On the Drake equation

– Ecology leads to a simplified equation and a solution of the problem

In 1995 mankind discovered the first extrasolar planet and since then we have detected thousands of them. We have also detected planet candidates that seem to be within a certain distance to their home stars so that liquid water should exist on their surface. We have detected enough of those worlds to get into statistic ranges, where extrapolations normally are quite good (significant). Meanwhile we can predict with a high certainty that our galaxy owns at least millions of planets with conditions that allow life as we know it. But where are the aliens?


Actually, if there are so many worlds with conditions that are similar to planet Earth, there should be an agile traffic between all that planets. Aliens should regularly visit us, one might expect. Why don’t they? Where are they? Do they actually exist? At least these alien civilizations should be capable to send radio signals into the surrounding universe, as we do. We are searching for that alien radio signals since decades now but never found anything. Why is space void if there are so many planets with possible life conditions? We call this discrepancy the Fermi Paradox.

There are some possible explanations for the Fermi Paradox. I will list them later in another article and rate them according their realism. First let’s start with the Drake equation itself to get a feeling for the problem. I will present a complete new biological perspective to find a proper solution for the problem. Dr. Fank Drake, president of the SETI institute (Search for Extra-Terrestrial Intelligence), published a handy equation in 1961:

N = R * Fp * Ne * Fl * Fi * Fc * L

The result N is the number of communicative civilizations within our milky way today.


R is the number of suitable stars, stars like the sun, that form in our galaxy per year. Astronomers estimate this number of new born suns per year is about one per year or R = 1/year

Fp is the fraction of these new suns that will develop planets. Probably half of all sun-like stars will develop planets. Many suns are too small to gravitationally support a planetary system, while some of the suns have a life span that is presumably too short to develop planets, so Fp = 0.5

Ne is the number of Earth-like planets per solar system, this is planets with liquid water on their surfaces (oceans). In our solar system the number of ocean worlds Ne is a minimum of one (Earth) to a maximum of four. Four, because Europa, Ganymede and Callisto, three moons of Jupiter might also have oceans beneath their icy surfaces. We have detected other solar systems with up to 3 Earth-like planets within the liquid water region and many Jupiter-like planets that might have several icy moons with oceans beneath their surfaces. Therefor this number is very difficult to predict at the moment. Very conservative one could say 0 to 1, more optimistic 1 to 4. Most authors take the classic view of our solar system as an example and choose a conservative Ne = 1. I think Ne = 1.5 is a good compromise for the moment, it is between being to optimistic and too pessimistic.

Fl is the fraction of Earth-like planets where life develops. Now it is becoming interesting:

  • If you have a strict anthropocentric religious motivated world view, this number may be Fl = 0.78. Because the value outbalances arbitrarily the rest of the values of the Drake equation and the end result of the Drake equation becomes exactly N = 1
  • If you believe in the random creation of life on Earth the value of Fl can either be randomly chosen (depending on your gusto) between some lowest limit, let’s say one in one million times Fl = 0.000001 and a very optimistic high probability, let’s say arbitrarily 0.9. The problem is, that we will presumably never find any evidence for any kind of realistic estimation of that value.
  • If you believe in the theory of Panspermia the value of Fl should be always quite high. This theory says the seed of life on Earth came via comets from outer space. Because DNA in an cold environment, near absolute zero, in perfect vacuum and well protected against radiation by several meters of ice can physically survive billions of years. Therefor it is only a question of time, until a water-planet is hit by a comet that is transporting life. Meanwhile we know that interstellar objects are crossing our solar system regularly. We have observed the first one with our instruments two years ago. Some of them may hit Earth. The theory of Panspermia is not proven so far. But its certainty is for sure endlessly higher than the certainty that life developed randomly on Earth. The biggest advantage of Panspermia over the established theory is that it is possible to proof the theory of Panspermia in the future by means of astronomical research and space probes. If you believe in Panspermia you can assume a very high certainty of life on Earth-like planets. Let’s assume a (still conservative) value of Fl = 0.9
  • In the Theory of Interstellar Ecology, that I will describe later, the value of Fl becomes trivial and is always one. This is because in an interstellar ecology all Earth-like ocean planets permanently interchange and mix and blend not only DNA but all higher life forms that have dauer-stages like eggs, seed and spores. Therefor it is trivially Fl = 1

Fi is the fraction of life sites where intelligent life develops.

  • Up to 2012 no complex theory was available to back this value. In 2012 P. Mueller developed the closed theory of Interstellar Ecology, where he predicted that comets do not only transport molecules or DNS like Panspermia theory demands. In the theory of Interstellar Ecology any planetary ecological system is actually not a closed system but an open system that interacts via several channels over long distances with other objects in space. One of these channels is the comets that are transporting dauer-stages of life forms like eggs, spores and seed. Any dauer-stage of life can also survive billions of years in space before it starts to grow on the shores of a new world. As long the DNA of the dauer-stage survives, the dauer-stage also survives. This means that higher life forms like trees, fish, octopus, mussels, slugs, insects, amphibians, saurians (and any other kind of species that develops eggs, seed or spores) are actually permanently blended on Earth-like planets over interstellar distances. The theory goes even further: just to minimize energy, any interstellar ecology system (a group of ecological deeply entangled planets) tries to develop at least one intelligent species, that develops more efficient ways to mix and blend life forms on those Earth-like planets. With the theory of Interstellar Ecology the prediction of Fi is no guessing or wishful thinking anymore. Within the theory of Interstellar Ecology the value can be estimated, depending of the typical size of a group of Earth-like planets that are blending life forms over interstellar distances. Further developments in astronomy and exobiology and Interstellar Ecology will give us more precise models. For the moment I will assume that a typical interstellar ecosystem of planets is about 100 Earth like planets, Nie = 100. If the ecosystem is forced to reduce overall energy (as any known ecosystem does), there should emerge at least one space fairing species in the overall interstellar ecosystem, that starts to travel between those planets and thereby exchanges life forms much more efficient than comets can do. The estimation of one per hundred leads to Fi = 1/Nie or Fi = 0.01
  • In a religious motivated world picture, there might the opinion exist that any world that god creates (independent on the uniqueness of creation) is made for intelligent human beings (the pride of creation) alone, therefor: Fi = 1
  • The mere anthropocentric person, even if not religious, would for trivial reasons also set Fi = 1

Fc is the fraction of intelligent life forms that uses radio communication.

  • From an anthropocentric point of view this is 100 years (since we invented radio communication) over 100,000 years (since homo sapiens sapiens exist), so Fc = 1/1000 = 0.001
  • The religious creationist may change this to 100 years over 6000 years (since god created the Earth and Adam and Eve in the Bible) and gets Fc = 1/60 = 0.017
  • In the theory of Interstellar Ecology any interstellar ecosystem develops at least one species that is capable to conduct directed space travel. Directed space travel is not possible without radio communication. Then the value of Fc only depends on the average time of existence of those intelligent species and how often they are created. If we assume that in an interstellar ecosystem, containing 100 planets or more, intelligent species are produced quite regularly and there is always at least a minimum of them in development, they are practically permanently created and the value of Fc only depends on the average time of existence of those species. If we further assume they exist in average as long as they need time to develop (in average) the value of Fc becomes Fc = 1. If we also assume there is not much more space in the Interstellar Ecosystem for more than one intelligent species and ecological regulatory phenomena (e.g. pray and predators) will hold the number of species down to this level of one, it becomes trivial to understand why the time they develop is in average as long as the time they exist. So in the theory of Interstellar Ecology we assume that any planet would always produce space fairing, radio transmitting species, if it could. For any interstellar ecosystem we always get Fc = 1

L is the typical lifetime in years of a communicative civilization.

  • We have developed radio communication a hundred years ago. So the minimum value from a mere anthropocentric view is L = 100 years.
  • If we take for the prediction of L the theory of Interstellar Ecology into account, the following is the case: Interstellar ecosystems develop space fairing species because of the reason of energy minimization. If an intelligent species is killed once by a natural catastrophe (asteroids, vulcanos, stellar outbursts) or by itself (environmental pollution, nuclear war), there will always immediately follow a new species that was suppressed by the former so far. So, as long Earth-like conditions on the majority of the planets of the interstellar ecosystem exist, the interstellar ecosystem will work properly and will always produce man-like creatures that can do space travel – one species after the other. Therefor we just have to take the average length of Earth-like conditions on planets into account. To be on the safe side we just take the value of years since Earth had quite similar living conditions as we know it today (with an atmosphere and plants on the surface). Therefor we take L = 500 Million years and assume this is in average a typical length of a period of life supporting conditions for the whole interstellar ecology.

Interstellar Ecology (biology based)

The result of the calculation of the Drake equation with the chosen values within the context of biology based Interstellar Ecology:

Inputs (more detailed explanation above)

  • R = 1/year : estimation based on astronomical observation
  • Fp = 0.5 : estimation, based on astronomical observation
  • Ne = 1.5: estimation, based on recent astronomical observation
  • Fl = 1: is a trivial value in the theory of Interstellar Ecology
  • Fi = 1/Nie = 0.01: due to the theory of Interstellare Ecology and with the assumption of the average size of an interstellar ecosystem of 100 Earth-like planets, Nie = 100
  • Fc = 1: this is a trivial value in the theory of Interstellar Ecology, because it predicts that any interstellar ecosystem of several planets develops permanently at least one space fearing species. And directed space travel cannot work without radio communication.
  • L = 500,000,000 years: this is a trivial value in the Interstellar Ecology, because Earth as we know it, with ocean and atmosphere and life on the surface of the continents exists since ca. 500 Million years, and we simply assume this would be the average value for most of the planets and therefor for any complete interstellar ecosystem with several planets.

In the context of the theory of Interstellar Ecology the Drake formula always reduces to

N = R * Fp * Ne * 1/Nie * L

and we get:

N = 1/year * 0.5 *  1.5 * 0.01 * 500,000,000 years

And the number of radio transmitting species in our galaxy becomes:

N = 3,75 Mio

This value can be further improved, when R, Fp, Ne, Nie become more detailed with the time by means of astronomical research of interstellar comets, star formation and of extrasolar planets. There is no completely unknown value left.

In the Interstellar Ecology, if we neglect the values that are relatively well known so far, we can say that the Drake equation becomes an equation, that depends mainly on the number of planets Nie in an interstellar ecology system:

N ≈ f(Nie)

More precise:

N = const / Nie

with const = (R * Fp * Ne * L) = 375 E6 †

N = 375 E6 / Nie

N = 375 E6 / 100 = 3,75 Mio

† (You can call the const the Shepherd Constant, and the remaining equation the Drake-Mueller equation if you like.)

The Shepherd Constant gives the number of possible Earth-like worlds in the galaxy that just underly an ongoing development process to get somehow intelligent space-fairing and thereby radio emitting species. This is not an evolution (it does not mean that species become better) but a solution for the ecological energy minimization of the interstellar ecosystems where these Earth-like planets are located. The Shepherd Constant gives the candidates. Because of the relatively stable factors that result in the constant, the Shepherd constant has only a moderate variation in uncertainty.

The Drake-Mueller Equation is actually quite simple. It says that the number of actual radio signal emitting intelligent species in the galaxy is the Shepherd constant (the possible candidates), divided by the average number of Earth-like planets in a typical interstellar ecosystem. This means that Fi (= 1/Nie) is actually a suppression-, extinction- or you can even call it an annihilation-factor. If a space fairing species once connects the Earth-like planets within a interstellar ecological system, it will suppress other species to become as powerful. Such a behavior for a complex resource consumptive species is normal for any kind of ecological systems with limited resources.

Interstellar Ecology by P. Mueller in a nutshell: A typical interstellar ecosystem is a system of many stars and their Earth-like planets that interchange higher life forms via dauer-stages that are transported by comets. Although there are millions of such interstellar comets that contain spores, seed and eggs, these comets typically need hundreds of millions of years to reach their destinations. Because comets are the perfect containers for dauer-stages of life, such a long travel time does not hinder the seeds to grew immediately when hitting fertile soil. How rock and permafrost soil with dauer-stages of plants and animals can leave a planet by cosmic impacts and even leave a solar system by planetary swing-by is both a well known process. Higher life forms are spread permanently through the galaxy and are mixed and blended in average quite regularly but with very long delay. The interstellar ecosystems of several Earth-like planets tend to minimize their overall energy (like any ecosystem does) by optimizing the transport of life. They develop human-like space fairing species – at least one per interstellar ecosystem. Therefor in biology human beings have only one sense: transporting life across space. They do this much more directed, faster and therefor much more energy efficient for the overall ecosystem than comets can do.

Common scientific use

A typical application of the Drake equation based on a scientific world view, but without the context of Interstellar Ecology:

Inputs (more detailed explanation above)

  • R = 1/year : estimation based on astronomical observation
  • Fp = 0.5 : estimation, based on astronomical observation
  • Ne = 1.5: estimation, based on recent astronomical observation
  • Fl = 0.9 as an conservative estimation in the theory of Panspermia or as an very optimistic estimation for planets that are developing life completely by themself
  • Fi = 0.5: this is an arbitrarily value between 0 and 1
  • Fc = 0.5: this is an arbitrarily value between 0 and 1
  • L = 5 Million years: this is an arbitrarily average value between 0 years and 500 Million years, assuming only one of hundred species would survive for a long time.

N = 1/year * 0.5 *  1.5 * 0.9 * 0.5 * 0.5 * 5,000,000 years

N = 843,750 radio transmitting species in our galaxy. But because of the arbitrariness of Fl, Fi, Fc and L the results can easily vary from N = 1 (at least mankind exists) to N = 375 Million (with Fl, Fi = 1, Fc = 1 and L = 500 Million years). But 375 Mio again is the value of the Shepherd constant and gives us as we have learned, only the number of possible candidate planets and not the real number of intelligent species. N = 1 is a religious motivated anthropocentric world view. This means the common scientific use of the Drake equation will always produce results ’somehow‘ between this two extremes.

There’s a big problem of the application of the Drake equation without using a biology based extension like Interstellar Ecology: the values for Fi, Fc, and L will always be mere crap.

Maybe Fl can be estimated better in the future by observing interstellar comets. If interstellar comets will contain DNA, Panspermia theory was right and life did not have it’s origin on Earth. Fl will be estimated then much more precise. But Fi, Fc and L still actually remain rubbish and therefor any calculation result using the classic Drake equation.

But if we once find out that interstellar comets contain not only DNA but also seeds, spores and eggs (dauer stages) then Interstellar Ecology is proven, and the application of the Drake equation will become very precise, because Fl, Fc and L become trivial and Fi can indirectly be observed by the counting of the average number of Earth-like planets Nie within the range of such comets, as showed in the chapter before.

Non-religious anthropocentric

Just for completeness, here comes the mere anthropocentric non-religious application of the Drake equation:

Inputs (more detailed explanation above)

  • R = 1/year : estimation based on astronomical observation
  • Fp = 0.5 : estimation, based on astronomical observation
  • Ne = 1.5: estimation, based on recent astronomical observation
  • Fl = 0.9 as an very optimistic estimation of planets that are developing life
  • Fi = 1: trivially 1 for an anthropocentric person
  • Fc = 0.001: 100 years in 100,000 years
  • L = 100 years

N = 1/year * 0.5 *  1.5 * 0.9 * 1 * 0.001 * 100 years

The result is:

N = 0,07

This is wrong, because we know: we are at least the one and only radio transmitting species in our galaxy, so N = 1 is the minimum value. Therefor a mere anthropocentric view on the world was always stupid in history of science and remains stupid, at least in the application of the Drake equation.


Now comes the religious world view as an variation of the anthropocentric view:

Inputs (more detailed explanation above)

  • R = 1/year : estimation based on astronomical observation
  • Fp = 0.5 : estimation, based on astronomical observation
  • Ne = 1.5: estimation, based on recent astronomical observation
  • Fl = 0.78 an arbitrarily value to balance the equation to the result N = 1
  • Fi = 1: a mere religious motivated assumption
  • Fc = 0.017: 100 years in 6000 years
  • L = 100 years

N = 1/year * 0.5 *  1.5 * 0.78 * 1 * 0.017 * 100 years

The result will always be:

N = 1

Fi, Fc and L are fixed and given due to religious reasons. Depending on astronomical research that might slightly deviate the values of R, Fp and Ne in the near future, Fl will always be adapted to get the evident result N = 1. This approach is not scientific, but at least better than the stupid result from a mere anthropocentric non-religious world view.

Results comparison

If the theory of Interstellar Ecology is right, then the Drake equation can be simplified to the Drake-Mueller equation. The Shepherd Constant has a relative moderate uncertainty and the factors that lead to the correct constant value seem to be in the range of near time improvement of astronomical measurement gear. The only uncertainty that will remain is the average age of life-sustaining conditions on Earth-like planets that we can only transfer from our geology of Earth to other Earth-like planets.

The common scientific well known use of the Drake equation includes 3 variables, Fi, Fc, and L that can never be predicted. They will always remain completely uncertain for individual planets without no interstellar ecosystem and therefor the Drake equation cannot be used in that form. Therefor a normal use of the Drake equation in its 1961 version, will always be meaningless. It is good for speculating or academic amusement.

The theory of Interstellar Ecology gets rid of the Drakes equations uncertainties by a change of the perspective. This can be understood similar to a coordinate transformation of thinking. In an interstellar ecology all planets are driven to produce intelligent life to have part on the overall reduction of energy. Ecological regulation mechanisms like pray and predator reduce the possible number of species to a lower levels, but there will always be at least one species that conducts space travel and the next species who are ready to spread out into the universe, and will only wait as long until room is made (e.g. mankind, one could guess). And a species that conducts directed space flight will always use radio. Therefor we get for the overall ecological system a trivial Fc = 1. Fi is simply given by Fi = 1/Nie. It may be possible that an ecological system allows for a short time more than one space fairing species and Fi becomes e.g. twice as big. But in the end one complicated (resource consumptive) species will typically dominate in an ecological system over the others and suppress them. Therefor we can call Fi an suppression factor. L becomes also trivial in an interstellar ecological system because of the reason that there is always at least one space fairing species available during the long time that the Earth-like conditions on most of the planets of the local interstellar ecosystem exist. But without those formulated closed biological-ecological demands you could never say this. Therefor the values of L = 500 Mio years, Fc = 1 and Fi = 1/Nie are only correct if the theory of Interstellar Ecology proves one day to be correct.

An non-religious anthropocentric use of the Drake equation is just idiotic as we have seen, even if it seems to be reasonable and scientific at first glance.

A religious use of the Drake equation is altogether not wrong. But it is no hard science anymore. It is believe to a certain amount and at least one of the values (Fl) is just manipulated to get the correct result. This kind of corrections of input values we can also see sometimes in engineering, especially in numerical calculation, where engineers change the formulas to fit to the observed results. So does religion: we see the result (only one available intelligent radio signal emitting species in the universe) and manipulate one value in the Drake formula to get the correct result N = 1.

Best regards

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