 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 mass 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 who was the first to mention the problem of points, which was incorrectly solved by the gambling scholar Cardano, but was correctly solved by Pascal 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 Doomsday Book, which really just means Judgment Day Book, by way of analogy to the finality of judgments on Judgment 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 the city they were invading to estimate the size of ladders they'd need to scale the wall. And in the 9th century, Arab mathematician Al-Kindi's work, with using letter frequencies to decipher 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 endeavor really took off. The word statistics, by the way, doesn't necessarily refer to numerical data. It actually comes from the new Latin, statistikus, affairs of state. So it really originally referred to collecting and studying any information about the state. It came into German as statistik, meaning of the collection and evaluation of data relating to the study of the state. And after the 18th century German political scientist Gottfried Achenwald, 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 barring the word from German but applying it to 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 R. Buffnott, 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 Scriblerist Club, an informal association of authors, including such satirical big wigs as Jonathan Swift, Alexander Pope, and John Gay. Our Buffnott may have even provided inspiration for elements of Swift's gulliver's travels and Pope's the Dunsead. In addition, he also likely invented the English national personification, John Bull, originally a figure of political satire. In more probability related endeavors, he translated Huygens book on probability, making it the first work on probability in English. But for our purposes, our Buffnott's most important mathematical contribution is in the study of birth rates. 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 birth rates, 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, write data, but wrong conclusions. Actually, before our Buffnott, John Grant made similar observations about birth and death rates, compiling the first life table in the 17th century. Grant 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 enough though, his house burned down in the great fire of London and he eventually went bankrupt, dying some 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. 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 Edmund Halley. Yes, that Edmund 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 the motifs of calculating the movement of celestial objects and to predicting the future. Actually, comets themselves had 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 Conqueror defeated King Harold, taking over the throne of England as we saw earlier. It's even pictured in the Bayou Tapestries. Also seemingly depicted in the tapestry is the death of King Harold, who legend has it, was killed by an arrow to the eye. Petty didn't see that coming. But as I mentioned before, it wasn't until probability mass 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 Adolf Kettelet, who was, by the way, deeply influenced by the astronomy work of Pierre Simon Laplace, who did most of the legwork on Bayes theorem, which was very important to probability. As an astronomer, Kettelet founded and directed the Brussels Observatory and studied periodicity in celestial objects. At the time, the probability mass were mainly being used in astronomy, like Carl Friedrich Gauss using the method of least squares to predict the orbit of Ceres. Well, Kettelet took what he learned from probability in astronomy and began applying 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 died in an 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 one to three shares at a fixed rate, and proceeds would then 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 Edmund 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 Morris, who worked on history and typography, picked up the baton and eventually got the equitable life insurance 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 Morris, 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 Morris 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 non-conformist 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 Kettle, 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 behavior. So instead they began frequenting one of the nearby coffee houses, in particular Jonathan's Coffee House, 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 behavior 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 bear-skin-jobber. From the proverb sell the bear-skin before one has caught the bear. And bull seems to go back to a slang expression used in Jonathan's Coffee House. The word bull itself comes from old Norse bolly, which can possibly be traced back to the Proto-Indo-European root bell, meaning to blow or 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 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 beowulf, 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 sort of complex calculations that are required for things like finding binary pulsars, the kind of astronomy we can do now as the result of all the mathematical advances of the past. Thanks for watching. Let me know how you've liked this miniseries, so I know if it's a good format to come back to. 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 at alliterative on Twitter and you can read more of my thoughts on my blog at alliterative.net.