How Not to Be Wrong : The Power of Mathematical Thinking (9780698163843)

by Ellenberg, Jordan

  “The unknown thing to be known”: From Grothendeick’s memoir Récoltes et Semailles, translated and quoted in McCarty, “Rising Sea,” 302.

  Gerald Selbee told me: Phone interview, Gerald Selbee, Feb. 11, 2013. All information about Selbee’s role is taken from this interview.

  friend of Boston Globe reporter Andrea Estes: E-mail from Andrea Estes, Feb. 5, 2013.

  the Globe ran a front-page story: Andrea Estes and Scott Allen, “A Game with a Windfall for a Knowing Few,” Boston Globe, July 31, 2011.

  In the early eighteenth century: The story of Voltaire and the lottery is drawn from Haydn Mason, Voltaire (Baltimore: Johns Hopkins University Press, 1981), 22–23, and from Brendan Mackie’s article “The Enlightenment Guide to Winning the Lottery,” www.damninteresting.com/the-enlightenment-guide-to-winning-the-lottery (accessed Jan. 14, 2014).

  “As long as the Lottery announced to the public”: Letter from Gregory W. Sullivan to Steven Grossman.

  “It’s a private lottery for skilled people”: Estes and Allen, “Game with a Windfall.”

  Chapter 12: Miss More Planes!

  “If you never miss the plane”: Or at least everyone says he used to say this. I couldn’t find any evidence he ever put it in writing.

  “The Social Security Administration’s inspector general on Monday said”: “Social Security Kept Paying Benefits to 1,546 Deceased,” Washington Wire (blog), Wall Street Journal, June 24, 2013.

  Nicholas Beaudrot observed: Nicholas Beaudrot, “The Social Security Administration Is Incredibly Well Run,” www.donkeylicious.com/2013/06/the-social-security-administration-is.html.

  “For, to talk frankly with you about Geometry”: Letter from Pascal to Fermat, August 10, 1660.

  devoted a long essay: The Voltaire here is all from the 25th of his “Philosophical Letters,” which consists of remarks on the Pensées.

  a widely circulated blog post: N. Gregory Mankiw, “My personal work incentives,” Oct. 26, 2008, gregmankiw.blogspot.com/2008/10/blog-post.html. Mankiw returned to the same theme in his column “I Can Afford Higher Taxes, but They’ll Make Me Work Less,” New York Times, BU3, Oct. 10, 2010.

  Fran Lebowitz tells a story: In the 2010 movie Public Speaking.

  “I dreamed about this problem some time”: Both quotes from Buffon’s “Essays on Moral Arithmetic,” 1777.

  After graduating third from his class at Harvard: Biographical material on Ellsberg drawn from Tom Wells, Wild Man: The Life and Times of Daniel Ellsberg (New York: St. Martin’s, 2001); and Daniel Ellsberg, Secrets: A Memoir of Vietnam and the Pentagon Papers (New York: Penguin, 2003).

  “There is the artist to study”: Daniel Ellsberg, “The Theory and Practice of Blackmail,” RAND Corporation, July 1968, unpublished at the time, available at www.rand.org/content/dam/rand/pubs/papers/2005/P3883.pdf (accessed Jan. 14, 2014).

  now known as Ellsberg’s paradox: Daniel Ellsberg, “Risk, Ambiguity, and the Savage Axioms,” Quarterly Journal of Economics 75, no.4 (1961): 643–69.

  Chapter 13: Where the Train Tracks Meet

  it worked for Long-Term Capital Management: LTCM itself didn’t survive for long, but the principal actors walked away rich men and stuck around in the financial sector despite the LTCM debacle.

  The eye must generate light: Otto-Joachim Gruesser and Michael Hagner, “On the History of Deformation Phosphenes and the Idea of Internal Light Generated in the Eye for the Purpose of Vision,” Documenta Ophthalmologica 74, no. 1–2 (1990): 57–85.

  “There is an ending as far as I’m concerned”: David Foster Wallace, interviewed at Word e-zine, May 17, 1996, www.badgerinternet.com/~bobkat/jest11a.html (accessed Jan. 14, 2014).

  “A base del nostro studio”: Gino Fano, “Sui postulati fondamentali della geometria proiettiva,” Giornale di matematiche 30.S 106 (1892).

  “As a basis for our study”: Translation adapted from that in C. H. Kimberling, “The Origins of Modern Axiomatics: Pasch to Peano,” American Mathematical Monthly 79, no.2 (Feb. 1972): 133–36.

  If you do Cartesian geometry using the Boolean number system: Highly abbreviated explanation: Remember, the projective plane can be thought of as the set of lines through the origin in three-dimensonal space, and the lines in the projective plane are planes through the origin. A plane through the origin in 3-space has an equation of the form ax + by + cz = 0. So a plane through the origin in 3-space over the Boolean numbers is also given by an equation ax + by + cz = 0, except that now a,b,c are required to be either 0 or 1. So there are eight possible equations of this form. What’s more, setting a= b = c = 0 gives an equation (0 = 0) which is satisfied for all x, y, and z, and thus doesn’t determine a plane; so in all there are seven planes through the origin in the Boolean 3-space, which means there are seven lines in the Boolean projective plane, just as there should be.

  Hamming, a young veteran of the Manhattan Project: Info on Hamming largely drawn from section 2 of Thomas M. Thompson, From Error-Correcting Codes Through Sphere Packing to Simple Groups (Washington, DC: Mathematical Association of America, 1984).

  “The Patent Department would not release the thing”: Ibid., 27

  Golay published first: Ibid., 5, 6.

  As for the patent: Ibid., 29.

  Ro was an artificial language: All material on Ro is from the “Dictionary of Ro” at www.sorabji.com/r/ro.

  it goes back to the astronomer Johannes Kepler: Historical material on sphere packing is taken from George Szpiro’s book The Kepler Conjecture (New York: Wiley, 2003).

  Henry Cohn and Abhinav Kumar proved: Henry Cohn and Abhinav Kumar, “Optimality and Uniqueness of the Leech Lattice Among Lattices,” Annals of Mathematics 170 (2009): 1003–50.

  a single giant roll of paper: Thompson, From Error-Correcting Codes, 121.

  was discovered by R. H. F. Denniston: Ralph H. F. Denniston, “Some New 5-designs,” Bulletin of the London Mathematical Society 8, no. 3 (1976): 263–67.

  “This man spends his life without weariness . . .”: Pascal, Pensées, no. 139.

  Even businesses that survive: Information about the “typical entrepreneur” comes from chapter 6 of Scott A. Shane’s book The Illusions of Entrepreneurship: The Costly Myths That Entrepreneurs, Investors, and Policy Makers Live By (New Haven, CT: Yale University Press, 2010).

  Chapter 14: The Triumph of Mediocrity

  a widely used statistics textbook: Horace Secrist, An Introduction to Statistical Methods: A Textbook for Students, a Manual for Statisticians and Business Executives (New York: Macmillan, 1917).

  “Mediocrity tends to prevail”: Horace Secrist, The Triumph of Mediocrity in Business (Chicago: Bureau of Business Research, Northwestern University, 1933), 7.

  “The results confront the business man”: Robert Riegel, Annals of the American Academy of Political and Social Science 170, no. 1 (Nov. 1933): 179.

  “Complete freedom to enter trade”: Secrist, Triumph of Mediocrity in Business, 24.

  “Pupils of all ages”: Ibid., 25.

  “I can cast up any sum in addition”: Karl Pearson, The Life, Letters and Labours of Francis Galton (Cambridge, UK: Cambridge University Press, 1930), 66.

  “devoured its contents and assimilated them”: Francis Galton, Memories of My Life (London: Methuen, 1908), 288. Both Galton’s memoir and Pearson’s biography are reproduced in full as part of the staggering collection of Galtoniana at galton.org.

  as one reviewer complained: quoted in Emel Aileen Gökyigit, “The Reception of Francis Galton’s Hereditary Genius,” Journal of the History of Biology 27, no. 2 (Summer 1994).

  “I attempted mathematics”: From Charles Darwin, “Autobiography,” in Francis Darwin, ed., The Life and Letters of Charles Darwin (New York and London: Appleton, 1911), 40.

  “Matt Kemp is off to a blazing start”: Eric Karabell, “Don’t Fall for Another Hot April for Ethier,” Eric Karabel
l Blog, Fantasy Baseball, http://insider.espn.go.com/blog/eric-karabell/post/_/id/275/andre-ethier-los-angeles-dodgers-great-start-perfect-sell-high-candidate-fantasy-baseball (accessed Jan. 14, 2014).

  first-half American League home run leaders: Data about midseason home run totals is drawn from “All-Time Leaders at the All-Star Break,” CNN Sports Illustrated, http://sportsillustrated.cnn.com/baseball/mlb/2001/allstar/news/2001/07/04/leaders_break_hr.

  famous statistical smackdown: Harold Hotelling, “Review of The Triumph of Mediocrity in Business by Horace Secrist,” Journal of the American Statistical Association 28, no. 184 (Dec. 1933): 463–65.

  Hotelling was a Minnesotan: Biographical information about Hotelling is drawn from Walter L. Smith, “Harold Hotelling, 1895–1973,” Annals of Statistics 6, no. 6 (Nov 1978).

  Then the hammer drops: My treatment of the Secrist/Hotelling story owes much to Stephen M. Stigler, “The History of Statistics in 1933,” Statistical Science 11, no. 3 (1996): 244–52.

  “Very few of those biologists”: Walter F. R. Weldon, “Inheritance in Animals and Plants” in Lectures on the Method of Science (Oxford: Clarendon Press, 1906). I learned of Weldon’s essay from Stephen Stigler.

  A 1976 British Medical Journal paper: A. J. M. Broadribb and Daphne M. Humphreys, “Diverticular Disease: Three Studies: Part II: Treatment with Bran,” British Medical Journal 1, no. 6007 (Feb. 1976): 425–28.

  When the program was put through randomized trials: Anthony Petrosino, Carolyn Turpin-Petrosino, and James O. Finckenauer, “Well-Meaning Programs Can Have Harmful Effects! Lessons from Experiments of Programs Such as Scared Straight,” Crime and Delinquency 46, no. 3 (2000): 354–79.

  Chapter 15: Galton’s Ellipse

  “I began with a sheet of paper”: Francis Galton, “Kinship and Correlation,” North American Review 150 (1890), 419–31.

  Or at least reinvented it: All material about the history of the scatterplot is drawn from Michael Friendly and Daniel Denis, “The Early Origins and Development of the Scatterplot,” Journal of the History of the Behavioral Sciences 41, no. 2 (Spring 2005): 103–30.

  [isopleth map]: Stanley A. Changnon, David Changnon, and Thomas R. Karl, “Temporal and Spatial Characteristics of Snowstorms in the Contiguous United States,” Journal of Applied Meteorology and Climatology 45, no. 8 (2006): 1141–55.

  the first published isoplethic map: Information on Halley’s isogonal map from Mark Monmonier, Air Apparent: How Meteorologists Learned to Map, Predict, and Dramatize Weather, (Chicago: University of Chicago Press, 2000), 24–25.

  And here are the 50 U.S. states: Data and image courtesy of Andrew Gelman.

  three of Thomas Pynchon’s major novels: Michael Harris, “An Automorphic Reading of Thomas Pynchon’s Against the Day” (2008). Available at www.math.jussieu.fr/~harris/Pynchon.pdf (accessed Jan. 14, 2014). See also Roberto Natalini, “David Foster Wallace and the Mathematics of Infinity,” in A Companion to David Foster Wallace Studies (New York: Palgrave MacMillan, 2013), 43–58, which interprets Infinite Jest in a similar way, finding there are not only parabolas and hyperbolas, but the cycloid, which is what you get when you subject a parabola to the mathematical operation of inversion.

  “The problem may not be difficult to an accomplished mathematician”: Francis Galton, Natural Inheritance (New York: Macmillan, 1889), 102.

  “The Bertillon cabinet”: Raymond B. Fosdick, “The Passing of the Bertillon System of Identification,”Journal of the American Institute of Criminal Law and Criminology 6, no. 3 (1915): 363–69.

  height versus “cubit”: Francis Galton, “Co-relations and Their Measurement, Chiefly from Anthropometric Data,” Proceedings of the Royal Society of London 45 (1888): 135–45; and “Kinship and Correlation,” North American Review 150 (1890): 419–31. In Galton’s own words, from the 1890 paper: “Then a question naturally arose as to the limits of refinement to which M. Bertillon’s system could be carried advantageously. An additional datum was no doubt obtained through the measurement of each additional limb or other bodily dimension; but what was the corresponding increase of accuracy in the means of identification? The sizes of the various parts of the body of the same person are in some degree related together. A large glove or shoe suggests that the person to whom it belongs is a large man. But the knowledge that a man has a large glove and a large shoe does not give us very much more information than if our knowledge had been confined to only one of the two facts. It would be most incorrect to suppose that the accuracy of the anthropometric method of identification increases with the number of measures in anything like the same marvellous rapidity that the security afforded by the better description of locks increases with the number of wards. The depths of the wards are made to vary quite independently of each other; consequently the addition of each new ward multiplies the previous security. But the lengths of the various limbs and bodily dimensions of the same person do not vary independently; so that the addition of each new measure adds to the security of the identification in a constantly-lessening degree.”

  “As in most other cases of novel views”: Francis Galton, Memories of My Life, 310.

  a recent Supreme Court oral argument: Briscoe v. Virginia, oral argument, Jan. 11, 2010, available at www.oyez.org/cases/2000-2009/2009/2009_07_11191 (accessed Jan. 14, 2014).

  “Like upscale areas everywhere”: David Brooks, “One Nation, Slightly Divisible,” Atlantic, Dec. 2001.

  statistician Andrew Gelman found: Andrew E. Gelman et al, “Rich State, Poor State, Red State, Blue State: What’s the Matter with Connecticut?” Quarterly Journal of Political Science 2, no. 4 (2007): 345–67.

  In some states, like Texas and Wisconsin: See Gelman’s book Rich State, Poor State, Red State, Blue State (Princeton, NJ: Princeton University Press, 2008), 68–70 for this data.

  was halted in 2011: “NIH Stops Clinical Trial on Combination Cholesterol Treatment,” NIH News, May 26, 2011, www.nih.gov/news/health/may2011/nhlbi-26.htm (accessed Jan. 14, 2014).

  appeared actually to increase the risk: “NHLBI Stops Trial of Estrogen Plus Progestin Due to Increased Breast Cancer Risk, Lack of Overall Benefit,” NIH press release, July 9, 2002, www.nih.gov/news/pr/jul2002/nhlbi-09.htm (accessed Jan. 14, 2014).

  or that estrogen alone: Philip M. Sarrel et al., “The Mortality Toll of Estrogen Avoidance: An Analysis of Excess Deaths Among Hysterectomized Women Aged 50 to 59 Years,” American Journal of Public Health 103, no. 9 (2013): 1583–88.

  Chapter 16: Does Lung Cancer Make You Smoke Cigarettes?

  the relation between smoking and lung cancer: Material on the early history of the link between smoking and lung cancer from Colin White, “Research on Smoking and Lung Cancer: A Landmark in the History of Chronic Disease Epidemiology,” Yale Journal of Biology and Medicine 63 (1990): 29–46.

  paper of Doll and Hill: Richard Doll and A. Bradford Hill, “Smoking and Carcinoma of the Lung,” British Medical Journal 2, no. 4682 (Sept. 30, 1950): 739–48.

  “Is it possible then, that lung cancer”: Fisher wrote this in 1958. Quoted in Paul D. Stolley, “When Genius Errs: R. A. Fisher and the Lung Cancer Controversy,” American Journal of Epidemiology 133, no. 5 (1991).

  more recent work has borne out his intuition: See, e.g., Dorret I. Boomsma, Judith R. Koopmans, Lorenz J. P. Van Doornen, and Jacob F. Orlebeke, “Genetic and Social Influences on Starting to Smoke: A Study of Dutch Adolescent Twins and Their Parents,” Addiction 89, no. 2 (Feb. 1994): 219–26.

  “if only the authors had been on the right side”: Jan P. Vandenbroucke, “Those Who Were Wrong,” American Journal of Epidemiology 130, no. 1 (1989), 3–5.

  “A number of authorities who have examined the same evidence cited by Dr. Burney”: quoted in Jon M. Harkness, “The U.S. Public Health Service and Smoking in the 1950s: The Tale of Two More Statements,” Journal of the History of Medicine and Allied Sciences 62, no. 2 (Apr. 2007): 171–212.


  the remarkable work: Ibid.

  “possible to conceive but impossible to conduct”: Jerome Cornfield, “Statistical Relationships and Proof in Medicine,” American Statistician 8, no. 5 (1954): 20.

  fell well short of disastrous: For the 2009 pandemic, see Angus Nicoll and Martin McKee, “Moderate Pandemic, Not Many Dead—Learning the Right Lessons in Europe from the 2009 Pandemic,” European Journal of Public Health 20, no. 5 (2010): 486–88. But note that more recent studies have suggested that the worldwide death toll was much larger than originally estimated, perhaps on the order of 250,000.

  “Cancer is a biologic”: Joseph Berkson, “Smoking and Lung Cancer: Some Observations on Two Recent Reports,” Journal of the American Statistical Association 53, no. 281 (Mar. 1958): 28–38.

  “It is as though”: Ibid.

  “If 85 to 95 per cent”: Ibid.

  Chapter 17: There Is No Such Thing as Public Opinion

  In a January 2011 CBS News poll: “Lowering the Deficit and Making Sacrifices,” Jan. 24, 2011, www.cbsnews.com/htdocs/pdf/poll_deficit_011411.pdf (accessed Jan. 14, 2014).

  A Pew Research poll from February 2011: “Fewer Want Spending to Grow, But Most Cuts Remain Unpopular,” Feb. 10, 2011, www.people-press.org/files/2011/02/702.pdf.

  “The most plausible reading of this data is that the public wants a free lunch”: Bryan Caplan, “Mises and Bastiat on How Democracy Goes Wrong, Part II” (2003), Library of Economics and Liberty, www.econlib.org/library/Columns/y2003/CaplanBastiat.html (accessed Jan. 14, 2014).

  “People want spending cut”: Paul Krugman, “Don’t Cut You, Don’t Cut Me,” New York Times, Feb. 11, 2011, http://krugman.blogs.nytimes.com/2011/02/11/dont-cut-you-dont-cut-me.

  “Many people seem to want to cut down the forest but to keep the trees”: “Cutting Government Spending May Be Popular but There Is Little Appetite for Cutting Specific Government Programs,” Harris Poll, Feb. 16, 2011, www.harrisinteractive.com/NewsRoom/HarrisPolls/tabid/447/mid/1508/articleId/693/ctl/ReadCustom%20Default/Default.aspx (accessed Jan. 14, 2014).