power law

Why Stock Markets Crash: Critical Events in Complex Financial Systems
by Didier Sornette
Published 18 Nov 2002

.  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
Published 31 Mar 2009

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
Published 27 Nov 2018

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
Published 1 Jan 2006

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
Published 24 Sep 2018

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 and Richard L. Hudson
Published 7 Mar 2006

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
Published 25 Jul 2011

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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When the frequency of something (i.e., number of occurrences of object or event) varies as a power (a.k.a., 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
Published 15 May 2017

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
Published 1 Nov 2008

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 and Blake Masters
Published 15 Sep 2014

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
Published 1 Feb 2022

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
Published 1 Feb 2003

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
Published 28 Feb 2008

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
Published 23 Feb 2012

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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Growth: From Microorganisms to Megacities
by Vaclav Smil
Published 23 Sep 2019

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
Published 1 Jan 2003

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 and Jon Kleinberg
Published 15 Nov 2010

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
Published 14 May 2006

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 and Tom Griffiths
Published 4 Apr 2016

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.

How Big Things Get Done: The Surprising Factors Behind Every Successful Project, From Home Renovations to Space Exploration
by Bent Flyvbjerg and Dan Gardner
Published 16 Feb 2023

Andriani, Pierpaolo, and Bill McKelvey. 2007. “Beyond Gaussian Averages: Redirecting International Business and Management Research Toward Extreme Events and Power Laws.” Journal of International Business Studies 38 (7): 1212–30. Andriani, Pierpaolo, and Bill McKelvey. 2009. “Perspective—from Gaussian to Paretian Thinking: Causes and Implications of Power Laws in Organizations.” Organization Science 20 (6): 1053–71. Andriani, Pierpaolo, and Bill McKelvey. 2011. “From Skew Distributions to Power-Law Science.” In Complexity and Management, eds. P. Allen, S. Maguire, and Bill McKelvey. Los Angeles: Sage, 254–73. Anguera, Ricard. 2006.

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The average overrun is 157 percent in real terms. Only nuclear waste storage has higher cost overruns of the twenty-plus project categories my team and I study. Scarier still, the overruns follow a power-law distribution, meaning that really extreme overruns are surprisingly common. The current holder of the one Olympic record no one wants—in cost overrun—is Montreal, which went 720 percent over budget in 1976. But thanks to the power law, it is likely only a matter of time before some unlucky city becomes the new Olympic champion.10 There are many reasons for the sorry record of the Olympics, but much of the explanation lies in the way the Games aggressively marginalize experience.

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The Strategic Management of Large Engineering Projects: Shaping Institutions, Risks, and Governance. Cambridge, MA: MIT Press. MIT Energy Initiative. 2018. The Future of Nuclear Energy in a Carbon-Constrained World. Cambridge, MA: MIT. Mitzenmacher, Michael. 2004. “A Brief History of Generative Models for Power Law and Lognormal Distributions.” Internet Mathematics 1 (2): 226–51. Mitzenmacher, Michael. 2005. “Editorial: The Future of Power Law Research.” Internet Mathematics 2 (4): 525–34. Molle, François, and Philippe Floch. 2008. “Megaprojects and Social and Environmental Changes: The Case of the Thai Water Grid.” AMBIO: A Journal of the Human Environment 37 (3): 199–204.

Rockonomics: A Backstage Tour of What the Music Industry Can Teach Us About Economics and Life
by Alan B. Krueger
Published 3 Jun 2019

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
Published 24 Sep 2012

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
Published 1 Mar 2016

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 and Andrew McAfee
Published 20 Jan 2014

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
Published 14 Oct 2005

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
Published 14 Jul 2012

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
Published 26 Feb 2017

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 .

NumPy Cookbook
by Ivan Idris
Published 30 Sep 2012

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.

Radical Uncertainty: Decision-Making for an Unknowable Future
by Mervyn King and John Kay
Published 5 Mar 2020

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.

The Middleman Economy: How Brokers, Agents, Dealers, and Everyday Matchmakers Create Value and Profit
by Marina Krakovsky
Published 14 Sep 2015

“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
Published 3 Jun 2019

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
Published 24 Mar 2020

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
Published 10 Nov 2011

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
Published 5 Jun 2023

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
Published 3 Feb 2015

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
Published 31 Mar 2015

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
Published 18 Jun 2018

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
Published 31 Aug 2012

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
Published 19 Mar 2019

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
Published 4 Mar 2014

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 and Milan M. Cirkovic
Published 2 Jul 2008

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
Published 2 Jan 2010

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
Published 31 Jul 2014

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 and Jeffrey David Ullman
Published 13 Nov 2014

” (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
Published 21 Sep 2015

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
Published 24 Jan 2017

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
Published 18 Jul 2016

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
Published 6 Nov 2012

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
Published 20 Feb 2018

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
Published 7 Feb 2017

“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
Published 1 Jun 2020

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
Published 14 Nov 2012

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
Published 16 Mar 2018

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.

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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
Published 14 May 2018

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).

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“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.

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“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
Published 1 Jan 2010

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 and Lauren McCann
Published 17 Jun 2019

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.

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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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Department of, 97 just world hypothesis, 22 Kahneman, Daniel, 9, 30, 90 karoshi, 82 Kauffman Foundation, 122 keeping up with the Joneses, 210–11 key person insurance, 305 King, Martin Luther, Jr., 129, 225 KISS (Keep It Simple, Stupid), 10 knowledge, institutional, 257 knowns: known, 197 unknown, 198, 203 known unknowns, 197–98 Knox, Robert E., 91 Kodak, 302–3, 308–10, 312 Koenigswald, Gustav Heinrich Ralph von, 50 Kohl’s, 15 Kopelman, Josh, 301 Korea, 229, 231, 235, 238 Kristof, Nicholas, 254 Krokodil, 49 Kruger, Justin, 269 Kuhn, Thomas, 24 Kutcher, Ashton, 121 labor market, 283–84 laggards, 116–17 landlords, 178, 179, 182, 188 Laplace, Pierre-Simon, 132 large numbers, law of, 143–44 Latané, Bibb, 259 late majority, 116–17 lateral thinking, 201 law of diminishing returns, 81–83 law of diminishing utility, 81–82 law of inertia, 102–3, 105–8, 110, 112, 113, 119, 120, 129, 290, 296 law of large numbers, 143–44 law of small numbers, 143, 144 Lawson, Jerry, 289 lawsuits, 231 leadership, 248, 255, 260, 265, 271, 275, 276, 278–80 learned helplessness, 22–23 learning, 262, 269, 295 from past events, 271–72 learning curve, 269 Le Chatelier, Henri-Louis, 193 Le Chatelier’s principle, 193–94 left to their own devices, 275 Leibniz, Gottfried, 291 lemons into lemonade, 121 Lernaean Hydra, 51 Levav, Jonathan, 63 lever, 78 leverage, 78–80, 83, 115 high-leverage activities, 79–81, 83, 107, 113 leveraged buyout, 79 leveraging up, 78–79 Levitt, Steven, 44–45 Levitt, Theodore, 296 Lewis, Michael, 289 Lichtenstein, Sarah, 17 lightning, 145 liking, 216–17, 220 Lincoln, Abraham, 97 Lindy effect, 105, 106, 112 line in the sand, 238 LinkedIn, 7 littering, 41, 42 Lloyd, William, 37 loans, 180, 182–83 lobbyists, 216, 306 local optimum, 195–96 lock-in, 305 lock in your gains, 90 long-term negative scenarios, 60 loose versus tight, in organizational culture, 274 Lorenz, Edward, 121 loss, 91 loss aversion, 90–91 loss leader strategy, 236–37 lost at sea, 68 lottery, 85–86, 126, 145 low-context communication, 273–74 low-hanging fruit, 81 loyalists versus mercenaries, 276–77 luck, 128 making your own, 122 luck surface area, 122, 124, 128 Luft, Joseph, 196 LuLaRoe, 217 lung cancer, 133–34, 173 Lyautey, Hubert, 276 Lyft, ix, 288 Madoff, Bernie, 232 magnetic resonance imaging (MRI), 291 magnets, 194 maker’s schedule versus manager’s schedule, 277–78 Making of Economic Society, The (Heilbroner), 49 mammograms, 160–61 management debt, 56 manager’s schedule versus maker’s schedule, 277–78 managing to the person, 255 Manhattan Project, 195 Man in the High Castle, The (Dick), 201 manipulative insincerity, 264 man-month, 279 Mansfield, Peter, 291 manufacturer’s suggested retail price (MSRP), 15 margin of error, 154 markets, 42–43, 46–47, 106 failure in, 47–49 labor, 283–84 market norms versus social norms, 222–24 market power, 283–85, 312 product/market fit, 292–96, 302 secondary, 281–82 winner-take-most, 308 marriage: divorce, 231, 305 same-sex, 117, 118 Maslow, Abraham, 177, 270–71 Maslow’s hammer, xi, 177, 255, 297, 317 Maslow’s hierarchy of needs, 270–71 mathematics, ix–x, 3, 4, 132, 178 Singapore math, 23–24 matrices, 2 × 2, 125–26 consensus-contrarian, 285–86, 290 consequence-conviction, 265–66 Eisenhower Decision Matrix, 72–74, 89, 124, 125 of knowns and unknowns, 197–98 payoff, 212–15, 238 radical candor, 263–64 scatter plot on top of, 126 McCain, John, 241 mean, 146, 149, 151 regression to, 146, 286 standard deviation from, 149, 150–51, 154 variance from, 149 measles, 39, 40 measurable target, 49–50 median, 147 Medicare, 54–55 meetings, 113 weekly one-on-one, 262–63 Megginson, Leon, 101 mental models, vii–xii, 2, 3, 31, 35, 65, 131, 289, 315–17 mentorship, 23, 260, 262, 264, 265 mercenaries versus loyalists, 276–77 Merck, 283 merry-go-round, 108 meta-analysis, 172–73 Metcalfe, Robert, 118 Metcalfe’s law, 118 #MeToo movement, 113 metrics, 137 proxy, 139 Michaels, 15 Microsoft, 241 mid-mortems, 92 Miklaszewski, Jim, 196 Milgram, Stanley, 219, 220 military, 141, 229, 279, 294, 300 milkshakes, 297 Miller, Reggie, 246 Mills, Alan, 58 Mindset: The New Psychology of Success (Dweck), 266 mindset, fixed, 266–67, 272 mindset, growth, 266–67 minimum viable product (MVP), 7–8, 81, 294 mirroring, 217 mission, 276 mission statement, 68 MIT, 53, 85 moats, 302–5, 307–8, 310, 312 mode, 147 Moltke, Helmuth von, 7 momentum, 107–10, 119, 129 Monday morning quarterbacking, 271 Moneyball (Lewis), 289 monopolies, 283, 285 Monte Carlo fallacy, 144 Monte Carlo simulation, 195 Moore, Geoffrey, 311 moral hazard, 43–45, 47 most respectful interpretation (MRI), 19–20 moths, 99–101 Mountain Dew, 35 moving target, 136 multiple discovery, 291–92 multiplication, ix, xi multitasking, 70–72, 74, 76, 110 Munger, Charlie, viii, x–xi, 30, 286, 318 Murphy, Edward, 65 Murphy’s law, 64–65, 132 Musk, Elon, 5, 302 mutually assured destruction (MAD), 231 MVP (minimum viable product), 7–8, 81, 294 Mylan, 283 mythical man-month, 279 name-calling, 226 NASA, 4, 32, 33 Nash, John, 213 Nash equilibrium, 213–14, 226, 235 National Football League (NFL), 225–26 National Institutes of Health, 36 National Security Agency, 52 natural selection, 99–100, 102, 291, 295 nature versus nurture, 249–50 negative compounding, 85 negative externalities, 41–43, 47 negative returns, 82–83, 93 negotiations, 127–28 net benefit, 181–82, 184 Netflix, 69, 95, 203 net present value (NPV), 86, 181 network effects, 117–20, 308 neuroticism, 250 New Orleans, La., 41 Newport, Cal, 72 news headlines, 12–13, 221 newspapers, 106 Newsweek, 290 Newton, Isaac, 102, 291 New York Times, 27, 220, 254 Nielsen Holdings, 217 ninety-ninety rule, 89 Nintendo, 296 Nobel Prize, 32, 42, 220, 291, 306 nocebo effect, 137 nodes, 118, 119 No Fly List, 53–54 noise and signal, 311 nonresponse bias, 140, 142, 143 normal distribution (bell curve), 150–52, 153, 163–66, 191 North Korea, 229, 231, 238 north star, 68–70, 275 nothing in excess, 60 not ready for prime time, 242 “now what” questions, 291 NPR, 239 nuclear chain reaction, viii, 114, 120 nuclear industry, 305–6 nuclear option, 238 Nuclear Regulatory Commission (NRC), 305–6 nuclear weapons, 114, 118, 195, 209, 230–31, 233, 238 nudging, 13–14 null hypothesis, 163, 164 numbers, 130, 146 large, law of, 143–44 small, law of, 143, 144 see also data; statistics nurses, 284 Oakland Athletics, 289 Obama, Barack, 64, 241 objective versus subjective, in organizational culture, 274 obnoxious aggression, 264 observe, orient, decide, act (OODA), 294–95 observer effect, 52, 54 observer-expectancy bias, 136, 139 Ockham’s razor, 8–10 Odum, William E., 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
Published 14 Apr 2014

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
Published 29 May 2009

“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
Published 1 Jan 2001

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).

…

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 and Ionut Florescu
Published 20 Dec 2011

A linear relationship between the F (n) and n (i.e., 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
Published 6 Jun 2016

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
Published 28 Jun 2009

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 and Erin Malone
Published 30 Sep 2009

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
Published 27 Jul 2015

“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
Published 3 Jan 2007

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
Published 25 Feb 2008

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.

Visions of Inequality: From the French Revolution to the End of the Cold War
by Branko Milanovic
Published 9 Oct 2023

Thicker upper tails of income distribution are therefore associated with higher synthetic measures of inequality. 46 Pareto’s Contributions It would be wrong to conclude from this chapter’s critique of Pareto’s findings that his contributions were small. They were important in several ways. Pareto defined the first power law, which is used in many instances and not only for distributions of income and wealth but also for distributions of cities by population, for sizes of floods, for numbers of publications by author, and even for numbers of Twitter followers. Pareto’s power law is used heuristically in income and wealth distributions today, when the need arises to estimate the extreme top of the distribution but the data are lacking—perhaps because the rich do not participate in surveys or incomes are underreported to fiscal authorities.

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He was thus the first to ask the question point blank: Does income inequality move according to some regularity as social institutions or incomes of society change? For him, the answer was in the negative, and we know by now that he was wrong. But the question was important to ask. a The relationship can be directly transformed into a power law distribution: b As Pareto himself realized, this was true only for top incomes, since only the rich were subject to direct taxation. c Pareto did, however, believe it was impossible for leaders to be entirely cynical and to fully disbelieve what they were teaching. They were bound to believe in their own propaganda, at least in part.

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Darcy (fictional character), 309n9 My Disillusionment in Russia (Goldman, E.), 329n41 Namibia, 179 Napoleonic wars, 86–89 , 98 , 112 narratives, 10–11 , 25–28 , 247–249 national product, 189 Navigation Act, 48 needs, 135–138 , 178 Netherlands, the, 51 , 68 , 69 , 70 , 73 net income, 45 , 90 , 93–94 , 96 net product, 11 , 45 , 93 , 94 , 100 , 121 , 123 net value added, 93 Nobel Memorial Prize in Economics, 254 nobility, 8 , 32 , 40 , 70 “nomad population,” 154 non-logico-experimental theories, 321n11 normal price, 120 , 223 North America, 47 , 49 , 51 , 59 , 73–74 , 76 , 308n67 Novokmet, Filip, 294 , 330n50 numerical examples: of Kuznets, 201 ; of Marx, 20–21 , 142–143 ; of Quesnay, 18 ; of Ricardo, 20–21 , 25 , 103 , 311n38 October Revolution, 23–24 Ofer, Gur, 326n14 Offer, Avner, 97 , 311n27 , 326n6 Okun, Arthur, 104 Olson, Mancur, 326n13 Omissions, in history of inequality studies, 11–12 “On Machinery” (Ricardo, D.), 20 , 100–101 , 300n21 “On the Jewish Question” (Marx, K.), 108 “On the People’s Democratic Dictatorship” (Mao Zedong), 236 ophelimity, 173 “optimum for a community” (Pareto optimum), 3 , 222 , 314n28 , 326n6 organic community, 67 , 304n10 , 306n33 organic composition of capital, 137–138 , 141–142 , 317n79 , 317n86 , 317n88 Ottoman Empire, 49 , 52 , 295 owners, 13 , 57 , 60 , 328n36 ; capital, 145 , 148 , 155 , 156 , 158 , 230 ; landowners, 35 , 37–38 , 40 , 45 , 59 , 61 , 83 , 125 , 127 , 129–130 , 197 , 241 , 243 , 304n37 ; petty bourgeoisie, 125 , 126 , 129 , 130 , 236 ; systems of non-private ownership of capital, 223–226 ; systems of state ownership of capital, 226–240 pan-mechanicism, 177–178 pan-organismic, 177 Pantaleoni, Maffeo, 180 paradis artificiels, Les (Baudelaire), 308n1 Pareto (coefficient) constant: calculated for different countries and at different parts of distribution, 181–183 , 183 ; Gini and, 184–185 ; guillotine, 175 , 181 , 182 , 184 , 185 ; income distribution among English and Welsh taxpayers, 1865, 159 , 160 ; inverse, 322n46 ; inverted, 322n46 ; Pareto’s law of income distribution and, 179–185 Pareto, Vilfredo, 1 , 241 , 244 ; body of work, 2 , 3 ; class struggle and, 164 ; contributions and legacy, 185–188 , 213 ; with elite and general population, 12 , 14 ; with inequality in France at turn of century, 168–172 ; interpersonal income inequality and, 158–160 ; Kuznets and, 25 , 187 ; legal inequality and, 29–30 ; letter to Pantaleoni from, 180 ; life of, 55 , 163–168 ; “logico-experimental” theories and, 166–167 , 187 , 321n11 ; Manual of Political Economy , 163 , 180 , 181 , 187 , 322n44 ; Marx, Karl, and, 17 , 164 , 172 , 187 , 194 ; with narrative, theory and empirics, 25 ; new ruling class and, 328n26 ; non-logico-experimental theories and, 321n11 ; in politics, 166 , 167 ; power law and, 175 , 185 ; on racism, 320nn3–4 ; social class and, 26–27 ; socialism and, 164–165 ; sociological theory and, 14 , 176 ; style and voice of, 24 ; with Swiss Canton of Vaud, 322n30 ; Les systèmes socialistes , 17 , 165 , 180 , 320n8 ; with taxes and income data, 322n44 ; timeline of, 6 ; with truth being harmful, 166 , 168 ; universalism and, 214 ; with vision of inequality, 12 , 14 ; Walras and, 3 Pareto optimum (“optimum for a community”), 3 , 222 , 314n28 , 326n6 Pareto’s law, 29 ; “circulation of the elites” with socialism, 172–179 ; empirical relationship in actual income distribution, 181 , 182 ; of income distribution and Pareto constant, 179–185 ; income distributions, 175 , 176 ; line drawn across highest amounts of corruption in China, 185 , 186 “patriotic capitalists,” 236 paupers, 32 , 34–35 , 57 , 59 , 203–204 , 302n18 peasantry, 4 , 37–38 , 59 , 60 , 79 , 238 ; dispossession of, 281 , 334n105 ; kulaks, 241 , 243 ; landowning, 35 , 127 , 129–130 , 197 , 241 , 243 ; poor and middle, 242 , 328n37 ; population, 43 ; Soviet Union, 127 , 328nn37–38 ; workers and, 78 , 236 Pen, Jan, 261 , 262 , 263 , 331n70 Penguin (publisher), 21 “pernicious system,” 307n41 Peru, 49 , 51 petty bourgeoisie, 125 , 126 , 129 , 130 , 236 Phelps Brown, Henry, 237 Philippines, 203 Philosophie rurale, La (Quesnay, F. and Mirabeau, V.

Television disrupted: the transition from network to networked TV
by Shelly Palmer
Published 14 Apr 2006

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).

Starstruck: The Business of Celebrity
by Currid
Published 9 Nov 2010

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

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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Pac-Man, 177 MTV, 176, 214 Mumford, Lewis, 38, 107, 112, 146–47, 154, 242n Murray, Arnold, 43 Museum of the Moving Image, 177 music, 45, 53, 128–29, 214, 217, 258n mutations, genetic, 58, 182–83 Myst, 183–84 Nakagaki, Toshiyuki, 11 Napier, Charles James, 35 Napster, 214, 217 NASDAQ, 117 Nation, 225 National Physical Laboratory, 42, 54 natural selection, 56–63, 83, 169, 170–74, 184, 185–86, 193, 203, 204 Nature of Economies, The (Jacobs), 156 NBC, 136 near-optimal solutions, 228 Negroponte, Nicholas, 159 neighborhoods, 18, 36–38, 41, 50–51, 87–91, 96, 99, 106, 115, 119, 123, 186, 203, 204, 205, 220, 229–30, 233, 246n Netscape browser, 124–25 networks: algorithms for, 88, 89, 161 information, 96–97, 116–26, 134–35, 204–5, 217–18 neural, 18, 21, 78, 115, 118–19, 121, 127, 133–34, 142–44, 146, 198–99, 203–4, 205, 209, 223, 238n, 241n, 256n, 261n, 262n–63n television, 135–36, 159, 160 see also Internet neurons, 18, 21, 78, 115, 118–19, 121, 127, 133–34, 142–44, 146, 198–99, 203–4, 205, 209, 223, 238n, 241n, 256n, 261n, 262n–63n neurotransmitters, 115 New Age, 113–14 New Economy, 224 New Republic, 135 newspapers, 159–60, 207 New Urbanist movement, 147, 230 New York City, 50, 93, 107, 113, 230 New York City Planning Commission, 50 New Yorker, 146 New York Times, 125, 131, 257n–58n Nightline, 135 Nintendo, 176 Nixon, Richard M., 132 nonequilibrium thermodynamics, 12, 43, 52 noosphere, 115–16 nucleic acids, 85 olfactory skills, 76 online communities, 17, 148–62, 204–5 Open Shortest Path First routine, 229 Open Source, 153 orangutans, 202 order: chaos vs., 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.

The Fractalist
by Benoit Mandelbrot
Published 30 Oct 2012

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.

…

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.

High-Frequency Trading
by David Easley , Marcos López de Prado and Maureen O'Hara
Published 28 Sep 2013

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.

…

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 .

Beautiful Visualization
by Julie Steele
Published 20 Apr 2010

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.

…

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.

Deep Survival: Who Lives, Who Dies, and Why
by Laurence Gonzales
Published 1 Dec 1998

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….

…

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 Data: The Stories Behind Elegant Data Solutions
by Toby Segaran and Jeff Hammerbacher
Published 1 Jul 2009

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
Published 31 Mar 2016

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
Published 13 Feb 2018

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 and Jian Pei
Published 21 Jun 2011

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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.; Bogdan, E.P., 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 and Alex McLean
Published 9 Nov 2012

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
Published 15 Jan 2011

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
Published 31 Mar 2013

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
Published 14 Aug 2015

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.

On the Edge: The Art of Risking Everything
by Nate Silver
Published 12 Aug 2024

“One thing that’s kind of a secret in the industry,” he told me, “is that most of the people I compete with, I’m actually pretty somewhere between real friends and very good friends with. So part of what I’m doing is mapping their brain. Like, will they or their fund appreciate this? Are they going to see the signals I’m seeing?” Sebastian Mallaby, the author of an excellent book about Silicon Valley called The Power Law, thinks that in certain respects it is an exceptionally conformist place. “In some ways, venture capitalists are the ultimate herders,” he said. “You go to Sand Hill Road, and you see that they all have offices on the same road. And there’s kind of one good restaurant on that road, at the Rosewood hotel, so they all bump into each other at the same bar.

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And while SBF is an extreme example, he’s of a certain type. Silicon Valley selects for highly (over)confident founders—people who are willing to gamble big on contrarian ideas that have a low intrinsic probability of success. We’re living in a world where focal points are becoming spikier, and wealth accumulation follows more of a power law. The ten richest people in the world were worth a combined $452 billion in 2013—by 2023, that had shot up to $1.17 trillion, about twice as much after adjusting for inflation.[*13] This is not, actually, intended as a standard lefty critique of capitalism, or necessarily as a critique of capitalism at all.

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Books, nytimes.com/2021/09/13/books/review-contrarian-peter-thiel-silicon-valley-max-chafkin.html. GO TO NOTE REFERENCE IN TEXT world’s unicorn companies: “The Complete List of Unicorn Companies,” CB Insights, instapage.cbinsights.com/research-unicorn-companies. GO TO NOTE REFERENCE IN TEXT nerds rebelling against: Sebastian Mallaby, The Power Law: Venture Capital and the Making of the New Future, Kindle ed. (New York: Penguin Press, 2022), 17. GO TO NOTE REFERENCE IN TEXT a semiconductor facility: David Leonhardt, “Holding On,” The New York Times, April 6, 2008, sec. Real Estate, nytimes.com/2008/04/06/realestate/keymagazine/406Lede-t.html.

Smarter Faster Better: The Secrets of Being Productive in Life and Business
by Charles Duhigg
Published 8 Mar 2016

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.

Rigged Money: Beating Wall Street at Its Own Game
by Lee Munson
Published 6 Dec 2011

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

Delete: The Virtue of Forgetting in the Digital Age
by Viktor Mayer-Schönberger
Published 1 Jan 2009

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
Published 21 Jun 2015

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.

When More Is Not Better: Overcoming America's Obsession With Economic Efficiency
by Roger L. Martin
Published 28 Sep 2020

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.

Lean Analytics: Use Data to Build a Better Startup Faster
by Alistair Croll and Benjamin Yoskovitz
Published 1 Mar 2013

Percentage of Mobile Users Who Pay If your application is paid-only, then this will naturally be “all of them,” but if you’re running a freemium model where users pay for enhanced functionality, then a good rule of thumb is that 2% of your users will actually sign up for the full offering. For a free-to-play mobile game with in-app purchases, Ken Seto says that across the industry roughly 1.5% of players will buy something within the game during their use of it. In-game purchases follow a typical power law, with a few “whales” spending significantly more on in-game activity and the majority spending little or nothing. A key factor in mobile application success is being able to strike a balance between gameplay quality (which increases good ratings and the number of players) and in-app purchases (which drives revenue).

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Sharing with Others (Sharing with others also applies to UGC sites) Sharing is the word-of-mouth form of virality. A March 2012 Adage article by Buzzfeed’s Jon Steinberg and StumbleUpon’s Jack Krawczyk looked at how much popular stories had been shared.[125] As with many other metrics, there was a strong power law. The vast majority of stories were shared with a small group, and only a tiny fraction was shared widely. On Facebook, the top 50 shared stories in the last five years had received hundreds of thousands—even millions—of views. But despite these outliers, the median ratio of views to shares is just nine.

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Reddit included only basic functionality, but made it easy for users to extend the site, then learned from what was working best and incorporated it into the platform. Engagement Funnel Changes Leading web usability consultant Jakob Nielsen once observed that in an online population, 90% of people lurk, 9% contribute intermittently, and 1% are heavy contributors.[129] His numbers suggest that there are power laws at work in engagement funnels. These patterns predate the Web—they occurred in online forums like CompuServe, AOL, and Usenet. Table 26-1 shows some of his estimates. Table 26-1. Jakob Nielsen’s engagement estimates Platform Lurkers Occasional Frequent Usenet ? 580,000 19,000 Blogs 95% 5% 0.1% Wikipedia 99.8% 0.2% 0.003% Amazon reviews 99% 1% Tiny Facebook donation app 99.3% 0.7% ?

A Man for All Markets
by Edward O. Thorp
Published 15 Nov 2016

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.

Cancel Cable: How Internet Pirates Get Free Stuff
by Chris Fehily
Published 1 Feb 2011

You’ll eventually settle on your favorite sites and keep others in reserve for hard-to-find or special materials. Sites come and go, and one day your favorite may go dark, block connections from your country, or be overrun with spam, malware, or ads. It’s not hard to find BitTorrent search engines but keep in mind that file-sharing traffic, like most types of internet traffic, follows a power law (also called the 80-20 rule): only a few sites get the vast majority of pirate visits while the rest fight for scraps. Try any of the following methods to find sites: Read Wikipedia’s comparison of BitTorrent sites. Search the web for file sharing news or torrent news and scan articles for promising sites.

The Connected Company
by Dave Gray and Thomas Vander Wal
Published 2 Dec 2014

In What Matters Now: How to Win in a World of Relentless Change, Ferocious Competition, and Unstoppable Innovation (Jossey-Bass), Gary Hamel writes: Without a lot of exciting new options, managers will inevitably opt for more of the same. That’s why renewal depends on a company’s ability to generate and test hundreds of new strategic options. There’s a power law here: Out of 1,000 crazy ideas, only 100 will merit a small-scale experiment. Of those, only 10 will be worth serious investment, and out of that bundle, only 1 or 2 will have the power to transform a business or spawn a new one. Google gets this. Within its core search business, the company tests more than 5,000 software changes a year and implements around 500.

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Emergent strategy requires that the company continually generate a broad range of hypotheses, testing them in small-scale experiments, and feeding the more successful experiments while pruning the failed ones. In order to innovate in a sustainable way, a company should have ongoing bets of all sizes, at all points in the power-law curve—a thousand small, a hundred medium, and one or two large—at any given point in time. In 2005, Google set a formula for distributing its engineering efforts: 70-20-10. Seventy percent of Google’s resources are devoted to improving search and advertising, Google’s primary source of revenue and profits.

Late Bloomers: The Power of Patience in a World Obsessed With Early Achievement
by Rich Karlgaard
Published 15 Apr 2019

When we force ourselves to do things we’re not naturally inclined to do, or that don’t fit our passion or purpose in life, we pay for it with reduced motivation and drive. In their book Designing Your Life, authors Bill Burnett and Dave Evans write of a woman who’d just made partner at her high-powered law firm. Let’s pause for a minute and examine what that means. The woman had performed exceptionally enough in college—straight A’s and summa cum laude—to get into one of the ten top law schools that her powerful law firm considers when recruiting newly minted lawyers. At law school she had to finish near the top. Then as an associate lawyer at her firm, she had to work eighty hours a week or more for at least five years before she was eligible for partnership in the firm.

Pale Blue Dot: A Vision of the Human Future in Space
by Carl Sagan
Published 8 Sep 1997

If the Universe were constructed with an inverse fourth power law rather than an inverse square law, soon there would be no planets for living beings to inhabit. So of all the possible gravitational force laws, why are we so lucky as to live in a universe sporting a law consistent with life? First of course, we're so "lucky," because if we weren't, we wouldn't be here to ask the question. It is no mystery that inquisitive beings who evolve on planets can be found only in universes that admit planets. Second, the inverse square law is not is the only one consistent with stability over billions of years. Any power law less steep than 1/ r 3 (1/ r 2.99 or 1/ r, for example) will keep a planet in the vicinity of a circular orbit even if it's given a shove.

Ghost Work: How to Stop Silicon Valley From Building a New Global Underclass
by Mary L. Gray and Siddharth Suri
Published 6 May 2019

When Work Looks More Like a Book Club Vilfredo Pareto was a famed 20th-century Italian scholar and a pioneer in the field of microeconomics. In measuring the concentrations and unequal distributions of income and housing access in social settings, Pareto observed that 20 percent of Italy’s population owned 80 percent of the land.17 Pareto’s principle is a special case of the more general “power law” distribution used to describe the natural and social phenomenon by which a resource is concentrated in the hands of a few. Pareto’s formulation, the 80/20 rule, has been used to describe phenomena ranging from the distribution of income—the richest 20 percent of the world’s population control roughly 80 percent of the world’s income—to software engineering.18 Microsoft engineers observed that fixing 20 percent of the bugs in a piece of software would take care of 80 percent of the glitches found in that computer program.

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See wages peer-to-peer sharing company, 155–56 Perez, Tom, 230 n26 permanent account number (PAN), 15 permatemps, 56–57 Pew Research Center, x, xxiv, 100–101, 145–46, 169 piecework, xix, 41–45, 46, 54, 227 n8, 228 n9 platforms choices made by, xvii cooperatives, 158–59 design flaws in, 19–20, 91–93, 170–71, 174 double bottom line, 140–41 head count of, 103–4 improvements to, 138–39 profit from workers, 144–47 Poonam, 128–29 Popexpert, xxv “power law” of distribution, 101–5, 163, 171 Pritzker, Penny, 230 n26 profit double bottom line, 141, 147–49 employee liability model, 54, 69 as goal, 39, 141 outsourcing, 55–56 in service industry, xix–xx, 4, 61 single bottom line, 32, 144–47 from workers, 144–47, 164, 224 n20 R Raja, 129 Rajee, 108–9 ratings or reputation score, 14, 70–71, 81–82, 89, 130, 179, 183–84 recession.

Freezing Order: A True Story of Money Laundering, Murder, and Surviving Vladimir Putin's Wrath
by Bill Browder
Published 11 Apr 2022

A secretary escorted me to a large, windowless conference room on the eighth floor, containing a long table and rows of shelves filled with red-spined law books. At the far end of the room was the seal of the SDNY. Although everything was government-issue and worn, I knew I was at the center of one of the most powerful law enforcement bodies in the world. The room could hold about 20 people, and I was surprised to find it half-full. I walked around the table and introduced myself. There was Duncan Levin and one of his assistants; Todd Hyman and a colleague from the Department of Homeland Security; and Sharon Levin, head of the asset forfeiture division (no relation to Duncan), along with two lawyers who worked for her.

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As long as they don’t serve you personally, this is just their wish list. Nothing more, nothing less.” I was hugely relieved, but I knew this was just John Moscow’s opening gambit. My lawyer in London was good, but if this carried on I needed to bring on some heavy firepower in the United States, and soon. I made a list of 10 of the most powerful law firms in New York and contacted each. Six immediately said they weren’t interested. None explained why, but I knew the reason. Russians were throwing around legal fees like confetti in New York. They were suing each other, getting divorces, buying luxury properties, applying for visas, and setting up bank accounts.

Natural Language Annotation for Machine Learning
by James Pustejovsky and Amber Stubbs
Published 14 Oct 2012

He noticed that frequency of a word, f(w), appears as a nonlinearly decreasing function of the rank of the word, r(w), in a corpus, and formulated the following relationship between these two variables: C is a constant that is determined by the particulars of the corpus, but for now, let’s say that it’s the frequency of the most frequent word in the corpus. Let’s assume that a is 1; then we can quickly see how frequency decreases with rank. Notice that the law is a power law: frequency is a function of the negative power of rank, –a. So the first word in the ranking occurs about twice as often as the second word in the ranking, and three times as often as the third word in the ranking, and so on. N-grams In this section we introduce the notion of an n-gram.

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The total number of types in a corpus gives us the vocabulary size. The rank/frequency profile of the words in a corpus assigns a ranking to the words, according to how many tokens there are of that word. The frequency spectrum of the word gives the number of word types that have a given frequency. Zipf’s law is a power law stating that the frequency of any word is inversely proportional to its rank. Constructing n-grams over the tokens in a corpus is the first step in building language models for many NLP applications. Pointwise mutual information is a measure of how dependent one word is on another in a text.

How Not to Network a Nation: The Uneasy History of the Soviet Internet (Information Policy)
by Benjamin Peters
Published 2 Jun 2016

The original formulation of his observation in the article is perhaps less elegant than information technologists might remember: “Given a large number of factories, the number of paired links between them is approximately equal to half of the square of the number of factories.”50 The law, in effect, prophesies a power law connection at the macro level between an industrial society and an information society. In 1965, the American computer businessman Gordon Moore expressed a distinct exponential law that has applied to the microscopic level of the compounding growth of silicon chip production—that the number of transistors on an integrated circuit doubles every two years (2N).51 Both men foresaw in 1962 the emerging information sector or what Austrian American economist Fritz Machlup called “the knowledge economy.”

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In 1965, the American computer businessman Gordon Moore expressed a distinct exponential law that has applied to the microscopic level of the compounding growth of silicon chip production—that the number of transistors on an integrated circuit doubles every two years (2N).51 Both men foresaw in 1962 the emerging information sector or what Austrian American economist Fritz Machlup called “the knowledge economy.” For Kharkevich, the amount of information that a society processes can be expressed as a power law function of the industries it contains, and for Moore, the amount of information that a society processes can be expressed as an exponential function of the transistors on the circuits its industries can produce.52 These sibling laws (Moore’s 2N and Kharkevich’s N2) diverge interestingly in complex systems (when N is larger than 4).

Custodians of the Internet: Platforms, Content Moderation, and the Hidden Decisions That Shape Social Media
by Tarleton Gillespie
Published 25 Jun 2018

Policy managers talked about surges of flags that turn out to be pranks inspired by 4chan users to disrupt the platform. Real-world events and widely shared pieces of contentious content might also lead to surges in flagging. Beyond that, it would be reasonable to guess that flagging is likely to resemble the 90/10 “power law” curves we see in participation on user-generated platforms.50 Probably a minority of users flag, and a tiny minority of that minority does most of the flagging. But again, this is only a guess, because none of the major social media platforms has made this kind of data available. Not all flags, or all surges of flags, are attended to in the same way.

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47Andrejevic et al., “Participations”; Bakioglu, “Exposing Convergence”; David and Pinch, “Six Degrees of Reputation”; Fast, Örnebring, and Karlsson, “Metaphors of Free Labor”; Herman, “Production, Consumption and Labor in the Social Media Mode of Communication”; Jarrett, “The Relevance of ‘Women’s Work’”; Postigo, “The Socio-Technical Architecture of Digital Labor”; van Doorn, “Platform Labor.” 48Matias et al., “Reporting, Reviewing, and Responding to Harassment on Twitter,” 9–12. 49Juniper Downs (YouTube), “Why Flagging Matters,” YouTube Official Blog, September 15, 2016, https://youtube.googleblog.com/2016/09/why-flagging-matters.html. 50Clay Shirky, “Power Laws, Weblogs, and Inequality,” Clay Shirky’s Writings about the Internet, February 8, 2003, http://www.shirky.com/writings/herecomeseverybody/powerlaw_weblog.html; Jakob Nielsen, “The 90-9-1 Rule for Participation Inequality in Social Media and Online Communities,” NN/g, October 9, 2006, https://www.nngroup.com/articles/participation-inequality/. 51Personal interview. 52Microsoft Xbox “Enforcement United,” http://enforcement.xbox.com/united/home.

Nobody's Fool: Why We Get Taken in and What We Can Do About It
by Daniel Simons and Christopher Chabris
Published 10 Jul 2023

When people think about what counts as random, they instead produce patterns. But randomness can have its own sort of predictability.33 When numbers describe the results of natural growth processes, such as the accumulation of followers, likes, or views online, they tend to occur in patterns that follow a power law, with bigger stopping values happening less and less often (many more YouTube videos have 100–200 views than have 1–2 million, and many more parties have 5–10 guests than 500–1,000). A principle called Benford’s law describes a regular pattern that results from randomness whenever a value can grow indefinitely and the range of possible values spans at least a few orders of magnitude.

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For example, some supporters of Donald Trump claimed to have found evidence of fraud in the 2020 presidential election by showing that Joe Biden’s vote totals across precincts did not adhere to Benford’s law. But the standard version of Benford’s law should not apply in this type of setting. Precincts are deliberately designed to include similarly sized segments of the population—they can’t continue growing in size indefinitely, so the distribution of precinct sizes won’t follow a power law. Moreover, vote totals for Biden constrain the possible totals for Trump, and vice versa. Imagine a Chicago precinct with 1,000 voters in which Biden got 900 votes. If there were no third-party candidates, Trump would have received 100 votes. Across a number of such districts, Trump might have vote counts starting with 1 or 2 fairly often, giving a Benford’s-like appearance.

Servants of the Damned: Giant Law Firms and the Corruption of Justice
by David Enrich
Published 5 Oct 2022

There was no settlement announced, leading to widespread speculation that the plaintiffs had simply given up. “What a royal tease,” a Bloomberg columnist wrote, wondering aloud whether the suit had been “a waste of time.” She noted that the case had been poised to “end in bright lights shining on the inner workings of a secretive, powerful law firm. So much for that. It promised so much yet delivered so little.” That wasn’t quite right. A number of the partners who were accused of sexist behavior—including Paul Rafferty and Eric Landau—left the firm. (It isn’t clear whether their departures were related to the allegations.) Jones Day also agreed to pay the plaintiffs an undisclosed amount.* Brogan issued a confidential memo to the firm’s lawyers.

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The lawyer on the case was Stephen Sozio, who had joined the firm two years earlier after a decade as a federal prosecutor pursuing organized crime. Now Sozio tapped out a letter to Mason, warning that the investigative files contained “highly confidential, personal, and intimate information” and therefore needed to remain secret; if they didn’t, Jones Day might sue. Rather than fight with Cleveland’s highest-powered law firm, Mason backpedaled. The files would never see the light of day. Around that time, Pilla, who was facing calls to resign as bishop, was spotted watching an Indians game from Jones Day’s luxury box at Jacobs Field. THE FIRM’S WORK FOR Catholic institutions and causes accelerated under Brogan, himself a Notre Dame alum and trustee.

Thank You for Being Late: An Optimist's Guide to Thriving in the Age of Accelerations
by Thomas L. Friedman
Published 22 Nov 2016

Lastly, we need to deploy AI to create more intelligent algorithms, or what Reid Hoffman calls “human networks”—so that we can much more efficiently connect people to all the job opportunities that exist, all the skills needed for each job, and all the educational opportunities to acquire those skills cheaply and easily. “When you have a compounding problem, you need a compounding solution,” added Hoffman. The jobs issue “is a power law problem, and the only way to solve a power law problem is with a power law solution” for improving humanity’s ability to adapt. Turning more forms of AI into more forms of IA is that solution. Ma Bell’s Intelligent Assistance I visited a lot of companies in researching this book, and none was more innovative in creating intelligent assistance to help its employees become lifelong learners than old, reliable AT&T.

Capital in the Twenty-First Century
by Thomas Piketty
Published 10 Mar 2014

Seeking to find out how rapidly the number of taxpayers decreases as one climbs higher in the income hierarchy, Pareto discovered that the rate of decrease could be approximated by a mathematical law that subsequently became known as “Pareto’s law” or, alternatively, as an instance of a general class of functions known as “power laws.”31 Indeed, this family of functions is still used today to study distributions of wealth and income. Note, however, that the power law applies only to the upper tail of these distributions and that the relation is only approximate and locally valid. It can nevertheless be used to model processes due to multiplicative shocks, like those described earlier. Note, moreover, that we are speaking not of a single function or curve but of a family of functions: everything depends on the coefficients and parameters that define each individual curve.

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The greater the difference r − g, the more powerful the divergent force. If the demographic and economic shocks take a multiplicative form (i.e., the greater the initial capital, the greater the effect of a good or bad investment), the long-run equilibrium distribution is a Pareto distribution (a mathematical form based on a power law, which corresponds fairly well to distributions observed in practice). One can also show fairly easily that the coefficient of the Pareto distribution (which measures the degree of inequality) is a steeply increasing function of the difference r − g.25 Concretely, what this means is that if the gap between the return on capital and the growth rate is as high as that observed in France in the nineteenth century, when the average rate of return was 5 percent a year and growth was roughly 1 percent, the model predicts that the cumulative dynamics of wealth accumulation will automatically give rise to an extremely high concentration of wealth, with typically around 90 percent of capital owned by the top decile and more than 50 percent by the top centile.26 In other words, the fundamental inequality r > g can explain the very high level of capital inequality observed in the nineteenth century, and thus in a sense the failure of the French Revolution.

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See Income and output; Per capita output growth Paine, Thomas, 197, 644n34 Palan, Ronen, 628n56 Pamuk, Orhan, 109 Pareto, Vilfredo, theory of, 364–­368, 610n19, 614nn25,30,32 Parsons, Talcott, 384, 621n55 Partnerships, 203 Pasinetti, Luigi, 231 Passeron, Jean-­Claude, 486 Patrimonial capitalism, 173, 237, 473 Patrimonial society: middle class and, 260–­262, 346–­347, 373; metamorphoses of, 339–­343; classic, 411–­414 “Pay for luck,” 335 PAYGO systems, 487–­490, 633n45, 648n13, 652n42, 653n50 Pension funds, 391–­392, 478, 487–­490, 627n47, 630n15 Per capita income, 106, 122, 590n31, 590–­591n8,9 Per capita output growth, 72–­74, 97, 510; stages of, 86–­87; purchasing power and, 87–­90; diversification of lifestyles and, 90–­93; end of, 93–­95; social change implications of 1 percent, 95–­96; in postwar period, 96–­99; bell curve of global, 99–­102; inflation and, 102–­103; monetary systems and, 103–­109 Père Goriot (Balzac), 104, 106, 113–­115, 238–­240, 343, 412, 440 Perfect capital market, 214 Persuasion (Austen), 362 Petroleum: investments and, 455–­460, 462, 627n49; rents, redistribution of, 537–­538 Petty, William, 56, 590n1 Phelps, Edmund, 651n40 Philip, André, 615n35 Pierson, Paul, 640n52 P90/P10 ratio, 267–­269 Po­liti­cal economy, 3–­5, 574 Poll tax, 495, 634n3 Pop­u­lar Front, 286, 649n25 Population. See Demographic growth; Demographic transition Postel-­Vinay, Gilles, 18, 582n28, 599n14, 612nn4,5,9 Power laws, 367–­368 Prices: inflation and, 102–­103; monetary stability and, 103–­104; effects of vs. volume effects, 176–­177 Price system, 5–­7 Primogeniture, 362–­363, 365 Prince­ton University, 447–­449 Private wealth/capital, 50–­51, 57, 170–­183, 541; abolition of, 10; slavery and, 46, 158–­163, 593n16; defined, 46–­49, 123; and public wealth/capital, 123–­131, 142–­145, 153–­154, 183–­187, 569; in Eu­rope vs.

In Our Own Image: Savior or Destroyer? The History and Future of Artificial Intelligence
by George Zarkadakis
Published 7 Mar 2016

They would have demonstrated our ability to transfer the lessons we’ve learned from nature – about life, complex computations and cognition – to an artificial medium. The algorithms of life would run in those tiny mechanical brains as they huddled together, exploring the controlled environment of the AI lab. But, as we saw, the algorithms of life can be scaled up by following a power law: every new generation will be many times more evolved than the previous one. From having the intelligence of tiny insects, artificial brains will quickly acquire the intelligence of reptiles, birds, mammals, primates, and finally that of human beings. At that point we will have created a mechanical and intelligent creature in our own image.

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Others may become scientists and solve all of humanity’s problems. Others may push the boundaries of the dynamic equilibrium that sustains them, fall in the abyss of self-destruction and re-emerge from it several orders of magnitude more intelligent. Let’s remember that self-organisation phenomena scale according to a power law. The next stage in the evolution of intelligent machines is impossible to describe, imagine, or comprehend – because it will be many orders of magnitude higher than our intelligence. The distance between the intelligence of those machines and ours will be similar to what separates us from the ants.

The Power of Habit: Why We Do What We Do in Life and Business
by Charles Duhigg
Published 1 Jan 2011

Langendam, “Breaking and Creating Habits on the Working Floor: A Field-Experiment on the Power of Implementation Intentions,” Journal of Experimental Social Psychology 42, no. 6 (2006): 776–83; Mindy Ji and Wendy Wood, “Purchase and Consumption Habits: Not Necessarily What You Intend,” Journal of Consumer Psychology 17, no. 4 (2007): 261–76; S. Bellman, E. J. Johnson, and G. Lohse, “Cognitive Lock-In and the Power Law of Practice,” Journal of Marketing 67, no. 2 (2003): 62–75; J. Bettman et al., “Adapting to Time Constraints,” in Time Pressure and Stressing Human Judgment and Decision Making, ed. O. Svenson and J. Maule (New York: Springer, 1993); Adwait Khare and J. Inman, “Habitual Behavior in American Eating Patterns: The Role of Meal Occasions,” Journal of Consumer Research 32, no. 4 (2006): 567–75; David Bell and R.

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Learning in the Evolution of Solidarity Networks: A Theoretical Comparison,” Computational and Mathematical Organization Theory 5, no. 2 (1999): 97–127; A. Flache and R. Hegselmann, “Dynamik Sozialer Dilemma-Situationen,” final research report of the DFG-Project Dynamics of Social Dilemma Situations, University of Bayreuth, Department of Philosophie, 2000; A. Flache and Michael Macy, “Stochastic Collusion and the Power Law of Learning,” Journal of Conflict Resolution 46, no. 5 (2002): 629–53; Michael Macy, “Learning to Cooperate: Stochastic and Tacit Collusion in Social Exchange,” American Journal of Sociology 97, no. 3 (1991): 808–43; E. P. H. Zeggelink, “Evolving Friendship Networks: An Individual-Oriented Approach Implementing Similarity,” Social Networks 17 (1996): 83–110; Judith Blau, “When Weak Ties Are Structured,” unpublished manuscript, Department of Sociology, State University of New York, Albany, 1980; Peter Blau, “Parameters of Social Structure,” American Sociological Review 39, no. 5 (1974): 615–35; Scott Boorman, “A Combinatorial Optimization Model for Transmission of Job Information Through Contact Networks,” Bell Journal of Economics 6, no. 1 (1975): 216–49; Ronald Breiger and Philippa Pattison, “The Joint Role Structure of Two Communities’ Elites,” Sociological Methods and Research 7, no. 2 (1978): 213–26; Daryl Chubin, “The Conceptualization of Scientific Specialties,” Sociological Quarterly 17, no. 4 (1976): 448–76; Harry Collins, “The TEA Set: Tacit Knowledge and Scientific Networks,” Science Studies 4, no. 2 (1974): 165–86; Rose Coser, “The Complexity of Roles as Seedbed of Individual Autonomy,” in The Idea of Social Structure: Essays in Honor of Robert Merton, ed.

Culture & Empire: Digital Revolution
by Pieter Hintjens
Published 11 Mar 2013

The biggest cost is probably the paper form one has to fill in, and the front office that types it in, and takes a copy of your ID "for security purposes." Now let's look at competitors. The largest competitor to Western Union is MoneyGram International, one tenth the size. There is a mathematical "power law" called Zipf's Law that models the distribution in natural systems such as free markets, earthquakes, cities in a country, and words in a language. Yes, all these follow the same rules of distribution. Normally, you'd expect the largest firm to be twice the size of its next competitor, three times the size of the one after, and so on.

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I also wrote an open source library called Zyre that does this -- if you run it on a phone, it will look for any other phone also running Zyre, connect to it, and then let applications exchange data. When you are out and about in the street, things become more fun. It's harder to find friendly WiFi hotspots. And even if you do, you have to stay within 10-30 yards of the hotspot for things to work. The "inverse power law" means that if two antennae (like the WiFi access point and your phone) move twice as far apart, they need to use four times as much energy to talk to each other. All modern smartphones -- since 2010 or so -- can create their own WiFi hotspots at will, unless the ability has been disabled by the phone company.

The Code of Capital: How the Law Creates Wealth and Inequality
by Katharina Pistor
Published 27 May 2019

Law creates the conditions for realizing our individual and social aspirations either as preference aggregating machines in a system in which efficiency is idolized, or as autonomous individuals in a deliberative polity, where reason, not just money, rules. Through law, societies commit to preserve formal rights, insulate them from political contestation, subordinate them to the market, but might also turn transitory rights into instruments of change. Second, without power, law is at best fleeting and at worse ineffective. As different as the two visions of Posner and Weyl on one hand, and Menke on the other, are, both will need to be implemented, and both will require at least the threat of coercion to do so. Just imagine the amount of resources that would have to be devoted to evict reluctant home owners from their houses, not because they defaulted, but because someone else came along and offered a price higher than their estimate and beyond their own means.

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A summary of the patterns of diffusion of Western legal systems can be found in Berkowitz, Pistor, and Richard, “Transplant Effect.” 3. For a succinct history of Japanese law, see Hiroshi Oda, Japanese Law, 2nd ed. (London, Dublin, Edinburgh: Butterworths, 1999); see also John Haley, Authority without Power: Law and the Japanese Paradox (Oxford: Oxford University Press, 1994) for a critical assessment of how Western legal transplants operate in a very different culture. After World War II, the United States occupied Japan and transplanted some of its own laws, with mixed success. 4. Alan Watson, Legal Transplants: An Approach to Comparative Law (Edinburgh: Scottish Academic Press; London: distributed by Chatto and Windus, 1974). 5.

For Profit: A History of Corporations
by William Magnuson
Published 8 Nov 2022

KKR’s accountant at Deloitte analyzed these assets and concluded that the company could increase its value by around $100 million, allowing additional tax-deductible depreciation for Houdaille of $15 million.12 Doing so would require complicated corporate structuring, though, and KKR hired Skadden, one of Wall Street’s most powerful law firms, to handle the documentation. Skadden, in turn, devised a transaction of Dickensian complexity. For example, on March 5, 1978, HH Holdings Inc. held a “meeting” at KKR’s office, which was attended by a single person, Kravis, who was its sole director. At this “meeting,” Kravis proposed eighteen resolutions to himself and approved them by a 1–0 vote.

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Nicholas Carlson, “Here’s the Email Zuckerberg Sent to Cut His Cofounder Out of Facebook,” Business Insider, May 15, 2012. 14. Alan J. Tabak, “Hundreds Register for New Facebook Website,” Harvard Crimson, Feb. 9, 2004. 15. Nicholas Carlson, “Well, These New Zuckerberg IMs Won’t Help Facebook’s Privacy Problems,” Business Insider, May 13, 2010. 16. Sebastian Mallaby, The Power Law: Venture Capital and the Making of the New Future (2022). 17. Levy, Facebook 214, 525. 18. Levy, Facebook 144. 19. Levy, Facebook 110. 20. Levy, Facebook 108; Henry Blodget, “Mark Zuckerberg on Innovation,” Business Insider, Oct. 1, 2009. 21. Levy, Facebook 123–27. 22. Hannah Kuchler, “How Facebook Grew Too Big to Handle,” Financial Times, Mar. 28, 2019. 23.

Website Optimization
by Andrew B. King
Published 15 Mar 2008

Reinforce the theme of your site The theme of a web page should flow through everything associated with that page: the title tag, the headers, the meta tags (keywords and description tags), the content, the links, the navigation, and even the URI of the page should all work together. Figure 1-3. The long tail (picture by Hay Kranen/PD) ora: Playing the Long Tail Given enough choice and a large population of consumers, search term selection patterns follow a power law distribution curve, or Pareto distribution. The first part of the curve contains 20% of the terms, which are deemed to be the most popular, and the rightmost long tail of the curve contains the remaining 80% of the terms, which are searched less frequently (as Figure 1-3 shows). With the widespread use of the Internet, targeting less popular terms has become a viable strategy.

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, Microsoft, and Everybody Else model numbers as long tail keywords, Target part and model numbers mod_cache module, Using mod_cache, Using mod_cache, Using mod_cache, Using mod_cache mod_deflate module, Using HTTP Compression, Compressing content in Apache mod_disk_cache module, Using mod_cache mod_expires module, A specific caching example, Target files by extension for caching mod_gzip module, Using HTTP Compression, Compressing content in Apache, Compressing content in Apache, Compressing content in Apache, Compressing content in Apache mod_headers module, A specific caching example mod_mem_cache module, Using mod_cache mod_proxy module, Using mod_cache mod_rewrite module, Rewriting URIs with mod_rewrite, How mod_rewrite works monitoring tools, Commercial Monitoring Tools mousemove event, Hybrid Analytics Systems Movable Type publishing platform, Write compelling summaries, Automatically categorize with blogs categorizing with blogs, Write compelling summaries, Automatically 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The Science of Hate: How Prejudice Becomes Hate and What We Can Do to Stop It
by Matthew Williams
Published 23 Mar 2021

.*2 Despite the depressing finding, Grodzin’s idea is fascinating, and it introduced the tipping point concept to the science of hate. Since the 1950s, the phrase ‘the tipping point’ has been used to describe other contexts in which a large group of people quickly adopt a behaviour that was previously rare. It draws on the power law, which suggests minor changes by a few people can have disproportionately dramatic effects on a population. The author Malcolm Gladwell famously applied the principle to understand the rapid spread of rumour and disease, explosive fashion trends, and the dramatic reduction in crime in New York City in the 1990s.3 These examples relate to changes in group behaviour.

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Abdallah, Abdalraouf, 1 Abedi, Salman, 1, 2, 3, 4 abortion, 1, 2 Abu Sayyaf Group, 1 abuse, 1, 2, 3, 4, 5 accelerants to hate, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 accelerationists, 1 addiction, 1, 2, 3, 4 Admiral Duncan bar, 1 adolescence, 1, 2, 3, 4, 5, 6, 7 advertising, 1, 2, 3, 4, 5 African Americans, 1, 2, 3, 4, 5, 6, 7 afterlife, 1, 2 age, 1, 2 aggression: brain and hate, 1, 2, 3, 4, 5; false alarms, 1; group threat, 1, 2, 3, 4, 5, 6; identity fusion, 1; mortality, 1; pyramid of hate, 1; trauma and containment, 1, 2 AI, see artificial intelligence Albright, Jonathan, 1 alcohol, 1, 2, 3, 4, 5, 6, 7, 8 algorithms: far-right hate, 1, 2, 3, 4; filter bubbles and bias, 1, 2; Google, 1, 2, 3; online hate speech, 1, 2, 3, 4, 5, 6; Tay, 1, 2; tipping point, 1, 2; YouTube, 1 Algotransparency.org, 1 Allport, Gordon, 1, 2, 3, 4 Al Noor Mosque, Christchurch, 1 al-Qaeda, 1, 2 Alternative für Deutschland (AfD), 1 alt-right: algorithms, 1, 2; brain and hate, 1; Charlottesville rally, 1, 2; counter-hate speech, 1; definition, 1n; Discord, 1; Facebook, 1, 2, 3; fake accounts, 1; filter bubbles, 1, 2; red-pilling, 1, 2; social media, 1, 2; Trump, 1, 2; YouTube, 1 Alzheimer’s disease, 1 American Crowbar Case, 1 American culture, 1 American Nazi Party, 1, 2 Amodio, David, 1n amygdala: brain and signs of prejudice, 1, 2; brain tumours, 1; disengaging the amygdala autopilot, 1; hate and feeling pain, 1, 2; and insula, 1; neuroscience of hate, 1n, 2, 3, 4; parts that edge us towards hate, 1; parts that process prejudice, 1; prepared versus learned amygdala responses, 1, 2; processing of ‘gut-deep’ hate, 1; recognising facial expressions, 1n, 2; stopping hate, 1, 2; trauma and containment, 1, 2; unlearning prejudiced threat detection, 1 anger, 1, 2, 3, 4, 5, 6, 7, 8 anonymity, 1, 2 anterior insula, 1n Antifa, 1, 2n, 3 anti-gay prejudice, 1, 2, 3, 4, 5, 6, 7, 8 anti-hate initiatives, 1, 2 antilocution, 1 anti-Muslim hate, 1, 2, 3, 4, 5, 6 anti-Semitism, 1, 2, 3, 4, 5, 6 anti-white hate crime, 1 Antonissen, Kirsten, 1, 2 anxiety: brain and hate, 1, 2, 3, 4; harm of hate speech, 1; intergroup contact, 1, 2; subcultures of hate, 1, 2; trauma and containment, 1; trigger events, 1, 2 Arab people, 1, 2, 3, 4, 5, 6 Arbery, Ahmaud, 1 Arkansas, 1, 2 artificial intelligence (AI), 1, 2, 3, 4 Asian Americans, 1, 2 Asian people, 1, 2, 3, 4 assault, 1, 2, 3 asylum seekers, 1, 2, 3, 4 Athens, 1 Atlanta attack, 1 Atran, Scott, 1, 2 attachment, 1 attention, 1, 2, 3 attitudes, 1, 2, 3, 4, 5, 6 Aung San Suu Kyi, 1 austerity, 1 Australia, 1 autism, 1 averages, 1, 2 avoidance, 1, 2, 3 Bali attack, 1 Bangladeshi people, 1 BBC (British Broadcasting Corporation), 1, 2, 3 behavioural sciences, 1, 2 behaviour change, 1, 2, 3 beliefs, 1, 2, 3 Bell, Sean, 1, 2 Berger, Luciana, 1 Berlin attacks, 1 bias: algorithms, 1; brain and hate, 1, 2, 3, 4, 5, 6, 7; filter bubbles, 1; Google Translate, 1; group threat, 1, 2, 3, 4; police racial bias, 1; predicting hate crime, 1; stopping hate, 1, 2, 3; unconscious bias, 1, 2, 3, 4 Bible, 1 Biden, Joe, 1 ‘Big Five’ personality traits, 1 biology, 1, 2, 3, 4, 5, 6, 7 Birstall, 1 bisexual people, 1 Black, Derek, 1, 2 Black, Don, 1, 2, 3 blackface, 1 Black Lives Matter, 1 Black Mirror, 1n black people: author’s brain and hate, 1, 2, 3, 4, 5; brain and signs of prejudice, 1, 2; brain parts that edge us towards hate, 1; brain parts that process prejudice, 1; Charlottesville rally, 1, 2; disengaging the amygdala autopilot, 1; Duggan shooting, 1; feeling pain, 1; Google searches, 1, 2; group threat, 1, 2, 3, 4; online hate speech, 1, 2, 3, 4; police relations, 1, 2; predicting hate crime, 1, 2; prepared versus learned amygdala responses, 1; pyramid of hate, 1, 2, 3n; recognising facial expressions, 1, 2; South Africa, 1; steps to stop hate, 1, 2, 3, 4; trauma and Franklin, 1, 2, 3, 4; trigger events, 1, 2, 3; unconscious bias, 1; unlearning prejudiced threat detection, 1, 2; white flight, 1 BNP, see British National Party Bolsonaro, Jair, 1 Bosnia and Herzegovina, 1, 2 bots, 1, 2, 3, 4, 5 Bowers, Robert Gregory, 1 boys, 1, 2 Bradford, 1 brain: ancient brains in modern world, 1; author’s brain and hate, 1; beyond the brain, 1; the brain and hate, 1; brain and signs of prejudice, 1; brain damage and tumours, 1, 2, 3, 4; brains and unconscious bias against ‘them’, 1; brain’s processing of ‘gut-deep’ hate, 1; defence mechanisms, 1; disengaging the amygdala autopilot, 1; figures, 1; finding a neuroscientist and brain scanner, 1; group threat detection, 1, 2; hacking the brain to hate, 1; hate and feeling pain, 1; locating hate in the brain, 1; neuroscience and big questions about hate, 1; overview, 1; parts that edge us towards hate, 1; parts that process prejudice, 1; prepared versus learned amygdala responses, 1; recognising facial expressions, 1; rest of the brain, 1; signs of prejudice, 1; steps to stop hate, 1, 2; tipping point to hate, 1, 2, 3, 4, 5; trauma and containment, 1, 2; unlearning prejudiced threat detection, 1; where neuroscience of hate falls down, 1 brain imaging: author’s brain and hate, 1; beyond the brain, 1; the brain and hate, 1; brain and signs of prejudice, 1, 2; brain injury, 1, 2; Diffusion MRI, 1; disengaging the amygdala autopilot, 1; finding a neuroscientist and brain scanner, 1; fusiform face area, 1; locating hate in the brain, 1; MEG, 1; neuroscience of hate, 1, 2, 3; parts that process prejudice, 1; prepared versus learned amygdala responses, 1; processing of ‘gut-deep’ hate, 1; subcultures of hate, 1, 2; unconscious bias, 1 brainwashing, 1, 2 Bray, Mark, 1n Brazil, 1, 2, 3 Breivik, Anders, 1, 2 Brexit, 1, 2, 3, 4n, 5, 6, 7, 8, 9 Brexit Party, 1, 2 Brick Lane, London, 1 Britain First, 1, 2 British identity, 1, 2 British National Party (BNP), 1, 2n, 3, 4, 5 Brixton, 1 Broadmoor Hospital, 1, 2 Brooker, Charlie, 1n Brooks, Rayshard, 1 Brown, Katie, 1, 2 Brown, Michael, 1, 2 Brussels attack, 1 Budapest Pride, 1 bullying, 1, 2 Bundy, Ted, 1 burka, 1, 2, 3 Burmese, 1 Bush, George W., 1 Byrd, James, Jr, 1 California, 1, 2n, 3 Caliskan, Aylin, 1 Cambridge Analytica, 1, 2 cancer, 1, 2 Cardiff University Brain Research Imaging Centre (CUBRIC), 1, 2, 3, 4 caregiving motivational system, 1 care homes, 1, 2 Casablanca, 1 cascade effect, 1, 2 categorisation, 1, 2, 3, 4 Catholics, 1 Caucasian Crew, 1 causality, 1, 2 celebrities, 1, 2, 3, 4 censorship, 1, 2 Centennial Olympic Park, Atlanta, 1 Centers for Disease Control (CDC), 1 change blindness, 1 charity, 1, 2, 3 Charlottesville rally, 1, 2, 3n, 4 chatbots, 1, 2, 3 Chauvin, Derek, 1 Chelmsford, 1 Chicago, 1 childhood: attachment issues, 1; child abuse, 1, 2, 3; child grooming, 1; child play, 1; failures of containment, 1, 2, 3, 4; group threat, 1, 2; intergroup contact, 1, 2; learned stereotypes, 1; online hate speech, 1, 2; predicting hate crime, 1; trauma and containment, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10; trigger events, 1, 2; understanding the ‘average’ hate criminal, 1; understanding the ‘exceptional’ hate offender, 1, 2, 3 China, 1, 2, 3, 4 Chinese people, 1, 2, 3 ‘Chinese virus,’ 1, 2 Cho, John, 1 Christchurch mosque attack, 1 Christianity, 1, 2, 3 cinema, 1 citizen journalism, 1 civilising process, 1 civil rights, 1, 2, 3, 4 class, 1, 2 cleaning, 1 climate change, 1, 2 Clinton, Hillary, 1, 2 cognitive behavioural therapy, 1 cognitive dissonance, 1 Cohen, Florette, 1, 2 Cold War, 1 collective humiliation, 1 collective quests for significance, 1, 2 collective trauma, 1, 2 colonialism, 1n, 2 Combat 1, 2 comedies, 1, 2, 3 Communications Acts, 1, 2 compassion, 1, 2, 3 competition, 1, 2, 3, 4, 5, 6, 7, 8 confirmation bias, 1 conflict, 1, 2, 3, 4 conflict resolution, 1, 2, 3, 4, 5 Connectome, 1 Conroy, Jeffrey, 1 Conservative Party, 1, 2, 3 conspiracy theories, 1, 2, 3 contact with others, 1, 2 containment: failures of, 1; hate as container of unresolved trauma, 1; understanding the ‘exceptional’ hate offender, 1, 2, 3 content moderation, 1, 2, 3 context, 1, 2, 3 Convention of Cybercrime, 1 cooperation, 1, 2, 3, 4, 5, 6 Copeland, David, 1, 2, 3, 4, 5, 6, 7 coping mechanisms, 1, 2, 3, 4, 5, 6, 7 Cordoba House (‘Ground Zero mosque’), 1 correction for multiple comparisons, 1, 2n ‘corrective rape’, 1, 2 cortisol, 1 Council of Conservative Citizens, 1n counter-hate speech, 1, 2, 3, 4 courts, 1, 2, 3, 4, 5, 6 COVID-19 pandemic, 1, 2, 3 Cox, Jo, 1, 2, 3 Criado Perez, Caroline, 1 crime, 1, 2, 3, 4, 5, 6, 7 Crime and Disorder Act 1998, 1n crime recording, 1, 2, 3, 4 crime reporting, 1, 2, 3, 4, 5, 6, 7 Crime Survey for England and Wales (CSEW), 1 criminal justice, 1, 2, 3 Criminal Justice Act, 1, 2n criminal prosecution, 1, 2 criminology, 1, 2, 3, 4, 5, 6 cross-categorisation, 1 cross-race or same-race effect, 1 Crusius, Patrick, 1, 2 CUBRIC (Cardiff University Brain Research Imaging Centre), 1, 2, 3, 4 cultural ‘feeding’, 1, 2, 3, 4, 5 cultural worldviews, 1, 2, 3, 4, 5, 6, 7 culture: definitions, 1; group threat, 1, 2, 3; steps to stop hate, 1, 2, 3; tipping point, 1, 2, 3, 4, 5; unlearning prejudiced threat detection, 1 culture machine, 1, 2, 3, 4, 5 culture wars, 1 Curry and Chips, 1 cybercrime, 1 dACC, see dorsal anterior cingulate cortex Daily Mail, 1, 2 Dailymotion, 1 Daily Stormer, 1, 2n Daley, Tom, 1, 2 Darfur, 1 dark matter, 1 death: events that remind us of our mortality, 1; newspapers, 1; predicting hate crime, 1; religion and hate, 1, 2; subcultures of hate, 1, 2; trigger events, 1, 2 death penalty, 1, 2 death threats, 1 decategorisation, 1 De Dreu, Carsten, 1, 2, 3, 4 deep learning, 1, 2 defence mechanisms, 1 defensive haters, 1, 2 dehumanisation, 1, 2, 3, 4, 5, 6 deindividuation, 1, 2 deindustrialisation, 1, 2, 3, 4 Democrats, 1, 2, 3 Denny, Reginald, 1 DeSalvo, Albert (the Boston Strangler), 1 desegregation, 1, 2, 3 Desmond, Matthew, 1 Dewsbury, 1, 2, 3 Diffusion Magnetic Resonance Imaging (Diffusion MRI), 1, 2 diminished responsibility, 1, 2 Director of Public Prosecutions (DPP), 1 disability: brain and hate, 1, 2; group threat, 1, 2, 3, 4, 5, 6; intergroup contact, 1; Japan care home, 1, 2; online hate speech, 1; profiling the hater, 1; suppressing prejudice, 1; victim perception, 1n Discord, 1, 2, 3, 4 discrimination: brain and hate, 1, 2; comedy programmes, 1; Google searches, 1; Japan laws, 1; preference for ingroup, 1; pyramid of hate, 1, 2, 3; questioning prejudgements, 1; trigger events, 1, 2, 3 disgust: brain and hate, 1, 2, 3, 4, 5, 6; group threat detection, 1, 2, 3; ‘gut-deep’ hate, 1, 2; Japan care home, 1; what it means to hate, 1, 2 disinformation, 1, 2, 3 displacement, 1, 2 diversity, 1, 2, 3 dlPFC, see dorsolateral prefrontal cortex domestic violence, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Doran, John, 1, 2, 3 dorsal anterior cingulate cortex (dACC), 1, 2, 3n, 4, 5, 6, 7, 8, 9 dorsolateral prefrontal cortex (dlPFC), 1n, 2, 3 Douglas, Mary, Purity and Danger, 1 drag queens, 1 drugs, 1, 2, 3, 4, 5, 6, 7, 8, 9 Duggan, Mark, 1 Duke, David, 1 Dumit, Joe, Picturing Personhood, 1 Durkheim, Emile, 1 Dykes, Andrea, 1 Earnest, John T., 1 Eastern Europeans, 1, 2, 3 Ebrahimi, Bijan, 1, 2, 3, 4, 5, 6 echo chambers, 1, 2n economy, 1, 2, 3, 4, 5, 6 EDL, see English Defence League education, 1, 2, 3, 4 Edwards, G., 1 8chan, 1, 2 elections, 1, 2, 3, 4, 5, 6 electroencephalography, 1n elites, 1 ELIZA (computer program), 1 The Ellen Show, 1 El Paso shooting, 1 Elrod, Terry, 1 Emancipation Park, Charlottesville, 1 Emanuel African Methodist Church, Charleston, 1 emotions: brain and hate, 1, 2, 3, 4n, 5, 6, 7, 8, 9; group threat, 1; subcultures of hate, 1; trigger events and mortality, 1; what it means to hate, 1, 2, 3, 4 empathy: brain and hate, 1, 2, 3, 4, 5, 6; feeling hate together, 1; group threat, 1, 2; steps to stop hate, 1, 2, 3; subcultures of hate, 1; trauma and containment, 1 employment, 1, 2, 3, 4, 5, 6, 7 English Defence League (EDL), 1, 2n, 3 epilepsy, 1, 2, 3, 4, 5 Epstein, Robert, 1 equality, 1, 2 Essex, 1 ethnicity, 1, 2n, 3, 4 ethnic minorities, 1, 2, 3, 4, 5, 6 ethnocentrism, 1 EU, see European Union European Commission, 1, 2 European Digital Services Act, 1 European Parliament, 1, 2 European Social Survey, 1 European Union (EU): Brexit referendum, 1, 2, 3, 4n, 5; Facebook misinformation, 1; group threat, 1, 2; online hate speech, 1, 2, 3; trigger events, 1 Eurovision, 1 evidence-based hate crime, 1 evolution, 1, 2, 3, 4, 5, 6, 7, 8 executive control area: brain and hate, 1, 2, 3, 4, 5, 6, 7, 8; disengaging the amygdala autopilot, 1, 2; extremism, 1; recognising false alarms, 1; trauma and containment, 1; trigger events, 1 exogenous shocks, 1 expert opinion, 1 extreme right, 1, 2, 3, 4, 5 extremism: Charlottesville and redpilling, 1, 2; feeling hate together, 1; online hate speech, 1; perceiving versus proving hate, 1; quest for significance, 1, 2, 3; subcultures of hate, 1, 2, 3, 4, 5, 6, 7; trauma and containment, 1; trigger events, 1, 2, 3 Facebook: algorithms, 1, 2; Charlottesville rally, 1, 2; Christchurch mosque attack, 1; far-right hate, 1, 2, 3, 4, 5; filter bubbles, 1, 2; how much online hate speech, 1, 2; Myanmar genocide, 1; online hate and offline harm, 1, 2, 3; redpilling, 1; stopping online hate speech, 1, 2, 3, 4 facial expression, 1, 2, 3, 4 faith, 1, 2 fake accounts, 1, 2; see also bots fake news, 1, 2, 3, 4 false alarms, 1, 2, 3 Farage, Nigel, 1, 2 far left, 1n, 2, 3, 4 Farook, Syed Rizwan, 1 far right: algorithms, 1, 2, 3, 4; brain injury, 1; Charlottesville rally, 1, 2, 3n, 4; COVID-19 pandemic, 1, 2; Facebook, 1, 2, 3, 4, 5; filter bubbles, 1, 2; gateway sites, 1; group threat, 1, 2; red-pilling, 1; rise of, 1; stopping online hate speech, 1; subcultures of hate, 1, 2, 3, 4, 5; terror attacks, 1, 2, 3; tipping point, 1, 2; trauma and containment, 1, 2, 3, 4n; trigger events, 1, 2; YouTube, 1 fathers, 1, 2, 3 FBI, see Federal Bureau of Investigation fear: brain and hate, 1, 2, 3, 4, 5, 6, 7; feeling hate together, 1; group threat, 1, 2, 3, 4, 5; mortality, 1; online hate speech, 1, 2, 3; steps to stop hate, 1, 2; trauma and containment, 1, 2; trigger events, 1, 2, 3 Federal Bureau of Investigation (FBI), 1, 2, 3, 4, 5, 6, 7 Federation of American Immigration Reform, 1 Ferguson, Missouri, 1 Festinger, Leon, 1 fiction, 1 Fields, Ted, 1 50 Cent Army, 1 ‘fight or flight’ response, 1, 2, 3 films, 1, 2 filter bubbles, 1, 2, 3, 4 Finland, 1, 2, 3, 4, 5, 6 Finsbury Park mosque attack, 1, 2, 3 first responders, 1 Fiske, Susan, 1 Five Star Movement, 1 flashbacks, 1 Florida, 1, 2 Floyd, George, 1, 2, 3 Flynt, Larry, 1 fMRI (functional Magnetic Resonance Imaging), 1, 2, 3, 4, 5, 6, 7 football, 1, 2, 3, 4, 5 football hooligans, 1, 2 Forever Welcome, 1 4chan, 1, 2 Fox News, 1, 2 Franklin, Benjamin, 1 Franklin, Joseph Paul, 1, 2, 3, 4, 5, 6, 7, 8 Fransen, Jayda, 1 freedom fighters, 1, 2 freedom of speech, 1, 2, 3, 4, 5, 6 frustration, 1, 2, 3, 4 functional Magnetic Resonance Imaging (fMRI), 1, 2, 3, 4, 5, 6, 7 fundamentalism, 1, 2 fusiform face area, 1 fusion, see identity fusion Gab, 1 Gadd, David, 1, 2n, 3, 4 Gaddafi, Muammar, 1, 2 Gage, Phineas, 1, 2 galvanic skin responses, 1 Gamergate, 1 gateway sites, 1 gay people: author’s experience, 1, 2, 3; brain and hate, 1, 2; Copeland attacks, 1, 2; COVID-19 pandemic, 1; filter bubbles, 1; gay laws, 1; gay marriage, 1, 2, 3; group associations, 1; group threat, 1, 2, 3, 4, 5; hate counts, 1, 2, 3, 4; physical attacks, 1, 2; profiling the hater, 1; Russia, 1, 2, 3, 4, 5; Section 1, 2, 3, 4; steps to stop hate, 1, 2, 3; trigger events, 1, 2; why online hate speech hurts, 1; see also LGBTQ+ people gay rights, 1, 2, 3, 4 gender, 1, 2, 3, 4, 5, 6, 7 Generation Identity, 1 Generation Z, 1, 2 genetics, 1n, 2, 3 genocide, 1, 2, 3, 4, 5, 6 Georgia (country), 1 Georgia, US, 1, 2, 3, 4 Germany, 1, 2, 3, 4, 5, 6, 7 Gilead, Michael, 1 ginger people, 1 girls, and online hate speech, 1 Gladwell, Malcolm, 1 Global Project Against Hate and Extremism, 1 glucocorticoids, 1, 2 God, 1, 2 God’s Will, 1, 2 Goebbels, Joseph, 1 Google, 1, 2, 3, 4, 5, 6, 7, 8 Google+, 1 Google Translate, 1 goth identity, 1, 2, 3, 4 governments, 1, 2, 3, 4, 5, 6 Grant, Oscar, 1 gravitational waves, 1 Great Recession (2007–9), 1 Great Replacement conspiracy theory, 1 Greece, 1, 2 Greenberg, Jeff, 1, 2, 3 Greene, Robert, 1 grey matter, 1 Grillot, Ian, 1, 2 Grodzins, Morton, 1 grooming, 1, 2, 3 ‘Ground Zero mosque’ (Cordoba House), 1 GroupMe, 1 groups: ancient brains in modern world, 1; brain and hate, 1, 2, 3, 4; childhood, 1; feeling hate together, 1; foundations of prejudice, 1; group threat and hate, 1; identity fusion, 1, 2, 3; intergroup hate, 1; pyramid of hate, 1; reasons for hate offending, 1; steps to stop hate, 1, 2; tipping point, 1, 2, 3, 4; warrior psychology, 1, 2, 3; what it means to hate, 1, 2 group threat, 1; beyond threat, 1; Bijan as the threatening racial other, 1; context and threat, 1; cultural machine, group threat and stereotypes, 1; evolution of group threat detection, 1; human biology and threat, 1; neutralising the perception of threat, 1; overview, 1; society, competition and threat, 1; threat in their own words, 1 guilt, 1, 2, 3, 4 guns, 1, 2 ‘gut-deep’ hate, 1, 2, 3, 4 Haines, Matt, 1 Haka, 1 Halle Berry neuron, 1, 2 harassment, 1, 2, 3, 4, 5 harm of hate, 1, 2, 3, 4, 5, 6, 7 Harris, Brendan, 1 Harris, Lasana, 1 Harris, Lovell, 1, 2, 3, 4 hate: author’s brain and hate, 1; the brain and hate, 1; definitions, 1, 2; feeling hate together, 1; foundations of prejudice and hate, 1, 2, 3; group threat and hate, 1; ‘gut-deep’ hate, 1, 2; hate counts, 1; hate in word and deed, 1; profiling the hater, 1; pyramid of hate, 1; rise of the bots and trolls, 1; seven steps to stop hate, 1; subcultures of hate, 1; tipping point from prejudice to hate, 1; trauma, containment and hate, 1; trigger events and ebb and flow of hate, 1; what it means to hate, 1 hate counts, 1; criminalising hate, 1; how they count, 1; overview, 1; perceiving versus proving hate, 1; police and hate, 1; rising hate count, 1; ‘signal’ hate acts and criminalisation, 1; Sophie Lancaster, 1; warped world of hate, 1 hate crime: author’s experience, 1, 2, 3; brain and hate, 1, 2, 3, 4, 5; definitions, 1; events and hate online, 1; events and hate on the streets, 1, 2; the ‘exceptional’ hate criminal, 1; far-right hate, 1, 2, 3; foundations of prejudice and hate, 1, 2, 3, 4; group threat, 1, 2, 3, 4, 5, 6, 7, 8; hate counts, 1, 2, 3, 4, 5; laws, 1n, 2, 3, 4, 5; number of crimes, 1, 2; online hate speech, 1, 2, 3, 4; predicting hate crime, 1; profiling the hater, 1; steps to stop hate, 1, 2, 3; trauma and containment, 1, 2, 3, 4; trigger events, 1, 2, 3, 4, 5, 6; understanding the ‘average’ hate criminal, 1; understanding the ‘exceptional’ hate offender, 1; what it means to hate, 1, 2, 3 hate groups, 1, 2, 3, 4, 5 hate in word and deed, 1; algorithmic far right, 1; Charlottesville rally, 1, 2, 3n, 4; extreme filter bubbles, 1; game changer for the far right, 1; gateway sites, 1; overview, 1; ‘real life effort post’ and Christchurch, 1; red-pilling, 1 HateLab, 1, 2, 3, 4, 5 hate speech: far-right hate, 1, 2, 3; filter bubbles and bias, 1; harm of, 1; how much online hate speech, 1; Japan laws, 1; pyramid of hate, 1; stopping online hate speech, 1; Tay chatbot, 1; trigger events, 1, 2, 3; why online hate speech hurts, 1 hate studies, 1, 2 ‘hazing’ practices, 1 health, 1, 2, 3, 4 Henderson, Russell, 1 Herbert, Ryan, 1 Hewstone, Miles, 1 Heyer, Heather, 1 Hinduism, 1, 2 hippocampus, 1, 2, 3, 4 history of offender, 1 Hitler, Adolf, 1, 2, 3, 4, 5, 6, 7 HIV/AIDS, 1, 2, 3, 4, 5, 6, 7 hollow mask illusion, 1, 2 Hollywood, 1, 2 Holocaust, 1, 2, 3, 4 Homicide Act, 1n homophobia: author’s experience, 1, 2, 3, 4; brain and hate, 1, 2, 3; evidence-based hate crime, 1; federal law, 1; jokes, 1; online hate speech, 1, 2; Russia, 1, 2; Shepard murder, 1; South Africa, 1; trauma and containment, 1; victim perception of motivation, 1n Homo sapiens, 1 homosexuality: author’s experience, 1; online hate speech, 1; policing, 1; questioning prejudgements, 1; Russia, 1, 2; trauma and containment, 1, 2; see also gay people hooligans, 1, 2 Horace, 1 hormones, 1, 2, 3 hot emotions, 1 hot-sauce study, 1, 2 housing, 1, 2, 3, 4, 5, 6 Huddersfield child grooming, 1 human rights, 1, 2, 3 humiliation, 1, 2, 3, 4, 5, 6 humour, 1, 2 Hungary, 1 hunter-gatherers, 1n, 2 Hustler, 1 IAT, see Implicit Association Test identity: author’s experience of attack, 1; British identity, 1, 2; Charlottesville rally, 1, 2; children’s ingroups, 1; group threat, 1, 2; online hate speech, 1, 2, 3, 4; steps to stop hate, 1, 2 identity fusion: fusion and hateful murder, 1; fusion and hateful violence, 1; fusion and self-sacrifice in the name of hate, 1; generosity towards the group, 1; tipping point, 1, 2; warrior psychology, 1, 2, 3 ideology, 1, 2, 3, 4 illegal hate speech, 1, 2, 3, 4 illocutionary speech, 1 imaging, see brain imaging immigration: Forever Welcome, 1; group threat, 1, 2, 3, 4, 5, 6, 7; hate counts, 1n, 2; HateLab Brexit study, 1; identity fusion, 1; intergroup contact, 1; negative stereotypes, 1; online hate speech, 1; Purinton, 1, 2; trauma and containment, 1, 2, 3; trigger events, 1, 2n, 3, 4, 5, 6, 7; YouTube algorithms, 1 immortality, 1, 2 Implicit Association Test (IAT), 1, 2, 3, 4, 5, 6, 7, 8, 9 implicit prejudice: author’s brain and hate, 1, 2, 3, 4; brain and hate, 1, 2, 3, 4, 5, 6; online hate speech, 1, 2 India, 1 Indonesia, 1 Infowars, 1, 2 Ingersoll, Karma, 1 ingroup: brain and hate, 1, 2, 3, 4; child play, 1; group threat, 1, 2, 3, 4, 5, 6, 7; HateLab Brexit study, 1; identity fusion, 1, 2; pyramid of hate, 1; reasons for hate offending, 1; trigger events, 1, 2, 3; what it means to hate, 1, 2, 3, 4, 5 Instagram, 1, 2, 3 Institute for Strategic Dialogue, 1 institutional racism, 1 instrumental crimes, 1 insula: brain and signs of prejudice, 1, 2, 3; facial expressions, 1, 2; fusiform face area, 1; hacking the brain to hate, 1; hate and feeling pain, 1; neuroscience of hate, 1n, 2, 3, 4, 5; parts that edge us towards hate, 1; parts that process prejudice, 1; processing of ‘gut-deep’ hate, 1, 2 Integrated Threat Theory (ITT), 1, 2, 3 integration, 1, 2, 3, 4 intergroup contact, 1, 2, 3 Intergroup Contact Theory, 1, 2, 3 intergroup hate, 1, 2, 3, 4 internet: algorithms, 1, 2; chatbots, 1; counterhate speech, 1; COVID-19 pandemic, 1; far-right hate, 1, 2, 3, 4, 5, 6, 7; filter bubbles, 1, 2, 3; Google searches, 1; hate speech harm, 1; how much online hate speech, 1; online news, 1; reasons for hate offending, 1; rise of the bots and trolls, 1; stopping online hate speech, 1; tipping point, 1, 2, 3; training the machine to count hate, 1; why online hate speech hurts, 1 interracial relations, 1, 2, 3, 4 intolerance, 1, 2 Iranian bots, 1 Iraq, 1 Irish Republican Army (IRA), 1 ISIS, 1, 2, 3, 4, 5, 6, 7, 8, 9 Islam: group threat, 1; online hate speech, 1, 2, 3, 4, 5; steps to stop hate, 1, 2, 3; subcultures of hate, 1, 2, 3, 4; trigger events, 1, 2, 3 Islamism: group threat, 1; online hate speech, 1, 2, 3, 4; profiling the hater, 1; subcultures of hate, 1, 2, 3; trigger events, 1, 2, 3 Islamophobia, 1, 2, 3, 4 Israel, 1, 2, 3 Italy, 1, 2 ITT, see Integrated Threat Theory James, Lee, 1, 2, 3, 4, 5, 6 Japan, 1, 2, 3 Jasko, Katarzyna, 1 Jefferson, Thomas, 1 Jenny Lives with Eric and Martin, 1 Jewish people: COVID-19 pandemic, 1, 2; far-right hate, 1, 2, 3, 4, 5; filter bubbles, 1; Google searches, 1, 2; group threat, 1; Nazism, 1, 2; negative stereotypes, 1 2 online hate speech, 1; pyramid of hate, 1; questioning prejudgements, 1; ritual washing, 1; subcultures of hate, 1, 2; trauma and Franklin, 1, 2, 3 jihad, 1, 2, 3, 4, 5 jokes, 1, 2, 3, 4, 5, 6, 7 Jones, Alex, 1 Jones, Terry, 1 Josephson junction, 1 Judaism, 1; see also Jewish people Jude, Frank, Jr, 1, 2, 3, 4, 5 Kansas, 1 Kerry, John, 1 Kik, 1 King, Gary, 1 King, Martin Luther, Jr, 1, 2 King, Rodney, 1, 2, 3 King, Ryan, 1 Kirklees, 1, 2 KKK, see Ku Klux Klan Kuchibhotla, Srinivas, 1, 2, 3, 4 Kuchibhotla, Sunayana, 1, 2 Ku Klux Klan (KKK), 1, 2, 3n, 4, 5, 6, 7 Labour Party, 1, 2, 3 Lancaster, Sophie, 1, 2 language, 1, 2, 3, 4, 5, 6, 7 LAPD (Los Angeles Police Department), 1 Lapshyn, Pavlo, 1 Lashkar-e-Taiba, 1 Las Vegas shooting, 1, 2 Latinx people, 1, 2, 3, 4, 5, 6, 7 law: brain and hate, 1, 2, 3; criminalising hate, 1; hate counts, 1, 2, 3; Kansas shooting, 1; limited laws, 1; online hate speech, 1; pyramid of hate, 1 Law Commission, 1 Lawrence, Stephen, 1 learned fears, 1, 2, 3 Leave.EU campaign, 1, 2 Leave voters, 1, 2, 3n Lee, Robert E., 1, 2, 3 left orbitofrontal cortex, 1n, 2n Legewie, Joscha, 1, 2, 3, 4 lesbians, 1, 2 Levin, Jack, 1 LGBTQ+ people, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17; see also gay people LIB, see Linguistic Intergroup Bias test Liberman, Nira, 1 Liberty Park, Salt Lake City, 1, 2 Libya, 1, 2, 3, 4 Light, John, 1 Linguistic Intergroup Bias (LIB) test, 1 Liverpool, 1, 2 Livingstone, Ken, 1, 2 Loja, Angel, 1 London: author’s experience of attack, 1; Copeland nail bombing, 1, 2; Duggan shooting, 1; far-right hate, 1; group threat, 1, 2, 3; online hate speech, 1, 2; Rigby attack, 1; terror attacks, 1, 2, 3, 4, 5, 6 London Bridge attack, 1, 2, 3 London School of Economics, 1 ‘lone wolf’ terrorists, 1, 2, 3, 4 long-term memory, 1, 2, 3, 4 Loomer, Laura, 1 Los Angeles, 1 loss: group threat, 1; subcultures of hate, 1, 2, 3, 4; tipping point, 1; trauma and containment, 1, 2, 3, 4, 5 love, 1, 2 Love Thy Neighbour, 1 Lucero, Marcelo, 1, 2 Luqman, Shehzad, 1 ‘Macbeth effect’, 1 machine learning, 1 Madasani, Alok, 1, 2, 3 Madrid attack, 1, 2 Magnetic Resonance Imaging (MRI): Diffusion MRI, 1, 2; functional MRI, 1, 2, 3, 4, 5, 6, 7 magnetoencephalography (MEG), 1, 2, 3 Maldon, 1 Malik, Tashfeen, 1 Maltby, Robert, 1, 2 Manchester, 1, 2 Manchester Arena attack, 1, 2, 3, 4, 5, 6 marginalisation, 1, 2 Martin, David, 1 Martin, Trayvon, 1, 2 MartinLutherKing.org, 1, 2 martyrdom, 1, 2, 3, 4n masculinity, 1, 2, 3, 4, 5 The Matrix, 1 Matthew Shepard and James Byrd Jr Hate Crimes Prevention Act, 1n, 2n Matz, Sandra, 1 Mauritius, 1 McCain, John, 1 McDade, Tony, 1 McDevitt, Jack, Levin McKinney, Aaron, 1 McMichael, Gregory, 1 McMichael, Travis, 1 media: far-right hate, 1, 2; group threat, 1, 2, 3; steps to stop hate, 1, 2, 3, 4, 5, 6; stereotypes in, 1, 2; subcultures of hate, 1; trigger events, 1 Meechan, Mark, 1 MEG (magnetoencephalography), 1, 2, 3 memory, 1, 2, 3, 4, 5, 6, 7 men, and online hate speech, 1 men’s rights, 1 mental illness, 1, 2, 3, 4, 5, 6 mentalising, 1, 2, 3 meta-analysis, 1 Metropolitan Police, 1 Mexican people, 1, 2, 3, 4 micro-aggressions, 1, 2n, 3, 4, 5, 6 micro-events, 1 Microsemi, 1n Microsoft, 1, 2, 3, 4, 5, 6 micro-targeting, 1, 2 Middle East, 1, 2 migration, 1, 2, 3, 4, 5, 6, 7; see also immigration Milgram, Stanley, 1 military, 1 millennials, 1 Milligan, Spike, 1 Milwaukee, 1, 2, 3 minimal groups, 1 Minneapolis, 1, 2, 3 minority groups: far-right hate, 1, 2; group threat, 1, 2, 3, 4, 5; police reporting, 1; questioning prejudgements, 1; trauma and containment, 1; trigger events, 1, 2 misinformation, 1, 2, 3, 4, 5, 6 mission haters, 1, 2, 3 mobile phones, 1, 2, 3 moderation of content, 1, 2, 3 Moore, Nik, 1 Moore, Thomas, 1 Moores, Manizhah, 1 Moore’s Ford lynching, 1 Moradi, Dr Zargol, 1, 2, 3, 4, 5, 6 Moral Choice Dilemma tasks, 1, 2, 3 moral cleansing, 1, 2, 3 moral dimension, 1, 2, 3, 4 moral outrage, 1, 2, 3, 4, 5 Moroccan people, 1, 2 mortality, 1, 2, 3 mortality salience, 1, 2, 3, 4, 5 Moscow, 1 mosques, 1, 2, 3, 4, 5, 6, 7 Moss Side Blood, 1 mothers, 1, 2, 3, 4, 5, 6 motivation, 1n, 2, 3, 4, 5, 6 Mphiti, Thato, 1 MRI, see Magnetic Resonance Imaging Muamba, Fabrice, 1 multiculturalism, 1, 2, 3, 4 murder: brain injury, 1, 2; group threat, 1, 2, 3; hate counts, 1; identity fusion and hateful murder, 1; police and hate, 1, 2; profiling the hater, 1; trauma and containment, 1, 2, 3, 4, 5 Murdered for Being Different, 1 music, 1, 2, 3 Muslims: COVID-19 pandemic, 1; far-right hate, 1, 2, 3, 4; Google searches, 1; group threat, 1, 2, 3, 4, 5, 6; negative stereotypes, 1; online hate speech, 1, 2; profiling the hater, 1, 2; Salah effect, 1; subcultures of hate, 1, 2, 3; trigger events, 1, 2, 3, 4, 5; and Trump, 1, 2, 3, 4n, 5, 6n Mvubu, Themba, 1 Myanmar, 1, 2 Myatt, David, 1 Nandi, Dr Alita, 1 National Action, 1 National Consortium for the Study of Terrorism and Responses to Terrorism, 1 national crime victimisation surveys, 1, 2 National Front, 1, 2, 3 nationalism, 1, 2 National Socialist Movement, 1, 2, 3, 4 natural experiments, 1, 2 Nature: Neuroscience, 1 nature vs nurture debate, 1 Nazism, 1, 2, 3, 4, 5, 6, 7, 8 NCVS (National Crime Victimisation Survey), 1, 2 negative stereotypes: brain and hate, 1, 2; feeling hate together, 1, 2; group threat, 1, 2, 3, 4, 5, 6; steps to stop hate, 1, 2, 3, 4, 5; tipping point, 1 Nehlen, Paul, 1 neo-Nazis, 1n, 2, 3, 4, 5, 6 Netherlands, 1, 2 Netzwerkdurchsetzungsgesetz (NetzDG) law, 1 neuroimaging, see brain imaging neurons, 1, 2, 3, 4, 5, 6, 7 neuroscience, 1, 2, 3, 4, 5, 6, 7, 8, 9 Newark, 1, 2 news, 1, 2, 3, 4, 5, 6, 7 newspapers, 1, 2, 3, 4 New York City, 1, 2, 3, 4, 5, 6 New York Police Department (NYPD), 1 New York Times, 1, 2 New Zealand, 1 n-grams, 1 Nimmo, John, 1 9/11 attacks, 1, 2, 3, 4, 5, 6, 7 911 emergency calls, 1 Nogwaza, Noxolo, 1 non-independence error, 1, 2n Al Noor Mosque, Christchurch, 1 Northern Ireland, 1 NWA, 1 NYPD (New York Police Department), 1 Obama, Barack, 1n, 2, 3, 4, 5, 6 Occupy Paedophilia, 1 ODIHR, see Office for Democratic Institutions and Human Rights Ofcom, 1 offence, 1, 2, 3, 4 Office for Democratic Institutions and Human Rights (ODIHR), 1, 2 Office for Security and Counter Terrorism, 1 office workers, 1 offline harm, 1, 2 Oklahoma City, 1 O’Mahoney, Bernard, 1 online hate speech: author’s experience, 1; COVID-19 pandemic, 1; far-right hate, 1, 2, 3, 4, 5; hate speech harm, 1; how much online hate speech, 1; individual’s role, 1; law’s role, 1; social media companies’ role, 1; steps to stop hate, 1; tipping point, 1, 2; training the machine to count hate, 1; trigger events, 1 Ono, Kazuya, 1 optical illusions, 1 Organization for Human Brain Mapping conference, 1 Orlando attack, 1 Orwell, George, Nineteen Eighty-Four, 1 Osborne, Darren, 1 ‘other’, 1, 2, 3, 4, 5, 6 Ottoman Empire, 1 outgroup: author’s brain and hate, 1, 2, 3; brain and hate, 1, 2, 3, 4, 5, 6, 7; child interaction and play, 1, 2; evolution of group threat detection, 1; feeling hate together, 1; group threat, 1, 2, 3, 4, 5, 6; ‘gut-deep’ hate, 1; HateLab Brexit study, 1; human biology and threat, 1; identity fusion, 1; prejudice formation, 1; profiling the hater, 1; push/pull factor, 1; pyramid of hate, 1; society, competition and threat, 1; steps to stop hate, 1, 2; tipping point, 1; trauma and containment, 1, 2, 3, 4, 5; trigger events, 1, 2, 3, 4, 5, 6, 7, 8 outliers, 1 Overton window, 1, 2, 3, 4 oxytocin, 1, 2, 3, 4 Paddock, Stephen, 1 Paddy’s Pub, Bali, 1 paedophilia, 1, 2, 3, 4, 5 page rank, 1 pain, 1, 2, 3, 4, 5, 6, 7 Pakistani people, 1, 2, 3, 4, 5 Palestine, 1 pandemics, 1, 2, 3, 4 Papua New Guinea, 1, 2, 3 paranoid schizophrenia, 1, 2 parents: caregiving, 1; subcultures of hate, 1; trauma and containment, 1, 2, 3, 4, 5; trigger events, 1, 2, 3 Paris attack, 1 Parsons Green attack, 1, 2 past experience: the ‘average’ hate criminal, 1; the ‘exceptional’ hate criminal, 1; trauma and containment, 1 perception-based hate crime, 1, 2 perception of threat, 1, 2, 3, 4, 5 perpetrators, 1, 2 personal contact, 1, 2 personality, 1, 2, 3 personality disorder, 1, 2 personal safety, 1, 2 personal significance, 1 perspective taking, 1, 2 PFC, see prefrontal cortex Philadelphia Police Department, 1 Philippines, 1 physical attacks, 1, 2, 3, 4, 5, 6, 7, 8 play, 1 Poland, 1, 2, 3 polarisation, 1, 2, 3, 4, 5 police: brain and hate, 1, 2; Duggan shooting, 1; group threat, 1, 2, 3; and hate, 1; NYPD racial bias, 1; online hate speech, 1, 2, 3, 4; perceiving versus proving hate, 1; police brutality, 1, 2, 3, 4; predicting hate crime, 1; recording crime, 1, 2, 3, 4; reporting crime, 1, 2, 3; rising hate count, 1, 2, 3; ‘signal’ hate acts and criminalisation, 1; steps to stop hate, 1, 2, 3; use of force, 1 Polish migrants, 1 politics: early adulthood, 1; far-right hate, 1, 2; filter bubbles and bias, 1; group threat, 1, 2, 3; online hate speech, 1, 2; seven steps to stop hate, 1, 2, 3, 4; trauma and containment, 1; trigger events, 1, 2, 3, 4, 5; Trump election, 1, 2 populism, 1, 2, 3, 4, 5 pornography, 1 Portugal, 1, 2 positive stereotypes, 1, 2 post-traumatic stress disorder (PTSD), 1, 2, 3, 4, 5 poverty, 1, 2, 3 Poway synagogue shooting, 1 power, 1, 2, 3, 4, 5 power law, 1 predicting the next hate crime, 1 prefrontal cortex (PFC): brain and signs of prejudice, 1; brain injury, 1; disengaging the amygdala autopilot, 1; feeling pain, 1; ‘gut-deep’ hate, 1; prejudice network, 1; psychological brainwashing, 1; recognising false alarms, 1; salience network, 1; trauma and containment, 1; trigger events, 1; unlearning prejudiced threat detection, 1, 2 prehistoric brain, 1, 2 prehistory, 1, 2 prejudgements, 1 prejudice: algorithms, 1; author’s brain and hate, 1, 2, 3, 4, 5, 6, 7; brain and hate, 1, 2, 3, 4, 5, 6, 7; brain and signs of prejudice, 1; cultural machine, 1; far-right hate, 1, 2; filter bubbles and bias, 1; foundations of, 1; Google, 2; group threat, 1, 2, 3, 4, 5, 6, 7, 8, 9; human biology and threat, 1; neuroscience of hate, 1, 2; online hate speech, 1, 2, 3; parts that process prejudice, 1; prejudice network, 1, 2, 3, 4; prepared versus learned amygdala responses, 1; pyramid of hate, 1; releasers, 1, 2; steps to stop hate, 1, 2, 3, 4; tipping point from prejudice to hate, 1; trauma and containment, 1, 2, 3, 4, 5; trigger events, 1, 2, 3, 4, 5, 6, 7, 8; Trump, 1, 2; unconscious bias, 1; unlearning prejudiced threat detection, 1; what it means to hate, 1, 2, 3, 4, 5 prepared fears, 1, 2 Prisoner’s Dilemma, 1 profiling the hater, 1 Proposition 1, 2 ProPublica, 1n, 2 prosecution, 1, 2, 3 Protestants, 1 protons, 1 psychoanalysis, 1 psychological development, 1, 2, 3, 4 psychological profiles, 1 psychological training, 1 psychology, 1, 2, 3, 4 psychosocial criminology, 1, 2 psy-ops (psychological operations), 1 PTSD, see post-traumatic stress disorder Public Order Act, 1 pull factor, 1, 2, 3, 4, 5 Pullin, Rhys, 1n Purinton, Adam, 1, 2, 3, 4, 5, 6, 7 push/pull factor, 1, 2, 3, 4, 5, 6 pyramid of hate, 1, 2 Q …, 1 al-Qaeda, 1, 2 quality of life, 1 queer people, 1, 2 quest for significance, 1, 2, 3 Quran burning, 1 race: author’s brain and hate, 1, 2, 3, 4; brain and hate, 1, 2, 3, 4, 5, 6, 7; brain and signs of prejudice, 1; far-right hate, 1, 2, 3; Google searches, 1; group threat, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10; hate counts, 1, 2, 3; online hate speech, 1; predicting hate crime, 1; pyramid of hate, 1; race relations, 1, 2, 3; race riots, 1, 2; race war, 1, 2, 3, 4, 5; steps to stop hate, 1, 2, 3; trauma and containment, 1, 2, 3, 4n, 5, 6; trigger events, 1, 2; unconscious bias, 1; unlearning prejudiced threat detection, 1 racism: author’s experience, 1; brain and hate, 1, 2, 3, 4, 5, 6; far-right hate, 1, 2; group threat, 1, 2, 3, 4, 5, 6, 7, 8; Kansas shooting, 1; NYPD racial bias, 1; online hate speech, 1, 2, 3, 4; steps to stop hate, 1n, 2, 3; Tay chatbot, 1; trauma and containment, 1, 2, 3, 4, 5, 6, 7; Trump election, 1; victim perception of motivation, 1n; white flight, 1 radicalisation: far-right hate, 1, 2, 3; group threat, 1; subcultures of hate, 1, 2, 3, 4, 5; trigger events, 1 rallies, 1, 2, 3; see also Charlottesville rally Ramadan, 1, 2 rape, 1, 2, 3, 4, 5 rap music, 1 realistic threats, 1, 2, 3, 4, 5 Rebel Media, 1 rebels, 1 recategorisation, 1 recession, 1, 2, 3, 4, 5 recommendation algorithms, 1, 2 recording crime, 1, 2, 3, 4 red alert, 1 Reddit, 1, 2, 3, 4 red-pilling, 1, 2, 3, 4 refugees, 1, 2, 3, 4, 5 rejection, 1, 2, 3, 4, 5, 6 releasers of prejudice, 1, 2 religion: group threat, 1, 2, 3; homosexuality, 1; online hate speech, 1, 2, 3; predicting hate crime, 1; pyramid of hate, 1; religion versus hate, 1; steps to stop hate, 1, 2; subcultures of hate, 1, 2; trauma and containment, 1n, 2; trigger events, 1, 2, 3, 4, 5; victim perception of motivation, 1n reporting crimes, 1, 2, 3, 4, 5, 6, 7 repression, 1 Republicans, 1, 2, 3, 4, 5 research studies, 1 responsibility, 1, 2, 3 restorative justice, 1 retaliatory haters, 1, 2, 3 Reuters, 1 Rieder, Bernhard, 1 Rigby, Lee, 1 rights: civil rights, 1, 2, 3, 4; gay rights, 1, 2, 3, 4; human rights, 1, 2, 3; men’s rights, 1; tipping point, 1; women’s rights, 1, 2 right wing, 1, 2, 3, 4, 5, 6; see also far right Right-Wing Authoritarianism (RWA) scale, 1 riots, 1, 2, 3, 4 risk, 1, 2, 3 rites of passage, 1, 2 rituals, 1, 2, 3 Robb, Thomas, 1 Robbers Cave Experiment, 1, 2, 3, 4, 5, 6 Robinson, Tommy (Stephen Yaxley-Lennon), 1, 2, 3, 4 Rohingya Muslims, 1, 2 Roof, Dylann, 1, 2 Roussos, Saffi, 1 Rudolph, Eric, 1 Rushin, S,, 1n Russia, 1, 2, 3, 4, 5, 6, 7, 8 Russian Internet Research Agency, 1 RWA (Right-Wing Authoritarianism) scale, 1 Rwanda, 1 sacred value protection, 1, 2, 3, 4, 5, 6, 7, 8 Saddam Hussein, 1 safety, 1, 2 Sagamihara care home, Japan, 1, 2 Salah, Mohamed, 1, 2, 3 salience network, 1, 2 salmon, brain imaging of, 1 Salt Lake City, 1 same-sex marriage, 1, 2 same-sex relations, 1, 2, 3 San Bernardino attack, 1n, 2, 3 Scanlon, Patsy, 1 scans, see brain imaging Scavino, Dan, 1n schizophrenia, 1, 2, 3, 4 school shootings, 1, 2 science, 1, 2, 3 scripture, 1, 2 SDO, see Social Dominance Orientation (SDO) scale Search Engine Manipulation Effect (SEME), 1 search queries, 1, 2, 3, 4 Second World War, 1, 2, 3 Section 1, Local Government Act, 1, 2, 3 seed thoughts, 1 segregation, 1, 2, 3 seizures, 1, 2, 3 selection bias problem, 1n self-defence, 1, 2 self-esteem, 1, 2, 3, 4 self-sacrifice, 1, 2, 3 Senior, Eve, 1 serial killers, 1, 2, 3 7/7 attack, London, 1 seven steps to stop hate, 1; becoming hate incident first responders, 1; bursting our filter bubbles, 1; contact with others, 1; not allowing divisive events to get the better of us, 1; overview, 1; putting ourselves in the shoes of ‘others’, 1; questioning prejudgements, 1; recognising false alarms, 1 sexism, 1, 2 sexual orientation, 1, 2, 3, 4, 5, 6, 7 sexual violence, 1, 2, 3, 4, 5 sex workers, 1, 2, 3, 4 Shakespeare, William, Macbeth, 1 shame, 1, 2, 3, 4, 5, 6, 7, 8, 9 shared trauma, 1, 2, 3 sharia, 1, 2 Shepard, Matthew, 1, 2 Sherif, Muzafer, 1, 2, 3, 4, 5, 6, 7 shitposting, 1, 2, 3n shootings, 1, 2, 3, 4, 5, 6, 7, 8 ‘signal’ hate acts, 1 significance, 1, 2, 3 Simelane, Eudy, 1 skin colour, 1, 2, 3n, 4, 5, 6, 7 Skitka, Linda, 1, 2 slavery, 1 Slipknot, 1 slurs, 1, 2, 3, 4, 5, 6 Snapchat, 1 social class, 1, 2 social desirability bias, 1, 2 Social Dominance Orientation (SDO) scale, 1 social engineering, 1 socialisation, 1, 2, 3, 4, 5 socialism, 1, 2 social media: chatbots, 1; COVID-19 pandemic, 1; far-right hate, 1, 2, 3, 4; filter bubbles and bias, 1; HateLab Brexit study, 1; online hate speech, 1, 2, 3, 4, 5; online news, 1; pyramid of hate, 1; steps to stop hate, 1, 2, 3; subcultures of hate, 1; trigger events, 1, 2; see also Facebook; Twitter; YouTube Social Perception and Evaluation Lab, 1 Soho, 1 soldiers, 1n, 2, 3 Sorley, Isabella, 1 South Africa, 1 South Carolina, 1 Southern Poverty Law Center, 1n, 2 South Ossetians, 1 Soviet Union, 1, 2 Spain, 1, 2, 3 Spencer, Richard B., 1 Spengler, Andrew, 1, 2, 3, 4 SQUIDs, see superconducting quantum interference devices Stacey, Liam, 1, 2 Stanford University, 1 Star Trek, 1, 2, 3 statistics, 1, 2, 3, 4, 5, 6, 7, 8 statues, 1 Stephan, Cookie, 1, 2 Stephan, Walter, 1, 2 Stephens-Davidowitz, Seth, Everybody Lies, 1 Stereotype Content Model, 1 stereotypes: brain and hate, 1, 2, 3, 4, 5, 6, 7; cultural machine, group threat and stereotypes, 1; definitions, 1; feeling hate together, 1, 2; group threat, 1, 2, 3, 4; homosexuality, 1; NYPD racial bias, 1; steps to stop hate, 1, 2, 3, 4, 5; study of prejudice, 1; tipping point, 1; trigger events, 1 Stoke-on-Trent, 1, 2 Stormfront website, 1, 2, 3 storytelling, 1 stress, 1, 2, 3, 4, 5, 6, 7, 8 striatum, 1, 2, 3n, 4 subcultures, 1, 2, 3, 4, 5 subcultures of hate, 1; collective quests for significance and extreme hate, 1; extremist ideology and compassion, 1; fusion and generosity towards the group, 1; fusion and hateful murder, 1; fusion and hateful violence, 1; fusion and self-sacrifice in the name of hate, 1; quest for significance and extreme hatred, 1; religion/belief, 1; warrior psychology, 1 subhuman, 1, 2 Sue, D.

Debunking Economics - Revised, Expanded and Integrated Edition: The Naked Emperor Dethroned?
by Steve Keen
Published 21 Sep 2011

Economics does not generate a sufficient volume of data, but financial markets do in abundance, with the price and volume data of financial transactions; as Joe McCauley put it, ‘the concentration is on financial markets because that is where one finds the very best data for a careful empirical analysis’ (McCauley 2004: xi). Given that it is a relatively new field, there are numerous explanations of the volatility of financial markets within Econophysics – including Power Law models of stock market movements (Gabaix, Gopikrishnan et al. 2006), Didier Sornette’s earthquake-based analysis (Sornette 2003), Joe McCauley’s empirically derived Fokker-Planck model (McCauley 2004), and Mandelbrot’s fractal geometry (Mandelbrot and Hudson 2004) – and it would require another book to detail them all.

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Concepts such as IS-LM and rational expectations often crop up in complexity or Econophysics models of the economy, with the authors rarely being aware of the origins of these ‘tools.’ While Econophysics has developed a very rich and empirically based analysis of financial markets to date, and their statistical analysis here – involving concepts like Power Law distributions and Tsallis-statistics – is far more accurate than neoclassical models, success here has led to neglect of the ‘econo’ part of the developing discipline’s name: at present it could more accurately be called ‘Finaphysics’ than ‘Econophysics.’ Econophysicists also occasionally succumb to the temptation to introduce one of the strongest weapons in their arsenal, which I believe has no place in economics: ‘conservation laws.’

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Phillips curve; short-run physiocrats piano playing Pick, A. Pigou, A. C. planetary behavior, theory of pleasure, pursuit of Poincaré, Henri policy ineffectiveness proposition politicians, influenced by neoclassical economics polynomialism Ponzi finance Popper, Karl positive economics post-Keynesianism potato famine in Ireland Power Law model Prescott, Edward price; changing, impact on consumer demand; controls imposed on; determination of; positive; theory of (‘additive’) pricing, of financial assets printing of money probability product rule production; Austrian theory of; economists’ assumptions about; neoclassical theory of; reswitching of; with a surplus; with explicit labor; with no surplus productivity: diminishing, causes rising price; does not determine wages; falls as output rises profit; definition of; falling tendency of; Marxian calculation of; maximization of (short-run); normal; rate of (determination of; falling); source of; super-normal proof by contradiction Property Income Limited Leverage (PILL) proto-energetics psychic income Pythagorean mathematics QE1 qualitative easing quantum uncertainty Quesnay, François Quesnay Economic Dynamics (QED) random numbers Rapping, Leonard rational behavior rational expectation see expectation, rational rational numbers rational private behavior rationality; definition of; in economics realism recession reductionism; fallacy of; reconstituted; strong Regulation Q regulatory capture rent; theory of Repast program representative agent passim Reserve Requirement reswitching returns to scale Ricardo, David; Marx’s critique of; Principles of Political Economy and Taxation; theory of rent risk; and return; measurement of; risk-averse behavior Robbins, L.

Tomorrow's Lawyers: An Introduction to Your Future
by Richard Susskind
Published 10 Jan 2013

There are over 50 firms in the world in which many of the partners earn over £1 million per year and, in some, their take is much greater than this. Many of these partners confess that when they entered the law they never dreamt of such incomes and that they had not chosen the law as a career because it would be well remunerated. In contrast, many high-powered law graduates today enter the law precisely because of the promise of considerable wealth. They may be disappointed. Although a handful of these global practices are likely to continue earning very substantial incomes, it may well be that the golden era for many law firms has passed. The more-for-less challenge will drive down profitability.

Hacking Politics: How Geeks, Progressives, the Tea Party, Gamers, Anarchists and Suits Teamed Up to Defeat SOPA and Save the Internet
by David Moon , Patrick Ruffini , David Segal , Aaron Swartz , Lawrence Lessig , Cory Doctorow , Zoe Lofgren , Jamie Laurie , Ron Paul , Mike Masnick , Kim Dotcom , Tiffiniy Cheng , Alexis Ohanian , Nicole Powers and Josh Levy
Published 30 Apr 2013

Perspective, opinions, and actions are developed and undertaken over time. Fluctuations in attention given progressive development of arguments and frames over time, allow for greater diversity of opportunity to participate in setting and changing the agenda early in the debate compared to the prevailing understanding of the power law structure of attention in the blogosphere. It also likely provides more pathways for participation than were available in the mass-mediated public sphere. Second, individuals play a much larger role than was feasible for all but a handful of major mainstream media in the past. A single post on reddit, by one user, launched the GoDaddy boycott; this is the clearest example in our narrative.

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It replicated with regard to online mobilization the same kind of innovation model we have seen for Internet innovation more generally: rapid experimentation and prototyping, cheap failure, adaptation, and ultimately rapid adoption of successful models. Fifth, highly visible sites within the controversy cluster were able to provide an attention backbone for less visible sites or speakers, overcoming the widely perceived effect of “power law” distribution of links. Fight for the Future benefited from links from more established sites, like the Mozilla front page. The phenomenon was not limited, however, to the largest emerging sites, but was available for more discrete interventions as well. Julian Sanchez of the Cato Institute, for example, authored a careful critique of the oft-repeated but poorly founded claim that piracy cost the copyright industries fifty-eight billion dollars a year.

The Controlled Demolition of the American Empire
by Jeff Berwick and Charlie Robinson
Published 14 Apr 2020

If Gold’s Gym could guarantee Wall Street that a huge chunk of their members would stay members for the next two decades, their stock price would spike too. The rise of “Mandatory Minimums” in sentencing happened at the same time that private prisons were coming online. That is not accidental. The people developing private prisons got together with their high power law firm partners that helped them to develop their business in the first place, and actively lobbied their political friends to create a way to guarantee a huge batch of new customers, not just for their current facilities, but for future facilities that have not even been built yet. Making long prison sentences mandatory removes discretion from the judge’s hands and forces them to impose unusually harsh incarceration terms on convicts that might have had a chance of receiving less time.

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Private investors arrange for new laws to be created, with a little help from their politician buddies whose campaigns they finance, that benefit the industry in which they wish to invest. These new laws usually do not have society’s best interests at heart, just their own financial goals. The investors partner up with powerful law firms that have a kind of revolving door that moves people between high government positions and their own boardroom. The powerful politicians arrange for large government contracts to be granted to the companies that have hired their old law firm to assist with the creation of a particular investment vehicle.

The End of Jobs: Money, Meaning and Freedom Without the 9-To-5
by Taylor Pearson
Published 27 Jun 2015

There have always been sailors, but not until the internet was it possible to reach them in a cost-effective way. Selling a few thousand CDs a month for a record company that had tens of thousands of dollars in overhead is a flop, but for an independent artist, it’s a full-time living.32 The same is true of businesses. If you look at sales in any market, it typically follows a power law distribution like the head to tail curve we saw earlier. If we plot the same curve on a logarithmic scale, where each step is a factor of ten ($1, $10, $100, $1000, etc), then it should form a straight line as in the graph below. Source: The Long Tail – Chris Anderson In this example from Chris Anderson’s The Long Tail, actual sales don’t follow the dotted line.

The Transhumanist Reader
by Max More and Natasha Vita-More
Published 4 Mar 2013

Technically, it does not involve any logistic limitation on growth, but rather a logistic-like limitation of increase of growth rate within each mode. It is also unique in predicting multiple past singularities (in the sense of type F radical phase transitions). Sornette (type A,F,G) Johansen and Sornette (2001) fit power laws of the form (T - t)β to world population, GDP, and financial data. β is allowed to be complex, implying not only a superexponential growth as time T is approached (due to the real part of the exponent) but also increasingly faster oscillations (due to the imaginary part). The use of this form is motivated with analogy with physics, for example cascades of Rayleigh-Taylor instabilities, black hole formation, phase separation, and material failure, which all show log-periodic oscillations before the final singularity.

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Rober Aunger has argued that thermodynamics represents a key factor in changing the organization of systems across history, and focused on the emergence of new mechanisms of control of energy flow within systems. Using a dataset of candidates he found an increasing trend of energy flow density and a power law decrease of gap length between transitions. Although he predicted the next transition to start near 2010 and to last 20–25 years, he argued that there has been a plateau in transition lengths for the last century that would preclude a technological singularity (Aunger 2007).8 Discussion Generically, mathematical models that exhibit growth tend to exhibit at least exponential growth since this is the signature of linear self-coupling terms.

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Students get smarter as they learn more, and learn how to learn. However, we teach the most valuable concepts first, and the productivity value of schooling eventually falls off, instead of exploding to infinity. Similarly, the productivity improvement of factory workers typically slows with time, following a power law. At the world level, average IQ scores have increased dramatically over the last century (the Flynn effect), as the world has learned better ways to think and to teach. Nevertheless, IQs have improved steadily, instead of accelerating. Similarly, for decades computer and communication aids have made engineers much “smarter,” without accelerating Moore’s law.

Blockchain: Blueprint for a New Economy
by Melanie Swan
Published 22 Jan 2014

More broadly, complementary currency systems and multicurrency systems are just the application of the same phenomenon that has been used to reinvent many other areas of modern life. Multicurrency systems are the granularification of currency, finance, and money; the seemingly infinite explosion of long-tail power-law personalization and choice making that has come to coffee (Starbucks), books and movies (Amazon, Netflix), information (blogs, Twitter), learning (YouTube, MOOCs), and relationships (polyamory). Now is merely the advent of these various systems of personalized multiplicity coming to money and finance.

Team Human
by Douglas Rushkoff
Published 22 Jan 2019

Connectivity may be the key to participation, but it also gives corporations more license and capacity to extract what little value people have left. Instead of retrieving the peer-to-peer marketplace, the digital economy exacerbates the division of wealth and paralyzes the social instincts for mutual aid that usually mitigate its effects. Digital platforms amplify the power law dynamics that determine winners and losers. While digital music platforms make space for many more performers to sell their music, their architecture and recommendation engines end up promoting many fewer artists than a diverse ecosystem of record stores or FM radio did. One or two superstars get all the plays, and everyone else sells almost nothing.

The Social Animal: The Hidden Sources of Love, Character, and Achievement
by David Brooks
Published 8 Mar 2011

The chairs would be in a rough circle, but each became slightly misaligned so that one guy would be looking at the window, another guy would be looking at a piece of corporate art on the wall, and a third would be facing the door. The members of the team could go an entire hour without ever making eye contact, even as they were talking together happily and productively. Harrison was about thirty-five, pale, large but nonathletic, and utterly brilliant. “What’s your favorite power law?” he asked Erica during one of her first meetings with the unit. Erica didn’t really know what one was. “It’s a polynomial with scale invariance. Like Zipf’s law.” Zipf’s law, Erica was told later, states that the most common word in any language will appear exactly twice as frequently as the next common word, and so on down to the least common.

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Kleiber’s law states that there is a constant relationship between mass and metabolism in any animal. Small animals have faster metabolisms and big animals have slower ones, and you can plot the ratio of mass to metabolism of all animals on a straight line, from the smallest bacteria to the largest hippopotami. The whole room was suddenly aflame with power laws. Everybody but her had their favorites. Erica felt astoundingly slow-witted next to these guys, but happy she’d get to work with them. Every day’s meeting was another intellectual-fireworks display. They’d plop down into their chairs—lower and lower as their meeting progressed until they were practically horizontal with their bellies sticking up and their wing tips crossed in front of them—and about once a meeting there’d be some brilliant outburst.

Civilization: The West and the Rest
by Niall Ferguson
Published 28 Feb 2011

Rather, if you plot the size of fires against the frequency of their occurrence, you get a straight line. Will the next fire be tiny or huge, a bonfire or a conflagration? The most that can be said is that a forest fire twice as large as last year’s is roughly four (or six or eight, depending on the forest) times less likely to happen this year. This kind of pattern – known as a ‘power-law distribution’ – is remarkably common in the natural world. It can be seen not just in forest fires but also in earthquakes and epidemics. Only the steepness of the line varies.11 The political and economic structures made by humans share many of the features of complex systems. Indeed, heterodox economists such as W.

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Of these, two magnitude-7 wars (the world wars) killed at least 36 million (60 per cent of the total), excluding victims of war-related famine or disease, and millions of magnitude-0 homicides (with one, two or three victims) claimed 9.7 million lives (16 per cent). These data appear at first sight to be completely random. But they, too, obey a power law.15 If the incidence of war is as unpredictable as the incidence of forest fires, the implications for any theory of the rise and fall of civilizations are immense, given the obvious causal role played by wars in both the ascent and descent of complex social organizations. A civilization is by definition a highly complex system.

The World According to Physics
by Jim Al-Khalili
Published 10 Mar 2020

Secondly, when we refer in mathematics to something being exponential, we mean that it varies slowly to begin with and then speeds up (the slope becoming steeper). This is a better way of thinking about the inflationary early universe. It started expanding slowly, then sped up. Then, at some point, this exponential expansion changed to what is called a ‘power law’ expansion, where instead of the expansion speeding up, it started to slow down again—until, that is, dark energy kicked in halfway through the universe’s life and started to speed the expansion up again. Of course, this tells you nothing about why the idea is so attractive, or why or how it works.

Gamification by Design: Implementing Game Mechanics in Web and Mobile Apps
by Gabe Zichermann and Christopher Cunningham
Published 14 Aug 2011

Based on these estimates, let’s create a simple table: Behavior Times Points Daily value Visit 1 5 5 Read 10 5 50 Review 0 50 0 Comment 1 25 25 Rate 3 10 30 Daily total 110 Yearly total 5720 Remember that in environments such as games and websites, participation is rarely a bell curve. Thus, your level design should recognize that the power law of distribution (e.g., the 80/20 rule of active users to passive users) is probably more relevant in anticipating possible usage. You don’t have to solve for this problem, but you should be aware of it. Level design recommendations To design levels effectively using the Badgeville system, it’s useful to consider a few design concepts that you can add to the strategies described earlier in this book: Create a profile of a common player and the actions she performs daily.

Likewar: The Weaponization of Social Media
by Peter Warren Singer and Emerson T. Brooking
Published 15 Mar 2018

Posobiec and his messages were retweeted multiple times by the most powerful social media platform in all the world, that of President Donald Trump. #Pizzagate shows how online virality—far from a measure of sincere popularity—is a force that can be manipulated and sustained by just a few influential social media accounts. In internet studies, this is known as “power law.” It tells us that, rather than a free-for-all among millions of people, the battle for attention is actually dominated by a handful of key nodes in the network. Whenever they click “share,” these “super-spreaders” (a term drawn from studies of biologic contagion) are essentially firing a Death Star laser that can redirect the attention of huge swaths of the internet.

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utm_term=.7ecbd9f78337. 129 “Nothing to suggest”: Jack Posobiec (@JackPosobiec), “DC Police Chief: ‘Nothing to suggest man w/gun at Comet Ping Pong had anything to do with #pizzagate’” (tweet deleted), available at Scoopnest, https://www.scoopnest.com/user/JackPosobiec/805559273426141184-dc-police-chief-nothing-to-suggest-man-w-gun-at-comet-ping-pong-had-anything-to-do-with-pizzagate. 129 livestreaming from the White House: Jared Holt and Brendan Karet, “Meet Jack Posobiec: The ‘Alt-Right’ Troll with Press Pass in White House,” Slate, August 16, 2017, https://www.salon.com/2017/08/16/meet-jack-posobiec-the-alt-right-troll-with-a-press-pass-in-white-house_partner/; Jack Posobiec (@JackPosobiec), “Free our people,” Twitter, May 9, 2017, 10:28 A.M., https://twitter.com/jackposobiec/status/861996422920536064. 129 retweeted multiple times: Colleen Shalby, “Trump Retweets Alt-Right Media Figure Who Published ‘Pizzagate’ and Seth Rich Conspiracy Theories,” Los Angeles Times, August 14, 2017, http://www.latimes.com/politics/la-pol-updates-everything-president-trump-retweets-alt-right-blogger-who-1502769297-htmlstory.html; Maya Oppenheim, “Donald Trump Retweets Far-Right Conspiracy Theorist Jack Posobiec Who Took ‘Rape Melania’ Sign to Rally,” Independent, January 15, 2018, https://www.independent.co.uk/news/world/americas/donald-trump-jack-posobiec-pizzagate-rape-melania-sign-twitter-conspiracy-theory-far-right-a8159661.html. 129 “power law”: Emma Pierson, “Twitter Data Show That a Few Powerful Users Can Control the Conversation,” Quartz, May 5, 2015, https://qz.com/396107/twitter-data-show-that-a-few-powerful-users-can-control-the-conversation/. 130 study of 330 million: Xu Wei, “Influential Bloggers Set Topics Online,” China Daily Asia, December 27, 2013, https://www.chinadailyasia.com/news/2013-12/27/content_15108347.html. 130 a mere 300 accounts: Ibid. 130 susceptibility to further falsehoods: Sander van der Linden, “The Conspiracy-Effect: Exposure to Conspiracy Theories (About Global Warming) Decreases Pro-Social Behavior and Science Acceptance,” Personality and Individual Differences 87 (December 2015): 171–73. 130 more supportive of “extremism”: Sander van der Linden, “The Surprising Power of Conspiracy Theories,” Psychology Today, August 24, 2015, https://www.psychologytoday.com/blog/socially-relevant/201508/the-surprising-power-conspiracy-theories. 130 spread about six times faster: Brian Dowling, “MIT Scientist Charts Fake News Reach,” Boston Herald, March 11, 2018, http://www.bostonherald.com/news/local_coverage/2018/03/mit_scientist_charts_fake_news_reach. 130 “Falsehood diffused”: Soroush Vosoughi, Deb Roy, and Sinan Aral, “The Spread of True and False News Online,” Science 359, no. 6380 (March 9, 2018): 1146–51. 131 fake political headlines: Silverman, “This Analysis Shows.” 131 study of 22 million tweets: Philip N.

Future Politics: Living Together in a World Transformed by Tech
by Jamie Susskind
Published 3 Sep 2018

Avent, Wealth of Humans, 119–20. 9. Erik Brynjolfsson and Andrew McAfee, The Second Machine Age:Work, Progress, and Prosperity in a Time of Brilliant Technologies (New York: W. W. Norton & Company, 2014), 118. 10. Erik Brynjolfsson, Andrew McAfee, and Michael Spence. ‘New World Order: Labor, Capital, and Ideas in the Power Law Economy’, Foreign Affairs, July/August 2014 <https://www.foreignaffairs. com/articles/united-states/2014-06-04/new-world-order> (accessed 8 December 2017). 11. Robert W. McChesney, Digital Disconnect: How Capitalism is Turning The Internet Against Democracy (New York:The New Press, 2014), 134. 12.

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Cambridge, Mass: MIT Press, 2013. Brownsword, Roger, and Morag Goodwin. Law and the Technologies of the Twenty-First Century: Texts and Materials. Cambridge: Cambridge University Press, 2012. Brynjolfsson, Erik, Andrew McAfee, and Michael Spence. ‘New World Order: Labor, Capital, and Ideas in the Power Law Economy’. Foreign Affairs, Jul./Aug. 2014 <https://www.foreignaffairs.com/articles/unitedstates/2014-06-04/new-world-order> (accessed 8 Dec. 2017). Brynjolfsson, Erik and Andrew McAfee. The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies. New York: W. W. Norton & Company, 2014.

Outliers
by Malcolm Gladwell
Published 29 May 2017

Skadden was so big, Kramer said, that it was hard to imagine the firm growing beyond that and being able to promote any of those hires. Flom told him, “Ahhh, we'll go to one thousand.” Flom never lacked for ambition. Today Skadden, Arps has nearly two thousand attorneys in twenty-three offices around the world and earns well over $i billion a year, making it one of the largest and most powerful law firms in the world. In his office, Flom has pictures of himself with George Bush Sr. and Bill Clinton. He lives in a sprawling apartment in a luxurious building on Manhattan's Upper East Side. For a period of almost thirty years, if you were a Fortune 500company about to be taken over or trying to take over someone else, or merely a big shot in some kind of fix, Joseph Flom has been your attorney and Skadden, Arps has been your law firmand if they weren't, you probably wished they were.

Bikenomics: How Bicycling Can Save the Economy (Bicycle)
by Elly Blue
Published 29 Nov 2014

Freeways were still being built, but the anti-freeway movement was celebrating some successes, and the spirit of social movements at the time gave people pause about what all that driving had wrought. In the Netherlands,196 the bicycle movement began in the streets, with citizen activists demanding an end to the free reign of automobility, with cries of “Stop the Child Murder.” Activists persisted, and won their point. Their momentum multiplied and reached the highest levels of power. Laws and infrastructure were reworked to make bicycles an attractive choice. As a result, bicycling became mainstream, as it had been once before, unremarkable, a normal way to get around from childhood to old age, with safe, comfortable, convenient facilities provided in every town and city as a matter of course.

Antifragile: Things That Gain From Disorder
by Nassim Nicholas Taleb
Published 27 Nov 2012

I myself spent some time with venture capitalists in California, with an eye on investing myself, and sure enough, that was the mold. Visibly the money should go to the tinkerers, the aggressive tinkerers who you trust will milk the option. Let us use statistical arguments and get technical for a paragraph. Payoffs from research are from Extremistan; they follow a power-law type of statistical distribution, with big, near-unlimited upside but, because of optionality, limited downside. Consequently, payoff from research should necessarily be linear to number of trials, not total funds involved in the trials. Since, as in Figure 7, the winner will have an explosive payoff, uncapped, the right approach requires a certain style of blind funding.

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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. Nonlinearities, Convexity Effects (smiles and frowns): Nonlinearities can be concave or convex, or a mix of both. The term convexity effects is an extension and generalization of the fundamental asymmetry. The technical name for fragility is negative convexity effects and for antifragility is positive convexity effects.

Circle of Greed: The Spectacular Rise and Fall of the Lawyer Who Brought Corporate America to Its Knees
by Patrick Dillon and Carl M. Cannon
Published 2 Mar 2010

As in criminal cases where sentencing guidelines punished holdouts, those who settled first now usually settled for less. AS SHE ASSUMED HER DUTIES as the new U.S. attorney in Los Angeles, Debra Yang inherited a case that had divided her office. It was one thing to allege ethical violations against a prominent and powerful law firm. It was quite another to bring criminal charges. Where were the victims? Who was really damaged? Milberg Weiss cases had been certified by sitting federal judges. Most had settled by virtue of agreements with defendant companies outside of court or with the court’s supervision. Some awards had been returned by juries.

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In his statement to the jury, Lerach had made a point of stressing the many good works of the Methodists, even acknowledging their noble intentions when launching the ill-fated retirement homes. One question raised by the case, Lerach told the jurors, was this: “How could something that should have been so good end up so bad?” As America’s most powerful law firm broke apart, and its top partners headed for prison, this was a question asked about Bill Lerach as well. “We may not be perfect,” Lerach had told William Greider of The Nation in 2002 when discussing trial lawyers, “but we are not corruptible.” Six years later Mother Jones, another liberal magazine, reprised that quote, with a different twist.

The Riders Come Out at Night: Brutality, Corruption, and Cover-Up in Oakland
by Ali Winston and Darwin Bondgraham
Published 10 Jan 2023

Louis Oaks, who ran the Los Angeles Police Department in the early 1920s, was also an open Klan member.13 One official who was not a Klansman, Los Angeles district attorney Thomas Woolwine, raided the terrorist group’s offices in 1922 following deadly KKK attacks against Mexican “bootleggers.” Woolwine’s men confiscated membership lists, then leaked the identity of Klansmen to the press and in letters to mayors and police chiefs to encourage a crackdown. This meant confronting some of California’s most powerful law enforcement leaders. Among the Klan’s members were Sheriff William Traeger of Los Angeles County, LAPD chief Oaks and at least a hundred of his officers, Bakersfield’s police chief, Charles Stone, and a Kern County judge. At least twenty-five San Francisco police officers were known Klansmen, as well as seven Fresno police officers, seven Sacramento deputy sheriffs, and three Kern County deputy sheriffs.

…

His attitudes changed notably while working in the California Attorney General’s Office under Robert Walker Kenny. Both Powers’s and Kenny’s attitudes toward civil rights and race repeatedly incurred the ire of FBI director J. Edgar Hoover and his subordinates for initiatives such as pathbreaking race relations training for police in Richmond, California. Powers, “Law Enforcement, Race Relations,” 58. 44. Mitford, Fine Old Conflict. 45. Gwynne Peirson, “An Introductory Study of Institutional Racism in Law Enforcement” (dissertation, University of California, Berkeley, 1978), 116–17. 46. “Prober Nabs Hostile Cop,” Daily People’s World (San Francisco), January 4, 1950; “Report Claims Oakland Cops Beat Negro,” San Francisco Chronicle, December 31, 1949. 47.

The Filter Bubble: What the Internet Is Hiding From You
by Eli Pariser
Published 11 May 2011

The possibilities are nearly limitless. To be sure, doing face recognition right takes an immense amount of computing power. The tool in Picasa is slow—on my laptop, it crunches for minutes. So for the time being, it may be too expensive to do it well for the whole Web. But face recognition has Moore’s law, one of the most powerful laws in computing, on its side: Every year, as processor speed per dollar doubles, it’ll get twice as cheap to do. Sooner or later, mass face recognition—perhaps even in real time, which would allow for recognition on security and video feeds—will roll out. Facial recognition is especially significant because it’ll create a kind of privacy discontinuity.

Whiplash: How to Survive Our Faster Future
by Joi Ito and Jeff Howe
Published 6 Dec 2016

And yet in hindsight, Professor Bell—son of a deaf mother, husband to a deaf wife, and pioneering student of sound waves and methods of using vibrating wires as a system of communicating sound to those who could not hear it—seems like the perfect choice.20 The shock of the new would become a common refrain in the century of marvels that followed the telegraph: From the sewing machine to the safety pin, from the elevator to the steam turbine, mankind hurtled forward, ever faster, the technology always outstripping our ability to understand it. Will genetic engineering eradicate cancer or become a cheap weapon of mass destruction? No one knows. As Moore’s law demonstrates, technology lopes along according to power laws of one or another magnitude. Our brains—or at least the sum of our brains working together in the welter of institutions, companies, governments, and other forms of collective endeavor—plod along slowly in its wake, struggling to understand just what God, or man, hath wrought. “The future,” science-fiction writer William Gibson once said, “is already here.

Empirical Market Microstructure: The Institutions, Economics and Econometrics of Securities Trading
by Joel Hasbrouck
Published 4 Jan 2007

Friedman, Daniel, and John Rust, 1993, The Double Auction Market: Institutions, Theories and Evidence (Addison-Wesley, New York). Fuller, Wayne A., 1996, Introduction to Statistical Time Series, 2nd ed. (John Wiley, New York). Gabaix, Xavier, Parameswaran Gopikrishnan, Vasiliki Plerou, and H. Eugene Stanley, 2003, A theory of power law distributions in financial market fluctuations, Nature 423, 267–70. Garman, Mark, 1976, Market microstructure, Journal of Financial Economics 3, 257–75. Gatev, Evan, William N. Goetzmann and K. Geert Rouwenhorst, 2006, Pairs trading: Performance of a relative-value arbitrage rule. Review of Financial Studies 19, 797–827.

The Nature of Technology
by W. Brian Arthur
Published 6 Aug 2009

So when I say that technologies are constructed from ones that previously exist, I mean this as shorthand for saying they are constructed from ones that previously exist or ones that can be constructed at one or two removes from those that previously exist. 171 In the beginning,… harnessed: See Ian McNeil, “Basic Tools, Devices, and Mechanisms,” in An Encyclopedia of the History of Technology, McNeil, ed., Routledge, London, 1990. 172 “The more there… curve: Ogburn, p. 104. 180 “gales of creative destruction”: Schumpeter, 1942, pp. 82–85. 181 An Experiment in Evolution: Arthur and Polak. 184 There is a parallel observation in biology: Richard Lenski, et al., “The evolutionary origin of complex features,” Nature, 423, 139–143, 2003. 185 This yielded avalanches: Polak and I found that these “sand-pile” avalanches of collapse followed a power law, which suggests, technically speaking, that our system of technologies exists at self-organized criticality. 187 More familiarly, larger… combinations: another important source of this is gene and genome duplication. The Jacob quote is from his The Possible and the Actual, Pantheon, New York, 1982, p. 30.

Deep Work: Rules for Focused Success in a Distracted World
by Cal Newport
Published 5 Jan 2016

For example, it might be the case that 80 percent of a business’s profits come from just 20 percent of its clients, 80 percent of a nation’s wealth is held by its richest 20 percent of citizens, or 80 percent of computer software crashes come from just 20 percent of the identified bugs. There’s a formal mathematical underpinning to this phenomenon (an 80/20 split is roughly what you would expect when describing a power law distribution over impact—a type of distribution that shows up often when measuring quantities in the real world), but it’s probably most useful when applied heuristically as a reminder that, in many cases, contributions to an outcome are not evenly distributed. Moving forward, let’s assume that this law holds for the important goals in your life.

Dataclysm: Who We Are (When We Think No One's Looking)
by Christian Rudder
Published 8 Sep 2014

In the male antithesis table I used “follow me” instead of “follow me on instagram.” In the female antithesis, I used “malcolm x” instead of “biography of malcolm x,” and in the words by orientation table in the next chapter I used “feminine women” instead of “attracted to feminine women.” something called Zipf’s law I was familiar with power law distributions already. However, I used the “Zipf’s law” Wikipedia page for more information on the law. “Zipf’s Law and Vocabulary,” by C. Joseph Sorell, The Encyclopedia of Applied Linguistics, November 5, 2012, was also a resource. The table in the text was excerpted from a longer table presented in that paper.

Empire of Illusion: The End of Literacy and the Triumph of Spectacle
by Chris Hedges
Published 12 Jul 2009

“It is especially difficult to fight against it,” warned Adorno, “because those manipulative people, who actually are incapable of true experience, for that very reason manifest an unresponsiveness that associates them with certain mentally ill or psychotic characters, namely schizoids.”25 Obama is a product of this elitist system. So are his degree-laden cabinet members. They come out of Harvard, Yale, Wellesley, and Princeton. Their friends and classmates made huge fortunes on Wall Street and in powerful law firms. They go to the same class reunions. They belong to the same clubs. They speak the same easy language of privilege, comfort, and entitlement. The education they have obtained has served to rigidify and perpetuate social stratification. These elite schools prevent, to use Arnold’s words, the “best selves” in the various strata in our culture from communicating across class lines.

The Half-Life of Facts: Why Everything We Know Has an Expiration Date
by Samuel Arbesman
Published 31 Aug 2012

“Exploring the Limits of the Technology S-Curve. Part I: Component Technologies.” Production and Operations Management 1, no. 4 (1992): 334–57. 46 they found mathematical regularities: More recent research has debated whether these are truly exponential or other fast-growing functions, such as power laws or double exponentials. The upshot is the same: There are regularities. See McNerney, James, et al. “Role of Design Complexity in Technology Improvement.” Proceedings of the National Academy of Sciences 108, no. 22 (May 31, 2011): 9008–13; Nagy, Béla, et al. “Superexponential Long-term Trends in Information Technology.”

Silk Road
by Eileen Ormsby
Published 1 Nov 2014

Silk Road was in no way immune to these scams, and those who tried to nab a bargain outside of escrow were given no sympathy. It’s been over two years and Silk Road is still here. We’ve had setbacks here and there, but I’m happy to say that mostly we’ve thrived. Everyone who’s taken their security seriously, and many who haven’t remain free and prosperous despite the wishes of the powerful law enforcement agencies that target us. It is easy to start feeling confident, invincible, even cocky. I encourage you to look for this in yourself and refrain from acting on it. A thread was recently started in this forum publishing the personal information of LE agents that users had a particular grudge with.

How to Predict the Unpredictable
by William Poundstone

Scherzer, Lisa (2012). “Cracking Your PIN Code: Easy as 1-2-3-4.” Yahoo! Finance, Sept. 21, 2012. finance.yahoo.com/blogs/the-exchange/cracking-pin-code-easy-1-2-3-4-130143629.html. Schiffman, Nathaniel (2005). Abracadabra! Amherst, NY: Prometheus Books. Schroeder, Manfred (1992). Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W.H. Freeman. Shannon, C.E. (1948). “A Mathematical Theory of Communication.” Bell System Technical Journal, Jul. and Oct. 1948, 379–423; 623–656. Shannon, Claude (1953). “A Mind-Reading (?) Machine.” Bell Laboratories memorandum, Mar. 18, 1953. ——— (1955).

How Democracy Ends
by David Runciman
Published 9 May 2018

Howard, Pax Technica: How the Internet of Things May Set Us Free or Lock Us Up (New Haven, CT: Yale University Press, 2015), p. 224. 86As above, pp. 161–2. 87Mason, Postcapitalism, p. 283. 88Alex Williams & Nick Srnicek, ‘#ACCELERATE MANIFESTO for an accelerationist politics’, Critical Legal Thinking, 14 May 2013, http://bit.ly/18usvb4 89Yuval Noah Harari, Homo Deus: A Brief History of Tomorrow (London: Harvill Secker, 2016). 90Derek Parfit, Reasons and Persons (Oxford: Oxford University Press, 1984), part 3. Conclusion 91‘UK to dodge Greek fate with tough budget – Osborne’, Reuters, 20 June 2010, http://reut.rs/2jSSnyZ 92Steven Pinker, The Better Angels of Our Nature: The Decline of Violence in History and Its Causes (London: Allen Lane, 2011). 93See Clay Shirky, ‘Power laws, weblogs and inequality’, 8 February 2003, http://bit.ly/1nyyc36 94Alex Cuadros, ‘Open talk of a military coup unsettles Brazil’, New Yorker, 13 October 2017, http://bit.ly/2gjbW25 Epilogue 95See Yuval, Homo Deus. Index A accelerationism, 199–202 Achen, Christopher see Bartels, Larry and Achen, Christopher Ackerman, Bruce, 54–5 advertising, 160 and elections, 158 internet, 157, 159 Afghanistan, 75 Africa, 79 see also Algeria; Zimbabwe Algeria: coup, 41–3 Amazon, 131, 137 anarchism, 192–3, 214 appeasement, 144 Apple, 131, 137 Arendt, Hannah, 85, 86–7, 98 Eichmann in Jerusalem, 84 Argentina, 162 Aristotle, 161 armies see military artificial intelligence (AI), 122–3, 126, 129–30, 189–91 Athens, ancient, 35–8, 142, 161 conspiracy theories, 60 epistocracy, 179 Athens, modern, 27–8; see also Greece austerity, 208 Australia, 162 authoritarianism, 154–5, 171–3 ‘competitive’, 175 pragmatic, 174–5, 176, 177–8, 181, 205 B bankers, 69, 116, 181 banks, 131, 135; see also European Central Bank Bannon, Steve, 13 Bartels, Larry and Achen, Christopher: Democracy for Realists, 184 Bell, David A., 176 Benn, Tony, 58 Bentham, Jeremy, 127, 151, 152 Bermeo, Nancy, 44, 45 bio-engineering, 102–3 Bitcoin, 136 Bostrom, Nick, 105–6 Bourne, Sam (pseudonym): To Kill the President, 57, 58 Brazil, 217 Brennan, Jason: Against Democracy, 183–5, 186–7, 188–9 Bryan, William Jennings, 68–9 bureaucracies, 85, 86–7, 99, 127, 164; see also civil service Burton, Robert, 159–60 Bush, President George W., 12, 55 C Cambridge Analytica (firm), 156, 157, 159 capitalism, 196, 199 Carson, Rachel, 85, 87–8 Silent Spring, 82–3, 89, 90–91, 93 catastrophes, 6, 7, 85–6 environmental, 82–3, 85, 87–93; see also climate change nuclear, 83–4, 97 total, 100 Chicago: violence, 211 China and climate change, 174 Communist Party, 172–3 economy, 172, 208 foreign policy, 30–31 government model, 174 as a meritocracy, 175–6 nationalism, 172 pollution, 89 view of Trump, 173 Churchill, Winston, 8, 75–6, 168–9, 177 civil service, 41, 55–6; see also bureaucracies Clark, Christopher: The Sleepwalkers: How Europe Went to War in 1914, 115 Clemenceau, Georges, 71, 75–6 climate change, 90–93 China and, 174 consciousness raising, 89, 92–93 conspiracy theories, 91–92 incremental nature of, 97 and risk, 101 support for, 108 and uncertainty, 96 see also global warming Clinton, President Bill, 54–5 Clinton, Hillary, 13–15, 16, 198 Cold War, 28–9, 67, 94, 95–6, 106–7, 108–9 communism 194; see also China: Communist Party; Marxism-Leninism; Stalinism consciousness raising, 85, 89, 92–3, 106 conspiracy theories, 60–71 climate change, 91–2 and division, 99 and fake news, 75 France, 69 India, 65–6 nuclear weapons, 96 Poland, 65, 66 and totalitarianism, 98 Turkey, 65, 66 United Kingdom, 62–3 United States, 62, 64–5, 67 and war, 77 conspiracy theorists, 153 Constantine I, king of Greece, 27, 28 consumerism, 166 Corbyn, Jeremy, 58, 94–5, 148–9, 150, 209 corporations, 129–32, 139, 166 coups, 3, 217 Algeria, 41–3 and catastrophes, 85 and clarity, 59 and conspiracies, 7, 60 and counter-coups, 56–7 Cyprus, 33, 38–9 economic conditions for, 31 in fiction, 57–8 Greece, 26–30, 27, 32, 33, 34–5, 38, 40, 45 Luttwak on, 41–2, 46 Turkey, 50–52, 53, 66 varieties of, 44–5 election-day vote fraud, 44 executive, 44 executive aggrandisement, 44, 52, 55 promissory, 44, 47, 50–51 strategic election manipulation, 44 Zimbabwe, 48 crises, 5–6 Cuban missile Crisis (1962), 107–8 mid-life, 5, 8, 169, 218 Cummings, Dominic, 179 currencies, 135 digital, 136 Cyprus: coups, 33, 38–9 D databases, 123 de Gaulle, General Charles, 41, 42 de Tocqueville, Alexis, 142, 187 death, 23–4, 204, 216–17 democracy appeal of, 6, 169–71 audience, 47, 117 direct, 35, 48, 143, 161, 162, 163 failure of, 50 obsolescence, 167–8 plebiscitary, 47 spectator, 47 spread of, 3 strong and weak, 59–60 threats to 6–7, 53–4, 108, 112; see also coups digital revolution, 152, 164, 200–201, 215, 219 dignity collective, 172, 173, 177 and elections, 170, 177 and loss, 175 disruption, 198–9 Dorsey, Jack, 137 Dreyfus, Alfred, 69 dystopias, 90–91, 113, 114, 118–19, 126, 220 E East India Company, 130–31 economic growth, 172, 192 accelerationists and, 200 and populism, 192 United States, 175 Western Europe, 175 Economist (journal), 133 Edgerton, David, 122 education, 109–10, 163–4, 183–4, 185 Eggers, David: The Circle, 139, 140, 141–2, 144 Egypt, 48–50 Eichmann, Adolf, 84, 85–6 elections 4, 218 and advertising, 158–9 computers and, 125 and coups, 44, 45 decision-making process, 188–9 and dignity, 170, 177 and disinformation, 156–7 Egypt, 48–9 France, 148 fraud, 44 Greece, 28, 29, 39, 40, 148 Italy, 148 manipulation of, 44 Netherlands, 148 online, 162 Turkey, 51 United Kingdom, 95 United States see under United States see also vote, right to elites, 75 and climate change, 91–2 corporate, 139 and nuclear disarmament, 95 and populism, 65 power of, 61 see also wealth environmentalists, 200 epistocracy, 178–9, 180, 181–8, 191, 205 equality, 202–3; see also inequality Erdogan, President Recep, 51–3, 66, 149, 213 Estlund, David: Democratic Authority, 185 Ethiopia, 154–5 European Central Bank (ECB), 33, 39, 116–17 European Union (EU) and corporations, 132 and Greece, 30, 32, 116–17 executive aggrandisement, 45–6 military, 55, 56 United States presidents, 92 experts see epistocracy; technocracy ExxonMobil, 92 F Facebook, 131, 132–3, 134–5, 136, 138–9, 140, 141, 145, 150, 157 fascism, 169 financial crash (2008), 79, 110, 116 Forster, E.

Genentech: The Beginnings of Biotech
by Sally Smith Hughes

“Detection of Two Restriction Endonuclease Activities in Hemophilus parainfluenzae Using Analytical Agarose-Ethidium Bromide Electrophoresis.” Biochemistry 12:3055–63. Southwick, Karen. 2001. The Kingmakers: Venture Capital and the Money behind the Net. New York: John Wiley & Sons. Stewart, James B. 1980. The Partners: Inside America’s Most Powerful Law Firms. New York: Simon & Schuster. Swann, John P. 1988. Academic Scientists and the Pharmaceutical Industry: Cooperative Research in Twentieth-Century America. Baltimore: Johns Hopkins University Press. Sylvester, Edward J., and Lynn C. Klotz. 1983. The Gene Age: Genetic Engineering and the Next Industrial Revolution.

Free Speech: Ten Principles for a Connected World
by Timothy Garton Ash
Published 23 May 2016

But these platforms are themselves an extreme example of simultaneous fragmentation and concentration. On the one hand, a platform like Facebook allows 1.5 billion people to speak directly to each other and in that sense can be described as radically open. On the other hand, near-monopoly concentration of ownership power is an extreme example of a power-law curve. Arguably, this is a double power-law curve, first of the platforms themselves, then of voices on those platforms, with the result that a very few reach very many, and very many reach very few. Recall Liebling’s description of a monopoly paper in a one-paper city: ‘a privately owned public utility’. That applies to Facebook, YouTube and Twitter today, with one small difference—their city is the world.

The Happiness Industry: How the Government and Big Business Sold Us Well-Being
by William Davies
Published 11 May 2015

Yet there is still a danger lurking in this worldview, which is the same problem that afflicts all forms of social network analysis. In reducing the social world to a set of mechanisms and resources available to individuals, the question repeatedly arises as to whether social networks might be redesigned in ways to suit the already privileged. Networks have a tendency towards what are called ‘power laws’, whereby those with influence are able to harness that power to win even greater influence. A combination of positive psychology with social media analytics has demonstrated that psychological moods and emotions travel through networks, much as Christakis found in relation to health behaviour.

SuperFreakonomics
by Steven D. Levitt and Stephen J. Dubner
Published 19 Oct 2009

But in truth, the book did have a unifying theme, even if it wasn’t obvious at the time, even to us. If pressed, you could boil it down to four words: People respond to incentives. If you wanted to get more expansive, you might say this: People respond to incentives, although not necessarily in ways that are predictable or manifest. Therefore, one of the most powerful laws in the universe is the law of unintended consequences. This applies to schoolteachers and Realtors and crack dealers as well as expectant mothers, sumo wrestlers, bagel salesmen, and the Ku Klux Klan. The issue of the book’s title, meanwhile, still lay unresolved. After several months and dozens of suggestions, including Unconventional Wisdom (eh), Ain’t Necessarily So (bleh), and E-Ray Vision (don’t ask), our publisher finally decided that perhaps Freakonomics wasn’t so bad after all—or, more precisely, it was so bad it might actually be good.

The Internet Is Not the Answer
by Andrew Keen
Published 5 Jan 2015

It was processing around 40,000 search queries each second, which computes into 3.5 billion daily searches or 1.2 trillion annual searches. The leviathan controls around 65% of search globally, with its dominance of some markets, such as Italy or Spain, being higher than 90%.72 Google’s domination of the Internet reveals the new power laws of this networked economy. Idealists like Kevin Kelly and Nicholas Negroponte believed that the “decentralizing” architecture of the Web would result in a “thousand points of wealth” economy. But the reverse is true. By mimicking the distributed architecture of the Web itself, Google has become a monopolist of information.

The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
by Mario Livio
Published 23 Sep 2003

“Fibonacci at Random,” Science News, 155 (1999): 376–377 Peterson, I. The Mathematical Tourist. New York: W H. Freeman and Company, 1988. Peterson, I. “A Quasicrystal Construction Kit,” Science News, 155 (1999): 60–61 Prechter, R.R. Jr., and Frost, A.J. Elliot Wave Principle. Gainesville, GA: New Classics Library, 1978. Schroeder, M. Fractals, Chaos, Power Laws. New York: W H. Freeman and Company, 1991. Steinhardt, P.J., Jeong, H.-C, Saitoh, K., Tanaka, M., Abe, E., andTsai, A.P. “Experimental Verification of the Quasi-Unit-Cell Model of Quasicrystal Structure,” Nature, 396 (1998): 55–57 Stewart, I. Does God Play Dice? London: Penguin Books, 1997. Walser, H.

DarkMarket: Cyberthieves, Cybercops and You
by Misha Glenny
Published 3 Oct 2011

From the FBI’s vantage point, the US Secret Service stood to gorge itself on three-quarters of a rich budgetary cake. First mover among the cybercops, and still basking in the glory of the Shadowcrew takedown, the US Secret Service was naturally eager to assert its primacy in this embryonic field. The FBI, the largest and most powerful law-enforcement agency in America, had other thoughts. Its Director, Robert Mueller, was keen to move into cyber both to get the funding but also because he was instrumental in trying to refashion the FBI to become less of a police force and more of a domestic intelligence agency. Mularksi’s plan was not merely about busting criminals, it was about gathering information as well.

Super Founders: What Data Reveals About Billion-Dollar Startups
by Ali Tamaseb
Published 14 Sep 2021

Venture-backed startups have created trillions of dollars in shareholder value and comprise a large proportion of the stock market. About 10 percent of billion-dollar startups were bootstrapped or self-financed. GitHub, Atlassian, UiPath, and Qualtrics all bootstrapped for at least four years. • Venture capital has an unintuitive math behind it, and the power laws of startup outcomes dictate why VCs prefer risky startups with massive potential to lower-risk startups with less perceived upside. The fund size of the VC firm you are raising money from dictates the minimum exit outcomes that would make the investors enough money to move the needle. • Startups still got funded and billion-dollar startups were still created in recessions, albeit with reduced dollar amounts and valuations.

Know Thyself
by Stephen M Fleming
Published 27 Apr 2021

The number of neurons in primate brains (which include monkeys, apes such as chimpanzees, and humans) increases linearly with brain mass. If one monkey brain is twice as large as another, we can expect it to have twice as many neurons. But in rodents (such as rats and mice), the number of neurons increases more slowly and then begins to flatten off, in a relationship known as a power law. This means that to get a rodent brain with ten times the number of neurons, you need to make it forty times larger in mass. Rodents are much less efficient than primates at packing neurons into a given brain volume.13 It’s important to put this result in the context of what we know about human evolution.

The Fabric of the Cosmos
by Brian Greene
Published 1 Jan 2003

And the more they spread out, the more precipitously the force of gravity drops with increasing separation. In four space dimensions, Newton’s law would be an inverse cube law (double the separation, force drops by a factor of 8); in five space dimensions, it would be an inverse fourth-power law (double the separation, force drops by a factor of 16); in six space dimensions, it would be an inverse fifth-power law (double the separation, force drops by a factor of 32); and so on for ever higher-dimensional universes. You might think that the success of the inverse square version of Newton’s law in explaining a wealth of data—from the motion of planets to the paths of comets—confirms that we live in a universe with precisely three space dimensions.

Death of the Liberal Class
by Chris Hedges
Published 14 May 2010

The anemic liberal class continues to assert, despite ample evidence to the contrary, that human freedom and equality can be achieved through the charade of electoral politics and constitutional reform. It refuses to acknowledge the corporate domination of traditional democratic channels for ensuring broad participatory power. Law has become, perhaps, the last idealistic refuge of the liberal class. Liberals, while despairing of legislative bodies and the lack of genuine debate in political campaigns, retain a naïve faith in law as an effective vehicle for reform. They retain this faith despite a manipulation of the legal system by corporate power that is as flagrant as the corporate manipulation of electoral politics and legislative deliberation.

The Big Oyster
by Mark Kurlansky
Published 20 Dec 2006

The economics were growing tougher because steam-powered dredges were greatly increasing the harvest. Each time a dredge was hauled across a bed, it hauled up seven to eight bushels of oysters. By 1880, the use of steam power was estimated to have increased the amount of oysters brought to market twelve times from the catch when oyster fleets had been purely sail-powered. Laws were passed to moderate the natural industriousness of men who earned their living by harvesting huge quantities of a low-priced product. Steam power was now commonplace, but steam-powered dredging was banned in much of New York, and even in the case of dredging from a sail-powered sloop, the size of the dredge was restricted to a maximum of thirty pounds.

What Algorithms Want: Imagination in the Age of Computing
by Ed Finn
Published 10 Mar 2017

On a philosophical level, Wiener’s vision of cybernetics depended on the transition from certainty to probability in the twentieth century.29 The advances of Einsteinian relativity and quantum mechanics suggested that uncertainty, or indeterminacy, was fundamental to the cosmos and that observation always affected the system being observed. This marked the displacement of a particular rationalist ideal of the Enlightenment, the notion that the universe operated by simple, all-powerful laws that could be discovered and mastered. Instead, as the growing complexity of mathematical physics in the twentieth and twenty-first centuries has revealed, the closer we look at a physical system, the more important probability becomes. It is unsettling to abandon the comfortable solidity of a table, that ancient prop for philosophers of materialism, and replace it with a probabilistic cloud of atoms.

More Blood, More Sweat and Another Cup of Tea
by Tom Reynolds
Published 30 Apr 2009

At the end of my shift the hospital’s theory was that he had suffered a transient ischaemic attack, or ‘mini-stroke’, which had resolved on its own. And they did take good care of his wife. On the Possible Causes for a Collapse It is funny how you find yourself going to the same people. I’m sure that some form of ‘Power Law’ applies to patients as much as everything else. While sometimes you can get seeming ‘clumps’, other times the reasons for the repeat calls are easy to understand. Take, for instance, a twelve-year-old boy. He had a history of collapsing at home and at school and previous medical tests had been performed to see if there was some cause for this.

Modern Monopolies: What It Takes to Dominate the 21st Century Economy
by Alex Moazed and Nicholas L. Johnson
Published 30 May 2016

More commoditized content platforms, such as Twitter or Instagram, typically have a large overlap between their consumers and producers, as producing content is quick and easy. However, less commoditized content platforms like YouTube have strongly differentiated producer and consumer user groups. These platforms tend to follow more of a power-law dynamic, where a small percentage of their users produce the vast majority of their content, and need to be designed accordingly. Platform Design The exchange versus maker split in platforms is not just a semantic difference. Although all platforms are focused on connecting consumers and producers, which category your platform falls under fundamentally alters the core value you will try to deliver.

The Art of Scalability: Scalable Web Architecture, Processes, and Organizations for the Modern Enterprise
by Martin L. Abbott and Michael T. Fisher
Published 1 Dec 2009

Fascinated by power and wealth distribution in societies, he studied the property ownership in Italy and observed in his 1909 publication that 20% of the population owned 80% of the land, thus giving rise to his Pareto Distribution. Technically, the Pareto Distribution is a power law of probability distribution, meaning that it has a special relationship between the frequency of an observed event and the size of the event. Another power law is Kleiber’s Law of metabolism, which states that the metabolic rate of an animal scales to the 3/4 power of the mass. As an example, a horse that is 50 times larger than a rabbit will have a metabolism 18.8 times greater than the rabbit.

Early Retirement Extreme
by Jacob Lund Fisker
Published 30 Sep 2010

These terms which, except for the top level, have been borrowed from the professional trades, are known in the educational system as high school, Associate's, Bachelor's, Master's, and PhD degrees; genius is beyond what can be obtained educationally. Note that the levels are close to being logarithmically spaced, suggesting that they are governed by a scaling power law. In other words, competence is judged by the rarity of the willingness and ability to put in the effort. The level at 30,000 hours is reserved for the Mozarts and da Vincis of the world, who spend every waking hour on their field of expertise. The hours are active learning hours. Mindless repetition doesn't count towards the total.

The Seventh Sense: Power, Fortune, and Survival in the Age of Networks
by Joshua Cooper Ramo
Published 16 May 2016

If you or I joined the service and found seven friends in ten days, we would most likely stay, enjoying the benefits of the gated world, making it that much harder (impossible, really) for friend number eight to wander somewhere else. Pretty soon, there was essentially nowhere else to go, anyhow. This was network Macht at work. Network theorists who came after Arthur call these rich-get-richer systems “power-law distributed” because if you line up all the firms in a digital industry, you find that the winners are exponentially—by a power of ten or one hundred—ahead of everyone else. They slip free from the normal bell curves that mark most business. A bell-curve distribution would shape up like a chart of people who own cars: 20 percent drive Fords, 10 percent Nissans and Toyotas, and so on.

Data and the City
by Rob Kitchin,Tracey P. Lauriault,Gavin McArdle
Published 2 Aug 2017

that there are at least two regimes characterizing travel in London. In fact, the scatter of trips in Figure 3.3 reveals a clear density map and in Figure 3.4 we show this as best we can. The intensity of very small trips is much greater than larger ones for the distribution of trip volumes follows some sort of power law. Figure 3.4 The density of the scatter: different patterns at different scales. 38 M. Batty In Figure 3.4, we have blown up the lower portion of the scatter to reveal this intensity and this reveals that this kind of data mining must be supplemented by many other kinds of visualization and analysis so that the true patterning of a system with this kind of complexity can be laid bare.

How to Turn Down a Billion Dollars: The Snapchat Story
by Billy Gallagher
Published 13 Feb 2018

As part of the deal, Evan and Bobby each sold a small portion of their equity in exchange for $10 million apiece in cash. For the venture capitalists, this was great—they got to buy more stock in a red-hot company, and it aligned the founders’ incentives with the VCs; venture capital firms see their returns follow a power law, where one investment makes them the majority of their money while most of their investments fail. If the founders have $10 million sitting in their pockets, they will be more likely to aim the company for the bigger, longer-run exits or IPOs rather than selling for less. Amazon CEO Jeff Bezos summed up this idea in a letter to his shareholders, writing, “We all know that if you swing for the fences, you’re going to strike out a lot, but you’re also going to hit some home runs.

RDF Database Systems: Triples Storage and SPARQL Query Processing
by Olivier Cure and Guillaume Blin
Published 10 Dec 2014

This structure is used for indexing subjects and objects. A third index is created for predicates. For each predicate a list of subjects and objects is stored. Default distribution of triples is hashing on the node IDs—that is they are randomly partitioned. Other partitioning methods can be used. The power law distribution is taken into account to model RDF data with the main objective of preventing communication between cluster nodes at query time. Because the data is modeled as a graph, the query processing uses graph navigation rather than joins.The project is relatively new and a first research paper has only been published in 2013 (Zeng et al., 2013). 5.4 COMPLEMENTARY SURVEYS Although we have presented a complete overview of existing RDF store systems, it seems fair to emphasize several comparable surveys of this active domain.

Decoding the World: A Roadmap for the Questioner
by Po Bronson
Published 14 Jul 2020

Nuclear fusion is a future industry; it will need fewer jobs than the coal and gas industry it replaces. Cryptocurrency and blockchain don’t create jobs. These technologies just make it easier to get paid in fractions of pennies. Even biotech is rapidly adopting robots to replace lab techs. All of the future industries will follow the Power Law, which is VC speak for “winners take all.” You can’t point to a single deep-tech field and argue, “That’s going to create a lot of jobs for everyone.” Sometimes politicians point at solar power and say it will create jobs; certainly the first-time installation takes some labor, but not after that.

Merchants of the Right: Gun Sellers and the Crisis of American Democracy
by Jennifer Carlson
Published 2 May 2023

Wisconsin: Second Amendment Rights Protected by Governor’s Emergency Order. Accessed August 2, 2021. https://www.nraila.org/articles/20200324/wisconsin-second-amendment-rights-protected-by-governors-emergency-order. Obert, J. and Schultz, E. (2020). Right Wing Militias, Guns, and the Technics of State Power. Law, Culture, and the Humanities, 16(2), 236–249. Oliver, J. E. and Rahn, W. M. (2016). Rise of the Trumpenvolk: Populism in the 2016 Election. The ANNALS of the American Academy of Political and Social Science, 667(1), 189–206. Omi, M. and Winant, H. (2014). Racial Formation in the United States.

Digital Empires: The Global Battle to Regulate Technology
by Anu Bradford
Published 25 Sep 2023

Historical Rev. 1348, 1381–1382 (2011). 100.See discussion in Chapter 7. 101.See discussion in Chapter 8. 102.See discussion in Chapter 9. 103.See discussion in Chapter 8 and conclusion. Chapter 1 1.See generally Margaret O’Mara, The Code: Silicon Valley and the Remaking of America (2019). 2.See generally Sebastian Mallaby, The Power Law: Venture Capital and the Making of the New Future (2022). 3.Id. at ch. 1. 4.O’Mara, supra note 1, at ch. 2. 5.Richard Barbrook & Andy Cameron, The Californian Ideology, 6 Sci. as Culture 44, 45, 49 (1996). 6.Id. at 44–45. 7.James A. Lewis, Sovereignty and the Role of Government in Cyberspace, 16 Brown J.

…

China (June 17, 2019), https://www.most.gov.cn/kjbgz/201906/t20190617_147107.html, translated in Graham Webster, Lorand Laskai, Translation: Chinese Expert Group Offers “Governance Principles” for “Responsible AI,” DigiChina (June 17, 2019), https://digichina.stanford.edu/work/translation-chinese-expert-group-offers-governance-principles-for-responsible-ai/. 147.Sebastian Mallaby, The Power Law: Venture Capital and the Making of the New Future 225 (2022). 148.Id. at 224. 149.Id. at 226. 150.Id. at 231–232. 151.James Kynge, For US Venture Funds, Next Jack Ma Is Outside China, Nikkei Asia (Mar. 5, 2020), https://asia.nikkei.com/Spotlight/Comment/For-US-venture-funds-next-Jack-Ma-is-outside-China. 152.Mallaby, supra note 147, 233 (2022). 153.Rolfe Winkler, Jing Yang, & Alexander Osipovich, Secretive High-Speed Trading Firm Hits Jackpot with TikTok, Wall St.

Is the Internet Changing the Way You Think?: The Net's Impact on Our Minds and Future
by John Brockman
Published 18 Jan 2011

The Internet immerses us in a milieu of information—not for almost twenty years has a Web user read every available page—and there’s more each minute: Twitter alone processes hundreds of tweets every second, from all around the world, all visible for anyone, anywhere, who cares to see. Of course, the majority of this information is worthless to the majority of people. Yet anything we care to know—What’s the function for opening files in Perl? How far is it from Hong Kong to London? What’s a power law?—is out there somewhere. I see today’s Internet as having three primary, broad consequences: (1) information is no longer stored and retrieved by people but is managed externally, by the Internet; (2) it is increasingly challenging and important for people to maintain their focus in a world where distractions are available everywhere; and (3) the Internet enables us to talk to and hear from people around the world effortlessly.

The Physics of Wall Street: A Brief History of Predicting the Unpredictable
by James Owen Weatherall
Published 2 Jan 2013

“This is a general property of fractals . . .”: There are many connections between fractals and fat-tailed distributions. That certain features of fractals exhibit fat tails is one such connection; another is that (some) fat-tailed distributions themselves exhibit self-similarity, in the form of power-law scaling in their tails. Mandelbrot was a central figure in identifying and exploring these relationships. See Mandelbrot (1997). “Known as the Butcher of Lyon . . .”: For more on Barbie, see Bower (1984) and McKale (2012). “. . . ‘there was no great distinction . . .’ ”: This quote is from Mandelbrot (1998)

The Boy Who Could Change the World: The Writings of Aaron Swartz
by Aaron Swartz and Lawrence Lessig
Published 5 Jan 2016

But they all do it on the same week [sweeps week], so the networks purposely introduce big guest stars and major cliffhangers that week to get more people to watch the show.) This sounds good, and it works reasonably well for TV, but it won’t work on the Internet. Popularity on the Internet doesn’t follow the old rules; it follows something called a power law. [. . .] There are hundreds of thousands of sites with tens of users and tens of sites with hundreds of thousands of users. And there are tens of thousands of sites with hundreds of users, and thousands of sites with thousands of users and so on. Sampling can’t cope with this kind of disparity.

Postcapitalism: A Guide to Our Future
by Paul Mason
Published 29 Jul 2015

Mason, Meltdown: The End of the Age of Greed (London, 2009) 4. http://www.telegraph.co.uk/finance/financetopics/davos/9041442/Davos-2012-Prudential-chief-Tidjane-Thiam-says-minimum-wage-is-a-machine-to-destroy-jobs.html 5. http://ftalphaville.ft.com/2014/02/07/1763792/a-lesson-from-japans-falling-real-wages/; http://www.social-europe.eu/2013/05/real-wages-in-the-eurozone-not-a-double-but-a-continuing-dip/; http://cep.lse.ac.uk/pubs/download/cp422.pdf 6. D. Fiaschi et al, ‘The Interrupted Power Law and the Size of Shadow Banking’, 4 April 2014, http://arxiv.org/pdf/1309.2130v4.pdf 7. http://www.theguardian.com/news/datablog/2015/feb/05/global-debt-has-grown-by-57-trillion-in-seven-years-following-the-financial-crisis 8. http://jenner.com/lehman/VOLUME%203.pdf p 742 9. http://www.sec.gov/news/studies/2008/craexamination070808.pdf p12 10. http://www.investmentweek.co.uk/investment-week/news/2187554/-done-for-boy-barclays-libor-messages 11.

This Will Make You Smarter: 150 New Scientific Concepts to Improve Your Thinking
by John Brockman
Published 14 Feb 2012

The Italian economist Vilfredo Pareto undertook a study of market economies a century ago and discovered that no matter what the country, the richest quintile of the population controlled most of the wealth. The effects of this Pareto distribution go by many names—the 80/20 rule, Zipf’s law, the power-law distribution, winner-take-all—but the basic shape of the underlying distribution is always the same: The richest or busiest or most connected participants in a system will account for much, much more wealth or activity or connectedness than average. Furthermore, this pattern is recursive. Within the top 20 percent of a system that exhibits a Pareto distribution, the top 20 percent of that slice will also account for disproportionately more of whatever is being measured, and so on.

Tower of Basel: The Shadowy History of the Secret Bank That Runs the World
by Adam Lebor
Published 28 May 2013

In fact, Dulles was running the American diplomatic intelligence operation for central Europe and courting and monitoring its émigrés, exiles, and revolutionaries. By 1930, when Dulles wrote to Leon Fraser, Dulles had left the Foreign Service. He and his brother, John Foster Dulles, became partners at Sullivan & Cromwell—the most powerful law firm in the United States, if not the world—headquartered at 48 Wall Street, in New York. Allen Dulles ran Sullivan & Cromwell’s office in Paris and knew Hjalmar Schacht well. In Paris in 1919, Dulles had learned about diplomacy. And in Paris in 1930, he would learn about the world of high finance and the BIS.

Age of Anger: A History of the Present
by Pankaj Mishra
Published 26 Jan 2017

See also Arjun Appadurai, Fear of Small Numbers: An Essay on the Geography of Anger (Durham, NC, 2006). The Pope’s encyclical about climate change is arguably the most important piece of intellectual criticism in our time. See Pope Francis, Laudato Si’: On Care for Our Common Home (London, 2015). For an example of fresh thinking, see David Kennedy, The World of Struggle: How Power, Law, and Expertise Shape Global Political Economy (Princeton, 2016). Acknowledgements Most of the books that guided me in the journey from eighteenth-century Europe to twenty-first-century India are mentioned above. But there are just too many political contexts, intellectual idioms and mentalities in this book for any reader to master adequately on his own, and I am very grateful to those who read Age of Anger, partially or fully, in manuscript, offered advice and encouragement, and demanded clarification: Manan Ahmed, Ian Almond, Negar Azimi, Fatima Bhutto, Isaac Chotiner, Siddhartha Deb, Faisal Devji, Paul Elie, Masoud Golsorkhi, Kia Golsorkhi-Ainslie, John Gray, Suzy Hansen, Hussein Omar Hussein, Shruti Kapila, Tabish Khair, Rebecca Liao, Arvind Krishna Mehrotra, Ferdinand Mount, Alok Rai, Joe Sacco, Kamila Shamsie, Adam Shatz, Ajay Skaria and Jeffrey Wasserstrom.

Licence to be Bad
by Jonathan Aldred
Published 5 Jun 2019

‘IT’S LIKE A MASSIVE EARTHQUAKE’ So said Kirsty McCluskey, a trader at the massive investment bank Lehmann Brothers on the day it went bust.8 And so true, because the risk of both earthquakes and the financial crisis which engulfed Lehmann Brothers can be described by the same underlying maths. Not the ‘never happen’ events at the end of a bell curve but a ‘power law’ or ‘fractal’ distribution of outcomes. Don’t worry: although much of the underlying maths is PhD level and beyond, the core ideas are more accessible. In some parts of the world earthquake activity is almost constant but at a very low level, much of it imperceptible to humans. Then, occasionally, there is an earthquake event which is hugely bigger than that background activity.

How I Built This: The Unexpected Paths to Success From the World's Most Inspiring Entrepreneurs
by Guy Raz
Published 14 Sep 2020

There is, in so many words, more than ample opportunity. Now the not-so-good news. Nearly 800,000 existing businesses close their doors every year. And while 80 percent of new businesses make it through one year, by year five or six survival is a fifty-fifty proposition. A coin flip. And the app market? Well, it is subject to a power law so steep it makes the streets of San Francisco, where many of the biggest apps have been developed, seem like gentle inclines. The top five apps, for example, account for 85 percent of all in-app time spent by users on their mobile devices. Which means that all the other 5 million–plus apps are competing for some portion of the remaining 15 percent of users’ in-app time.

Fortunes of Change: The Rise of the Liberal Rich and the Remaking of America
by David Callahan
Published 9 Aug 2010

Raised in Dallas by a lawyer dad and an accountant mom—typical parents for a new-economy billionaire—Arnold and his wife, Laura, gave more than $120,000 to the Democratic Party in 2008. (Laura is not the kind of wife you would have met in River Oaks in earlier times; she holds degrees from Harvard, Yale, and Cambridge and left a high-powered law career to focus her philanthropic energies on poor kids.) c01.indd 14 5/11/10 6:17:15 AM educated, rich, and liberal 15 Houston is still the capital of the U.S. energy industry, but finance and services now account for a larger share of the city’s economy, and this is where much of the Democratic money is coming from—not to mention many of the votes.

The New Jim Crow: Mass Incarceration in the Age of Colorblindness
by Michelle Alexander
Published 24 Nov 2011

If people were informed about what could be done, they might actually ask for help.”67 Bad Deal Almost no one ever goes to trial. Nearly all criminal cases are resolved through plea bargaining—a guilty plea by the defendant in exchange for some form of leniency by the prosecutor. Though it is not widely known, the prosecutor is the most powerful law enforcement official in the criminal justice system. One might think that judges are the most powerful, or even the police, but in reality the prosecutor holds the cards. It is the prosecutor, far more than any other criminal justice official, who holds the keys to the jailhouse door. After the police arrest someone, the prosecutor is in charge.

Chaos: Making a New Science
by James Gleick
Published 18 Oct 2011

None of these books will be valuable to readers without some technical background. In describing the events of this book and the motivations and perspectives of the scientists, I have avoided the language of science wherever possible, assuming that the technically aware will know when they are reading about integrability, power-law distribution, or complex analysis. Readers who want mathematical elaboration or specific references will find them in the chapter notes below. In selecting a few journal articles from the thousands that might have been cited, I chose either those which most directly influenced the events chronicled in this book or those which will be most broadly useful to readers seeking further context for ideas that interest them.

The Fugitive Game: Online With Kevin Mitnick
by Jonathan Littman
Published 1 Jan 1996

It's the big Hawaiian, Special Agent Stan Ornellas, a bear of a man at six foot three, well over 230 pounds, with a hand made for crushing things. Ornellas is from the FBI's old school. He talks tough; he's fond of phrases like "I think I'll go over and squeeze that little pinhead." Ornellas doesn't like De Payne. The feeling is mutual. De Payne is enjoying every minute. The comedy, the irony of it all. The FBI, the most powerful law enforcement agency in the most technologically advanced nation on earth, has come to search his modest condo for evidence of his computer hacking. But it's De Payne who knows everything about the FBI, not the other way around. De Payne knows the numbers of the agents' cellular phones, pagers, and bank accounts, the names of their wives, their children, their friends at the FBI and the CIA, along with more mundane personal secrets the agents wouldn't want to share with the public.

The Upstarts: How Uber, Airbnb, and the Killer Companies of the New Silicon Valley Are Changing the World
by Brad Stone
Published 30 Jan 2017

They built a food-ordering website that catered to law firms and investment banks. They called it SeamlessWeb. SeamlessWeb launched in April of 2000 and ran right into the teeth of the dot-com bust. Finger raised less than half a million dollars, paltry by the overcaffeinated standards that came later, but the service caught on quickly with the employees at several high-powered law firms and investment banks. SeamlessWeb contracted with hundreds of Manhattan restaurants and gave its corporate customers and their employees a way to browse menus and place orders over a website, expense meals to the company, and coordinate the flurry of deliveries. The business, headquartered in midtown Manhattan on the corner of Thirty-Eighth Street and Sixth Avenue, grew briskly.

City on the Verge
by Mark Pendergrast
Published 5 May 2017

The state finally changed that law in 2015, letting people sign leases with solar companies, which often required little or no money down and saved on monthly electricity bills. The city of Atlanta pledged to install solar panels atop twenty-eight city buildings. Almost as remarkable as the change in solar power law was the fact that Mayor Reed was talking about climate change—a topic traditionally ignored or denied by Georgia politicians and businesspeople. The Atlanta Office of Sustainability announced its Climate Action Plan at a 2015 Sustainable Atlanta Roundtable, providing an overview of best practices to reduce greenhouse gas emissions while requesting the assistance of some fifty sustainability experts across the city.

Palace Coup: The Billionaire Brawl Over the Bankrupt Caesars Gaming Empire
by Sujeet Indap and Max Frumes
Published 16 Mar 2021

Any bankruptcy judge experienced in large cases would have laughed Bennett’s motion to compel out of court. Five of the six individuals were famously wealthy. Moreover, the settlement contribution could come from multiple sources—Caesars stock, insurance, or the firms they worked at. But Goldgar has demonstrated that he was an earnest judge not deferential to powerful law firms or private equity firms simply out of convention. But Bennett’s timing was fortuitous. Just three weeks earlier, Goldgar had lifted the injunction on the guarantee litigation though Caesars had won a delay on enforcement while it appealed. Bennett was laser focused on how little the private equity firms were directly contributing to the settlement.

Paved Paradise: How Parking Explains the World
by Henry Grabar
Published 8 May 2023

By 1970, 95 percent of U.S. cities with over twenty-five thousand people had made the parking spot as legally indispensable as the front door. And though it is true that parking in America is disorderly, it is not quite true that parking is exclusively grappled over by angry neighbors and drivers with guns. There is a powerful law of parking, too—this third step that virtually every U.S. jurisdiction took in the 1950s and ’60s to mandate the provision of parking spaces with every new home, store, school, office, doughnut shop, movie theater, or tennis court. Over time, it was this decision, more than the highways or the malls or the tax-poaching suburbs themselves, that would prove the most influential legacy of the midcentury downtown parking crisis.

Market Risk Analysis, Quantitative Methods in Finance
by Carol Alexander
Published 2 Jan 2007

This has a density that converges to a mass at  as  → −. The lower tail remains finite in the Weibull density. • If  > 0 we have the Fréchet distribution. This also has a density that converges to a mass at , this time as  → . But it converges more slowly than the Weibull density since the tail in the Fréchet declines by a power law. • Figure I.3.20 depicts the GEV density for β = 5,  = 10 and  = 1. Readers may use the spreadsheet to explore the density function for other GEV distributions with  = 0. 0.12 0.10 0.08 0.06 0.04 0.02 45 40 35 30 25 20 15 10 5 0 0.00 Figure I.3.20 A Fréchet density Although we have derived the GEV distributions as distributions of sample maxima it is important to note that their application is not limited to this type of random variable.

Digital Disconnect: How Capitalism Is Turning the Internet Against Democracy
by Robert W. McChesney
Published 5 Mar 2013

And, ironically, as Matthew Hindman points out, personalization of websites “systematically advantages the very largest websites over smaller ones.”95 A paradox of the Internet, John Naughton writes, “is that a relatively small number of websites get most of the links and attract the overwhelming volume of traffic.” If your site isn’t in that elite group, it will likely be very small, and stay very small.96 As Matthew Hindman’s research on journalism, news media, and political websites demonstrates, what has emerged is a “power law” distribution whereby a small number of political or news media websites get the vast majority of traffic.97 They are dominated by the traditional giants with name recognition and resources. There is a “long tail” of millions of websites that exist but get little or no traffic, and only a small number of people have any idea that they exist.

Hacker, Hoaxer, Whistleblower, Spy: The Story of Anonymous
by Gabriella Coleman
Published 4 Nov 2014

Then he wrapped up with some shout-outs, giving props to “Jeremy and Donncha”—two of the most technically savvy and hardworking hackers in Anonymous, who had themselves refused to offer anything to law enforcement (and whose capture had largely been the result of his actions). Then he said a parting word: “I still think the idea of Anonymous is beautiful. Decentralization is power.” Law-Breaking and Snitches Around this time, Anonymous participants and some independent journalists like Nigel Parry began raising questions about the official story that had coalesced around the Stratfor hack. On March 25, 2012, Parry penned a detailed blog post titled “Sacrificing Stratfor: How the FBI waited three weeks to close the stable door.”23 He noted how bizarre it was that Stratfor’s thorough pwning could occur right under the FBI’s nose.

The New Digital Age: Transforming Nations, Businesses, and Our Lives
by Eric Schmidt and Jared Cohen
Published 22 Apr 2013

Perhaps a fully integrated information system, with all manner of data inputs, software that can interpret and predict behavior and humans at the controls is simply too powerful for anyone to handle responsibly. Moreover, once built, such a system will never be dismantled. Even if a dire security situation were to improve, what government would willingly give up such a powerful law-enforcement tool? And the next government in charge might not exhibit the same caution or responsibility with its information as the preceding one. Such totally integrated information systems are in their infancy now, and to be sure they are hampered by various challenges (like consistent data-gathering) that impose limits on their effectiveness.

Happy City: Transforming Our Lives Through Urban Design
by Charles Montgomery
Published 12 Nov 2013

This is why most retrofits have grown from dead and dying malls—large parcels of land with single owners. But the biggest obstacle to the retrofit project has almost nothing to do with demand or landowners’ resistance to change. It is that the system that built sprawl—huge state subsidies, financial incentives, and powerful laws—is still in place. In fact, in most jurisdictions in the United States and Canada, the sprawl-repair vision is not merely unfamiliar. It is totally against the law. Mableton is a perfect example. Most of the things that Robin Meyer imagined—things that would make Mableton more walkable, slower, safer, healthier, and more welcoming for kids and seniors—are forbidden by zoning codes and road standards in Cobb County.

Giving the Devil His Due: Reflections of a Scientific Humanist
by Michael Shermer
Published 8 Apr 2020

In a model I developed in the late 1980s and early 1990s to explain how history unfolds – the Model of Contingent-Necessity1 – I defined contingency as: a conjuncture of events occurring without design; and necessity as: constraining circumstances compelling a certain course of action. Contingencies are the sometimes small, apparently insignificant, and usually unexpected events of life – the kingdom hangs in the balance awaiting the horseshoe nail. Necessities are the large and powerful laws of nature and trends of history – once the kingdom has collapsed, the arrival of 100,000 horseshoe nails will not save it. The past is composed of both contingencies and necessities. Therefore, it is useful to combine the two into one term that expresses this interrelationship – contingent-necessity – taken to mean: a conjuncture of events compelling a certain course of action by constraining prior conditions.

The Lords of Easy Money: How the Federal Reserve Broke the American Economy
by Christopher Leonard
Published 11 Jan 2022

Even that figure understated the narrowness of the impact. Fully 25 percent of all the PPP went to 1 percent of the companies. These were the big law firms and national food chains, which got the maximum PPP amount of $10 million. Those beneficiaries included the Boston Market restaurant chain and the high-powered law firm of Boies Schiller Flexner. An analysis by the Federal Reserve and others found that the PPP program saved about 2.3 million jobs at a cost of $286,000 per job, after President Trump claimed it would save or support 50 million jobs. About $651 billion of the CARES Act was in the form of tax breaks for businesses, which were often complicated to obtain.

Rationality: What It Is, Why It Seems Scarce, Why It Matters
by Steven Pinker
Published 14 Oct 2021

There are also two-humped or bimodal distributions, such as men’s relative degree of sexual attraction to women and to men, which has a large peak at one end for heterosexuals and a smaller peak at the other end for homosexuals, with still fewer bisexuals in between. And there are fat-tailed distributions, where extreme values are rare but not astronomically rare, such as the populations of cities, the incomes of individuals, or the number of visitors to websites. Many of these distributions, such as those generated by “power laws,” have a high spine on the left with lots of low values and a long, thick tail on the right with a modicum of extreme ones.4 But bell curves—unimodal, symmetrical, thin-tailed—are common in the world; they arise whenever a measurement is the sum of a large number of small causes, like many genes together with many environmental influences.5 Let’s turn to the subject at hand, observations on whether or not something happened in the world.

Red-Blooded Risk: The Secret History of Wall Street
by Aaron Brown and Eric Kim
Published 10 Oct 2011

Investigate days when you lose more than the VaR amount, but supplement the observations with hypothetical scenarios and days in the past when your current positions would have suffered large losses. On the basis of the previous point’s analysis, estimate a left tail of the distribution—that is, the distribution of rare big losses. A power law fit is often appropriate. Don’t try to go to the worst possible case; accept a nonzero chance of catastrophic failure. Also on the basis of trans-VaR scenarios, consider risk factors not measured in the P&L. These include leverage risk, liquidity risk, counterparty credit risk, model risk, fraud risk, and others.

The Death of Money: The Coming Collapse of the International Monetary System
by James Rickards
Published 7 Apr 2014

pagewanted=all. “Money: DeGaulle v. the Dollar.” Time, February 12, 1965, http://content.time.com/time/magazine/article/0,9171,840572,00.html. Mundell, Robert A. “A Theory of Optimum Currency Areas.” American Economic Review 51, no. 4 (September 1961), pp. 657–65, esp. 659. Newman, Mark. “Power Laws, Pareto Distributions and Zipf’s Law.” Contemporary Physics 46 (September 2005), pp. 323–51. Nixon, Richard M. Address to the Nation Outlining a New Economic Policy, August 15, 1971, http://www.presidency.ucsb.edu/ws/index.php?pid=3115#axzz1LXd02JEK. O’Neill, Jim. “Building Better Global Economic BRICs.”

Smart Cities: Big Data, Civic Hackers, and the Quest for a New Utopia
by Anthony M. Townsend
Published 29 Sep 2013

And cities in Europe tend to run into one another, whereas in the United States (where the data fit the Santa Fe model best), there are wide-open spaces separating them. So while superlinear scaling in cities can be found in some places, it clearly isn’t as universal as West has argued. The only universal thing about urban scaling may be just how easily it yields to our interventions. “[T]he elegant hypothesis of power-law scaling marked a step forward in our understanding of cities,” Shalizi concludes. “But it is now time to leave it behind.”56 Urban scaling isn’t quite cold fusion, but it doesn’t seem to be the quantum theory of cities either. This is an important cautionary tale, for the convergence of urbanization and ubiquity will drive demand for rigorous empirical research on cities.

Virtual Competition
by Ariel Ezrachi and Maurice E. Stucke
Published 30 Nov 2016

Reeder-Simco GMC, Inc., 546 U.S. 164 (2006), raised the standard for “secondary line” cases, “which occur when favored customers of a supplier are given a price advantage over competing customers,” requiring that the supplier show that the different pricing policies made it harder to compete for the same customers at the same time; Federal Trade Commission, Price Discrimination: Robinson-Patman Violations (n.d.), https://www.ftc.gov/tips-advice/competition-guidance/guide-antitrust -laws/price-discrimination-robinson-patman; see also Robert J. Toth, “A Powerful Law Has Been Losing a Lot of Its Punch,” Wall Street Journal, May 1, 2002, http://www.wsj.com/articles/SB100014240527023047466045773801727 54953842. 302 Notes to Pages 128–130 51. Edwards, “Price and Prejudice,” 596, quoting Howard J. Alperin and Roland F. Chase, Consumer Law: Sales Practices and Credit Regulation, 2004 Supplement (St.

Londongrad: From Russia With Cash; The Inside Story of the Oligarchs
by Mark Hollingsworth and Stewart Lansley
Published 22 Jul 2009

The brothers even started to emulate the lifestyles of their Londongrad clients, buying their own £10 million second-hand yacht, Candyscape, joining the private jet set, and moving to Monte Carlo. Like many of their clients, the brothers’ business is based in a complex offshore structure. Gradually, Berezovsky integrated himself into the British way of life. He bought property in the right areas, hired some of the most powerful law firms in the country, and even, in December 2003, spoke at that most respected of London institutions, the Reform Club. While his initial arrival was barely noticed, his wealth - he was prepared to spend £1 million a month on his private jet and £40,000 for a QC’s opinion on a property dispute - and dynamic political apparatus soon began to open doors.

The Profiteers
by Sally Denton

While some of the files had been splashed on the front page of the New York Times in an explosive article written by Seymour Hersh, nearly all of the several thousand pages of documents from the investigation were classified and hidden from public view for the next thirty-five years. Meanwhile, Weinberger had become such a lightning rod in the Arab boycott controversy that the Bechtels and Shultz decided to bring in outside counsel, soliciting the help of one of Washington’s powerful law firms, Hogan and Hartson. Bechtel did not deny that it had complied with the boycott but argued that doing so did not violate federal law, and claimed that the company had been singled out. Sharp disagreements permeated the discussions within Bechtel’s executive suite about how the company should handle the lawsuit.

Unscripted: The Epic Battle for a Media Empire and the Redstone Family Legacy
by James B Stewart and Rachel Abrams
Published 14 Feb 2023

STEWART Deep State: Trump, the FBI, and the Rule of Law Tangled Webs: How False Statements Are Undermining America: From Martha Stewart to Bernie Madoff Disney War: The Battle for the Magic Kingdom Heart of a Soldier: A Story of Love, Heroism, and September 11th Blind Eye: The Terrifying Story of a Doctor Who Got Away with Murder Blood Sport: The President and His Adversaries Den of Thieves The Prosecutors: Inside the Offices of the Government’s Most Powerful Lawyers The Partners: Inside America’s Most Powerful Law Firms PENGUIN PRESS An imprint of Penguin Random House LLC penguinrandomhouse.com Copyright © 2023 by James B. Stewart and Rachel Abrams Penguin Random House supports copyright. Copyright fuels creativity, encourages diverse voices, promotes free speech, and creates a vibrant culture.

ZeroMQ
by Pieter Hintjens
Published 12 Mar 2013

It’s not ideal, but it works well enough to let us solve some interesting problems. Let me give you a rapid status report. First, point-to-point versus AP-to-client. Traditional WiFi is all AP-client. Every packet has to go from client A to AP, then to client B. You cut your bandwidth by 50%—but that’s only half the problem. I explained about the inverse power law. If A and B are very close together but both are far from the AP, they’ll both be using a low bit rate. Imagine your AP is in the garage, and you’re in the living room trying to stream video from your phone to your TV. Good luck! There is an old “ad hoc” mode that lets A and B talk to each other, but it’s way too slow for anything fun, and of course, it’s disabled on all mobile chipsets.

Crisis and Leviathan: Critical Episodes in the Growth of American Government
by Robert Higgs and Arthur A. Ekirch, Jr.
Published 15 Jan 1987

See also Conscription Du Pont Co., 214 Dye, Thomas, 46, 69 Economic growth, 11, 13, 79, 107 Economic royalists, 190 Economic Stabilization Act, 210, 215, 252 Economic Stabilization Agency, 245 Edison, Thomas, 71 Eisenhower, Dwight D., 246, 256 Ekirch, Arthur A., 122 Ely, Richard T., 116 Emergency Banking Act, 171 Emergency Coun of Appeals, 208, 222 Emergency Farm Mortgage Act, 176 Emergency Fleet Corporation, 126, 138, 140, 153 Emergency powers laws in 1970s, 251 Emergency Price Control Act, 207-208, 210,221,223 Emergency Relief and Construction Act, 164 Emergency workers in Great Depression, 25-26 Employment Act, 190,227,235 Energy controls, 238, 253-254 Engels, Friedrich, 49-50, 53 Environmental Protection Agency, 9, 29 Equal Employment Opportunity Act, 247 Espionage Act, 133, 148-149 European Recovery Program, 261.

Wealth and Poverty: A New Edition for the Twenty-First Century
by George Gilder
Published 30 Apr 1981

Economists now look with perplexity at the failure of the price level to go back down to an earlier level after World War II. But the London study showed that never throughout measurable history has inflation gone back down. Several times, though, it has moved massively and persistently up. Phelps-Brown and Hopkins conclude, describing the critical upsurges,For a century or more, it seems, prices will obey one all-powerful law; it changes, and a new law prevails: a war that would have cast the trend up to new heights in one dispensation is powerless to deflect it in another. Do we yet know what are the factors that set this stamp on an age; and why, after they have held on so long through such shakings, they give way quickly and completely to others?

Them And Us: Politics, Greed And Inequality - Why We Need A Fair Society
by Will Hutton
Published 30 Sep 2010

There is an enormous intellectual and financial investment in the status quo. Academics have built careers, reputations and tenure on a particular view of the world being right. Only an earthquake can persuade them to put up their hands and acknowledge they were wrong. When the mathematician Benoit Mandelbrot began developing his so-called fractal mathematics and power laws in the early 1960s, arguing that the big events outside the normal distribution are the ones that need explaining and assaulting the whole edifice of mathematical theory and the random walk, MIT’s Professor Paul Cootner (the great random walk theorist) exclaimed: ‘surely, before consigning centuries of work to the ash pile, we should like some assurance that all our work is truly useless’.

Rigged: How the Media, Big Tech, and the Democrats Seized Our Elections
by Mollie Hemingway
Published 11 Oct 2021

And leaders of the Democratic Party did not just push to make mail-in voting more popular; they lobbied to eliminate the rules designed to decrease coercion and fraud. * * * One Democrat in particular had spent years coordinating the party’s efforts to increase mail-in balloting and decrease measures to fight fraud. Marc Elias has chaired the political law practice at the Democratic Party’s powerful law firm Perkins Coie for years. He was John Kerry’s general counsel in his 2004 run for president, as well as Hillary Clinton’s general counsel in her 2016 run.43 While much of Elias’s reputation is thanks to the fact that he is an amazing self-promoter who amplifies his victories and hides his many defeats, Elias has operated on a level well beyond that of his Republican counterparts, particularly when it comes to dirty tricks that have undermined confidence in America’s elections.

A History of France
by John Julius Norwich
Published 30 Sep 2018

The National Assembly was granted fresh powers to institute reforms and to frame a constitution, but for the urban poor and the peasants across the country life was becoming harder every day. ‘A horrible anarchy’, reported the Venetian ambassador, ‘is the first aspect of the regeneration it is desired to bestow on France … There no longer exist either executive power, laws, magistrates or police.’ Riots were breaking out all over the country. At Troyes they murdered the mayor; the royal garrison at Rennes deserted en masse, that at Marseille was forcibly disbanded by an armed mob. Prisons were broken into, their prisoners released, arsenals were emptied, hôtels de ville taken over.

The New Map: Energy, Climate, and the Clash of Nations
by Daniel Yergin
Published 14 Sep 2020

Bill Hayton, The South China Sea: The Struggle for Power in Asia (New Haven: Yale University Press, 2014), pp. 28, 121 (“not wise enough”). 3. Carlyle A. Thayer, “Recent Developments in the South China Sea: Implications for Peace, Stability, and Cooperation in the Region,” South China Sea Studies, March 24, 2011, p. 3; U.S. Department of State, “Limits in the Seas”; Tran Truong Thuy and Le Thuy Trang, Power, Law, and Maritime Order in the South China Sea (Lanham: Lexington Books, 2015), pp. 103–15. 4. Interviews; Hillary Rodham Clinton, Hard Choices (New York: Simon & Schuster, 2014), p. 79; Edward Wong, “Chinese Military Seeks to Extend Its Naval Power,” New York Times, July 23, 2010. Chapter 21: The Role of History 1.

Lifespan: Why We Age—and Why We Don't Have To
by David A. Sinclair and Matthew D. Laplante
Published 9 Sep 2019

But today, we can plainly see that the city is flourishing not in spite of its population but because of it, such that today the capital of and most populous city in the United Kingdom is home to a myriad of museums, restaurants, clubs, and culture. It is home to several Premier League football clubs, the world’s most prestigious tennis tournament, and two of the best cricket teams on the globe. It is home to one of the world’s largest stock exchanges, a booming tech sector, and many of the world’s biggest and most powerful law firms. It is home to dozens of institutions of higher education and hundreds of thousands of university students. And it is home to what is arguably the most prestigious national scientific association in the world, the Royal Society. Founded in the 1600s during the Age of Enlightenment and formerly headed by Australia’s catalyst, the botanist Sir Joseph Banks, as well as such legendary minds as Sir Isaac Newton and Thomas Henry Huxley, the society’s cheeky motto is a pretty good one to live by: “Nullius in Verba,” it says underneath the society’s coat of arms.

Spies, Lies, and Algorithms: The History and Future of American Intelligence
by Amy B. Zegart
Published 6 Nov 2021

See Fox Jr., “Bureaucratic wrangling over counterintelligence.” 77. Quoted in Andrew, For the President’s Eyes Only, 56 (original source: Arthur S. Link, ed., The Papers of Woodrow Wilson, Vol. 45 [Princeton: Princeton University Press, 1966–1992], 75). 78. Federal Bureau of Investigation, “Brief History”; Ronald Kessler, Inside the FBI: The World’s Most Powerful Law Enforcement Agency (New York: Pocket, 1994); Weiner, Enemies. 79. Andrew, For the President’s Eyes Only, 69–70; Jeffrey T. Richelson, A Century of Spies: Intelligence in the Twentieth Century (New York: Oxford University Press, 1995), 69–77. 80. Henry L. Stimson and McGeorge Bundy, On Active Service in Peace and War (New York: Harper & Brothers, 1947), 188. 81.

Grand Transitions: How the Modern World Was Made
by Vaclav Smil
Published 2 Mar 2021

In 1900 17 of the world’s 25 largest cities were in Europe and the Americas and 6 in Asia; by the year 2000 Europe and the Americas had only 8 such cities and the Asian total rose to 16 (UN 2016). Ranking of city populations by size has been characterized by a high degree of regularity conforming to an inverse power formula: the size of the population residing in the country’s nth largest city is equal to 1/n of the largest city’s total, corresponding to a power law with a coefficient of –1 (Zipf [1949]; Figure 2.6; Smil 2019a). The law is valid on the global level, and we do not need actual census data to demonstrate it: it is better to use satellite images which offer visible delineations of large settlements (Jiang et al. 2015). Figure 2.6 In his book Human Behavior and the Principle of Least Effort, George Kingsley Zipf extended his pioneering studies of word rank frequency to many other phenomena, including the ranking of the 100 largest US metropolitan areas.

Traffic: Why We Drive the Way We Do (And What It Says About Us)
by Tom Vanderbilt
Published 28 Jul 2008

In a traffic system that is always congested, any good alternative routes will have already been discovered by other drivers. Another shortcoming of real-time routing is due to a curious fact about urban road networks. As a group of researchers observed after studying traffic patterns and road networks in the twenty largest cities in Germany, roads follow what’s called a “power law”—in other words, a small minority of roads carry a huge majority of the traffic. In Dresden, for example, while 50 percent of the total road length carried hardly any traffic at all (0.2 percent), 80 percent of the total traffic ran on less than 10 percent of the roads. The reason is rather obvious: Most drivers tend to drive on the largest roads, because they are the fastest.

The Best of Kim Stanley Robinson
by Kim Stanley Robinson
Published 1 Mar 2001

· A nation’s fortunes depend on its success in war. · A society’s culture is determined by its economic system. · Belief systems exist to disguise inequality. · Lastly, unparalleled in both elegance and power, subsuming many of the examples listed above: power corrupts. So there do seem to be some quite powerful laws of historical explanation. But consider another: · For want of a nail, the battle was lost. For instance: on July 29th, 1945, a nomad in Kirgiz walked out of his yurt and stepped on a butterfly. For lack of the butterfly flapping its wings, the wind in the area blew slightly less. A low-pressure front therefore moved over east China more slowly than it would have.

The Economic Weapon
by Nicholas Mulder
Published 15 Mar 2021

Olive Anderson, “The Russian Loan of 1855: A Postscript,” Economica 28, no. 112 (November 1961): 425–426. See also Arnold D. McNair, The Law of Treaties: British Practice and Opinions (New York: Columbia University Press, 1938), p. 550. 34. About the Russo-Dutch loan, see House of Commons debate, 1 August 1854, in Hansard, vol. 135, p. 1118. 35. Jan Lemnitzer, Power, Law and the End of Privateering (Basingstoke: Palgrave, 2014). 36. As A. J. P. Taylor commented, “In that civilized age, it was thought a reasonable demand that political refugees should be allowed to draw enormous revenues from their estates while conducting revolutionary propaganda against the ruler of the country in which the estates lay” (The Struggle for Mastery in Europe, 1848–1918 [Oxford: Oxford University Press, 1971], p. 71n3). 37.

Peer-to-Peer
by Andy Oram
Published 26 Feb 2001

The distribution of links in Freenet was an important factor in its robustness, so let’s look at Gnutella’s corresponding distribution, shown in Figure 14.25. Figure 14-25. Histogram showing the distribution of links in Gnutella Mathematically, this is a “Poisson” distribution peaked around the average connectivity of 3. Its tail drops off exponentially, rather than according to a power law as Freenet’s does. This can be seen more clearly in the log-log plot of Figure 14.26. Figure 14-26. Log-log scatter plot of the distribution of links in Gnutella Comparing this plot to Figure 14.20, we can see that Figure 14.26 drops off much more sharply at high link numbers. As a result, highly connected nodes are much less of a factor in Gnutella than they are in Freenet.

Dreams and Shadows: The Future of the Middle East
by Robin Wright
Published 28 Feb 2008

From the Muqata, Arafat ran the new Palestinian Authority for the next decade as autocratically as he had the Palestine Liberation Organization. He also ensured that Fatah dominated all branches of government, the best private sector jobs, monopolies on lucrative imports, and the top security positions. Patronage was the lever of power. Laws passed by an elected legislature, including some impressive judicial and executive-branch reforms, sat on his desk ignored and unsigned for years.4 Critics were often picked up and released at his whim rather than the dictates of a court. In 2004, a public opinion poll found that eighty-seven percent of Palestinians surveyed believed that Arafat’s government was corrupt and that its leaders were opportunists who became rich off their powers.

The Red and the Blue: The 1990s and the Birth of Political Tribalism
by Steve Kornacki
Published 1 Oct 2018

Quietly, some regulators began poking around, but the topic of Whitewater played no meaningful role in the ’92 race. What it did, though, was plant the seed of an idea: that in the Clintons’ Arkansas past there might be things that weren’t quite on the level—maybe a lot of things. After all, he’d been the governor for twelve years. She’d been a partner in the state’s most powerful law firm. They’d gone into business with a politically connected banker. And it had all transpired far off the national radar, in the outpost town of Little Rock, where the clubby elite had plenty of incentives to look the other way. Suspicion was widely shared by the media in D.C., and would be fed by the Clintons and their own behavior when they moved to the White House.

The Musical Human: A History of Life on Earth
by Michael Spitzer
Published 31 Mar 2021

Looking for 1/f relationships in Western rhythm (in 1,788 movements from 558 compositions), Levitin’s team found that Beethoven’s rhythms tend towards the regular pole; Mozart’s towards the unpredictable. See Daniel Levitin, Parag Chordia and Vinod Menon, ‘Musical rhythm spectra from Bach to Joplin obey a 1/f power law’, Proceedings of the National Academy of Sciences of the United States of America 109/10 (2011), pp. 3716–20 (p. 3716). 60Martin Gardner, ‘White, Brown, and Fractal Music’, in his Fractal Music, Hypercards and More Mathematical Recreations from SCIENTIFIC AMERICAN Magazine (New York: W. H. Freeman and Company, 1992), pp. 1–23. 61Philip Ball, Patterns in Nature: Why the Natural World Looks the Way it Does (Chicago: The University of Chicago Press, 2016). 62Gabriel Pareyon, On Musical Self-Similarity: Intersemiosis as Synecdoche and Analogy (Imatra: International Semiotics Institute, 2011). 63Benjamin Ayotte and Benjamin McKay Ayotte, Heinrich Schenker: A Guide to Research (London: Routledge, 2004). 64Arnold Schoenberg, The Musical Idea and the Logic, Technique and Art of Its Presentation (Bloomington: Indiana University Press, 2006). 65For example Rolf Bader, ‘Fractal dimension analysis of complexity in Ligeti’s piano pieces’, The Journal of the Acoustical Society of America 117/4 (2005), p. 2477. 66Fernández and Vico, ‘AI Methods in Algorithmic Composition’, p. 557. 67https://www.samwoolfe.com/2014/03/could-universe-be-fractal.html Chapter 12 1Yuk Hui, Recursivity and Contingency (Lanham, Maryland: Rowman & Littlefield International, 2019). 2As I mentioned in Chapter 1, Ernst Haeckel’s discredited theory that ontogeny ‘recapitulates’ phylogeny, that the gestation of the human embryo echoes the stages of evolution, has sprung back to life in the most recent work in the psychology of musical emotion.

The Black Banners: The Inside Story of 9/11 and the War Against Al-Qaeda
by Ali H. Soufan and Daniel Freedman
Published 11 Sep 2011

But after I submitted the application, I spent some time researching the FBI. The information was mostly new to me. I discovered that the bureau was created in 1908—given its prominence today, I had thought it would have been around longer. I also learned that only under J. Edgar Hoover had it been built into the powerful law enforcement tool it is today, which makes the bureau’s successes and reputation even more impressive. The application process includes tests of all sorts, from physical to aptitude, along with lots of interviews, often spaced out over months. As I jumped through the hoops, my friends started a pool betting on how long I’d last.

Galileo's Dream
by Kim Stanley Robinson
Published 29 Dec 2009

He had seen the evidence for the laws of both inertia and gravity, he had used them in his parabolic description of falling bodies, but he had not understood what he had used, and now he floated above them, abashed, glowing before their utter simplicity. The force of gravity was simply an inverse power law, easy as kiss your hand, and resulting in obvious solutions to things like Kepler’s orbits, which Kepler had only groped his way to after years of observation and analysis. So planetary orbits were naturally ellipses, with the sun occupying the major focus, and the other gravitational pulls together locating the minor focus.

Tribe of Mentors: Short Life Advice From the Best in the World
by Timothy Ferriss
Published 14 Jun 2017

They think, draw conclusions, make predictions, look for explanations and even do experiments. . . . In fact, scientists are successful precisely because they emulate what children do naturally.” Much of the human brain’s power derives from its massive synaptic interconnectivity. Geoffrey West from the Santa Fe Institute observed that across species, synapses/neuron fanout grows as a power law with brain mass. At the age of two to three years old, children hit their peak with ten times the synapses and two times the energy burn of an adult brain. And it’s all downhill from there. The UCSF Memory and Aging Center has graphed the pace of cognitive decline, and finds the same slope of decline in our 40s as in our 80s.

The Taking of Getty Oil: Pennzoil, Texaco, and the Takeover Battle That Made History
by Steve Coll
Published 12 Jun 2017

In a city that sometimes resembled a casino, they were the only ones in town who never rolled the dice. Instead, they stood quietly beside the table, ever so often raking off a pile of money. In January 1984, when an embittered Hugh Liedtke returned home without a single barrel of oil to show for his bid to take control of Getty Oil, there were three exceptionally large and powerful law firms headquartered in downtown Houston: Fulbright & Jaworski, Vinson & Elkins, and Baker & Botts, Liedtke’s firm for more than twenty-five years. In those first days after Pennzoil’s defeated takeover attempt, gossip circulated in the legal establishment that Liedtke blamed his lawyers for his uncharacteristic failure in New York, and that he was so angry that he might take his lucrative business away from Baker & Botts.

Persian Gulf Command: A History of the Second World War in Iran and Iraq
by Ashley Jackson
Published 15 May 2018

The Americans believed that the mission existed to help improve Iran’s economy, whereas ‘Iranians seem to want it to stay more for political purposes of having the US as a buffer’.29 Dreyfus detected a ‘deeprooted and concerted campaign against our advisers’ on the part of the Iranians. ‘This springs undoubtedly from corrupt and selfish political elements in the Majlis who stand to lose personally with the institution of the kind of regime our advisers contemplate.’30 Under Millspaugh’s direction an income tax was levied via the Full Powers Law of May 1943 for the collection of grain and the equitable distribution of bread and the ‘monopoly commodities’. This was resented by the wealthy: Millspaugh encountered opposition from landowners, merchants, speculators and the possessing classes in general, because he threatened to attack their interests.

Types and Programming Languages
by Benjamin C. Pierce
Published 4 Jan 2002

The search for appropriate semantic domains for modeling various language features has given rise to a rich and elegant research area known as domain theory. One major advantage of denotational semantics is that it abstracts from the gritty details of evaluation and highlights the essential concepts of the language. Also, the properties of the chosen collection of semantic domains can be used to derive powerful laws for reasoning about program behaviors-laws for proving that two programs have exactly the same behavior, for example, or that a program's behavior satisfies some specification. Finally, from the properties of the chosen collection of semantic domains, it is often immediately evident that various (desirable or undesirable) things are impossible in a language.

The Concepts and Practice of Mathematical Finance
by Mark S. Joshi
Published 24 Dec 2003

This observation is at the heart of the BlackScholes approach to pricing options. Before proceeding to the derivation of the Black-Scholes equation, we look at a further example of the application of Ito's lemma. Suppose our stock movements were not strictly proportional to level but instead obeyed a power law: dSt = Sr sdt + St adWt, (5.47) with P * 0, 1. Such a process is called a constant elasticity of variance process or a CEV process. In order to solve the SDE we would like to make the process constant coefficient. If we take d(f (s)) for some smooth function f then the volatility term of the new process will be, from Ito's lemma, f'(S)SPQ.

An Empire of Their Own: How the Jews Invented Hollywood
by Neal Gabler
Published 17 Nov 2010

He came from an old-line Los Angeles Jewish family that was so deeply assimilated it practiced Christian Science and raised him that way. After working briefly at the Los Angeles Times, he became an attorney, but when the head of his firm brought in his son as an associate, Silberberg and a close friend named Shepard Mitchell quit and formed a firm of their own. Years later, when it had become one of the most powerful law firms in Los Angeles, they liked to reminisce about its infancy. Their income was so paltry that they served their own papers and ate at a local bar where the lunch came gratis with the beer. Nevertheless, Silberberg upbraided their principal client for recommending they do something illicit. “If you weren’t my partner and didn’t have to bear half the cost,” he told Mitchell when the partner poked his head in to see what the commotion was, “I’d throw this son of a bitch through this partition.”

The Children of the Sky
by Vernor Vinge
Published 11 Oct 2011

The structure forming in the space between the kids didn’t look like art. There were thousands of points of light, variously connected by colored lines. Will someone please explain this to me? thought Ravna. It might be a network simulation, but there was no labelling. Ah, wait, she could almost guess at the power law on the connections. Maybe this was a— Øvin was talking again: “This was hell to put together using Oobii’s interface, but we’ve visualized a whole-body map of the transduction network in a modern human. Well, it’s what Oobii has on file, a racial average across Sjandra Kei. We Straumers can’t be much different.

Tools of Titans: The Tactics, Routines, and Habits of Billionaires, Icons, and World-Class Performers
by Timothy Ferriss
Published 6 Dec 2016

But the idea that the worst player on one of the lower-rated teams would be the undisputed champion simply through an innovation that was that profound shows you what the power of one of these ideas is. [TF: “These ideas” = having a “secret” as described in Peter Thiel’s Zero to One: knowing or believing something that the rest of the world thinks is nonsense.] The power laws are just so unbelievably in your favor if you win that it makes [venturing outside the norm] worthwhile.” TIM: “Or Dick Fosbury, who went backwards over the high jump bar for the first time in the Olympics, winning gold —” ERIC: “1968, you got it.” TIM: “Ridiculed, then mimicked, and eventually made standard.”

Thinking Without a Banister: Essays in Understanding, 1953-1975
by Hannah Arendt
Published 6 Mar 2018

The differences between the various forms of government depended on the distribution of power, whether one single man or the most distinguished citizens or the people possessed the power to rule. The good or bad nature of each of these was judged according to the role played by law in the exercise of power: lawful government was good and lawless bad. The criterion of law, however, as a yardstick for good or bad government was very early replaced, already in Aristotle’s political philosophy, by the altogether different notion of interest, with the result that bad government became the exercise of power in the interest of the rulers, and good government the use of power in the interest of the ruled.

The Singularity Is Near: When Humans Transcend Biology
by Ray Kurzweil
Published 14 Jul 2005

However, if we have an exponential growth rate of the form: (10) where C > 1, this has the solution: (11) which has a slow logarithmic growth while t < 1/lnC but then explodes close to the singularity at t = 1/lnC. Even the modest dW/dt = W2 results in a singularity. Indeed any formula with a power law growth rate of the form: (12) where a > 1, leads to a solution with a singularity: (12) at the time T. The higher the value of a, the closer the singularity. My view is that it is hard to imagine infinite knowledge, given apparently finite resources of matter and energy, and the trends to date match a double exponential process.

The Internationalists: How a Radical Plan to Outlaw War Remade the World
by Oona A. Hathaway and Scott J. Shapiro
Published 11 Sep 2017

And whether and how they change is largely up to us. We can update the rules to respond to global challenges—as have those who have endeavored to create ever more inventive and creative mechanisms for outcasting rule breakers—or we can disregard them. The choice is ours. Many have argued that the world is best explained by reference to state power. Law is just words on a piece of paper, incapable of true influence. We reject this account not because states or those within them care more about law than power. Instead, if this book shows anything, it is that the choice between law and power is a false one. Real power—power useful for achieving important and lasting political objectives—does not exist in the absence of law.

Palo Alto: A History of California, Capitalism, and the World
by Malcolm Harris
Published 14 Feb 2023

David Shephardson and Karen Pierog, “Foxconn Mostly Abandons $10 Billion Wisconsin Project Touted by Trump,” Reuters, April 20, 2021. 21. Filip Novokmet et al., “From Communism to Capitalism: Private versus Public Property and Inequality in China and Russia,” AEA Papers and Proceedings 108 (May 2018): 111. 22. Ibid., 112. 23. Ibid. 24. Ibid. 25. Sebastian Mallaby, The Power Law: Venture Capital and the Making of the New Future (New York: Penguin Press, 2022), 273–75. 26. Michael Arrington, “Exclusive Video: Mark Zuckerberg and Yuri Milner Talk about Facebook’s New Investment,” TechCrunch, May 26, 2009, https://techcrunch.com/2009/05/26/mark-zuckerberg-and-yuri-milner-talk-about-facebooks-new-investment-video. 27.

Ashes to Ashes: America's Hundred-Year Cigarette War, the Public Health, and the Unabashed Triumph of Philip Morris
by Richard Kluger
Published 1 Jan 1996

The TCJL effort achieved partial success during the 1987 legislative session: claimants held to be 50 percent or more responsible could not be awarded damages, and claims were capped at $200,000 or four times actual losses like hospital costs and lost wages, whichever was higher. But those limitations fell well short of a satisfying victory, and so the drive was renewed in 1989 under chief lobbyist Jack Gullahorn, a Dan Quayle look-alike and a disarmingly smooth member of one of the most powerful law firms in Texas—Akin, Gump, Strauss, Hauer & Feld. Gullahorn had eighteen other clients beside the TCJL that he lobbied for at that time, including Texaco, several banks, the fireworks and billboard industries, and the Gulf Coast Conservation Association, and was so well connected around Austin, the state capital, that in the days before mobile phones were commonplace, a pay telephone booth just outside the Texas House chamber was set aside largely for his personal use and decorated with flowers, family photos, and a deer head in humorous tribute to his influence.

The Year's Best Science Fiction: Twenty-Sixth Annual Collection
by Gardner Dozois
Published 23 Jun 2009

If you have random noise you’d expect roughly equal numbers of the letters, so you’d get a flat distribution. If you have a clean signal without information content, a string of identical letters, A, A, A, you’d get a graph with a spike. Meaningful information gives you a slope, somewhere in between those horizontal and vertical extremes. “And we get a beautiful log-scale minus one power law,” he said, showing me. “There’s information in there all right. But there is a lot of controversy over identifying the elements themselves. The Eaglets did not send down neat binary code. The data is frequency modulated, their language full of growths and decays. More like a garden growing on fast-forward than any human data stream.

God's Bankers: A History of Money and Power at the Vatican
by Gerald Posner
Published 3 Feb 2015

The Pope was quiet when accused pedophile priests threatened litigation against their bishops for violating their employment rights by defrocking them.64 And the Pontiff also did not respond publicly when a support group for sex abuse victims beseeched him to prevent priests from filing malicious defamation lawsuits against their accusers. John Paul was a bystander as the American church quietly approved an aggressive new legal strategy that included, as The Washington Post uncovered, “hiring high-powered law firms and private detectives to examine the personal lives of the church’s accusers, fighting to keep documents secret and engaging in new tactics to minimize settlements.”65 To the great dismay of victims’ rights groups, what did prompt the Pope and Vatican to intervene was when the American bishops were told that they did not have the authority to administratively remove a priest charged with sexual abuse.

Executive Orders
by Tom Clancy
Published 2 Jan 1996

But this guy is rebuilding the whole fucking government, and he's building it in his image, in case you didn't notice. Every appointment he's made, they're all people he's worked with, some for a long time-or they were selected for him by close associates. Murray running the FBI. Do you want Dan Murray in charge of America's most powerful law enforcement agency? You want these two people picking the Supreme Court? Where will he take us?” Webb paused, and sighed. “I hate doing this. He's one of us at Langley, but he isn't supposed to be President, okay? I have an obligation to my country, and my country isn't Jack Ryan.” Webb collected the photos and tucked them back in the folders.