A History of Random Numbers
Who are you?
Win Treese
What is your project?
I’m writing a history of random numbers, a hidden, essential resource in our world today. We need random numbers for sampling in polls and clinical trial, computer simulations that forecast the weather, for the cryptography underlying security on the Internet.
Where do we get them? Are they any good? What does it even mean for them to be good? Where else are they used?
All of that is part of their history, which, as a distinct concept, is not quite a hundred years old. I aim to be comprehensive and engaging, without skimping on the math and the code.
Can we see some photos?
Some code! Here’s the pseudocode from the Wikipedia entry on a widely-used contemporary random number generator. Don’t worry, it won’t be on the test!
This is Win :)
A link to your work:
My work online is at https://win.treese.org, occasionally updated. There’s also information there about In the Cloud: Poems for a Technological Age, a collection of poetry I published last year (which, by the way, came directly out of Writing in Community!).
A preview, snippet, or glimpse of your work in progress:
A sample from the chapter on Tables of Random Numbers
In 1923, L.H.C. Tippett arrived at University College, London, to study statistics with Karl Pearson. A recent graduate in physics from the Royal College of Science, Tippett was sent to Pearson by the British Cotton Research Institute, generally known as the Shirley Institute. The Shirley Institute was established in 1919 to conduct research for the cotton industry in improving the production of textiles. Within its first few years, it seemed that newly emerging techniques in statistics might be valuable in that work, and the Institute decided that one way to bring in expertise was to send a student to train under Pearson as well as for a while with R. A. Fisher.
Of course, Pearson had his own research agenda and put Tippett to work on it. Tippett’s first paper with Pearson, “On the stability of the cephalic indices within the race,”
appeared in 1924, in line with Pearson’s research on racial differences.
The following year, Tippett published a solo paper, “On the extreme individuals and the range of samples taken from a normal population”. Without going into details here, he was investigating an important question in statistical analysis: if you take a random sample of a population, are extreme values likely to be in the sample?
Tippett had a real challenge working on that paper. It turns out, that at roughly the same, another of Pearson’s colleagues, A.E.R. Church, was having a similar problem. To do convincing statistical work for those papers, they needed a better way to select samples for analysis.
Pearson suggested something that might help: making a table of random numbers.
Making such a table is not an obvious thing to do, but Pearson’s group was positioned to do it. In the foreword to Random Sampling Numbers, Pearson wrote:
In the case of many problems we may both check theory and prevent the pure algebraist, as he is apt to do, outrunning statistical experience by an appeal to the test of artificial sampling. Even when we are dealing with small samples—since we have as a rule to take a large number of them— the work of testing is very laborious. It is complicated by the fact that drawing balls or tickets from a bag or urn, however pleasing in theory to the mathematician, transcends the powers of the practical statistician. Given a frequency distribution of, say, 20 categories, with proportions varying between 5 and 60 say, this may clearly involve as many as 1000 or 1200 balls in the bag, or a like number of tickets in an urn. Practical experiment has demonstrated that it is impossible to mix the balls or shuffle the tickets between each draw adequately. Even if marbles be replaced by the more manageable beads of commerce their very differences in size and weight are found to tell on the sampling. The dice of commerce are always loaded, however imperceptibly. The records of whist, even those of long experienced players, show how the shuffling is far from perfect, and to get theoretically correct whist returns we must deal the cards without playing them. In short, tickets and cards, balls and beads fail in large scale random sampling tests; it is as difficult to get artificially true random samples as it is to sample effectively a cargo of coal or of barley.
They had tried, and been frustrated by, drawing numbered tickets, pulling balls from a bag, rolling dice, picking colored beads, and shuffling cards. Despite the possible uses in other situations, from games to lotteries, the results simply weren’t random enough for statisticians who were investigating randomness more seriously. In a way, making a table of random numbers would—if they were good enough—be a predictable, reliable base for selecting samples.
Moreover, Pearson’s lab had started publishing numerical tables to help with statistical work beginning in 1919, in a series called “Tracts for Computers”. (At the time, “computer” meant “a person who does computations”, and the first one was “Tables of the Digamma and Trigamma Functions”). Tippett’s table would be number 15 in the series, so working on them was a constant activity at the University College London Department of Applied Statistics. One can imagine that in such an environment it became obvious what needed to be done.
What will you ship at the end of 6 months?
Two complete draft chapters, one on tables of random numbers and one to be determined. (Also, in that time frame I need to ship a new version of my class, “Introduction to Computer Security”, which goes live in front of students in January!)
Along the way, I hope for feedback on fragments of the drafts on whether the writing is clear and engaging, especially for getting through some of the math, code, and other technical details. (Admittedly this will be hard sometimes when there’s not enough context available in the fragments!)