Welcome to the Endless Knot!
Today is the final part of a three episode series about the word Average, in which we
look at stats and stocks!
In the previous videos we started from the word ‘average’ and its origins in maritime
shipping, and looked at the development of probability maths and their role in property
insurance: how Islamic scholar Al-Kindi did early work on probability and statistics,
and passed on Arabic numerals to Europe, which were picked up by Fibonacci, who inspired
Pacioli, who was the first to mention the problem of points, which was incorrectly solved
by the gambling scholar Cardano, but was correctly solved by Pascale and Fermat, whose math became
the backbone of probability theory, which was written up by astronomer Huygens, and
became useful in solving astronomical problems, like Gauss locating the dwarf planet Ceres,
and was added to by other mathematicians like Bayes, Laplace, and Poisson, which eventually
became useful to property insurance companies, which earlier had got their start after the
Great Fire of London.
Well, the other thing that the insurance game really needed to get going, particularly life
insurance, was statistics, and the lack of good mathematical ways of dealing with statistics
was holding things back.
Sure, there had been some fairly basic forms of life insurance since the ancient world,
such as burial societies in Rome.
You pay a regular fee, and when you die, the society makes sure you get a proper funeral
and assists your survivors.
And you can find statistics being collected and used in some fairly basic ways since the
ancient world.
Again, the Romans collected census data, and in medieval England, shortly after William
the Conqueror and the Normans defeated King Harold and the Anglo-Saxons at the Battle
of Hastings, the Normans went about compiling census data for taxation purposes, into a
document known as the Domesday Book, which really just means Judgement Day book, by way
of analogy to the finality of the judgements on Judgement Day, and not actually as apocalyptic
as the Norse Ragnarok we started off with back in the first video.
In a surprisingly sophisticated use of statistics, the Greek historian Thucydides records how
the Athenians used what we would now call the mode, loosely speaking a kind of average,
of a number of attempts to count bricks in the wall of a city they were invading to estimate
the size of ladders they’d need to scale the wall.
And the 9th century Arab mathematician Al-Kindi’s work with using letter frequencies to decypher
encrypted texts can also be seen as a mathematical foundation to statistics.
But it wasn’t until the 19th century when the new probability math was brought to bear
on the analysis of statistics that statistics as a mathematical endeavour really took off.
The word statistics, by the way, doesn’t necessarily refer to numerical data.
It actually comes from the New Latin statisticus “affairs of state”, so it really originally
referred to collecting and studying any information about the state.
It came into German as statistich to mean “of the collection and evaluation of data…relating
to the study of the state”, and after the 18th century German political scientist Gottfried
Achenwall coined the noun form Statistik, the word began to narrow in meaning.
It was introduced into English by Sir John Sinclair in his 21 volume Statistical Account
of Scotland, in which he acknowledges borrowing the word from German but applying to it a
slightly different meaning, in his words “an inquiry into the state of a country, for the
purpose of ascertaining the quantum of happiness enjoyed by its inhabitants, and the means
of its future improvement”.
So the data was still not specifically numerical.
But by 1829 the word had further narrowed in sense to “numerical data collected and
classified”, and no longer referred specifically to data about the state.
But for the advancement of numerical statistics (even if not by that name), and specifically
leading to the use of statistics in life insurance, we turn to Sinclair’s earlier fellow Scotsman
John Arbuthnot, a physician by trade, who also engaged in literary and mathematical
pursuits in his off-time.
As a writer, he was a member of the early 18th century Scriblerus Club, an informal
association of authors including such satirical bigwigs as Johnathan Swift, Alexander Pope,
and John Gay.
Arbuthnot may have even provided inspiration for elements in Swift’s Gulliver’s Travels
and Pope’s The Dunciad.
In addition, he also likely invented the English national personification John Bull, originally
a figure of political satire.
In more probability-related endeavours he translated Huygens’s book on probability,
making it the first work on probability in English.
But for our purposes Arbuthnot’s most important mathematical contribution is in the study
of birthrates.
In doing that study, he made one of the first inferences from statistical data when he noted
that there was a slightly higher proportion of girls to boys in the birthrates, which
he took to be evidence of divine providence, as it allowed for the fact that males die
young more often than females, due to fighting in wars and such.
Well, right data, but wrong conclusions.
Actually, before Arbuthnot, John Graunt made similar observations about birth and death
rates, compiling the first life table in the 17th century.
Graunt was in fact a haberdasher by trade but is now remembered as one of the first
demographers, and in recognition of his statistical work was elected to the Royal Society, and
is now sometimes referred to as the “father of statistics”.
Not bad for a haberdasher.
Sadly though, his house burned down in the Great Fire of London and he eventually went
bankrupt, dying some eight years after the fire of jaundice and liver disease.
Too bad he didn’t have insurance.
But the other 17th century person to work on the mortality tables which were necessary
for life insurance was economist Sir William Petty.
A charter member of the Royal Society, Petty also apparently came up with the idea of laissez-faire
government.
As a statistician his only statistical technique was the basic use of simple averages, but
he was nevertheless able to estimate population sizes.
But the first to work out a life table relating the death rate to age, which you can imagine
would be crucial for life insurance, was Edmond Halley.
Yes that Edmond Halley, who “discovered” the comet that came to be known as Halley’s
Comet by studying earlier sightings and thereby predicting its return in 1758, some 16 years
after his death, bringing us to motifs of calculating the movements of celestial objects
and to predicting the future.
Actually comets had themselves been seen as predictors of great calamity since time immemorial.
Indeed Halley’s Comet itself was taken as an omen, at least retrospectively, of the
Norman Conquest when William the Conquerer defeated King Harold taking over the throne
of England, as we saw earlier.
It’s even pictured in the Bayeux Tapestry.
Also seemingly depicted in the tapestry is the death of King Harold, who legend has it
was killed by an arrow to the eye.
Bet he didn’t see that coming!
But as I mentioned before it wasn’t until probability maths were applied to statistics
that statistics as a field could begin in earnest, and one of the first to do this was
Belgian astronomer and mathematician Adolphe Quetelet, who was by the way deeply influenced
by the astronomy work by Pierre-Simon Laplace, who did most of the legwork on Bayes’ theorem,
which was very important to probability.
As an astronomer, Quetelet founded and directed the Brussels Observatory, and studied periodicity
in celestial objects.
At the time the probability maths were mainly being used in astronomy — like Carl Friedrich
Gauss using the method of least squares to predict the orbit of Ceres.
Well Quetelet took what he learnt from probability in astronomy and began to apply it to other
things, including the statistics of human populations, and came up with the concept
of the “average man” — there’s that word average again — who is characterized
by the mean values of measured variables that follow a normal distribution.
Which means that he’s responsible for the Body Mass Index or BMI.
So you can blame him as you diet in the attempt to reach some unrealistic expectation of the
ideal body!
And that brings us to the first life insurance company, which was actually founded sometime
earlier in 1706 by William Talbot, bishop of Oxford, and Sir Thomas Allen and was called
the Amicable Society for a Perpetual Assurance Office.
The scheme was basically that members, who had to be between the ages of 12 and 45, could
purchase 1 to 3 shares at a fixed rate and proceeds would be divided between the families
of deceased members proportional to the number of shares purchased.
So not taking into account probability at all.
Plus, anyone over 45 was out of luck.
Like the British mathematician James Dodson.
Dodson worked as an accountant and math teacher, and when he tried to join the Amicable Society,
he was turned down as he was then over 45.
So he decided to do something about it, hatching a scheme for a more equitable insurance company.
He would build on the tables of Edmond Halley so that the premiums charged would be calculated
on age-based life expectancy.
Unfortunately Dodson wasn’t able to get his scheme off the ground before he died at
the age of 52, leaving three motherless children unprovided for.
Fortunately antiquarian and scholar Edward Rowe Mores, who worked on history and typography,
picked up the baton, and eventually got The Equitable Life Assurance Society founded in
1762.
Oh, and in case you were worried, Dodson’s children were eventually provided for by Equitable
Life in recognition of Dodson’s work on the life tables.
As for Mores, he decided that the chief official of the company would be termed an actuary,
a word which had previously been used to refer to a “registrar or clerk”, but since then
gained its more specific sense in the world of insurance.
Though Mores was the first to use that title, he wasn’t really a statistician, so the
first actual actuary was Welsh physician, physicist, and statistician William Morgan,
when he was hired as Assistant Actuary in 1774.
In addition to working for Equitable Life, Morgan published papers on actuarial science
and is considered the father of that field.
He got the job on the recommendation of his uncle Richard Price.
Price was a mathematician and nonconformist preacher who was, among other things, the
literary executor of mathematician Thomas Bayes, gathering for publication all of Bayes’
unpublished work, including the work on probability and Bayes’ Theorem.
Price continued the work on life tables for the Equitable Society.
Now one thing you may have noticed from the preceding discussion is that these early life
insurance companies were actually assurance companies.
Indeed the terms were used rather interchangeably and assurance is actually the older term,
coming through French from the Latin ad- “to” and securus “safe”.
And indeed to this day many British life insurance companies are called assurance companies,
whereas insurance is used to refer to marine and fire insurance.
This distinction between assurance and insurance was suggested by Charles Babbage, inventor
of the analytical engine, the world’s first computer.
And Babbage fits into our story in more ways than one, for he along with our friend Quetelet,
inventor of the “average man”, formed the Royal Statistical Society, a group which
fostered the continuing work on statistics and promoted the use of statistics for the
common good.
As a bit of a coda, aside from the insurance market, there’s another kind of market to
come out of those coffee shops I mentioned way back in the first episode: the stock market.
The first company that issued stocks was the Dutch East India Company.
Not to be outdone by their trading rivals, Britain followed suit.
But the problem was, where could the exchange of stock be carried out?
At first they did so in the Royal Exchange, but were banned from there, reportedly on
account of their rude behaviour.
So instead they began frequenting one of the nearby coffeehouses, in particular Jonathan’s
Coffeehouse, where there were regular postings of stock and commodity prices, so the first
stock market in England.
And this was the beginning of the London Stock Exchange or LSE.
Many similar institutions subsequently popped up around the world, including the New York
Stock Exchange in the US.
And this is where American journalist Charles Dow founded the Wall Street Journal to report
on business and finance.
Dow also, along with statistician Edward Jones, invented the Dow Jones Industrial Average.
Basically by averaging the stock prices of certain companies thought to be indicators
of how the market was doing as a whole, you could make a pretty good prediction of market
behaviour overall.
When the average is rising we call that a bull market.
The opposite is the bear market.
Basically a bear is a trader who is pessimistic about how the market is going and wants to
sell stock, whereas a bull is a trader who intends to buy believing the price of the
stocks will go up.
It’s all about predicting the future.
And where did the bear and bull terms come from?
Well some suggest the analogy that bulls fight with their horns pointing up, whereas bears
fight with their claws pointing down.
However, bear seems to get this sense from the expression bearskin jobber, from the proverb
sell the bearskin before one has caught the bear.
And bull seems to go back to a slang expression used in Jonathan’s Coffeehouse.
The word bull itself comes from Old Norse boli, which can possibly be traced back to
the Proto-Indo-European root *bhel- meaning “to blow, swell”.
As for bear, well that’s an interesting one.
The usual Proto-Indo-European root meaning “bear” leads to Latin ursus as in ursa
minor, the little bear constellation which now contains the north star.
In ancient Greece, when astronomers like Ptolemy were charting the skies, the north star didn’t
exactly line up with the North Pole as it does now, so the whole constellation of ursa
minor indicated north.
The Greek derivative of this root is arktos meaning “bear”.
And we get the word arctic from this Greek word because that ursa minor constellation
marks out the arctic (not because of polar bears).
But the English word bear doesn’t come from this root at all.
Instead it comes from the Proto-Germanic *bero- meaning “dark” so the dark animal.
This is what’s called a taboo replacement.
When a culture believes a certain object or concept can’t be named directly, perhaps
for religious reasons or other social taboos, they come up with an indirect way of referring
to it.
So the bear becomes instead the dark animal.
And this may also lie behind the name of the hero Beowulf, from the Anglo-Saxon eponymous
epic poem.
One explanation of his name is that it means “bee-wolf”, which is what’s called a
kenning, a kind of metaphorical play on words.
What acts like a predatory wolf to bees?
A bear, who steals their honey.
So another way of saying bear, without actually saying bear.
And the final upshot of all this is that Beowulf, who was no average man and was said to have
the strength of 30 men in his hand grip, has for that reason lent his name to the Beowulf
cluster, a way of using a network of ordinary (or should we say average) personal computers
(our old friend Babbage’s progeny) to cheaply produce a system capable of large computational
power.
Beowulf clusters are popular with universities, who don’t have a lot of cash, but need to
do the sorts of complex calculations that are required for things like finding binary
pulsars—the kind of astronomy we can do now, as a result of all the mathematical advances
of the past.
Thanks for watching!
If you’ve enjoyed these etymological explorations and cultural connections, please subscribe
to this channel or share it.
And check out our Patreon, where you can make a contribution to help me make more videos.
I’m @Alliterative on Twitter, and you can read more of my thoughts on my blog at alliterative.net