The Black Swan

by Nassim Nicholas Taleb

  CHAPTERS 11–13

  Serendipity: See Koestler (1959) and Rees (2004). Rees also has powerful ideas on fore-castability. See also Popper’s comments in Popper (2002), and Waller (2002a), Cannon (1940), Mach (1896) (cited in Simonton [1999]), and Merton and Barber (2004). See Simonton (2004) for a synthesis. For serendipity in medicine and anesthesiology, see Vale et al. (2005).

  “Renaissance man”: See www.bell-labs.com/project/feature/archives/cosmology/.

  Laser: As usual, there are controversies as to who “invented” the technology. After a successful discovery, precursors are rapidly found, owing to the retrospective distortion. Charles Townsend won the Nobel prize, but was sued by his student Gordon Gould, who held that he did the actual work (see The Economist, June 9, 2005).

  Darwin/Wallace: Quammen (2006).

  Popper’s attack on historicism: See Popper (2002). Note that I am reinterpreting Popper’s idea in a modern manner here, using my own experiences and knowledge, not commenting on comments about Popper’s work—with the consequent lack of fidelity to his message. In other words, these are not directly Popper’s arguments, but largely mine phrased in a Popperian framework. The conditional expectation of an unconditional expectation is an unconditional expectation.

  Forecast for the future a hundred years earlier: Bellamy (1891) illustrates our mental projections of the future. However, some stories might be exaggerated: “A Patently False Patent Myth still! Did a patent official really once resign because he thought nothing was left to invent? Once such myths start they take on a life of their own.” Skeptical Inquirer, May–June, 2003.

  Observation by Peirce: Olsson (2006), Peirce (1955).

  Predicting and explaining: See Thom (1993).

  Poincaré: The three body problem can be found in Barrow-Green (1996), Rollet (2005), and Galison (2003). On Einstein, Pais (1982). More recent revelations in Hladik (2004).

  Billiard balls: Berry (1978) and Pisarenko and Sornette (2004).

  Very general discussion on “complexity”: Benkirane (2002), Scheps (1996), and Ruelle (1991). For limits, Barrow (1998).

  Hayek: See www.nobel.se. See Hayek (1945, 1994). Is it that mechanisms do not correct themselves from railing by influential people, but either by mortality of the operators, or something even more severe, by being put out of business? Alas, because of contagion, there seems to be little logic to how matters improve; luck plays a part in how soft sciences evolve. See Ormerod (2006) for network effects in “intellectuals and socialism” and the power-law distribution in influence owing to the scale-free aspect of the connections—and the consequential arbitrariness. Hayek seems to have been a prisoner of Weber’s old differentiation between Natur-Wissenschaften and Geistes Wissenschaften—but thankfully not Popper.

  Insularity of economists: Pieters and Baumgartner (2002). One good aspect of the insularity of economists is that they can insult me all they want without any consequence: it appears that only economists read other economists (so they can write papers for other economists to read). For a more general case, see Wallerstein (1999). Note that Braudel fought “economic history.” It was history.

  Economics as religion: Nelson (2001) and Keen (2001). For methodology, see Blaug (1992). For high priests and lowly philosophers, see Boettke, Coyne, and Leeson (2006). Note that the works of Gary Becker and the Platonists of the Chicago School are all marred by the confirmation bias: Becker is quick to show you situations in which people are moved by economic incentives, but does not show you cases (vastly more numerous) in which people don’t care about such materialistic incentives.

  The smartest book I’ve seen in economics is Gave et al. (2005) since it transcends the constructed categories in academic economic discourse (one of the authors is the journalist Anatole Kaletsky).

  General theory: This fact has not deterred “general theorists.” One hotshot of the Platonifying variety explained to me during a long plane ride from Geneva to New York that the ideas of Kahneman and his colleagues must be rejected because they do not allow us to develop a general equilibrium theory, producing “time-inconsistent preferences.” For a minute I thought he was joking: he blamed the psychologists’ ideas and human incoherence for interfering with his ability to build his Platonic model.

  Samuelson: For his optimization, see Samuelson (1983). Also Stiglitz (1994).

  Plato’s dogma on body symmetry: “Athenian Stranger to Cleinias: In that the right and left hand are supposed to be by nature differently suited for our various uses of them; whereas no difference is found in the use of the feet and the lower limbs; but in the use of the hands we are, as it were, maimed by the folly of nurses and mothers; for although our several limbs are by nature balanced, we create a difference in them by bad habit,” in Plato’s Laws. See McManus (2002).

  Drug companies: Other such firms, I was told, are run by commercial persons who tell researchers where they find a “market need” and ask them to “invent” drugs and cures accordingly—which accords with the methods of the dangerously misleading Wall Street security analysts. They formulate projections as if they know what they are going to find.

  Models of the returns on innovations: Sornette and Zajdenweber (1999) and Silverberg and Verspagen (2005).

  Evolution on a short leash: Dennet (2003) and Stanovich and West (2000).

  Montaigne: We don’t get much from the biographies of a personal essayist; some information in Frame (1965) and Zweig (1960).

  Projectibility and the grue paradox: See Goodman (1955). See also an application (or perhaps misapplication) in King and Zheng (2005).

  Constructionism: See Berger and Luckmann (1966) and Hacking (1999).

  Certification vs, true skills or knowledge: See Donhardt (2004). There is also a franchise protection. Mathematics may not be so necessary a tool for economics, except to protect the franchise of those economists who know math. In my father’s days, the selection process for the mandarins was made using their abilities in Latin (or Greek). So the class of students groomed for the top was grounded in the classics and knew some interesting subjects. They were also trained in Cicero’s highly probabilistic view of things—and selected on erudition, which carries small side effects. If anything it allows you to handle fuzzy matters. My generation was selected according to mathematical skills. You made it based on an engineering mentality; this produced mandarins with mathematical, highly structured, logical minds, and, accordingly, they will select their peers based on such criteria. So the papers in economics and social science gravitated toward the highly mathematical and protected their franchise by putting high mathematical barriers to entry. You could also smoke the general public who is unable to put a check on you. Another effect of this franchise protection is that it might have encouraged putting “at the top” those idiot-savant-like researchers who lacked in erudition, hence were insular, parochial, and closed to other disciplines.

  Freedom and determinism: a speculative idea in Penrose (1989) where only the quantum effects (with the perceived indeterminacy there) can justify consciousness.

  Projectibility: uniqueness assuming least squares or MAD.

  Chaos theory and the backward/forward confusion: Laurent Firode’s Happenstance, a.k.a. Le battement d’ailes du papillon / The Beating of a Butterfly’s Wings (2000).

  Autism and perception of randomness: See Williams et al. (2002).

  Forecasting and misforecasting errors in hedonic states: Wilson, Meyers, and Gilbert (2001), Wilson, Gilbert, and Centerbar (2003), and Wilson et al. (2005). They call it “emotional evanescence.”

  Forecasting and consciousness: See the idea of “aboutness” in Dennett (1995, 2003) and Humphrey (1992). However, Gilbert (2006) believes that we are not the only animal that forecasts—which is wrong as it turned out. Suddendorf (2006) and Dally, Emery, and Clayton (2006) show that animals too forecast!

  Russell’s comment on Pascal’s wager: Ayer (1988) reports this as a private communication.

  History: Carr (1961), Hexter (
1979), and Gaddis (2002). But I have trouble with historians throughout, because they often mistake the forward and the backward processes. Mark Buchanan’s Ubiquity and the quite confused discussion by Niall Ferguson in Nature. Neither of them seem to realize the problem of calibration with power laws. See also Ferguson, Why Did the Great War?, to gauge the extent of the forward-backward problems.

  For the traditional nomological tendency, i.e., the attempt to go beyond cause into a general theory, see Muqaddamah by Ibn Khaldoun. See also Hegel’s Philosophy of History.

  Emotion and cognition: Zajonc (1980, 1984).

  Catastrophe insurance: Froot (2001) claims that insurance for remote events is overpriced. How he determined this remains unclear (perhaps by backfitting or bootstraps), but reinsurance companies have not been making a penny selling “overpriced” insurance.

  Postmodernists: Postmodernists do not seem to be aware of the differences between narrative and prediction.

  Luck and serendipity in medicine: Vale et al. (2005). In history, see Cooper (2004). See also Ruffié (1977). More general, see Roberts (1989).

  Affective forecasting: See Gilbert (1991), Gilbert et al. (1993), and Montier (2007).

  CHAPTERS 14–17

  This section will also serve another purpose. Whenever I talk about the Black Swan, people tend to supply me with anecdotes. But these anecdotes are just corroborative: you need to show that in the aggregate the world is dominated by Black Swan events. To me, the rejection of nonscalable randomness is sufficient to establish the role and significance of Black Swans.

  Matthew effects: See Merton (1968, 1973a, 1988). Martial, in his Epigrams: “Semper pauper eris, si pauper es, Aemiliane./Dantur opes nullis (nunc) nisi divitibus.” (Epigr. V 81). See also Zuckerman (1997, 1998).

  Cumulative advantage and its consequences on social fairness: review in DiPrete et al. (2006). See also Brookes-Gun and Duncan (1994), Broughton and Mills (1980), Dannefer (2003), Donhardt (2004), Hannon (2003), and Huber (1998). For how it may explain precocity, see Elman and O’Rand (2004).

  Concentration and fairness in intellectual careers: Cole and Cole (1973), Cole (1970), Conley (1999), Faia (1975), Seglen (1992), Redner (1998), Lotka (1926), Fox and Kochanowski (2004), and Huber (2002).

  Winner take all: Rosen (1981), Frank (1994), Frank and Cook (1995), and Attewell (2001).

  Arts: Bourdieu (1996), Taleb (2004e).

  Wars: War is concentrated in an Extremistan manner: Lewis Fry Richardson noted last century the uneveness in the distribution of casualties (Richardson [1960]).

  Modern wars: Arkush and Allen (2006). In the study of the Maori, the pattern of fighting with clubs was sustainable for many centuries—modern tools cause 20,000 to 50,000 deaths a year. We are simply not made for technical warfare. For an anecdotal and causative account of the history of a war, see Ferguson (2006).

  S&P 500: See Rosenzweig (2006).

  The long tail: Anderson (2006).

  Cognitive diversity: See Page (2007). For the effect of the Internet on schools, see Han et al. (2006).

  Cascades: See Schelling (1971, 1978) and Watts (2002). For information cascades in economics, see Bikhchandani, Hirshleifer, and Welch (1992) and Shiller (1995). See also Surowiecki (2004).

  Fairness: Some researchers, like Frank (1999), see arbitrary and random success by others as no different from pollution, which necessitates the enactment of a tax. De Vany, Taleb, and Spitznagel (2004) propose a market-based solution to the problem of allocation through the process of voluntary self-insurance and derivative products. Shiller (2003) proposes cross-country insurance.

  The mathematics of preferential attachment: This argument pitted Mandelbrot against the cognitive scientist Herbert Simon, who formalized Zipf’s ideas in a 1955 paper (Simon [1955]), which then became known as the Zipf-Simon model. Hey, you need to allow for people to fall from favor!

  Concentration: Price (1970). Simon’s “Zipf derivation,” Simon (1955). More general bibliometrics, see Price (1976) and Glänzel (2003).

  Creative destruction revisited: See Schumpeter (1942).

  Networks: Barabási and Albert (1999), Albert and Barabási (2000), Strogatz (2001, 2003), Callaway et al. (2000), Newman et al. (2000), Newman, Watts, and Strogatz (2000), Newman (2001), Watts and Strogatz (1998), Watts (2002, 2003), and Amaral et al. (2000). It supposedly started with Milgram (1967). See also Barbour and Reinert (2000), Barthélémy and Amaral (1999). See Boots and Sasaki (1999) for infections. For extensions, see Bhalla and Iyengar (1999). Resilence, Cohen et al. (2000), Barabási and Bonabeau (2003), Barabási (2002), and Banavar et al. (2000). Power laws and the Web, Adamic and Huberman (1999) and Adamic (1999). Statistics of the Internet: Huberman (2001), Willinger et al. (2004), and Faloutsos, Faloutsos, and Faloutsos (1999). For DNA, see Vogelstein et al. (2000).

  Self-organized criticality: Bak (1996).

  Pioneers of fat tails: For wealth, Pareto (1896), Yule (1925, 1944). Less of a pioneer Zipf (1932, 1949). For linguistics, see Mandelbrot (1952).

  Pareto: See Bouvier (1999).

  Endogenous vs. exogenous: Sornette et al. (2004).

  Sperber’s work: Sperber (1996a, 1996b, 1997).

  Regression: If you hear the phrase least square regression, you should be suspicious about the claims being made. As it assumes that your errors wash out rather rapidly, it underestimates the total possible error, and thus overestimates what knowledge one can derive from the data.

  The notion of central limit: very misunderstood: it takes a long time to reach the central limit—so as we do not live in the asymptote, we’ve got problems. All various random variables (as we started in the example of Chapter 16 with a +1 or −1, which is called a Bernouilli draw) under summation (we did sum up the wins of the 40 tosses) become Gaussian. Summation is key here, since we are considering the results of adding up the 40 steps, which is where the Gaussian, under the first and second central assumptions becomes what is called a “distribution.” (A distribution tells you how you are likely to have your outcomes spread out, or distributed.) However, they may get there at different speeds. This is called the central limit theorem: if you add random variables coming from these individual tame jumps, it will lead to the Gaussian.

  Where does the central limit not work? If you do not have these central assumptions, but have jumps of random size instead, then we would not get the Gaussian. Furthermore, we sometimes converge very slowly to the Gaussian. For preasymptotics and scalability, Mandelbrot and Taleb (2007a), Bouchaud and Potters (2003). For the problem of working outside asymptotes, Taleb (2007).

  Aureas mediocritas: historical perspective, in Naya and Pouey-Mounou (2005) aptly called Éloge de la médiocrité.

  Reification (hypostatization): Lukacz, in Bewes (2002).

  Catastrophes: Posner (2004).

  Concentration and modern economic life: Zajdenweber (2000).

  Choices of society structure and compressed outcomes: The classical paper is Rawls (1971), though Frohlich, Oppenheimer, and Eavy (1987a, 1987b), as well as Lissowski, Tyszka, and Okrasa (1991), contradict the notion of the desirability of Rawl’s veil (though by experiment). People prefer maximum average income subjected to a floor constraint on some form of equality for the poor, inequality for the rich type of environment.

  Gaussian contagion: Quételet in Stigler (1986). Francis Galton (as quoted in Ian Hacking’s The Taming of Chance): “I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by ‘the law of error.’”

  “Finite variance” nonsense: Associated with CLT is an assumption called “finite variance” that is rather technical: none of these building-block steps can take an infinite value if you square them or multiply them by themselves. They need to be bounded at some number. We simplified here by making them all one single step, or finite standard deviation. But the problem is that some fractal payoffs may have finite variance, but still not take us there rapidly. See Bouchaud and Potters (2003).

&nb
sp; Lognormal: There is an intermediate variety that is called the lognormal, emphasized by one Gibrat (see Sutton [1997]) early in the twentieth century as an attempt to explain the distribution of wealth. In this framework, it is not quite that the wealthy get wealthier, in a pure preferential attachment situation, but that if your wealth is at 100 you will vary by 1, but when your wealth is at 1,000, you will vary by 10. The relative changes in your wealth are Gaussian. So the lognormal superficially resembles the fractal, in the sense that it may tolerate some large deviations, but it is dangerous because these rapidly taper off at the end. The introduction of the lognormal was a very bad compromise, but a way to conceal the flaws of the Gaussian.

  Extinctions: Sterelny (2001). For extinctions from abrupt fractures, see Courtillot (1995) and Courtillot and Gaudemer (1996). Jumps: Eldredge and Gould.

  FRACTALS, POWER LAWS, and SCALE-FREE DISTRIBUTIONS

  Definition: Technically, P>x= K x-α where α is supposed to be the power-law exponent. It is said to be scale free, in the sense that it does not have a characteristic scale: relative deviation of does not depend on x, but on n—for x “large enough.” Now, in the other class of distribution, the one that I can intuitively describe as nonscalable, with the typical shape p(x) = Exp[-a x], the scale will be a.

  Problem of “how large”: Now the problem that is usually misunderstood. This scalability might stop somewhere, but I do not know where, so I might consider it infinite. The statements very large and I don’t know how large and infinitely large are epistemologically substitutable. There might be a point at which the distributions flip. This will show once we look at them more graphically.

  Log P>x = -α Log X +Ct for a scalable. When we do a log-log plot (i.e., plot P>x and x on a logarithmic scale), as in Figures 15 and 16, we should see a straight line.

  Fractals and power laws: Mandelbrot (1975, 1982). Schroeder (1991) is imperative. John Chipman’s unpublished manuscript The Paretian Heritage (Chipman [2006]) is the best review piece I’ve seen. See also Mitzenmacher (2003).