Drake equations. The new Fermi paradox and the Drake equation. Historical parameter estimates
The number of extraterrestrial civilizations wishing to come into contact with ours is predictable.
Generally speaking, few major scientific discoveries are strictly dated - not only by year, but also by month and date. However, at least one of them can be dated literally to the minute. On the night of November 1–2, 1961, several scientists attending a conference held in Green Bank, Virginia, USA, sat up late in a bar discussing an article written by physicist Philip Morrison (b. 1915). and Giuseppe Cocconi (b. 1914). They argued whether terrestrial scientists, who had just begun to build serious radio telescopes, could actually detect radio signals sent by extraterrestrial civilizations from deep space. If somewhere in the depths of the Universe there really is at least one extraterrestrial civilization seeking to contact us, it is likely sending us radio signals, and we just need to catch them, they reasoned. At the same time, the task for the next day of the conference was formulated: to estimate the likely number of extraterrestrial civilizations ready to come into contact with us.
The question was posed, and the answer was proposed the very next day by the American radio astronomer Frank Drake. According to his formula, the number of extraterrestrial civilizations N is:
where R is the number of stars formed annually in the Universe; P is the probability of a star having a planetary system; N e is the probability that among the planets there is an terrestrial planet on which the origin of life is possible; L is the probability of the real origin of life on the planet; C is the probability that intelligent life has followed the technogenic path of development, has developed means of communication and wants to make contact, and, finally, T is the average time during which a civilization wishing to make contact sends radio signals into space to contact us. The meaning of Drake's formula is, if you like, not to completely confuse everything, but to clearly show the full extent of human ignorance regarding the real state of affairs in the Universe and, at least approximately, to break down one purely guesswork estimate of the total number of civilizations in it into several probabilistic estimates. At least this way things start to look less mysterious.
At the time of the Green Bank conference, the only more or less known number on the right side of the formula was the number of stars formed annually R. As for other numbers, terrestrial planets (N e) even in our Solar system could be classified as one (only Earth) to five (Venus, Earth, Mars and one of each of the large satellites of Jupiter and Saturn) space objects of a planetary type. With optimistic forecasts of this kind, it turned out that the Galaxy is literally teeming with millions of technologically advanced civilizations (N), and we are, in fact, juniors in this “galactic league”. This information immediately flooded the media, and through them, the mass consciousness, and people simply ceased to doubt that the existence of extraterrestrial intelligence is an immutable truth.
However, more than one decade has passed since 1961, and the further we go, the more we become convinced that it is necessary to moderate the optimism initially generated by Drake’s formula in the mass consciousness of earthlings who yearned for brothers in mind. Today we know, for example, unlike the overly optimistic members of the Greenbank group, that the existence of life within our solar system outside of Earth is extremely unlikely (unless it exists under a thick ice sheet in the ocean of Saturn's fourth largest moon, which, ironically, is called Europa ). And, although after 1961 we discovered many planetary systems around previously known stars, they all look little like our Solar system, since the planets there, for the most part, revolve in elongated elliptical orbits with a very significant eccentricity, which means an annual difference temperatures on them seem unacceptable from the point of view of the development of protein life. In fact, it turned out that the conditions conducive to retaining water on the surface of a planetary body for billions of years without its evaporation and/or freezing out are so severe that, apart from the Earth, such planets have not yet been found - and this is not surprising, since even a few percent changes in the radius of the earth's orbit will lead to our planet becoming uninhabitable.
It so happened that in 1981, my fellow astronomer Robert Rood (b. 1942) and I came across Drake's formula and decided to critically rethink it in the light of modern scientific knowledge. Substituting all the estimates of quantities at hand on the right side of the formula, we received a value of N approximately equal to 0.003. That is, three out of a thousand (or approximately one in three hundred) star systems contain a technologically advanced civilization that wants to communicate with us. Or, if you like, this means that interstellar signals from extraterrestrial intelligence appeared in our Galaxy only in the last 1/300th of its existence. In any case, our chances of finding them are extremely poor: 1:300. Naturally, nothing has changed over the past twenty-odd years, and extraterrestrial civilizations have not shown any signs of life. Their search has been going on for decades, financed both at public expense and by private foundations. Alas... To this day we have not found the notorious extraterrestrial brothers in mind, not to mention trying to make contact with them. Okay. But we have accumulated a lot of absolutely reliable data regarding what is not there.\
Frank Donald DRAKE
Frank Donald Drake, b. 1930
American astronomer. Born in Chicago, he studied electronics at Cornell University. After listening to a course of lectures by the famous astronomer Otto Struve (1897–1963) on the formation of planetary systems, he developed a lifelong interest in issues of extraterrestrial life and civilizations. After serving in the US Navy, he successively worked at the National Radio Astronomy Observatory (NRAO), Cornell University and the University of California (Santa Cruz). With Struve's support, Drake organized the construction of a 28-meter radio telescope based on NRAO (Project Ozma), the world's first measuring and recording instrument specifically designed to try to identify extraterrestrial life
Does such a beach exist anywhere outside of Earth? The answer to this question is provided by the Drake equation.
The Drake Equation is a formula designed to determine the number of alien civilizations with which humans may come into contact. It was developed in 1960 by astrophysicist Frank Drake to justify the science of SETI, the search for extraterrestrial intelligence program.
What's the point?
The purpose of the formula is to find the number N - the number of civilizations capable of communicating with each other. It is obtained by multiplying six main factors:
- R is the number of stars born per year (10, hereinafter according to Drake’s own estimates).
- f p – the proportion of stars with planets. (0.5)
- n e – the number of habitable planets around the star. (2)
- f l – the chance of life appearing in favorable conditions. (1 – if there are conditions, then life will definitely appear)
- f with – the ratio of the number of planets where there are inhabitants looking for contact to the number of planets on which there is simply life. (0.01 or 1 percent)
- f i – the chance of intelligent life appearing where there is simply life. (0.01)
- L is the lifespan of developed life that wants to enter into interplanetary contact (10 thousand years).
The final result for Drake is 10. As many as ten extraterrestrial societies that can contact us! But why are they silent then?
While working at Los Alamos National Laboratory in New Mexico in 1950, physicist Enrico Fermi asked his colleagues the now famous question: “Where are they?” . The Nobel Prize winner noted the discrepancy, which he found strange. With so many stars in our galaxy, even the tiny chance of life existing near any given star means the presence of a large number of alien civilizations. Further, assuming reasonable probabilities about the ability of aliens to travel interstellarly, physically change the surrounding space or communicate, we should already see evidence of their existence. But we don't see. This discrepancy became known as Fermi paradox, and the corresponding absence of life in the observable Universe is usually called Fermi's observation.
Many hypotheses have tried to explain the Fermi Paradox. For example, that other civilizations deliberately hide themselves or self-destruct before they learn to travel between stars or establish long-distance communications. The main problem with such hypotheses is that the proposed mechanism for concealing one's existence or self-destruction must be extremely reliable: if only 99% of civilizations destroy themselves, this does little to resolve the paradox.
Thus, all of these hypotheses remain highly speculative and largely rely only on assumptions about some universal motives or social dynamics of aliens, while we cannot claim similar knowledge about our own world. These hypotheses are not considered for their independent scientific plausibility, but only because they offer a solution to the Fermi Paradox.
Scientists from the Future of Humanity Institute at the University of Oxford have published a scientific paper in which they show that "the correct handling of scientific uncertainties dissolves the Fermi Paradox." In other words, our uniqueness in the Universe and the absence of observable alien life becomes not a “paradox” or an unlikely event.
The authors of the scientific work criticize the fact that the Drake formula is usually used with point estimates. However, such point estimates "imply knowledge about processes (especially those related to the origin of life) that are untenable given the current state of science." According to British scientists, taking into account realistic uncertainty, point estimates should be replaced probability distributions, which reflect current scientific understanding. And then, according to Drake’s formula, a completely different picture emerges - and any reason to be sure that the Galaxy (or the observable Universe) contains other civilizations disappears.
The second result of the scientific work: the scientists showed that, given the observed limits of the dominance of other civilizations, “our updated probabilities suggest that there is a significant probability that we are alone.” The authors found qualitatively similar results using two different methods: using the authors' estimates of current scientific knowledge relevant to key parameters, and using diverging estimates of these parameters in the astrobiological literature as a proxy for current scientific uncertainty.
Calculation using this method showed a fairly high probability that humanity is alone in its native Milky Way galaxy (53−99.6%) or even in the entire observable Universe (39−85%). Accordingly, to the famous question “Where are they?” the authors of the scientific work answer: “Probably very far away, and quite possibly beyond the cosmological horizon and forever unattainable.”
From all of the above, the third conclusion follows that pessimism for the survival of mankind, based on the Fermi paradox, is unfounded. In other words, humanity has a good chance of survival, and one cannot draw conclusions about the inevitability of the self-destruction of civilization based on the fact that there is not a single sufficiently developed civilization in the observable Universe. This is perhaps the most optimistic result from a published scientific work.
The article was published on June 6, 2018 on the preprint site arXiv.org (arXiv:1806.02404v1).
Elon Musk responded to the calculations of British specialists. "So strange", -
Drake's formula was formulated by American astronomer Frank Drake to estimate number of civilizations in the Galaxy.
(Yes, this is not really on the topic of the site. But it’s still interesting.)
Appearing in 1960, Drake’s formula was very fashionable in the era of “great cosmic hopes,” but then, due to resentment that the hopes did not come true, it began to be criticized, and as a rule, not substantive, but methodological. The main complaint about Drake’s formula is that it is “about nothing”; anything can be counted with this formula; the formula is unfalsifiable, and therefore unscientific.
I will leave the statement about non-falsifiability to the conscience of the critics: they either do not understand the meaning of this concept, or deliberately mislead the reader with a beautiful term. The emotional thesis “the formula is about nothing” is deciphered as follows: the problem area of the problem is so undefined that it seems pointless to derive any formula: we get false accuracy on too shaky ground.
This is true, but this is exactly how the task is posed: to give a reasonable estimate of a certain value under extremely uncertain conditions affecting it. This situation is not at all unique. Very often in science, and in astronomy in particular, at the initial stage of research it is necessary to make assumptions under conditions of extreme uncertainty. Surprisingly, from general considerations one can draw correct conclusions and obtain numerical estimates that do not diverge much from the truth.
- How many hairs is there on the head of the President of Venezuela?
- What is the mass of a female Porcula salvania?
- What is the viscosity in the photosphere of the Sun?
Such questions can be answered from general considerations and a number that is not catastrophically different from the correct one can be obtained. In conditions of complete misunderstanding of the initial conditions, an error of a couple of orders of magnitude is already a worthy result!
This is precisely the situation that Drake was in, offering his generally banal formula. He reduced a completely incomprehensible task (to determine the number of extraterrestrial civilizations) to a set of subtasks that can be assessed. We may be wrong by several orders of magnitude, but in our situation this is already good!
Here is Drake's formula in its original formulation:
N = R * f p n e f l f i f c L ,
- R* - star formation rate (stars per year)
- f p - fraction of stars with planetary systems
- n e - average number of planets in the system that are ecologically suitable for life
- f l - probability of life appearing on such a planet
- f i - probability of evolution to reasonable
- f c - probability of civilization formation
- L - time of existence of civilization (years).
Some comments should be made.
Firstly, Drake himself discussed the radio search for extraterrestrial civilizations and therefore meant technically advanced civilizations using radio communications, and estimated the L parameter specifically for them. Without losing generality, you can define civilization at your own discretion and, accordingly, estimate its lifespan.
For example
...civilization can be understood in the most general form, as a socio-cultural structure distinct from isolated tribes. In this case, earthly civilization begins with the Sumerians and today spans approximately 5 millennia.
...following Jaspers, start counting from the axial time, when humanity formed the axiology in which we still exist (presumably, this is a necessary axiology of civilizational development). In this case we have two and a half millennia.
...we can limit ourselves to technical civilizations that are only a couple of centuries old.
Secondly, the dependence on the star formation rate seems somewhat unclear. At first glance, it is paradoxical that the number of extraterrestrial civilizations does not depend on the number of stars in the galaxy, but only on the frequency of star formation. In fact, the size of the galaxy is implicitly included in this parameter, because the larger the star system, the more new stars are born in it. However, in modifications of the formula the number of stars in the Galaxy can also be used, but then one has to use the obscure parameter “lifetime of the Galaxy”. The original version of the form is more accurate.
I'll explain what I'm talking about.
It is clear that f = f p n e f l f i f c is the probability of the appearance of a civilization at an arbitrary random star. R* stars are born per year. After the required period, n = R * f civilizations will arise on these stars. During the existence of a civilization (L years), its contemporaries will be n L other civilizations. This, in particular, means that R * is the star formation rate not at the present time, but approximately when the Sun was born. (Drake himself spoke about the rate of star formation averaged over the lifetime of the Galaxy, which is generally incorrect.) Within the limits of acceptable accuracy, this detail can be neglected.
There are serious factors that are usually not mentioned when talking about the Drake formula that can seriously correlate the result. Some of them work to increase, others - to decrease the probability.
I'll start with the bitter.
"Ecological habitability" depends primarily on surface temperature, that is, on the temperature of the central star and its distance. It is important that the temperature regime should not go beyond acceptable limits during the entire period from the appearance of life to the death of civilization. Using our example, we should talk about 4-5 billion years, which means discarding too hot stars, unstable stars and stars above the Hertzsprung-Russell Main Sequence (fortunately there are not so many of them). In general, it would be worth redefining the f p parameter as “the fraction of stable stars with planetary systems,” where the meaning of “stability” is explained above.
Here's something nice.
The formula implies that civilization is a one-time phenomenon in the history of the planet. That is, the scenario is this: life appeared on the planet, evolved to intelligent life, a civilization formed, and the civilization died. That's all.
That's all? Why can't a new civilization arise based on the same mind? Why can't a new mind arise (and create a civilization) if the old one has died? Why can’t a new life arise if the old one was destroyed, say, as a result of a catastrophe, evolve to intelligence, etc.? The "disposability" of civilization is a very strong and completely unfounded limitation in Drake's formula. If civilization is a renewable thing, then in its present form the formula is significantly inaccurate: the parameter L must be multiplied by the number of reincarnations n r , and its growth will lead to nonlinearity when the total time L n r becomes correlated with the age of the star.
Of course, the question of the n r factor is highly speculative. In particular, it depends on the scenario of the death of civilization, and this is an area of pure futurism, and not at all a serious scientific forecast.
During a conference in the city of Green Bank, located in the state of Virginia, USA, which took place in 1961, a dispute arose between scientific participants, astronomers and astrophysicists on the topic of a report by physicists Philip Morrison (born in 1915) and Giuseppe Cocconi (born in 1914) . It discussed the possibility of scientists around the globe, who had just begun to break through to a serious level of receiving and decoding radio signals, to receive a message and contact the civilizations of other worlds in the galaxy through radio telescopes. There were also thoughts that if such intelligent extraterrestrial civilizations exist, then most likely they are already sending signals and may be ready for contact with earthlings. It is only necessary to receive these signals and accurately decipher them. Moreover, during the conference a problem was posed: how can one calculate the number of such intelligent civilizations ready to contact us?
Literally the next day (namely, on the night from November 1 to 2), after this question was voiced, American radio astronomer Frank Drake recommended using the following formula to calculate the number of extraterrestrial civilizations (EC, aka N)
N = R?P?Ne?L?C?T?L, in which:
- R is the number of stars that are formed in the Universe annually;
- P is the chance that the star has a planetary system;
- Ne is the probability that between these planets there will be one on which there will be a chance of the origin of life;
- L - the possibility that life can actually arise on such a planet;
- F is the probability of the emergence of intelligent life forms on the planet;
- C - the real probability that life that originated on the specified planet chose a technogenically developing path, it has the means by which it can communicate through signals in space and is ready to contact other worlds;
- T is the standard average time during which a civilization that would like to contact other worlds constantly sends radio signals in the hope of communicating with the CC.
N = N*?P?Ne?L?F?C?T/Tg, in which:
- N* - the number of all stellar objects in our galaxy;
- Tg is the lifetime of our galaxy.
- R - the number of stars equal to 10 that are discovered every year;
- P - it is assumed that half of the stellar objects have planets;
- Ne - it is found that only two planetary objects can have life;
- L - equals 1, if conditions allow, then life on the planet will definitely arise;
- F is just a hundredth of the probability that life on the planet will be intelligent;
- C - only 1% of intelligent worlds that are ready and express desires for contact with other worlds;
- T - an indicator of 10,000 years (a civilization that leads technological development lives about 10,000 years).
However, during the above-mentioned conference, only the number of stars that can be formed from year to year could be known, that is, the variable R. Regarding other parameters in this formula, for example, Ne (the number of terrestrial planets), it is very ambiguous . If we take our Solar system as a basis, then in it we can choose either the singular Ne (our Earth) or the plural (for example, the five planets of our system, such as Venus, Earth and Mars and any one large satellite of the giant planets Jupiter or Saturn) space objects with properties and descriptions of planets.
If we take forecasts with an optimistic future, then our Galaxy is simply crammed with worlds that have sufficient technological development (N), and our civilization is simply a young and inexperienced creature in comparison with them. Thanks to this, the news immediately became accessible to the media, and then the idea was formed and established in the minds of all people that earthly civilization is not the only one in the Universe and that extraterrestrial intelligence exists.
However, over time, the optimistic forecast that Drake's formula generated becomes very distant. If we take the Solar System as an example, the possible origin of life on the planets is very unlikely, and if it is possible, then only under a huge layer of ocean ice on Saturn’s moon Europa. Since 1961 (the year of the Green Bank Conference), terrestrial astronomers have discovered multiple planetary systems around stars that had long been known, but, alas, they very vaguely resembled our own, Solar. Since their planetary objects have orbits with the shape of highly elongated ellipses, with a very large eccentricity (the degree of deviation from the circle of the numerical characteristic of the canonical section). That is, the temperature indicators that occur on these planets throughout the year have a very large difference and are not suitable for the development of protein life on these planets.
It was also found that the necessary indicators that characterize the ability to retain water on its surface for a body that is considered a planet for a huge period of time (which is calculated in billions of years), without its evaporation and (or) freezing, are quite large. And so far only our Earth corresponds to them, since no other such planetary objects have been discovered. This is explained by the fact that the radius of the body, if it does not correspond to certain parameters even by a few hundredths, then life on the planet will not arise or will be destroyed.
In 1981, astronomers rethought Drake's formula to apply it to contemporary scientific research and discoveries. The value of N was calculated to be equal to 0.003 in approximate calculations. That is, 3 out of a thousand (or one out of three hundred) star cluster systems should have a civilization that has a sufficiently developed technogenic base and expresses a desire to communicate. That is, following calculations, the percentage of detection of such a civilization is 1:300.
Over the past period of time, no progress has been made to increase this figure. There is a lot of criticism about this formula, which cannot give an exact result, but its consideration led to the development and allocation of funds (several million dollars) for the promotion of astronomy and many natural sciences (biology, geology, etc.), as well as computer search programs. Although using this formula you can definitely substitute two variables:
- R is the number of stars formed per year in the Universe and which can be determined;
- P is the probability that the star has a system of planets.
