Nader, Ralph, 378–80, 383–84, 400–401
National Review, 427
Natural History (Buffon), 214
Natural Inheritance (Galton), 301
Natural Theology; or, Evidence of the Existence and Attributes of the Deity, Collected from the Appearances of Nature (Paley), 185–86
negative numbers
employment statistics and, 77–79
income inequality and, 80–82
women, and job loss statistics, 82–84
word problems and, 84–85
Nelson, Edward, 46, 410–11
Netflix, 165–66
New Frontiers of the Mind (Rhine), 171–72
Newton, Isaac, 12, 39–41, 51
New York Times, 80, 82, 101, 305, 426
Neyman, Jerzy, 158–60, 242, 394
Nicomachean Ethics (Aristotle), 24
Nightingale, Florence, 312
Noether, Emmy, 417
nonlinearity
distinguished from linearity, 23–24
of utility, 244
nonstandard analysis, 46
normal distribution, 68–74
Notices of the American Mathematical Society, 94
NSA, 171
null hypothesis, 112
null hypothesis significance test, 112–130, 145–57
criticisms of and problems associated with, 117
divine creation and, 115–16
false positives generated by, 147–48
file drawer problem, 152
haruspicy and, 145–46
“hot hand,” analysis of, 125–30
mechanics of, 112–15
oral contraceptive warning and, 118–20
p-hacking problem and, 153–55
p-values, 110, 114, 171
as reductio ad unlikely, 133
relevance of significance, 117–21
underpowered analysis, 125–28, 149
winner’s curse problem and, 150
Numb3rs (tv show), 137
Obama, Barack, 246, 320, 368, 426–28
obesity, 50–51, 59–61
O’Connor, Sandra Day, 372
“Ode to Joy” (Beethoven), 328–29
Olsen, Nils, 382
Oprah Winfrey Show, The (tv show), 93
oral contraceptive scare, 118–20
Origin of Species, The (Darwin), 298
orthogonal vectors, 339–40
Paley, William, 185–86
parabolas, 324
parallel postulate, 394–99
Paramore (ship), 318
Parsons code, 328–29
partially ordered set, 75
Pascal, Blaise, 191, 237–42, 271, 289–90, 389–90, 404, 425–26
Pascal’s wager, 239–42
Peano, Guiseppe, 406
Pearson, Egon, 158–60, 242, 394
Pearson, Karl, 336, 339
Penry v. Lynaugh, 371, 372–73
Pensées (Pascal), 191, 239, 241
Peres, Shimon, 93–94
Perot, H. Ross, 369, 374
perspective, 261
Peruggia Vincenzo, 327
p-hacking problem, 153–55
Philosophical Essay on Probabilities, A (Laplace), 248
pi, 36, 432
Piketty, Thomas, 80–82
Pinker, Stephen, 64–65
p (movie), 223–24
Planck, Max, 417
plane geometry, 58
Plato, 262
Platonism, 411–12
Pleiades, 133–36
Podesta, John, 93–94
Poincaré, Henri, 413–14
points at infinity, 264, 265
Poisson, Siméon-Denis, 67–68
political logic, 416–18
political polls, computing standard error in, 72
Politico, 427
polygons, 37, 40
Posner, Richard, 403–4
posterior probabilities, 178
Powerball, 201–6
precision, 430–32
Presumed Innocent (Turow), 224
prime numbers, distribution of, 137–44
Prime Number Theorem, 139, 140
principle of explosion, 433
principle of indifference, 187
probability, 110–21. See also improbability
as degree of belief, 178
frequentist view of, 111
Law of Large Numbers and, 111
posterior, 178
a priori, 175
significance testing and (See null hypothesis significance test)
product rule, 96
projective geometry, 261–69
projective plane, 264–66, 398–99
“Promise and Pitfalls of Using Imprecise School Accountability Measures, The” (Kane & Staiger), 70
Proofiness (Seife), 431
Proof (movie), 223–24
proportions, 62–65, 74–75
prosecutor’s fallacy, 170
Psychological Science, 149
Ptolemy, 17
public health decisions, and expected value, 354–57
public opinion, 365–92
Atkins v. Virginia and, 370–76
Condorcet paradoxes and, 387, 391–92
in Florida 2000 presidential election, 378–80, 383–84, 400–401, 430–31
independence of irrelevant alternatives, effect of, 377–83
instant-runoff voting and, 383–86
jury theorem and, 387–88
polls and, 365–70
Putnam, Hilary, 405
p-values, 110, 114, 171
Pynchon, Thomas, 324
Pythagoras, 34
Pythagoreans, 33–34
Pythagorean Theorem, 32–33, 35, 132–33
quadratic equations, 105–9, 323–24
quadrics (conic sections), 322–24
Quine, W. O. V., 429
radio psychics, 171–73
Ramanujan, Srinivasa, 412
RAND Corporation, 249
A Random Walk down Wall Street (Malkiel), 256
randomness
prime numbers and, 140–44
regression and (See regression)
star clusters and, 133–36
ranking systems, 62–76
atrocities and disasters and, 62–65, 74–76
bell curve and, 68–74
brain cancer incidence and, 65
coin flips and, 65–68, 71–74
law of averages and, 73–74
Law of Large Numbers and, 67–74
NBA shooting percentages and, 68–69
proportions and, 62–65, 74–75
simple averages and, 68–70
test scores and, 69–70
weighted averages and, 70–71
Rattner, Steven, 80–81
Reagan, Ronald, 27, 246
Rector, Robert, 156
reductio ad absurdum, 131–32
reductio ad unlikely, 133–44, 157
argument by design as, 186
null hypothesis significance test and, 133
pitfalls of, 136–37
Pleaides as cluster versus random distribution, 133–36
prime clusters and, 137–44
Reed-Solomon code, 276
reform math, 56–57
Registered Replication Reports, 162
regression, 293–362
baseball statistics and, 304–6
correlation and, 319, 325–27, 329–30, 335–62
ellipses and, 311–25
Galton’s hereditary studies and, 298–302, 311–20
/> oral-anal transit and, 309
Secrist’s triumph of mediocrity and, 295–98, 302, 306–8
weather and, 331–34
“Regression Towards Mediocrity in Hereditary Stature” (Galton), 317
Reid, Constance, 418
Reid, Ryan, 69
replication, 161–62
Republican Party, 79–80
Review of Finance, 9
Rhine, J. B., 171–72
Riegel, Robert, 296
Riemann, Bernhard, 396–98
Rips, Eliyahu, 90–91, 92–93, 100, 101
risk, 251
risk ratios, 119–20
Ro, 278
Roberts, John, 402, 403
Robinson, Abraham, 46
Robinson, Julia, 405
Roentgen, Wilhelm, 417
Romberg, Justin, 330
Romney, Mitt, 82, 426–27
Romney campaign, 82–84
Roosevelt, Theodore, 422–24, 425
Rosenberg, Yoav, 90–91, 92–93, 100, 101
Rousseau, Jean-Jacques, 387
Rumsfeld, Donald, 25, 251
Russell, Bertrand, 122, 409, 433
Russell’s paradox, 409
Rwanda genocide, 63–64, 75
Saez, Emmanuel, 80–82
sample size, 68–69
Saunders, Percy, 121
Savage, Leonard Jimmy, 5, 249, 288
Savant Capital study of mutual fund performance, 8–9
Scacco, Alexandra, 173
Scalia, Antonin, 372–73, 374, 375–76, 401–2, 403, 404, 410
Scared Straight, 309–10
scatterplots, 312–13
second incompleteness theorem, 410
Secrist, Horace, 295–96, 297–98, 301, 302, 303, 306–8
Sedikides, Constantine, 382
Seife, Charles, 431
Selbee, Gerald, 210–11, 224–25, 227, 228–29, 253, 257
Selbee, Marjorie, 211
Sensenbrenner, Jim, 80
set theory, 408–409
Shakespeare, William, 123–25
Shalizi, Cosma, 145
Shannon, Claude, 271, 272, 276, 283–84, 330, 436
significance testing. See null hypothesis significance test
Silver, Nate, 426–30
Simonsohn, Uri, 153, 161
simple averages, 68–70
Sinclair, Mary, 171–72
Sinclair, Upton, 171–72
“Sitting on a Fence” (The Housemartins), 425
Six Cornered Snowflake, The (Kepler), 279–80
Sketch for a Historical Picture of the Progress of the Human Mind (Condorcet), 419–20
Skinner, B. F., 121–25
slime mold, 376–77, 380–82
Smith, Adam, 196, 197, 206, 231, 288
social decision making, 387–93, 418–20
socks, sandals worn with, 405
“Soonest Mended” (Ashbery), 424–25
Sotomayor, Sonia, 156
Spence, Michael, 77, 79
sphere packing problem, 279–81
spherical geometry, 396–99
St. Petersburg paradox, 243–48
Staiger, Douglas, 70
“Statistical Inquiries into the Efficacy of Prayer” (Galton), 299
Statistical Research Group (SRG), 4–5, 6
Statistical Science, 93, 94, 101
Stein, Ben, 24–25
Sternberg, Shlomo, 94
Stevens, John Paul, 375
Stigler, George, 233, 235, 236, 357
Stillwell, Michael, 128
stock portfolio, variance of, 255–56
Stockman, David, 27
straight locally, curved globally, 31–49
calculus and, 39–49
circle, area of, 31–39
exhaustion, method of, 34–39
infinitesimal quantities, defining, 41–49
Strena Seu De Nive Sexanula (Kepler), 279–80
Sullivan, Gregory W., 209, 230, 231
Supreme Court, 156, 340, 370–71, 401–404
surrogate endpoint problem, 350
survivorship bias
mutual fund performance and, 8–9
Wald’s bullet hole problem and, 8
Talbott, John, 353, 354
Tao, Terry, 143, 144, 330, 410–11, 414, 415–16
Tarasco, Tony, 402–3
Target, 163, 166, 170
Tarski, Alfred, 391
taxation, and revenue generated, 24–30
teaching math, 56–58
telepathy, 171–73
terrorist attacks, 62–63, 64
terrorist-finding algorithms, 166–71
Terry, Luther, 354
test scores, 69–70
Thabeet, Hasheem, 69
Theory of Games and Economic Behavior, The (Von Neumann & Morgenstern), 249
Thirty Years War, 64–65, 75
title of book, apology for, 335
Tolstoy, Leo, 100
Torah codes, 89–95, 99–101, 111, 114–15
Toronto Star, 62
traditional math, 56–57
transitivity, 342–44
Transylvania lottery, 258–60
Treatise on Probabilities (Keynes), 181
Triumph of Mediocrity in Business, The (Secrist), 296
Trop v. Dulles, 372
Tsarnaev, Dzhokar, 184
Turgot, Jacques, 387
Turiaf, Ronny, 69
Turow, Scott, 224
Tversky, Amos, 125–28, 129, 134–35, 288–89
Twain, Mark, 55, 415
twin primes conjecture, 138, 142–43
uncertainty, 251, 424–30
unconditional expectation, 314
uncorrelated variables, 344–46
underpowered statistical analysis, 125–28, 149
unknown unknowns (uncertainty), 251
utility, 233–52
airport wait times versus missed flights and, 233–36
of buying lottery ticket, 288–89
Ellsberg’s paradox and, 250–51
of entrepreneurship, 290–91
expected utility theory, 248–52
of religious belief, 239–42
governmental waste, cost of eliminating, 236–37
of money, 242–48
utility curve, 235
utils, 234
Vallone, Robert, 125–28, 129, 134–35
Vandenbroucke, Jan, 353
vanishing point, 264
variables, setting to zero, 6–7
Varian, Hal, 27
variance, 253–61
Cash Winfall lottery and, 257–61
stock portfolio and, 255–56
vector, 337
Viète, François, 78
Voevodsky, Vladimir, 411
Voltaire, 228, 241–42, 389–90
Von Neumann, John, 13–14, 17, 249, 252
voting
in Burlington, Vermont 2009 mayoral race, 384–87, 391–92
Condorcet paradoxes and, 387, 391–92
in Florida 2000 presidential election, 378–80, 383–84, 400–401, 430–31
instant-runoff voting, 383–86
patterns of (See voting patterns, statistical analysis of)
Silver’s predictions for 2012 presidential election, 426–30
voting patterns, statistical analysis of
Iranian election vote totals, 173
Obama versus Kerry vote share, 320
wealth and votes for Republicans versus Democrats, 322, 341–42
voxels, 102–4
Wald, Abra
ham, 3–8, 9–10, 152, 153, 406, 418, 424, 436
Walker, Scott, 80
Wallace, David Foster, 223, 224, 242, 265, 435
Wallis, W. Allen, 4, 5
Wall Street Journal, 306, 309
Wall Street Journal’s Washington Wire blog, 236
Wang, Youfa, 59, 60
Wanniski, Jude, 25, 26–27, 30
War and Peace (Tolstoy), 93, 100, 101
Washington Post, 84
Watson, John, 122
Way the World Works, The (Wanniski), 26
Wealth of Nations, The (Smith), 196
weather
algorithms and forecasting of, 164–65
regression to the mean and, 331–34
weighted averages, 70–71
Weil, Sandy, 129
Weissmandl, Michael Dov, 91–92
Weldon, Walter R. F., 308–9
welfare state, 21–24
When Genius Failed (Lowenstein), 255
White, Matthew, 74
Who Wants to Be a Millionaire? (TV show), 388
“Why Is Obama Trying to Make America More Like Sweden When Swedes Are Trying to Be Less Like Sweden?” (Mitchell), 21
“Why Most Published Research Findings Are False” (Ioannidis), 147
Wiener, Norbert, 5
wiggle room, 99–101, 153
Wiles, Andrew, 143
“Will All Americans Become Overweight or Obese?” (Wang, et al.), 50
William III, King, 199
Williams, William Carlos, 58
winner’s curse, 150
Witztum, Doron, 90–91, 92–93, 100, 101, 114
Wolfowitz, Jack, 4–5, 8
women, and job loss statistics, 82–84
Worstward Ho (Beckett), 436
Wright, Kurt, 384–86
Zenith Radio Corporation, 172
Zeno, 41
Zeno’s paradox, 41–42
Zhang, Ying, 210, 228–29
Zhang, Yitang, 138, 140, 141, 144
* Paul’s dad.
* Savage was almost totally blind, able to see only out of one corner of one eye, and at one point spent six months living only on pemmican in order to prove a point about Arctic exploration. Just thought that was worth mentioning.
* To be fair, the S&P 500 index itself did even better, gaining 212.5% over the same period.
* Von Neumann’s view of the nature of math is solid, but it’s fair to feel a bit queasy about his characterization of mathematics carried out for purely aesthetic ends as “degenerate.” Von Neumann is writing this just ten years after the entartene Kunst (“degenerate art”) exhibition in Hitler’s Berlin, whose point was that “l’art pour l’art” was the sort of thing that Jews and Communists liked, and was designed to undercut the healthy “realist” art required by a vigorous Teutonic state. Under the circumstances, one feels a little defensive toward mathematics that serves no apparent purpose. A writer with different political commitments than my own would, at this point, bring up von Neumann’s energetic work on the development and delivery of nuclear weapons.
How Not to Be Wrong : The Power of Mathematical Thinking (9780698163843) Page 49
