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Chaos by James Gleick
Benoit Mandelbrot, butterfly effect, cellular automata, Claude Shannon: information theory, discrete time, Edward Lorenz: Chaos theory, experimental subject, Georg Cantor, Henri Poincaré, Isaac Newton, iterative process, John von Neumann, Louis Pasteur, mandelbrot fractal, Murray Gell-Mann, Norbert Wiener, pattern recognition, Richard Feynman, Richard Feynman, Stephen Hawking, stochastic process, trade route
* With a parameter of 3.5, say, and a starting value of .4, he would see a string of numbers like this: .4000, .8400, .4704, .8719, .3908, .8332, .4862, .8743, .3846, .8284, .4976, .8750, .3829, .8270, .4976, .8750, .3829, .8270, .5008, .8750, .3828, .8269, .5009, .8750, .3828, .8269, .5009, .8750, etc. A Geometry of Nature And yet relation appears, A small relation expanding like the shade Of a cloud on sand, a shape on the side of a hill. —WALLACE STEVENS “Connoisseur of Chaos” A PICTURE OF REALITY built up over the years in Benoit Mandelbrot’s mind. In 1960, it was a ghost of an idea, a faint, unfocused image. But Mandelbrot recognized it when he saw it, and there it was on the blackboard in Hendrik Houthakker’s office. Mandelbrot was a mathematical jack-of–all-trades who had been adopted and sheltered by the pure research wing of the International Business Machines Corporation. He had been dabbling in economics, studying the distribution of large and small incomes in an economy.
Yet the picture of reality that was forming in his mind in 1960 evolved from an oddity into a full-fledged geometry. To the physicists expanding on the work of people like Lorenz, Smale, Yorke, and May, this prickly mathematician remained a sideshow—but his techniques and his language became an inseparable part of their new science. The description would not have seemed apt to anyone who knew him in his later years, with his high imposing brow and his list of titles and honors, but Benoit Mandelbrot is best understood as a refugee. He was born in Warsaw in 1924 to a Lithuanian Jewish family, his father a clothing wholesaler, his mother a dentist. Alert to geopolitical reality, the family moved to Paris in 1936, drawn in part by the presence of Mandelbrot’s uncle, Szolem Mandelbrojt, a mathematician. When the war came, the family stayed just ahead of the Nazis once again, abandoning everything but a few suitcases and joining the stream of refugees who clogged the roads south from Paris.
Lamont-Doherty is where Christopher Scholz, a Columbia University professor specializing in the form and structure of the solid earth, first started thinking about fractals. While mathematicians and theoretical physicists disregarded Mandelbrot’s work, Scholz was precisely the kind of pragmatic, working scientist most ready to pick up the tools of fractal geometry. He had stumbled across Benoit Mandelbrot’s name in the 1960s, when Mandelbrot was working in economics and Scholz was an M.I.T. graduate student spending a great deal of time on a stubborn question about earthquakes. It had been well known for twenty years that the distribution of large and small earthquakes followed a particular mathematical pattern, precisely the same scaling pattern that seemed to govern the distribution of personal incomes in a free-market economy.
activist fund / activist shareholder / activist investor, Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, bank run, beat the dealer, Benoit Mandelbrot, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, card file, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, corporate raider, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discovery of the americas, diversification, diversified portfolio, Edward Glaeser, Edward Thorp, endowment effect, Eugene Fama: efficient market hypothesis, experimental economics, financial innovation, Financial Instability Hypothesis, fixed income, floating exchange rates, George Akerlof, Henri Poincaré, Hyman Minsky, implied volatility, impulse control, index arbitrage, index card, index fund, information asymmetry, invisible hand, Isaac Newton, John Meriwether, John Nash: game theory, John von Neumann, joint-stock company, Joseph Schumpeter, Kenneth Arrow, libertarian paternalism, linear programming, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market design, Myron Scholes, New Journalism, Nikolai Kondratiev, Paul Lévy, Paul Samuelson, pension reform, performance metric, Ponzi scheme, prediction markets, pushing on a string, quantitative trading / quantitative ﬁnance, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, road to serfdom, Robert Bork, Robert Shiller, Robert Shiller, rolodex, Ronald Reagan, shareholder value, Sharpe ratio, short selling, side project, Silicon Valley, South Sea Bubble, statistical model, The Chicago School, The Myth of the Rational Market, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Thomas L Friedman, Thorstein Veblen, Tobin tax, transaction costs, tulip mania, value at risk, Vanguard fund, Vilfredo Pareto, volatility smile, Yogi Berra
He recommended to his professors that they bring Osborne to the Business School for a semester, but Osborne demurred because his large family made relocation problematic.10 Another early member of the gang was Houthakker. While serving on the Stanford faculty with Holbrook Working in the 1950s, he began to focus on the commodity price series that he had criticized Maurice Kendall for bothering to study. He brought this avocation with him to Harvard, where one day in 1960 Benoit Mandelbrot came calling. Mandelbrot was a mathematician who had emigrated from France to work at IBM’s research center in Yorktown Heights, New York, studying—like Osborne at the Naval Research Laboratory—most anything that interested him. He had been looking at the mathematics of income distribution, and Houthakker invited him up to Harvard to speak about it. When Mandelbrot arrived he saw a chart on Houthakker’s blackboard of what appeared to be his income data.
At Tufts, Fama had crunched numbers for a stock market newsletter published by one of his professors. He found lots of interesting patterns in stock prices, but noticed that they tended to disappear as soon as he had identified them. With this experience he gravitated toward the random walk work begun by statistics professor Harry Roberts. He also hooked up with wandering IBM mathematician Benoit Mandelbrot. His first published work was a Mandelbrot-guided exploration of the statistical distribution of stock price changes. Fama stayed on for his doctorate, and under the influence of the newly arrived Miller he began to steer a course away from purely statistical work toward a research program shaped by economic theory. He still devoted the bulk of his 1964 doctoral dissertation, which was reprinted in full in the Business School’s quarterly Journal of Business, to Mandelbrot’s statistical ideas, but that wasn’t the part to which people paid attention.
That day it dropped 13.5 percent, the next 11.7 percent. On October 30, it rose 12.3 percent. In statistical terms these rare but significant events are called fat tails, because they are found at the tail ends of a statistical distribution and keep them from converging quickly with zero—as they would in a true bell curve. The tendency of fat-tail events to follow upon one another is called dependence. IBM MATHEMATICIAN BENOIT MANDELBROT SAW fat tails and dependence in a chart of cotton futures prices at Harvard in 1960. Mandelbrot was a Polish Jew who had emigrated to France in 1936, spent what would have been his high school years hiding from the Nazis, and then got a doctorate in mathematics at the Sorbonne. It was a 1949 book by Harvard linguist George Zipf that first piqued his interest in strange statistical distributions.
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
But as the exchange with Lévy shows, many of the most influential people working in France during Bachelier’s lifetime, including people who worked on topics quite close to Bachelier’s specialties, were either unaware of him or dismissed his work as unimportant or flawed. Given the importance that ideas like his have today, one is left to conclude that Bachelier was simply too far ahead of his time. Soon after his death, though, his ideas reappeared in the work of Samuelson and his students, but also in the work of others who, like Bachelier, had come to economics from other fields, such as the mathematician Benoît Mandelbrot and the astrophysicist M.F.M. Osborne. Change was afoot in both the academic and financial worlds that would bring these later prophets the kind of recognition that Bachelier never enjoyed while he was alive. 2 Swimming Upstream MAURY OSBORNE’S MOTHER, AMY OSBORNE, WAS AN AVID GARDENER. She was also a practical woman. Rather than buy commercial fertilizer, she would go out to the horse pastures near her home, in Norfolk, Virginia, to collect manure and bring it back for her garden.
He was a founding member of a group of French mathematicians who, under the pseudonym Nicolas Bourbaki, endeavored to bring the highest possible level of rigor and abstraction to the field; the group’s collected works set the tone for two generations of mathematicians. When his mentor, Jacques Hadamard, one of the most famous mathematicians of the late nineteenth century, retired from his position at the prestigious Collège de France, the Collège invited Mandelbrojt to replace him. He was a serious man, doing serious work. Or at least he would have been doing serious work if his nephew hadn’t been constantly hounding him. In 1950, Benoît Mandelbrot was a doctoral student at the University of Paris, Szolem’s alma mater, seeking (Szolem imagined) to follow in his eminent uncle’s footsteps. When Szolem first learned that Benoît wanted to pursue mathematics, he was thrilled. But gradually, Szolem began to question Benoît’s seriousness. Despite his uncle’s advice, Benoît showed no interest in the pressing mathematical matters of the day. His work lacked the rigor that had brought Szolem such success.
He often found himself at the fringes of respectability: esteemed, though never as highly as he deserved; criticized and dismissed as much for his style as for the unconventionality of his work. Yet over the past four decades, as Wall Street and the scientific community have encountered new, seemingly insurmountable challenges, Mandelbrot’s insights into randomness have seemed ever more prescient — and more essential to understand. Benoît Mandelbrot was born in 1924, to Lithuanian parents living in Warsaw, Poland. Although his father was a businessman, two of his uncles (including Szolem) were scholars. Many of his father’s other relatives were, in Mandelbrot’s words, “wise men” with no particular employment, but with a group of followers in the community who would trade money or goods in exchange for advice or learning. His mother, meanwhile, was also well educated, trained as a physician.
The Quants by Scott Patterson
Albert Einstein, asset allocation, automated trading system, beat the dealer, Benoit Mandelbrot, Bernie Madoff, Bernie Sanders, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, buttonwood tree, buy low sell high, capital asset pricing model, centralized clearinghouse, Claude Shannon: information theory, cloud computing, collapse of Lehman Brothers, collateralized debt obligation, commoditize, computerized trading, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Donald Trump, Doomsday Clock, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, Gordon Gekko, greed is good, Haight Ashbury, I will remember that I didn’t make the world, and it doesn’t satisfy my equations, index fund, invention of the telegraph, invisible hand, Isaac Newton, job automation, John Meriwether, John Nash: game theory, law of one price, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, merger arbitrage, money market fund, Myron Scholes, NetJets, new economy, offshore financial centre, old-boy network, Paul Lévy, Paul Samuelson, Ponzi scheme, quantitative hedge fund, quantitative trading / quantitative ﬁnance, race to the bottom, random walk, Renaissance Technologies, risk-adjusted returns, Rod Stewart played at Stephen Schwarzman birthday party, Ronald Reagan, Sergey Aleynikov, short selling, South Sea Bubble, speech recognition, statistical arbitrage, The Chicago School, The Great Moderation, The Predators' Ball, too big to fail, transaction costs, value at risk, volatility smile, yield curve, éminence grise
Was there a worm in the apple, a fatal flaw in the quants’ theory? This haunting fear, brought on by Black Monday, would hover over them like a bad dream time and time again, from the meltdown in October 1987 until the financial catastrophe that erupted in August 2007. The flaw had already been identified decades earlier by one of the most brilliant mathematicians in the world: Benoit Mandelbrot. When German tanks rumbled into France in 1940, Benoit Mandelbrot was sixteen years old. His family, Lithuanian Jews, had lived in Warsaw before moving to Paris in 1936 amid a spreading economic depression. Mandelbrot’s uncle, Szolem Mandelbrojt, had moved to Paris in 1929 and quickly rose to prominence among the city’s mathematical elite. Young Mandelbrot studied under his uncle and entered a French secondary school. But his life was upended when the Nazis invaded.
Aaron Brown, the quant who used his math smarts to thoroughly humiliate Wall Street’s old guard at their trademark game of Liar’s Poker, and whose career provided him with a front-row view of the explosion of the mortgage-backed securities industry. Paul Wilmott, quant guru extraordinaire and founder of the mathematical finance program at Oxford University. In 2000, Wilmott began warning of a mathematician-led market meltdown. Benoit Mandelbrot, mathematician who as early as the 1960s warned of the dangers wild market swings pose to quant models—but was soon forgotten in the world of quants as little more than a footnote in their long march to a seemingly inevitable victory. “We have involved ourselves in a colossal muddle, having blundered in the control of a delicate machine, the working of which we do not understand. The result is that our possibilities of wealth may run to waste for a time—perhaps for a long time.”
The market moves PDT and other quant funds started to see early that week defied logic. The fine-tuned models, the bell curves and random walks, the calibrated correlations—all the math and science that had propelled the quants to the pinnacle of Wall Street—couldn’t capture what was happening. It was utter chaos driven by pure human fear, the kind that can’t be captured in a computer model or complex algorithm. The wild, fat-tailed moves discovered by Benoit Mandelbrot in the 1950s seemed to be happening on an hourly basis. Nothing like it had ever been seen before. This wasn’t supposed to happen! The quants did their best to contain the damage, but they were like firefighters trying to douse a raging inferno with gasoline—the more they tried to fight the flames by selling, the worse the selling became. The downward-driving force of the deleveraging market seemed unstoppable.
Currency Wars: The Making of the Next Gobal Crisis by James Rickards
Asian financial crisis, bank run, Benoit Mandelbrot, Berlin Wall, Big bang: deregulation of the City of London, Black Swan, borderless world, Bretton Woods, BRICs, British Empire, business climate, capital controls, Carmen Reinhart, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, currency peg, Daniel Kahneman / Amos Tversky, Deng Xiaoping, diversification, diversified portfolio, Fall of the Berlin Wall, family office, financial innovation, floating exchange rates, full employment, game design, German hyperinflation, Gini coefficient, global rebalancing, global reserve currency, high net worth, income inequality, interest rate derivative, John Meriwether, Kenneth Rogoff, labour mobility, laissez-faire capitalism, liquidity trap, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, Mexican peso crisis / tequila crisis, money market fund, money: store of value / unit of account / medium of exchange, Myron Scholes, Network effects, New Journalism, Nixon shock, offshore financial centre, oil shock, one-China policy, open economy, paradox of thrift, Paul Samuelson, price mechanism, price stability, private sector deleveraging, quantitative easing, race to the bottom, RAND corporation, rent-seeking, reserve currency, Ronald Reagan, sovereign wealth fund, special drawing rights, special economic zone, The Myth of the Rational Market, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, time value of money, too big to fail, value at risk, War on Poverty, Washington Consensus, zero-sum game
., Judgment under Uncertainty: Heuristics and Biases, Cambridge: Cambridge University Press, 1982. 201 If they are diverse they will respond differently to various inputs producing . . . The extended analysis that follows, including elements of diversity, connectedness, interdependence and adaptability, draws on a series of lectures under the title “Understanding Complexity,” delivered in 2009 by Professor Scott E. Page of the University of Michigan. 207 However, there is strong empirical evidence, first reported by Benoît Mandelbrot . . . This discussion of fractal dimensions in market prices draws on Benoît Mandelbrot and Richard L. Hudson, The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward, New York: Basic Books, 2004. 218 Chaisson posits that the universe is best understood . . . The discussion of Chaisson’s theory of free energy rate densities is from Eric J. Chaisson, Cosmic Evolution: The Rise of Complexity in Nature, Cambridge: Harvard University Press, 2001.
Based on an enormous body of statistical and social science research, it is clear that markets are not efficient, that price movements are not random and risk is not normally distributed. The academic counterattack on these tenets of financial economics have come from two directions. From the fields of psychology, sociology and biology came a flood of studies showing that investors are irrational after all, at least from the perspective of wealth maximization. From iconoclastic mathematical genius Benoît Mandelbrot came insights that showed future prices are not independent of the past—that the market had a kind of “memory” that could cause it to react or overreact in disruptive ways, giving rise to alternating periods of boom and bust. Daniel Kahneman and his colleague Amos Tversky demonstrated in a series of simple but brilliantly constructed experiments that individuals were full of irrational biases.
The peaks and valleys, “double tops,” “head and shoulders” and other technical chart patterns are examples of emergence from the complexity of the overall system. Phase transitions—rapid extreme changes—are present in the form of market bubbles and crashes. Much of the work on capital markets as complex systems is still theoretical. However, there is strong empirical evidence, first reported by Benoît Mandelbrot, that the magnitude and frequency of certain market prices plot out as a power-law degree distribution. Mandelbrot showed that a time series chart of these price moves exhibited what he called a “fractal dimension.” A fractal dimension is a dimension greater than one and less than two, expressed as a fraction such as 1½; the word “fractal” is just short for “fractional.” A line has one dimension (length) and a square has two dimensions (length and width).
Capitalism 4.0: The Birth of a New Economy in the Aftermath of Crisis by Anatole Kaletsky
bank run, banking crisis, Benoit Mandelbrot, Berlin Wall, Black Swan, bonus culture, Bretton Woods, BRICs, Carmen Reinhart, cognitive dissonance, collapse of Lehman Brothers, Corn Laws, correlation does not imply causation, creative destruction, credit crunch, currency manipulation / currency intervention, David Ricardo: comparative advantage, deglobalization, Deng Xiaoping, Edward Glaeser, Eugene Fama: efficient market hypothesis, eurozone crisis, experimental economics, F. W. de Klerk, failed state, Fall of the Berlin Wall, financial deregulation, financial innovation, Financial Instability Hypothesis, floating exchange rates, full employment, George Akerlof, global rebalancing, Hyman Minsky, income inequality, information asymmetry, invisible hand, Isaac Newton, Joseph Schumpeter, Kenneth Arrow, Kenneth Rogoff, laissez-faire capitalism, Long Term Capital Management, mandelbrot fractal, market design, market fundamentalism, Martin Wolf, money market fund, moral hazard, mortgage debt, new economy, Northern Rock, offshore financial centre, oil shock, paradox of thrift, Pareto efficiency, Paul Samuelson, peak oil, pets.com, Ponzi scheme, post-industrial society, price stability, profit maximization, profit motive, quantitative easing, Ralph Waldo Emerson, random walk, rent-seeking, reserve currency, rising living standards, Robert Shiller, Robert Shiller, Ronald Reagan, shareholder value, short selling, South Sea Bubble, sovereign wealth fund, special drawing rights, statistical model, The Chicago School, The Great Moderation, The inhabitant of London could order by telephone, sipping his morning tea in bed, the various products of the whole earth, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, too big to fail, Vilfredo Pareto, Washington Consensus, zero-sum game
But in contrast to other cyclical theories that suggest that financial markets are intrinsically unstable, behavioral finance treats trend-following behavior as a temporary, and perhaps avoidable, aberration. The behavioral view is therefore less challenging to the fundamental assumption of textbook economics that markets are, on average, driven by rational calculation and are always self-stabilizing in the long term. Chaos theory was developed in the 1960s by Benoit Mandelbrot, one of the leading mathematicians of the twentieth century. Mandelbrot spent thirty years demonstrating that this theory, which transformed the study of biology, meteorology, geology, and other complex systems, could be applied also to financial markets. Mandelbrot’s research program undermined most of the mathematical assumptions of modern portfolio theory, which is the basis for the conventional risk models used by regulators, credit-rating agencies, and unsophisticated financial institutions.
Brian Arthur, along with colleagues at the Santa Fe Institute, has spent a lifetime developing the mathematics of nonlinear complex systems and applying them to the self-organizing emergent behavior of economies and markets that involve properties defying the assumptions of standard economics, for example, increasing returns and winner-takes-all positive feedbacks. Such work has produced impressive results on industrial organization that are widely divergent from conventional economics, but these ideas have never been integrated into the study of macroeconomic policy and financial markets, where new ideas are most needed because conventional economics has clearly failed. Benoit Mandelbrot, one of the most creative mathematicians of the twentieth century and a founder of the theories of chaos and complex systems, devoted a large part of his career to studying economics and financial markets. Many of the mathematical ideas that Mandelbrot developed and that found fruitful applications in the study of earthquakes, weather, galaxies, and biological systems from the 1960s onward were inspired by his studies of finance and economics—and could be applied to these subjects with great effect.
For more details, see Chapter 11. 4 This accelerator-multiplier concept, first proposed by Sir Roy Harrod, was later refined by Paul Samuelson and Sir John Hicks and became the standard Keynesian business cycle model. 5 Justin Lahart, “In Time of Tumult, Obscure Economist Gains Currency,” Wall Street Journal, August 18, 2007. 6 George Soros, The Soros Lectures: At the Central European University. 7 Alan Greenspan, “The Challenge of Central Banking,” remarks at the Annual Dinner and Francis Boyer Lecture of the American Enterprise Institute for Public Policy Research, Washington, DC, December 5, 1996. Available from http://www.federalreserve.gov/boarddocs/speeches/1996/19961205.htm. 8 Robert Shiller, Irrational Exuberance. 9 Benoit Mandelbrot and Richard Hudson, The (Mis)behavior of Markets: A Fractal View of Risk, Ruin and Reward, 4. 10 Nassim Nicholas Taleb, Fooled by Randomness: The Hidden Role of Chance in the Markets and in Life and the Black Swan: The Impact of the Highly Probable. 11 The term normal distribution describes prices or any other form of data that cluster predictably and reliably around a mean value in a bell curve pattern. 12 Malcolm C.
How Markets Fail: The Logic of Economic Calamities by John Cassidy
Albert Einstein, Andrei Shleifer, anti-communist, asset allocation, asset-backed security, availability heuristic, bank run, banking crisis, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Black-Scholes formula, Bretton Woods, British Empire, capital asset pricing model, centralized clearinghouse, collateralized debt obligation, Columbine, conceptual framework, Corn Laws, corporate raider, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, Daniel Kahneman / Amos Tversky, debt deflation, diversification, Elliott wave, Eugene Fama: efficient market hypothesis, financial deregulation, financial innovation, Financial Instability Hypothesis, financial intermediation, full employment, George Akerlof, global supply chain, Gunnar Myrdal, Haight Ashbury, hiring and firing, Hyman Minsky, income per capita, incomplete markets, index fund, information asymmetry, Intergovernmental Panel on Climate Change (IPCC), invisible hand, John Nash: game theory, John von Neumann, Joseph Schumpeter, Kenneth Arrow, laissez-faire capitalism, Landlord’s Game, liquidity trap, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, market clearing, mental accounting, Mikhail Gorbachev, money market fund, Mont Pelerin Society, moral hazard, mortgage debt, Myron Scholes, Naomi Klein, negative equity, Network effects, Nick Leeson, Northern Rock, paradox of thrift, Pareto efficiency, Paul Samuelson, Ponzi scheme, price discrimination, price stability, principal–agent problem, profit maximization, quantitative trading / quantitative ﬁnance, race to the bottom, Ralph Nader, RAND corporation, random walk, Renaissance Technologies, rent control, Richard Thaler, risk tolerance, risk-adjusted returns, road to serfdom, Robert Shiller, Robert Shiller, Ronald Coase, Ronald Reagan, shareholder value, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, statistical model, technology bubble, The Chicago School, The Great Moderation, The Market for Lemons, The Wealth of Nations by Adam Smith, too big to fail, transaction costs, unorthodox policies, value at risk, Vanguard fund, Vilfredo Pareto, wealth creators, zero-sum game
If a person repeatedly tosses a fair coin, the odds that he will get three heads in a row are one in eight. The odds that he will get six heads in a row are one in sixty-four. The coin-tossing view of finance that Bachelier pioneered today goes under the name of the “random walk” theory, because it implies that the prices of stocks and other speculative assets will wander about aimlessly like an inebriated person. Benoit Mandelbrot, another eminent French mathematician, described the theory this way: “Suppose you see a blind drunk staggering across an open field. If you pass by again later on, how far will he have gotten? Well, he could go two steps left, three right, four backwards, and so on in an aimless jagged path. On average—just like the coin-toss game—he gets nowhere.” If you were asked to predict where the drunk will end up in an hour’s time, the best guess you could make would be to say he will be where he is now.
But if nobody finds and processes information, stock prices won’t reflect that information, and the market won’t be efficient. For the market to work at all, there must be some level of inefficiency! Grossman and Stiglitz entitled their paper “On the Impossibility of Informationally Efficient Markets.” Other economic theorists admired its terse logic, but it didn’t have much immediate impact on Wall Street. The aforementioned Benoit Mandelbrot, who is perhaps best known as one of the founders of chaos theory, was another skeptic of the efficient market hypothesis. In the early 1960s, when he was working in the research department at IBM, Mandelbrot got interested in some of the new theories that were being developed to explain how financial markets worked, and he started to gather evidence on how they performed. The Harvard economist Hendrik Houthakker, whom he met while giving a talk in Cambridge, gave him the records of daily movements in the prices of cotton and cotton futures going back more than a century, which he had obtained from the New York Cotton Exchange.
As I explain in Part I, Eugene Fama and other defenders of the efficient market hypothesis claimed that stocks moved randomly, but during the 1980s and ’90s, strong evidence emerged that this wasn’t the case. Researchers showed that stocks did better in January than in other months, and did better on Mondays than on other days of the week. They also showed that small cap stocks outperform large cap stocks; and that value stocks—those with a low price-to-dividend ratio or price-to-earnings ratio—outperform growth stocks. Confirming the point Benoit Mandelbrot made as early as 1963, researchers also demonstrated that successive movements in the market are correlated. Upward moves tend to come in clumps, and so do downward moves. And it isn’t just price changes that display this pattern: trading volumes and volatility are clustered, too. Fama himself coauthored two revisionist papers. In one of them, which The Journal of Finance published in June 1992, he and Kenneth French, of Dartmouth, showed that between 1963 and 1990, stocks that traded at low prices relative to the value of the physical and intellectual assets of the company (value stocks) systematically outperformed stocks that traded at high prices relative to book value (growth stocks).
Antifragile: Things That Gain From Disorder by Nassim Nicholas Taleb
Air France Flight 447, Andrei Shleifer, banking crisis, Benoit Mandelbrot, Berlin Wall, Black Swan, Chuck Templeton: OpenTable, commoditize, creative destruction, credit crunch, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discrete time, double entry bookkeeping, Emanuel Derman, epigenetics, financial independence, Flash crash, Gary Taubes, George Santayana, Gini coefficient, Henri Poincaré, high net worth, hygiene hypothesis, Ignaz Semmelweis: hand washing, informal economy, invention of the wheel, invisible hand, Isaac Newton, James Hargreaves, Jane Jacobs, joint-stock company, joint-stock limited liability company, Joseph Schumpeter, Kenneth Arrow, knowledge economy, Lao Tzu, Long Term Capital Management, loss aversion, Louis Pasteur, mandelbrot fractal, Marc Andreessen, meta analysis, meta-analysis, microbiome, money market fund, moral hazard, mouse model, Myron Scholes, Norbert Wiener, pattern recognition, Paul Samuelson, placebo effect, Ponzi scheme, principal–agent problem, purchasing power parity, quantitative trading / quantitative ﬁnance, Ralph Nader, random walk, Ray Kurzweil, rent control, Republic of Letters, Ronald Reagan, Rory Sutherland, selection bias, Silicon Valley, six sigma, spinning jenny, statistical model, Steve Jobs, Steven Pinker, Stewart Brand, stochastic process, stochastic volatility, The Great Moderation, the new new thing, The Wealth of Nations by Adam Smith, Thomas Bayes, Thomas Malthus, too big to fail, transaction costs, urban planning, Vilfredo Pareto, Yogi Berra, Zipf's Law
And many of the problems of society come from the argument “other people are doing it.” So if I call someone a dangerous ethically challenged fragilista in private after the third glass of Lebanese wine (white), I will be obligated to do so here. Calling people and institutions fraudulent in print when they are not (yet) called so by others carries a cost, but is too small to be a deterrent. After the mathematical scientist Benoît Mandelbrot read the galleys of The Black Swan, a book dedicated to him, he called me and quietly said: “In what language should I say ‘good luck’ to you?” I did not need any luck, it turned out; I was antifragile to all manner of attacks: the more attacks I got from the Central Fragilista Delegation, the more my message spread as it drove people to examine my arguments. I am now ashamed of not having gone further in calling a spade a spade.
From the outside, it looks like there is hormesis, but from the inside, there are winners and losers. How does this layering operate? A tree has many branches, and these look like small trees; further, these large branches have many more smaller branches that sort of look like even smaller trees. This is a manifestation of what is called fractal self-similarity, a vision by the mathematician Benoît Mandelbrot. There is a similar hierarchy in things and we just see the top layer from the outside. The cell has a population of intercellular molecules; in turn the organism has a population of cells, and the species has a population of organisms. A strengthening mechanism for the species comes at the expense of some organisms; in turn the organism strengthens at the expense of some cells, all the way down and all the way up as well.
For one example of a trick for debunking causality: I am not even dead yet, but am already seeing distortions about my work. Authors theorize about some ancestry of my ideas, as if people read books then developed ideas, not wondering whether perhaps it is the other way around; people look for books that support their mental program. So one journalist (Anatole Kaletsky) saw the influence of Benoît Mandelbrot on my book Fooled by Randomness, published in 2001 when I did not know who Mandelbrot was. It is simple: the journalist noticed similarities of thought in one type of domain, and seniority of age, and immediately drew the false inference. He did not consider that like-minded people are inclined to hang together and that such intellectual similarity caused the relationship rather than the reverse.
The Misbehavior of Markets by Benoit Mandelbrot
Albert Einstein, asset allocation, Augustin-Louis Cauchy, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black-Scholes formula, British Empire, Brownian motion, buy low sell high, capital asset pricing model, carbon-based life, discounted cash flows, diversification, double helix, Edward Lorenz: Chaos theory, Elliott wave, equity premium, Eugene Fama: efficient market hypothesis, Fellow of the Royal Society, full employment, Georg Cantor, Henri Poincaré, implied volatility, index fund, informal economy, invisible hand, John Meriwether, John von Neumann, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market microstructure, Myron Scholes, new economy, paper trading, passive investing, Paul Lévy, Paul Samuelson, Plutocrats, plutocrats, price mechanism, quantitative trading / quantitative ﬁnance, Ralph Nelson Elliott, RAND corporation, random walk, risk tolerance, Robert Shiller, Robert Shiller, short selling, statistical arbitrage, statistical model, Steve Ballmer, stochastic volatility, transfer pricing, value at risk, Vilfredo Pareto, volatility smile
She helped review and research portions of the book; patiently transcribed many hours of tape-recorded discussions between the authors; and provided—as ever—her generous encouragement and wise companionship. For the art, we thank M. Gruskin, H. Kanzer, and M. Logan. PRELUDE by Richard L. Hudson Introducing a Maverick in Science INDEPENDENCE IS A GREAT VIRTUE. To illustrate that, Benoit Mandelbrot relates how, during the German occupation of France in World War II, his father escaped death. One day, a band of Resistance fighters attacked the prison camp where he was being held. They disarmed the guards and told the inmates to flee before the main German force struck back. So the surprised and disoriented prisoners set off towards nearby Limoges, en masse and on the high road. After half a kilometer, Mandelbrot père decided this way was folly.
Quantitative Finance 1 (5): 482-483. Bouchaud, Jean-Philippe. 2002. An introduction to statistical finance. Physica A 313: 238-251. Buffett, Warren E. 1988. To the Shareholders of Berkshire Hathaway Inc. Annual Report. Omaha, Neb.: Berkshire Hathaway Inc. Burton, Jonathan. 1998. Revisiting the capital asset pricing model. Dow Jones Asset Manager May-June: 20-28. Calvet, Laurent, Adlai Fisher, and Benoit Mandelbrot. 1997. Large deviations and the distribution of price changes. Cowles Foundation Discussion Paper 1165 (September). Calvet, Laurent and Adlai Fisher. 2002. Multifractality in asset returns: Theory and evidence. Review of Economics and Statistics 84 (3): 381-406. Campbell, John Y., Andrew W. Low, and A. Craig MacKinlay. 1997. The Econometrics of Financial Markets. Princeton, NJ : Princeton University Press.
An Introduction to Probability Theory and Its Applications. New York: Wiley. Fillol, Jérôme, 2003. Multifractality: theory and evidence. An application to the French stock market. Economics Bulletin 3 (31): 1-12. Financial Executives Research Foundation. 2003. Valuing Employee Stock Options: A Comparison of Alternative Models. Research report available at: http://www.ferf.org. Fisher, Adlai, Laurent Calvet, and Benoit Mandelbrot. 1997. Multifractality of Deutschemark/US dollar exchange rates. Cowles Foundation Discussion Paper 1166. Frame, Michael and Benoit B. Mandelbrot. 2002. Fractals, Graphics and Mathematics Education. Washington, D.C.: Mathematical Association of America. Gleick, James. 1987. Chaos: Making a New Science. New York: Viking Penguin. Gleria, Iram, Raul Matsushita, and Sergio Da Silva. 2002. Scaling power laws in the Sao Paulo Stock Exchange.
23andMe, Albert Einstein, Alfred Russel Wallace, banking crisis, Barry Marshall: ulcers, Benoit Mandelbrot, Berlin Wall, biofilm, Black Swan, butterfly effect, Cass Sunstein, cloud computing, congestion charging, correlation does not imply causation, Daniel Kahneman / Amos Tversky, dark matter, data acquisition, David Brooks, delayed gratification, Emanuel Derman, epigenetics, Exxon Valdez, Flash crash, Flynn Effect, hive mind, impulse control, information retrieval, Intergovernmental Panel on Climate Change (IPCC), Isaac Newton, Jaron Lanier, John von Neumann, Kevin Kelly, lifelogging, mandelbrot fractal, market design, Mars Rover, Marshall McLuhan, microbiome, Murray Gell-Mann, Nicholas Carr, open economy, Pierre-Simon Laplace, place-making, placebo effect, pre–internet, QWERTY keyboard, random walk, randomized controlled trial, rent control, Richard Feynman, Richard Feynman, Richard Feynman: Challenger O-ring, Richard Thaler, Satyajit Das, Schrödinger's Cat, security theater, selection bias, Silicon Valley, stem cell, Steve Jobs, Steven Pinker, Stewart Brand, the scientific method, Thorstein Veblen, Turing complete, Turing machine, Vilfredo Pareto, Walter Mischel, Whole Earth Catalog, zero-sum game
Implicitly it gives you an excellent glimpse of what some of the world’s leading thinkers are obsessed with at the moment. You can see their optimism (or anxiety) about how technology is changing culture and interaction. You’ll observe a frequent desire to move beyond deductive reasoning and come up with more rigorous modes of holistic or emergent thinking. You’ll also get a sense of the emotional temper of the group. People in this culture love neat puzzles and cool questions. Benoit Mandelbrot asked his famous question “How long is the coast of Britain?” long before this symposium was written, but it perfectly captures the sort of puzzle people in this crowd love. The question seems simple. Just look it up in the encyclopedia. But as Mandelbrot observed, the length of the coast of Britain depends on what you use to measure it. If you draw lines on a map to approximate the coastline, you get one length, but if you try to measure the real bumps in every inlet and bay, the curves of each pebble and grain of sand, you get a much different length.
The idea of recursive structure came into its own with the advent of computer science (that is, software science) in the 1950s. The hardest problem in software is controlling the tendency of software systems to grow incomprehensibly complex. Recursive structure helps convert impenetrable software rain forests into French gardens—still (potentially) vast and complicated but much easier to traverse and understand than a jungle. Benoit Mandelbrot famously recognized that some parts of nature show recursive structure of a sort: A typical coastline shows the same shape or pattern whether you look from six inches or sixty feet or six miles away. But it also happens that recursive structure is fundamental to the history of architecture, especially to the Gothic, Renaissance, and Baroque architecture of Europe—covering roughly the five hundred years between the thirteenth and eighteenth centuries.
Lately, one of many projects has been to revisit the aesthetic space of scientific visualizations, and another the epitome of mathematics made tangible: fractals, which I had done almost twenty years ago with virtuoso coder Ben Weiss, now enjoying them via realtime flythroughs on a handheld little smartphone. Here was the most extreme example: A tiny formula, barely one line on paper, used recursively, yields worlds of complex images of amazing beauty. (Ben had the distinct pleasure of showing Benoit Mandelbrot an alpha version at a TED conference just months before Mandelbrot’s death.) My hesitation about overuse of parsimony was expressed perfectly in a quote from Albert Einstein, arguably the counterpart blade to Ockham’s razor: “Things should be made as simple as possible—but not simpler.” And there we have the perfect application of its truth, used recursively on itself: Neither Einstein nor Ockham actually used the exact words as quoted!
Overcomplicated: Technology at the Limits of Comprehension by Samuel Arbesman
3D printing, algorithmic trading, Anton Chekhov, Apple II, Benoit Mandelbrot, citation needed, combinatorial explosion, Danny Hillis, David Brooks, digital map, discovery of the americas, en.wikipedia.org, Erik Brynjolfsson, Flash crash, friendly AI, game design, Google X / Alphabet X, Googley, HyperCard, Inbox Zero, Isaac Newton, iterative process, Kevin Kelly, Machine translation of "The spirit is willing, but the flesh is weak." to Russian and back, mandelbrot fractal, Minecraft, Netflix Prize, Nicholas Carr, Parkinson's law, Ray Kurzweil, recommendation engine, Richard Feynman, Richard Feynman, Richard Feynman: Challenger O-ring, Second Machine Age, self-driving car, software studies, statistical model, Steve Jobs, Steve Wozniak, Steven Pinker, Stewart Brand, superintelligent machines, Therac-25, Tyler Cowen: Great Stagnation, urban planning, Watson beat the top human players on Jeopardy!, Whole Earth Catalog, Y2K
You can’t have a futuristic starship that is all angles and smooth sides; you need to add ports and vents and sundry other impenetrable doodads and whatsits, pipes and bumps, indentations and grooves. Think of the ships in Battlestar Galactica or Star Wars. They are more visually intriguing thanks to their complications of unknown purpose. This process of greebling is closely related to a well-known quote from the mathematician Benoit Mandelbrot, who coined the term “fractal”: “Why is geometry often described as ‘cold’ and ‘dry’? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” So, too, our technological systems, once embedded in the real world, are far from the cleanly pristine logical constructions of the drawing board; they are full of the miscellaneous details of biology that have accreted over time, much like the evolutionary hodgepodge found within living systems.
Corky Ramirez: Note that in the episode “The Van Buren Boys,” someone is referred to as “Ramirez” in a bar (though I believe his name is stressed differently than Kramer’s pronunciation of Corky Ramirez). Perhaps he is visible in the room, but it is unclear. Seinfeld superfans: please send me mail. delightfully evocative term: “greeblies”: : Or, alternatively, “greebles.” Kelly, What Technology Wants, 318. the mathematician Benoit Mandelbrot: Benoit B. Mandelbrot, The Fractal Geometry of Nature (New York: W. H. Freeman and Company, 1982), 1. Recall “Funes the Memorious”: Borges, “Funes, His Memory,” in Collected Fictions, 131–37. “The patterns of a river network”: Philip Ball, Branches, vol. 3 of Nature’s Patterns: A Tapestry in Three Parts (Oxford, UK: Oxford University Press, 2009), 181. researchers analyzed the United States Code: William Li et al., “Law Is Code: A Software Engineering Approach to Analyzing the United States Code,” Journal of Business and Technology Law 10, no. 2 (2015): 297–372.
The Bed of Procrustes: Philosophical and Practical Aphorisms by Nassim Nicholas Taleb
– Randomness is indistinguishable from complicated, undetected, and undetectable order; but order itself is indistinguishable from artful randomness. * Moore’s Law stipulates that computational power doubles every eighteen months. * Say, Sarah Palin. † The biggest error since Socrates has been to believe that lack of clarity is the source of all our ills, not the result of them. AESTHETICS Art is a one-sided conversation with the unobserved. – The genius of Benoît Mandelbrot is in achieving aesthetic simplicity without having recourse to smoothness. – Beauty is enhanced by unashamed irregularities; magnificence by a façade of blunder. – To understand “progress”: all places we call ugly are both man-made and modern (Newark), never natural or historical (Rome). – We love imperfection, the right kind of imperfection; we pay up for original art and typo-laden first editions
Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies by Geoffrey West
Alfred Russel Wallace, Anton Chekhov, Benoit Mandelbrot, Black Swan, British Empire, butterfly effect, carbon footprint, Cesare Marchetti: Marchetti’s constant, clean water, complexity theory, computer age, conceptual framework, continuous integration, corporate social responsibility, correlation does not imply causation, creative destruction, dark matter, Deng Xiaoping, double helix, Edward Glaeser, endogenous growth, Ernest Rutherford, first square of the chessboard, first square of the chessboard / second half of the chessboard, Frank Gehry, Geoffrey West, Santa Fe Institute, Guggenheim Bilbao, housing crisis, Index librorum prohibitorum, invention of agriculture, invention of the telephone, Isaac Newton, Jane Jacobs, Jeff Bezos, Johann Wolfgang von Goethe, John von Neumann, Kenneth Arrow, laissez-faire capitalism, life extension, Mahatma Gandhi, mandelbrot fractal, Marchetti’s constant, Masdar, megacity, Murano, Venice glass, Murray Gell-Mann, New Urbanism, Peter Thiel, profit motive, publish or perish, Ray Kurzweil, Richard Feynman, Richard Feynman, Richard Florida, Silicon Valley, smart cities, Stephen Hawking, Steve Jobs, Stewart Brand, technological singularity, The Coming Technological Singularity, The Death and Life of Great American Cities, the scientific method, too big to fail, transaction costs, urban planning, urban renewal, Vernor Vinge, Vilfredo Pareto, Von Neumann architecture, Whole Earth Catalog, Whole Earth Review, wikimedia commons, working poor
The traditional framework that many of us have been painfully and joyfully exposed to implicitly assumes that all lines and surfaces are smooth and continuous. Novel ideas that evoked concepts of discontinuities and crinkliness, which are implicit in the modern concept of fractals, were viewed as fascinating formal extensions of academic mathematics but were not generally perceived as playing any significant role in the real world. It fell to the French mathematician Benoit Mandelbrot to make the crucial insight that, quite to the contrary, crinkliness, discontinuity, roughness, and self-similarity—in a word, fractality—are, in fact, ubiquitous features of the complex world we live in.17 In retrospect it is quite astonishing that this insight had eluded the greatest mathematicians, physicists, and philosophers for more than two thousand years. Like many great leaps forward, Mandelbrot’s insight now seems almost “obvious,” and it beggars belief that his observation hadn’t been made hundreds of years earlier.
Once again we see that underlying the daunting complexity of the natural world lies a surprising simplicity, regularity, and unity when viewed through the coarse-grained lens of scale. Although Richardson discovered this strange, revolutionary, nonintuitive behavior in his investigations of borders and coastlines and understood its origins, he didn’t fully appreciate its extraordinary generality and far-reaching implications. This bigger insight fell to Benoit Mandelbrot. Measuring the lengths of coastline using different resolutions (Britain in the example). (13) The lengths increase systematically with resolution following a power law as indicated by the examples in the graph. (14) The slope gives the fractal dimension for the coastline: the more squiggly it is, the steeper the slope. Richardson’s discovery was almost entirely ignored by the scientific community.
This is not too surprising because it was published in a relatively obscure journal and, in addition, it was buried in the middle of his investigations into the origins of war. His paper, published in 1961, carries the marvelously obscure title “The Problem of Contiguity: An Appendix to Statistics of Deadly Quarrels,” barely revealing, even to the cognoscenti, what the content might be. Who was to know that this was to herald a paradigm shift of major significance? Well, Benoit Mandelbrot did. He deserves great credit not only for resurrecting Richardson’s work but for recognizing its deeper significance. In 1967 he published a paper in the high-profile journal Science with the more transparent title “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension.”22 This brought Richardson’s work to light by expanding on his findings and generalizing the idea.
A Mathematician Plays the Stock Market by John Allen Paulos
Benoit Mandelbrot, Black-Scholes formula, Brownian motion, business climate, butterfly effect, capital asset pricing model, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, diversified portfolio, Donald Trump, double entry bookkeeping, Elliott wave, endowment effect, Erdős number, Eugene Fama: efficient market hypothesis, four colour theorem, George Gilder, global village, greed is good, index fund, intangible asset, invisible hand, Isaac Newton, John Nash: game theory, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, mental accounting, Myron Scholes, Nash equilibrium, Network effects, passive investing, Paul Erdős, Paul Samuelson, Ponzi scheme, price anchoring, Ralph Nelson Elliott, random walk, Richard Thaler, Robert Shiller, Robert Shiller, short selling, six sigma, Stephen Hawking, survivorship bias, transaction costs, ultimatum game, Vanguard fund, Yogi Berra
Most commonly the market rises in five distinct waves and declines in three distinct waves for obscure psychological or systemic reasons. Elliott believed as well that these patterns exist at many levels and that any given wave or cycle is part of a larger one and contains within it smaller waves and cycles. (To give Elliott his due, this idea of small waves within larger ones having the same structure does seem to presage mathematician Benoit Mandelbrot’s more sophisticated notion of a fractal, to which I’ll return later.) Using Fibonacci-inspired rules, the investor buys on rising waves and sells on falling ones. The problem arises when these investors try to identify where on a wave they find themselves. They must also decide whether the larger or smaller cycle of which the wave is inevitably a part may temporarily be overriding the signal to buy or sell.
A shoreline, to cite a classic example, has a characteristic jagged shape at whatever scale we draw it; that is, whether we use satellite photos to sketch the whole coast, map it on a fine scale by walking along some small section of it, or examine a few inches of it through a magnifying glass. The surface of the mountain looks roughly the same whether seen from a height of 200 feet by a giant or close up by an insect. The branching of a tree appears the same to us as it does to birds, or even to worms or fungi in the idealized limiting case of infinite branching. As the mathematician Benoit Mandelbrot, the discoverer of fractals, has famously written, “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” These and many other shapes in nature are near fractals, having characteristic zigzags, push-pulls, bump-dents at almost every size scale, greater magnification yielding similar but ever more complicated convolutions.
Andrei Shleifer, asset-backed security, bank run, banking crisis, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Bretton Woods, capital controls, carbon footprint, Carmen Reinhart, Cass Sunstein, centre right, choice architecture, cloud computing, collective bargaining, conceptual framework, Corn Laws, corporate governance, creative destruction, credit crunch, Credit Default Swap, debt deflation, decarbonisation, Deng Xiaoping, discovery of DNA, discovery of the americas, discrete time, diversification, double helix, Edward Glaeser, financial deregulation, financial innovation, financial intermediation, first-past-the-post, floating exchange rates, Francis Fukuyama: the end of history, Frank Levy and Richard Murnane: The New Division of Labor, full employment, George Akerlof, Gini coefficient, global supply chain, Growth in a Time of Debt, Hyman Minsky, I think there is a world market for maybe five computers, income inequality, inflation targeting, interest rate swap, invisible hand, Isaac Newton, James Dyson, James Watt: steam engine, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, knowledge economy, knowledge worker, labour market flexibility, liberal capitalism, light touch regulation, Long Term Capital Management, Louis Pasteur, low-wage service sector, mandelbrot fractal, margin call, market fundamentalism, Martin Wolf, mass immigration, means of production, Mikhail Gorbachev, millennium bug, money market fund, moral hazard, moral panic, mortgage debt, Myron Scholes, Neil Kinnock, new economy, Northern Rock, offshore financial centre, open economy, Plutocrats, plutocrats, price discrimination, private sector deleveraging, purchasing power parity, quantitative easing, race to the bottom, railway mania, random walk, rent-seeking, reserve currency, Richard Thaler, Right to Buy, rising living standards, Robert Shiller, Robert Shiller, Ronald Reagan, Rory Sutherland, Satyajit Das, shareholder value, short selling, Silicon Valley, Skype, South Sea Bubble, Steve Jobs, The Market for Lemons, the market place, The Myth of the Rational Market, the payments system, the scientific method, The Wealth of Nations by Adam Smith, too big to fail, unpaid internship, value at risk, Vilfredo Pareto, Washington Consensus, wealth creators, working poor, zero-sum game, éminence grise
It could only be a legitimate question if the markets were not efficient, prices were not randomly distributed and events were not distributed on Gaussian principles, but nobody who wanted to stay in the mainstream could suggest such things. There is an enormous intellectual and financial investment in the status quo. Academics have built careers, reputations and tenure on a particular view of the world being right. Only an earthquake can persuade them to put up their hands and acknowledge they were wrong. When the mathematician Benoit Mandelbrot began developing his so-called fractal mathematics and power laws in the early 1960s, arguing that the big events outside the normal distribution are the ones that need explaining and assaulting the whole edifice of mathematical theory and the random walk, MIT’s Professor Paul Cootner (the great random walk theorist) exclaimed: ‘surely, before consigning centuries of work to the ash pile, we should like some assurance that all our work is truly useless’.
See Brad DeLong, Andrei Shleifer, Larry Summers and Michael Waldman (1990) ‘Noise Trader Risk in Financial Markets’, Journal of Political Economy 98: 703–38. 35 Anil Kashyap, Raghuram Rajan and Jeremy Stein (2008) ‘Rethinking Capital: Regulation’, paper for the Federal Reserve Bank of Kansas City. 36 Andrew Haldane (2009) ‘Why Banks Failed the Stress Test’, presentation to the Marcus-Evans Conference on Stress-Testing, 9–10 February. 37 James G. Rickards, ‘The Risks of Financial Modeling: VaR and the Economic Meltdown’, testimony before the Subcommittee on Investigations and Oversight Committee on Science and Technology, US House of Representatives, 10 September 2009. 38 Benoit Mandelbrot (2008) The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin and Reward, Profile Books. For another interesting example of cross-fertilisation, see Didier Sornette (2003) Why Stockmarkets Crash: Critical Events in Complex Financial Systems, Princeton University Press. 39 See Justin Fox (2009) The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street, HarperBusiness. 40 The following example is paraphrased from Baseline Scenario: http://baselinescenario.com/2009/10/01/the-economics-of-models/. 41 Gillian Tett (2009) Fool’s Gold: How Unrestrained Greed Corrupted a Dream, Shattered Global Markets and Unleashed a Catastrophe, Little, Brown. 42 Lucien Bebchuk and Jesse Fried (2004) Pay without Performance: The Unfulfilled Promise of Executive Compensation, Harvard University Press. 43 Lucian Bebchuk and Holger Spamann (2009) ‘Regulating Bankers’ Pay’, Harvard Law and Economics Discussion Paper No. 641. 44 Jesse Eisinger, ‘London Banks, Falling Down’, Portfolio, 13 August 2008, at http://www.portfolio.com/views/columns/wall-street/2008/08/13/Problemsin-British-Banking-System/. 45 Philip Augar (2009) Chasing Alpha: How Reckless Growth and Unchecked Ambition Ruined the City’s Golden Decade, The Bodley Head. 46 Albert-Laszlo Baraasi (2002) Linked: The New Science of Networks, Basic Books.
See also Matthew Jackson (2008) Social and Economic Networks, Princeton University Press. 47 Nicholas Christakis and James Fowler (2010) Connected: The Amazing Power of Social Lives and How They Shape Our Lives, Harper Press. 48 Robert M. May, Simon A. Levin and George Sugihara (2008) ‘Ecology for Bankers’, Nature 451 (21): 893–5. 49 Richard Bookstaber (2007) A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation, John Wiley & Sons. 50 Cited by Benoit Mandelbrot (2008) The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin and Reward, Profile Books, p. 154. 51 Ibid. 52 Andrew Haldane (2009) ‘Rethinking the Financial Network’, presentation to the Financial Students Association, Amsterdam. 53 Bobbi Low, Elinor Ostrom, Carl Simon and James Wilson, ‘Redundancy and Diversity’, in Wilson Fikret Berkes, Johan Colding and Carl Folke (eds) (2003) Navigating Social-Ecological Systems: Building Resilience for Complexity and Change, Cambridge University Press. 54 Scott Page (2007) The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies, Princeton University Press.
Near and Distant Neighbors: A New History of Soviet Intelligence by Jonathan Haslam
active measures, Albert Einstein, Benoit Mandelbrot, Berlin Wall, Bolshevik threat, Bretton Woods, British Empire, cuban missile crisis, falling living standards, John von Neumann, Robert Hanssen: Double agent, Ronald Reagan, Valery Gerasimov, Vladimir Vetrov: Farewell Dossier, éminence grise
It was the gifted son of Russian emigrés in the United States, William Friedman, who discovered the index of coincidence: the likelihood of a given letter in any text finding itself in exactly the same position in another text, even a ciphered text.39 This approach was then trumped by research into the application of statistics to linguistics pioneered by George Zipf in 193540 and more rigorously articulated in mathematical form by Benoît Mandelbrot after the war, funded by the U.S. armed services.41 Zipf found degrees of probability of a word appearing in a text; more than that, a fixed ratio of repetition between the commonest word and the next most common word, and so forth. As he wrote, words are not deliberately chosen for their frequency, but they “have a frequency distribution of great orderliness which for a large portion of the curve seems to be constant for language in general.”42 In the United States, cryptolinguistics was coming into being as a field in its own right.
The Russians, they were relieved to discover, “had yet to perfect their cryptosecurity procedures.”53 New American comparators (such as Warlock) were already operating at speed by weighing each letter according to language frequency.54 The next step was to replicate the chi-square distribution test mechanically, to compare the frequency with which a letter appeared in one text to the frequency with which it appeared in another, and testing to ensure that this was not just a matter of chance. This had to be done through thousands of multiplications and additions—and at speed.55 Meanwhile, cryptolinguistics were developing with increasing sophistication under Benoît Mandelbrot. Though apparently produced at random with respect to the probability of repetition, words emerge in the text in a discernible pattern that bears no relationship to grammar or meaning. This means that even were a text enciphered, the probability of a word appearing remained just as it did in plain text. Mandelbrot, who linked these insights to information theory, summed it up when he said that word frequency is in inverse proportion to ranking.
London: Hodder and Stroughton, 1990. Andrew, Christopher, and Vasili, Mitrokhin. The Mitrokhin Archive: The KGB in Europe and the West. London and New York: Allen Lane, 2000. ______. The Mitrokhin Archive II: The KGB and the World. London and New York: Allen Lane, 2005. Antonov, Vladimir, and Vladimir Karpov. Tainye informatory Kremlya: Vollenberg, Artuzov i drugie. Moscow: Geia Iterum, 2001. Apostel, Léo, Benoît Mandelbrôt, and Albert Morf. Logique, Langage et Théorie de l’Information. Paris: Presses Universitaires de France, 1957. Benson, Robert. The Venona Story. Meade, MD: NSA, 2000. Bezymensky, Lev. Budapeshtskaya missiya: Raul’ Vallenberg. Moscow: Kollektsiya “Sovershenno Sekretno,” 2001. Boltunov, Mikhail. “Zolotoe Ukho” voennoi razvedki. Moscow: Veche, 2011. Bondarenko, V. I., V. V. Andronenko, and M.
Money Changes Everything: How Finance Made Civilization Possible by William N. Goetzmann
Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, banking crisis, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, Cass Sunstein, collective bargaining, colonial exploitation, compound rate of return, conceptual framework, corporate governance, Credit Default Swap, David Ricardo: comparative advantage, debt deflation, delayed gratification, Detroit bankruptcy, disintermediation, diversified portfolio, double entry bookkeeping, Edmond Halley, en.wikipedia.org, equity premium, financial independence, financial innovation, financial intermediation, fixed income, frictionless, frictionless market, full employment, high net worth, income inequality, index fund, invention of the steam engine, invention of writing, invisible hand, James Watt: steam engine, joint-stock company, joint-stock limited liability company, laissez-faire capitalism, Louis Bachelier, mandelbrot fractal, market bubble, means of production, money market fund, money: store of value / unit of account / medium of exchange, moral hazard, Myron Scholes, new economy, passive investing, Paul Lévy, Ponzi scheme, price stability, principal–agent problem, profit maximization, profit motive, quantitative trading / quantitative ﬁnance, random walk, Richard Thaler, Robert Shiller, Robert Shiller, shareholder value, short selling, South Sea Bubble, sovereign wealth fund, spice trade, stochastic process, the scientific method, The Wealth of Nations by Adam Smith, Thomas Malthus, time value of money, too big to fail, trade liberalization, trade route, transatlantic slave trade, transatlantic slave trade, tulip mania, wage slave
In particular, they led to the development of financial derivatives—financial tools referred to by investor Warren Buffett as “weapons of mass destruction,”1 but which are also are widely recognized as the fundamental tools of insurance and risk mitigation. We shall see that the work of three of the giants of modern finance, Robert Merton, Fischer Black, and Myron Scholes, built directly on the insights and techniques of the French mathematical tradition—both in terms of its strength and also its weakness. This last point is reserved for a discussion about a modern French mathematician, and my former Yale colleague, Benoit Mandelbrot. RANDOM WALKS Almost nothing is known about the nineteenth-century French stockbroker Jules Regnault (1834–1894). What we do know comes from the efforts of Franck Jovanovic, a lecturer in finance at Leicester University. Over the past decade, Jovanovic has studied the intellectual development of mathematical finance and traced a key logical foundation of modern quantitative methods to Jules Regnault, a successful broker on the Paris Bourse during the middle of the nineteenth century.2 In 1863, Regnault wrote a strikingly novel book, Calcul des Chances et Philosophie de la Bourse, arguing that it is impossible to profit by speculating in the market.
A drop of 22% in a couple of days was not in Mark Rubenstein’s game plan, because standard models used for option pricing effectively assume that the logarithm of stock prices are “normal”—that is, they conform to the standard bell-curve distribution. In fact, the non-normality of security prices had been well known for decades prior to the crash of 2008—and for that matter the crash of 1987, as was the potential for extreme events. The “high priest” of non-normality before Nassim Taleb ever started to trade or write about extreme events was Benoit Mandelbrot, the creator of fractal geometry, a mathematician who both carried the mantle of French mathematical finance and who also believed he had discovered its fatal flaw. Mandelbrot was a student of Paul Lévy’s—the son of the man who gave Bachelier bad marks at his examination at the École Polytechnique in 1900. Lévy’s research focused on “stochastic processes”: mathematical models that describe the behavior of some variable through time.
Paul Lévy formalized these prior random walk models into a very general family of stochastic processes referred to as Lévy processes. Brownian motion was just one process in the family of Lévy processes—and perhaps the best behaved of them. Other stochastic processes have such things as discontinuous jumps and unusually large shocks (which might, for example, explain the crash of 1987, when the US stock market lost 22.6% of its value in a single day). In the 1960s, Benoit Mandelbrot began to investigate whether Lévy processes described economic time series like cotton prices and stock prices. He found that the ones that generated jumps and extreme events better described financial markets. He developed a mathematics around these unusual Lévy processes that he called “fractal geometry.” He argued that unusual events—Taleb’s black swan—were in fact much more common phenomena than Brownian motion would suggest.
Albert Einstein, Andrei Shleifer, Benoit Mandelbrot, bitcoin, Brownian motion, Claude Shannon: information theory, cloud computing, cognitive dissonance, computer age, conceptual framework, continuation of politics by other means, crony capitalism, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Graeber, Dissolution of the Soviet Union, Donald Davies, double helix, Drosophila, Francis Fukuyama: the end of history, From Mathematics to the Technologies of Life and Death, hive mind, index card, informal economy, information asymmetry, invisible hand, Jacquard loom, Jacquard loom, John von Neumann, Kevin Kelly, knowledge economy, knowledge worker, linear programming, mandelbrot fractal, Marshall McLuhan, means of production, Menlo Park, Mikhail Gorbachev, mutually assured destruction, Network effects, Norbert Wiener, packet switching, Pareto efficiency, pattern recognition, Paul Erdős, Peter Thiel, Philip Mirowski, RAND corporation, rent-seeking, road to serfdom, Ronald Coase, scientific mainstream, Steve Jobs, Stewart Brand, stochastic process, technoutopianism, The Structural Transformation of the Public Sphere, transaction costs, Turing machine
In 1947, the year before he published Cybernetics with the MIT Press, Wiener attended Szolem Mandelbrot’s congress on harmonic analysis in Nancy, France, which resulted in a French book contract for the book that, while initially resisted by the MIT Press, sold a sensational 21,000 copies over three reprints in six months after its release in 1948. Three years later, in 1951, at the invitation of Benoit Mandelbrot, the founder of fractals and Szolem’s nephew, Wiener returned to lecture at Collège de France. Between 1947 and 1952, a flurry of press coverage and public controversy sprung up between two camps of anticybernetic communists and anticommunist cyberneticists.32 (Jacques Lacan, who served in the French army, may very well have been among the anticommunists and early cyberneticists at the time.)
Aleksandr Bogdanov—old Bolshevik revolutionary, right-hand man to Vladimir Lenin, and philosopher—developed a wholesale theory that analogized between society and political economy, which he published in 1913 as Tektology: A Universal Organizational Science, a proto-cybernetics minus the mathematics, whose work Wiener may have seen in translation in the 1920s or 1930s.39 Stefan Odobleja was a largely ignored Romanian whose pre–World War II work prefaced cybernetic thought.40 John von Neumann, the architect of the modern computer, a founding game theorist, and a Macy Conference participant, was a Hungarian émigré. Szolem Mandelbrojt, a Jewish Polish scientist and uncle of fractal founder Benoit Mandelbrot, organized Wiener’s collaboration on harmonic analysis and Brownian motion in 1950 in Nancy, France. Roman Jakobson, the aforementioned structural linguist, a collaborator in the Macy Conferences, and a Russian émigré, held the chair in Slavic studies at Harvard founded by Norbert Wiener’s father. And finally, Wiener’s own domineering and brilliant father, Leo Wiener, was a self-made polymath, the preeminent translator of Tolstoy into English in the twentieth-century, the founder of Slavic studies in America, an émigré from a Belarusian shtetl, and like his son, a humanist committed to uncovering methods for nearly universal communication.41 Although summarizing the intellectual and international sources for the consolidation of cybernetics as a midcentury science for self-governing systems is beyond the scope of this project, the following statement is probably not too far of a stretch.
Capital Ideas: The Improbable Origins of Modern Wall Street by Peter L. Bernstein
Albert Einstein, asset allocation, backtesting, Benoit Mandelbrot, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, buy low sell high, capital asset pricing model, corporate raider, debt deflation, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, financial intermediation, fixed income, full employment, implied volatility, index arbitrage, index fund, interest rate swap, invisible hand, John von Neumann, Joseph Schumpeter, Kenneth Arrow, law of one price, linear programming, Louis Bachelier, mandelbrot fractal, martingale, means of production, money market fund, Myron Scholes, new economy, New Journalism, Paul Samuelson, profit maximization, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, Robert Shiller, Robert Shiller, Ronald Reagan, stochastic process, the market place, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, Thorstein Veblen, transaction costs, transfer pricing, zero-coupon bond, zero-sum game
Twenty years after writing his dissertation, he remarked that his analysis had embodied “images taken from natural phenomena . . . a strange and unexpected linkage and a starting point for great progress.” His superiors did not agree. Although Poincarè, his teacher, wrote that “M. Bachelier has evidenced an original and precise mind,” he also observed that “The topic is somewhat remote from those our candidates are in the habit of treating.”5 Benoit Mandelbrot, the pioneer of fractal geometry and one of Bachelier’s great admirers, recently suggested that no one knew where to pigeonhole Bachelier’s findings. There was no ready means to retrieve them, assuming that someone wanted to. Sixty years were to pass before anyone took the slightest notice of his work. ••• The key to Bachelier’s insight is his observation, expressed in a notably modern manner, that “contradictory opinions concerning [market] changes diverge so much that at the same instant buyers believe in a price increase and sellers believe in a price decrease.”6 Convinced that there is no basis for believing that—on the average—either sellers or buyers consistently know any more about the future than the other, he arrived at an astonishing conjecture: “It seems that the market, the aggregate of speculators, at a given instant can believe in neither a market rise nor a market fall, since, for each quoted price, there are as many buyers as sellers.”7 (emphasis added) The fond hopes of home buyers in California during the 1980s provide a vivid example of Bachelier’s perception.
The final section of the book contained five articles on the statistical analysis of options prices, an area that was only just beginning to attract the attention of finance specialists; two of these articles were by Samuelson’s protege Richard Kruizenga. These five works formed the basis for the important and farreaching research into this question that was to emerge at MIT around 1970 and that will occupy our attention later on. Cootner’s book also contained a short article by Fama, reprinted from the Journal of Business for October 1963, in which Fama expanded on an analysis of market behavior conducted by Benoit Mandelbrot, a French mathematician living in the United States whose work was published in the same issue of the journal. Mandelbrot proposed that stock prices fluctuate so irregularly because they are not sufficiently well behaved to submit to the kind of rigorous statistical analysis recommended by Bachelier and Samuelson. Mandelbrot’s research implied that stocks are riskier than had been assumed, that diversification might not work as well as Markowitz had indicated, that measures like variance could be highly unstable, and that major price movements would cluster more closely than anticipated.
Think Complexity by Allen B. Downey
Benoit Mandelbrot, cellular automata, Conway's Game of Life, Craig Reynolds: boids flock, discrete time, en.wikipedia.org, Frank Gehry, Gini coefficient, Guggenheim Bilbao, mandelbrot fractal, Occupy movement, Paul Erdős, peer-to-peer, Pierre-Simon Laplace, sorting algorithm, stochastic process, strong AI, Thomas Kuhn: the structure of scientific revolutions, Turing complete, Turing machine, Vilfredo Pareto, We are the 99%
Similarly, Pruessner and Jensen studied large-scale versions of the forest fire model (using an algorithm similar to Newman and Ziff’s). In their 2004 paper, “Efficient algorithm for the forest fire model,” they present evidence that the system is not critical after all (http://pre.aps.org/abstract/PRE/v70/i6/e066707). How do these results bear on Bak’s claim that SOC explains the prevalence of critical phenomena in nature? Example 9-8. In The Fractal Geometry of Nature, Benoit Mandelbrot proposes what he calls a “heretical” explanation for the prevalence of long-tailed distributions in natural systems (page 344). It may not be, as Bak suggests, that many systems can generate this behavior in isolation. Instead there may be only a few, but there may be interactions between systems that cause the behavior to propagate. To support this argument, Mandelbrot points out the following: The distribution of observed data is often “the joint effect of a fixed underlying ‘true distribution’ and a highly variable ‘filter.’”
Infinite Ascent: A Short History of Mathematics by David Berlinski
Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Andrew Wiles, Benoit Mandelbrot, Douglas Hofstadter, Eratosthenes, four colour theorem, Georg Cantor, Gödel, Escher, Bach, Henri Poincaré, Isaac Newton, John von Neumann, Murray Gell-Mann, Stephen Hawking, Turing machine, William of Occam
Nonetheless, no mathematician has suggested that Appel and Haken’s proof is less certain than it would be had all the calculations been done by hand. Those calculations represent dog work, and mathematicians are notably inferior to the computer when it comes to going to the dogs. (Many mathematicians cannot, in fact, add a simple column of figures with the accuracy expected of a German greengrocer.) An uneasy feeling nonetheless persists that the method of proof has somehow been compromised. No one has quite said why. Benoit Mandelbrot—a distant cousin of mine, a remote family connection—is a mathematician who has immensely enriched the ordinary happiness of mankind by showing how beautiful pictures can be made simply on the computer. His images are now everywhere and are everywhere known as Mandelbrot sets. Their construction depends on recursive iteration and a computer program that can assign colors to regions of the complex plane.
algorithmic trading, Benoit Mandelbrot, Chance favours the prepared mind, constrained optimization, Dava Sobel, George Santayana, Long Term Capital Management, Louis Pasteur, mandelbrot fractal, market clearing, market fundamentalism, merger arbitrage, pattern recognition, price discrimination, profit maximization, quantitative trading / quantitative ﬁnance, risk tolerance, Sharpe ratio, statistical arbitrage, statistical model, stochastic volatility, systematic trading, transaction costs
The phenomenon of ‘‘noise at rest,’’ the random wandering about the local mean just exemplified, is known as stochastic resonance. As you read the foregoing description, you may feel a sense of deja vu. The description of modeling the variation about the mean during periods of zero forecast activity is quite the same as the general description of the variation of the spread overall. Such self-similarity occurs throughout nature according to Benoit Mandelbrot, who invented a branch of mathematics called fractals for the study and analysis of such patterns. Mandelbrot, 2004, has argued that fractal analysis provides a better model for understanding the movements of prices of financial instruments than anything currently in the mathematical finance literature. It is unknown whether any successful trading strategies have been built using fractal analysis; Mandelbrot himself does not believe his tools are yet sufficiently developed for prediction of financial series to be feasible. 3.8 PRACTICAL MATTERS Forecasts of stock price movements are incredibly inaccurate.
Albert Einstein, Benoit Mandelbrot, correlation does not imply causation, discovery of DNA, double helix, Drosophila, epigenetics, Isaac Newton, Mahatma Gandhi, mandelbrot fractal, Mars Rover, On the Revolutions of the Heavenly Spheres, phenotype, placebo effect, randomized controlled trial, selective serotonin reuptake inhibitor (SSRI), stem cell
However, Euclidian geometry does not apply to nature. For example, you cannot map a tree, a cloud, or a mountain using the mathematical formulas of this geometry. In nature, most organic and inorganic structures display more irregular and chaotic-appearing patterns. These natural images can only be created by using the recently discovered mathematics called fractal geometry. French mathematician Benoit Mandelbrot launched the field of fractal mathematics and geometry in 1975. Like quantum physics, fractal (fractional) geometry forces us to consider those irregular patterns, a quirkier world of curvy shapes and objects with more than three dimensions. The mathematics of fractals is amazingly simple because you need only one equation, using only simple multiplication and addition. The same equation is then repeated ad infinitum.
The Simpsons and Their Mathematical Secrets by Simon Singh
Albert Einstein, Andrew Wiles, Benoit Mandelbrot, cognitive dissonance, Donald Knuth, Erdős number, Georg Cantor, Grace Hopper, Isaac Newton, John Nash: game theory, mandelbrot fractal, Menlo Park, Norbert Wiener, Norman Mailer, P = NP, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, Richard Feynman, Richard Feynman, Rubik’s Cube, Schrödinger's Cat, Simon Singh, Stephen Hawking, Wolfskehl Prize, women in the workforce
(And he solved them by hand, without determinants.) When I asked him how he knew the formula would be a cubic polynomial, he said: “What else would it be?” APPENDIX 4 Fractals and Fractional Dimensions We normally think of fractals as patterns that consist of self-similar patterns at every scale. In other words, the overall pattern associated with an object persists as we zoom in and out. As the father of fractals Benoit Mandelbrot pointed out, these self-similar patterns are found in nature: “A cauliflower shows how an object can be made of many parts, each of which is like a whole, but smaller. Many plants are like that. A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don’t get something smooth but irregularities at a smaller scale.” Fractals are also recognizable because they exhibit fractional dimensions.
Albert Einstein, Atul Gawande, Benoit Mandelbrot, big-box store, Black Swan, Checklist Manifesto, Clayton Christensen, Daniel Kahneman / Amos Tversky, Exxon Valdez, Gordon Gekko, housing crisis, information asymmetry, Isaac Newton, Kenneth Arrow, Long Term Capital Management, Mahatma Gandhi, mandelbrot fractal, NetJets, pattern recognition, pre–internet, random walk, Ronald Reagan, South Sea Bubble, Steve Jobs, winner-take-all economy, young professional, zero-sum game
Tartakower and J. du Mont Homo Ludens: A Study of the Play Element in Culture by Johan Huizinga Reality Is Broken: Why Games Make Us Better and How They Can Change the World by Jane McGonigal Winning Chess Tactics for Juniors by Lou Hays Wise Choices: Decisions, Games, and Negotiations by Richard Zeckhauser, Ralph Keeney, and James Sebenius Investing A Zebra in Lion Country by Ralph Wanger with Everett Mattlin Active Value Investing: Making Money in Range-Bound Markets by Vitaliy Katsenelson Beating the Street by Peter Lynch Common Stocks and Uncommon Profits by Philip Fisher Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by Nassim Nicholas Taleb Fooling Some of the People All of the Time: A Long Short Story by David Einhorn and Joel Greenblatt Fortune’s Formula: The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street by William Poundstone Investing: The Last Liberal Art by Robert Hagstrom Investment Biker: Around the World with Jim Rogers by Jim Rogers More Mortgage Meltdown: 6 Ways to Profit in These Bad Times by Whitney Tilson and Glenn Tongue More Than You Know: Finding Financial Wisdom in Unconventional Places by Michael Mauboussin Of Permanent Value: The Story of Warren Buffett by Andrew Kilpatrick Pioneering Portfolio Management: An Unconventional Approach to Institutional Investment by David Swensen Security Analysis by Benjamin Graham and David Dodd Seeking Wisdom: From Darwin to Munger by Peter Bevelin Short Stories from the Stock Market: Uncovering Common Themes behind Falling Stocks to Find Uncommon Ideas by Amit Kumar The Dhandho Investor: The Low-Risk Value Method to High Returns by Mohnish Pabrai The Manual of Ideas: The Proven Framework for Finding the Best Value Investments by John Mihaljevic The Misbehavior of Markets: A Fractal View of Financial Turbulence by Benoit Mandelbrot and Richard Hudson The Most Important Thing: Uncommon Sense for the Thoughtful Investor by Howard Marks The Warren Buffett Way by Robert Hagstrom Value Investing: From Graham to Buffett and Beyond by Bruce Greenwald, Judd Kahn, Paul Sonkin, and Michael van Biema Where Are the Customers’ Yachts? Or, A Good Hard Look at Wall Street by Fred Schwed Your Money and Your Brain: How the New Science of Neuroeconomics Can Help Make You Rich by Jason Zweig Literature 100 Years of Solitude by Gabriel García Márquez Hamlet by William Shakespeare Jonathan Livingston Seagull by Richard Bach Oliver Twist by Charles Dickens Zen and the Art of Motorcycle Maintenance: An Inquiry into Values by Robert Pirsig Miscellaneous Autobiography: The Story of My Experiments with the Truth by Mahatma Gandhi City Police by Jonathan Rubinstein Endurance: Shackleton’s Incredible Voyage by Alfred Lansing Long Walk to Freedom: The Autobiography of Nelson Mandela by Nelson Mandela Metaphors We Live By by George Lakoff and Mark Johnson Reagan: A Life in Letters by Ronald Reagan The Autobiography of Benjamin Franklin by Benjamin Franklin The Checklist Manifesto: How to Get Things Right by Atul Gawande The Hero with a Thousand Faces by Joseph Campbell The New British Constitution by Vernon Bogdanor The Power of Myth by Joseph Campbell with Bill Moyers Vor 1914: Erinnerungen an Frankfurt geschrieben in Israel by Selmar Spier Walden: or, Life in the Woods by Henry David Thoreau Why America Is Not a New Rome by Vaclav Smil Philosophy and Theology A Theory of Justice by John Rawls Anarchy, the State, and Utopia by Robert Nozick Destination Torah: Reflections on the Weekly Torah Readings by Isaac Sassoon Halakhic Man by Joseph Soloveitchik Letters from a Stoic by Lucius Annaeus Seneca Man’s Search for Meaning by Viktor Frankl Meditations by Marcus Aurelius Pirke Avot: A Modern Commentary on Jewish Ethics by Leonard Kravits and Kerry Olitzky Plato, not Prozac!
Memory Machines: The Evolution of Hypertext by Belinda Barnet
augmented reality, Benoit Mandelbrot, Bill Duvall, British Empire, Buckminster Fuller, Claude Shannon: information theory, collateralized debt obligation, computer age, conceptual framework, Douglas Engelbart, Douglas Engelbart, game design, hiring and firing, Howard Rheingold, HyperCard, hypertext link, information retrieval, Internet Archive, John Markoff, linked data, mandelbrot fractal, Marshall McLuhan, Menlo Park, nonsequential writing, Norbert Wiener, publish or perish, Robert Metcalfe, semantic web, Steve Jobs, Stewart Brand, technoutopianism, Ted Nelson, the scientific method, Vannevar Bush, wikimedia commons
Machine-Enhanced (Re)minding: The Development of Storyspace 115 Conclusion 137 Notes 143 Bibliography 149 Index 157 Foreword TO MANDELBROT IN HEAVEN Stuart Moulthrop A certain confusion may befall us when we praise pioneers, especially while they are still with us. This hazard was apparent to the troubadour and know-hit wonder Jonathan Coulton, when he wrote one of the great tunes of popular science, ‘Mandelbrot Set’: Mandelbrot’s in heaven At least he will be when he’s dead Right now he’s still alive and teaching math at Yale The song was released in October 2004, giving it a nice run of six years before its lyrics were compromised by Benoît Mandelbrot’s passing in 2010. Even thus betrayed to history, ‘Mandelbrot Set’ still marks the contrast between extraordinary and ordinary lives, dividing those who change the world, in ways tiny or otherwise, from those who sing about them or merely ruminate. The life of ideas, perhaps like ontogeny, works through sudden transformations and upheavals, apparent impasses punctuated by instant, lateral shift.
The Wisdom of Finance: Discovering Humanity in the World of Risk and Return by Mihir Desai
activist fund / activist shareholder / activist investor, Albert Einstein, Andrei Shleifer, assortative mating, Benoit Mandelbrot, Brownian motion, capital asset pricing model, carried interest, collective bargaining, corporate governance, corporate raider, discounted cash flows, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, follow your passion, George Akerlof, Gordon Gekko, greed is good, housing crisis, income inequality, information asymmetry, Isaac Newton, Jony Ive, Kenneth Rogoff, Louis Bachelier, moral hazard, Myron Scholes, new economy, out of africa, Paul Samuelson, Pierre-Simon Laplace, principal–agent problem, Ralph Waldo Emerson, random walk, risk/return, Robert Shiller, Robert Shiller, Ronald Coase, Silicon Valley, Steve Jobs, The Market for Lemons, The Nature of the Firm, The Wealth of Nations by Adam Smith, Tim Cook: Apple, transaction costs, zero-sum game
Capital Ideas: The Improbable Origins of Modern Wall Street. 1st ed. New York: Free Press, 1992. The original works in this stream of research are well discussed in this pioneering paper: Fama, Eugene. “Efficient Capital Markets: A Review of Theory and Empirical Work.”Journal of Finance 25, no. 2 (May 1970): 383–417. In particular, Fama is generous with his referencing of earlier work, including that of Paul Samuelson, Bill Sharpe, Benoit Mandelbrot, Paul Cootner, Jack Treynor, and others. This lecture is an excellent source on the ideas of efficient markets: Fama, Eugene. “A Brief History of the Efficient Market Hypothesis.” Lecture, Masters of Finance. February 12, 2014. https://www.youtube.com/watch?v=NUkkRdEknjI. An alternative stream of important research on this topic was triggered by Grossman, Sanford J., and Joseph E. Stiglitz.
Extreme Money: Masters of the Universe and the Cult of Risk by Satyajit Das
affirmative action, Albert Einstein, algorithmic trading, Andy Kessler, Asian financial crisis, asset allocation, asset-backed security, bank run, banking crisis, banks create money, Basel III, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Black Swan, Bonfire of the Vanities, bonus culture, Bretton Woods, BRICs, British Empire, capital asset pricing model, Carmen Reinhart, carried interest, Celtic Tiger, clean water, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, corporate governance, corporate raider, creative destruction, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, debt deflation, Deng Xiaoping, deskilling, discrete time, diversification, diversified portfolio, Doomsday Clock, Edward Thorp, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, eurozone crisis, Fall of the Berlin Wall, financial independence, financial innovation, financial thriller, fixed income, full employment, global reserve currency, Goldman Sachs: Vampire Squid, Gordon Gekko, greed is good, happiness index / gross national happiness, haute cuisine, high net worth, Hyman Minsky, index fund, information asymmetry, interest rate swap, invention of the wheel, invisible hand, Isaac Newton, job automation, Johann Wolfgang von Goethe, John Meriwether, joint-stock company, Joseph Schumpeter, Kenneth Arrow, Kenneth Rogoff, Kevin Kelly, labour market flexibility, laissez-faire capitalism, load shedding, locking in a profit, Long Term Capital Management, Louis Bachelier, margin call, market bubble, market fundamentalism, Marshall McLuhan, Martin Wolf, mega-rich, merger arbitrage, Mikhail Gorbachev, Milgram experiment, money market fund, Mont Pelerin Society, moral hazard, mortgage debt, mortgage tax deduction, mutually assured destruction, Myron Scholes, Naomi Klein, negative equity, Network effects, new economy, Nick Leeson, Nixon shock, Northern Rock, nuclear winter, oil shock, Own Your Own Home, Paul Samuelson, pets.com, Philip Mirowski, Plutocrats, plutocrats, Ponzi scheme, price anchoring, price stability, profit maximization, quantitative easing, quantitative trading / quantitative ﬁnance, Ralph Nader, RAND corporation, random walk, Ray Kurzweil, regulatory arbitrage, rent control, rent-seeking, reserve currency, Richard Feynman, Richard Feynman, Richard Thaler, Right to Buy, risk-adjusted returns, risk/return, road to serfdom, Robert Shiller, Robert Shiller, Rod Stewart played at Stephen Schwarzman birthday party, rolodex, Ronald Reagan, Ronald Reagan: Tear down this wall, Satyajit Das, savings glut, shareholder value, Sharpe ratio, short selling, Silicon Valley, six sigma, Slavoj Žižek, South Sea Bubble, special economic zone, statistical model, Stephen Hawking, Steve Jobs, survivorship bias, The Chicago School, The Great Moderation, the market place, the medium is the message, The Myth of the Rational Market, The Nature of the Firm, the new new thing, The Predators' Ball, The Wealth of Nations by Adam Smith, Thorstein Veblen, too big to fail, trickle-down economics, Turing test, Upton Sinclair, value at risk, Yogi Berra, zero-coupon bond, zero-sum game
Cliff Asness, a student of Fama and founder of hedge fund AQR Capital Management, exploited these anomalies. Hearing complaints that his strategies were not working, Asness’ wife asked him incredulously: “Let me get this straight. I thought you said you make your money because people aren’t completely rational. Yet now you’re mad because they’re too irrational.”24 Risk management assumes that price changes are normally distributed. The mathematician Benoit Mandelbrot demonstrated that normal distributions do not exist in practice. In Fooled by Randomness and Black Swan, Nicholas Nassim Taleb argued against the application of statistical methods in finance, especially the normal distribution curve to measure risk. Taleb drew on John Stuart Mill, himself rephrasing a problem posed by Scottish philosopher David Hume: “no amount of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute that conclusion.”
Like the philosoher of science Thomas Kuhn, financial markets persisted with flawed models, arguing that they worked in normal conditions and were superior to alternatives. David Einhorn compared risk systems to: “an airbag which works all the time except when you get into a crash.”25 Financiers were reluctant to use qualitative approaches that were inconsistent with their scientific self-image. As Benoit Mandelbrot, the creator of chaos theory, observed: “Human Nature yearns to see order and hierarchy in the world. It will invent it if it cannot find it.”26 Psychologist B.F. Skinner created “superstitious pigeons.” Unlike in normal experiments, he fed the pigeons with no reference to the bird’s behavior. Even though the food was given out on a fixed schedule, each bird developed its own superstitious behavior, trying to uncover a pattern associated with food.
Bad Data Handbook by Q. Ethan McCallum
Amazon Mechanical Turk, asset allocation, barriers to entry, Benoit Mandelbrot, business intelligence, cellular automata, chief data officer, Chuck Templeton: OpenTable, cloud computing, cognitive dissonance, combinatorial explosion, commoditize, conceptual framework, database schema, en.wikipedia.org, Firefox, Flash crash, Gini coefficient, illegal immigration, iterative process, labor-force participation, loose coupling, natural language processing, Netflix Prize, quantitative trading / quantitative ﬁnance, recommendation engine, selection bias, sentiment analysis, statistical model, supply-chain management, survivorship bias, text mining, too big to fail, web application
To see this idea in action, consider a classic technique for defining a complex graphical object by starting with two simple objects: “One begins with two shapes, an initiator and a generator…each stage of the construction begins with a broken line and consists in replacing each straight interval with a copy of the generator, reduced and displaced so as to have the same end points as those of the interval being replaced.” Benoît Mandelbrot In just three iterations of this algorithm, we can create a famous shape known as the Koch snowflake. Not so different than what just happened with our relational schema, is it? Our entities play the role of the “straight interval,” and the associative many-to-many entities act as the complexity generators. The Hidden Network Emerges Let’s step back. If we were to just step up to a whiteboard and draw out what we were trying to accomplish with the asset allocations for our servers, our sketch might look something like Figure 13-2.
A Declaration of the Independence of Cyberspace, Albert Einstein, AltaVista, Amazon Mechanical Turk, Asperger Syndrome, availability heuristic, Benoit Mandelbrot, biofilm, Black Swan, British Empire, conceptual framework, corporate governance, Danny Hillis, Douglas Engelbart, Douglas Engelbart, Emanuel Derman, epigenetics, Flynn Effect, Frank Gehry, Google Earth, hive mind, Howard Rheingold, index card, information retrieval, Internet Archive, invention of writing, Jane Jacobs, Jaron Lanier, John Markoff, Kevin Kelly, lifelogging, lone genius, loss aversion, mandelbrot fractal, Marc Andreessen, Marshall McLuhan, Menlo Park, meta analysis, meta-analysis, New Journalism, Nicholas Carr, out of africa, Paul Samuelson, peer-to-peer, Ponzi scheme, pre–internet, Richard Feynman, Richard Feynman, Rodney Brooks, Ronald Reagan, Schrödinger's Cat, Search for Extraterrestrial Intelligence, SETI@home, Silicon Valley, Skype, slashdot, smart grid, social graph, social software, social web, Stephen Hawking, Steve Wozniak, Steven Pinker, Stewart Brand, Ted Nelson, telepresence, the medium is the message, the scientific method, The Wealth of Nations by Adam Smith, theory of mind, trade route, upwardly mobile, Vernor Vinge, Whole Earth Catalog, X Prize
This year, I enlisted the aid of Hans Ulrich Obrist, curator of the Serpentine Gallery in London, and the artist April Gornik, one of the early members of the Reality Club, to help broaden the Edge conversation—or, rather, to bring it back to where it was in the late 1980s and early 1990s, when April gave a talk at a Reality Club meeting and discussed the influence of chaos theory on her work, and Benoit Mandelbrot showed up to discuss fractal theory. Every artist in New York City wanted to be there. What then happened was very interesting. When the Reality Club went online as Edge, the scientists were all on e-mail—and the artists weren’t. Thus did Edge, surprisingly, become a science site, whereas my own background (beginning in 1965, when Jonas Mekas hired me to manage the Film-Makers’ Cinematheque) was in the visual and performance arts.
A Place of My Own: The Architecture of Daydreams by Michael Pollan
A Pattern Language, back-to-the-land, Benoit Mandelbrot, dematerialisation, Frank Gehry, interchangeable parts, Marshall McLuhan, Mercator projection, Peter Eisenman, place-making, Stewart Brand, telemarketer, The Great Good Place, urban renewal, zero-sum game
(Cambridge: MIT Press, 1972). Mostafavi, Mohsen, and David Leatherbarrow. On Weathering (Cambridge: MIT Press, 1993). My principal sources on trees and woods were Herbert L. Edlin’s What Wood Is That? A Manual of Wood Identification (New York: Viking Press, 1969) and Donald Culross Peattie’s A Natural History of Trees of Eastern and Central North America (Boston: Houghton Mifflin, 1966). Benoit Mandelbrot’s ideas about architectural ornament are discussed briefly in James Gleick’s Chaos: Making a New Science (New York: Viking, 1987). On the history of the study and the rise of the modern individual the key work is A History of Private Life, edited by Philippe Ariès and Georges Duby. See Volume III, Passions of the Renaissance, especially Ariès’s introduction, as well as “The Refuges of Intimacy” by Orest Ranum, and “The Practical Impact of Writing” by Roger Chartier.
Present Shock: When Everything Happens Now by Douglas Rushkoff
algorithmic trading, Andrew Keen, bank run, Benoit Mandelbrot, big-box store, Black Swan, British Empire, Buckminster Fuller, cashless society, citizen journalism, clockwork universe, cognitive dissonance, Credit Default Swap, crowdsourcing, Danny Hillis, disintermediation, Donald Trump, double helix, East Village, Elliott wave, European colonialism, Extropian, facts on the ground, Flash crash, game design, global supply chain, global village, Howard Rheingold, hypertext link, Inbox Zero, invention of agriculture, invention of hypertext, invisible hand, iterative process, John Nash: game theory, Kevin Kelly, laissez-faire capitalism, Law of Accelerating Returns, loss aversion, mandelbrot fractal, Marshall McLuhan, Merlin Mann, Milgram experiment, mutually assured destruction, negative equity, Network effects, New Urbanism, Nicholas Carr, Norbert Wiener, Occupy movement, passive investing, pattern recognition, peak oil, price mechanism, prisoner's dilemma, Ralph Nelson Elliott, RAND corporation, Ray Kurzweil, recommendation engine, selective serotonin reuptake inhibitor (SSRI), Silicon Valley, Skype, social graph, South Sea Bubble, Steve Jobs, Steve Wozniak, Steven Pinker, Stewart Brand, supply-chain management, the medium is the message, The Wisdom of Crowds, theory of mind, Turing test, upwardly mobile, Whole Earth Catalog, WikiLeaks, Y2K, zero-sum game
They believe that, unlike traditional measurement and prediction, these nonlinear, systems approaches transcend the human inability to imagine the unthinkable. Even Black Swan author Nassim Taleb, who made a career of warning economists and investors against trying to see the future, believes in the power of fractals to predict the sudden shifts and wild outcomes of real markets. He dedicated the book to Benoit Mandelbrot. While fractal geometry can certainly help us find strong, repeating patterns within the market activity of the 1930s Depression, it did not predict the crash of 2007. Nor did the economists using fractals manage to protect their banks and brokerages from the systemic effects of bad mortgage packages, overleveraged European banks, or the impact of algorithmic trading on moment-to-moment volatility.
Albert Einstein, anti-communist, asset allocation, beat the dealer, Benoit Mandelbrot, Black-Scholes formula, Brownian motion, buy low sell high, capital asset pricing model, Claude Shannon: information theory, computer age, correlation coefficient, diversified portfolio, Edward Thorp, en.wikipedia.org, Eugene Fama: efficient market hypothesis, high net worth, index fund, interest rate swap, Isaac Newton, Johann Wolfgang von Goethe, John Meriwether, John von Neumann, Kenneth Arrow, Long Term Capital Management, Louis Bachelier, margin call, market bubble, market fundamentalism, Marshall McLuhan, Myron Scholes, New Journalism, Norbert Wiener, offshore financial centre, Paul Samuelson, publish or perish, quantitative trading / quantitative ﬁnance, random walk, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Reagan, Rubik’s Cube, short selling, speech recognition, statistical arbitrage, The Predators' Ball, The Wealth of Nations by Adam Smith, transaction costs, traveling salesman, value at risk, zero-coupon bond, zero-sum game
At the time he was designing the roulette computer with Thorp, Shannon kept notes in an MIT notebook. Part of the notebook is devoted to the roulette device and part to a wildly disconnected set of stock market musings. Shannon wondered about the statistical structure of the market’s random walk and whether information theory could provide useful insights. He mentions such diverse names as Bachelier, (Benjamin) Graham and (David) Dodd, (John) Magee, A. W. Jones, (Oskar) Morgenstern, and (Benoit) Mandelbrot. He considered margin trading and short-selling; stop-loss orders and the effects of market panics; capital gains taxes and transaction costs. Shannon graphs short interest in Litton Industries (shorted shares vs. price: the values jump all over with no evident pattern). He notes such success stories as Bernard Baruch, the Lone Wolf, who ran about $10,000 into a million in about ten years, and Hetty Green, the Witch of Wall Street, who ran a million into a hundred million in thirty years.
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
Are these “critical points” not quite points but progressions (the so-called Pareto power laws)? While it is clear that the world produces clusters it is also sad that these may be too difficult to predict (outside of physics) for us to take their models seriously. Once again the important fact is knowing the existence of these nonlinearities, not trying to model them. The value of the great Benoit Mandelbrot’s work lies more in telling us that there is a “wild” type of randomness of which we will never know much (owing to their unstable properties). Our Brain Our brain is not cut out for nonlinearities. People think that if, say, two variables are causally linked, then a steady input in one variable should always yield a result in the other one. Our emotional apparatus is designed for linear causality.
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
Like the roulette balls Farmer had attempted to track while a student, the players’ choices bounced around unpredictably. The researchers found that as the number of players increased, this chaotic decision making became more common. When games are complicated, it seems that it may be impossible to anticipate players’ choices. Other patterns also emerged, including ones that had previously been spotted in real-life games. When mathematician Benoit Mandelbrot looked at financial markets in the early 1960s, he noticed that volatile periods in stock markets tended to cluster together. “Large changes tend to be followed by large changes,” he noted, “and small changes tend to be followed by small changes.” The appearance of “clustered volatility” has intrigued economists ever since. Galla and Farmer spotted the phenomenon in their game, too, suggesting the pattern may just be a consequence of lots of people trying to learn the complexities of the financial markets.
Places of the Heart: The Psychogeography of Everyday Life by Colin Ellard
augmented reality, Benoit Mandelbrot, Berlin Wall, Broken windows theory, Buckminster Fuller, carbon footprint, commoditize, crowdsourcing, Frank Gehry, Google Glasses, Guggenheim Bilbao, haute couture, Howard Rheingold, Internet of things, Jaron Lanier, mandelbrot fractal, Marshall McLuhan, Masdar, mass immigration, megastructure, more computing power than Apollo, Oculus Rift, Peter Eisenman, RFID, Richard Florida, risk tolerance, sentiment analysis, smart cities, the built environment, theory of mind, urban decay, urban planning, urban sprawl, Victor Gruen
Fractal dimensions for scenes lie between the numbers one and two, suggesting that they are neither quite one- nor two-dimensional geometric objects. In fact, the very name “fractal” is meant to convey this property of having a fractional dimensionality lying somewhere between whole numbers. Though this might seem a bit puzzling to picture, what it really means is that fractal objects defy some of the rules of conventional nonfractal geometry. In his original formulation of fractal dimension, the Polish mathematician Benoit Mandelbrot considered how one might go about measuring the length of a jagged coastline using a measuring stick. Because it contains a vast number of detailed curves and angles, the measured length of the coastline will depend on the length of the stick. As the stick becomes shorter and shorter, the length of the coastline will seem to become longer and longer. Fractal dimension describes the relationship between the length of the measuring stick and the measured length of the coastline.
Benoit Mandelbrot, clockwork universe, double helix, Drosophila, Geoffrey West, Santa Fe Institute, Louis Pasteur, mandelbrot fractal, out of africa, phenotype, random walk, Richard Feynman, Richard Feynman, stem cell, unbiased observer
Their densely mathematical model was published in Science in 1997, and the ramiﬁcations (if not the maths) swiftly captured the imagination of many. The fractal tree of life Fractals (from the Latin fractus, broken) are geometric shapes that look similar at any scale. If a fractal is broken into its constituent parts, each part still looks more or less the same, because, as the pioneer of fractal geometry Benoit Mandelbrot put it, ‘the shapes are made of parts similar to the whole in some way’. Fractals can be formed randomly by natural forces such as wind, rain, ice, erosion, and gravity, to generate natural fractals, like mountains, clouds, rivers, and coastlines. Indeed, Mandelbrot described fractals as ‘the geometry of nature’, and in his landmark paper, published in Science, in 1967, he applied this approach to the question advanced in its title: How Long is the Coast of Britain?
Red-Blooded Risk: The Secret History of Wall Street by Aaron Brown, Eric Kim
activist fund / activist shareholder / activist investor, Albert Einstein, algorithmic trading, Asian financial crisis, Atul Gawande, backtesting, Basel III, Bayesian statistics, beat the dealer, Benoit Mandelbrot, Bernie Madoff, Black Swan, capital asset pricing model, central bank independence, Checklist Manifesto, corporate governance, creative destruction, credit crunch, Credit Default Swap, disintermediation, distributed generation, diversification, diversified portfolio, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, experimental subject, financial innovation, illegal immigration, implied volatility, index fund, Long Term Capital Management, loss aversion, margin call, market clearing, market fundamentalism, market microstructure, money market fund, money: store of value / unit of account / medium of exchange, moral hazard, Myron Scholes, natural language processing, open economy, Pierre-Simon Laplace, pre–internet, quantitative trading / quantitative ﬁnance, random walk, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, road to serfdom, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, special drawing rights, statistical arbitrage, stochastic volatility, The Myth of the Rational Market, Thomas Bayes, too big to fail, transaction costs, value at risk, yield curve
Narang, and Multifractal Volatility: Theory, Forecasting, and Pricing by Laurent E. Calvet. The view of quantitative finance described in Red-Blooded Risk has a lot of overlap with two pathbreaking but eccentric works: The Handbook of Portfolio Mathematics: Formulas for Optimal Allocation & Leverage by Ralph Vince and Finding Alpha: The Search for Alpha When Risk and Return Break Down by Eric Falkenstein. A more famous pathbreaking and eccentric work is Benoit Mandelbrot’s The (Mis)behavior of Markets. Two of the best books on the future of finance are The New Financial Order: Risk in the 21st Century by Robert J. Shiller and Financing the Future: Market-Based Innovations for Growth by Franklin Allen and Glenn Yago. Both cover quite a bit of history to ground their predictions in something solid. If you like to study your quantitative finance through people, Espen Haug’s Derivatives Models on Models is an excellent choice.
New Market Wizards: Conversations With America's Top Traders by Jack D. Schwager
backtesting, beat the dealer, Benoit Mandelbrot, Berlin Wall, Black-Scholes formula, butterfly effect, commodity trading advisor, computerized trading, Edward Thorp, Elliott wave, fixed income, full employment, implied volatility, interest rate swap, Louis Bachelier, margin call, market clearing, market fundamentalism, money market fund, paper trading, pattern recognition, placebo effect, prediction markets, Ralph Nelson Elliott, random walk, risk tolerance, risk/return, Saturday Night Live, Sharpe ratio, the map is not the territory, transaction costs, War on Poverty
A robust statistical estimator is one that is not perturbed much by mistaken assumptions about the nature of the distribution. Why do you feel such techniques are more appropriate for trading system analysis? Because I believe that price distributions are pathological. In what way? As one example, price distributions have more variance [a statistical measure of the variability in the data] than one would expect on the basis of normal distribution theory. Benoit Mandelbrot, the originator of the concept of fractional dimension, has conjectured that price change distributions actually have infinite variance. The sample variance [i.e., the implied variability in prices] just gets larger and larger as you add more data. If this is true, then most standard statistical techniques are invalid for price data applications. I don’t understand. How can the variance be infinite?
3D printing, Albert Einstein, Amazon Mechanical Turk, Arthur Eddington, basic income, Bayesian statistics, Benoit Mandelbrot, bioinformatics, Black Swan, Brownian motion, cellular automata, Claude Shannon: information theory, combinatorial explosion, computer vision, constrained optimization, correlation does not imply causation, creative destruction, crowdsourcing, Danny Hillis, data is the new oil, double helix, Douglas Hofstadter, Erik Brynjolfsson, experimental subject, Filter Bubble, future of work, global village, Google Glasses, Gödel, Escher, Bach, information retrieval, job automation, John Markoff, John Snow's cholera map, John von Neumann, Joseph Schumpeter, Kevin Kelly, lone genius, mandelbrot fractal, Mark Zuckerberg, Moneyball by Michael Lewis explains big data, Narrative Science, Nate Silver, natural language processing, Netflix Prize, Network effects, NP-complete, off grid, P = NP, PageRank, pattern recognition, phenotype, planetary scale, pre–internet, random walk, Ray Kurzweil, recommendation engine, Richard Feynman, Richard Feynman, Second Machine Age, self-driving car, Silicon Valley, speech recognition, statistical model, Stephen Hawking, Steven Levy, Steven Pinker, superintelligent machines, the scientific method, The Signal and the Noise by Nate Silver, theory of mind, Thomas Bayes, transaction costs, Turing machine, Turing test, Vernor Vinge, Watson beat the top human players on Jeopardy!, white flight, zero-sum game
Otto Creutzfeldt makes the case that the cortex is one algorithm in “Generality of the functional structure of the neocortex” (Naturwissenschaften, 1977), as does Vernon Mountcastle in “An organizing principle for cerebral function: The unit model and the distributed system,” in The Mindful Brain, edited by Gerald Edelman and Vernon Mountcastle (MIT Press, 1978). Gary Marcus, Adam Marblestone, and Tom Dean make the case against in “The atoms of neural computation” (Science, 2014). “The unreasonable effectiveness of data,” by Alon Halevy, Peter Norvig, and Fernando Pereira (IEEE Intelligent Systems, 2009), argues for machine learning as the new discovery paradigm. Benoît Mandelbrot explores the fractal geometry of nature in the eponymous book* (Freeman, 1982). James Gleick’s Chaos (Viking, 1987) discusses and depicts the Mandelbrot set. The Langlands program, a research effort that seeks to unify different subfields of mathematics, is described in Love and Math, by Edward Frenkel (Basic Books, 2014). The Golden Ticket, by Lance Fortnow (Princeton University Press, 2013), is an introduction to NP-completeness and the P = NP problem.
additive manufacturing, Atul Gawande, backtesting, Benoit Mandelbrot, buy low sell high, Checklist Manifesto, computerized trading, deliberate practice, diversification, Elliott wave, endowment effect, loss aversion, mandelbrot fractal, margin call, offshore financial centre, paper trading, Ponzi scheme, price stability, psychological pricing, quantitative easing, random walk, risk tolerance, short selling, South Sea Bubble, systematic trading, The Wisdom of Crowds, transaction costs, transfer pricing, traveling salesman, tulip mania, zero-sum game
Resistance is where sellers sell with greater intensity than buyers buy (see Chapter 18). Channels show where to expect support and resistance in the future. Channels help identify buying and selling opportunities and avoid bad trades. The original research into trading channels was conducted by J. M. Hurst and described in his 1970 book, The Profit Magic of Stock Transaction Timing. The late great mathematician Benoit Mandelbrot was hired by the Egyptian government to create a mathematical model of cotton prices—the main agricultural export of that country. After extensive study, the scientist made this finding: “prices oscillate above and below value.” It may sound simple, but in fact it's profound. If we accept this mathematical finding and if we have the means to define value and measure an average oscillation, we'll have a trading system.
A Splendid Exchange: How Trade Shaped the World by William J. Bernstein
Admiral Zheng, asset allocation, bank run, Benoit Mandelbrot, British Empire, call centre, clean water, Columbian Exchange, Corn Laws, David Ricardo: comparative advantage, deindustrialization, Doha Development Round, domestication of the camel, double entry bookkeeping, Eratosthenes, financial innovation, Gini coefficient, God and Mammon, ice-free Arctic, imperial preference, income inequality, intermodal, James Hargreaves, John Harrison: Longitude, Khyber Pass, low skilled workers, non-tariff barriers, Paul Samuelson, placebo effect, Port of Oakland, refrigerator car, Silicon Valley, South China Sea, South Sea Bubble, spice trade, spinning jenny, Steven Pinker, The Wealth of Nations by Adam Smith, Thomas L Friedman, Thomas Malthus, trade liberalization, trade route, transatlantic slave trade, transatlantic slave trade, transcontinental railway, upwardly mobile, working poor, zero-sum game
At a ratio of twelve to one for gold to silver, then, one ounce of gold or silk represented ninety-six days' wages. 6. S. D. Goitein, A Mediterranean Society (Berkeley: University of California Press, 1967), I: 347-348. 7. Ibid., 298. 8. Ibid., 299-300. 9. Ibid., 340-342. 10. Ibid., 219. Only in the twentieth century did economists begin to fully appreciate the unpredictability of market prices. By a strange coincidence, the founder of chaos theory, Benoit Mandelbrot, drew his original inspiration by connecting the pattern of cotton prices with that of the flooding pattern of the Nile. 11. The dinar, like most of the standard gold coins of the premodern period, weighed about one-eighth of an ounce, worth about eighty dollars at current value. Thus, an annual income of one hundred dinars corresponds to about $8,000 per year in today's currency. 12. Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations (Chicago: University of Chicago Press, 1976), I: 17. 13.
Wireless by Stross, Charles
anthropic principle, back-to-the-land, Benoit Mandelbrot, Buckminster Fuller, Cepheid variable, cognitive dissonance, colonial exploitation, cosmic microwave background, epigenetics, finite state, Georg Cantor, gravity well, hive mind, jitney, Khyber Pass, lifelogging, Magellanic Cloud, mandelbrot fractal, peak oil, phenotype, Pluto: dwarf planet, security theater, sensible shoes, Turing machine
(True names have power, so the Laundry is big on call by reference, not call by value; I’m no more “Bob Howard” than the “Alan Turing” in room two is the father of computer science and applied computational demonology.) She continues. “The real Alan Turing would be nearly a hundred by now. All our long-term residents are named for famous mathematicians. We’ve got Alan Turing, Kurt Godel, Georg Cantor, and Benoit Mandelbrot. Turing’s the oldest, Benny is the most recent—he actually has a payroll number, sixteen.” I’m in five digits—I don’t know whether to laugh or cry. “Who’s the nameless one?” I ask. “That would be Georg Cantor,” she says slowly. “He’s probably in room four.” I bend over the indicated periscope, remove the brass cap, and peer into the alien world of the nameless K. Syndrome survivor. I see a whitewashed room, quite spacious, with a toilet area off to one side and a bedroom accessible through a doorless opening—much like the short-term ward.
Dead or Alive by Tom Clancy, Grant (CON) Blackwood
active measures, affirmative action, air freight, airport security, Bay Area Rapid Transit, Benoit Mandelbrot, defense in depth, failed state, friendly fire, Google Earth, Panamax, post-Panamax, Skype, uranium enrichment, urban sprawl
A former IBM employee, he’d lost two brothers in Vietnam, and thereafter had come to work for the federal government, then to be talent-scouted and cherry-picked to the Fort Meade headquarters of the National Security Agency, the government’s premier center for communications and electronic security. His government salary had long since topped him out as a Senior Executive Service genius, and indeed he still collected his reasonably generous government pension. But he loved the action and had snapped up the offer to join The Campus within seconds of its being made. He was, professionally, a mathematician, with a doctorate from Harvard, where he’d studied under Benoit Mandelbrot himself, and he occasionally lectured at MIT and Caltech as well in his area of expertise. Biery was a geek through and through, right down to the heavy black-rimmed glasses and doughy complexion, but he kept The Campus’s electronic gears oiled and the machines purring. “Compartmentalization?” Brian said. “Don’t gimme that cloak-and-dagger shit.” Jack held up his hands and shrugged. “Sorry.”
The Singularity Is Near: When Humans Transcend Biology by Ray Kurzweil
additive manufacturing, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anthropic principle, Any sufficiently advanced technology is indistinguishable from magic, artificial general intelligence, Asilomar, augmented reality, autonomous vehicles, Benoit Mandelbrot, Bill Joy: nanobots, bioinformatics, brain emulation, Brewster Kahle, Brownian motion, business intelligence, c2.com, call centre, carbon-based life, cellular automata, Claude Shannon: information theory, complexity theory, conceptual framework, Conway's Game of Life, cosmological constant, cosmological principle, cuban missile crisis, data acquisition, Dava Sobel, David Brooks, Dean Kamen, disintermediation, double helix, Douglas Hofstadter, en.wikipedia.org, epigenetics, factory automation, friendly AI, George Gilder, Gödel, Escher, Bach, informal economy, information retrieval, invention of the telephone, invention of the telescope, invention of writing, Isaac Newton, iterative process, Jaron Lanier, Jeff Bezos, job automation, job satisfaction, John von Neumann, Kevin Kelly, Law of Accelerating Returns, life extension, lifelogging, linked data, Loebner Prize, Louis Pasteur, mandelbrot fractal, Mikhail Gorbachev, mouse model, Murray Gell-Mann, mutually assured destruction, natural language processing, Network effects, new economy, Norbert Wiener, oil shale / tar sands, optical character recognition, pattern recognition, phenotype, premature optimization, randomized controlled trial, Ray Kurzweil, remote working, reversible computing, Richard Feynman, Richard Feynman, Robert Metcalfe, Rodney Brooks, Search for Extraterrestrial Intelligence, selection bias, semantic web, Silicon Valley, Singularitarianism, speech recognition, statistical model, stem cell, Stephen Hawking, Stewart Brand, strong AI, superintelligent machines, technological singularity, Ted Kaczynski, telepresence, The Coming Technological Singularity, Thomas Bayes, transaction costs, Turing machine, Turing test, Vernor Vinge, Y2K, Yogi Berra
In other words, the principles of the design of the brain are simpler than they appear. To understand this, let's first consider the fractal nature of the brain's organization, which I discussed in chapter 2. A fractal is a rule that is iteratively applied to create a pattern or design. The rule is often quite simple, but because of the iteration the resulting design can be remarkably complex. A famous example of this is the Mandelbrot set devised by mathematician Benoit Mandelbrot.20 Visual images of the Mandelbrot set are remarkably complex, with endlessly complicated designs within designs. As we look at finer and finer detail in an image of the Mandelbrot set, the complexity never goes away, and we continue to see ever finer complication. Yet the formula underlying all of this complexity is amazingly simple: the Mandelbrot set is characterized by a single formula Z = Z2 + C, in which Z is a "complex" (meaning two-dimensional) number and C is a constant.
More Money Than God: Hedge Funds and the Making of a New Elite by Sebastian Mallaby
Andrei Shleifer, Asian financial crisis, asset-backed security, automated trading system, bank run, barriers to entry, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Bonfire of the Vanities, Bretton Woods, capital controls, Carmen Reinhart, collapse of Lehman Brothers, collateralized debt obligation, computerized trading, corporate raider, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, currency manipulation / currency intervention, currency peg, Elliott wave, Eugene Fama: efficient market hypothesis, failed state, Fall of the Berlin Wall, financial deregulation, financial innovation, financial intermediation, fixed income, full employment, German hyperinflation, High speed trading, index fund, John Meriwether, Kenneth Rogoff, Long Term Capital Management, margin call, market bubble, market clearing, market fundamentalism, merger arbitrage, money market fund, moral hazard, Myron Scholes, natural language processing, Network effects, new economy, Nikolai Kondratiev, pattern recognition, Paul Samuelson, pre–internet, quantitative hedge fund, quantitative trading / quantitative ﬁnance, random walk, Renaissance Technologies, Richard Thaler, risk-adjusted returns, risk/return, rolodex, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, statistical arbitrage, statistical model, survivorship bias, technology bubble, The Great Moderation, The Myth of the Rational Market, the new new thing, too big to fail, transaction costs
The efficient-market hypothesis had always been based on a precarious assumption: that price changes conformed to a “normal” probability distribution—the one represented by the familiar bell curve, in which numbers at and near the median crop up frequently while numbers in the tails of the distribution are rare to the point of vanishing. Even in the early 1960s, a maverick mathematician named Benoit Mandelbrot argued that the tails of the distribution might be fatter than the normal bell curve assumed; and Eugene Fama, the father of efficient-market theory, who got to know Mandelbrot at the time, conducted tests on stock-price changes that confirmed Mandelbrot’s assertion. If price changes had been normally distributed, jumps greater than five standard deviations should have shown up in daily price data about once every seven thousand years.
I Am a Strange Loop by Douglas R. Hofstadter
Albert Einstein, Andrew Wiles, Benoit Mandelbrot, Brownian motion, double helix, Douglas Hofstadter, Georg Cantor, Gödel, Escher, Bach, Isaac Newton, James Watt: steam engine, John Conway, John von Neumann, mandelbrot fractal, pattern recognition, Paul Erdős, place-making, probability theory / Blaise Pascal / Pierre de Fermat, publish or perish, random walk, Ronald Reagan, self-driving car, Silicon Valley, telepresence, Turing machine
This was the case because the most unpredictable of the visual phenomena always seemed to happen right in the vicinity of that central point where the infinite regress converges down to a magical dot. My explorations did not teach me that any shape whatsoever can arise as a result of video feedback, but they did show me that I had entered a far richer universe of possibilities than I had expected. Today, this visual richness reminds me of the amazing visual universe discovered around 1980 by mathematician Benoit Mandelbrot when he studied the properties of the simple iteration defined by z → z2 + c, where c is a fixed complex number and z is a variable complex number whose initial value is 0. This is a mathematical feedback loop where one value of z goes in and a new value comes out, ready to be fed back in again, just as in audio or video feedback. The key question is this: If you, playing the role of microphone and loudspeaker (or camera and TV), do this over and over again, will the z values you get grow unboundedly, sailing off into the wild blue (or wild yellow or wild red) yonder, or will they instead home in on a finite value?
Clojure Programming by Chas Emerick, Brian Carper, Christophe Grand
Amazon Web Services, Benoit Mandelbrot, cloud computing, continuous integration, database schema, domain-specific language, don't repeat yourself, en.wikipedia.org, failed state, finite state, Firefox, game design, general-purpose programming language, Guido van Rossum, Larry Wall, mandelbrot fractal, Paul Graham, platform as a service, premature optimization, random walk, Ruby on Rails, Schrödinger's Cat, semantic web, software as a service, sorting algorithm, Turing complete, type inference, web application
Of course, that callback function should have its primitive arguments declared as we just did for escape to avoid boxing. * * *  See http://en.wikipedia.org/wiki/Mandlebrot_set for a gentle introduction to the Mandelbrot Set, the mathematics behind it, and how you can go about generating visualizations of it. We’d also be remiss if we didn’t point you toward Jonathan Coulton’s fantastic song and music video about the Mandelbrot Set and its creator/discoverer Benoît Mandelbrot: http://www.youtube.com/watch?v=ES-yKOYaXq0.  Simpler implementations are possible; for example, by using the iterate function to lazily calculate the result of the complex polynomial, and take-ing only as many results from the head of that lazy seq as dictated by our maximum iteration count. Such approaches are much more concise, but because they utilize lazy seqs and collections, the results of our calculations will be boxed—and thus, much slower
airport security, availability heuristic, Bayesian statistics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, big-box store, Black Swan, Broken windows theory, Carmen Reinhart, Claude Shannon: information theory, Climategate, Climatic Research Unit, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, complexity theory, computer age, correlation does not imply causation, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, Daniel Kahneman / Amos Tversky, diversification, Donald Trump, Edmond Halley, Edward Lorenz: Chaos theory, en.wikipedia.org, equity premium, Eugene Fama: efficient market hypothesis, everywhere but in the productivity statistics, fear of failure, Fellow of the Royal Society, Freestyle chess, fudge factor, George Akerlof, haute cuisine, Henri Poincaré, high batting average, housing crisis, income per capita, index fund, Intergovernmental Panel on Climate Change (IPCC), Internet Archive, invention of the printing press, invisible hand, Isaac Newton, James Watt: steam engine, John Nash: game theory, John von Neumann, Kenneth Rogoff, knowledge economy, locking in a profit, Loma Prieta earthquake, market bubble, Mikhail Gorbachev, Moneyball by Michael Lewis explains big data, Monroe Doctrine, mortgage debt, Nate Silver, negative equity, new economy, Norbert Wiener, PageRank, pattern recognition, pets.com, Pierre-Simon Laplace, prediction markets, Productivity paradox, random walk, Richard Thaler, Robert Shiller, Robert Shiller, Rodney Brooks, Ronald Reagan, Saturday Night Live, savings glut, security theater, short selling, Skype, statistical model, Steven Pinker, The Great Moderation, The Market for Lemons, the scientific method, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, too big to fail, transaction costs, transfer pricing, University of East Anglia, Watson beat the top human players on Jeopardy!, wikimedia commons
How to Make a Chess Master Blink Deep Blue was born at IBM’s Thomas J. Watson Center—a beautiful, crescent-shaped, retro-modern building overlooking the Westchester County foothills. In its lobby are replicas of early computers, like the ones designed by Charles Babbage. While the building shows a few signs of rust—too much wood paneling and too many interior offices—many great scientists have called it home, including the mathematician Benoit Mandelbrot, and Nobel Prize winners in economics and physics. I visited the Watson Center in the spring of 2010 to see Murray Campbell, a mild-mannered and still boyish-looking Canadian who was one of the chief engineers on the project since its days as Deep Thought at Carnegie Mellon. (Today, Campbell oversees IBM’s statistical modeling department.) In Campbell’s office is a large poster of Kasparov glaring menacingly at a chessboard with the caption: How Do You Make a Computer Blink?
accounting loophole / creative accounting, banking crisis, banks create money, barriers to entry, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black Swan, Bonfire of the Vanities, butterfly effect, capital asset pricing model, cellular automata, central bank independence, citizen journalism, clockwork universe, collective bargaining, complexity theory, correlation coefficient, creative destruction, credit crunch, David Ricardo: comparative advantage, debt deflation, diversification, double entry bookkeeping, en.wikipedia.org, Eugene Fama: efficient market hypothesis, experimental subject, Financial Instability Hypothesis, fixed income, Fractional reserve banking, full employment, Henri Poincaré, housing crisis, Hyman Minsky, income inequality, information asymmetry, invisible hand, iterative process, John von Neumann, laissez-faire capitalism, liquidity trap, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, market clearing, market microstructure, means of production, minimum wage unemployment, money market fund, open economy, Pareto efficiency, Paul Samuelson, place-making, Ponzi scheme, profit maximization, quantitative easing, RAND corporation, random walk, risk tolerance, risk/return, Robert Shiller, Robert Shiller, Ronald Coase, Schrödinger's Cat, scientific mainstream, seigniorage, six sigma, South Sea Bubble, stochastic process, The Great Moderation, The Wealth of Nations by Adam Smith, Thorstein Veblen, time value of money, total factor productivity, tulip mania, wage slave, zero-sum game
The Lorenz model, noted in Chapter 8, has both these attributes: the nonlinear relations between displacement and temperature lead to behavior which on the surface is ‘chaotic,’ but behind which lies the beautiful organizing force of Lorenz’s ‘strange attractor.’ Complexity theorists argue that the economy demonstrates similar attributes, and these are what give rise to the cycles which are a self-evident aspect of real-world economies. Econophysics substantially adds to the contribution made by the early proponents of complexity in economics – such as Richard Goodwin (Goodwin 1990, 1991), Benoit Mandelbrot (Mandelbrot 1971, 2005), Hans-Walter Lorenz (Lorenz 1987a, 1987b, 1989), Paul Ormerod (Ormerod 1997, 2001, 2004); Ormerod and Heineike (2009), Carl Chiarella (Chiarella and Flaschel 2000, Chiarella, Dieci et al. 2002, Chiarella et al. 2003) and myself, among many others – by bringing both the techniques and the empirical mindset of physicists to bear upon economic data. Over the last century, physicists have developed a vast array of techniques to interpret the equally vast range of physical processes encountered in everything from fluid dynamics to the behavior of subatomic particles.
Surfaces and Essences by Douglas Hofstadter, Emmanuel Sander
affirmative action, Albert Einstein, Arthur Eddington, Benoit Mandelbrot, Brownian motion, Chance favours the prepared mind, cognitive dissonance, computer age, computer vision, dematerialisation, Donald Trump, Douglas Hofstadter, Ernest Rutherford, experimental subject, Flynn Effect, Georg Cantor, Gerolamo Cardano, Golden Gate Park, haute couture, haute cuisine, Henri Poincaré, Isaac Newton, l'esprit de l'escalier, Louis Pasteur, Mahatma Gandhi, mandelbrot fractal, Menlo Park, Norbert Wiener, place-making, Sapir-Whorf hypothesis, Silicon Valley, statistical model, Steve Jobs, Steve Wozniak, theory of mind, upwardly mobile, urban sprawl, yellow journalism, zero-sum game
.), and mathematicians in the early twentieth century who were interested in abstract spaces — especially the German mathematician Felix Haussdorff — came up with ways to generalize the concept of dimensionality, thus leading to the idea of spaces having, say, 0.73 dimensions or even π dimensions. These discoveries later turned out to be ideally suited for characterizing the dimensionality of “fractal objects”, as they were dubbed by the Franco–Polish mathematician Benoît Mandelbrot. After such richness, one might easily presume that there must be spaces having a negative or imaginary number of dimensions — but oddly enough, despite the appeal of the idea, this notion has not yet been explored, or at any rate, if it has, we are ignorant of the fact. But the mindset of today’s mathematicians is so generalization-prone that even the hint of such an idea might just launch an eager quest for all the beautiful new abstract worlds that are implicit in the terms.
The Sum of All Fears by Tom Clancy
accounting loophole / creative accounting, airport security, Benoit Mandelbrot, British Empire, colonial exploitation, complexity theory, cuban missile crisis, demand response, financial independence, index card, mandelbrot fractal, trade route, uranium enrichment
The KGB's Eighth Chief Directorate is tasked to communications intelligence and communications security. It has a long and distinguished history that has benefited from another traditional Russian strength, a fascination with theoretical mathematics. The relationship between ciphers and mathematics is a logical one, and the most recent manifestation of this was the work of a bearded, thirtyish gnome of a man who was fascinated with the work of Benoit Mandelbrot at Harvard University, the man who had effectively invented fractal geometry. Uniting this work with that of MacKenzie's work on Chaos Theory at Cambridge University in England, the young Russian genius had invented a genuinely new theoretical way of looking at mathematical formulae. It was generally conceded by that handful of people who understood what he was talking about that his work was easily worth a Planck Medal.
The Man Who Knew: The Life and Times of Alan Greenspan by Sebastian Mallaby
airline deregulation, airport security, Andrei Shleifer, anti-communist, Asian financial crisis, balance sheet recession, bank run, barriers to entry, Benoit Mandelbrot, Bretton Woods, central bank independence, centralized clearinghouse, collateralized debt obligation, conceptual framework, corporate governance, correlation does not imply causation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency peg, energy security, equity premium, fiat currency, financial deregulation, financial innovation, fixed income, Flash crash, forward guidance, full employment, Hyman Minsky, inflation targeting, information asymmetry, interest rate swap, inventory management, invisible hand, Kenneth Rogoff, Kitchen Debate, laissez-faire capitalism, Long Term Capital Management, low skilled workers, market bubble, market clearing, Martin Wolf, money market fund, moral hazard, mortgage debt, Myron Scholes, new economy, Nixon shock, Northern Rock, paper trading, paradox of thrift, Paul Samuelson, Plutocrats, plutocrats, popular capitalism, price stability, RAND corporation, rent-seeking, Robert Shiller, Robert Shiller, rolodex, Ronald Reagan, Saturday Night Live, savings glut, secular stagnation, short selling, The Great Moderation, the payments system, The Wealth of Nations by Adam Smith, too big to fail, trade liberalization, unorthodox policies, upwardly mobile, WikiLeaks, women in the workforce, Y2K, yield curve, zero-sum game
At that time, the fathers of modern portfolio theory confronted a highly inconvenient truth: contrary to their efficient-market assumptions, price changes in asset markets do not follow the “normal distribution” depicted by a bell curve; rather, very large price moves occur far more frequently than the thin tails of the bell curve anticipate. At first the efficient marketers responded open-mindedly to this objection, acknowledging that its main proponent, the maverick mathematician Benoit Mandelbrot, was right. But then they swept Mandelbrot’s protests under the carpet because his message was too difficult to live with. Deprived of their bell-curve assumption, the efficient marketers’ mathematical techniques would cease to work. “Mandelbrot, like Prime Minister Churchill before him, promises us not utopia but blood, sweat, toil and tears,” Paul Cootner, an efficient marketer, objected.