AAWSAP DIRD, An Introduction to the Statistical Drake Equation, March 2010

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After having found the above two distances (1933 and 2670 light years, respectively),
the next natural question that arises is: "what is the range, back and forth around the
mean value of the distance, within which we can expect to find extraterrestrials with
"the highest hopes?" The answer to this question is given by the notion of standard
deviation that we already found to be given by (11) and (13),
I'
0'2
~
CTET_Distance = Ce 3 e •8 Ve 9 -1 ""1309 light years .
More precisely, this is the so-called 1-sigma (distance) level. Probability theory then
shows that the nearest extraterrestrial civilization is expected to be located within this
range, i.e. within the two distances of (2670-1309) = 1361 light years and
(2670+1309) = 3979 light years, with probability given by the integral of fET_oistance(r)
taken in between these two lower and upper limits, that is:
i
3979 1igh1 years
fET Disiance (r) dr:::: 0.75 = 75 %
(15)
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In plain words: with 75 percent probability, the nearest extraterrestrial civilization is
located in between the distances of 1361 and 3979 light years from us, having assumed
the input values to the Drake Equation given by table 1. If we change those input
values, then all the numbers change again, of course.
9. The "Data Enrichment Principle" as the Best CLT
Consequence Upon the Statistical Drake Equation (Any
Number of Factors Allowed)
As a fitting climax to all the statistical equations developed so far, let us now state our
"DATA ENRICHMENT PRINCIPLE." It simply states that "The Higher the Number of
Factors in the Statistical Drake equation, The Better."
Put in this simple way, it simply looks like a new way of saying that the CLT lets the
random variable Y approach the normal distribution when the number of terms in the
sum (4) approaches infinity. And this is the case, indeed.
10. Conclusions
We have sought to extend the classical Drake equation to let it encompass Statistics
and Probability.
This approach appears to pave the way to future, more profound investigations
intended not only to associate "error bars" to each factor in the Drake equation, but
especially to increase the number of factors themselves. In fact, this seems to be the
only way to incorporate into the Drake equation more and more new scientific
information as soon as it becomes available. In the long run, the Statistical Drake
equation might just become a huge computer code, growing in size and especially in
the depth of the scientific information it contains. It would thus be Humanity's first
"Encyclopaedia Galactica."
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