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The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow
Albert Einstein, Alfred Russel Wallace, Antoine Gombaud: Chevalier de Méré, Atul Gawande, Brownian motion, butterfly effect, correlation coefficient, Daniel Kahneman / Amos Tversky, Donald Trump, feminist movement, forensic accounting, Gerolamo Cardano, Henri Poincaré, index fund, Isaac Newton, law of one price, pattern recognition, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, Richard Feynman, Richard Feynman, Ronald Reagan, Stephen Hawking, Steve Jobs, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Bayes, V2 rocket, Watson beat the top human players on Jeopardy!
His sister Gilberte called it “the time of his life that was worst employed.”9 Though he put some effort into self-promotion, his scientific research went almost nowhere, but for the record, his health was the best it had ever been. Often in history the study of the random has been aided by an event that was itself random. Pascal’s work represents such an occasion, for it was his abandonment of study that led him to the study of chance. It all began when one of his partying pals introduced him to a forty-five-year-old snob named Antoine Gombaud. Gombaud, a nobleman whose title was chevalier de Méré, regarded himself as a master of flirtation, and judging by his catalog of romantic entanglements, he was. But de Méré was also an expert gambler who liked the stakes high and won often enough that some suspected him of cheating. And when he stumbled on a little gambling quandary, he turned to Pascal for help. With that, de Méré initiated an investigation that would bring to an end Pascal’s scientific dry spell, cement de Méré’s own place in the history of ideas, and solve the problem left open by Galileo’s work on the grand duke’s dice-tossing question.
Fermat’s Last Theorem by Simon Singh
Albert Einstein, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, Augustin-Louis Cauchy, Fellow of the Royal Society, Georg Cantor, Henri Poincaré, Isaac Newton, John Conway, John von Neumann, kremlinology, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, Rubik’s Cube, Simon Singh, Wolfskehl Prize
The mathematical hermit was introduced to the subject by Pascal, and so, despite his desire for isolation, he felt obliged to maintain a dialogue. Together Fermat and Pascal would discover the first proofs and cast-iron certainties in probability theory, a subject which is inherently uncertain. Pascal’s interest in the subject had been sparked by a professional Parisian gambler, Antoine Gombaud, the Chevalier de Méré, who had posed a problem which concerned a game of chance called points. The game involves winning points on the roll of a dice, and whichever player is the first to earn a certain number of points is the winner and takes the prize money. Gombaud had been involved in a game of points with a fellow-gambler when they were forced to abandon the game half-way through, owing to a pressing engagement.
Wonderland: How Play Made the Modern World by Steven Johnson
Ada Lovelace, Alfred Russel Wallace, Antoine Gombaud: Chevalier de Méré, Berlin Wall, bitcoin, Book of Ingenious Devices, Buckminster Fuller, Claude Shannon: information theory, Clayton Christensen, colonial exploitation, computer age, conceptual framework, crowdsourcing, cuban missile crisis, Drosophila, Edward Thorp, Fellow of the Royal Society, game design, global village, Hedy Lamarr / George Antheil, HyperCard, invention of air conditioning, invention of the printing press, invention of the telegraph, Islamic Golden Age, Jacquard loom, Jacquard loom, Jacques de Vaucanson, James Watt: steam engine, Jane Jacobs, John von Neumann, joint-stock company, Joseph-Marie Jacquard, land value tax, Landlord’s Game, lone genius, mass immigration, megacity, Minecraft, moral panic, Murano, Venice glass, music of the spheres, Necker cube, New Urbanism, Oculus Rift, On the Economy of Machinery and Manufactures, pattern recognition, peer-to-peer, pets.com, placebo effect, probability theory / Blaise Pascal / Pierre de Fermat, profit motive, QWERTY keyboard, Ray Oldenburg, spice trade, spinning jenny, statistical model, Steve Jobs, Steven Pinker, Stewart Brand, supply-chain management, talking drums, the built environment, The Great Good Place, the scientific method, The Structural Transformation of the Public Sphere, trade route, Turing machine, Turing test, Upton Sinclair, urban planning, Victor Gruen, Watson beat the top human players on Jeopardy!, white flight, white picket fence, Whole Earth Catalog, working poor, Wunderkammern
He also demonstrated the multiplicative nature of probability when predicting the results of a sequence of dice rolls: the chance of rolling three sixes in a row is one in 216: 1⁄6 x 1⁄6 x 1⁄6. Written in 1564, Cardano’s book wasn’t published for another century. By the time his ideas got into wider circulation, an even more important breakthrough had emerged out of a famous correspondence between Blaise Pascal and Pierre de Fermat in 1654. This, too, was prompted by a compulsive gambler, the French aristocrat Antoine Gombaud, who had written Pascal for advice about the most equitable way to predict the outcome of a dice game that had been interrupted. Their exchange put probability theory on a solid footing and created the platform for the modern science of statistics. Within a few years, Edward Halley (of comet legend) was using these new tools to calculate mortality rates for the average Englishman, and the Dutch scientist Christiaan Huygens and his brother Lodewijk had set about to answer “the question . . . to what age a newly conceived child will naturally live.”
The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling by Adam Kucharski
Ada Lovelace, Albert Einstein, Antoine Gombaud: Chevalier de Méré, beat the dealer, Benoit Mandelbrot, butterfly effect, call centre, Chance favours the prepared mind, Claude Shannon: information theory, collateralized debt obligation, correlation does not imply causation, diversification, Edward Lorenz: Chaos theory, Edward Thorp, Everything should be made as simple as possible, Flash crash, Gerolamo Cardano, Henri Poincaré, Hibernia Atlantic: Project Express, if you build it, they will come, invention of the telegraph, Isaac Newton, John Nash: game theory, John von Neumann, locking in a profit, Louis Pasteur, Nash equilibrium, Norbert Wiener, p-value, performance metric, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative ﬁnance, random walk, Richard Feynman, Richard Feynman, Ronald Reagan, Rubik’s Cube, statistical model, The Design of Experiments, Watson beat the top human players on Jeopardy!, zero-sum game
In the decades that followed, other researchers chipped away at the mysteries of probability, too. At the request of a group of Italian nobles, Galileo investigated why some combinations of dice faces appeared more often than others. Astronomer Johannes Kepler also took time off from studying planetary motion to write a short piece on the theory of dice and gambling. The science of chance blossomed in 1654 as the result of a gambling question posed by a French writer named Antoine Gombaud. He had been puzzled by the following dice problem. Which is more likely: throwing a single six in four rolls of a single die, or throwing double sixes in twenty-four rolls of two dice? Gombaud believed the two events would occur equally often but could not prove it. He wrote to his mathematician friend Blaise Pascal, asking if this was indeed the case. To tackle the dice problem, Pascal enlisted the help of Pierre de Fermat, a wealthy lawyer and fellow mathematician.
Against the Gods: The Remarkable Story of Risk by Peter L. Bernstein
Albert Einstein, Alvin Roth, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Bayesian statistics, Big bang: deregulation of the City of London, Bretton Woods, buttonwood tree, capital asset pricing model, cognitive dissonance, computerized trading, Daniel Kahneman / Amos Tversky, diversified portfolio, double entry bookkeeping, Edmond Halley, Edward Lloyd's coffeehouse, endowment effect, experimental economics, fear of failure, Fellow of the Royal Society, Fermat's Last Theorem, financial deregulation, financial innovation, full employment, index fund, invention of movable type, Isaac Newton, John Nash: game theory, John von Neumann, Kenneth Arrow, linear programming, loss aversion, Louis Bachelier, mental accounting, moral hazard, Myron Scholes, Nash equilibrium, Paul Samuelson, Philip Mirowski, probability theory / Blaise Pascal / Pierre de Fermat, random walk, Richard Thaler, Robert Shiller, Robert Shiller, spectrum auction, statistical model, The Bell Curve by Richard Herrnstein and Charles Murray, The Wealth of Nations by Adam Smith, Thomas Bayes, trade route, transaction costs, tulip mania, Vanguard fund, zero-sum game
In the course of that experiment he demonstrated that barometric pressure could be measured at varying altitudes with the use of mercury in a tube emptied of all air. About this time, Pascal became acquainted with the Chevalier de Mere, who prided himself on his skill at mathematics and on his ability to figure the odds at the casinos. In a letter to Pascal some time in the late 1650s, he boasted, "I have discovered in mathematics things so rare that the most learned of ancient times have never thought of them and by which the best mathematicians in Europe have been surprised."5 Leibniz himself must have been impressed, for he described the Chevalier as "a man of penetrating mind who was both a gambler and a philosopher." But then Leibniz must have had second thoughts, for he went on to say, "I almost laughed at the airs which the Chevalier de Mere takes on in his letter to Pascal."6 Pascal agreed with Leibniz. "M. de Mere," he wrote to a colleague, "has good intelligence but he is not a geometer and this, as you realize, is a great defect."'
But the serious study of risk began during the Renaissance, when people broke loose from the constraints of the past and subjected longheld beliefs to open challenge. This was a time when much of the world was to be discovered and its resources exploited. It was a time of religious turmoil, nascent capitalism, and a vigorous approach to science and the future. In 1654, a time when the Renaissance was in full flower, the Chevalier de Mere, a French nobleman with a taste for both gambling and mathematics, challenged the famed French mathematician Blaise Pascal to solve a puzzle. The question was how to divide the stakes of an unfinished game of chance between two players when one of them is ahead. The puzzle had confounded mathematicians since it was posed some two hundred years earlier by the monk Luca Paccioli. This was the man who brought double-entry bookkeeping to the attention of the business managers of his day-and tutored Leonardo da Vinci in the multiplication tables.
By this time Martin Luther had had his say and halos had disappeared from most paintings of the Holy Trinity and the saints. William Harvey had overthrown the medical teachings of the ancients with his discovery of the circulation of blood-and Rembrandt had painted "The Anatomy Lesson," with its cold, white, naked human body. In such an environment, someone would soon have worked out the theory of probability, even if the Chevalier de Mere had never confronted Pascal with his brainteaser. As the years passed, mathematicians transformed probability theory from a gamblers' toy into a powerful instrument for organizing, interpreting, and applying information. As one ingenious idea was piled on top of another, quantitative techniques of risk management emerged that have helped trigger the tempo of modern times. By 1725, mathematicians were competing with one another in devising tables of life expectancies, and the English government was financing itself through the sale of life annuities.
Alex's Adventures in Numberland by Alex Bellos
Andrew Wiles, Antoine Gombaud: Chevalier de Méré, beat the dealer, Black Swan, Black-Scholes formula, Claude Shannon: information theory, computer age, Daniel Kahneman / Amos Tversky, Edward Thorp, family office, forensic accounting, game design, Georg Cantor, Henri Poincaré, Isaac Newton, Myron Scholes, pattern recognition, Paul Erdős, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, random walk, Richard Feynman, Richard Feynman, Rubik’s Cube, SETI@home, Steve Jobs, The Bell Curve by Richard Herrnstein and Charles Murray, traveling salesman
Step 3: So, the probability of rolling a six is 1 – 0.482 = 0.518. A probability of 0.518 means that if you threw four dice a thousand times, you could expect to get at least one six about 518 times, and get no sixes about 482 times. If you gambled on the chance of at least one six, you would win on average more than you would lose, so you would end up profiting. The seventeenth-century writer Chevalier de Méré was a regular at the dicing table, as he was at the most fashionable salons in Paris. The chevalier was as interested in the mathematics of dicing as he was in winning money. He had a couple of questions about gambling, though, that he was unable to answer himself, so in 1654 he approached the distinguished mathematician Blaise Pascal. His chance enquiry was the random event that set in motion the proper study of randomness.
Nevertheless, his amateur ruminations had made him one of the most respected mathematicians of the first half of the seventeenth century. The short correspondence between Pascal and Fermat about chance – which they called hasard – was a landmark in the history of science. Between them the men solved both of the literary bon vivant’s problems, and in so doing, set the foundations of modern probability theory. Now for the answers to Chevalier de Méré’s questions. How many times do you need to throw a pair of dice so that it is more likely than not that a double six will appear? In one throw of two dice the chance of a double six is , or 0.028. The chance of a double six appearing in two throws of two dice is 1 minus the probability of no double sixes appearing in two throws, or 1 – ( ). This works out to be , or 0.055. (Note: the chance of a double six in two throws is not .
Perhaps the cause was the near-death accident in which his coach hung perilously off a bridge after the horses plunged over the parapet, or perhaps it was a moral reaction to the decadence of the dicing tables of pre-revolutionary France – in any case, it revitalized his commitment to Jansenism, a strict Catholic cult, and he abandoned maths for theology and philosophy. Nonetheless, Pascal could not help but think mathematically. His most famous contribution to philosophy – an argument about whether or not one should believe in God – was a continuation of the new approach to analysing chance that he had first discussed with Fermat. In simple terms, expected value is what you can expect to get out of a bet. For example, what could Chevalier de Méré expect to win by betting £10 on getting a six when rolling four dice? Imagine that he wins £10 if there is a six and loses everything if there is no six. We know that the chance of winning this bet is 0.518. So, just over half the time he wins £10, and just under half he loses £10. The expected value is calculated by multiplying the probability of each outcome with the value of each outcome, and then adding them up.
Is God a Mathematician? by Mario Livio
Albert Einstein, Antoine Gombaud: Chevalier de Méré, Brownian motion, cellular automata, correlation coefficient, correlation does not imply causation, cosmological constant, Dava Sobel, double helix, Edmond Halley, Eratosthenes, Georg Cantor, Gerolamo Cardano, Gödel, Escher, Bach, Henri Poincaré, Isaac Newton, John von Neumann, music of the spheres, Myron Scholes, probability theory / Blaise Pascal / Pierre de Fermat, Russell's paradox, The Design of Experiments, the scientific method, traveling salesman
Engineers trying to decide which safety mechanisms to install into the Crew Exploration Vehicle for astronauts, particle physicists analyzing results of accelerator experiments, psychologists rating children in IQ tests, drug companies evaluating the efficacy of new medications, and geneticists studying human heredity all have to use the mathematical theory of probability. Games of Chance The serious study of probability started from very modest beginnings—attempts by gamblers to adjust their bets to the odds of success. In particular, in the middle of the seventeenth century, a French nobleman—the Chevalier de Méré—who was also a reputed gamester, addressed a series of questions about gambling to the famous French mathematician and philosopher Blaise Pascal (1623–62). The latter conducted in 1654 an extensive correspondence about these questions with the other great French mathematician of the time, Pierre de Fermat (1601–65). The theory of probability was essentially born in this correspondence. Let’s examine one of the fascinating examples discussed by Pascal in a letter dated July 29, 1654.
The Physics of Wall Street: A Brief History of Predicting the Unpredictable by James Owen Weatherall
Albert Einstein, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Asian financial crisis, bank run, beat the dealer, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, butterfly effect, capital asset pricing model, Carmen Reinhart, Claude Shannon: information theory, collateralized debt obligation, collective bargaining, dark matter, Edward Lorenz: Chaos theory, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, George Akerlof, Gerolamo Cardano, Henri Poincaré, invisible hand, Isaac Newton, iterative process, John Nash: game theory, Kenneth Rogoff, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, martingale, Myron Scholes, new economy, Paul Lévy, Paul Samuelson, prediction markets, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative ﬁnance, random walk, Renaissance Technologies, risk-adjusted returns, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Coase, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, statistical arbitrage, statistical model, stochastic process, The Chicago School, The Myth of the Rational Market, tulip mania, V2 rocket, Vilfredo Pareto, volatility smile
Cardano never published his book — after all, why give your best gambling tips away? — but the manuscript was found among his papers when he died and ultimately was published over a century after it was written, in 1663. By that time, others had made independent advances toward a full-fledged theory of probability. The most notable of these came at the behest of another gambler, a French writer who went by the name of Chevalier de Méré (an affectation, as he was not a nobleman). De Méré was interested in a number of questions, the most pressing of which concerned his strategy in a dice game he liked to play. The game involved throwing dice several times in a row. The player would bet on how the rolls would come out. For instance, you might bet that if you rolled a single die four times, you would get a 6 at least one of those times.
Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by Nassim Nicholas Taleb
Antoine Gombaud: Chevalier de Méré, availability heuristic, backtesting, Benoit Mandelbrot, Black Swan, commoditize, complexity theory, corporate governance, corporate raider, currency peg, Daniel Kahneman / Amos Tversky, discounted cash flows, diversified portfolio, endowment effect, equity premium, fixed income, global village, hindsight bias, Kenneth Arrow, Long Term Capital Management, loss aversion, mandelbrot fractal, mental accounting, meta analysis, meta-analysis, Myron Scholes, Paul Samuelson, quantitative trading / quantitative ﬁnance, QWERTY keyboard, random walk, Richard Feynman, Richard Feynman, road to serfdom, Robert Shiller, Robert Shiller, selection bias, shareholder value, Sharpe ratio, Steven Pinker, stochastic process, survivorship bias, too big to fail, Turing test, Yogi Berra
Rozan’s book: Rozan (1999). Mental accounting: Thaler (1980) and Kahneman, Knetch and Thaler (1991). Portfolio theory (alas): Markowitz (1959). The conventional probability paradigm: Most of the conventional discussions on probabilistic thought, especially in the philosophical literature, present minor variants of the same paradigm with the succession of the following historical contributions: Chevalier de Méré, Pascal, Cardano, De Moivre, Gauss, Bernouilli, Laplace, Bayes, von Mises, Carnap, Kolmogorov, Borel, De Finetti, Ramsey, etc. However, these concern the problems of calculus of probability, perhaps fraught with technical problems, but ones that are hair-splitting and, to be derogatory, academic. They are not of much concern in this book—because, inspite of my specialty, they do not seem to provide any remote usefulness for practical matters.
How I Became a Quant: Insights From 25 of Wall Street's Elite by Richard R. Lindsey, Barry Schachter
Albert Einstein, algorithmic trading, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, asset allocation, asset-backed security, backtesting, bank run, banking crisis, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, business process, buy low sell high, capital asset pricing model, centre right, collateralized debt obligation, commoditize, computerized markets, corporate governance, correlation coefficient, creative destruction, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, discounted cash flows, disintermediation, diversification, Donald Knuth, Edward Thorp, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, full employment, George Akerlof, Gordon Gekko, hiring and firing, implied volatility, index fund, interest rate derivative, interest rate swap, John von Neumann, linear programming, Loma Prieta earthquake, Long Term Capital Management, margin call, market friction, market microstructure, martingale, merger arbitrage, Myron Scholes, Nick Leeson, P = NP, pattern recognition, Paul Samuelson, pensions crisis, performance metric, prediction markets, profit maximization, purchasing power parity, quantitative trading / quantitative ﬁnance, QWERTY keyboard, RAND corporation, random walk, Ray Kurzweil, Richard Feynman, Richard Feynman, Richard Stallman, risk-adjusted returns, risk/return, shareholder value, Sharpe ratio, short selling, Silicon Valley, six sigma, sorting algorithm, statistical arbitrage, statistical model, stem cell, Steven Levy, stochastic process, systematic trading, technology bubble, The Great Moderation, the scientific method, too big to fail, trade route, transaction costs, transfer pricing, value at risk, volatility smile, Wiener process, yield curve, young professional
In contrast, the Enlightenment view of science (the view of Francis Bacon and his intellectual followers) defines science in terms of improving the understanding of the forces at work in the world with which we interact. In this context, utility is a natural measure of scientific contribution. Fermat, in the seventeenth century, was the first to correctly solve certain problems related to games of chance, problems posed to him (and to Blaise Pascal, a mathematician famous for his triangle, among other things) by a well-known player of such games, the Chevalier de Mere, who was looking, not for Aristotelian truth, but for the proper rules to use to split the pot of cash wagered in a game that ends before there is a winner. If Fermat wasn’t a quant by Joshi’s definition, then we can’t tell a quant from a quail. As Douglas Adams (author of the science fiction classic, The Hitchhiker’s Guide to the Galaxy) said, “If it looks like a duck, and quacks like a duck, we have at least to consider the possibility that we have a small aquatic bird of the family anatidae on our hands.”