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.

    N_g = R_* × f_p × n_e ×f_l × f_i × f_c × L

where N_g = number of communicating intelligent civilizations in the galaxy, R_* = rate of star formation, f_p =  fraction of stars that have planets, n_e = fraction of these planet that have an environment that could support life, f_l = fraction of those that actually support life, f_i = fraction of those with intelligent life, f_c = 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 f_p = 1, n_e = 1, f_l = 1, f_i = 1 and f_c = 1. The equation then reduces to N_g = 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, N_u. If the number of galaxies is 5e11, then N_u = 5e11 × L.

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

We have information about N_tot; 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 =  n_e ×f_l × f_i × f_c. I'm working up to writing a different Drake equation, but for now let's evaluate f. The original Drake equation can be written:

    N_g = R_* × f × L

and similarly,

    N_tot = R_* × f × L_u / L

Solving for f yields:

    f = N_tot / (R_* × L_u / L)

Substituting values for N_tot, R_* and L_u 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 n_e × f_l × f_i × f_c.

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 = n_e × f_l.

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 = n_e × f_l: 

    N_g = R_* × (G₁ × f_i × f_c × 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 f_c =1, L₁ = 100 years, and adopt the following reasonable bounds for f_i, G₂ and L₂:

    1e-6 < f_i < 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_*, f_p, f_l, f_c that we can simply set them to 1, and set and L₁ =100 years, and rewrite the Drake Equation using both Gaian Bottleneck terms:

     N_g = G₁ × f_i × 100 + G₁ × f_i × G₂ × L₂

     N_g = (G₁ × f_i ) × (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.

Implications

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., N_g = 2, what parameter combinations would allow that? Setting f_i= 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 N_g = 20. In order to arrive at greater values for N_g 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 N_g<< 10, and that we are probably "alone" in the galaxy.

References 

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

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

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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. Gary.  Nothing on this web page is copyrighted. This site opened:  2016.02.11.  Last Update:  2016.02.12.