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

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million or even billions in the optimist's opinion. A lot of uncertainty is thus affecting our
knowledge of N as of 2010. In all cases, however, the final result about N has always
been a sheer number, i.e., a positive integer number ranging from 1 to millions or
billions. This is precisely the aspect of the Drake equation that this author regarded as
"too simplistic" and improved mathematically in his paper #IAC-08-A4.1.4, entitled
"The Statistical Drake Equation" and presented on October 1st , 2008, at the 59th
International Astronautical Congress (IAC) held in Glasgow, Scotland, UK, September
29th thru October 3rd, 2008. That paper is attached herewith as Appendix B. Newcomers
to SETI and to the Drake equation, however, may find that paper too difficult to be
understood mathematically at a first reading. Thus, I shall now explain the content of
that paper "by speaking easily." I thank the reader for his or her attention.
5. The Statistical Drake Equation
We start by an example.
Consider the first independent variable in the Drake equation (7), i.e., Ns, the number
of stars in the Milky Way galaxy. Astronomers tell us that approximately there should
be about 350 millions stars in the galaxy. Of course, nobody has counted (or even seen
in the photographic plates) all the stars in the galaxy! There are too many practical
difficulties preventing us from doing so: just to name one, the dust clouds that don't
allow us to see even the Galactic Bulge (i.e. the central region of the galaxy) in the
visible light (although we may "see it" at radio frequencies like the famous neutral
hydrogen line at 1420 MHz). So, it doesn't make any sense to say that Ns = 350 x 106,
or, say (even worse) that the number of stars in the galaxy is (say) 354,233,321, or
similar fanciful exact integer numbers. That is just silly and non-scientific. Much more
scientific, on the contrary, is to say that the number of stars in the galaxy is 350 million
plus or minus, say, 50 millions (or whatever values the astronomers may regard as
more appropriate, since this is just an example to let the reader understand the
difficulty).
Thus, it makes sense to REPLACE each of the seven independent variables in the Drake
equation (7) by a MEAN VALUE (350 millions, in the above example) PLUS OR MINUS A
CERTAIN STANDARD DEVIATION (SO millions, in the above example).
By doing so, we have made a great step ahead: we have abandoned the too-simplistic
equation (7) and replaced it by something more sophisticated and scientifically more
serious: the STATISTICAL Drake equation. In other words, we have transformed the
classical and simplistic Drake equation (7) into an advanced statistical tool for the
investigation of a host of facts hardly known to us in detail. In other words still:
•
We replace each independent variable in (7) by a RANDOM VARIABLE, labeled
D, (from Drake).
•
We assume that the MEAN VALUE of each D, is the same numerical value previously
attributed to the corresponding independent variable in (7).
•
But now we also ADD A STANDARD DEVIATION cr0; on each side of the mean value,
that is provided by the knowledge gathered by scientists in each discipline
encompassed by each D,.
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