How Not to Be Wrong : The Power of Mathematical Thinking (9780698163843)
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Condorcet paradoxes, 387, 391–92
confidence intervals, 157–60
conic sections, 322–24
consistency of math, 404–12
conspiracy theories, 183–84
contradiction, 404–12, 432–36
Conway, John, 281
Cornfield, Jerry, 355
correlation, 7–8, 319, 325–27, 329–30, 335–62
Berkson’s fallacy and, 357–62
Bertillon system and, 325–27, 329–30
binary variables and, 347–49
causal relationships and, 335–36, 349–62
cigarette smoking/lung cancer, 350–55
drug efficacy studies and, 343–44
geometry and, 336–44
HDL cholesterol/heart attacks, 343, 349–50
hormone replacement therapy/heart disease, 344
public health decisions and, 354–57
uncorrelated variables, 344–46
coxcomb graphs, 312–13
“Crack-Up, The” (Fitzgerald), 434
Cramer, Gabriel, 214, 247
creation, divine. See divine creation
cubic equations, 109–10
Curious Incident of the Dog in the Night-Time, The (Haddon), 224
D’Alembert, Jean le Rond, 389
Darwin, Charles, 116, 117, 186, 298, 299–300, 336
dating advice, 361, 382
Daubechies, Ingrid, 330
Davis, Martin, 405
Davis, Philip, 411
Dawkins, Darryl, 126
Dayton, Mark, 80
De la Vallée Poussin, Charles-Jean, 139
dead salmon, 102
Deligne, Pierre, 222
De Moivre, Abraham, 71–72, 73
Denniston, R. H. F., 285–86
derivatives, 40
Descartes, René, 268, 311, 336–37
Dewey, Melvil, 278
Dewey Decimal System, 278
Dial, The, 122
Dickson, J. D. Hamilton, 325
Diogenes the Cynic, 42
disasters
as partially ordered set, 75–76
proportional comparison of, 62–65, 74–75
divergent series, 48
Divergent Series (Hardy), 47
divine creation
argument by design, 185–91
faith, utility of, 239–42
significance testing and, 115–16
Torah codes and, 89–95, 99–101, 111, 114–15
Doctrine of Chances, The (De Moivre), 71
Doll, Richard, 350–51, 359
Doll & Hill study, 350–51, 359
Drosnin, Michael, 93–94, 101
drug efficacy studies
and correlation, 343–44
interpreting, 113–14
ears, cutting off of, 372
eccentricity of an ellipse, 319–20
Economist, The, 77
Edgeworth, Francis Ysidro, 72
Eighth Amendment, 371–72
Einstein, Albert, 171–72, 416–17
Elements (Euclid), 395
ellipses, 311–25
data sets exhibiting, examples of, 320–22
eccentricity of, 319–20
Galton’s, 311–20
as quadrics, 322–24
Ellsberg, Daniel, 248–52, 288
Ellsberg’s paradox, 250–51
Emanuel, Simcha, 100
employment statistics
job growth, state versus national, 79–80
job growth by sector, 77–79
women, and job loss statistics, 82–84
entrepreneurship, 290–91
equidistant letter sequence (ELS), 91–95
error-correcting code, 271–79
error-detecting codes, 276
Erving, Julius, 126–27
An Essay Towards Making the Doctrine of Chances Easy to those Who Understand Vulgar Arithmetic only . . . . (Hoyle), 71
Essay on the Application of Analysis to the Probability of Majority Decisions (Condorcet), 387–88
Estes, Andrea, 227
Euclid, 17, 34, 139, 262, 390–91, 394–95
Eudoxus of Cnidus, 34, 37, 221
eugenics, 334–35
Euler, Leonhard, 45
evidentiary standards for assessing results, 102–30, 145–62
Bayesian inference (See Bayesian inference)
confidence intervals, use of, 157–60
dead salmon fMRI study, statistical results from, 102–4
probability theory and, 110–30
replication of results, 161–62
reverse engineering and, 105–10
significance testing and (See null hypothesis significance test)
ex falso quodlibet (principle of explosion), 433
exhaustion, method of, 34–39
existence, 363–420
consistency of math and, 404–12
formalism and, 400–412
genius cult, 412–16
parallel postulate and, 394–99
political logic and, 416–18
public opinion and, 365–92
expectation, 193–291
coding theory and, 269–87
lotteries and, 195–232
projective geometry and, 261–69
utility and, 233–52, 288–91
variance and, 253–61
expected utility theory, 248–52
expected value, 197–206
additivity of, 212, 214–22
of bets, 198–99
of religious belief, 239–42
insurance pricing and, 199–200
of lottery tickets, 197–98, 201–13
and public health decisions, 354–57
explosion, principle of, 433
“Exposition on a New Theory of the Measurement of Risk” (Bernoulli), 243
Facebook, 166–71
face-centered cubic lattice, 280
faith, utility of, 239–42
false linearity, 23
false positives, in significance testing, 147–48
Fano, Gino, 267
Fano plane, 267–269
Fermat, Pierre de, 143, 237, 239
Fermat conjecture, 143
Ferris Bueller’s Day Off (movie), 24–25
Feynman, Richard, 182
file drawer problem, 152
financial collapse of 2008, 255–56
fingerprinting, 327
finite symmetry groups, 281
Fisher, R. A., 99, 112, 114, 115, 116, 131, 136, 156, 159, 160, 162, 171, 180, 181, 351–53, 357, 394
Fitzgerald, F. Scott, 433, 434–35
flash drives, 276
flogarithm, 139–40
Florida 2000 presidential election, 378–80, 383–84, 400–401, 430–31
fluxions, 40
Foreign Affairs, 62
formalism, 400–412
Fosdick, Raymond, 326
Foster, Edward Powell, 278
franc-carreau, 214–22
Franken, Al, 431
Franklin, Benjamin, 432
Frege, Gottlob, 407–8, 433
frequentist view of probability, 111
Friedman, Milton, 5, 28, 288
Frost, Robert, 122
Galton, Francis, 298–302, 308, 311–20, 324–25, 326–27, 329–30, 334–35, 336, 436
Galvin, William, 231
Garcia, Rich, 403
Gascoigne, George, 124–25
Gauss, Carl Friedrich, 16, 396
Gelman, Andrew, 341
gendarme’s hat, 68–74
Genesis, 93, 100
genius, cult of, 412–16
geometry, 336
Buffon’s needle, 214–22
correlation and, 336–44
ellipses and, 311–25
Euclid’s axioms, 390–91, 396–97
of Hamming code, 274–75
non-Euclidean, 394–99
plane, 58
projective, 261–69
Pythagorean Theorem, 32–33, 35, 132–33
sphere packing problem and, 279–81
Gilovich, Thomas, 125–28, 129, 134–35
Gingrich, Newt, 62
Girshik, Abe, 5
global thermonuclear war, 249, 252
Gödel, Kurt, 410, 416–17
Godfrey, Thomas, 432
Golay, Marcel, 276
Goldblach conjecture, 143
Gombaud, Antoine (Chevalier de Méré), 237
Google, 164, 166
Gore, Al, 341, 378–80, 383–84, 400–401
governmental waste, cost of eliminating, 236–37
Grandi, Guido, 45
Grandi’s series, 45, 48
Gravity’s Rainbow (Pynchon), 324
Great Big Book of Horrible Things (White), 74
Great Square of Men, 361
Green, Ben, 143, 144
Grothendieck, Alexander, 222, 223
Grundgesetze (Frege), 409
Hadamard, Jacques, 139
Hadamard code, 275–76
Haddon, Mark, 224
Hales, Thomas, 282
Halley, Edmond, 199–200, 318
Hamming, Richard, 272–73, 276, 277, 284, 436
Hamming code, 273–75, 283, 284–85
Hamming distance, 277–79
Hamming sphere, 279
hand, horribly severed, 55
Hardy, G. H., 47, 48, 142, 400
Harkness, Jon, 354
Harmelin v. Michigan, 375
haruspicy, 145–46
Harvey, James, 210, 225–26, 227, 228–29, 230, 231, 253, 260, 291
HDL cholesterol/heart attacks, and correlation, 343, 349–50
height, and regression to the mean, 301–2, 311–20
Hereditary Genius (Galton), 298–99, 300
Hersh, Reuben, 411
Hick, W. E., 160
Hilbert, David, 405–7, 410, 411–12, 416–18
Hill, A. Bradford, 350–51, 359
Hipparchus, 340
Hippasus, 34
Hlatshwayo, Sandile, 77, 79
Home Run Derby, curse of the, 305–6
homotopy theory, 411
Horace, 24
hormone replacement therapy/heart disease correlation, 344
Hotelling, Harold, 306–8
“hot hand,” myth of the myth of, 125–30
The Housemartins, 425
Hoyle, Edmond, 71
Huizinga, John, 129
human behavior, algorithms predicting, 163–71
Target’s pregnancy predicting algorithm, 163, 166, 170
terrorist-finding, 166–71
hyperbolas, 324
Ibn al-Haytham, ‘Ali al-Hasan, 262
improbability, 89–102. See also probability
Baltimore stockbroker parable and, 95–99, 152
lotteries and, 98–99, 112, 137
Torah codes and, 89–95, 99–101, 111, 114–15
wiggle room and, 99–101
incubation of mutual funds, 97
independence of irrelevant alternatives, 377–83
indifference, principle of, 187
inference, 87–191
Bayesian, 171–91
evidentiary standards for assessing results, 102–30, 145–62
human behavior, algorithms predicting, 163–71
improbable occurrences and, 89–102
null hypothesis significance test and, 112–130, 145–57
reductio ad unlikely and, 133–44, 157
Infinite Jest (Wallace), 242, 265
infinitesimal quantities, 41–49
In Re Troy Anthony Davis, 402
inscribed square, 35
instant-runoff voting, 383–86
insurance pricing, and expected value, 199–200
intelligent design, 186
investment advisor performance, 129
Ioannidis, John, 147, 150, 161
Iranian election vote totals, analysis of, 173
isobars, 317
isogons, 318
isonephs, 317
isopleths, 317
isotherms, 317
Jefferson, Thomas, 388
Jeter, Derek, 305, 402–3
job growth, 77–79
Johnson, Armon, 69, 70
Johnson, Kirk, 156
Jones, William, 370
Jordan, Josh, 427
Journal of the American Medical Association, 353
Journal of the American Statistical Association, 306, 308
Jungle, The (Sinclair), 171
jury theorem, 387–88
Kahnemann, Daniel, 288–89
Kane, Thomas, 70
Kass, Robert, 93, 99
Kazhdan, David, 94
Kemp, Jack, 27
Kemp, Matt, 304, 306
Kennedy, Anthony, 326
Kepler, Johannes, 279–80, 282, 322–23
Kerrich, J. E., 66–67
Kerry, John, 320
Keynes, John Maynard, 181
Kiss, Bob, 384–86
Kitab al-Manazire (Ibn al-Haytham), 262
Klein, Felix, 417
Klem, Bill, 402, 403
known unknowns (risk), 251
Korb, Kevin, 128
Kronecker, Leopold, 104
Krugman, Paul, 366
Kumar, Abhinav, 281
La Condamine, Charles-Marie de La, 227–28, 389
Laffer, Arthur, 25, 30
Laffer curve, 24–30, 235
Laplace, Pierre-Simon, 248
Latty, Tanya, 376, 381
law of averages, 73–74
Law of Large Numbers, 67–74, 111
Lawson, Donald, 202, 203
Lebowitz, Fran, 247
Leech, John, 281
Leech lattice, 281
Leibniz, Gottfried W., 45
Le Peletier des Forts, Michel, 227
Less Like Sweden fallacy, 21–24
Life on the Mississippi (Twain), 55
Liggins, DeAndre, 69
limit, 47
linearity, 19–85
false, 23
Laffer curve and, 24–30
linear regression, 51–55, 59–61
negative numbers, impact of, 77–85
nonlinearity distinguished from, 23–24
ranking systems and, 62–76
straight locally, curved globally, 31–49
linear regression, 51–55, 59–61
college tuition/SAT scores and, 51–53
missile flight and, 54–55
obesity and, 50–51, 59–61
lineocentrism, 63
Littlewood, J. E., 142
Livermore, Samuel, 371–72, 376
Lobachevskii, Nikolai, 396
logarithm, 139–40
Lojban, 279
Long Beach Press-Telegram, 50
Long-Term Capital Management, 255
Lorenz, Edward, 164–65
Los Angeles Times, 62
lotteries, 112, 137, 195–232
additivity of expected value, 212, 214–22
Cash Winfall, 206–13, 224�
�32, 253, 256–61, 258–60
Denniston’s code and, 258–60
expected value and, 197–98, 201–13
Fano plane and, 267–69
improbability and, 98–99
Powerball, 201–6
Transylvania lottery, 258–60
utility of playing, 288–89
variance and, 253, 256–61
Lowenstein, Roger, 255
Lu, Yuran, 224, 253, 287, 291
lung cancer/cigarette smoking correlation, 350–55
McKay, Brendan, 99–100, 101
McNamara, Robert, 63
Maier, Jeffrey, 403
Maimonides, 89–90, 91–92
Malkiel, Burton, 256
Mallat, Stéphane, 330
Malthus, Thomas, 420
Mankiw, Greg, 27–29, 246–47
Many Labs project, 162
Mariner 9 (Mars orbiter), 275–76
Maryland v. King, 326
Mason & Dixon (Pynchon), 324
“A Mathematical Theory of Communication” (Shannon), 271
“Mathematician, The” (Von Neumann), 13–14, 17
mathematics
as common sense, 9–14
complicated facts of, 14–16
existence (See existence)
expectation (See expectation)
four quadrants of, 15
inference (See inference)
linearity (See linearity)
regression (See regression)
teaching, 56–58
understanding of, and insight into everyday problems, 1–3
Wald, and bullet hole problem, 3–10
“Math Melodrama” myth, 223
math education, 56–58
Matijasevic, Yuri, 405
Matrixx, 155–56
Maynard, James, 141
Melville, Herman, 101
Menaechmus, 17
Mental Radio (Sinclair), 171–72
Meyer, Yves, 330
Michell, John, 133, 135–36, 137
Mill, John Stuart, 384
Million Act, 199–200
Minard, Charles, 312
Minkowski, Hermann, 412
Mirman, Eugene, 50
Mishneh Torah, 89–90
missile flight
linear regression and, 54–55
quadratic equation and, 105–9
missing bullet hole problem, 5–8, 9–10
Mitchell, Daniel J., 21, 23
Mitchell, John, 133–34
Moby Dick (Melville), 101
Mona Lisa (painting), 327
money, utility of, 242–48
Montroll, Andy, 384–86
Moor, Ahmed, 62
Morgenstern, Oskar, 3–4, 249, 416–17
Morlet, Jean, 330
Mosteller, Frederick, 5
multiple comparisons correction, 104
Mumford, David, 58
mutual fund performance
Baltimore stockbroker parable and, 97–98
survivorship bias and, 8–9