Yes, I've been busy again: there's some teaching happening (I am a volunteer scientific visitor in a local school), and I have been cleaning up two new books.
One of these is called Playwiths, and it is based on a website of mine that has pulled in around 4 million hits over 20 years. The following is a small sample from the completed text, which as the first link reveals, is about STEAM: Science, Technology, Engineering, Arts and Mathematics.
Consider the number of years between events designated as “once
in a thousand years”, such as floods. To the lay person, this immediately
raises the question: how can the authorities access data, covering several
thousand years. The answer is that they can’t, but they have what is usually
referred to as the Poisson distribution to fall back on, and to understand
that, we need to consider an old tale of Prussian cavalrymen who were kicked in
the head by their horses.
If you know any French, the Poisson distribution has nothing
to do with handing out fishes. It was developed by (and named after)
Siméon-Denis Poisson. It describes the probability of clusters in random
events, given nothing more than the average occurrence of such events. Poisson
died in 1840, before the kicked Prussians died. Ladislaus Bortkiewicz published
a book in 1898 in which he tried out the distribution of head kicks in each of
the 14 corps of Prussian cavalry over a 20-year period, to see if it conformed to
Poisson’s predictions.
Basically, the Poisson distribution works like this given a
sample average (or better, a population average), you can predict the
probability of clusters of, say, breast cancer cases in a workplace, the number
of calls to a call centre in a given minute, power failures on a grid, some
types of traffic accident, the number of typos on a page and the failure of
light bulbs. And given some flood data for a few inundations, the Poisson
distribution can predict about how often there would be a flood of a certain
level.
Let us consider the Prussian data: there were several cases
where a significant number of kicks had happened, and many more where no kicks had
happened, and Bortkiewicz got hold of the data for 200 corps-years. In 109 cases,
there were no injuries, 65 instances of one injury, 22 cases of two, 3 cases of
three head-kicks and one unfortunate corps, in one year, had four instances, a
total of 122 cases. That meant the probability of a case in any given corps in
any given year was about 6/10, or if you want precision, 0.61.
Bortkiewicz triumphantly showed that the known distribution
was an almost perfect fit to the theoretical prediction. After that, people
everywhere took up Poisson’s idea enthusiastically.
This sort of thing always catches on with the mob, because
most of the world favoured the idea of Prussian cavalry being kicked in the
head, but the main point was to say that there would be variation, and a high “score”
did not necessarily imply carelessness or anything else. Ask anybody who has
done some basic stats, and they will all know about the Prussian head-kicks.
It’s the one that is always mentioned. What is
less-mentioned is that you can calculate the flood height that, based on prior
data, would happen once in a thousand years. This figure would be approximate,
and the estimates would be refined after each flood, and they would be slightly
invalidated if the risk is increasing rather than steady, but it’s better than
nothing as a predictor.
I actually began looking into this issue, revisiting it
after several decades, because somebody was questioning the science behind
global warming, and as a throw-away line, poked fun at councils in Australia
which have maps showing the limits of one-in-a-thousand-year floods.
Those who know my interests will not be surprised to learn
that I point to 1859 as the year when scientists in unrelated disciplines began
to be unable to understand one another. The public had started to be lost a few
years earlier, but after the 1860s, a great deal of science was either
counter-intuitive or relied on obscure methods, and it all got progressively
more complicated.
Counter-intuitive science is in some ways the worst source
of dissent and confusion: if we know that mathematicians have a clever wrinkle
that lets them estimate what a one-in-a-thousand-year flood would be like, we
can accept that. Science that flies in the face of uninformed “common sense”,
science that causes fears to arise, these are the sorts of science that cause
trouble. Even if the ancient Greeks knew that the world was a sphere, peasant
minds were happy to say that the world they saw was clearly flat.
In the same way, other equally simple and fearful minds
attack the idea of evolution, misrepresenting what evolution is, even as they
deny it. Climate is another case: everybody who watches the weather on TV
thinks he or she understands climate, which is a very different kettle of
poissons.
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