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So - You're Telling Me There's A Chance. . . .

On Sunday, The New York Times published an article by Adam Frank titled Yes, There Have Been Aliens.  Frank, a professor of astrophysics at the University of Rochester, maintains that the probability of advanced life in the universe at some time is quite high.  To use his words, it "almost certainly existed."  I find it fascinating to see what I think could be called eagerness approaching desperation on the part of so many in this field to find evidence of alien presence.  Frank's article provides a window into such a mindset.

The Details

Frank, along with his colleague Woodruff Sullivan of the University of Washington, arrive at their conclusions by massaging the somewhat famous Drake Equation.  The equation was designed to outline the factors on which the likelihood of an existing advanced alien civilization would depend.  The equation looks like this:

N = R* ⋅ fp ⋅ ne ⋅ fl ⋅ fi ⋅ fc ⋅ L

Before you leave, let me assure you this isn't as math-intensive as it seems.  Drake's equation is basically telling us that the number of existing advanced civilizations (N) is equal to the product of the average rate of star formation in a given area of space (R*), the fraction of extant stars with planets (fp), the average planets per star with planets capable of supporting life (fl), the fraction of those planets that have developed life (fi), the fraction of those lifeforms that have developed communication skills (fc), and the length of time over which such communications - detectable radio signals - could be sent (L).

Fair enough.  Fair, too, is the massaging done by Frank and Sullivan ("F&S").  Rather than analyzing existing advanced civilizations, they take a more modest approach and examine the likelihood of such a civilization existing at any time - what they refer to as an archaeological approach.  F&S begin by splitting the Drake equation into its two logical components as follows:

A = [N*fpnp] ⋅ [flfift]

Here, they replace N with A, as they are looking not for existing civilizations, but any ('A' is for archaeology).  On the other side of the equation, we see that they have compartmentalized the equation whereby the first set of brackets involves the astrophysical components (number of starts, stars with planets, number of such planets in the habitable zone of the star), and the second set involves the biological/technical advancement components (the probability of life on a habitable planet, the probability of intelligent life, and the probability of technologically advanced life).  As such, the equation is further simplified for ease:

A = Nast ⋅ fbt

So:  The probability of the existence at any time of a civilization capable of sending/receiving radio communications (A) is a function of (i) the number of life permitting planets, and (ii) the likelihood of technologically advanced life actually developing (by means of evolution) on such planets. If nothing else, perhaps F&S have done us all a service by clearly distinguishing the different components of the Drake equation. 

The Results

Now that F&S have the equation just how they want it (again, fairly so), all of these mathematical symbols need some real numbers if they wish to sustain their claim.

Astrophysics

For the calculation of Nast, they rely on recent developments in astronomy and astrophysics.  Whereas the discovery of a planet outside of our solar system was once deemed an incredible find, these exoplanets are now discovered - as the author says - on a wholesale level.  As is typical in these types of stories, there is a slight of hand at play.  Frank writes, "We now know, for example, that every star in the sky likely hosts at least one planet;" while later he writes, "We know that the percentage of stars hosting planets is about 100."  To me, this seems like a bit of an unexplained leap: that every star likely hosts a planet to simply stating that the proportion is about 100%.  We have actual knowledge of about 3,000 or so planets in a universe with 2x1022 stars (using figures provided by F&S), but I will grant them the benefit of the doubt on this point.  Further, I will grant them that of all the planets around all the stars, approximately 20% of them are in the "habitable zone," i.e., not too close and not too far from their star.  As such we can use their figures for calculating Nast :

Nast = N* ⋅ fp ⋅ np (from above, before simplification)

         = 2x1022 ⋅ ∼ 1 ⋅ 0.20 (data used by S&F: number of stars x stars with planets x fraction of planets in habitable zone)

         = 4x1021

These figures would mean that there are 4 sextillion habitable planets in our observable universe.  Not too shabby, as these things go, but does it get us any closer to their claim of near certainty for the existence of advanced life?

 Bio-Technical*

Now that we have some idea of how many habitable planets there are, we must next examine F&S's second component: the probability of advanced civilization developing by means of evolution on such a world, or fbt.  The NYT article claims that a probability of 1 in 10 billion has been used in the Drake equation as a pessimistic assumption, but how can this be?  Remember, we need not only life, but intelligent life that has used that capacity to achieve technological advancement (in this case, the use of radio waves).  As we saw above, fbt is equal to f⋅ f⋅ ft.  Let's look at each of these.

The authors don't give us much hope as we begin:

Given that we have only one known example of a planet where such evolution has occurred (and also only one example of where even microbial life has evolved), there seems to be little hope in determining the fecundity of the Universe in producing technological species. 

Why don't we just use that one example we do have - Earth.  I believe it is reasonable to break down our analysis of technologically advanced, intelligent, and basic life by using humans, mammals (open to other opinions), and bacterial life as our samples, respectively.  Remember, the authors are looking at probabilities throughout time, so the calculations for what types of life have existed here on Earth should similarly take this broader approach.

Technologically Advanced Life

Certainly human beings would qualify as the type of life the authors are seeking.  It is estimated that 107,602,707,791, or 1.08x1011, human beings have inhabited this planet.  It is further estimated that the total number of mammals that have inhabited the earth is approximately 1020.  That means that the probability of technologically advanced life developing from mere intelligent life would be roughly 1.08x10-9.  Already, the supposedly "pessimistic" figure of 1:10,000,000,000 seems optimistic.  We can place a value on ft:

ft = 1.08x10-9

Intelligent Life

The mammals that have lived on earth are part of a larger grouping - basic life.  Using bacteria as a parent group, there have been approximately 5.95x1039 living organisms on earth.  Therefore, the probability of basic life developing into intelligent (animal) life is roughly 1.68x10-19.

fi = 1.68x10-19

Let's pause here, as our numbers are starting to point against the authors' claim.  Assuming we have life to begin with (a huge assumption), the odds of that life evolving into technologically advanced life can be calculated as follows:

fbt = f⋅ fi ⋅ ft

       = fl ⋅ 1.08x10-9 ⋅ 1.68x10-19

       = fl ⋅ 1.815x10-28

Frank makes this claim in the NYT:

You might assume [the likelihood of the creation of life, intelligent life and technological capacity] is low, and thus the chances remain small that another technological civilization arose. But what our calculation revealed is that even if this probability is assumed to be extremely low, the odds that we are not the first technological civilization are actually high. Specifically, unless the probability for evolving a civilization on a habitable-zone planet is less than one in 10 billion trillion, then we are not the first.

Well, unfortunately, the probability for evolving such a civilization - without considering the development of initial life - is quite a bit lower.  1.815x10-28 is considerably smaller than 1x10-22.  Over 18,000,000 times smaller.

Basic Life

We still haven't examined the final probability in S&F's bio-technical component: The development of life itself.  Again, we can turn to our very own planet for some guidance.  Using bacteria, we have 5.95x1039 examples to look at.  That's 5,950,000,000,000,000,000,000,000,000,000,000,000,000 different samples.  How many of these samples give evidence of abiogenesis (life from non-life)?  Zero.  If we want to see the flip-side of this, we could look at the 7,400,000,000 people living, or the 20,000,121,091,000,000,000 animals currently living, or the . . . (you get the idea) and see that every single one has something in common: it did not come from non-life, but from life.  For the sake of computation, let's assume one - just one - example of abiogenesis to get the ball rolling (No, I don't think there has ever been even one example - but we all know what happens when we multiply by 0).  This allows us to finish the bio-technical component of the equation that we paused above:

fbt = f⋅ fi ⋅ ft

       = fl ⋅1.08x10-9 ⋅ 1.68x10-19

       = fl ⋅ 1.815x10-28

     = 5.0x10-20 ⋅ 1.815x10-28

     = 9.076x10-48

We are now in a position to look at the entirety of the F&S formula:

A = Nast ⋅ fbt

     = 4x1021 ⋅ 9.076x10-48

    = 3.63x10-26

The probability of humanity being the only technologically advanced civilization in the history of the universe is  363,000,000,000,000,000,000,000,000 to 1.  I'm afraid I'll have to disagree with Frank in the NYT:

[T]he degree of pessimism required to doubt the existence, at some point in time, of an advanced extraterrestrial civilization borders on the irrational.

Conclusion

As I started out, there is an eagerness to believe, to hope, to find some other life forms out there in the cosmos that borders on desperation.  Perhaps Carl Sagan gives us the best explanation:

Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.

Or, as Frank, Sullivan and so many others would add, panting with anticipation, "Yet."

Personally, I find it much more rational - and less math-intensive - to simply read: "In the beginning, God," and follow the story all the way to the Cross and beyond.


* This section has been slightly modified since original publication to use mammals as the "intelligent life" sample.

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