Another Drake Equation

I propose to estimate a lower bound for the probability of passage through the Gaian bottleneck. The first Gaian bottleneck is converting a wet, rocky planet that forms in the HZ to one that is Gaian regulated in a way that assures habitable stability for billions of years, thus providing an opportunity for intelligent life to evolve. The second Gaian bottleneck is passage of an evolved intelligent species through those dangerous centuries when the intelligent species so dominates the planet's atmosphere that it risks destroying the Gaian regulation of the past billions of years, which is equivalent to humanity surviving its Anthropocene Era. I claim that the probability of passage through the first Gaian bottleneck, G1, is so difficult to predict that its uncertainty dominates any calculation of the abundance of intelligent life in the universe. I claim that a lower limit for it can be derived based on the fact that the Earth passed it. I derive that G1 > 5e-21. Using plausible estimates for the other factors in a revised Drake equation I conclude that "we are alone" in our galaxy.   

Classical Drake Equation

In 1960 Frank D. Drake presented the "Drake Equation" for the purpose of stimulating a conversation about intelligent life in the galaxy with the hope of encouraging a search for extraterrestrial intelligent beings.

    Ng = R* fp ne fl fi fc L

where Ng = number of communicating intelligent civilizations in the galaxy, R* = rate of star formation, fp =  fraction of stars that have planets, ne = fraction of these planet that have an environment that could support life, fl = fraction of those that actually support life, fi = fraction of those with intelligent life, fc = fraction of those that are technologically capable of communicating over interstellar distances, and L = average lifetime of those civilizations. Notice that the "units" for the answer is simply a number, since R* time L have units that cancel.

Let's interpret R* to be the rate of star formation for sun-like stars, ~ 1/year. An optimist would set fp = 1, ne = 1, fl = 1, fi = 1 and fc = 1. The equation then reduces to Ng = L. So if L = 100 years (an approximate lower limit for humanity), then there would be 100 communicating civilizations in the galaxy at any one time. An optimist might argue for L = 1000 or 10,000 years, but for now let's just say we don't know L.

Let's ask how many communicating civilizations there might be in the universe at any given time, Nu. If the number of galaxies is 5e11, then Nu = 5e11 L.

Now let's ask how many communicating civilizations have ever existed during the history of the universe, Ntot. Since the lifetime of the universe is Lu ~ 20 billion years = 2e10 years, Ntot = 2e10 5e11 / L = 1e22 / L.

We have information about Ntot; it's > 1 (i.e., humans).

We are safe in estimating L > 100 years, so what could be the meaning of the last equation. We're now in a position to re-evaluate some of the less certain f-values in the Drake equation, or place limits on them.

I'm going to take the position that he most uncertain combination of terms is the product f =  ne fl fi fc. I'm working up to writing a different Drake equation, but for now let's evaluate f. The original Drake equation can be written:

    Ng = R* f L

and similarly,

    Ntot = R* f Lu / L

Solving for f yields:

    f = Ntot / (R* Lu / L)

Substituting values for Ntot, R* and Lu yields:

    f  > 5e-23 [year-1] L

and since we're safe is stating that L > 100 years, we have:

    f > 5e-21

We now have an evidence-based estimate for ne fl fi fc.

Gaian Bottleneck

The Gaian Bottleneck is customarily described as a wet planet in the circumstellar habitable zone (CHZ) evolving life early in the planet's history that produces negative feedback dynamics regulating the atmosphere in a way that overcomes the positive feedback dynamics of an otherwise abiotic planet that would lead to either the runaway greenhouse sterility or albedo ice cube sterility. It is thought that this biotic intervention must occur during the first 1/2 to 1 billion years after the end of the heavy bombardment, which for Earth was 3.8 Gya. However, I am unaware of a derivation of the probability that such a Gaian regulation should occur. I will refer to this probability as G1. As an approximation, G1 = ne fl.

For any planet that survives this first Gaian Bottleneck there is a possibility that life will continue to evolve, and eventually produce an "intelligent" species. Humanity is usually used as an example of what is meant by an intelligent species. Given that humans today have had such a profound influence over the Earth's climate, raising the possibility of an atmosphere that warms to such a level as to threaten the extinction of humanity, and other species, it is reasonable to ask if the Gaian regulation of the Earth's past 3.8 billion years is again under threat. I refer to this as the Second Gaian Bottleneck.

How long does a communicating species exist before it confronts Second Gaian Bottleneck? Let's call it L1, and assign it with a round number of 100 years. Then, if it succeeds in passing the Second Gaian bottleneck, with probability G2, how long will species endure? Let's call it L2. The Drake equation now has two components, one associated with G1 and the other associated with G2. Substituting G1 = ne fl

    Ng = R* (G1 fi fc L1 + G2 L2)

where G1 and G2 are the two Gaian Bottleneck passage probabilities. This equation assumes that after passage through the Second Gaian Bottleneck a species will remain communicative for L2 years.

In the previous section I derived that the right side of the above equation is f > 5e-21. We can therefore begin to place bounds on the terms on the left side of the equation. It is my opinion that the least known of the 3 terms on the left side is G1. Let's set fc =1, L1 = 100 years, and adopt the following reasonable bounds for fi, G2 and L2:

    1e-6 < fi < 1 
    1e-3 < G2 < 1
    0 < L2 < 1e6 years

Solving for G1 is now possible:

    G1 > 5e-21 / (100 (1e-6 to 1) + (0 to 1e-6) (1e-3 to 1)), or

    G1 > 5e-21 / ((1e-4 to 1) + (0 to 1e-6)), or

    G1 > 5e-21

This may be the first evidence-based derivation of G1, the probability of a wet planet in the HZ developing life (shortly after its heavy bombardment ends) that happens to produce negative feedback climate dynamics that overcome the normally present abiotic positive climate dynamics leading to runaway greenhouse or high albedo ice cube sterile end states, such that the planet can remain habitable for the billions of years necessary for life to evolve sufficiently long as to produce an intelligent species. 

Another Drake Equation

Implicit in the above is the assumption that whenever an intelligent species evolves, and becomes technologically "communicative," it has ~ 100 years before it faces the Second Gaian Bottleneck. I believe G1 is so much more uncertain than R*, fp, fl, fc that we can simply set them to 1, and set and L1 =100 years, and rewrite the Drake Equation using both Gaian Bottleneck terms:

     Ng = G1 fi 100 + G1 fi G2 L2

     Ng = (G1 fi ) (100 + G2 L2)

The right side has two terms, one associated with a "free pass" 100 years before facing the Second Gaian Bottleneck, and the second term for the possibility that it could pass the bottleneck and endure for L2 years.


Let's play with some assumptions. Working backwards, if we want to be somewhat optimistic and believe that we have the company of one other intelligent and communicating civilization in the galaxy, at this time, i.e., Ng = 2, what parameter combinations would allow that? Setting fi= 1, G2 = 0.1, and L2 = 1000 years, this can be achieved with G1 = 0.01. If G1 << 0.01, then we'd have to increase G2 or L2 to maintain the likely presence of company in our galaxy.

Let's be wildly optimistic and adopt G1 = 0.1 and G2 = 0.1. With L2 = 1000 years we calculate Ng = 20. In order to arrive at greater values for Ng we have to assume that L2 > 1000 years.

Is it likely that L2 > 1000 years? I don't think so, based on sampling theory applied to the human situation (as described in my book Genetic Enslavement, 2014). To date ~ 6e10 humans have existed (since 50,000 years ago). With plausible future population scenarios an equal number of humans will be born during the next 300 years. If humanity disappears at that time, then we now will be close to the 50 percentile of all humans in the entire past/present/future sequence. I have shown that if we require the present generation of humans to reside within the 25% to 75% range of birth sequences, which can be stated as encompassing 50% of future scenarios, then humanity's demise will occur sometime between 2100 AD and 2500 AD. In other words, sampling theory states that humanity will be "communicative" for ~ 350 200 years. If humanity's G1 = 1, then humanity's L2 < 450 years. This is just a suggestion of what values for L2 should be considered.

I conclude that Ng<< 10, and that we are probably "alone" in the galaxy.


Chopra, A. and C. Lineweaver, 2016, Astrobiology, 16, 1.

Gary, B. L. 2014, Genetic Enslavement: A Call to Arms for Individual Liberation, link


For those who don't want to believe that "we are alone" in the universe, I remind you that "If intelligent life originated only once throughout the universe, during the entire lifetime of the universe, we, of necessity, must be it!"

Another things to remember was stated by Einstein, when a reporter pressed him for an example of infinity: "The size of the universe, and human stupidity; but I'm not sure about the first one."


WebMaster: B. GaryNothing on this web page is copyrighted. This site opened:  2016.02.11 Last Update:  2016.02.12.