Drake equation

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Frank Drake

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

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). The equation summarizes the main concepts which scientists must contemplate when considering the question of other radio-communicative life. 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:

$${\displaystyle N=R_{\ast }\cdot f_{\mathrm{p}}\cdot n_{\mathrm{e}}\cdot f_{\mathrm{l}}\cdot f_{\mathrm{i}}\cdot f_{\mathrm{c}}\cdot L}$$

where

• N = the number of civilizations in the Milky Way galaxy with which communication might be possible (i.e. which are on the 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 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.

This form of the equation first appeared in Drake's 1965 paper.

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". 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."

Seven months after Cocconi and Morrison published their article, Drake began searching for extraterrestrial intelligence in an experiment called Project Ozma. It was the first systematic search for signals from communicative extraterrestrial civilizations. Using the 85 ft (26 m) 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, slowly scanning frequencies close to the 21 cm wavelength for six hours per day from April to July 1960. 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.

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. These participants called 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.

Usefulness

The Allen Telescope Array for SETI

The Drake equation results in a summary of the factors affecting the likelihood that we might detect radio-communication from intelligent extraterrestrial life. The last three parameters, f_i, f_c, and L, 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, 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.

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. 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. SETI efforts since 1961 have conclusively ruled out widespread alien emissions near the 21 cm wavelength of the hydrogen frequency.

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:

• 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 = 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 this Galaxy, R_∗

Calculations in 2010, from NASA and the European Space Agency indicate that the rate of star formation in this Galaxy is about 0.68–1.45 M_☉ of material per year. 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 0.5 M_☉. This gives a star formation rate of about 1.5–3 stars per year.

Fraction of those stars that have planets, f_p

Analysis of microlensing surveys, in 2012, has found that f_p 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.

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

In November 2013, astronomers reported, based on Kepler space telescope 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. 11 billion of these estimated planets may be orbiting sun-like stars. Since there are about 100 billion stars in the galaxy, this implies f_p · n_e 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 n_e had a minimum value between 3 and 5. Dutch science journalist Govert Schilling has opined that this is optimistic. Even if planets are in the habitable zone, the number of planets with the right proportion of elements is difficult to estimate. 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.

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, although the flaring behavior of these stars might speak against this. 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.

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.

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 f_l 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 f_l 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. 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." 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, f_l, f_i, and f_c 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).

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 f_i. Likewise, the Rare Earth hypothesis, notwithstanding their low value for n_e above, also think a low value for f_i dominates the analysis. Those who favor higher values note the generally increasing complexity of life over time, concluding that the appearance of intelligence is almost inevitable, implying an f_i 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 the estimate of f_l 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 ${\displaystyle f_{\mathrm{l}}\cdot f_{\mathrm{i}}}$. 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.

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).

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 human 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 present day humans. 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.

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. 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 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.^[52] 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 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.

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. Paleobiologist Olev 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.

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

Range of results

As many skeptics have pointed out, the Drake equation can give a very wide range of values, depending on the assumptions, as the values used in portions of the Drake equation are not well established. 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.

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, Mayr's view on intelligence arising, Drake's view of communication, and Shermer's estimate of lifetime:

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

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, f_p = 1, n_e = 0.2, f_l = 0.13, f_i = 1, f_c = 0.2, and L = 10⁹ years

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.

Possible former technological civilizations

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) 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 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 2.5×10⁻²⁴. 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 than 1.7×10⁻¹¹ (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.

Modifications

As many observers have pointed out, the Drake equation is a very simple model that omits potentially relevant parameters, 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. 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. 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, 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". 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 v, and establishes additional sites that survive for a lifetime L. The result is a more complex set of 3 equations.

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 n_r 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 1 + n_r, 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 n_r may be almost zero. In the case of total life extinction, a similar factor may be applicable for f_l, 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. 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. These gases are produced by living organisms that can accumulate in a planet atmosphere to levels that can be detected with remote space telescopes.

The Seager equation looks like this:

$${\displaystyle N=N_{\ast }\cdot F_{\mathrm{Q}}\cdot F_{\mathrm{H}\mathrm{Z}}\cdot F_{\mathrm{O}}\cdot F_{\mathrm{L}}\cdot F_{\mathrm{S}}}$$

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?"

Carl Sagan's version of the Drake equation

American astronomer Carl Sagan made some modifications in the Drake equation and presented it in the 1980 program Cosmos: A Personal Voyage. The modified equation is shown below

$${\displaystyle N=N_{\ast }\cdot f_{\mathrm{p}}\cdot n_{\mathrm{e}}\cdot f_{\mathrm{l}}\cdot f_{\mathrm{i}}\cdot f_{\mathrm{c}}\cdot f_{\mathrm{L}}}$$ where

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

and

• N_∗ = Number of stars in the Milky Way 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 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.
• f_L = fraction of a planetary lifetime graced by a technological civilization

Criticism

Criticism of the Drake equation is varied. Firstly, many of the 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 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.

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.

One reply to such criticisms 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.

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 present-day technology. However, no confirmed signs of civilizations or intelligent life elsewhere have been found, either in this Galaxy or in the observable universe of 2 trillion galaxies. 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?".

A large number of explanations have been proposed to explain this lack of contact; a book published in 2015 elaborated on 75 different explanations. 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 · n_e · f_l · f_i, has a low value. The most common suspect is f_i, but explanations such as the rare Earth hypothesis argue that n_e is the small term.
• Intelligent civilizations exist, but we see no evidence, meaning f_c 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 L 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, 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 (predicted) probability of there being no other intelligent life in our observable universe".

In fiction and popular culture

Commemorative plate on Europa Clipper

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. The invented equation created by Roddenberry is:

$${\displaystyle F{f}^2(MgE)-C^{1}R{i}^1\cdot M=L/So}$$

Regarding Roddenberry's fictional version of the equation, Drake himself commented that a number raised to the first power is just the number itself.

A commemorative plate on NASA's Europa Clipper mission, planned for launch in October 2024, features a poem by the U.S. Poet Laureate Ada Limón, waveforms of the word 'water' in 103 languages, a schematic of the water hole, the Drake equation, and a portrait of planetary scientist Ron Greeley on it.

The track Abiogenesis on the Carbon Based Lifeforms album World of Sleepers features the Drake equation in a spoken voice-over.

Prime Directive

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Prime_Directive

In the fictional universe of Star Trek, the Prime Directive (also known as "Starfleet General Order 1", and the "non-interference directive") is a guiding principle of Starfleet that prohibits its members from interfering with the natural development of alien civilizations. Its stated aim is to protect unprepared civilizations from the danger of starship crews introducing advanced technology, knowledge, and values before they are ready. Since its introduction in the first season of the original Star Trek series, the directive has been featured in many Star Trek episodes as part of a moral question over how best to establish diplomatic relations with new alien worlds.

The Prime Directive

The Prime Directive is one of many guidelines for Starfleet's mandate to explore the galaxy and "seek out new life and new civilizations." Although the concept of the Prime Directive has been alluded to and paraphrased by many Star Trek characters during the television series and feature films, the text of the directive was only revealed to viewers in 2021 during the Star Trek: Prodigy episode "First Con-Tact" set in 2383. Two sections of the text were shown, and are as follows:

Section 1:

Starfleet crew will obey the following with any civilization that has not achieved a commensurate level of technological and/or societal development as described in Appendix 1.

a) No identification of self or mission.

b) No interference with the social, cultural, or technological development of said planet.

c) No reference to space, other worlds, or advanced civilizations.

d) The exception to this is if said society has already been exposed to the concepts listed herein. However, in that instance, section 2 applies.

Section 2:

If said species has achieved the commensurate level of technological and/or societal development as described in Appendix 1, or has been exposed to the concepts listed in section 1, no Starfleet crew person will engage with said society or species without first gathering extensive information on the specific traditions, laws, and culture of that species civilization. Then Starfleet crew will obey the following.

a) If engaged with diplomatic relations with said culture, will stay within the confines of said culture's restrictions.

b) No interference with the social development of said planet.

The Prime Directive was frequently applied to less developed planets which had not yet discovered warp travel or subspace communication technology. The Prime Directive was also sometimes applied to advanced civilizations that already knew of life on other worlds but were protected by empires outside the Federation's jurisdiction. First contact could be made by the Federation with alien worlds that had either discovered warp or were on the verge of it, or with highly advanced civilizations that simply hadn't ventured into space yet. In those cases, the Prime Directive was used as a general policy to not disrupt or interfere with their culture when establishing peaceful diplomatic relations.

Consequences for violating the Prime Directive could range from a stern reprimand to a demotion, depending on the severity of the infraction. However, enforcement of these rules -- and interpretations of the Prime Directive itself -- varied greatly and were at the discretion of the commanding officer. In many instances, prominent Starfleet personnel like captains James T. Kirk, Jean-Luc Picard, Kathryn Janeway and Benjamin Sisko willingly broke the Prime Directive but faced no real punishment or consequence for doing so.

However, the Prime Directive is not absolute. Starship captains have been known to violate it to protect their ships and crews, and certain Starfleet regulations such as The Omega Directive can even render it null and void in certain circumstances.

Creation and evolution

Creation of the Prime Directive is generally credited to Original Series producer Gene L. Coon. Later writers have suggested that the Prime Directive was influenced by the Vietnam War or designed to show a civilization that had evolved beyond colonialism. This would have been consistent with Coon and Roddenberry's political outlooks, but the notion of science fictional first contact and its possible harms already had a decades-long history by 1966.

Notable on-screen references

The Original Series

• The first filmed reference to the Prime Directive occurs in the first season TOS episode "The Return of the Archons" (1966), when Spock begins to caution Captain Kirk of the starship Enterprise when he proposes to destroy a computer controlling an entire civilization. Kirk interrupts him after Spock says, "Captain, our Prime Directive of non-interference" with, "That refers to a living, growing culture..." Later, Kirk argues the computer into self-destruction and leaves behind a team of sociologists to help restore the society to a "human" form.
• In the second-season episode "The Apple", Spock says of Kirk's plan to destroy Vaal, "If we do what it seems we must, in my opinion, it will be in direct violation of the non-interference directive."
• In the second-season episode "A Piece of the Action", Kirk, briefing Spock and McCoy before beaming down on possible interference 100 years earlier by the Federation ship, the Horizon, Kirk explicitly states, "the contact came before the non-interference directive".
• In the second-season episode "A Private Little War", two different factions on a planet were at war with each other and it is discovered that the Klingons were furnishing one faction with advanced weapons. Kirk responded by arming the other faction with the same weapons. This resulted in an arms race on that world, as a fictionalized parallel to the then-current Cold War arms race, in which the United States often armed one side of a dispute and the Soviet Union armed the other.
  • In a similar storyline on TNG, "Too Short a Season", a Starfleet admiral admits he interpreted the Prime Directive to mean equally arming two different factions on a planet, intended to reach a stalemate, but which resulted in 40 years of war.
• In the second-season episode "Patterns of Force," Federation cultural observer and historian John Gill created a regime based on Nazi Germany on a primitive planet in an effort to create a society which combined the high efficiency of a fascist dictatorship with a more benign philosophy. In doing so, he contaminated the normal and healthy development of the planet's culture, with disastrous effects; the regime adopts the same racial supremacist and genocidal ideologies of the original. Eventually, this leaves investigating Starfleet officers with no other option but to arrange the overthrow of the government in order to mitigate the harm of Gill's interference.
• In the second-season episode "The Omega Glory", after finding out that Captain Tracy may have violated the Prime Directive, Captain Kirk states, "A starship captain's most solemn oath is that he will give his life, even his entire crew, rather than violate the Prime Directive."
• In the second-season episode "Bread and Circuses", the crew discusses that the Prime Directive is in effect, saying, "No identification of self or mission. No interference with the social development of said planet. No references to space, or the fact that there are other worlds, or more advanced civilizations."

The Next Generation

• In the Star Trek: The Next Generation (TNG) first-season episode "Symbiosis", Captain Jean-Luc Picard of the starship Enterprise-D states that, "The Prime Directive is not just a set of rules; it is a philosophy... and a very correct one. History has proven again and again that whenever mankind interferes with a less developed civilization, no matter how well-intentioned that interference may be, the results are invariably disastrous."
• In the third season episode "Who Watches the Watchers", the crew of the Enterprise expose a pre-warp civilization on Mintaka III to Federation technology. Despite an attempted mind wipe, the Mintakans remember and now revere Picard as a god. Picard intentionally breaks the Prime Directive again by beaming one of the Mintakans aboard the Enterprise and explaining they are on a starship, and not gods, showing them their world from space and encouraging them to spread the truth to the others. Eventually, he allowed himself to be shot by an arrow to prove he was mortal.
• In the fourth season episode "The Drumhead", the captain of the Enterprise is being interrogated by retired Admiral Norah Satie, who says the Prime Directive is "Starfleet General Order Number One". She claims that Picard had "violated the Prime Directive a total of nine times since you took command of the Enterprise". (To this he responds "My reports to Starfleet document the circumstances in each of those instances".)
• In the fourth season episode "First Contact", Commander Riker goes undercover to scout a pre-warp civilization that is on the verge of discovering warp technology, preparing to establish diplomatic relations. When he is captured, Captain Picard and Deanna Troi make first contact early, but Picard refuses to share Federation technology with them due to the Prime Directive. After worries of social upheaval, the alien scientists developing warp travel believe their society isn't ready for knowledge of extraterrestrial life, and they ask the Enterprise to leave without announcing their presence to the public, agreeing to delay developing warp technology until their culture is ready.
• In the seventh season episode "Homeward", it is said that Starfleet had allowed 60 races to die out rather than interfere with their fate. However, in the episodes "Homeward" and "Pen Pals", the crew debates the Prime Directive and the saving of civilizations.

Deep Space Nine

• In the Star Trek: Deep Space Nine (DS9) first season episode "Captive Pursuit", Commander Sisko references the Prime Directive as his reason for choosing not to interfere in a hunt of a member of sentient species from the Gamma Quadrant that is bred to be hunted. In the end, Sisko does allow Chief O'Brien to assist the hunted being to escape from his captors to continue the hunt.
• In the episode "The Circle", the government of the planet Bajor experiences an internal, civil war-like conflict. Starfleet Commander Benjamin Sisko's superior orders him to evacuate all Starfleet personnel from the station, noting, "The Cardassians may involve themselves in other people's civil wars, but we don't."
• In the episode "In the Pale Moonlight", Sisko and Garak plant evidence to force the Romulans to enter the Dominion War under false pretenses, with full knowledge and approval from Starfleet Command, despite this violating the Prime Directive's edict of not interfering with other cultures or civilizations. Participation in the war by the Romulans resulted in massive military and civilian casualties within Romulan society.

Voyager

• In the Star Trek: Voyager episode "The Omega Directive," an exception to the Prime Directive was introduced. Starfleet's Omega Directive authorizes a captain to take any and all means necessary to destroy Omega particles including interference with any society that creates them.
• In the episode "Infinite Regress", Naomi Wildman informs Seven of Nine that she was familiar with the Prime Directive including all 47 suborders.
• In the episode "Natural Law," Chakotay and Seven of Nine encounter a primitive culture protected by an energy barrier that they crash a shuttle into which protects the culture from the rest of the planet's more advanced inhabitants. Although the two try to avoid contact, the natives encounter and help an injured Chakotay and start mimicking the pair and collecting shuttle debris as jewellery. After Seven manages to use the shuttle's deflector to lower the barrier, Voyager is able to beam out all of the loose technology and minimize the Prime Directive violation. However, this leads to another issue when the other culture on the planet -- who have achieved spaceflight and openly engaged in friendly relations with Voyager -- seek to use the downed barrier to explore the previously blocked portion of their planet and civilize the natives. While such an idea has its benefits and detractors, Janeway cites the Prime Directive as the reason for taking down the barrier. In response, the natives knock out Voyager's transporters and actively try to force the crew to leave the deflector behind, forcing Tom Paris to destroy it with the Delta Flyer instead. However, Seven worries that as her deflector modifications were already scanned, they may be replicated in time to take down the barrier again.
• In the episode "Endgame" the Future Admiral Janeway warns the present Captain Janeway against holding on to the "Prime Directive" when the Future Janeway goes back in time to change history by having Voyager get back to Earth in only 7 years instead of 23 years.

Enterprise

• Filmed between 2001 and 2005, Star Trek: Enterprise (ENT) is a prequel to Star Trek: The Original Series (TOS), set before the implementation of the Prime Directive. The first-season episode "Dear Doctor" sees the ship's doctor Phlox struggle with the ethics of providing a cure to a pre-warp species with a deadly disease. Captain Jonathan Archer notes that as humanity grapples with their newfound reach, they will have to develop "a doctrine, something that tells us what we can and can't do out here, should and shouldn't do."
• Additionally, the ENT episodes "Fight or Flight" and "Civilization", make reference to a Vulcan policy of non-interference, a possible model for Starfleet's Prime Directive.

Discovery

• In "New Eden", the second episode in season two of Star Trek: Discovery aired in 2019, the away party is selected and briefed to ensure that their interactions with humans from pre-warp capable Earth does not interfere with their development. The regulation is exclusively referred to as General Order 1. Captain Christopher Pike later breaks the Prime Directive to reveal the truth to one of the locals in exchange for a World War III era helmet camera, but the man promises to keep quiet about it to his people. Commander Michael Burnham argued to Pike that the helmet camera and the answers it might contain to solve the mystery, was more important than the Prime Directive, and that one would have to be sacrificed to uphold the other – and only the captain could make that choice.
• In "Whistlespeak" of season five, the Discovery encounters the Halem'nites, a pre-warp, pre-industrial society that is protected by a Denobulan weather tower which shields the only habitable part of the planet against sandstorms and generates rain. The Denobulans had installed the weather tower and four others like it in secret and masked them as mountains in order to avoid breaking the Prime Directive. However, the other four failed and the last one is failing, leading the Halemn'ites to build a whole religion around them. While Captain Michael Burnham and Lieutenant Sylvia Tilly at first discreetly infiltrate the locals, allowing Burnham to repair the tower in secret, Tilly's life is put in danger when the Halem'nites prepare to sacrifice her as part of a ritual to bring rain. Burnham expressly chooses to violate the Prime Directive to save her friend, arguing that Tilly and a local named Ravah should not suffer a pointless death and, without learning how to properly maintain the tower themselves, the Halem'nites will eventually go extinct.

Prodigy

• The villain of the first season, the Diviner, came from the future. In his original timeline the Vau N'Akat saw the arrival of a Federation ship to its planet. This divided their society between those who wanted to join the Federation and those who refused, and the ensuing civil war destroyed them. The Federation refused to take sides in the civil war. The Diviner considered it a subtle act of aggression and jumped to the past, the series' present, to destroy the Federation before it makes first contact with his people.
• In "First Con-tact," a holographic version of Kathryn Janeway informs the young crew of the USS Protostar of the Prime Directive before they attempt a first contact mission. However, captain Dal R'El is tricked by his old Ferengi mentor DaiMon Nandi, resulting in a disastrous first contact. Although the crew returns what Nandi stole, Janeway furiously berates them as not only was the Prime Directive broken, but the way that things went down will have a negative impact on any possible relations that the race that they had met will have with outsiders going forwards.
• In "All the World's a Stage," the crew of the Protostar meet a civilization, the Enderprizians, that experienced massive cultural contamination due to a visit by the USS Enterprise around a hundred years before. According to the locals' history, the Enterprise detected a danger to the Enderprizians that Ensign David Garrovick volunteered for a solo mission to address without breaking the Prime Directive. However, Garrovick crashed and was saved by the locals with his presence, technology and stories leading to them basing their whole culture around Starfleet and the Enterprise. One local, Doctor Boons (named after Leonard McCoy's nickname of Bones), reveals that Garrovick had told the people about the Prime Directive and that they weren't ready for the Federation or their technology, but the Enderprizians saw the Federation and its ideals as something to believe in. The Protostar's meeting with the Enderprizians is treated as second contact rather than a Prime Directive violation. In the season finale, an Enderprizian is seen in a Starfleet class, suggesting that they ended up making more official contact with Starfleet in the end.
• In "Brink," The Doctor mentions that sending the Protostar crew to Solum wouldn't technically violate the Prime Directive or Voyager's direct orders as the crew are not Starfleet personnel. However, when Gwyn asks to rescue her father Ilthuran -- the present day version of the Diviner -- Commander Tysess worries that doing so would be taking sides in the brewing civil war which the Prime Directive prohibits. Janeway agrees to allow the rescue, pointing out that nothing prevents them from granting Ilthuran political asylum, particularly as he is the best hope for a peaceful resolution to the conflict. While Janeway states that Starfleet will disavow their actions if they're caught, she allows Voyager to supply the crew with various technologies for their mission.
• In "Touch of Grey," despite Janeway previously declaring that the Protostar crew would be disavowed if they were caught, she personally leads Chakotay, The Doctor and Wesley Crusher to rescue them. As civil war breaks out on Solum, just like it did in the future that the Diviner came from, Gwyn asks Janeway for help in saving her homeworld which would be taking sides and thus violating the Prime Directive. Rather than staying out of it like the Federation did in the Diviner's future, Janeway instantly agrees to help, having been reminded that boldness isn't only for the young.
• In "Ouroboros, Part I," Voyager and the Protostar engage Asencia's forces to buy time for the Protostar crew to enact their plan. While the battle results in the defeat of Asencia and the favorable end of the civil war, the Federation's direct role is minimal, limited primarily to Voyager and the Protostar engaging Asencia's fleet which is in the middle of launching to attack every major Federation outpost across three quadrants. Like in "Brink," the forces sent to the ground who take direct part in Asencia's defeat are non-Starfleet personnel. In the following episode, Janeway leads official first contact between the Federation and the Vau N'Akat which Gwyn had previously tried and failed to establish.

Strange New Worlds

• In "Strange New Worlds", the first episode of season one of Star Trek: Strange New Worlds, Captain Pike reveals the Enterprise to a society that has reverse engineered a matter-anti-matter reactor as a weapon after witnessing the Battle near Xahea. However, the Federation Council could not address how the weapon was created because the Battle near Xahea was classified information, which prevented them from charging Pike with violating General Order 1. The Federation Council is also considering renaming General Order 1 as the Prime Directive, which Captain Pike says will "never stick".
• In "Among the Lotus Eaters," Pike orders the removal of a radioactive asteroid from the surface of the planet Rigel VII. Spock argues that they are violating the Prime Directive, but Pike counters that the asteroid's effects were stunting the growth of the local civilization and as such, they are merely setting things right rather than interfering which Spock concedes is a logical argument.

Picard

• In "Vox," Geordi La Forge mentions that Starfleet had raised the wrecked saucer section of the USS Enterprise-D off of the surface of Veridian III following the events of Star Trek Generations in order to avoid breaking the Prime Directive due to the pre-warp civilization living in the star system. This allowed La Forge the chance to spend twenty years secretly rebuilding the ship.

Films

• In the feature film Star Trek: Insurrection, Picard violates orders to protect the rights of a planet's population when he feels an admiral is breaking the Prime Directive.
• In the feature film Star Trek Into Darkness, Captain Kirk violates the prime directive by saving Spock's life while attempting to stop an active volcano that threatens the native inhabitants, and then by exposing the Enterprise to those inhabitants. As punishment, Kirk is removed from command of the Enterprise and demoted to first officer instead. Initially, his punishment was to be sent back to Starfleet Academy, but Admiral Pike intervened on Kirk's behalf. The subsequent actions of Khan Noonien Singh lead to Kirk being reinstated soon afterwards.

Criticism

The Prime Directive has been criticized in-universe because of the inconsistencies in which it is applied. In the TOS episodes "Friday's Child," "For the World Is Hollow and I Have Touched the Sky," "The Cloud Minders," "The Apple," "The Return of the Archons," "Space Seed" and "A Taste of Armageddon," the crew of the Enterprise either interferes with laws or customs of alien worlds or outright colonizes an alien planet to achieve a Federation objective, to save the lives of the crew, or to better the lives of the inhabitants.

Out-of-universe criticisms focus on the above problems; that the Prime Directive is simply a plot device and is manipulated by the writers. Janet D. Stemwedel points out a potential conflict between the anti-colonialist intentions of the Federation and the "ethical project of sharing a universe" which would require "a kind of reciprocity — even if your technological attainment is quite different, it means recognizing you are owed the same moral consideration." Stemwedel writes, "If your concern is not to change the natural behavior or development of alien citizens at any cost, your best bet is to stay at home rather than to explore new worlds." Ars Technica asked lawyers to comment on the Prime Directive and other Star Trek legal issues. Criticism included interpreting the Prime Directive as a product of the Cold War environment in which Roddenberry wrote, as well as indicating that enforcement would be lacking.

Temporal Prime Directive

The "Temporal Prime Directive" is a fictional guideline for time travelers (from the past or future) from interfering in the natural development of a timeline.

In the TNG episode "A Matter of Time", Picard compares the Prime Directive to a possible Temporal Prime Directive:

"Of course, you know of the Prime Directive, which tells us that we have no right to interfere with the natural evolution of alien worlds. Now I have sworn to uphold it, but nevertheless I have disregarded that directive on more than one occasion because I thought it was the right thing to do. Now, if you are holding on to some temporal equivalent of that directive, then isn't it possible that you have an occasion here to make an exception, to help me to choose, because it's the right thing to do?"

As 31st-century time traveler Daniels revealed to Captain Jonathan Archer in the Star Trek: Enterprise episode "Cold Front", as time travel technology became practical, the Temporal Accords were established sometime before the 31st century, to allow the use of time travel for the purposes of studying history, while prohibiting the use of it to alter history.

As revealed in the Star Trek: Discovery episode "Face the Strange," the Temporal Prime Directive is still in effect in the late 32nd century.