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A History of Western Philosophy by Aaron Finkel
When the popes became politically subservient to France, the sovereigns hostile to the French king were necessarily hostile to the Pope. This led to the protection of William of Occam and Marsiglio of Padua by the Emperor; at a slightly later date, it led to the protection of Wycliffe by John of Gaunt. Bishops, in general, were by this time completely in subjection to the Pope; in an increasing proportion, they were actually appointed by him. The monastic orders and the Dominicans were equally obedient, but the Franciscans still had a certain spirit of independence. This led to their conflict with John XXII (1316-34), which we have already considered in connection with William of Occam. During this conflict, Marsiglio persuaded the Emperor to march on Rome, where the imperial crown was conferred on him by the populace, and a Franciscan antipope was elected after the populace had declared John XXII deposed.
They devoted themselves to reconciling Aristotle and Christ; Albertus Magnus and Thomas Aquinas, both Dominicans, accomplished this task as well as it is capable of being accomplished. The authority of Thomas Aquinas was so overwhelming that subsequent Dominicans did not achieve much in philosophy; though Francis, even more than Dominic, had disliked learning, the greatest names in the immediately following period are Franciscan: Roger Bacon, Duns Scotus, and William of Occam were all Franciscans. What the friars accomplished for philosophy will be the subject of the following chapters. CHAPTER XIII Saint Thomas Aquinas THOMAS AQUINAS (b. 1225 or 1226, d. 1274) is regarded as the greatest of scholastic philosophers. In all Catholic educational institutions that teach philosophy his system has to be taught as the only right one; this has been the rule since a rescript of 1879 by Leo XIII.
I cannot, therefore, feel that he deserves to be put on a level with the best philosophers either of Greece or of modern times. CHAPTER XIV Franciscan Schoolmen FRANCISCANS, on the whole, were less impeccably orthodox than Dominicans. Between the two orders there was keen rivalry, and the Franciscans were not inclined to accept the authority of Saint Thomas. The three most important of Franciscan philosophers were Roger Bacon, Duns Scotus, and William of Occam. Saint Bonaventura and Matthew of Aquasparta also call for notice. Roger Bacon (ca. 1214-ca. 1294) was not greatly admired in his own day, but in modern times has been praised far beyond his deserts. He was not so much a philosopher, in the narrow sense, as a man of universal learning with a passion for mathematics and science. Science, in his day, was mixed up with alchemy, and thought to be mixed up with black magic; Bacon was constantly getting into trouble through being suspected of heresy and magic.
The Music of the Primes by Marcus Du Sautoy
Ada Lovelace, Andrew Wiles, Arthur Eddington, Augustin-Louis Cauchy, computer age, Dava Sobel, Dmitri Mendeleev, Eratosthenes, Erdős number, four colour theorem, Georg Cantor, German hyperinflation, global village, Henri Poincaré, Isaac Newton, Jacquard loom, Jacquard loom, music of the spheres, New Journalism, Paul Erdős, Richard Feynman, Richard Feynman, Search for Extraterrestrial Intelligence, Simon Singh, Solar eclipse in 1919, Stephen Hawking, Turing machine, William of Occam, Wolfskehl Prize, Y2K
It is a religious belief that it has to be true or else the whole world would be wrong if it weren’t.’ Indeed, as Bombieri elaborated, ‘When I was in the eleventh grade I studied several of the medieval philosophers. One of them, William of Occam, elevated the idea that when one must choose between two explanations, one should always choose the simpler. Occam’s razor as the principle is called cuts out the difficult and chooses the simple.’ For Bombieri, a zero off the line would be like an instrument in the orchestra ‘that drowns out the others – an aesthetically distasteful situation. As a follower of William of Occam, I reject that conclusion, and so I accept the truth of the Riemann Hypothesis.’ Things came to a head when Bombieri visited the Institute in Bonn, and discussion over tea turned to the Riemann Hypothesis.
and Ramanujan 134, 135, 137–41, 143 and the Riemann Hypothesis 150, 160 Lobachevsky, Nikolai Ivanovic 110 logarithms 46–9, 55, 62, 72, 74, 91, 104, 105, 168, 189, 206 Logue, Donal 240 Louis XV, King of France 41 Louis XVI, King of France 41 Lovelace, Ada 190 Lucas, Édouard 205, 206 Lucas-Lehmer numbers 206, 207 m-commerce 248 Manasse, Mark 239 mathematics: a creative art under constraints 34 irrespective of race 184, 199 plunged into crisis 156 pursuit of order 6 Matijasevich, Yuri 198–9, 201 Mendeleev, Dmitri 23, 32, 36–7 Mendelssohn, Felix 75 Mersenne, Marin 40, 41, 44, 93, 204–5 Mersenne primes 17, 206–9, 224, 236 Mertens Conjecture 219, 221–2 Miller-Rabin test 245 Millennium Problems and Prizes 14–16, 33, 242, 246, 250, 252 Miller, Gary 245 Miller, Victor 248 Minkowski, Hermann 108, 114, 116, 211 MISPAR (a computer language) 4 modular arithmetic 9 Monbeig, M. 290 Montgomery, Hugh 254, 255–64, 267, 269–72, 275, 278, 307, 312 Mordell, Louis 258 Motchane, Léon 299, 303 music 77–9, 84, 125 ‘music of the spheres’ 77 of the primes 93–7, 310, 311 Riemann’s 278–9 Nachlass 151–153, 286–287 Napier, Baron John 46 Napoleon Bonaparte 17, 53, 57, 59, 60, 64, 78, 94, 96, 265, 266, 289, 299, 311 Nasar, Sylvia 304 Nash, John Forbes 304 National Bureau of Standards’ Institute for Numerical Analysis 207 National Physics Laboratory, Teddington, Middlesex 191 National Security Agency (NSA) (US) 12, 249 NATO 302 negative numbers 67–8, 68 neutrons 265, 268 Nevanlinna, Rolf 294 Neville, E.H. 139, 140–41 Newman, Max 183, 184, 186, 187, 191, 204,207 Newton, Sir Isaac 119, 123, 269 Noether, Emmy 194 non-communicative space of Adele classes 307 Norwegian Mathematical Society 157 Nth Fermat number 39 nucleus 264–5 Occam’s razor 215 Odlyzko, Andrew 220, 221–2, 221, 253, 254, 270, 271, 272, 275–6, 278, 279, 280, 312 Oppenheimer, Robert 263 parallel lines 109–10 particle accelerators 270 particle physics 4 partition function 143 partition numbers 141–3, 142, 158 Periodic Table of chemical elements 23, 32, 36, 224, 264, 265, 268 Peter the Great 41 physics 74, 84 pi (film) 28 Piazzi, Giuseppe 19 planetary orbits 188 Poincaré, Henri 1, 6 Pomerance, Carl 238–9, 240, 245 Prime Number Conjecture (later Theorem) see under Gauss, Carl Friedrich prime numbers: apparent randomness 5, 6, 7, 9, 47 and cicadas 27–8 definition 5 Fermat’s Little Theorem see under Fermat, Pierre de and Germany’s educational revolution 60 hunting for 38–41 importance to mathematics 5 infinity of 36, 76, 81, 106–7, 163, 205, 310 largest known 204, 205, 207, 208, 209 list of 5–6, 5, 22, 23, 24, 37, 199 and logarithms 46–9, 55, 62, 72, 74, 104, 105, 168, 206 and longevity 311–12 masters of disguise 130 music of 93–7, 310, 311 Riemann’s formula for the number of 89, 90–91, 90 story of primes as a social mirror 34 tables of 47–8, 48, 205–6 an unanswered riddle 314 probability theory 165, 166, 272, 313 Problem of the Bridges of Königsberg 43, 44, 106 Project Orion 263 protons 265, 268 Proust, Marcel 255 Prussia 59 Pryce, Maurice 187 Ptolemy I 36 Putnam, Hilary 198 Pythagoras 67, 77, 78, 93 Pythagoras’ theorem 67 quadratic sieve 238–9, 240 quantum billiards 275–80, 277, 282, 288 quantum chaos 279, 280, 281, 283, 298, 307, 311 quantum mechanics 279 quantum physics 4, 117, 166, 263, 264, 266, 267, 269, 273, 276, 280, 284, 286, 296, 305, 306, 307,311, 313 Rabin, Michael 245 Rademacher, Hans 158 Ramanujan, Srinivasa 27, 132–47, 133, 157–8, 164, 245, 262, 294 Ramanujan’s Tau Conjecture 16, 146 Rameau, Jean-Philippe 77 real numbers 68, 68, 69, 85 Redford, Robert 240 Reid, Legh Wilber 102 Ribenboim, Paulo 245 Riemann, Bernhard (main references) 63, 286–7 creates the Hypothesis 9 and Dirichlet 168 education 61–5, 72–5, 84 formula for number of primes 89, 90–91, 90 geometry 74, 113, 289, 307 imaginary numbers 66, 84, 88, 251, 286, 287 influences 61–2, 63, 66, 75–6, 82, 132 mathematical looking-glass 9, 90, 99, 167, 168 notebook 153–4 order out of chaos 97–101 paper on prime numbers 82–3, 84, 96, 100, 103, 106, 149, 150, 153 perfectionism 61, 82, 101 rescued notes 101, 151 Siegel discovers his secret formula 152–3, 213 succeeds Dirichlet 83, 100 visits Italy 100–101 and zeta function 81–2, 84–7, 137 Riemann, Elise (née Koch) 100, 101, 151 Riemann Hypothesis 33, 166, 176 assumed to be true 130, 131, 143 Bombieri’s interest see under Bombieri Cohen and 202 and commercial interest 11, 12 Connes’ work 3, 4, 288–289, 305, 307–9 Hilbert and 1–2, 114, 115, 243 importance 138–9 Landau’s criticism 149–50 a Millennium Problem 14, 15, 309–10, 312 probabilistic interpretation of 167 proof issue 4, 5, 9–10, 11, 14, 17, 18, 114–15, 159–60, 171–5, 178, 181, 182, 183, 188, 192, 196, 204, 212–16, 218–19, 222, 243, 245, 279, 281, 287, 288, 290, 294,297, 298, 301–2, 304, 307–10, 312,313 published 83 Selberg on 159–60, 173–4 Stieltjes’ claim 103 Rivest, Ron 11, 227–31, 229, 233–6, 238, 239, 242, 244, 249–50 Robinson, Julia 193–9, 195, 201, 202, 204, 205 Robinson, Raphael 196, 197, 207 Rota, Gian-Carlo 172 Royal Society 145, 189, 190 Computing Laboratory 191 RSA 12, 230, 231, 232, 235–9, 241–4, 246–50, 252, 253 ECC Central 249, 250 RSA 129 challenge 236–7, 239 RSA 155 challenge 240 Russell, Bertrand 128, 136, 138, 144, 178 Sacks, Oliver 8, 9, 39 Sagan, Carl 1, 7–8, 9, 28, 271, 280 Sarnak, Peter 127, 224, 281–3, 287, 296, 298, 307, 308, 309 Saxena, Nitin 245 Scandinavian Congress of Mathematicians (Copenhagen, 1946) 159 Schmalfuss (director of the Gymnasium Johanneum) 60–61, 63 Schneier, Bruce 242 Schoenberg, I.J. 154 Schrödinger, Erwin 284 Schwartz, Laurent 172 Science Museum, London 189 Second World War 154, 155–6, 160, 174, 175, 190, 192, 225, 241, 263, 289, 293–4 Selberg, trace formula 17 Selberg, Atle 16, 156–60, 157, 162, 167–74, 176, 177, 212–13, 261, 262, 263, 285, 288, 294, 295, 301–2, 307–8, 311–12 Severi, Francesco 296 Shamir, Adi 11, 228–9, 229, 230, 236, 238, 249 Shimura, Goro 298 Siegel, Carl Ludwig 148–9, 151–4, 156,188,213,251,297 Siegel zero 17 sieve of Eratosthenes 17, 23, 24, 239 Silverman, Joseph 250, 252, 253 sine function 72 sine waves 95, 96, 188 Skewes, Stanley 129, 130 Skewes Number 129 Slowinski, David 207, 208 Snaith, Nina 284, 285 Sneakers (film) 240, 242 Snow, C.P. 136–7, 147 space, as curved and non-Euclidean 128 spectroscopy 88, 224 Stalin, Joseph 293 Standards Western Automatic Computer (SWAC) 207 Stark, Harold 220, 221 Stieltjes, Thomas 102–5 string theory 306 super-symmetric fermionic-bosonic systems 4 Survive 303 Swinnerton-Dyer, Sir Peter 127, 250–52 Tarski, Alfred 197 te Riele, Herman 217, 218, 222 Teichmüller, Oswald 155 Thomson, J.J. 128 tides 188–9 Titchmarsh, Ted 188, 190, 192 triangular numbers 24–5, 26, 26, 29, 32, 52 trivial zeros 98 Trinity College, Cambridge 122–4, 124, 127–8, 144 Truman, Harry 172 Turán, Paul 169, 170 Turing, Alan 175–7, 177, 227 artificial intelligence 176 at Bell Laboratory 219 and the Enigma code 175, 190–91, 205, 206 and Hardy 187, 188 death 192 homosexuality 192 and the Riemann Hypothesis 175, 188, 191, 212 Turing machines 182–93, 197, 198, 199, 202–3, 204, 207, 213, 215 twin autistic-savants 8–9, 39 Twin Primes Conjecture 39, 181, 257, 258 uranium 268 van de Lune, Jan 219 Vernon, Dai 271–2 Vijayaraghavan 293, 294, 296 Wagner, Richard 59 Waring’s Problem 116 wave equation 266 Weber, Heinrich 154 Weber, Wilhelm 73–4 Weil, André 31, 180, 288–300, 293, 302, 305, 306, 308 Weyl, Hermann 160, 171 Wigner, Eugene 268–9, 270 Wiles, Andrew 4–5, 12–17, 29, 34, 115, 118, 171, 248, 251, 252, 282, 298, 313 William of Occam 215 Wittgenstein, Ludwig 128 Wolfskehl, Paul 15, 118 Wolfskehl Prize 15, 136 Woltman, George 208 Zagier, Don 213–19,214, 217, 252, 278 Zeilberger, Doron 309 zeta function 76–82, 84–6, 86, 88, 89, 128, 137, 144, 153, 158, 167, 168, 190, 220, 251, 258, 273, 283, 295 P.S. Ideas, interviews & features … About the Author * * * Portrait of Marcus du Sautoy Snapshot Top Ten Favourite Books About the Book * * * A Critical Eye Jerzy Grotowski Read On * * * If You Loved This, You’ll Like … Find Out More Bookshop About the Author Portrait of Marcus du Sautoy By Josh Lacey WHEN I MEET Marcus du Sautoy I take along one of the books which he discusses in The Music of the Primes and recommends in his ‘top ten’.
The Clash of the Cultures by John C. Bogle
asset allocation, collateralized debt obligation, corporate governance, corporate social responsibility, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, diversified portfolio, estate planning, Eugene Fama: efficient market hypothesis, financial innovation, financial intermediation, fixed income, Flash crash, Hyman Minsky, income inequality, index fund, interest rate swap, invention of the wheel, market bubble, market clearing, mortgage debt, new economy, Occupy movement, passive investing, Ponzi scheme, principal–agent problem, profit motive, random walk, rent-seeking, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, shareholder value, short selling, South Sea Bubble, statistical arbitrage, The Wealth of Nations by Adam Smith, transaction costs, Vanguard fund, William of Occam
Even earlier, in the first edition of his remarkable book A Random Walk Down Wall Street (1973), Princeton professor Burton G. Malkiel also issued a challenge for someone to start “a mutual fund that simply buys the hundreds of stocks making up the market averages.” Alas, I didn’t read his book until the early 1980s. 2 My thinking has long been informed by a fifteenth-century maxim known as Occam’s Razor (after English philosopher Sir William of Occam): When there are multiple solutions to a problem, pick the simplest one. 3 That high cost was justified by a Wells Fargo spokesperson because “we (the manager) can make a lot of money. The fund is our cash cow.” 4 The typical investor owns about four equity mutual funds; the typical fund manager lasts for five years. So in the course of, say, a 60-year investment lifetime, the investor’s portfolio will have been managed by almost 50 different managers.
., impact of change in P/E) They also forecast that “the return to the 10-year government bond over the next 10 years is just the yield on that bond.” While Grinold and Kroner failed to mention my 1991 publication that introduced essentially the same methodology more than a decade earlier, Professor Javier Estrada of the IESE Business School was extremely gracious in this regard. In his article from the journal Corporate Finance Review, “Investing in the Twenty-First Century: With Occam’s Razor and Bogle’s Wit,” he concluded “Sir William of Occam taught us to focus on the essentials, and Bogle showed us how to apply that lesson to forecasting the long-term returns of stock markets.4 Taking a cue from both, I evaluate the forecasting ability of two simple models, and show that they are surprisingly successful.” Also generous in recognizing my methodology are Princeton professor Burton G. Malkiel and professors Earl Benson and Sophie Kong of Western Washington University, along with investment analyst Ben D.
Mindware: Tools for Smart Thinking by Richard E. Nisbett
affirmative action, Albert Einstein, availability heuristic, big-box store, Cass Sunstein, choice architecture, cognitive dissonance, correlation coefficient, correlation does not imply causation, cosmological constant, Daniel Kahneman / Amos Tversky, dark matter, endowment effect, experimental subject, feminist movement, fundamental attribution error, glass ceiling, Henri Poincaré, Isaac Newton, job satisfaction, lake wobegon effect, libertarian paternalism, loss aversion, low skilled workers, Menlo Park, meta analysis, meta-analysis, quantitative easing, Richard Thaler, Ronald Reagan, Socratic dialogue, Steve Jobs, Steven Levy, the scientific method, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, William of Occam, Zipcar
Stich and his colleagues have shown that intuitions about the nature of the world, what one can call knowledge, and what one regards as moral can be so diverse across cultures and from individual to individual that it often makes no sense to appeal to a chimera called “our intuitions.”1 15. KISS and Tell We consider it a good principle to explain the phenomena by the simplest hypothesis possible. —Claudius Ptolemy It is futile to do with more things that which can be done with fewer. —William of Occam To the same natural effects we must, so far as possible, assign the same causes. —Isaac Newton Whenever possible, substitute constructions out of known entities for inferences to unknown entities. —Bertrand Russell What counts as knowledge, and what qualifies as an explanation, are two of the main questions discussed in this book. They are also central concerns for philosophers of science.
Smith, Adam social conflict social desirability bias social facilitation effect social psychology; context in; experiments in; founding of; fundamental attribution error in; microeconomics and; in political campaigns; reality in; social influence in Social Security Social Text Socrates Socratic dialogue Sokal, Alan South Carolina Soviet Union Speed (movie) Spender, Stephen Sperber, Dan spreading activation standard deviation (SD); for IQs; for observations Standard & Poor’s Stanford University; Graduate School of Business statistical dependence statistical heuristics statistical independence status quo stereotypes Stich, Stephen stimuli; incidental Stoic philosophers Stoler, Ann Structure of Scientific Revolutions, The (Kuhn) Subaru subliminal perception and persuasion Summers, Lawrence sunk costs Sunstein, Cass Sweden syllogisms Talmudic scholars Tanzania Tao Tennessee Texas text, reality as Thaler, Richard theology Thorndike, Edward Time magazine Towers of Hanoi problem Toyota tragedy of the commons training, transfer of traits; behaviors related to; correlations for; role-related “Transgressing the Boundaries” (Sokal) Triplett, Norman Turkish language Tversky, Amos Twain, Mark uncertainty unconscious mind; rational Unitarians United States; academic performance in; allergies in; autism diagnosis in; crime prevention programs in; death penalty in; dialectical thinking in; health issues in; history teachers in; homicide versus suicide deaths in; incarceration rate in; income ranges in; life insurance coverage in; manufacturing in; minority advancement in armed forces of; national election polls in; oil reserves of; per capita GDP in; pragmatism in; product choice in; Social Security program in; subjectivist view in; vaccination in; values and beliefs in vaccination validity; of arguments; reliability and value: expected; of human life; monetary, in cost-benefit analysis; sentimental; of sunk costs and opportunity costs Van Buren, Abigail (Dear Abby) variables; continuous; control; correlation of; economic; outcome; predictor; regression to the mean of; see also dependent variables; independent variables Varnum, Michael Venn, John Venn diagrams Vermont Volkswagen von Neuman, John Wall Street Journal, The Washington, University of Washington State Institute for Public Policy Western culture, difference between Eastern culture and, see cultural differences West Germany What Works Clearinghouse Whitehead, Alfred North William of Occam Wilson, Timothy within designs World Economic Forum Zajonc, Robert Zen Buddhism Zeno Zhang, Yitang Zipcars A NOTE ABOUT THE AUTHOR Richard E. Nisbett is Distinguished University Professor of Psychology at the University of Michigan and one of the world’s most respected psychologists. He has been awarded the Distinguished Scientific Contribution Award of the American Psychological Association and the William James Fellow Award for Distinguished Scientific Achievements of the Association for Psychological Science, among others.
Trend Following: How Great Traders Make Millions in Up or Down Markets by Michael W. Covel
Albert Einstein, asset allocation, Atul Gawande, backtesting, Bernie Madoff, Black Swan, buy low sell high, capital asset pricing model, Clayton Christensen, commodity trading advisor, correlation coefficient, Daniel Kahneman / Amos Tversky, delayed gratification, deliberate practice, diversification, diversified portfolio, Elliott wave, Emanuel Derman, Eugene Fama: efficient market hypothesis, fiat currency, fixed income, game design, hindsight bias, housing crisis, index fund, Isaac Newton, John Nash: game theory, linear programming, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, market fundamentalism, market microstructure, mental accounting, Nash equilibrium, new economy, Nick Leeson, Ponzi scheme, prediction markets, random walk, Renaissance Technologies, Richard Feynman, Richard Feynman, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, South Sea Bubble, Stephen Hawking, systematic trading, the scientific method, Thomas L Friedman, too big to fail, transaction costs, upwardly mobile, value at risk, Vanguard fund, volatility arbitrage, William of Occam
In any scientific realm, when a new set of data requires the creation of a new theory, many hypotheses are proposed, studied, and rejected. Yet, even when all unfit hypotheses are thrown out, several might remain, in some cases reaching the same end, but having different underlying assumptions. To choose among similar theories, scientists use Occam’s razor. Occam’s razor is a principle attributed to logician and Franciscan friar William of Occam. The principle states that entities must not be multiplied unnecessarily. In its original Latin form, Occam’s razor is “Pluralitas non est ponenda sine neccesitate.” This underlies all scientific modeling and theory building. A common interpretation of the principle is that the simplest of two or more competing theories is preferable.7 Occam’s razor does not guarantee that the simplest solution will be correct, but it does focus priorities. 213 We could still imagine that there is a set of laws that determines events completely for some supernatural being who could observe the present state of the universe without disturbing it.
., 40, 66, 243, 272 volatility, 99-105 measuring, 180 risk versus, 104 upside volatility, 102-105 Voltaire, xvii von Metternich, Klemens, 270 von Mises, Ludwig, xviii, 3, 97, 99, 202, 264 Wachtel, Larry, 235 Waksman, Sol, 253 Watts, Dickson, 92 Weaver, Earl, 182 web sites, 397 Weill, Sandy, 156 Weintraub, Neal T., 233 Wells, Herbert George (H.G.), 225 Welton, Patrick, 15 what to trade, 254-256 when to buy/sell, 259-262 whipsaws, 263 Wigdor, Paul, 126 Wilcox, Cole, 268, 307 William of Occam, 213 Williams, Ted, 261 winners Long-Term Capital Management (LTCM) collapse, 156-164 losers versus, 123-125 “The Winners and Losers of the Zero-Sum Game: The Origins of Trading Profits, Price Efficiency and Market Liquidity” (white paper) (Harris), 115 winning investment philosophies, 4-6 winning positions, when to exit, 263-265 Winton Capital Management, 29, 372-373 Winton Futures Fund, 230 “The Winton Papers” (Harding), 31 Wittgenstein, Ludwig, 395 Womack, Kent, 241 The World is Flat (Friedman), 143 WorldCom, 241 Wright, Charlie, 244 Yahoo!
Pathfinders: The Golden Age of Arabic Science by Jim Al-Khalili
agricultural Revolution, Albert Einstein, Andrew Wiles, Book of Ingenious Devices, colonial rule, Commentariolus, Dmitri Mendeleev, Eratosthenes, Henri Poincaré, invention of the printing press, invention of the telescope, invention of the wheel, Isaac Newton, Islamic Golden Age, Joseph Schumpeter, retrograde motion, Silicon Valley, Simon Singh, stem cell, Stephen Hawking, the scientific method, Thomas Malthus, trade route, William of Occam
But if so, what use is there for the original rays emitted by the eye? The light could come directly from the object if it is luminous, or be reflected from it if it is not. Thus, the rays from the eye are an unnecessary complication and should be dropped. In this way, he used a form of Occam’s Razor, the dictum that a phenomenon should be explained using as few assumptions as necessary, attributed to the fourteenth-century English philosopher William of Occam. But Ibn al-Haytham went further than philosophical arguments, for he did something quite astounding. He used Euclid’s geometrical model of the emission theory and applied it to the intromission theory. Now, it is rays emanating from the object that spread out radially in straight lines. In this way, he ‘mathematized’ his theory of vision. Interestingly, what he did not do, despite giving the first optical description of the camera obscura,12 was to connect this to the way the eye works (by projecting an inverted image of the objects we see onto the retina).
It would be wrong to dismiss completely any form of original scientific scholarship in Europe during the Islamic golden age, for there are always isolated pockets of intellectual activity and excellence wherever and whenever one looks in world history. Two notable lights and original thinkers who shone in the medieval darkness were the Italian Thomas Aquinas (c. 1225–74), and the Englishman William of Occam (c. 1288–1347). However, there were very few other Christian scholars whose achievements could rival their Muslim counterparts until the end of the fifteenth century and the arrival of Renaissance geniuses such as Leonardo da Vinci. By that time, European universities would have contained the Latin translations of the works of all the giants of Islam, such as Ibn Sīna, Ibn al-Haytham, Ibn Rushd, al-Rāzi, al-Khwārizmi and many others.
Infinite Ascent: A Short History of Mathematics by David Berlinski
Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Andrew Wiles, Benoit Mandelbrot, Douglas Hofstadter, Eratosthenes, four colour theorem, Georg Cantor, Gödel, Escher, Bach, Henri Poincaré, Isaac Newton, John von Neumann, Murray Gell-Mann, Stephen Hawking, Turing machine, William of Occam
But the Romans possessed no mathematical gift whatsoever, their incompetence as striking as it would have been had classical Greek culture given out directly to modern-day Rwanda or the Sudan. Mathematical curiosity died in the Roman Empire and it stayed dead in the Christian West for more than one thousand years. There were great theologians and philosophers, to be sure: the Church fathers, the Venerable Bede, Anselm, Abélard, Albertus Magnus, Thomas Aquinas, Duns Scotus, William of Occam; but no one on fire with the Pythagorean rapture, only men prepared indifferently to sift its ashes. In the great Moslem Empire that from the eighth century AD to the middle of the thirteenth century stretched from Spain in the west to the borders of India in the east, things were otherwise. Arabic was the language of literate men and women, the suave and supple intermediary between Greek and Latin antiquity and medieval Europe, and the perfumed city of Baghdad was their dimpled pleasure pool, the center of the Arab archipelago.
The Golden Ticket: P, NP, and the Search for the Impossible by Lance Fortnow
Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Andrew Wiles, Claude Shannon: information theory, cloud computing, complexity theory, Erdős number, four colour theorem, Gerolamo Cardano, Isaac Newton, John von Neumann, linear programming, new economy, NP-complete, Occam's razor, P = NP, Paul Erdős, Richard Feynman, Richard Feynman, smart grid, Stephen Hawking, traveling salesman, Turing machine, Turing test, Watson beat the top human players on Jeopardy!, William of Occam
, 33–34 one-time pad encryption, 129–30 On the Calculation with Hindu Numerals (al-Khwārizmī), 32 “On the Computational Complexity of Algorithms” (Hartmanis and Stearns), 76 “On the Impossibility of Constructing Minimal Disjunctive Normal Forms for Boolean Functions by Algorithms of a Certain Class” (Zhuravlev), 80 “On the Impossibility of Eliminating Perebor in Solving Some Problems of Circuit Theory” (Yablonsky), 80 OR, in logic, 52–53 OR gates, 79, 114, 114, 116, 116 P (polynomial): circuits size in, 116; efficiency in, 36; examples of, 46; meaning of, ix, 4 pad encryption, 129–30 parallel computing, 155, 156–58 partition into triangles problem, 59 partition puzzle, 4–5, 10 Pass the Rod, 37–38, 38, 39–40, 40, 45–46 “Paths, Trees, and Flowers” (Edmonds), 35–36, 76–77 perebor (Пepeбop), 71, 80 Perelman, Grigori, 7, 12 personalized recommendations, 23, 25 physics, NP problems in, 48, 48 Pippenger, Nicholas, 157 Pitts, Walter, 75 P = NC, 157–58 P = NP: big data and, 159; cryptography and, 129–30; imagined possibilities of, 12–19, 23–27; implications of, ix, 6, 9, 10, 46; importance of question, 46; likelihood of, 9, 28; meaning of, 4; NP-complete problems and, 59; proving, versus P ≠ NP, 120–21; random number generation and, 140; as satisfiability, 54–55; very cozy groups and, 104 P ≠ NP: attempts to prove, 118–21; implications of, ix–x, 46; meaning of, 4; mistakes in proving, 119–21; proving, 46, 57, 109–21, 161–62; very cozy groups and, 104 Poe, Edgar Allan, 124 Poincaré conjecture, 7 poker protocol, 137 polyalphabetic cipher, 124 polytope, 69–70, 70 prime numbers, 67–69, 129 privacy, and P = NP, 26–27 private-key cryptography, 26 probability theory, Kolmogorov and, 81–82, 167 products, in computations, 138 programs: contradictions in, 112; for hand control, 5–6 protein folding, 47–48 protein threading, 48 pseudorandomness, 140 public-key cryptography: factoring in, 140–41; P = NP and, 26, 127; randomness in, 136–37 public randomness, 136 P versus NP: circuit size in, 116; clique circuit computation and, 117; Eastern history of, 78–85; efficiency in, 36; future of, 155–62; Gödel’s description of, 85–86; hardest problems of, 55–57; history of, 6–7; as natural concept, 87; origin of problem, 54–55; paradox approach to, 112–13; parallel computing and, 157; resolving, 161–62; sources for technical formulation, 119; terminology used for, 58–59; Western history of, 72–78 quantum adiabatic systems, 147 quantum annealing, 147 quantum bits (qubits): copying, 148, 152; definition of, 144; dimensions of, 145; entanglement of, 145, 145, 147, 151, 151–52; transporting, 150, 150–53, 151, 152; values of, 145, 145 quantum computers: capabilities of, 9, 143, 146–47; future of, 153–54 quantum cryptography, 130, 148–49 quantum error-correction, 147 quantum states, observing, 146 quantum teleportation, 149–53, 150 randomness: creating, 139–40; public, 136 random sequences, 82–83 Razborov, Alexander, 85, 117–18 reduction, 54 relativity theory, 21 Rivest, Ronald, 127–28 robotic hand, 5–6 rock-paper-scissors, 139, 139 routes, finding shortest, 7–8 RSA cryptography, 127–28, 138 Rubik’s Cube, 64, 64 Rudich, Steven, 118 rule of thumb, 92 Salt, Veruca, 1–2, 157 satisfiability: cliques and, 54, 55; competition for, 96–97; as NP, 54–55 SAT Race, 96–97 Scherbius, Arthur, 124 Scientific American, 149–50 secret key cryptography, 126 security: of computer networks, 127; on Internet, 128–29 sensor data, 158 sentences, 75, 75–76 Seven Bridges of Königsberg puzzle, 38–39, 39 Shamir, Adi, 127–28 Shannon, Claude, 79 shared private keys, 129–30 shipping containers, 160–61 Shor, Peter, 146–47 simplex method, 69 simulations, data from, 158 Sipser, Michael, 117 Six Degrees of Kevin Bacon, 31–32 six degrees of separation, 30–33 Skynet effect, 13 small world phenomenon, 30–33 smart cards, finding key to, 106–7 social networking, and Frenemy relationships, 29 Solomonoff, Ray, 83 Soviet Union: genetics research in, 81; probability theory in, 81, 167 speeches, automated creation of, 24 sports broadcasting, 17–18 Sports Scheduling Group, 16 Stalin, Josef, 81 Stanford University, 126, 139 Stearns, Richard, 76 Steklov Mathematical Institute, 117 Stephenson, Henry and Holly, 16 strategy, and equilibrium states, 49 Sudoku: large games, 60, 60–61, 61; zero-knowledge, 130–36, 131, 132, 133, 134 sums, in computations, 138 Sun Microsystems, 160 Switzerland, 94, 94–95, 95 Symposium on the Complexity of Computer Computations, 78 Symposium on the Theory of Computing (STOC), 52 Tait, Peter, 42 technological innovations, dealing with, 160–61 technology, failure of, 161 teleportation, quantum, 149–53, 150 television, 3-D renderings used by, 17–18 Terminator movies, 13 Tetris, 63, 63 theoretical cybernetics, 79–85 tracking, over Internet, 159–60 Trakhtenbrot, Boris, 83–84 transistors, in circuits, 113 translation, 18, 23 traveling salesman problem: approximation of, 99–100, 100, 101; description of, 2–4, 3; size of problem, 91, 91 Tsinghua University, 12 Turing, Alan, 73–74; in computer science, 112; in Ultra, 125–26; work on Entscheidungs-problem, 49 Turing Award: for Blum, 78; for computational complexity, 76; naming of, 74; for P versus NP, 57, 85; for RSA cryptography, 128 Turing machine, 73, 73–74, 86–87 Turing test, 74 Twitter, 161 Ultra project, 124–25 unique games problem, 104 universal search algorithm, 84 universal search problems, 84–85 University of Chicago, 121 University of Illinois, 12–14 University of Montreal, 148 University of Oxford, 19–20 University of Toronto, 51 University of Washington, 5–6 Unofficial Guide to Disney World (Sehlinger and Testa), 56–57 Urbana algorithm, 12–19, 23–27 U.S. Combined DNA Index System (CODIS), 25–26 Vardi, Moshe, x vertex cover problem (very cozy group): approximating, 101–4, 102, 103; hardness of, 97, 97–99, 98 video games, automated creation of, 25 voice recognition, 23 Wallach, Eli, and Kevin Bacon, 31–32 Watson (computer), 156–57 weather prediction, 16 Wiles, Andrew, 7, 110 William of Occam, 19–20 Williamson, David, 45 wire, electric charge carried by, 113–14 workers, effect of P = NP on, 27 World War II, 125–26 Xbox, 25 Yablonsky, Sergey, 78, 79–80 zero-knowledge proofs, 131; for Sudoku, 130–36
The Eureka Factor by John Kounios
Albert Einstein, call centre, Captain Sullenberger Hudson, deliberate practice, en.wikipedia.org, Flynn Effect, Google Hangouts, impulse control, invention of the telephone, invention of the telescope, Isaac Newton, Louis Pasteur, meta analysis, meta-analysis, Necker cube, pattern recognition, Silicon Valley, Skype, Steve Jobs, theory of mind, Wall-E, William of Occam
It you want to have more insights, then it’s important to understand where they come from and how they arrive. This knowledge will help you to chart a reliable path to enhanced creativity. The second reason is more theoretical. Science aims for parsimony—never settle for a complicated explanation when a simple one will do the job. This is known as “Occam’s razor,” named after the fourteenth-century English scholar William of Occam. During the 1970s and ’80s, psychologists started to amass substantial evidence for the existence of gradually changing, or “continuous,” thought processes, but little support for truly sudden or “discrete” ones. In the interest of parsimony, some researchers questioned whether sudden cognitive processes exist. Insight, thought to be a quintessential sudden process, was not spared this scrutiny.
The Productive Programmer by Neal Ford
anti-pattern, business process, c2.com, continuous integration, database schema, domain-specific language, Firefox, general-purpose programming language, knowledge worker, side project, type inference, web application, William of Occam
Noticing what is essential may lead you toward abandoning something whose contribution to the real problem outweighs the amount of complexity it introduces to the overall problem. For example, you may think you need a data warehouse, but the amount of complexity it adds to the overall problem isn’t worth the benefits it might provide. You can never kill all accidental complexity with software, but you can continually try to minimize it. NOTE Maximize work on essential complexity; kill accidental complexity. Occam’s Razor Sir William of Occam was a monk who disdained ornate, elaborate explanations. His contribution to philosophy and science is known as Occam’s Razor, which says that given multiple explanations for something, the simplest is the most likely. Obviously, this ties in nicely with our discussion of essential versus accidental complexity. How far into the software stack this goes, however, is surprising. As an industry, we’ve been engaged in an experiment for the last decade or so.
Empire by Michael Hardt, Antonio Negri
Berlin Wall, Bretton Woods, collective bargaining, colonial rule, conceptual framework, discovery of the americas, Dissolution of the Soviet Union, equal pay for equal work, European colonialism, Fall of the Berlin Wall, feminist movement, Francis Fukuyama: the end of history, global village, Haight Ashbury, informal economy, invention of the printing press, invisible hand, labour mobility, late capitalism, low skilled workers, means of production, Monroe Doctrine, New Urbanism, open borders, Peace of Westphalia, post-industrial society, postindustrial economy, Scramble for Africa, The Wealth of Nations by Adam Smith, union organizing, urban planning, William of Occam
Just as in philosophy and science, in politics, too, humanity reappropriated in this early period of modernity what medieval transcendence had taken away from it. In the span of three or four centuries, the process of the refoundation of authority on the basis of a human universal and through the action of a multitude of singularities was accomplished with great force, amid dreadful tragedies and heroic conquests. William of Occam, for example, claimed that the church is the multitude of the faithful—‘‘Ecclesia est multitudo ﬁdelium’’9 —meaning that it is not superior to and distinct from the community of Christians but immanent to that community. Marsilius of Padua posed the same deﬁnition for the Republic: the power of the Republic and the power of its laws derive not from superior principles but from the assembly of citizens.10 A new understanding of power and a new conception of liberation were set in motion: from Dante and the late medieval apologia of the ‘‘possible intellect’’ to Thomas More and the celebration of the ‘‘immense and inexplicable power’’ of natural life and labor as foundation for the political arrangement; from the democracy of the Protestant sects to Spinoza and his notion of the absoluteness of the democracy.
., 249 truth, 155–156 tactics and strategy, 58–59, 63 Taylorism, 240, 242, 247–248, 255–256, 267–268, 383, 409 teleology, 51–52, 100, 165, 383; materialist, 63–66, 368, 395–396, 403–407, 470n25 temporality, 401–403 Thatcher, Margaret, 348 Third Worldism, 264 Third World versus First World, xiii, 253–254, 263–264, 333–335, 362–363 Thucydides, 182 Tiananmen Square events, 54, 56 Wallerstein, Immanuel, 334 Weber, Max, 41, 88–90, 340, 377 welfare state, 301 William of Occam, 73 Wilson, Woodrow, 174–176, 180, 242 Wittgenstein, Ludwig, 378–379 working class, industrial, 53, 256, 402 world market, 150–154, 190, 235–237, 251–256, 310, 332–335; construction of, 221–222, 346. See also delinking World War I, 233 World War II, 243 ultra-imperialism, 230–231 underdevelopment theories, 283–284 United Nations, 4–6, 8, 18, 31, 40, 132, 181, 309 U.S. constitutional history, phases of, 167–168 variable capital, 294, 405 Versailles Conference, 241 Vico, Giambattista, 100 Vietnam War, 178–179, 260, 275 Virgil, 167 virtual, 357–360, 366 Vogelfrei, 157–158 Zavattini, Cesare, 158
23andMe, airport security, Albert Einstein, Black Swan, Buckminster Fuller, carbon footprint, cognitive dissonance, Columbine, correlation does not imply causation, Dean Kamen, game design, Gary Taubes, index card, Kevin Kelly, knowledge economy, life extension, Mahatma Gandhi, microbiome, p-value, Parkinson's law, Paul Buchheit, placebo effect, Productivity paradox, publish or perish, Ralph Waldo Emerson, Ray Kurzweil, Richard Feynman, Richard Feynman, Silicon Valley, Silicon Valley startup, Skype, stem cell, Steve Jobs, Thorstein Veblen, wage slave, William of Occam
That’s 89 McDonald’s double cheeseburgers or 97 chicken breasts per day. Even with chicken breasts, poor Casey would have also gained an unfortunate 189 pounds of fat at the same time, according to the same math, leaving him looking like Cartman on “Weight Gain 4000.” 15. 1.7 g/kg * 56.7 kg * 80%. OCCAM’S PROTOCOL I A Minimalist Approach to Mass It is vain to do with more what can be done with less. —William of Occam (c. 1288–1348), “Occam’s Razor” 100 FEET OFFSHORE, MALIBU, CALIFORNIA I was sitting on my surfboard 20 feet to the side of Neil Strauss, bestselling author of The Game. The afternoon sun was shimmering off the rolling sets of blue water, and he was catching wave after wave. Me, not so much. In between bouts of falling into whitewash like an injured seal, I mentioned that my next book was a hacker’s guide to the human body.
., 14.1, 17.1 sucrose sugar substitutes, 8.1, 9.1 Sulis, Talulah, 19.1, 19.2, 19.3, 19.4 sun, exposure to Superhuman, Effortless superoxide dismutase (SOD) supine groin progressive, 25.1, 25.2, 25.3 supplements author’s regimen and insulin sensitivity in strength training for vegetarians, 47.1, 48.1 Swaraj Sweet Potatoes (recipe) swimming author’s tips breathing gear getting started stroke length Total Immersion, 34.1, 34.2 Szent-Gyorgyi, Albert T TA-65 (telomerase activator) Tabata protocol, 30.1, 31.1 Takeuchi, Shinji, 34.1, 34.2 Taleb, Nassim, 43.1, 43.2 Tapalla, Rudy Tarahumara Indians Tate, Dave, 30.1, 33.1 Taubes, Gary Taylor, Jeff tea, 9.1, 9.2, 10.1, 10.2 TEF (thermal effect of food) telomerase activators Tempeh Tacos (recipe) tensegrity testing, 40.1, 48.1 BioPhysical BodPod Cardio Lipid Panel Comprehensive Blood Panel DEXA for fertility Food Allergies Genetic Insights Inflammatory Markers insurance coverage, 40.1, 48.1 Liver Enzymes repeating SpectraCell Stool Analysis timing of Urine Toxic Metals ZRT at-home Vitamin D kits testosterone: and cell phones exogenous levels of, 21.1, 46.1 and nuts and pheromones production of Protocol #1 for Protocol #2 for and SHBG and steroids and women testosterone enanthate tetracycline T-handle theobromine theophylline thermodynamics thermogenics, 8.1, 46.1 Thomas, Kurt Thompson, Clive three-cone drill Thun, Michael thyme TI (Total Immersion), 34.1, 34.2 TI (total inches), 5.1, 6.1 tibialis anterior time under tension (TUT) tomatoes Torine, Jon, 27.1, 27.2 Torres, Dara Total Immersion (TI), 34.1, 34.2 total inches (TI), 5.1, 6.1 transfer Traumeel travel, and diet, 8.1, 47.1 Trevor triglycerides Tsatsouline, Pavel, 32.1, 32.2 tuna TUT (time under tension) Twain, Mark Tyler, Alison U ultrasound, 5.1, 5.2 Uno, Caol urine testing UV exposure V Valsalva Technique vampire myth Vanilla Walnut Protein Cookies (recipe) Van Voorhies, Wayne Veblen, Thorstein, 42.1 vegetables, 7.1, 8.1, 8.2 vegetarians: lacto-ovo mistakes of plant-based diet, 47.1, 48.1 and protein, 8.1, 47.1, 48.1 questions and concerns supplements for, 47.1, 48.1 and travel use of term Vergel, Nelson Vesper, scratches from vests, weighted Vetterlein, Ray Viator, Casey, 2.1, 16.1 vibrators vinegar vitamin A, 46.1, 46.2, 46.3 vitamin C vitamin D, 21.1, 46.1, 46.2 vitamin E vitamin K(2) vitamins, fat-soluble W waist-to-hip ratio (WHR) WakeMate walking, timed wall presses, 9.1, 9.2, 9.3 WAT (white adipose tissue) water: drinking gulping retention of thermal load of water weight Wegener, Alfred weight: fluctuations in gain (recipe) metric conversion Wells, H. G. West, Mae WHI (Women’s Health Initiative) WHR (waist-to-hip ratio) Wie, Michelle, 27.1, 27.2 Wilde, Oscar William of Occam Williams, Ted, 35.1, 37.1 Wilson, Clyde wine, 7.1, 8.1 and sleep Wired WOE (ways of eating) Wolfer, Lee, 1.1, 25.1, 25.2 women: fertility tests and menstruation, 8.1, 8.2, 21.1 orgasms of and testosterone Women’s Health Initiative (WHI) Wooden, John Y Yates, Dorian, 17.1, 17.2, 33.1 yerba mate tea yogurt yo-yo dieting Z Zaru, Nathan zdeel Zeiger, Roni Zeisel, Steven Zeo, 23.1, 23.2 Zepeda, Lydia Zobrist, Ben, 35.1, 35.2 ZRT at-home Vitamin D kits ABOUT THE AUTHOR TIMOTHY FERRISS, nominated as one of Fast Company’s “Most Innovative Business People of 2007,” is the author of the #1 New York Times, Wall Street Journal, and BusinessWeek bestseller The 4-Hour Workweek, which has been published in 35 languages.
Data Mining the Web: Uncovering Patterns in Web Content, Structure, and Usage by Zdravko Markov, Daniel T. Larose
Firefox, information retrieval, Internet Archive, iterative process, natural language processing, pattern recognition, random walk, recommendation engine, semantic web, speech recognition, statistical model, William of Occam
Both situations are undesirable in learning because neither the most general nor the least general hypothesis provides a meaningful description of the data that can be used for explanation or classiﬁcation. Minimum Description Length Principle After all these considerations a natural question comes in mind: Is there any connection between the simplicity of the hypothesis and the quality of the clustering it describes? Interestingly, there is a natural answer to this question, known as Occam’s razor. In the fourteenth century William of Occam formulated a very general principle stating that “Entities are not to be multiplied beyond necessity.” In other words, among several alternatives, the simplest is usually the best choice. Occam’s razor has proven its validity in many areas; however, its application to formal decision making such as clustering and classiﬁcation requires a formal deﬁnition of simplicity. The minimum description length (MDL) principle suggested by Rissanen  provides a formal framework for the application of Occam’s razor.
The 4-Hour Workweek: Escape 9-5, Live Anywhere, and Join the New Rich by Timothy Ferriss
Albert Einstein, Amazon Mechanical Turk, call centre, clean water, Donald Trump, en.wikipedia.org, Firefox, follow your passion, game design, global village, Iridium satellite, knowledge worker, late fees, Maui Hawaii, oil shock, paper trading, Parkinson's law, passive income, pre–internet, Ralph Waldo Emerson, remote working, Richard Feynman, risk tolerance, Ronald Reagan, side project, Silicon Valley, Silicon Valley startup, Skype, Steve Jobs, wage slave, William of Occam
It is not daily increase but daily decrease. The height of cultivation always runs to simplicity. —BRUCE LEE The End of Time Management ILLUSIONS AND ITALIANS Perfection is not when there is no more to add, but no more to take away. —ANTOINE DE SAINT-EXUPÉRY, pioneer of international postal flight and author of Le Petit Prince (The Little Prince) It is vain to do with more what can be done with less. —WILLIAM OF OCCAM (1300–1350), originator of “Occam’s Razor” Just a few words on time management: Forget all about it. In the strictest sense, you shouldn’t be trying to do more in each day, trying to fill every second with a work fidget of some type. It took me a long time to figure this out. I used to be very fond of the results-by-volume approach. Being busy is most often used as a guise for avoiding the few critically important but uncomfortable actions.
Day We Found the Universe by Marcia Bartusiak
Albert Einstein, Albert Michelson, Arthur Eddington, California gold rush, Cepheid variable, Copley Medal, cosmic microwave background, cosmological constant, Edmond Halley, Edward Charles Pickering, Fellow of the Royal Society, fudge factor, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, horn antenna, invention of the telescope, Isaac Newton, Louis Pasteur, Magellanic Cloud, Occam's razor, Pluto: dwarf planet, Solar eclipse in 1919, William of Occam
For Curtis the faint novae were bona fide proof that the nebulae resided far beyond the borders of the Milky Way. But Curtis was championing this idea too early, before the physics could explain it. Many of his fellow astronomers were still fairly skeptical, unwilling to conjure up new celestial creatures willy-nilly. For them “Occam's Razor” prevailed, the long-standing rule of thumb established by the English philosopher William of Occam in the fourteenth century. “Pluralitas non est ponenda sine necessitate,” declared Occam, which can be translated as “plurality must not be posited without necessity.” Best to choose the simplest interpretation over an unnecessarily complex one—unless forced to do otherwise. One type of nova was far more preferable than two. Arrows point to the novae discovered by Heber Curtis in photos of NGC-4321 taken in 1901 and 1914.
Big Bang by Simon Singh
Albert Einstein, Albert Michelson, All science is either physics or stamp collecting, Andrew Wiles, anthropic principle, Arthur Eddington, Astronomia nova, Brownian motion, carbon-based life, Cepheid variable, Chance favours the prepared mind, Commentariolus, Copley Medal, cosmic abundance, cosmic microwave background, cosmological constant, cosmological principle, dark matter, Dava Sobel, Defenestration of Prague, discovery of penicillin, Dmitri Mendeleev, Edmond Halley, Edward Charles Pickering, Eratosthenes, Ernest Rutherford, Erwin Freundlich, Fellow of the Royal Society, fudge factor, Hans Lippershey, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, Henri Poincaré, horn antenna, if you see hoof prints, think horses—not zebras, Index librorum prohibitorum, invention of the telescope, Isaac Newton, John von Neumann, Karl Jansky, Louis Daguerre, Louis Pasteur, luminiferous ether, Magellanic Cloud, Murray Gell-Mann, music of the spheres, Olbers’ paradox, On the Revolutions of the Heavenly Spheres, Paul Erdős, retrograde motion, Richard Feynman, Richard Feynman, scientific mainstream, Simon Singh, Solar eclipse in 1919, Stephen Hawking, the scientific method, Thomas Kuhn: the structure of scientific revolutions, unbiased observer, V2 rocket, Wilhelm Olbers, William of Occam
In fact, the only attribute of the Sun-centred model that made it clearly better than the Earth-centred model was still its simplicity. Although Copernicus did toy with epicycles, his model essentially employed a simple circular orbit for each planet, whereas Ptolemy’s model was inordinately complex, with its finely tuned epicycles, deferents, equants and eccentrics for each and every planet. Fortunately for Copernicus, simplicity is a prized asset in science, as had been pointed out by William of Occam, a fourteenth-century English Franciscan theologian who became famous during his lifetime for arguing that religious orders should not own property or wealth. He propounded his views with such fervour that he was run out of Oxford University and had to move to Avignon in the south of France, from where he accused Pope John XII of heresy. Not surprisingly, he was excommunicated. After succumbing to the Black Death in 1349, Occam became famous posthumously for his legacy to science, known as Occam’s razor, which holds that if there are two competing theories or explanations, then, all other things being equal, the simpler one is more likely to be correct.
The Beginning of Infinity: Explanations That Transform the World by David Deutsch
agricultural Revolution, Albert Michelson, anthropic principle, artificial general intelligence, Bonfire of the Vanities, conceptual framework, cosmological principle, dark matter, David Attenborough, discovery of DNA, Douglas Hofstadter, Eratosthenes, Ernest Rutherford, first-past-the-post, Georg Cantor, Gödel, Escher, Bach, illegal immigration, invention of movable type, Isaac Newton, Islamic Golden Age, Jacquard loom, Jacquard loom, John Conway, John von Neumann, Joseph-Marie Jacquard, Loebner Prize, Louis Pasteur, pattern recognition, Richard Feynman, Richard Feynman, Search for Extraterrestrial Intelligence, Stephen Hawking, supervolcano, technological singularity, The Coming Technological Singularity, the scientific method, Thomas Malthus, Thorstein Veblen, Turing test, Vernor Vinge, Whole Earth Review, William of Occam
Science would be impossible if it were not for the fact that the overwhelming majority of false theories can be rejected out of hand without any experiment, simply for being bad explanations. Good explanations are often strikingly simple or elegant – as I shall discuss in Chapter 14. Also, a common way in which an explanation can be bad is by containing superfluous features or arbitrariness, and sometimes removing those yields a good explanation. This has given rise to a misconception known as ‘Occam’s razor’ (named after the fourteenth-century philosopher William of Occam, but dating back to antiquity), namely that one should always seek the ‘simplest explanation’. One statement of it is ‘Do not multiply assumptions beyond necessity.’ However, there are plenty of very simple explanations that are nevertheless easily variable (such as ‘Demeter did it’). And, while assumptions ‘beyond necessity’ make a theory bad by definition, there have been many mistaken ideas of what is ‘necessary’ in a theory.