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

“. . . something known as a log-normal distribution”: for background on prob-
ability distributions, including log-normal distributions, see casella and Berger (2002) 
and forbes et al. (2011).
38 “. . . principle known as the Weber-Fechner law”: See osborne (1959).
39 “. . . he picked up a book by Einstein, the Meaning of relativity . . .”: this is 
einstein (1946).
40 “So Osborne wrote Einstein a letter . . .”: the original letters are kept at the 

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einstein archive at the Hebrew University of Jerusalem. osborne’s family provided me 
with photocopies (osborne and einstein 1946).
41 “Other researchers, such as the statistician Maurice Kendall . . .” See Kendall 
(1953) in particular. Kendall’s work on the randomness of stock prices is described in 
detail in Bernstein (1993).
42 “As Osborne would later put it . . .”: the quote is from osborne (1987a, p. 137).
42
“The third idea concerned the migratory efficiency of salmon”: this work was 
ultimately published as osborne (1961).
44 “Osborne proposed a new model for deep ocean currents”: this work was pub-
lished as osborne (1973).
44
“. . . it was impossible to predict how individual stock prices would change . . .”: 
osborne makes this point in several places, but he dwells on it (and the related question 
of how analyses such as his might be put into use in practice) in his book, osborne (1977, 
pp. 96–100).
45 “. . . ‘unrelieved bedlam’ . . .”: See, for instance, osborne (1962, p. 378) for 
the quote. for a clear example of where osborne relentlessly sought empirical evidence 
against his own hypothesis, see osborne (1967).
45
“He showed that the volume of trading . . .”: See osborne (1962). note that this 
work appeared just one year after the migratory salmon paper was published.
45
“. . . Osborne and a collaborator . . .”: the article I have in mind is niederhof-
fer and osborne (1966); the collaborator was victor niederhoffer, the now-(in)famous 
hedge fund manager. for more on niederhoffer, see his autobiography, niederhoffer 
(1998), or the recent New Yorker profile (cassidy 2007).
48 “. . . Osborne proposed the first trading program . . .”: In other words, the first 
systematic, fully deterministic trading strategy that could be programmed into a com-
puter — a system for what today would be called algorithmic trading. the proposal is 
made in niederhoffer and osborne (1966).
3. from coastlines to cotton Prices
49 “Szolem Mandelbrojt was the very model . . .”: Information about Mandelbrojt 
comes from o’connor and robertson (2005), as well as from the biographical materials 
related to Mandelbrot cited below.
49
“In 1950, Benoît Mandelbrot . . .”: Unfortunately, Mandelbrot passed away in 
2010, before I had an opportunity to interview him in connection with this book. Bio-
graphical material in this chapter comes from Mandelbrot and Hudson (2004), Man-
delbrot (1987, 2004a), Gleick (1987), Barcellos (1985), and davis (1984), as well as from 
a number of filmed interviews of Mandelbrot produced shortly before he died — espe-
cially Mandelbrot (1998, 2010).
50 “This is for you . . .”: this story, including the quote, is told in Mandelbrot and 
Hudson (2004).
50
“. . . linguist named George Kingsley Zipf . . .”: for more on Zipf, see Man-
delbrot’s biographical notes at the end of Mandelbrot (1982). for the most up-to-date 

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236 
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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
take on the mathematics of Zipf’s law, see Saichev et al. (2010) — a book coauthored by 
didier Sornette, who is the subject of chapter 7 of this book.
51 “. . . which he named ‘fractal geometry’ . . .”: for more on fractal geometry, see, 
for instance, falconer (2003).
52 “. . . indeed, in a speech he gave . . .”: this is Mandelbrot (2004a).
53 “. . . of the more than 3 million Jews who lived in Poland . . .”: Background mate-
rial on World War II and the Holocaust in particular is from dwork and van Pelt (2002), 
fischel (1998), rossel (1992), and Yahil (1987).
54 “How long is Britain’s coastline?”: this question is taken up in Mandelbrot 
(1967).
55 “. . . a coastline doesn’t have a length . . .”: the more precise version of this 
claim is that a coastline should be understood to have non-integer Hausdorff dimension, 
which means that the correct “measure” of a coastline does not behave like a length.
55