According to Ramsey theory , ideal randomness is impossible especially for large structures. For example, professor Theodore Motzkin pointed out that “while disorder is more probable in general, complete disorder is impossible”. Misunderstanding of this can lead to numerous conspiracy theories and misunderstandings. I got off on this subject because of a news item today about the military draft that ended in 1973. It was based on a “random” selection of birthdates which many complained was not truly random.
My issues with the idea of random came when I was asked to “randomly select” medical samples for testing. I used a simple random number generator to choose which samples would be used. Problem was that the person in charge saw a pattern in the dates, times, sex, blood types or sample numbers of the resulting group and so felt the result was not truly random. One of his complaints was that all the samples selected happened to all be A+. I pointed out that over 90 percent of the samples were A+ so it would be natural for a large number of the random samples chosen to be A+. For example, if a group has 10 red balls and 90 black balls a selection of ten from this group will not necessarily result in 1 red and 9 black. There might not be any red at all. Similar issues came with time – most samples were drawn between noon and 2:00 with very few drawn outside that timeframe, most samples were from males, so I wasn’t too surprised that all samples chosen were male and all were drawn between noon and 2:00.
The final “random” sample list was chosen by printing the sample numbers on slips of paper, dropping them in a hat and drawing slips. Even then most samples were male, all were A+ and drawn between noon and 2:00pm a very good representation of the samples and not unexpected based on the distribution of the original data. The doctor in charge changed out some of the samples to include additional females, some drawn outside the noon -2:00pm timeframe and at least one sample that was not A+. He created a sample list that suited his idea of what “random” should look like.