Drunkard's Walk - Leonard Mlodinow [117]
12. Blaise Pascal, quoted in Bishop, Pascal, p. 196.
13. Blaise Pascal, quoted in David, Gods, Games and Gambling, p. 252.
14. Bruce Martin, “Coincidences: Remarkable or Random?” Skeptical Inquirer 22, no. 5 (September/October 1998).
15. Holland, What Are the Chances? pp. 86–89.
Chapter 5: The Dueling Laws of Large and Small Numbers
1. Tijms, Understanding Probability, p. 53.
2. Scott Kinney, “Judge Sentences Kevin L. Lawrence to 20 Years Prison in Znetix/HMC Stock Scam,” Washington State Department of Financial Institutions, press release, November 25, 2003; http://www.dfi.wa.gov/sd/kevin_laurence_sentence.htm.
3. Interview with Darrell Dorrell, August 1, 2005.
4. Lee Berton, “He’s Got Their Number: Scholar Uses Math to Foil Financial Fraud,” Wall Street Journal, July 10, 1995.
5. Charles Sanders Peirce, Max Harold Fisch, and Christian J. W. Kloesel, Writings of Charles S. Peirce: A Chronological Edition (Bloomington: Indiana University Press, 1982), p. 427.
6. Rand Corporation, A Million Random Digits with 100,000 Normal Deviates (1955; repr., Santa Monica, Calif.: Rand, 2001), pp. ix–x. See also Lola L. Lopes, “Doing the Impossible: A Note on Induction and the Experience of Randomness,” Journal of Experimental Psychology: Learning, Memory, and Cognition 8, no. 6 (November 1982): 626–36.
7. The account of Joseph Jagger (sometimes spelled Jaggers) is from John Grochowski, “House Has a Built-in Edge When Roulette Wheel Spins,” Chicago Sun-Times, February 21, 1997.
8. For details about the Bernoulli family and Jakob’s life, see E. S. Pearson, ed., The History of Statistics in the 17th and 18th Centuries against the Changing Background of Intellectual, Scientific and Religious Thought: Lectures by Karl Pearson Given at University College, London, during the Academic Sessions 1921–1933 (New York: Macmillan, 1978), pp. 221–37; J. O. Fleckenstein, “Johann und Jakob Bernoulli,” in Elemente der Mathematik, Beihefte zur Zeitschrift, no. 6 (Basel, 1949); and Stephen Stigler, “The Bernoullis of Basel,” Journal of Econometrics 75, no. 1 (1996): 7–13.
9. Quoted in Pearson, The History of Statistics in the 17th and 18th Centuries, p. 224.
10. Stephen Stigler, The History of Statistics: The Measurement of Uncertainty before 1900 (Cambridge, Mass.: Harvard University Press, 1986), p. 65.
11. Pearson, The History of Statistics in the 17th and 18th Centuries, p. 226.
12. William H. Cropper, The Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking (London: Oxford University Press, 2001), p. 31.
13. Johann Bernoulli, quoted in Pearson, The History of Statistics in the 17th and 18th Centuries, p. 232.
14. This depends, of course, on what you identify as “the modern concept.” I am using the definition employed by Hankel’s 1871 history of the topic, described in great detail in Gert Schubring, Conflicts between Generalization, Rigor, and Intuition: Number Concepts Underlying the Development of Analysis in 17th–19th Century France and Germany (New York: Springer, 2005), pp. 22–32.
15. David Freedman, Robert Pisani, and Roger Purves, Statistics, 3rd ed. (New York: W. W. Norton, 1998), pp. 274–75.
16. The Hacking quote is from Ian Hacking, The Emergence of Probability (Cambridge: Cambridge University Press, 1975), p. 143. The Bernoulli quote is from David, Gods, Games and Gambling, p. 136.
17. For a discussion of what Bernoulli actually proved, see Stigler, The History of Statistics, pp. 63–78, and Ian Hacking, The Emergence of Probability, pp. 155–65.
18. Amos Tversky and Daniel Kahneman, “Belief in the Law of Small Numbers,” Psychological Bulletin 76, no. 2 (1971): 105–10.
19. Jakob Bernoulli, quoted in L. E. Maistrov, Probability Theory: A Historical Sketch, trans. Samuel Kotz (New York: Academic Press, 1974), p. 68.
20. Stigler, The History of Statistics, p. 77.
21. E. T. Bell, Men of Mathematics (New York: Simon & Schuster, 1937), p. 134.
Chapter 6: False Positives and Positive Fallacies
1.