"Average" Transcript

By Mark Sundaram

Welcome to the Endless Knot! Today is no ordinary episode. Today is an Average episode! Actually, I have so much to say that it won’t fit into one episode, so I’m averaging it out over a three-episode series!

People often seem to want to predict the future. I mean, after all, horoscopes are still regularly published in newspapers and magazines. Businesses are always trying to predict what consumers will want and what the economy’s going to be like next year. And in Norse mythology, the god Odin was always after wisdom and knowledge, particularly about the impending Ragnarok, the Norse version of Doomsday, so much so that he even gives up one of his eyes for wisdom. And speaking of astrology, it’s thanks to that that humans started studying the universe around us. It’s why we invented constellations and star charts. But soon enough people started to use those constellations and star charts for navigation. One of the most influential star charts was produced by the Greek Ptolemy. The work was originally titled Mathematike Syntaxis meaning “Mathematical Treatise”, and in fact was a work on Greek mathematics with a special focus on the maths of the apparent motion of the celestial bodies as the Greeks saw it. No mean feat as the Greek conception of the cosmos had the earth in the centre with everything else revolving around it like giant glass spheres, a notion first introduced by the philosopher Aristotle. This geocentric conception came to be known as the Ptolemaic model. The catalogue of 1022 stars within their constellations was only a part of this great work, but it would come to be important to celestial navigation in later eras, especially when European sailors gained the necessary naval technology to sail away from sight of land into the deep ocean. But it was due to the Islamic world that the medieval west had access to this treatise, as it had been translated into Arabic, and from there into Latin in the 12th century, making it available to Europeans. Its name had shifted to Greek He Megale Syntaxis “The Great Treatise” to simply Megiste “greatest” which was rendered in Arabic as Al-majisti, leading to the European name Almagest. This is an example of the enormously important contribution of the Islamic world, who transmitted and built upon the knowledge of ancient Greece, to European learning. Christian Europeans generally had no access to or ability to read ancient Greek texts in their original forms. As we’ll see, the Islamic world is above average in importance to our story in a number of ways.

And this brings us to the word average. The earliest senses of the word have to do with maritime shipping. In English contexts it originally referred to a customs-duty or expense over and above the freight incurred in the shipment of goods and payable by their owner. But the word seems to come from the Old French availe which meant “damage to shipping” and by extension any expense, with the -age ending coming by way of a parallel to the semantically related damage. And since the usual practise was to share out these expenses between all the owners of freight on the ship as well as the ship owners, kind of like an early form of insurance, the term gained the mathematical sense of the ‘arithmetic mean’ from the idea of distributing a sum between a number of people, and the sense of “typical” or “usual” developed from there. Now the deeper etymology of this word is a matter of some speculation and disagreement. As the Oxford English Dictionary puts it “few words have received more etymological investigation”. But the explanation that seems to carry the most weight, and the one we’re going to go with here, is that it comes from Arabic ‘awariya “damaged goods”, from ‘awar “fault, blemish, defect, flaw”, from ‘awira “to lose an eye”, from a Proto-Semitic root that means “to be or become blind”. Kind of recalls Odin giving up his eye, and in a way this is fitting since average in its maritime shipping sense, which is the beginnings of insurance, is all about making plans for future contingencies.

The practise, now referred to as general average, was to share out the losses in freight if for instance some had to be jettisoned overboard in the event of a storm at sea in order to save the ship. The sailors therefore weren’t faced with the decision of what to jettison on the basis of who owned it since all the freight owners would share the expense of the loss. This practise goes back a long way, and can be found in the Lex Rhodia, a maritime code from Rhodes around 800 BCE. The law disappeared after the fall of Rome, but the principle was revived in the Rolls of Oléron promulgated by Eleanore of Aquitaine after returning from the Second Crusade around 1160 CE. There were of course other ancient forerunners of insurance by distributing or transferring risk, such as the 3rd century BCE Chinese practise of distributing goods among several vessels in case one capsized in river rapids. And in the Code of Hammurabi from around 1750 BCE a merchant taking a loan to fund a shipment could pay an additional fee guaranteeing the loan would be cancelled in the event of theft or loss. By the way, the code of Hammurabi also records the first evidence of interest-bearing loans. But in any case the first example of actual contract insurance for maritime shipping dates to 1347 CE in Genoa. Actual insurance laws became codified first in 15th century Barcelona, with the first statute in England in 1601.
Insurance brokers kind of grew up organically from there, and funnily enough we have coffee to thank for it. Which is appropriate since coffee is another of those things that Europe got from the Islamic world. The word coffee came into English through Dutch and Italian from Turkish kahveh, which in turn came from Arabic qahwah. The ultimate origin of the word is debated. Some trace it back to the Kaffa region of Ethiopia, where coffee was originally grown. But a more likely etymology is that it comes from a Proto-Semitic root which means “to be or become weak, dim, dull, dark”, thus meaning “dark stuff”, appropriately enough. Interestingly, the word seems to have originally referred to a kind of wine, also dark in colour, until the Islamic prohibition against drinking alcohol made the word obsolete, whereupon it shifted over to refer to coffee, a non-alcoholic drink which nonetheless has a pleasant effect on the drinker. The drink itself made it to Europe in the 16th century by way of Turkey. It arrived in England before the end of that century through trading by the Dutch and British East India Companies, and soon coffeehouses sprang up in Europe, and they soon became centres of social life and business. For instance the Café Procope in Paris was where Denis Diderot and Jean le Rond d’Alembert brewed up the idea of creating the first modern Encyclopedia.

But more important to our story is the coffeehouse opened in London in 1686 by a man named Edward Lloyd. You see, shortly after it opened, it was relocated in 1691 to an area called Exchange Alley which was conveniently located near the Royal Exchange where the exchange of goods was carried out. As a result people involved in trade and commerce began to congregate at the nearby coffeehouses such as Lloyd’s Coffeehouse. Lloyd installed a pulpit from which shipping news could be announced, and for the benefit of his patrons engaged in their wheelings and dealings began to compile a list of ships engaged in trade which included information about the condition and seaworthiness of the ships both in terms of the state of their hulls and the quality of their equipment. That way you’d know what trade venture to underwrite. He used an alphanumerical rating system — A1 was top notch both in terms of hull and equipment. That’s where we get the expression A1 for something that is first-rate. At the time, a ship’s hull was vulnerable to shipworms, actually a species of salt-water clam which bored into the hull. The solution for shipworm was to coat the hull with a mixture of tar and pitch. No problem for England as their American colonies produced the necessary stuff. But after American Independence, England was in a bit of a pickle. Eventually a solution was found in sheathing the hull in copper. And that’s where we get the expression copper-bottomed, as in a copper-bottomed investment—a really safe bet. The practise began with the navy but soon was adopted by commercial ships, and in 1777 the first such ship was listed in Lloyd’s register, and by 1786 there were 275 copper-bottomed vessels. And in case you hadn’t guessed by now Lloyd’s Coffeehouse eventually became the great insurance market Lloyd’s of London. So thanks to Islamic prohibition and maritime shipping with its distributed averages, we have insurance brokers.

Thanks for watching, and I'll be back very soon with part two of our look at the word Average, in which we’ll investigate the history of probability mathematics and property insurance. 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

Welcome to the Endless Knot! Today is part two of a three episode series about the word Average, in which we look at property and probability!

As we saw in the last video, the word average, which comes from an Arabic word that means ‘blemish’ and ultimately from a Proto-Semitic root that means “to be one eyed”, originally referred damage to shipping and how averaging out those losses was an early form of insurance. We also saw how Ptolemy had a geocentric model of the universe, and how his star charts were passed on to medieval Europe by Islamic scholars, and how the Islamic world also passed along coffee to European society, where coffeehouses became hives for business transactions, including the Italian invention of contract insurance, which led to insurance brokers in Lloyd’s Coffeehouse in London to become the insurance market Lloyd’s of London.

Well the other thing the insurance business needed to really get going was a way of predicting the likelihood or chances of unfavourable events. So we’re back to predicting the future again. The word likely, by the way, which around 1300 had the sense of “having the appearance of truth or fact” and from that gained its sense of “probable” in the late 14th century, comes from Old Norse likligr, replacing the native Anglo-Saxon cognate geliclic. The word chance, on the other hand, comes through French from Latin cado “to fall, die”, and when it entered English around 1300 it had the sense “something that takes place, what happens, an occurrence”, in other words how matters fall, but reminding us I suppose of how the dice fall, and thus became a synonym for probability. And the word probability itself comes from Latin as well, from probabilitas. This in turn is cognate with the word prove and comes from the Latin verb probare “to make good, esteem, represent as good, make credible, show” from probus “worthy, good, upright, virtuous” from Proto-Indo-European *pro-bhwo- “being in front”.

As for calculating probabilities, we again have the Islamic world to thank. For the first name in the history of probability theory is Al-Kindi the 9th century Arab mathematician, philosopher and, if you’ll pardon the pun, all around polymath. As a philosopher he adopted and adapted Greek ideas, and as a mathematician he was the first to use statistics and probability to decode a cipher by working out what the letter frequencies were. But in addition to his kicking off the study and use of probability and statistics, he is probably best known for introducing Indian numerals to the Islamic world, and thence to Christian Europe, where they became known as Arabic numerals. The 12th to 13th century Italian mathematician Fibonacci was the first to popularize the so-called Arabic numerals in Europe through his 1202 book Liber Abaci or Book of Calculation. You probably know him from the Fibonacci numbers, which he also introduced in that book. It was an important and influential work, and was the inspiration and one of the main sources for the book Summa arithmetica or Summary of arithmetic, by the 15th to 16th century Italian mathematician Luca Pacioli, itself containing a number of firsts. It was the first description of double-entry bookkeeping, useful I suppose for all those later coffeehouse financial transactions, which led to Pacioli often being referred to as the “father of accounting and bookkeeping”. But for our purposes Pacioli’s book is important for another first, the first mention of the problem of points, to which he, incorrectly, offered a solution. The problem of points can be explained thusly: imagine two gamblers are playing a coin toss game upon which is riding a monetary prize. The game is to see who is the first to win ten coin tosses. But for some reason the game is interrupted and the players want to figure out how to fairly distribute the stakes between them. Simple enough to divide it in half if they were tied, but harder to work out if one had a lead. It’s clear in that case that one of the players has a greater chance of winning than the other, but what chance? This problem kicked off the development of probability theory and the maths to solve problems of probability.

Our next stop in the history of probability was one Gerolamo Cardano, who was inspired by Pacioli’s work. You see Cardano was another one of these polymath types, working as a physician, but also a part-time mathematician and inventor, inventing for instance the combination lock. He was also an avid and disreputable gambler — you can see why he was so interested in Pacioli’s probability work — and he was often short on funds, keeping himself afloat by gambling and playing chess. He was thus the first to write systematically about probability and games of chance, publishing his Liber de ludo aleae or Book about Games of Chance in 1539, which included not only the mathematical treatment of probability, but also ways to cheat like rubbing a card you want to draw from a deck with soap. He wrote about the use of expressing odds as the ratio of favourable to unfavourable outcomes, like there’s a 1 in 6 chance of rolling a six with one die, and even worked on figuring out the probability of rolling a seven with two dice. As a result of all this, Cardano is sometimes referred to as “the gambling scholar”. So we also have gambling to thank for probability theory.

Speaking of gambling, the word gamble is related to the word game, as in games of chance, coming from Old English gamenian “to play, joke, pun” ultimately from the Proto-Germanic collective prefix *ga- plus *mann meaning “person” giving a sense of “people together”. Gamble probably gained its “b” by influence from the otherwise unrelated word gambol, as in a lamb gambolling. I suppose you need good luck when gambling, and luck is an odd word with an uncertain etymology. It probably comes from Middle Dutch luk, a shortening of gheluk meaning “happiness, good fortune” and cognate with modern German Glück meaning “fortune, good luck”. But where this word ultimately comes from is entirely unknown. Another unexpectedly luck-related word is speed, which comes from Old English sped “luck, prosperity, success”. It comes ultimately from Proto-Indo-European *spe- “to thrive, prosper”. The sense of “quickness”, now the dominant sense, didn’t emerge until late Old English, but there is a remnant of the older meaning in the expression Godspeed which actually means “may God prosper you” or even just “good luck” and has nothing to do with quickness, though I’m sure God is very fast.
But getting back to the gambling scholar Cardano, he was also into astrology — there’s predicting the future again — and struck up a friendship with fellow astrologer and Lutheran theologian Andreas Osiander. Osiander edited a number of Cardano’s books and even received a dedication in one of them. Another writer that Osiander edited, who didn’t get along so well with him, was Nicolaus Copernicus. You see in his De revolutionibus orbium coelestium or On the Revolutions of the Celestial Spheres, Copernicus challenged that old Ptolemaic geocentric model of the universe, presenting instead a solar system with the sun in the centre and the planets in orbit around it and the various moons in orbit around the planets. Made more sense of the apparent movement of the celestial objects. But while editing, unbeknownst to Copernicus, Cardano slipped in his own preface to the book stating that it wasn’t meant to be taken literally, it was just a mathematical model. Copernicus was furious but by then it was too late and there was nothing that could be done about it, and soon after Copernicus died.

But coming back to Pacioli’s problem of points, it was finally solved in 1654. The problem came to the attention of a French writer named Antoine Gombaud who is more commonly known as the Chevalier de Méré. He wasn’t actually an aristocrat, it was just a name he invented for his dialogues, but soon his friends started to refer to him that way and the name just stuck. In addition to being a writer, the Chevalier de Méré was also a proficient gambler as well as an amateur mathematician, but his math skills weren’t up to solving the problem, so he brought it to his friend Blaise Pascal. Pascal was a child prodigy in mathematics, making many discoveries while still a teenager. In 1650 he had something of a religious epiphany while suffering from ill health, and abandoned mathematics, turning instead to religious meditation and philosophy. He eventually did return to mathematics but died at the unfortunately young age of 39. As a result of all this he is known as greatest might-have-been of mathematics. Well, he started corresponding with fellow French mathematician Pierre de Fermat about that problem of points which the Chevalier de Méré brought to him. Actually Fermat was a lawyer with no formal mathematical training. Indeed he didn’t even get onto mathematics until he was in his thirties. But unlike his friend Pascal his life was long and mathematically productive. Perhaps best known for Fermat’s Last Theorem, his contributions to mathematics were so great that he is often referred to as “the prince of amateurs”. Well between them in their correspondence, Pascal and Fermat worked out two entirely different ways of solving the problem which produced the same results, and the methods they developed became the backbone of probability mathematics. And in keeping with Pascal’s vacillation between mathematics and religion and philosophy, Pascal united these two interests in the realm of probability, writing “We know neither the existence nor the nature of God … Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is”.

In 1657, just three years after Pascal and Fermat created probability maths, the Dutch astronomer and physicist Christiaan Huygens wrote it all up in the first formal treatise called De ratiociniis in ludo aleae or On Reasoning in Games of Chance. And it’s perhaps fitting that Huygens is best known today as an astronomer, since probability came to be very useful in that field. For instance, years later another child prodigy mathematician Carl Friedrich Gauss used the method of least squares to accurately predict the location of the dwarf planet Ceres from only a few observations as data points. Imagine you have a graph with just a few data points on it. The method of least squares allows you to find the line of best fit for that scant data. So once again we return to the effort to determine the motion of celestial objects, just like Ptolemy and Copernicus.
Another important early contributer to probability and statistics was Thomas Bayes, a Presbyterian minister by calling. He is most famous for Bayes Theorem, which basically allows one to accurately work out the probability of an event based on prior knowledge. Bayes actually published very little on mathematics during his lifetime, and it was up to French aristocrat and scholar Pierre-Simon Laplace to further develop Bayes’ Theorem. And in a nice bit of interconnection, Laplace had also tried but was unable to calculate the orbit of the dwarf planet Ceres, a problem which you remember Gauss solved. One of Leplace’s students, Joseph Fourier made important contributions to both mathematics and physics, but it’s, oddly enough, his work on heat transfer that interests us. Fourier was very interested in heat, and is credited with discovering the greenhouse effect. You see, Fourier got into an academic argument with Siméon Denis Poisson over the theory of heat — Poisson was forced to retract. However Poisson had more luck in his work on probability theory, which included the Poisson distribution, which allows one to know the probability of a given number of events occurring in a fixed interval of time, exactly the sort of thing an insurance company needs to know.

After marine insurance, the next type to develop was property insurance, specifically fire insurance. Unfortunately it’s a bit of a shut-the-barn-door-after-the-horse-has-bolted sort of thing, because what really pointed out the need for fire insurance was the Great Fire of London in 1666, in which more than 13,000 homes burned down. The job of rebuilding fell to architect Christopher Wren, also a sometime physicist and mathematician whose scientific work was highly regarded by our friend Pascal. Clearly Wren observed the need for an insurance office as he included in his rebuilding plans a site for one. Wren’s assistant was polymath Robert Hooke, the trajectory of whose life ran from being a penniless scientist, to a wealthy and admired member of society, to eventually an old man in ill health, jealous and bitter towards his scientific contemporaries. However, Hooke’s efforts as surveyor after the Great Fire of London won him much acclaim. In addition, Hooke worked on the problem of timekeeping and celestial navigation. You see in order to calculate longitude (how far east or west you were) you needed to know the time back home where all your star charts were calibrated to. If you take a reading of a star’s position and find out how far out it is compared to the star chart, you can work out how far east or west you are to see the star in that position. But you can’t use a pendulum clock at sea, and spring driven clocks weren’t accurate enough. So Hooke invented a balance spring pocket watch which was up to the challenge, and tried to patent and develop the technology, but was unable to finance it, no doubt adding to the bitterness of his later years. What’s more our astronomer friend Christiaan Huygens independently came up with the same idea some five years later.

But getting back to the insurance office, the first one to be established was founded by a man with an unusual middle name: Nicholas If-Christ-had-not-died-for-thee-thou-hadst-been-damned Barbon. Yes that’s actually his legal middle name, the practise of giving such hortatory middle names being popular with the Puritans at the time. Well, Barbon and eleven associates founded the Insurance Office for Houses located at the back of the Royal Exchange, the first fire insurance company, and soon other companies were started. And once those new insurance companies got their hands on all of that new probability math such as the Poisson distribution, insurance companies could estimate how often claims would come in and thus set their premiums appropriately to average out their risks and losses.

Thanks for watching! I'll be back soon with the final part in our look at the word Average, in which we investigate statistics and stock markets. 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

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.

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