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, G_{1}, 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 G_{1}> 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 G_{1}.
As an approximation, G_{1} = 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 L_{1}, and assign
it with a round number of 100 years. Then, if it succeeds in
passing the Second Gaian bottleneck, with probability G_{2},
how long will species endure? Let's call it L_{2}. The
Drake equation now has two components, one associated with G_{1}
and the other associated with G_{2}. Substituting G_{1}
= n_{e} × f_{l}:

N_{g} = R_{*} × (G_{1}_{}
× f_{i} × f_{c} × L_{1} + G_{2} ×
L_{2})_{}

where G_{1} and G_{2} are the two Gaian
Bottleneck passage probabilities. This equation assumes that after
passage through the Second Gaian Bottleneck a species will remain
communicative for L_{2} 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 G_{1}.
Let's set f_{c} =1, L_{1} = 100 years, and adopt
the following reasonable bounds for f_{i}, G_{2}
and L_{2}:

1e-6 < f_{i} < 1

1e-3 < G_{2} < 1

0 < L_{2} < 1e6 years

Solving for G_{1} is now possible:

G_{1} > 5e-21 / (100 × (1e-6 to 1)
+ (0 to 1e-6) × (1e-3 to 1)), or

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

G_{1} > 5e-21

This may be the first evidence-based derivation of G_{1},
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 G_{1} is so much more
uncertain than R_{*}, f_{p}, f_{l}, f_{c}
that we can simply set them to 1, and set and L_{1} =100
years, and rewrite the Drake Equation using both Gaian Bottleneck
terms:

N_{g} = G_{1} × f_{i}
× 100 + G_{1} × f_{i} × G_{2} × L_{2}

N_{g} = (G_{1} × f_{i}
) × (100 + G_{2} × L_{2})

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 L_{2} 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, G_{2}
= 0.1, and L_{2} = 1000 years, this can be achieved with G_{1}
= 0.01. If G_{1} << 0.01, then we'd have to increase
G_{2} or L_{2} 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
L_{2} = 1000 years we calculate N_{g} = 20. In
order to arrive at greater values for N_{g} we have to
assume that L_{2} > 1000 years.

Is it likely that L_{2} > 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 G_{1}
= 1, then humanity's L_{2} < 450 years. This is just a
suggestion of what values for L_{2} 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."

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*WebMaster: *B. Gary*. **Nothing on this web page is copyrighted. **This
site opened: 2016.02.11*