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This Defense Intelligence Reference Document, dated 11 March 2010, was prepared by the Defense Intelligence Agency's Defense Warning Office under the Advanced Aerospace Weapon System Applications Program. It introduces the Statistical Drake Equation, which treats each Drake factor as a random variable with a mean value and a standard deviation. Using its example inputs, the paper estimates that the nearest extraterrestrial civilization lies between 1,361 and 3,979 light years away with 75% probability. The author's 2008 International Astronautical Congress paper is attached as an appendix.
From the source:Release of 2026-09-18 Incident: 3/11/10, Las Vegas, Nevada. Released with redactions. This document is a Defense Intelligence Reference Document (DIRD), a technical reference format used by the Defense Intelligence Agency (DIA) to capture baseline knowledge on a specific topic for later analytic use. DIRDs are best understood as reference and synthesis products rather than as original research. It is one of 38 DIRDs produced under the Advanced Aerospace Weapon System Applications Program (AAWSAP) between 2009 and 2011. Because AAWSAP’s scope permitted a broad range of supporting topics, not every DIRD in the series directly concerns aerospace systems or future threat assessment. The following summary reflects the DIRD’s scope and framing at the time of writing and should not be read as implying current validation of the concepts discussed. This DIRD introduces the Drake Equation, a well-known thought framework for estimating how many communicative extraterrestrial civilizations might exist in the galaxy. It reformulates the equation in statistical terms, arguing that the usual approach of assigning fixed values to its variables is too simplistic because major inputs are uncertain and are better modeled as probability distributions. Using that approach, it concludes that, if one accepts the underlying logic of the Drake Equation, the estimated number of communicating civilizations should be treated as a range of possible values, and that the likely distance between neighboring civilizations can likewise be expressed statistically rather than as a single figure. The document is primarily a mathematical and methodological exercise, and its worked examples rely on assumed values to illustrate the framework rather than to establish a firm astrophysical estimate. Overall, it is an attempt to formalize uncertainty within the Drake framework rather than an attempt to bound the actual likelihood, prevalence, or proximity of extraterrestrial civilizations.
UNCLASSIFIED/ /FO R OFFIEil.t.k W&i Q~lls¥ 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 up in size and especially in the depth of the scientific information it contained. It would thus be Humanity's fast "Encyclopaedia Galactica," Unfortunately, to extend the Drake equation to Statistics, it was necessary to use a mathematical apparatus that is more sophisticated than just the simple product of seven numbers. When this author had the honour and privilege to present his results at the SETI Institute on April lJlh, 2008, in front of an audjence also including Professor Frank Drake, he felt he had to add these words: " My apologies, Frank, for disrupting the beautiful simplicity of your equation," ACKNOWLEDGEMENTS The author is grateful to Drs. Jill Tarter, Paul Davies, Seth Shostak, Doug Vakoch, Tom Pierson, Carol Oliver, Paul Shuch and Kathryn Denning for attending his first presentation ever about these topics at the "Beyond" Center of the University of Arizona at Phoenix on February 8th , 2008. He also would like to thank Dan Werthi.mer and rus School of SETI young experts for keeping alive the interplay between experimental and theoretical SETI. But the greatest "thanks" goes of course to the Teacher to all of us: Professor Frank D. Drake, whose equation opened a new way of thinking about the past and the future of Human in the Galaxy. REFERE CES [I] http://en.wikipedia.org/wiki/Drake equation [2] http://en.wikipedia.org/wiki/SETI [3] http://en.wikipedia.org/wiki/ Astrobiology [4] http://en.wikipedia.org/wiki/Frank Drake l5J Athanasios Papoulis and S. Unnikrishna Pillai, "Probability, Random Variables and Stochastic Processes", Fourth Edition, Tata McGraw-Hill, ew Delhi, 2002, ISBN 0-07-048658-l. [6) http://en.wikipedia.org/wiki/Gamma distribution [7] http://en.wikipedia.org/wiki/Central limit theore ill [8] http://en.wikipedia.org/wiki/Cumulants (9) http://en.wikipedia.org/wiki/Median [ I0]Jeffrey Bennett and Seth Shostak, "Life in the Universe", Second Edition, Pearson - Addison Wesley, San Francisco, 2007, ISBN 0-8053- 4753-4. See in particular page 404. UNCLASSIFIED/ /FOR 8FFI&l.t.k Wii ,>DIis¥ 54
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