Edward Lorenz: Chaos theory

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pages: 396 words: 112,748

Chaos by James Gleick

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Benoit Mandelbrot, butterfly effect, cellular automata, Claude Shannon: information theory, discrete time, Edward Lorenz: Chaos theory, experimental subject, Georg Cantor, Henri Poincaré, Isaac Newton, iterative process, John von Neumann, Louis Pasteur, mandelbrot fractal, Murray Gell-Mann, Norbert Wiener, pattern recognition, Richard Feynman, Richard Feynman, Stephen Hawking, stochastic process, trade route

CHAOS Making a New Science James Gleick To Cynthia human was the music, natural was the static… —JOHN UPDIKE Contents Prologue The Butterfly Effect Edward Lorenz and his toy weather. The computer misbehaves. Long-range forecasting is doomed. Order masquerading as randomness. A world of nonlinearity. “We completely missed the point.” Revolution A revolution in seeing. Pendulum clocks, space balls, and playground swings. The invention of the horseshoe. A mystery solved: Jupiter’s Great Red Spot. Life’s Ups and Downs Modeling wildlife populations. Nonlinear science, “the study of non-elephant animals.” Pitchfork bifurcations and a ride on the Spree. A movie of chaos and a messianic appeal. A Geometry of Nature A discovery about cotton prices. A refugee from Bourbaki.

For the young physicists and mathematicians leading the revolution, a starting point was the Butterfly Effect. The Butterfly Effect Physicists like to think that all you have to do is say, these are the conditions, now what happens next? —RICHARD P. FEYNMAN THE SUN BEAT DOWN through a sky that had never seen clouds. The winds swept across an earth as smooth as glass. Night never came, and autumn never gave way to winter. It never rained. The simulated weather in Edward Lorenz’s new electronic computer changed slowly but certainly, drifting through a permanent dry midday midseason, as if the world had turned into Camelot, or some particularly bland version of southern California. Outside his window Lorenz could watch real weather, the early-morning fog creeping along the Massachusetts Institute of Technology campus or the low clouds slipping over the rooftops from the Atlantic.

Given a slightly different starting point, the weather should unfold in a slightly different way. A small numerical error was like a small puff of wind—surely the small puffs faded or canceled each other out before they could change important, large-scale features of the weather. Yet in Lorenz’s particular system of equations, small errors proved catastrophic. HOW TWO WEATHER PATTERNS DIVERGE. From nearly the same starting point, Edward Lorenz saw his computer weather produce patterns that grew farther and farther apart until all resemblance disappeared. (From Lorenz’s 1961 printouts.) He decided to look more closely at the way two nearly identical runs of weather flowed apart. He copied one of the wavy lines of output onto a transparency and laid it over the other, to inspect the way it diverged. First, two humps matched detail for detail.


pages: 317 words: 100,414

Superforecasting: The Art and Science of Prediction by Philip Tetlock, Dan Gardner

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Affordable Care Act / Obamacare, Any sufficiently advanced technology is indistinguishable from magic, availability heuristic, Black Swan, butterfly effect, cloud computing, cuban missile crisis, Daniel Kahneman / Amos Tversky, desegregation, Edward Lorenz: Chaos theory, forward guidance, Freestyle chess, fundamental attribution error, germ theory of disease, hindsight bias, index fund, Jane Jacobs, Jeff Bezos, Mikhail Gorbachev, Mohammed Bouazizi, Nash equilibrium, Nate Silver, obamacare, pattern recognition, performance metric, place-making, placebo effect, prediction markets, quantitative easing, random walk, randomized controlled trial, Richard Feynman, Richard Feynman, Richard Thaler, Robert Shiller, Robert Shiller, Ronald Reagan, Saturday Night Live, Silicon Valley, Skype, statistical model, stem cell, Steve Ballmer, Steve Jobs, Steven Pinker, the scientific method, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Watson beat the top human players on Jeopardy!

Indeed, you could have said that about Tunisia, Egypt, and several other countries for decades. They may have been powder kegs but they never blew—until December 17, 2010, when the police pushed that one poor man too far. In 1972 the American meteorologist Edward Lorenz wrote a paper with an arresting title: “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?” A decade earlier, Lorenz had discovered by accident that tiny data entry variations in computer simulations of weather patterns—like replacing 0.506127 with 0.506—could produce dramatically different long-term forecasts. It was an insight that would inspire “chaos theory”: in nonlinear systems like the atmosphere, even small changes in initial conditions can mushroom to enormous proportions. So, in principle, a lone butterfly in Brazil could flap its wings and set off a tornado in Texas—even though swarms of other Brazilian butterflies could flap frantically their whole lives and never cause a noticeable gust a few miles away.

He meant that if that particular butterfly hadn’t flapped its wings at that moment, the unfathomably complex network of atmospheric actions and reactions would have behaved differently, and the tornado might never have formed—just as the Arab Spring might never have happened, at least not when and as it did, if the police had just let Mohamed Bouazizi sell his fruits and vegetables that morning in 2010. Edward Lorenz shifted scientific opinion toward the view that there are hard limits on predictability, a deeply philosophical question.4 For centuries, scientists had supposed that growing knowledge must lead to greater predictability because reality was like a clock—an awesomely big and complicated clock but still a clock—and the more scientists learned about its innards, how the gears grind together, how the weights and springs function, the better they could capture its operations with deterministic equations and predict what it would do.

These are false dichotomies, the first of many we will encounter. We live in a world of clocks and clouds and a vast jumble of other metaphors. Unpredictability and predictability coexist uneasily in the intricately interlocking systems that make up our bodies, our societies, and the cosmos. How predictable something is depends on what we are trying to predict, how far into the future, and under what circumstances. Look at Edward Lorenz’s field. Weather forecasts are typically quite reliable, under most conditions, looking a few days ahead, but they become increasingly less accurate three, four, and five days out. Much beyond a week, we might as well consult that dart-throwing chimpanzee. So we can’t say that weather is predictable or not, only that weather is predictable to some extent under some circumstances—and we must be very careful when we try to be more precise than that.


pages: 338 words: 106,936

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

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Albert Einstein, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Asian financial crisis, bank run, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, butterfly effect, capital asset pricing model, Carmen Reinhart, Claude Shannon: information theory, collateralized debt obligation, collective bargaining, dark matter, Edward Lorenz: Chaos theory, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial innovation, George Akerlof, Gerolamo Cardano, Henri Poincaré, invisible hand, Isaac Newton, iterative process, John Nash: game theory, Kenneth Rogoff, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, martingale, new economy, Paul Lévy, prediction markets, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk-adjusted returns, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Coase, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, statistical arbitrage, statistical model, stochastic process, The Chicago School, The Myth of the Rational Market, tulip mania, V2 rocket, volatility smile

“Jobs at the top universities were filled . . .”: For an example of the kind of recommendation I have in mind, see Wheeler (2011). This letter is the origin of the quote “best men” in the next sentence. “. . . Silver City was a paradigm Western mining town”: This background on Silver City is from Wallis (2007). “. . . first developed by a man named Edward Lorenz”: The biographical and historical details concerning Lorenz and the history of chaos theory are from Gleick (1987) and Lorenz (1993). “. . . the work of two physicists named James Yorke and Tien-Yien Li . . .”: The article is Li and Yorke (1975). “. . . the so-called butterfly effect . . .”: The paper is Lorenz (2000). Lorenz never used the metaphor of a butterfly flapping its wings, though he sometimes used a similar metaphor involving a seagull

He got in, and instead of finishing high school in Silver City, he moved into Ingerson’s attic in Moscow, Idaho, to start his career as a physicist. After a year in Idaho, though, Farmer was ready for bigger pastures. In 1970, he transferred to Stanford University. True to his ambitions, he majored in physics — laying the groundwork for a career that would change science, and finance, forever. The ideas at the heart of Farmer’s and Packard’s work were first developed by a man named Edward Lorenz. As a young boy, Lorenz thought he wanted to be a mathematician. He had a clear talent for mathematics, and when it came time to select a major at Dartmouth, he had few doubts about what he would choose. He graduated in 1938 and went on to Harvard, planning to pursue a PhD. But World War II interfered with his plans: in 1942, he joined the U.S. Army Air Corps. His job was to predict the weather for Allied pilots.

It is tempting to say that Farmer, Packard, and their Prediction Company collaborators “used chaos theory to predict the markets” or something along those lines. In fact, this is how their enterprise is usually characterized. But that isn’t quite right. Farmer and Packard didn’t use chaos theory as a meteorologist or a physicist might. They didn’t do things such as attempt to find the fractal geometry underlying markets, or derive the deterministic laws that govern financial systems. Instead, the fifteen years that Farmer and Packard spent working on chaos theory gave them an unprecedented (by 1991 standards) understanding of how complex systems work, and the ability to use computers and mathematics in ways that someone trained in economics (or even in most areas of physics) would never have imagined possible. Their experience with chaos theory helped them appreciate how regular patterns — patterns with real predictive power — could be masked by the appearance of randomness.


pages: 239 words: 68,598

The Vanishing Face of Gaia: A Final Warning by James E. Lovelock

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Ada Lovelace, butterfly effect, carbon footprint, Clapham omnibus, cognitive dissonance, continuous integration, David Attenborough, decarbonisation, discovery of DNA, Edward Lorenz: Chaos theory, Henri Poincaré, mandelbrot fractal, megacity, Northern Rock, oil shale / tar sands, phenotype, planetary scale, short selling, Stewart Brand, University of East Anglia

The mathematics of dynamic self‐regulating systems frequently involves differential equations that are difficult or impossible to solve by traditional methods. It is too easy to slip into the practice of making what are called ‘linearizing approximations’, and then forget their presence as the model evolves. Scientists of these separated disciplines should have realized that they were on the wrong track when quite independently the geophysicist Edward Lorenz, in 1961, and the neo‐Darwinist biologist Robert May, in 1973, made the remarkable discovery that deterministic chaos was an inherent part of the computer models they researched. Deterministic chaos is not an oxymoron, however much it may seem like one. Up until Lorenz and May started using computers to solve systems rich in difficult equations almost all science clung to the comforting idea put forward in 1814 by the French mathematician Pierre‐Simon Laplace that the universe was deterministic and if the precise location and momentum of every particle in the universe were known, then by using Newton’s laws we could reveal the entire course of cosmic events, past, present and future.

It took the discovery of the utter incomprehensibility of quantum phenomena to force the acceptance of a statistical more than a deterministic world; this was later consummated by the discoveries that came from the availability of affordable computers. These have enabled scientists to explore the world of dynamics – the mathematics of moving, flowing and living systems. The insights from the numerical analysis of fluid dynamics by Edward Lorenz and of population biology by Robert May revealed what is called ‘deterministic chaos’. Systems like the weather, the motion of more than two astronomical bodies linked by gravitation, or more than two species in competition, are exceedingly sensitive to the initial conditions of their origin, and they evolve in a wholly unpredictable manner. The study of these systems is a rich and colourful new field of science enlivened by the visual brilliance of the strange images of fractal geometry.

Vernadsky expanded the definition of biosphere to include the concept that life is an active participant in geological evolution, encapsulating this notion in the phrase, ‘Life is a geological force.’ Vernadsky was following a tradition set by Darwin, Huxley, Lotka, Redfield and many others, but unlike them his ideas were mostly anecdotal. Biosphere is now mainly used, in Vernadsky’s sense, as an imprecise word that acknowledges the power of life on Earth without surrendering human sovereignty. CHAOS THEORY Certainty and confidence in science marked its development in the nineteenth and much of the twentieth centuries, but now it carries on unaware that the determinism that had so long enlivened it is dead. The recognition that science was provisional and could never be certain was always there in the minds of good scientists. The nineteenth‐century application of statistics, first in commerce then in science, made probabilistic thinking more intelligible than faith‐based certainties.


pages: 208 words: 70,860

Paradox: The Nine Greatest Enigmas in Physics by Jim Al-Khalili

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Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, butterfly effect, clockwork universe, complexity theory, dark matter, Edmond Halley, Edward Lorenz: Chaos theory, Ernest Rutherford, Henri Poincaré, invention of the telescope, Isaac Newton, luminiferous ether, Magellanic Cloud, Olbers’ paradox, Schrödinger's Cat, Search for Extraterrestrial Intelligence, The Present Situation in Quantum Mechanics, Wilhelm Olbers

If you make a certain decision one morning on your way to work, like pausing for a second before crossing the road, then you might miss the opportunity of bumping into an old friend who gives you some information that leads to your applying for a new job that changes your life; a split second later still in crossing that road and you could be hit by a bus. Our destiny may be mapped out for us in a deterministic universe, but it is totally unpredictable. The man who first brought these ideas to the world and in doing so helped create the new concept of chaos was Edward Lorenz, an American mathematician and meteorologist who hit upon the phenomenon by accident while he was working on modeling weather patterns in the early 1960s. He was using an early “desktop” computer, the LGP-30, to run his simulation. At one point he wanted to repeat a simulation by running the computer program again with identical inputs. To do this he used a number the computer had calculated and printed out halfway through its run.

Chaos is not really a theory as such (although “chaos theory” has become a commonly used term, and I still plan to use it). It is a concept, or phenomenon, that we find to be almost ubiquitous in nature and has spawned a whole new discipline in science with the rather less imaginative title of nonlinear dynamics—a description which derives from the main mathematical property of chaotic systems, namely that cause and effect are not related in a linear, proportional way. By this I mean that it had been assumed before chaos was fully understood that, while effect must follow cause, simple causes would always lead to simple effects and complex causes to complex effects. The notion that a simple cause could lead to a complex effect was quite unexpected. This is what mathematicians mean by “nonlinear.” Chaos theory tells us that order and determinism can breed what appears to be randomness.

The answer, I believe, despite what I have said about determinism, is yes, we still do. And it is rescued not by quantum mechanics, as some physicists argue, but by chaos theory. For it doesn’t matter that we live in a deterministic universe in which the future is, in principle, fixed. That future would be knowable only if we were able to view the whole of space and time from the outside. But for us, and our consciousnesses, embedded within space-time, that future is never knowable to us. It is that very unpredictability that gives us an open future. The choices we make are, to us, real choices, and because of the butterfly effect, tiny changes brought about by our different decisions can lead to very different outcomes, and hence different futures. So, thanks to chaos theory, our future is never knowable to us. You might prefer to say that the future is preordained and that our free will is just an illusion—but the point remains that our actions still determine which of the infinite number of possible futures is the one that gets played out.


pages: 239 words: 56,531

The Secret War Between Downloading and Uploading: Tales of the Computer as Culture Machine by Peter Lunenfeld

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Albert Einstein, Andrew Keen, Apple II, Berlin Wall, British Empire, Brownian motion, Buckminster Fuller, Burning Man, butterfly effect, computer age, crowdsourcing, cuban missile crisis, Dissolution of the Soviet Union, don't be evil, Douglas Engelbart, Dynabook, East Village, Edward Lorenz: Chaos theory, Fall of the Berlin Wall, Francis Fukuyama: the end of history, Frank Gehry, Grace Hopper, gravity well, Guggenheim Bilbao, Honoré de Balzac, Howard Rheingold, invention of movable type, Isaac Newton, Jacquard loom, Jacquard loom, Jane Jacobs, Jeff Bezos, John von Neumann, Mark Zuckerberg, Marshall McLuhan, Mercator projection, Mother of all demos, mutually assured destruction, Network effects, new economy, Norbert Wiener, PageRank, pattern recognition, planetary scale, Plutocrats, plutocrats, Post-materialism, post-materialism, Potemkin village, RFID, Richard Feynman, Richard Feynman, Richard Stallman, Robert X Cringely, Schrödinger's Cat, Search for Extraterrestrial Intelligence, SETI@home, Silicon Valley, Skype, social software, spaced repetition, Steve Ballmer, Steve Jobs, Steve Wozniak, Ted Nelson, the built environment, The Death and Life of Great American Cities, the medium is the message, Thomas L Friedman, Turing machine, Turing test, urban planning, urban renewal, Vannevar Bush, walkable city, Watson beat the top human players on Jeopardy!, William Shockley: the traitorous eight

If you connect the links one way, you will track the following movement: Cubism ‰ Suprematism ‰ Constructivism ‰ Bauhaus Follow another line, and you will get to the Bauhaus this way: Synthetism ‰ Fauvism ‰ Expressionism ‰ Bauhaus Barr’s chart is a teleological document that culminates with the presentation of these objects in MOMA’s galleries. The exactitude of Barr’s chart is unlikely to emerge from the process of bespoke futures. The skewing of the classic scenario-building process undermines such vectoral surety and fixed relationships. Instead, a better model might be found in the dynamic imagescapes of the Lorenz strange attractor, one of the earliest and still most potent visualizations of chaotic systems.26 Edward Lorenz, a mathematician and meteorologist at MIT, needed a new way to analyze atmospheric conditions. He came up with 117 CHAPTER 5 a dynamic model in which seemingly random and chaotic outliers were eventually contained within a definite figure (often described as looking like an owl’s eyes) in which solutions approach but do not replicate each other exactly. The equations are described as deterministic, yet they are extremely sensitive to their initial conditions.

A minor change in the original condition can effect a hugely different outcome—better known as the “butterfly effect”—and can also create a different attractor, collapsing it into a fixed solution or tumbling it back into apparent chaos before a new strange attractor establishes itself. This effect is readily visible when you watch an animation of the strange attractor, many of which are now available on the World Wide Web. Disequilibrium can fall into a dynamic equilibrium with a slight shift, and can again be thrown into a new disequilibrium by yet another shift. The strange attractor can be any point within an orbit that appears to pull the entire system toward it. Chaos theory is based in part on the fact that Newtonian paradigms of predictability do not actually work. Accepting nonlinear systems creates a challenge to scenario planning. Recasting scenario planning to create bespoke futures acknowledges the unpredictability of strange attractors, but hopes to use the process itself (as well as its result) to move the system toward a tipping point. Returning to Barr’s diagram, bespoke futures are more like strange attractors than oppositional or political avant-gardist objects.27 The bespoke futures process can develop attractors to pull the entire system toward new and more hopeful visions of worlds to come.

., 123–124 Berners-Lee, Tim, 144, 167–169, 175 Bespoke futures adopting future as client and, 110–113 anticipated technology and, 108–110 crafting, 113–116 design and, 102, 105–106, 110–111, 115–116, 119–120, 124–125, 137 downloading and, 97, 123, 132, 138 dynamic equilibrium and, 117–120 89/11 and, xvi, 97, 100–102, 105, 130 Enlightenment and, xvi, 129–139 information and, 98, 100–101, 124–126 lack of vision and, 106–108 markets and, 97–104, 118, 120, 127, 131–132, 137–138 MaSAI (Massively Synchronous Applications of the Imagination) and, xvi, 112, 120–123, 127, 193n32 199 modernists and, 105–108 mutants and, 105–108 networks and, 98–101, 108, 112–113, 116, 119–126, 133, 137 New Economy and, 97, 99, 104, 131, 138, 144–145, 190n3 participation and, 98–99, 120–121, 129 plutopian meliorism and, xvi, 127–129, 133, 137–138 prosumers and, 120–121 reperceiving and, 112–113 R-PR (Really Public Relations) and, 123–127 scenario planning and, 111–119, 191n19, 192n20 simulation and, 98, 121, 124, 126–127 strange attractors and, xvi, 117–120, 192n27 technology and, 98–104, 107–113, 116, 119, 125–127, 131–133, 136–139 television and, 101, 108, 124, 127–129, 133–137 unfinish and, 127–129, 136 uploading and, 97, 120–123, 128–129, 132 Best use, 10, 13–15, 138 Bezos, Jeff, 145 Bible, 28, 137 BitTorrent, 92 Black Album, The (Jay Z), 55 Blade Runner (Scott), 107 Blogger, 177 Blogosphere, xvii bespoke futures and, 101 culture machine and, 175, 177 Facebook and, 81, 145, 180n2 stickiness and, 30, 34 Twitter and, 34, 180n2 unimodernism and, 49, 68 Web n.0 and, 80, 92–93 INDEX Bohème, La (Puccini), 61 Boing Boing magazine, 68–69 Bollywood, 62 Bourgeoisie, 31 Bowie, David, 62 Braque, Georges, 93 Breuer, Marcel, 45 Brillat-Savarin, Jean Anthèlme, 3 Brin, Sergey, 144, 174–176 Broadband technology, 9, 57 Brownian motion, 49 Burroughs, Allie Mae, 40–42 Burroughs, William, 52 Bush, Vannevar, 52, 194n6 culture machine and, 144, 147–152, 157 Engelbart and, 157 Memex and, 108, 149–151 Oppenheimer and, 150 systems theory and, 151 war effort and, 150–151 Business 2.0 magazine, 145 C3I , 146–147 Cabrini Green, 85 Calypso, 25–27 Cambodia, 107 Cambridge, 17, 36 “Can-Can” (“Orpheus in the Underworld”) (Offenbach), 62 Capitalism, 4, 13 bespoke futures and, 97–100, 103–105 Sears and, 103–105 stickiness and, 13 unimodernism and, 66, 75 Web n.0 and, 90 Capitulationism, 7, 24, 30, 182n1 Carnegie, Andrew, 166 Casablanca (film), 90 Cassette tapes, 2 CATIA 3–D software, 39 Cell phones, xiii, xvii, 17, 23, 42, 53, 56, 76, 101 Chaos theory, 117–120 Chaplin, Charlie, 45 Cheney, Dick, 99 China, 104, 107 Christians, 135 Cicero, 47 Cinema, 8, 10 micro, 56–60 stickiness and, 15 unimodernism and, 47, 52, 56–60, 63, 71 Clarke, Arthur C., 174 CNN, 58 Cobain, Kurt, 62 Code breaking, 17–18 Cold war, 101 Cole, Nat King, 62 Commercial culture, 4–5, 8 bespoke futures and, 98, 102, 108, 120, 132–134 culture machine and, 153–156, 167, 170, 172, 175–177 copyright and, 54, 88–95, 123, 164, 166, 173, 177 Mickey Mouse Protection Act and, 90 open source and, 36, 61, 69, 74–75, 91–92, 116, 121–126, 144, 170– 173, 177, 189n12 propaganda and, 124 scenario planning and, 111–119 stickiness and, 23, 28–31, 37 unimodernism and, 41, 69 Web n.0 and, 82–86 Commercial syndrome, 85–86 Communism, 97–98, 103 Compact discs (CDs), 2, 48, 53 Complex City (Simon), 39 “Computable Numbers, On” (Turing), 18 Computer Data Systems, 145 Computers, xi.

Exploring Everyday Things with R and Ruby by Sau Sheong Chang

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Alfred Russel Wallace, bioinformatics, business process, butterfly effect, cloud computing, Craig Reynolds: boids flock, Debian, Edward Lorenz: Chaos theory, Gini coefficient, income inequality, invisible hand, p-value, price stability, Skype, statistical model, stem cell, Stephen Hawking, text mining, The Wealth of Nations by Adam Smith, We are the 99%, web application, wikimedia commons

We have discussed emergent behavior, where small local rules result in complex, macro-level, group behavior. The pattern we have observed here, rather than emergent behavior, can be classified as a kind of “butterfly effect”; see the sidebar Butterfly Effect. Figure 8-6. Population fluctuation swings, resulting in extinction of the roids Butterfly Effect In chaos theory, the butterfly effect is the sensitive dependence on initial conditions, where a small change somewhere in a nonlinear system can result in large differences at a later stage. This name was coined by Edward Lorenz, one of the pioneers of chaos theory (and no relation to Max Lorenz of the Lorenz curve fame). In 1961, Lorenz was using a computer model to rerun a weather prediction when he entered the shortened decimal value .506 instead of entering the full .506127. The result was completely different from his original prediction.

: (question mark, colon), in Ruby ternary conditional expression, if and unless > (right angle bracket), The R Console, Variables and Functions -> assignment operator, R, Variables and Functions > R console prompt, The R Console ' ' (single quotes), enclosing Ruby strings, Strings [ ] (square brackets), Vectors, Matrices, Data frames accessing subset of R data frame, Data frames enclosing R matrix indexes, Matrices enclosing R vector indexes, Vectors [[ ]] (square brackets, double), enclosing single R vector index, Vectors A aes() function, R, Aesthetics An Inquiry into the Nature and Causes of the Wealth of Nations (University of Chicago Press), The Invisible Hand apply() function, R, Interpreting the Data Armchair Economist (Free Press), How to Be an Armchair Economist array() function, R, Arrays arrays, R, Arrays–Arrays arrays, Ruby, Arrays and hashes–Arrays and hashes, Arrays and hashes artificial society, Money (see Utopia example) as.Date() function, R, Number of Messages by Day of the Month ascultation, Auscultation assignment operators, R, Variables and Functions at sign, double (@@), preceding Ruby class variables, Class methods and variables attr keyword, Ruby, Classes and objects Audacity audio editor, Homemade Digital Stethoscope average, Interpreting the Data (see mean() function, R) Axtell, Robert (researcher), It’s a Good Life Growing Artificial Societies: Social Science from the Bottom Up (Brookings Institution Press/MIT Press), It’s a Good Life B backticks (` `), enclosing R operators as functions, Variables and Functions bar charts, Plotting charts, Interpreting the Data–Interpreting the Data, The Second Simulation–The Second Simulation, The Third Simulation–The Third Simulation, The Final Simulation–The Final Simulation barplot() function, R, Plotting charts batch mode, R, Sourcing Files and the Command Line Bioconductor repository, Packages birds flocking, Schooling Fish and Flocking Birds (see flocking example) bmp() function, R, Basic Graphs Boids algorithm, Schooling Fish and Flocking Birds–The Origin of Boids Box, George Edward Pelham (statistician), regarding usefulness of models, The Simple Scenario break keyword, R, Conditionals and Loops brew command, Installing Ruby using your platform’s package management tool butterfly effect, The Changes C c() function, R, Vectors CALO Project, The Emailing Habits of Enron Executives camera, pulse oximeter using, Homemade Pulse Oximeter case expression, Ruby, case expression chaos theory, The Changes charts, Charting–Adjustments, Plotting charts, Statistical transformation, Geometric object, Interpreting the Data–Interpreting the Data, Interpreting the Data–Interpreting the Data, Interpreting the Data–Interpreting the Data, The Second Simulation, The Second Simulation–The Second Simulation, The Third Simulation–The Third Simulation, The Third Simulation–The Third Simulation, The Final Simulation–The Final Simulation, The Final Simulation–The Final Simulation, Analyzing the Simulation–Analyzing the Simulation, Analyzing the Second Simulation–Analyzing the Second Simulation, Number of Messages by Day of the Month–Number of Messages by Hour of the Day, Generating the Heart Sounds Waveform–Generating the Heart Sounds Waveform, Generating the Heartbeat Waveform and Calculating the Heart Rate–Generating the Heartbeat Waveform and Calculating the Heart Rate, Money–Money, Money–Money, Implementation bar charts, Plotting charts, Interpreting the Data–Interpreting the Data, The Second Simulation–The Second Simulation, The Third Simulation–The Third Simulation, The Final Simulation–The Final Simulation histograms, Statistical transformation, Geometric object, Money–Money line charts, Interpreting the Data–Interpreting the Data, Analyzing the Simulation–Analyzing the Simulation, Analyzing the Second Simulation–Analyzing the Second Simulation Lorenz curves, Money–Money scatterplots, Interpreting the Data–Interpreting the Data, The Second Simulation, The Third Simulation–The Third Simulation, The Final Simulation–The Final Simulation, Number of Messages by Day of the Month–Number of Messages by Hour of the Day, Implementation waveforms, Generating the Heart Sounds Waveform–Generating the Heart Sounds Waveform, Generating the Heartbeat Waveform and Calculating the Heart Rate–Generating the Heartbeat Waveform and Calculating the Heart Rate class methods, Ruby, Class methods and variables class variables, Ruby, Class methods and variables–Class methods and variables classes, R, Programming R classes, Ruby, Classes and objects–Classes and objects code examples, Using Code Examples (see example applications) colon (:), Symbols, Vectors creating R vectors, Vectors preceding Ruby symbols, Symbols comma-separated value (CSV) files, Importing data from text files (see CSV files) Comprehensive R Archive Network (CRAN), Packages conditionals, R, Conditionals and Loops conditionals, Ruby, Conditionals and loops–case expression contact information for this book, How to Contact Us conventions used in this book, Conventions Used in This Book cor() function, R, The R Console Core library, Ruby, Requiring External Libraries corpus, Text Mining correlation, R, The R Console CRAN (Comprehensive R Archive Network), Packages CSV (comma-separated value) files, Importing data from text files, The First Simulation–The First Simulation, The First Simulation, Interpreting the Data, The Simulation, Extracting Data from Sound–Extracting Data from Sound, Extracting Data from Video extracting video data to, Extracting Data from Video extracting WAV data to, Extracting Data from Sound–Extracting Data from Sound reading data from, Interpreting the Data writing data to, The First Simulation–The First Simulation, The Simulation csv library, Ruby, The First Simulation, The Simulation, Grab and Parse curl utility, Ruby Version Manager (RVM) D data, Data, Data, Everywhere–Data, Data, Everywhere, Bringing the World to Us, Importing Data–Importing data from a database, Importing data from text files, The First Simulation–The First Simulation, Interpreting the Data, How to Be an Armchair Economist, The Simulation, Grab and Parse–Grab and Parse, The Emailing Habits of Enron Executives–The Emailing Habits of Enron Executives, Homemade Digital Stethoscope–Extracting Data from Sound, Extracting Data from Sound–Extracting Data from Sound, Homemade Pulse Oximeter–Extracting Data from Video, Extracting Data from Video analyzing, Data, Data, Everywhere–Data, Data, Everywhere, Bringing the World to Us, How to Be an Armchair Economist charts for, How to Be an Armchair Economist (see charts) obstacles to, Data, Data, Everywhere–Data, Data, Everywhere simulations for, Bringing the World to Us (see simulations) audio, from stethoscope, Homemade Digital Stethoscope–Extracting Data from Sound CSV files for, Importing data from text files, The First Simulation–The First Simulation, Interpreting the Data, The Simulation, Extracting Data from Sound–Extracting Data from Sound, Extracting Data from Video from Enron, The Emailing Habits of Enron Executives–The Emailing Habits of Enron Executives from Gmail, Grab and Parse–Grab and Parse importing, R, Importing Data–Importing data from a database video, from pulse oximeter, Homemade Pulse Oximeter–Extracting Data from Video data frames, R, Data frames–Data frames data mining, The Idea data.frame() function, R, Data frames database, importing data from, Importing data from a database–Importing data from a database dbConnect() function, R, Importing data from a database dbGet() function, R, Importing data from a database DBI packages, R, Importing data from a database–Importing data from a database Debian system, installing Ruby on, Installing Ruby using your platform’s package management tool def keyword, Ruby, Classes and objects dimnames() function, R, Matrices distribution, normal, Money dollar sign ($), preceding R list item names, Lists doodling example, Shoes doodler–Shoes doodler double quotes (" "), enclosing Ruby strings, Strings duck typing, Ruby, Code like a duck–Code like a duck dynamic typing, Ruby, Code like a duck–Code like a duck E economics example, A Simple Market Economy–A Simple Market Economy, The Producer–The Producer, The Consumer–The Consumer, Some Convenience Methods–Some Convenience Methods, The Simulation–The Simulation, Analyzing the Simulation–Analyzing the Simulation, The Producer–The Producer, The Consumer–The Consumer, Market–Market, The Simulation–The Simulation, Analyzing the Second Simulation–Analyzing the Second Simulation, Price Controls–Price Controls charts for, Analyzing the Simulation–Analyzing the Simulation, Analyzing the Second Simulation–Analyzing the Second Simulation Consumer class for, The Consumer–The Consumer, The Consumer–The Consumer Market class for, Some Convenience Methods–Some Convenience Methods, Market–Market modeling, A Simple Market Economy–A Simple Market Economy price controls analysis, Price Controls–Price Controls Producer class for, The Producer–The Producer, The Producer–The Producer simulations for, The Simulation–The Simulation, The Simulation–The Simulation email example, Grab and Parse–Grab and Parse, The Emailing Habits of Enron Executives–The Emailing Habits of Enron Executives, Number of Messages by Day of the Month–Number of Messages by Day of the Month, Number of Messages by Day of the Month–Number of Messages by Hour of the Day, MailMiner–MailMiner, Number of Messages by Day of Week–Number of Messages by Hour of the Day, Interactions–Comparative Interactions, Text Mining–Text Mining charts for, Number of Messages by Day of the Month–Number of Messages by Hour of the Day content of messages, analyzing, Text Mining–Text Mining data for, Grab and Parse–Grab and Parse Enron data for, The Emailing Habits of Enron Executives–The Emailing Habits of Enron Executives interactions in email, analyzing, Interactions–Comparative Interactions number of messages, analyzing, Number of Messages by Day of the Month–Number of Messages by Day of the Month, Number of Messages by Day of Week–Number of Messages by Hour of the Day R package for, creating, MailMiner–MailMiner emergent behavior, The Origin of Boids (see also flocking example) Enron Corporation scandal, The Emailing Habits of Enron Executives Epstein, Joshua (researcher), It’s a Good Life Growing Artificial Societies: Social Science from the Bottom Up (Brookings Institution Press/MIT Press), It’s a Good Life equal sign (=), assignment operator, R, Variables and Functions Euclidean distance, Roids evolution, Evolution example applications, Using Code Examples, Shoes stopwatch–Shoes stopwatch, Shoes doodler–Shoes doodler, The R Console–Sourcing Files and the Command Line, Data frames–Introducing ggplot2, qplot–qplot, Statistical transformation–Geometric object, Adjustments–Adjustments, Offices and Restrooms, A Simple Market Economy, Grab and Parse, My Beating Heart, Schooling Fish and Flocking Birds, Money artificial utopian society, Money (see Utopia example) birds flocking, Schooling Fish and Flocking Birds (see flocking example) doodling, Shoes doodler–Shoes doodler economics, A Simple Market Economy (see economics example) email, Grab and Parse (see email example) fuel economy, qplot–qplot, Adjustments–Adjustments heartbeat, My Beating Heart (see heartbeat example) height and weight, The R Console–Sourcing Files and the Command Line league table, Data frames–Introducing ggplot2 movie database, Statistical transformation–Geometric object permission to use, Using Code Examples restrooms, Offices and Restrooms (see restrooms example) stopwatch, Shoes stopwatch–Shoes stopwatch expressions, R, Programming R external libraries, Ruby, Requiring External Libraries–Requiring External Libraries F factor() function, R, Factors, Text Mining factors, R, Factors–Factors FFmpeg library, Extracting Data from Video, Extracting Data from Video field of vision (FOV), Roids fish, schools of, Schooling Fish and Flocking Birds (see flocking example) flocking example, Schooling Fish and Flocking Birds–The Origin of Boids, The Origin of Boids, Simulation–Simulation, Roids–Roids, The Boid Flocking Rules–Putting in Obstacles, The Boid Flocking Rules–The Boid Flocking Rules, A Variation on the Rules–A Variation on the Rules, Going Round and Round–Going Round and Round, Putting in Obstacles–Putting in Obstacles Boids algorithm for, Schooling Fish and Flocking Birds–The Origin of Boids centering path for, Going Round and Round–Going Round and Round obstacles in path for, Putting in Obstacles–Putting in Obstacles research regarding, A Variation on the Rules–A Variation on the Rules Roid class for, Roids–Roids rules for, The Origin of Boids, The Boid Flocking Rules–The Boid Flocking Rules simulations for, Simulation–Simulation, The Boid Flocking Rules–Putting in Obstacles flows, Shoes, Shoes stopwatch fonts used in this book, Conventions Used in This Book–Conventions Used in This Book for loop, R, Conditionals and Loops format() function, R, Number of Messages by Day of the Month FOV (field of vision), Roids fuel economy example, qplot–qplot, Adjustments–Adjustments function class, R, Programming R functions, R, Variables and Functions–Variables and Functions G GAM (generalized addictive model), The Changes gem command, Ruby, Requiring External Libraries .gem file extension, Requiring External Libraries generalized addictive model (GAM), The Changes Gentleman, Robert (creator of R), Introducing R geom_bar() function, R, Interpreting the Data, The Second Simulation, The Final Simulation geom_histogram() function, R, Geometric object geom_line() function, R, Analyzing the Simulation geom_point() function, R, Plot, Interpreting the Data, Generating the Heart Sounds Waveform geom_smooth() function, R, Interpreting the Data ggplot() function, R, Plot ggplot2 package, R, Introducing ggplot2–Adjustments Gini coefficient, Money Git utility, Ruby Version Manager (RVM) Gmail, retrieving message data from, Grab and Parse–Grab and Parse graphics device, opening, Basic Graphs graphics package, R, Basic Graphs graphs, Charting (see charts) Growing Artificial Societies: Social Science from the Bottom Up (Brookings Institution Press/MIT Press), It’s a Good Life H hash mark, curly brackets (#{ }), enclosing Ruby string escape sequences, Strings hashes, Ruby, Arrays and hashes–Arrays and hashes heart, diagram of, Generating the Heart Sounds Waveform heartbeat example, My Beating Heart, My Beating Heart, My Beating Heart, Homemade Digital Stethoscope, Homemade Digital Stethoscope, Homemade Digital Stethoscope–Extracting Data from Sound, Generating the Heart Sounds Waveform–Generating the Heart Sounds Waveform, Generating the Heart Sounds Waveform, Finding the Heart Rate–Finding the Heart Rate, Homemade Pulse Oximeter–Homemade Pulse Oximeter, Homemade Pulse Oximeter–Extracting Data from Video, Generating the Heartbeat Waveform and Calculating the Heart Rate–Generating the Heartbeat Waveform and Calculating the Heart Rate, Generating the Heartbeat Waveform and Calculating the Heart Rate–Generating the Heartbeat Waveform and Calculating the Heart Rate charts for, Generating the Heart Sounds Waveform–Generating the Heart Sounds Waveform, Generating the Heartbeat Waveform and Calculating the Heart Rate–Generating the Heartbeat Waveform and Calculating the Heart Rate data for, Homemade Digital Stethoscope–Extracting Data from Sound, Homemade Pulse Oximeter–Extracting Data from Video audio from stethoscope, Homemade Digital Stethoscope–Extracting Data from Sound video from pulse oximeter, Homemade Pulse Oximeter–Extracting Data from Video heart rate, My Beating Heart, Finding the Heart Rate–Finding the Heart Rate, Generating the Heartbeat Waveform and Calculating the Heart Rate–Generating the Heartbeat Waveform and Calculating the Heart Rate finding from video file, Generating the Heartbeat Waveform and Calculating the Heart Rate–Generating the Heartbeat Waveform and Calculating the Heart Rate finding from WAV file, Finding the Heart Rate–Finding the Heart Rate health parameters for, My Beating Heart heart sounds, My Beating Heart, My Beating Heart, Homemade Digital Stethoscope, Generating the Heart Sounds Waveform health parameters for, My Beating Heart recording, Homemade Digital Stethoscope types of, My Beating Heart, Generating the Heart Sounds Waveform homemade pulse oximeter for, Homemade Pulse Oximeter–Homemade Pulse Oximeter homemade stethoscope for, Homemade Digital Stethoscope height and weight example, The R Console–Sourcing Files and the Command Line here-documents, Ruby, Strings hex editor, Extracting Data from Sound histograms, Statistical transformation, Geometric object, Money–Money Homebrew tool, Installing Ruby using your platform’s package management tool hyphen (-), Variables and Functions, Variables and Functions -> assignment operator, R, Variables and Functions <- assignment operator, R, Variables and Functions I icons used in this book, Conventions Used in This Book if expression, R, Conditionals and Loops if expression, Ruby, if and unless–if and unless Ihaka, Ross (creator of R), Introducing R ImageMagick library, Extracting Data from Video IMAP (Internet Message Access Protocol), Grab and Parse importing data, R, Importing Data–Importing data from a database inheritance, Ruby, Inheritance–Inheritance initialize method, Ruby, Classes and objects inner product, Roids–Roids installation, Installing Ruby–Installing Ruby using your platform’s package management tool, Installing Shoes–Installing Shoes, Introducing R, Installing packages–Installing packages R, Introducing R R packages, Installing packages–Installing packages Ruby, Installing Ruby–Installing Ruby using your platform’s package management tool Shoes, Installing Shoes–Installing Shoes Internet Message Access Protocol (IMAP), Grab and Parse Internet Message Format, The Emailing Habits of Enron Executives invisible hand metaphor, The Invisible Hand irb application, Running Ruby–Running Ruby J jittering, Adjustments jpeg() function, R, Basic Graphs L Landsburg, Stephen E.


pages: 289 words: 113,211

A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation by Richard Bookstaber

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affirmative action, Albert Einstein, asset allocation, backtesting, Black Swan, Black-Scholes formula, Bonfire of the Vanities, butterfly effect, commodity trading advisor, computer age, disintermediation, diversification, double entry bookkeeping, Edward Lorenz: Chaos theory, family office, financial innovation, fixed income, frictionless, frictionless market, George Akerlof, implied volatility, index arbitrage, Jeff Bezos, London Interbank Offered Rate, Long Term Capital Management, loose coupling, margin call, market bubble, market design, merger arbitrage, Mexican peso crisis / tequila crisis, moral hazard, new economy, Nick Leeson, oil shock, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk tolerance, risk/return, Robert Shiller, Robert Shiller, rolodex, Saturday Night Live, shareholder value, short selling, Silicon Valley, statistical arbitrage, The Market for Lemons, time value of money, too big to fail, transaction costs, tulip mania, uranium enrichment, yield curve, zero-coupon bond

The mathematical system may be demonstrably incomplete, and the world might not be pinned down on the fringes, but for all practical purposes the world can be known. Unfortunately, while “almost” might work for horseshoes and hand grenades, 30 years after Godel and Heisenberg yet a third limitation of our knowledge was in the wings, a limitation that would close the door on any attempt to block out the implications of microscopic uncertainty on predictability in our macroscopic world. Based on observations made by Edward Lorenz in the early 1960s and popularized by the so-called butterfly effect—the fanciful notion that the beating wings of a butterfly could change the predictions of an otherwise perfect weather forecasting system—this limitation arises because in some important cases immeasurably small errors can compound over time to limit prediction in the larger scale. Half a century after the limits of measurement and thus of physical knowledge were demonstrated by Heisenberg in the world of quantum mechanics, Lorenz piled on a result that showed how microscopic errors could propagate to have a stultifying impact in nonlinear dynamic systems.

Half a century after the limits of measurement and thus of physical knowledge were demonstrated by Heisenberg in the world of quantum mechanics, Lorenz piled on a result that showed how microscopic errors could propagate to have a stultifying impact in nonlinear dynamic systems. This limitation could come into the forefront only with the dawning of the computer age, because it is manifested in the subtle errors of computational accuracy. The essence of the butterfly effect is that small perturbations can have large repercussions in massive, random forces such as weather. Edward Lorenz was a professor of meteorology at MIT, and in 1961 he was testing and tweaking a model of weather dynamics on a rudimentary vacuumtube computer. The program was based on a small system of simultaneous equations, but seemed to provide an inkling into the variability of weather patterns. At one point in his work, Lorenz decided to examine in more detail one of the solutions he had generated. To save time, rather than starting the run over from the beginning, he picked some intermediate conditions that had been printed out by the computer and used those as the new starting point.

For his application in the narrow scientific discipline of weather prediction, this meant that no matter how precise the starting measurements of weather conditions, there was a limit after which the residual imprecision would lead to unpredictable results, so that “long-range forecasting of specific weather conditions would be impossible.” And since this occurred in a very simple laboratory model of weather dynamics, it could only be worse in the more complex equations that would be needed to properly reflect the weather. Lorenz discovered the principle that would emerge over time into the field of chaos theory, where a deterministic system generated with simple nonlinear dynamics unravels into an unrepeated and apparently random path. The simplicity of the dynamic system Lorenz had used suggests a farreaching result: Because we cannot measure without some error (harking back to Heisenberg), for many dynamic systems our forecast errors will grow to the point that even an approximation will be out of our hands.


pages: 364 words: 101,286

The Misbehavior of Markets by Benoit Mandelbrot

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Albert Einstein, asset allocation, Augustin-Louis Cauchy, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black-Scholes formula, British Empire, Brownian motion, buy low sell high, capital asset pricing model, carbon-based life, discounted cash flows, diversification, double helix, Edward Lorenz: Chaos theory, Elliott wave, equity premium, Eugene Fama: efficient market hypothesis, Fellow of the Royal Society, full employment, Georg Cantor, Henri Poincaré, implied volatility, index fund, informal economy, invisible hand, John von Neumann, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market microstructure, new economy, paper trading, passive investing, Paul Lévy, Plutocrats, plutocrats, price mechanism, quantitative trading / quantitative finance, Ralph Nelson Elliott, RAND corporation, random walk, risk tolerance, Robert Shiller, Robert Shiller, short selling, statistical arbitrage, statistical model, Steve Ballmer, stochastic volatility, transfer pricing, value at risk, volatility smile

Zoom again, and yet more fine detail emerges. You can do this forever, and at each stage get an entirely different picture. Its study has become a classic problem in pure mathematics. The Mandelbrot set belongs to both fractal geometry and chaos theory. A chaotic system, far from being disorganized or non-organized, starts with one particular point and cranks it through a repeating process; the outcome is unpredictable if you do not know the process—and it depends heavily on the starting point. The most famous example of chaos was proposed by meteorologist Edward Lorenz in 1972: Can the flap of a butterfly’s wings in Brazil set off a tornado in Texas? The basic idea is that if you stand a pencil on its point and let it fall through force of gravity, exactly where it lands depends on where it began, whether it was leaning infinitesimally in one direction or another.

Studying roughness, Mandelbrot found fractal order where others had only seen troublesome disorder. His manifesto, The Fractal Geometry of Nature, appeared in 1982 and became a scientific bestseller. Soon, T-shirts and posters of his most famous fractal creation, the bulbous but infinitely complicated Mandelbrot Set, were being made by the thousands. His ideas were also embraced immediately by another scientific movement, chaos theory. “Fractals” and “chaos” entered the popular vocabulary. In 1993, on receiving the prestigious Wolf Prize for Physics, Mandelbrot was cited for “having changed our view of nature.” MANDELBROT’S LIFE story has been a tale of roughness, irregularity,. and what he calls “wild” chance. He was born in Warsaw in 1924, and tutored privately by an uncle who despised rote learning; to this day, Mandelbrot says, the alphabet and times tables trouble him mildly.

My key contribution was to found a new branch of mathematics that perceives the hidden order in the seemingly disordered, the plan in the unplanned, the regular pattern in the irregularity and roughness of nature. This mathematics, called fractal geometry, has much to say in the natural sciences. It has helped model the weather, study river flows, analyze brainwaves and seismic tremors, and understand the distribution of galaxies. It was immediately embraced as an essential mathematical tool in the 1980s by “chaos” theory, the study of order in the seeming-chaos of a whirlpool or a hurricane. It is routinely used today in the realm of man-made structures, to measure Internet traffic, compress computer files, and make movies. It was the mathematical engine behind the computer animation in the movie, Star Trek II: the Wrath of Khan. I believe it has much to contribute to finance, too. For forty years in fits and starts, as allowed by my personal interests, by unfolding events, and by the availability of colleagues to talk to, the development of fractal geometry has continually interacted with my studies of financial markets and economic systems.


pages: 297 words: 98,506

Deep Survival: Who Lives, Who Dies, and Why by Laurence Gonzales

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business climate, butterfly effect, complexity theory, Edward Lorenz: Chaos theory, impulse control, Lao Tzu, loose coupling, Louis Pasteur, V2 rocket

Traditional economics assumed perfectly rational agents. So does traditional survival training. Neither assumption reflects the messy real world. The idea of chaos theory is that what appears to be a very complex, turbulent system (the weather, for example) can begin with simple components (water, air, earth), operating under a few simple rules (heat and gravity). One of the characteristics of such a system is that a small change in the initial conditions, often too small to measure, can lead to radically different behavior. Run the equations two, four, eight times, and they may seem to be giving similar results. But the harder you drive the system, the more iterations result and the more unpredictable it becomes. Edward Lorenz, a meteorologist at MIT, was modeling weather systems on a computer in the early 1960s when he accidentally discovered that a tiny change in the initial state (1 part in 1,000) was enough to produce totally different weather patterns.

Just when you think you’ve found the smallest piece, you find another even smaller one. The theory of self-organized criticality, sometimes called Complexity theory, was developed hard on the heels of chaos theory by some of the same people. It asked and suggested answers to questions as fundamental as: Where does order come from? How do you reconcile it with the second law of thermodynamics, which says that everything is heading toward more disorder? In a sense, complexity was an extension of the thinking that gave rise to chaos theory; indeed, it was often referred to as existing at “the edge of chaos.” (There has also been strong objection to linking complexity and chaos and to using the term “complexity.”) Like chaos theory, complexity theory postulated “upheaval and change and enormous consequences flowing from trivial-seeming events—and yet with a deep law hidden beneath.”

(For that matter, if they had not misperceived which way was down, they might not have positioned themselves over Hillman and Biggs.) But the accident was still no one’s fault. There is no cause for such system accidents in the traditional sense, no blame, as the I Ching says. The cause is in the nature of the system. It’s self-organizing. WHEN NORMAL ACCIDENTS was published, neither chaos theory nor the theory of self-organizing systems was widely known or accepted. But it is possible to see hints of both in Perrow’s work. Chaos theory arose out of a huge vacuum in the physical sciences: disorder. We see it everywhere we look, from the functioning of a living organism to the behavior of flowing water: turbulence; erratic behavior; nonperiodic natural cycles from weather to animal populations. Classical physics ignored all that and used idealized systems to explain the world.


pages: 268 words: 75,850

The Formula: How Algorithms Solve All Our Problems-And Create More by Luke Dormehl

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3D printing, algorithmic trading, Any sufficiently advanced technology is indistinguishable from magic, augmented reality, big data - Walmart - Pop Tarts, call centre, Cass Sunstein, Clayton Christensen, computer age, death of newspapers, deferred acceptance, Edward Lorenz: Chaos theory, Erik Brynjolfsson, Filter Bubble, Flash crash, Florence Nightingale: pie chart, Frank Levy and Richard Murnane: The New Division of Labor, Google Earth, Google Glasses, High speed trading, Internet Archive, Isaac Newton, Jaron Lanier, Jeff Bezos, job automation, Kevin Kelly, Kodak vs Instagram, Marshall McLuhan, means of production, Nate Silver, natural language processing, Netflix Prize, pattern recognition, price discrimination, recommendation engine, Richard Thaler, Rosa Parks, self-driving car, sentiment analysis, Silicon Valley, Silicon Valley startup, Slavoj Žižek, social graph, speech recognition, Steve Jobs, Steven Levy, Steven Pinker, Stewart Brand, the scientific method, The Signal and the Noise by Nate Silver, upwardly mobile, Wall-E, Watson beat the top human players on Jeopardy!, Y Combinator

What difference does that make in your system?’ He wasn’t trying to catch us out; he was trying to grasp what we do. I was never able to explain to his satisfaction that it all depends. Is this a change that can be made without altering any of the other variables that the neural network ranks upon? Very seldom is there a movie where any significant alteration doesn’t mean changes elsewhere.” To modify a phrase coined by chaos theory pioneer Edward Lorenz, a butterfly that flaps its wings in the first minute of a movie may well cause a hurricane in the middle of the third act. The studio boss to whom Meaney refers was likely picking a purposely arbitrary detail by mentioning the color of a character’s shirt. After all, who ever formed their opinion about which movie to go and see on a Saturday night, or which film to recommend to friends, on the basis of whether the protagonist wears a blue shirt or a red shirt?


pages: 302 words: 92,507

Cold: Adventures in the World's Frozen Places by Bill Streever

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Albert Einstein, carbon footprint, Edward Lorenz: Chaos theory, Exxon Valdez, Mason jar, refrigerator car, South China Sea, the scientific method, University of East Anglia

The data, one might think, would be adequate: more than ten thousand weather stations check conditions around the globe, another five thousand ships and planes send in information, unmanned buoys transmit data from remote reaches of the world’s oceans, more than a thousand weather balloons go up each day to sample the sky, and satellites circle endlessly with their gaze turned back toward earth. But the data are not adequate. In 1963, Edward Lorenz set up weather models on a computer. He compared models run with data offering three decimal points of accuracy and those run with data offering six decimal points of accuracy. The results were completely different. Tiny differences in the starting point resulted in major differences at the end point. It would be comparable to a banker counting his wealth in dollars and in pennies, only to discover that he was well positioned in dollars but flat broke in pennies. It made no sense. It led to what was later called chaos theory. Lorenz delivered a talk to the American Academy for the Advancement of Science titled “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”

This so-called Richardson effect is often ignored in technical papers attempting to relate shoreline length to various ecological phenomena and political or economic statistics. Some sources suggest that Lorenz had planned to mention a seagull’s wings rather than a butterfly’s wings. Lorenz was swayed to the butterfly by another meteorologist, Philip Merilees. The ideas expressed in the talk — intended to explain why accurate weather forecasting is so challenging — led to a blossoming of the much-misunderstood chaos theory, popularized in books and movies, including Jurassic Park. The essence of chaos theory is that small differences in initial conditions can result in huge differences in subsequent outcomes. Lorenz died on April 16, 2008, at age ninety. James Glaisher wrote a full account of his balloon ascent, published on September 5, 1862, as “Greatest Height Ever Reached” in the British Association Report (1862, pp. 383–85). During the ascent, Glaisher describes himself fading in and out of consciousness at high altitudes.


pages: 346 words: 92,984

The Lucky Years: How to Thrive in the Brave New World of Health by David B. Agus

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3D printing, active transport: walking or cycling, Affordable Care Act / Obamacare, Albert Einstein, butterfly effect, clean water, cognitive dissonance, crowdsourcing, Danny Hillis, Drosophila, Edward Lorenz: Chaos theory, en.wikipedia.org, epigenetics, Kickstarter, medical residency, meta analysis, meta-analysis, microbiome, microcredit, mouse model, Murray Gell-Mann, New Journalism, pattern recognition, personalized medicine, phenotype, placebo effect, publish or perish, randomized controlled trial, risk tolerance, statistical model, stem cell, Steve Jobs, Thomas Malthus, wikimedia commons

Having to create our own incentives—finishing the “I shall . . .” statement by making commitments to ourselves. And that process begins by knowing who you are and, perhaps more important, how you feel. Flap Your Wings For every intervention you adopt, you create change. This was articulated beautifully by the late Edward Lorenz: when a butterfly flutters its wings in one part of the world, it can eventually cause a hurricane in another. Lorenz was an MIT meteorologist who tried to explain why it is so hard to make good weather forecasts; he wound up starting a scientific revolution called chaos theory. In the early 1960s, he noticed that small differences in a dynamic system such as the atmosphere could give rise to vast and often unexpected results. These observations ultimately led him to develop what became known as the butterfly effect, a term that grew out of an academic paper he presented in 1972 entitled “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”

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cell division, 5 cells: death of (apoptosis), 59 endoplasmic reticulum in, 40 oxidative damage to, 40 receptors on, 59 Center for the Study of Aging and Human Development (Duke University), 45 Center for Translational Neuromedicine (University of Rochester), 208 Center for Translational Research in Aging and Longevity (University of Arkansas for Medical Sciences), 194 Centers for Disease Control and Prevention (CDC), 47, 103, 133, 205 ceritinib (Zykadia), 53 change, self-assessment of, past vs. future in, 38–40, 39 chaos theory, 236–37 Charaka, 113 Charlottesville Neurology and Sleep Medicine, 204 checkpoint blockage therapy, 29–30 chemotherapy, 29, 60, 190–91 exercise and, 191, 192 Chicago, University of, 17 children, obesity and overweight in, 133 Chittagong University, 232 cholera, 234 cholesterol, 150, 195, 217, 219 dietary vs. blood, 162 online calculator for, 218 chronic disease, 128–29 age-related, 128, 136 diet and, 141–44 management of, 144–46 overweight and, 141 sleep habits and, 147 chronological age, 45, 46, 46, 47, 135–36, 232 circadian rhythm, 123, 138, 139–40, 148, 205 Circulation, 86 climate change, 159 Clinical Practice Research Datalink, 219 clinical trials, 52 double-blind, 53, 155 IRBs and, 52 randomized, 52–53 ClinVar, 9 coarse graining, 229–32, 230 cognitive abilities, 45, 46 cognitive dissonance, 159 Cohen, Jacques, 111–12 colds, 205, 214 Cold War, 94 Coley, William B., 27–29, 28, 33, 48 colitis, 121–22 Collins, Francis, 114, 118 colonoscopies, 93 Colorado, 47 colorectal cancer, 55, 123–24, 190, 217 statin use and, 220 Columbia University, 138 complex carbohydrates, 162 comprehensive metabolic panel (CMP), 151 Congress, US, 114, 237 context: adapting to new data in, 159 aging and, 45 baselines for, 150 changes in, 22 databases as, 83, 91–94 data mining and, 101 diet and, 163, 165 disease and, 13–14, 20 genes and, 14, 20–21, 118 health and, 48, 76–78, 84, 89–90, 91–94, 101, 113, 114–15, 117, 124–25 heart disease and, 22 identifying and optimizing, 135–52 lab tests in, 150–52 medical data and, 78–82 medical education and, 75 Cooper Center Longitudinal Study, 192 coordination, 45 Cornell University, 2 coronary artery disease, 151 cortisol, 123 counterfeit drugs, 10–11 C-reactive protein, 175 CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats), 24–25, 26, 45 Critical Care, 222 Crohn’s disease, 25, 121 CTLA-4, 29–30 cystic fibrosis, 115–16 Cystic Fibrosis Foundation Vertex, 115–16 cytokines, 123 cytoplasm, 111 cytosol, 40 Dana-Farber Cancer Institute, Profile program of, 118 Dannon, 235 Dartmouth College, 157 Darwin, Charles, 112 data, medical: context and, 78–82 individual’s role in collection of, 81 databases, medical, 82–83, 95 as context, 83, 91–94 security of, 88–89 data mining, 84–89, 92 context and, 101 infectious diseases and, 100–101 Davos, Switzerland, 161 Dawkins, Richard, 17 death, leading causes of, 129 death certificates, 96 decision-making, 225, 227–28 dehydration, 234 dementia, 5, 41, 90, 91, 151, 204, 210, 215, 221 see also Alzheimer’s disease depression, 122, 211, 215 exercise and, 186 Dhaka, 232 diabetes, 22, 24, 25, 47, 59, 108, 114, 123, 128, 147, 151, 166, 175, 186, 187, 188, 215, 221, 237 gut bacteria and, 120–21 incidence of, 120–21 diet, 22, 114 chronic disease and, 141–44 as contextual, 163 honesty about, 133–34 low-cholesterol, 162 low-fat, 162 moderation in, 144 research on, see nutritional studies weight and, 141 diphtheria, 161 disease: autoimmune, 85, 125, 175 context and, 13–14, 20 genetic markers for, 22, 113–14, 127 surrogate markers for, 127–28 see also chronic disease; infectious diseases; noncommunicable diseases disorders, inherited, newborn screening and, 12 DNA, see genes, genome DNA mismatch repair, 32, 57 docosahexaenoic acid (DHA), 182 dopamine, 211 Doudna, Jennifer A., 25 dreaming, 203 drug abuse, 22 drugs, see medications Duke Cancer Institute (DCI), 191 Duke University, 30 Center for the Study of Aging and Human Development at, 45 Dulken, Ben, 63 Dunedin Study, 45–47, 46 Dyerberg, Jorn, 182–83 Dyson, Esther, 173 Earls, Felton, 213 East Africa, 44, 107 Eat, Sleep, Poop (Cohen), 137 eating patterns, heart disease and, 138–40 Ebola, 18, 221–22 E. coli, 123 eicosapentaenoic acid (EPA), 182 Einstein, Albert, 2, 223 Elder, William, Jr., 115–16 electrodermal response, 230–31 Elledge, Stephen J., 84 emotions, touch and, 214 emulsifiers, microbiome and, 121–22 “end of history illusion,” 38–40, 39 End of Illness, The (Agus), 18 endoplasmic reticulum, 40 endorphins, 211 energy levels, 149 England, see Great Britain environment, see context epidemics: global spread of, 103 prediction of, 103–4 epigenetics, 20–21 esomeprazole (Nexium), 86 esophageal cancer, 217 estrogen, 64 ethics: genome editing and, 24–25 medical advances and, 10, 24 technology and, 25–26 Europe, 77 European Journal of Immunology, 34 exercise, 21, 114, 140, 185–201 chemotherapy and, 191, 192 honesty about, 133–34 ideal amount of, 196–200 intensity of, 197–98 life expectancy and, 189–90 mortality rates and, 148 Exeter, University of, 157 “Experimental Prolongation of the Life Span” (McCay, Lunsford, and Pope), 2 experimental treatments, quicker access to, 56 Facebook, 27 fasting lipid profile, 150 feebleness, aging and, 43 fertility, aging and, 43 Field, Tiffany, 214 financial industry, information technology and, 89 Finland, 220 fish oil, 182–83 Florida, 103 flu vaccine: misinformation about, 157–58 public distrust of, 160 FODMAPs (fermentable oligo-di-monosaccharides and polyols), 164 Fodor, George, 183 food, safety of, 11 Food and Drug Administration, US (FDA), 2, 18, 51, 55, 56, 86, 111, 112, 127–28, 146, 182, 201 Accelerated Approval provisions of, 128 Foundation Medicine, 50 Framingham Heart Study, 47, 118 Fred Hutchinson Cancer Research Center, 169 free radicals, 208 fruit flies, eating pattern studies with, 138–40 fungi, 119 gait, 45 galvanic skin response (GSR), 230–31 gastroesophageal reflux disease (GERD), 86 Gates, Bill, 2 Genentech, 56 genes, genome, 45, 83–84 aging and, 20, 41 bacterial, 107, 119 context and, 14, 20–21, 118 DNA mismatch repair and, 32 expression of, 20–21, 125, 139 mitochondrial, see mitochondrial DNA sequencing of, 20, 23, 49–52, 112 SNPs in, 113–14 as switches, 41 viruses and, 119–20 genes, genome, editing of, 24–25, 45 ethics of, 102–5 genetically modified foods (GMOs), 18 genetic markers, 22, 113–14, 127 genetic mutations: aging and, 41 cancer and, 14, 21–22, 50 disease risk and, 9, 12 genetic screening, 103, 117, 137 flawed results in, 8–10 of newborns, 11–12 Georgia State University, 121 Gewirtz, Andrew, 121 Gibson, Peter, 164 Gilbert, Daniel, 38, 39, 40 Gillray, James, 161 Gladwell, Malcolm, 225, 227, 228 Gleevec (imatinib), 55 glial cells, 209 glioblastoma, 30 “Global Recommendations on Physical Activity for Health” (WHO), 187 gluten, debate over, 163–65 Goldstein, Irwin, 211 Google, 87, 88, 101 Google Flu Trends, 101 Grameen Bank, 232, 233–34, 235 Grameen Danone, 235 Graunt, John, 100 Great Britain, 96, 97, 100, 110, 155 Black Death in, 95–101, 98, 99, 100 Greatist.com, 200 Greenland, 182 Grove, Andy, 7, 7 growth factors, 59 gun violence, 91 gut: inflammation of, 120, 122 microbiome of, see microbiome H2 blockers, 86 habits and routines, 136, 137–41, 228, 237–38 see also diet; lifestyle choices Harlow, Harry, 213 Harvard Medical School, 84 Harvard School of Public Health, 142–43 Harvard University, 3, 23, 24, 37, 178, 186, 196, 212, 213, 216 hash tables, health care and, 87–88 Hawaii, 47 HDL cholesterol, 150 health: biological age and, 47 context and, 48, 76–78, 84, 89–90, 91–94, 101, 113, 114–15, 117, 124–25 family history of, 136–37 honesty about, 131–34 inflection point in, 8 lifestyle and, see lifestyle choices optimism and, 65–69 personal baselines for, 150 retirement and, 91–92 technology and, 37–70 health and fitness apps, 200 Health and Human Services Department, US, 103 health care: Affordable Care Act and, 69–70 hash tables and, 87–88 individual’s responsibility in, 12–13, 26, 70, 75, 78, 131–32 misinformation about, 14–15, 18, 19, 154, 157–58 politics and, 11–12 portable electronic devices and, 79, 90–91 Health Professionals Follow-up Study, 142–43, 217 health threats, prediction of, 103–4 heart: biological age of, 47–48 health of, 48 heart attacks, 76, 86, 182, 217, 218 heart disease, 59, 128, 150, 166, 175, 183, 186, 187, 215, 217, 221 context and, 22 diet and, 163 eating patterns and, 138–40 lifestyle choices and, 22 muscle mass and, 195 heart rates, 231 heart rate variability (HRV), 230 Heathrow Airport, 92 “hedonic reactions,” 38–40 heel sticks, 11–12 hemoglobin A1C test, 151 hepatitis B, 175 hepatitis C, 175 Herceptin (trastuzumab), 55 high blood pressure, 22, 188, 195 high-sensitivity C-reactive protein (CRP) test, 151 hippocampus, 214 Hippocrates, 71, 113, 122, 216 HIV/AIDS, 18, 24, 25, 59, 84, 127–28, 131, 159 Hoffmann, Felix, 215, 216 Holland, 41 Homeland Security Department, US, 103 homeostasis, 137–38, 140 Homo sapiens, evolution of, 107 honesty: about health, 131–34 nutritional studies and, 162 hormones, 219 hormone therapy, 201 Horton, Richard, 178 Hospital for the Ruptured and Crippled (Hospital for Special Surgery), 28 house calls, 80 Houston Methodist, 86 “how do you feel” question, 231 hugs, 214 Human Genome Project, 113, 120 human growth hormone, 200 Human Molecular Genetics, 65 human papilloma virus (HPV), 161, 175 Hurricane Sandy, 84 Huxley, Aldous, viii, 6, 159, 238 Hydra magnipapillata, 42, 42 hyperglycemia, 122 hypertension, 125, 195, 203 IBM, 88–89 imatinib (Gleevec), 55 immune reactions, 5 immune system, 175, 190, 209, 211 aging and, 44 impact of hugs on, 214 immunotherapy, 28–33 polio virus and, 30, 31 incentives, 235–36 Indiana University Bloomington School of Informatics and Computing’s Center for Complex Networks and Systems Research, 94–95 infant mortality, 87, 97 infants: genetic screening of, 11–12 premature, 87 infections, 175–76 infectious diseases, 129 antibiotic-resistant, 67–69, 68 data mining and, 100–101 inflammation, 34, 151, 174–77, 181, 187, 190, 195, 215–22 inflammatory bowel disease, 121 inflection points, 7–8, 7 influenza, 161 risks from, 157 vaccine for, see flu vaccine information, sorting good from bad, 19–20 information technology, financial industry and, 89 inherited disorders, newborn genetic screening and, 12 insomnia, 122 Institute for Sexual Medicine, 211 insulin, 56, 190 insulin sensitivity, 5, 87, 120, 122, 151, 195 insurance companies, off-label drugs and, 55 Intel, 7 International Agency for Research on Cancer, 170 International Prevention Research Institute, 180 intuition, 224–29 Inuits, 182–83 in vitro fertilization (IVF), three-person, 109–12, 110 Ioannidis, John, 178 IRBs (institutional review boards), 52 iron deficiency, 231 irritable bowel syndrome (IBS), 164 Islam, 234 Italy, 183 ivacaftor (Kalydeco), 115–16 JAMA Internal Medicine, 142, 143, 192, 196 Jenner, Edward, 160, 161 Jobs, Steve, 2, 23–24, 26, 49 Johns Hopkins Hospital, 71, 72, 128 Hurd Hall at, 74 Osler Medical Housestaff Training Program at, 73–75, 74 Johns Hopkins Sidney Kimmel Comprehensive Cancer Center, 32 Johns Hopkins University, 23, 169, 170, 171, 173, 174, 175, 176, 215 Jolie, Angelina, 21 Jones, Owen, 43 Journal of Sexual Medicine, 211 Journal of the American Medical Association (JAMA), 72, 114–15, 173, 201, 220, 221 Journal of the American Osteopathic Association, 154 Journal of the National Cancer Institute, 169 Journal of Urology, 168 journals, medical, misinformation in, 154, 179 J.


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Earth Wars: The Battle for Global Resources by Geoff Hiscock

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Admiral Zheng, Asian financial crisis, Bakken shale, Bernie Madoff, BRICs, butterfly effect, clean water, cleantech, corporate governance, demographic dividend, Deng Xiaoping, Edward Lorenz: Chaos theory, energy security, energy transition, eurozone crisis, Exxon Valdez, flex fuel, global rebalancing, global supply chain, hydraulic fracturing, Long Term Capital Management, Malacca Straits, Masdar, megacity, Menlo Park, Mohammed Bouazizi, new economy, oil shale / tar sands, oil shock, Panamax, purchasing power parity, Ralph Waldo Emerson, RAND corporation, Shenzhen was a fishing village, Silicon Valley, smart grid, South China Sea, sovereign wealth fund, special economic zone, spice trade, trade route, uranium enrichment, urban decay, working-age population, Yom Kippur War

But he was more positive about the United States, calling it “a pragmatic nation that doesn’t give up easily, and has the determination and the optimism to keep trying new things until it solves a problem.” As for China, du Plessis had little doubt that its long-term growth rate remained in place, “keeping China firmly in position as the world’s primary engine of growth.”17 This is the human element of the Earth wars, but there is a natural element at play as well. In classic chaos theory, tiny differences at the start of a sequence of events lead to vastly different outcomes—the so-called butterfly effect popularised by the U.S. mathematician and meteorologist Edward Lorenz in his work on computerised weather prediction in the 1960s. Lorenz, a professor emeritus at Massachusetts University of Technology (MIT) when he died in 2008 at the age of 90, wrote a paper in 1972 titled “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?” to explain his theory of sensitive dependence on initial conditions.


pages: 1,205 words: 308,891

Bourgeois Dignity: Why Economics Can't Explain the Modern World by Deirdre N. McCloskey

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Admiral Zheng, agricultural Revolution, Albert Einstein, BRICs, British Empire, butterfly effect, Carmen Reinhart, clockwork universe, computer age, Corn Laws, dark matter, David Ricardo: comparative advantage, Donald Trump, Edward Lorenz: Chaos theory, European colonialism, experimental economics, financial innovation, Fractional reserve banking, full employment, George Akerlof, germ theory of disease, Gini coefficient, greed is good, Howard Zinn, income per capita, interchangeable parts, invention of agriculture, invention of air conditioning, invention of writing, invisible hand, Isaac Newton, James Watt: steam engine, John Maynard Keynes: technological unemployment, John Snow's cholera map, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, knowledge economy, means of production, Naomi Klein, New Economic Geography, New Urbanism, purchasing power parity, rent-seeking, road to serfdom, Robert Gordon, Ronald Coase, Ronald Reagan, Scientific racism, Scramble for Africa, Shenzhen was a fishing village, Simon Kuznets, Slavoj Žižek, spinning jenny, Steven Pinker, The Wealth of Nations by Adam Smith, Thorstein Veblen, too big to fail, total factor productivity, transaction costs, tulip mania, union organizing, Upton Sinclair, urban renewal, V2 rocket, very high income, working poor, World Values Survey, Yogi Berra

But the other half is unhelpful, too. It is not — pace Marx — the surplus value stored up by Mr. Moneybags (Herr Geldsack) that propels modern innovation. Such profit is merely a hope tempting to the imagination. Profit comes mostly from productivity, not as the pessimists of the left and right insist mostly from monopoly. Paul Sweezy, Paul Baran, Stephen Marglin, William Lazonick, Bernard Elbaum, Edward Lorenz, Jon Cohen, Robert Allen, and other economic scholars on the left — an astonishing group, by the 239 way, presenting a scientific challenge largely ignored by the Samuelsonian/ Friedmanian orthodoxy in modern economics — have been claiming for a long time that innovation was determined by the struggle over the spoils (in a phrase, by monopoly capitalism), for good [Galbraith, Lazonick] or evil [Baran and Sweezy]).

What we are looking at is the inception of something which was at first insignificant and even bizarre,” though “destined to change the life of every man and woman in the West.” 29 In the case of the Industrial Revolution now the East. Yet one might wonder—the point will be made many times here in various different ways—why then it did not happen before. “Sensitive dependence on initial conditions” is the technical term for some “nonlinear” models—a piece of so called “chaos theory.” But under such 87 circumstances a history becomes untellable. 30 It may be so—the world may be in fact nonlinear dynamic, as Basil Moore argues. But then we will need to give up our project of telling its history, because the true causes will consist of lost horseshoe nails and butterfly effects too small to be detected. The reasons are the same as those that make it impossible to forecast distant weather: “Current forecasts are useful for about five days,” writes a leading student of such matters, “but it is theoretically impossible to extend the window more than two weeks into the future.” 31 It is “theoretically” impossible because the fluid mechanics, the radiative transfer, the photochemistry, the air-sea interactions, and so forth “are violently non-linear and strongly coupled.”

As Emerson noted, “an idealist can never go backward to be a materialist.”3 A piling up of rejected alternatives, all of the same re-allocative character, does suggest by sober scientific criteria that we may be looking in the wrong place — perhaps under the lamppost of static economics, or under a somewhat grander lamppost of a dynamics depending on statics, or under the grandest lamppost discovered so far, of a non-linear dynamics of chaos theory. Perhaps we are looking in such places not because the evidence leads us to them but on account of the excellent mathematical light shining under all these impressively ornamented lampposts. Yet one after another of the proffered material explanations has failed. No believable case can be made that adding them all together would change much, or that other countries and other times did not have equally favorable material conjunctures — not if we are trying to explain the unprecedented factors of growing production per head.


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

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airport security, availability heuristic, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, big-box store, Black Swan, Broken windows theory, Carmen Reinhart, Claude Shannon: information theory, Climategate, Climatic Research Unit, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, complexity theory, computer age, correlation does not imply causation, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, Daniel Kahneman / Amos Tversky, diversification, Donald Trump, Edmond Halley, Edward Lorenz: Chaos theory, en.wikipedia.org, equity premium, Eugene Fama: efficient market hypothesis, everywhere but in the productivity statistics, fear of failure, Fellow of the Royal Society, Freestyle chess, fudge factor, George Akerlof, haute cuisine, Henri Poincaré, high batting average, housing crisis, income per capita, index fund, Internet Archive, invention of the printing press, invisible hand, Isaac Newton, James Watt: steam engine, John Nash: game theory, John von Neumann, Kenneth Rogoff, knowledge economy, locking in a profit, Loma Prieta earthquake, market bubble, Mikhail Gorbachev, Moneyball by Michael Lewis explains big data, Monroe Doctrine, mortgage debt, Nate Silver, new economy, Norbert Wiener, PageRank, pattern recognition, pets.com, prediction markets, Productivity paradox, random walk, Richard Thaler, Robert Shiller, Robert Shiller, Rodney Brooks, Ronald Reagan, Saturday Night Live, savings glut, security theater, short selling, Skype, statistical model, Steven Pinker, The Great Moderation, The Market for Lemons, the scientific method, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, too big to fail, transaction costs, transfer pricing, University of East Anglia, Watson beat the top human players on Jeopardy!, wikimedia commons

They’re relatively Newtonian: the uncertainty principle—interesting as it might be to physicists—won’t bother you much. You’ve gotten your hands on a state-of-the-art piece of equipment like the Bluefire. You’ve hired Richard Loft to design the computer’s software and to run its simulations. What could possibly go wrong? How Chaos Theory Is Like Linsanity What could go wrong? Chaos theory. You may have heard the expression: the flap of a butterfly’s wings in Brazil can set off a tornado in Texas. It comes from the title of a paper19 delivered in 1972 by MIT’s Edward Lorenz, who began his career as a meteorologist. Chaos theory applies to systems in which each of two properties hold: The systems are dynamic, meaning that the behavior of the system at one point in time influences its behavior in the future; And they are nonlinear, meaning they abide by exponential rather than additive relationships.

After spending weeks double-checking their hardware and trying to debug their program, Lorenz and his team eventually discovered that their data wasn’t exactly the same: one of their technicians had truncated it in the third decimal place. Instead of having the barometric pressure in one corner of their grid read 29.5168, for example, it might instead read 29.517. Surely this couldn’t make that much difference? Lorenz realized that it could. The most basic tenet of chaos theory is that a small change in initial conditions—a butterfly flapping its wings in Brazil—can produce a large and unexpected divergence in outcomes—a tornado in Texas. This does not mean that the behavior of the system is random, as the term “chaos” might seem to imply. Nor is chaos theory some modern recitation of Murphy’s Law (“whatever can go wrong will go wrong”). It just means that certain types of systems are very hard to predict. The problem begins when there are inaccuracies in our data. (Or inaccuracies in our assumptions, as in the case of mortgage-backed securities).

“I did a bold and stupid thing—I made a testable prediction. That’s what we’re supposed to do, but it can bite you when you’re wrong.” Bowman’s idea had been to identify the root causes of earthquakes—stress accumulating along a fault line—and formulate predictions from there. In fact, he wanted to understand how stress was changing and evolving throughout the entire system; his approach was motivated by chaos theory. Chaos theory is a demon that can be tamed—weather forecasters did so, at least in part. But weather forecasters have a much better theoretical understanding of the earth’s atmosphere than seismologists do of the earth’s crust. They know, more or less, how weather works, right down to the molecular level. Seismologists don’t have that advantage. “It’s easy for climate systems,” Bowman reflected.


pages: 493 words: 172,533

Best of Kim Stanley Robinson by Kim Stanley Robinson

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Albert Einstein, butterfly effect, Edward Lorenz: Chaos theory, late capitalism, Murano, Venice glass, Richard Feynman, Richard Feynman

The scientific term for it is “sensitive dependence on initial conditions.” It is an aspect of chaos theory first studied by the meteorologist Edward Lorenz, who, while running computer simulations of weather patterns, discovered that the slightest change in the initial conditions of the simulation would quickly lead to completely different weather. So the strong covering law model said that historical explanation should equal the rigor of scientific explanation. Then its defenders, bringing the model into the quantum world, conceded that predictions can never be anything but probabilistic at best. The explanandum was no longer deducible from the explanans; one could only suggest probabilities. Now chaos theory has added new problems. And yet consider: Captain Frank January chose to miss Hiroshima.

“The Lucky Strike” One day in 1983, when we were living in our little place in downtown Davis, the image came to me of the Enola Gay, flying toward Japan but then tipping over and falling into the sea. That was a story for sure, but what? After a few weeks of reading I wrote it out pretty quickly. “A Sensitive Dependence on Initial Conditions” After I wrote “The Lucky Strike,” I began to have second thoughts about the postwar alternative history described at the end of that story. Back in DC after our Swiss adventure, I was reading all the new stuff about chaos theory, and some historiography in preparation for the Mars books, and it seemed to me human history might be regarded as a kind of chaotic system. This story was the result. It had a strange form, but it did what I wanted; and “form follows function” is one of the great rules. “Arthur Sternbach Brings the Curveball to Mars” This one I wrote in 1998, but the inspiration for it came from our two years in Zürich (1986–87), when I was a member of the baseball team Züri 85.