I just read a mystery novel 1 set in London in 1719, the year before the stock market crash of the `South Sea Bubble'. Our hero investigates his father's murder.
In the novel, the author has our hero learn about probability although that word is never mentioned, so he could learn to think about possibilities.
That caused me to think of other notions that people could understand at that time, but did not.
As far as I can see, in 1700, school children could have learned three aspects of judgement. This learning could have been formal — hardly anyone would then (or now) apply the concepts in everyday life, except as a time consuming effort to help in making a few difficult judgements.
1. The first concept would have been a method for combining different qualities of evidence. It goes without saying that we do this all the time without the need or time wasted by a formal method. A major purpose for teaching a formal technique would have been to focus students' attention on the quality of evidence that comes from new and previously unknown sources.
The mathematics are those that David McAllister invented for what he called `certainty factors':
A certainty factor expresses how accurate, truthful, or reliable you judge a statement. It is your judgement of the evidence.
McAllister did not invent the mathematics until the mid 1980s, but the ideas are straightforward. They could have been invented centuries earlier, but, as far as I know, were not. (In this respect, certainty factors are like other notions invented `after their time'.)
Had `certainty factors' been invented, school children could have worked their way through home work assignments in which they assessed various qualities of evidence: how `suggestive' it is. To avoid sensitive issues such as those in contemporary politics or religion, teachers could have asked how suggestive the evidence is that `Nero fiddled while Rome burned.'
2. By 1700, part of the second concept was already a centuries old business; but other parts were new. The old practice was to insure ships; the new practices included government borrowing that was funded by annuities.
Insurers had found that sinking and death were common and regular when applied to large numbers of ships or people, but unpredictable when applied to a specific ship or person.
As far as I know, the first insurers priced their offers to handle the past frequency of sinkings and death. They presumed the future would be similar to the past and choose a price that would make them a profit so long as the future repeated the past, more or less. They applied what they knew of past frequencies to future events.
3. A third concept consists of an estimate of the likelihood of a one-time-only event, such as whether the `Titanic' will sink on its first voyage. Such estimates often use the same language as that used for insurance based on past frequencies. However, such likelihood estimates tend to depend on people's hopes and fears, even when they are analyzed into components, such as whether the captain of a new ship might try to speed across the Atlantic in a fast, new ship.
Because of the similarity in language, and because both deal with the future, it is easy to confuse an estimate of the likelihood of a one-time-only event with an estimate of the likelihood of multiple future events that also have a past history.
Generally, the reasons for a one-time-only event can be divided into their components. These components are what might be considered `other indicators'. After all, when judging the chance that a particular ship will sink on a particular voyage, general statistics are of little use.
Moreover, these `other indicators' can be judged as to their certainty. The `other indicators' are not estimates of the future, but of the past — for example, how suggestive is the evidence that over his career, a particular captain sped through regions frequented by icebergs although he never came near any? The past is then applied to making a judgement about the future.
Although no one does so formally, it would be possible to list and combine the certainty factors that appear to apply to a particular judgement of a past event.
This means that even though certainty factors apply to judgements of the past, their use could well be to help suggest chances for the future. Put another way, an estimate of the likelihood of a one-time-only event may use the same language as insurance. However, it does not depend on a history of similar occurrences, but on evidence from other indicators.
Of course, a history of similar occurrences depends on how you judge that history. How good are your reports of ship sinkings? Nowadays, they will be fairly good -- only occasionally do you hear of pirates stealing a ship and providing it with new papers and a new name. In centuries past, this was more likely.
As I write this, people who are not sailors are beginning to accept the notion that occasional large waves will sink large ships. The large waves have been photographed by satellites; before that, their existence was dismissed as sailors' exaggeration. But rather than use language such as `dismissed as sailors' exaggeration', it is more illuminating to describe the change in the language of certainty factors: from weakly suggestive to highly suggestive. With this language, no one denies that before the satellite discoveries, some people who were not sailors figured the sailors were telling the truth, or that some effort was made to investigate reports. The language also suggests a task for journalists and historians: to report how much was spent when, for the most part, the ship owners, insurers, and government weather forecasters thought the evidence was `weakly suggestive', and how much is spent when they think the evidence is `strongly suggestive'?
I wonder whether, and if so how, our history would be different if over the past few centuries everyone receiving a high school education had learned of certainty factors, frequency-based probabilities, and single-time estimates. I am not suggesting that the tools be used by anyone after they left high school, only that they learned about this way of thinking about evidence and the future.
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