Only 47% of Americans: These numbers are from the January 2011 CBS poll cited above.
In an October 2010 poll of likely voters: “The AP-GfK Poll, November 2010,” questions HC1 and HC14a, http://surveys.ap.org/data/GfK/AP-GfK%20Poll%20November%20Topline-nonCC.pdf.
“The clause seems to express a great deal of humanity”: Annals of the Congress of the United States, Aug. 17, 1789. (Washington, DC: Gales and Seaton, 1834), 782.
“The Court pays lip service”: Atkins v. Virginia, 536 US 304 (2002).
Akhil and Vikram Amar: “Akhil Reed Amar and Vikram David Amar, Eighth Amendment Mathematics (Part One): How the Atkins Justices Divided When Summing,” Writ, June 28, 2002, writ.news.findlaw.com/amar/20020628.html (accessed Jan. 14, 2014).
Just over six hundred people in all: Numbers of executions taken from the Death Penalty Information Center, www.deathpenaltyinfo.org/executions-year (accessed Jan. 14, 2014).
you can train a slime mold to run through a maze: See, e.g., Atsushi Tero, Ryo Kobayashi, and Toshiyuki Nakagaki, “A Mathematical Model for Adaptive Transport Network in Path Finding by True Slime Mold,”Journal of Theoretical Biology 244, no. 4 (2007): 553–64.
Tanya Latty and Madeleine Beekman: Tanya Latty and Madeleine Beekman, “Irrational Decision-Making in an Amoeboid Organism: Transitivity and Context-Dependent Preferences,” Proceedings of the Royal Society B: Biological Sciences 278, no. 1703 (Jan. 2011): 307–12.
jays, honeybees, and hummingbirds: Susan C. Edwards and Stephen C. Pratt, “Rationality in Collective Decision-Making by Ant Colonies,” Proceedings of the Royal Society B: Biological Sciences 276, no. 1673 (2009): 3655–61.
Psychologists Constantine Sedikides, Dan Ariely, and Nils Olsen: Constantine Sedikides, Dan Ariely, and Nils Olsen, “Contextual and Procedural Determinants of Partner Selection: Of Asymmetric Dominance and Prominence,” Social Cognition 17, no. 2 (1999): 118–39. But note also Shane Frederick, Leonard Lee, and Ernest Baskin, “The Limits of Attraction” (working paper), which argues that the evidence for the asymmetric domination effect in humans outside artificial lab scenarios is very weak.
“among the very greatest improvements”: John Stuart Mill, On Liberty and Other Essays (Oxford: Oxford University Press, 1991), 310.
the 2009 mayoral race in Burlington, Vermont: The vote totals here are all drawn from “Burlington Vermont IRV Mayor Election,” http://rangevoting.org/Burlington.html (accessed Jan. 15, 2014). See also University of Vermont political scientist Anthony Gierzynski’s assessment of the election, “Instant Runoff Voting,” www.uvm.edu/~vlrs/IRVassessment.pdf (accessed Jan. 15, 2014).
“le mouton enragé”: Ian MacLean and Fiona Hewitt, eds., Condorcet: Foundations of Social Choice and Political Theory (Cheltenham, UK: Edward Elgar Publishing, 1994), 7.
“I must act not by what I think reasonable”: From Condorcet’s “Essay on the Applications of Analysis to the Probability of Majority Decisions,” in Ian MacLean and Fiona Hewitt, Condorcet, 38.
“mathematical charlatan”: Material on Condorcet, Jefferson, and Adams from MacLean and Hewitt, Condorcet, 64.
made an extended visit to Voltaire’s house: The material about the relationship between Voltaire and Condorcet in this section is largely drawn from David Williams, “Signposts to the Secular City: The Voltaire-Condorcet Relationship,” in T. D. Hemming, Edward Freeman, and David Meakin, eds., The Secular City: Studies in the Enlightenment (Exeter, UK: University of Exeter Press, 1994), 120–33.
Condorcet, like R. A. Fisher after him: Lorraine Daston, Classical Probability in the Enlightenment (Princeton, NJ: Princeton University Press, 1995), 99.
“so beautiful that it was frightening”: recounted in a letter of Mme. Suard of June 3, 1775, quoted in Williams, “Signposts,” 128.
Chapter 18: “Out of Nothing I Have Created a Strange New Universe”
“You must not attempt this approach to parallels”: This quote, and much of the historical discussion of Bolyai’s work on non-Euclidean geometry, is drawn from Amir Alexander, Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics (Cambridge, MA: Harvard University Press, 2011), part 4.
“To praise it would amount to praising myself”: Steven G. Krantz, An Episodic History of Mathematics (Washington, DC: Mathematical Association of America, 2010), 171.
the U.S. Supreme Court said no: In Bush v. Gore, 531 U.S. 98 (2000).
“Long live formalism”: Antonin Scalia, A Matter of Intepretation: Federal Courts and the Law (Princeton, NJ: Princeton University Press, 1997), 25.
“The best-umpired game”: Quoted widely, e.g. in Paul Dickson, Baseball’s Greatest Quotations, rev. ed. (Glasgow: Collins, 2008), 298.
Jeter knew it wasn’t a home run: To be fair, the question “What did Derek Jeter know and when did he know it?” has never been completely settled. In a 2011 interview with Cal Ripken, Jr., he conceded that the Yankees “caught a break” on the play but wasn’t willing to go so far as to say he should have been out. But he should have been out.
“Most of the cases the Supreme Court agrees to decide”: from Richard A. Posner, “What’s the Biggest Flaw in the Opinions This Term?” Slate, June 21, 2013.
what Congress must have meant: See, e.g., Scalia’s concurrence in Green v. Bock Laundry Machine Co., 490 U.S. 504 (1989).
“When we are engaged in investigating”: From the translation of Hilbert’s speech by Mary Winston Newson, Bulletin of the American Mathematical Society, July 1902, 437–79.
“tables, chairs, and beer mugs”: Reid, Hilbert, 57.
“A careful reader”: Hilbert, “Über das unendliche,” Mathematische Annalen 95 (1926): 161–90; trans. Erna Putnam and Gerald J. Massey, “On the Infinite,” in Paul Benacerraf and Hilary Putnam, Philosophy of Mathematics, 2d ed. (Cambridge, UK: Cambridge University Press, 1983).
Terry Tao found a mistake: If you want to see what it looks like when serious mathematicians go toe-to-toe, you can watch the whole thing play out in real time in the comment section of the math blog The N-Category Café from September 27, 2011, “The Inconsistency of Arithmetic,” http://golem.ph.utexas.edu/category/2011/09/the_inconsistency_of_arithmeti.html (accessed Jan. 15, 2014).
“The typical working mathematician”: Phillip J. Davis and Reuben Hersh, The Mathematical Experience (Boston: Houghton Mifflin, 1981), 321.
Ramanujan was a prodigy from southern India: Robert Kanigel’s book The Man Who Knew Infinity (New York: Scribner, 1991) is a thorough popular account of Ramanujan’s life and work, if you want to know more.
that was Hermann Minkowski: Reid, Hilbert, 7.
Psychologists nowadays call it “grit”: See, e.g., the work of Angela Lee Duckworth.
“It takes a thousand men”: From a letter Twain wrote on Mar. 17, 1903, to the young Helen Keller, available as “The Bulk of All Human Utterances Is Plagiarism,” Letters of Note, www.lettersofnote.com/2012/05/bulk-of-all-human-utterances-is.html (accessed Jan. 15, 2014).
“The popular image”: Terry Tao, “Does One Have to Be a Genius to Do Maths?” http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths (accessed Jan. 15, 2014).
As to the nature of the contradiction: The story and the quoted conversation come from “Kurt Gödel and the Institute,” Institute for Advanced Study, www.ias.edu/people/godel/institute.
he refused to sign the 1914 Declaration to the Cultural World: Reid, Hilbert, 137.
recounts the conversation: Constance Reid, Hilbert (Berlin: Springer-Verlag, 1970), 210.
“We cannot usually avoid being presented with decisions of this kind”: From “An Election Between Three Candidates,” a section of Condorcet’s “Essay on the Applications of Analysis,” in MacLean and Hewitt, Condorcet.
How to Be Right
went his whole life without lifting a weapon in anger: Wald did fulfill his compulsory service in the Rumanian army,
though, so I can’t say for sure he didn’t.
“Soonest Mended”: It appears in Ashbery’s 1966 book The Double Dream of Spring. You can read the poem online at www.poetryfoundation.org/poem/177260 (accessed Jan. 15, 2014).
“Sitting on a fence”: “Sitting on a Fence” appears on the Housemartins’s debut record, London 0 Hull 4.
I think of Silver as a kind of Kurt Cobain of probability: Some of this material is adapted from my review of Silver’s book The Signal and the Noise in the Boston Globe, Sept. 29, 2012.
“On September 30, leading into the debates”: Josh Jordan, “Nate Silver’s Flawed Model,” National Review Online, Oct. 22, 2012, www.nationalreview.com/articles/331192/nate-silver-s-flawed-model-josh-jordan (accessed Jan. 15, 2014).
“So should Mitt Romney win on Nov. 6”: Dylan Byers, “Nate Silver: One-Term Celebrity?” Politico, Oct. 29, 2012.
states Silver considered potentially competitive: Nate Silver, “October 25: The State of the States,” New York Times, Oct. 26, 2012.
“To believe something is to believe that it is true”: Willard Van Orman Quine, Quiddities: An Intermittently Philosophical Dictionary (Cambridge, MA: Harvard University Press, 1987), 21.
Obama had a 67% chance: These aren’t Silver’s actual numbers, which aren’t archived as far as I can tell, just numbers made up to illustrate the kind of predictions he was making before the election.
Sometimes the people speak and they say “I dunno”: The discussion of close elections is adapted from my article “To Resolve Wisconsin’s State Supreme Court Election, Flip a Coin,” Washington Post, Apr. 11, 2011.
“He knew little out of his way”: From The Autobiography of Benjamin Franklin (New York: Collier, 1909), www.gutenberg.org/cache/epub/148/pg148.html (accessed Jan. 15, 2014).
their reasoning modules frazzle and halt: See, e.g., “I, Mudd,” Star Trek, air date Nov. 3, 1967.
“The test of a first-rate intelligence”: F. Scott Fitzgerald, “The Crack-Up,” Esquire, Feb. 1936.
it’s said of the topologist R. H. Bing: For instance, in George G. Szpiro, Poincaré’s Prize: The Hundred-Year Quest to Solve One of Math’s Greatest Puzzles (New York: Dutton, 2007).
“I can’t go on, I’ll go on”: Samuel Beckett, The Unnameable (New York: Grove Press, 1958).
Determined to record and neutralize: My take on DFW’s language is taken from an article I published in Slate on Sept. 18, 2008, “Finite Jest: Editors and Writers Remember David Foster Wallace,” www.slate.com/articles/arts/culturebox/2008/09/finite_jest_2.html.
“and you go the way of Hippasos”: Samuel Beckett, Murphy (London: Routledge, 1938).
INDEX
The page numbers in this index refer to the printed version of this book. The link provided will take you to the beginning of that print page. You may need to scroll forward from that location to find the corresponding reference on your e-reader.
ABC News, 50
Abel, Niels Henrik, 48
Abraham, 89–90
Adams, John, 388
additivity of expected value, 212, 214–22
Affordable Care Act, 368
Against the Day (Pynchon), 324
Ahmadinejad, Mahmoud, 173
airport wait times versus missed flights, 233–36
Albrecht, Spike, 125, 126, 129
Alcmaeon of Croton, 262
Alexander the Great, 17
algebra, 104–10, 336
algorithms, 56–58
asteroid trajectory, forecasting, 164
Target’s pregnancy predicting, 163, 166, 170
terrorist-finding, 166–71
weather forecasting, 164–65
for solving equations in whole numbers, 405
Alhazen. See Ibn al-Haytham, ‘Ali al-Hasan
Allen, Scott, 227
alliteration, statistical analysis of, 123–25
Amar, Akhil, 373, 375
Amar, Vikram, 373, 375
Amgen, 150
annuities, pricing of, 199–200
Appolonius of Perga, 319–20, 322
a priori probabilities, 175
Arbuthnot, John, 115, 116
Archimedes, 31, 32, 34–38, 40, 221
area, of circle, 31–39
“An Argument for Divine Providence, Taken from the Constant Regularity Observed in the Births of Both Sexes” (Arbuthnot), 115
argument by design, 185–91
Ariely, Dan, 382
Aristotle, 24, 99, 131
Arrow, Kenneth, 419
Ashbery, John, 424–25
Association for Psychological Science, 162
asteroid trajectory, forecasting, 164
asymmetric domination effect, 382
Atkins, Daryl Renard, 370, 372
Atkins v. Virginia, 370–76, 403
atrocities
as partially ordered set, 75–76
proportional comparison of, 62–65, 74–75
Attali, Yigal, 129
“Axiomatic Thought” (Hilbert), 416
Bakan, David, 117
Baltimore stockbroker, 95–99, 152
Banach-Tarski paradox, 391
Barbier, Jospeh-Émile, 217, 218, 222, 223
Bar-Natan, Dror, 99–100, 101
Baseball
formalism in, 403
regression to the mean in, 304–6
basketball
“hot hand,” statistical analysis of, 125–28
NBA shooting percentages, and ranking systems, 68–69
Bayesian inference, 171–91
argument by design and, 186–91
mechanics of, 174–78
Bayes theorem, 178
Beal, Andrew, 143
Beaudrot, Nicholas, 236
Beautiful Mind, A (movie), 223–24
Beber, Bernd, 173
Beckett, Samuel, 434–36
Beekman, Madeleine, 376, 381
Beethoven, Ludwig van, 328
Bell, 272, 276
bell curve, 68–74
Benitez, Armando, 402–3
Bennett, Craig, 102–4
Bennett, Jim, 166
Berkeley, George, 40, 46
Berkson, Jospeh, 136, 357–59
Berkson’s fallacy, 357–62
Bernoulli, Daniel, 243, 244–46, 247, 248, 252, 271
Bernoulli, Jakob, 68
Bernoulli, Nicolas, 115–16, 243
Bertillon, Alphonse, 325–26
bertillonage, 325–29
Bertrand, Joseph, 223
Better Angels of Our Nature, The (Pinker), 64
Bible Code, The (Drosnin), 93–94
Bible codes, 89–95, 99–101, 111, 114–15
binary variables, and correlation, 347–49
Bing, R. H., 433
bits, 269
bivariate normal distribution, 319
Blumenthal, Otto, 418
Bolyai, Farkas, 395
Bolyai, János, 395–96, 399, 434, 436
Book of Isaiah, 93
Borda, Jean-Charles de, 379–80, 390
Bose-Chaudhuri-Hocquenghem codes, 276
Boston Globe, 227, 228, 231
Bostrom, Nick, 189
bounded gaps conjecture, 138, 140–42, 144
brain cancer incidence, 65
British Medical Journal, 309
Brooks, David, 341
Broom of the System, The (Wallace), 435
Brown, Derren, 97
Brunelleschi, Filippo, 262, 264, 398
Buchanan, Pat, 400
Buffon, Georges-Louis LeClerc, Comte de, 214–17, 222, 223, 247–48
Buffon’s needle problem, 216–22
Buffon’s noodle p
roblem, 222
bullet hole problem, 5–8, 9–10
Burlington, Vermont 2009 mayoral election, 384–87, 391–92
Burney, Leroy E., 353, 354
Bush, George H. W., 369, 374
Bush, George W., 322, 341, 378–80, 383–84, 400–401
Bush v. Gore, 404
business performance, and regression to the mean, 295–98, 302
Byers, Dylan, 427
Byman, Daniel, 62
calculus, 39–49, 56
Candès, Emmanuel, 330
Cantor, Georg, 271, 410
capacity of a communication channel, 272
capital punishment, 370–76
Caplan, Bryan, 366
Caplan, Gerald, 62–63
calculus, 12, 39–41, 47
Caramello, Olivia, 399
Cardano, Girolamo, 67–68, 78
Cash Winfall, 206–13, 224–32, 253, 256–61, 258–60
cat in the hat problem, 184–85
Cato Institute, 21–23
Cauchy, Augustin-Louis, 47–49
causal relationships, and correlation, 335–36, 349–62
Chabris, Christopher, 150
Chandler, Tyson, 69
Chao, Lu, 431–32
chaos, 164–65
checksum, 276
Cheney, Dick, 25
Churchill, Winston, 265
cigarette smoking/lung cancer correlation, 350–55
circle, area of, 31–39
circumscribed square, 36
“Citizenship in a Republic” (Roosevelt), 422–23
Clausewitz, Carl von, 13
cleanest man in school, 188
clinical trials. See drug efficacy studies
Clinton, Bill, 77, 369, 374
CNN, 93
Cobain, Kurt, 426
code words, 273
Cohn, Henry, 281
coin flips, 65–68, 71–74
Coleman, Norm, 431
combinatorial explosion, 261
common sense, 9–14
compact discs, 276
compression, 330
conditional expectation, 314
conditional probabilities, 170
Condorcet, Marie-Jean-Antoine-Nicolas de Caritat, Marquis de, 387–93, 400–401, 418–20, 424, 436
How Not to Be Wrong : The Power of Mathematical Thinking (9780698163843) Page 47