Drake equations. New Fermi Paradox and Drake Equation

The number of extraterrestrial civilizations wishing to come into contact with ours is predictable.

Generally speaking, few major scientific discoveries are strictly dated—not just 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— the number of stars formed annually in the Universe; R - the probability of a star having a planetary system; N e - the probability that among the planets there is an Earth-like planet on which the origin of life is possible; L— the likelihood of the real origin of life on the planet; WITH - the likelihood that intelligent life has followed a technogenic path of development, has developed means of communication and wants to make contact and, finally, T- 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, then to terrestrial planets ( N e) even in our solar system, it was possible to classify from one (only the Earth) to five (Venus, Earth, Mars, and one of each of the large satellites of Jupiter and Saturn) space objects of the planetary type. With optimistic forecasts of this kind, it turned out that the Galaxy was literally teeming with millions of technologically advanced civilizations ( N), and we are essentially 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 that the annual temperature difference on them looks 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, no such planets have 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 available to us on the right side of the formula, we obtained the value 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 there No.

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?

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.

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, no such planets have 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

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Not long ago, our resource “” published a material called “”, which touched upon the question of the existence of alien intelligent civilizations in the Universe. But if there this very possibility was questioned, here we will consider a formula that often serves as a refutation of the above-mentioned paradox. This formula is called the Drake equation.

Some general information

It’s worth starting with the fact that there is a special project under the general name “SETI” (an abbreviation for Search for Extraterrestrial Intelligence). It includes various projects and activities aimed at searching for extraterrestrial civilizations and making contact with them. The project has existed for several decades (since 1959), almost from the moment when American astronomer Frank Drake conducted his first experiment. SETI searches are based on listening to radio waves that may be sent by other civilizations from the depths of space. Drake himself even then considered this an indicator of a high-tech society, as well as the most acceptable and reasonable means for searching for extraterrestrial life forms.

The probability of detecting any signal at a distance of more than 500 light years is practically zero, i.e. 500 light years is the limit within which modern technologies can generally detect any radio signal. It follows from this that the so-called “Great Silence”, which radio telescopes are constantly detecting, does not mean that other life in the Universe is not possible. And higher chances of approving something with a more or less significant degree of confidence can only appear if earthly “receivers” can increase the range of signal reception by at least another 900 light years.

In the middle of the last century, humanity had even less data on this topic. However, already at the time when the Soviet cosmonaut Yuri Gagarin became the first person to orbit the Earth (1961), Frank Drake developed his equation to approximately estimate the number of possible alien civilizations in our galaxy, called the Milky Way. This equation is based on methods for detecting electromagnetic pulses.

Drake equation

The Drake equation is formulated as follows:

N = R * Fp * Ne * Fl * Fi * Fc * L, where:

N – the number of intelligent civilizations that are ready to make contact

R is the number of stars appearing during the year in the Milky Way galaxy.

Fp – percentage of stars that have planets in their orbits

Ne is the average number of planets and their satellites whose conditions are suitable for the origin of life

Fl – probability of life appearing on a suitable planet

Fi – the probability of the appearance of intelligent life forms on planets where life is possible at all

Fc – the ratio of the number of planets on which intelligent life forms are capable of contact and seek it, to the number of planets on which there are intelligent life forms at all

L – time during which intelligent life exists, can come into contact and wants to do so

Analysis of the Drake Equation

Looking at the Drake equation, it becomes obvious that the value of N cannot be determined exactly. In addition, if you move along the equation from left to right, estimates of all quantities become more and more abstract. However, this equation should not be assessed by numbers alone. Some researchers are convinced that this formula is only a way of organizing human ignorance. And if we consider the hypothesis of the existence of extraterrestrial intelligence from a purely mathematical point of view, then the possibility of obtaining an answer to the question about the number of alien civilizations is significantly limited. The L value is the most important in the entire equation. A person cannot know how long a technologically advanced civilization can survive. And even if we assume that there is only one alien civilization, and has existed for billions of years or even eternity, then this will be enough to equate N and L in the equation.

But searching for extraterrestrial intelligence only by listening to radio waves would be a mistake. Thanks to the development of astrobiology and cosmology, man's perception of space and the ways of development of other forms of life has changed greatly. At the beginning of the existence of SETI, its experts predicted the rapid development of terrestrial radio technologies and the growth of radio traffic, but the “dot-dash-dot” connection faded against the background of satellites sending their signals to the Earth, and the emphasis in telecommunications shifted from radio to fiber optics for the Internet. traffic and cable TV, which means that no serious radio signals will be received from the Earth for at least another hundred years.

Another weak point of the formula is the number of planets on which intelligent life forms can develop. Presumably, their number should be within 10 thousand in our galaxy. But at present there is no evidence that there is any fundamental principle that could direct the primordial substance towards the development of Homo Sapiens. And this question will remain unanswered until evidence of life is found on at least one planet in the solar system.

Among other things, the Drake equation does not take into account such indicators as the age of the galaxy itself and chemical-mechanical parameters, for example, the presence of certain elements necessary for the formation of planets and the origin of life. According to some experts, the Drake equation does not imply a Universe that is constantly in dynamics, but a special cosmological constancy.

The formula contains the approximate number of Earth-type planets, but does not provide estimates of when intelligent life forms appear on these planets. The enormous age of our galaxy and the likelihood that intelligent life on its planets could have been present 2 and 4.5 billion years ago, but could have already died out, do not provide practically any space for detecting radio waves.

To date, astronomers have already found approximately two thousand extrasolar planets. And the total number of stars similar to the Sun can be over 40%. But many planets are too large and are in orbits very close to “their” stars. These planets are called "Hot Jupiters". However, scientists predict that if search methods are improved, it will be possible to find planets of a smaller size and with more suitable orbital characteristics. Plus, over the past twenty years of research, it has been possible to find out that there may be billions of planets in the Milky Way, on which life is possible, capable of existing in extreme conditions, for example, with high levels of carbon dioxide, at a depth of up to 10,000 meters and even in sulfuric acid. acid.

But despite its “flaws,” the Drake equation greatly influenced people’s thinking. Mainly, it served as the starting point for the emergence of astrobiological science. The eminent American astrophysicist Carl Sagan praised the fact that the equation showed a high percentage of detection of intelligent extraterrestrial life. And not so long ago, in 2010, Italian astronomer Claudio Maccone published his version of the Drake equation - the statistical Drake equation, which is more complex, but also more reliable. Using the new formula, Maccone was able to determine that within the Milky Way alone there could be 4,590 extraterrestrial civilizations, which is more than 1,000 more than the number that was obtained in the classic version of the equation. In addition to this, the new formula showed that in addition to human civilization there may be up to 15,785 others possessing high technology.

But even if the different galactic communities were at the same distance from each other, the average distance would be 28,845 light years, which makes any contact between these communities impossible, even if it were carried out using electromagnetic radiation traveling at the speed Sveta. And even if such a number of civilizations existed, interstellar communication between them would experience very serious technological problems.

In fact, the Drake equation is subject to scrupulous and detailed study, and, without being an expert in the relevant field, it is quite difficult to really understand what’s what. But our goal was by no means an exhaustive explanation of the equation, but only an indication that scientists around the world are approaching the question of the existence of extraterrestrial intelligence more than seriously, and this has very good reasons.