omits potentially relevant parameters,[66]
and many changes and modifications to the equation have been proposed. One line of modification, for example, attempts to business relationship for the uncertainty inherent in many of the terms.[67]
Combining the estimates of the original half-dozen factors by major researchers via a Monte Carlo procedure leads to a best value for the non-longevity factors of 0.85 1/years.[68]
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 instance, David Brin states: “The Drake equation merely speaks of the number of sites at which ETIs spontaneously arise. The equation says nothing directly virtually the contact cantankerous-department between an ETIS and contemporary human society”.[69]
Because it is the contact cross-department that is of interest to the SETI community, many additional factors and modifications of the Drake equation take 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
v, and establishes additional sites that survive for a lifetime
L. The consequence is a more complex set of iii equations.[69]
Reappearance factor
The Drake equation may furthermore be multiplied past
how many times
an intelligent civilization may occur on planets where it has happened once. Even if an intelligent civilisation reaches the end of its lifetime subsequently, for example, x,000 years, life may still prevail on the planet for billions of years, permitting the adjacent culture to evolve. Thus, several civilizations may come up and go during the lifespan of one and the same planet. Thus, if

n
r

is the average number of times a new culture reappears on the same planet where a previous civilization once has appeared and ended, then the full number of civilizations on such a planet would exist
ane +
northward
r
, which is the actual
reappearance factor
added to the equation.
The factor depends on what generally is the cause of culture extinction. If it is by and large by temporary uninhabitability, for example a nuclear winter, and so

northward
r

may be relatively high. On the other manus, if it is by and large by permanent uninhabitability, such equally stellar evolution, then

n
r

may be virtually zero. In the example of total life extinction, a like cistron may be applicable for

f
l
, that is,
how many times
life may appear on a planet where it has appeared one time.
METI factor
Alexander Zaitsev said that to be in a chatty stage and emit dedicated letters are not the aforementioned. For example, humans, although being in a chatty phase, are not a communicative civilisation; nosotros 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.[seventy]
He defined the factor every bit “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 manual of letters by a civilization is non required for them to receive a broadcast sent by some other that is seeking start contact. Information technology is simply required they have capable and compatible receiver systems operational; all the same, 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.[71]
These gases are produced by living organisms that can accumulate in a planet atmosphere to levels that tin can be detected with remote space telescopes.[72]
The Seager equation looks like this:[72]
[a]




N
=

N










F


Q







F


H
Z







F


O







F


50







F


South





{\displaystyle N=N_{*}\cdot F_{\mathrm {Q} }\cdot F_{\mathrm {HZ} }\cdot F_{\mathrm {O} }\cdot F_{\mathrm {L} }\cdot F_{\mathrm {S} }}

where:

Northward

= the number of planets with detectable signs of life

North


= 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 exist 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 upwards with the equation, we have discovered thousands of exoplanets. We equally a community accept had our views revolutionized equally to what could peradventure exist out in that location. And at present we have a existent question on our hands, one that’s not related to intelligent life: Tin can nosotros detect any signs of life in any way in the very nigh hereafter?”[73]

Criticism

[edit]

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 audio 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 civilisation, not physics. No statistical estimates are possible for some of the parameters, where merely i example is known. The net result is that the equation cannot be used to describe firm conclusions of whatsoever kind, and the resulting margin of error is huge, far across what some consider acceptable or meaningful.[74]
[75]

Ane reply to such criticisms[76]
is that even though the Drake equation currently involves speculation most unmeasured parameters, it was intended every bit a way to stimulate dialogue on these topics. Then the focus becomes how to proceed experimentally. Indeed, Drake originally formulated the equation just equally an agenda for word at the Green Banking concern conference.[77]

Fermi paradox

[edit]

A culture 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 engineering. However, no confirmed signs of civilizations or intelligent life elsewhere have been plant, either in our Milky way or in the observable universe of 2 trillion galaxies.[78]
[79]
According to this line of thinking, the tendency to make full upwards (or at to the lowest degree explore) all bachelor territory seems to be a universal trait of living things, so the World should have already been colonized, or at least visited, merely no evidence of this exists. Hence Fermi’southward question “Where is everybody?”.[80]
[81]

A large number of explanations have been proposed to explain this lack of contact; a volume published in 2015 elaborated on 75 different explanations.[82]
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

    ·
    f
    p
    ·
    due north
    e
    ·
    f
    50
    ·
    f
    i
    , has a low value. The most common suspect is

    f
    i
    , but explanations such as the rare Earth hypothesis debate that

    n
    e

    is the small term.
  • Intelligent civilizations exist, but we see no show, pregnant

    f
    c

    is pocket-sized. Typical arguments include that civilizations are too far apart, it is too expensive to spread throughout the milky way, civilizations circulate signals for merely a brief period of fourth dimension, advice is unsafe, and many others.
  • The lifetime of intelligent, communicative civilizations is brusque, meaning the value of
    50
    is small-scale. Drake suggested that a large number of extraterrestrial civilizations would course, and he further speculated that the lack of show of such civilizations may be because technological civilizations tend to disappear rather rapidly. Typical explanations include information technology 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 Slap-up Filter hypothesis,[83]
which states that since in that location are no observed extraterrestrial civilizations despite the vast number of stars, at least one step in the procedure must be acting as a filter to reduce the terminal 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 being must exist 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”.[84]

In fiction and popular culture

[edit]

The equation was cited past Gene Roddenberry as supporting the multiplicity of inhabited planets shown on
Star Trek, the tv set serial he created. Even so, Roddenberry did non take the equation with him, and he was forced to “invent” it for his original proposal.[85]
The invented equation created by Roddenberry is:





F

f

2


(
M
g
E
)




C

ane


R

i

ane





Grand
=
L

/

S
o


{\displaystyle Ff^{2}(MgE)-C^{1}Ri^{ane}\cdot Grand=L/Then}



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

See also

[edit]

  • Astrobiology – Science concerned with life in the universe
  • Goldilocks principle – Analogy for optimal atmospheric condition
  • Kardashev scale – Measure of the development of a civilization
  • Planetary habitability – Known extent to which a planet is suitable for life
  • Ufology – Study of UFOs
  • Lincoln index – Statistical measure
  • The Search for Life: The Drake Equation, BBC documentary

Notes

[edit]


  1. ^

    The rendering of the equation here is slightly modified for clarity of presentation from the rendering in the cited source.[72]

References

[edit]

  1. ^


    a




    b




    c




    d




    Burchell, M.J. (2006). “W(h)ither the Drake equation?”.
    International Journal of Astrobiology.
    5
    (3): 243–250. Bibcode:2006IJAsB…five..243B. doi:10.1017/S1473550406003107. S2CID 121060763.



  2. ^


    Glade, North.; Ballet, P.; Bastien, O. (2012). “A stochastic process approach of the drake equation parameters”.
    International Journal of Astrobiology.
    xi
    (2): 103–108. arXiv:1112.1506. Bibcode:2012IJAsB..11..103G. doi:x.1017/S1473550411000413. S2CID 119250730.


  3. ^


    a




    b




    c




    “Affiliate 3 – Philosophy: “Solving the Drake Equation”.
    Enquire Dr. SETI. SETI League. December 2002. Retrieved
    ten April
    2013
    .



  4. ^


    Drake, North. (30 June 2014). “How my Dad’due south Equation Sparked the Search for Extraterrestrial Intelligence”.
    National Geographic
    . Retrieved
    2 Oct
    2016
    .


  5. ^


    a




    b




    Aguirre, Fifty. (1 July 2008). “The Drake Equation”.
    Nova ScienceNow. PBS. Retrieved
    vii March
    2010
    .



  6. ^


    “What do we need to know almost to discover life in space?”. SETI Institute. Retrieved
    16 April
    2013
    .



  7. ^


    Cocconi, G.; Morisson, P. (1959). “Searching for Interstellar Communications”
    (PDF).
    Nature.
    184
    (4690): 844–846. Bibcode:1959Natur.184..844C. doi:10.1038/184844a0. S2CID 4220318. Retrieved
    10 April
    2013
    .


  8. ^


    a




    b




    Schilling, M.; MacRobert, A. 1000. (2013). “The Adventure of Finding Aliens”.
    Sky & Telescope. Archived from the original on 14 February 2013. Retrieved
    10 Apr
    2013
    .



  9. ^


    newspaper, staff (8 November 1959). “Life On Other Planets?”.
    Sydney Morning Herald
    . Retrieved
    2 October
    2015
    .



  10. ^


    “The Drake Equation Revisited: Part I”.
    Astrobiology Mag. 29 September 2003. Retrieved
    20 May
    2017
    .



  11. ^


    Zaun, H. (1 November 2011). “Es war wie eine 180-Grad-Wende von diesem peinlichen Geheimnis!” [It was like a 180 degree turn from this embarrassing secret].
    Telepolis
    (in High german). Retrieved
    13 August
    2013
    .



  12. ^


    “Drake Equation Plaque”. Retrieved
    thirteen Baronial
    2013
    .



  13. ^


    Darling, D. J. “Green Bank conference (1961)”.
    The Encyclopedia of Scientific discipline. Archived from the original on 18 May 2013. Retrieved
    thirteen August
    2013
    .



  14. ^


    Jones, D. S. (26 September 2001). “Beyond the Drake Equation”. Retrieved
    17 Apr
    2013
    .



  15. ^


    “The Search For Life : The Drake Equation 2010 – Part one”. BBC Four. 2010. Retrieved
    17 April
    2013
    .



  16. ^

    SETI: A celebration of the commencement 50 years. Keith Cooper.
    Astronomy At present. 2000

  17. ^


    Drake, F.; Sobel, D. (1992).
    Is Anyone Out In that location? The Scientific Search for Extraterrestrial Intelligence. Delta. pp. 55–62. ISBN0-385-31122-2.



  18. ^


    Glade, N.; Ballet, P.; Bastien, O. (2012). “A stochastic process approach of the drake equation parameters”.
    International Journal of Astrobiology.
    11
    (2): 103–108. arXiv:1112.1506. Bibcode:2012IJAsB..11..103G. doi:10.1017/S1473550411000413. S2CID 119250730.


    Note: This reference has a table of 1961 values, claimed to be taken from Drake & Sobel, just these differ from the book.
  19. ^


    a




    b




    c




    Robitaille, Thomas P.; Barbara A. Whitney (2010). “The present-mean solar day star formation rate of the Galaxy determined from Spitzer-detected immature stellar objects”.
    The Astrophysical Periodical Letters.
    710
    (i): L11. arXiv:1001.3672. Bibcode:2010ApJ…710L..11R. doi:ten.1088/2041-8205/710/1/L11. S2CID 118703635.



  20. ^


    Wanjek, C. (ii July 2015).
    The Drake Equation. Cambridge University Printing. ISBN9781107073654
    . Retrieved
    nine September
    2016
    .



  21. ^


    Kennicutt, Robert C.; Evans, Neal J. (22 September 2012). “Star Formation in the Galaxy and Nearby Galaxies”.
    Annual Review of Astronomy and Astrophysics.
    50
    (1): 531–608. arXiv:1204.3552. Bibcode:2012ARA&A..l..531K. doi:x.1146/annurev-astro-081811-125610. S2CID 118667387.


  22. ^


    a




    b




    Palmer, J. (11 January 2012). “Exoplanets are around every star, study suggests”. BBC. Retrieved
    12 January
    2012
    .



  23. ^


    Cassan, A.; et al. (11 January 2012). “1 or more jump planets per Galaxy star from microlensing observations”.
    Nature.
    481
    (7380): 167–169. arXiv:1202.0903. Bibcode:2012Natur.481..167C. doi:ten.1038/nature10684. PMID 22237108. S2CID 2614136.



  24. ^


    Overbye, Dennis (iv November 2013). “Far-Off Planets Like the Globe Dot the Galaxy”.
    The New York Times. Archived from
    the original
    on 1 Jan 2022. Retrieved
    5 November
    2013
    .



  25. ^


    Petigura, Eric A.; Howard, Andrew W.; Marcy, Geoffrey W. (31 Oct 2013). “Prevalence of Earth-size planets orbiting Sunday-similar stars”.
    Proceedings of the National University of Sciences of the United States of America.
    110
    (48): 19273–19278. arXiv:1311.6806. Bibcode:2013PNAS..11019273P. doi:10.1073/pnas.1319909110. PMC3845182. PMID 24191033.



  26. ^


    Khan, Amina (4 November 2013). “Milky way may host billions of Earth-size planets”.
    Los Angeles Times
    . Retrieved
    5 November
    2013
    .


  27. ^


    a




    b




    Govert Schilling (November 2011). “The Chance of Finding Aliens: Reevaluating the Drake Equation”.
    astro-tom.com.



  28. ^


    Trimble, V. (1997). “Origin of the biologically important elements”.
    Origins of Life and Evolution of the Biosphere.
    27
    (1–three): 3–21. Bibcode:1997OLEB…27….3T. doi:10.1023/A:1006561811750. PMID 9150565. S2CID 7612499.



  29. ^


    Lineweaver, C. H.; Fenner, Y.; Gibson, B. Yard. (2004). “The Galactic Habitable Zone and the Age Distribution of Complex Life in the Milky Way”.
    Science.
    303
    (5654): 59–62. arXiv:astro-ph/0401024. Bibcode:2004Sci…303…59L. doi:ten.1126/science.1092322. PMID 14704421. S2CID 18140737.



  30. ^


    Dressing, C. D.; Charbonneau, D. (2013). “The Occurrence Rate of Modest Planets around Small Stars”.
    The Astrophysical Periodical.
    767
    (one): 95. arXiv:1302.1647. Bibcode:2013ApJ…767…95D. doi:10.1088/0004-637X/767/i/95. S2CID 29441006.



  31. ^


    “Carmine Dwarf Stars Could Leave Habitable Earth-Like Planets Vulnerable to Radiation”.
    SciTech Daily. two July 2013. Retrieved
    22 September
    2015
    .



  32. ^


    Heller, René; Barnes, Rory (29 Apr 2014). “Constraints on the Habitability of Extrasolar Moons”.
    Proceedings of the International Astronomical Union.
    8
    (S293): 159–164. arXiv:1210.5172. Bibcode:2014IAUS..293..159H. doi:10.1017/S1743921313012738. S2CID 92988047.


  33. ^


    a




    b




    Ward, Peter D.; Brownlee, Donald (2000).
    Rare Globe: Why Complex Life is Uncommon in the Universe. Copernicus Books (Springer Verlag). ISBN0-387-98701-0.



  34. ^


    Davies, P. (2007). “Are Aliens Amidst The states?”.
    Scientific American.
    297
    (6): 62–69. Bibcode:2007SciAm.297f..62D. doi:10.1038/scientificamerican1207-62.



  35. ^


    Crick, F. H. C.; Orgel, L. East. (1973). “Directed Panspermia”
    (PDF).
    Icarus.
    xix
    (3): 341–346. Bibcode:1973Icar…19..341C. doi:10.1016/0019-1035(73)90110-three.



  36. ^


    Westby, Tom; Conselice, Christopher J. (15 June 2020). “The Astrobiological Copernican Weak and Strong Limits for Intelligent Life”.
    The Astrophysical Journal.
    896
    (1): 58. arXiv:2004.03968. Bibcode:2020ApJ…896…58W. doi:10.3847/1538-4357/ab8225. S2CID 215415788.



  37. ^


    Davis, Nicola (15 June 2020). “Scientists say most likely number of contactable alien civilisations is 36”.
    The Guardian
    . Retrieved
    nineteen June
    2020
    .


  38. ^


    a




    b




    “Ernst Mayr on SETI”. The Planetary Lodge. Archived from the original on vi December 2010.


  39. ^

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


    a




    b




    Campbell, A. (13 March 2005). “Review of
    Life’south Solution
    by Simon Conway Morris”. Archived from the original on xvi July 2011.



  41. ^


    Bonner, J. T. (1988).

    The evolution of complication past means of natural selection
    . Princeton University Printing. ISBN0-691-08494-7.



  42. ^


    Kipping, David (eighteen May 2020). “An objective Bayesian analysis of life’s early outset and our late arrival”.
    Proceedings of the National Academy of Sciences.
    117
    (22): 11995–12003. arXiv:2005.09008. doi:10.1073/pnas.1921655117. PMC7275750. PMID 32424083.



  43. ^


    Columbia Academy. “New study estimates the odds of life and intelligence emerging beyond our planet”.
    Phys.org. Phys.org. Retrieved
    23 May
    2020
    .



  44. ^


    Lee, Pascal. “N~1: Alone in the Galaxy, Mt Tam”.
    YouTube. Archived from the original on 11 December 2021.



  45. ^


    Lee, Pascal. “Northward~one: Lonely in the Milky Mode – Kalamazoo Astronomical Gild”.
    YouTube. Archived from the original on 15 March 2021.



  46. ^


    Forgan, D.; Elvis, M. (2011). “Extrasolar Asteroid Mining as Forensic Evidence for Extraterrestrial Intelligence”.
    International Journal of Astrobiology.
    10
    (4): 307–313. arXiv:1103.5369. Bibcode:2011IJAsB..x..307F. doi:10.1017/S1473550411000127. S2CID 119111392.



  47. ^


    Tarter, Jill C. (September 2001). “The Search for Extraterrestrial Intelligence (SETI)”.
    Almanac Review of Astronomy and Astrophysics.
    39: 511–548. Bibcode:2001ARA&A..39..511T. doi:10.1146/annurev.astro.39.ane.511.


  48. ^


    a




    b




    Shermer, M. (Baronial 2002). “Why ET Hasn’t Called”.
    Scientific American.
    287
    (2): 21. Bibcode:2002SciAm.287b..33S. doi:ten.1038/scientificamerican0802-33.


  49. ^


    a




    b




    Grinspoon, D. (2004).
    Solitary Planets.



  50. ^


    Goldsmith, D.; Owen, T. (1992).
    The Search for Life in the Universe
    (2d ed.). Addison-Wesley. p. 415. ISBN1-891389-16-five.



  51. ^


    Aatif Sulleyman (2 Nov 2017). “Stephen Hawking warns artificial intelligence ‘may supersede humans altogether’“.
    independent.co.uk.



  52. ^

    “The value of
    Northward
    remains highly uncertain. Fifty-fifty if we had a perfect knowledge of the first two terms in the equation, there are yet v remaining terms, each of which could exist uncertain past factors of 1,000.” from
    Wilson, TL (2001). “The search for extraterrestrial intelligence”.
    Nature. Nature Publishing Group.
    409
    (6823): 1110–1114. Bibcode:2001Natur.409.1110W. doi:x.1038/35059235. PMID 11234025. S2CID 205014501.

    , or more than informally, “The Drake Equation can accept whatever value from “billions and billions” to zero”, Michael Crichton, equally quoted in
    Douglas A. Vakoch; et al. (2015).
    The Drake Equation: Estimating the prevalence of extraterrestrial life through the ages. Cambridge University Press. ISBN978-i-10-707365-iv.

    , p. 13

  53. ^


    “The Drake Equation”.
    psu.edu.



  54. ^


    Devin Powell, Astrobiology Magazine (four September 2013). “The Drake Equation Revisited: Interview with Planet Hunter Sara Seager”.
    Space.com.



  55. ^


    Govert Schilling; Alan M. MacRobert (three June 2009). “The Chance of Finding Aliens”.
    Sky & Telescope.



  56. ^


    [
    meliorate source needed
    ]

    Dean, T. (10 August 2009). “A review of the Drake Equation”.
    Cosmos Magazine. Archived from the original on 3 June 2013. Retrieved
    sixteen April
    2013
    .



  57. ^

    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 one% 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 look that a much college number volition have microbial life.)”

  58. ^


    von Bloh, W.; Bounama, C.; Cuntz, M.; Franck, S. (2007). “The habitability of super-Earths in Gliese 581”.
    Astronomy & Astrophysics.
    476
    (iii): 1365–1371. arXiv:0705.3758. Bibcode:2007A&A…476.1365V. doi:x.1051/0004-6361:20077939. S2CID 14475537.



  59. ^


    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. arXiv:0710.5294. Bibcode:2007A&A…476.1373S. doi:10.1051/0004-6361:20078091. S2CID 11492499.



  60. ^


    Lineweaver, C. H.; Davis, T. Yard. (2002). “Does the rapid advent of life on World suggest that life is mutual in the universe?”.
    Astrobiology.
    ii
    (three): 293–304. arXiv:astro-ph/0205014. Bibcode:2002AsBio…ii..293L. doi:10.1089/153110702762027871. PMID 12530239. S2CID 431699.



  61. ^


    Forgan, D. (2009). “A numerical testbed for hypotheses of extraterrestrial life and intelligence”.
    International Journal of Astrobiology.
    8
    (ii): 121–131. arXiv:0810.2222. Bibcode:2009IJAsB…viii..121F. doi:ten.1017/S1473550408004321. S2CID 17469638.



  62. ^


    “Are we alone? Setting some limits to our uniqueness”. phys.org. 28 April 2016.


  63. ^


    “Are We Alone? Galactic Culture Challenge”.
    PBS Space Time. 5 October 2016. PBS Digital Studios.



  64. ^


    Adam Frank (10 June 2016). “Yes, In that location Have Been Aliens”.
    The New York Times.



  65. ^


    A. Frank; W.T. Sullivan III (22 April 2016). “A New Empirical Constraint on the Prevalence of Technological Species in the Universe”.
    Astrobiology
    (published 13 May 2016).
    sixteen
    (5): 359–362. arXiv:1510.08837. Bibcode:2016AsBio..xvi..359F. doi:10.1089/ast.2015.1418. PMID 27105054.



  66. ^


    Hetesi, Z.; Regaly, Z. (2006). “A new interpretation of Drake-equation”
    (PDF).
    Periodical of the British Interplanetary Society.
    59: 11–14. Bibcode:2006JBIS…59…11H. Archived from the original
    (PDF)
    on five Feb 2009.



  67. ^


    Maccone, C. (2010). “The Statistical Drake Equation”.
    Acta Astronautica.
    67
    (xi–12): 1366–1383. Bibcode:2010AcAau..67.1366M. doi:10.1016/j.actaastro.2010.05.003. S2CID 121239391.



  68. ^

    Gilded, Leslie K. (2021) “A articulation 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
  69. ^


    a




    b




    Brin, Chiliad. D. (1983). “The Great Silence – The Controversy Apropos Extraterrestrial Intelligent Life”.
    Quarterly Journal of the Purple Astronomical Lodge.
    24
    (3): 283–309. Bibcode:1983QJRAS..24..283B.



  70. ^


    Zaitsev, A. (May 2005). “The Drake Equation: Adding a METI Gene”. SETI League. Retrieved
    20 April
    2013
    .



  71. ^


    Jones, Chris (7 Dec 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
    . Retrieved
    viii December
    2016
    .


  72. ^


    a




    b




    c



    The Drake Equation Revisited: Interview with Planet Hunter Sara Seager Devin Powell,
    Astrobiology Magazine
    iv September 2013.

  73. ^


    “A New Equation Reveals Our Exact Odds of Finding Alien Life”. io9. 21 June 2013.


  74. ^


    Dvorsky, Thou. (31 May 2007). “The Drake Equation is obsolete”.
    Sentient Developments
    . Retrieved
    21 Baronial
    2013
    .



  75. ^


    Sutter, Paul (27 December 2018). “Alien Hunters, End Using the Drake Equation”.
    Space.com
    . Retrieved
    eighteen February
    2019
    .



  76. ^


    Tarter, Jill C. (May–June 2006). “The Cosmic Haystack Is Large”.
    Skeptical Inquirer.
    30
    (3). Retrieved
    21 Baronial
    2013
    .



  77. ^


    Alexander, A. “The Search for Extraterrestrial Intelligence: A Short History – Office 7: The Birth of the Drake Equation”. The Planetary Society. Archived from the original on 6 March 2005.


  78. ^


    Christopher J. Conselice; et al. (2016). “The Development of Milky way Number Density at

    z
    < 8

    and its Implications”.
    The Astrophysical Journal.
    830
    (2): 83. arXiv:1607.03909. Bibcode:2016ApJ…830…83C. doi:ten.3847/0004-637X/830/ii/83. S2CID 17424588.



  79. ^


    Fountain, Henry (17 October 2016). “Two Trillion Galaxies, at the Very To the lowest degree”.
    The New York Times. Archived from
    the original
    on 1 January 2022. Retrieved
    17 Oct
    2016
    .



  80. ^


    Jones, East. K. (one March 1985). “Where is everybody?” An account of Fermi’south question
    (PDF)
    (Report). Los Alamos National Laboratory. Bibcode:1985STIN…8530988J. doi:10.2172/5746675. OSTI5746675
    . Retrieved
    21 August
    2013
    .



  81. ^


    Krauthammer, C. (29 Dec 2011). “Are we alone in the Universe?”.
    The Washington Mail
    . Retrieved
    21 August
    2013
    .



  82. ^


    Webb, Due south. (2015).
    If the Universe Is Teeming with Aliens … WHERE IS EVERYBODY?: Seventy-5 Solutions to the Fermi Paradox and the Problem of Extraterrestrial Life. Springer International Publishing. ISBN978-3319132358.



  83. ^


    Hanson, R. (15 September 1998). “The Great Filter — Are We Nearly Past It?”. Retrieved
    21 August
    2013
    .



  84. ^


    Sandberg, Anders; Drexler, Eric; Ord, Toby (half-dozen June 2018). “Dissolving the Fermi Paradox”. arXiv:1806.02404
    [physics.pop-ph].



  85. ^


    The Making of Star Trek
    by Stephen Due east. Whitfield and Gene Roddenberry, New York: Ballantine Books, 1968

Further reading

[edit]

  • Morton, Oliver (2002). “A Mirror in the Heaven”. In Graham Formelo (ed.).
    It Must Be Beautiful. Granta Books. ISBN1-86207-555-7.

  • Rood, Robert T.; James South. Trefil (1981).
    Are We Lonely? The Possibility of Extraterrestrial Civilizations. New York: Scribner. ISBN0684178427.

  • Vakoch, Douglas A.; Dowd, Matthew F., eds. (2015).
    The Drake Equation: Estimating the Prevalence of Extraterrestrial Life Through the Ages. Cambridge, Great britain: Cambridge University Press. ISBN978-1-ten-707365-4.

External links

[edit]

  • Interactive Drake Equation Estimator
  • 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 Eastward.T. Equation, Recalculated”.
    Wired.

  • Macromedia Wink folio allowing the user to modify Drake’s values from PBS Nova
  • The Drake Equation
    Astronomy Bandage
    episode #23, includes full transcript.
  • Animated simulation of the Drake equation.
  • The Conflicting Equation 22 September 2010, BBC Radio program
    Discovery.
  • “Reflections on the Equation” (PDF), past Frank Drake, 2013



Source: https://en.wikipedia.org/wiki/Drake_equation