Chance has no memory.
I’m not a statistician, though I did have to learn some of it years ago. I now know what a point of inflexion is, even if I didn’t then. We were taught about probability and odds, but it’s mostly a distant memory now.
Still, I can remember some of the important things. Like chance — randomness. A chance or random event can’t be forecast from previous behaviour — previous behaviour doesn’t and can’t influence the present or future. This does sound a bit like the advice given to investors, about past performance not being an indicator of the future.
A common example of a chance event is tossing a coin; it will come down either heads or tails — if you really want to be pedantic, it might come down on edge, but let’s forget this. If it came down tails this time, it will still be either heads or tails next time, and so on. (Unless you toss it thousands of times, when something about large numbers comes into play.) Roulette wheels are supposed to be another chance event, though the advantage is always just in favour of the bank. Methods to predict the spin of the wheel may succeed if the wheel isn’t perfectly balanced — but this is then not a chance event.
Cot deaths (sudden infant death syndrome*) are seemingly random, chance events. This is a way of saying that we don’t really know what the causes of cot death are, we can only try to look for patterns. And having one cot death still leaves you at the same chance of another. You might say that there must be a cause or causes, and indeed there must be; and these causes, whether hereditary or environmental or a mixture, could well make you more likely to suffer a second.
Münchausen’s† syndrome was first described by Richard Asher, a London physician, clear thinker and father of Jane. He described patients whose symptoms were fictitious, but who sought medical attention. They might present with bleeding, strange neurological symptoms or abdominal pain — and many of the latter had multiple scars from operations.
Münchausen’s syndrome by proxy was described by Professor Sir Roy Meadow. These people harm others, often children, to draw attention to themselves. They may even kill their children, leading Sir Roy to state: “one sudden infant death is a tragedy, two is suspicious and three is murder, until proved otherwise“ . This became known as Meadow’s Law, though the research he used to be able to formulate the law was apparently “destroyed”.
You may recall the story of Sally Clark, whose first two (infant) children died suddenly, and who was subsequently convicted of their murder. Sir Roy gave ‘expert medical’ evidence at her trial, invoking some quite remarkable statistical prestidigitation — a feat for which he was not ‘expertly’ qualified. Sally Clark was freed on her second appeal, but died a few years later — a life destroyed.
Sir Roy was struck off by the General Medical Council, but this was subsequently reversed in the Courts.
More recently, the requirements for (and limitations of) expert witnesses have been significantly strengthened.
* A syndrome is a collection of three or more signs and symptoms.
† The stories of Baron von Münchausen were written by Rudolf Raspe, who after a colourful life ended up working at the copper mines in Killarney, where he died and was buried. I once met a patient with this syndrome, who had been in most of the hospitals in Ireland, including Killarney. The physician there, in a discharge note, suggested that the patient was on a pilgrimage to the grave of his ‘progenitor’.