The Physics of Wall Street: a brief History of Predicting the Unpredictable

“. . . discovered by one of his professors in Paris, Paul Lévy”: Mandelbrot offers 
some biographical background on Lévy in Mandelbrot (1982) and describes his interac-
tions with him in Mandelbrot and Hudson (2004).
69 “. . . a class of probability distribution now called Lévy-stable distributions”: 
they are also called α-stable distributions. throughout the text (and in Mandelbrot’s 
popular writing), “wildness” is code for “α < 2.” for a Lévy-stable distribution with 1 < 
α < 2, the mean is defined, but the variance is not; if α ≤ 1, neither mean nor variance is 
defined. notably, the central limit theorem fails for Lévy-stable distributions, or rather, 
the following more general theorem holds: a random variable that can be modeled as a 
sum of sufficiently many independent and identically Lévy-stable-distributed variables 
must also be Lévy-stable distributed. for more on the mathematics of Lévy-stable dis-
tributions, see Mantegna and Stanley (2000) and Zolotarev (1986).
70 “. . . early enough that Paul Cootner . . .”: See Mandelbrot (1964) and cootner 
(1964).
71 “Cootner made the argument . . .”: the passage is quoted in Mandelbrot and 
Hudson (2004, p. xxiii).
71
“. . . most notably, Nassim Taleb . . .”: See taleb (2004, 2007a). Mandelbrot 

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t h e p h y s i c s o f wa l l s t r e e t
makes related arguments in Mandelbrot and Hudson (2004). for a more moderate ver-
sion of taleb’s argument — one that is sympathetic with the central arguments of this 
book, though perhaps not regarding the present point on the direction history took in 
1962 — see taleb (2007b).
72 “On a typical day, there aren’t going to be any extreme events . . .”: While true, 
this remark obscures some important points, often emphasized by Mandelbrot. for one, 
the statistical tools that one uses in the context of normal and log-normal distributions 
often do not make any sense — and certainly do not work — in the context of Lévy-
stable-distributed variables. for this reason, assuming normal or log-normal distribu-
tions can lead to extremely misleading results and, moreover, produce a false sense of 
confidence regarding the likelihood of certain kinds of extreme events. for another, de-
spite the fact that extreme events happen infrequently on both models, in Mandelbrot’s 
models of financial markets, they happen often enough that it is the extreme events that 
dominate market behavior in the long run. And so, even if there are similarities in how 
the models predict markets on a typical day, there is a significant difference in how one 
should view the importance of a “typical day” for the long-term behavior of markets.
73 “It is also too simple to say that Mandelbrot was ignored . . .”: for instance, see 
fama (1964).
73
“Today, the best evidence indicates . . .”: See, for instance, cont (2001) and 
references therein; this point was also emphasized in conversation by didier Sornette, 
whose work is the subject of chapter 7.
74 “. . . there is disagreement about how to interpret the data”: In particular, it can 
be extremely difficult to tell whether empirical data are governed by distributions that 
are Lévy-stable and distributions that are fat-tailed but not Lévy-stable, since the differ-
ences often turn on the frequency of extreme events that occur very infrequently. See, 
for instance, Weron (2001).
4. Beating the dealer
76 “The year is 1961”: I have taken some liberties with this opening story (des 
Moines; whiskey sours), but the basics are correct; it is based on an autobiographical 
essay (thorp 1998). More generally, the biographical material on thorp is from that 
essay, as well as thorp (1966, 2004), Poundstone (2005), Patterson (2010), and Schwager 
(2012). In addition, I interviewed thorp, and he was kind enough to read and comment 
on an earlier draft of this chapter.
78 “. . . the 1973 book A random Walk down Wall Street . . .”: this is Malkiel 
(1973).
80 “. . . about $850 in 2012 dollars . . .”: this calculation is based on the Bureau of 
Labor Statistics’ online inflation calculator at http://www.bls.gov/data/inflation_calcula-
tor.htm.
81 “. . . the pioneering mathematician profiled by Sylvia Nasar . . .”: See nasar 
(1998).

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82 for more on Shannon, see Kahn (1967), Poundstone (2005), Gleick (2011), 
and the two biographies in Wyner and Sloane (1993). An excellent modern introduction 
to information theory is Gray (2011); for Shannon’s contributions specifically, see Wyner 
and Sloane (1993) and Shannon and Weaver (1949).
85 “. . . as Shannon’s secretary would later inform Thorp . . .”: this quote is from 
thorp (1998).
86 “. . . a colleague passed along a recent academic article . . .”: the article was 
Baldwin et al. (1956).
86