Documents / Report
This Defense Intelligence Agency reference document, dated 11 March 2010, is one of the advanced technology reports produced in FY 2009 under the Advanced Aerospace Weapon System Applications (AAWSA) program. It introduces the Statistical Drake Equation, which replaces each factor of Frank Drake's 1961 equation with a uniform random variable to estimate how far away the nearest extraterrestrial civilization is. In the worked example, there is a 75% probability that the nearest civilization lies between 1,361 and 3,979 light years from Earth.
UNCLASSIFIED/ /f81il 8ffll1Als WliEii SUllslf 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 ist, 2008, at the 59 th International Astronautical Congress (IAC) held in Glasgow, Scotland, UK, September 29 th 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. S. 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 Di is the same numerical value previously attributed to the corresponding independent variable in (7). • But now we also ADD A STANDARD DEVIATION un, on each side of the mean value, that is provided by the knowledge gathered by scientists in each discipline encompassed by each D,. 11 UNCLASSIFIED/ ,'f811. 8ffllil,,.I! l!l!II! 8111!1/
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Report, from the dia collection. The PDF is mirrored here; the original link is above. 55 pages are in the text index: search them above, or from the library's search.