Book review: A Million Random Digits with 100,000 Normal Deviates

the RAND Corporation, 1955
Free Press Publishers, Glencoe Illinois

This is a strange book, possibly the oddest book I own, and I have a few oddballs on my shelves. On it's face, it's a rigorous mathematical table, the intended audience those working in specialized mathematical fields, so it's strangeness is not that obvious.

First, a bit of background...

However useful mathematical tables are, their very nature makes them dull as warm water to most people, but their creation was once considered a worthwhile lifetime's work.

The history of mathematical tables is as old as written language. In the last few hundred years the work of calculating and printing mathematical tables exactly parallels that of calculating/computing machinery; in fact Babbage intended his machines to produce error-free mathematical tables.

It's hard to grasp, today, just how critically important accurate math tables are. Thousands of people have died due to tabular errors; navigators lost, bridges collapsed, pipes burst, often due to "mere" typographical errors. Tables published in the 18th century often had addendums to addendums to addendums, just to correct transcription and calculator errors accumulated over decades of use.

But in one recent historic moment, millennia of human effort was tossed in the trash and forgotten: the production of the automatic electronic computer. A crappy $5 calculator from the grocery store either culminates, or renders pointless, depending on your view, the work and suffering of centuries of mathematicians.

The need for large amounts of random numbers however didn't appear until the advent of electronic calculating machines, in the late 1940's, and the major driving force was the mathematical characterization of the nuclear processes that produce fission, in other words, the 'atom bomb' of the Manhattan Project.

(If you're not excessively math literate, you'll have to accept at face value that truly random numbers are not only excruciatingly useful, but extremely hard to produce. So-called "Monte Carlo" techniques, where a random starting point is chosen for working out a problem, require them. Basically, numbers are random when the next number in a series is completely unpredictable, like tossing a coin. In other words, there is no information contained in one number that can be used to determine the value of the next, or previous.)

Viewed another way...

Mathematical tables are essentially distilled information and order, human intellectual production of the finest kind, selfless and pure.

Then there is this book, a monstrous anti-table, a work of intentional disorder, produced by machine, an undoing of order itself, by one of the key strategic tools of the Cold War order. A MILLION RANDOM DIGITS is guarenteed to contain absolutely no information , and this is proven in the first 25 pages, where the method used to produce the table is given.

The method of production is essentially this: an electronic "roulette wheel" was made that generated digits with "a random frequency pulse source" (see note below). These digits were transposed in a particular way outlined in the book, and fed into an IBM card punch (IBM punched cards were a digital storage medium). This "file" of punched cards was then transformed and the results checked for statistical meaninglessness -- really -- as outlined. The final results were output to an IBM Model 856 Cardatype and reproduced photographically for the book.

Note: The barely mentioned "random frequency pulse source" is in fact the critical heart of their system. Willis Ware wrote, in a history of RAND accomplishments, that it was "probably an ordinary gas voltage regulator tube". Not a very forceful statement; however the most common random-noise source in the late 1940's was the 6D4 triode thyratron, wired as a diode (grid tied to cathode). If RAND did not use a 6D4, it seems certain that they used the same principle -- a gas-filled electron tube operating in a transverse magnetic field. (Corrected 21 May 2009)

As mentioned above, the mechanical production and reproduction of math tables was a holy grail for over a century and the precise target of Babbages decades of efforts. A particularly proud (bold, arrogant, whatever) remark in the book rubs salt into the wound of Babbage's failure: "...Because of the very nature of the tables, it did not seem necessary to proofread every page of the final manuscript...". In previous centuries, entire professional careers was spent proofreading tables!

(This isn't a place for any synopsis of RAND, but for flavor here are a few RAND published books, listed in the book's frontispiece:


The suggestions for use of the tables reads as a bizarre magical rite, outside it's mathematical context: " the book to an unselected page... blindly choose a 5-digit number; this number reduced modulo 2 determines the starting line; the two digits to the right... determine the starting column...", complete with suggestions on avoiding the obvious pitfalls of books that fall open to the same page, human tendencies to choose numbers in the middle of a page, etc, all precisely the opposite of how mathematical tables are used. And it's of course perfectly, verifyably correct.

In the tail of the book is a list of other books published by The Free Press, which appears to be Ayn Rand's reading list.

This is the stuff Illuminati/Masonic conspiracies are made of...