Benoit Mandelbrot

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pages: 396 words: 112,748

Chaos: Making a New Science by James Gleick

Benoit Mandelbrot, business cycle, butterfly effect, cellular automata, Claude Shannon: information theory, discrete time, Edward Lorenz: Chaos theory, experimental subject, Georg Cantor, Henri Poincaré, Herbert Marcuse, Isaac Newton, iterative process, John von Neumann, Louis Pasteur, mandelbrot fractal, military-industrial complex, Murray Gell-Mann, Norbert Wiener, pattern recognition, power law, Richard Feynman, scientific management, 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.

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.

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.


pages: 461 words: 128,421

The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street by Justin Fox

"Friedman doctrine" OR "shareholder theory", Abraham Wald, activist fund / activist shareholder / activist investor, Alan Greenspan, Albert Einstein, Andrei Shleifer, AOL-Time Warner, asset allocation, asset-backed security, bank run, beat the dealer, behavioural economics, Benoit Mandelbrot, Big Tech, Black Monday: stock market crash in 1987, Black-Scholes formula, book value, Bretton Woods, Brownian motion, business cycle, buy and hold, capital asset pricing model, card file, Carl Icahn, Cass Sunstein, collateralized debt obligation, compensation consultant, complexity theory, corporate governance, corporate raider, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, democratizing finance, Dennis Tito, discovery of the americas, diversification, diversified portfolio, Dr. Strangelove, Edward Glaeser, Edward Thorp, endowment effect, equity risk premium, Eugene Fama: efficient market hypothesis, experimental economics, financial innovation, Financial Instability Hypothesis, fixed income, floating exchange rates, George Akerlof, Glass-Steagall Act, Henri Poincaré, Hyman Minsky, implied volatility, impulse control, index arbitrage, index card, index fund, information asymmetry, invisible hand, Isaac Newton, John Bogle, John Meriwether, John Nash: game theory, John von Neumann, joint-stock company, Joseph Schumpeter, junk bonds, Kenneth Arrow, libertarian paternalism, linear programming, Long Term Capital Management, Louis Bachelier, low interest rates, mandelbrot fractal, market bubble, market design, Michael Milken, Myron Scholes, New Journalism, Nikolai Kondratiev, Paul Lévy, Paul Samuelson, pension reform, performance metric, Ponzi scheme, power law, prediction markets, proprietary trading, prudent man rule, 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, rolodex, Ronald Reagan, seminal paper, shareholder value, Sharpe ratio, short selling, side project, Silicon Valley, Skinner box, Social Responsibility of Business Is to Increase Its Profits, South Sea Bubble, statistical model, stocks for the long run, tech worker, 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, Two Sigma, Tyler Cowen, 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.

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.

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.


pages: 374 words: 114,600

The Quants by Scott Patterson

Alan Greenspan, Albert Einstein, AOL-Time Warner, asset allocation, automated trading system, Bear Stearns, beat the dealer, Benoit Mandelbrot, Bernie Madoff, Bernie Sanders, Black Monday: stock market crash in 1987, Black Swan, Black-Scholes formula, Blythe Masters, Bonfire of the Vanities, book value, Brownian motion, buttonwood tree, buy and hold, buy low sell high, capital asset pricing model, Carl Icahn, 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, Dr. Strangelove, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial engineering, Financial Modelers Manifesto, fixed income, Glass-Steagall Act, global macro, 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, Jim Simons, job automation, John Meriwether, John Nash: game theory, junk bonds, Kickstarter, law of one price, Long Term Capital Management, Louis Bachelier, low interest rates, mandelbrot fractal, margin call, Mark Spitznagel, merger arbitrage, Michael Milken, military-industrial complex, money market fund, Myron Scholes, NetJets, new economy, offshore financial centre, old-boy network, Paul Lévy, Paul Samuelson, Ponzi scheme, proprietary trading, quantitative hedge fund, quantitative trading / quantitative finance, race to the bottom, random walk, Renaissance Technologies, risk-adjusted returns, Robert Mercer, Rod Stewart played at Stephen Schwarzman birthday party, Ronald Reagan, Savings and loan crisis, Sergey Aleynikov, short selling, short squeeze, 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

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.

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 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 Fractalist by Benoit Mandelbrot

Albert Einstein, Benoit Mandelbrot, Brownian motion, business cycle, Claude Shannon: information theory, discrete time, double helix, financial engineering, Georg Cantor, Henri Poincaré, Honoré de Balzac, illegal immigration, Isaac Newton, iterative process, Johannes Kepler, John von Neumann, linear programming, Louis Bachelier, Louis Blériot, Louis Pasteur, machine translation, mandelbrot fractal, New Journalism, Norbert Wiener, Olbers’ paradox, Paul Lévy, power law, Richard Feynman, statistical model, urban renewal, Vilfredo Pareto

Copyright © 2012 by The Estate of Benoit Mandelbrot Afterword copyright © by Michael Frame All rights reserved. Published in the United States by Pantheon Books, a division of Random House, Inc., New York, and in Canada by Random House of Canada Limited, Toronto. Pantheon Books and colophon are registered trademarks of Random House, Inc. Library of Congress Cataloging-in-Publication Data Mandelbrot, Benoit B. The fractalist : memoir of a scientific maverick / Benoit Mandelbrot. p. cm. eISBN: 978-0-307-37860-6 1. Mandelbrot, Benoit B. 2. Mathematicians—France—Biography. 3. Fractals. I.

I. Title. QA29.M34A3 2012 510.92—dc22 [B] 2012017896 www.pantheonbooks.com Cover image Benoit Mandelbrot. Emilio Segre Visual Archives/American Institute of Physics/Photo Researchers, Inc. Cover design by Peter Mendelsund v3.1 My long, meandering ride through life has been lonely and often very rough. Without loving help, it would have been short, nasty, and unproductive. But I have been lucky. Father and Mother taught me the art of survival. Uncle took me as an unruly but grateful student. Aliette later joined them, and she, our sons, and our grandchildren taught me how to smile.

He smiled and answered, “What a surprise. Nice to see you. Of course I remember you.” I breathed again—he would not tell on me. My papers cautiously downgraded my baccalaureate from its dangerously conspicuous summa to an adequate magna. One day, a student approached. “I hear that you come from Tulle. You must have known Benoit Mandelbrot.” “Of course, of course, I know him well.” “Is it true that he is un crack who got a summa at the bachot?” Back in 1944, “crack” was French slang for a high achiever. Imagine my panic. Did the student suspect the truth? Was he testing me? Trembling and with feigned nonchalance, I started telling stories about myself, how stressful it had been for “me,” a mere future magna, to be in the same classroom as “that guy.”


pages: 436 words: 127,642

When Einstein Walked With Gödel: Excursions to the Edge of Thought by Jim Holt

Ada Lovelace, Albert Einstein, Andrew Wiles, anthropic principle, anti-communist, Arthur Eddington, Benoit Mandelbrot, Bletchley Park, Brownian motion, cellular automata, Charles Babbage, classic study, computer age, CRISPR, dark matter, David Brooks, Donald Trump, Dr. Strangelove, Eddington experiment, Edmond Halley, everywhere but in the productivity statistics, Fellow of the Royal Society, four colour theorem, Georg Cantor, George Santayana, Gregor Mendel, haute couture, heat death of the universe, Henri Poincaré, Higgs boson, inventory management, Isaac Newton, Jacquard loom, Johannes Kepler, John von Neumann, Joseph-Marie Jacquard, Large Hadron Collider, Long Term Capital Management, Louis Bachelier, luminiferous ether, Mahatma Gandhi, mandelbrot fractal, Monty Hall problem, Murray Gell-Mann, new economy, Nicholas Carr, Norbert Wiener, Norman Macrae, Paradox of Choice, Paul Erdős, Peter Singer: altruism, Plato's cave, power law, probability theory / Blaise Pascal / Pierre de Fermat, quantum entanglement, random walk, Richard Feynman, Robert Solow, Schrödinger's Cat, scientific worldview, Search for Extraterrestrial Intelligence, selection bias, Skype, stakhanovite, Stephen Hawking, Steven Pinker, Thorstein Veblen, Turing complete, Turing machine, Turing test, union organizing, Vilfredo Pareto, Von Neumann architecture, wage slave

., Touchstone, 1986). 7. THE AVATARS OF HIGHER MATHEMATICS G. H. Hardy, A Mathematician’s Apology (Cambridge, 1940). Michael Harris, Mathematics Without Apologies: Portrait of a Problematic Vocation (Princeton, 2015). 8. BENOIT MANDELBROT AND THE DISCOVERY OF FRACTALS Benoit Mandelbrot, The Fractalist: Memoir of a Scientific Maverick (Pantheon, 2012). Benoit Mandelbrot and Richard L. Hudson, The (Mis)behavior of Markets: A Fractal View of Financial Turbulence (Basic, 2006). 9. GEOMETRICAL CREATURES Edwin A. Abbott, The Annotated Flatland: A Romance of Many Dimensions, with an introduction and notes by Ian Stewart (Perseus, 2002).

Indeed, the discovery of such an inconsistency would be fatal to pure mathematics, at least as we know it today. The distinction between truth and falsehood would be breached, the ladder of avatars would come crashing down, and the One Big Theorem would take a truly terrible form: 0 = 1. Yet, oddly enough, e-commerce and financial derivatives would be left untouched. 8 Benoit Mandelbrot and the Discovery of Fractals Benoit Mandelbrot, the brilliant Polish-French-American mathematician who died in 2010, had a poet’s taste for complexity and strangeness. His genius for noticing deep links among far-flung phenomena led him to create a new branch of geometry, one that has deepened our understanding of both natural forms and patterns of human behavior.

Simon Blackburn, Truth: A Guide (Oxford, 2005). Richard Rorty, Truth and Progress: Philosophical Papers, vol. 3 (Cambridge, 1998). Acknowledgments The longer essays in this volume previously appeared, in somewhat different form, in the following publications: “A Mathematical Romance,” “The Avatars of Higher Mathematics,” “Benoit Mandelbrot and the Discovery of Fractals,” “Geometrical Creatures,” “A Comedy of Colors,” “The Dangerous Idea of the Infinitesimal,” “Dr. Strangelove Makes a Thinking Machine,” and “Einstein, ‘Spooky Action,’ and the Reality of Space” in The New York Review of Books; “When Einstein Walked with Gödel,” “Numbers Guy: The Neuroscience of Math,” “Sir Francis Galton, the Father of Statistics … and Eugenics,” “Infinite Visions: Georg Cantor v.


pages: 338 words: 106,936

The Physics of Wall Street: A Brief History of Predicting the Unpredictable by James Owen Weatherall

Alan Greenspan, Albert Einstein, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Apollo 11, Asian financial crisis, bank run, Bear Stearns, beat the dealer, behavioural economics, Benoit Mandelbrot, Black Monday: stock market crash in 1987, Black Swan, Black-Scholes formula, Bonfire of the Vanities, book value, Bretton Woods, Brownian motion, business cycle, butterfly effect, buy and hold, capital asset pricing model, Carmen Reinhart, Claude Shannon: information theory, coastline paradox / Richardson effect, collateralized debt obligation, collective bargaining, currency risk, dark matter, Edward Lorenz: Chaos theory, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial engineering, financial innovation, Financial Modelers Manifesto, fixed income, George Akerlof, Gerolamo Cardano, Henri Poincaré, invisible hand, Isaac Newton, iterative process, Jim Simons, John Nash: game theory, junk bonds, Kenneth Rogoff, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, Market Wizards by Jack D. Schwager, martingale, Michael Milken, military-industrial complex, Myron Scholes, Neil Armstrong, new economy, Nixon triggered the end of the Bretton Woods system, Paul Lévy, Paul Samuelson, power law, prediction markets, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk free rate, risk-adjusted returns, Robert Gordon, Robert Shiller, Ronald Coase, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, statistical arbitrage, statistical model, stochastic process, Stuart Kauffman, The Chicago School, The Myth of the Rational Market, tulip mania, Vilfredo Pareto, volatility smile

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.

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.

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.


pages: 283 words: 81,376

The Doomsday Calculation: How an Equation That Predicts the Future Is Transforming Everything We Know About Life and the Universe by William Poundstone

Albert Einstein, anthropic principle, Any sufficiently advanced technology is indistinguishable from magic, Arthur Eddington, Bayesian statistics, behavioural economics, Benoit Mandelbrot, Berlin Wall, bitcoin, Black Swan, conceptual framework, cosmic microwave background, cosmological constant, cosmological principle, CRISPR, cuban missile crisis, dark matter, DeepMind, digital map, discounted cash flows, Donald Trump, Doomsday Clock, double helix, Dr. Strangelove, Eddington experiment, Elon Musk, Geoffrey Hinton, Gerolamo Cardano, Hans Moravec, heat death of the universe, Higgs boson, if you see hoof prints, think horses—not zebras, index fund, Isaac Newton, Jaron Lanier, Jeff Bezos, John Markoff, John von Neumann, Large Hadron Collider, mandelbrot fractal, Mark Zuckerberg, Mars Rover, Neil Armstrong, Nick Bostrom, OpenAI, paperclip maximiser, Peter Thiel, Pierre-Simon Laplace, Plato's cave, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, Richard Feynman, ride hailing / ride sharing, Rodney Brooks, Ronald Reagan, Ronald Reagan: Tear down this wall, Sam Altman, Schrödinger's Cat, Search for Extraterrestrial Intelligence, self-driving car, Silicon Valley, Skype, Stanislav Petrov, Stephen Hawking, strong AI, tech billionaire, Thomas Bayes, Thomas Malthus, time value of money, Turing test

To the right of Mitchell, though easily missed, is the familiar face of Albert Einstein, shown in profile. The speeding rocket and slow-growing hemlock allude to Einstein’s thought experiments of racing trains and light beams, used to develop his theory of relativity. Standing in front of Einstein is Benoit Mandelbrot, the IBM mathematician who described the concept of fractals. The hemlock tree and rocket blast are fractals, complex shapes in which each part resembles the whole. Zeno of Elea, a Greek philosopher whose features are known from ancient busts, dangles a cigarette. Zeno propounded the paradox of Achilles and the Tortoise.

“According to a law established and promulgated by bald-headed, cigar-chomping know-it-alls who foregather every night at [New York deli] Lindy’s… the life expectancy of a television comedian is proportional to the total amount of his exposure on the medium.” Many comics who score a Tonight Show shot are soon forgotten, but it’s safe to assume that Jerry Seinfeld will be around awhile. Mathematician Benoit Mandelbrot came across Lindy’s law and wrote about it, saying that it applies to many things other than show business. That was Gott’s point. Before I heard of the Copernican method, I formulated a semiserious law for waiting on hold to speak to a customer support agent. Your future wait to speak to a live human is approximately equal to however long you’ve already waited.

The reason, says Caves, is scale invariance. We need to be dealing with a process that has no characteristic time scale or lifespan, or at any rate, none that we know about. Fractals and Scale Invariance “Scale invariance” may be an unfamiliar term. Here’s one more likely to ring a bell: “fractal.” That word was coined by Benoit Mandelbrot to describe the fascinating unruliness of nature. Coastlines, snowflakes, clouds, and landscapes resist the straitjackets of Euclidean geometry. A coastline is not a “line.” A snowflake is not a hexagon. The defining quality of a fractal is scale invariance, or self-similarity. When a picture or diagram or chart of a fractal is zoomed in or out, its crinkly detail looks pretty much the same.


pages: 256 words: 60,620

Think Twice: Harnessing the Power of Counterintuition by Michael J. Mauboussin

affirmative action, Alan Greenspan, asset allocation, Atul Gawande, availability heuristic, Benoit Mandelbrot, Bernie Madoff, Black Swan, butter production in bangladesh, Cass Sunstein, choice architecture, Clayton Christensen, cognitive dissonance, collateralized debt obligation, Daniel Kahneman / Amos Tversky, deliberate practice, disruptive innovation, Edward Thorp, experimental economics, financial engineering, financial innovation, framing effect, fundamental attribution error, Geoffrey West, Santa Fe Institute, George Akerlof, hindsight bias, hiring and firing, information asymmetry, libertarian paternalism, Long Term Capital Management, loose coupling, loss aversion, mandelbrot fractal, Menlo Park, meta-analysis, money market fund, Murray Gell-Mann, Netflix Prize, pattern recognition, Performance of Mutual Funds in the Period, Philip Mirowski, placebo effect, Ponzi scheme, power law, prediction markets, presumed consent, Richard Thaler, Robert Shiller, statistical model, Steven Pinker, systems thinking, the long tail, The Wisdom of Crowds, ultimatum game, vertical integration

Taleb, The Black Swan, discusses a similar concept he calls the “ludic fallacy.” 15. Donald MacKenzie, An Engine, Not a Camera: How Financial Models Shape Markets (Cambridge: MIT Press, 2006). 16. Benoit Mandelbrot, “The Variation of Certain Speculative Prices,” in The Random Character of Stock Market Prices, ed. Paul H. Cootner, (Cambridge: MIT Press, 1964), 369–412. This is also a core theme of Taleb, The Black Swan. See also Benoit Mandelbrot and Richard L. Hudson, The (Mis)Behavior of Markets (New York: Basic Books, 2004). 17. Paul H. Cootner, “Comments on The Variation of Certain Speculative Prices,” in Cootner, The Random Character of Stock Market Prices, 413–418. 18.

If you have ever heard a financial expert refer to the stock market using terms like alpha, beta, or standard deviation, you have witnessed reductive bias in action. Most economists characterize markets using simpler, but wrong, price-change distributions. A number of high-profile financial blowups, including Long-Term Capital Management, show the danger of this bias.15 Benoit Mandelbrot, a French mathematician and the father of fractal geometry, was one of the earliest and most vocal critics of using normal distributions to explain how asset prices move.16 His chapter in The Random Character of Stock Market Prices, published in 1964, created a stir because it demonstrated that asset price changes were much more extreme than previous models had assumed.


Turing's Cathedral by George Dyson

1919 Motor Transport Corps convoy, Abraham Wald, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anti-communist, Benoit Mandelbrot, Bletchley Park, British Empire, Brownian motion, cellular automata, Charles Babbage, cloud computing, computer age, Computing Machinery and Intelligence, Danny Hillis, dark matter, double helix, Dr. Strangelove, fault tolerance, Fellow of the Royal Society, finite state, Ford Model T, Georg Cantor, Henri Poincaré, Herman Kahn, housing crisis, IFF: identification friend or foe, indoor plumbing, Isaac Newton, Jacquard loom, John von Neumann, machine readable, mandelbrot fractal, Menlo Park, Murray Gell-Mann, Neal Stephenson, Norbert Wiener, Norman Macrae, packet switching, pattern recognition, Paul Erdős, Paul Samuelson, phenotype, planetary scale, RAND corporation, random walk, Richard Feynman, SETI@home, social graph, speech recognition, The Theory of the Leisure Class by Thorstein Veblen, Thorstein Veblen, Turing complete, Turing machine, Von Neumann architecture

Archivists Christine Di Bella, Erica Mosner, and all the staff at the Institute, especially Linda Cooper, helped in every capacity, and the current trustees, especially Jeffrey Bezos, have lent continuing encouragement and support. Many of the surviving eyewitnesses—including Alice Bigelow, Julian Bigelow, Andrew and Kathleen Booth, Raoul Bott, Martin and Virginia Davis, Akrevoe Kondopria Emmanouilides, Gerald and Thelma Estrin, Benoît Mandelbrot, Harris Mayer, Jack Rosenberg, Atle Selberg, Joseph and Margaret Smagorinsky, Françoise Ulam, Nicholas Vonneumann, Willis Ware, and Marina von Neumann Whitman—took time to speak with me. “You’re within about five years of not having a testifiable witness,” Joseph Smagorinsky warned me in 2004.

Verena Huber-Dyson (1923–): Swiss American logician and group theorist; arrived at the IAS as a postdoctoral fellow in 1948. James Brown Horner (Desmond) Kuper (1909–1992): American physicist and second husband of Mariette (Kovesi) von Neumann. Herbert H. Maass (1878–1957): Attorney and founding trustee of the IAS. Benoît Mandelbrot (1924–2010): Polish-born French American mathematician; invited by von Neumann to the IAS to study word frequency distributions in 1953. John W. Mauchly (1907–1980): American physicist, electrical engineer, and cofounder of the ENIAC project. Harris Mayer (1921–): American Manhattan Project physicist and collaborator with Edward Teller and John von Neumann.

They tended more to think of it as a lifetime fellowship for themselves.” Veblen, adds Montgomery, “said he and Einstein and Weyl didn’t feel up to that.”49 The other Institute was the annually changing group of mostly young visitors at the beginning of their careers, interspersed with occasional established scholars taking a year off. Benoît Mandelbrot, who arrived at von Neumann’s invitation in the fall of 1953 to begin a study of word frequency distributions (sampling the occurrence of probably, sex, and Africa) that would lead to the field known as fractals, notes that the Institute “had a clear purpose and a rather strange structure in which to assemble people: heavenly bodies in residence, and then nobody, nobody, nobody, and then mostly young people.


pages: 484 words: 136,735

Capitalism 4.0: The Birth of a New Economy in the Aftermath of Crisis by Anatole Kaletsky

"World Economic Forum" Davos, Alan Greenspan, bank run, banking crisis, Bear Stearns, behavioural economics, Benoit Mandelbrot, Berlin Wall, Black Swan, bond market vigilante , bonus culture, Bretton Woods, BRICs, business cycle, buy and hold, Carmen Reinhart, classic study, cognitive dissonance, collapse of Lehman Brothers, Corn Laws, correlation does not imply causation, creative destruction, credit crunch, currency manipulation / currency intervention, currency risk, David Ricardo: comparative advantage, deglobalization, Deng Xiaoping, eat what you kill, Edward Glaeser, electricity market, 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, foreign exchange controls, full employment, geopolitical risk, George Akerlof, global rebalancing, Goodhart's law, Great Leap Forward, Hyman Minsky, income inequality, information asymmetry, invisible hand, Isaac Newton, Joseph Schumpeter, Kenneth Arrow, Kenneth Rogoff, Kickstarter, laissez-faire capitalism, long and variable lags, Long Term Capital Management, low interest rates, mandelbrot fractal, market design, market fundamentalism, Martin Wolf, military-industrial complex, Minsky moment, Modern Monetary Theory, Money creation, money market fund, moral hazard, mortgage debt, Nelson Mandela, new economy, Nixon triggered the end of the Bretton Woods system, Northern Rock, offshore financial centre, oil shock, paradox of thrift, Pareto efficiency, Paul Samuelson, Paul Volcker talking about ATMs, 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 Solow, Ronald Reagan, Savings and loan crisis, seminal paper, shareholder value, short selling, South Sea Bubble, sovereign wealth fund, special drawing rights, statistical model, systems thinking, 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.

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.


pages: 545 words: 137,789

How Markets Fail: The Logic of Economic Calamities by John Cassidy

Abraham Wald, Alan Greenspan, Albert Einstein, An Inconvenient Truth, Andrei Shleifer, anti-communist, AOL-Time Warner, asset allocation, asset-backed security, availability heuristic, bank run, banking crisis, Bear Stearns, behavioural economics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Black Monday: stock market crash in 1987, Black-Scholes formula, Blythe Masters, book value, Bretton Woods, British Empire, business cycle, capital asset pricing model, carbon tax, Carl Icahn, 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, different worldview, diversification, Elliott wave, Eugene Fama: efficient market hypothesis, financial deregulation, financial engineering, financial innovation, Financial Instability Hypothesis, financial intermediation, full employment, Garrett Hardin, George Akerlof, Glass-Steagall Act, 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, junk bonds, Kenneth Arrow, Kickstarter, laissez-faire capitalism, Landlord’s Game, liquidity trap, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, low interest rates, mandelbrot fractal, margin call, market bubble, market clearing, mental accounting, Mikhail Gorbachev, military-industrial complex, Minsky moment, money market fund, Mont Pelerin Society, moral hazard, mortgage debt, Myron Scholes, Naomi Klein, negative equity, Network effects, Nick Leeson, Nixon triggered the end of the Bretton Woods system, Northern Rock, paradox of thrift, Pareto efficiency, Paul Samuelson, Phillips curve, Ponzi scheme, precautionary principle, price discrimination, price stability, principal–agent problem, profit maximization, proprietary trading, 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 Solow, Ronald Coase, Ronald Reagan, Savings and loan crisis, shareholder value, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, statistical model, subprime mortgage crisis, tail risk, Tax Reform Act of 1986, technology bubble, The Chicago School, The Great Moderation, The Market for Lemons, The Wealth of Nations by Adam Smith, too big to fail, Tragedy of the Commons, transaction costs, Two Sigma, unorthodox policies, value at risk, Vanguard fund, Vilfredo Pareto, wealth creators, zero-sum game

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.

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.

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.


pages: 381 words: 101,559

Currency Wars: The Making of the Next Gobal Crisis by James Rickards

"World Economic Forum" Davos, Alan Greenspan, Asian financial crisis, bank run, Bear Stearns, behavioural economics, Benoit Mandelbrot, Berlin Wall, Big bang: deregulation of the City of London, Black Swan, borderless world, Bretton Woods, BRICs, British Empire, business climate, buy and hold, capital controls, Carmen Reinhart, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, cross-border payments, currency manipulation / currency intervention, currency peg, currency risk, Daniel Kahneman / Amos Tversky, deal flow, Deng Xiaoping, diversification, diversified portfolio, Dr. Strangelove, 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, Great Leap Forward, guns versus butter model, high net worth, income inequality, interest rate derivative, it's over 9,000, John Meriwether, Kenneth Rogoff, laissez-faire capitalism, liquidity trap, Long Term Capital Management, low interest rates, mandelbrot fractal, margin call, market bubble, Mexican peso crisis / tequila crisis, Money creation, money market fund, money: store of value / unit of account / medium of exchange, Myron Scholes, Network effects, New Journalism, Nixon shock, Nixon triggered the end of the Bretton Woods system, offshore financial centre, oil shock, one-China policy, open economy, paradox of thrift, Paul Samuelson, power law, price mechanism, price stability, private sector deleveraging, proprietary trading, quantitative easing, race to the bottom, RAND corporation, rent-seeking, reserve currency, Ronald Reagan, short squeeze, sovereign wealth fund, special drawing rights, special economic zone, subprime mortgage crisis, 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, vertical integration, War on Poverty, Washington Consensus, zero-sum game

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.

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.”


pages: 651 words: 180,162

Antifragile: Things That Gain From Disorder by Nassim Nicholas Taleb

"World Economic Forum" Davos, Air France Flight 447, Alan Greenspan, Andrei Shleifer, anti-fragile, banking crisis, Benoit Mandelbrot, Berlin Wall, biodiversity loss, Black Swan, business cycle, caloric restriction, caloric restriction, Chuck Templeton: OpenTable:, commoditize, creative destruction, credit crunch, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discrete time, double entry bookkeeping, Emanuel Derman, epigenetics, fail fast, financial engineering, financial independence, Flash crash, flying shuttle, Gary Taubes, George Santayana, Gini coefficient, Helicobacter pylori, Henri Poincaré, Higgs boson, high net worth, hygiene hypothesis, Ignaz Semmelweis: hand washing, informal economy, invention of the wheel, invisible hand, Isaac Newton, James Hargreaves, Jane Jacobs, Jim Simons, joint-stock company, joint-stock limited liability company, Joseph Schumpeter, Kenneth Arrow, knowledge economy, language acquisition, Lao Tzu, Long Term Capital Management, loss aversion, Louis Pasteur, mandelbrot fractal, Marc Andreessen, Mark Spitznagel, meta-analysis, microbiome, money market fund, moral hazard, mouse model, Myron Scholes, Norbert Wiener, pattern recognition, Paul Samuelson, placebo effect, Ponzi scheme, Post-Keynesian economics, power law, 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, Rupert Read, selection bias, Silicon Valley, six sigma, spinning jenny, statistical model, Steve Jobs, Steven Pinker, Stewart Brand, stochastic process, stochastic volatility, synthetic biology, tacit knowledge, tail risk, Thales and the olive presses, Thales of Miletus, 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

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.

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.


pages: 348 words: 83,490

More Than You Know: Finding Financial Wisdom in Unconventional Places (Updated and Expanded) by Michael J. Mauboussin

Alan Greenspan, Albert Einstein, Andrei Shleifer, Atul Gawande, availability heuristic, beat the dealer, behavioural economics, Benoit Mandelbrot, Black Swan, Brownian motion, butter production in bangladesh, buy and hold, capital asset pricing model, Clayton Christensen, clockwork universe, complexity theory, corporate governance, creative destruction, Daniel Kahneman / Amos Tversky, deliberate practice, demographic transition, discounted cash flows, disruptive innovation, diversification, diversified portfolio, dogs of the Dow, Drosophila, Edward Thorp, en.wikipedia.org, equity premium, equity risk premium, Eugene Fama: efficient market hypothesis, fixed income, framing effect, functional fixedness, hindsight bias, hiring and firing, Howard Rheingold, index fund, information asymmetry, intangible asset, invisible hand, Isaac Newton, Jeff Bezos, John Bogle, Kenneth Arrow, Laplace demon, Long Term Capital Management, loss aversion, mandelbrot fractal, margin call, market bubble, Menlo Park, mental accounting, Milgram experiment, Murray Gell-Mann, Nash equilibrium, new economy, Paul Samuelson, Performance of Mutual Funds in the Period, Pierre-Simon Laplace, power law, quantitative trading / quantitative finance, random walk, Reminiscences of a Stock Operator, Richard Florida, Richard Thaler, Robert Shiller, shareholder value, statistical model, Steven Pinker, stocks for the long run, Stuart Kauffman, survivorship bias, systems thinking, The Wisdom of Crowds, transaction costs, traveling salesman, value at risk, wealth creators, women in the workforce, zero-sum game

However, a run of thirty provides a $1.1 billion payoff, but this is only a 1-in-1.1 billion probability. Lots of small events and a few very large events characterize a fractal system. Further, the average winnings per game is unstable with the St. Petersburg game, so no average accurately describes the game’s long-term outcome. Are stock market returns fractal? Benoit Mandelbrot shows that by lengthening or shortening the horizontal axis of a price series—effectively speeding up or slowing down time—price series are indeed fractal. Not only are rare large changes interspersed with lots of smaller ones, the price changes look similar at various scales (e.g., daily, weekly, and monthly returns).

If the largest city, Madrid, has 3 million inhabitants, the second-largest city, Barcelona, has one-half as many, the third-largest city, Valencia, one-third as many, and so forth. Zipf’s law does describe some systems well, but is too narrow to describe the variety of systems that exhibit power laws. The brilliant polymath Benoit Mandelbrot showed that two modifications to Zipf’s law make it possible to obtain a more general power law.5 The first modification is to add a constant to the rank. This changes the sequence to 1/(1 + constant), 1/(2 + constant), 1/(3 + constant), etc. The second modification is to add a constant to the power of 1 in the denominator.

The pictures will only get better with time. • Statistical properties of markets—from description to prediction? When describing markets, financial economists generally assume a definable tradeoff between risk and reward. Unfortunately, the empirical record defies a simple risk-reward relationship. As Benoit Mandelbrot has argued, failure to explain is caused by failure to describe.Starting in earnest with Mandelbrot’s work in finance in the early 1960s, statistical studies have shown that stock price changes are not distributed along a bell-shaped curve but rather follow a power law.1 Practitioners acknowledged this fact long ago and have modified their models—even if through intuition—to accommodate this reality.


pages: 476 words: 121,460

The Man From the Future: The Visionary Life of John Von Neumann by Ananyo Bhattacharya

Ada Lovelace, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Alvin Roth, Andrew Wiles, Benoit Mandelbrot, business cycle, cellular automata, Charles Babbage, Claude Shannon: information theory, clockwork universe, cloud computing, Conway's Game of Life, cuban missile crisis, Daniel Kahneman / Amos Tversky, DeepMind, deferred acceptance, double helix, Douglas Hofstadter, Dr. Strangelove, From Mathematics to the Technologies of Life and Death, Georg Cantor, Greta Thunberg, Gödel, Escher, Bach, haute cuisine, Herman Kahn, indoor plumbing, Intergovernmental Panel on Climate Change (IPCC), Isaac Newton, Jacquard loom, Jean Tirole, John Conway, John Nash: game theory, John von Neumann, Kenneth Arrow, Kickstarter, linear programming, mandelbrot fractal, meta-analysis, mutually assured destruction, Nash equilibrium, Norbert Wiener, Norman Macrae, P = NP, Paul Samuelson, quantum entanglement, RAND corporation, Ray Kurzweil, Richard Feynman, Ronald Reagan, Schrödinger's Cat, second-price auction, side project, Silicon Valley, spectrum auction, Steven Levy, Strategic Defense Initiative, technological singularity, Turing machine, Von Neumann architecture, zero-sum game

Von Neumann receives his Medal of Freedom from President Eisenhower. Cancer had come at a particularly cruel time. The truth was that von Neumann had been unhappy at the IAS for several years before his death. ‘Von Neumann, when I was there at Princeton, was under extreme pressure,’ says Benoît Mandelbrot, who had come to the IAS in 1953 at von Neumann’s invitation, ‘from mathematicians, who were despising him for no longer being a mathematician; by the physicists, who were despising him for never having been a real physicist; and by everybody for having brought to Princeton this collection of low-class individuals called “programmers”’.

‘He was always gentle, always kind, always penetrating and always magnificently lucid.’3 Shy of revealing too much of himself, his good deeds were quietly done behind people’s backs. When a Hungarian-speaking factory worker in Tennessee wrote to him in 1939 asking how he could learn secondary school mathematics, von Neumann asked his friend Ortvay to send school books.4 Benoît Mandelbrot, whose stay at the IAS had been sponsored by von Neumann, unexpectedly found himself in his debt again many years later. Sometime after von Neumann’s death, prompted by a clash of personalities with his manager at IBM, Mandelbrot went looking for a new job – and found that the way had been made easier for him.

Stan isław Ulam,’John von Neumann 1903–1957’, Bulletin of the American Mathematical Society, 64(3) (1958), pp. 1–49. 100. John von Neumann, Documentary Mathematical Association of America, 1966. Many thanks to David Hoffman, the film’s producer, for sending me the DVD in 2019. Now available to watch here: https://archive.org/details/JohnVonNeumannY2jiQXI6nrE. 101. Macrae, John von Neumann. 102. ‘Benoît Mandelbrot – Post-doctoral Studies: Weiner and Von Neumann (36/144)’, Web of Stories – Life Stories of Remarkable People, https://www.youtube.com/watch?v=U9kw6Reml6s. 103. https://rjlipton.wpcomstaging.com/the-gdel-letter/. Also see Richard J. Lipton, 2010, The P=NP Question and Gödel’s Lost Letter, Springer, New York. 104.


pages: 578 words: 168,350

Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies by Geoffrey West

"World Economic Forum" Davos, Alfred Russel Wallace, Anthropocene, Anton Chekhov, Benoit Mandelbrot, Black Swan, British Empire, butterfly effect, caloric restriction, caloric restriction, carbon footprint, Cesare Marchetti: Marchetti’s constant, clean water, coastline paradox / Richardson effect, complexity theory, computer age, conceptual framework, continuous integration, corporate social responsibility, correlation does not imply causation, cotton gin, creative destruction, dark matter, Deng Xiaoping, double helix, driverless car, Dunbar number, 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, Great Leap Forward, 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, Large Hadron Collider, Larry Ellison, Lewis Mumford, life extension, Mahatma Gandhi, mandelbrot fractal, Marc Benioff, Marchetti’s constant, Masdar, megacity, Murano, Venice glass, Murray Gell-Mann, New Urbanism, Oklahoma City bombing, Peter Thiel, power law, profit motive, publish or perish, Ray Kurzweil, Richard Feynman, Richard Florida, Salesforce, seminal paper, Silicon Valley, smart cities, Stephen Hawking, Steve Jobs, Stewart Brand, Suez canal 1869, systematic bias, systems thinking, technological singularity, The Coming Technological Singularity, The Death and Life of Great American Cities, the scientific method, the strength of weak ties, time dilation, 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

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.

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.

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.


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The Misbehavior of Markets: A Fractal View of Financial Turbulence by Benoit Mandelbrot, Richard L. Hudson

Alan Greenspan, Albert Einstein, asset allocation, Augustin-Louis Cauchy, behavioural economics, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black Monday: stock market crash in 1987, Black-Scholes formula, British Empire, Brownian motion, business cycle, buy and hold, buy low sell high, capital asset pricing model, carbon-based life, discounted cash flows, diversification, double helix, Edward Lorenz: Chaos theory, electricity market, Elliott wave, equity premium, equity risk premium, Eugene Fama: efficient market hypothesis, Fellow of the Royal Society, financial engineering, 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, power law, price mechanism, quantitative trading / quantitative finance, Ralph Nelson Elliott, RAND corporation, random walk, risk free rate, risk tolerance, 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.

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.

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.


pages: 289 words: 95,046

Chaos Kings: How Wall Street Traders Make Billions in the New Age of Crisis by Scott Patterson

"World Economic Forum" Davos, 2021 United States Capitol attack, 4chan, Alan Greenspan, Albert Einstein, asset allocation, backtesting, Bear Stearns, beat the dealer, behavioural economics, Benoit Mandelbrot, Bernie Madoff, Bernie Sanders, bitcoin, Bitcoin "FTX", Black Lives Matter, Black Monday: stock market crash in 1987, Black Swan, Black Swan Protection Protocol, Black-Scholes formula, blockchain, Bob Litterman, Boris Johnson, Brownian motion, butterfly effect, carbon footprint, carbon tax, Carl Icahn, centre right, clean tech, clean water, collapse of Lehman Brothers, Colonization of Mars, commodity super cycle, complexity theory, contact tracing, coronavirus, correlation does not imply causation, COVID-19, Credit Default Swap, cryptocurrency, Daniel Kahneman / Amos Tversky, decarbonisation, disinformation, diversification, Donald Trump, Doomsday Clock, Edward Lloyd's coffeehouse, effective altruism, Elliott wave, Elon Musk, energy transition, Eugene Fama: efficient market hypothesis, Extinction Rebellion, fear index, financial engineering, fixed income, Flash crash, Gail Bradbrook, George Floyd, global pandemic, global supply chain, Gordon Gekko, Greenspan put, Greta Thunberg, hindsight bias, index fund, interest rate derivative, Intergovernmental Panel on Climate Change (IPCC), Jeff Bezos, Jeffrey Epstein, Joan Didion, John von Neumann, junk bonds, Just-in-time delivery, lockdown, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, Mark Spitznagel, Mark Zuckerberg, market fundamentalism, mass immigration, megacity, Mikhail Gorbachev, Mohammed Bouazizi, money market fund, moral hazard, Murray Gell-Mann, Nick Bostrom, off-the-grid, panic early, Pershing Square Capital Management, Peter Singer: altruism, Ponzi scheme, power law, precautionary principle, prediction markets, proprietary trading, public intellectual, QAnon, quantitative easing, quantitative hedge fund, quantitative trading / quantitative finance, Ralph Nader, Ralph Nelson Elliott, random walk, Renaissance Technologies, rewilding, Richard Thaler, risk/return, road to serfdom, Ronald Reagan, Ronald Reagan: Tear down this wall, Rory Sutherland, Rupert Read, Sam Bankman-Fried, Silicon Valley, six sigma, smart contracts, social distancing, sovereign wealth fund, statistical arbitrage, statistical model, stem cell, Stephen Hawking, Steve Jobs, Steven Pinker, Stewart Brand, systematic trading, tail risk, technoutopianism, The Chicago School, The Great Moderation, the scientific method, too big to fail, transaction costs, University of East Anglia, value at risk, Vanguard fund, We are as Gods, Whole Earth Catalog

Someone told her the exotic-looking bearded gentleman in the studio had written a book about randomness. Curious, she approached him. When she discovered he was a trader, she declared she was against the market system and stomped away as Taleb sputtered in confusion. Later that day, Taleb met a man he’d soon come to idolize: Benoit Mandelbrot. The maverick French mathematician, inventor of fractal geometry, and pioneer of chaos theory, was giving a lecture at NYU’s Courant Institute about two seemingly disconnected topics—fractals and finance. Taleb was intrigued. He had no idea how finance could have anything to do with fractals.

The French physicist was claiming to have unearthed a phantom. A phenomenon that, according to prevailing economic and financial theory, couldn’t exist. The market, according to this theory, behaves like a random walk. It was the theory first proposed in 1900 by Bachelier, the neurotic French mathematician described by Benoit Mandelbrot at NYU. Sometimes called a drunkard’s walk, the theory claims that markets—all markets—are completely random and therefore unpredictable. Imagine a drunk staggering away from a light pole. Each stagger goes in a different direction, sometimes toward the pole and sometimes away from it. By the math, it’s impossible to predict how far from the pole he’ll be by the end of the night.

Black Swans lurk in the shadows, he warned—be careful! In the spring of 2007, The Black Swan: The Impact of the Highly Improbable hit bookstores across the U.S. It was an instant hit, debuting on the New York Times bestseller list at number five. An entire chapter, “The Aesthetics of Randomness,” was a paean to Benoit Mandelbrot, the French mathematician whose fractal geometry deeply informed Taleb’s vision of extreme events and fat tails—a land Taleb dubbed “Extremistan.” The mundane territory in the middle of the bell curve he called “Mediocristan”—the tame Gaussian world Mandelbrot had shown mostly doesn’t apply to the wild rock-’n’-roll nature of financial markets.


pages: 222 words: 53,317

Overcomplicated: Technology at the Limits of Comprehension by Samuel Arbesman

algorithmic trading, Anthropocene, Anton Chekhov, Apple II, Benoit Mandelbrot, Boeing 747, Chekhov's gun, citation needed, combinatorial explosion, Computing Machinery and Intelligence, Danny Hillis, data science, David Brooks, digital map, discovery of the americas, driverless car, en.wikipedia.org, Erik Brynjolfsson, Flash crash, friendly AI, game design, Google X / Alphabet X, Googley, Hans Moravec, HyperCard, Ian Bogost, Inbox Zero, Isaac Newton, iterative process, Kevin Kelly, machine translation, Machine translation of "The spirit is willing, but the flesh is weak." to Russian and back, mandelbrot fractal, Minecraft, Neal Stephenson, Netflix Prize, Nicholas Carr, Nick Bostrom, Parkinson's law, power law, Ray Kurzweil, recommendation engine, Richard Feynman, Richard Feynman: Challenger O-ring, Second Machine Age, self-driving car, SimCity, software studies, statistical model, Steve Jobs, Steve Wozniak, Steven Pinker, Stewart Brand, superintelligent machines, synthetic biology, systems thinking, the long tail, Therac-25, Tyler Cowen, 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.”

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.


pages: 416 words: 106,582

This Will Make You Smarter: 150 New Scientific Concepts to Improve Your Thinking by John Brockman

23andMe, adjacent possible, Albert Einstein, Alfred Russel Wallace, Anthropocene, banking crisis, Barry Marshall: ulcers, behavioural economics, Benoit Mandelbrot, Berlin Wall, biofilm, Black Swan, Bletchley Park, butterfly effect, Cass Sunstein, cloud computing, cognitive load, congestion charging, correlation does not imply causation, Daniel Kahneman / Amos Tversky, dark matter, data acquisition, David Brooks, delayed gratification, Emanuel Derman, epigenetics, Evgeny Morozov, Exxon Valdez, Flash crash, Flynn Effect, Garrett Hardin, Higgs boson, hive mind, impulse control, information retrieval, information security, Intergovernmental Panel on Climate Change (IPCC), Isaac Newton, Jaron Lanier, Johannes Kepler, John von Neumann, Kevin Kelly, Large Hadron Collider, lifelogging, machine translation, mandelbrot fractal, market design, Mars Rover, Marshall McLuhan, microbiome, Murray Gell-Mann, Nicholas Carr, Nick Bostrom, ocean acidification, open economy, Pierre-Simon Laplace, place-making, placebo effect, power law, pre–internet, QWERTY keyboard, random walk, randomized controlled trial, rent control, Richard Feynman, Richard Feynman: Challenger O-ring, Richard Thaler, Satyajit Das, Schrödinger's Cat, scientific management, security theater, selection bias, Silicon Valley, Stanford marshmallow experiment, stem cell, Steve Jobs, Steven Pinker, Stewart Brand, Stuart Kauffman, sugar pill, synthetic biology, the scientific method, Thorstein Veblen, Turing complete, Turing machine, twin studies, Vilfredo Pareto, Walter Mischel, Whole Earth Catalog, WikiLeaks, zero-sum game

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.

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!


pages: 1,239 words: 163,625

The Joys of Compounding: The Passionate Pursuit of Lifelong Learning, Revised and Updated by Gautam Baid

Abraham Maslow, activist fund / activist shareholder / activist investor, Airbnb, Alan Greenspan, Albert Einstein, Alvin Toffler, Andrei Shleifer, asset allocation, Atul Gawande, availability heuristic, backtesting, barriers to entry, beat the dealer, Benoit Mandelbrot, Bernie Madoff, bitcoin, Black Swan, book value, business process, buy and hold, Cal Newport, Cass Sunstein, Checklist Manifesto, Clayton Christensen, cognitive dissonance, collapse of Lehman Brothers, commoditize, corporate governance, correlation does not imply causation, creative destruction, cryptocurrency, Daniel Kahneman / Amos Tversky, deep learning, delayed gratification, deliberate practice, discounted cash flows, disintermediation, disruptive innovation, Dissolution of the Soviet Union, diversification, diversified portfolio, dividend-yielding stocks, do what you love, Dunning–Kruger effect, Edward Thorp, Elon Musk, equity risk premium, Everything should be made as simple as possible, fear index, financial independence, financial innovation, fixed income, follow your passion, framing effect, George Santayana, Hans Rosling, hedonic treadmill, Henry Singleton, hindsight bias, Hyman Minsky, index fund, intangible asset, invention of the wheel, invisible hand, Isaac Newton, it is difficult to get a man to understand something, when his salary depends on his not understanding it, Jeff Bezos, John Bogle, Joseph Schumpeter, junk bonds, Kaizen: continuous improvement, Kickstarter, knowledge economy, Lao Tzu, Long Term Capital Management, loss aversion, Louis Pasteur, low interest rates, Mahatma Gandhi, mandelbrot fractal, margin call, Mark Zuckerberg, Market Wizards by Jack D. Schwager, Masayoshi Son, mental accounting, Milgram experiment, moral hazard, Nate Silver, Network effects, Nicholas Carr, offshore financial centre, oil shock, passive income, passive investing, pattern recognition, Peter Thiel, Ponzi scheme, power law, price anchoring, quantitative trading / quantitative finance, Ralph Waldo Emerson, Ray Kurzweil, Reminiscences of a Stock Operator, reserve currency, Richard Feynman, Richard Thaler, risk free rate, risk-adjusted returns, Robert Shiller, Savings and loan crisis, search costs, shareholder value, six sigma, software as a service, software is eating the world, South Sea Bubble, special economic zone, Stanford marshmallow experiment, Steve Jobs, Steven Levy, Steven Pinker, stocks for the long run, subscription business, sunk-cost fallacy, systems thinking, tail risk, Teledyne, the market place, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, time value of money, transaction costs, tulip mania, Upton Sinclair, Walter Mischel, wealth creators, Yogi Berra, zero-sum game

According to Sebastian Mallaby, 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 a daily price data about once every seven thousand years. Instead, they cropped up about once every three to four years [emphasis added].9 Benoit Mandelbrot was a Polish-born mathematician and polymath who developed a new branch of mathematics known as fractal geometry, which recognizes the hidden order in the seemingly disordered, the plan in the unplanned, the regular pattern in the irregularity of nature.

Charles Mackay, Charles Kindleberger, John Galbraith, John Brooks, Edward Chancellor, Robert Shiller, and Maggie Mahar educated me on the history of market cycles, speculative manias, and the subsequent busts. Peter Senge and Donella Meadows educated me on systems thinking and a more interconnected view of the world. George Soros, Benoit Mandelbrot, and Richard Bookstaber made me aware of the intricate and highly dynamic feedback loops present in markets and social systems. John Maynard Keynes enlightened me on the significance of prevailing sentiments in markets and economies, and the critical role of timely government intervention. Burton Malkiel, Charles Ellis, and John Bogle taught me the importance of minimizing costs and staying the course.

Hagstrom, The Warren Buffett Way, 2nd ed. (Hoboken, NJ: Wiley, 2005). 7. Quoted in Foulke, “Warren Buffett on LTCM.” 8. Buffett FAQ, 2006 Berkshire Hathaway Annual Meeting, http://buffettfaq.com. 9. Sebastian Mallaby, More Money Than God: Hedge Funds and the Making of a New Elite (London: Penguin, 2011). 10. Benoit Mandelbrot and Richard L. Hudson, The (Mis)Behavior of Markets: A Fractal View of Financial Turbulence (New York: Basic Books, 2006), 20, 217, 248. 11. Benjamin Graham and David Dodd, Security Analysis: The Classic 1934 Edition (New York: McGraw-Hill Education, 1996). 12. Howard Marks, The Most Important Thing Illuminated: Uncommon Sense for the Thoughtful Investor (New York: Columbia University Press, 2013). 13.


pages: 57 words: 11,522

The Bed of Procrustes: Philosophical and Practical Aphorisms by Nassim Nicholas Taleb

Benoit Mandelbrot, Black Swan, commoditize, knowledge worker, Republic of Letters

* 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)


pages: 524 words: 120,182

Complexity: A Guided Tour by Melanie Mitchell

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Albert Michelson, Alfred Russel Wallace, algorithmic management, anti-communist, Arthur Eddington, Benoit Mandelbrot, bioinformatics, cellular automata, Claude Shannon: information theory, clockwork universe, complexity theory, computer age, conceptual framework, Conway's Game of Life, dark matter, discrete time, double helix, Douglas Hofstadter, Eddington experiment, en.wikipedia.org, epigenetics, From Mathematics to the Technologies of Life and Death, Garrett Hardin, Geoffrey West, Santa Fe Institute, Gregor Mendel, Gödel, Escher, Bach, Hacker News, Hans Moravec, Henri Poincaré, invisible hand, Isaac Newton, John Conway, John von Neumann, Long Term Capital Management, mandelbrot fractal, market bubble, Menlo Park, Murray Gell-Mann, Network effects, Norbert Wiener, Norman Macrae, Paul Erdős, peer-to-peer, phenotype, Pierre-Simon Laplace, power law, Ray Kurzweil, reversible computing, scientific worldview, stem cell, Stuart Kauffman, synthetic biology, The Wealth of Nations by Adam Smith, Thomas Malthus, Tragedy of the Commons, Turing machine

If you then view the same coastline from your car on the coast highway, it still appears to have the exact same kind of ruggedness, but on a smaller scale (Figure 7.2, bottom). Ditto for the close-up view when you stand on the beach and even for the ultra close-up view of a snail as it crawls on individual rocks. The similarity of the shape of the coastline at different scales is called “self-similarity.” The term fractal was coined by the French mathematician Benoit Mandelbrot, who was one of the first people to point out that the world is full of fractals—that is, many real-world objects have a rugged self-similar structure. Coastlines, mountain ranges, snowflakes, and trees are often-cited examples. Mandelbrot even proposed that the universe is fractal-like in terms of the distribution of galaxies, clusters of galaxies, clusters of clusters, et cetera.

Zipf himself proposed that, on the one hand, people in general operate by a “Principle of Least Effort”: once a word has been used, it takes less effort to use it again for similar meanings than to come up with a different word. On the other hand, people want language to be unambiguous, which they can accomplish by using different words for similar but nonidentical meanings. Zipf showed mathematically that these two pressures working together could produce the observed power-law distribution. In the 1950s, Benoit Mandelbrot, of fractal fame, had a somewhat different explanation, in terms of information content. Following Claude Shannon’s formulation of information theory (cf. chapter 3), Mandelbrot considered a word as a “message” being sent from a “source” who wants to maximize the amount of information while minimizing the cost of sending that information.

., Proceedings of the 2004 Winter Simulation Conference, pp. 130–141. Piscataway, NJ: IEEE Press, 2004. “This relation is now called Zipf’s law”: Zipf’s original publication on this work is a book: Zipf, G. K., Selected Studies of the Principle of Relative Frequency in Language. Cambridge, MA: Harvard University Press, 1932. “Benoit Mandelbrot … had a somewhat different explanation”: Mandelbrot. B., An informational theory of the statistical structure of languages. In W. Jackson (editor), Communicaiton Theory, Woburn, MA: Butterworth, 1953, pp. 486–502. “Herbert Simon proposed yet another explanation”: Simon, H. A., On a class of skew distribution functions.”


pages: 295 words: 66,824

A Mathematician Plays the Stock Market by John Allen Paulos

Alan Greenspan, AOL-Time Warner, Benoit Mandelbrot, Black-Scholes formula, book value, Brownian motion, business climate, business cycle, butter production in bangladesh, butterfly effect, capital asset pricing model, confounding variable, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, diversified portfolio, dogs of the Dow, Donald Trump, double entry bookkeeping, Elliott wave, endowment effect, equity risk premium, 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, it's over 9,000, John Bogle, John Nash: game theory, Larry Ellison, 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, Plato's cave, Ponzi scheme, power law, price anchoring, Ralph Nelson Elliott, random walk, Reminiscences of a Stock Operator, Richard Thaler, risk free rate, Robert Shiller, short selling, six sigma, Stephen Hawking, stocks for the long run, survivorship bias, transaction costs, two and twenty, ultimatum game, UUNET, Vanguard fund, Yogi Berra

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.

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.


pages: 525 words: 131,496

Near and Distant Neighbors: A New History of Soviet Intelligence by Jonathan Haslam

active measures, Albert Einstein, Benoit Mandelbrot, Berlin Wall, Bletchley Park, Bolshevik threat, Bretton Woods, British Empire, cuban missile crisis, disinformation, falling living standards, false flag, John von Neumann, lateral thinking, military-industrial complex, Robert Hanssen: Double agent, Ronald Reagan, Strategic Defense Initiative, 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.

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.


pages: 695 words: 194,693

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, book value, Bretton Woods, Brownian motion, business cycle, capital asset pricing model, Cass Sunstein, classic study, collective bargaining, colonial exploitation, compound rate of return, conceptual framework, Cornelius Vanderbilt, 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, equity risk premium, financial engineering, 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, land bank, Louis Bachelier, low interest rates, 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, public intellectual, quantitative trading / quantitative finance, random walk, Richard Thaler, Robert Shiller, shareholder value, short selling, South Sea Bubble, sovereign wealth fund, spice trade, stochastic process, subprime mortgage crisis, Suez canal 1869, Suez crisis 1956, the scientific method, The Wealth of Nations by Adam Smith, Thomas Malthus, time value of money, tontine, too big to fail, trade liberalization, trade route, transatlantic slave trade, tulip mania, wage slave

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.

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.

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.”


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Them And Us: Politics, Greed And Inequality - Why We Need A Fair Society by Will Hutton

Abraham Maslow, Alan Greenspan, Andrei Shleifer, asset-backed security, bank run, banking crisis, Bear Stearns, behavioural economics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Blythe Masters, Boris Johnson, bread and circuses, Bretton Woods, business cycle, capital controls, carbon footprint, Carmen Reinhart, Cass Sunstein, centre right, choice architecture, cloud computing, collective bargaining, conceptual framework, Corn Laws, Cornelius Vanderbilt, corporate governance, creative destruction, credit crunch, Credit Default Swap, debt deflation, decarbonisation, Deng Xiaoping, discovery of DNA, discovery of the americas, discrete time, disinformation, diversification, double helix, Edward Glaeser, financial deregulation, financial engineering, 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, general purpose technology, George Akerlof, Gini coefficient, Glass-Steagall Act, 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, Japanese asset price bubble, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, knowledge economy, knowledge worker, labour market flexibility, language acquisition, Large Hadron Collider, liberal capitalism, light touch regulation, Long Term Capital Management, long term incentive plan, Louis Pasteur, low cost airline, low interest rates, low-wage service sector, mandelbrot fractal, margin call, market fundamentalism, Martin Wolf, mass immigration, means of production, meritocracy, Mikhail Gorbachev, millennium bug, Money creation, money market fund, moral hazard, moral panic, mortgage debt, Myron Scholes, Neil Kinnock, new economy, Northern Rock, offshore financial centre, open economy, plutocrats, power law, price discrimination, private sector deleveraging, proprietary trading, 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, Ronald Reagan, Rory Sutherland, Satyajit Das, Savings and loan crisis, shareholder value, short selling, Silicon Valley, Skype, South Sea Bubble, Steve Jobs, systems thinking, tail risk, 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, three-masted sailing ship, too big to fail, unpaid internship, value at risk, Vilfredo Pareto, Washington Consensus, wealth creators, work culture , working poor, world market for maybe five computers, zero-sum game, éminence grise

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.


pages: 299 words: 92,782

The Success Equation: Untangling Skill and Luck in Business, Sports, and Investing by Michael J. Mauboussin

Amazon Mechanical Turk, Atul Gawande, Benoit Mandelbrot, Black Swan, Boeing 747, Checklist Manifesto, Clayton Christensen, cognitive bias, commoditize, Daniel Kahneman / Amos Tversky, David Brooks, deliberate practice, disruptive innovation, Emanuel Derman, fundamental attribution error, Gary Kildall, Gini coefficient, hindsight bias, hiring and firing, income inequality, Innovator's Dilemma, John Bogle, Long Term Capital Management, loss aversion, Menlo Park, mental accounting, moral hazard, Network effects, power law, prisoner's dilemma, random walk, Richard Thaler, risk-adjusted returns, shareholder value, Simon Singh, six sigma, Steven Pinker, transaction costs, winner-take-all economy, zero-sum game, Zipf's Law

Michael Bar-Eli, Simcha Avugos, and Markus Raab, “Twenty Years of ‘Hot Hand’ Research: Review and Critique,” Psychology of Sport and Exercise 7, no. 6 (November 2006): 525–553; and Alan Reifman, Hot Hands: The Statistics Behind Sports' Greatest Streaks (Washington, DC: Potomac Books, 2011). 7. Frank H. Knight, Risk, Uncertainty, and Profit (New York: Houghton and Mifflin, 1921), and http://www.econlib.org/library/Knight/knRUP.html. Benoit Mandelbrot distinguishes between “mild” and “wild” chance. These terms neatly capture the spirit of this discussion; see Benoit Mandelbrot and Richard L. Hudson, The (Mis)Behavior of Markets (New York: Basic Books, 2004), 32–33. 8. William Goldman, Adventures in the Screen Trade: A Personal View of Hollywood and Screenwriting (New York: Warner Books, 1983), 39. 9.


pages: 518 words: 107,836

How Not to Network a Nation: The Uneasy History of the Soviet Internet (Information Policy) by Benjamin Peters

Albert Einstein, American ideology, Andrei Shleifer, Anthropocene, Benoit Mandelbrot, bitcoin, Brownian motion, Charles Babbage, Claude Shannon: information theory, cloud computing, cognitive dissonance, commons-based peer production, computer age, conceptual framework, continuation of politics by other means, crony capitalism, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Graeber, disinformation, 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, Gabriella Coleman, hive mind, index card, informal economy, information asymmetry, invisible hand, Jacquard loom, John von Neumann, Kevin Kelly, knowledge economy, knowledge worker, Lewis Mumford, linear programming, mandelbrot fractal, Marshall McLuhan, means of production, megaproject, Menlo Park, Mikhail Gorbachev, military-industrial complex, mutually assured destruction, Network effects, Norbert Wiener, packet switching, Pareto efficiency, pattern recognition, Paul Erdős, Peter Thiel, Philip Mirowski, power law, RAND corporation, rent-seeking, road to serfdom, Ronald Coase, scientific mainstream, scientific management, Steve Jobs, Stewart Brand, stochastic process, surveillance capitalism, systems thinking, technoutopianism, the Cathedral and the Bazaar, the strength of weak ties, The Structural Transformation of the Public Sphere, transaction costs, Turing machine, work culture , Yochai Benkler

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.


pages: 453 words: 111,010

Licence to be Bad by Jonathan Aldred

"Friedman doctrine" OR "shareholder theory", Affordable Care Act / Obamacare, Alan Greenspan, Albert Einstein, availability heuristic, Ayatollah Khomeini, behavioural economics, Benoit Mandelbrot, Berlin Wall, Black Monday: stock market crash in 1987, Black Swan, Capital in the Twenty-First Century by Thomas Piketty, Carmen Reinhart, Cass Sunstein, Charles Babbage, clean water, cognitive dissonance, corporate governance, correlation does not imply causation, cuban missile crisis, Daniel Kahneman / Amos Tversky, Donald Trump, Douglas Engelbart, Douglas Engelbart, Dr. Strangelove, Edward Snowden, fake news, Fall of the Berlin Wall, falling living standards, feminist movement, framing effect, Frederick Winslow Taylor, From Mathematics to the Technologies of Life and Death, full employment, Gary Kildall, George Akerlof, glass ceiling, Glass-Steagall Act, Herman Kahn, Intergovernmental Panel on Climate Change (IPCC), invisible hand, Isaac Newton, Jeff Bezos, John Nash: game theory, John von Neumann, Linda problem, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, meta-analysis, Mont Pelerin Society, mutually assured destruction, Myron Scholes, Nash equilibrium, Norbert Wiener, nudge unit, obamacare, offshore financial centre, Pareto efficiency, Paul Samuelson, plutocrats, positional goods, power law, precautionary principle, profit maximization, profit motive, race to the bottom, RAND corporation, rent-seeking, Richard Thaler, ride hailing / ride sharing, risk tolerance, road to serfdom, Robert Shiller, Robert Solow, Ronald Coase, Ronald Reagan, scientific management, Skinner box, Skype, Social Responsibility of Business Is to Increase Its Profits, spectrum auction, The Nature of the Firm, The Wealth of Nations by Adam Smith, Tragedy of the Commons, transaction costs, trickle-down economics, Vilfredo Pareto, wealth creators, zero-sum game

If there was an answer, it would surely be revealed by the physical properties of snowflakes. But if we look at snowflakes under a magnifying lens we find a different kind of property. Snowflakes are called ‘scale-invariant’ by physicists because their crystal structure looks the same no matter how much we magnify them. Snowflakes are an example of what the mathematician Benoît Mandelbrot calls fractals – structures with no natural or normal size and which recur at different scales. (Another example is trees: the pattern of branches looks like the pattern of leaves on a branch, and also the pattern of veins in a leaf). Mandelbrot noticed that prices in financial markets have this property: a graph showing the price over time of some stock or market index will look much the same, whether the time period covered is several decades, a few seconds, or anything in between.

., CEO Pay in 2012 was Extraordinarily High Relative to Typical Workers and Other High Earners (Economic Policy Institute, 2013). 3 Speech at the Royal Geographical Society Presidential Dinner, London, 1991. 4 On histories of the effect of Reagan’s and Thatcher’s ideas, one inspiration for this book was Daniel Rodgers’s superb Age of Fracture (Harvard: Harvard University Press, 2011). See especially chapter 2. 5 Strathern, P. (2001), Dr Strangelove’s Game (London: Hamish Hamilton), 227. 6 Atkinson, 19–20. 7 See Economist, 13 October 2012, ‘The Rich and the Rest’, and research cited there. 8 Quoted in Benoit Mandelbrot; Hudson, Richard L. (2004), The (Mis) behavior of Markets: A Fractal View of Risk, Ruin, and Reward (New York: Basic Books), 155. 9 Hacker, J., and Pierson, P. (2010), ‘Winner-Take-All Politics’, Politics and Society, 38 (2010), 152–204. 10 See for instance Atkinson, 80–81 and J. Stiglitz (2012), The Price of Inequality (London: Allen Lane), 27–8. 11 Norton, M., and Ariely, Dan, ‘Building a Better America – One Wealth Quintile at a Time’, Perspectives in Psychological Science, 6 (2011), 9–12; Davidai, S., and Gilovich, T. (2015), ‘Building a More Mobile America – One Income Quintile at a Time’, in ibid., 10, 60–71; survey conducted by Fondation-Jean-Jaurès at https://jean-jaures.org/nos-productions/la-perception-des-inegalites-dans-le-monde. 12 See for instance M.


pages: 425 words: 122,223

Capital Ideas: The Improbable Origins of Modern Wall Street by Peter L. Bernstein

Albert Einstein, asset allocation, backtesting, Benoit Mandelbrot, Black Monday: stock market crash in 1987, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, business cycle, buy and hold, 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, Glass-Steagall Act, Great Leap Forward, guns versus butter model, implied volatility, index arbitrage, index fund, interest rate swap, invisible hand, John von Neumann, Joseph Schumpeter, junk bonds, Kenneth Arrow, law of one price, linear programming, Louis Bachelier, mandelbrot fractal, martingale, means of production, Michael Milken, money market fund, Myron Scholes, new economy, New Journalism, Paul Samuelson, Performance of Mutual Funds in the Period, profit maximization, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk free rate, risk/return, Robert Shiller, Robert Solow, Ronald Reagan, stochastic process, Thales and the olive presses, 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.

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.


pages: 247 words: 43,430

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, Laplace demon, mandelbrot fractal, Occupy movement, Paul Erdős, peer-to-peer, Pierre-Simon Laplace, power law, seminal paper, sorting algorithm, stochastic process, strong AI, Thomas Kuhn: the structure of scientific revolutions, Turing complete, Turing machine, Vilfredo Pareto, We are the 99%

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.


pages: 193 words: 51,445

On the Future: Prospects for Humanity by Martin J. Rees

23andMe, 3D printing, air freight, Alfred Russel Wallace, AlphaGo, Anthropocene, Asilomar, autonomous vehicles, Benoit Mandelbrot, biodiversity loss, blockchain, Boston Dynamics, carbon tax, circular economy, CRISPR, cryptocurrency, cuban missile crisis, dark matter, decarbonisation, DeepMind, Demis Hassabis, demographic transition, Dennis Tito, distributed ledger, double helix, driverless car, effective altruism, Elon Musk, en.wikipedia.org, Geoffrey Hinton, global village, Great Leap Forward, Higgs boson, Hyperloop, Intergovernmental Panel on Climate Change (IPCC), Internet of things, James Webb Space Telescope, Jeff Bezos, job automation, Johannes Kepler, John Conway, Large Hadron Collider, life extension, mandelbrot fractal, mass immigration, megacity, Neil Armstrong, Nick Bostrom, nuclear winter, ocean acidification, off-the-grid, pattern recognition, precautionary principle, quantitative hedge fund, Ray Kurzweil, Recombinant DNA, Rodney Brooks, Search for Extraterrestrial Intelligence, sharing economy, Silicon Valley, smart grid, speech recognition, Stanford marshmallow experiment, Stanislav Petrov, stem cell, Stephen Hawking, Steven Pinker, Stuxnet, supervolcano, technological singularity, the scientific method, Tunguska event, uranium enrichment, Walter Mischel, William MacAskill, Yogi Berra

Conway indulged in a lot of ‘trial and error’ before he came up with a simple ‘virtual world’ that allowed for interesting emergent variety. He used pencil and paper, before the days of personal computers, but the implications of the Game of Life only emerged when the greater speed of computers could be harnessed. Likewise, early PCs enabled Benoit Mandelbrot and others to plot out the marvellous patterns of fractals—showing how simple mathematical formulas can encode intricate apparent complexity. Most scientists resonate with the perplexity expressed in a classic essay by the physicist Eugene Wigner, titled ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’.2 And also with Einstein’s dictum that ‘the most incomprehensible thing about the universe is that it is comprehensible’.


pages: 158 words: 49,168

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

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.


pages: 807 words: 154,435

Radical Uncertainty: Decision-Making for an Unknowable Future by Mervyn King, John Kay

Airbus A320, Alan Greenspan, Albert Einstein, Albert Michelson, algorithmic trading, anti-fragile, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, autonomous vehicles, availability heuristic, banking crisis, Barry Marshall: ulcers, battle of ideas, Bear Stearns, behavioural economics, Benoit Mandelbrot, bitcoin, Black Swan, Boeing 737 MAX, Bonfire of the Vanities, Brexit referendum, Brownian motion, business cycle, business process, capital asset pricing model, central bank independence, collapse of Lehman Brothers, correlation does not imply causation, credit crunch, cryptocurrency, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, DeepMind, demographic transition, discounted cash flows, disruptive innovation, diversification, diversified portfolio, Donald Trump, Dutch auction, easy for humans, difficult for computers, eat what you kill, Eddington experiment, Edmond Halley, Edward Lloyd's coffeehouse, Edward Thorp, Elon Musk, Ethereum, Eugene Fama: efficient market hypothesis, experimental economics, experimental subject, fear of failure, feminist movement, financial deregulation, George Akerlof, germ theory of disease, Goodhart's law, Hans Rosling, Helicobacter pylori, high-speed rail, Ignaz Semmelweis: hand washing, income per capita, incomplete markets, inflation targeting, information asymmetry, invention of the wheel, invisible hand, Jeff Bezos, Jim Simons, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Snow's cholera map, John von Neumann, Kenneth Arrow, Kōnosuke Matsushita, Linda problem, Long Term Capital Management, loss aversion, Louis Pasteur, mandelbrot fractal, market bubble, market fundamentalism, military-industrial complex, Money creation, Moneyball by Michael Lewis explains big data, Monty Hall problem, Nash equilibrium, Nate Silver, new economy, Nick Leeson, Northern Rock, nudge theory, oil shock, PalmPilot, Paul Samuelson, peak oil, Peter Thiel, Philip Mirowski, Phillips curve, Pierre-Simon Laplace, popular electronics, power law, price mechanism, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, railway mania, RAND corporation, reality distortion field, rent-seeking, Richard Feynman, Richard Thaler, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Solow, Ronald Coase, sealed-bid auction, shareholder value, Silicon Valley, Simon Kuznets, Socratic dialogue, South Sea Bubble, spectrum auction, Steve Ballmer, Steve Jobs, Steve Wozniak, Suez crisis 1956, Tacoma Narrows Bridge, Thales and the olive presses, Thales of Miletus, The Chicago School, the map is not the territory, The Market for Lemons, The Nature of the Firm, The Signal and the Noise by Nate Silver, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Bayes, Thomas Davenport, Thomas Malthus, Toyota Production System, transaction costs, ultimatum game, urban planning, value at risk, world market for maybe five computers, World Values Survey, Yom Kippur War, zero-sum game

The nineteenth of October 1987, on which the principal American stock indices fell by around 20% during the day, is the financial analogue of the Valdivia earthquake. Extreme events are common with power laws and rare in normal distributions. The application of power laws to economics was pioneered in the early 1960s by the Polish-French-American mathematician Benoit Mandelbrot. He established that movements in cotton prices could be described by a power law. 9 Power laws have a property of ‘scale invariance’. If you look at a snowflake under a powerful microscope, the shape of every small part you see is the same as the shape you see with the naked eye. The property which creates this beautiful structure is called fractal geometry.

Lorraine Daston provides a comprehensive account of the development of probabilistic reasoning in Classical Probability in the Enlightenment (1995) and its application to insurance is described in Niall Ferguson’s The Ascent of Money (2008). In 2019 the American Statistical Association devoted an entire issue to the misuse of probabilistic reasoning to make inferences about causation. The editorial concluded ‘it is time to stop using the term “statistically significant” entirely’. * The study of power laws was pioneered by Benoit Mandelbrot, and Mark Buchanan’s Ubiquity (2002) is a survey of many applications. Again as we went to press, we saw Ian Stewart’s Do Dice Play God? (2019) which reviews several of the puzzles and paradoxes in the early chapters of this book. ____________ * Ronald L. Wasserstein, Allen L. Schirm and Nicole A.


pages: 239 words: 69,496

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, AOL-Time Warner, assortative mating, Benoit Mandelbrot, book value, Brownian motion, capital asset pricing model, Carl Icahn, carried interest, Charles Lindbergh, collective bargaining, corporate governance, corporate raider, discounted cash flows, diversified portfolio, Eugene Fama: efficient market hypothesis, financial engineering, financial innovation, follow your passion, George Akerlof, Gordon Gekko, greed is good, housing crisis, income inequality, information asymmetry, Isaac Newton, Jony Ive, Kenneth Rogoff, longitudinal study, Louis Bachelier, low interest rates, Monty Hall problem, 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, Ronald Coase, short squeeze, Silicon Valley, Steve Jobs, Thales and the olive presses, Thales of Miletus, The Market for Lemons, The Nature of the Firm, The Wealth of Nations by Adam Smith, Tim Cook: Apple, tontine, transaction costs, vertical integration, zero-sum game

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.


pages: 220 words: 66,518

The Biology of Belief: Unleashing the Power of Consciousness, Matter & Miracles by Bruce H. Lipton

Albert Einstein, Benoit Mandelbrot, Boeing 747, correlation does not imply causation, data science, discovery of DNA, double helix, Drosophila, epigenetics, Isaac Newton, Mahatma Gandhi, mandelbrot fractal, Mars Rover, nocebo, On the Revolutions of the Heavenly Spheres, phenotype, placebo effect, randomized controlled trial, selective serotonin reuptake inhibitor (SSRI), stem cell, sugar pill

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.


pages: 257 words: 13,443

Statistical Arbitrage: Algorithmic Trading Insights and Techniques by Andrew Pole

algorithmic trading, Benoit Mandelbrot, constrained optimization, Dava Sobel, deal flow, financial engineering, George Santayana, Long Term Capital Management, Louis Pasteur, low interest rates, mandelbrot fractal, market clearing, market fundamentalism, merger arbitrage, pattern recognition, price discrimination, profit maximization, proprietary trading, quantitative trading / quantitative finance, risk tolerance, Sharpe ratio, statistical arbitrage, statistical model, stochastic volatility, systematic trading, transaction costs

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.


pages: 262 words: 65,959

The Simpsons and Their Mathematical Secrets by Simon Singh

Albert Einstein, Andrew Wiles, Apollo 13, Benoit Mandelbrot, Bletchley Park, cognitive dissonance, Donald Knuth, Erdős number, Georg Cantor, Grace Hopper, Higgs boson, Isaac Newton, John Nash: game theory, Kickstarter, mandelbrot fractal, Menlo Park, Norbert Wiener, Norman Mailer, P = NP, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, quantum cryptography, Richard Feynman, Rubik’s Cube, Schrödinger's Cat, Simon Singh, Stephen Hawking, Wolfskehl Prize, women in the workforce

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.”


pages: 741 words: 179,454

Extreme Money: Masters of the Universe and the Cult of Risk by Satyajit Das

"RICO laws" OR "Racketeer Influenced and Corrupt Organizations", "there is no alternative" (TINA), "World Economic Forum" Davos, affirmative action, Alan Greenspan, Albert Einstein, algorithmic trading, Andy Kessler, AOL-Time Warner, Asian financial crisis, asset allocation, asset-backed security, bank run, banking crisis, banks create money, Basel III, Bear Stearns, behavioural economics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Black Swan, Bonfire of the Vanities, bonus culture, book value, Bretton Woods, BRICs, British Empire, business cycle, buy the rumour, sell the news, capital asset pricing model, carbon credits, Carl Icahn, 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, currency risk, Daniel Kahneman / Amos Tversky, deal flow, debt deflation, Deng Xiaoping, deskilling, discrete time, diversification, diversified portfolio, Doomsday Clock, Dr. Strangelove, Dutch auction, Edward Thorp, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, eurozone crisis, Everybody Ought to Be Rich, Fall of the Berlin Wall, financial engineering, financial independence, financial innovation, financial thriller, fixed income, foreign exchange controls, full employment, Glass-Steagall Act, global reserve currency, Goldman Sachs: Vampire Squid, Goodhart's law, Gordon Gekko, greed is good, Greenspan put, happiness index / gross national happiness, haute cuisine, Herman Kahn, high net worth, Hyman Minsky, index fund, information asymmetry, interest rate swap, invention of the wheel, invisible hand, Isaac Newton, James Carville said: "I would like to be reincarnated as the bond market. You can intimidate everybody.", job automation, Johann Wolfgang von Goethe, John Bogle, John Meriwether, joint-stock company, Jones Act, Joseph Schumpeter, junk bonds, Kenneth Arrow, Kenneth Rogoff, Kevin Kelly, laissez-faire capitalism, load shedding, locking in a profit, Long Term Capital Management, Louis Bachelier, low interest rates, margin call, market bubble, market fundamentalism, Market Wizards by Jack D. Schwager, Marshall McLuhan, Martin Wolf, mega-rich, merger arbitrage, Michael Milken, Mikhail Gorbachev, Milgram experiment, military-industrial complex, Minsky moment, money market fund, Mont Pelerin Society, moral hazard, mortgage debt, mortgage tax deduction, mutually assured destruction, Myron Scholes, Naomi Klein, National Debt Clock, negative equity, NetJets, Network effects, new economy, Nick Leeson, Nixon shock, Northern Rock, nuclear winter, oil shock, Own Your Own Home, Paul Samuelson, pets.com, Philip Mirowski, Phillips curve, planned obsolescence, plutocrats, Ponzi scheme, price anchoring, price stability, profit maximization, proprietary trading, public intellectual, quantitative easing, quantitative trading / quantitative finance, Ralph Nader, RAND corporation, random walk, Ray Kurzweil, regulatory arbitrage, Reminiscences of a Stock Operator, rent control, rent-seeking, reserve currency, Richard Feynman, Richard Thaler, Right to Buy, risk free rate, risk-adjusted returns, risk/return, road to serfdom, 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, short squeeze, Silicon Valley, six sigma, Slavoj Žižek, South Sea Bubble, special economic zone, statistical model, Stephen Hawking, Steve Jobs, stock buybacks, survivorship bias, tail risk, Teledyne, 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 Theory of the Leisure Class by Thorstein Veblen, The Wealth of Nations by Adam Smith, Thorstein Veblen, too big to fail, trickle-down economics, Turing test, two and twenty, Upton Sinclair, value at risk, Yogi Berra, zero-coupon bond, zero-sum game

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.


pages: 193 words: 19,478

Memory Machines: The Evolution of Hypertext by Belinda Barnet

augmented reality, Benoit Mandelbrot, Bill Duvall, British Empire, Buckminster Fuller, Charles Babbage, Claude Shannon: information theory, collateralized debt obligation, computer age, Computer Lib, conceptual framework, Douglas Engelbart, Douglas Engelbart, game design, hiring and firing, Howard Rheingold, HyperCard, hypertext link, Ian Bogost, information retrieval, Internet Archive, John Markoff, linked data, mandelbrot fractal, Marshall McLuhan, Menlo Park, nonsequential writing, Norbert Wiener, Project Xanadu, publish or perish, Robert Metcalfe, semantic web, seminal paper, Steve Jobs, Stewart Brand, technoutopianism, Ted Nelson, the scientific method, Vannevar Bush, wikimedia commons

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.


pages: 240 words: 73,209

The Education of a Value Investor: My Transformative Quest for Wealth, Wisdom, and Enlightenment by Guy Spier

Albert Einstein, Atul Gawande, Bear Stearns, Benoit Mandelbrot, big-box store, Black Swan, book value, Checklist Manifesto, classic study, 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, mirror neurons, Nelson Mandela, NetJets, pattern recognition, pre–internet, random walk, Reminiscences of a Stock Operator, risk free rate, Ronald Reagan, South Sea Bubble, Steve Jobs, Stuart Kauffman, TED Talk, two and twenty, 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?


pages: 789 words: 207,744

The Patterning Instinct: A Cultural History of Humanity's Search for Meaning by Jeremy Lent

Admiral Zheng, agricultural Revolution, Albert Einstein, Alfred Russel Wallace, Anthropocene, Atahualpa, Benoit Mandelbrot, Bretton Woods, British Empire, Buckminster Fuller, Capital in the Twenty-First Century by Thomas Piketty, cognitive dissonance, commoditize, complexity theory, conceptual framework, dematerialisation, demographic transition, different worldview, Doomsday Book, Easter island, en.wikipedia.org, European colonialism, failed state, Firefox, Ford Model T, Francisco Pizarro, Garrett Hardin, Georg Cantor, Great Leap Forward, Hans Moravec, happiness index / gross national happiness, hedonic treadmill, income inequality, Intergovernmental Panel on Climate Change (IPCC), Internet of things, invention of gunpowder, invention of writing, Isaac Newton, Jevons paradox, Johann Wolfgang von Goethe, Johannes Kepler, language acquisition, Lao Tzu, Law of Accelerating Returns, mandelbrot fractal, mass immigration, megacity, Metcalfe's law, Mikhail Gorbachev, move 37, Neil Armstrong, Nicholas Carr, Nick Bostrom, Norbert Wiener, oil shale / tar sands, out of africa, peak oil, Pierre-Simon Laplace, Plato's cave, QWERTY keyboard, Ray Kurzweil, Robert Solow, Sapir-Whorf hypothesis, scientific management, Scientific racism, scientific worldview, seminal paper, shareholder value, sharing economy, Silicon Valley, Simon Kuznets, social intelligence, South China Sea, Stephen Hawking, Steven Pinker, Stuart Kauffman, synthetic biology, systems thinking, technological singularity, the scientific method, The Theory of the Leisure Class by Thorstein Veblen, theory of mind, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, Thorstein Veblen, Tragedy of the Commons, Turing test, ultimatum game, urban sprawl, Vernor Vinge, wikimedia commons

The li of a thing is one with the li of all things…. There is only one li in the world.” While this might sound rather mystical, recent breakthroughs in mathematics have demonstrated Cheng's statements to be a perceptive insight into the nature of reality. Fractal geometry, pioneered by mathematician Benoit Mandelbrot, shows how nature forms intricate patterns that replicate themselves at different scales, each pattern nested inside another. Examples of these fractal patterns are observable in clouds, coastlines, ferns, and sand dunes.41 Since Mandelbrot's discovery, biologists have come to recognize that the design of life itself is fractal, with cells self-organizing to form organisms, which then self-organize into communities of organisms and ecosystems.

In pursuing their disciplines, scientists would often use the Latin phrase ceteribus paribus—“other things being equal”—to dismiss the random noise that didn't fit into the theory. Now, in systems thinking, a new set of methods was emerging to investigate the unequal world of those other things.20 A brilliant mathematician, Benoit Mandelbrot, developed a new branch of mathematics, called fractal geometry, to describe this non-Newtonian world. His 1983 book The Fractal Geometry of Nature had a profound effect on the field of mathematics. Mandelbrot explained in clear terms the limitations of classical theory: Most of nature is very, very complicated.


pages: 306 words: 82,765

Skin in the Game: Hidden Asymmetries in Daily Life by Nassim Nicholas Taleb

anti-fragile, availability heuristic, behavioural economics, Benoit Mandelbrot, Bernie Madoff, Black Swan, Brownian motion, Capital in the Twenty-First Century by Thomas Piketty, Cass Sunstein, cellular automata, Claude Shannon: information theory, cognitive dissonance, complexity theory, data science, David Graeber, disintermediation, Donald Trump, Edward Thorp, equity premium, fake news, financial independence, information asymmetry, invisible hand, knowledge economy, loss aversion, mandelbrot fractal, Mark Spitznagel, mental accounting, microbiome, mirror neurons, moral hazard, Murray Gell-Mann, offshore financial centre, p-value, Paradox of Choice, Paul Samuelson, Ponzi scheme, power law, precautionary principle, price mechanism, principal–agent problem, public intellectual, Ralph Nader, random walk, rent-seeking, Richard Feynman, Richard Thaler, Ronald Coase, Ronald Reagan, Rory Sutherland, Rupert Read, Silicon Valley, Social Justice Warrior, Steven Pinker, stochastic process, survivorship bias, systematic bias, tail risk, TED Talk, The Nature of the Firm, Tragedy of the Commons, transaction costs, urban planning, Yogi Berra

Chapter 13 The Merchandising of Virtue Sontag is about Sontag—Virtue is what you do when nobody is looking—Have the guts to be unpopular—Meetings breed meetings—Call someone lonely on Saturdays after tennis Lycurgus, the Spartan lawmaker, responded to a suggestion to allow democracy there, saying “begin with your own family.” I will always remember my encounter with the writer and cultural icon Susan Sontag, largely because I met the great Benoit Mandelbrot on the same day. It took place in 2001, two months after the terrorist event of September, in a radio station in New York. Sontag, who was being interviewed, was piqued by the idea of a fellow who “studies randomness” and came to engage me. When she discovered that I was a trader, she blurted out that she was “against the market system” and turned her back to me as I was in mid-sentence, just to humiliate me (note here that courtesy is an application of the Silver Rule), while her assistant gave me a look as if I had been convicted of child killing.


pages: 360 words: 85,321

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, behavioural economics, Benoit Mandelbrot, Bletchley Park, butterfly effect, call centre, Chance favours the prepared mind, Claude Shannon: information theory, collateralized debt obligation, Computing Machinery and Intelligence, 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, Johannes Kepler, 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, Ronald Reagan, Rubik’s Cube, statistical model, The Design of Experiments, Watson beat the top human players on Jeopardy!, zero-sum game

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.


pages: 301 words: 85,263

New Dark Age: Technology and the End of the Future by James Bridle

AI winter, Airbnb, Alfred Russel Wallace, AlphaGo, Anthropocene, Automated Insights, autonomous vehicles, back-to-the-land, Benoit Mandelbrot, Bernie Sanders, bitcoin, Boeing 747, British Empire, Brownian motion, Buckminster Fuller, Cambridge Analytica, Capital in the Twenty-First Century by Thomas Piketty, carbon footprint, coastline paradox / Richardson effect, cognitive bias, cognitive dissonance, combinatorial explosion, computer vision, congestion charging, cryptocurrency, data is the new oil, disinformation, Donald Trump, Douglas Engelbart, Douglas Engelbart, Douglas Hofstadter, Dr. Strangelove, drone strike, Edward Snowden, Eyjafjallajökull, Fairchild Semiconductor, fake news, fear of failure, Flash crash, fulfillment center, Google Earth, Greyball, Haber-Bosch Process, Higgs boson, hive mind, income inequality, informal economy, Internet of things, Isaac Newton, ITER tokamak, James Bridle, John von Neumann, Julian Assange, Kickstarter, Kim Stanley Robinson, Large Hadron Collider, late capitalism, Laura Poitras, Leo Hollis, lone genius, machine translation, mandelbrot fractal, meta-analysis, Minecraft, mutually assured destruction, natural language processing, Network effects, oil shock, p-value, pattern recognition, peak oil, recommendation engine, road to serfdom, Robert Mercer, Ronald Reagan, security theater, self-driving car, Seymour Hersh, Silicon Valley, Silicon Valley ideology, Skype, social graph, sorting algorithm, South China Sea, speech recognition, Spread Networks laid a new fibre optics cable between New York and Chicago, stem cell, Stuxnet, technoutopianism, the built environment, the scientific method, Uber for X, undersea cable, University of East Anglia, uranium enrichment, Vannevar Bush, warehouse robotics, WikiLeaks

The reason, as he came to understand, was that the length of the border depended upon the tools used to measure it: as these became more accurate, the length actually increased, as smaller and smaller variations in the line were taken into account.41 Coastlines were even worse, leading to the realisation that it is in fact impossible to give a completely accurate account of the length of a nation’s borders. This ‘coastline paradox’ came to be known as the Richardson effect, and formed the basis for Benoît Mandelbrot’s work on fractals. It demonstrates, with radical clarity, the counterintuitive premise of the new dark age: the more obsessively we attempt to compute the world, the more unknowably complex it appears. 3 Climate There was a video on YouTube that I watched over and over again, until it got taken down.


The Golden Ratio: The Story of Phi, the World's Most Astonishing Number by Mario Livio

Albert Einstein, Albert Michelson, Alfred Russel Wallace, Benoit Mandelbrot, Brownian motion, Buckminster Fuller, classic study, cosmological constant, Elliott wave, Eratosthenes, Gödel, Escher, Bach, Isaac Newton, Johann Wolfgang von Goethe, Johannes Kepler, mandelbrot fractal, music of the spheres, Nash equilibrium, power law, Ralph Nelson Elliott, Ralph Waldo Emerson, random walk, Richard Feynman, Ronald Reagan, Thales of Miletus, the scientific method

Investors know, however, that even with the application of all the bells and whistles of modern portfolio theory, which is supposed to maximize the returns for a decided-on level of risk, fortunes can be made or lost in a heartbeat. You may have noticed that Elliott's wave interpretation has as one of its ingredients the concept that each part of the curve is a reduced-scale version of the whole, a concept central to fractal geometry. Indeed, in 1997, Benoit Mandelbrot published a book entitled Fractals and Scaling in Finance: Discontinuity, Concentration, Risk, which introduced well-defined fractal models into market economics. Mandelbrot built on the known fact that fluctuations in the stock market look the same when charts are enlarged or reduced to fit the same price and time scales.


pages: 313 words: 92,053

Places of the Heart: The Psychogeography of Everyday Life by Colin Ellard

Apollo 11, augmented reality, Benoit Mandelbrot, Berlin Wall, Broken windows theory, Buckminster Fuller, carbon footprint, classic study, cognitive load, commoditize, crowdsourcing, data science, Dunbar number, Frank Gehry, gentrification, Google Glasses, Guggenheim Bilbao, haute couture, Howard Rheingold, Internet of things, Jaron Lanier, Lewis Mumford, mandelbrot fractal, Marshall McLuhan, Masdar, mass immigration, megastructure, mirror neurons, Mondo 2000, more computing power than Apollo, Oculus Rift, overview effect, Peter Eisenman, RFID, Richard Florida, risk tolerance, sentiment analysis, Skinner box, smart cities, starchitect, TED Talk, the built environment, theory of mind, time dilation, urban decay, urban planning, urban sprawl, Victor Gruen

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.


pages: 315 words: 89,861

The Simulation Hypothesis by Rizwan Virk

3D printing, Albert Einstein, AlphaGo, Apple II, artificial general intelligence, augmented reality, Benoit Mandelbrot, bioinformatics, butterfly effect, Colossal Cave Adventure, Computing Machinery and Intelligence, DeepMind, discovery of DNA, Dmitri Mendeleev, Elon Musk, en.wikipedia.org, Ernest Rutherford, game design, Google Glasses, Isaac Newton, John von Neumann, Kickstarter, mandelbrot fractal, Marc Andreessen, Minecraft, natural language processing, Nick Bostrom, OpenAI, Pierre-Simon Laplace, Plato's cave, quantum cryptography, quantum entanglement, Ralph Waldo Emerson, Ray Kurzweil, Richard Feynman, Schrödinger's Cat, Search for Extraterrestrial Intelligence, Silicon Valley, Stephen Hawking, Steve Jobs, Steve Wozniak, technological singularity, TED Talk, time dilation, Turing test, Vernor Vinge, Zeno's paradox

Figure 32: Fractal patterns resemble natural processes.78 According to the Fractal Foundation, “A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop.”79 Fractals have been around since the 1980s. Benoit Mandelbrot, as a young mathematician and researcher, found patterns of self-similarity at different scales in many different kinds of problems, ranging from error codes in telephone lines, to the pattern of prices of commodities in the markets, to the structure of a coastline. The coastline example is perhaps the best way to understand fractals.


pages: 398 words: 86,855

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, data science, database schema, DevOps, en.wikipedia.org, Firefox, Flash crash, functional programming, Gini coefficient, hype cycle, illegal immigration, iterative process, labor-force participation, loose coupling, machine readable, natural language processing, Netflix Prize, One Laptop per Child (OLPC), power law, quantitative trading / quantitative finance, recommendation engine, selection bias, sentiment analysis, SQL injection, 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[62] In just three iterations of this algorithm, we can create a famous shape known as the Koch snowflake.[63] 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.


pages: 339 words: 94,769

Possible Minds: Twenty-Five Ways of Looking at AI by John Brockman

AI winter, airport security, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Alignment Problem, AlphaGo, artificial general intelligence, Asilomar, autonomous vehicles, basic income, Benoit Mandelbrot, Bill Joy: nanobots, Bletchley Park, Buckminster Fuller, cellular automata, Claude Shannon: information theory, Computing Machinery and Intelligence, CRISPR, Daniel Kahneman / Amos Tversky, Danny Hillis, data science, David Graeber, deep learning, DeepMind, Demis Hassabis, easy for humans, difficult for computers, Elon Musk, Eratosthenes, Ernest Rutherford, fake news, finite state, friendly AI, future of work, Geoffrey Hinton, Geoffrey West, Santa Fe Institute, gig economy, Hans Moravec, heat death of the universe, hype cycle, income inequality, industrial robot, information retrieval, invention of writing, it is difficult to get a man to understand something, when his salary depends on his not understanding it, James Watt: steam engine, Jeff Hawkins, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John von Neumann, Kevin Kelly, Kickstarter, Laplace demon, Large Hadron Collider, Loebner Prize, machine translation, market fundamentalism, Marshall McLuhan, Menlo Park, military-industrial complex, mirror neurons, Nick Bostrom, Norbert Wiener, OpenAI, optical character recognition, paperclip maximiser, pattern recognition, personalized medicine, Picturephone, profit maximization, profit motive, public intellectual, quantum cryptography, RAND corporation, random walk, Ray Kurzweil, Recombinant DNA, Richard Feynman, Rodney Brooks, self-driving car, sexual politics, Silicon Valley, Skype, social graph, speech recognition, statistical model, Stephen Hawking, Steven Pinker, Stewart Brand, strong AI, superintelligent machines, supervolcano, synthetic biology, systems thinking, technological determinism, technological singularity, technoutopianism, TED Talk, telemarketer, telerobotics, The future is already here, the long tail, the scientific method, theory of mind, trolley problem, Turing machine, Turing test, universal basic income, Upton Sinclair, Von Neumann architecture, Whole Earth Catalog, Y2K, you are the product, zero-sum game

The Fifth Generation: Artificial Intelligence and Japan’s Computer Challenge to the World was published in 1983. We had a code name for the project: “It’s coming, it’s coming!” But it didn’t come; it went. From that point on I’ve worked with researchers in nearly every variety of AI and complexity, including Rodney Brooks, Hans Moravec, John Archibald Wheeler, Benoit Mandelbrot, John Henry Holland, Danny Hillis, Freeman Dyson, Chris Langton, J. Doyne Farmer, Geoffrey West, Stuart Russell, and Judea Pearl. AN ONGOING DYNAMICAL EMERGENT SYSTEM From the initial meeting in Washington, Connecticut, to the present, I arranged a number of dinners and discussions in London and Cambridge, Massachusetts, as well as a public event at London’s City Hall.


Concentrated Investing by Allen C. Benello

activist fund / activist shareholder / activist investor, asset allocation, barriers to entry, beat the dealer, Benoit Mandelbrot, Bob Noyce, Boeing 747, book value, business cycle, buy and hold, carried interest, Claude Shannon: information theory, corporate governance, corporate raider, delta neutral, discounted cash flows, diversification, diversified portfolio, Dutch auction, Edward Thorp, family office, fixed income, Henry Singleton, high net worth, index fund, John Bogle, John von Neumann, junk bonds, Louis Bachelier, margin call, merger arbitrage, Paul Samuelson, performance metric, prudent man rule, random walk, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, shareholder value, Sharpe ratio, short selling, survivorship bias, technology bubble, Teledyne, transaction costs, zero-sum game

His research led him to fill three library shelves with books, including Adam Smith’s Wealth of Nations, John von Neumann and Oskar Morgenstern’s Theory of Games and Economic Behavior, Paul Samuelson’s Economics, and Fred Schwed’s Where Are the Customer’s Yachts? In a notebook Shannon recorded a varied list of thinkers, including French mathematician Louis Bachelier, Benjamin 74 Concentrated Investing Graham, and Benoit Mandelbrot. He took notes about margin trading; short selling; stop‐loss orders; the effects of market panics; capital gains taxes and transaction costs. The only surviving document from Shannon’s research is a mimeographed handout from one of the lectures he delivered at MIT in the spring term of 1956, in a class called Seminar of Information Theory.


pages: 292 words: 94,660

The Loop: How Technology Is Creating a World Without Choices and How to Fight Back by Jacob Ward

2021 United States Capitol attack, 4chan, Abraham Wald, AI winter, Albert Einstein, Albert Michelson, Amazon Mechanical Turk, assortative mating, autonomous vehicles, availability heuristic, barriers to entry, Bayesian statistics, Benoit Mandelbrot, Big Tech, bitcoin, Black Lives Matter, Black Swan, blockchain, Broken windows theory, call centre, Cass Sunstein, cloud computing, contact tracing, coronavirus, COVID-19, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, dark matter, data science, deep learning, Donald Trump, drone strike, endowment effect, George Akerlof, George Floyd, hindsight bias, invisible hand, Isaac Newton, Jeffrey Epstein, license plate recognition, lockdown, longitudinal study, Lyft, mandelbrot fractal, Mark Zuckerberg, meta-analysis, natural language processing, non-fungible token, nudge unit, OpenAI, opioid epidemic / opioid crisis, pattern recognition, QAnon, RAND corporation, Richard Thaler, Robert Shiller, selection bias, self-driving car, seminal paper, shareholder value, smart cities, social contagion, social distancing, Steven Levy, survivorship bias, TikTok, Turing test

Goldman titled his article “Lindy’s Law,” and successive generations of writers seized on his theme as a way of predicting the longevity of certain ideas and works of art. This wasn’t just wannabe Late Night writers ruminating over bad coffee. Goldman’s concept launched a whole world of statistical thinking. The mathematician Benoit Mandelbrot updated the model in a 1982 book about fractals to posit that comedians who have made appearances in the past are more likely to make them in the future. Nicholas Taleb carried Mandelbrot’s concept into his book Black Swan, and in his book Antifragile put a specific math to the notion that as an idea survives, its longevity increases.


pages: 347 words: 101,586

Descartes' Error: Emotion, Reason and the Human Brain by António R. Damásio

Albert Einstein, Benoit Mandelbrot, Daniel Kahneman / Amos Tversky, discovery of DNA, experimental subject, longitudinal study, mandelbrot fractal, placebo effect, Richard Feynman, social intelligence, theory of mind

If those symbols were not imageable, we would not know them and would not be able to manipulate them consciously. In this regard, it is interesting to observe that some insightful mathematicians and physicists describe their thinking as dominated by images. Often the images are visual, and they even can be somatosensory. Not surprisingly, Benoit Mandelbrot, whose life work is fractal geometry, says he always thinks in images.14 He relates that the physicist Richard Feynman was not fond of looking at an equation without looking at the illustration that went with it (and note that both equation and illustration were images, in fact). As for Albert Einstein, he had no doubts about the process: The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought.


pages: 111 words: 1

Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by Nassim Nicholas Taleb

Alan Greenspan, Antoine Gombaud: Chevalier de Méré, availability heuristic, backtesting, behavioural economics, 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, financial engineering, fixed income, global village, hedonic treadmill, hindsight bias, junk bonds, Kenneth Arrow, Linda problem, Long Term Capital Management, loss aversion, mandelbrot fractal, Mark Spitznagel, Market Wizards by Jack D. Schwager, mental accounting, meta-analysis, Michael Milken, Myron Scholes, PalmPilot, Paradox of Choice, Paul Samuelson, power law, proprietary trading, public intellectual, quantitative trading / quantitative finance, QWERTY keyboard, random walk, Richard Feynman, risk free rate, road to serfdom, Robert Shiller, selection bias, shareholder value, Sharpe ratio, Steven Pinker, stochastic process, survivorship bias, too big to fail, Tragedy of the Commons, Turing test, Yogi Berra

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.


pages: 337 words: 103,522

The Creativity Code: How AI Is Learning to Write, Paint and Think by Marcus Du Sautoy

3D printing, Ada Lovelace, Albert Einstein, algorithmic bias, AlphaGo, Alvin Roth, Andrew Wiles, Automated Insights, Benoit Mandelbrot, Bletchley Park, Cambridge Analytica, Charles Babbage, Claude Shannon: information theory, computer vision, Computing Machinery and Intelligence, correlation does not imply causation, crowdsourcing, data is the new oil, data science, deep learning, DeepMind, Demis Hassabis, Donald Trump, double helix, Douglas Hofstadter, driverless car, Elon Musk, Erik Brynjolfsson, Fellow of the Royal Society, Flash crash, Gödel, Escher, Bach, Henri Poincaré, Jacquard loom, John Conway, Kickstarter, Loebner Prize, machine translation, mandelbrot fractal, Minecraft, move 37, music of the spheres, Mustafa Suleyman, Narrative Science, natural language processing, Netflix Prize, PageRank, pattern recognition, Paul Erdős, Peter Thiel, random walk, Ray Kurzweil, recommendation engine, Rubik’s Cube, Second Machine Age, Silicon Valley, speech recognition, stable marriage problem, Turing test, Watson beat the top human players on Jeopardy!, wikimedia commons

Perhaps the answer lies in the fact that they do not form a bridge between two conscious worlds. Computer-generated fractals have nonetheless made their creators big money, as fractals have proven to be a highly effective way to simulate the natural world. In his seminal book The Fractal Geometry of Nature, Benoit Mandelbrot explained how Nature uses fractal algorithms to make ferns, clouds, waves, mountains. It was reading this book that inspired Loren Carpenter, an engineer working at Boeing, to experiment with code to simulate natural worlds on the computer. Using the Boeing computers at night-time, he put together a two-minute animation of a fly-through of his computer-generated fractal landscape.


pages: 268 words: 109,447

The Cultural Logic of Computation by David Golumbia

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, American ideology, Benoit Mandelbrot, Bletchley Park, borderless world, business process, cellular automata, citizen journalism, Claude Shannon: information theory, computer age, Computing Machinery and Intelligence, corporate governance, creative destruction, digital capitalism, digital divide, en.wikipedia.org, finite state, folksonomy, future of work, Google Earth, Howard Zinn, IBM and the Holocaust, iterative process, Jaron Lanier, jimmy wales, John von Neumann, Joseph Schumpeter, late capitalism, Lewis Mumford, machine readable, machine translation, means of production, natural language processing, Norbert Wiener, One Laptop per Child (OLPC), packet switching, RAND corporation, Ray Kurzweil, RFID, Richard Stallman, semantic web, Shoshana Zuboff, Slavoj Žižek, social web, stem cell, Stephen Hawking, Steve Ballmer, Stewart Brand, strong AI, supply-chain management, supply-chain management software, technological determinism, Ted Nelson, telemarketer, The Wisdom of Crowds, theory of mind, Turing machine, Turing test, Vannevar Bush, web application, Yochai Benkler

The CCS should be remembered as the first major center to use the words cognitive science, and once again it is fascinating to note who else backed this project: Over the years [the CCS] became a gathering place for those scientists who were most active in the blending of psychology, linguistics, computer modeling, philosophy, and information theory that Miller and Bruner were backing. Noam Chomsky, Nelson Goodman, Benoit Mandelbrot, Donald Norman, Jerrold Katz, Thomas Bever, Eric Lennenberg, and Joseph Weizenbaum were only a few of the dozens of visitors who spent a year or more at the Center between 1960 and 1966. More than $2 million in grant money flowed into the Center’s coffers, mostly from the Carnegie Corporation, the National Institutes of Health, and ARPA.


pages: 323 words: 95,939

Present Shock: When Everything Happens Now by Douglas Rushkoff

"Hurricane Katrina" Superdome, algorithmic trading, Alvin Toffler, Andrew Keen, bank run, behavioural economics, Benoit Mandelbrot, big-box store, Black Swan, British Empire, Buckminster Fuller, business cycle, 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, Future Shock, game design, global pandemic, global supply chain, global village, Howard Rheingold, hypertext link, Inbox Zero, invention of agriculture, invention of hypertext, invisible hand, iterative process, James Bridle, John Nash: game theory, Kevin Kelly, laissez-faire capitalism, lateral thinking, Law of Accelerating Returns, Lewis Mumford, loss aversion, mandelbrot fractal, Marshall McLuhan, Merlin Mann, messenger bag, Milgram experiment, mirror neurons, mutually assured destruction, negative equity, Network effects, New Urbanism, Nicholas Carr, Norbert Wiener, Occupy movement, off-the-grid, passive investing, pattern recognition, peak oil, Peter Pan Syndrome, price mechanism, prisoner's dilemma, Ralph Nelson Elliott, RAND corporation, Ray Kurzweil, recommendation engine, scientific management, selective serotonin reuptake inhibitor (SSRI), Silicon Valley, SimCity, Skype, social graph, South Sea Bubble, Steve Jobs, Steve Wozniak, Steven Pinker, Stewart Brand, supply-chain management, technological determinism, the medium is the message, The Wisdom of Crowds, theory of mind, Tragedy of the Commons, 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.


Growth: From Microorganisms to Megacities by Vaclav Smil

2013 Report for America's Infrastructure - American Society of Civil Engineers - 19 March 2013, 3D printing, agricultural Revolution, air freight, Alan Greenspan, American Society of Civil Engineers: Report Card, Anthropocene, Apollo 11, Apollo Guidance Computer, autonomous vehicles, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Boeing 747, Bretton Woods, British Empire, business cycle, caloric restriction, caloric restriction, carbon tax, circular economy, colonial rule, complexity theory, coronavirus, decarbonisation, degrowth, deindustrialization, dematerialisation, demographic dividend, demographic transition, Deng Xiaoping, disruptive innovation, Dissolution of the Soviet Union, Easter island, endogenous growth, energy transition, epigenetics, Fairchild Semiconductor, Ford Model T, general purpose technology, Gregor Mendel, happiness index / gross national happiness, Helicobacter pylori, high-speed rail, hydraulic fracturing, hydrogen economy, Hyperloop, illegal immigration, income inequality, income per capita, industrial robot, Intergovernmental Panel on Climate Change (IPCC), invention of movable type, Isaac Newton, James Watt: steam engine, knowledge economy, Kondratiev cycle, labor-force participation, Law of Accelerating Returns, longitudinal study, low interest rates, mandelbrot fractal, market bubble, mass immigration, McMansion, megacity, megaproject, megastructure, meta-analysis, microbiome, microplastics / micro fibres, moral hazard, Network effects, new economy, New Urbanism, old age dependency ratio, optical character recognition, out of africa, peak oil, Pearl River Delta, phenotype, Pierre-Simon Laplace, planetary scale, Ponzi scheme, power law, Productivity paradox, profit motive, purchasing power parity, random walk, Ray Kurzweil, Report Card for America’s Infrastructure, Republic of Letters, rolodex, Silicon Valley, Simon Kuznets, social distancing, South China Sea, synthetic biology, techno-determinism, technoutopianism, the market place, The Rise and Fall of American Growth, three-masted sailing ship, total factor productivity, trade liberalization, trade route, urban sprawl, Vilfredo Pareto, yield curve

Jaromír Korčák called attention to the duality of statistical distribution, with the outcome of organic growth organized in normal fashion, while the distribution of the planet’s physical characteristics—area and depth of lakes, size of islands, area of watersheds, length of rivers—follows inverse power law with distributions highly skewed leftward (Korčák 1938 and 1941). Korčák’s law was later made better known, via Fréchet (1941), by Benoit Mandelbrot in his pioneering work on fractals (Mandelbrot 1967, 1975, 1977, 1982). But a recent reexamination of Korčák’s law concluded that his ranked properties cannot be described with a single power-law exponent and hence the law is not strictly valid even for sets consisting of strictly similar fractal objects presented in his original publications (Imre and Novotný 2016).

In the equation N = 10a−bM a indicates the activity rate (how many earthquakes of a given magnitude in a year) and b is usually close to 1 for interplate events but it is higher along oceanic ridges and lower for intraplate earthquakes. Quincy Wright (1942) and Lewis F. Richardson (1948) used power law to explain the variation of the frequency of fatal conflicts with their magnitude. And Benoit Mandelbrot’s pioneering studies of self-similarity and fractal structures further expanded the applications of power laws: after all, the “probability distribution of a self-similar random variable X must be of the form Pr(X>x) = x-D, which is commonly called hyperbolic or Pareto distribution” (Mandelbrot 1977, 320).


pages: 354 words: 105,322

The Road to Ruin: The Global Elites' Secret Plan for the Next Financial Crisis by James Rickards

"World Economic Forum" Davos, Affordable Care Act / Obamacare, Alan Greenspan, Albert Einstein, asset allocation, asset-backed security, bank run, banking crisis, barriers to entry, Bayesian statistics, Bear Stearns, behavioural economics, Ben Bernanke: helicopter money, Benoit Mandelbrot, Berlin Wall, Bernie Sanders, Big bang: deregulation of the City of London, bitcoin, Black Monday: stock market crash in 1987, Black Swan, blockchain, Boeing 747, Bonfire of the Vanities, Bretton Woods, Brexit referendum, British Empire, business cycle, butterfly effect, buy and hold, capital controls, Capital in the Twenty-First Century by Thomas Piketty, Carmen Reinhart, cellular automata, cognitive bias, cognitive dissonance, complexity theory, Corn Laws, corporate governance, creative destruction, Credit Default Swap, cuban missile crisis, currency manipulation / currency intervention, currency peg, currency risk, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, debt deflation, Deng Xiaoping, disintermediation, distributed ledger, diversification, diversified portfolio, driverless car, Edward Lorenz: Chaos theory, Eugene Fama: efficient market hypothesis, failed state, Fall of the Berlin Wall, fiat currency, financial repression, fixed income, Flash crash, floating exchange rates, forward guidance, Fractional reserve banking, G4S, George Akerlof, Glass-Steagall Act, global macro, global reserve currency, high net worth, Hyman Minsky, income inequality, information asymmetry, interest rate swap, Isaac Newton, jitney, John Meriwether, John von Neumann, Joseph Schumpeter, junk bonds, Kenneth Rogoff, labor-force participation, large denomination, liquidity trap, Long Term Capital Management, low interest rates, machine readable, mandelbrot fractal, margin call, market bubble, Mexican peso crisis / tequila crisis, Minsky moment, Money creation, money market fund, mutually assured destruction, Myron Scholes, Naomi Klein, nuclear winter, obamacare, offshore financial centre, operational security, Paul Samuelson, Peace of Westphalia, Phillips curve, Pierre-Simon Laplace, plutocrats, prediction markets, price anchoring, price stability, proprietary trading, public intellectual, quantitative easing, RAND corporation, random walk, reserve currency, RFID, risk free rate, risk-adjusted returns, Robert Solow, Ronald Reagan, Savings and loan crisis, Silicon Valley, sovereign wealth fund, special drawing rights, stock buybacks, stocks for the long run, tech billionaire, The Bell Curve by Richard Herrnstein and Charles Murray, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, theory of mind, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, too big to fail, transfer pricing, value at risk, Washington Consensus, We are all Keynesians now, Westphalian system

Good Money Part I: The New World. Indianapolis: Liberty Fund, 1999. ———. Good Money Part II: The Standard. Indianapolis: Liberty Fund, 1999. Hudson, Michael. Killing the Host: How Financial Parasites and Debt Destroy the Global Economy. Bergenfield, NJ: ISLET, 2015. Hudson, Richard L., and Benoit Mandelbrot. The (Mis)behavior of Markets: A Fractal View of Risk, Ruin, and Reward. New York: Basic Books, 2004. Hui, Pak Ming, Paul Jefferies, and Neil F. Johnson. Financial Market Complexity: What Physics Can Tell Us About Market Behavior. Oxford: Oxford University Press, 2003. Jensen, Henrik Jeldtoft.


pages: 389 words: 109,207

Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street by William Poundstone

"RICO laws" OR "Racketeer Influenced and Corrupt Organizations", Albert Einstein, anti-communist, asset allocation, Bear Stearns, beat the dealer, Benoit Mandelbrot, Black Monday: stock market crash in 1987, Black-Scholes formula, Bletchley Park, Brownian motion, buy and hold, 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, financial engineering, Henry Singleton, high net worth, index fund, interest rate swap, Isaac Newton, Johann Wolfgang von Goethe, John Meriwether, John von Neumann, junk bonds, Kenneth Arrow, Long Term Capital Management, Louis Bachelier, margin call, market bubble, market fundamentalism, Marshall McLuhan, Michael Milken, Myron Scholes, New Journalism, Norbert Wiener, offshore financial centre, Paul Samuelson, publish or perish, quantitative trading / quantitative finance, random walk, risk free rate, risk tolerance, risk-adjusted returns, Robert Shiller, Ronald Reagan, Rubik’s Cube, short selling, speech recognition, statistical arbitrage, Teledyne, The Predators' Ball, The Wealth of Nations by Adam Smith, transaction costs, traveling salesman, value at risk, zero-coupon bond, zero-sum game

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.


pages: 317 words: 107,653

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, Lewis Mumford, Marshall McLuhan, Mercator projection, off-the-grid, Peter Eisenman, place-making, Stewart Brand, telemarketer, The Great Good Place, urban renewal, zero-sum game

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.


pages: 379 words: 109,612

Is the Internet Changing the Way You Think?: The Net's Impact on Our Minds and Future by John Brockman

A Declaration of the Independence of Cyberspace, Albert Einstein, AltaVista, Amazon Mechanical Turk, Asperger Syndrome, availability heuristic, Benoit Mandelbrot, biofilm, Black Swan, bread and circuses, British Empire, conceptual framework, corporate governance, Danny Hillis, disinformation, Douglas Engelbart, Douglas Engelbart, Emanuel Derman, epigenetics, Evgeny Morozov, financial engineering, Flynn Effect, Frank Gehry, Future Shock, Google Earth, hive mind, Howard Rheingold, index card, information retrieval, Internet Archive, invention of writing, Jane Jacobs, Jaron Lanier, John Markoff, John Perry Barlow, Kevin Kelly, Large Hadron Collider, lifelogging, lone genius, loss aversion, mandelbrot fractal, Marc Andreessen, Marshall McLuhan, Menlo Park, meta-analysis, Neal Stephenson, New Journalism, Nicholas Carr, One Laptop per Child (OLPC), out of africa, Paul Samuelson, peer-to-peer, pneumatic tube, Ponzi scheme, power law, pre–internet, Project Xanadu, Richard Feynman, Rodney Brooks, Ronald Reagan, satellite internet, Schrödinger's Cat, search costs, Search for Extraterrestrial Intelligence, SETI@home, Silicon Valley, Skype, slashdot, smart grid, social distancing, social graph, social software, social web, Stephen Hawking, Steve Wozniak, Steven Pinker, Stewart Brand, synthetic biology, Ted Nelson, TED Talk, telepresence, the medium is the message, the scientific method, the strength of weak ties, The Wealth of Nations by Adam Smith, theory of mind, trade route, upwardly mobile, Vernor Vinge, Whole Earth Catalog, X Prize, Yochai Benkler

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.


pages: 319 words: 106,772

Irrational Exuberance: With a New Preface by the Author by Robert J. Shiller

Alan Greenspan, Andrei Shleifer, asset allocation, banking crisis, benefit corporation, Benoit Mandelbrot, book value, business cycle, buy and hold, computer age, correlation does not imply causation, Daniel Kahneman / Amos Tversky, demographic transition, diversification, diversified portfolio, equity premium, Everybody Ought to Be Rich, experimental subject, hindsight bias, income per capita, index fund, Intergovernmental Panel on Climate Change (IPCC), Joseph Schumpeter, Long Term Capital Management, loss aversion, Mahbub ul Haq, mandelbrot fractal, market bubble, market design, market fundamentalism, Mexican peso crisis / tequila crisis, Milgram experiment, money market fund, moral hazard, new economy, open economy, pattern recognition, Phillips curve, Ponzi scheme, price anchoring, random walk, Richard Thaler, risk tolerance, Robert Shiller, Ronald Reagan, Small Order Execution System, spice trade, statistical model, stocks for the long run, Suez crisis 1956, survivorship bias, the market place, Tobin tax, transaction costs, tulip mania, uptick rule, urban decay, Y2K

The literature on applications of chaos theory to economics usually does not stress the kind of price feedback model discussed here, but it may nonetheless offer some insights into the sources of complexity in financial markets. See Michael Boldrin and Michael Woodford, “Equilibrium Models Displaying Endogenous Fluctuations and Chaos: A Survey,” Journal of Monetary Economics, 25(2) (1990): 189–222, for a survey of this literature. See also Benoit Mandelbrot, Fractals and Scaling in Finance: Discontinuity, Concentration, Risk (New York: Springer-Verlag, 1997); and Brian Arthur, John H. Holland, Blake LeBaron, Richard Palmer, and Paul Tayler, “Asset Pricing under Endogenous Expectations in an Artificial Stock Market,” in W. B. Arthur, S. Durlauf, and D.


pages: 407 words: 104,622

The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution by Gregory Zuckerman

affirmative action, Affordable Care Act / Obamacare, Alan Greenspan, Albert Einstein, Andrew Wiles, automated trading system, backtesting, Bayesian statistics, Bear Stearns, beat the dealer, behavioural economics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Black Monday: stock market crash in 1987, blockchain, book value, Brownian motion, butter production in bangladesh, buy and hold, buy low sell high, Cambridge Analytica, Carl Icahn, Claude Shannon: information theory, computer age, computerized trading, Credit Default Swap, Daniel Kahneman / Amos Tversky, data science, diversified portfolio, Donald Trump, Edward Thorp, Elon Musk, Emanuel Derman, endowment effect, financial engineering, Flash crash, George Gilder, Gordon Gekko, illegal immigration, index card, index fund, Isaac Newton, Jim Simons, John Meriwether, John Nash: game theory, John von Neumann, junk bonds, Loma Prieta earthquake, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, Mark Zuckerberg, Michael Milken, Monty Hall problem, More Guns, Less Crime, Myron Scholes, Naomi Klein, natural language processing, Neil Armstrong, obamacare, off-the-grid, p-value, pattern recognition, Peter Thiel, Ponzi scheme, prediction markets, proprietary trading, quantitative hedge fund, quantitative trading / quantitative finance, random walk, Renaissance Technologies, Richard Thaler, Robert Mercer, Ronald Reagan, self-driving car, Sharpe ratio, Silicon Valley, sovereign wealth fund, speech recognition, statistical arbitrage, statistical model, Steve Bannon, Steve Jobs, stochastic process, the scientific method, Thomas Bayes, transaction costs, Turing machine, Two Sigma

A quarter century later, legendary New York Times financial columnist Floyd Norris called it, “the beginning of the destruction of markets by dumb computers. Or, to be fair to the computers, by computers programmed by fallible people and trusted by people who did not understand the computer programs’ limitations. As computers came in, human judgment went out.” During the 1980s, Professor Benoit Mandelbrot—who had demonstrated that certain jagged mathematical shapes called fractals mimic irregularities found in nature—argued that financial markets also have fractal patterns. This theory suggested that markets will deliver more unexpected events than widely assumed, another reason to doubt the elaborate models produced by high-powered computers.


pages: 432 words: 106,612

Trillions: How a Band of Wall Street Renegades Invented the Index Fund and Changed Finance Forever by Robin Wigglesworth

Albert Einstein, algorithmic trading, asset allocation, Bear Stearns, behavioural economics, Benoit Mandelbrot, Big Tech, Black Monday: stock market crash in 1987, Blitzscaling, Brownian motion, buy and hold, California gold rush, capital asset pricing model, Carl Icahn, cloud computing, commoditize, coronavirus, corporate governance, corporate raider, COVID-19, data science, diversification, diversified portfolio, Donald Trump, Elon Musk, Eugene Fama: efficient market hypothesis, fear index, financial engineering, fixed income, Glass-Steagall Act, Henri Poincaré, index fund, industrial robot, invention of the wheel, Japanese asset price bubble, Jeff Bezos, Johannes Kepler, John Bogle, John von Neumann, Kenneth Arrow, lockdown, Louis Bachelier, machine readable, money market fund, Myron Scholes, New Journalism, passive investing, Paul Samuelson, Paul Volcker talking about ATMs, Performance of Mutual Funds in the Period, Peter Thiel, pre–internet, RAND corporation, random walk, risk-adjusted returns, road to serfdom, Robert Shiller, rolodex, seminal paper, Sharpe ratio, short selling, Silicon Valley, sovereign wealth fund, subprime mortgage crisis, the scientific method, transaction costs, uptick rule, Upton Sinclair, Vanguard fund

And that’s how the precocious former jock ended up at the University of Chicago. Aside from a two-year stint as a visiting professor at the University of Leuven in Belgium in the mid-1970s, Fama has stayed true to Chicago ever since the fateful call, and is still teaching in his eighties. It was at Chicago that Fama first met Benoit Mandelbrot, a brilliant Polish-French American mathematician. The peripatetic polymath would occasionally visit the university and give presentations to its graduate students, and ended up taking many long walks around the university’s quadrangles with the young Fama. Crucially, it was Mandelbrot who told the young Italian American about the apparent randomness of financial markets, and Bachelier’s groundbreaking work over half a century earlier.


pages: 396 words: 117,149

The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World by Pedro Domingos

Albert Einstein, Amazon Mechanical Turk, Arthur Eddington, backpropagation, basic income, Bayesian statistics, Benoit Mandelbrot, bioinformatics, Black Swan, Brownian motion, cellular automata, Charles Babbage, Claude Shannon: information theory, combinatorial explosion, computer vision, constrained optimization, correlation does not imply causation, creative destruction, crowdsourcing, Danny Hillis, data is not the new oil, data is the new oil, data science, deep learning, DeepMind, double helix, Douglas Hofstadter, driverless car, Erik Brynjolfsson, experimental subject, Filter Bubble, future of work, Geoffrey Hinton, global village, Google Glasses, Gödel, Escher, Bach, Hans Moravec, incognito mode, information retrieval, Jeff Hawkins, job automation, John Markoff, John Snow's cholera map, John von Neumann, Joseph Schumpeter, Kevin Kelly, large language model, lone genius, machine translation, mandelbrot fractal, Mark Zuckerberg, Moneyball by Michael Lewis explains big data, Narrative Science, Nate Silver, natural language processing, Netflix Prize, Network effects, Nick Bostrom, NP-complete, off grid, P = NP, PageRank, pattern recognition, phenotype, planetary scale, power law, pre–internet, random walk, Ray Kurzweil, recommendation engine, Richard Feynman, scientific worldview, Second Machine Age, self-driving car, Silicon Valley, social intelligence, speech recognition, Stanford marshmallow experiment, statistical model, Stephen Hawking, Steven Levy, Steven Pinker, superintelligent machines, the long tail, 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, yottabyte, zero-sum game

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).


pages: 464 words: 117,495

The New Trading for a Living: Psychology, Discipline, Trading Tools and Systems, Risk Control, Trade Management by Alexander Elder

additive manufacturing, Atul Gawande, backtesting, behavioural economics, Benoit Mandelbrot, buy and hold, buy low sell high, Checklist Manifesto, computerized trading, deliberate practice, diversification, Elliott wave, endowment effect, fear index, loss aversion, mandelbrot fractal, margin call, offshore financial centre, paper trading, Ponzi scheme, price stability, psychological pricing, quantitative easing, random walk, Reminiscences of a Stock Operator, risk tolerance, short selling, South Sea Bubble, systematic trading, systems thinking, The Wisdom of Crowds, transaction costs, transfer pricing, traveling salesman, tulip mania, zero-sum game

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.


Wireless by Charles Stross

air gap, anthropic principle, back-to-the-land, Benoit Mandelbrot, Buckminster Fuller, Cepheid variable, cognitive dissonance, colonial exploitation, cosmic microwave background, Easter island, epigenetics, finite state, Georg Cantor, gravity well, hive mind, hydroponic farming, jitney, Khyber Pass, Late Heavy Bombardment, launch on warning, lifelogging, Magellanic Cloud, mandelbrot fractal, MITM: man-in-the-middle, Neil Armstrong, peak oil, phenotype, Pluto: dwarf planet, security theater, sensible shoes, Turing machine, undersea cable

(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.


Human Frontiers: The Future of Big Ideas in an Age of Small Thinking by Michael Bhaskar

"Margaret Hamilton" Apollo, 3D printing, additive manufacturing, AI winter, Albert Einstein, algorithmic trading, AlphaGo, Anthropocene, artificial general intelligence, augmented reality, autonomous vehicles, backpropagation, barriers to entry, basic income, behavioural economics, Benoit Mandelbrot, Berlin Wall, Big bang: deregulation of the City of London, Big Tech, Bletchley Park, blockchain, Boeing 747, brain emulation, Brexit referendum, call centre, carbon tax, charter city, citizen journalism, Claude Shannon: information theory, Clayton Christensen, clean tech, clean water, cognitive load, Columbian Exchange, coronavirus, cosmic microwave background, COVID-19, creative destruction, CRISPR, crony capitalism, cyber-physical system, dark matter, David Graeber, deep learning, DeepMind, deindustrialization, dematerialisation, Demis Hassabis, demographic dividend, Deng Xiaoping, deplatforming, discovery of penicillin, disruptive innovation, Donald Trump, double entry bookkeeping, Easter island, Edward Jenner, Edward Lorenz: Chaos theory, Elon Musk, en.wikipedia.org, endogenous growth, energy security, energy transition, epigenetics, Eratosthenes, Ernest Rutherford, Eroom's law, fail fast, false flag, Fellow of the Royal Society, flying shuttle, Ford Model T, Francis Fukuyama: the end of history, general purpose technology, germ theory of disease, glass ceiling, global pandemic, Goodhart's law, Google Glasses, Google X / Alphabet X, GPT-3, Haber-Bosch Process, hedonic treadmill, Herman Kahn, Higgs boson, hive mind, hype cycle, Hyperloop, Ignaz Semmelweis: hand washing, Innovator's Dilemma, intangible asset, interchangeable parts, Internet of things, invention of agriculture, invention of the printing press, invention of the steam engine, invention of the telegraph, invisible hand, Isaac Newton, ITER tokamak, James Watt: steam engine, James Webb Space Telescope, Jeff Bezos, jimmy wales, job automation, Johannes Kepler, John von Neumann, Joseph Schumpeter, Kenneth Arrow, Kevin Kelly, Kickstarter, knowledge economy, knowledge worker, Large Hadron Collider, liberation theology, lockdown, lone genius, loss aversion, Louis Pasteur, Mark Zuckerberg, Martin Wolf, megacity, megastructure, Menlo Park, Minecraft, minimum viable product, mittelstand, Modern Monetary Theory, Mont Pelerin Society, Murray Gell-Mann, Mustafa Suleyman, natural language processing, Neal Stephenson, nuclear winter, nudge unit, oil shale / tar sands, open economy, OpenAI, opioid epidemic / opioid crisis, PageRank, patent troll, Peter Thiel, plutocrats, post scarcity, post-truth, precautionary principle, public intellectual, publish or perish, purchasing power parity, quantum entanglement, Ray Kurzweil, remote working, rent-seeking, Republic of Letters, Richard Feynman, Robert Gordon, Robert Solow, secular stagnation, shareholder value, Silicon Valley, Silicon Valley ideology, Simon Kuznets, skunkworks, Slavoj Žižek, sovereign wealth fund, spinning jenny, statistical model, stem cell, Steve Jobs, Stuart Kauffman, synthetic biology, techlash, TED Talk, The Rise and Fall of American Growth, the scientific method, The Wealth of Nations by Adam Smith, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, TikTok, total factor productivity, transcontinental railway, Two Sigma, Tyler Cowen, Tyler Cowen: Great Stagnation, universal basic income, uranium enrichment, We wanted flying cars, instead we got 140 characters, When a measure becomes a target, X Prize, Y Combinator

It encompassed mathematics, meteorology, population ecology, epidemiology, physics and economics, underwritten by advances in computing and computer science and applied to topics as various as the organs of the human body, atmospheric storms and a beam of particles. Names like Edward Lorenz, Mary Cartright, Benoit Mandelbrot and Mitchell Feigenbaum were all closely connected, but it didn't have one great progenitor in the manner of a Darwin or Pasteur. The study of complexity is itself, perhaps unsurprisingly, complex, transdisciplinary, composed of different foci and sub-ideas, while nonetheless adding up to something big and revolutionary.


pages: 483 words: 141,836

Red-Blooded Risk: The Secret History of Wall Street by Aaron Brown, Eric Kim

Abraham Wald, activist fund / activist shareholder / activist investor, Albert Einstein, algorithmic trading, Asian financial crisis, Atul Gawande, backtesting, Basel III, Bayesian statistics, Bear Stearns, beat the dealer, Benoit Mandelbrot, Bernie Madoff, Black Swan, book value, business cycle, capital asset pricing model, carbon tax, central bank independence, Checklist Manifesto, corporate governance, creative destruction, credit crunch, Credit Default Swap, currency risk, disintermediation, distributed generation, diversification, diversified portfolio, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, experimental subject, fail fast, fear index, financial engineering, financial innovation, global macro, illegal immigration, implied volatility, independent contractor, index fund, John Bogle, junk bonds, Long Term Capital Management, loss aversion, low interest rates, managed futures, margin call, market clearing, market fundamentalism, market microstructure, Money creation, 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, power law, pre–internet, proprietary trading, quantitative trading / quantitative finance, random walk, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, road to serfdom, Robert Shiller, shareholder value, Sharpe ratio, special drawing rights, statistical arbitrage, stochastic volatility, stock buybacks, stocks for the long run, tail risk, The Myth of the Rational Market, Thomas Bayes, too big to fail, transaction costs, value at risk, yield curve

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.


pages: 502 words: 132,062

Ways of Being: Beyond Human Intelligence by James Bridle

Ada Lovelace, Airbnb, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Anthropocene, Any sufficiently advanced technology is indistinguishable from magic, autonomous vehicles, behavioural economics, Benoit Mandelbrot, Berlin Wall, Big Tech, Black Lives Matter, blockchain, Californian Ideology, Cambridge Analytica, carbon tax, Charles Babbage, cloud computing, coastline paradox / Richardson effect, Computing Machinery and Intelligence, corporate personhood, COVID-19, cryptocurrency, DeepMind, Donald Trump, Douglas Hofstadter, Elon Musk, experimental subject, factory automation, fake news, friendly AI, gig economy, global pandemic, Gödel, Escher, Bach, impulse control, James Bridle, James Webb Space Telescope, John von Neumann, Kickstarter, Kim Stanley Robinson, language acquisition, life extension, mandelbrot fractal, Marshall McLuhan, microbiome, music of the spheres, negative emissions, Nick Bostrom, Norbert Wiener, paperclip maximiser, pattern recognition, peer-to-peer, planetary scale, RAND corporation, random walk, recommendation engine, self-driving car, SETI@home, shareholder value, Silicon Valley, Silicon Valley ideology, speech recognition, statistical model, surveillance capitalism, techno-determinism, technological determinism, technoutopianism, the long tail, the scientific method, The Soul of a New Machine, theory of mind, traveling salesman, trolley problem, Turing complete, Turing machine, Turing test, UNCLOS, undersea cable, urban planning, Von Neumann architecture, wikimedia commons, zero-sum game

On each measurement, the reading would get more accurate, with more and more of the coastline accounted for. But the result, as Richardson realized, was not that the measurement converged on the correct answer but rather, the more closely it was measured, the longer it got. What Richardson had discovered was what the mathematician Benoit Mandelbrot would later term ‘fractals’: structures which repeat to infinite complexity. Instead of resolving into order and clarity, ever-closer examination reveals only more, and more splendid, detail and variation.26 The Richardson effect applies to biology, archaeology, evolution and, it seems, to life itself.


pages: 573 words: 142,376

Whole Earth: The Many Lives of Stewart Brand by John Markoff

A Pattern Language, air freight, Anthropocene, Apple II, back-to-the-land, Benoit Mandelbrot, Bernie Madoff, Beryl Markham, Big Tech, Bill Atkinson, Biosphere 2, Brewster Kahle, Buckminster Fuller, Burning Man, butterfly effect, Claude Shannon: information theory, cloud computing, complexity theory, computer age, Computer Lib, computer vision, Danny Hillis, decarbonisation, demographic transition, disinformation, Douglas Engelbart, Douglas Engelbart, Dynabook, El Camino Real, Electric Kool-Aid Acid Test, en.wikipedia.org, experimental subject, feminist movement, Fillmore Auditorium, San Francisco, Filter Bubble, game design, gentrification, global village, Golden Gate Park, Hacker Conference 1984, Hacker Ethic, Haight Ashbury, Herman Kahn, housing crisis, Howard Rheingold, HyperCard, intentional community, Internet Archive, Internet of things, Jane Jacobs, Jaron Lanier, Jeff Bezos, John Gilmore, John Markoff, John Perry Barlow, Kevin Kelly, Kickstarter, knowledge worker, Lao Tzu, Lewis Mumford, Loma Prieta earthquake, Marshall McLuhan, megacity, Menlo Park, Michael Shellenberger, microdosing, Mitch Kapor, Morris worm, Mother of all demos, move fast and break things, New Urbanism, Norbert Wiener, Norman Mailer, North Sea oil, off grid, off-the-grid, paypal mafia, Peter Calthorpe, Ponzi scheme, profit motive, public intellectual, Ralph Nader, RAND corporation, Ray Kurzweil, Richard Stallman, Sand Hill Road, self-driving car, shareholder value, Silicon Valley, South of Market, San Francisco, speech recognition, Steve Jobs, Steve Wozniak, Steven Levy, Stewart Brand, systems thinking, technoutopianism, Ted Nelson, Ted Nordhaus, TED Talk, The Death and Life of Great American Cities, The Hackers Conference, Thorstein Veblen, traveling salesman, Turing test, upwardly mobile, Vernor Vinge, We are as Gods, Whole Earth Catalog, Whole Earth Review, young professional

The event, held in a hotel conference center in Monterey in February of 1984, was a little-noticed affair attended by a relatively intimate group (compared to later conferences) of 250 artists, writers, musicians, corporate execs, and scientists united by their “faith in the computer.”[18] IBM mathematician Benoit Mandelbrot and Megatrends futurist John Naisbitt both spoke, but it was Negroponte who stole the show. Dressed in a dapper gray suit and tie and with a rich mane of longish hair, he showed off in his “TED Talk” (the term had yet to become a marque—and, in some quarters, a pigeonhole) a variety of futuristic technologies for interacting with computers, including touch screen manipulation, which would not become commonplace until a quarter century later with the introduction of the iPhone.


pages: 369 words: 153,018

Power, Sex, Suicide: Mitochondria and the Meaning of Life by Nick Lane

Benoit Mandelbrot, caloric restriction, caloric restriction, clockwork universe, double helix, Drosophila, Geoffrey West, Santa Fe Institute, Louis Pasteur, mandelbrot fractal, out of africa, phenotype, power law, random walk, Recombinant DNA, Richard Feynman, seminal paper, 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?


pages: 608 words: 150,324

Life's Greatest Secret: The Race to Crack the Genetic Code by Matthew Cobb

a long time ago in a galaxy far, far away, Anthropocene, anti-communist, Asilomar, Asilomar Conference on Recombinant DNA, Benoit Mandelbrot, Berlin Wall, bioinformatics, Claude Shannon: information theory, conceptual framework, Copley Medal, CRISPR, dark matter, discovery of DNA, double helix, Drosophila, epigenetics, factory automation, From Mathematics to the Technologies of Life and Death, Gregor Mendel, heat death of the universe, James Watt: steam engine, John von Neumann, Kickstarter, Large Hadron Collider, military-industrial complex, New Journalism, Norbert Wiener, phenotype, post-materialism, Recombinant DNA, Stephen Hawking, synthetic biology

For a biologist, argued Lwoff, the only meaning of information was ‘a sequence of small molecules and the set of functions they carry out’.30 Wiener and the philosophers who were present could not see what the problem was, thereby inadvertently illustrating the gulf between the information theoreticians and the biologists. Similar mutual incomprehension was revealed in the other sessions, which were often fractious. The mathematician Benoît Mandelbrot suggested that such information-focused cross-disciplinary meetings were pointless: The implications of the strict meaning of information have sufficiently explored for its consequences to be quite clear. What remains is so difficult that it can usefully be discussed only in private … we must consider that its scientific usefulness has ceased, at least for the time being’.31 Alongside these rather sterile plenary discussions there were workshops in which experts in the various fields explored their topic in more detail.


The Volatility Smile by Emanuel Derman,Michael B.Miller

Albert Einstein, Asian financial crisis, Benoit Mandelbrot, Black Monday: stock market crash in 1987, book value, Brownian motion, capital asset pricing model, collateralized debt obligation, continuous integration, Credit Default Swap, credit default swaps / collateralized debt obligations, discrete time, diversified portfolio, dividend-yielding stocks, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial engineering, fixed income, implied volatility, incomplete markets, law of one price, London Whale, mandelbrot fractal, market bubble, market friction, Myron Scholes, prediction markets, quantitative trading / quantitative finance, risk tolerance, riskless arbitrage, Sharpe ratio, statistical arbitrage, stochastic process, stochastic volatility, transaction costs, volatility arbitrage, volatility smile, Wiener process, yield curve, zero-coupon bond

We can use Equation 24.48 to get the approximate formula for the smile in Figure 24.6, which is (√ √ 𝜆 𝜏e−𝜆𝜏 J 𝜋 ) ( ) K 1 + √ ln 𝛴 ≈𝜎+ 2 𝜎 𝜏 S S ( ) K ≈ 0.102 + 0.56 × ln S (24.50) which is a good approximation to the exact results near at-the-money. 416 THE VOLATILITY SMILE FURTHER THOUGHTS AND READING Merton’s model of jump-diffusion regards jumps as “abnormal” market events that have to be superimposed upon “normal” diffusion. The view that the market has two regimes of behavior, normal and abnormal, is regarded as contrived both by Benoit Mandelbrot and by Eugene Stanley and his econophysics collaborators. To paraphrase their view, a single model rather than a mixture of “normal” and “abnormal” models should ideally explain all events. END-OF-CHAPTER PROBLEMS 24-1. Estimate the price of a 24,000 strike put with two weeks to expiration on the Hang Seng Index (HSI).


pages: 542 words: 145,022

In Pursuit of the Perfect Portfolio: The Stories, Voices, and Key Insights of the Pioneers Who Shaped the Way We Invest by Andrew W. Lo, Stephen R. Foerster

Alan Greenspan, Albert Einstein, AOL-Time Warner, asset allocation, backtesting, behavioural economics, Benoit Mandelbrot, Black Monday: stock market crash in 1987, Black-Scholes formula, Bretton Woods, Brownian motion, business cycle, buy and hold, capital asset pricing model, Charles Babbage, Charles Lindbergh, compound rate of return, corporate governance, COVID-19, credit crunch, currency risk, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, Donald Trump, Edward Glaeser, equity premium, equity risk premium, estate planning, Eugene Fama: efficient market hypothesis, fake news, family office, fear index, fiat currency, financial engineering, financial innovation, financial intermediation, fixed income, hiring and firing, Hyman Minsky, implied volatility, index fund, interest rate swap, Internet Archive, invention of the wheel, Isaac Newton, Jim Simons, John Bogle, John Meriwether, John von Neumann, joint-stock company, junk bonds, Kenneth Arrow, linear programming, Long Term Capital Management, loss aversion, Louis Bachelier, low interest rates, managed futures, mandelbrot fractal, margin call, market bubble, market clearing, mental accounting, money market fund, money: store of value / unit of account / medium of exchange, Myron Scholes, new economy, New Journalism, Own Your Own Home, passive investing, Paul Samuelson, Performance of Mutual Funds in the Period, prediction markets, price stability, profit maximization, quantitative trading / quantitative finance, RAND corporation, random walk, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Solow, Ronald Reagan, Savings and loan crisis, selection bias, seminal paper, shareholder value, Sharpe ratio, short selling, South Sea Bubble, stochastic process, stocks for the long run, survivorship bias, tail risk, Thales and the olive presses, Thales of Miletus, The Myth of the Rational Market, The Wisdom of Crowds, Thomas Bayes, time value of money, transaction costs, transfer pricing, tulip mania, Vanguard fund, yield curve, zero-coupon bond, zero-sum game

He later mused, “I wonder what path my professional life would have taken if Jeff didn’t answer the phone that day. Serendipity!”12 Fama attended Chicago’s PhD program in economics between 1960 and 1964. In his second year, near the completion of his coursework, he began to attend the department’s Econometrics Workshop. An occasional presenter was Benoit Mandelbrot, a highly regarded mathematician on staff as a researcher at the IBM Thomas J. Watson Research Center and a visiting professor at Harvard University, today best known for his work on fractals and their irregular geometry. Fama enjoyed strolling the campus with Mandelbrot and learned much about probability distributions from him, including Mandelbrot’s research on cotton prices.


pages: 565 words: 164,405

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, cotton gin, David Ricardo: comparative advantage, death from overwork, deindustrialization, Doha Development Round, domestication of the camel, double entry bookkeeping, Easter island, Eratosthenes, financial innovation, flying shuttle, Gini coefficient, God and Mammon, high-speed rail, 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, Suez canal 1869, The Wealth of Nations by Adam Smith, Thomas L Friedman, Thomas Malthus, trade liberalization, trade route, transatlantic slave trade, transcontinental railway, two and twenty, upwardly mobile, working poor, zero-sum game

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.


pages: 512 words: 162,977

New Market Wizards: Conversations With America's Top Traders by Jack D. Schwager

backtesting, beat the dealer, Benoit Mandelbrot, Berlin Wall, Black-Scholes formula, book value, butterfly effect, buy and hold, commodity trading advisor, computerized trading, currency risk, Edward Thorp, Elliott wave, fixed income, full employment, implied volatility, interest rate swap, Louis Bachelier, margin call, market clearing, market fundamentalism, Market Wizards by Jack D. Schwager, money market fund, paper trading, pattern recognition, placebo effect, prediction markets, proprietary trading, Ralph Nelson Elliott, random walk, Reminiscences of a Stock Operator, risk tolerance, risk/return, Saturday Night Live, Sharpe ratio, the map is not the territory, transaction costs, uptick rule, War on Poverty

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.


pages: 923 words: 163,556

Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures by Frank J. Fabozzi

algorithmic trading, Benoit Mandelbrot, Black Monday: stock market crash in 1987, capital asset pricing model, collateralized debt obligation, correlation coefficient, distributed generation, diversified portfolio, financial engineering, fixed income, global macro, index fund, junk bonds, Louis Bachelier, Myron Scholes, p-value, power law, quantitative trading / quantitative finance, random walk, risk free rate, risk-adjusted returns, short selling, stochastic volatility, subprime mortgage crisis, Thomas Bayes, transaction costs, value at risk

The immense threat radiating from heavy tails in stock return distributions made industry professionals aware of the urgency to take them serious and reflect them in their models. Many distributional alternatives providing more realistic chances to severe price movements have been presented earlier, such as the Student’s t in Chapter 11 or GEV distributions earlier in this chapter, for example. In the early 1960s, Benoit Mandelbrot suggested as a distribution for commodity price changes the class of stable distributions. The reason is that, through their particular parameterization, they are capable of modeling moderate scenarios as supported by the normal distribution as well as extreme ones beyond the scope of most of the distributions that we have presented in this chapter.


pages: 614 words: 174,226

The Economists' Hour: How the False Prophets of Free Markets Fractured Our Society by Binyamin Appelbaum

90 percent rule, airline deregulation, Alan Greenspan, Alvin Roth, Andrei Shleifer, anti-communist, battle of ideas, Benoit Mandelbrot, Big bang: deregulation of the City of London, Bretton Woods, British Empire, business cycle, capital controls, Carmen Reinhart, Cass Sunstein, Celtic Tiger, central bank independence, clean water, collective bargaining, Corn Laws, correlation does not imply causation, Credit Default Swap, currency manipulation / currency intervention, David Ricardo: comparative advantage, deindustrialization, Deng Xiaoping, desegregation, Diane Coyle, Donald Trump, Dr. Strangelove, ending welfare as we know it, financial deregulation, financial engineering, financial innovation, fixed income, flag carrier, floating exchange rates, full employment, George Akerlof, George Gilder, Gini coefficient, greed is good, Greenspan put, Growth in a Time of Debt, Ida Tarbell, income inequality, income per capita, index fund, inflation targeting, invisible hand, Isaac Newton, It's morning again in America, Jean Tirole, John Markoff, Kenneth Arrow, Kenneth Rogoff, land reform, Les Trente Glorieuses, long and variable lags, Long Term Capital Management, low cost airline, low interest rates, manufacturing employment, means of production, Menlo Park, minimum wage unemployment, Mohammed Bouazizi, money market fund, Mont Pelerin Society, Network effects, new economy, Nixon triggered the end of the Bretton Woods system, oil shock, Paul Samuelson, Philip Mirowski, Phillips curve, plutocrats, precautionary principle, price stability, profit motive, public intellectual, Ralph Nader, RAND corporation, rent control, rent-seeking, Richard Thaler, road to serfdom, Robert Bork, Robert Gordon, Robert Solow, Ronald Coase, Ronald Reagan, Sam Peltzman, Savings and loan crisis, Silicon Valley, Simon Kuznets, starchitect, Steve Bannon, Steve Jobs, supply-chain management, The Chicago School, The Great Moderation, The Myth of the Rational Market, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, transaction costs, trickle-down economics, ultimatum game, Unsafe at Any Speed, urban renewal, War on Poverty, Washington Consensus, We are all Keynesians now

Fama, “Efficient Capital Markets: A Review of Theory and Empirical Work,” Journal of Finance 25, no. 2 (1970). 15. The theory said nobody, no matter how smart, could predict the future movements of stock prices based on the information already in existence. The movement would be determined by what happened next. The economist Benoit Mandelbrot compared markets to a drunken man in an open field: he might stumble in any direction; he might double back on his own tracks. The only useful information about where he would end up was where he stood at the start. The theory actually comes in three progressively stronger formulations. The weakest version says past price movements cannot be used to forecast future price movements.


pages: 584 words: 187,436

More Money Than God: Hedge Funds and the Making of a New Elite by Sebastian Mallaby

Alan Greenspan, Andrei Shleifer, Asian financial crisis, asset-backed security, automated trading system, bank run, barriers to entry, Bear Stearns, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Bonfire of the Vanities, book value, Bretton Woods, business cycle, buy and hold, 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, deal flow, do well by doing good, Elliott wave, Eugene Fama: efficient market hypothesis, failed state, Fall of the Berlin Wall, financial deregulation, financial engineering, financial innovation, financial intermediation, fixed income, full employment, German hyperinflation, High speed trading, index fund, Jim Simons, John Bogle, John Meriwether, junk bonds, Kenneth Rogoff, Kickstarter, Long Term Capital Management, low interest rates, machine translation, margin call, market bubble, market clearing, market fundamentalism, Market Wizards by Jack D. Schwager, Mary Meeker, merger arbitrage, Michael Milken, money market fund, moral hazard, Myron Scholes, natural language processing, Network effects, new economy, Nikolai Kondratiev, operational security, pattern recognition, Paul Samuelson, pre–internet, proprietary trading, public intellectual, quantitative hedge fund, quantitative trading / quantitative finance, random walk, Renaissance Technologies, Richard Thaler, risk-adjusted returns, risk/return, Robert Mercer, rolodex, Savings and loan crisis, Sharpe ratio, short selling, short squeeze, Silicon Valley, South Sea Bubble, sovereign wealth fund, statistical arbitrage, statistical model, survivorship bias, tail risk, technology bubble, The Great Moderation, The Myth of the Rational Market, the new new thing, too big to fail, transaction costs, two and twenty, uptick rule

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.


pages: 626 words: 181,434

I Am a Strange Loop by Douglas R. Hofstadter

Albert Einstein, Andrew Wiles, Benoit Mandelbrot, Brownian motion, Charles Babbage, double helix, Douglas Hofstadter, Georg Cantor, Gödel, Escher, Bach, Hans Moravec, Isaac Newton, James Watt: steam engine, John Conway, John von Neumann, language acquisition, 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

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.


pages: 999 words: 194,942

Clojure Programming by Chas Emerick, Brian Carper, Christophe Grand

Amazon Web Services, Benoit Mandelbrot, cloud computing, cognitive load, continuous integration, database schema, domain-specific language, don't repeat yourself, drop ship, duck typing, en.wikipedia.org, failed state, finite state, Firefox, functional programming, game design, general-purpose programming language, Guido van Rossum, higher-order functions, Larry Wall, mandelbrot fractal, no silver bullet, Paul Graham, platform as a service, premature optimization, random walk, Ruby on Rails, Schrödinger's Cat, semantic web, software as a service, sorting algorithm, SQL injection, Turing complete, type inference, web application

* * * [349] 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. [350] 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.


pages: 829 words: 186,976

The Signal and the Noise: Why So Many Predictions Fail-But Some Don't by Nate Silver

airport security, Alan Greenspan, Alvin Toffler, An Inconvenient Truth, availability heuristic, Bayesian statistics, Bear Stearns, behavioural economics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, big-box store, Black Monday: stock market crash in 1987, Black Swan, Boeing 747, book value, Broken windows theory, business cycle, buy and hold, Carmen Reinhart, Charles Babbage, classic study, 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, disinformation, 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, Ford Model T, Freestyle chess, fudge factor, Future Shock, George Akerlof, global pandemic, Goodhart's law, haute cuisine, Henri Poincaré, high batting average, housing crisis, income per capita, index fund, information asymmetry, Intergovernmental Panel on Climate Change (IPCC), Internet Archive, invention of the printing press, invisible hand, Isaac Newton, James Watt: steam engine, Japanese asset price bubble, John Bogle, John Nash: game theory, John von Neumann, Kenneth Rogoff, knowledge economy, Laplace demon, 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, Oklahoma City bombing, PageRank, pattern recognition, pets.com, Phillips curve, Pierre-Simon Laplace, Plato's cave, power law, prediction markets, Productivity paradox, proprietary trading, public intellectual, random walk, Richard Thaler, Robert Shiller, Robert Solow, Rodney Brooks, Ronald Reagan, Saturday Night Live, savings glut, security theater, short selling, SimCity, 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, Timothy McVeigh, too big to fail, transaction costs, transfer pricing, University of East Anglia, Watson beat the top human players on Jeopardy!, Wayback Machine, wikimedia commons

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.)


pages: 823 words: 220,581

Debunking Economics - Revised, Expanded and Integrated Edition: The Naked Emperor Dethroned? by Steve Keen

accounting loophole / creative accounting, Alan Greenspan, banking crisis, banks create money, barriers to entry, behavioural economics, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black Swan, Bonfire of the Vanities, book value, business cycle, 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, equity risk premium, Eugene Fama: efficient market hypothesis, experimental subject, Financial Instability Hypothesis, fixed income, Fractional reserve banking, full employment, Glass-Steagall Act, Greenspan put, Henri Poincaré, housing crisis, Hyman Minsky, income inequality, information asymmetry, invisible hand, iterative process, John von Neumann, Kickstarter, laissez-faire capitalism, liquidity trap, Long Term Capital Management, low interest rates, mandelbrot fractal, margin call, market bubble, market clearing, market microstructure, means of production, minimum wage unemployment, Money creation, money market fund, open economy, Pareto efficiency, Paul Samuelson, Phillips curve, place-making, Ponzi scheme, Post-Keynesian economics, power law, profit maximization, quantitative easing, RAND corporation, random walk, risk free rate, risk tolerance, risk/return, Robert Shiller, Robert Solow, Ronald Coase, Savings and loan crisis, 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

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.


pages: 795 words: 212,447

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, dual-use technology, failed state, false flag, friendly fire, Google Earth, Panamax, post-Panamax, Skype, uranium enrichment, urban sprawl

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?”


pages: 824 words: 218,333

The Gene: An Intimate History by Siddhartha Mukherjee

Albert Einstein, Alfred Russel Wallace, All science is either physics or stamp collecting, Any sufficiently advanced technology is indistinguishable from magic, Asilomar, Asilomar Conference on Recombinant DNA, autism spectrum disorder, Benoit Mandelbrot, butterfly effect, CRISPR, dark matter, discovery of DNA, double helix, Drosophila, epigenetics, Ernest Rutherford, experimental subject, Gregor Mendel, Internet Archive, invisible hand, Isaac Newton, longitudinal study, medical residency, military-industrial complex, moral hazard, mouse model, New Journalism, out of africa, phenotype, Pierre-Simon Laplace, planned obsolescence, Ponzi scheme, Ralph Waldo Emerson, Recombinant DNA, Scientific racism, seminal paper, stem cell, The Bell Curve by Richard Herrnstein and Charles Murray, Thomas Malthus, twin studies

“Important Biological Objects Come in Pairs” One could not be a successful scientist without realizing that, in contrast to the popular conception supported by newspapers and the mothers of scientists, a goodly number of scientists are not only narrow-minded and dull, but also just stupid. —James Watson It is the molecule that has the glamour, not the scientists. —Francis Crick Science [would be] ruined if—like sports—it were to put competition above everything else. —Benoit Mandelbrot Oswald Avery’s experiment achieved another “transformation.” DNA, once the underdog of all biological molecules, was thrust into the limelight. Although some scientists initially resisted the idea that genes were made of DNA, Avery’s evidence was hard to shrug off (despite three nominations, however, Avery was still denied the Nobel Prize because Einar Hammarsten, the influential Swedish chemist, refused to believe that DNA could carry genetic information).


pages: 745 words: 207,187

Accessory to War: The Unspoken Alliance Between Astrophysics and the Military by Neil Degrasse Tyson, Avis Lang

active measures, Admiral Zheng, airport security, anti-communist, Apollo 11, Arthur Eddington, Benoit Mandelbrot, Berlin Wall, British Empire, Buckminster Fuller, Carrington event, Charles Lindbergh, collapse of Lehman Brothers, Colonization of Mars, commoditize, corporate governance, cosmic microwave background, credit crunch, cuban missile crisis, dark matter, Dava Sobel, disinformation, Donald Trump, Doomsday Clock, Dr. Strangelove, dual-use technology, Eddington experiment, Edward Snowden, energy security, Eratosthenes, European colonialism, fake news, Fellow of the Royal Society, Ford Model T, global value chain, Google Earth, GPS: selective availability, Great Leap Forward, Herman Kahn, Higgs boson, invention of movable type, invention of the printing press, invention of the telescope, Isaac Newton, James Webb Space Telescope, Johannes Kepler, John Harrison: Longitude, Karl Jansky, Kuiper Belt, Large Hadron Collider, Late Heavy Bombardment, Laura Poitras, Lewis Mumford, lone genius, low earth orbit, mandelbrot fractal, Maui Hawaii, Mercator projection, Mikhail Gorbachev, military-industrial complex, mutually assured destruction, Neil Armstrong, New Journalism, Northpointe / Correctional Offender Management Profiling for Alternative Sanctions, operation paperclip, pattern recognition, Pierre-Simon Laplace, precision agriculture, prediction markets, profit motive, Project Plowshare, purchasing power parity, quantum entanglement, RAND corporation, Ronald Reagan, Search for Extraterrestrial Intelligence, skunkworks, South China Sea, space junk, Stephen Hawking, Strategic Defense Initiative, subprime mortgage crisis, the long tail, time dilation, trade route, War on Poverty, wikimedia commons, zero-sum game

Today (presumably taking into account only some of the ins and outs), according to the Ordnance Survey, Britain’s national mapping agency, “The coastline length around mainland Great Britain is 11,072.76 miles,” www.ordnancesurvey.co.uk/oswebsite/freefun/didyouknow/ (accessed May 17, 2010). But as Benoit Mandelbrot famously proposed in “How Long Is the Coastline of Britain?” there is no end of different numbers. Nevertheless, Pytheas was certainly on the right track compared with contemporaries of his, such as the disbelieving Strabo. 20.Roseman, Pytheas, 7–20, writes that eighteen known ancient writers referred to Pytheas by name between 300 BC and AD 550, notably Eratosthenes, Hipparkhos, Polybius, Strabo, and Pliny the Elder.


pages: 761 words: 231,902

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, backpropagation, Benoit Mandelbrot, Bill Joy: nanobots, bioinformatics, brain emulation, Brewster Kahle, Brownian motion, business cycle, business intelligence, c2.com, call centre, carbon-based life, cellular automata, Charles Babbage, Claude Shannon: information theory, complexity theory, conceptual framework, Conway's Game of Life, coronavirus, cosmological constant, cosmological principle, cuban missile crisis, data acquisition, Dava Sobel, David Brooks, Dean Kamen, digital divide, disintermediation, double helix, Douglas Hofstadter, en.wikipedia.org, epigenetics, factory automation, friendly AI, functional programming, George Gilder, Gödel, Escher, Bach, Hans Moravec, hype cycle, informal economy, information retrieval, information security, invention of the telephone, invention of the telescope, invention of writing, 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, Marshall McLuhan, Mikhail Gorbachev, Mitch Kapor, mouse model, Murray Gell-Mann, mutually assured destruction, natural language processing, Network effects, new economy, Nick Bostrom, Norbert Wiener, oil shale / tar sands, optical character recognition, PalmPilot, pattern recognition, phenotype, power law, precautionary principle, premature optimization, punch-card reader, quantum cryptography, quantum entanglement, radical life extension, randomized controlled trial, Ray Kurzweil, remote working, reversible computing, Richard Feynman, Robert Metcalfe, Rodney Brooks, scientific worldview, Search for Extraterrestrial Intelligence, selection bias, semantic web, seminal paper, Silicon Valley, Singularitarianism, speech recognition, statistical model, stem cell, Stephen Hawking, Stewart Brand, strong AI, Stuart Kauffman, superintelligent machines, technological singularity, Ted Kaczynski, telepresence, The Coming Technological Singularity, Thomas Bayes, transaction costs, Turing machine, Turing test, two and twenty, Vernor Vinge, Y2K, Yogi Berra

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.


The Sum of All Fears by Tom Clancy

"RICO laws" OR "Racketeer Influenced and Corrupt Organizations", accounting loophole / creative accounting, airport security, Benoit Mandelbrot, Boeing 747, British Empire, colonial exploitation, complexity theory, cuban missile crisis, demand response, disinformation, false flag, financial independence, flag carrier, Herman Kahn, index card, mandelbrot fractal, operational security, Suez crisis 1956, trade route, uranium enrichment

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.


pages: 1,079 words: 321,718

Surfaces and Essences by Douglas Hofstadter, Emmanuel Sander

Abraham Maslow, affirmative action, Albert Einstein, Arthur Eddington, Benoit Mandelbrot, Brownian motion, Charles Babbage, cognitive dissonance, computer age, computer vision, dematerialisation, Donald Trump, Douglas Hofstadter, Eddington experiment, Ernest Rutherford, experimental subject, Flynn Effect, gentrification, Georg Cantor, Gerolamo Cardano, Golden Gate Park, haute couture, haute cuisine, Henri Poincaré, Isaac Newton, l'esprit de l'escalier, Louis Pasteur, machine translation, Mahatma Gandhi, mandelbrot fractal, Menlo Park, Norbert Wiener, place-making, Sapir-Whorf hypothesis, Silicon Valley, statistical model, Steve Jobs, Steve Wozniak, theory of mind, time dilation, 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.


pages: 1,242 words: 317,903

The Man Who Knew: The Life and Times of Alan Greenspan by Sebastian Mallaby

airline deregulation, airport security, Alan Greenspan, Alvin Toffler, Andrei Shleifer, anti-communist, Asian financial crisis, balance sheet recession, bank run, barriers to entry, Bear Stearns, behavioural economics, Benoit Mandelbrot, Black Monday: stock market crash in 1987, bond market vigilante , book value, Bretton Woods, business cycle, central bank independence, centralized clearinghouse, classic study, 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, Dr. Strangelove, energy security, equity premium, fiat currency, financial deregulation, financial engineering, financial innovation, fixed income, Flash crash, forward guidance, full employment, Future Shock, Glass-Steagall Act, Greenspan put, Hyman Minsky, inflation targeting, information asymmetry, interest rate swap, inventory management, invisible hand, James Carville said: "I would like to be reincarnated as the bond market. You can intimidate everybody.", junk bonds, Kenneth Rogoff, Kickstarter, Kitchen Debate, laissez-faire capitalism, Lewis Mumford, Long Term Capital Management, low interest rates, low skilled workers, market bubble, market clearing, Martin Wolf, Money creation, money market fund, moral hazard, mortgage debt, Myron Scholes, Neil Armstrong, new economy, Nixon shock, Nixon triggered the end of the Bretton Woods system, Northern Rock, paper trading, paradox of thrift, Paul Samuelson, Phillips curve, plutocrats, popular capitalism, price stability, RAND corporation, Reminiscences of a Stock Operator, rent-seeking, Robert Shiller, Robert Solow, rolodex, Ronald Reagan, Saturday Night Live, Savings and loan crisis, savings glut, secular stagnation, short selling, stock buybacks, subprime mortgage crisis, The Great Moderation, the payments system, The Wealth of Nations by Adam Smith, Tipper Gore, too big to fail, trade liberalization, unorthodox policies, upwardly mobile, We are all Keynesians now, 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.


The Master and His Emissary: The Divided Brain and the Making of the Western World by Iain McGilchrist

Albert Einstein, Asperger Syndrome, autism spectrum disorder, Benoit Mandelbrot, Berlin Wall, classic study, cognitive bias, cognitive dissonance, computer age, Donald Trump, double helix, Douglas Hofstadter, epigenetics, experimental subject, Fellow of the Royal Society, Georg Cantor, hedonic treadmill, Henri Poincaré, language acquisition, Lao Tzu, longitudinal study, Louis Pasteur, mandelbrot fractal, meta-analysis, mirror neurons, music of the spheres, Necker cube, Panopticon Jeremy Bentham, pattern recognition, randomized controlled trial, Sapir-Whorf hypothesis, Schrödinger's Cat, social intelligence, social web, source of truth, stem cell, Steven Pinker, the scientific method, theory of mind, traumatic brain injury

., pp. 9–11. 153. Fractality is the property of forms as diverse as plants, river systems, coast lines, snowflakes and blood vessels that dictates that their form at higher levels of magnification replicates their form at lower levels. Although the term is modern, and derives from the mathematics of Benoît Mandelbrot in the mid-1970s, Leibniz may already have intuited, possibly on the basis of microscope findings, that nature is fractal: see Leibniz, 1992, §67–8, pp. 25–6, and commentary on pp. 41 & 234 ff. Elsewhere in this aphoristic late work, Leibniz relates his description of these worlds within worlds that formed part of his monadology to two further concepts of relevance for the theme of this book: the way that each body mirrors its environing universe, and each soul mirrors its environing body (and consequently the entire universe) (§61–2); and the way in which ‘all bodies are in a perpetual flux, like rivers, and some parts enter into them and some pass out continually’ (§71–2). 154.


pages: 1,544 words: 391,691

Corporate Finance: Theory and Practice by Pierre Vernimmen, Pascal Quiry, Maurizio Dallocchio, Yann le Fur, Antonio Salvi

"Friedman doctrine" OR "shareholder theory", accelerated depreciation, accounting loophole / creative accounting, active measures, activist fund / activist shareholder / activist investor, AOL-Time Warner, ASML, asset light, bank run, barriers to entry, Basel III, Bear Stearns, Benoit Mandelbrot, bitcoin, Black Swan, Black-Scholes formula, blockchain, book value, business climate, business cycle, buy and hold, buy low sell high, capital asset pricing model, carried interest, collective bargaining, conceptual framework, corporate governance, correlation coefficient, credit crunch, Credit Default Swap, currency risk, delta neutral, dematerialisation, discounted cash flows, discrete time, disintermediation, diversification, diversified portfolio, Dutch auction, electricity market, equity premium, equity risk premium, Eugene Fama: efficient market hypothesis, eurozone crisis, financial engineering, financial innovation, fixed income, Flash crash, foreign exchange controls, German hyperinflation, Glass-Steagall Act, high net worth, impact investing, implied volatility, information asymmetry, intangible asset, interest rate swap, Internet of things, inventory management, invisible hand, joint-stock company, joint-stock limited liability company, junk bonds, Kickstarter, lateral thinking, London Interbank Offered Rate, low interest rates, mandelbrot fractal, margin call, means of production, money market fund, moral hazard, Myron Scholes, new economy, New Journalism, Northern Rock, performance metric, Potemkin village, quantitative trading / quantitative finance, random walk, Right to Buy, risk free rate, risk/return, shareholder value, short selling, Social Responsibility of Business Is to Increase Its Profits, sovereign wealth fund, Steve Jobs, stocks for the long run, supply-chain management, survivorship bias, The Myth of the Rational Market, time value of money, too big to fail, transaction costs, value at risk, vertical integration, volatility arbitrage, volatility smile, yield curve, zero-coupon bond, zero-sum game

A number of “anomalies” that tend to go against the efficiency of markets have been highlighted: Excess volatility. The first issue with efficient market theory seems very intuitive: how can markets be so volatile? Information on Sanofi is not published every second. Nevertheless, the share price does move at each instant. There seems to be some kind of noise around fundamental value. As described by Benoit Mandelbrot, who first used fractals in economics, prices evolve in a discrete way rather than in a continuous manner. Dual listing and closed-end funds. Dual listings are shares of twin companies listed on two different markets. Their stream of dividends is, by definition, identical but we can observe that their price can differ over a long period of time.