Historical research guide · 0327 · 2010

DIRD An Introduction to the Statistical Drake Equation

DIA / AAWSAP contractor

In one minute

This is the Defense Intelligence Reference Document about arithmetic rather than hardware. Its author — Appendix B reproduces Claudio Maccone’s 2008 congress paper under his own name — takes Frank Drake’s 1961 equation for the number of communicating civilisations in the galaxy and points out that multiplying seven guesses together gives one tidy number that hides how uncertain every guess was. His repair is to replace each of the seven factors with a random variable carrying a mean value and a spread. Taking logarithms turns the product into a sum, and the central limit theorem then forces the answer into a lognormal distribution whose mean, spread, median and peak can all be written down exactly. Worked through with one plausible set of inputs, the classical equation returns 3,500 civilisations; the statistical version returns a mean of about 4,590, and makes the distance to the nearest one a random variable too — most likely 1,933 light years, with a 75 percent chance of lying between 1,361 and 3,979 light years.

Connection

Chapter 1’s point about the DIRD list is that the Defense Intelligence Agency commissioned an engineering and physics reading list, and this is the page of it that teaches the manners the rest of the list is read with: state the spread, not just the number, and let the error bars do the arguing. Chapter 13’s unified picture needs exactly that discipline whenever the subject turns to who else is out there and how far away they are.

From the source

The classical Drake equation is over-simplified: it multiplies seven uncertain numbers into a single sheer integer, when each factor should instead be a random variable carrying both a mean value and a standard deviation.Section 4, p. 10; Section 5, p. 11
Because each Drake factor is non-negative and its true distribution is unknown, Shannon’s 1948 theorem — that the uniform distribution carries maximum entropy over any finite range — makes the uniform distribution the honest choice for every input.Section 5, p. 12; Appendix A, pp. 25–27
Taking natural logarithms turns the product into a sum, so the central limit theorem makes the number of communicating civilisations N a lognormal random variable whose mean, variance, mode, median and every moment follow analytically.Section 6, p. 13; Table 1, p. 14
For one worked set of inputs the classical equation returns N = 3500, while the statistical version returns a mean of about 4590 with a standard deviation of 11,195 — the statistical extension raises rather than lowers the expected number.Section 7, pp. 16–17
The distance to the nearest civilisation becomes a random variable with its own probability density: mode 1,933 light years, mean 2,670 light years, standard deviation 1,309 light years, and a 75 percent probability of lying between 1,361 and 3,979 light years.Section 8, pp. 18–22, equations (9) through (15)
The Data Enrichment Principle: because the central limit theorem allows any number of factors, new factors can be added to the equation as scientific knowledge grows, until it becomes a growing computer code — humanity’s first Encyclopaedia Galactica.Section 9, p. 23; Section 10: Conclusions, p. 23

The way in

https://documents2.theblackvault.com/documents/dia/AAWSAP-DIRDs/DIRD_25-DIRD_An_Introduction_to_the_Statistical_Drake_Equation.pdf

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

Defense Intelligence Reference Document, Acquisition Threat Support, 11 March 2010 (IOD: 1 December 2009), one in the series of advanced technology reports produced in FY 2009 under the DIA Advanced Aerospace Weapon System Applications (AAWSA) Program. Released under FOIA and published by The Black Vault. The preparing office is withheld under 10 USC 424 and the author’s name under FOIA exemption (b)(5)/(b)(6); internal evidence is unusually direct — Appendix B reproduces the author’s own congress paper IAC-08-A4.1.4, printed there under the name Claudio Maccone of the International Academy of Astronautics SETI Permanent Study Group — so the redacted author is inferred to be Maccone, but the released copy itself names no one. Sections 1 through 10, the body of the report, are given here in full. Appendix A (a reproduction of Shannon’s 1948 maximum-entropy proof) and Appendix B (the complete original congress paper, 27 pages in two-column facsimile) are omitted for length; the complete text is at the source. Equations that the released scan rendered unreadable are transcribed in plain notation or noted in place, and the two summary tables of lognormal properties did not survive the scan.

How to cite it

DIA / AAWSAP contractor (2010) DIRD An Introduction to the Statistical Drake Equation https://documents2.theblackvault.com/documents/dia/AAWSAP-DIRDs/DIRD_25-DIRD_An_Introduction_to_the_Statistical_Drake_Equation.pdf

Where it sits in the curriculum

The reference documents and the institutional record