power law

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Why Stock Markets Crash: Critical Events in Complex Financial Systems by Didier Sornette

Alan Greenspan, Asian financial crisis, asset allocation, behavioural economics, Berlin Wall, Black Monday: stock market crash in 1987, Bretton Woods, Brownian motion, business cycle, buy and hold, buy the rumour, sell the news, capital asset pricing model, capital controls, continuous double auction, currency peg, Deng Xiaoping, discrete time, diversified portfolio, Elliott wave, Erdős number, experimental economics, financial engineering, financial innovation, floating exchange rates, frictionless, frictionless market, full employment, global village, implied volatility, index fund, information asymmetry, intangible asset, invisible hand, John von Neumann, joint-stock company, law of one price, Louis Bachelier, low interest rates, mandelbrot fractal, margin call, market bubble, market clearing, market design, market fundamentalism, mental accounting, moral hazard, Network effects, new economy, oil shock, open economy, pattern recognition, Paul Erdős, Paul Samuelson, power law, quantitative trading / quantitative finance, random walk, risk/return, Ronald Reagan, Schrödinger's Cat, selection bias, short selling, Silicon Valley, South Sea Bubble, statistical model, stochastic process, stocks for the long run, Tacoma Narrows Bridge, technological singularity, The Coming Technological Singularity, The Wealth of Nations by Adam Smith, Tobin tax, total factor productivity, transaction costs, tulip mania, VA Linux, Y2K, yield curve

The human population data from 0 to 1998 was retrieved from the website of The United Nations Population Division, Depart- 363 2 05 0: the end of t h e g r o w t h e r a? 10000 Real power law Complex power law Dow Jones Standard & Poor EAFE Europe Latin America Index 1000 World 100 10 1800 1850 1900 Date 1950 2000 Fig. 10.2. Financial indices in logarithmic scale as a function of time (linear scale). The two largest time series, the Dow Jones extrapolated back to 1790 and the S&P (500) index from 1871, are fitted by a power law Atc − tm shown as continuous lines. The log-periodic law (corresponding to a complex exponent of the power law) is shown only for the Dow Jones time series as a dashed line. A sophisticated power law analysis suggests an abrupt transition at around 2050 [219].

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A crash is not the critical or singular point itself, but its triggering rate is strongly influenced by the proximity of the critical point: the closer to the critical time, the more probable is the crash. We have seen that the hallmark of critical behavior is a power law acceleration of the price, of its volatility, or of the crash hazard rate, as the critical time tc is approached. The purpose of the present chapter is to extend this analysis and suggest that additional important ingredients and patterns beyond the simple power law acceleration should be expected. An important motivation is that a power law acceleration is notoriously difficult to detect and to qualify in practice in the presence of the ubiquitous noise and irregularities of the trajectories of stock market prices.

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The right panel shows five realizations with different initial configurations of waiting times, in a double logarithmic scale, such that a power law acceleration of the form shown in Figures 6.3 and 6.4 is represented as a straight line. One can indeed observe a characteristic power law acceleration, which is decorated by log-periodic structures at many different scales as the critical time is approached. It turns out to be possible to explicitly solve this model and demonstrate rigorously the existence of these log-periodic structures decorating the average power law [398]. hier archies and l o g - p e r i o d i c i t y 185 Fig. 6.8. Left panel: Number of traders who have made buy orders as a function of time.

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

All scale-free networks have the small-world property, though not all networks with the small-world property are scale-free. In more scientific terms, a scale-free network always has a power law degree distribution. Recall that the approximate in-degree distribution for the Web is Number of Web pages with in-degree k is proportional to . Perhaps you will remember from high school math that also can be written as k−2. This is a “power law with exponent −2.” Similarly, (or, equivalently, k−1) is a power law with exponent −1.” In general, a power-law distribution has the form of xd, where x is a quantity such as in-degree. The key number describing the distribution is the exponent d; different exponents cause very different-looking distributions.

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The theory, called metabolic scaling theory (or simply metabolic theory), combines biology and physics in equal parts, and has ignited both fields with equal parts excitement and controversy. Power Laws and Fractals Metabolic scaling theory answers two questions: (1) why metabolic scaling follows a power law at all; and (2) why it follows the particular power law with exponent 3/4. Before I describe how it answers these questions, I need to take a brief diversion to describe the relationship between power laws and fractals. Remember the Koch curve and our discussion of fractals from chapter 7? If so, you might recall the notion of “fractal dimension.”

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More generally, if each level is scaled by a factor of x from the previous level and is made up of N copies of the previous level, then xdimension = N. Now, after having read chapter 15, you can recognize that this is a power law, with dimension as the exponent. This illustrates the intimate relationship between power laws and fractals. Power law distributions, as we saw in chapter 15, figure 15.6, are fractals—they are self-similar at all scales of magnification, and a power-law’s exponent gives the dimension of the corresponding fractal (cf. chapter 7), where the dimension quantifies precisely how the distribution’s self-similarity scales with level of magnification.

Model Thinker: What You Need to Know to Make Data Work for You by Scott E. Page

Airbnb, Albert Einstein, Alfred Russel Wallace, algorithmic trading, Alvin Roth, assortative mating, behavioural economics, Bernie Madoff, bitcoin, Black Swan, blockchain, business cycle, Capital in the Twenty-First Century by Thomas Piketty, Checklist Manifesto, computer age, corporate governance, correlation does not imply causation, cuban missile crisis, data science, deep learning, deliberate practice, discrete time, distributed ledger, Easter island, en.wikipedia.org, Estimating the Reproducibility of Psychological Science, Everything should be made as simple as possible, experimental economics, first-price auction, Flash crash, Ford Model T, Geoffrey West, Santa Fe Institute, germ theory of disease, Gini coefficient, Higgs boson, High speed trading, impulse control, income inequality, Isaac Newton, John von Neumann, Kenneth Rogoff, knowledge economy, knowledge worker, Long Term Capital Management, loss aversion, low skilled workers, Mark Zuckerberg, market design, meta-analysis, money market fund, multi-armed bandit, Nash equilibrium, natural language processing, Network effects, opioid epidemic / opioid crisis, p-value, Pareto efficiency, pattern recognition, Paul Erdős, Paul Samuelson, phenotype, Phillips curve, power law, pre–internet, prisoner's dilemma, race to the bottom, random walk, randomized controlled trial, Richard Feynman, Richard Thaler, Robert Solow, school choice, scientific management, sealed-bid auction, second-price auction, selection bias, six sigma, social graph, spectrum auction, statistical model, Stephen Hawking, Supply of New York City Cabdrivers, systems thinking, tacit knowledge, The Bell Curve by Richard Herrnstein and Charles Murray, The Great Moderation, the long tail, The Rise and Fall of American Growth, the rule of 72, the scientific method, The Spirit Level, the strength of weak ties, The Wisdom of Crowds, Thomas Malthus, Thorstein Veblen, Tragedy of the Commons, urban sprawl, value at risk, web application, winner-take-all economy, zero-sum game

In Chapter 12 when we cover entropy, we learn a third model in which a power-law maximizes uncertainty given a fixed mean. And in Chapter 13, we show that return times in a random walk model also satisfy a power law. Still other models show that power laws result from optimal encodings, random stopping rules, and combining distributions.4 The remainder of the chapter covers the structure, logic, and functions of power-law distributions, followed by a discussion. The discussion reconsiders the implications of large events and describes the limits of our ability to prevent and plan for them. Power Laws: Structure In a power-law distribution, the probability of an event is proportional to its size raised to a negative exponent.

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So for example, the familiar function describes a power law. In a power-law distribution, the probability of an event is inversely related to its size: the larger the event, the less likely it occurs. Power-law distributions, therefore, have many more small events than large ones. Power-Law Distributions A power-law distribution5 defined over the interval [xmin, ∞) can be written as follows: p(x) = Cx-a where the exponent a > 1 determines the length of the tail, and the constant term ensures the distribution has a total probability of one. The size of the power law’s exponent determines the likelihood and size of large events.

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If deaths due to terrorist attacks followed a normal distribution with mean 20 and a standard deviation of 5, a one-in-a-million event would involve fewer than 50 deaths. A power-law distribution has a precise definition. Not all long-tailed distributions are power laws. Plotting a distribution on a log-log scale creates a crude test of whether the distribution is a power law. A log-log plot transforms event sizes and their probabilities to their logged values and transforms a power-law distribution into a straight line.8 Figure 6.2: Power Law (Black) vs. Lognormal (Gray) on Log-Log Scale In other words, a straight line on a log-log plot is evidence of a power law, while an initially straight line that gradually falls off is consistent with a lognormal (or an exponential) distribution.

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

Zipf’s law, as scientists came to call it, is actually only one example among many of a “power law.” To take language as an example, a power law implies that you see a few words very frequently and many words relatively rarely. Zipf erroneously argued that his law distinguished the social sciences from the physical sciences. Since his work, scientists have discovered power laws in many areas, including physical and biological systems. For example, scientists use power laws to explain relationships between the mass and metabolic rates of animals, frequency and magnitude of earthquakes (the Gutenberg-Richter law), and frequency and size of avalanches. Power laws are also very prominent in social systems, including income distribution (Pareto’s law), city size, Internet traffic, company size, and changes in stock price.

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Many people recognize power laws through the more colloquial “80/20 rule.”3 Why should investors care about power laws? First, the existence of power law distributions can help reorient our understanding of risk. Most of finance theory—including models of risk—is based on the idea of normal or lognormal distributions of stock price changes. A power law distribution suggests periodic, albeit infrequent price movements that are much larger than the theory predicts. This fat-tail phenomenon is important for portfolio construction and leverage. Second, the existence of power laws suggests some underlying order in self-organizing systems.

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Another way investors can use power laws is to understand the topology of the Internet. A classic example of a self-organizing network, the Internet has spawned a host of power law relationships—including the number of links per site, the number of pages per site, and the popularity of sites. These power laws suggest uneven benefits for companies that make heavy use of the Web.11 The development of the Web may be instructive for the organization of future networks. Power laws represent a number of social, biological, and physical systems with fascinating accuracy. Further, many of the areas where power laws exist intersect directly with the interests of investors.

The Internet Trap: How the Digital Economy Builds Monopolies and Undermines Democracy by Matthew Hindman

A Declaration of the Independence of Cyberspace, accounting loophole / creative accounting, activist fund / activist shareholder / activist investor, AltaVista, Amazon Web Services, barriers to entry, Benjamin Mako Hill, bounce rate, business logic, Cambridge Analytica, cloud computing, computer vision, creative destruction, crowdsourcing, David Ricardo: comparative advantage, death of newspapers, deep learning, DeepMind, digital divide, discovery of DNA, disinformation, Donald Trump, fake news, fault tolerance, Filter Bubble, Firefox, future of journalism, Ida Tarbell, incognito mode, informal economy, information retrieval, invention of the telescope, Jeff Bezos, John Perry Barlow, John von Neumann, Joseph Schumpeter, lake wobegon effect, large denomination, longitudinal study, loose coupling, machine translation, Marc Andreessen, Mark Zuckerberg, Metcalfe’s law, natural language processing, Netflix Prize, Network effects, New Economic Geography, New Journalism, pattern recognition, peer-to-peer, Pepsi Challenge, performance metric, power law, price discrimination, recommendation engine, Robert Metcalfe, search costs, selection bias, Silicon Valley, Skype, sparse data, speech recognition, Stewart Brand, surveillance capitalism, technoutopianism, Ted Nelson, The Chicago School, the long tail, The Soul of a New Machine, Thomas Malthus, web application, Whole Earth Catalog, Yochai Benkler

This section will briefly discuss power laws and the mathematics of dynamical systems that underlie our simulations. The first order of business is to address a sometimes unhelpful debate on what counts as a power law in empirical data. In formal terms, a power law distribution is characterized by a density function that is proportional to 1/x α , where the (negative) power α corresponds to the slope of the line when plotted on a log-log scale. A profusion of papers on power laws from the late 1990s onward, and a subsequent popular press discussion of power laws and “long tails,” has sparked a corrective backlash among some researchers (e.g., Clauset et al., 2009).

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Appendix • 185 For the data sources used here, there is little substantive difference whether the distribution of audience is a power law, an extreme lognormal, a power law with exponential cutoff, etc. Most real-world datasets show deviations from a pure power law in the “head” with the largest observations. This volume often uses the term “log-linear distribution” to denote this broad family of related distributions. In general, though, there are good reasons to prefer the power law label, even when other distributions may fit the data slightly better. Of course other related distributions often fit better: they have two or more parameters, while pure power laws have only one. Parsimony is a cardinal virtue in model building, and each additional parameter provides latitude for mischief.

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Web traffic is roughly power law distributed, in which a highly concentrated “head” of the web is coupled with a long, diffuse “tail” of tiny sites. These power law–like patterns have provoked vigorous debate about whether the web is dominated by new or old elites.3 Amidst this debate crucial questions have remained unanswered. First, where did these power laws come from? After all, as we saw in chapter 1, the World Wide Web was specifically designed to prevent this sort of inequality. Some scholarship has suggested that rich-get-richer effects are the culprit.4 But power law patterns can be produced by many different kinds of rich-getricher loops, and also by some processes that are different altogether.5 84 • Chapter 5 Second, and just as important, how stable are these winners-take-all patterns?

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

His book, Human Behavior and the Principle of Least Effort, saw power laws as an omnipresent pattern in the social sciences. Such power laws are common in physics, and are a form of what I now call fractal scaling. Seismologists have a mathematical formula that shows the number of earthquakes varying by a power law with their intensity, on the famous Richter scale. Put another way: Small quakes are common while big ones are rare, with a precise formula relating intensity to frequency. But at that time only a few examples were known—to very few persons. Zipf, an encyclopedist obsessed by an idée fixe, claimed that power laws do not occur only in physical sciences but are the rule in all manner of human behavior, organization, and anatomy—even in the size of sexual organs.

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If a spaceship doubles its distance from Earth, the gravitational pull on it falls to a fourth its original value. In economics, one classic power law was discovered by Italian economist Vilfredo Pareto a century ago. It describes the distribution of income in the upper reaches of society. That power law concentrates much more of a society’s wealth among the very few; a bell curve would be more equitable, scattering incomes more evenly around an average. Now we reach one of my main findings. A power law also applies to positive or negative price movements of many financial instruments. It leaves room for many more big price swings than would the bell curve.

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Funny coincidence: Two is also the value of the exponent by which you raise the length to get the area. In short, the slope of the line is also the “power” in the power law. It works with other powers, too. If you fill a boxcar with cubic boxes, the volume increases by the power of three and the slope will be steeper. If you create a long string by lining up shorter strings end to end, the power is one. Of course, bathroom tiles, boxcars, and strings make for particularly silly power laws; other, more complex data may show steeper or shallower slopes on the paper. Regardless: If a power law is in play, some kind of straight line will appear. It is a simple test, childishly simple.

Understanding Sponsored Search: Core Elements of Keyword Advertising by Jim Jansen

AltaVista, AOL-Time Warner, barriers to entry, behavioural economics, Black Swan, bounce rate, business intelligence, butterfly effect, call centre, Claude Shannon: information theory, complexity theory, content marketing, correlation does not imply causation, data science, en.wikipedia.org, first-price auction, folksonomy, Future Shock, information asymmetry, information retrieval, intangible asset, inventory management, life extension, linear programming, longitudinal study, machine translation, megacity, Nash equilibrium, Network effects, PageRank, place-making, power law, price mechanism, psychological pricing, random walk, Schrödinger's Cat, sealed-bid auction, search costs, search engine result page, second-price auction, second-price sealed-bid, sentiment analysis, social bookmarking, social web, software as a service, stochastic process, tacit knowledge, telemarketer, the market place, The Present Situation in Quantum Mechanics, the scientific method, The Wisdom of Crowds, Vickrey auction, Vilfredo Pareto, yield management

We see this in the searching behavior mentioned, such as query length, session length, click-through rates, and sites visited among the aggregate set of searchers. All this leads us to what we are most interested in€– the power law distribution. The powerful impact of power laws Most searchers’ keyterm behavior, and therefore keyphrases, can be modeled using power law distributions. Why are these aggregate behaviors explainable by power laws? It is an outgrowth of the aggregate of the individual behavior resulting from the principle of least effort and information obtainability constructs. First though, what is a power law? The graph shown in Figure 3.5 is a power law. A power law is a special kind of mathematical relationship between two quantities.

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The number p may vary from 50 (which is the case of equal distribution, in which 100 percent of the population have equal shares of the resource) to nearly 100 (where a few participants have almost all of the resources). How do we model power laws? Mathematically, a quantity x obeys a power law if it is drawn from a probability distribution where α is a constant parameter of the distribution known as the exponent or scaling parameter. P(x) = Cx-α Equation 3.3.╇ Mathematical model of a power law Many times, we see power law distributions display a logarithmic chart. For the power law, the distribution when plotted in this fashion follows a straight line quite closely. The C represents the percentage of data from a single category.

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., exponent, 50 Understanding Sponsored Search a mathematical notation indicating the number of times a quantity is multiplied by itself) of some attribute of that object (e.g., its size, its rank, its height), the frequency is said to follow a power law. Like the more standard normal or bell curve, the power law is a probability distribution. There are many phenomena that follow a power law distribution. Many aspects of sponsored search follow power laws, including frequencies of terms used in queries, the frequency of visits to Web sites, and the frequency of clicks on SERP links. This is specifically why some keyphrases are much more expensive than others in the same vertical.

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

Mandelbrot’s insights imply that when viewed through a coarse-grained lens of varying resolution, a hidden simplicity and regularity is revealed underlying the extraordinary complexity and diversity in much of the world around us. Furthermore, the mathematics that describes self-similarity and its implicit recursive rescaling is identical to the power law scaling discussed in previous chapters. In other words, power law scaling is the mathematical expression of self-similarity and fractality. Consequently, because animals obey power law scaling both within individuals, in terms of the geometry and dynamics of their internal network structures, as well as across species, they, and therefore all of us, are living manifestations of self-similar fractals.

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So as we saw when discussing the Richter scale for earthquakes in the previous chapter, there are very practical reasons for using logarithmic coordinates for representing data such as this which span many orders of magnitude. But there are also deep conceptual reasons for doing so related to the idea that the structures and dynamics being investigated have self-similar properties, which are represented mathematically by simple power laws, as I will now explain. We’ve seen that a straight line on a logarithmic plot represents a power law whose exponent is its slope (⅔ in the case of the scaling of strength, shown in Figure 7). In Figure 1 you can readily see that for every four orders of magnitude increase in mass (along the horizontal axis), metabolic rate increases by only three orders of magnitude (along the vertical axis), so the slope of the straight line is ¾, the famous exponent in Kleiber’s law.

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This repetitive behavior, the recurrence in this case of the same factor 32 as we move up in mass by the same repetitive factor of 100, is an example of the general self-similar feature of power laws. More generally: if the mass is increased by any arbitrary factor at any scale (100, in the example), then the metabolic rate increases by the same factor (32, in the example) no matter what the value of the initial mass is, that is, whether it’s that of a mouse, cat, cow, or whale. This remarkably systematic repetitive behavior is called scale invariance or self-similarity and is a property inherent to power laws. It is closely related to the concept of a fractal, which will be discussed in detail in the following chapter.

Topics in Market Microstructure by Ilija I. Zovko

Brownian motion, computerized trading, continuous double auction, correlation coefficient, financial intermediation, Gini coefficient, information asymmetry, market design, market friction, market microstructure, Murray Gell-Mann, p-value, power law, quantitative trading / quantitative finance, random walk, stochastic process, stochastic volatility, transaction costs

This supports the obvious hypothesis that traders are reasonably aware of the volatility distribution when placing orders, an effect that may contribute to the phenomenon of clustered volatility. Plerou et al. (1999) have observed a power law for the unconditional distribution of price fluctuations. It seems that the power law for price fluctuations should be related to that of relative limit prices, but the precise nature and the cause of this relationship is not clear. The exponent for price fluctuations of individual companies reported by Plerou et al. is roughly 3, but the exponent we have measured here is roughly 1.5. Why these particular exponents? Makoto Nirei has suggested that if traders have power law utility functions, under the assumption that they optimize this utility, it is possible to derive an expression for β in terms of the exponent of price fluctuations and the coefficient of risk aversion.

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The main graphs of figure 5.1 represent the estimated density function2 of normalized order sizes pooled across all stocks. The left panel represents on-book trading, while the right represents off-book trading. Both densities show power-law behaviour in the tails with exponents around 3 for on-book and 3/2 for off-book trading, which were obtained by fitting a power-law to the tails of the distribution for values larger than 10. Looking at the Hill plots in figure 5.2 we see that the power law behavior in the on-book indeed seems to be valid for orders larger than 10 times the average size. For the off-book market the threshold is not as clear. Disaggregating the volume on hourly intervals we obtain strikingly similar distributions and the same exponents.

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Furthermore, we checked whether there are significant differences in the estimated parameters for stocks with high vs. low order arrival rates. The results ranged from β = 1.5 5 The functional form we use to fit the distribution has to satisfy two requirements: it has to be a power law for large δ and finite for δ = 0. A pure power law is either not integrable at 0 or at ∞. If the functional form is to be interpreted as a probability density then it necessarily has to be truncated at one end. In our case the natural truncation point is 0. Clearly there is some arbitrariness in the choice of the exact form, but since we are mainly interested in the behavior for large δ, this functional form seems satisfactory. 14 CHAPTER 2.

Zero to One: Notes on Startups, or How to Build the Future by Peter Thiel, Blake Masters

Airbnb, Alan Greenspan, Albert Einstein, Andrew Wiles, Andy Kessler, Berlin Wall, clean tech, cloud computing, crony capitalism, discounted cash flows, diversified portfolio, do well by doing good, don't be evil, Elon Musk, eurozone crisis, Fairchild Semiconductor, heat death of the universe, income inequality, Jeff Bezos, Larry Ellison, Lean Startup, life extension, lone genius, Long Term Capital Management, Lyft, Marc Andreessen, Mark Zuckerberg, Max Levchin, minimum viable product, Nate Silver, Network effects, new economy, Nick Bostrom, PalmPilot, paypal mafia, Peter Thiel, pets.com, power law, profit motive, Ralph Waldo Emerson, Ray Kurzweil, self-driving car, shareholder value, Sheryl Sandberg, Silicon Valley, Silicon Valley startup, Singularitarianism, software is eating the world, Solyndra, Steve Jobs, strong AI, Suez canal 1869, tech worker, Ted Kaczynski, Tesla Model S, uber lyft, Vilfredo Pareto, working poor

If you do start your own company, you must remember the power law to operate it well. The most important things are singular: One market will probably be better than all others, as we discussed in Chapter 5. One distribution strategy usually dominates all others, too—for that see Chapter 11. Time and decision-making themselves follow a power law, and some moments matter far more than others—see Chapter 9. However, you can’t trust a world that denies the power law to accurately frame your decisions for you, so what’s most important is rarely obvious. It might even be secret. But in a power law world, you can’t afford not to think hard about where your actions will fall on the curve. 8 SECRETS EVERY ONE OF TODAY’S most famous and familiar ideas was once unknown and unsuspected.

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The biggest cities dwarf all mere towns put together. And monopoly businesses capture more value than millions of undifferentiated competitors. Whatever Einstein did or didn’t say, the power law—so named because exponential equations describe severely unequal distributions—is the law of the universe. It defines our surroundings so completely that we usually don’t even see it. This chapter shows how the power law becomes visible when you follow the money: in venture capital, where investors try to profit from exponential growth in early-stage companies, a few companies attain exponentially greater value than all others.

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This chapter shows how the power law becomes visible when you follow the money: in venture capital, where investors try to profit from exponential growth in early-stage companies, a few companies attain exponentially greater value than all others. Most businesses never need to deal with venture capital, but everyone needs to know exactly one thing that even venture capitalists struggle to understand: we don’t live in a normal world; we live under a power law. THE POWER LAW OF VENTURE CAPITAL Venture capitalists aim to identify, fund, and profit from promising early-stage companies. They raise money from institutions and wealthy people, pool it into a fund, and invest in technology companies that they believe will become more valuable. If they turn out to be right, they take a cut of the returns—usually 20%.

The Power Law: Venture Capital and the Making of the New Future by Sebastian Mallaby

"Susan Fowler" uber, 23andMe, 90 percent rule, Adam Neumann (WeWork), adjacent possible, Airbnb, Apple II, barriers to entry, Ben Horowitz, Benchmark Capital, Big Tech, bike sharing, Black Lives Matter, Blitzscaling, Bob Noyce, book value, business process, charter city, Chuck Templeton: OpenTable:, Clayton Christensen, clean tech, cloud computing, cognitive bias, collapse of Lehman Brothers, Colonization of Mars, computer vision, coronavirus, corporate governance, COVID-19, cryptocurrency, deal flow, Didi Chuxing, digital map, discounted cash flows, disruptive innovation, Donald Trump, Douglas Engelbart, driverless car, Dutch auction, Dynabook, Elon Musk, Fairchild Semiconductor, fake news, family office, financial engineering, future of work, game design, George Gilder, Greyball, guns versus butter model, Hacker Ethic, Henry Singleton, hiring and firing, Hyperloop, income inequality, industrial cluster, intangible asset, iterative process, Jeff Bezos, John Markoff, junk bonds, Kickstarter, knowledge economy, lateral thinking, liberal capitalism, Louis Pasteur, low interest rates, Lyft, Marc Andreessen, Mark Zuckerberg, market bubble, Marshall McLuhan, Mary Meeker, Masayoshi Son, Max Levchin, Metcalfe’s law, Michael Milken, microdosing, military-industrial complex, Mitch Kapor, mortgage debt, move fast and break things, Network effects, oil shock, PalmPilot, pattern recognition, Paul Graham, paypal mafia, Peter Thiel, plant based meat, plutocrats, power law, pre–internet, price mechanism, price stability, proprietary trading, prudent man rule, quantitative easing, radical decentralization, Recombinant DNA, remote working, ride hailing / ride sharing, risk tolerance, risk/return, Robert Metcalfe, ROLM, rolodex, Ronald Coase, Salesforce, Sam Altman, Sand Hill Road, self-driving car, shareholder value, side project, Silicon Valley, Silicon Valley startup, Skype, smart grid, SoftBank, software is eating the world, sovereign wealth fund, Startup school, Steve Jobs, Steve Wozniak, Steven Levy, super pumped, superconnector, survivorship bias, tech worker, Teledyne, the long tail, the new new thing, the strength of weak ties, TikTok, Travis Kalanick, two and twenty, Uber and Lyft, Uber for X, uber lyft, urban decay, UUNET, vertical integration, Vilfredo Pareto, Vision Fund, wealth creators, WeWork, William Shockley: the traitorous eight, Y Combinator, Zenefits

Accel Telecom more than conformed to the so-called 80/20 rule: a whopping 95 percent of its profits came from the top 20 percent of its investments.[23] Other early Accel funds exhibited similar power-law effects. In the firm’s first five funds, the top 20 percent of the investments accounted for never less than 85 percent of the profits, and the average was 92 percent. In short, the power law was inexorable. Even a methodical, anti-Kleiner, prepared-mind partnership could not escape it. The dominance of the power law was illustrated by UUNET, one of several unforeseen grand slams in Accel’s first dozen years in business. Now a forgotten company, subsumed into Verizon’s vast telecom empire, UUNET, pronounced “you-you-net,” sounds like a throwback to a different age: this strange non-acronym, vaguely inspired by software protocols loved only by engineers, is a world away from the brand-conscious zippiness of later startup names—think Zoom or Snap or Stripe or Spotify.[24] Yet UUNET is worth recalling because, in addition to illustrating the power law, it illuminates two features of venture investing.

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If Jeff Bezos walks out of the cinema, the average wealth of those who stay behind will plummet. Power Law Distribution This sort of skewed distribution is sometimes referred to as the 80/20 rule: the idea that 80 percent of the wealth is held by 20 percent of the people, that 80 percent of the people live in 20 percent of the cities, or that 20 percent of all scientific papers earn 80 percent of the citations. In reality, there is nothing magical about the numbers 80 or 20: it could be that just 10 percent of the people hold 80 percent of the wealth, or perhaps 90 percent of it. But whatever the precise numbers, all these distributions are examples of the power law, so called because the winners advance at an accelerating, exponential rate, so that they explode upward far more rapidly than in a linear progression.

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The celebrated hedge-fund stock picker Julian Robertson used to say that he looked for shares that might plausibly double in three years, an outcome he would view as “fabulous.”[22] But if venture capitalists embarked on the same quest, they would almost guarantee failure, because the power law generates relatively few startups that merely double in value. Most fail completely, in which case the value of their equity rounds to zero—an unthinkable catastrophe for a stock market investor. But each year brings a handful of outliers that hit the proverbial grand slam, and the only thing that matters in venture is to own a piece of them.[23] When today’s venture capitalists back flying cars or space tourism or artificial intelligence systems that write film scripts, they are following this power-law logic. Their job is to look over the horizon, to reach for high-risk, huge-reward possibilities that most people believe to be unreachable.

Six Degrees: The Science of a Connected Age by Duncan J. Watts

AOL-Time Warner, Berlin Wall, Bretton Woods, business process, corporate governance, Drosophila, Erdős number, experimental subject, fixed income, Frank Gehry, Geoffrey West, Santa Fe Institute, independent contractor, industrial cluster, invisible hand, it's over 9,000, Long Term Capital Management, market bubble, Milgram experiment, MITM: man-in-the-middle, Murray Gell-Mann, Network effects, new economy, Norbert Wiener, PalmPilot, Paul Erdős, peer-to-peer, power law, public intellectual, rolodex, Ronald Coase, Savings and loan crisis, scientific worldview, Silicon Valley, social contagion, social distancing, Stuart Kauffman, supply-chain management, The Nature of the Firm, the strength of weak ties, The Wealth of Nations by Adam Smith, Toyota Production System, Tragedy of the Commons, transaction costs, transcontinental railway, vertical integration, Vilfredo Pareto, Y2K

Instead, they follow what is known as a power law. Power laws are another very widespread kind of distribution in natural systems, although their origin is a good deal murkier than the origins of normal-type distributions like Poisson’s. Power laws have two features that make them strikingly different from normal distributions. First, unlike a normal distribution, a power law doesn’t have a peak at its average value. Rather, like Figure 4.2, it starts at its maximum value and then decreases relentlessly all the way to infinity. Second, the rate at which the power law decays is much slower than the decay rate for a normal distribution, implying a much greater likelihood of extreme events.

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By contrast, the population of New York City, at just over eight million people, is almost 300 times the size of a town like Ithaca. Extreme differences like this would be inconceivable in a normal distribution but are entirely routine for power laws. Figure 4.2. A power-law distribution. Although it decreases rapidly with k, it does so much slower than the normal distribution in figure 4.1, implying than large values of k are more likely. The distribution of wealth in the United States, for instance, resembles a power law. The nineteenth-century Parisian engineer Vilfredo Pareto was the first person to note this phenomenon, subsequently called Pareto’s law, and demonstrated that it held true in every European country for which the relevant statistics existed.

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Rather than plotting the probability of an event as a function of its size (as in Figure 4.2), the easiest way to determine the exponent of a power law is to plot the logarithm of the probability versus the logarithm of the size. Conveniently, in this form (called a log-log plot), a pure power-law distribution will always be a straight line, just like in Figure 4.3. The exponent then is revealed simply as the slope of this straight line. So once we have enough data, all we need to do is plot it on a log-log scale and measure the slope of the resulting line. Pareto, for example, showed that regardless of which country he looked at, the wealth distribution was a power law with a slope somewhere between two and three where the lower the exponent, the greater the inequality.

Here Comes Everybody: The Power of Organizing Without Organizations by Clay Shirky

Andrew Keen, Andy Carvin, Berlin Wall, bike sharing, bioinformatics, Brewster Kahle, c2.com, Charles Lindbergh, commons-based peer production, crowdsourcing, digital rights, en.wikipedia.org, Free Software Foundation, Garrett Hardin, hiring and firing, hive mind, Howard Rheingold, Internet Archive, invention of agriculture, invention of movable type, invention of the printing press, invention of the telegraph, jimmy wales, John Perry Barlow, Joi Ito, Kuiper Belt, liberation theology, Mahatma Gandhi, means of production, Merlin Mann, Metcalfe’s law, Nash equilibrium, Network effects, Nicholas Carr, Picturephone, place-making, Pluto: dwarf planet, power law, prediction markets, price mechanism, prisoner's dilemma, profit motive, Richard Stallman, Robert Metcalfe, Ronald Coase, Silicon Valley, slashdot, social software, Stewart Brand, supply-chain management, the Cathedral and the Bazaar, the long tail, The Nature of the Firm, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Tragedy of the Commons, transaction costs, ultimatum game, Vilfredo Pareto, Wayback Machine, Yochai Benkler, Yogi Berra

Though the word “ecosystem” is overused as a way to make simple situations seem more complex, it is merited here, because large social systems cannot be understood as a simple aggregation of the behavior of some nonexistent “average” user. The most salient characteristic of a power law is that the imbalance becomes more extreme the higher the ranking. The operative math is simple—a power law describes data in which the nth position has 1/nth of the first position’s rank. In a pure power law distribution, the gap between the first and second position is larger than the gap between second and third, and so on. In Wikipedia article edits, for example, you would expect the second most active user to have committed only half as many edits as the most active user, and the tenth most active to have committed one-tenth as many.

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Instead, you have to change your focus, to concentrate not on the individual users but on the behavior of the collective. The power law also helps explain the difference between the many small but tightly integrated clusters of friends using weblogs and the handful of the most famous and best-trafficked weblogs. The pressures are reflected in Figure 5-2, which shows the relationship between a power law distribution and the kinds of communication patterns that can be supported. Figure 5-2: The relationship between audience size and conversational pattern. The curved line represents the power-law distribution of weblogs ranked by audience size. Weblogs at the left-hand side of the graph have so many readers that they are limited to the broadcast pattern, because you can’t interact with millions of readers.

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Though I first did the research on Mermaid Parade photos, the subject doesn’t matter very much; there is some variation in the steepness of the falloff from the most popular items and the length of the tail of one-off contributors, but the basic power law distribution is stable over most of Flickr (and indeed, over most large social systems.) Page 124: power law distribution A good guide to the ubiquity and interpretive importance of power law distributions in social systems is Linked: The New Science of Networks, by Albert-Laszlo Barabasi, Perseus (2002). Page 126: The Long Tail: Why the Future of Business Is Selling Less of More, by Chris Anderson, Hyperion (2006).

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%

Finally, they show that graphs generated by this model have a distribution of degrees that obeys a power law. Graphs that have this property are sometimes called scale-free networks; see http://en.wikipedia.org/wiki/Scale-free_network. That name can be confusing because it is the distribution of degrees that is scale-free, not the network. In order to maximize confusion, distributions that obey the power law are sometimes called scaling distributions because they are invariant under a change of scale. That means that if you change the units in which the quantities are expressed, the slope parameter, , doesn’t change. You can read http://en.wikipedia.org/wiki/Power_law for the details, but it is not important for what we are doing here.

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Use the BA model to generate a graph with about 1,000 vertices, and compute the characteristic length and clustering coefficient as defined in the Watts and Strogatz paper. Do scale-free networks have the characteristics of a small world graph? Zipf, Pareto, and Power Laws At this point, we have seen three phenomena that yield a straight line on a log-log plot: Zipf plot Frequency as a function of rank Pareto CCDF The complementary CDF of a Pareto distribution Power law plot A histogram of frequencies The similarity in these plots is not a coincidence; these visual tests are closely related. Starting with a power law distribution, we have: If we choose a random node in a scale free network, is the probability that its degree equals k.

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, Percolation PIL, CADrawer pink noise, Sand Piles, Pink Noise pitch, Spectral Density planetary motion, A New Kind of Science, What Kind of Explanation Is That? Popper, Karl, Falsifiability population, Pareto Distributions porosity, Percolation Postscript (EPS), CADrawer postulated entity, Realism power, Spectral Density power law, Barabási and Albert, Zipf, Pareto, and Power Laws, Sand Piles power spectral density, Spectral Density practical analysis of algorithms, Order of Growth precondition, A New Kind of Thinking prediction, Falsifiability, SOC, Causation, and Prediction predictive model, A New Kind of Model preferential attachment, Barabási and Albert, Explanatory Models prevalence, Reductionism and Holism principle of computational equivalence, Universality Prisoner’s Dilemma, Prisoner’s Dilemma, Prisoner’s Dilemma iterated, Prisoner’s Dilemma PRNG, Randomness problem formulation, What’s a Graph?

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

On linear scales, plots of such distributions produce curves that are best characterized either by exponential functions or by a power-law function. A perfect power-law function (approximating the form f(x) = ax − k where a and k are constant) produces a nearly L-shaped curve on a linear plot, and when both axes are converted to decadic logarithms, it produces a straight line. Obviously, neither exponential nor power-law functions can be well characterized by their modal or average values; in the real world there are many deviations from the straight line, and the linear fit may not be always sufficient to identify true power-law behavior. Between 1881 and 1949 these asymmetric distributions were repeatedly and independently identified by observers in both natural and social sciences, and a number of these empirical observations earned their authors fame as they became known as eponymous laws.

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Their rigorous tests found that 17 of 24 data sets were consistent with power-law distribution—but, remarkably, they also concluded that the lognormal distribution could not be ruled out for any sets save one, because “it is extremely difficult to tell the difference between log-normal and power-law behavior. Indeed over realistic ranges of x the two distributions are very closely equal, so it appears unlikely that any test would be able to tell them apart unless we have an extremely large data set” (Clauset et al. 2009, 689). Mitzenmacher (2004) came to the same conclusion as far as lognormal and power-law distributions are concerned, and Lima-Mendez and van Helden (2009) showed how an apparent power law can disappear when data are subjected to more rigorous testing. Most instances of power-law distributions do not even have strong statistical support, and any purely empirical fitting—while interesting, perhaps even remarkable—does not justify unsubstantiated suggestions of universality.

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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). Mandelbrot’s D, fractal dimension, has many properties of a “dimension” but it is fractional (Mandelbrot 1967). Mandelbrot (1977) had introduced a more general power law—nearly the most general, as Gell-Mann put it—by modifying the inverse sequence, by adding a constant to the rank, and by allowing squares, cubes, square roots or any other powers of fractions (Gell-Mann 1994).

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

Kozlowski, Dennis Kraus, Karl Krauthammer, Charles Kudlow, Larry Lakonishok, Josef Landsburg, Steven Lay, Ken LeBaron, Blake Lefevre, Edwin Leibweber, David linguistics, power law and Lo, Andrew logistic curve lognormal distribution Long-Term Capital Management (LTCM) losing through winning loss aversion lotteries present value and as tax on stupidity Lynch, Peter MacKinlay, Craig mad money Malkiel, Burton management, manipulating stock prices Mandelbrot, Benoit margin calls margin investments buying on the margin as investment type margin calls selling on the margin market makers decimalization and World Class Options Market Maker (WCOMM) Markowitz, Harry mathematics, generally Greek movies and plays about outguessing the average guess risk and stock markets and Mathews, Eddie “maximization of expected value” principle mean value. see also expected value arithmetic mean deviation from the mean geometric mean regression to the mean using interchangeably with expected value media celebrities and crisis mentality and impact on market volatility median rate of return Merrill Lynch Merton, Robert mnemonic rules momentum investing money, categorizing into mental accounts Morgenson, Gretchen Motley Fool contrarian investment strategy PEG ratio and moving averages complications with evidence supporting example of generating buy-sell rules from getting the big picture with irrelevant in efficient market phlegmatic nature of mu (m) multifractal forgeries mutual funds expert picks and hedge funds index funds politically incorrect rationale for socially regressive funds mutual knowledge, contrasted with common knowledge Nash equilibrium Nash, John Neff, John negatively correlated stocks as basis of mutual fund selection as basis of stock selection stock portfolios and networks Internet as example of price movements and six degrees of separation and A New Kind of Science (Wolfram) Newcomb, Simon Newcombe, William Newcombe’s paradox Niederhoffer, Victor Nigrini, Mark nominal value A Non-Random Walk Down Wall Street (Lo and MacKinlay) nonlinear systems billiards example “butterfly effect” or sensitive dependence of chaos theory and fractals and investor behavior and normal distribution Nozick, Robert numbers anchoring effect Benford’s Law and Fibonacci numbers and off-shore entities, Enron Once Upon a Number (Paulos) online chatrooms online trading optimal portfolio balancing with risk-free portfolio Markowitz efficient frontier of options. see stock options Ormerod, Paul O’Shaughnessy, James P/B (price-to-book) ratio P/E ratio interpreting measuring future earnings expectations PEG variation on stock valuation and P/S (price to sales) ratio paradoxes Efficient Market Hypothesis and examples of Newcombe’s paradox Parrondo’s paradox St. Petersburg paradox Pareto laws. see power law Parrondo, Juan patterns, random events and PEG ratio personal accounting Peters, Tom Pi Pitt, Harvey Poincare, Henri politics campaign contributions politically incorrect funds power law and Ponzi schemes portfolios. see stock portfolios pound-euro/euro-pound exchange rate power law complex systems economic power “flocking effect” on Internet linguistics media influence political power price movements Pradilla, Charles Prechter, Bob predictability, of stock market complexity of cross-correlations over time and Efficient Market Hypothesis multifractal forgeries price anomalies leading to private information randomness vs.

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This means, for example, that there are approximately one-eighth as many documents with twenty links as there are documents with ten links since 1/203 is one-eighth of 1/103. Thus the number of documents with k links declines quickly as k increases, but nowhere near as quickly as a normal bell-shaped distribution would predict. This is why the power law distribution has a fatter tail (more instances of very large values of k) than does the normal distribution. The power laws (sometimes called scaling laws, sometimes Pareto laws) that characterize the web also seem to characterize many other complex systems that organize themselves into a state of skittish responsiveness. The physicist Per Bak, who has made an extensive study of them, described in his book How Nature Works, claims that such 1/km laws (for various exponents m) are typical of many biological, geological, musical, and economic processes, and that they tend to arise in a wide variety of complex systems.

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The physicist Per Bak, who has made an extensive study of them, described in his book How Nature Works, claims that such 1/km laws (for various exponents m) are typical of many biological, geological, musical, and economic processes, and that they tend to arise in a wide variety of complex systems. Traffic jams, to cite a different domain and seemingly unrelated dynamic, also seem to obey a power law, with jams involving k cars occurring with a probability roughly proportional to 1/km for an appropriate m. There is even a power law in linguistics. In English, for example, the word “the” appears most frequently and is said to have rank order 1; the words “of,” “and,” and “to” rank 2, 3, and 4, respectively. “Chrysanthemum” has a much higher rank order. Zipf’s Law relates the frequency of a word to its rank order k and states that a word’s frequency in a written text is proportional to 1/k1; that is, inversely proportional to the first power of k.

Networks, Crowds, and Markets: Reasoning About a Highly Connected World by David Easley, Jon Kleinberg

Albert Einstein, AltaVista, AOL-Time Warner, Apollo 13, classic study, clean water, conceptual framework, Daniel Kahneman / Amos Tversky, Douglas Hofstadter, Dutch auction, Erdős number, experimental subject, first-price auction, fudge factor, Garrett Hardin, George Akerlof, Gerard Salton, Gerard Salton, Gödel, Escher, Bach, incomplete markets, information asymmetry, information retrieval, John Nash: game theory, Kenneth Arrow, longitudinal study, market clearing, market microstructure, moral hazard, Nash equilibrium, Network effects, Pareto efficiency, Paul Erdős, planetary scale, power law, prediction markets, price anchoring, price mechanism, prisoner's dilemma, random walk, recommendation engine, Richard Thaler, Ronald Coase, sealed-bid auction, search engine result page, second-price auction, second-price sealed-bid, seminal paper, Simon Singh, slashdot, social contagion, social web, Steve Jobs, Steve Jurvetson, stochastic process, Ted Nelson, the long tail, The Market for Lemons, the strength of weak ties, The Wisdom of Crowds, trade route, Tragedy of the Commons, transaction costs, two and twenty, ultimatum game, Vannevar Bush, Vickrey auction, Vilfredo Pareto, Yogi Berra, zero-sum game

Second, do you expect that adding this feature will cause the popularity distribution of the articles to follow a power-law distribution more closely or less closely, 570 CHAPTER 18. POWER LAWS AND RICH-GET-RICHER PHENOMENA compared to the version of the site before these counters were added? Give an explanation for your answer. 2. When we covered power laws in Chapter 18, we discussed a number of cases in which power laws arise, generally reflecting some notion of “popularity” or a close analogue. Consider, for example, the fraction of news articles each day that are read by k people: if f (k) represents this fraction as a function of k, then f (k) approximately follows a power-law distribution of the form f (k) ≈ k−c for some exponent c.

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In Section 18.7 at the end of this chapter, we show how to turn this reasoning into a calculation that produces the correct exponent on the power-law distribution. As with any simple model, the goal is not to capture all the reasons why people create links on the Web, or in any other network, but to show that a simple and very natural principle behind link creation leads directly to power laws — and hence, one should not find them as surprising as they might first appear. Indeed, rich-get-richer models can suggest a basis for power laws in a wide array of settings, including some that have nothing at all to do with human decision-making. For example, the populations of cities have been observed to follow a power law distribution: the fraction of cities with population k is roughly 1/kc for some constant c [365].

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One sees similar power laws arising in measures of popularity in many other domains as well: for example, the fraction of telephone numbers that receive k calls per day is roughly proportional to 1/k2; the fraction of books that are bought by k people is roughly proportional to 1/k3; the fraction of scientific papers that receive k citations 556 CHAPTER 18. POWER LAWS AND RICH-GET-RICHER PHENOMENA Figure 18.2: A power law distribution (such as this one for the number of Web page in-links, from Broder et al. [79]) shows up as a straight line on a log-log plot. in total is roughly proportional to 1/k3; and there are many related examples [11, 314]. Indeed, just as the normal distribution is widespread in a family of settings in the natural sciences, power laws seem to dominate in cases where the quantity being measured can be viewed as a type of popularity.

The Wealth of Networks: How Social Production Transforms Markets and Freedom by Yochai Benkler

affirmative action, AOL-Time Warner, barriers to entry, bioinformatics, Brownian motion, business logic, call centre, Cass Sunstein, centre right, clean water, commoditize, commons-based peer production, dark matter, desegregation, digital divide, East Village, Eben Moglen, fear of failure, Firefox, Free Software Foundation, game design, George Gilder, hiring and firing, Howard Rheingold, informal economy, information asymmetry, information security, invention of radio, Isaac Newton, iterative process, Jean Tirole, jimmy wales, John Markoff, John Perry Barlow, Kenneth Arrow, Lewis Mumford, longitudinal study, machine readable, Mahbub ul Haq, market bubble, market clearing, Marshall McLuhan, Mitch Kapor, New Journalism, optical character recognition, pattern recognition, peer-to-peer, power law, precautionary principle, pre–internet, price discrimination, profit maximization, profit motive, public intellectual, radical decentralization, random walk, Recombinant DNA, recommendation engine, regulatory arbitrage, rent-seeking, RFID, Richard Stallman, Ronald Coase, scientific management, search costs, Search for Extraterrestrial Intelligence, SETI@home, shareholder value, Silicon Valley, Skype, slashdot, social software, software patent, spectrum auction, subscription business, tacit knowledge, technological determinism, technoutopianism, The Fortune at the Bottom of the Pyramid, the long tail, The Nature of the Firm, the strength of weak ties, Timothy McVeigh, transaction costs, vertical integration, Vilfredo Pareto, work culture , Yochai Benkler

Strogatz, "Collective Dynamics of `Small World' Networks," Nature 393 (1998): 440-442; D. J. Watts, Small Worlds: The Dynamics of Networks Between Order and Randomness (Princeton, NJ: Princeton University Press, 1999). 89. Clay Shirky, "Power Law, Weblogs, and Inequality" (February 8, 2003), http:// www.shirky.com/writings/powerlaw_weblog.htm; Jason Kottke, "Weblogs and Power Laws" (February 9, 2003), ‹http://www.kottke.org/03/02/weblogs-and-power-laws›. 90. Ravi Kumar et al., "On the Bursty Evolution of Blogspace," Proceedings of WWW2003, May 20-24, 2003, ‹http://www2003.org/cdrom/papers/refereed/p477/› p477-kumar/p477-kumar.htm. 91. Both of these findings are consistent with even more recent work by Hargittai, E., J.

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Strogatz, "Collective Dynamics of `Small World' Networks," Nature 393 (1998): 440-442; D. J. Watts, Small Worlds: The Dynamics of Networks Between Order and Randomness (Princeton, NJ: Princeton University Press, 1999). 89. Clay Shirky, "Power Law, Weblogs, and Inequality" (February 8, 2003), http:// www.shirky.com/writings/powerlaw_weblog.htm; Jason Kottke, "Weblogs and Power Laws" (February 9, 2003), ‹http://www.kottke.org/03/02/weblogs-and-power-laws›. 90. Ravi Kumar et al., "On the Bursty Evolution of Blogspace," Proceedings of WWW2003, May 20-24, 2003, ‹http://www2003.org/cdrom/papers/refereed/p477/› p477-kumar/p477-kumar.htm. 91. Both of these findings are consistent with even more recent work by Hargittai, E., J.

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If users avoid information overload by focusing on a small subset of sites in an otherwise [pg 242] open network that allows them to read more or less whatever they want and whatever anyone has written, policy interventions aimed to force a different pattern would be hard to justify from the perspective of liberal democratic theory. 439 The sustained study of the distribution of links on the Internet and the Web is relatively new--only a few years old. There is significant theoretical work in a field of mathematics called graph theory, or network topology, on power law distributions in networks, on skew distributions that are not pure power law, and on the mathematically related small-worlds phenomenon in networks. The basic intuition is that, if indeed a tiny minority of sites gets a large number of links, and the vast majority gets few or no links, it will be very difficult to be seen unless you are on the highly visible site.

Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian, Tom Griffiths

4chan, Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, algorithmic bias, algorithmic trading, anthropic principle, asset allocation, autonomous vehicles, Bayesian statistics, behavioural economics, Berlin Wall, Big Tech, Bill Duvall, bitcoin, Boeing 747, Charles Babbage, cognitive load, Community Supported Agriculture, complexity theory, constrained optimization, cosmological principle, cryptocurrency, Danny Hillis, data science, David Heinemeier Hansson, David Sedaris, delayed gratification, dematerialisation, diversification, Donald Knuth, Donald Shoup, double helix, Dutch auction, Elon Musk, exponential backoff, fault tolerance, Fellow of the Royal Society, Firefox, first-price auction, Flash crash, Frederick Winslow Taylor, fulfillment center, Garrett Hardin, Geoffrey Hinton, George Akerlof, global supply chain, Google Chrome, heat death of the universe, Henri Poincaré, information retrieval, Internet Archive, Jeff Bezos, Johannes Kepler, John Nash: game theory, John von Neumann, Kickstarter, knapsack problem, Lao Tzu, Leonard Kleinrock, level 1 cache, linear programming, martingale, multi-armed bandit, Nash equilibrium, natural language processing, NP-complete, P = NP, packet switching, Pierre-Simon Laplace, power law, prediction markets, race to the bottom, RAND corporation, RFC: Request For Comment, Robert X Cringely, Sam Altman, scientific management, sealed-bid auction, second-price auction, self-driving car, Silicon Valley, Skype, sorting algorithm, spectrum auction, Stanford marshmallow experiment, Steve Jobs, stochastic process, Thomas Bayes, Thomas Malthus, Tragedy of the Commons, traveling salesman, Turing machine, urban planning, Vickrey auction, Vilfredo Pareto, Walter Mischel, Y Combinator, zero-sum game

The average population of a town: This figure comes from Clauset, Shalizi, and Newman, “Power-Law Distributions in Empirical Data,” which in turn cites the 2000 US Census. can plausibly range over many scales: The general form of a power-law distribution on a quantity t is p(t) ∝ t−γ, where the value of γ describes how quickly the probability of t decreases as t gets larger. As with the uninformative prior, the form of the distribution doesn’t change if we take s = ct, changing the scale. a domain full of power laws: The observation that wealth is distributed according to a power-law function is credited to Pareto, Cours d’économie politique.

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Movie box-office grosses, which can range from four to ten figures, are another example. Most movies don’t make much money at all, but the occasional Titanic makes … well, titanic amounts. In fact, money in general is a domain full of power laws. Power-law distributions characterize both people’s wealth and people’s incomes. The mean income in America, for instance, is $55,688—but because income is roughly power-law distributed, we know, again, that many more people will be below this mean than above it, while those who are above might be practically off the charts. So it is: two-thirds of the US population make less than the mean income, but the top 1% make almost ten times the mean.

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These three very different patterns of optimal prediction—the Multiplicative, Average, and Additive Rules—all result directly from applying Bayes’s Rule to the power-law, normal, and Erlang distributions, respectively. And given the way those predictions come out, the three distributions offer us different guidance, too, on how surprised we should be by certain events. In a power-law distribution, the longer something has gone on, the longer we expect it to continue going on. So a power-law event is more surprising the longer we’ve been waiting for it—and maximally surprising right before it happens. A nation, corporation, or institution only grows more venerable with each passing year, so it’s always stunning when it collapses.

Rockonomics: A Backstage Tour of What the Music Industry Can Teach Us About Economics and Life by Alan B. Krueger

"Friedman doctrine" OR "shareholder theory", accounting loophole / creative accounting, Affordable Care Act / Obamacare, Airbnb, Alan Greenspan, autonomous vehicles, bank run, behavioural economics, Berlin Wall, bitcoin, Bob Geldof, butterfly effect, buy and hold, congestion pricing, creative destruction, crowdsourcing, digital rights, disintermediation, diversified portfolio, Donald Trump, endogenous growth, Gary Kildall, George Akerlof, gig economy, income inequality, independent contractor, index fund, invisible hand, Jeff Bezos, John Maynard Keynes: Economic Possibilities for our Grandchildren, Kenneth Arrow, Kickstarter, Larry Ellison, Live Aid, Mark Zuckerberg, Moneyball by Michael Lewis explains big data, moral hazard, Multics, Network effects, obamacare, offshore financial centre, opioid epidemic / opioid crisis, Paul Samuelson, personalized medicine, power law, pre–internet, price discrimination, profit maximization, random walk, recommendation engine, rent-seeking, Richard Thaler, ride hailing / ride sharing, Saturday Night Live, Skype, Steve Jobs, the long tail, The Wealth of Nations by Adam Smith, TikTok, too big to fail, transaction costs, traumatic brain injury, Tyler Cowen, ultimatum game, winner-take-all economy, women in the workforce, Y Combinator, zero-sum game

This ability to create superstars in music is amplified by another feature, one that increasingly applies to other industries: the popularity of a song or artist grows geometrically rather than linearly. This is often called a power law. The popularity of the top performer is a multiple of the second-most-popular performer, which in turn is a multiple of the third-most-popular performer, and so on. Scientists have documented power laws in all kinds of outcomes, from the frequency of use of various words to the size of cities and the number of hurricanes in a year. Networks help to create power laws. Popularity ricochets through networks of friends and acquaintances, creating power law relationships where a small number of performers garner almost all the attention.

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Once you start looking at the world in terms of power laws, or extremely skewed distributions, you can’t miss them. Power laws have been used to describe the frequency of words used in the English language (and practically all other languages), the number of people living in cities, the number of electrical grid failures, the distribution of income, stock market returns, the pattern of musical notes in songs, the number of people joining protests, the frequency of web page links, and multiple physical phenomena.19 More important, the social or physical network mechanism that can generate a power law illuminates the process that leads to spectacular success or dismal failure.

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Second, the determination of what is most popular is highly susceptible to random perturbations in the ways in which new products are introduced to a market and ripple through networks of potential customers. In statistical jargon, the cascade of information and musical preferences through networks of fans generates a power law distribution of popularity—the popularity of the most popular item is a multiple of the next-most-popular item, and so on down the line. As a result, a small number of players—superstars—come to dominate a market. The so-called 80/20 rule (Pareto’s law), where 20 percent of a firm’s customers are responsible for 80 percent of sales, is an example of a power law that is common in business. To conceptualize the way in which social influence operates, suppose each person who is considering making a purchase of a song sometimes follows her own judgment and at other times follows the behavior of a friend.

The Better Angels of Our Nature: Why Violence Has Declined by Steven Pinker

1960s counterculture, affirmative action, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, availability heuristic, behavioural economics, Berlin Wall, Boeing 747, Bonfire of the Vanities, book value, bread and circuses, British Empire, Broken windows theory, business cycle, California gold rush, Cass Sunstein, citation needed, classic study, clean water, cognitive dissonance, colonial rule, Columbine, computer age, Computing Machinery and Intelligence, conceptual framework, confounding variable, correlation coefficient, correlation does not imply causation, crack epidemic, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Brooks, delayed gratification, demographic transition, desegregation, Doomsday Clock, Douglas Hofstadter, Dr. Strangelove, Edward Glaeser, en.wikipedia.org, European colonialism, experimental subject, facts on the ground, failed state, first-past-the-post, Flynn Effect, food miles, Francis Fukuyama: the end of history, fudge factor, full employment, Garrett Hardin, George Santayana, ghettoisation, Gini coefficient, global village, Golden arches theory, Great Leap Forward, Henri Poincaré, Herbert Marcuse, Herman Kahn, high-speed rail, Hobbesian trap, humanitarian revolution, impulse control, income inequality, informal economy, Intergovernmental Panel on Climate Change (IPCC), invention of the printing press, Isaac Newton, lake wobegon effect, libertarian paternalism, long peace, longitudinal study, loss aversion, Marshall McLuhan, mass incarceration, McMansion, means of production, mental accounting, meta-analysis, Mikhail Gorbachev, mirror neurons, moral panic, mutually assured destruction, Nelson Mandela, nuclear taboo, Oklahoma City bombing, open economy, Peace of Westphalia, Peter Singer: altruism, power law, QWERTY keyboard, race to the bottom, Ralph Waldo Emerson, random walk, Republic of Letters, Richard Thaler, Ronald Reagan, Rosa Parks, Saturday Night Live, security theater, Skinner box, Skype, Slavoj Žižek, South China Sea, Stanford marshmallow experiment, Stanford prison experiment, statistical model, stem cell, Steven Levy, Steven Pinker, sunk-cost fallacy, technological determinism, The Bell Curve by Richard Herrnstein and Charles Murray, the long tail, The Wealth of Nations by Adam Smith, theory of mind, Timothy McVeigh, Tragedy of the Commons, transatlantic slave trade, trolley problem, Turing machine, twin studies, ultimatum game, uranium enrichment, Vilfredo Pareto, Walter Mischel, WarGames: Global Thermonuclear War, WikiLeaks, women in the workforce, zero-sum game

Technically they are not “proportional,” since there is usually a nonzero intercept, but are “linearly related.” 52. Power-law distribution in the Correlates of War Dataset: Cederman, 2003. 53. Plotting power-law distributions: Newman, 2005. 54. Power-law distributions, theory and data: Mitzenmacher, 2004, 2006; Newman, 2005. 55. Zipf’s laws: Zipf, 1935. 56. Word type and token frequencies: Francis & Kucera, 1982. 57. Things with power-law distributions: Hayes, 2002; Newman, 2005. 58. Examples of normal and power-law distributions: Newman, 2005. 59. Newman presented the percentages of cities with an exact population size, rather than in a range of population sizes, to keep the units commensurable in the linear and logarithmic graphs (personal communication, February 1, 2011). 60.

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When the axes are stretched out like this, something interesting happens to the distribution: the L straightens out into a nice line. And that is the signature of a power-law distribution. FIGURE 5–10. Populations of cities (a power-law distribution), plotted on linear and log scales Source: Graph adapted from Newman, 2005, p. 324. Which brings us back to wars. Since wars fall into a power-law distribution, some of the mathematical properties of these distributions may help us understand the nature of wars and the mechanisms that give rise to them. For starters, power-law distributions with the exponent we see for wars do not even have a finite mean. There is no such thing as a “typical war.”

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How can the intuition that size doesn’t matter be implemented in models of armed conflict that actually generate power-law distributions?61 The simplest is to assume that the coalitions themselves are power-law-distributed in size, that they fight each other in proportion to their numbers, and that they suffer losses in proportion to their sizes. We know that some human aggregations, namely municipalities, are power-law-distributed, and we know the reason. One of the commonest generators of a power-law distribution is preferential attachment: the bigger something is, the more new members it attracts. Preferential attachment is also known as accumulated advantage, the-rich-get-richer, and the Matthew Effect, after the passage in Matthew 25:29 that Billie Holiday summarized as “Them that’s got shall get, them that’s not shall lose.”

Throwing Rocks at the Google Bus: How Growth Became the Enemy of Prosperity by Douglas Rushkoff

activist fund / activist shareholder / activist investor, Airbnb, Alan Greenspan, algorithmic trading, Amazon Mechanical Turk, Andrew Keen, bank run, banking crisis, barriers to entry, benefit corporation, bitcoin, blockchain, Burning Man, business process, buy and hold, buy low sell high, California gold rush, Capital in the Twenty-First Century by Thomas Piketty, carbon footprint, centralized clearinghouse, citizen journalism, clean water, cloud computing, collaborative economy, collective bargaining, colonial exploitation, Community Supported Agriculture, corporate personhood, corporate raider, creative destruction, crowdsourcing, cryptocurrency, data science, deep learning, disintermediation, diversified portfolio, Dutch auction, Elon Musk, Erik Brynjolfsson, Ethereum, ethereum blockchain, fiat currency, Firefox, Flash crash, full employment, future of work, gamification, Garrett Hardin, gentrification, gig economy, Gini coefficient, global supply chain, global village, Google bus, Howard Rheingold, IBM and the Holocaust, impulse control, income inequality, independent contractor, index fund, iterative process, Jaron Lanier, Jeff Bezos, jimmy wales, job automation, Joseph Schumpeter, Kickstarter, Large Hadron Collider, loss aversion, low interest rates, Lyft, Marc Andreessen, Mark Zuckerberg, market bubble, market fundamentalism, Marshall McLuhan, means of production, medical bankruptcy, minimum viable product, Mitch Kapor, Naomi Klein, Network effects, new economy, Norbert Wiener, Oculus Rift, passive investing, payday loans, peer-to-peer lending, Peter Thiel, post-industrial society, power law, profit motive, quantitative easing, race to the bottom, recommendation engine, reserve currency, RFID, Richard Stallman, ride hailing / ride sharing, Ronald Reagan, Russell Brand, Satoshi Nakamoto, Second Machine Age, shareholder value, sharing economy, Silicon Valley, Snapchat, social graph, software patent, Steve Jobs, stock buybacks, TaskRabbit, the Cathedral and the Bazaar, The Future of Employment, the long tail, trade route, Tragedy of the Commons, transportation-network company, Turing test, Uber and Lyft, Uber for X, uber lyft, unpaid internship, Vitalik Buterin, warehouse robotics, Wayback Machine, Y Combinator, young professional, zero-sum game, Zipcar

But instead of a new fatter, longer tail for formerly obscure products to thrive, we got an extraordinarily “hit heavy, skinny tail.”9 Instead of a flatter bell curve with a big “middle class” of participants, it maps out like a steep slope upward, from losers with nothing at the bottom to winners with everything at the top. This is what’s meant by a power-law distribution—basically, a winner-takes-all disparity, like the infamous 1 percent. For some reason, the original industrial-age mandate for extractive, monopolized growth was not only still in force but getting worse. Net economists were quick to defend these market dynamics as natural phenomena. “This has nothing to do with moral weakness, selling out, or any other psychological explanation,” explained Clay Shirky in 2003. “The very act of choosing, spread widely enough and freely enough, creates a power-law distribution.”10 Others went on to use these naturally occurring power-law dynamics to rationalize the injustices of capitalism and increasing wealth inequality.

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See also advertising big data and, 42 branding and, 20, 35–37 “likes” economy and, 35–37 mass, 19–20 social graphs generated by, 40 market makers, 178–79 market money, 127–28, 130 Marx, Karl, 83, 138 mass media, 20–21 maturity, 98 Mecklenburg, George, 159 medical debt, 153 Meetup, 196–97 microfinancing platforms, 202–4 Microsoft, 83 Microventures, 202–3 Mill, John Stuart, 135 mining, of bitcoins, 145, 147 MIT Technology Review,53 Mondragon Corporation, 220, 222 money basket of commodities approach to backing of, 139 blockchains and, 144–51, 222 central currency system and (See central currency system) cooperative currencies, 160–65 debt and, 152–54 digital transaction networks and, 140–51 extractive purpose of, 128–31 free money theory, currencies based on, 156–59 gold standard and, 139 grain receipts, 128 history of, 126–31 local currencies, 154–65 manipulating human financial behavior to serve, 151–52 market, 127–28, 130 operating system nature of centrally-issued, 125–26 outlawing of local currencies and replacement with coin of the realm, 128–29 precious metals and, 128 reprogramming of, 138–51 traditional bank’s role in serving communities, 165–67 traditional purpose of, 126 as unbound, 212–13 velocity of, 140–41 monopolies chartered, 18, 56, 70, 101, 125, 131 platform, 82–93, 101 power-law dynamics and, 27–28 Monsanto, 218 Morgan Stanley, 195 Mozilla Corporation, 122–23 Mozilla Foundation, 122–23 Mr. Clean Magic Eraser, 107 music industry, 100 positive reinforcement feedback loop and, 28 power-law dynamics and, 26–27 360 deals and, 34 Musk, Elon, 121 Myspace, 31 Nakamoto, Satoshi, 143, 145 National Commission on Technology, Automation and Economic Progress, 52–53 negative income tax, 64 Neilsen Soundscan, 26–27 Nelson, Jonathan, 26 Nelson, Matthew, 25, 26 Netflix, 29, 48 New Deal, 99 New York Stock Exchange (NYSE), 182 New York Times,37–38, 87, 177 99designs, 200 Nixon, Richard, 63 not-for-profits (NFPs), 121–23 obsolescence Amazon business model and, 89–90 corporations and, 70–71, 73 employment opportunities, technology as replacing and obsolescing, 51–54 Occupy Wall Street movement, 100, 152, 153 Oculus Rift, 201 offshoring, 78–79 Olen, Helaine, 170 OMGPop, 192, 193 online trading platforms, 176–78 open-source corporate strategies, 106–7 Open Source Ecology project, 217 Organic, Inc., 26 Ostrom, Elinor, 216 Pacific Lumber Company, 117 Palmer, Amanda, 38–39, 199 PandoDaily, 197–98 Pandora, 34, 218 Parker, Sean, 191–92 PayPal, 140–41 paywalls, 37–38 peer-to-peer economy/marketplaces, 16–17, 18 alternative corporate models for fostering, 93–97 Bandcamp and, 29–30 central currency as means of shutting down, 128–29 digital transaction networks and, 141 distribution of ability to create and exchange value by, 29–30 eBay and, 29 Known business model versus Blackboard’s in fostering, 95–97 obsolescence of, as effect of corporations, 70–71, 73 Sidecar business model versus Uber’s in fostering, 93–94 pensions, 170–71 Perez, Carlota, 98, 99 personhood, of corporations, 72, 73–74 Amazon and, 90 artificial intelligence and, 91 perspective painting, 235 Piketty, Thomas, 53–54, 131 Pitbull, 36 Pius X, Pope, 228–29, 230 platform cooperatives, 220–23 platform monopolies, 82–93, 101 acceleration in extraction of value and opportunity from economy and, 92–93 Amazon (publishing industry) and, 87–90 becoming entire environment and, 87 creative destruction and, 83–87 distributive alternatives to, 93–97 Uber (transportation industry) and, 85–87 Plum Organics, 119 Poole, Steven, 201 populists, 99–100 positive reinforcement, 28 Pound Foolish (Olen), 170 power-law distribution, 26–29, 30 precious metals currencies, 128 present shock, 6 price gouging, 86 privatization, 114–16 Proctor & Gamble, 107–8 productivity gains corporations failure to capitalize on, 77 great decoupling and, 53 income disparity and, 53–54 sharing of, with employees, 60–62 Prosper Marketplace, 203, 204 publishing industry, 87–89 Publix Super Markets, 117–18 quantitative easing, 137 Quirky, 199 Reagan, Ronald, 64 Real Pickles, 205–6 Renaissance, 45, 71, 230, 235–37 repatriation of jobs, 80 retirement savings plans, 170–75 fees and commissions charged for, 173–74 financial services industry and, 171–73, 175 401(k) plans and, 171–74 individual retirement accounts (IRAs), 171 pension accounts and, 170–71 performance of, 173–75 retrieval, 71–72, 73 return on assets (ROA), 76–77 Rifkin, Jeremy, 62 Roaring Twenties, 99 robotic ad-viewing programs, 37 Rolling Jubilee, 153 Rosenberg, Dan, 205–6 Rothschild, Lynn Forester de, 111 Ryan, Paul, 138 Ryan, William F., 63 Santa Barbara Missions, 156 scarcity, 62 Scholz, Trebor, 50, 223 Schor, Juliet, 58 Schumpeter, Joseph, 83, 84, 85 Second Machine Age, The (Brynjolfsson & McAfee), 23 secrecy, 106–7 seed-sharing networks, 217 self-help cooperatives, 159 Series A round of investment, 188–89 shareholder.

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It’s the pressure rendering CEOs powerless to prioritize the sustainability of their enterprises over the interests of impatient shareholders. It is the unidentified culprit behind the news headlines of economic crises from the Greek default to skyrocketing student debt. It is the force exacerbating wealth disparity, increasing the pay gap between employees and executives, and generating the power-law dynamics separating winners from losers. It is the black box extracting value from the stock market before human traders know what has happened, and the mindless momentum expanding the tech bubble to proportions dangerously too big to burst. To use the metaphor of our era, we are running an extractive, growth-driven economic operating system that has reached the limits of its ability to serve anyone, rich or poor, human or corporate.

The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies by Erik Brynjolfsson, Andrew McAfee

2013 Report for America's Infrastructure - American Society of Civil Engineers - 19 March 2013, 3D printing, access to a mobile phone, additive manufacturing, Airbnb, Alan Greenspan, Albert Einstein, Amazon Mechanical Turk, Amazon Web Services, American Society of Civil Engineers: Report Card, Any sufficiently advanced technology is indistinguishable from magic, autonomous vehicles, barriers to entry, basic income, Baxter: Rethink Robotics, Boston Dynamics, British Empire, business cycle, business intelligence, business process, call centre, carbon tax, Charles Lindbergh, Chuck Templeton: OpenTable:, clean water, combinatorial explosion, computer age, computer vision, congestion charging, congestion pricing, corporate governance, cotton gin, creative destruction, crowdsourcing, data science, David Ricardo: comparative advantage, digital map, driverless car, employer provided health coverage, en.wikipedia.org, Erik Brynjolfsson, factory automation, Fairchild Semiconductor, falling living standards, Filter Bubble, first square of the chessboard / second half of the chessboard, Frank Levy and Richard Murnane: The New Division of Labor, Freestyle chess, full employment, G4S, game design, general purpose technology, global village, GPS: selective availability, Hans Moravec, happiness index / gross national happiness, illegal immigration, immigration reform, income inequality, income per capita, indoor plumbing, industrial robot, informal economy, intangible asset, inventory management, James Watt: steam engine, Jeff Bezos, Jevons paradox, jimmy wales, job automation, John Markoff, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, Joseph Schumpeter, Kevin Kelly, Khan Academy, Kiva Systems, knowledge worker, Kodak vs Instagram, law of one price, low skilled workers, Lyft, Mahatma Gandhi, manufacturing employment, Marc Andreessen, Mark Zuckerberg, Mars Rover, mass immigration, means of production, Narrative Science, Nate Silver, natural language processing, Network effects, new economy, New Urbanism, Nicholas Carr, Occupy movement, oil shale / tar sands, oil shock, One Laptop per Child (OLPC), pattern recognition, Paul Samuelson, payday loans, post-work, power law, price stability, Productivity paradox, profit maximization, Ralph Nader, Ray Kurzweil, recommendation engine, Report Card for America’s Infrastructure, Robert Gordon, Robert Solow, Rodney Brooks, Ronald Reagan, search costs, Second Machine Age, self-driving car, sharing economy, Silicon Valley, Simon Kuznets, six sigma, Skype, software patent, sovereign wealth fund, speech recognition, statistical model, Steve Jobs, Steven Pinker, Stuxnet, supply-chain management, TaskRabbit, technological singularity, telepresence, The Bell Curve by Richard Herrnstein and Charles Murray, the Cathedral and the Bazaar, the long tail, The Signal and the Noise by Nate Silver, The Wealth of Nations by Adam Smith, total factor productivity, transaction costs, Tyler Cowen, Tyler Cowen: Great Stagnation, Vernor Vinge, warehouse robotics, Watson beat the top human players on Jeopardy!, winner-take-all economy, Y2K

Thus, there are very few people at the extremes. FIGURE 10.1 In contrast, superstar (and long tail) markets are often better described by a power law, or Pareto curve, in which a small number of people reap a disproportionate share of sales. This is often characterized as the 80/20 rule, where 20 percent of the participants get 80 percent of the gains, but it can be more extreme than that.22 For instance, research by Erik and his coauthors found that book sales at Amazon were characterized by a power law distribution.23 Power law distributions have a ‘fat tail,’ which means the likelihood of extreme events is much greater than one would expect to see in a normal distribution.24 They are also ‘scale invariant,’ which means that the top-selling book accounts for about the same share of the top ten books’ sales as the top ten books do for the top one hundred, or the top one hundred do for the top one thousand.

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This is often characterized as the 80/20 rule, where 20 percent of the participants get 80 percent of the gains, but it can be more extreme than that.22 For instance, research by Erik and his coauthors found that book sales at Amazon were characterized by a power law distribution.23 Power law distributions have a ‘fat tail,’ which means the likelihood of extreme events is much greater than one would expect to see in a normal distribution.24 They are also ‘scale invariant,’ which means that the top-selling book accounts for about the same share of the top ten books’ sales as the top ten books do for the top one hundred, or the top one hundred do for the top one thousand. Power laws describe many phenomena, from frequency of earthquakes to the frequency of words in most languages. They also describe the sales distribution of books, DVD, apps, and other information products. Other markets are mixtures of different types of distributions. The U.S. economy as a whole can be described as a mixture of a log-normal distribution (a variant of the classical normal distribution) and power law, with the power law fitting the incomes at the top best.25 Some of our current research at MIT is trying to better understand the causes and consequences of this mixture, and how it may be evolving over time.

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However, the mean (or average) of a power-law distribution is generally much, much higher than the median or the mode.27 For instance, in 2009, the average salary for major league baseball players was $3,240,206, roughly three times the median salary of $1,150,000.28 In practical terms, this means that when income is distributed according to a power law, most people will be below average—say goodbye, Lake Wobegon! Furthermore, over time, average income can increase without any increase in the median income or, for that matter, without any increase in income for most people. Power-law distributions don’t just increase income inequality; they also mess with our intuitions

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

It comes up with an answer that is found empirically not to be true. The empirical failings of a theory may inculcate a fantastic new theory—the failings of the Newtonian universe ushered in relativity—but they also lead, of course, to the demise of the original model. In our The Power Laws of Biology 167 case here, fractal geometry can only explain the power laws of biology if the power laws really exist—if the exponent really is a constant, the value of 0.75 genuinely universal. I mentioned that Alfred Heusner and others have for decades contested the validity of the 3/4 exponent, arguing that Max Rubner’s original 2/3 scaling was in fact more accurate.

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The Hydrogen Hypothesis 19 27 38 51 Part 2 The Vital Force: Proton Power and the Origin of Life 4. The Meaning of Respiration 5. Proton Power 6. The Origin of Life 65 71 85 94 Part 3 Insider Deal: The Foundations of Complexity 7. Why Bacteria are Simple 8. Why Mitochondria Make Complexity Possible 105 114 130 Part 4 Power Laws: Size and the Ramp of Ascending Complexity 9. The Power Laws of Biology 10. The Warm-Blooded Revolution 149 156 178 Part 5 Murder or Suicide: The Troubled Birth of the Individual 11. Conflict in the Body 12. Foundations of the Individual 189 200 215 Part 6 Battle of the Sexes: Human Pre-History and the Nature of Gender 13.

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If being larger demands greater complexity, which has an immediate cost—a need for new genes, better organization, more energy—was there any immediate payback, some advantage to being bigger for its own sake, which could counter-balance the costly new organization? In Part 4, we’ll consider the possibility that the ‘power laws’ of biological scaling may have underpinned the apparent trajectory towards greater complexity that seems to have characterized the rise of the eukaryotes, while forever defying the bacteria. 9 The Power Laws of Biology They say that in London everyone lives within 6 feet of a rat. Denizens of the night, these rats are presumably dozing the day away somewhere beneath the floorboards, or in the drains.

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

Matthew Salganik, “Prediction and Surprise,” presentation at the Thought Leader Forum, Legg Mason Capital Management, October 14, 2011. 10. More formally, a power law is expressed in the form: p(x) = Cx−α, where C and α are constants. The exponent, α, is often shown as positive, although it is negative. Since x is raised to the power of α, the distribution is called a power law. The value of the exponent is typically 2 < α < 3. See M. E. J. Newman, “Power Laws, Pareto Distributions, and Zipf's Law,” Contemporary Physics 46, no. 5 (September–October 2005): 323–351; and Aaron Clauset, Cosma Rohilla Shalizi, and M. E. J. Newman, “Power-law Distributions in Empirical Data,” SIAM Review 51, no. 4 (2009): 661–703. 11.

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FIGURE 6-4 Top U.S. cities, rank and size on a logarithmic scale (based on 2010 data) Source: United States Census Bureau and analysis by author. The term power law comes from the fact that an exponent (or power) determines the slope of the line. An astonishingly diverse range of socially driven phenomena follow power laws, including the rank and number of book sales, the rank and frequency of citations for scientific papers, the rank and number of deaths in acts of terrorism, and the rank and deaths in war.10 One of the key features of distributions that follow a power law is that there are very few large values and lots of small values. As a result, the idea of an “average” has no meaning.

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The process of social influence and cumulative advantage frequently generates a distribution that is best described by a power law. Figure 6-4 shows the rank and size of the largest 275 cities in the United States as of 2010. The rank of the cities is on the horizontal axis, and the size of the cities is on the vertical axis. Both the horizontal and vertical axes are on logarithmic scales, which means that the percentage change between tick marks is the same (the percentage difference between 1 and 10 is the same as between 10 and 100). The data fall close to a straight line, which can be expressed with a relatively simple formula known as a power law. For example, the formula for the United States would be able to tell you the size of the seventh-largest city (San Antonio, Texas; population 1,325,000) as well as the seventieth (Buffalo, New York; population 260,000).

The Blockchain Alternative: Rethinking Macroeconomic Policy and Economic Theory by Kariappa Bheemaiah

"World Economic Forum" Davos, accounting loophole / creative accounting, Ada Lovelace, Adam Curtis, Airbnb, Alan Greenspan, algorithmic trading, asset allocation, autonomous vehicles, balance sheet recession, bank run, banks create money, Basel III, basic income, behavioural economics, Ben Bernanke: helicopter money, bitcoin, Bletchley Park, blockchain, Bretton Woods, Brexit referendum, business cycle, business process, call centre, capital controls, Capital in the Twenty-First Century by Thomas Piketty, cashless society, cellular automata, central bank independence, Charles Babbage, Claude Shannon: information theory, cloud computing, cognitive dissonance, collateralized debt obligation, commoditize, complexity theory, constrained optimization, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, cross-border payments, crowdsourcing, cryptocurrency, data science, David Graeber, deep learning, deskilling, Diane Coyle, discrete time, disruptive innovation, distributed ledger, diversification, double entry bookkeeping, Ethereum, ethereum blockchain, fiat currency, financial engineering, financial innovation, financial intermediation, Flash crash, floating exchange rates, Fractional reserve banking, full employment, George Akerlof, Glass-Steagall Act, Higgs boson, illegal immigration, income inequality, income per capita, inflation targeting, information asymmetry, interest rate derivative, inventory management, invisible hand, John Maynard Keynes: technological unemployment, John von Neumann, joint-stock company, Joseph Schumpeter, junk bonds, Kenneth Arrow, Kenneth Rogoff, Kevin Kelly, knowledge economy, large denomination, Large Hadron Collider, Lewis Mumford, liquidity trap, London Whale, low interest rates, low skilled workers, M-Pesa, machine readable, Marc Andreessen, market bubble, market fundamentalism, Mexican peso crisis / tequila crisis, Michael Milken, MITM: man-in-the-middle, Money creation, money market fund, money: store of value / unit of account / medium of exchange, mortgage debt, natural language processing, Network effects, new economy, Nikolai Kondratiev, offshore financial centre, packet switching, Pareto efficiency, pattern recognition, peer-to-peer lending, Ponzi scheme, power law, precariat, pre–internet, price mechanism, price stability, private sector deleveraging, profit maximization, QR code, quantitative easing, quantitative trading / quantitative finance, Ray Kurzweil, Real Time Gross Settlement, rent control, rent-seeking, robo advisor, Satoshi Nakamoto, Satyajit Das, Savings and loan crisis, savings glut, seigniorage, seminal paper, Silicon Valley, Skype, smart contracts, software as a service, software is eating the world, speech recognition, statistical model, Stephen Hawking, Stuart Kauffman, supply-chain management, technology bubble, The Chicago School, The Future of Employment, The Great Moderation, the market place, The Nature of the Firm, the payments system, the scientific method, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, too big to fail, trade liberalization, transaction costs, Turing machine, Turing test, universal basic income, Vitalik Buterin, Von Neumann architecture, Washington Consensus

Complexity economics treats such variations as the intrinsic characteristics of interrelated systems. Non - linearity thus plays a central role in complexity economics. Power Laws The effects of agents on a non-linear dynamic system follow rules of power laws . Power laws imply that small occurrences are very common, but large eco-system changes are rare. For example- patterns involving incomes, the growth of cities, firms, the stock market and fluctuations of returns, order flow, volume, liquidity and even natural calamities such as hurricanes and earthquakes, all follow power laws. A power law, can also be called a scaling law, as there is a direct relationship between two variables.

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The study of power laws in markets has increasingly been a subject of interest to econophysicists25 (a complimentary offshoot of complexity economics) as power laws signal the occurrence of scale independent behaviour that is closely related to phase transitions and critical phenomenon . Some reliable examples of power law distributions occur in financial markets (Sinha et al., 2010) (Also see, ‘Power Laws in Finance’, Chapter 5, ‘Econophysics: An Introduction’, Sinha et al., (2010); ‘Power Laws in Economics: An Introduction’, Xavier Gabaix (2008)). Complex systems are more commonly characterised by probability distributions that are better described by a power laws instead of normal distributions, as these gradually decreasing mathematical functions are better at probabilistically predicting the future states of even highly complex systems (Levy D.

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Mathematically this can be interpreted as, where ‘Y’ and ‘X’ are variables of interest, “is called the power law exponent, and ‘a’ is typically an unremarkable constant. So, if X is multiplied by a factor of 10, then Y is multiplied by 10; i.e.: Y ‘scales’ as X to the power. Power laws or scaling laws are seen in different disciplines of study, particularly physics. A commonly known power law is the Pareto principle (used in marketing studies for example) or the also known as the 80/20 rule, which states that, for many events, roughly 80% of the effects come from 20% of the causes. The study of power laws in markets has increasingly been a subject of interest to econophysicists25 (a complimentary offshoot of complexity economics) as power laws signal the occurrence of scale independent behaviour that is closely related to phase transitions and critical phenomenon .

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

In particular, extreme outcomes are much more frequent, and the average value of some power law distributions cannot be calculated. 8 If height was distributed in a similar way to word usage, most men would be dwarfs (the majority of words are hardly used at all) but a few would be hundreds of feet tall (the human equivalent of ‘the’ and ‘of’). Power laws have much wider application than word frequencies. The Australian Don Bradman was the greatest batsman in the history of cricket, and the fitted power law enables us to estimate how many batsmen there would have to be before there was another as good as Bradman, how many batsmen are as bad as the authors, and even to conjecture how good Bradman was relative to other fine players of other sports (stunningly good).

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Nor could a normal distribution describe earthquakes; if it could there would never have been an earthquake like that which hit Valdivia in Chile in 1960, the largest measured by modern recording equipment. Earthquakes follow a power law – there are many small earthquakes, so small they pass unnoticed, every day. And so do asteroids – the Yucatán crater was created by the largest of which we have knowledge, but Earth is regularly hit by objects from space. 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.

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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. The graph of securities price movements in every minute looks very similar to the graph of securities price movements on every day. Power laws do better than normal and lognormal distributions in picking up the extremes of market fluctuations, which is important for controlling risk and understanding long-run patterns of returns.

NumPy Cookbook by Ivan Idris

business intelligence, cloud computing, computer vision, data science, Debian, en.wikipedia.org, Eratosthenes, mandelbrot fractal, p-value, power law, sorting algorithm, statistical model, transaction costs, web application

eig Returns the eigenvalues and eigenvectors of an array. See also The Installing Matplotlib recipe in Chapter 1, Winding Along with IPython Discovering a power law For the purpose of this recipe, imagine that we are operating a Hedge Fund. Let it sink in; you are part of the one percent now! Power laws occur in a lot of places, see http://en.wikipedia.org/wiki/Power_law for more information. The Pareto principle (http://en.wikipedia.org/wiki/Pareto_principle) for instance, which is a power law, states that wealth is unevenly distributed. This principle tells us that if we group people by their wealth, the size of the groups will vary exponentially.

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This principle tells us that if we group people by their wealth, the size of the groups will vary exponentially. To put it simply, there are not a lot of rich people, and there are even less billionaires; hence the one percent. Assume that there is a power law in the closing stock prices log returns. This is a big assumption, of course, but power law assumptions seem to pop up all over the place. We don't want to trade too often, because of involved transaction costs per trade. Let's say that we would prefer to buy and sell once a month based on a significant correction (in other words a big drop). The issue is to determine an appropriate signal given that we want to initiate a transaction every one out of about 20 days.

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Get to Grips with Commonly Used Functions In this chapter, we will cover a number of commonly used functions: sqrt, log, arange, astype, and sum ceil, modf, where, ravel, and take sort and outer diff, sign, eig histogram and polyfit compress and randint We will be discussing these functions through the following recipes: Summing Fibonacci numbers Finding prime factors Finding palindromic numbers The steady state vector determination Discovering a power law Trading periodically on dips Simulating trading at random Sieving integers with the Sieve of Eratosthenes Introduction This chapter is about the commonly used functions. These are the functions that you will be using on a daily basis. Obviously, the usage may differ for you. There are so many NumPy functions that it is virtually impossible to know all of them, but the functions in this chapter will be the bare minimum with which we must be familiar.

The Middleman Economy: How Brokers, Agents, Dealers, and Everyday Matchmakers Create Value and Profit by Marina Krakovsky

Affordable Care Act / Obamacare, Airbnb, Al Roth, Ben Horowitz, Benchmark Capital, Black Swan, buy low sell high, Chuck Templeton: OpenTable:, Credit Default Swap, cross-subsidies, crowdsourcing, deal flow, disintermediation, diversified portfolio, experimental economics, George Akerlof, Goldman Sachs: Vampire Squid, income inequality, index fund, information asymmetry, Jean Tirole, Joan Didion, John Zimmer (Lyft cofounder), Kenneth Arrow, Lean Startup, Lyft, Marc Andreessen, Mark Zuckerberg, market microstructure, Martin Wolf, McMansion, Menlo Park, Metcalfe’s law, moral hazard, multi-sided market, Network effects, patent troll, Paul Graham, Peter Thiel, pez dispenser, power law, real-name policy, ride hailing / ride sharing, Robert Metcalfe, Sand Hill Road, search costs, seminal paper, sharing economy, Silicon Valley, social graph, supply-chain management, TaskRabbit, the long tail, The Market for Lemons, the strength of weak ties, too big to fail, trade route, transaction costs, two-sided market, Uber for X, uber lyft, ultimatum game, Y Combinator

“It is the asymmetry between upside and downside that allows antifragile tinkering to benefit from disorder and uncertainty.”33 When your downside is limited and your upside is potentially infinite, you should embrace risk taking. That rule fits venture capital perfectly because returns in venture capital follow a power-law distribution, a pattern many of us are familiar with as the 80/20 rule,34 although many power-law distributions are even more extreme. For example, according to a study released today, the 80 wealthiest individuals in the world collectively own $1.9 trillion—a total about equal to the “wealth” of all the people in the poorer half of the world.35 In The Black Swan, Taleb coined a memorable word to refer to such highly skewed distributions: they occur in “Extremistan,” where a single event or data point has a disproportionate impact on the total.36 Venture capital lives in Extremistan in that only about 15 start-ups out of several thousand vying for VC funding each year are responsible for the vast majority of profits: just one of those megahits—the next Google or Facebook or Twitter—will make you a monumental winner even if all your other investments lose money.

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I think so because middlemen often live in Extremistan: lots of other uncertain outcomes besides the success of start-ups follow a power-law distribution rather than the normal (bell-shaped) distribution that most of us learned about in grade school. Several years ago, a pair of psychologists who analyzed the performance of more than half a million people in a variety of jobs—academic researchers, athletes, entertainers, and politicians—found that across the board (in more than 93 percent of the cases), individual performance outcomes fit the power-law pattern, distributions in which the majority of the people performed below average. That is not so much an indictment of ordinary performers as it is a direct result of the fact that the most extraordinary people in each field performed so spectacularly well: the superstars pushed the average up significantly despite a large total number of contenders.47 Put another way, the big winners are outliers, just like they would be in a normal distribution—but the losers in the long tail of the distribution are more or less the norm.

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In a 2003 study of blogs (back when they were still often called “weblogs”), the social media scholar Clay Shirky counted the number of inbound links to each of 433 blogs, finding that the top dozen (or fewer than 3 percent of the total) had 20 percent of the links from other blogs; it’s not quite the 80/20 rule, but it points in the same direction.48 Popularity on Twitter follows power-law patterns,49 as well, as do videos on YouTube.50 There’s every reason to believe that similar winner-take-all effects also occur in other online networks. What does that mean for middlemen deciding which risky prospects to back? The answer undoubtedly depends on the costs of those bets. In The Long Tail, Chris Anderson explored the implications of power-law dynamics on the Internet, where the costs of storing and distributing products are low (as they are for digital middlemen like Amazon and Netflix); for such middlemen, Anderson argued, it makes economic sense to carry a wide selection: though each niche product brings in a miniscule amount of revenue, “all those niches add up,” he wrote,51 suggesting that collectively the long tail can rival the hits in the short head, especially if offering a wide variety makes the long tail not only longer but fatter.

Secrets of Sand Hill Road: Venture Capital and How to Get It by Scott Kupor

activist fund / activist shareholder / activist investor, Airbnb, Amazon Web Services, asset allocation, barriers to entry, Ben Horowitz, Benchmark Capital, Big Tech, Blue Bottle Coffee, carried interest, cloud computing, compensation consultant, corporate governance, cryptocurrency, discounted cash flows, diversification, diversified portfolio, estate planning, family office, fixed income, Glass-Steagall Act, high net worth, index fund, information asymmetry, initial coin offering, Lean Startup, low cost airline, Lyft, Marc Andreessen, Myron Scholes, Network effects, Paul Graham, pets.com, power law, price stability, prudent man rule, ride hailing / ride sharing, rolodex, Salesforce, Sand Hill Road, seminal paper, shareholder value, Silicon Valley, software as a service, sovereign wealth fund, Startup school, the long tail, Travis Kalanick, uber lyft, VA Linux, Y Combinator, zero-sum game

If you are an institutional investor who is lucky enough to have built a roster of successful firms whose returns are not the median but in the high-return section of the power-law curve, you don’t want to diversify. Returns in the top end of VC funds can often be as much as 3,000 basis points higher than at the bottom end; dispersion of returns is huge when you have power-law distributions. In general, diversification is likely to push you toward the median/low-return section of the power-law curve and thus be dilutive to overall returns. Thus, many institutional investors seek to have a concentrated venture portfolio—which, by the way, probably further exacerbates that power-law distribution of returns. And that brings us to the second implication—it’s very hard for new firms to break into the industry and be successful.

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These are the investments where the VC is expecting to return ten to one hundred times her money. If you’re paying attention, this distribution of returns should remind you of the power-law curve discussion from the last section. It turns out that not only does the performance of VC firms follow the power-law curve, but so does the distribution of deals within a given fund. Over time, funds that generate two and a half to three times net returns to their investors will be in the good portion of the power-law curve distribution and continue to have access to institutional capital. We’ll talk about fees later, but to achieve two and a half to three times net returns (after all fees), VCs probably need to generate three to four times gross returns.

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That is, most institutional investors could choose a manager to invest in and have a high expectation that that manager’s returns would fall within that distribution. Instead, VC firm results tend to follow more of a power-law curve. That is, the distribution of returns is not normal, but rather heavily skewed, such that a small percentage of firms capture a large percentage of the returns to the industry. BELL CURVE POWER-LAW CURVE So if you are an institutional investor in this paradigm, the likelihood of your investing in one of the few firms that generates excess returns is small. And if you invest in the median firm, the results generated by that firm are likely to be in the long tail of returns that are subpar.

The Precipice: Existential Risk and the Future of Humanity by Toby Ord

3D printing, agricultural Revolution, Albert Einstein, Alignment Problem, AlphaGo, Anthropocene, artificial general intelligence, Asilomar, Asilomar Conference on Recombinant DNA, availability heuristic, biodiversity loss, Columbian Exchange, computer vision, cosmological constant, CRISPR, cuban missile crisis, decarbonisation, deep learning, DeepMind, defense in depth, delayed gratification, Demis Hassabis, demographic transition, Doomsday Clock, Dr. Strangelove, Drosophila, effective altruism, Elon Musk, Ernest Rutherford, global pandemic, Goodhart's law, Hans Moravec, Herman Kahn, Higgs boson, Intergovernmental Panel on Climate Change (IPCC), Isaac Newton, James Watt: steam engine, Large Hadron Collider, launch on warning, Mark Zuckerberg, Mars Society, mass immigration, meta-analysis, Mikhail Gorbachev, mutually assured destruction, Nash equilibrium, Nick Bostrom, Norbert Wiener, nuclear winter, ocean acidification, OpenAI, p-value, Peter Singer: altruism, planetary scale, power law, public intellectual, race to the bottom, RAND corporation, Recombinant DNA, Ronald Reagan, self-driving car, seminal paper, social discount rate, Stanislav Petrov, Stephen Hawking, Steven Pinker, Stewart Brand, supervolcano, survivorship bias, synthetic biology, tacit knowledge, the scientific method, Tragedy of the Commons, uranium enrichment, William MacAskill

There is much debate about whether the distributions of various disasters are really power laws. For example, log-normal distributions have right-hand tails that approximate a power law, so could be mistaken for them, but have a lower probability of small events than in a true power law. For our purpose, we don’t really need to distinguish between different heavy-tailed distributions. We are really just interested in whether the right-hand tail (the distribution of large events) behaves as a power law (∼xα), what its exponent is, and over what domain the power law relationship actually holds. Any actual distribution will only be well fitted by a power law up to some level.

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This is the case with climate change, where even though the catastrophic damages would be felt a long time from now, lowering emissions or developing alternative energy sources makes more difference the sooner we do it. 35 The diameter of NEOs fits a power-law distribution with exponent –3.35 (Chapman, 2004). The size of measles epidemics in isolated communities fits a power law with exponent –1.2 (Rhodes & Anderson, 1996). Fatalities from many other natural disasters—tsunamis, volcanoes, floods, hurricanes, tornadoes—also fit power-law distributions. This fit usually fails beyond some large size, where the actual probabilities of extremely large events are typically lower than a power law would predict (e.g., measles outbreaks are eventually limited by the size of the population).

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Another suggestion is that tacit knowledge and operational barriers make it much harder to deploy bioweapons than it may first appear.44 But the answer may also just be that we have too little data. The patterns of disease outbreaks, war deaths and terrorist attacks all appear to follow power law distributions. Unlike the familiar “normal” distribution where sizes are clustered around a central value, power law distributions have a “heavy tail” of increasingly large events, where there can often be events at entirely different scales, with some being thousands, or millions, of times bigger than others. Deaths from war and terror appear to follow power laws with especially heavy tails, such that the majority of the deaths happen in the few biggest events. For instance, warfare deaths in the last hundred years are dominated by the two World Wars, and most US fatalities from terrorism occurred in the September 11 attacks.45 When events follow a distribution like this, the average size of events until now systematically under-represents the expected size of events to come, even if the underlying risk stays the same.46 And it is not staying the same.

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 degree distribution that describes many events in complex systems is called a power law. A curve that corresponds to a power law is shown below as Figure 2. FIGURE 2: A curve illustrating a power-law degree distribution In this degree distribution, the frequency of events appears on the vertical axis and the severity of events appears on the horizontal axis. As in a bell curve, extreme events occur less frequently than mild events. This is why the curve slopes downward (less frequent events) as it moves off to the right (more extreme events). However, there are some crucial differences between the power law and the bell curve. For one thing, the bell curve (see Figure 1) is “fatter” in the region close to the vertical axis.

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This means that mild events happen more frequently in bell curve distributions and less frequently in power law distributions. Crucially, this power law curve never comes as close to the horizontal axis as the bell curve. The “tail” of the curve continues for a long distance to the right and remains separated from the horizontal axis. This is the famous “fat tail,” which in contrast with the tail on the bell curve does not appear to touch the horizontal axis. This means that extreme events happen more frequently in power law distributions. Television and blogs are filled with discussions of fat tails, although the usage often seems more like cliché than technical understanding.

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A similar fractal pattern appears whether the chart is magnified to cover hours, days, months or years, and similar results come from looking at other charts in currency, bond and derivatives markets. Such charts show price movements, and therefore risk, distributed according to a power law and chart patterns with a fractal dimension significantly greater than 1.0. These features are at odds with a normal distribution of risk and are consistent with the power-law degree distribution of events in complex systems. While more work needs to be done in this area, so far the case for understanding capital markets as complex systems with power-law degree distributions is compelling. This brings the analysis back to the question of scale. What is the scale of currency and capital markets, and how does it affect risk?

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

It measured phenomena that had smooth step-by-step transitions, with most samples falling within the safe confines of the middle of the bell curve. The bell curve didn’t capture the extreme volatility that can occur in a fractal world—the world of power laws, sudden jumps, wild leaps. Much of Mandelbrot’s work was based on power laws driving all sorts of phenomena, from cotton prices to income distributions to population densities in cities. Rather than adding up in linear fashion (1 + 2 + 3 etc.), which fit well within the bell curve, things governed by power laws can make dramatic, unexpected moves that live in the tails of the curve. Mandelbrot—his big-eared, balding basketball-size head glistening over an Apple laptop perched on the podium—told the NYU audience filled with quants, traders, and finance professors that if the bell curve truly captured the reality of the stock market, big crashes in the market like Black Monday would never happen.

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The math behind the Johansen-Ledoit-Sornette model was first discovered by Sornette in the 1990s when he was diagnosing those critical rupture points in pressure tanks on the Ariane rocket as well as a method to predict earthquakes. The phenomenon, which had parallels in Mandelbrot’s fractals, was something he said was bigger than standard power laws—it was a super-power law marked by dizzyingly fast up-and-down oscillations. 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.

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“Let me speak,” Sornette snapped. “I let you speak. Let me speak. Dragon, dragon, like animals, mystical animals with special properties. That’s exactly what are the Dragon Kings, predictable, but outliers. Second point. Excuse me Nassim, you’re not going to like it. You confuse a little bit the power laws. You are speaking about power laws in terms of statistics and indeed the fragility of estimation with respect to fat tails. I’m speaking of a different type of predictive model which is fundamentally dynamic, not statistical. That is the underlying theme of everything I showed.” Sornette was saying that Taleb’s analysis was based on the wrong kind of math—statistics.

The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation by Hannah Fry

Brownian motion, John Nash: game theory, linear programming, Nash equilibrium, Pareto efficiency, power law, recommendation engine, Skype, stable marriage problem, statistical model, TED Talk

Nor does it follow the normal bell curve–type distribution that is usually associated with things to do with humans, like height or IQ. Instead, the formula suggests that the number of sexual partners follows what’s known as a ‘power-law’ distribution. When it comes to height, almost all of us fall within a small window, with most people between five foot and six foot five. There are some outliers, of course, but generally there is little difference between the tallest and shortest people in a typical population. The power-law distribution, on the other hand, allows for a much, much bigger range. If the number of sexual partners followed the same rules as height, finding someone with over a thousand partners would be like meeting a person who was taller than the Eiffel Tower.

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Partly inspired by this study, scientists and mathematicians have begun to look for and find power-law distributions in a range of unusual places in the last decade. The distribution pattern behind sexual contacts is also found in the way that websites are linked on the internet, the way we form connections on Twitter and Facebook, the way that words sit next to each other in a sentence, even how different ingredients are used in recipes. The simple equation of x-α unites them all. The reason for all this becomes clearer when we return to the idea of links in a network. It’s these connections that are causing the distribution. Power-law distributions are created by links in a network with a very particular shape, known to mathematicians as ‘scale-free’.10 An example of what these scale-free networks look like is on the right.

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Power-law distributions are created by links in a network with a very particular shape, known to mathematicians as ‘scale-free’.10 An example of what these scale-free networks look like is on the right. Most people have roughly the same number of connections, but there are some – like the darker circle in the middle – who have a huge number of links. These people are known as the ‘hubs’ of the network and are the secret to the similarities between all the seemingly unrelated power-law distributions. Katy Perry, with 57,000,000 followers (as of September 2014), is the biggest hub of the Twitter network, Wikipedia is a hub of the World Wide Web and the onion is a hub of the recipe-ingredient network. The hubs are created because of a ‘rich-get-richer’ rule in all of these scenarios.

Work Rules!: Insights From Inside Google That Will Transform How You Live and Lead by Laszlo Bock

Abraham Maslow, Abraham Wald, Airbnb, Albert Einstein, AltaVista, Atul Gawande, behavioural economics, Black Swan, book scanning, Burning Man, call centre, Cass Sunstein, Checklist Manifesto, choice architecture, citizen journalism, clean water, cognitive load, company town, correlation coefficient, crowdsourcing, Daniel Kahneman / Amos Tversky, deliberate practice, en.wikipedia.org, experimental subject, Fairchild Semiconductor, Frederick Winslow Taylor, future of work, Google Earth, Google Glasses, Google Hangouts, Google X / Alphabet X, Googley, helicopter parent, immigration reform, Internet Archive, Kevin Roose, longitudinal study, Menlo Park, mental accounting, meta-analysis, Moneyball by Michael Lewis explains big data, nudge unit, PageRank, Paul Buchheit, power law, Ralph Waldo Emerson, Rana Plaza, random walk, Richard Thaler, Rubik’s Cube, self-driving car, shareholder value, Sheryl Sandberg, side project, Silicon Valley, six sigma, statistical model, Steve Ballmer, Steve Jobs, Steven Levy, Steven Pinker, survivorship bias, Susan Wojcicki, TaskRabbit, The Wisdom of Crowds, Tony Hsieh, Turing machine, Wayback Machine, winner-take-all economy, Y2K

The 2011 Japan earthquake (magnitude 9.0), Bill Gates’s net worth (over $70 billion), and even the population of New York City (8.3 million people) are too far from average to show up as a likely scenario in a Gaussian model, yet we know they exist.129 Statistically, these phenomena are better described by a “power law” distribution, which is compared to a Gaussian distribution below. Comparison of the distribution of human height and earthquake magnitude. Height varies evenly around an average with roughly half of people above and half below average in height. In contrast, the large majority of earthquakes are below average size. The name “power law” is used because if you wrote an equation describing the shape of the curve, you’d need to use an exponent to describe it, where one number is raised to the power of another number (e.g., in y = x-½, the exponent is −½ and x is “raised to the power of −½.”

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Schmidt assumed that performance was normally distributed. It’s not. Professors Ernest O’Boyle and Herman Aguinis, whom we met in chapter 8, reported in the journal Personnel Psychology that human performance actually follows a power law distribution171—pop back to the first few pages of chapter 8 for a refresher. The biggest difference between a normal (also known as a Gaussian) and a power law distribution is that, for some phenomena, normal distributions massively underpredict the likelihood of extreme events. For example, most financial models used by banks up until the 2008 economic crisis assumed a normal distribution of stock market returns.

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Nassim Nicholas Taleb, in his book The Black Swan, made exactly this point, explaining that extreme events were much more likely than most banks’ models assumed.172 As a result, swings and downturns happen far more often than predicted when using a normal distribution, but about as often as you would expect using a power law or similar distribution. Individual performance also follows a power law distribution. In many fields it’s easy to point to people whose performance surpasses their peers’ by an inhuman amount. Jack Welch as CEO of GE or Steve Jobs as CEO of Apple and Pixar. Walt Disney and his twenty-six Academy Awards, the most ever for an individual.173 The Belgian novelist Georges Simenon wrote 570 books and stories (many featuring his detective Jules Maigret), selling between 500 and 700 million copies, and Dame Barbara Cartland of the United Kingdom published more than 700 romance stories, selling between 500 million and one billion copies.174 (I am clearly writing the wrong kind of book.)

Outnumbered: From Facebook and Google to Fake News and Filter-Bubbles – the Algorithms That Control Our Lives by David Sumpter

affirmative action, algorithmic bias, AlphaGo, Bernie Sanders, Brexit referendum, Cambridge Analytica, classic study, cognitive load, Computing Machinery and Intelligence, correlation does not imply causation, crowdsourcing, data science, DeepMind, Demis Hassabis, disinformation, don't be evil, Donald Trump, Elon Musk, fake news, Filter Bubble, Geoffrey Hinton, Google Glasses, illegal immigration, James Webb Space Telescope, Jeff Bezos, job automation, Kenneth Arrow, Loebner Prize, Mark Zuckerberg, meta-analysis, Minecraft, Nate Silver, natural language processing, Nelson Mandela, Nick Bostrom, Northpointe / Correctional Offender Management Profiling for Alternative Sanctions, p-value, post-truth, power law, prediction markets, random walk, Ray Kurzweil, Robert Mercer, selection bias, self-driving car, Silicon Valley, Skype, Snapchat, social contagion, speech recognition, statistical model, Stephen Hawking, Steve Bannon, Steven Pinker, TED Talk, The Signal and the Noise by Nate Silver, traveling salesman, Turing test

In situations where there are a large number of items that can be ‘also liked’ – such as the hundreds of thousands of scientific articles that have been written – then popularity can often be captured by a mathematical relationship known as a ‘power law’. To understand power laws, think about a plot of the proportion of papers that are cited more than a certain number of times. We are most used to graphs with points that increase on a linear scale, i.e. in equally spaced steps, like 1, 2, 3, 4 etc. or 10 per cent, 20 per cent, 30 per cent etc. Power laws are revealed when we plot data on a double logarithmic scale, in which we increase the steps in successive powers of a number. For example, the positive (or strictly speaking, the non-negative) powers of 10 are 1, 10, 100, 1,000, 10,000, etc.

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There is a straight-line relationship between the proportion of articles and number of citations (for articles cited more than about 10 times). It is this straight line that is known as a power law.*. Figure 10.1 The number of times an article is cited plotted against the proportion of articles cited more than that number of times for scientific articles in 2008. Data collected by Young-Ho Eom and Santo Fortunato.3 Power laws are a sign of vast inequality. In 2008, 73 per cent of scientific articles had been cited once or less. A very depressing thought for anyone who has spent those many months required to write an article.

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Chapter 9 : We ‘ Also Liked ’ the Internet 1 This model is usually called ‘preferential attachment’ in mathematical literature, but has a variety of names reflecting the variety of times it has been discovered. The best mathematical description about how it is used and works can be found in Mark Newman’s article on power laws: Newman, M. E. J. 2005. ‘Power laws, Pareto distributions and Zipf’s law.’ Contemporary Physics 46, no. 5: 323–51. 2 The detailed description of the ‘also liked’ model is as follows. On each step of the model a new customer arrives and looks at the site of their favourite author. The probability that a particular author, i, is this new customer’s favourite depends on previous sales is given by: where n i is the number of books sold by author i and N=S25 i=1n i is the total number of books sold by all authors.

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

This type of pattern—a very small number of cases causing a very large proportion of the total impact—is characteristic of a power-law distribution, the type of distribution that earthquakes obey. Clauset’s insight was that terror attacks abide by a power-law distribution as well. Suppose that we draw a graph (figure 13-4) plotting the frequency of terror attacks on one axis and their death tolls on the other. At first, this doesn’t seem terribly useful. You can clearly see the power-law relationship: the number of attacks decreases very steeply with their frequency. But the slope is so steep that it seems to obscure any meaningful signal: you see a large number of very small attacks, and a small number of very large ones, with seemingly little room in between.

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When plotted on a double-logarithmic scale, the relationship between the frequency and the severity of terror attacks appears to be, more or less,47 a straight line. This is, in fact, a fundamental characteristic of power-law relationships: when you plot them on a double-logarithmic scale, the pattern that emerges is as straight as an arrow. Power laws have some important properties when it comes to making predictions about the scale of future risks. In particular, they imply that disasters much worse than what society has experienced in the recent past are entirely possible, if infrequent. For instance, the terrorism power law predicts that a NATO country (not necessarily the United States) would experience a terror attack killing at least one hundred people about six times over the thirty-one-year period from 1979 through 2009.

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There is some evidence that their approach is successful: Israel is the one country that has been able to bend Clauset’s curve. If we plot the fatality tolls from terrorist incidents in Israel using the power-law method (figure 13-8), we find that there have been significantly fewer large-scale terror attacks than the power-law would predict; no incident since 1979 has killed more than two hundred people. The fact that Israel’s power-law graph looks so distinct is evidence that our strategic choices do make some difference. How to Read Terrorists’ Signals Whatever strategic choices we make, and whatever trade-off we are willing to accept between security and freedom, we must begin with the signal.

Loonshots: How to Nurture the Crazy Ideas That Win Wars, Cure Diseases, and Transform Industries by Safi Bahcall

accounting loophole / creative accounting, Alan Greenspan, Albert Einstein, AOL-Time Warner, Apollo 11, Apollo 13, Apple II, Apple's 1984 Super Bowl advert, Astronomia nova, behavioural economics, Boeing 747, British Empire, Cass Sunstein, Charles Lindbergh, Clayton Christensen, cognitive bias, creative destruction, disruptive innovation, diversified portfolio, double helix, Douglas Engelbart, Douglas Engelbart, Dunbar number, Edmond Halley, Gary Taubes, Higgs boson, hypertext link, industrial research laboratory, invisible hand, Isaac Newton, Ivan Sutherland, Johannes Kepler, Jony Ive, knowledge economy, lone genius, Louis Pasteur, Mark Zuckerberg, Menlo Park, Mother of all demos, Murray Gell-Mann, PageRank, Peter Thiel, Philip Mirowski, Pierre-Simon Laplace, power law, prediction markets, pre–internet, Ralph Waldo Emerson, RAND corporation, random walk, reality distortion field, Richard Feynman, Richard Thaler, Sheryl Sandberg, side project, Silicon Valley, six sigma, stem cell, Steve Jobs, Steve Wozniak, synthetic biology, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Tim Cook: Apple, tulip mania, Wall-E, wikimedia commons, yield management

The frequency should vary in inverse proportion to size: Twenty-acre fires should occur half as often as ten-acre fires. Forty-acre fires should occur one-quarter as often as ten-acre fires. Hundred-acre fires should occur one-tenth as often, and so on. That pattern, called a power law, is a surprising prediction—a mathematical clue that a forest is on the verge of erupting. The pattern has been seen elsewhere. As we will discuss below, the power-law pattern is seen not only in forest-fire models, but in financial markets and terrorist attacks. It would take another decade, however, for these three seemingly unrelated systems to come together. Outside of the forest-fire world, interest in Hammersley and Broadbent’s percolation theory began to dwindle.

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By building a model that was simple, but not simplistic—that is, it captured the essence of trading, without getting lost in the details—Johnson showed that his trading cliques model seemed to explain the fat tail distribution in financial markets pretty well. That fat tail took on a characteristic shape: a power law. There were 32 times fewer cliques of 40 people than cliques of 10. There were 32 times fewer cliques of 160 than cliques of 40. And so on. The number of cliques decreased with the size of the clique by an unusual power: 2.5. The data on casualties from decades of civil war in Colombia showed a near-perfect power law as well. There were 32 times fewer attacks with 40 casualties than attacks with 10 casualties. There were 32 times fewer attacks with 160 casualties than attacks with 40 casualties.

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The number of recorded attacks decreased with casualty size by the same unusual power: 2.5. The similarity between trading data and one set of guerrilla warfare data, from just one country, could be a coincidence. But it would be a strange coincidence. Such a neatly ordered power law is rare. So Johnson and his collaborators began looking at other conflicts. Remarkably, data from wars in Iraq and Afghanistan showed the same pattern: casualties from attacks followed the same power-law form, with the same 2.5 exponent. Over the next three years, they recruited help and data from a broader set of researchers around the world, eventually assembling a database of 54,679 violent events across nine wars (or “insurgent conflicts”): Senegal, Peru, Sierra Leone, Indonesia, Israel, and Northern Ireland, in addition to their original three—Iraq, Colombia, and Afghanistan.

The People's Platform: Taking Back Power and Culture in the Digital Age by Astra Taylor

"World Economic Forum" Davos, A Declaration of the Independence of Cyberspace, Aaron Swartz, Alan Greenspan, American Legislative Exchange Council, Andrew Keen, AOL-Time Warner, barriers to entry, Berlin Wall, big-box store, Brewster Kahle, business logic, Californian Ideology, citizen journalism, cloud computing, collateralized debt obligation, Community Supported Agriculture, conceptual framework, content marketing, corporate social responsibility, creative destruction, cross-subsidies, crowdsourcing, David Brooks, digital capitalism, digital divide, digital Maoism, disinformation, disintermediation, don't be evil, Donald Trump, Edward Snowden, Evgeny Morozov, Fall of the Berlin Wall, Filter Bubble, future of journalism, Gabriella Coleman, gentrification, George Gilder, Google Chrome, Google Glasses, hive mind, income inequality, informal economy, Internet Archive, Internet of things, invisible hand, Jane Jacobs, Jaron Lanier, Jeff Bezos, job automation, John Markoff, John Perry Barlow, Julian Assange, Kevin Kelly, Kickstarter, knowledge worker, Laura Poitras, lolcat, Mark Zuckerberg, means of production, Metcalfe’s law, Naomi Klein, Narrative Science, Network effects, new economy, New Journalism, New Urbanism, Nicholas Carr, oil rush, peer-to-peer, Peter Thiel, planned obsolescence, plutocrats, post-work, power law, pre–internet, profit motive, recommendation engine, Richard Florida, Richard Stallman, self-driving car, shareholder value, sharing economy, Sheryl Sandberg, Silicon Valley, Silicon Valley billionaire, Silicon Valley ideology, slashdot, Slavoj Žižek, Snapchat, social graph, Steve Jobs, Stewart Brand, technological solutionism, technoutopianism, TED Talk, the long tail, trade route, Tragedy of the Commons, vertical integration, Whole Earth Catalog, WikiLeaks, winner-take-all economy, Works Progress Administration, Yochai Benkler, young professional

Over the entire Web, traffic and links are distributed according to “power laws.” These distributions tend to follow what’s known as the 80/20 rule, exemplified by a situation in which 80 percent of a desirable resource goes to 20 percent of the population: 20 percent of a society’s citizens possessing 80 percent of the wealth or land are the classic examples. They are winner-take-all, rich-get-richer scenarios, which means that power laws are less equal than the classic bell curve. Human height, for example, follows a bell curve. If our size followed a power-law distribution, a small percentage of the population would be thousands of feet tall while the majority of people would be very short.

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If our size followed a power-law distribution, a small percentage of the population would be thousands of feet tall while the majority of people would be very short. Because power laws are so heavily weighted toward the top (the head), most elements are actually below average (the tail), however strange that sounds: a handful of large events coexist with numerous small ones. Consequently, power laws are starkly inegalitarian. The top elements are far more popular than those in the middle, and those, in turn, are far more popular than the ones on the bottom. They are also ubiquitous online, a fact that has serious ramifications for political and cultural democracy and diversity.

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Preferential attachment, network effects, and the power laws they produce matter, in part, because they intensify and epitomize the old inequities we hoped the Internet would overthrow, from the star system to the hit-driven manufacturing of movies, music, and books. Winner-take-all markets promote certain types of culture at the expense of others, can make it harder for niche cultures and late bloomers to flourish, and contribute to broader income inequality.26 More specifically, where cultural production is concerned, the persistence of power laws refutes the myth of independent creators competing on even ground.

Global Catastrophic Risks by Nick Bostrom, Milan M. Cirkovic

affirmative action, agricultural Revolution, Albert Einstein, American Society of Civil Engineers: Report Card, anthropic principle, artificial general intelligence, Asilomar, availability heuristic, backpropagation, behavioural economics, Bill Joy: nanobots, Black Swan, carbon tax, carbon-based life, Charles Babbage, classic study, cognitive bias, complexity theory, computer age, coronavirus, corporate governance, cosmic microwave background, cosmological constant, cosmological principle, cuban missile crisis, dark matter, death of newspapers, demographic transition, Deng Xiaoping, distributed generation, Doomsday Clock, Drosophila, endogenous growth, Ernest Rutherford, failed state, false flag, feminist movement, framing effect, friendly AI, Georg Cantor, global pandemic, global village, Great Leap Forward, Gödel, Escher, Bach, Hans Moravec, heat death of the universe, hindsight bias, information security, Intergovernmental Panel on Climate Change (IPCC), invention of agriculture, Kevin Kelly, Kuiper Belt, Large Hadron Collider, launch on warning, Law of Accelerating Returns, life extension, means of production, meta-analysis, Mikhail Gorbachev, millennium bug, mutually assured destruction, Nick Bostrom, nuclear winter, ocean acidification, off-the-grid, Oklahoma City bombing, P = NP, peak oil, phenotype, planetary scale, Ponzi scheme, power law, precautionary principle, prediction markets, RAND corporation, Ray Kurzweil, Recombinant DNA, reversible computing, Richard Feynman, Ronald Reagan, scientific worldview, Singularitarianism, social intelligence, South China Sea, strong AI, superintelligent machines, supervolcano, synthetic biology, technological singularity, technoutopianism, The Coming Technological Singularity, the long tail, The Turner Diaries, Tunguska event, twin studies, Tyler Cowen, uranium enrichment, Vernor Vinge, War on Poverty, Westphalian system, Y2K

Addressing such disputes is beyond the scope of this chapter. We will instead consider power law distributed disasters as an analysis reference case. Our conclusions would apply directly to types of disasters that continue to be distributed as a power law even up to very large severity. Compared to this reference case, we should worry less about types of disasters whose frequency of very large events is below a power law, and more about types of disasters whose frequency is greater. The higher the power a, the fewer larger disasters there are, relative to small disasters. For example, if they followed a power law, then car accidents would have a high power, as most accidents involve only one or two cars, and very few accidents involve one hundred or more cars.

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Each such catastrophic event can be described by its severity, which might be defined in terms ofenergy released, deaths induced, and so on. 368 Global catastrophic risks For many kinds of catastrophes. the distribution of event severity appears to follow a power law over a wide severity range. That is, sometimes the chance that within a small time interval one will see an event with severity S that is greater than a threshold s is given by P(S > s) = ks- a , (17.1) where k is a constant and a is the power of this type of disaster. Now we should keep in mind that these powers a can only be known to apply within the scales sampled by available data, and that many have disputed how widely such power laws apply (Bilham, 2004) , and whether power laws are the best model form, compared, for example, to the lognormal distribution (Clauset et al., 2007a) .

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Events/Year Catastrophe, social collapse, and human extinction 371 Of course the data to which these power laws have been fitted do not include events where most of humanity was destroyed. So in the absence of direct data, we must make guesses about how to project the power law into the regime where most people are killed. If S is the severity of a disaster, to which a power law applies, T is the total population just before the disaster, and D is the number killed by the disaster, then one simple approach would be to set D = (17.2) max(T, S) This would produce a very hard cut-off. In this case, much of the population would be left alive or everyone would be dead; there would be little chance of anything close to the borderline.

Gnuplot in Action: Understanding Data With Graphs by Philipp Janert

bioinformatics, business intelligence, Debian, general-purpose programming language, iterative process, mandelbrot fractal, pattern recognition, power law, random walk, Richard Stallman, six sigma, sparse data, survivorship bias

Double logarithmic plots serve a different purpose: they help us identify power law behavior—that is, data that follows an equation such as the following (C is a constant): y( x ) = C x k The analysis goes through as previously, but we end up with logarithms now on both sides of the equation: log( y( x ) ) = k log( x ) + log( C ) The resulting graph is a straight line, with a slope that depends on the exponent k. We’ve seen an example of this in chapter 1, when estimating the completion time of a long-running computer program. Double logarithmic plots are very important. Power laws occur in many different contexts in the real world, but aren’t always easy to spot.

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Go back to figure 1.3 in chapter 1: many different curves will seem to fit the data about equally well. But once plotted on a double-log plot (see figure 1.4), the linear shape of the data stands out and provides a strong and easily recognizable indicator of the underlying power law behavior. Log and log-log plots are part of the standard toolset. When faced with a new data set, I typically plot it both ways, just to see whether there’s some obvious (exponential or power law) behavior in it that wasn’t apparent immediately. They’re also useful when dealing with data that changes over many orders of magnitude. Learn how to use them! 3.7 Summary In this chapter, we covered what’s really the “meat” of gnuplot: working with data.

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Naively, we may attempt a nonlinear fit here, but in reality, the value of m that will give the best fit is simply the mean of all the values: m = (1/N)#i xi. Can we transform the equation in such a way that it becomes linear? For example, let’s assume that we suspect our data to follow a power-law with unknown exponent. Rather than fitting f(x;a,n) = a xn, we can take logarithms on both sides, or (equivalently) plot the data on a double-log plot. If the power-law relation holds, the data will fall on a straight line and we can obtain the exponent from the slope of this line. (We showed an example in figure 1.4.) Check for instance Numerical Recipes, section 15.1 for more details on this. 198 CHAPTER 10 ■ Advanced plotting concepts Even if no such a transformation is possible, can we identify and isolate the dominant behavior and perform a transformation to a linear form on that?

With Liberty and Dividends for All: How to Save Our Middle Class When Jobs Don't Pay Enough by Peter Barnes

adjacent possible, Alfred Russel Wallace, banks create money, basic income, Buckminster Fuller, carbon tax, collective bargaining, computerized trading, creative destruction, David Ricardo: comparative advantage, declining real wages, deindustrialization, diversified portfolio, driverless car, en.wikipedia.org, Fractional reserve banking, full employment, Glass-Steagall Act, hydraulic fracturing, income inequality, It's morning again in America, Jaron Lanier, Jevons paradox, John Maynard Keynes: Economic Possibilities for our Grandchildren, Joseph Schumpeter, land reform, Mark Zuckerberg, Money creation, Network effects, oil shale / tar sands, Paul Samuelson, power law, profit maximization, quantitative easing, rent-seeking, Ronald Coase, Ronald Reagan, Silicon Valley, sovereign wealth fund, Stuart Kauffman, the map is not the territory, The Spirit Level, The Wealth of Nations by Adam Smith, Thorstein Veblen, transaction costs, Tyler Cowen, Tyler Cowen: Great Stagnation, Upton Sinclair, Vilfredo Pareto, wealth creators, winner-take-all economy

This led him to posit that in market economies, about 20 percent of the people will always acquire about 80 percent of the wealth … because that’s how market economies work. Pareto’s formula wasn’t purely random; it reflects what mathematicians call a power law, meaning a curve that’s exponentially skewed to one end, as depicted in figure 3.1. The alternative to a power law is a bell curve, which has a large middle with small tails on both ends. What Pareto noticed was that in untempered market economies, wealth distribution follows a power law rather than a bell curve. A century later, this thesis seems as valid as ever: the 80/20 rule understates wealth concentration in the United States today.

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We also know that because money has the loudest voice in politics, the willingness of government to tax the rich wanes as their wealth waxes, a process that tax-reform advocate Chuck Collins calls the “inequality death spiral.”3 Though not startling, Epstein and Axtell’s finding is nevertheless sobering. It means that small initial differences, such as those in a bell curve, are inexorably magnified until they become extreme differences, such as those in a power law. Which means that, over time, our economic system will necessarily create a small upper crust and a shrunken middle. This is a crucial point. We know that people have different capacities and drives. Some are smarter than others, and some work harder. But those different abilities don’t explain the far greater differences in rewards.

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See also Alaska model dividends in countries with, 130 Oregon, wind energy dividends in, 128 O’Reilly, Bill, 86 Organization for Economic Cooperation and Development, 95 Orszag, Peter, 102 Outsourcing, 16–17 P Paine, Thomas, 1, 3, 7–9, 39, 70, 137 Palin, Sarah, 75, 76, 94 Pareto, Vilfredo, 30–31 Parijs, Philippe van, 130 Patents, rent from, 144 Peabody Energy, 102 Pelosi, Nancy, 109 Pensions as deferred wage, 27 defined-benefits pensions, 123 Perkins, Frances, 38 Pigou, Arthur, 63–64, 113 Pitt, William, 8 Pollin, Robert, 143 Pollution. See also Carbon capping carbon pollution permits, 93 co-owned wealth and, 88 externalities and, 63 Pollution, Property & Prices (Dales), 98 Poverty Alaska model and, 74 job training and, 25 Powell, Colin, 130 Power law, 30–31 Pragmatism, 121 Pre-distribution of wealth, 125–127 Price-setting, 63–64 Private wealth, 49 Privileges, rent and income from, 52–53 “The Problem of Social Cost” (Coase), 98–99 Progress and Poverty (George), 51 Property rights. See also Intellectual property rights externalities and, 98–99 Paine, Thomas on, 8 Punctuated equilibrium, 120 Q Quantitative easing, 22 R Reagan, Ronald, 16 Recession, stimulus and, 22 Recycled rent, 43, 59–68.

Mining of Massive Datasets by Jure Leskovec, Anand Rajaraman, Jeffrey David Ullman

cloud computing, crowdsourcing, en.wikipedia.org, first-price auction, G4S, information retrieval, John Snow's cholera map, Netflix Prize, NP-complete, PageRank, pattern recognition, power law, random walk, recommendation engine, second-price auction, sentiment analysis, social graph, statistical model, the long tail, web application

” (3)Sizes of Web Sites: Count the number of pages at Web sites, and order sites by the number of their pages. Let y be the number of pages at the xth site. Again, the function y(x) follows a power law. (4)Zipf’s Law: This power law originally referred to the frequency of words in a collection of documents. If you order words by frequency, and let y be the number of times the xth word in the order appears, then you get a power law, although with a much shallower slope than that of Fig. 1.3. Zipf’s observation was that y = cx−1/2. Interestingly, a number of other kinds of data follow this particular power law. For example, if we order states in the US by population and let y be the population of the xth most populous state, then x and y obey Zipf’s law approximately.

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Then or approximately e1/2 = 1.64844. Let x = −1. Then or approximately e−1 = 0.36786.□ 1.3.6Power Laws There are many phenomena that relate two variables by a power law, that is, a linear relationship between the logarithms of the variables. Figure 1.3 suggests such a relationship. If x is the horizontal axis and y is the vertical axis, then the relationship is log10 y = 6 − 2 log10 x. Figure 1.3 A power law with a slope of −2 EXAMPLE 1.7We might examine book sales at Amazon.com, and let x represent the rank of books by sales. Then y is the number of sales of the xth best-selling book over some period.

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The implication that above rank 1000 the sales are a fraction of a book is too extreme, and we would in fact expect the line to flatten out for ranks much higher than 1000.□ The general form of a power law relating x and y is log y = b + a log x. If we raise the base of the logarithm (which doesn’t actually matter), say e, to the values on both sides of this equation, we get y = ebea log x = ebxa. Since eb is just “some constant,” let us replace it by constant c. Thus, a power law can be written as y = cxa for some constants a and c. EXAMPLE 1.8In Fig. 1.3 we see that when x = 1, y = 106, and when x = 1000, y = 1. Making the first substitution, we see 106 = c.

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

Whether it’s playing games or the guitar, the curve of performance improvement over time—how well you do something or how long it takes you to do it—has a very specific form: This type of curve is called a power law, because performance varies as time raised to some negative power. For example, in the figure above, time to completion is proportional to the number of trials raised to minus two (or equivalently, one over the number of trials squared). Pretty much every human skill follows a power law, with different powers for different skills. (In contrast, Windows never gets faster with practice—something for Microsoft to work on.) In 1979, Allen Newell and Paul Rosenbloom started wondering what could be the reason for this so-called power law of practice. Newell was one of the founders of AI and a leading cognitive psychologist, and Rosenbloom was one of his graduate students at Carnegie Mellon University.

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Rosenbloom and Newell set their chunking program to work on a series of problems, measured the time it took in each trial, and lo and behold, out popped a series of power law curves. But that was only the beginning. Next they incorporated chunking into Soar, a general theory of cognition that Newell had been working on with John Laird, another one of his students. Instead of working only within a predefined hierarchy of goals, the Soar program could define and solve a new subproblem every time it hit a snag. Once it formed a new chunk, Soar generalized it to apply to similar problems, in a manner similar to inverse deduction. Chunking in Soar turned out to be a good model of lots of learning phenomena besides the power law of practice. It could even be applied to learning new knowledge by chunking data and analogies.

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See also Multilayer perceptron Perceptrons (Minsky & Papert), 100–101, 113 Personal data ethical responsibility to share some types of, 272–273 as model, 267–270 professional management of, 273–276 sharing or not, 270–276 types of, 271–273 value of, 274 Phase transitions, 105–107, 288 Physical symbol system hypothesis, 89 Physics, 29–31, 46–47, 50 Pitts, Walter, 96 Planetary-scale machine learning, 256–259 Planets, computing duration of year of, 131–133 Plato, 58 Point mutation, 124 Poisson’s equation, 30 Policing, predictive, 20 Politics, machine learning and, 16–19, 299 Positive examples, 67, 69 Posterior probability, 146–147, 241, 242, 243, 249 Poverty of the stimulus argument, 36–37 Power law of practice, 224–225 The Power of Habit (Duhigg), 223 Practice learning and, 223 power law of, 224–225 Predictive analytics, 8. See also Machine learning Predictive policing, 20 Presidential election, machine learning and 2012, 16–19 Principal-component analysis (PCA), 211–217, 255, 308 Principia (Newton), 65 Principal components of the data, 214 Principle of association, 93 Principle of indifference, 145 Principle of insufficient reason, 145 Principles of Psychology (James), 93 Prior probability, 146–147 Privacy, personal data and, 275 Probabilistic inference, 52, 53, 161–166, 242, 256, 305 Probability applied to poetry, 153–154 Bayesian networks and, 156–158 Bayesians and meaning of, 149, 169–170 Bayes’ theorem and, 145–149 estimating, 148–149 frequentist interpretation of, 149 logic and, 173–175, 245–246, 306, 309 Master Algorithm and, 245–246 posterior, 146–147 prior, 146–147 Probability theory, Laplace and, 145 Probably Approximately Correct (Valiant), 75 Problem solving learning as, 226 theory of, 225 Procedures, learners and, 8 Programming by example, 298 Programming, machine learning vs., 7–8 Programs, 4 computers writing own, 6 survival of the fittest, 131–134 Program trees, 131–133 Prolog programming language, 252–253 Punctuated equilibria, 127, 303 Pushkin, Alexander, 153 Python, 4 Quinlan, J.

SUPERHUBS: How the Financial Elite and Their Networks Rule Our World by Sandra Navidi

"World Economic Forum" Davos, activist fund / activist shareholder / activist investor, Alan Greenspan, Anthropocene, assortative mating, bank run, barriers to entry, Bear Stearns, Bernie Sanders, Black Swan, Blythe Masters, Bretton Woods, butterfly effect, Capital in the Twenty-First Century by Thomas Piketty, Carmen Reinhart, central bank independence, cognitive bias, collapse of Lehman Brothers, collateralized debt obligation, commoditize, conceptual framework, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, digital divide, diversification, Dunbar number, East Village, eat what you kill, Elon Musk, eurozone crisis, fake it until you make it, family office, financial engineering, financial repression, Gini coefficient, glass ceiling, Glass-Steagall Act, Goldman Sachs: Vampire Squid, Google bus, Gordon Gekko, haute cuisine, high net worth, hindsight bias, income inequality, index fund, intangible asset, Jaron Lanier, Jim Simons, John Meriwether, junk bonds, Kenneth Arrow, Kenneth Rogoff, Kevin Roose, knowledge economy, London Whale, Long Term Capital Management, longitudinal study, Mark Zuckerberg, mass immigration, McMansion, mittelstand, Money creation, money market fund, Myron Scholes, NetJets, Network effects, no-fly zone, offshore financial centre, old-boy network, Parag Khanna, Paul Samuelson, peer-to-peer, performance metric, Peter Thiel, plutocrats, Ponzi scheme, power law, public intellectual, quantitative easing, Renaissance Technologies, rent-seeking, reserve currency, risk tolerance, Robert Gordon, Robert Shiller, rolodex, Satyajit Das, search costs, shareholder value, Sheryl Sandberg, Silicon Valley, social intelligence, sovereign wealth fund, Stephen Hawking, Steve Jobs, subprime mortgage crisis, systems thinking, tech billionaire, The Future of Employment, The Predators' Ball, The Rise and Fall of American Growth, too big to fail, Tyler Cowen, women in the workforce, young professional

According to physicist Albert-László Barabási, “If a node has twice as many links as another node, then it is twice as likely to receive a new link.”10 Thus, a few hubs—superhubs—will be connected to almost all nodes.11 This is called a “power-law distribution.” The behavior of a network is governed by the interactions between nodes, hubs, and superhubs. The interactions are primarily determined by the network’s purpose and to some degree by randomness.12 Due to power-laws, you can anticipate that the behavior of the network will be influenced by many nodes trying to create links to hubs and especially to superhubs. Thus, a few nodes, the superhubs, will have the most influence within the network, and their actions and interactions will have broad effects throughout the network.

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MONEY + INFORMATION + SOCIAL CAPITAL = INFINITE OPPORTUNITIES Through their networks, the financial elite are ideally suited to create circumstances favorable to advancing their interests. Opportunities are both the cause and the effect of inextricable links between people, money, and information—with social capital serving as a conduit. They are also subject to power laws, according to which the more you have, the more you get. The sociologist Robert Merton described this phenomenon as the “Matthew Effect,” since Matthew states in the Bible, “For unto every one that hath shall be given, and he shall have abundance; but from him that hath not shall be taken away even that which he hath.”31 The more quality connections you have, the greater your access to additional connections, capital, and information, which in turn leads to more opportunities.

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The central bank governor of the Bank of England during the crisis was Mervyn King, who had also once taught in MIT’s economics department. It is quite incredible how much our world has been shaped by the few who attended the same school. The epitome of the old boys’ network is Goldman Sachs. It is the most exclusive of all exclusive clubs and artfully illustrates how the power-laws of network science correlate with actual network power. Due to the fact that Goldman always seems to make money regardless of the circumstances, it has been vilified as the “great vampire squid wrapped around the face of humanity”17 and alleged to have caused as well as profited from various financial crises.

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

When a corpus is all (or nearly all) we have of an entire language, such as the Hebrew Bible in the case of biblical Hebrew, hapax words can sometimes be quite vexing, since we might have little idea of their meaning. But hapax legomena aren’t strange statistical flukes or curiosities. Not only are they more common as a category than we might realize, but their existence is related to certain mathematical rules of language. The frequency of words in a language is described by what is known as a power law or, more commonly, a long tail. These types of distributions, unlike the bell curves we are used to for such quantities as human height, have values that extend far out into the upper reaches of the scale, allowing both for exceedingly common words such as “the” and for much rarer words like “flother.”

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Dean, TEAMS Middle English Texts Series (Kalamazoo, MI: Medieval Institute Publications, 1991); available online at Robbins Library Digital Projects, University of Rochester, accessed April 30, 2015, http://d.lib.rochester.edu/teams/text/dean-six-ecclesiastical-satires-friar-daws-reply. more commonly, a long tail: Note that not all heavy-tailed distributions, or long tails, are necessarily power laws. Often about half of the words: András Kornai, Mathematical Linguistics (London: Springer-Verlag, 2008), 71. According to this source, the percentage of the words in a corpus that occur only once each—hapax legomena—is about 40–60 percent for many corpora. To avoid losing our exceptions and edge cases: Related ideas are explored, along with the notion of language as a complex system, in William A.

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Balkin, “The Crystalline Structure of Legal Thought,” Rutgers Law Review 39, no. 1 (1986): 1–108, http://www.yale.edu/lawweb/jbalkin/articles/crystal.pdf; Yale Law School Faculty Scholarship Series, Paper 294. The law professor David Post and the biologist Michael Eisen: Post and Eisen, “How Long Is the Coastline of the Law?” they find features indicative of fractals: Post and Eisen find power laws. “the value of good contracts and good lawyering”: Mark D. Flood and Oliver Goodenough, “Contract as Automaton: The Computational Representation of Financial Agreements,” OFR (Office of Financial Research) Working Paper no. 15-04, March 26, 2015, https://financialresearch.gov/working-papers/files/OFRwp-2015-04_Contract-as-Automaton-The-Computational-Representation-of-Financial-Agreements.pdf.

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

Approximately 95 percent of people vary no more than 15 centimeters (about 6 inches) from the average height. Heights have a narrow and predictable range of outcomes. But there are systems with heavily skewed distributions, where the idea of average holds little or no meaning. These distributions are better described by a power law, which implies that a few of the outcomes are really large (or have a large impact) and most observations are small. Look at city sizes. New York City, with about 8 million inhabitants, is the largest city in the United States. The smallest town has about 50 people. So the ratio of the largest to the smallest is more than 150,000 to 1.

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So the ratio of the largest to the smallest is more than 150,000 to 1. Other social phenomena, like book or movie sales, show such extreme differences as well. City sizes have a much wider range of outcomes than human heights do.8 Nassim Taleb, an author and former derivatives trader, calls the extreme outcomes within power law distributions black swans. He defines a black swan as an outlier event that has a consequential impact and that humans seek to explain after the fact.9 In large part owing to Taleb’s efforts, more people are aware of black swans and distributions that deviate from the bell curve. What most people still don’t appreciate is the mechanism that propagates black swans.

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The equivalent of the turkey’s plight—sharp losses following a period of prosperity—has occurred repeatedly in business. For example, Merrill Lynch (which was acquired by Bank of America) suffered losses over a two-year period from 2007 to 2008 that were in excess of one-third of the profits it had earned cumulatively in its thirty-six years as a public company.13 Dealing with a system governed by a power law is like the farmer feeding us while he holds the axe behind his back. If you stick around long enough, the axe will fall. The question is not if, but when. The term black swan reflects the criticism of induction by the philosopher Karl Popper. Popper argued that seeing lots of white swans doesn’t prove the theory that all swans are white, but seeing one black swan does disprove it.

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

Among the categories of distributions that are often distinguished due to the convergence properties of moments are: (1) Having a support that is compact but not degenerate, (2) Subgaussian, (3) Gaussian, (4) Subexponential, (5) Power law with exponent greater than 3, (6) Power law with exponent less than or equal to 3 and greater than 2, (7) Power law with exponent less than or equal to 2. In particular, power law distributions have a finite mean only if the exponent is greater than 1, and have a finite variance only if the exponent exceeds 2. Our interest is in distinguishing between cases where tail events dominate impacts, as a formal definition of the boundary between the categories of distributions to be considered as Mediocristan and Extremistan.

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No single observation can meaningfully affect the aggregate. Also called “thin-tailed,” or member of the Gaussian family of distributions. Extremistan: a process where the total can be conceivably impacted by a single observation (say, income for a writer). Also called “fat-tailed.” Includes the fractal, or power-law, family of distributions. See subexponentiality in the Appendix. Minority Rule: an asymmetry by which the behavior of the total is dictated by the preferences of a minority. Smokers can be in smoke-free areas but nonsmokers cannot be in smoking ones, so nonsmokers will prevail, not because they are initially a majority, but because they are asymmetric.

Hit Makers: The Science of Popularity in an Age of Distraction by Derek Thompson

Airbnb, Albert Einstein, Alexey Pajitnov wrote Tetris, always be closing, augmented reality, Clayton Christensen, data science, Donald Trump, Downton Abbey, Ford Model T, full employment, game design, Golden age of television, Gordon Gekko, hindsight bias, hype cycle, indoor plumbing, industrial cluster, information trail, invention of the printing press, invention of the telegraph, Jeff Bezos, John Snow's cholera map, Kevin Roose, Kodak vs Instagram, linear programming, lock screen, Lyft, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Mary Meeker, Menlo Park, Metcalfe’s law, Minecraft, Nate Silver, Network effects, Nicholas Carr, out of africa, planned obsolescence, power law, prosperity theology / prosperity gospel / gospel of success, randomized controlled trial, recommendation engine, Robert Gordon, Ronald Reagan, Savings and loan crisis, Silicon Valley, Skype, Snapchat, social contagion, statistical model, Steve Ballmer, Steve Jobs, Steven Levy, Steven Pinker, subscription business, TED Talk, telemarketer, the medium is the message, The Rise and Fall of American Growth, Tyler Cowen, Uber and Lyft, Uber for X, uber lyft, Vilfredo Pareto, Vincenzo Peruggia: Mona Lisa, women in the workforce

“Movies are complex products,” they wrote in a follow-up paper, “and the cascade of information among filmgoers during the course of a film’s run can evolve along so many paths that it is impossible to attribute the success of a movie to individual causal factors.” In short, Hollywood is chaos. Success in Hollywood does not follow a normal distribution, with many films earning the box office average. Instead, movies follow a power law distribution, which means most of the winnings come from a tiny minority of films. The best way to imagine a power law market is to think of a lottery. The vast majority of people win nothing, and a few people win millions of dollars. So it makes little sense to talk about the “average” lottery outcome. It’s the same in Hollywood. Hollywood’s six major studios released just over one hundred movies in 2015.

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At some point in time, they will cluster around an unforeseeable cultural product by buying the same book or attending the same movie. Recall Duncan Watts’s big idea: Like a massive earthquake, some “global cascades” are mathematically inevitable, but they are also impossible to predict too far ahead of time. “Pareto’s power law characteristics”: Vilfredo Pareto, an Italian economist, is credited with discovering that income within a country follows a “power law,” such that 80 percent of wealth is held by 20 percent of the population. This Pareto principle has been extended to mean that 80 percent of sales often comes from 20 percent of products. In the movie sample De Vany studied, one fifth of the movies took four fifths of the box office.

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What is the best way to understand a market both filled with flops and driven by hits? Al Greco, a professor of marketing at Fordham University and an expert in book publishing, summarizes the entertainment business this way: “A complex, adaptive, semi-chaotic industry with Bose-Einstein distribution dynamics and Pareto power law characteristics with dual-sided uncertainty.” That is quite the disfluent multisyllabic mouthful, but it’s worth breaking down word by word: “Complex”: Every year, there are hundreds of movies released to billions of potential viewers, who are watching ads, reading critics, and mimicking each other to decide what movie ticket they will buy next.

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

Kaufman’s approach provides a framework of general laws that have stood the test of time—invariant, unchanging lenses that we can use to focus and arrive at workable answers. A foundational principle that aligns with the world and is applicable across the geologic time scale of human, organic, and inorganic history is compounding. Compounding is one of the most powerful forces in the world. In fact, it is the only power law in the universe that exists with a variable in its exponent. The power law of compounding not only is applicable to investing but also, and more important, can be applied to continued learning. The fastest way to simplify things is to spot the symmetries, or invariances—that is, the fundamental properties that do not change from one object under study to another.

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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. Mandelbrot found that the underlying power law that was evident in random patterns in nature also applies to the positive and negative price movements of many financial instruments. The movement of stock prices followed a power law rather than a Gaussian or normal distribution. In his book The (Mis)Behavior of Markets, written with Richard Hudson, Mandelbrot invoked the important concept of “clustering”: Market turbulence tends to cluster.

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Because of such constraints and the limits of our knowledge, random variation of attributes exists in Mediocristan and can be usefully described by Gaussian probability models (i.e., the bell curve or other distributions having a family resemblance to it). In Extremistan, variation within distributions is far less constrained than in Mediocristan. It is the land of scalability and power laws. Generators of events produce distributions with large or small extreme values, frequently. Those extreme values affect the sum of attribute values in a sample distribution, and the mean value of such distributions. The probability of occurrence of extreme values varies greatly from Gaussian models.

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

One could infer from this that even if there are no intersections to worry about, it is worth confirming the direction one is going in. There is a specific trap when working with data that can have an equally devastating effect: producing results that are entirely off the mark—and you won’t even know it! I am speaking of highly skewed (specifically: power-law) point distributions. Unless they are diagnosed and treated properly, they will ruin all standard calculations. Deceivingly, the results will look just fine but will be next to meaningless. Such datasets occur all the time. A company may serve 2.6 million web pages per month and count 100,000 unique visitors, thus concluding that the “typical visitor” consumes about 26 page views per month.

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A service provider has 20,000 accounts, generating a total of $5 million in revenue, and therefore figures that “each account” is worth $250. Figure 7-4. Histogram of the number of page views generated by each user in a month. The inset shows the same data using double-logarithmic scales, revealing power-law behavior. In all these cases (and many, many more), the apparently obvious conclusions will turn out to be very, very wrong. Figure 7-4 shows a histogram for the first example, which exhibits the features typical of all such situations. The two most noteworthy features are the very large number of visitors producing only very few (one or two) page views per month, and the very small number of visitors generating an excessively large number of views.

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The graph suggests therefore to partition the population into three groups, each of which is in itself either relatively homogeneous (the bottom 90% and the middle 9%) or so small that it can almost be treated on an individual basis (the top 1%, or an even smaller set of extremely high-frequency users). Datasets exhibiting power-law distributions come close to being “bad data”: datasets for which standard methods silently fail and that need to be treated carefully on a case-by-case basis. On the other hand, once properly diagnosed, such datasets become manageable and even offer real opportunities. For instance, we can go tell the account manager that he or she doesn’t have to worry about all of the 20,000 accounts individually, but instead can focus on the top 150 and still capture 85% of expected revenue!

Globalists: The End of Empire and the Birth of Neoliberalism by Quinn Slobodian

"World Economic Forum" Davos, Alan Greenspan, Asian financial crisis, Berlin Wall, bilateral investment treaty, borderless world, Bretton Woods, British Empire, business cycle, capital controls, central bank independence, classic study, collective bargaining, David Ricardo: comparative advantage, Deng Xiaoping, desegregation, Dissolution of the Soviet Union, Doha Development Round, eurozone crisis, Fall of the Berlin Wall, floating exchange rates, full employment, Garrett Hardin, Greenspan put, Gunnar Myrdal, Hernando de Soto, invisible hand, liberal capitalism, liberal world order, Mahbub ul Haq, market fundamentalism, Martin Wolf, Mercator projection, Mont Pelerin Society, Norbert Wiener, offshore financial centre, oil shock, open economy, pattern recognition, Paul Samuelson, Pearl River Delta, Philip Mirowski, power law, price mechanism, public intellectual, quantitative easing, random walk, rent control, rent-seeking, road to serfdom, Ronald Reagan, special economic zone, statistical model, Suez crisis 1956, systems thinking, tacit knowledge, The Chicago School, the market place, The Wealth of Nations by Adam Smith, theory of mind, Thomas L Friedman, trade liberalization, urban renewal, Washington Consensus, Wolfgang Streeck, zero-sum game

Alan Cafruny and Glenda Rosenthal (Boulder, NOTES TO PAGES 209–213 173. 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193. 194. 195. 196. 343 CO: Lynne Rienner, 1993), 407. On the diverse uses of the concept, see Simona Piattoni, The Theory of Multi-­level Governance: Conceptual, Empirical, and Normative Challenges (Oxford: Oxford University Press, 2010). Kowitz, Alfred Müller-­Armack, 271. Mestmäcker, “Power, Law and Economic Constitution,” 190. Mestmäcker, “Competition Law,” 73. Mestmäcker, “Power, Law and Economic Constitution,” 190. Mestmäcker, “Offene Märkte,” 391. Joerges, “Science of Private Law and the Nation-­State,” 79. Michelle Cini and Lee McGowan, Competition Policy in the Eu­ro­pean Union (New York: St. Martin’s Press, 1998), 22. Von der Groeben, The Eu­ro­pean Community, 195.

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Ernst Joachim Mestmäcker, Hans Möller, and Hans-­Peter Schwarz (Baden-­Baden: Nomos, 1987), 11. 159. Peter Behrens, “The Ordoliberal Concept of ‘Abuse’ of a Dominant Position and Its Impact on Article 102 TFEU,” Discussion Paper, Europa-­Kolleg Hamburg, Institute for Eu­ro­pean Integration, No. 7 / 15, 2015, http://­hdl​.­handle​.­net​/­10419​ /­120873. 160. Ernst​-­Joachim Mestmäcker, “Power, Law and Economic Constitution,” German Economic Review 11, no. 3 (1973): 182. 161. Ernst-­Joachim Mestmäcker, “Offene Märkte im System unverfälschten Wettbewerbs in der Europäischen Wirtschaftsgmeinschaft,” in Wirtschaftsordnung und Rechtsordnung, ed. Helmut Coing, Heinrich Kronstein, and Ernst-­Joachim Mestmäcker (Karlsruhe: C.

…

Christian Joerges, “The Science of Private Law and the Nation-­State,” in The Eu­ ro­pe­anisation of Law: The L ­ egal Effects of Eu­ro­pean Integration, ed. Francis G. Snyder (Portland, OR: Hart, 2000), 69. 163. Mestmäcker, “Offene Märkte,” 348. 164. Ibid., 353. 165. Ibid., 390. 166. Mestmäcker, “Power, Law and Economic Constitution,” 187. 167. Ernst Joachim Mestmäcker, A ­Legal Theory without Law: Posner v. Hayek on Economic Analy­sis of Law (Tübingen: Mohr Siebeck, 2007), 40. 168. Fritz W. Scharpf, “Economic Integration, Democracy and the Welfare State,” Journal of Eu­ro­pean Public Policy 4, no. 1 (March 1997): 28. 169.

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

But the same basic principle turns out to be valid for a great variety of phenomena, including the size of islands, the populations of cities, the amount of time a book spends on the bestseller list, the number of links to a given website, and—as the Italian economist Vilfredo Pareto had discovered in the 1890s—a country’s distribution of income and wealth. All of these are examples of “power law” distributions. (The word “power” here refers not to the political or electrical kind but to the mathematical exponent that determines the precise shape of a given distribution.) Power laws apply, in nature or society, where there is extreme inequality or unevenness: where a high peak (corresponding to a handful of huge cities, or frequently used words, or very rich people) is followed by a low “long tail” (corresponding to a multitude of small towns, or rare words, or wage slaves).

…

“In one of the very few clear-cut eureka moments of my life,” he tells us, “I saw that it might be deeply linked to information theory and hence to statistical thermodynamics—and became hooked on power law distributions for life.” He proceeded to write his Ph.D. thesis on Zipf’s law. Neither his uncle Szolem nor his dissertation committee (headed by Louis de Broglie, one of the founders of quantum theory) paid much heed to his effort to explain the significance of power laws, and for a long time thereafter Mandelbrot was the only mathematician to take such laws and their long tails seriously—which is why, when their importance was finally appreciated half a century later, he became known as the father of long tails.

…

“At that point, the computing center staff had to assign passwords,” he says. “So I can boast—if that’s the right term—of having been at the origin of the police intrusion that this change represented.” It was chance again that led to Mandelbrot’s next breakthrough. Visiting Harvard to give a lecture on power laws and the distribution of wealth, he was struck by a diagram that he happened to see on a chalkboard in the office of an economics professor there. The diagram was almost identical in shape to the one Mandelbrot was about to present in his lecture, yet it concerned not wealth distribution but price jumps on the New York Cotton Exchange.

Priceless: The Myth of Fair Value (And How to Take Advantage of It) by William Poundstone

availability heuristic, behavioural economics, book value, Cass Sunstein, collective bargaining, Daniel Kahneman / Amos Tversky, delayed gratification, Donald Trump, Dr. Strangelove, East Village, en.wikipedia.org, endowment effect, equal pay for equal work, experimental economics, experimental subject, feminist movement, game design, German hyperinflation, Henri Poincaré, high net worth, index card, invisible hand, John von Neumann, Kenneth Arrow, laissez-faire capitalism, Landlord’s Game, Linda problem, loss aversion, market bubble, McDonald's hot coffee lawsuit, mental accounting, meta-analysis, Nash equilibrium, new economy, no-fly zone, Paul Samuelson, payday loans, Philip Mirowski, Potemkin village, power law, price anchoring, price discrimination, psychological pricing, Ralph Waldo Emerson, RAND corporation, random walk, RFID, Richard Thaler, risk tolerance, Robert Shiller, rolodex, social intelligence, starchitect, Steve Jobs, The Chicago School, The Wealth of Nations by Adam Smith, three-martini lunch, ultimatum game, working poor

Perceptions of heat follow different power curves depending on whether it’s a warm piece of metal touching the arm, the irradiation of a small area of skin, or sauna-like heat enveloping the whole body. But for a given experiment, the curves are remarkably consistent. By 1965, two of Stevens’s colleagues could write, “As an experimental fact, the power law is established beyond any reasonable doubt, possibly more firmly established than anything else in psychology.” Five Black Is White S. S. Stevens tried to explain why the senses obey a power law. He noted that most of the laws of physics (like E=mc2) are power laws. By adapting to the form of physical law, the senses are better able to “tell us how matters stand out there.” In his posthumously published text, Psychophysics, Stevens wrote, For example, is it the differences or the proportions and ratios that need to remain constant in perception?

…

Doubling the subjective effect means quadrupling the wattage (and, unfortunately, your December electric bill). Stevens noted with satisfaction that his power curve rule can be stated in seven words: Equal stimulus ratios produce equal subjective ratios. This is often called Stevens’s law, or the psychophysical law. Within a generation, Stevens and contemporaries established that the power law is a very general one, applying not just to brightness of lights but also to perceptions of warmth, cold, taste, smell, vibration, and electric shock. The factor connecting the two ratios varies with the type of stimulus. It’s not always “four times the stimulus doubles the response.” For instance, it takes only about 1.7 times as much sugar, in a watery soft drink, to double the perception of sweetness.

…

Wearing a Cartier says you’re rich and don’t care who knows it. The Rolex says the same thing, only louder. The Rolex presumably has a higher bling rating than the Cartier, but not anywhere near ten times more. As Indow’s students appreciated, a massive increase in price buys only an incremental increase in cachet. There were also studies finding power laws for the social status attached to income and the seriousness of a theft of money. To double your social status, you need to earn about 2.6 times as much, according to one study cited by Stevens. The seriousness of thefts rose the slowest with dollar value. A thief would need to steal 60 times as much to double the seriousness of the crime.

Super Thinking: The Big Book of Mental Models by Gabriel Weinberg, Lauren McCann

Abraham Maslow, Abraham Wald, affirmative action, Affordable Care Act / Obamacare, Airbnb, Albert Einstein, anti-pattern, Anton Chekhov, Apollo 13, Apple Newton, autonomous vehicles, bank run, barriers to entry, Bayesian statistics, Bernie Madoff, Bernie Sanders, Black Swan, Broken windows theory, business process, butterfly effect, Cal Newport, Clayton Christensen, cognitive dissonance, commoditize, correlation does not imply causation, crowdsourcing, Daniel Kahneman / Amos Tversky, dark pattern, David Attenborough, delayed gratification, deliberate practice, discounted cash flows, disruptive innovation, Donald Trump, Douglas Hofstadter, Dunning–Kruger effect, Edward Lorenz: Chaos theory, Edward Snowden, effective altruism, Elon Musk, en.wikipedia.org, experimental subject, fake news, fear of failure, feminist movement, Filter Bubble, framing effect, friendly fire, fundamental attribution error, Goodhart's law, Gödel, Escher, Bach, heat death of the universe, hindsight bias, housing crisis, if you see hoof prints, think horses—not zebras, Ignaz Semmelweis: hand washing, illegal immigration, imposter syndrome, incognito mode, income inequality, information asymmetry, Isaac Newton, Jeff Bezos, John Nash: game theory, karōshi / gwarosa / guolaosi, lateral thinking, loss aversion, Louis Pasteur, LuLaRoe, Lyft, mail merge, Mark Zuckerberg, meta-analysis, Metcalfe’s law, Milgram experiment, minimum viable product, moral hazard, mutually assured destruction, Nash equilibrium, Network effects, nocebo, nuclear winter, offshore financial centre, p-value, Paradox of Choice, Parkinson's law, Paul Graham, peak oil, Peter Thiel, phenotype, Pierre-Simon Laplace, placebo effect, Potemkin village, power law, precautionary principle, prediction markets, premature optimization, price anchoring, principal–agent problem, publication bias, recommendation engine, remote working, replication crisis, Richard Feynman, Richard Feynman: Challenger O-ring, Richard Thaler, ride hailing / ride sharing, Robert Metcalfe, Ronald Coase, Ronald Reagan, Salesforce, school choice, Schrödinger's Cat, selection bias, Shai Danziger, side project, Silicon Valley, Silicon Valley startup, speech recognition, statistical model, Steve Jobs, Steve Wozniak, Steven Pinker, Streisand effect, sunk-cost fallacy, survivorship bias, systems thinking, The future is already here, The last Blockbuster video rental store is in Bend, Oregon, The Present Situation in Quantum Mechanics, the scientific method, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Tragedy of the Commons, transaction costs, uber lyft, ultimatum game, uranium enrichment, urban planning, vertical integration, Vilfredo Pareto, warehouse robotics, WarGames: Global Thermonuclear War, When a measure becomes a target, wikimedia commons

While every relationship is not always 80/20, there is a common pattern for outcomes to be far from evenly distributed. This particular 80/20 arrangement of outcomes is known as a power law distribution, where relatively few occurrences account for a significantly outsized proportion of the total. (It is named after mathematical exponentiation, aka power, because the math that creates the distribution involves this operation.) U.S. Health Spending Concentration In the figure above, we see a power law distribution at work in the people who spend the most on healthcare. Other examples with similar patterns include the returns from venture capital, the strength of volcanic eruptions, and the size of power outages.

…

By contrast, women shorter than four feet ten inches or taller than five feet ten inches make up less than about 5 percent of all women (outside two standard deviations from the mean). Probability Distributions Log-normal distribution Applies to phenomena that follow a power law relationship, such as wealth, the size of cities, and insurance losses. Poisson distribution Applies to independent and random events that occur in an interval of time or space, such as lightning strikes or numbers of murders in a city. Exponential distribution Applies to the timing of events, such as the survival of people and products, service times, and radioactive particle decay.

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., 38 oil, 105–6 Olympics, 209, 246–48, 285 O’Neal, Shaquille, 246 one-hundred-year floods, 192 Onion, 211–12 On the Origin of Species by Means of Natural Selection (Darwin), 100 OODA loop, 294–95 openness to experience, 250 Operation Ceasefire, 232 opinion, diversity of, 205, 206 opioids, 36 opportunity cost, 76–77, 80, 83, 179, 182, 188, 305 of capital, 77, 179, 182 optimistic probability bias, 33 optimization, premature, 7 optimums, local and global, 195–96 optionality, preserving, 58–59 Oracle, 231, 291, 299 order, 124 balance between chaos and, 128 organizations: culture in, 107–8, 113, 273–80, 293 size and growth of, 278–79 teams in, see teams ostrich with its head in the sand, 55 out-group bias, 127 outliers, 148 Outliers (Gladwell), 261 overfitting, 10–11 overwork, 82 Paine, Thomas, 221–22 pain relievers, 36, 137 Pampered Chef, 217 Pangea, 24–25 paradigm shift, 24, 289 paradox of choice, 62–63 parallel processing, 96 paranoia, 308, 309, 311 Pareto, Vilfredo, 80 Pareto principle, 80–81 Pariser, Eli, 17 Parkinson, Cyril, 74–75, 89 Parkinson’s law, 89 Parkinson’s Law (Parkinson), 74–75 Parkinson’s law of triviality, 74, 89 passwords, 94, 97 past, 201, 271–72, 309–10 Pasteur, Louis, 26 path dependence, 57–59, 194 path of least resistance, 88 Patton, Bruce, 19 Pauling, Linus, 220 payoff matrix, 212–15, 238 PayPal, 72, 291, 296 peak, 105, 106, 112 peak oil, 105 Penny, Jonathon, 52 pent-up energy, 112 perfect, 89–90 as enemy of the good, 61, 89–90 personality traits, 249–50 person-month, 279 perspective, 11 persuasion, see influence models perverse incentives, 50–51, 54 Peter, Laurence, 256 Peter principle, 256, 257 Peterson, Tom, 108–9 Petrified Forest National Park, 217–18 Pew Research, 53 p-hacking, 169, 172 phishing, 97 phones, 116–17, 290 photography, 302–3, 308–10 physics, x, 114, 194, 293 quantum, 200–201 pick your battles, 238 Pinker, Steven, 144 Pirahã, x Pitbull, 36 pivoting, 295–96, 298–301, 308, 311, 312 placebo, 137 placebo effect, 137 Planck, Max, 24 Playskool, 111 Podesta, John, 97 point of no return, 244 Polaris, 67–68 polarity, 125–26 police, in organizations and projects, 253–54 politics, 70, 104 ads and statements in, 225–26 elections, 206, 218, 233, 241, 271, 293, 299 failure and, 47 influence in, 216 predictions in, 206 polls and surveys, 142–43, 152–54, 160 approval ratings, 152–54, 158 employee engagement, 140, 142 postmortems, 32, 92 Potemkin village, 228–29 potential energy, 112 power, 162 power drills, 296 power law distribution, 80–81 power vacuum, 259–60 practice, deliberate, 260–62, 264, 266 precautionary principle, 59–60 Predictably Irrational (Ariely), 14, 222–23 predictions and forecasts, 132, 173 market for, 205–7 superforecasters and, 206–7 PredictIt, 206 premature optimization, 7 premises, see principles pre-mortems, 92 present bias, 85, 87, 93, 113 preserving optionality, 58–59 pressure point, 112 prices, 188, 231, 299 arbitrage and, 282–83 bait and switch and, 228, 229 inflation in, 179–80, 182–83 loss leader strategy and, 236–37 manufacturer’s suggested retail, 15 monopolies and, 283 principal, 44–45 principal-agent problem, 44–45 principles (premises), 207 first, 4–7, 31, 207 prior, 159 prioritizing, 68 prisoners, 63, 232 prisoner’s dilemma, 212–14, 226, 234–35, 244 privacy, 55 probability, 132, 173, 194 bias, optimistic, 33 conditional, 156 probability distributions, 150, 151 bell curve (normal), 150–52, 153, 163–66, 191 Bernoulli, 152 central limit theorem and, 152–53, 163 fat-tailed, 191 power law, 80–81 sample, 152–53 pro-con lists, 175–78, 185, 189 procrastination, 83–85, 87, 89 product development, 294 product/market fit, 292–96, 302 promotions, 256, 275 proximate cause, 31, 117 proxy endpoint, 137 proxy metric, 139 psychology, 168 Psychology of Science, The (Maslow), 177 Ptolemy, Claudius, 8 publication bias, 170, 173 public goods, 39 punching above your weight, 242 p-values, 164, 165, 167–69, 172 Pygmalion effect, 267–68 Pyrrhus, King, 239 Qualcomm, 231 quantum physics, 200–201 quarantine, 234 questions: now what, 291 what if, 122, 201 why, 32, 33 why now, 291 quick and dirty, 234 quid pro quo, 215 Rabois, Keith, 72, 265 Rachleff, Andy, 285–86, 292–93 radical candor, 263–64 Radical Candor (Scott), 263 radiology, 291 randomized controlled experiment, 136 randomness, 201 rats, 51 Rawls, John, 21 Regan, Ronald, 183 real estate agents, 44–45 recessions, 121–22 reciprocity, 215–16, 220, 222, 229, 289 recommendations, 217 red line, 238 referrals, 217 reframe the problem, 96–97 refugee asylum cases, 144 regression to the mean, 146, 286 regret, 87 regulations, 183–84, 231–32 regulatory capture, 305–7 reinventing the wheel, 92 relationships, 53, 55, 63, 91, 111, 124, 159, 271, 296, 298 being locked into, 305 dating, 8–10, 95 replication crisis, 168–72 Republican Party, 104 reputation, 215 research: meta-analysis of, 172–73 publication bias and, 170, 173 systematic reviews of, 172, 173 see also experiments resonance, 293–94 response bias, 142, 143 responsibility, diffusion of, 259 restaurants, 297 menus at, 14, 62 RetailMeNot, 281 retaliation, 238 returns: diminishing, 81–83 negative, 82–83, 93 reversible decisions, 61–62 revolving door, 306 rewards, 275 Riccio, Jim, 306 rise to the occasion, 268 risk, 43, 46, 90, 288 cost-benefit analysis and, 180 de-risking, 6–7, 10, 294 moral hazard and, 43–45, 47 Road Ahead, The (Gates), 69 Roberts, Jason, 122 Roberts, John, 27 Rogers, Everett, 116 Rogers, William, 31 Rogers Commission Report, 31–33 roles, 256–58, 260, 271, 293 roly-poly toy, 111–12 root cause, 31–33, 234 roulette, 144 Rubicon River, 244 ruinous empathy, 264 Rumsfeld, Donald, 196–97, 247 Rumsfeld’s Rule, 247 Russia, 218, 241 Germany and, 70, 238–39 see also Soviet Union Sacred Heart University (SHU), 217, 218 sacrifice play, 239 Sagan, Carl, 220 sales, 81, 216–17 Salesforce, 299 same-sex marriage, 117, 118 Sample, Steven, 28 sample distribution, 152–53 sample size, 143, 160, 162, 163, 165–68, 172 Sánchez, Ricardo, 234 sanctions and fines, 232 Sanders, Bernie, 70, 182, 293 Sayre, Wallace, 74 Sayre’s law, 74 scarcity, 219, 220 scatter plot, 126 scenario analysis (scenario planning), 198–99, 201–3, 207 schools, see education and schools Schrödinger, Erwin, 200 Schrödinger’s cat, 200 Schultz, Howard, 296 Schwartz, Barry, 62–63 science, 133, 220 cargo cult, 315–16 Scientific Autobiography and other Papers (Planck), 24 scientific evidence, 139 scientific experiments, see experiments scientific method, 101–2, 294 scorched-earth tactics, 243 Scott, Kim, 263 S curves, 117, 120 secondary markets, 281–82 second law of thermodynamics, 124 secrets, 288–90, 292 Securities and Exchange Commission, U.S., 228 security, false sense of, 44 security services, 229 selection, adverse, 46–47 selection bias, 139–40, 143, 170 self-control, 87 self-fulfilling prophecies, 267 self-serving bias, 21, 272 Seligman, Martin, 22 Semmelweis, Ignaz, 25–26 Semmelweis reflex, 26 Seneca, Marcus, 60 sensitivity analysis, 181–82, 185, 188 dynamic, 195 Sequoia Capital, 291 Sessions, Roger, 8 sexual predators, 113 Shakespeare, William, 105 Sheets Energy Strips, 36 Shermer, Michael, 133 Shirky, Clay, 104 Shirky principle, 104, 112 Short History of Nearly Everything, A (Bryson), 50 short-termism, 55–56, 58, 60, 68, 85 side effects, 137 signal and noise, 311 significance, 167 statistical, 164–67, 170 Silicon Valley, 288, 289 simulations, 193–95 simultaneous invention, 291–92 Singapore math, 23–24 Sir David Attenborough, RSS, 35 Skeptics Society, 133 sleep meditation app, 162–68 slippery slope argument, 235 slow (high-concentration) thinking, 30, 33, 70–71 small numbers, law of, 143, 144 smartphones, 117, 290, 309, 310 smoking, 41, 42, 133–34, 139, 173 Snap, 299 Snowden, Edward, 52, 53 social engineering, 97 social equality, 117 social media, 81, 94, 113, 217–19, 241 Facebook, 18, 36, 94, 119, 219, 233, 247, 305, 308 Instagram, 220, 247, 291, 310 YouTube, 220, 291 social networks, 117 Dunbar’s number and, 278 social norms versus market norms, 222–24 social proof, 217–20, 229 societal change, 100–101 software, 56, 57 simulations, 192–94 solitaire, 195 solution space, 97 Somalia, 243 sophomore slump, 145–46 South Korea, 229, 231, 238 Soviet Union: Germany and, 70, 238–39 Gosplan in, 49 in Cold War, 209, 235 space exploration, 209 spacing effect, 262 Spain, 243–44 spam, 37, 161, 192–93, 234 specialists, 252–53 species, 120 spending, 38, 74–75 federal, 75–76 spillover effects, 41, 43 sports, 82–83 baseball, 83, 145–46, 289 football, 226, 243 Olympics, 209, 246–48, 285 Spotify, 299 spreadsheets, 179, 180, 182, 299 Srinivasan, Balaji, 301 standard deviation, 149, 150–51, 154 standard error, 154 standards, 93 Stanford Law School, x Starbucks, 296 startup business idea, 6–7 statistics, 130–32, 146, 173, 289, 297 base rate in, 157, 159, 160 base rate fallacy in, 157, 158, 170 Bayesian, 157–60 confidence intervals in, 154–56, 159 confidence level in, 154, 155, 161 frequentist, 158–60 p-hacking in, 169, 172 p-values in, 164, 165, 167–69, 172 standard deviation in, 149, 150–51, 154 standard error in, 154 statistical significance, 164–67, 170 summary, 146, 147 see also data; experiments; probability distributions Staubach, Roger, 243 Sternberg, Robert, 290 stock and flow diagrams, 192 Stone, Douglas, 19 stop the bleeding, 234 strategy, 107–8 exit, 242–43 loss leader, 236–37 pivoting and, 295–96, 298–301, 308, 311, 312 tactics versus, 256–57 strategy tax, 103–4, 112 Stiglitz, Joseph, 306 straw man, 225–26 Streisand, Barbra, 51 Streisand effect, 51, 52 Stroll, Cliff, 290 Structure of Scientific Revolutions, The (Kuhn), 24 subjective versus objective, in organizational culture, 274 suicide, 218 summary statistics, 146, 147 sunk-cost fallacy, 91 superforecasters, 206–7 Superforecasting (Tetlock), 206–7 super models, viii–xii super thinking, viii–ix, 3, 316, 318 surface area, 122 luck, 122, 124, 128 surgery, 136–37 Surowiecki, James, 203–5 surrogate endpoint, 137 surveys, see polls and surveys survivorship bias, 140–43, 170, 272 sustainable competitive advantage, 283, 285 switching costs, 305 systematic review, 172, 173 systems thinking, 192, 195, 198 tactics, 256–57 Tajfel, Henri, 127 take a step back, 298 Taleb, Nassim Nicholas, 2, 105 talk past each other, 225 Target, 236, 252 target, measurable, 49–50 taxes, 39, 40, 56, 104, 193–94 T cells, 194 teams, 246–48, 275 roles in, 256–58, 260 size of, 278 10x, 248, 249, 255, 260, 273, 280, 294 Tech, 83 technical debt, 56, 57 technologies, 289–90, 295 adoption curves of, 115 adoption life cycles of, 116–17, 129, 289, 290, 311–12 disruptive, 308, 310–11 telephone, 118–19 temperature: body, 146–50 thermostats and, 194 tennis, 2 10,000-Hour Rule, 261 10x individuals, 247–48 10x teams, 248, 249, 255, 260, 273, 280, 294 terrorism, 52, 234 Tesla, Inc., 300–301 testing culture, 50 Tetlock, Philip E., 206–7 Texas sharpshooter fallacy, 136 textbooks, 262 Thaler, Richard, 87 Theranos, 228 thermodynamics, 124 thermostats, 194 Thiel, Peter, 72, 288, 289 thinking: black-and-white, 126–28, 168, 272 convergent, 203 counterfactual, 201, 272, 309–10 critical, 201 divergent, 203 fast (low-concentration), 30, 70–71 gray, 28 inverse, 1–2, 291 lateral, 201 outside the box, 201 slow (high-concentration), 30, 33, 70–71 super, viii–ix, 3, 316, 318 systems, 192, 195, 198 writing and, 316 Thinking, Fast and Slow (Kahneman), 30 third story, 19, 92 thought experiment, 199–201 throwing good money after bad, 91 throwing more money at the problem, 94 tight versus loose, in organizational culture, 274 timeboxing, 75 time: management of, 38 as money, 77 work and, 89 tipping point, 115, 117, 119, 120 tit-for-tat, 214–15 Tōgō Heihachirō, 241 tolerance, 117 tools, 95 too much of a good thing, 60 top idea in your mind, 71, 72 toxic culture, 275 Toys “R” Us, 281 trade-offs, 77–78 traditions, 275 tragedy of the commons, 37–40, 43, 47, 49 transparency, 307 tribalism, 28 Trojan horse, 228 Truman Show, The, 229 Trump, Donald, 15, 206, 293 Trump: The Art of the Deal (Trump and Schwartz), 15 trust, 20, 124, 215, 217 trying too hard, 82 Tsushima, Battle of, 241 Tupperware, 217 TurboTax, 104 Turner, John, 127 turn lemons into lemonade, 121 Tversky, Amos, 9, 90 Twain, Mark, 106 Twitter, 233, 234, 296 two-front wars, 70 type I error, 161 type II error, 161 tyranny of small decisions, 38, 55 Tyson, Mike, 7 Uber, 231, 275, 288, 290 Ulam, Stanislaw, 195 ultimatum game, 224, 244 uncertainty, 2, 132, 173, 180, 182, 185 unforced error, 2, 10, 33 unicorn candidate, 257–58 unintended consequences, 35–36, 53–55, 57, 64–65, 192, 232 Union of Concerned Scientists (UCS), 306 unique value proposition, 211 University of Chicago, 144 unknown knowns, 198, 203 unknowns: known, 197–98 unknown, 196–98, 203 urgency, false, 74 used car market, 46–47 U.S.

Essentialism: The Disciplined Pursuit of Less by Greg McKeown

90 percent rule, Albert Einstein, Clayton Christensen, Daniel Kahneman / Amos Tversky, David Sedaris, deliberate practice, double helix, en.wikipedia.org, endowment effect, impact investing, Isaac Newton, iterative process, Jeff Bezos, Lao Tzu, lateral thinking, loss aversion, low cost airline, Mahatma Gandhi, microcredit, minimum viable product, Nelson Mandela, North Sea oil, Peter Thiel, power law, Ralph Waldo Emerson, Richard Thaler, Rosa Parks, Salesforce, Shai Danziger, side project, Silicon Valley, Silicon Valley startup, sovereign wealth fund, Stanford prison experiment, Steve Jobs, TED Talk, Vilfredo Pareto

Sometimes what you don’t do is just as important as what you do.”6 In short, he makes big bets on the essential few investment opportunities and says no to the many merely good ones.7 Some believe the relationship between efforts and results is even less linear, following what scientists call a “power law.” According to the power law theory, certain efforts actually produce exponentially more results than others. For example, as Nathan Myhrvold, the former chief technology officer for Microsoft, has said (and then confirmed to me in person), “The top software developers are more productive than average software developers not by a factor of 10X or 100X or even 1,000X but by 10,000X.”8 It may be an exaggeration, but it still makes the point that certain efforts produce exponentially better results than others.

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Joseph Moses Juran, Quality-Control Handbook (New York: McGraw Hill, 1951). 3. I originally wrote this in a blog post for the Harvard Business Review, called “The Unimportance of Practically Everything,” May 29, 2012 4. Richard Koch, The 80/20 Principle: The Secret of Achieving More with Less (London: Nicholas Brealey, 1997); The Power Laws (London: Nicholas Brealey, 2000), published in the United States as The Natural Laws of Business (New York: Doubleday, 2001); The 80/20 Revolution (London: Nicholas Brealey, 2002), published in the United States as The 80/20 Individual (New York: Doubleday, 2003); and Living the 80/20 Way (London: Nicholas Brealey, 2004). 5.

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

“The curve does not fall smoothly from most common to least common word,” Mandelbrot observed. “It plunges vertiginously at first, then declines more slowly—like the profile of a ski jumper leaping into space, to land and coast down the gentler slope below.”1 Such statistical distributions have become known as “power laws,” because one variable is exponentially related to the other. These patterns, which allow far more room for outliers than the standard bell curve, had first been observed around the turn of the nineteenth century in the distribution of wealth,2 and it was the statistics of wealth and income that Mandelbrot studied.

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He authored a paper that appeared not long after Samuelson’s in 1965 showing mathematically that a random market would be a rational one.3 “The first period was very nice,” Mandelbrot recalled. “They were receptive, but with an ominous cloud.” The “cloud” was the frustration that developed among economists as they discovered how hard it was to work with Mandelbrot’s power laws. In his depiction of security price movements, variance—the measure of how widely scattered the different data points are—was infinite. For scholars who were just getting acquainted with Markowitz’s depiction of portfolio selection as a tradeoff between mean and variance, infinity was not helpful.

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To make sense of the fat tails in stock price data observed by Mandelbrot, for example, Rosenberg demonstrated in 1972 that one could account for most of them by cobbling together a series of different bell curves, and using economic data to predict when you were moving from one normal distribution to another. This may sound awfully complicated, but it was easier to work with than Mandelbrot’s power laws. Rosenberg never got around to publishing his insight, and a decade later another economist, Robert Engle, arrived independently at the same idea. Engle won a Nobel Prize for it in 2002. Rosenberg didn’t have time to see the paper into print because he was building a consulting business upon his ideas.

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

A Pareto-Levy distribution does not provide them with such luxury. For economic discussions on the ideas of Pareto, see Zajdenweber (2000), Bouvier (1999). For a presentation of the mathematics of Pareto-Levy distributions, see Voit (2001), and Mandelbrot (1997). There is a recent rediscovery of power law dynamics. Intuitively a power law distribution has the following property: If the power exponent were 2, then there would be 4 times more people with an income higher than $1 million than people with $2 million. The effect is that there is a very small probability of having an event of an extremely large deviation.

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The more connected a network, the higher the probability of someone hitting it and the more connected it will be, especially if there is no meaningful limitation on such capacity. Note that it is sometimes foolish to look for precise “critical points” as they may be unstable and impossible to know except, like many things, after the fact. Are these “critical points” not quite points but progressions (the so-called Pareto power laws)? While it is clear that the world produces clusters it is also sad that these may be too difficult to predict (outside of physics) for us to take their models seriously. Once again the important fact is knowing the existence of these nonlinearities, not trying to model them. The value of the great Benoit Mandelbrot’s work lies more in telling us that there is a “wild” type of randomness of which we will never know much (owing to their unstable properties).

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By some argument, the boss of the company may be unskilled labor but one who presents the necessary attributes of charisma and the package that makes for good MBA talk. In other words, he may be subjected to the monkey-on-the-typewriter problem. There are so many companies doing all kinds of things that some of them are bound to make “the right decision.” It is a very old problem. It is just that, with the acceleration of the power law–style winner-takes-all effects in our environment, such differences in outcomes are more accentuated, more visible, and more offensive to people’s sense of fairness. In the old days, the CEO was getting ten to twenty times what the janitor earned. Today, he can get several thousand times that. I am excluding entrepreneurs from this discussion for the obvious reason: These are people who stuck their necks out for some idea, and risked belonging to the vast cemetery of those who did not make it.

Handbook of Modeling High-Frequency Data in Finance by Frederi G. Viens, Maria C. Mariani, Ionut Florescu

algorithmic trading, asset allocation, automated trading system, backtesting, Bear Stearns, Black-Scholes formula, book value, Brownian motion, business process, buy and hold, continuous integration, corporate governance, discrete time, distributed generation, fear index, financial engineering, fixed income, Flash crash, housing crisis, implied volatility, incomplete markets, linear programming, machine readable, mandelbrot fractal, market friction, market microstructure, martingale, Menlo Park, p-value, pattern recognition, performance metric, power law, principal–agent problem, random walk, risk free rate, risk tolerance, risk/return, short selling, statistical model, stochastic process, stochastic volatility, transaction costs, value at risk, volatility smile, Wiener process

., box size) in a log–log plot reveals that the fluctuations can be characterized by a scaling exponent (α), the slope of the line relating log F (n) to log n. For data series with no correlations or short-range correlation, α is expected to be 0.5. For data series with long-range power law correlations, α would lie between 0.5 and 1 and for power law anticorrelations; α would lie between 0 and 0.5. This method was used to measure correlations in financial series of high frequencies and in the daily evolution of some of the most relevant indices. 6.2.4 STATIONARITY AND UNIT-ROOT TEST In order to study the fractional behavior of a times series using the R/S or the DFA analysis, it is important to investigate whether the underlying time series is stationary or not.

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In this case, the characteristic function takes the form: α ϕ(q) = e−γ |q| (6.2) As the characteristic function of a distribution is its Fourier transform, the stable distribution of index α and scale factor γ is 1 PL (x) ≡ π ∞ α e−γ |q| cos(qx) dq (6.3) 0 The asymptotic behavior of the distribution for large values of the absolute value of x is given by 123 6.2 Methods Used for Data Analysis PL (|x|) ≈ γ (1 + α) sin(πα/2) ≈ |x|−(1+α) π|x|1+α (6.4) and the value in zero PL (x = 0) by PL (x = 0) = (1/α) παγ 1/α (6.5) The fact that the asymptotic behavior for huge values of x is a power law has as a consequence that the stable Levy processes have infinite variance. To avoid the problems arising in the infinite second moment, Mantegna and Stanley [19] considered a stochastic process with finite variance that follows scale relations called TLF . The TLF distribution is defined by ⎧ ⎪ x>l ⎨0 (6.6) P(x) = cPL (x) −l <x <l ⎪ ⎩0 x < −l where PL (x) is a symmetric Levy distribution and c is a normalization constant.

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Peng CK, Havlin S, Stanley HE, Goldberger AL. In: Glass L, editor. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series, Chaos, Vol. 5; 1995. p 82–87 [Proceedings of NATO Dynamical Disease Conference]. 34. Koscienly-Bunde E, Roman HE, Bunde A, Havlin S, Schellnhuber HJ. Longrange power-law correlations in local daily temperature fluctuations. Philos Mag B 1998;77:1331–1339. 35. Koscienly-Bunde E, Bunde A, Havlin S, Roman HE, Goldreich Y, Schellnhuber HJ. Indication of universal persistence law governing atmospheric variability. Phys Rev Lett 1998;81:729–732. 36. Kantelhardt JW, Berkovits R, Havlin S, Bunde A.

The Inner Lives of Markets: How People Shape Them—And They Shape Us by Tim Sullivan

Abraham Wald, Airbnb, airport security, Al Roth, Alvin Roth, Andrei Shleifer, attribution theory, autonomous vehicles, barriers to entry, behavioural economics, Brownian motion, business cycle, buy and hold, centralized clearinghouse, Chuck Templeton: OpenTable:, classic study, clean water, conceptual framework, congestion pricing, constrained optimization, continuous double auction, creative destruction, data science, deferred acceptance, Donald Trump, Dutch auction, Edward Glaeser, experimental subject, first-price auction, framing effect, frictionless, fundamental attribution error, George Akerlof, Goldman Sachs: Vampire Squid, Gunnar Myrdal, helicopter parent, information asymmetry, Internet of things, invisible hand, Isaac Newton, iterative process, Jean Tirole, Jeff Bezos, Johann Wolfgang von Goethe, John Nash: game theory, John von Neumann, Joseph Schumpeter, Kenneth Arrow, late fees, linear programming, Lyft, market clearing, market design, market friction, medical residency, multi-sided market, mutually assured destruction, Nash equilibrium, Occupy movement, opioid epidemic / opioid crisis, Pareto efficiency, Paul Samuelson, Peter Thiel, pets.com, pez dispenser, power law, pre–internet, price mechanism, price stability, prisoner's dilemma, profit motive, proxy bid, RAND corporation, ride hailing / ride sharing, Robert Shiller, Robert Solow, Ronald Coase, school choice, school vouchers, scientific management, sealed-bid auction, second-price auction, second-price sealed-bid, sharing economy, Silicon Valley, spectrum auction, Steve Jobs, Tacoma Narrows Bridge, techno-determinism, technoutopianism, telemarketer, The Market for Lemons, The Wisdom of Crowds, Thomas Malthus, Thorstein Veblen, trade route, transaction costs, two-sided market, uber lyft, uranium enrichment, Vickrey auction, Vilfredo Pareto, WarGames: Global Thermonuclear War, winner-take-all economy

Among Pareto’s enduring contributions were his incisive observations on the distribution of income. Building from his calculation that the richest 20 percent of Italians owned 80 percent of the country’s land, Pareto posited that incomes in an economy tend to be distributed according to a “power law.” (Power law distributions will often generate extreme inequality, making Pareto an unlikely hero of the Occupy movement.) Most memorably, though, he used his mathematical skills to extend Smith’s invisible hand arguments, introducing a particular criterion by which economists could assess social well-being.5 This welfare principle, named Pareto efficiency by British economist I.

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Woods store, 1–2 person’s life, value of, 166–167 philanthropic commitments, 72–75 Pillow Pets, 128–129 platforms babysitting, 121 Champagne fairs as, 126–128 competition, 124–126 credit card, 113–116 economics of, 107–112 greed in, 128–129 mobile market, 116 multisided, 14 rules for, 112–117 video game system, 116 See also economics Podolny, Joel, 39, 43 poker, bluffing in, 26 See also chess; Cold War Pontiff, Jeffrey, 11–12 posting system, 79–81, 100–101 POW camps, 7–13, 175–177 power law distributions, 22 practice, market, 14–15 Prendergast, Canice, 154–160 “Price and Advertising Signals of Product Quality” (Milgrom and Roberts), 70–71 price discovery, 83 priceless, when something is, 132–133 prisoners’ dilemma game, 178–179 property, expected value of, 56 Radford, R. A., 7–10, 22–23 Ranau Japanese POW camp, 10–11 RAND Corporation, 25, 27, 134–136 reality-based economic modeling, 35–37, 49–51, 141 See also lemon markets theory recessions, 36, 48, 75 Roberts, John, 66, 70–71 Ross, Lee, 177–179 Roth, Al, 140, 141, 163–165 rush, fraternity/sorority, 140 Rutland, VT, 1 Rysman, Marc, 109 Samuelson, Paul, 28–29, 44 Samuelson, William, 55–57 San Fernando Valley gangs, 61–62 San Fers gang, 61–62 Sandakan camp, Borneo, 10–11 Sauget, IL, 168–169 scams internet, 52–55 money-back, 69–70 Scarf, Herbert, 163–164 school choice, in Sweden, 151–152 school to student matching, 138–139, 141–142, 143–149 Schultz, Theodore, 35 Schumpeter, Joseph, 24, 49–50 Scottish auctions, 82 Sears, 115–116 second-bid auction, 81–82 second-price sealed-bid auctions, 87–89 “Selection process starts with choices, ends with luck” (article), 146 self-destructive behaviors, signaling theory and, 67–68 selfish, markets making us, 177–179 seller misrepresentation, 52–55 sellers, knowing more than buyers, 41, 44–55 Seven Minute Abs, 172 Shakin’ Cat Midgets gang, 61 Shapley, Lloyd, 134–136, 137–138, 163–164 Shapley-Gale algorithm, 137–140 Shi, Peng, 148 Shleifer, Andrei, 180–181 shopping malls, as two-sided markets, 122–123 Shoup, Carl, 85 sick organizations, 142–143 signaling model applications of, 66–68 commitment signs, 62–66 competitive signaling, 69–71 integrity, 71–75 Silicon Valley, market friction and, 169–173 Skoll, Jeff, 39–40, 43, 51 Smith, Adam, 21 Snider, James, 42 social efficiency, auctions, 89 social well-being, assessing, 22 Solow, Robert, 35 Solow model, 35 Sönmez, Tayfun, 144 Sony’s Blu-ray format war, 125–126 sorority rush, 140 spectrum auction theory, 102–103 Spence, Michael, 62–66 Stack, Charles, 42–43 Stalag VII-A POW camp market, 5–6, 7–10, 13 stamp collecting, 82–84 Stiglitz, Joseph, 35–36, 76, 182 strategy proofness mechanism, 145 student to school matching, 138–139, 141–142, 143–149 Summers, Larry, 166–167 Super Bowl advertising, 70–71 supply and demand, 96 survival rates, of Japanese vs.

Who's Your City?: How the Creative Economy Is Making Where to Live the Most Important Decision of Your Life by Richard Florida

Abraham Maslow, active measures, assortative mating, back-to-the-city movement, barriers to entry, big-box store, blue-collar work, borderless world, BRICs, business climate, Celebration, Florida, correlation coefficient, creative destruction, dark matter, David Brooks, David Ricardo: comparative advantage, deindustrialization, demographic transition, edge city, Edward Glaeser, epigenetics, extreme commuting, financial engineering, gentrification, Geoffrey West, Santa Fe Institute, happiness index / gross national happiness, high net worth, income inequality, industrial cluster, invention of the telegraph, Jane Jacobs, job satisfaction, Joseph Schumpeter, knowledge economy, knowledge worker, low skilled workers, megacity, new economy, New Urbanism, Peter Calthorpe, place-making, post-work, power law, Richard Florida, risk tolerance, Robert Gordon, Robert Shiller, Seaside, Florida, Silicon Valley, Silicon Valley startup, superstar cities, The Death and Life of Great American Cities, the strength of weak ties, The Wealth of Nations by Adam Smith, Thomas L Friedman, Tyler Cowen, urban planning, World Values Survey, young professional

To test this idea, the researchers collected data from the United States, Europe, and China at a variety of times, and looked at a wide range of characteristics, such as crime rate, disease transmission, demographics, infrastructure energy consumption, economic activity, and innovation. Sure enough: “Social organizations, like biological organisms, consume energy and resources, depend on networks for the flow of information and materials, and produce artifacts and waste. . . . Cities manifest power-law scaling similar to the economy-of-scale relationships observed in biology: a doubling of population requires less than a doubling of certain resources. The material infrastructure that is analogous to biological transport networks—gas stations, lengths of electrical cable, miles of road surface—consistently exhibits sublinear [less than one] scaling with population.”

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While they tend to last longer, even the largest megaregions can eventually decline. This model is a near perfect simulation of our world today. Creative people and their firms cluster tightly to form the top of a hierarchy of city regions in a way that strikingly reflects George Zipf’s famous power law.9 In the middle of the distribution, individual cities and regions constantly vie for prime spots, while at the top there is far less moving around. This is more than a hierarchy of places. It is a hierarchy of productivity rates, metabolic rates, and costs. Places at the top are more productive, operate at faster speed, and are more expensive than those further down the hierarchy.

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Pittsburgh Pittsburgh Post-Gazette Pixar Place aesthetics of attribute clusters for basic services of career choice influencing children and choosing class division and death of economic activity and economic stability and empty nesters/retirees and evaluating family and freedom to choose getting around and globalization and happiness and importance of industry and key factors for leadership of Leamer on life stages and marriage and offerings of personality and Porter on pride in research on setting priorities for short-listing for spark factor for technology and trade-offs in types of values of venture capital and visiting wrong Place and Happiness Survey basic services in culture/nightlife in fit in key factors identified by key results from leadership in meeting people in New Orleans and occupation and openness in physical environment in safety/security in United States differences with global cities in Place pyramid(fig.) Poona Popsicle Index Population density(fig.) Population growth Porter, Michael Portland, Oregon housing in openness and Positive psychology Postindustrial society Postrel, Virginia Powdthavee, Nattavudh Power law Prada Prague(fig.) Preferential attachment Princeton Productivity clustering and creative Psychosocial environment Public transportation Putnam, Robert Quality of life rankings of Quarterly Journal of Economics Quebec City Queen’s University Raconteurs, The Railroads Ratner, Albert Real estate globalization of innovation and mobility limited by price factors in stickiness of superstar cities and unemployment and Real Networks REI Relationships, happiness and Relocating Rentfrow, Jason Research in Motion Research Triangle Retirees Reykjavik(fig.)

Designing Social Interfaces by Christian Crumlish, Erin Malone

A Pattern Language, Amazon Mechanical Turk, anti-pattern, barriers to entry, c2.com, carbon footprint, cloud computing, collaborative editing, commons-based peer production, creative destruction, crowdsourcing, en.wikipedia.org, Firefox, folksonomy, Free Software Foundation, game design, ghettoisation, Howard Rheingold, hypertext link, if you build it, they will come, information security, lolcat, Merlin Mann, Nate Silver, Network effects, Potemkin village, power law, recommendation engine, RFC: Request For Comment, semantic web, SETI@home, Skype, slashdot, social bookmarking, social graph, social software, social web, source of truth, stealth mode startup, Stewart Brand, systems thinking, tacit knowledge, telepresence, the long tail, the strength of weak ties, The Wisdom of Crowds, web application, Yochai Benkler

Instead, consider calling out only the most remarkable levelholders in the community (“Level 10 Contributor!”). Exclusivity Exclusivity in the Numbered Levels pattern relates to the distribution of reputations across the available levels. Ideally, from the high end of the register to the low, your numbered levels should follow a power-law distribution. (For a good general discussion of power laws in a social web context, see Clay Shirky’s “Power Laws, Weblogs, and Inequality” at http://www.shirky.com/writings/powerlaw_weblog.html.) Examples World of Warcraft tracks an individual’s progress via a numbered level (Figure 6-5). Download at WoweBook.Com 162 Chapter 6: Would You Buy a Used Car from This Person?

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By itself, a widget that asks people to compare friends doesn’t get you much, but if you can accumulate a data store with a rich web of crowdsourced comparisons, then you can start calculating some, well, rankings, and publish or display them in an attempt to spur further engagement with your service. Reputation interfaces like the one shown in Figure 6-27 present the known issues of leaderboards, and more broadly demonstrate the way social networks cluster around highly connected “hub” people who then end up getting recommended to everyone or singled out in a power law–driven, self-perpetuating trend. Figure 6-27. Another friend-ranking tool powered by Facebook notified me by email of the Top 10 most trusted (and by extension, it reasons, most powerful) friends in my network. Download at WoweBook.Com Further Reading 185 Further Reading “I Love My Chicken Wire Mommy,” by Ben Brown, http://benbrown.com/says/2007/10/29/i-love-my-chicken-wire-mommy/ “Is Harriet Klausner for real?

Doing Good Better: How Effective Altruism Can Help You Make a Difference by William MacAskill

barriers to entry, basic income, behavioural economics, Black Swan, Branko Milanovic, Cal Newport, Capital in the Twenty-First Century by Thomas Piketty, carbon footprint, clean water, corporate social responsibility, correlation does not imply causation, Daniel Kahneman / Amos Tversky, David Brooks, Edward Jenner, effective altruism, en.wikipedia.org, end world poverty, experimental subject, follow your passion, food miles, immigration reform, income inequality, index fund, Intergovernmental Panel on Climate Change (IPCC), Isaac Newton, job automation, job satisfaction, Lean Startup, M-Pesa, mass immigration, meta-analysis, microcredit, Nate Silver, Peter Singer: altruism, power law, public intellectual, purchasing power parity, quantitative trading / quantitative finance, randomized controlled trial, self-driving car, Skype, Stanislav Petrov, Steve Jobs, Steve Wozniak, Steven Pinker, The Future of Employment, The Wealth of Nations by Adam Smith, Tyler Cowen, universal basic income, William MacAskill, women in the workforce

“even those of us labeled as ‘aid critics’”: William Easterly, “Some Cite Good News on Aid,” Aid Watch, February 18, 2009, http://aidwatchers.com/2009/02/some-cite-good-news-on-aid/. Look at the following graph: This graph uses the same data as for the one in chapter one. most people live in a small number of cities: For this and the other examples mentioned, see Mark E. J. Newman, “Power Laws, Pareto Distributions and Zipf’s Law,” Contemporary Physics 46, no. 5 (2005), 323–51. The effectiveness of different aid activities forms a fat-tailed distribution: Ramanan Laxminarayan, Jeffrey Chow, and Sonbol A. Shahid-Salles, “Intervention Cost-Effectiveness: Overview of Main Messages,” in Dean Jamison et al.

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The situation could be exacerbated if geoengineering, previously used to cool the planet, was discontinued during the societal collapse, which could cause even more warming. Even in a situation of this sort it is unlikely that the human race would end, however. (the death tolls from disasters form a fat-tailed distribution): A comprehensive overview is given by Anders Sandberg, “Power Laws in Global Catastrophic and Existential Risks,” unpublished paper, 2014. (Nassim Taleb describes these as Black Swans): Nassim Nicholas Taleb, The Black Swan: The Impact of the Highly Improbable (New York: Random House, 2007). most people who’ve died in war have died in the very worst wars: Steven Pinker, The Better Angels of Our Nature: Why Violence Has Declined (New York: Viking, 2011).

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this field has improved our ability to cause desirable behavior change: For examples, see “Poor Behaviour: Behavioural Economics Meets Development Policy,” The Economist, December 6, 2014, and Dean Karlan and Jacob Appel, More Than Good Intentions: How a New Economics Is Helping to Solve Global Poverty (New York: Dutton, 2011). the distribution of book sales: Newman, “Power Laws,” 5. as is the distribution of Twitter follower counts: State of the Social Media Marketing Industry, HubSpot, January 2010, http://www.hubspot.com/Portals/53/docs/01.10.sot.report.pdf. the main reason they use volunteers: See Holden Karnofsky, “Is Volunteering Just a Show?” GiveWell Blog, November 12, 2008, http://blog.givewell.org/2008/11/12/is-volunteering-just-a-show/.

Frequently Asked Questions in Quantitative Finance by Paul Wilmott

Abraham Wald, Albert Einstein, asset allocation, beat the dealer, Black-Scholes formula, Brownian motion, butterfly effect, buy and hold, capital asset pricing model, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, currency risk, delta neutral, discrete time, diversified portfolio, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial engineering, fixed income, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, iterative process, lateral thinking, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, martingale, Myron Scholes, Norbert Wiener, Paul Samuelson, power law, quantitative trading / quantitative finance, random walk, regulatory arbitrage, risk free rate, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, transaction costs, urban planning, value at risk, volatility arbitrage, volatility smile, Wiener process, yield curve, zero-coupon bond

As long as none of the random variables has too much more impact on the average than the others then it still works. You are even allowed to have some weak dependence between the variables. A generalization that is important in finance applies to distributions with infinite variance. If the tails of the individual distributions have a power-law decay, |x|−1−α with 0 < α < 2 then the average will tend to a stable Lévy distribution. If you add random numbers and get normal, what happens when you multiply them? To answer this question we must think in terms of logarithms of the random numbers. Logarithms of random numbers are themselves random (let’s stay with logarithms of strictly positive numbers).

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Mean. a Variance Note that the nth moment only exists if c > n. Pareto Bounded below, unbounded above. It has two parameters: a > 0, scale; b > 0 shape. Its probability density function is given by Student’s t Pareto Commonly used to describe the distribution of wealth, this is the classical power-law distribution. Mean Variance Note that the nth moment only exists if b > n. Uniform Bounded below and above. It has two location parameters, a and b. Its probability density function is given by Uniform Mean Variance Inverse normal Bounded below, unbounded above. It has two parameters: a > 0, location; b > 0 scale.

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From Itô we have Therefore the expected return on the option is and the risk is Since both the underlying and the option must have the same compensation, in excess of the risk-free rate, for unit risk Now rearrange this. The µ drops out and we are left with the Black-Scholes equation. Utility Theory The utility theory approach is probably one of the least useful of the ten derivation methods, requiring that we value from the perspective of an investor with a utility function that is a power law. This idea was introduced by Rubinstein (1976). The steps along the way to finding the Black-Scholes formulæ are as follows. We work within a single-period framework, so that the concept of continuous hedging, or indeed anything continuous at all, is not needed. We assume that the stock price at the terminal time (which will shortly also be an option’s expiration) and the consumption are both lognormally distributed with some correlation.

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 tails of the Pareto as well as the α-stable distribution decay at a rate with fixed power α, x-α (i.e., power law), which is in contrast to the normal distribution whose tails decay at an exponential rate (i.e., roughly e − x2 / 2). We illustrate the effect focusing on the probability of exceeding some value x somewhere in the upper tail, say x = 3. Moreover, we choose the parameter of stability to be α = 1.5. under the normal law, the probability of exceedance is roughly e−32 /2 = 0.011 while under the power law it is about 3-1.5 = 0.1925. Next, we let the benchmark x become gradually larger. Then the probability of assuming a value at least twice or four times as large (i.e., 2x or 4x) is roughly or for the normal distribution.

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Then the probability of assuming a value at least twice or four times as large (i.e., 2x or 4x) is roughly or for the normal distribution. In contrast, under the power law, the same exceedance probabilities would be (2 × 3)-1.5 = 0.068 or (4 × 3)-1.5 ≈ 0.024. This is a much slower rate than under the normal distribution. Note that the value of x = 3 plays no role for the power tails while the exceedance probability of the normal distribution decays the faster the further out we are in the tails (i.e., the larger is x). The same reasoning applies to the lower tails considering the probability of falling below a benchmark x rather than exceeding it.

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CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION) Heavy tails Generalized extreme value distributions Standardized data Extreme value theory Gumbel distribution Fréchet distribution Weibull distribution Generalized Pareto distribution Normal inverse Gaussian distribution Bessel function of the third kind Scaling property α-stable distributions Stable distributions Tail index Characteristic exponent Excess kurtosis Power law Skewness Scale Location Stability property Generalized central limit theorem CHAPTER 13 Parameters of Location and Scale of Random Variables In the previous four chapters, we presented discrete and continuous probability distributions. It is common to summarize distributions by various measures.

Starstruck: The Business of Celebrity by Currid

barriers to entry, Bernie Madoff, Big Tech, Donald Trump, income inequality, index card, industrial cluster, Mark Zuckerberg, Metcalfe’s law, natural language processing, place-making, Ponzi scheme, post-industrial society, power law, prediction markets, public intellectual, Renaissance Technologies, Richard Florida, Robert Metcalfe, Robert Solow, rolodex, search costs, shareholder value, Silicon Valley, slashdot, Stephen Fry, the long tail, The Theory of the Leisure Class by Thorstein Veblen, transaction costs, Tyler Cowen, upwardly mobile, urban decay, Vilfredo Pareto, Virgin Galactic, winner-take-all economy

Harvard Business Review (November–December 1998): 77–90. Preston, Peter. “A Dozen Reasons to Be Cheerful About the State of the British Media.” Observer, December 27, 2009. Reed, David. “The Law of the Pack.” Harvard Business Review (February 2001): 23–24. Reed, William J. “The Pareto, Zipf and Other Power Laws.” Economics Letters 74, no. 1 (2001): 15–19. Rein, Irving, Philip Kotler, Michael Hamlin, and Martin Stoller. High Visibility: Transforming Your Personal and Professional Brand. 3rd ed. New York: McGraw-Hill, 2005. Rice, Lynette. “TLC Halts Production on ‘Jon and Kate Plus 8.’” Entertainment Weekly, October 1, 2009. http://news-briefs.ew.com/2009/10/01/tlc-halts-production-on-jon-and-kate-plus-8/. ———.

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While some results point toward a median of 5.5 and others may report 7 connections, on the whole the average is about 6. 7. Overall, the Getty Images photographic network exhibits the characteristics of a small-world network and properties of a scale-free network (see Appendix B). Scale-free networks possess power law distribution connections between actors as compared to random-network connections. Most people photographed in the Getty database (95 percent) are connected to fewer than five other people, but our “celebrity core” (the 6.5 percent of individuals photographed four or more times) tend to be very connected (possessing greater than 5 degrees).

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Social network analysts use the term “clustering coefficient” to measure the degree to which people are closely connected. 10. See Barabási, Linked. 11. Weinberg, “In Health-Care Reform, the 20–80 Solution.” 12. Gladwell, The Tipping Point; Pareto, “Manual of Political Economy” Reed, “The Pareto, Zipf and Other Power Laws.” 13. Barabási and Albert, “Emergence of Scaling in Random Networks.” For a more reader-friendly version of the phenomenon, see Barabási, Linked. In social network analysis, this network structure is called a “scale free network.” Such a network is present if the nodes’ degree frequency distributes according to the power distribution. 14.

Emergence by Steven Johnson

A Pattern Language, agricultural Revolution, AOL-Time Warner, Brewster Kahle, British Empire, Claude Shannon: information theory, complexity theory, Danny Hillis, Douglas Hofstadter, edge city, epigenetics, game design, garden city movement, Gödel, Escher, Bach, hive mind, Howard Rheingold, hypertext link, invisible hand, Jane Jacobs, Kevin Kelly, late capitalism, Lewis Mumford, Marshall McLuhan, mass immigration, Menlo Park, mirror neurons, Mitch Kapor, Murano, Venice glass, Naomi Klein, new economy, New Urbanism, Norbert Wiener, PalmPilot, pattern recognition, pez dispenser, phenotype, Potemkin village, power law, price mechanism, profit motive, Ray Kurzweil, SimCity, slashdot, social intelligence, Socratic dialogue, stakhanovite, Steven Pinker, The Death and Life of Great American Cities, The Wealth of Nations by Adam Smith, theory of mind, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, trickle-down economics, Turing machine, Turing test, urban planning, urban renewal, Vannevar Bush

It’s called a brain tumor. Still, in the midst of all that networked chaos, a few observers have begun to detect macropatterns in the Web’s development, patterns that are invisible to anyone using the Web, and thus mostly useless. The distribution of Web sites and their audiences appears to follow what is called a power law: the top ten most popular sites are ten times larger than the next hundred more popular sites, which are themselves ten times more popular than the next thousand sites. Other online cartographers have detected “hub” and “spoke” patterns in traffic flows. But none of these macroshapes, even if they do exist, actually makes the Web a more navigable or informative system.

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New York: Basic Books, 1997. Schelling, Thomas. Micromotives and Macrobehavior. New York and London: W. W. Norton, 1978. Schreiber, Darren. “The Emergence of Parties: An Agent-Based Model.” Online posting. www.swarm.org/community-links.html. March 20, 2000. Schroeder, Manfred. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W. H. Freeman and Co., 1991. Selfridge, O. G. “Pandemonium: A Paradigm for Learning.” In Mechanization of Thought Processes. Proceedings of a Symposium Held at the National Physical Laboratory in November 1958. London: Her Majesty’s Stationery Office, 1959.

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., 38, 52, 65, 117–23, 154, 169, 179, 218–20, 226, 237n global vs. local, 39–40, 74–80, 82, 86, 90, 93, 108–9, 218–19, 224 see also control Organic Art, 182 “organic clocks,” 20 organization: global, 224–26 goal-directed, 118 hierarchical, 15, 98, 132, 136, 145, 148–49, 153, 208, 223, 225, 263n–64n political, 67, 225–26 self-, see self-organization size limitations of, 259n–60n social, 9, 27, 33–41, 92–94, 97–100, 109, 204, 252n–54n see also systems OSS code, 175 Out of Control (Kelly), 168–69 pacemaker cells, 14–15, 16, 17, 23, 40, 64, 67, 164 PalmPilots, 54 “Pandemonium: A Paradigm for Learning” (Selfridge), 54 Pandemonium model, 53–57, 65, 169, 231 Papert, Seymour, 65, 164, 166 paradigm shift, 48–49, 64 Paradise Lost (Milton), 53–54 Pattern on the Stone, The (Hillis), 173 patterns: of behavior, see behavior development of, 49, 184–85, 246n feedback on, 40–41 of heredity, 46 hub-and-spoke, 119 letter, 54–57, 65 mathematical, 42 of movement, 18–20, 41, 168 musical, 45 recognition of, 18, 21, 22, 44–45, 52, 54–57, 65, 103–4, 123–24, 126–29, 199, 206, 220, 221, 226, 231, 233 social, 18, 36–40, 41, 49–50, 52, 91, 95, 137, 185 spatial, 20, 27, 48, 90–91, 159, 223 speech, 44–45 spontaneous, 180 temporal, 20, 27, 48, 91, 104–5 urban, 40–41, 90–91, 146, 147, 159, 223 “Perceptrons” (Minsky and Papert), 65 phase transitions, 111–12 phenotypes, 58, 59 pheromone, 52, 60–63, 64, 74, 75–76, 78, 79, 84–85, 98, 115, 167, 206, 226, 228–29, 243n–44n Phillips Interactive, 178 physics, 21, 105 Picasso, Pablo, 23 Pinker, Steven, 118 planets, rotation of, 46 “platform agonistic,” 139–40 Pleistocene era, 202, 262n plow, wheeled, 112 politics, 39–40, 67, 94–95, 161, 224–26, 264n population growth, 34, 99, 110–11, 112, 116, 164–65, 252n–53n pornography, 208 post-structuralism, 65 power law, 119 Powers of Ten, 231–32 predictions, 9, 47 Prelude, The (Wordsworth), 39 pricing, 155–56 Prigogine, Ilya, 43, 52, 64–65 prioritization, 78 probability theory, 46–47 problem-solving, 74, 79–80, 120, 126–27, 227–29, 251n–52n product placement, 214 programs, computer: artificial-life, 59–63, 65 branching paths in, 58 codes in, 169, 170–71, 173–74, 175, 180, 205–6 evolution of, 57–59, 60, 205–6 mini-, 170–74 number-sorting, 170–74, 209, 231 predator, 172–73 see also software proteins, 85 Proverbs, Book of, 71 “pseudo events,” 145 purchase circles, 221–22 Quake, 182, 183, 208–9 quality management, 67 racial diversity, 89, 95, 247n randomness, 19, 62, 77, 78–79, 87, 121, 163, 171, 220, 222–23, 244n, 247n recognition systems, 103 redwood forests, 258n reentry, neural, 256 reflexes, 38–39 Reliable Sources, 135 Renaissance, 101–2, 147 Replay, 211 “Residence in London” (Wordsworth), 27 Resnick, Mitch, 16–17, 23, 64, 76, 163–69, 180, 189, 260n Restak, Richard, 133–34 retina, 201 Rheingold, Howard, 148 Ridley, Matt, 82, 86 Rizzollati, Giaccamo, 198–99 Rockefeller Foundation, 46, 50 Roman Empire, 33, 109–10 Rosenstiel, Tom, 135 rules, 19, 180–81, 226 St.

Television disrupted: the transition from network to networked TV by Shelly Palmer

AOL-Time Warner, barriers to entry, call centre, commoditize, disintermediation, en.wikipedia.org, folksonomy, Golden age of television, hypertext link, interchangeable parts, invention of movable type, Irwin Jacobs: Qualcomm, James Watt: steam engine, Leonard Kleinrock, linear programming, Marc Andreessen, market design, Metcalfe’s law, pattern recognition, peer-to-peer, power law, recommendation engine, Saturday Night Live, shareholder value, Skype, spectrum auction, Steve Jobs, subscription business, Telecommunications Act of 1996, the long tail, There's no reason for any individual to have a computer in his home - Ken Olsen, Vickrey auction, Vilfredo Pareto, yield management

Key Takeaways • The practical exploitation of transactional databases is a goal of networked television, although pricing based on actual response metrics is extremely dispassionate and represents a seriously two-edged sword. • The 80/20 rule is the best way to evaluate ROI for back catalog. A power law like a Zipf ’s Distribution is an excellent way to evaluate demand. • Walled gardens are valuable assets, but as consumers acquire new, more powerful technology, they will start to push back. • Broadband is a commodity and will become even less expensive in the future. Copyright © 2006, Shelly Palmer.

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In order to maintain a competitive advantage, media providers are going to have to offer the benefit of “intelligent” media or consumers will switch to providers who can more adequately service their needs. However, there is a group of companies that don’t need to be told anything about the value of content, the long tail or how a power law might relate to consumer needs —the contact providers. Contact Providers Contact providers are not just search engines. Certainly Google enjoys an extraordinary market cap for a company that does not create any original content. (In practice, they do create some content, but the bulk of their business and most of their profit Copyright © 2006, Shelly Palmer.

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Lean forward Industry slang for using a computer leaning forward in your chair from about 2' away. Linear Channels Traditional television channels that broadcast one signal 24 hrs. a day. Long Tail The phrase The Long Tail (as a proper noun with capitalized letters) was first coined by Chris Anderson in a 2004 Wired Magazine article to describe a power law known as a Zipf ’s Distribution. Master File A database file, often created manually as needed, that contains static records used to identify items, customers, vendors, bills of material, work centers, etc. as opposed to files used to track the dynamic status of orders and inventory balances. Mb or MEGABIT 106 bits of information (usually used to express a data transfer rate; as in, 1 megabit/second = 1Mbps).

High-Frequency Trading by David Easley, Marcos López de Prado, Maureen O'Hara

algorithmic trading, asset allocation, backtesting, Bear Stearns, Brownian motion, capital asset pricing model, computer vision, continuous double auction, dark matter, discrete time, finite state, fixed income, Flash crash, High speed trading, index arbitrage, information asymmetry, interest rate swap, Large Hadron Collider, latency arbitrage, margin call, market design, market fragmentation, market fundamentalism, market microstructure, martingale, National best bid and offer, natural language processing, offshore financial centre, pattern recognition, power law, price discovery process, price discrimination, price stability, proprietary trading, quantitative trading / quantitative finance, random walk, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, Tobin tax, transaction costs, two-sided market, yield curve

Most models use common explanatory variables such as the size of the order relative to the average or median daily volume, the average participation rate during the execution interval and asset-specific attributes, such as spread and volatility. Price impact is either modelled using parametric functional forms involving power laws and decay kernels (Gatheral 2010; Obizhaeva and Wang 2013) or estimated non-parametrically for various buckets of order size and participation rate. We shall not discuss in detail the structure of these models here. Instead, we shall look at the realised cost of large order samples and break it down by the algorithm used for their execution.

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The ACF of trade signs is plotted in Figure 2.5 for a high (Microsoft Corp symbol: MSFT) and a medium (BEAM Inc symbol: BEAM) capitalisation stock. We note significant correlation over several lags, in particular for the high capitalisation stock. The autocorrelation of trade signs is due primarily to algorithms splitting large client orders (Tóth et al 2011). The log–log plot in Figure 2.5 provides evidence of a power law decay of the correlation ρ at lag h as ρ ∝ h−γ . We estimate the decay exponent γ = 0. 50 for MSFT and γ = 0. 65 for BEAM. The predictability of the trade signs means that an indicator that measures trade arrival separately for buy and sell trades will be relatively stable. Following Almgren (2006), we generalise the trade sign from the discrete variable with ±1 values to two continuous variables, the “askness” a and the “bidness” b, both within the [0, 1] range.

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Instead, we use the Kaplan–Meier estimator (sometimes also known as the product limit estimator), which is the maximum likelihood estimator for censored data (Ganchev et al 2010). Furthermore, since empirically the execution data frequently exhibits instances in which no submitted shares are executed, combined with occasional executions of large volumes (Figure 5.7), we adapt this estimator for a parametric model for the Pi that has the form of a power law with a separate parameter for zero shares. 119 i i i i i i “Easley” — 2013/10/8 — 11:31 — page 120 — #140 i i HIGH-FREQUENCY TRADING 3. For each desired volume V to execute, the algorithm simply behaves as if its current approximate distributions Pi are in fact the true liquidity distributions, and chooses the allocations Vi according to the greedy algorithm applied to the Pi .

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

Instead, I wrote a somewhat strange two-part dissertation for the Doctorat d’État ès Sciences, which was soon overtaken by far better work. But it largely determined the course of my life and—arguably—the work that led to changes in the course of several sciences. The first part of the dissertation concerned George Kingsley Zipf’s universal power law distribution for words. The other part was an incursion into the foundation of an ancient area of physics: generalized statistical thermodynamics. One of my models of word frequencies relied on that second part in a very exotic form. Unfortunately, this mixture was dreadful academic politics. More important, my thoughts in physics were still very much in flux.

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My luck was to begin with the distribution of word frequencies—a thoroughly atypical example without any important consequences, and uniquely easy to handle. Incidentally, in 1952, my first involvement with long tails involved no computers. I first saw a computer in 1953 and first used one in 1958, after I went to IBM. Zipf’s Universal Power Law for Words In written text or in speech, some words, such as “the” or “this,” have a well-defined frequency. Other words are so rarely used that they have no defined frequency. Here was Zipf’s game: Pick a text and count how many times each word appears in it. Then give each word a rank: 1 for the most common word, 2 for the second most common word, and so on.

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The fact that it applies to all languages—is universal—implies that Zipf’s law is irrelevant to the core of linguistics, which is grammar. In one of the very few clear-cut eureka moments of my life, I saw that it might be deeply linked to information theory and hence to statistical thermodynamics—and became hooked on power law distributions for life. Those “details” had eluded not only Zipf—not trained as a scientist or mathematician—but also Walsh. Anyhow, appreciating the history of ideas does not make a street-smart scientific explorer. My good fortune resided in an unfair advantage. I was to be the first—and for an interminable time, the only—trained mathematical scientist to take Zipf’s law seriously.

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

business climate, butterfly effect, complexity theory, Edward Lorenz: Chaos theory, impulse control, Lao Tzu, loose coupling, Louis Pasteur, Neil Armstrong, power law, systems thinking

But collapses of all sizes do happen with an inevitability that can be described mathematically as inversely proportional to some power of the size (with earthquakes it’s the 3/2 power, which curiously is the same power as the one used to determine the time that planets take to go around the sun: the square root of the cube of the size of the orbit). Similarly, fender benders are common, while sixty-car fatal pileups are rare. But they both happen. Murder is common; six-state murder sprees are rare. Mountaineering falls are common; nine people falling into a crevasse with three fatalities is rare. That so-called power law is found extensively in nature. It’s a more precise way of saying what Perrow was saying: Large accidents, while rare, are normal. Efforts to prevent them always fail. Both the Sand Pile Effect and normal accident theory predict that space shuttle accidents in which the entire craft and crew are lost will happen, albeit with long intervals between them.

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Every step was another chance for a slip—a collapse—of any size. Most were small—1 inch, 5 inches—and died out. At a less frequent rate, bigger slips occurred. Hillman saw Biggs fall that morning. He quickly arrested himself with his ice ax. There are ten thousand climbers on Mount Hood each year and only one death on average. The power law applies: The bigger the accident, the less likely it is. I like Perrow’s description of such accidents, because while he was talking about a nuclear power plant, he could just as easily have been talking about Mount Hood: “processes happen very fast and can’t be turned off…recovery from the initial disturbance is not possible; it will spread quickly and irretrievably for at least some time….

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Despite the existence of four other much easier descent routes, seventy-five people have died at Lambs Slide since Elkannah Lamb gave it its name. The death rate isn’t that high, but it nevertheless means that a lot of people have been unpleasantly surprised in a pretty place that has a reputation as a beginner’s peak. And the frequency of fatalities probably follows a power law. We are human. Our attention is fragmentary. We get excited. We get tired. We get stupid. Of course, you can’t make adventure safe, for then it’s not adventure. In an almost comic treatment of the paradox, the Mount Hood recreation officer told me, “If you made it so safe for everybody to get up there, you’d have a lot more fatalities because people wouldn’t recognize the risk.”

Beautiful Visualization by Julie Steele

barriers to entry, correlation does not imply causation, data acquisition, data science, database schema, Drosophila, en.wikipedia.org, epigenetics, global pandemic, Hans Rosling, index card, information retrieval, iterative process, linked data, Mercator projection, meta-analysis, natural language processing, Netflix Prize, no-fly zone, pattern recognition, peer-to-peer, performance metric, power law, QR code, recommendation engine, semantic web, social bookmarking, social distancing, social graph, sorting algorithm, Steve Jobs, the long tail, web application, wikimedia commons, Yochai Benkler

Notice also the use of font weight (boldness) to enhance the contrast between different word weights. Figure 3-9. Squashing the scale of differences between word weights In effect, del.icio.us is scaling the word weights—roughly—by logarithm. It’s sensible to scale weights using logarithms or square roots when the source data follows a power-law distribution, as tags seem to do.[8] Somewhere between these earnest, useful designs and the fanciful world that Wordle inhabits, there are other, more experimental interfaces. The WP-Cumulus[9] blog plug-in, for example, provides a rotating, three-dimensional sphere of tags (see Figure 3-10).

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(In a regular linear projection, the slope of each distribution would be so steep that we would not see anything interesting.) It is striking that there is not a single Gaussian bell curve in the plots, as we would expect for, say, the average heights of people. Instead, we find a whole zoology of long tails ranging from beautiful power-laws to log-linear curves, with less clean, bumpier distributions in between. Nearly all IN and OUT distribution pairs appear to be asymmetric. Birth Dates, for example, are connected to Persons in a 1:n manner, where n is highly heterogeneous. This is no surprise, as this area of information is not subject to the multiplicity of opinion, as we would expect in a prosopographic database, which would focus on people instead of objects.

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Science 298, no. 5594: 824–827. Nesselrath, Arnold. 1993. “Die Erstellung einer wissenschaftlichen Datenbank zum Nachleben der Antike: Der Census of Ancient Works of Art Known to the Renaissance.” Habilitation thesis, Universität Mainz. Available at the CENSUS office at HU-Berlin. Newman, Mark E.J. 2005. “Power laws, Pareto distributions and Zipf’s law.” Contemporary Physics 46: 323–351. doi:10.1080/00107510500052444. Newman, Mark E.J., Albert-László Barabási, and Duncan J. Watts, eds. 2006. The Structure and Dynamics of Networks. Princeton, NJ: Princeton University Press. Penfield, W., and T. Rasmussen. 1950.

Beautiful Data: The Stories Behind Elegant Data Solutions by Toby Segaran, Jeff Hammerbacher

23andMe, airport security, Amazon Mechanical Turk, bioinformatics, Black Swan, business intelligence, card file, cloud computing, computer vision, correlation coefficient, correlation does not imply causation, crowdsourcing, Daniel Kahneman / Amos Tversky, DARPA: Urban Challenge, data acquisition, data science, database schema, double helix, en.wikipedia.org, epigenetics, fault tolerance, Firefox, Gregor Mendel, Hans Rosling, housing crisis, information retrieval, lake wobegon effect, Large Hadron Collider, longitudinal study, machine readable, machine translation, Mars Rover, natural language processing, openstreetmap, Paradox of Choice, power law, prediction markets, profit motive, semantic web, sentiment analysis, Simon Singh, social bookmarking, social graph, SPARQL, sparse data, speech recognition, statistical model, supply-chain management, systematic bias, TED Talk, text mining, the long tail, Vernor Vinge, web application

Tag frequencies for top 1,000 tags. We can check to see whether we have a power-law distribution by plotting our word frequencies in log space (see Figure 17-11): Plot log ranks against log frequency. > log_ranks = log(1:length(sorted_counts)) > plot(log_ranks, log(sorted_counts)) Log frequency vs. log rank Frequency of use 10,000 1,000 100 10 1 cute happy sexy ew dull hip Gothic Sloot Tags ordered by rank cops F I G U R E 1 7 - 1 1 . Tags’ log frequencies by log rank, with fitted line from the power law model. 292 CHAPTER SEVENTEEN Download at Boykma.Com chiiin A power-law distribution should look linear in the log-log space: Fit a model of log count against log rank and draw it on Figure 17-10

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From our table of common tags, we see that the most common tag, “cute”, has 36,000 occurrences, but the second most common, “pretty”, has just half of that. (See Figure 17-10.) For the top 1,000 tags, draw a plot of their counts. > s = sorted_counts[1:1000] > barplot(s) In 1935, the linguist George Zipf observed that word frequency distributions often follow a “power law,” where the frequency of the nth word is proportional to (1/ns), where s is a constant. Unlike a Gaussian distribution, this distribution has infinite variance, which can make it somewhat unwieldy for certain statistical algorithms. Popular books such as Nassim Nicholas Taleb’s The Black Swan (Random House) and Chris Anderson’s The Long Tail (Hyperion) have made these distributions famous as “fat tail” and “long tail” distributions, respectively.

The Age of Em: Work, Love and Life When Robots Rule the Earth by Robin Hanson

8-hour work day, artificial general intelligence, augmented reality, Berlin Wall, bitcoin, blockchain, brain emulation, business cycle, business process, Clayton Christensen, cloud computing, correlation does not imply causation, creative destruction, deep learning, demographic transition, Erik Brynjolfsson, Ethereum, ethereum blockchain, experimental subject, fault tolerance, financial intermediation, Flynn Effect, Future Shock, Herman Kahn, hindsight bias, information asymmetry, job automation, job satisfaction, John Markoff, Just-in-time delivery, lone genius, Machinery of Freedom by David Friedman, market design, megaproject, meta-analysis, Nash equilibrium, new economy, Nick Bostrom, pneumatic tube, power law, prediction markets, quantum cryptography, rent control, rent-seeking, reversible computing, risk tolerance, Silicon Valley, smart contracts, social distancing, statistical model, stem cell, Thomas Malthus, trade route, Turing test, Tyler Cowen, Vernor Vinge, William MacAskill

As discussed in Chapter 18, Cities section, while most farmers lived near small villages, in our industrial era people are spread rather evenly across towns and cities of all feasible sizes. Also, for most industrial products today, market shares are relatively concentrated within transport-cost-limited market areas. That is, for each type of product in an area, only a small number of firms supply most customers. Power laws are mathematical forms that often usefully describe such inequality. That is, power laws often fit the large-unit end of the distributions of how such items are grouped into units. In such cases, a power of one describes a uniform distribution of items across feasible unit sizes. Powers greater than one describe more equal distributions, wherein most items reside in small units, and powers less than one describe less equal distributions, wherein most items are clumped into fewer larger units.

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Forecasting Some say that there is little point in trying to foresee the non-immediate future. But in fact there have been many successful forecasts of this sort. For example, we can reliably predict the future cost changes for devices such as batteries or solar cells, as such costs tend to follow a power law of the cumulative device production (Nagy et al. 2013). As another example, recently a set of a thousand published technology forecasts were collected and scored for accuracy, by comparing the forecasted date of a technology milestone with its actual date. Forecasts were significantly more accurate than random, even forecasts 10 to 25 years ahead.

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Eric 33 dust 103 E early scans 148, 150 earthquakes 93 eating 298 economic analysis, v economic growth 28 economics 37–9, 382 economy 130, 179, 190, 276, 278, 374 doubling time of 190–4, 201–2, 221 early em 360 growth of 10, 92 size of 194 efficiency 155–65, 278 clan concentration 155–6 competition 156–9 eliteness 161–3 implications 159–61 qualities 163–5 elections 182, 183, 265 eliteness 161–3 ems see emulations emotion words 217 emulations 2, 6–7, 130, 338 assumptions 47–8 brain 2 compared to ordinary humans 11–2 enough 151–4 envisioning a world of 34–7 inequality 244–6 introduction to 1–2 many 122–4 mass 308 models 48 niche 308 one-name 155–6 opaque 61 open source 61 overview of 5–8 precedents 13–15 slow 257 start of 5–11 summary of conclusions 8–11 technologies 46 time-sharing 65, 222 energy 70, 71, 74, 75, 82 see also entropy control of 126 influence on behavior 83 entrenchment 344 entropy 77–80 see also energy eras 13–14, 15 see also farming era; foraging era; industrial era present 18–21 prior 15–18 values 21–3 erasures of bits 81, 82, 83 logical78rate of 80 reversible 79 eunuchs 285, 343 evaluations 367–70 evolution 22, 24, 25, 26, 134, 153 animal 24 em 153, 154 foragers 24, 25, 238 human 134, 153, 227 systems 344 existence 119–26 copying 119–21 many ems 122–4 rights 121–2 surveillance 124–6 existential risk 369 expenses 357 experimental art 203 experts, fake 254–5 exports 87, 95, 224 F faces 102, 297 factions 268–70 factories 96–7, 190, 191, 192, 193 failures 208 fake experts 254–5 fakery 113–14 farmers 1, 5, 8, 13, 16–17 communities 216 culture 326–8 farming era 5, 13, 14, 190, 252 firms 253 inequality 243 marriages 289 stories 331 wars 251 fashions 257, 268, 298, 310, 325, 326 clothes 18 intellectual 301 local 296 music 28 fast ems 257 fears 343 feelings 217 fertility 25, 26 fiction 1, 2, 41, 334 see also science fiction finance 195–7 financial inequality 247 fines 273 firms 231–4, 245 cost-focused 233 family-based 232 firm-clan relations 235–7 managers 234 mass versus niche teams 239–41 novelty-focused 233 private-equity owned 232 quality-focused 233 teams 237–9 first ems 147–50 flexibility 184, 202, 206, 224, 288, 378 flow projects 192 foragers 1, 5, 6, 8, 24–5, 29, 156, 190, 238 communities 13 pair bonds 289 foraging era 14, 16 inequality 243 stories 331 forecasting 33–4 fractal reversing 79, 81 fractional factorial experiment design 115 fragility 127–30 friendship 320, 371 future, vi 1, 26, 28, 31–2, 381 abstract construal of 42 analysis of 382, 383 em 384 eras 27, 29 evaluation of 367 technology 2, 7 futurists 35 G gates, computer 77–8 gender 290–1, 325 imbalance 291–3 geographical divisions 326 ghosts 132–3 global laws 124 God 316 governance 197, 258–62 clan 262–4 global 358 governments 364 gravity 74, 101 grit 164, 379 groups 227–41 clans 227–9 firm-clan relations 235–7 firms 231–4 managing clans 229–31 mass versus niche teams 239–41 signals 299–302 teams 237–9 growth 14, 15, 27, 28, 29, 189–97 estimate 192–4 faster 189–92 financial 195–7 modes 14 myths 194–5 H happiness 42, 165, 204–5, 232, 238, 247, 253, 303, 311, 320, 339, 370–1 hardware 54, 56–60, 63, 65, 278 clan-specific 355 communication 86 computer 86 deterministic 58, 86, 97, 174 digital 58 fault-tolerant 58 parallel 63–5 reversible 82 signal-processing 46, 57, 59 variable speed 82 heat transport 91–2 historians vi, 35 history 31, 32, 41, 248, 301 leisure 204, 207 personal 111 homosexual ems 292 homosexuality 10 hospitals 302 humans 1, 5, 7, 8, 14 introduction of 13 I identical twins 227 identity 49, 303–8, 317 ideologies 326 illness 305 implementation of emulations 55–65 hardware 56–60 mindreading 55–6 parallelism 63–5 security 60–3 impressions 295, 300 incentives 180, 181, 182, 183, 274 inclinations 342 income tax 182 individualism 20 industrial era 18–21 firms 253 stories 332 industrial organization 158 industrial revolution 232, 363 industry 5, 6, 13, 14 inequality 243–7 information 109–17 fake 113–14 records 111–2 simulations 115–17 views 109–11 infrastructure 85–98 air and water 90–2 buildings 92–5 climate controlled 85 cooling 86–9 manufacturing 95–8 innovation 189, 193, 275–7 institutions 179–80 new 181–4 intellectual property 124, 125, 147, 276, 277, 324, 362, 378 intelligence 163, 194, 295, 297, 299, 346–7 intelligence explosion 347–50 interactions 83, 109–10 interest rates 131, 196–7, 224 J job(s) categories 153 evaluations 159, 233 performance 164 tasks 356 see also careers; work judges 133, 173, 174, 261, 262, 267, 270, 272, 277, 286 K Kahn, Herman 33 kilo-ems 224 Kingdom Tower, Jeddah 93 L labor 54, 143–54, 190, 361 enough ems 151–4 first ems 147–50 Malthusian wages 146–7 markets 237 selection 150–1 supply and demand 143–5 languages 16, 128, 172, 217, 278, 345 law 229, 271–3 efficient 273–5 lawsuits 274 leisure 100, 102, 129, 168, 207, 374 activities 329 fast 258 speeds 222 liability 229, 273, 274, 277 liberals 327 lifecycle 199–212 careers 199–202 childhood 210–2 maturity 204–5 peak age 202–4 preparation for tasks 206–8 training 208–10 lifespan 11, 245, 246, 247 limits 27–9 logic gates 78, 79 loyalty 115, 117, 297, 299 lying 205 M machine reproduction estimates 192–3 machine shops 192 maladaptive behaviors 26 maladaptive cultures 25 Malthusian wages 146–7 management 200 of physical systems 109 practices 232–3 manic-depressive disorder 165 marketing 331 mass labor markets 239, 324 mass market teams 239–41 mass production 96 mating 285–93, 320, 342 gender 290–1 gender imbalance 291–3 open-source lovers 287–8 pair bonds 288–90 sexuality 285–7 maturity 204–5 meetings 75–7, 310 memories 48, 112, 136, 149, 207, 221, 304, 307 memory 63–5, 70–1, 79, 145, 219 mental fatigue 170 mental flexibility 203 mental speeds see mind speeds messages 81–2, 104 delays 77 methods 33, 34, 37, 40, 41, 42 Microsoft 91 military 359–60 mindfulness 165 minds 10, 335–50 features 344–5 humans 335–9 intelligence 346–7 intelligence explosion 347–50 merging 358 partial 341–3 psychology 343–6 quality 74 reading 55–6, 265, 271, 310, 314 speeds 65, 194, 199, 221–4 see also speed(s) theft 10, 61, 62, 76, 124, 302 unhumans 339–41 modeling, brain cell 364 modes of civilization 13–30 dreamtime 23–6 era values 21–3 limits 27–9 our era 18–21 precedents 13–15 prior eras 15–18 modular buildings 94 functional units 49 Moore’s law 54, 59, 80 moral choices 303 morality 2, 368 motivation, for studying future emulations 31–3 multitasking 171 music 311, 312, 328 myths 194–5 N nanotech manufacturing 97 nations 39, 87, 159, 163, 184, 195, 216, 243, 244, 245, 253 democratic 264 poor 22 rich 22, 39, 73, 94, 216, 234 war between 259 nature 81, 303 Neanderthals 21 nepotism 252–4 networks, talk 237 neurons 69 niche ems 308 niche labor markets 239, 324 niche market teams 239–41 normative considerations 44 nostalgia 308 nuclear weapons 251 O office politics 236 offices 100, 102, 104 older people 204–5 see also aging; retirement open-source lovers 287–8 outcome measures 260 ownership 120 P pair bonds 286, 288–90, 292–3 parallel computing 63–5, 278, 279, 280, 353 parents 383 partial sims 115 past, the see history patents 277 pay-for-performance 181–2 peak age 202–4 period 64–5, 70, 72, 76, 110 reversing 79–83 perseverance 164 personality, gender differences 290 personal signals 296–9 phase 65, 76, 81, 83, 110, 222 physical bodies 73, 75–6 physical jobs 73 physical violence 103 physical worlds 81 pipes 87, 88 plants 16, 87, 190, 303 police spurs 358 policy analysis 372–6 political power 354 politics 257–70, 322, 333 clan governance 262–4 coalitions 266–8 democracy 264–6 factions 268–70 governance 258–62 population 125 portable brain hardware 251 portfolios 196, 264, 378 positive considerations 44 poverty 246, 247, 249, 250 em 147, 153, 325 human 338 power 175–7 power laws 243 prediction markets 184, 186–8, 252, 255, 274, 317 city auctions 220 estimates 231 use of 276 pre-human primates 15–16 pre-skills 143–4, 152–3, 158, 356 preparation for tasks 206–8 prices 181–4, 187 of manufactured goods 145 for resources 179 printers, 3D 192 prison 273 privacy 172 productivity 12, 163, 171, 209–10, 211, 371 progress 2, 46–7, 49, 52, 53, 54 psychology 343–6 punishments 229, 273 purchasing 97, 182, 183, 277, 304 Q qualities 163–5 quality of life 370–2 quantum computing 357 R random access memory (RAM) 70 rare products 299 reaction time 72–3, 76–8, 83, 217 body size and 73 physical em body 223 real world, merging virtual and 105–7 records 111–2 redistribution 246–50 regulations 28, 37–8, 106, 110, 123, 151, 159, 217, 221, 264, 356, 358, 359 religion 276, 311–2, 326 research 194–5, 376 retirement 110, 127, 129–33, 135, 170, 174, 221–2, 336–9 human 8 reversibility 77–80, 82, 83 rewards 159–60 rights 121–2 rituals 309–11 rulers 259 rules 164, 271–81 S safes 172–3 salt water 91 scales 69–83 bodies 72–4 Lilliputian 74–5 speeds 69–72 scanning 148, 151, 363 scans 148–50 scenarios 34–7, 354–9, 363, 364 schools v, 20, 164, 168, 181, 233, 295–6, 302, 309, 333, 382 science fiction v, 2, 6, 312 scope 39–40 search teams 210 security 60–3, 71, 101, 104, 110, 117, 231, 306, 354, 357 breaches 85, 117 computer 104, 252, 357 costs 76 selection 5, 24, 26, 112, 137, 150–1, 153, 158, 162, 175, 263, 292, 339, 346 self-deception 173, 261, 296 self-governance 230 serial computing 353 sexuality 285–7, 328 shared spaces 103–5 showing off 295–6 sight perception 341 signals 295–308 copy identity 305–8 groups 299–302 identity 303–5 personal 296–9 processing 46 sim administrators 116 simulations 115–17 singing 311 sins 312 size 69, 72, 73, 74, 75, 110 slaves 16, 60, 121, 123–4, 147, 149, 245, 302, 327, 342 sleep 18, 60, 83, 133, 165 sleeping beauty strategy 131 social bonds 239 social gatherings 267 social interactions 238 social power 175–7 social reasoning 342 social relations 323 social science 382 social status 258 society 12, 321–34 software 54, 126, 277–9, 355 software developers 280–1 software engineers 200, 278, 280 souls 106 sound perception 341 spaces 110–14 space travel 225 speculation 39 speed(s) 69, 110, 137, 245, 246, 332 alternative scenario 355, 358 divisions 325, 326 em 8, 10, 353–4 em era 353 ghosts 132, 133 human-speed emulation 47 redistribution based on 248 retirement 130, 131 talking 298 time-shared em 65 top cheap 69, 70, 82, 89, 133, 222, 280, 281 travel 329, 330 variable speed hardware 82 walking 74 spurs 9, 110, 136, 169–71, 271, 292 social interactions 171 uses of 171–4 stability 131, 132 status 257–8, 301 stories 32, 35, 102, 325, 330–3 see also fiction clan 333–4 stress 20, 103, 134, 137, 164, 313 structure, city 217–19 subclans 227, 229 conflicting 356 inequality between 248 subordinates 200 subsistence levels 249 success 377–9 suicide 138–9 supply and demand 143–5 surveillance 124–6, 271 swearing 312–14 synchronization 309, 318–20 T takeovers 196 talk networks 237 taxes 249–50, 337 teams 237–9, 296, 299, 301, 306, 307 application 210 intelligence 346 mass versus niche teams 239–41 training 204 technologies 362–4 temperature 85, 88–91 territories 374 tests 114–17 theory 37, 39, 143 tools, non-computer-based 279 top cheap speed 69, 70, 82, 89, 133, 222, 280, 281 track records 181, 255 training 147, 151, 208–10, 212 transexuality 10 transgender conversions 292 transition, from our world to the em world 359–62 transport 224–6 travel 18, 22, 29, 43, 75, 102, 215, 218–19, 303, 329–30 travel times 102 trends 353–4 trust 208, 236 clans 227, 228, 234, 235 maturity and 204, 205 Tsiolkovsky, Konstantin 33 tweaking 150, 151 U undo action 104–5 unhumans, minds of 339–41 unions 236 United States of America 23 uploads see emulations utilitarianism 370, 372 V vacations 207 values 21–3, 237–8, 322, 383, 384 variety 20, 23, 96, 156, 157, 160, 189, 199, 234, 298, 375 views 109–11, 381, 382, 383 virtual meetings 217 virtual reality 8, 102, 103–4, 112, 217, 288, 291, 362 appearances 99–101 authentication 113 cultures 324 design of 104 leisure environments 102 meetings 76 merging real and 105–7 nature 81 travel, 224voices, pitch of 297 voting 183, 265–6 W wages 9, 12, 124, 143–5, 245, 336, 358 inequality 234, 248 Malthusian wages 146–7 rules 121, 122, 123 subsistence 354 war 16–17, 36, 131, 134, 250–2, 327, 354, 361 water 87, 90–2 Watkins, John 33 wealth 23, 26, 245–6, 321–2, 325, 336–8 weapons 251 Whole Brain Emulation Roadmap (Sandberg and Bostrom) 47 Wiener, Anthony 33 wind pressures 92, 93 work 167–77, 327, 328, 331 conditions 169 culture 321, 322, 323, 324 hours 167–9, 299, 372 methods 202 social power 175–7 speeds 222 spurs 169–71 teams 237–9 workers, time spent “loafing” 170 workaholics 165, 167 World Wide Web 34 Y Year 2000, The (Kahn and Wiener) 33 youth 11, 30, 376 see also children Z zoning 184, 185

Enlightenment Now: The Case for Reason, Science, Humanism, and Progress by Steven Pinker

3D printing, Abraham Maslow, access to a mobile phone, affirmative action, Affordable Care Act / Obamacare, agricultural Revolution, Albert Einstein, Alfred Russel Wallace, Alignment Problem, An Inconvenient Truth, anti-communist, Anton Chekhov, Arthur Eddington, artificial general intelligence, availability heuristic, Ayatollah Khomeini, basic income, Berlin Wall, Bernie Sanders, biodiversity loss, Black Swan, Bonfire of the Vanities, Brexit referendum, business cycle, capital controls, Capital in the Twenty-First Century by Thomas Piketty, carbon footprint, carbon tax, Charlie Hebdo massacre, classic study, clean water, clockwork universe, cognitive bias, cognitive dissonance, Columbine, conceptual framework, confounding variable, correlation does not imply causation, creative destruction, CRISPR, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, dark matter, data science, decarbonisation, degrowth, deindustrialization, dematerialisation, demographic transition, Deng Xiaoping, distributed generation, diversified portfolio, Donald Trump, Doomsday Clock, double helix, Eddington experiment, Edward Jenner, effective altruism, Elon Musk, en.wikipedia.org, end world poverty, endogenous growth, energy transition, European colonialism, experimental subject, Exxon Valdez, facts on the ground, fake news, Fall of the Berlin Wall, first-past-the-post, Flynn Effect, food miles, Francis Fukuyama: the end of history, frictionless, frictionless market, Garrett Hardin, germ theory of disease, Gini coefficient, Great Leap Forward, Hacker Conference 1984, Hans Rosling, hedonic treadmill, helicopter parent, Herbert Marcuse, Herman Kahn, Hobbesian trap, humanitarian revolution, Ignaz Semmelweis: hand washing, income inequality, income per capita, Indoor air pollution, Intergovernmental Panel on Climate Change (IPCC), invention of writing, Jaron Lanier, Joan Didion, job automation, Johannes Kepler, John Snow's cholera map, Kevin Kelly, Khan Academy, knowledge economy, l'esprit de l'escalier, Laplace demon, launch on warning, life extension, long peace, longitudinal study, Louis Pasteur, Mahbub ul Haq, Martin Wolf, mass incarceration, meta-analysis, Michael Shellenberger, microaggression, Mikhail Gorbachev, minimum wage unemployment, moral hazard, mutually assured destruction, Naomi Klein, Nate Silver, Nathan Meyer Rothschild: antibiotics, negative emissions, Nelson Mandela, New Journalism, Norman Mailer, nuclear taboo, nuclear winter, obamacare, ocean acidification, Oklahoma City bombing, open economy, opioid epidemic / opioid crisis, paperclip maximiser, Paris climate accords, Paul Graham, peak oil, Peter Singer: altruism, Peter Thiel, post-truth, power law, precautionary principle, precision agriculture, prediction markets, public intellectual, purchasing power parity, radical life extension, Ralph Nader, randomized controlled trial, Ray Kurzweil, rent control, Republic of Letters, Richard Feynman, road to serfdom, Robert Gordon, Rodney Brooks, rolodex, Ronald Reagan, Rory Sutherland, Saturday Night Live, science of happiness, Scientific racism, Second Machine Age, secular stagnation, self-driving car, sharing economy, Silicon Valley, Silicon Valley ideology, Simon Kuznets, Skype, smart grid, Social Justice Warrior, sovereign wealth fund, sparse data, stem cell, Stephen Hawking, Steve Bannon, Steven Pinker, Stewart Brand, Stuxnet, supervolcano, synthetic biology, tech billionaire, technological determinism, technological singularity, Ted Kaczynski, Ted Nordhaus, TED Talk, The Rise and Fall of American Growth, the scientific method, The Signal and the Noise by Nate Silver, The Spirit Level, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, total factor productivity, Tragedy of the Commons, union organizing, universal basic income, University of East Anglia, Unsafe at Any Speed, Upton Sinclair, uranium enrichment, urban renewal, W. E. B. Du Bois, War on Poverty, We wanted flying cars, instead we got 140 characters, women in the workforce, working poor, World Values Survey, Y2K

Since we cannot replay history thousands of times and count the outcomes, a statement that some event will occur with a probability of .01 or .001 or .0001 or .00001 is essentially a readout of the assessor’s subjective confidence. This includes mathematical analyses in which scientists plot the distribution of events in the past (like wars or cyberattacks) and show they fall into a power-law distribution, one with “fat” or “thick” tails, in which extreme events are highly improbable but not astronomically improbable.7 The math is of little help in calibrating the risk, because the scattershot data along the tail of the distribution generally misbehave, deviating from a smooth curve and making estimation impossible.

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Michaud, “One in Seven Thinks End of World Is Coming: Poll,” Reuters, May 1, 2012, http://www.reuters.com/article/us-mayancalendar-poll-idUSBRE8400XH20120501. The rate for the United States was 22 percent, and in a 2015 YouGov poll, 31 percent: http://cdn.yougov.com/cumulus_uploads/document/i7p20mektl/toplines_OPI_disaster_20150227.pdf. 7. Power-law distributions: Johnson et al. 2006; Newman 2005; see Pinker 2011, pp. 210–22, for a review. See the references in note 17 of chapter 11 for an explanation of the complexities in estimating the risks from the data. 8. Overestimating the probability of extreme risks: Pinker 2011, pp. 368–73. 9.

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Ineffective charitable altruism suggests adaptations for partner choice. Presented at the Annual Meeting of the Human Behavior and Evolution Society, Vancouver. New York Times. 2016. Election 2016: Exit polls. https://www.nytimes.com/interactive/2016/11/08/us/politics/election-exit-polls.html?_r=0. Newman, M. E. J. 2005. Power laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46, 323–51. Nietzsche, F. 1887/2014. On the genealogy of morals. New York: Penguin. Nisbet, R. 1980/2009. History of the idea of progress. New Brunswick, NJ: Transaction. Norberg, J. 2016. Progress: Ten reasons to look forward to the future.

Data Mining: Concepts and Techniques: Concepts and Techniques by Jiawei Han, Micheline Kamber, Jian Pei

backpropagation, bioinformatics, business intelligence, business process, Claude Shannon: information theory, cloud computing, computer vision, correlation coefficient, cyber-physical system, database schema, discrete time, disinformation, distributed generation, finite state, industrial research laboratory, information retrieval, information security, iterative process, knowledge worker, linked data, machine readable, natural language processing, Netflix Prize, Occam's razor, pattern recognition, performance metric, phenotype, power law, random walk, recommendation engine, RFID, search costs, semantic web, seminal paper, sentiment analysis, sparse data, speech recognition, statistical model, stochastic process, supply-chain management, text mining, thinkpad, Thomas Bayes, web application

The scale-free model assumes that the network follows the power law distribution (also known as the Pareto distribution or the heavy-tailed distribution). In most large-scale social networks, a small-world phenomenon is observed, that is, the network can be characterized as having a high degree of local clustering for a small fraction of the nodes (i.e., these nodes are interconnected with one another), while being no more than a few degrees of separation from the remaining nodes. Social networks exhibit certain evolutionary characteristics. They tend to follow the densification power law, which states that networks become increasingly dense over time.

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., Predictive learning via rule ensembles, Ann. Applied Statistics 2 (2008) 916–954. [FBF77] Friedman, J.H.; Bentley, J.L.; Finkel, R.A., An algorithm for finding best matches in logarithmic expected time, ACM Transactions on Math Software 3 (1977) 209–226. [FFF99] Faloutsos, M.; Faloutsos, P.; Faloutsos, C., On power-law relationships of the internet topology, In: Proc. ACM SIGCOMM’99 Conf. Applications, Technologies, Architectures, and Protocols for Computer Communication Cambridge, MA. (Aug. 1999), pp. 251–262. [FG02] Fishelson, M.; Geiger, D., Exact genetic linkage computations for general pedigrees, Disinformation 18 (2002) 189–198.

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seedata mining DBSCAN 471–473 algorithm illustration 474 core objects 472 density estimation 477 density-based cluster 472 density-connected 472, 473 density-reachable 472, 473 directly density-reachable 472 neighborhood density 471see alsocluster analysis; density-based methods DDPMine 422 decimal scaling, normalization by 115 decision tree analysis, discretization by 116 decision tree induction 330–350, 385 algorithm differences 336 algorithm illustration 333 attribute selection measures 336–344 attribute subset selection 105 C4.5 332 CART 332 CHAID 343 gain ratio 340–341 Gini index 332, 341–343 ID3 332 incremental versions 336 information gain 336–340 multivariate splits 344 parameters 332 scalability and 347–348 splitting criterion 333 from training tuples 332–333 tree pruning 344–347, 385 visual mining for 348–350 decision trees 18, 330 branches 330 illustrated 331 internal nodes 330 leaf nodes 330 pruning 331, 344–347 root node 330 rule extraction from 357–359 deep web 597 default rules 357 DENCLUE 476–479 advantages 479 clusters 478 density attractor 478 density estimation 476 kernel density estimation 477–478 kernels 478see alsocluster analysis; density-based methods dendrograms 460 densification power law 592 density estimation 476 DENCLUE 477–478 kernel function 477–478 density-based methods 449, 471–479, 491 DBSCAN 471–473 DENCLUE 476–479 object division 449 OPTICS 473–476 STING as 480see alsocluster analysis density-based outlier detection 564–567 local outlier factor 566–567 local proximity 564 local reachability density 566 relative density 565 descendant cells 189 descriptive mining tasks 15 DIANA (Divisive Analysis) 459, 460 dice operation 148 differential privacy 622 dimension tables 136 dimensional cells 189 dimensionality reduction 86, 99–100, 120 dimensionality reduction methods 510, 519–522, 538 list of 587 spectral clustering 520–522 dimension/level application of 297 constraints 294 dimensions 10, 136 association rule 281 cardinality of 159 concept hierarchies and 142–144 in multidimensional view 33 ordering of 210 pattern 281 ranking 225 relevance analysis 175 selection 225 shared 204see alsodata warehouses direct discriminative pattern mining 422 directed acyclic graphs 394–395 discernibility matrix 427 discovery-driven exploration 231–234, 235 discrepancy detection 91–93 discrete attributes 44 discrete Fourier transform (DFT) 101, 587 discrete wavelet transform (DWT) 100–102, 587 discretization 112, 120 by binning 115 by clustering 116 by correlation analysis 117 by decision tree analysis 116 by histogram analysis 115–116 techniques 113 discriminant analysis 600 discriminant rules 16 discriminative frequent pattern-based classification 416, 419–422, 437 basis for 419 feature generation 420 feature selection 420–421 framework 420–421 learning of classification model 421 dispersion of data 44, 48–51 dissimilarity asymmetric binary 71 between attributes of mixed type 76–77 between binary attributes 71–72 measuring 65–78, 79 between nominal attributes 69 on numeric data 72–74 between ordinal attributes 75 symmetric binary 70–71 dissimilarity matrix 67, 68 data matrix versus 67–68 n-by-n table representation 68 as one-mode matrix 68 distance measures 461–462 Euclidean 72–73 Manhattan 72–73 Minkowski 73 supremum 73–74 types of 72 distance-based cluster analysis 445 distance-based outlier detection 561–562 nested loop algorithm 561, 562see alsooutlier detection distributed data mining 615, 624 distributed privacy preservation 622 distributions boxplots for visualizing 49–50 five-number summary 49 distributive measures 145 Divisive Analysis (DIANA) 459, 460 divisive hierarchical method 459 agglomerative hierarchical clustering versus 459–460 DIANA 459, 460 DNA chips 512 document classification 430 documents language model 26 topic model 26–27 drill-across operation 148 drill-down operation 11, 146–147 drill-through operation 148 dynamic itemset counting 256 E eager learners 423, 437 Eclat (Equivalence Class Transformation) algorithm 260, 272 e-commerce 609 editing method 425 efficiency Apriori algorithm 255–256 backpropagation 404 data mining algorithms 31 elbow method 486 email spam filtering 435 engineering applications 613 ensemble methods 378–379, 386 bagging 379–380 boosting 380–382 for class imbalance problem 385 random forests 382–383 types of 378, 386 enterprise warehouses 132 entity identification problem 94 entity-relationship (ER) data model 9, 139 epoch updating 404 equal-frequency histograms 107, 116 equal-width histograms 107, 116 equivalence classes 427 error rates 367 error-correcting codes 431–432 Euclidean distance 72 mathematical properties 72–73 weighted 74see alsodistance measures evaluation metrics 364–370 evolution, of database system technology 3–5 evolutionary searches 579 exception-based, discovery-driven exploration 231–234, 235 exceptions 231 exhaustive rules 358 expectation-maximization (EM) algorithm 505–508, 538 expectation step (E-step) 505 fuzzy clustering with 505–507 maximization step (M-step) 505 for mixture models 507–508 for probabilistic model-based clustering 507–508 steps 505see alsoprobabilistic model-based clustering expected values 97 cell 234 exploratory data mining.

Speaking Code: Coding as Aesthetic and Political Expression by Geoff Cox, Alex McLean

4chan, Amazon Mechanical Turk, augmented reality, bash_history, bitcoin, Charles Babbage, cloud computing, commons-based peer production, computer age, computer vision, Computing Machinery and Intelligence, crowdsourcing, dematerialisation, Donald Knuth, Douglas Hofstadter, en.wikipedia.org, Everything should be made as simple as possible, finite state, Free Software Foundation, Gabriella Coleman, Gödel, Escher, Bach, Hacker Conference 1984, Ian Bogost, Jacques de Vaucanson, language acquisition, Larry Wall, late capitalism, means of production, natural language processing, Neal Stephenson, new economy, Norbert Wiener, Occupy movement, packet switching, peer-to-peer, power law, Richard Stallman, Ronald Coase, Slavoj Žižek, social software, social web, software studies, speech recognition, SQL injection, stem cell, Stewart Brand, systems thinking, The Nature of the Firm, Turing machine, Turing test, Vilfredo Pareto, We are Anonymous. We are Legion, We are the 99%, WikiLeaks, Yochai Benkler

Networks are often viewed as inherently random, simply because their operations appear too complex to comprehend; but randomness remains a misleading description, as “relative connectedness” is articulated through the density of connections in scale-free networks. Albert-László Barabási uses the mathematical concept of the “power law” to explain how complex networks demonstrate “directedness,” in other words how they are organized preferentially.69 The Italian economist Vilfredo Pareto observed that 80 percent of peas were produced by 20 percent of pea pods;70 and many other phenomena seem to fall into similar inverse relationships (as in the popular adage that 80 percent of wealth is owned by 20 percent of the population). Although this 80/20 rule (an example of a power law) seems rather imprecise, it does offer some scientific insight into the politics of self-organization.

Mining the Social Web: Finding Needles in the Social Haystack by Matthew A. Russell

Andy Rubin, business logic, Climategate, cloud computing, crowdsourcing, data science, en.wikipedia.org, fault tolerance, Firefox, folksonomy, full text search, Georg Cantor, Google Earth, information retrieval, machine readable, Mark Zuckerberg, natural language processing, NP-complete, power law, Saturday Night Live, semantic web, Silicon Valley, slashdot, social graph, social web, sparse data, statistical model, Steve Jobs, supply-chain management, text mining, traveling salesman, Turing test, web application

A few values are between 2 and 9, indicating that those nodes are connected to anywhere between 2 and 9 other nodes. The extreme outlier is the node with a degree of 37. The gist of the graph is that it’s mostly composed of disjoint nodes, but there is one very highly connected node. Figure 1-1 illustrates a distribution of degree as a column chart. The trendline shows that the distribution closely follows a Power Law and has a “heavy” or “long” tail. Although the characteristics of distributions with long tails are by no means treated with rigor in this book, you’ll find that lots of distributions we’ll encounter exhibit this property, and you’re highly encouraged to take the initiative to dig deeper if you feel the urge.

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For example, just over 533 of Tim’s tweets weren’t retweeted at all as denoted by the far left column, 50 of his tweets were retweeted 50 times, and over 60 of his tweets were retweeted over 100 times[32] as denoted by the far right column. Figure 5-3. Sample results from Example 5-12 The distribution isn’t too surprising in that it generally trends according to the power law and that there are a fairly high number of tweets that went viral and were retweeted what could have been many hundreds of times. The high-level takeaways are that of over 3,000 total tweets, 2,536 of them were retweeted at least one time (a ratio of about 0.80) and generated over 50,000 retweets in all (a factor about 16).

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, Visualizing with spreadsheets (the old-fashioned way) part-of-speech (POS) tagging, A Typical NLP Pipeline with NLTK Penn Treebank Project, A Typical NLP Pipeline with NLTK Penn Treebank Tags, full listing of, Entity-Centric Analysis: A Deeper Understanding of the Data pickling your data, Frequency Analysis and Lexical Diversity PMI (Pointwise Mutual Information), How the Collocation Sausage Is Made: Contingency Tables and Scoring Functions POP3 (Post Office Protocol version 3), Analyzing Your Own Mail Data POS (part-of-speech) tagging, A Typical NLP Pipeline with NLTK Power Law, Extracting relationships from the tweets precision, Quality of Analytics, Quality of Analytics calculating, Quality of Analytics privacy controls, Facebook data, Facebook’s Query APIs profiles, Fetching Extended Profile Information, Fetching Extended Profile Information, From Zero to Access Token in Under 10 Minutes Facebook users, accessing data from, From Zero to Access Token in Under 10 Minutes fetching extended profile information for LinkedIn members, Fetching Extended Profile Information, Fetching Extended Profile Information Prolog logic-based programming language, Open-World Versus Closed-World Assumptions protocols, used on Internet, An Evolutionary Revolution?

Cities Are Good for You: The Genius of the Metropolis by Leo Hollis

Airbnb, Alvin Toffler, banking crisis, Berlin Wall, Big Tech, Boris Johnson, Broken windows theory, Buckminster Fuller, call centre, car-free, carbon footprint, cellular automata, classic study, clean water, cloud computing, complexity theory, congestion charging, creative destruction, credit crunch, Credit Default Swap, crowdsourcing, Deng Xiaoping, digital divide, digital map, Disneyland with the Death Penalty, Donald Shoup, East Village, Edward Glaeser, Elisha Otis, Enrique Peñalosa, export processing zone, Firefox, Frank Gehry, General Motors Futurama, Geoffrey West, Santa Fe Institute, Gini coefficient, Google Earth, Great Leap Forward, Guggenheim Bilbao, haute couture, Hernando de Soto, high-speed rail, housing crisis, illegal immigration, income inequality, informal economy, Internet of things, invisible hand, Jane Jacobs, Jevons paradox, Kickstarter, knowledge economy, knowledge worker, Leo Hollis, Lewis Mumford, Long Term Capital Management, M-Pesa, Mahatma Gandhi, Mark Zuckerberg, Masdar, mass immigration, megacity, negative equity, Neil Armstrong, new economy, New Urbanism, Occupy movement, off-the-grid, openstreetmap, packet switching, Panopticon Jeremy Bentham, place-making, power law, Quicken Loans, Ray Oldenburg, Richard Florida, sharing economy, Silicon Valley, Skype, smart cities, smart grid, spice trade, Steve Jobs, technoutopianism, the built environment, The Chicago School, The Death and Life of Great American Cities, The Great Good Place, the High Line, The Spirit Level, the strength of weak ties, The Wisdom of Crowds, Thomas Malthus, trade route, traveling salesman, urban planning, urban renewal, urban sprawl, walkable city, white flight, Y2K, Yom Kippur War

Klieber’s original law of energy consumption worked on a sublinear quarter-rule, so that the metabolic rate does not correspond exactly to an increase in body size. Rather than the metabolic rate increasing by 100 per cent whenever the animal doubles in size, it follows a ‘sublinear’ path and increases by only 75 per cent. The city, on the other hand, follows a similar ‘superlinear’ power law, so that every time it doubles in size, it increases its efficiency and energy use. West’s results can be seen across the board: moving to a city that is twice the size will increase per capita income, it will also be a more creative and industrious place; as the pace of all socio-economic activity accelerates, this leads to higher productivity while economic and social activities diversify.12 The increased complexity that comes from the agglomeration that one finds in the city, therefore, is what makes cities special.

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As West said in a 2010 interview with the New York Times, he offers a scientific bedrock to Jane Jacobs’s imaginative hunch: ‘One of my favourite compliments is when people come up to me and say, “You have done what Jane Jacobs would have done, if only she could do mathematics” … What the data clearly shows, and what she was clever enough to anticipate, is that when people come together, they become much more productive.’13 While Jacobs focused her attention on her own front stoop and observed life on her local street, West’s superlinear power law shows how this complexity is applicable wherever people gather. The city of the twenty-first century will not be a rational or ordered place; the world city will more likely resemble the chaotic lives of the hundreds of thousands who have just arrived and are looking for a home. It will be a dynamic place of transition and transformation, discovering for itself the underlying laws of how it works.

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From an economic view, this makes sense.’4 It might make sense, and has clearly worked in Bilbao, but this is not the only way to define a creative city, nor does it truly tell us why they will become so important in the future. Recall Geoffrey West’s study into the metabolism of the city. Gathering together all possible data on the urban world, West and his team at the Santa Fe Institute discovered that cities display a superlinear power law when it came to size and output. Thus the city that grows by, say, ten times does not just improve its performance by ten but by sixteen times its original. This was, they proposed, true of the city’s economic power, energy efficiency, even crime rate and levels of disease; surprisingly, it is also true for the city’s creativity: ‘wages, income, domestic product, bank deposits, as well as rates of invention, measured by new patents and employment in creative sectors all scale superlinearly with city size’.5 Thus, the complex interweave of connections and people, the agglomeration of knowledge and ideas, is an amazing incubator of innovation.

The Nature of Software Development: Keep It Simple, Make It Valuable, Build It Piece by Piece by Ron Jeffries

Amazon Web Services, anti-pattern, bitcoin, business cycle, business intelligence, business logic, business process, c2.com, call centre, cloud computing, continuous integration, Conway's law, creative destruction, dark matter, data science, database schema, deep learning, DevOps, disinformation, duck typing, en.wikipedia.org, fail fast, fault tolerance, Firefox, Hacker News, industrial robot, information security, Infrastructure as a Service, Internet of things, Jeff Bezos, Kanban, Kubernetes, load shedding, loose coupling, machine readable, Mars Rover, microservices, Minecraft, minimum viable product, MITM: man-in-the-middle, Morris worm, move fast and break things, OSI model, peer-to-peer lending, platform as a service, power law, ransomware, revision control, Ruby on Rails, Schrödinger's Cat, Silicon Valley, six sigma, software is eating the world, source of truth, SQL injection, systems thinking, text mining, time value of money, transaction costs, Turing machine, two-pizza team, web application, zero day

Beware of the way that patterns of relationships can change from QA to production as well. Early social media sites assumed that the number of connections per user would be distributed on something like a bell curve. In fact it’s a power law distribution, which behaves totally differently. If you test with bell-curve distributed relationships, you would never expect to load an entity that has a million times more relationships than the average. But that’s guaranteed to happen with a power law. If you’re handcrafting your own SQL, use one of these recipes to limit the number of rows to fetch: ​ ​-- Microsoft SQL Server​ ​ ​SELECT​ TOP 15 colspec ​FROM​ tablespec ​ ​ ​-- Oracle (since 8i)​ ​ ​SELECT​ colspec ​FROM​ tablespec ​ ​WHERE​ rownum <= 15 ​ ​ ​-- MySQL and PostgreSQL​ ​ ​SELECT​ colspec ​FROM​ tablespec ​ ​LIMIT​ 15 An incomplete solution (but better than nothing) would be to query for the full results but break out of the processing loop after reaching the maximum number of rows.

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A Note on Microservices Microservices are a technological solution to an organizational problem. As an organization grows, the number of communication pathways grows exponentially. Similarly, as a piece of software grows, the number of possible dependencies within the software grows exponentially. Classes tend toward a power-law distribution. Most classes have one or a few dependencies, while a very small number have hundreds or thousands. That means any particular change is likely to encounter one of those and incur a large risk of “action at a distance.” This makes developers hesitant to touch the problem classes, so necessary refactoring pressure is ignored and the problem gets worse.

Smarter Faster Better: The Secrets of Being Productive in Life and Business by Charles Duhigg

Air France Flight 447, Asperger Syndrome, Atul Gawande, behavioural economics, Black Swan, cognitive dissonance, Daniel Kahneman / Amos Tversky, data science, David Brooks, digital map, epigenetics, Erik Brynjolfsson, framing effect, high-speed rail, hiring and firing, index card, John von Neumann, knowledge worker, Lean Startup, Malcom McLean invented shipping containers, meta-analysis, new economy, power law, Saturday Night Live, Silicon Valley, Silicon Valley startup, statistical model, Steve Jobs, the scientific method, the strength of weak ties, theory of mind, Toyota Production System, William Langewiesche, Yom Kippur War

They were interested in these events because if you were to graph multiple examples of each one, a distinct pattern would emerge. Box office totals, for instance, typically conform to a basic rule: There are a few blockbusters each year that make a huge amount of money, and lots of other films that never break even. Within mathematics, this is known as a “power law distribution,” and when the revenues of all the movies released in a given year are graphed together, it looks like this: Graphing other kinds of events results in different patterns. Take life spans. A person’s odds of dying in a specific year spike slightly at birth—because some infants perish soon after they arrive—but if a baby survives its first few years, it is likely to live decades longer.

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How long will he or she live? A cake has been baking for fourteen minutes. How much longer does it need to stay in the oven? You meet a U.S. congressman who has served for fifteen years. How long will he serve in total? The students weren’t given any additional information. They weren’t told anything about power law distributions or Erlang curves. Rather, they were simply asked to make a prediction based on one piece of data and no guidance about what kinds of probabilities to apply. Despite those handicaps, the students’ predictions were startlingly accurate. They knew that a movie that’s earned $60 million is a blockbuster, and is likely to take in another $30 million in ticket sales.

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In fact, when Tenenbaum and Griffiths graphed all of the students’ predictions for each question, the resulting distribution curves almost perfectly matched the real patterns the professors had found in the data they had collected online. Just as important, each student intuitively understood that different kinds of predictions required different kinds of reasoning. They understood, without necessarily knowing why, that life spans fit into a normal distribution curve whereas box office grosses tend to conform to a power law. Some researchers call this ability to intuit patterns “Bayesian cognition” or “Bayesian psychology,” because for a computer to make those kinds of predictions, it must use a variation of Bayes’ rule, a mathematical formula that generally requires running thousands of models simultaneously and comparing millions of results.*2 At the core of Bayes’ rule is a principle: Even if we have very little data, we can still forecast the future by making assumptions and then skewing them based on what we observe about the world.

Delete: The Virtue of Forgetting in the Digital Age by Viktor Mayer-Schönberger

digital divide, en.wikipedia.org, Erik Brynjolfsson, Firefox, full text search, George Akerlof, information asymmetry, information retrieval, information security, information trail, Internet Archive, invention of movable type, invention of the printing press, John Markoff, Joi Ito, lifelogging, moveable type in China, Network effects, packet switching, Panopticon Jeremy Bentham, pattern recognition, power law, RFID, slashdot, Steve Jobs, Steven Levy, systematic bias, The Market for Lemons, The Structural Transformation of the Public Sphere, Vannevar Bush, Yochai Benkler

There is one small exception: Information that is acquired without explicit attention may be able to bypass short-term memory to reach long-term memory, but this is not the intentional memorizing of sensory stimuli that we refer to when talking about remembering and forgetting. 6. It is likely that procedural memory is captured through different biological processes compared with declarative memory; see The Economist, “H.M.,” Dec. 18, 2008, 146. 7. Wixted and Carpenter, “The Wickelgren Power Law and the Ebbinghaus Savings Function,” 133–34. 8. Schacter, How the Mind Forgets and Remembers, 134. 9. See Berg, “Remembering Every Day of Your Life.” 10. This is simply another way to state that, in regards to entropy and information, as randomness increases so does the information in the system, and vice versa. 11.

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“The Advantages of Amnesia.” Boston Globe. Sept. 23, 2007. http://www.boston.com/news/globe/ideas/articles/2007/09/23/ the_advantages_of_amnesia/?page=full. Wired. “Raw Data.” April 2000. http://www.wired.com/wired/archive/8.04/mustread.html?pg=15. Wixted, John T. and Shana K. Carpenter. “The Wickelgren Power Law and the Ebbinghaus Savings Function.” Psychological Science 18 (2007): 133–34. Wylie, Glenn R., John J. Foxe, and Tracy L. Taylor. “Forgetting as an Active Process: An fMRI Investigation of Item-Method–Directed Forgetting.” Cerebral Cortex 18(3) (2008): 670–82. Yu, Peter K. “Of Monks, Medieval Scribes, and Middlemen.”

Mastering Pandas by Femi Anthony

Amazon Web Services, Bayesian statistics, correlation coefficient, correlation does not imply causation, data science, Debian, en.wikipedia.org, Internet of things, Large Hadron Collider, natural language processing, p-value, power law, random walk, side project, sparse data, statistical model, Thomas Bayes

This rarely happens in practice and the points do not all fit neatly on a straight line. Then the relationship is imperfect. In some cases, a linear relationship only occurs among log-transformed variables. This is a log-log model. An example of such a relationship would be a power law distribution in physics where one variable varies as a power of another. Thus, an expression such as results in the linear relationship. For more information see: http://en.wikipedia.org/wiki/Power_law To construct the best-fit line, the method of least squares is used. In this method, the best-fit line is the optimal line that is constructed between the points for which the sum of the squared distance from each point to the line is the minimum.

Rigged Money: Beating Wall Street at Its Own Game by Lee Munson

affirmative action, Alan Greenspan, asset allocation, backtesting, barriers to entry, Bear Stearns, Bernie Madoff, Bretton Woods, business cycle, buy and hold, buy low sell high, California gold rush, call centre, Credit Default Swap, diversification, diversified portfolio, estate planning, fear index, fiat currency, financial engineering, financial innovation, fixed income, Flash crash, follow your passion, German hyperinflation, Glass-Steagall Act, global macro, High speed trading, housing crisis, index fund, joint-stock company, junk bonds, managed futures, Market Wizards by Jack D. Schwager, Michael Milken, military-industrial complex, money market fund, moral hazard, Myron Scholes, National best bid and offer, off-the-grid, passive investing, Ponzi scheme, power law, price discovery process, proprietary trading, random walk, Reminiscences of a Stock Operator, risk tolerance, risk-adjusted returns, risk/return, Savings and loan crisis, short squeeze, stocks for the long run, stocks for the long term, too big to fail, trade route, Vanguard fund, walking around money

The first clue that you need to upgrade your adviser is simple: A pie chart is used. Rarely will you see a pie chart being used by someone who studies statistics. One of the reasons is that people don’t perceive a visual area as well as they perceive length. There are some theories about this, including Stevens’ power law. It suggests that people don’t see visual space like in a pie chart as accurately as they do length. A simple bar chart is easier for a human to decipher as shown in Figure 2.1. I think pie charts are the preferred method of delivering information because they are visually pleasing and suggest a cohesive unit to talk about.

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See Securities and Exchange Commission Section 28(e) sectors Securities Act of 1944 Securities and Exchange Commission Securities Reform Act of 1975 Security Analysis sell Ship of Gold in the Deep Blue Sea short sideways markets silver, gold versus small business, 401(k) and Smith, Adam soft dollars Sorkin, Andrew sounding board spiders Spitzer, Elliott Standard and Poor’s ETF Stevens’ power law sticky clients stock brokers stock exchanges, Amsterdam stock sales, investment banking and story super cycle sustainability, investment T tax-deferred investment plan third-party administrator (TPA) third-party research time Top Stocks TPA. See third-party administrator track record tracking error trade aways traders, becoming trading rates Treasury yields types of investors U United Copper Company upgrade V volatility, S&P 500 versus W Wilson, Woodrow

When More Is Not Better: Overcoming America's Obsession With Economic Efficiency by Roger L. Martin

activist fund / activist shareholder / activist investor, Affordable Care Act / Obamacare, autism spectrum disorder, banking crisis, Black Monday: stock market crash in 1987, butterfly effect, call centre, cloud computing, complexity theory, coronavirus, COVID-19, David Ricardo: comparative advantage, do what you love, Edward Lorenz: Chaos theory, financial engineering, Frederick Winslow Taylor, Glass-Steagall Act, High speed trading, income inequality, industrial cluster, inflation targeting, Internet of things, invisible hand, Lean Startup, low interest rates, Lyft, Mark Zuckerberg, means of production, Network effects, new economy, obamacare, open economy, Phillips curve, Pluto: dwarf planet, power law, Renaissance Technologies, Richard Florida, Ronald Reagan, scientific management, shareholder value, Silicon Valley, Snapchat, Spread Networks laid a new fibre optics cable between New York and Chicago, Tax Reform Act of 1986, The future is already here, the map is not the territory, The Wealth of Nations by Adam Smith, Tobin tax, Toyota Production System, transaction costs, trickle-down economics, two-sided market, uber lyft, very high income, Vilfredo Pareto, zero-sum game

At the turn of the twentieth century, Italian economist Vilfredo Pareto noted that, at the time, 20 percent of Italian families owned 80 percent of Italy’s land.1 Most of the remaining 80 percent, who owned no land, farmed the land owned by their rich and often oppressive landlords. The Pareto distribution named in his honor—or Power Law distribution to most statisticians—takes the shape of the curve seen in figure 3-1. On this curve the many poor Italians with little to no land are on the left side and the very few superrich, landowning families are in the long tapered end to the right. Along with a very different shape, a Pareto distribution has markedly different characteristics than a Gaussian distribution.

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See New York Stock Exchange Obamacare, 92 Office of the Superintendent of Financial Institutions (OFSI), 139–141 off-shoring, 155 oligopolies, 63 optimal financial structure, 173 options trading, 55 outsourcing, 155 Pareto, Vilfredo, 59 Pareto distribution, 46, 57, 59–76, 100 challenge of, 75–76 in companies, 71–73 of income, 161–162 monocultures and, 73–75 Parker, Jeffrey, 86 Parkland shooting, 197 participatory budgeting, 199–200 Penner, Elliot, 188 perfection, 103–106, 113, 126 performance management, 173 Pershing Square, 158 Persona Project, 2, 4, 14–16, 206 Phillips curve, 24 pitch-count restrictions, 102 platform businesses, 71 policy making long-term thinking and, 155–159 mental proximity and, 145–149 revision and, 142–145 political economy, 38 political leaders, 113–114 agenda for, 137–163 political parties, 92, 201–205 political relationships, 197–200 politicians, 197–205 politics, disengagement from, 3, 198 Porter, Michael, 17, 67, 128 power, abuse of, 152–153 power blackouts, 106–107 Power Law distribution. See Pareto distribution preferential attachment, 61 pressure, 100–103, 113 prices, decline in, 9–10 Principles of Scientific Management, The (Taylor), 42 private markets, 91 Private Securities Litigation Reform Act, 87, 112 Private Sponsorship of Refugees Program, 196 problem solving, 172–174 procurement costs, 50, 63 production-cost efficiencies, 54 productive friction, 102, 113, 142, 149–152 productivity growth, 8–10, 42 Progressive Era, 53 progressive taxation, 14, 159–162 protectionism, 151 proxies in business, 49–53 in economic policy, 53–56 in education, 45–49 lineage of, 56–57 long-term, 155–159 for measuring progress, 46 multiple measurements as, 127–129, 135 outcomes and, 57 problem with, 46–57 surrogation and, 127–129 public companies, 91 public policy models, 29–30 schools of, 180 public utilities, 152 purchasing power, 188–192, 207 Putnam, Robert, 199 Qualcomm, 154 qualities, appreciation of, 181–184 quantities, 181, 182 QuikTrip, 125 Rajgopal, Shiva, 155 random-access memory (RAM), 177 Reagan, Ronald, 54, 160 real income, 10, 11 real world, interaction with, 178–181 reciprocal political relationships, 197–200 Reckitt Benckiser Group, 188 reductionism, 119–123, 134, 173–178 redundancies, 111, 133–134 reflectiveness, 172, 213–214 refugees, 196 regulations, financial, 107–108, 112, 139–141, 143 Reichheld, Fred, 27, 48, 147–148 Renaissance Technologies, 157 Repo 105, 85, 86, 104, 137 Report on the Subject of Manufactures (Hamilton), 40 representative government, 201 Republicans, 160–161, 197–198 See also political parties; politicians resilience, 98–99 balance between efficiency and, 15, 99–114, 210 monopolies and, 132 restaurant industry, 115–116 restrictor plates, 102, 103 retailers, 124–126 revision, of laws, 142–145 Ricardo, David, 40–42, 56 Riel, Jennifer, 171 Ries, Eric, 156 Rise of the Creative Class, The (Florida), 67–68 robber barons, 53 Rockefeller, John D., 129 Rodrik, Dani, 150 Ronaldo, Cristiano, 61, 64–65 Roosevelt, Franklin, 12 Rotman School of Management, 176, 180, 212–213 routine-intensive jobs, 68–70 rules, 142–145 safe harbor provision, 87 Sandy Hook shooting, 197 Santa Fe Institute, 177 Sarbanes-Oxley Act (SOX), 84–85, 142 Sawitz, Stephen, 116–119 Scherer, Stephen, 111–112 school reform, 29–30, 49 school shootings, 197 scientific management, 42 SeaWorld Entertainment, 192 Securities and Exchange Commission (SEC), 64, 90, 112–113, 156 self-interest, 94, 203 Senate, 201, 202 separation, 106–113 September 11, 2001, 111 shareholder value, 50–52 Sharp, Isadore, 122, 123 Sherman Antitrust Act, 53, 152 short-term capital, 157 short-term efficiency, 155 siloes, 32, 122 Sinatra, Frank, 64, 65 Singapore, 93–94 slack, 50, 56, 63, 123–127, 132, 134–135 Sloan School of Management, 177 smartphones, 131 Smith, Adam, 39–40, 41, 56 Smoot-Hawley Tariff Act, 41 Snapchat, 129, 191, 192 social media, 61, 65, 191 South Korea, 151 Southwest Airlines, 127–128 SOX.

A Man for All Markets by Edward O. Thorp

"RICO laws" OR "Racketeer Influenced and Corrupt Organizations", 3Com Palm IPO, Alan Greenspan, Albert Einstein, asset allocation, Bear Stearns, beat the dealer, Bernie Madoff, Black Monday: stock market crash in 1987, Black Swan, Black-Scholes formula, book value, Brownian motion, buy and hold, buy low sell high, caloric restriction, caloric restriction, carried interest, Chuck Templeton: OpenTable:, Claude Shannon: information theory, cognitive dissonance, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Edward Thorp, Erdős number, Eugene Fama: efficient market hypothesis, financial engineering, financial innovation, Garrett Hardin, George Santayana, German hyperinflation, Glass-Steagall Act, Henri Poincaré, high net worth, High speed trading, index arbitrage, index fund, interest rate swap, invisible hand, Jarndyce and Jarndyce, Jeff Bezos, John Bogle, John Meriwether, John Nash: game theory, junk bonds, Kenneth Arrow, Livingstone, I presume, Long Term Capital Management, Louis Bachelier, low interest rates, margin call, Mason jar, merger arbitrage, Michael Milken, Murray Gell-Mann, Myron Scholes, NetJets, Norbert Wiener, PalmPilot, passive investing, Paul Erdős, Paul Samuelson, Pluto: dwarf planet, Ponzi scheme, power law, price anchoring, publish or perish, quantitative trading / quantitative finance, race to the bottom, random walk, Renaissance Technologies, RFID, Richard Feynman, risk-adjusted returns, Robert Shiller, rolodex, Sharpe ratio, short selling, Silicon Valley, Stanford marshmallow experiment, statistical arbitrage, stem cell, stock buybacks, stocks for the long run, survivorship bias, tail risk, The Myth of the Rational Market, The Predators' Ball, the rule of 72, The Wisdom of Crowds, too big to fail, Tragedy of the Commons, uptick rule, Upton Sinclair, value at risk, Vanguard fund, Vilfredo Pareto, Works Progress Administration

To those who balk at changing their ways we can only ask, along with Regis Philbin, “Who wants to be a millionaire?” Investors I dealt with typically were not just millionaires but multimillionaires with fortunes of $5 million and up. How many households have reached these rarefied heights? The great Italian economist Vilfredo Pareto studied the distribution of income and in 1897 came up with a “power law” formula that seems then and now to describe fairly well how many top wealth holders in a modern society have reached various levels. To calibrate the formula we need just these two facts: The Forbes 400 cutoff for the United States, which was $1.55 billion in 2014, and the total wealth of those four hundred, an amazing $2.3 trillion.

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saves $6 each day He saves more each day in later years assuming the price of cigarettes increases along with inflation. An article http://quickenloans.quicken.com/​Articles/​fthbc_afford_budget.asp. $10,000 difference grows Mentally calculated by the rule of 240 in Appendix C. The formula Assume the power law N = AW–B, where W is a high enough wealth level to exclude most people, and N is the number having wealth at least W, and A and B are unknowns. The two facts I used to find A and B were (1) when N = 400, W = $1.3 billion, and (2) the total wealth of the 400 was $1.2 trillion, giving an average value of three times the cutoff.

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$37 million each Bloomberg, August 17, 2009, citing UC–Berkeley economics professor Emmanuel Saez, noted for his continuing studies of, and statistics on, the distribution of income and wealth in America. Note that the average of $37 million, divided by the cutoff of $11.5 million, is 3.2, very close to the result of the same calculation for the wealth distribution of the Forbes 400, suggesting that 2007 superrich taxable income followed the same, or nearly the same, power law as that for wealth. CHAPTER 24 disputed origin The claimed sources include Benjamin Franklin, various Rothschilds, Albert Einstein, Bernard Baruch, and “unknown.” $22 million result These figures do not include trading costs or income taxes. A buy-and-hold investor loses little to trading costs and is taxed only on dividends.

Lean Analytics: Use Data to Build a Better Startup Faster by Alistair Croll, Benjamin Yoskovitz

Airbnb, Amazon Mechanical Turk, Amazon Web Services, Any sufficiently advanced technology is indistinguishable from magic, barriers to entry, Bay Area Rapid Transit, Ben Horowitz, bounce rate, business intelligence, call centre, cloud computing, cognitive bias, commoditize, constrained optimization, data science, digital rights, en.wikipedia.org, Firefox, Frederick Winslow Taylor, frictionless, frictionless market, game design, gamification, Google X / Alphabet X, growth hacking, hockey-stick growth, Infrastructure as a Service, Internet of things, inventory management, Kickstarter, lateral thinking, Lean Startup, lifelogging, longitudinal study, Marshall McLuhan, minimum viable product, Network effects, PalmPilot, pattern recognition, Paul Graham, performance metric, place-making, platform as a service, power law, price elasticity of demand, reality distortion field, recommendation engine, ride hailing / ride sharing, rolodex, Salesforce, sentiment analysis, skunkworks, Skype, social graph, social software, software as a service, Steve Jobs, subscription business, telemarketer, the long tail, transaction costs, two-sided market, Uber for X, web application, Y Combinator