DOW-UAP-D127, AAWSAP DIRD, An Introduction to the Statistical Drake Equation, March 2010
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.
The summary above is sourced from the released file metadata as published to war.gov. The analysis sections below are original to this tracker.
Text of the document
Machine-extracted from the PDF war.gov published (its text layer or OCR), so expect errors, especially in names, numbers and handwriting; the PDF is the authoritative copy. Lines that did not extract as readable text are left out. Showing about 997 words from pages 2, 3, 4, 5, 6 of 55.
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An Introduction to the Statistical Drake Equation Prepared by: Acquisition Support Division (DW0-3) Defense Warning Office Directorate for Analysis Defense Intelligence Agency AAP Person 80 Administrative Note COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized. This product is one in a series of advanced technology reports produced in FY 2009 under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace Weapon System Applications (AAWSA) Program. Comments or questions pertaining to this document should be addressed to !AAP Person 1 ~ AAWSA Program Manager, Defense Intelligence Agency, ATTN: CLAR/DWO-3, Bldg 6000, Washington,
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2. The Key Question: How Far are They ? .............................................................. 4 4. The Drake Equation is Over-Simplified ............................................................. 10 6. Solving the Statistical Drake Equation By Virtue of the Central Limit Theorem 7. An Example Explaining the Statistical Drake Equation ..................................... 15 8. Finding the Probability Distribution of the Et-Distance By Virtue of the Statistical Drake Equation................................................................................................. 18 9. The "Data Enrichment Principle" as the Best CLT Consequence Upon the Statistical Drake Equation (Any Number of Factors Allowed) ........................... 23 Appendix A: Proof of Shannon's 1948 Theorem Stating That the Uniform Distribution is the "Most Uncertain" One Over a Finite Range of Appendix B: Original Text of the Author's Paper #IAC-08-A4.1.4 Entitled the Statistical Drake Equation ............................................................... 28
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An Introduction to the Statistical Drake Equation SETI (an acronym for "Search for Extraterrestrial Intelligence") is a relatively new branch of scientific research, having begun only in 1959. Its goal is to ascertain whether alien civilizations exist in the universe, how far from us they exist, and possibly how much more advanced than us they may be. As of 2009, the only physical tools we know that could help us get in touch with aliens are the electromagnetic waves an alien civilization could emit and we could detect. This forces us to use the largest radiotelescopes on Earth for SETI research, because the higher our collecting area of electromagnetic radiation is, the higher our sensitivity is (that is, the farther in space we can probe). Yet, even by using the largest radiotelescopes on Earth (the 310-meter dish at Arecibo, for instance), we cannot search for aliens beyond, say, a few hundred light years away. This is a very, very small amount of space around us within our galaxy, the Milky Way, that is about 100,000 light years in diameter. Thus, current SETI can cover only a very tiny fraction of the galaxy, and it is not surprising that in the past 50 years of SETI searches, NO extraterrestrial civilization was discovered. Quite simply, we did not get far enough! This demands the construction of much more powerful and radically new radiotelescopes. Rather than big and heavy metal dishes, whose mechanical problems hamper SETI research too much, we are now turning to "software radiotelescopes," where a large number of small dishes (ATA = Allen Telescope Array, and ALMA= Atacama Large Millimeter/submillimeter Array) or even just of simple dipoles (LOFAR = Low Frequency Array) using state-of the-art electronics and very-high-speed computing can outperform the classical radiotelescopes in many regards. The final dream in this field is the SKA ( = Square Kilometer Array), currently being designed and expected to be completed around 2020. 2. The Key Question: How Far are They? But still, the key question remains: how far are they? Or, more correctly, how far do we expect the NEAREST extraterrestrial civilization to be from the Solar System in the galaxy? This question was first faced in a scientific manner back in 1961 by the same scientist who also was the first experimental SETI radio astronomer ever: the American, Frank Donald Drake (born 1930). He first considered the shape and size of the galaxy where we are living: the Milky Way. This is a spiral galaxy measuring some 100,000 light years in diameter and some 16,000 light years in thickness of the Galactic Disk at half way from its center. That is: The diameter of the galaxy is (about) 100,000 light years, (abbreviated ly) i.e., its radius, is about 50,000 ly.
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The thickness of the Galactic Disk at half-way from its center, is about 16,000 ly. The volume of the galaxy may then be approximated as the volume of the corresponding cylinder, i.e. Now consider the sphere around us having a radius r. The volume of such a sphere is In the last equation, we had to divide the distance "ET_ Distance" between ourselves and the nearest ET civilization by 2 because we are now going to make the unwarranted assumption that all ET civilizations are equally spaced from each other in the galaxy! This is a crazy assumption, clearly, and should be replaced by more scientifically-grounded assumptions as soon as we know more about our Galactic Neighborhood. At the moment, however, this is the best guess that we can make, and so we shall take it for granted, although we are aware that this is a weak point in the Furthermore, let us denote by N the total number of civilizations now living in the galaxy, including ourselves. Of course, this number N is unknown. We only know that N ~ 1 since one civilization does at least exist! Having thus assumed that ET civilizations are UNIFORMLY SPACED IN THE GALAXY, we can then write down the proportion: That is, upon replacing both (1) and (2) into (3): The last equation contains two unknowns: N and ET_Distance, and so we don't know which one it is better to solve for. However, we may suppose that, by resorting to the (rather uncertain) knowledge that we have about the Evolution of the galaxy through the last 10 billion years or so, we might somehow compute an approximate value for N. Then, we may solve (4) for ET_Distance thus obtaining the (AVERAGE) DISTANCE BETWEEN ANY PAIR OF NEIGHBORING CIVILIZATIONS IN THE GALAXY (DISTANCE
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where the positive constant C is defined by Equations (5) and (6) are the starting point to understand the origin of the Drake
Where this file fits in the PURSUE archive
This file is one of DoD's 282 files in the Trump PURSUE disclosure. Within the DoD agency block it ranks #243 of 282 by Anomalousness Index. Across the entire 478-file archive it ranks #418 of 478.
That places it in the lower-scoring band of the archive (418 of 478 by score), typical of investigative-record style files where the report is paper-based rather than instrumented.
Anomalousness Index: 53/100
This is a reference document, not an encounter report, so the index has no encounter to measure here. The value above is the rubric's default for a document that describes no event, shown so every file in the archive can be ranked the same way. Not a probability of extraterrestrial origin - that number is not honestly computable from the released files and this tracker refuses to publish it.
🤖 AI-ASSISTED SCORING · methodology
The six rubric components break down for this file as follows. Each component has a weighted contribution to the final score; the per-component explanation below describes what this file's particular value on that component means in the rubric's framework.
This file is a reference document, not an observation, so no sensor, camera, or witness captured anything. The rubric's sensor axis has no not-applicable option, so a document with no instrument record sits on its lowest tier by default.
There is no witness: this is a document released by the Department of War, not a first-hand account. The rubric assigns this axis from the originating body, so the value reflects the source of the record, not anyone's testimony.
Nothing is being corroborated, because the file does not report an event. Like every file in the archive it takes the rubric's single-source default.
The file describes no object and no motion, so the kinematic axis takes the archive-wide 'no kinematic data' default.
Every file in the archive scores this tier. For a document that describes no event it carries no information about the record at all.
The rubric's default for the file's release status (files released with redactions are catalogued as unresolved, unredacted ones as open). For a document that reports no event this describes how the file was released, not anything that happened.
Bottom line on the score: the 53/100 is the rubric's default for a document that reports no encounter, so it is not a finding about any event and should not be compared with the scores of sighting reports. For the full per-axis weights and the rubric JSON, see /methodology.
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DOW-UAP-PR109, Unresolved UAP Report, Eastern United States, 2015
DOW-UAP-PR110, Unresolved UAP Report, Eastern United States, 2020
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