The Black Swan: The Impact of the Highly Improbable

NOTES BEHIND THE CURTAIN: ADDITIONAL NOTES, TECHNICAL COMMENTS, REFERENCES, AND READING RECOMMENDATIONS

I separate topics thematically; so general references will mostly be found in the chapter in which they first occur. I prefer to use a logical sequence here rather than stick to chapter division.

PROLOGUE and CHAPTER 1

Black Swan in logic: First, mine is not a problem in logic. The philosophical problem is about the possibility of a Black Swan. Mine is about the impact. Also, it may not be too relevant who came up with the metaphor first, but the earliest mention of Black Swan problem I could find is in John Stuart Mill’s A System of Logic. It was later used by many (including Charles Sanders Peirce) before it became associated with Karl Popper.

Bell curve: when I write bell curve I mean the Gaussian bell curve, a.k.a. normal distribution. All curves look like bells, so this is a nickname. Also, when I write the Gaussian basin I mean all distributions that are similar and for which the improbable is inconsequential and of low impact (more technically, nonscalable – all moments are finite). Note that the visual presentation of the bell curve in histogram form masks the contribution of the remote event, as such an event will be a point to the far right or far left of the center.

Diamonds: see Eco (2002).

Platonicity: I’m simply referring to incurring the risk of using a wrong form – not that forms don’t exist. I am not against essentialisms; I am often skeptical of our reverse engineering and identification of the right form. It is an inverse problem!

Empiricist: If I call myself an empiricist, or an empirical philosopher, it is because I am just suspicious of confirmatory generalizations and hasty theorizing. Do not confuse this with the British empiricist tradition. Also, many statisticians, as we will see with the Makridakis competition, call themselves “empirical” researchers, but are in fact just the opposite – they fit theories to the past.

Mention of Christ: see Flavius Josephus’s The Jewish War.

Great War and prediction: Ferguson (2006b).

Hindsight bias (retrospective distortion): see Fischhoff (1982b).

Historical fractures: Braudel (1985), p.169, quotes a little known passage from Gautier. He writes, “‘This long history,’ wrote Emile-Felix Gautier, ‘lasted a dozen centuries, longer than the entire history of France. Encountering the first Arab sword, the Greek language and thought, all that heritage went up in smoke, as if it never happened’” For discussions of discontinuity, see also Gurvitch (1957), Braudel (1953), Harris (2004).

Religions spread as bestsellers: Veyne (1971). See also Veyne (2005).

Clustering in political opinions: Pinker (2002).

Categories: Rosch (1973, 1978). See also Umberto Eco’s Kant and the Platypus.

Ontological uncertainty: Some of the literature discusses my categorization problem as ontological uncertainty, meaning there can be uncertainty concerning the entities themselves.

Historiography and philosophy of history: Bloch (1953), Carr (1961), Gaddis (2002), Braudel (1969, 1990), Bourde and Martin (1989), Certeau (1975), Muqaddamat Ibn Khaldoun illustrate the search for causation, which we see already present in Herodotus. For philosophy of history, Aron (1961), Fukuyama (1992). For postmodern views, see Jenkins (1991). I show in Part Two how historiographers are unaware of the epistemological difference between forward and backward processes (i.e., between projection and reverse engineering).

Information and markets: See Shiller (1981, 1989), Delong et al. (1991), and Cutler et al. (1989). The bulk of market moves does not have a “reason”, just a contrived explanation.

Of descriptive value for crashes: See Galbraith (1997), Shiller (2000), and Kindleberger (2001).

CHAPTER 3

Movies: see De Vany (2002). See also Salganik et al. (2006) for the contagion in music buying.

Religion and domains of contagion: See Boyer (2001).

Wisdom (madness) of crowds: Collectively, we can both get wiser or far more foolish. We may collectively have intuitions for Mediocristan-related matters, such as the weight of an ox (see Surowiecki, 2004), but my conjecture is that we fail in more complicated predictions (economic variables for which crowds incur pathologies – two heads are worse than one). For decision errors and groups, see Sniezek and Buckley (1993). Classic: Charles Mackay’s Extraordinary Popular Delusions and the Madness of Crowds.

Increase in the severity of events: Zajdenweber (2000).

Modern life: The nineteenth-century novelist Emile Zola welcomed the arrival of the market for culture in the late 1800s, of which he seemed to be one of the first beneficiaries. He predicted that the writers’ and artists’ ability to exploit the commercial system freed them from a dependence on patrons’ whims. Alas, this was accompanied with more severe concentration – very few people benefited from the system. Lahire (2006) shows how most writers, throughout history, have starved. Remarkably, we have ample data from France about the literary tradition.

CHAPTER 4

Titanic: The quote is from Dave Ingram’s presentation at the Enterprise Risk Management Symposium in Chicago on May 2, 2005. For more on LTCM, see Lowenstein (2000), Dunbar (1999).

Hume’s exposition: Hume (1748, 2000).

Sextus Empriricus: “It is easy, I think, to reject the method of induction (???????). For since by way of it they want to make universals convincing on the basis of particulars, they will do this surveying all the particulars or some of them. But if some, the induction will be infirm, it being that some of the particulars omitted in the induction should be contrary to the universal; and if all, they will labor at an impossible task, since the particulars and infinite are indeterminate. Thus in either case it results, I think, that induction totters”. Outline of Pyrrhonism, Book II, p. 204.

Bayle: the Dictionnaire historique etcritique is long (twelve volumes, close to 6,000 pages) and heavy (40 pounds), yet it was an intellectual bestseller in its day, before being supplanted by the philosophes. It can be downloaded from the French Bibliotheque Nationale at www.bn.fr.

Hume’s inspiration from Bayle: see Popkin (1951, 1955). Any reading of Bishop Huet