February 20, 2011

A Million Random Digits

Posted by Evelyn Mervine

First page of random digits in “A Million Random Digits” book. Image taken from Amazon.com.

Earlier this evening I met up with three classmates (all girls, by the way; my statistics class is about 90% female) to work on programming our latest statistics homework into MATLAB. Working in a group is easier as four pairs of eyes tend to catch code errors faster than one pair of eyes. Also, we can eat Chinese food and giggle and have fun as we work.

One of the things we had to do this evening was use the “rand” function in MATLAB. This function calls upon a computer algorithm that generates random– or really pseudorandom since they’re calculated by a computer– numbers. The “rand” function calls upon a random number between 0 and 1 as a default, though you can tell it to use other ranges.  Random numbers are very important for many types of statistical analyses and numerical simulations. These days, many computer programs, such as MATLAB, have pseudorandom number generators built in. For most types of applications in mathematics and science, a pseduorandom number is nearly as good as a random number.

But what if you need actual random numbers?

And how did people generate random numbers before computers became fancy enough to generate pseudorandom numbers?

We started wondering about these two questions this evening. During our discussion about this, one of my classmates said, “Have you ever heard of that book that is nothing but random numbers?”

Of course, we had to immediately google this book, procrastinating our coding for a few minutes.

Cover of the book “A Million Random Digits.” Image taken from here.

Indeed, there is a book that contains nothing but a short introduction and then page after page of random numbers– 1 million of them, in fact! The book is titled “A Million Random Digits with 100,000 Normal Deviates.”

This book was first published by the RAND Corporation in 1955. If you go to the RAND website about the book, you can actually download the book for free. The text parts of the book come as PDF files and you can download the million random numbers as a data file. In the old computing days, you could order punch cards with these million random numbers. If you want a hard copy of this book (magicians and mentalists– wouldn’t this book make a great prop for your shows?), you can order it either from the RAND website or from Amazon.com.

A book of random numbers might seem incredibly boring; you wouldn’t want to read this book cover-to-cover, that’s for sure. Yet however boring, this book is very useful. Even though pseudorandom number generators are much easier and more commonly used these days, there are still times when mathematicians and scientists need truly random numbers. And for this, the RAND compilation remains the largest published source of random digits.

You might be wondering how these million random digits were generated. If you read the introduction to the book, the method of number generating is explained in detail. Basically, the numbers were generated on a roulette wheel. So, if you went to Las Vegas and played roulette for days (years?), you could generate a million random numbers, assuming there are no biases in the wheel.

Roulette Wheel. Image taken from wikipedia here.

The wheel that was used to generate the random numbers was actually an electronic roulette wheel that was hooked up to a very early computer. At first, the numbers looked random, based on various statistical tests. However, after awhile the RAND employees evaluating the randomness of the numbers realized that their electronic roulette wheel wasn’t perfectly random– there was some drift over time, probably as the machine aged and changed slightly in operation. You can read more about the biases of the electronic roulette machine here. To make the numbers truly random, the RAND employees- to put it simplistically- shuffled them up a bit.

I think this book of numbers is really great. I’m even tempted order this book as a coffee table book. I can just imagine my in-laws (who already think I’m strange) picking this book up off the coffee table and wondering why on Earth we have a book of numbers. I can’t quite justify the purchase (the book is about $70) on my graduate student budget, but perhaps I’ll order it sometime in the future.

Many people find this book of numbers both interesting and amusing. If you go to Amazon.com and read the reviews for this book, there are a plethora of hilarious ones. Below are a few reviews I found particularly entertaining:

“The book is a promising reference concept, but the execution is somewhat sloppy. Whatever algorithm they used was not fully tested. The bulk of each page seems random enough. However at the lower left and lower right of alternate pages, the number is found to increment directly.”

-B. McGroarty

“Such a terrific reference work! But with so many terrific random digits, it’s a shame they didn’t sort them, to make it easier to find the one you’re looking for.”

-A Curious Reader

“I definitely prefer books like ‘One million sequential numbers’ as the story always steadily progresses. By comparison this book is just so and so.”

-Devide Cerri

“For those who thought that ‘Atlas Shrugged’ could not be surpassed, here Rand refutes all doubters and utterly tops that opus in a style so rarefied and refined that words themselves have been transcended, with the essence–no, the ethereal, mystical quintessence–of Rand’s philosophy expressed as its ultimate ur-truth of a million unrelated symbols floating forever in pure mindless randomness. Rand’s myrmidons will find this most congenial, and I recommend that they spend the rest of their days reading this ne plus ultra masterpiece, meeting 24/7 in pure white Randian temples, there to pontificate and meditate on this wonder and that way stop bothering everybody else.”

-George Zadoronzy

“Wow, what can I say. A very insightful novel. The way the author manages to manipulate those numbers was wonderful.


I have to admit, there were many twists that I didn’t expect, especially when he decided to follow up 9238399 with 2883002. I have to admit, the beginning was rather slow, but it began to pick up pace somewhere on page 7. My only regret is that there isn’t a sequel, because the author left it at a cliffhanger.

At times spontaneous, blunt, and errant, this is a book that you can definitely share with your friends.”

-Anna Huynh