Quotations

p. 45

on the Marilyn vos Savant column on Monty Hall Problem

From Georgetown: “How many irate mathematicians are needed to change your mind?” And someone from the U.S. Army Research Institute remarked, “if  all those PhDs are wrong the country would be in serious trouble.”

p. 49

Not all the chapters of Cardano’s book treat technical issues. For instance, chapter 26 is titled “Do Those Who Teach Well Also Play Well?” he concludes, “it seems to be a different thing to know and to execute”.

p.56

While in college he had written a paper, “On Differing Opinions of Physicians,” that essentially called the medical establishment a bunch of quacks. The Milan College of Physicians now returned the favor, refusing to admit him.

p.83

Benford’s Law, observation -> theorem-> proof

…the American astronomer Simon Newcomb. Around 1881, Newcomb noticed that the pages of books of logarithms that dealt with numbers beginning with the numeral 1 were dirtier and more frayed in the pages corresponding to numbers beginning with the numeral 2, and so on, down to the numeral 9, whose pages, in comparison, looked clean.

…when scrutinizing the log tables at the General Electric Research Laboratory in Schenectady, New York. But neithei man proved the law. That didn’t happen until 1995, in work by Ted Hill ,mathematician at the Georgia Institute of Technology.

p. 95

In the 1940s a South African mathematician named John Kerrich decided to test this out in a practical experiment, tossing a coin what must have seemed like 1 zillion times—  actually it was 10,000—and recording the results of each toss You might think Kerrich would have had better things to do, but he was a war prisoner at the time, having had the bad luck of being a visitor in Copenhagen when the Germans invaded Denmark in April 1940.

p.98

One reason Bernoulli’s numerical estimate was so far from optimal was that his proof was based on many approximations. Another was that he chose 99.9 percent as his standard of certainty—that is, he required that he get the wrong answer less than 1 time in 1,000. That is a very demanding standard/Bernoulli called it “moral certainty”

p.100

Jakob Bernoulli

One should not appraise human action on the basis of its results

p.109

Actuary Founding and Failure

Richard Price was…credited with founding actuary science, a field he developed when, in 1765, three men from an insurance company, the Equitable Society, requested his assistance.Six years after that encounter he published his work in a book titled Observations on Reversionary Payments. Though the book served as a)ible for actuaries well into the nineteenth century, because of some poor data and estimation methods, he appears to have underestimated life expectancies. The resulting inflated life insurance premiums enriched his pals at the Equitable Society. The hapless British government, on the other hand, based annuity payments on Price’s tables and took a bath when the pensioners did not proceed to keel over at the predicted rate.

p.118

Abuse of Probability

For example, the case in Britain of Sally Clark.lark’s first child died at 11 weeks. The death was reported as Sudden infant death syndrome, or SIDS…

p.128

In 1794, Lavoisier was arrested with the rest of the association and quickly sentenced todeath. Ever the dedicated scientist, he requested time to completdesome of his research so that it would be available to posterity. To that the presiding judge famously replied, “The republic has no need of scientists.”

p.131

hx of the wine industry

Back in the 1970s the winebusiness was a sleepy enterprise, growing, but mainly in the sales of low-grade jug wines. Then, in 1978, an event often credited with the rapid growth  of that industry occurred:  a lawyer turned  self-proclaimed wine critic, Robert M. Parker Jr., decided that, in addition to his reviews he would rate wines numerically on a 100-pointscale.

p.147

philosopher Immanuel Kant wrote in 1784, “Each, according to his own inclination follows his own purpose, often in opposition to others; yet each individual and people, as if following some guiding thread, go toward a natural but to each of them unknown goal; all work toward furthering it, even if they would set little store by it if they did know it.”

p.153

The term statistics entered the English language from the German word Statistik through a 1770 translation of the book Bielfield’s Elementary Universal Education, which stated that “The science thats called statistics teaches us what is the political arrangement of all the modern states in the known world”

p.155

In the height of 100,000 young Frenchmen called up for the draft he also found meaning in a deviation from the normal distribution. In that data, when the number of conscripts was plotted against their height,the bell ell-shaped curve was distorted: too few prospects were just above five feet two and a compensating surplus was just below that height. Quetelet argued that the difference—about 2,200 extra “short men’—was due to fraud or, you might say friendly fudging, as those-low five feet two were excused from service.

Decades later the great French mathematician Jules-Henri Poincare employed Quetelet’s method to nab a baker who was short- changing his customers.

p.158

inventory loss runs pretty steadily from year to year at about 1.6 percent and that consistently about 45 percent to 48 percent of it is due to employee theft. Crime, Quetelet wrote, is “like a budget that is paid with frightening regularity. Quetelet recognized that I’homme moyen would be different for different cultures and that it could change with changing social conditions.

p.174 that was rather starkly illustrated by the mathematician George Spencer-Brown, who wrote that in a random series of 10^1,000,007 zeroes and ones, you should expect at least 10 nonoverlapping subsequences of 1 million consecutive zeros.

p.189

philosopher Francis Bacon put it in 1620, “the human understanding,   once  it has  adopted  an  opinion,  collects  any instances that confirm it, and though the contrary instances may be more numerous and more weighty, it either does not notice them or  rejects them, in order that this opinion will remain unshaken.”46

p.195

as the Nobel laureate Max Born wrote, “Chance is a more fundamental conception than causality.”

p.201

the socialist historian Richard Henry Tawney, for example, put it like this: “Historians give an appearance of inevitability … by dragging into prominence the forces which have triumphed and thrusting into the background those which they have swallowed up.”

Works to Pull

Amos Tversky and Daniel Kahneman, “Extensional versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment,” Psychological Review 90 no4 (October 1983): 293-315.

Craig R. Fox and Richard Birke, “Forecasting Trial Outcomes: Lawyers Assign Higher Probabilities to Possibilities That Are Described in Greater Detail,” Law and Human Behavior 26, no. 2 (April 2002): 159-73.

Bruce Schechter, My Brain Is Open: The Mathematical Journeys of Paul Erdos (New York: Touchstone, 1998), pp. 107-9

Kline, Mathematical Thought, pp. 178-79.

Alan Wykes, Doctor Cardano: Physician Extraordinary (London- Frederick Muller, 1969). See also Oystein Ore, Cardano: The Gambling Scholar, with aanslation of Cardano’s Boofc on Games of Chance by Sydney Henry Gould Princeton University Press, 1953).

Jerome Cardan, The Book of My Life: De Vita Propia Liber, trans. Jean Stoner (Whitefish, Mont: Kessinger, IUUV, p.5>.

18. Amos Tversky and Daniel Kahneman, “Belief in the Law of Small Numbers,” Psychological Bulletin 76, no. 2 (1971): 105-10.

19. Probability Theory: A Historical Sketch, trans. Samuel Kotz (New York: Academic Press, 1974), p. 68.

8. Gerd Gigerenzer, Calculated Risks: How to Know When Numbers Deceive You (New York: Simon & Schuster, 2002), pp. 40-44.

22. Gregg E. A. Solomon, “Psychology of Novice and Expert Wine Talk,”American Journal of Psychology 103, no. 4 (Winter 1990): 495-517.

30. James J. Fogarty, “Why Is Expert Opinion on Wine Valueless?” (discussion paper 02.17, Department of Economics, University of Western Australia, Perth,2001

For Graunt’s story, see Hacking, The Emergence of Probability, pp. 103-9;David, Gods, Games and Gambling, pp. 98-109; and Newman, The World of Mathematics, 3:1416-18.

8. Justin Wolfers, “Point Shaving: Corruption in NCAA Basketball,” American Economic Review 96, no. 2 (May 2006): 279-83.

21. Richard C. Hollinger et al., National-Retail Security Survey: Final Report Gainesville: Security Research Project, Department of Sociology and Center for Studies in Criminal Law, University of Florida, 2002-2006).

Jeffrey Kluger, “Why We Worry about the Things We Shouldn’t… and ignore the Things We Should,” Time, December 4, 2006, pp. 65-71.

Malkiel, A random walk down Wall Street

18. Andrew Metrick, “Performance Evaluation with Transactions Data: The Stock Selection of Investment Newsletters, Journal of Finance 54, no. 5 (October/
1999): 1743-75; and “The Equity Performance of Investment Newsletters” (dis-ission paper no. 1805, Harvard Institute of Economic Research, Cambridge,lass., November 1997).

Atul Gawande, “The Cancer Cluster Myth,” The New Yorker, February 28,998, pp. 34-37.

9. W. Brian Arthur, “Positive Feedbacks in the Economy,” Scientific American, 9.
February 1990, pp. 92-99.).

Perrow, Normal Accidents.

Melvin J. Lerner, “Evaluation of Performance as a Function of Performer sReward and Attractiveness,” Journal of Personality and Social Psychology 1 (1965)

Melvin J. Lerner and C. H. 9immons, “Observer’s Reactions to the ‘Innocent Victim’: Compassion or Rejection?” Journal of of Personality and Social Psy-chology 4 (1966): 203-10.

David L. Rosenhan, “On Being Sane in Insane Places,” Science 179 (Janu-ary 19,1973): 237-55.