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

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/ /fOR OFFI&IAk Wlii QPU,¥
3 6 R2 h
Ef ff (N) Ca!a,y
_ ,stance = VN C (5)
VN
where the posit ive constant C is defined by
C = V6 R ~ala.,y h ca /axy ,., 28845 light years . (6)
Equations (5) and (6) are the starting point to understand t he orig in of the Drake
equation that we discuss in detail in Section 3 of th is paper.
Let us just complete this section by pointing out three different numerical cases of the
distance law (5):
• We know that we exist, so N may not be smaller tha n 1, i.e., N ~ 1. Suppose then
that we are alone in the galaxy, i.e., that N=l. Then the distance law (5) yields as
distance to the nearest civilization from us just the constant C, i.e., 28,845 light
years. Th is is about the distance in between ourselves and the center of the galaxy
(i. e. the Galactic Bulge) . Thus, this result seems to suggest that, if we do not find
any extraterrestrial civilization around us in these outskirts of the galaxy where we
live, we should look around the Galactic Center first. And this is indeed what is
happening, i.e., many SETI searches are actually point ing the antennas towards the
Galactic Center, looking for beacons (see, for instance ref. [1]).
• Suppose next that N=l000, i.e. there are about a thousand extraterrestrial
communicating civilizations in the whole galaxy right now. Then the distance law (5)
yields an average distance of 2,885 light yea rs. This is a distance that most
radiotelescopes in Earth may not reach for SETI searches right now: hence the need
to build larger radiotelescopes, like ALMA, LOFAR and the SKA.
• Suppose finally that N=l00000O, i.e., there are a million communicating civilizations
now in the galaxy. Then the distance law (5) yields an average dista nce of 288 light
years. Th is is with in the (upper) range of distances that our current rad iotelescopes
may reach for SETI searches, and that justifies all SETI searches that have been
done so far in t he first fifty years of SETI (1960-2010).
In conclusion, interpolating the above three special cases of N, we may say that the
distance law (5) yields t he following key diagram of the average ET distance vs. the
assumed number of communicating civilizations, N, in the galaxy right now (Figure 1):
UNCLASSIFIED/ J'FOA. OFlilCI0 I. P!SE ON! X
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