Kathryn:
That LA Times article on the Poisson distribution brought many things surging to mind.
One: An elderly friend of my family whose wife died some years ago after a long and stable marriage blessed with two fine children. Talking to him soon afterwards, he admitted he had never loved his wife, nor she him, and they had been up front about this with each other. I forget what her side of it was, but his went like this: “When I was young I was deeply in love with a girl who loved me equally. We were together only a few months, then she died of rheumatic fever. After that I never hoped to again be loved by someone who loved me back, and decided I would marry the first person I felt I could get along with decently well. Doris [not wife’s real name] filled the bill, and it worked out pretty much as I’d hoped it would.” This person was English. I read Mornings on Horseback soon after, and wondered if that was also TR’s case.
Two: Arthur Koestler’s remarks about “the law of large numbers” inChapter 1 of The Roots of Coincidence, thus:
“Another mystery of the theory of chance is reflected in the following quotation from [mathematician] Warren Weaver: ‘The circumstances which result in a dog biting a person seriously enough so that the matter gets reported to the health authorities would seem to be complex and unpredictable indeed. In New York City, in the year 1955, there were, on the average, 75.3 reports per day to the Department of Health of bitings of people. In 1956 the corresponding number was 73.6. In 1957 it was 73.2. In 1957 and 1958 [sic: this is probably a typo for “1958 and 1959”] the figures were 74.5 and 72.6.’
“Weaver comments: ‘One of the most striking and fundamental things about probability theory is that it leads to an understanding [sic–this sic is Koestler’s, not mine] of the otherwise strange fact that events which are individually capricious and unpredictable can, when treated en masse, lead to very stable average performances.’
“But does it really lead to an understanding? How do those German Army horses adjust the frequency of their lethal kicks to the requirements of the Poisson equation? How do the dogs in New York know that their daily ration of biting is exhausted? How does the roulette ball know that in the long run zero must come up once in thirty-seven times, if the casino is to be kept going? The soothing explanation that the countless minute influences on horses, dogs, or roulette balls must in the long run “cancel out,” is in fact begging the question. It cannot answer the hoary paradox resulting from the fact that the outcome of the croupier’s throw is not causally related to the outcome of previous throws: that if red came up twenty-eight times in a row (which, I believe, is the longest series ever recorded), the chances of it coming up yet once more are still fifty-fifty..
“Probability theory is the offspring of paradox wedded to mathematics…”
[Derb] Brian Aldiss wrote a short story in which the laws of probability temporarily break down. The protagonist’s colleague’s pet monkey, which he’s looking after as a favor, escapes, gets into his office, and starts dancing on the typewriter — it produces Two Gentlemen of Verona, complete with stage directions… etc. etc.