 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 protosemitic root that means to be one-eyed, originally referred to 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 coffee houses became hives or business transactions, including the Italian invention of contract insurance, which led insurance brokers in Lloyd's coffee house 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 unfavorable 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 Lickliger, replacing the native Anglo-Saxon cognate Yilichlich. The word chance, on the other hand, comes through French, from Latin cateau to fall or die, and when it entered English around 1300 it had the sense something that takes place, 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. 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 or show, from probis, worthy or good, from proto-Indo-European probo, 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 of the 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, Lieber-Abbaki, 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 writing a monetary prize. The game is to see who is the first to win 10 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 math 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 in games of chance, publishing his Viber De Ludo Allaei, 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 favorable to unfavorable outcomes, like there's a one in six 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, gamenean, ultimately from the proto-Germanic collective prefix ga plus man, meaning person, giving the sense of people together. Gamble probably gained its B by influence from the otherwise unrelated word gamble, as in a lamb gambling. 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 geluk, meaning happiness or good fortune, and cognate with modern German gluk, meaning fortune or 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 or prosperity. It comes ultimately from proto-Indo-European spay to thrive or 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 Ossiander. Ossiander edited a number of Cardano's books and even received a dedication in one of them. Another writer that Ossiander edited, who didn't get along so well with him, was Nicholas Copernicus. You see, in his De Revolutionebus 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 center and the planets in orbit around it and various moons in orbit around the planets, made more sense of the apparent movement of the celestial objects. But while editing, unbeknownst to Copernicus, Ossiander 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 Paceoli's problem of points, it was finally solved in 1654. The problem came to the attention of a French writer named Antoine Gambo, who is more commonly known as the Chevalier de Meret. 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 Meret 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 the attention of 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 the greatest might've been of mathematics. Well, he started corresponding with fellow French mathematician Pierre de Fermat about that problem of points, which the Chevalier de Meret 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 30s, 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's 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, Christiane Huygens, wrote it up in the first formal treatise called De Ratio Kiniees in Ludo Allaeae, or On the 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 series 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 contributor 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 series, a problem which you remember Gauss solved. One of Laplace'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 Simeon 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 is 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 who 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 Hook, 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, Hook's efforts as surveyor after the Great Fire of London won him much acclaim. In addition, Hook 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 Hook invented a balanced 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 his bitterness in his later years. What's more, our astronomer friend, Christiane 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 had spin damned, barbun. Yes, that's actually his legal middle name. The practice of giving such hortatory middle names being popular with the Puritans at the time. Well, barbun and 11 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 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 very 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 at alliterative on Twitter and you can read more of my thoughts on my blog at alliterative.net.