Pierre-Simon Laplace

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pages: 561 words: 120,899

The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant From Two Centuries of Controversy by Sharon Bertsch McGrayne

Bayesian statistics, bioinformatics, British Empire, Claude Shannon: information theory, Daniel Kahneman / Amos Tversky, double helix, Edmond Halley, Fellow of the Royal Society, full text search, Henri Poincaré, Isaac Newton, Johannes Kepler, John Markoff, John Nash: game theory, John von Neumann, linear programming, longitudinal study, meta analysis, meta-analysis, Nate Silver, p-value, Pierre-Simon Laplace, placebo effect, prediction markets, RAND corporation, recommendation engine, Renaissance Technologies, Richard Feynman, Richard Feynman: Challenger O-ring, Robert Mercer, Ronald Reagan, speech recognition, statistical model, stochastic process, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, Turing machine, Turing test, uranium enrichment, Yom Kippur War

For the next two centuries few read the Bayes-Price article. In the end, this is the story of two friends, Dissenting clergymen and amateur mathematicians, whose labor had almost no impact. Almost, that is, except on the one person capable of doing something about it, the great French mathematician Pierre Simon Laplace. 2. the man who did everything Just across the English Channel from Tunbridge Wells, about the time that Thomas Bayes was imagining his perfectly smooth table, the mayor of a tiny village in Normandy was celebrating the birth of a son, Pierre Simon Laplace, the future Einstein of his age. Pierre Simon, born on March 23, 1749, and baptized two days later, came from several generations of literate and respected dignitaries. His mother’s relatives were well-to-do farmers, but she died when he was young, and he never referred to her.

. ———. (1994) Le role de Laplace à l’École Polytechnique. In La Formation polytechnicienne, 1794–1994, eds., B. Belhoste, A. Dahan and A. Picon. Seyssel. ———. (1995) Lavoisier et ses collaborateurs: Une Équipe au Travail. In Il y a 200 Ans Lavoisier, ed., C. Demeulenaere-Douyère, Paris: Technique et Documentation Lavoisier. 55–63. ———. (2005) Pierre Simon Laplace, 1749–1827: A Determined Scientist. Harvard University Press; (2004) Le Système du Monde: Pierre Simon Laplace, Un Itinéraire dans la Science. Trans. Patrick Hersant. Éditions Gallimard. These are the same book, the original in English, the translation in French. These books are my primary sources for Laplace’s life. Hald, Anders. (1998) A History of Mathematical Statistics from 1750 to 1930. John Wiley and Sons. A classic. Hankins, Thomas L. (1970) Jean d’Alembert: Science and the Enlightenment.

To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. In the first-ever account of Bayes’ rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information, even breaking Germany’s Enigma code during World War II, and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes’ rule is used everywhere from DNA de-coding to Homeland Security.


pages: 634 words: 185,116

From eternity to here: the quest for the ultimate theory of time by Sean M. Carroll

Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, Brownian motion, cellular automata, Claude Shannon: information theory, Columbine, cosmic microwave background, cosmological constant, cosmological principle, dark matter, dematerialisation, double helix, en.wikipedia.org, gravity well, Harlow Shapley and Heber Curtis, Henri Poincaré, Isaac Newton, Johannes Kepler, John von Neumann, Lao Tzu, Laplace demon, lone genius, low earth orbit, New Journalism, Norbert Wiener, pets.com, Pierre-Simon Laplace, Richard Feynman, Richard Stallman, Schrödinger's Cat, Slavoj Žižek, Stephen Hawking, stochastic process, the scientific method, wikimedia commons

They are often portrayed as something relatively mundane: “Objects where the gravitational field is so strong that light itself cannot escape.” The reality is more interesting. Even in Newtonian gravity, there’s nothing to stop us from contemplating an object so massive and dense that the escape velocity is greater than the speed of light, rendering the body “black.” Indeed, the idea was occasionally contemplated, including by British geologist John Michell in 1783 and by Pierre-Simon Laplace in 1796.73 At the time, it wasn’t clear whether the idea quite made sense, as nobody knew whether light was even affected by gravity, and the speed of light didn’t have the fundamental importance it attains in relativity. More important, though, there is a very big distinction hidden in the seemingly minor difference between “an escape velocity greater than light” and “light cannot escape.”

Having laid sufficient groundwork, it’s time to confront the mystery of time’s direction head-on. PART THREE ENTROPY AND TIME’S ARROW 7 RUNNING TIME BACKWARD This is what I mean when I say I would like to swim against the stream of time: I would like to erase the consequences of certain events and restore an initial condition. —Italo Calvino, If on a Winter’s Night a Traveler Pierre-Simon Laplace was a social climber at a time when social climbing was a risky endeavor.102 When the French Revolution broke out, Laplace had established himself as one of the greatest mathematical minds in Europe, as he would frequently remind his colleagues at the Académie des Sciences. In 1793 the Reign of Terror suppressed the Académie; Laplace proclaimed his Republican sympathies, but he also moved out of Paris just to be safe.

It seems unlikely that Napoleon read the whole thing (or any of it), but someone at court did let him know that the name of God was entirely absent. Napoleon took the opportunity to mischievously ask, “M. Laplace, they tell me you have written this large book on the system of the universe, and have never even mentioned its Creator.” To which Laplace answered stubbornly, “I had no need of that hypothesis.”103 Figure 31: Pierre-Simon Laplace, mathematician, physicist, swerving politician, and unswerving determinist. One of the central tenets of Laplace’s philosophy was determinism. It was Laplace who truly appreciated the implications of Newtonian mechanics for the relationship between the present and the future: Namely, if you understood everything about the present, the future would be absolutely determined. As he put it in the introduction to his essay on probability: We may regard the present state of the universe as the effect of its past and the cause of its future.


pages: 523 words: 143,139

Algorithms to Live By: The Computer Science of Human Decisions by Brian Christian, Tom Griffiths

4chan, Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, algorithmic trading, anthropic principle, asset allocation, autonomous vehicles, Bayesian statistics, Berlin Wall, Bill Duvall, bitcoin, Community Supported Agriculture, complexity theory, constrained optimization, cosmological principle, cryptocurrency, Danny Hillis, David Heinemeier Hansson, delayed gratification, dematerialisation, diversification, Donald Knuth, double helix, Elon Musk, fault tolerance, Fellow of the Royal Society, Firefox, first-price auction, Flash crash, Frederick Winslow Taylor, George Akerlof, global supply chain, Google Chrome, Henri Poincaré, information retrieval, Internet Archive, Jeff Bezos, Johannes Kepler, John Nash: game theory, John von Neumann, Kickstarter, knapsack problem, Lao Tzu, Leonard Kleinrock, linear programming, martingale, Nash equilibrium, natural language processing, NP-complete, P = NP, packet switching, Pierre-Simon Laplace, prediction markets, race to the bottom, RAND corporation, RFC: Request For Comment, Robert X Cringely, Sam Altman, sealed-bid auction, second-price auction, self-driving car, Silicon Valley, Skype, sorting algorithm, spectrum auction, Stanford marshmallow experiment, Steve Jobs, stochastic process, Thomas Bayes, Thomas Malthus, traveling salesman, Turing machine, urban planning, Vickrey auction, Vilfredo Pareto, Walter Mischel, Y Combinator, zero-sum game

But thinking about the probabilities of probabilities can get a bit head-spinning. What’s more, if someone pressed us, “Well, fine, but what do you think the raffle odds actually are?” we still wouldn’t know what to say. The answer to this question—how to distill all the various possible hypotheses into a single specific expectation—would be discovered only a few years later, by the French mathematician Pierre-Simon Laplace. Laplace’s Law Laplace was born in Normandy in 1749, and his father sent him to a Catholic school with the intent that he join the clergy. Laplace went on to study theology at the University of Caen, but unlike Bayes—who balanced spiritual and scientific devotions his whole life—he ultimately abandoned the cloth entirely for mathematics. In 1774, completely unaware of the previous work by Bayes, Laplace published an ambitious paper called “Treatise on the Probability of the Causes of Events.”

Sampling In 1777, George-Louis Leclerc, Comte de Buffon, published the results of an interesting probabilistic analysis. If we drop a needle onto a lined piece of paper, he asked, how likely is it to cross one of the lines? Buffon’s work showed that if the needle is shorter than the gap between the blines, the answer is 2⁄π times the needle’s length divided by the length of the gap. For Buffon, deriving this formula was enough. But in 1812, Pierre-Simon Laplace, one of the heroes of chapter 6, pointed out that this result has another implication: one could estimate the value of π simply by dropping needles onto paper. Laplace’s proposal pointed to a profound general truth: when we want to know something about a complex quantity, we can estimate its value by sampling from it. This is exactly the kind of calculation that his work on Bayes’s Rule helps us to perform.

we need to first reason forward: To be precise, Bayes was arguing that given hypotheses h and some observed data d, we should evaluate those hypotheses by calculating the likelihood p(d|h) for each h. (The notation p(d|h) means the “conditional probability” of d given h—that is, the probability of observing d if h is true.) To convert this back into a probability of each h being true, we then divide by the sum of these likelihoods. Laplace was born in Normandy: For more details on Laplace’s life and work, see Gillispie, Pierre-Simon Laplace. distilled down to a single estimate: Laplace’s Law is derived by working through the calculation suggested by Bayes—the tricky part is the sum over all hypotheses, which involves a fun application of integration by parts. You can see a full derivation of Laplace’s Law in Griffiths, Kemp, and Tenenbaum, “Bayesian Models of Cognition.” From the perspective of modern Bayesian statistics, Laplace’s Law is the posterior mean of the binomial rate using a uniform prior.


pages: 317 words: 100,414

Superforecasting: The Art and Science of Prediction by Philip Tetlock, Dan Gardner

Affordable Care Act / Obamacare, Any sufficiently advanced technology is indistinguishable from magic, availability heuristic, Black Swan, butterfly effect, buy and hold, cloud computing, cuban missile crisis, Daniel Kahneman / Amos Tversky, desegregation, drone strike, Edward Lorenz: Chaos theory, forward guidance, Freestyle chess, fundamental attribution error, germ theory of disease, hindsight bias, index fund, Jane Jacobs, Jeff Bezos, Kenneth Arrow, Laplace demon, longitudinal study, Mikhail Gorbachev, Mohammed Bouazizi, Nash equilibrium, Nate Silver, Nelson Mandela, obamacare, pattern recognition, performance metric, Pierre-Simon Laplace, place-making, placebo effect, prediction markets, quantitative easing, random walk, randomized controlled trial, Richard Feynman, Richard Thaler, Robert Shiller, Robert Shiller, Ronald Reagan, Saturday Night Live, scientific worldview, Silicon Valley, Skype, statistical model, stem cell, Steve Ballmer, Steve Jobs, Steven Pinker, the scientific method, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Thomas Bayes, Watson beat the top human players on Jeopardy!

Edward Lorenz shifted scientific opinion toward the view that there are hard limits on predictability, a deeply philosophical question.4 For centuries, scientists had supposed that growing knowledge must lead to greater predictability because reality was like a clock—an awesomely big and complicated clock but still a clock—and the more scientists learned about its innards, how the gears grind together, how the weights and springs function, the better they could capture its operations with deterministic equations and predict what it would do. In 1814 the French mathematician and astronomer Pierre-Simon Laplace took this dream to its logical extreme: We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

A Presbyterian minister, educated in logic, Bayes was born in 1701, so he lived at the dawn of modern probability theory, a subject to which he contributed with “An Essay Towards Solving a Problem in the Doctrine of Chances.” That essay, in combination with the work of Bayes’ friend Richard Price, who published Bayes’ essay posthumously in 1761, and the insights of the great French mathematician Pierre-Simon Laplace, ultimately produced Bayes’ theorem. It looks like this: P(H|D)/P(-H|D) = P(D|H) • P(D|-H) • P(H)/P(-H) Posterior Odds = Likelihood Ratio • Prior Odds The Bayesian belief-updating equation In simple terms, the theorem says that your new belief should depend on two things—your prior belief (and all the knowledge that informed it) multiplied by the “diagnostic value” of the new information.

I submit that it is logically impossible to engage in policy advocacy (which pundits routinely do) without making assumptions about whether we would be better or worse off if we went down one or another policy path. Show me a pundit who does not make at least implicit forecasts and I will show you one who has faded into Zen-like irrelevance. 4. See James Gleick, Chaos: Making a New Science (New York: Viking, 1987); Donald N. McCloskey, “History, Differential Equations, and the Problem of Narration,” History and Theory 30 (1991): 21–36. 5. Pierre-Simon Laplace, A Philosophical Essay on Probabilities, trans. Frederick Wilson Truscott and Frederick Lincoln Emory (New York: Dover Publications, 1951), p. 4. 6. Yet even historians who should know better continue to make grand pronouncements like this one, by Oxford professor Margaret MacMillan, quoted in Maureen Dowd’s September 7, 2014, New York Times column: “the 21st century will be a series of low grade, very nasty wars that will go on and on without clear outcomes, doing dreadful things to any civilians in their paths”—a good summary of the recent past but a dubious guide to the world of 2083.


pages: 208 words: 70,860

Paradox: The Nine Greatest Enigmas in Physics by Jim Al-Khalili

Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, butterfly effect, clockwork universe, complexity theory, dark matter, Edmond Halley, Edward Lorenz: Chaos theory, Ernest Rutherford, Henri Poincaré, invention of the telescope, Isaac Newton, Johannes Kepler, Laplace demon, luminiferous ether, Magellanic Cloud, Olbers’ paradox, Pierre-Simon Laplace, Schrödinger's Cat, Search for Extraterrestrial Intelligence, The Present Situation in Quantum Mechanics, Wilhelm Olbers

“Prediction is very difficult, especially about the future.” So said the Danish quantum physicist Niels Bohr. The quote might sound trite and frivolous, but hidden behind it, as was so often the case with the utterances of Bohr, are profound ideas about the nature of fate, free will, and our ability to determine how the future will unfold. Let me first set up the paradox. The French mathematician Pierre-Simon Laplace devised his own imaginary demon half a century before Maxwell proposed his. Laplace’s demon is far more powerful than Maxwell’s since it has the ability to know the exact position and state of motion not merely of every air molecule in a box, but of every particle in the Universe, and fully understands the laws of physics that describe how they interact with each other. This means that, in principle, such an all-knowing demon could work out how the Universe will evolve over time and be able to predict its state in the future.

And when it comes to the workings of the human brain, no one can be sure when the next breakthrough will come. It might even turn out that the probabilistic nature of the quantum world does indeed have a direct impact on the world of the very large, particularly inside living cells, and possibly the brain. We may have resolved the Paradox of Laplace’s Demon; but in doing so we have not answered all these questions. 3 Pierre-Simon Laplace, A Philosophical Essay on Probabilities (1814), trans. F. W. Truscott and F. L. Emory, 6th ed. (New York: Dover, 1951), p. 4. 9 THE PARADOX OF SCHRÖDINGERS CAT The cat in the box is both dead and alive—until we look. In 1935 one of the founders of quantum mechanics, the Austrian genius Erwin Schrödinger, had had enough of the weird interpretations of its mathematics. Following lengthy discussions with, among others, Albert Einstein himself, he proposed one of the most famous thought experiments in the history of science.


pages: 829 words: 186,976

The Signal and the Noise: Why So Many Predictions Fail-But Some Don't by Nate Silver

"Robert Solow", airport security, availability heuristic, Bayesian statistics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, big-box store, Black Swan, Broken windows theory, business cycle, buy and hold, Carmen Reinhart, Claude Shannon: information theory, Climategate, Climatic Research Unit, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, complexity theory, computer age, correlation does not imply causation, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, Daniel Kahneman / Amos Tversky, diversification, Donald Trump, Edmond Halley, Edward Lorenz: Chaos theory, en.wikipedia.org, equity premium, Eugene Fama: efficient market hypothesis, everywhere but in the productivity statistics, fear of failure, Fellow of the Royal Society, Freestyle chess, fudge factor, George Akerlof, global pandemic, haute cuisine, Henri Poincaré, high batting average, housing crisis, income per capita, index fund, information asymmetry, Intergovernmental Panel on Climate Change (IPCC), Internet Archive, invention of the printing press, invisible hand, Isaac Newton, James Watt: steam engine, John Nash: game theory, John von Neumann, Kenneth Rogoff, knowledge economy, Laplace demon, locking in a profit, Loma Prieta earthquake, market bubble, Mikhail Gorbachev, Moneyball by Michael Lewis explains big data, Monroe Doctrine, mortgage debt, Nate Silver, negative equity, new economy, Norbert Wiener, PageRank, pattern recognition, pets.com, Pierre-Simon Laplace, prediction markets, Productivity paradox, random walk, Richard Thaler, Robert Shiller, Robert Shiller, Rodney Brooks, Ronald Reagan, Saturday Night Live, savings glut, security theater, short selling, Skype, statistical model, Steven Pinker, The Great Moderation, The Market for Lemons, the scientific method, The Signal and the Noise by Nate Silver, The Wisdom of Crowds, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, too big to fail, transaction costs, transfer pricing, University of East Anglia, Watson beat the top human players on Jeopardy!, wikimedia commons

Isaac Newton’s mechanics had seemed to suggest that the universe was highly orderly and predictable, abiding by relatively simple physical laws. The idea of scientific, technological, and economic progress—which by no means could be taken for granted in the centuries before then—began to emerge, along with the notion that mankind might learn to control its own fate. Predestination was subsumed by a new idea, that of scientific determinism. The idea takes on various forms, but no one took it further than Pierre-Simon Laplace, a French astronomer and mathematician. In 1814, Laplace made the following postulate, which later came to be known as Laplace’s Demon: We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.13 Given perfect knowledge of present conditions (“all positions of all items of which nature is composed”), and perfect knowledge of the laws that govern the universe (“all forces that set nature in motion”), we ought to be able to make perfect predictions (“the future just like the past would be present”).

Probability and Progress We might notice how similar this claim is to the one that Bayes made in “Divine Benevolence,” in which he argued that we should not confuse our own fallibility for the failures of God. Admitting to our own imperfections is a necessary step on the way to redemption. However, there is nothing intrinsically religious about Bayes’s philosophy.27 Instead, the most common mathematical expression of what is today recognized as Bayes’s theorem was developed by a man who was very likely an atheist,28 the French mathematician and astronomer Pierre-Simon Laplace. Laplace, as you may remember from chapter 4, was the poster boy for scientific determinism. He argued that we could predict the universe perfectly—given, of course, that we knew the position of every particle within it and were quick enough to compute their movement. So why is Laplace involved with a theory based on probabilism instead? The reason has to do with the disconnect between the perfection of nature and our very human imperfections in measuring and understanding it.

“The Weatherman,” Curb Your Enthusiasm, season 4, episode 4, HBO, January. 25, 2004. 10. joesixpacker, “The Mitt Romney Weathervane,” YouTube, December. 24, 2011. http://www.youtube.com/watch?v=PWPxzDd661M. 11. Willis I. Milham, Meteorology. A Text-Book on the Weather, the Causes of Its Changes, and Weather Forecasting for the Student and General Reader (New York: Macmillan, 1918). 12. Aristotle, Meteorology, translated by E. W. Webster. Internet Classics Archive. http://classics.mit.edu/Aristotle/meteorology.html. 13. Pierre-Simon Laplace, “A Philosophical Essay on Probabilities” (Cosmo Publications, 2007). 14. The uncertainty principle should not be confused with the observer effect, which is the idea that the act of measuring a system (such as shooting a laser beam at a particle of light) necessarily disrupts it. The two beliefs are not inherently incompatible—but the uncertainty principle is a stronger statement and is not so satisfyingly intuitive.


pages: 105 words: 18,832

The Collapse of Western Civilization: A View From the Future by Naomi Oreskes, Erik M. Conway

anti-communist, correlation does not imply causation, creative destruction, en.wikipedia.org, energy transition, Intergovernmental Panel on Climate Change (IPCC), invisible hand, laissez-faire capitalism, market fundamentalism, mass immigration, means of production, oil shale / tar sands, Pierre-Simon Laplace, road to serfdom, Ronald Reagan, stochastic process, the built environment, the market place

Overwhelmingly male, they emphasized study of the world’s physical constituents and processes—the elements and compounds; atomic, magnetic, and gravitational forces; chemical reactions, flows of air and water—to the neglect of biological and social realms and focused on reductionist methodologies that impeded understanding of the crucial interactions between the physical, biological, and social realms. positivism The intellectual philosophy, promoted in the late nineteenth century by the French sociologist Auguste Comte (but also associated with earlier thinkers such as Francis Bacon and Pierre Simon LaPlace and later thinkers such as Ernst Mach and A. J. Ayer), which stressed that reliable knowledge must be grounded in observation. Statements that could not be tested through observation were considered to be outside the realm of “positive knowledge”— or science—and this included most metaphysical and religious claims. Logical positivists (sometimes also referred to as logical empiricists) stressed the linguistic aspects of this problem and focused on finding theoretically neutral means to articulate observation statements.


pages: 348 words: 83,490

More Than You Know: Finding Financial Wisdom in Unconventional Places (Updated and Expanded) by Michael J. Mauboussin

Albert Einstein, Andrei Shleifer, Atul Gawande, availability heuristic, beat the dealer, Benoit Mandelbrot, Black Swan, Brownian motion, butter production in bangladesh, buy and hold, capital asset pricing model, Clayton Christensen, clockwork universe, complexity theory, corporate governance, creative destruction, Daniel Kahneman / Amos Tversky, deliberate practice, demographic transition, discounted cash flows, disruptive innovation, diversification, diversified portfolio, dogs of the Dow, Drosophila, Edward Thorp, en.wikipedia.org, equity premium, Eugene Fama: efficient market hypothesis, fixed income, framing effect, functional fixedness, hindsight bias, hiring and firing, Howard Rheingold, index fund, information asymmetry, intangible asset, invisible hand, Isaac Newton, Jeff Bezos, Kenneth Arrow, Laplace demon, Long Term Capital Management, loss aversion, mandelbrot fractal, margin call, market bubble, Menlo Park, mental accounting, Milgram experiment, Murray Gell-Mann, Nash equilibrium, new economy, Paul Samuelson, Pierre-Simon Laplace, quantitative trading / quantitative finance, random walk, Richard Florida, Richard Thaler, Robert Shiller, Robert Shiller, shareholder value, statistical model, Steven Pinker, stocks for the long run, survivorship bias, The Wisdom of Crowds, transaction costs, traveling salesman, value at risk, wealth creators, women in the workforce, zero-sum game

Investors who insist on understanding the causes for the market’s moves risk focusing on faulty causality or inappropriately anchoring on false explanations. Many of the big moves in the market are not easy to explain. Laplace’s Demon Two hundred years ago, determinism ruled in science. Inspired by Newton, scientists largely embraced the notion of a clockwork universe. The French mathematician Pierre Simon Laplace epitomized this thinking with a famous passage from A Philosophical Essay on Probabilities:An intellect which at any given moment knew all of the forces that animate Nature and the mutual positions of the beings that comprise it, if this intellect were vast enough to submit its data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom: for such an intellect nothing could be uncertain; and the future just like the past would be present before its eyes.

See also psychology of investing investment process investment profession investors: average holding period diversity of evolution of understanding of power laws Iowa Electronic Markets (IEM) janitor’s dream jellybean-jar experiment Johnson, Norman judgment Kahneman, Daniel; decision-making model Kaplan, Sarah Karceski, Jason Kasparov, Garry Kaufman, Peter Keynes, John Maynard Knight, Frank Krugman, Paul kurtosis lack of representation Lakonishok, Joseph Laplace, Pierre Simon Laplace’s demon leader/challenger dynamics LeDoux, Joseph Legg Mason Value Trust Leinweber, David Lev, Baruch Lewis, Michael life cycle: clockspeed of companies of fruit flies of industries liking limited-time offers linear models lions liquidity lollapalooza effects long term, management for strategies for winners strategy as simple rules Long Term Capital Management long-term investment, loss aversion and Lorie, James loss, risk and loss aversion equity-risk premium exhibits myopic portfolio turnover ratio of risk to reward utility lottery players Lowenstein, Roger luck MacGregor, Donald G.


pages: 283 words: 81,376

The Doomsday Calculation: How an Equation That Predicts the Future Is Transforming Everything We Know About Life and the Universe by William Poundstone

Albert Einstein, anthropic principle, Any sufficiently advanced technology is indistinguishable from magic, Arthur Eddington, Bayesian statistics, Benoit Mandelbrot, Berlin Wall, bitcoin, Black Swan, conceptual framework, cosmic microwave background, cosmological constant, cosmological principle, cuban missile crisis, dark matter, digital map, discounted cash flows, Donald Trump, Doomsday Clock, double helix, Elon Musk, Gerolamo Cardano, index fund, Isaac Newton, Jaron Lanier, Jeff Bezos, John Markoff, John von Neumann, mandelbrot fractal, Mark Zuckerberg, Mars Rover, Peter Thiel, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, Richard Feynman, ride hailing / ride sharing, Rodney Brooks, Ronald Reagan, Ronald Reagan: Tear down this wall, Sam Altman, Schrödinger's Cat, Search for Extraterrestrial Intelligence, self-driving car, Silicon Valley, Skype, Stanislav Petrov, Stephen Hawking, strong AI, Thomas Bayes, Thomas Malthus, time value of money, Turing test

Had the chosen ball been number 11 or higher, then he could have deduced, with ironclad certainty, that the draw was from the urn with a thousand balls. But there’s a ball number 7 in both urns. The evidence supplied by drawing a number 7 ball is circumstantial but not to be neglected by any fully reasonable party. “Rational belief is constrained,” Nick Bostrom wrote, “not only by chains of deduction but also by the rubber bands of probabilistic inference.” Doubting Thomas Bayes’s Essay found a most influential reader. He was Pierre-Simon Laplace (1749–1827), a French marquis, mathematician, physicist, astronomer, and atheist. Laplace slapped Bayes’s wreck of a paper into rigorous math. There are those who judge Laplace to be the true originator of Bayesian probability, leaving Bayes as simply a brand. Everyone read Laplace. But Laplace’s enthusiasm for the probability of causes couldn’t change reality. In the simplest instances Bayes’s result was obvious even without the math.

In certain troublesome cases like the Presumptuous Philosopher, Occam’s razor might lead one to discount the effect of SIA and vice versa. Still, it’s not always clear how to apply Occam’s razor (or SIA). What if a relatively simple theory, well grounded in evidence, predicts an infinity of observers? That’s not a hypothetical question for today’s cosmologists. Tarzan Meets Jane The theory of probability is, in the most profound way, only common sense reduced to calculus.” So wrote Pierre-Simon Laplace in 1814. The historical record paints a murkier picture. Probability theory can be a quagmire with no firm footing. It has entrapped many of the smartest people who ever lived. Gottfried Leibniz was the universal genius who invented calculus, independently of Newton, and who inspired Voltaire’s consummate know-it-all, Dr. Pangloss. Leibniz believed that throwing an 11 with dice was just as likely as throwing a 12.


pages: 310 words: 89,653

The Interstellar Age: Inside the Forty-Year Voyager Mission by Jim Bell

Albert Einstein, crowdsourcing, dark matter, Edmond Halley, Edward Charles Pickering, en.wikipedia.org, Eratosthenes, gravity well, Isaac Newton, Johannes Kepler, Kuiper Belt, Mars Rover, Pierre-Simon Laplace, planetary scale, Pluto: dwarf planet, polynesian navigation, Ronald Reagan, Saturday Night Live, Search for Extraterrestrial Intelligence, Stephen Hawking

That is, like the hour, minute, and second hands of a clock, those three worlds occasionally line up with one another, and thus their gravitational attractions nudge them each away from what would otherwise be perfectly circular orbits. Each of them, then, is sometimes slightly closer to or slightly farther from Jupiter than usual. The mathematics of the orbital resonance of Io, Europa, and Ganymede had been worked out in detail around 1800 by the French astronomer Pierre-Simon Laplace (indeed, the resonance is named after him). But the implications of the Laplace resonance weren’t fully appreciated until just before the Voyagers arrived at Jupiter. In fact, in a scientific publication intentionally timed to appear in print just three days before Voyager 1’s flyby, a team of three celestial mechanics experts led by Stan Peale of UC Santa Barbara published a prediction in Science magazine that the resonance that was slightly changing the inner Galilean satellites’ distances from Jupiter would result in a gentle squeezing and relaxing of their interiors.

When my colleagues on the navigation team at JPL, for example, want to study a possible trajectory for a new space mission, they load their computers with the positions and masses of the sun, all the planets and their fifty or so large moons, and more than a half million asteroids, to make sure that every single possible “perturber” of the spacecraft is taken into consideration in their calculations. When astronomers and mathematicians like Edmond Halley and Pierre-Simon Laplace were working out the theory of motions of comets and asteroids, they were working on what physicists call the three-body problem, for example needing to account for the gravity and motions of the sun, Jupiter, and one of the Galilean satellites; or maybe the sun, Jupiter, and a newly discovered comet. Today’s more sophisticated computer modeling of solar-system motions search for solutions to what is known as the n-body problem, whereby n is some very large number of objects.


pages: 343 words: 102,846

Trees on Mars: Our Obsession With the Future by Hal Niedzviecki

"Robert Solow", Ada Lovelace, agricultural Revolution, Airbnb, Albert Einstein, anti-communist, big data - Walmart - Pop Tarts, big-box store, business intelligence, Colonization of Mars, computer age, crowdsourcing, David Brooks, Elon Musk, en.wikipedia.org, Erik Brynjolfsson, Flynn Effect, Google Glasses, hive mind, Howard Zinn, if you build it, they will come, income inequality, Internet of things, invention of movable type, Jaron Lanier, Jeff Bezos, job automation, John von Neumann, knowledge economy, Kodak vs Instagram, life extension, Lyft, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Peter H. Diamandis: Planetary Resources, Peter Thiel, Pierre-Simon Laplace, Ponzi scheme, precariat, prediction markets, Ralph Nader, randomized controlled trial, Ray Kurzweil, ride hailing / ride sharing, rising living standards, Ronald Reagan, self-driving car, shareholder value, sharing economy, Silicon Valley, Silicon Valley startup, Skype, Steve Jobs, TaskRabbit, technological singularity, technoutopianism, Ted Kaczynski, Thomas L Friedman, Uber and Lyft, uber lyft, working poor

She went on: “This is the most general definition, and would include all subjects in the universe.”18 Lovelace, dubbed everything from “the prophet of the computer age” to “the enchantress of numbers,” had that rare combination of mathematical genius and inherited gift for language; as a result she had a vision for what a language of pure information could make possible—just about anything. She writes with beauty and scope about the information landscape to come: “A new, a vast, and a powerful language is developed . . . in which to wield its truths so that these may become of more speedy and accurate practical application for the purposes of mankind than the means hitherto in our possession have rendered possible.”19 Around the same time, Pierre-Simon Laplace, the great French astronomer and mathematician, an advocate for Newtonian principles, wrote of a new kind of “intelligence” that “would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.”20 Uncertainty banished. The future brought under our control.

Martin Davis, The Universal Computer: The Road from Leibniz to Turing, Turing centenary ed (Boca Raton, Fla: CRC Press, 2012), 16. 16. George Dyson, Turing’s Cathedral: The Origins of the Digital Universe, 1st ed (New York: Pantheon Books, 2012), 104. 17. Ibid., 105. 18. Charles Babbage, Charles Babbage and His Calculating Engines: Selected Writings (Dover Publications, 1961), 247. 19. Ibid., 252. 20. Pierre-Simon Laplace, A Philosophical Essay on Probabilities (Wiley, 1902). 21. Dyson, Turing’s Cathedral, 2012, 130. 22. “The Atlantic Telegraph,” The New York Times, August 6, 1858. 23. Marshall McLuhan, Understanding Media: The Extensions of Man, 1st MIT Press ed (Cambridge, Mass: MIT Press, 1994). 24. John Archibald Wheeler, “It from Bit,” in At Home in the Universe: The Search for Laws of Self-Organization and Complexity, ed.


pages: 416 words: 112,268

Human Compatible: Artificial Intelligence and the Problem of Control by Stuart Russell

3D printing, Ada Lovelace, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Alfred Russel Wallace, Andrew Wiles, artificial general intelligence, Asilomar, Asilomar Conference on Recombinant DNA, augmented reality, autonomous vehicles, basic income, blockchain, brain emulation, Cass Sunstein, Claude Shannon: information theory, complexity theory, computer vision, connected car, crowdsourcing, Daniel Kahneman / Amos Tversky, delayed gratification, Elon Musk, en.wikipedia.org, Erik Brynjolfsson, Ernest Rutherford, Flash crash, full employment, future of work, Gerolamo Cardano, ImageNet competition, Intergovernmental Panel on Climate Change (IPCC), Internet of things, invention of the wheel, job automation, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, John Nash: game theory, John von Neumann, Kenneth Arrow, Kevin Kelly, Law of Accelerating Returns, Mark Zuckerberg, Nash equilibrium, Norbert Wiener, NP-complete, openstreetmap, P = NP, Pareto efficiency, Paul Samuelson, Pierre-Simon Laplace, positional goods, probability theory / Blaise Pascal / Pierre de Fermat, profit maximization, RAND corporation, random walk, Ray Kurzweil, recommendation engine, RFID, Richard Thaler, ride hailing / ride sharing, Robert Shiller, Robert Shiller, Rodney Brooks, Second Machine Age, self-driving car, Shoshana Zuboff, Silicon Valley, smart cities, smart contracts, social intelligence, speech recognition, Stephen Hawking, Steven Pinker, superintelligent machines, Thales of Miletus, The Future of Employment, Thomas Bayes, Thorstein Veblen, transport as a service, Turing machine, Turing test, universal basic income, uranium enrichment, Von Neumann architecture, Wall-E, Watson beat the top human players on Jeopardy!, web application, zero-sum game

Often, the utility of a sequence of states is expressed as a sum of rewards for each of the states in the sequence. Given a purpose defined by a utility or reward function, the machine aims to produce behavior that maximizes its expected utility or expected sum of rewards, averaged over the possible outcomes weighted by their probabilities. Modern AI is partly a rebooting of McCarthy’s dream, except with utilities and probabilities instead of goals and logic. Pierre-Simon Laplace, the great French mathematician, wrote in 1814, “The theory of probabilities is just common sense reduced to calculus.”57 It was not until the 1980s, however, that a practical formal language and reasoning algorithms were developed for probabilistic knowledge. This was the language of Bayesian networks,C introduced by Judea Pearl. Roughly speaking, Bayesian networks are the probabilistic cousins of propositional logic.

For example, Shakey believed that by executing “push object A through door D into room B,” object A would end up in room B. This belief was false because Shakey could get stuck in the doorway or miss the doorway altogether or someone might sneakily remove object A from Shakey’s grasp. Shakey’s plan execution module could detect plan failure and replan accordingly, so Shakey was not, strictly speaking, a purely logical system. 57. An early commentary on the role of probability in human thinking: Pierre-Simon Laplace, Essai philosophique sur les probabilités (Mme. Ve. Courcier, 1814). 58. Bayesian logic described in a fairly nontechnical way: Stuart Russell, “Unifying logic and probability,” Communications of the ACM 58 (2015): 88–97. The paper draws heavily on the PhD thesis research of my former student Brian Milch. 59. The original source for Bayes’ theorem: Thomas Bayes and Richard Price, “An essay towards solving a problem in the doctrine of chances,” Philosophical Transactions of the Royal Society of London 53 (1763): 370–418. 60.


pages: 137 words: 36,231

Information: A Very Short Introduction by Luciano Floridi

agricultural Revolution, Albert Einstein, bioinformatics, carbon footprint, Claude Shannon: information theory, conceptual framework, double helix, Douglas Engelbart, Douglas Engelbart, George Akerlof, Gordon Gekko, industrial robot, information asymmetry, intangible asset, Internet of things, invention of writing, John Nash: game theory, John von Neumann, Laplace demon, moral hazard, Nash equilibrium, Nelson Mandela, Norbert Wiener, Pareto efficiency, phenotype, Pierre-Simon Laplace, prisoner's dilemma, RAND corporation, RFID, Thomas Bayes, Turing machine, Vilfredo Pareto

The problem is that, if this were true, the universe would `run out of memory' because, as Philip Ball has remarked: To simulate the Universe in every detail since time began, the computer would have to have 109° bits - binary digits, or devices capable of storing a I or a 0 - and it would have to perform 10120 manipulations of those bits. Unfortunately there are probably only around 1080 elementary particles in the Universe. Moreover, if the world were a computer, this would imply the total predictability of its developments and the resuscitation of another demon, that of Laplace. Pierre-Simon Laplace (1749-1827), one of the founding fathers of mathematical astronomy and statistics, suggested that if a hypothetical being (known as Laplace's demon) could have all the necessary information about the precise location and momentum of every atom in the universe, he could then use Newton's laws to calculate the entire history of the universe. This extreme form of determinism was still popular in the 19th century, but in the 20th century was undermined by the ostensibly probabilistic nature of quantum phenomena.


pages: 147 words: 39,910

The Great Mental Models: General Thinking Concepts by Shane Parrish

Albert Einstein, Atul Gawande, Barry Marshall: ulcers, bitcoin, Black Swan, colonial rule, correlation coefficient, correlation does not imply causation, cuban missile crisis, Daniel Kahneman / Amos Tversky, dark matter, delayed gratification, feminist movement, index fund, Isaac Newton, Jane Jacobs, mandelbrot fractal, Pierre-Simon Laplace, Ponzi scheme, Richard Feynman, statistical model, stem cell, The Death and Life of Great American Cities, the map is not the territory, the scientific method, Thomas Bayes, Torches of Freedom

There are three important aspects of probability that we need to explain so you can integrate them into your thinking to get into the ballpark and improve your chances of catching the ball: Bayesian thinking Fat-tailed curves Asymmetries Thomas Bayes and Bayesian thinking: Bayes was an English minister in the first half of the 18th century, whose most famous work, “An Essay Toward Solving a Problem in the Doctrine of Chances”, was brought to the attention of the Royal Society by his friend Richard Price in 1763—two years after his death. The essay concerned how we should adjust probabilities when we encounter new data, and provided the seeds for the great mathematician Pierre Simon Laplace to develop what we now call Bayes’s Theorem. The core of Bayesian thinking (or Bayesian updating, as it can be called) is this: given that we have limited but useful information about the world, and are constantly encountering new information, we should probably take into account what we already know when we learn something new. As much of it as possible. Bayesian thinking allows us to use all relevant prior information in making decisions.


pages: 407 words: 116,726

Infinite Powers: How Calculus Reveals the Secrets of the Universe by Steven Strogatz

Albert Einstein, Asperger Syndrome, Astronomia nova, Bernie Sanders, clockwork universe, complexity theory, cosmological principle, Dava Sobel, double helix, Edmond Halley, Eratosthenes, four colour theorem, fudge factor, Henri Poincaré, invention of the telescope, Isaac Newton, Islamic Golden Age, Johannes Kepler, John Harrison: Longitude, Khan Academy, Laplace demon, lone genius, music of the spheres, pattern recognition, Paul Erdős, Pierre-Simon Laplace, precision agriculture, retrograde motion, Richard Feynman, Socratic dialogue, Solar eclipse in 1919, Steve Jobs, the rule of 72, the scientific method

They could alter the nature of prediction forever and lead to a new era in calculus—and in science more generally—where human insight may begin to fade, although science itself will still go on. To clarify what I mean by this somewhat apocalyptic warning, we need to understand how prediction is possible at all, what it meant classically, and how our classical notions are being revised by discoveries made in the past several decades in studies of nonlinearity, chaos, and complex systems. Early in the 1800s, the French mathematician and astronomer Pierre Simon Laplace took the determinism of Newton’s clockwork universe to its logical extreme. He imagined a godlike intellect (now known as Laplace’s demon) that could keep track of all the positions of all the atoms in the universe as well as all the forces acting on them. “If this intellect were also vast enough to submit these data to analysis,” he wrote, “nothing would be uncertain and the future just like the past would be present before its eyes.”

The Future of Calculus 275 writhing number: Fuller, “The Writhing Number.” See also Pohl, “DNA and Differential Geometry.” 275 geometry and topology of DNA: Bates and Maxwell, DNA Topology, and Wasserman and Cozzarelli, “Biochemical Topology.” 275 knot theory and tangle calculus: Ernst and Sumners, “Calculus for Rational Tangles.” 276 targets for cancer-chemotherapy drugs: Liu, “DNA Topoisomerase Poisons.” 277 Pierre Simon Laplace: Kline, Mathematics in Western Culture; C. Hoefer, “Causal Determinism,” https://plato.stanford.edu/entries/determinism-causal/. 277 “nothing would be uncertain”: Laplace, Philosophical Essay on Probabilities, 4. 277 Sofia Kovalevskaya: Cooke, Mathematics of Sonya Kovalevskaya, and Goriely, Applied Mathematics, 54–57. She is often referred to by other names; Sonia Kovalevsky is a common variant.


pages: 247 words: 43,430

Think Complexity by Allen B. Downey

Benoit Mandelbrot, cellular automata, Conway's Game of Life, Craig Reynolds: boids flock, discrete time, en.wikipedia.org, Frank Gehry, Gini coefficient, Guggenheim Bilbao, Laplace demon, mandelbrot fractal, Occupy movement, Paul Erdős, peer-to-peer, Pierre-Simon Laplace, sorting algorithm, stochastic process, strong AI, Thomas Kuhn: the structure of scientific revolutions, Turing complete, Turing machine, Vilfredo Pareto, We are the 99%

The center of mass of world opinion swings along this range in response to historical developments and scientific discoveries. Prior to the scientific revolution, many people regarded the working of the universe as fundamentally unpredictable or controlled by supernatural forces. After the triumphs of Newtonian mechanics, some optimists came to believe something like D4. For example, in 1814, Pierre-Simon Laplace wrote: We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.


The Book of Why: The New Science of Cause and Effect by Judea Pearl, Dana Mackenzie

affirmative action, Albert Einstein, Asilomar, Bayesian statistics, computer age, computer vision, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, Edmond Halley, Elon Musk, en.wikipedia.org, experimental subject, Isaac Newton, iterative process, John Snow's cholera map, Loebner Prize, loose coupling, Louis Pasteur, Menlo Park, pattern recognition, Paul Erdős, personalized medicine, Pierre-Simon Laplace, placebo effect, prisoner's dilemma, probability theory / Blaise Pascal / Pierre de Fermat, randomized controlled trial, selection bias, self-driving car, Silicon Valley, speech recognition, statistical model, Stephen Hawking, Steve Jobs, strong AI, The Design of Experiments, the scientific method, Thomas Bayes, Turing test

Only after gamblers invented intricate games of chance, sometimes carefully designed to trick us into making bad choices, did mathematicians like Blaise Pascal (1654), Pierre de Fermat (1654), and Christiaan Huygens (1657) find it necessary to develop what we today call probability theory. Likewise, only when insurance organizations demanded accurate estimates of life annuity did mathematicians like Edmond Halley (1693) and Abraham de Moivre (1725) begin looking at mortality tables to calculate life expectancies. Similarly, astronomers’ demands for accurate predictions of celestial motion led Jacob Bernoulli, Pierre-Simon Laplace, and Carl Friedrich Gauss to develop a theory of errors to help us extract signals from noise. These methods were all predecessors of today’s statistics. Ironically, the need for a theory of causation began to surface at the same time that statistics came into being. In fact, modern statistics hatched from the causal questions that Galton and Pearson asked about heredity and their ingenious attempts to answer them using cross-generational data.

This pattern has a mathematical explanation. The path of any individual ball is like a sequence of independent coin flips. Each time a ball hits a pin, it bounces either to the left or the right, and from a distance its choice seems completely random. The sum of the results—say, the excess of the rights over the lefts—determines which slot the ball ends up in. According to the central limit theorem, proven in 1810 by Pierre-Simon Laplace, any such random process—one that amounts to a sum of a large number of coin flips—will lead to the same probability distribution, called the normal distribution (or bell-shaped curve). The Galton board is simply a visual demonstration of Laplace’s theorem. The central limit theorem is truly a miracle of nineteenth-century mathematics. Think about it: even though the path of any individual ball is unpredictable, the path of 1,000 balls is extremely predictable—a convenient fact for the producers of The Price Is Right, who can estimate accurately how much money the contestants will win at Plinko over the long run.


pages: 486 words: 148,485

Being Wrong: Adventures in the Margin of Error by Kathryn Schulz

affirmative action, anti-communist, banking crisis, Bernie Madoff, car-free, Cass Sunstein, cognitive dissonance, colonial rule, conceptual framework, cosmological constant, cuban missile crisis, Daniel Kahneman / Amos Tversky, dark matter, desegregation, Johann Wolfgang von Goethe, lake wobegon effect, longitudinal study, mandatory minimum, Pierre-Simon Laplace, Ronald Reagan, six sigma, stem cell, Steven Pinker, Tenerife airport disaster, the scientific method, The Wisdom of Crowds, theory of mind, Thomas Kuhn: the structure of scientific revolutions, trade route

This is another important dispute in the history of how we think about being wrong: whether error represents an obstacle in the path toward truth, or the path itself. The former idea is the conventional one. The latter, as we have seen, emerged during the Scientific Revolution and continued to evolve throughout the Enlightenment. But it didn’t really reach its zenith until the early nineteenth century, when the French mathematician and astronomer Pierre-Simon Laplace refined the theory of the distribution of errors, illustrated by the now-familiar bell curve. Also known as the error curve or the normal distribution, the bell curve is a way of aggregating individually meaningless, idiosyncratic, or inaccurate data points in order to generate a meaningful and accurate big picture. Laplace, for instance, used the bell curve to determine the precise orbit of the planets.

Whether or not this method has ever been practiced as such (that is, to what extent scientists, especially as individuals, seek to replicate experiments and falsify hypotheses) is an open question, as Thomas Kuhn made abundantly clear in The Structure of Scientific Revolutions. But my point here concerns the method as an intellectual ideal more than an actual practice. “For Satan himself.” The Bible, New International Version (HarperTorch, 1993), 2 Corinthians 11:14–15. errors as ignes fatui. Bates, 46. Pierre-Simon Laplace. Bates touches on this development toward the end of Enlightenment Aberrations (248), but my primary source here was Steven M. Stigler’s History of Statistics: The Measurement of Uncertainty Before 1900 (Harvard University Press, 1990), especially 31–38 and 109–148. “The genius of statistics.” Louis Menand, The Metaphysical Club: A Story of Ideas in America (Farrar, Straus and Giroux, 2002), 182.


What We Cannot Know: Explorations at the Edge of Knowledge by Marcus Du Sautoy

Albert Michelson, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, banking crisis, bet made by Stephen Hawking and Kip Thorne, Black Swan, Brownian motion, clockwork universe, cosmic microwave background, cosmological constant, dark matter, Dmitri Mendeleev, Edmond Halley, Edward Lorenz: Chaos theory, Ernest Rutherford, Georg Cantor, Hans Lippershey, Harvard Computers: women astronomers, Henri Poincaré, invention of the telescope, Isaac Newton, Johannes Kepler, Magellanic Cloud, mandelbrot fractal, MITM: man-in-the-middle, Murray Gell-Mann, music of the spheres, Necker cube, Paul Erdős, Pierre-Simon Laplace, Richard Feynman, Skype, Slavoj Žižek, Solar eclipse in 1919, stem cell, Stephen Hawking, technological singularity, Thales of Miletus, Turing test, wikimedia commons

At the beginning of the nineteenth century French mathematician Joseph Fourier found equations to describe heat flow. Fellow compatriots Pierre-Simon Laplace and Siméon-Denis Poisson took Newton’s equations to produce more generalized equations for gravitation, which were then seen to control other phenomena like hydrodynamics and electrostatics. The behaviours of viscous fluids were described by the Navier–Stokes equations, and electromagnetism by Maxwell’s equations. With the discovery of the calculus and the laws of motion, it seemed that Newton had turned the universe into a deterministic clockwork machine controlled by mathematical equations. Scientists believed they had indeed discovered the Theory of Everything. In his Philosophical Essay on Probabilities published in 1812, the mathematician Pierre-Simon Laplace summed up most scientists’ belief in the extraordinary power of mathematics to tell you everything about the physical universe.


pages: 807 words: 154,435

Radical Uncertainty: Decision-Making for an Unknowable Future by Mervyn King, John Kay

"Robert Solow", Airbus A320, Albert Einstein, Albert Michelson, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, autonomous vehicles, availability heuristic, banking crisis, Barry Marshall: ulcers, battle of ideas, Benoit Mandelbrot, bitcoin, Black Swan, Bonfire of the Vanities, Brownian motion, business cycle, business process, capital asset pricing model, central bank independence, collapse of Lehman Brothers, correlation does not imply causation, credit crunch, cryptocurrency, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, demographic transition, discounted cash flows, disruptive innovation, diversification, diversified portfolio, Donald Trump, easy for humans, difficult for computers, Edmond Halley, Edward Lloyd's coffeehouse, Edward Thorp, Elon Musk, Ethereum, Eugene Fama: efficient market hypothesis, experimental economics, experimental subject, fear of failure, feminist movement, financial deregulation, George Akerlof, germ theory of disease, Hans Rosling, Ignaz Semmelweis: hand washing, income per capita, incomplete markets, inflation targeting, information asymmetry, invention of the wheel, invisible hand, Jeff Bezos, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Snow's cholera map, John von Neumann, Kenneth Arrow, Long Term Capital Management, loss aversion, Louis Pasteur, mandelbrot fractal, market bubble, market fundamentalism, Moneyball by Michael Lewis explains big data, Nash equilibrium, Nate Silver, new economy, Nick Leeson, Northern Rock, oil shock, Paul Samuelson, peak oil, Peter Thiel, Philip Mirowski, Pierre-Simon Laplace, popular electronics, price mechanism, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, railway mania, RAND corporation, rent-seeking, Richard Feynman, Richard Thaler, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Coase, sealed-bid auction, shareholder value, Silicon Valley, Simon Kuznets, Socratic dialogue, South Sea Bubble, spectrum auction, Steve Ballmer, Steve Jobs, Steve Wozniak, Tacoma Narrows Bridge, Thales and the olive presses, Thales of Miletus, The Chicago School, the map is not the territory, The Market for Lemons, The Nature of the Firm, The Signal and the Noise by Nate Silver, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Bayes, Thomas Davenport, Thomas Malthus, Toyota Production System, transaction costs, ultimatum game, urban planning, value at risk, World Values Survey, Yom Kippur War, zero-sum game

From the earliest days of probabilistic thinking, attempts were made to apply such reasoning outside the domain of the observable frequencies of games of chance and human mortality, to use probabilistic language and mathematics in the description of unique events such as the Yucatán asteroid or the bin Laden raid. And from the earliest days of probabilistic thinking, such extension was resisted. Opponents of extension for long had the upper hand. In his 1843 System of Logic , the British philosopher John Stuart Mill criticised the French mathematician Pierre-Simon Laplace for applying probability theory ‘to things of which we are completely ignorant’. 2 Another French mathematician, Joseph Bertrand, went further. 3 He lambasted his countrymen for making absurd assumptions in the application of probabilities to problems outside the domain of games of chance. We believe that the sun will rise tomorrow, he said, because of ‘the discovery of astronomical laws and not by renewed success in the same game of chance’. 4 Even this belief depends on the astronomical laws remaining stationary.

Donoghue (1983). 18 Márquez and Stone (1981). 19 Tuckett and Nikolic (2017) p. 502. 20 Ibid. p. 501. 21 Walton and Huey (1993) p. 298. 22 Serling (1992) p. 68. 23 Ibid. p. 285. 24 Kay (2011) pp. 21–2. 25 Shubber (2018). 26 Wolfe (1988) p. 57. 27 Shiller (2017) and Chong and Tuckett (2015). 13. TELLING STORIES THROUGH NUMBERS 1 That distribution was subsequently, and seemingly independently, discovered by another Frenchman, Pierre-Simon Laplace, and by the German Carl Gauss, and is still often called the Gaussian distribution. 2 Quetelet (1835). 3 We owe these discoveries to distinguished professors of applied mathematics in the early twentieth century, scholars such as Francis Galton, Karl Pearson and Jerzy Neyman – and to ‘Student’, who published anonymously. We now know ‘Student’ to have been W. J. Gossett, an employee of the Guinness Brewery in Dublin.


Growth: From Microorganisms to Megacities by Vaclav Smil

2013 Report for America's Infrastructure - American Society of Civil Engineers - 19 March 2013, 3D printing, agricultural Revolution, air freight, American Society of Civil Engineers: Report Card, autonomous vehicles, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Bretton Woods, British Empire, business cycle, colonial rule, complexity theory, coronavirus, decarbonisation, deindustrialization, dematerialisation, demographic dividend, demographic transition, Deng Xiaoping, disruptive innovation, Dissolution of the Soviet Union, endogenous growth, energy transition, epigenetics, happiness index / gross national happiness, hydraulic fracturing, hydrogen economy, Hyperloop, illegal immigration, income inequality, income per capita, industrial robot, Intergovernmental Panel on Climate Change (IPCC), invention of movable type, Isaac Newton, James Watt: steam engine, knowledge economy, labor-force participation, Law of Accelerating Returns, longitudinal study, mandelbrot fractal, market bubble, mass immigration, McMansion, megacity, megastructure, meta analysis, meta-analysis, microbiome, moral hazard, Network effects, new economy, New Urbanism, old age dependency ratio, optical character recognition, out of africa, peak oil, Pearl River Delta, phenotype, Pierre-Simon Laplace, planetary scale, Ponzi scheme, Productivity paradox, profit motive, purchasing power parity, random walk, Ray Kurzweil, Report Card for America’s Infrastructure, Republic of Letters, rolodex, Silicon Valley, Simon Kuznets, South China Sea, technoutopianism, the market place, The Rise and Fall of American Growth, total factor productivity, trade liberalization, trade route, urban sprawl, Vilfredo Pareto, yield curve

The second most common name besides normal is the Gaussian distribution, named after Carl Friedrich Gauss, although Gauss was not the first mathematician to identify its existence (figure 1.22). His first published work on that topic came more than three decades after Pierre-Simon Laplace published his Mémoire sur la probabilité which contains normal curve function (Gauss 1809; Laplace 1774). Laplace’s distribution should have been a more accurate attribution—until Pearson (1924) discovered that the work of de Moivre antedates that of Laplace (figure 1.22). Figure 1.22 Carl Friedrich Gauss, Pierre-Simon Laplace, and Abraham de Moivre. Portraits from the author’s collection. In 1730 Abraham de Moivre published his Miscellanea Analytica and three years later attached a short supplement entitled Approximatio ad Summam Terminorum Binomii (a+b)n in Seriem expansi which contains the first known treatment of what we now know as the normal curve and was included in the second edition of his Doctrine of Chances (de Moivre 1738).

Figure 1.19    Actual trajectories of primary energy shares show that this has not been a system with an immutable “schedule, a will, and a clock.” Shares plotted from data in Smil (2017b). Figure 1.20    Logistic growth trajectory (inflection point in 2024, asymptote at 625.5 Wh/kg) of battery energy densities, 1900–2017. Plotted from data in Zu and Li (2011) and from subsequent news reports. Figure 1.21    Examples of confined exponential growth curves (based on Banks 1994). Figure 1.22    Carl Friedrich Gauss, Pierre-Simon Laplace, and Abraham de Moivre. Portraits from the author’s collection. Figure 1.23    Characteristics of the normal distribution curve. Figure 1.24    Lognormal species abundance distributions (x axes in log2 classes) of North American fish and birds and less regular distributions of North American and Asian vegetation. Simplified from Antão et al. (2017). Figure 1.25    Peaks of two asymmetric distributions, one natural and one anthropogenic: there is only one Qomolangma and one Tokyo.


pages: 233 words: 62,563

Zero: The Biography of a Dangerous Idea by Charles Seife

Albert Einstein, Albert Michelson, Arthur Eddington, Cepheid variable, cosmological constant, dark matter, Edmond Halley, Georg Cantor, Isaac Newton, Johannes Kepler, John Conway, Pierre-Simon Laplace, place-making, probability theory / Blaise Pascal / Pierre de Fermat, retrograde motion, Richard Feynman, Solar eclipse in 1919, Stephen Hawking

In the mid-twelfth century the first adaptations of al-Khowarizmi’s Aljabr were working their way through Spain, England, and the rest of Europe. Zero was on the way, and just as the church was breaking the shackles of Aristotelianism, it arrived. Zero’s Triumph …a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it lent to all computations put our arithmetic in the first rank of useful inventions. —PIERRE-SIMON LAPLACE Christianity initially rejected zero, but trade would soon demand it. The man who reintroduced zero to the West was Leonardo of Pisa. The son of an Italian trader, he traveled to northern Africa. There the young man—better known as Fibonacci—learned mathematics from the Muslims and soon became a good mathematician in his own right. Fibonacci is best remembered for a silly little problem he posed in his book, Liber Abaci, which was published in 1202.


pages: 855 words: 178,507

The Information: A History, a Theory, a Flood by James Gleick

Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, AltaVista, bank run, bioinformatics, Brownian motion, butterfly effect, citation needed, Claude Shannon: information theory, clockwork universe, computer age, conceptual framework, crowdsourcing, death of newspapers, discovery of DNA, Donald Knuth, double helix, Douglas Hofstadter, en.wikipedia.org, Eratosthenes, Fellow of the Royal Society, Gödel, Escher, Bach, Henri Poincaré, Honoré de Balzac, index card, informal economy, information retrieval, invention of the printing press, invention of writing, Isaac Newton, Jacquard loom, Jaron Lanier, jimmy wales, Johannes Kepler, John von Neumann, Joseph-Marie Jacquard, lifelogging, Louis Daguerre, Marshall McLuhan, Menlo Park, microbiome, Milgram experiment, Network effects, New Journalism, Norbert Wiener, Norman Macrae, On the Economy of Machinery and Manufactures, PageRank, pattern recognition, phenotype, Pierre-Simon Laplace, pre–internet, Ralph Waldo Emerson, RAND corporation, reversible computing, Richard Feynman, Rubik’s Cube, Simon Singh, Socratic dialogue, Stephen Hawking, Steven Pinker, stochastic process, talking drums, the High Line, The Wisdom of Crowds, transcontinental railway, Turing machine, Turing test, women in the workforce

“No thought can perish,”♦ he wrote in 1845, in a dialogue between two angels. “Did there not cross your mind some thought of the physical power of words? Is not every word an impulse on the air?” Further, every impulse vibrates outward indefinitely, “upward and onward in their influences upon all particles of all matter,” until it must, “in the end, impress every individual thing that exists within the universe.” Poe was also reading Newton’s champion Pierre-Simon Laplace. “A being of infinite understanding,” wrote Poe, “—one to whom the perfection of the algebraic analysis lay unfolded” could trace the undulations backward to their source. Babbage and Poe took an information-theoretic view of the new physics. Laplace had expounded a perfect Newtonian mechanical determinism; he went further than Newton himself, arguing for a clockwork universe in which nothing is left to chance.

♦ “OUR HERESIARCH UNCLE”: William Gibson, “An Invitation,” introduction to Labyrinths, xii. ♦ “WHAT A STRANGE CHAOS”: Charles Babbage, The Ninth Bridgewater Treatise: A Fragment, 2nd ed. (London: John Murray, 1838), 111. ♦ “NO THOUGHT CAN PERISH”: Edgar Allan Poe, “The Power of Words” (1845), in Poetry and Tales (New York: Library of America, 1984), 823–24. ♦ “IT WOULD EMBRACE IN THE SAME FORMULA”: Pierre-Simon Laplace, A Philosophical Essay on Probabilities, trans. Frederick Wilson Truscott and Frederick Lincoln Emory (New York: Dover, 1951). ♦ “IN TURNING OUR VIEWS”: Charles Babbage, The Ninth Bridgewater Treatise, 44. ♦ “THE ART OF PHOTOGENIC DRAWING”: Nathaniel Parker Willis, “The Pencil of Nature: A New Discovery,” The Corsair 1, no. 5 (April 1839): 72. ♦ “IN FACT, THERE IS A GREAT ALBUM OF BABEL”: Ibid., 71


pages: 239 words: 68,598

The Vanishing Face of Gaia: A Final Warning by James E. Lovelock

Ada Lovelace, butterfly effect, carbon footprint, Clapham omnibus, cognitive dissonance, continuous integration, David Attenborough, decarbonisation, discovery of DNA, Edward Lorenz: Chaos theory, Henri Poincaré, Intergovernmental Panel on Climate Change (IPCC), mandelbrot fractal, mass immigration, megacity, Northern Rock, oil shale / tar sands, phenotype, Pierre-Simon Laplace, planetary scale, short selling, Stewart Brand, University of East Anglia

Scientists of these separated disciplines should have realized that they were on the wrong track when quite independently the geophysicist Edward Lorenz, in 1961, and the neo‐Darwinist biologist Robert May, in 1973, made the remarkable discovery that deterministic chaos was an inherent part of the computer models they researched. Deterministic chaos is not an oxymoron, however much it may seem like one. Up until Lorenz and May started using computers to solve systems rich in difficult equations almost all science clung to the comforting idea put forward in 1814 by the French mathematician Pierre‐Simon Laplace that the universe was deterministic and if the precise location and momentum of every particle in the universe were known, then by using Newton’s laws we could reveal the entire course of cosmic events, past, present and future. The first indication that this was too good to be true came in 1890 when Henri Poincaré studied the interaction of three bodies held together by gravity while orbiting in space; he found that the behaviour of the system was wholly unpredictable.


pages: 212 words: 65,900

Symmetry and the Monster by Ronan, Mark

Albert Einstein, Andrew Wiles, conceptual framework, Everything should be made as simple as possible, G4S, Henri Poincaré, John Conway, John von Neumann, Kickstarter, New Journalism, Pierre-Simon Laplace, Richard Feynman, V2 rocket

Mark Ronan, February 2006 Contents Prologue 1 Theaetetus’s Icosahedron 2 Galois: Death of a Genius 3 Irrational Solutions 4 Groups 5 Sophus Lie 6 Lie Groups and Physics 7 Going Finite 8 After the War 9 The Man from Uccle 10 The Big Theorem 11 Pandora’s Box 12 The Leech Lattice 13 Fischer’s Monsters 14 The Atlas 15 A Monstrous Mystery 16 Construction 17 Moonshine Notes Appendix 1: The Golden Section Appendix 2: The Witt Design Appendix 3: The Leech Lattice Appendix 4: The 26 Exceptions Glossary Index To Grace Varndell, my headmistress from primary school, who still remembers exactly where I sat in class. Prologue What we know is not much. What we do not know is immense. Pierre-Simon Laplace (1749–1827), said to be his last words In November 1978 an English mathematician named John McKay was reading a research paper at his home in Montreal. He worked in a branch of mathematics called group theory, which deals with the study of symmetry. It was an area that had recently produced some exceptional objects in many dimensions, but McKay was taking a break by reading a paper in number theory, the part of mathematics that deals with the whole numbers.


pages: 257 words: 66,480

Strange New Worlds: The Search for Alien Planets and Life Beyond Our Solar System by Ray Jayawardhana

Albert Einstein, Albert Michelson, Arthur Eddington, cosmic abundance, dark matter, Donald Davies, Edmond Halley, invention of the telescope, Isaac Newton, Johannes Kepler, Kuiper Belt, Louis Pasteur, Pierre-Simon Laplace, planetary scale, Pluto: dwarf planet, Search for Extraterrestrial Intelligence, Solar eclipse in 1919

Unfortunately, soon after his book was printed, Kant’s publisher went bankrupt, and not even King Frederick the Great, to whom it was dedicated, got to see Kant’s ambitiously titled book Universal Natural History and Theory of the Heavens: An Essay on the Constitution and Mechanical Origin of the Whole Universe according to Newton’s Principles. Forty years later, the French mathematician Pierre Simon Laplace came up with a somewhat different version of the “solar nebula” model. He suggested that a fast-spinning young Sun cast off rings of material, out of which the planets condensed. Again, the implication is that the same could happen with other stars. Laplace’s scenario accounted for the planets orbiting the Sun in the same plane and the same direction. He interpreted Saturn’s rings as evidence in favor of his theory, adding that they may condense into moons in the future.


pages: 229 words: 67,599

The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age by Paul J. Nahin

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Any sufficiently advanced technology is indistinguishable from magic, Claude Shannon: information theory, conceptual framework, Edward Thorp, Fellow of the Royal Society, finite state, four colour theorem, Georg Cantor, Grace Hopper, Isaac Newton, John von Neumann, knapsack problem, New Journalism, Pierre-Simon Laplace, reversible computing, Richard Feynman, Schrödinger's Cat, Steve Jobs, Steve Wozniak, thinkpad, Thomas Bayes, Turing machine, Turing test, V2 rocket

Boole argued that this is not so, using the ideas of the previous section, and showed that P( | X) is given by a considerably more involved expression than simply “p.” What Boole did was not really original, as conditional probability had been studied a century before by the English philosopher and minister Thomas Bayes (1701–1761), whose work was published posthumously in 1764 in the Philosophical Transactions of the Royal Society of London, where it was then promptly forgotten for twenty years until the great French mathematician Pierre-Simon Laplace (1749–1827) endorsed Bayes’s results. What Boole did, then, with the following analysis, was remind his readers what the Reverend Bayes had done a hundred years before. From the previous section—see (6.2.6) and (6.2.7)—we have But and so and so Or, from (6.2.8), we rewrite the denominator of (6.3.1) to get or, at last, we arrive at Boole’s result (in our modern notation): which is (most definitely!)


pages: 239 words: 69,496

The Wisdom of Finance: Discovering Humanity in the World of Risk and Return by Mihir Desai

activist fund / activist shareholder / activist investor, Albert Einstein, Andrei Shleifer, assortative mating, Benoit Mandelbrot, Brownian motion, capital asset pricing model, carried interest, Charles Lindbergh, collective bargaining, corporate governance, corporate raider, discounted cash flows, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, follow your passion, George Akerlof, Gordon Gekko, greed is good, housing crisis, income inequality, information asymmetry, Isaac Newton, Jony Ive, Kenneth Rogoff, longitudinal study, Louis Bachelier, moral hazard, Myron Scholes, new economy, out of africa, Paul Samuelson, Pierre-Simon Laplace, principal–agent problem, Ralph Waldo Emerson, random walk, risk/return, Robert Shiller, Robert Shiller, Ronald Coase, Silicon Valley, Steve Jobs, Thales and the olive presses, Thales of Miletus, The Market for Lemons, The Nature of the Firm, The Wealth of Nations by Adam Smith, Tim Cook: Apple, transaction costs, zero-sum game

One might imagine that the balls would fall willy-nilly across those wooden lanes and ultimately land in each lane equally—after all, the balls are just bouncing off wooden pegs randomly on their way down the board. But the quincunx, like many outcomes that are the product of multiple random processes, actually results in the wonderfully soothing bell-shaped distribution where most balls fall in the center. This regularity was found so often and in so many intriguing places that it gave rise to a conviction that what seemed like chance was illusory and that nature followed ironclad laws. Pierre-Simon Laplace, a pioneer of statistics and probability during this period, was characteristic of the ironic confusion: the discoverers of the tools to analyze randomness came to believe in determinism. Laplace began a famous volume on probability by asserting that “all events, even those which on account of their insignificance do not seem to follow the great laws of nature, are a result of it just as necessarily as the revolutions of the sun.”


God Created the Integers: The Mathematical Breakthroughs That Changed History by Stephen Hawking

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Antoine Gombaud: Chevalier de Méré, Augustin-Louis Cauchy, British Empire, Edmond Halley, Eratosthenes, Fellow of the Royal Society, G4S, Georg Cantor, Henri Poincaré, Isaac Newton, Johannes Kepler, John von Neumann, p-value, Pierre-Simon Laplace, Richard Feynman, Stephen Hawking, Turing machine

Latham courtesy of Dover Publications. Selections from Isaac Newton’s Principia, notes by David Eugene Smith, courtesy of New York: Daniel Adee, © 1848. English translation of Leonhard Euler’s On the sums of series of reciprocals (De summis serierum reciprocarum) courtesy of Jordan Bell. Leonhard Euler’s The Seven Bridges of Konigsberg and Proof that Every Integer is A Sum of Four Squares courtesy of Dover Publications. Pierre Simon Laplace’s A Philosophical Essay on Probabilities, introductory note by E.T. Bell, courtesy of Dover Publications. Selection from Jean Baptiste Joseph Fourier’s The Analytical Theory of Heat courtesy of Dover Publications. Selections from Carl Friedrich Gauss’s Disquisitiones Arithmeticae courtesy of Yale University Press. Selections from Oeuvres complètes d’Augustin Cauchy reprinted from 1882 version published by Gauthier-Villars, Paris.

CONTENTS Introduction EUCLID (C. 325BC–265BC) His Life and Work Selections from Euclid’s Elements Book I: Basic Geometry—Definitions, Postulates, Common Notions; and Proposition 47, (leading up to the Pythagorean Theorem) Book V: The Eudoxian Theory of Proportion—Definitions & Propositions Book VII: Elementary Number Theory—Definitions & Propositions Book IX: Proposition 20: The Infinitude of Prime Numbers Book IX: Proposition 36: Even Perfect Numbers Book X: Commensurable and Incommensurable Magnitudes ARCHIMEDES (287BC–212BC) His Life and Work Selections from The Works of Archimedes On the Sphere and Cylinder, Books I and II Measurement of a Circle The Sand Reckoner The Methods DIOPHANTUS (C. 200–284) His Life and Work Selections from Diophantus of Alexandria, A Study in the History of Greek Algebra Book II Problems 8–35 Book III Problems 5–21 Book V Problems 1–29 RENÉ DESCARTES (1596–1650) His Life and Work The Geometry of Rene Descartes ISAAC NEWTON (1642–1727) His Life and Work Selections from Principia On First and Last Ratios of Quantities LEONHARD EULER (1707–1783) His Life and Work On the sums of series of reciprocals (De summis serierum reciprocarum) The Seven Bridges of Konigsberg Proof that Every Integer is A Sum of Four Squares PIERRE SIMON LAPLACE (1749–1827) His Life and Work A Philosophical Essay on Probabilities JEAN BAPTISTE JOSEPH FOURIER (1768–1830) His Life and Work Selection from The Analytical Theory of Heat Chapter III: Propagation of Heat in an Infinite Rectangular Solid (The Fourier series) CARL FRIEDRICH GAUSS (1777–1855) His Life and Work Selections from Disquisitiones Arithmeticae (Arithmetic Disquisitions) Section III Residues of Powers Section IV Congruences of the Second Degree AUGUSTIN-LOUIS CAUCHY (1789–1857) His Life and Work Selections from Oeuvres complètes d’Augustin Cauchy Résumé des leçons données à l’École Royale Polytechnique sur le calcul infinitésimal (1823), series 2, vol. 4 Lessons 3–4 on differential calculus Lessons 21–24 on the integral NIKOLAI IVANOVICH LOBACHEVSKY (1792–1856) His Life and Work Geometrical Researches on the Theory of Parallels JÁNOS BOLYAI (1802–1860) His Life and Work The Science of Absolute Space ÉVARISTE GALOIS (1811–1832) His Life and Work On the conditions that an equation be soluble by radicals Of the primitive equations which are soluble by radicals On Groups and Equations and Abelian Integrals GEORGE BOOLE (1815–1864) His Life and Work An Investigation of the Laws of Thought BERNHARD RIEMANN (1826–1866) His Life and Work On the Representability of a Function by Means of a Trigonometric Series (Ueber die Darstellbarkeit eine Function durch einer trigonometrische Reihe) On the Hypotheses which lie at the Bases of Geometry (Ueber die Hypothesen, welche der Geometrie zu Grunde liegen) On the Number of Prime Numbers Less than a Given Quantity (Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse) KARL WEIERSTRASS (1815–1897) His Life and Work Selected Chapters on the Theory of Functions, Lecture Given in Berlin in 1886, with the Inaugural Academic Speech, Berlin 1857 § 7 Gleichmässige Stetigkeit (Uniform Continuity) RICHARD DEDEKIND (1831–1916) His Life and Work Essays on the Theory of Numbers GEORG CANTOR (1848–1918) His Life and Work Selections from Contributions to the Founding of the Theory of Transfinite Numbers Articles I and II HENRI LEBESGUE (1875–1941) His Life and Work Selections from Integrale, Longeur, Aire (Intergral, Length, Area) Preliminaries and Integral KURT GÖDEL (1906–1978) His Life and Work On Formally Undecidable Propositions of Principia Mathematica and Related Systems ALAN TURING (1912–1954) His Life and Work On computable numbers with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society INTRODUCTION WE ARE LUCKY TO LIVE IN AN AGE LN WHICH WE ARE STILL MAKING DISCOVERIES.

It is hard to imagine the development of either electrodynamics or quantum theory without the methods of Jean Baptiste Joseph Fourier or the work on calculus and the theory of complex functions pioneered by Carl Friedrich Gauss and Augustin-Louis Cauchy—and it was Henri Lebesgue’s work on the theory of measure that enabled John von Neumann to formulate the rigorous understanding of quantum theory that we have today. Albert Einstein could not have completed his general theory of relativity had it not been for the geometric ideas of Bernhard Riemann. And practically all of modern science would be far less potent (if it existed at all) without the concepts of probability and statistics pioneered by Pierre Simon Laplace. All through the ages, no intellectual endeavor has been more important to those studying physical science than has the field of mathematics. But mathematics is more than a tool and language for science. It is also an end in itself, and as such, it has, over the centuries, affected our worldview in its own right. Karl Weierstrass provided a new idea of what it means for a function to be continuous, and Georg Cantors work revolutionized peoples idea of infinity.


pages: 253 words: 80,074

The Man Who Invented the Computer by Jane Smiley

1919 Motor Transport Corps convoy, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anti-communist, Arthur Eddington, British Empire, c2.com, computer age, Fellow of the Royal Society, Henri Poincaré, IBM and the Holocaust, Isaac Newton, John von Neumann, Karl Jansky, Norbert Wiener, Norman Macrae, Pierre-Simon Laplace, RAND corporation, Turing machine, Vannevar Bush, Von Neumann architecture

He also employed his students in investigating ways of calculating. One of these students came up with an idea for a type of small analog calculator, something like a slide rule, that measured fourteen inches by three inches by three inches. Atanasoff, the student, and another colleague designed it to calculate the geometry of surfaces and called it a “Laplaciometer,” after the eighteenth-century French mathematician and astronomer Pierre-Simon Laplace, but its uses were limited. Most calculators in the 1930s were analog, that is, they were similar to a slide rule in that something is measured in order to ascertain a number. As Atanasoff later explained to Clark Mollenhoff, his first biographer, the thing measured “can be anything: a distance, an electric voltage, a current of electricity, air pressure, etc.” Calculating ever larger numbers requires ever more sensitive measurements, so that, for example, a slide rule, which calculates numbers by measuring distance, would have to be enormous (“the length of a football field, or in some instances a mile or more”) in order to represent the numbers Atanasoff was interested in calculating.


pages: 317 words: 84,400

Automate This: How Algorithms Came to Rule Our World by Christopher Steiner

23andMe, Ada Lovelace, airport security, Al Roth, algorithmic trading, backtesting, big-box store, Black-Scholes formula, call centre, cloud computing, collateralized debt obligation, commoditize, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, Donald Trump, Douglas Hofstadter, dumpster diving, Flash crash, G4S, Gödel, Escher, Bach, High speed trading, Howard Rheingold, index fund, Isaac Newton, John Markoff, John Maynard Keynes: technological unemployment, knowledge economy, late fees, Marc Andreessen, Mark Zuckerberg, market bubble, medical residency, money market fund, Myron Scholes, Narrative Science, PageRank, pattern recognition, Paul Graham, Pierre-Simon Laplace, prediction markets, quantitative hedge fund, Renaissance Technologies, ride hailing / ride sharing, risk tolerance, Robert Mercer, Sergey Aleynikov, side project, Silicon Valley, Skype, speech recognition, Spread Networks laid a new fibre optics cable between New York and Chicago, transaction costs, upwardly mobile, Watson beat the top human players on Jeopardy!, Y Combinator

GIVING VISUAL SHAPE TO ALGORITHMS In 1791, the famous Austrian composer Joseph Haydn attended a grandly staged version of George Frideric Handel’s Messiah at Westminster Abbey in London. At the close of the performance, put on by a thousand choral and orchestra members, Haydn wept. Through his tears, he declared of Handel, his contemporary, “He is the master of us all.”37 At about the same time, Pierre-Simon Laplace, the French mathematician and one of the thought giants who developed the field of statistics, was exclaiming the same thing, but not of the Messiah’s composer. The man Laplace proclaimed the “master of us all” was Leonhard Euler.38 Euler was another product of the University of Basel, a world-altering cluster of intelligence. Pope Pius II founded the university, the oldest in Switzerland, in 1460, and for centuries it drew in high intellects such as Erasmus of Rotterdam, the Bernoullis, the Eulers, Jacob Burckhardt, Friedrich Nietzsche, and Carl Jung.


pages: 360 words: 85,321

The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling by Adam Kucharski

Ada Lovelace, Albert Einstein, Antoine Gombaud: Chevalier de Méré, beat the dealer, Benoit Mandelbrot, butterfly effect, call centre, Chance favours the prepared mind, Claude Shannon: information theory, collateralized debt obligation, correlation does not imply causation, diversification, Edward Lorenz: Chaos theory, Edward Thorp, Everything should be made as simple as possible, Flash crash, Gerolamo Cardano, Henri Poincaré, Hibernia Atlantic: Project Express, if you build it, they will come, invention of the telegraph, Isaac Newton, Johannes Kepler, John Nash: game theory, John von Neumann, locking in a profit, Louis Pasteur, Nash equilibrium, Norbert Wiener, p-value, performance metric, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, random walk, Richard Feynman, Ronald Reagan, Rubik’s Cube, statistical model, The Design of Experiments, Watson beat the top human players on Jeopardy!, zero-sum game

Probability theory, which Bolton used to analyze horse races, is one of the most valuable analytical tools ever created. It gives us the ability to judge the likelihood of events and assess the reliability of information. As a result, it is a vital component of modern scientific research, from DNA sequencing to particle physics. Yet the science of probability emerged not in libraries or lecture theaters but among the cards and dice of bars and game rooms. For eighteenth-century mathematician Pierre Simon Laplace, it was a strange contrast. “It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge.” Cards and casinos since have inspired many other scientific ideas. We have seen how roulette helped Henri Poincaré develop the early ideas of chaos theory and allowed Karl Pearson to test his new statistical techniques.


pages: 301 words: 85,126

AIQ: How People and Machines Are Smarter Together by Nick Polson, James Scott

Air France Flight 447, Albert Einstein, Amazon Web Services, Atul Gawande, autonomous vehicles, availability heuristic, basic income, Bayesian statistics, business cycle, Cepheid variable, Checklist Manifesto, cloud computing, combinatorial explosion, computer age, computer vision, Daniel Kahneman / Amos Tversky, Donald Trump, Douglas Hofstadter, Edward Charles Pickering, Elon Musk, epigenetics, Flash crash, Grace Hopper, Gödel, Escher, Bach, Harvard Computers: women astronomers, index fund, Isaac Newton, John von Neumann, late fees, low earth orbit, Lyft, Magellanic Cloud, mass incarceration, Moneyball by Michael Lewis explains big data, Moravec's paradox, more computing power than Apollo, natural language processing, Netflix Prize, North Sea oil, p-value, pattern recognition, Pierre-Simon Laplace, ransomware, recommendation engine, Ronald Reagan, self-driving car, sentiment analysis, side project, Silicon Valley, Skype, smart cities, speech recognition, statistical model, survivorship bias, the scientific method, Thomas Bayes, Uber for X, uber lyft, universal basic income, Watson beat the top human players on Jeopardy!, young professional

In his forties, Bayes became a member of one such society, in a spa town in Kent called Tunbridge Wells, where he’d taken a job as a minister—and where he came up with the rule that now bears his name, sometime during the 1750s. Surprisingly, his discovery didn’t make much of an impact at first. Bayes didn’t even publish it during his lifetime; he died in 1761, and his manuscript was read posthumously to the Royal Society in 1763, by his friend Richard Price. There was a brief period around the turn of the nineteenth century when Bayesian ideas flourished, mainly in the hands of the great French mathematician Pierre-Simon Laplace. But upon Laplace’s death in 1827, Bayes’s rule fell into obscurity and irrelevance for more than a century. Bayesian Updating and Robot Cars Today, however, Bayes’s rule is back, better than ever, and sitting right behind the steering wheel of every robot car out there. Bayes’s rule is an equation that tells us how to update our beliefs in light of new information, turning prior probabilities into posterior probabilities.


pages: 315 words: 89,861

The Simulation Hypothesis by Rizwan Virk

3D printing, Albert Einstein, Apple II, artificial general intelligence, augmented reality, Benoit Mandelbrot, bioinformatics, butterfly effect, discovery of DNA, Dmitri Mendeleev, Elon Musk, en.wikipedia.org, Ernest Rutherford, game design, Google Glasses, Isaac Newton, John von Neumann, Kickstarter, mandelbrot fractal, Marc Andreessen, Minecraft, natural language processing, Pierre-Simon Laplace, Ralph Waldo Emerson, Ray Kurzweil, Richard Feynman, Schrödinger's Cat, Search for Extraterrestrial Intelligence, Silicon Valley, Stephen Hawking, Steve Jobs, Steve Wozniak, technological singularity, Turing test, Vernor Vinge, Zeno's paradox

Let’s take a quick look at what’s often called the old (“classical”) physics models, which were built on the works of Sir Isaac Newton, and the new (“relativistic and quantum”) physics, which began with Albert Einstein but was really fleshed out by a number of eminent physicists in the early 20th century, including Niels Bohr, Werner Heisenberg, Wolfgang Pauli, Erwin Schrödinger, and others. In the classical view of physics, the universe operates independently of people like us (or observers) and does so in a purely mechanistic way. Newton’s laws of motion could be used to describe the movements of heavenly bodies simply based on their mass and position using basic physics equations. In fact, utilizing Newton’s equations, Pierre-Simon Laplace put together two tomes that described the motions of every heavenly body that was known at the time, Exposition du système du monde and the Mécanique celeste. In this model, each of the planetary bodies is an independent physical entity that acts on the others per the laws of classical mechanics. It is a purely deterministic model—in order to know where things end up, you simply need to know where they started and which forces are acting on them.


pages: 383 words: 92,837

Incognito: The Secret Lives of the Brain by David Eagleman

Ada Lovelace, Albert Einstein, Any sufficiently advanced technology is indistinguishable from magic, Columbine, Daniel Kahneman / Amos Tversky, delayed gratification, endowment effect, facts on the ground, impulse control, invisible hand, Isaac Newton, Johann Wolfgang von Goethe, out of africa, Pierre-Simon Laplace, Ralph Waldo Emerson, Robert Shiller, Robert Shiller, Rodney Brooks, Saturday Night Live, selective serotonin reuptake inhibitor (SSRI), Steven Pinker, Thales of Miletus

To understand this, we need only to examine its historical roots. Over recent centuries, thinking men and women watched the growth of deterministic science around them in the form of the deterministic equations of Galileo, Newton, and others. These scientists pulled springs and rolled balls and dropped weights, and increasingly they were able to predict what the objects would do with simple equations. By the nineteenth century, Pierre-Simon Laplace had proposed that if one could know the position of every particle in the universe, then one could compute forward to know the entire future (and crank the equations in the other direction to know everything past). This historical success story is the heart of reductionism, which essentially proposes that everything big can be understood by discerning smaller and smaller pieces of it. In this viewpoint, the arrows of understanding all point to the smaller levels: humans can be understood in terms of biology, biology in the language of chemistry, and chemistry in the equations of atomic physics.


pages: 293 words: 88,490

The End of Theory: Financial Crises, the Failure of Economics, and the Sweep of Human Interaction by Richard Bookstaber

"Robert Solow", asset allocation, bank run, bitcoin, business cycle, butterfly effect, buy and hold, capital asset pricing model, cellular automata, collateralized debt obligation, conceptual framework, constrained optimization, Craig Reynolds: boids flock, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, dark matter, disintermediation, Edward Lorenz: Chaos theory, epigenetics, feminist movement, financial innovation, fixed income, Flash crash, Henri Poincaré, information asymmetry, invisible hand, Isaac Newton, John Conway, John Meriwether, John von Neumann, Joseph Schumpeter, Long Term Capital Management, margin call, market clearing, market microstructure, money market fund, Paul Samuelson, Pierre-Simon Laplace, Piper Alpha, Ponzi scheme, quantitative trading / quantitative finance, railway mania, Ralph Waldo Emerson, Richard Feynman, risk/return, Saturday Night Live, self-driving car, sovereign wealth fund, the map is not the territory, The Predators' Ball, the scientific method, Thomas Kuhn: the structure of scientific revolutions, too big to fail, transaction costs, tulip mania, Turing machine, Turing test, yield curve

HEISENBERG’S UNCERTAINTY PRINCIPLE Just four years before Gödel defined the limits of our ability to conquer the intellectual world of mathematics and logic with the publication of his undecidability theorem, the German physicist Werner Heisenberg’s celebrated uncertainty principle delineated the limits of inquiry into the physical world, thereby undoing the efforts of another celebrated intellect, the great mathematician Pierre-Simon Laplace. In the early 1800s, Laplace had worked extensively to demonstrate the purely mechanical and predictable nature of planetary motion. He later extended this theory to the interaction of molecules. In the Laplacian view, molecules are just as subject to the laws of physical mechanics as the planets are. In theory, if we knew the position and velocity of each molecule, we could trace its path as it interacted with other molecules, and trace the course of the physical universe at the most fundamental level.


pages: 327 words: 103,336

Everything Is Obvious: *Once You Know the Answer by Duncan J. Watts

active measures, affirmative action, Albert Einstein, Amazon Mechanical Turk, Black Swan, business cycle, butterfly effect, Carmen Reinhart, Cass Sunstein, clockwork universe, cognitive dissonance, coherent worldview, collapse of Lehman Brothers, complexity theory, correlation does not imply causation, crowdsourcing, death of newspapers, discovery of DNA, East Village, easy for humans, difficult for computers, edge city, en.wikipedia.org, Erik Brynjolfsson, framing effect, Geoffrey West, Santa Fe Institute, George Santayana, happiness index / gross national happiness, high batting average, hindsight bias, illegal immigration, industrial cluster, interest rate swap, invention of the printing press, invention of the telescope, invisible hand, Isaac Newton, Jane Jacobs, Jeff Bezos, Joseph Schumpeter, Kenneth Rogoff, lake wobegon effect, Laplace demon, Long Term Capital Management, loss aversion, medical malpractice, meta analysis, meta-analysis, Milgram experiment, natural language processing, Netflix Prize, Network effects, oil shock, packet switching, pattern recognition, performance metric, phenotype, Pierre-Simon Laplace, planetary scale, prediction markets, pre–internet, RAND corporation, random walk, RFID, school choice, Silicon Valley, social intelligence, statistical model, Steve Ballmer, Steve Jobs, Steve Wozniak, supply-chain management, The Death and Life of Great American Cities, the scientific method, The Wisdom of Crowds, too big to fail, Toyota Production System, ultimatum game, urban planning, Vincenzo Peruggia: Mona Lisa, Watson beat the top human players on Jeopardy!, X Prize

As Newton himself wrote: If only we could derive the other phenomena of nature from mechanical principles by the same kind of reasoning! For many things lead me to have a suspicion that all phenomena may depend on certain forces by which particles of bodies, by causes not yet known, either are impelled toward one another and cohere in regular figures, or are repelled from one another and recede.6 A century later, the French mathematician and astronomer Pierre-Simon Laplace pushed Newton’s vision to its logical extreme, claiming in effect that Newtonian mechanics had reduced the prediction of the future—even the future of the universe—to a matter of mere computation. Laplace envisioned an “intellect” that knew all the forces that “set nature in motion, and all positions of all items of which nature is composed.” Laplace went on, “for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.”7 The “intellect” of Laplace’s imagination eventually received a name—“Laplace’s demon”—and it has been lurking around the edges of mankind’s view of the future ever since.


pages: 439 words: 104,154

The Clockwork Universe: Saac Newto, Royal Society, and the Birth of the Modern WorldI by Edward Dolnick

Albert Einstein, Apple's 1984 Super Bowl advert, Arthur Eddington, clockwork universe, complexity theory, double helix, Edmond Halley, Isaac Newton, Johannes Kepler, lone genius, music of the spheres, Pierre-Simon Laplace, Richard Feynman, Saturday Night Live, scientific worldview, Simon Singh, Stephen Hawking, Thomas Kuhn: the structure of scientific revolutions

Newton would have wept with rage to know that his scientific descendants spent their lifetimes proving conclusively that the clockwork universe ran even more smoothly than he had ever believed. It ran so marvelously well, in fact, that a new consensus quickly arose—just as Newton’s enemies had claimed, Newton had built a universe that had no place within it for God. The crowning glory of eighteenth-century astronomy was the proof, by the French mathematician Pierre Simon Laplace, that although the planets did wobble a bit as they circled the sun, those wobbles stayed within a narrow, predictable range. Since the wobbles did not grow larger and larger as time passed, as Newton had believed, they did not require that God step in to smooth things out. Laplace presented his masterpiece, a tome called Celestial Mechanics, to Napoleon. How was it, Napoleon asked, that in all those hundreds of pages, Laplace had made not a single mention of God?


Interplanetary Robots by Rod Pyle

autonomous vehicles, Elon Musk, Jeff Bezos, Kickstarter, low earth orbit, Mars Rover, orbital mechanics / astrodynamics, Pierre-Simon Laplace, Pluto: dwarf planet, Search for Extraterrestrial Intelligence, Stephen Hawking, X Prize

In 1655, Christiaan Huygens (who would doubtless be quite pleased to have a probe named after him for a moon he discovered) used an improved telescope to observe that the apparition was in fact a ring of some kind surrounding the planet. He noted that the planet was “surrounded by a thin, flat, ring, nowhere touching, inclined to the ecliptic.”7 Twenty years later, Giovanni Cassini saw the ring divisions (one of which is named after him, the Cassini Division) and realized that the rings were separate structures in a flat plane around the distant world. Over the next two hundred years, scientists like Pierre-Simon Laplace and James Clerk Maxwell intuited that the rings must be made of particles—they could not be solids or liquids as others had theorized; mathematical calculations showed that such structures would not be stable in orbits around a large planet. As the decades sped by, other astronomers used ever-larger instruments to study Saturn's rings, but the real cornucopia of data prior to the Cassini mission came from the Pioneer and Voyager spacecraft as they sped past the planet, with Voyager 2 passing at about 23,000 miles.8 Only then did the real structure and composition of the rings become entrenched in the science books.


pages: 319 words: 100,984

The Moon: A History for the Future by Oliver Morton

Charles Lindbergh, commoditize, Dava Sobel, Donald Trump, Elon Musk, facts on the ground, gravity well, Isaac Newton, Jeff Bezos, Johannes Kepler, low earth orbit, Mark Zuckerberg, Menlo Park, multiplanetary species, Norman Mailer, Pierre-Simon Laplace, planetary scale, Pluto: dwarf planet, plutocrats, Plutocrats, Silicon Valley, South China Sea, Steve Jobs, Stewart Brand, UNCLOS, Whole Earth Catalog, X Prize

The now changeless Moon had previously undergone “a constant progression from one stage of development to the next . . . a perpetual mutation of form and nature”; it had evolved. And an understanding of that evolution could explain the history of other planets, most importantly the Earth, in new ways. The book follows the account of the solar system’s origin given by the great French astronomer Pierre-Simon Laplace: a nebula of dust and gas collapsed in on itself because of Newtonian gravitation. As it did so, an enormous amount of potential energy was given up, and the first law of thermodynamics stated that that energy could not just vanish. Instead, it went into heat. As one of the first law’s framers, Julius von Mayer, had put it, the nebula’s collapse was a source of heat “powerful enough to melt worlds”.


Gaming the Vote: Why Elections Aren't Fair (And What We Can Do About It) by William Poundstone

affirmative action, Albert Einstein, business cycle, Debian, desegregation, Donald Trump, en.wikipedia.org, Everything should be made as simple as possible, global village, guest worker program, hiring and firing, illegal immigration, invisible hand, jimmy wales, John Nash: game theory, John von Neumann, Kenneth Arrow, manufacturing employment, Nash equilibrium, Paul Samuelson, Pierre-Simon Laplace, prisoner's dilemma, Ralph Nader, RAND corporation, Ronald Reagan, Silicon Valley, slashdot, the map is not the territory, Thomas Bayes, transcontinental railway, Unsafe at Any Speed, Y2K

They released him after a short term of captivity, and he returned to France. There he pursued a career as a mathematician and surveyor. A share of his fame rests with his role in devising the metric system. Borda was chairman of the Commission of Weights and Measures, which included many of the great scientists of the age, among them Condorcet, the chemist Antoine Lavoisier, and the mathematician 136 Trouble in Kiribati Pierre Simon Laplace. The illustrious group considered defining the fundamental unit, the meter, as the length of a pendulum that would complete precisely one swing per second. Accurate clocks could be carried to any corner of the globe, and a simple experiment with string and a plumb bob could determine the accurate length. Borda rejected the idea. He did not like the fact that it made the meter dependent on the second, since the second was not an evenpower-of-ten unit (being one sixtieth of a minute), The second was "Babylonian," to use Borda's pejorative.


pages: 400 words: 99,489

The Sirens of Mars: Searching for Life on Another World by Sarah Stewart Johnson

Albert Einstein, Alfred Russel Wallace, Astronomia nova, back-to-the-land, cuban missile crisis, dark matter, Drosophila, Elon Musk, invention of the printing press, Isaac Newton, Johannes Kepler, low earth orbit, Mars Rover, Mercator projection, Pierre-Simon Laplace, Ronald Reagan, scientific mainstream, sensible shoes

It fit perfectly with his interpretation of planetary formation and the idea that planets would march toward an evolutionarily advanced state—both physically and biologically. As an undergraduate at Harvard, Lowell had completed a thesis on the nebular hypothesis. The theory, first suggested on a somewhat intuitive basis by the philosopher Immanuel Kant during a foray into astronomy, and later by the celebrated French mathematical astronomer Pierre-Simon Laplace, held that rings of gas shed by the cooling, contracting sun condensed to form planets. Since entropy—the tendency toward disorder—was unidirectional, it would eventually lead to the senescence of the solar system, with the smaller planets dying first. So, from the time of their birth as molten masses, Lowell reasoned, the planets progressed through stages of development. Mars was clearly in a terrestrial stage where oceans had disappeared, but it was rapidly approaching a dead stage, an airless stage, the stage of Mercury and the stage “so sadly typified by our moon, a body now practically past possibility of change.”


pages: 416 words: 106,582

This Will Make You Smarter: 150 New Scientific Concepts to Improve Your Thinking by John Brockman

23andMe, Albert Einstein, Alfred Russel Wallace, banking crisis, Barry Marshall: ulcers, Benoit Mandelbrot, Berlin Wall, biofilm, Black Swan, butterfly effect, Cass Sunstein, cloud computing, congestion charging, correlation does not imply causation, Daniel Kahneman / Amos Tversky, dark matter, data acquisition, David Brooks, delayed gratification, Emanuel Derman, epigenetics, Exxon Valdez, Flash crash, Flynn Effect, hive mind, impulse control, information retrieval, Intergovernmental Panel on Climate Change (IPCC), Isaac Newton, Jaron Lanier, Johannes Kepler, John von Neumann, Kevin Kelly, lifelogging, mandelbrot fractal, market design, Mars Rover, Marshall McLuhan, microbiome, Murray Gell-Mann, Nicholas Carr, open economy, Pierre-Simon Laplace, place-making, placebo effect, pre–internet, QWERTY keyboard, random walk, randomized controlled trial, rent control, Richard Feynman, Richard Feynman: Challenger O-ring, Richard Thaler, Satyajit Das, Schrödinger's Cat, security theater, selection bias, Silicon Valley, Stanford marshmallow experiment, stem cell, Steve Jobs, Steven Pinker, Stewart Brand, the scientific method, Thorstein Veblen, Turing complete, Turing machine, twin studies, Vilfredo Pareto, Walter Mischel, Whole Earth Catalog, WikiLeaks, zero-sum game

But it wasn’t until our understanding of physics was advanced by thinkers such as Avicenna, Galileo, and Newton that it became reasonable to conceive of the universe evolving under its own power, free of guidance and support from anything beyond itself. Theologians sometimes invoke “sustaining the world” as a function of God. But we know better; the world doesn’t need to be sustained, it can simply be. Pierre-Simon Laplace articulated the very specific kind of rule that the world obeys: If we specify the complete state of the universe (or any isolated part of it) at some particular instant, the laws of physics tell us what its state will be at the very next moment. Applying those laws again, we can figure out what it will be a moment later. And so on, until (in principle, obviously) we can build up a complete history of the universe.


pages: 409 words: 105,551

Team of Teams: New Rules of Engagement for a Complex World by General Stanley McChrystal, Tantum Collins, David Silverman, Chris Fussell

Airbus A320, Albert Einstein, Atul Gawande, autonomous vehicles, bank run, barriers to entry, Black Swan, butterfly effect, call centre, Captain Sullenberger Hudson, Chelsea Manning, clockwork universe, crew resource management, crowdsourcing, Edward Snowden, Flash crash, Frederick Winslow Taylor, global supply chain, Henri Poincaré, high batting average, interchangeable parts, invisible hand, Isaac Newton, Jane Jacobs, job automation, job satisfaction, John Nash: game theory, knowledge economy, Mark Zuckerberg, Mohammed Bouazizi, Nate Silver, Pierre-Simon Laplace, RAND corporation, self-driving car, Silicon Valley, Silicon Valley startup, Skype, Steve Jobs, supply-chain management, The Wealth of Nations by Adam Smith, urban sprawl, US Airways Flight 1549, WikiLeaks, zero-sum game

But at the scale of industrial production, where these gains were multiplied across hundreds of identical machines and thousands of workers, small savings added up to significant differences in productivity and profits. By 1890, Midvale had become an industry leader and Taylor departed to pursue the broader potential of “a workplace ruled by science.” Taylor’s efforts dovetailed nicely with contemporary scientific thought, heavily influenced by the elegant simplicity of earlier thinkers such as Newton and “the French Newton,” Pierre-Simon Laplace. Science at the time was dominated by the notion of determinism—the idea that any initial conditions has only one, inevitable outcome: a ball thrown at a certain speed will have a predictable trajectory, as will a planet in orbit. Throughout the nineteenth century, phenomena that had once been written off as the work of God fell under human mastery. The vision was of a “clockwork universe” in which all laws were coherent and all causes and effects predictable.


pages: 354 words: 105,322

The Road to Ruin: The Global Elites' Secret Plan for the Next Financial Crisis by James Rickards

"Robert Solow", Affordable Care Act / Obamacare, Albert Einstein, asset allocation, asset-backed security, bank run, banking crisis, barriers to entry, Bayesian statistics, Ben Bernanke: helicopter money, Benoit Mandelbrot, Berlin Wall, Bernie Sanders, Big bang: deregulation of the City of London, bitcoin, Black Swan, blockchain, Bonfire of the Vanities, Bretton Woods, British Empire, business cycle, butterfly effect, buy and hold, capital controls, Capital in the Twenty-First Century by Thomas Piketty, Carmen Reinhart, cellular automata, cognitive bias, cognitive dissonance, complexity theory, Corn Laws, corporate governance, creative destruction, Credit Default Swap, cuban missile crisis, currency manipulation / currency intervention, currency peg, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, debt deflation, Deng Xiaoping, disintermediation, distributed ledger, diversification, diversified portfolio, Edward Lorenz: Chaos theory, Eugene Fama: efficient market hypothesis, failed state, Fall of the Berlin Wall, fiat currency, financial repression, fixed income, Flash crash, floating exchange rates, forward guidance, Fractional reserve banking, G4S, George Akerlof, global reserve currency, high net worth, Hyman Minsky, income inequality, information asymmetry, interest rate swap, Isaac Newton, jitney, John Meriwether, John von Neumann, Joseph Schumpeter, Kenneth Rogoff, labor-force participation, large denomination, liquidity trap, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, Mexican peso crisis / tequila crisis, money market fund, mutually assured destruction, Myron Scholes, Naomi Klein, nuclear winter, obamacare, offshore financial centre, Paul Samuelson, Peace of Westphalia, Pierre-Simon Laplace, plutocrats, Plutocrats, prediction markets, price anchoring, price stability, quantitative easing, RAND corporation, random walk, reserve currency, RFID, risk-adjusted returns, Ronald Reagan, Silicon Valley, sovereign wealth fund, special drawing rights, stocks for the long run, The Bell Curve by Richard Herrnstein and Charles Murray, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, theory of mind, Thomas Bayes, Thomas Kuhn: the structure of scientific revolutions, too big to fail, transfer pricing, value at risk, Washington Consensus, Westphalian system

Investors who use complexity theory can leave mainstream analysis behind and get better forecasting results. The third tool in addition to behavioral psychology and complexity theory is Bayesian statistics, a branch of etiology also referred to as causal inference. Both terms derive from Bayes’ theorem, an equation first described by Thomas Bayes and published posthumously in 1763. A version of the theorem was elaborated independently and more formally by the French mathematician Pierre-Simon Laplace in 1774. Laplace continued work on the theorem in subsequent decades. Twentieth-century statisticians have developed more rigorous forms. Normal science including economics assembles massive data sets and uses deductive methods to derive testable hypotheses from the data. These hypotheses often involve correlations and regressions used to forecast future events deemed likely to resemble past events.


pages: 370 words: 107,983

Rage Inside the Machine: The Prejudice of Algorithms, and How to Stop the Internet Making Bigots of Us All by Robert Elliott Smith

Ada Lovelace, affirmative action, AI winter, Alfred Russel Wallace, Amazon Mechanical Turk, animal electricity, autonomous vehicles, Black Swan, British Empire, cellular automata, citizen journalism, Claude Shannon: information theory, combinatorial explosion, corporate personhood, correlation coefficient, crowdsourcing, Daniel Kahneman / Amos Tversky, desegregation, discovery of DNA, Douglas Hofstadter, Elon Musk, Fellow of the Royal Society, feminist movement, Filter Bubble, Flash crash, Gerolamo Cardano, gig economy, Gödel, Escher, Bach, invention of the wheel, invisible hand, Jacquard loom, Jacques de Vaucanson, John Harrison: Longitude, John von Neumann, Kenneth Arrow, low skilled workers, Mark Zuckerberg, mass immigration, meta analysis, meta-analysis, mutually assured destruction, natural language processing, new economy, On the Economy of Machinery and Manufactures, p-value, pattern recognition, Paul Samuelson, performance metric, Pierre-Simon Laplace, precariat, profit maximization, profit motive, Silicon Valley, social intelligence, statistical model, Stephen Hawking, stochastic process, telemarketer, The Bell Curve by Richard Herrnstein and Charles Murray, The Future of Employment, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, theory of mind, Thomas Bayes, Thomas Malthus, traveling salesman, Turing machine, Turing test, twin studies, Vilfredo Pareto, Von Neumann architecture, women in the workforce

Gauss’s new use of the Bell Curve was an inspired idea, but it must be evaluated in the context of Galileo’s critical point: in the case of physical bodies, there is only one true value for the distance from the centre of the Earth to a star. Gauss’s theory was so seductively simple it appeared to offer an almost magical way to predict previously unknowable things with startling accuracy. Perhaps it could be used to illuminate truths in other complex physical, social and economic phenomena in the increasingly complex industrial world of the late eighteenth century? It was Pierre-Simon Laplace (1749–1827) who, in 1785, found a way to broaden the application of the Bell Curve with the publication of his Central Limit Theorem (CLT). This theory establishes that measurements of all sorts of phenomena tend to be distributed according to a Bell Curve, even if the variations of the thing being measured aren’t distributed by a Bell Curve. To understand how CLT works in the real world, let’s consider its application in presidential approval polls.


pages: 289 words: 113,211

A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation by Richard Bookstaber

"Robert Solow", affirmative action, Albert Einstein, asset allocation, backtesting, beat the dealer, Black Swan, Black-Scholes formula, Bonfire of the Vanities, butterfly effect, commoditize, commodity trading advisor, computer age, computerized trading, disintermediation, diversification, double entry bookkeeping, Edward Lorenz: Chaos theory, Edward Thorp, family office, financial innovation, fixed income, frictionless, frictionless market, George Akerlof, implied volatility, index arbitrage, intangible asset, Jeff Bezos, John Meriwether, London Interbank Offered Rate, Long Term Capital Management, loose coupling, margin call, market bubble, market design, merger arbitrage, Mexican peso crisis / tequila crisis, moral hazard, Myron Scholes, new economy, Nick Leeson, oil shock, Paul Samuelson, Pierre-Simon Laplace, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk tolerance, risk/return, Robert Shiller, Robert Shiller, rolodex, Saturday Night Live, selection bias, shareholder value, short selling, Silicon Valley, statistical arbitrage, The Market for Lemons, time value of money, too big to fail, transaction costs, tulip mania, uranium enrichment, William Langewiesche, yield curve, zero-coupon bond, zero-sum game

Just four years before Godel had defined the limits of our ability to conquer the intellectual world of mathematics and logic with the publication of his Undecidability Theorem, the German physicist Werner Heisenberg’s celebrated Uncertainty Principle had delineated the limits of inquiry into the physical world, thereby undoing the efforts of another celebrated intellect, the great mathematician Pierre-Simon Laplace. In the early 1800s Laplace had worked extensively to demonstrate the purely mechanical and predictable nature of planetary motion. He later extended this theory to the interaction of molecules. In the Laplacean view, molecules are just as subject to the laws of physical mechanics as the planets are. In theory, if we knew the position and velocity of each molecule, we could trace its path as it interacted with other molecules, and trace the course of the physical universe at the most fundamental level.


pages: 393 words: 115,217

Loonshots: How to Nurture the Crazy Ideas That Win Wars, Cure Diseases, and Transform Industries by Safi Bahcall

accounting loophole / creative accounting, Albert Einstein, Apple II, Apple's 1984 Super Bowl advert, Astronomia nova, British Empire, Cass Sunstein, Charles Lindbergh, Clayton Christensen, cognitive bias, creative destruction, disruptive innovation, diversified portfolio, double helix, Douglas Engelbart, Douglas Engelbart, Edmond Halley, Gary Taubes, hypertext link, invisible hand, Isaac Newton, Johannes Kepler, Jony Ive, knowledge economy, lone genius, Louis Pasteur, Mark Zuckerberg, Menlo Park, Mother of all demos, Murray Gell-Mann, PageRank, Peter Thiel, Philip Mirowski, Pierre-Simon Laplace, prediction markets, pre–internet, Ralph Waldo Emerson, RAND corporation, random walk, Richard Feynman, Richard Thaler, side project, Silicon Valley, six sigma, Solar eclipse in 1919, stem cell, Steve Jobs, Steve Wozniak, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Tim Cook: Apple, tulip mania, Wall-E, wikimedia commons, yield management

In other words, what we know today as Newton’s laws most likely would go by some other name—or names. Gottfried Leibniz, for example, developed calculus independently, in Germany, around the same time as Newton. Christiaan Huygens, in the Netherlands, developed the idea of centripetal force, the wave theory of light, modern probability theory—and he invented the pendulum clock. Daniel Bernoulli in Switzerland, Leonhard Euler in Germany, Pierre-Simon Laplace in France—all were giants of mathematics and physics who arrived not long after Newton. The Royal Society helped Newton and England win a race against time, a competition to discover truths of nature. But the Society didn’t come together purely for basic research: “Science was to be fostered and nurtured as leading to the improvement of man’s lot on earth by facilitating technologic invention.”


Super Thinking: The Big Book of Mental Models by Gabriel Weinberg, Lauren McCann

affirmative action, Affordable Care Act / Obamacare, Airbnb, Albert Einstein, anti-pattern, Anton Chekhov, autonomous vehicles, bank run, barriers to entry, Bayesian statistics, Bernie Madoff, Bernie Sanders, Black Swan, Broken windows theory, business process, butterfly effect, Cal Newport, Clayton Christensen, cognitive dissonance, commoditize, correlation does not imply causation, crowdsourcing, Daniel Kahneman / Amos Tversky, David Attenborough, delayed gratification, deliberate practice, discounted cash flows, disruptive innovation, Donald Trump, Douglas Hofstadter, Edward Lorenz: Chaos theory, Edward Snowden, effective altruism, Elon Musk, en.wikipedia.org, experimental subject, fear of failure, feminist movement, Filter Bubble, framing effect, friendly fire, fundamental attribution error, Gödel, Escher, Bach, hindsight bias, housing crisis, Ignaz Semmelweis: hand washing, illegal immigration, income inequality, information asymmetry, Isaac Newton, Jeff Bezos, John Nash: game theory, lateral thinking, loss aversion, Louis Pasteur, Lyft, mail merge, Mark Zuckerberg, meta analysis, meta-analysis, Metcalfe’s law, Milgram experiment, minimum viable product, moral hazard, mutually assured destruction, Nash equilibrium, Network effects, nuclear winter, offshore financial centre, p-value, Parkinson's law, Paul Graham, peak oil, Peter Thiel, phenotype, Pierre-Simon Laplace, placebo effect, Potemkin village, prediction markets, premature optimization, price anchoring, principal–agent problem, publication bias, recommendation engine, remote working, replication crisis, Richard Feynman, Richard Feynman: Challenger O-ring, Richard Thaler, ride hailing / ride sharing, Robert Metcalfe, Ronald Coase, Ronald Reagan, school choice, Schrödinger's Cat, selection bias, Shai Danziger, side project, Silicon Valley, Silicon Valley startup, speech recognition, statistical model, Steve Jobs, Steve Wozniak, Steven Pinker, survivorship bias, The Present Situation in Quantum Mechanics, the scientific method, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, transaction costs, uber lyft, ultimatum game, uranium enrichment, urban planning, Vilfredo Pareto, wikimedia commons

Despite this uncertainty, you still have to make a lot of choices, from decisions about your health to deciding whom to vote for to taking a risk with a new project at work. This chapter is about helping you think about wading through such uncertainty in the context of decision making. What advice should you listen to and why? Probability and statistics are the branches of mathematics that give us the most useful mental models for these tasks. As French mathematician Pierre-Simon Laplace wrote in his 1812 book Théorie Analytique des Probabilités: “The most important questions of life are indeed, for the most part, really only problems of probability.” We will discuss the useful mental models from the fields of probability and statistics along with common traps to avoid. While many of the basic concepts of probability are fairly intuitive, your intuition often fails you (as we’ve seen throughout this book).


pages: 395 words: 116,675

The Evolution of Everything: How New Ideas Emerge by Matt Ridley

"Robert Solow", affirmative action, Affordable Care Act / Obamacare, Albert Einstein, Alfred Russel Wallace, AltaVista, altcoin, anthropic principle, anti-communist, bank run, banking crisis, barriers to entry, bitcoin, blockchain, Boris Johnson, British Empire, Broken windows theory, Columbian Exchange, computer age, Corn Laws, cosmological constant, creative destruction, Credit Default Swap, crony capitalism, crowdsourcing, cryptocurrency, David Ricardo: comparative advantage, demographic transition, Deng Xiaoping, discovery of DNA, Donald Davies, double helix, Downton Abbey, Edward Glaeser, Edward Lorenz: Chaos theory, Edward Snowden, endogenous growth, epigenetics, Ethereum, ethereum blockchain, facts on the ground, falling living standards, Ferguson, Missouri, financial deregulation, financial innovation, Frederick Winslow Taylor, Geoffrey West, Santa Fe Institute, George Gilder, George Santayana, Gunnar Myrdal, Henri Poincaré, hydraulic fracturing, imperial preference, income per capita, indoor plumbing, interchangeable parts, Intergovernmental Panel on Climate Change (IPCC), invisible hand, Isaac Newton, Jane Jacobs, Jeff Bezos, joint-stock company, Joseph Schumpeter, Kenneth Arrow, Kevin Kelly, Khan Academy, knowledge economy, land reform, Lao Tzu, long peace, Lyft, M-Pesa, Mahatma Gandhi, Mark Zuckerberg, means of production, meta analysis, meta-analysis, mobile money, money: store of value / unit of account / medium of exchange, Mont Pelerin Society, moral hazard, Necker cube, obamacare, out of africa, packet switching, peer-to-peer, phenotype, Pierre-Simon Laplace, price mechanism, profit motive, RAND corporation, random walk, Ray Kurzweil, rent-seeking, reserve currency, Richard Feynman, rising living standards, road to serfdom, Ronald Coase, Ronald Reagan, Satoshi Nakamoto, Second Machine Age, sharing economy, smart contracts, South Sea Bubble, Steve Jobs, Steven Pinker, The Wealth of Nations by Adam Smith, Thorstein Veblen, transaction costs, twin studies, uber lyft, women in the workforce

The leading Irish scientist Richard Kirwan even went as far as to hint that ideas like Hutton’s contributed to dangerous events like the French Revolution, remarking on how they had ‘proved too favourable to the structure of various systems of atheism or infidelity, as these have been in their turn to turbulence and immorality’. No need of that hypothesis The physicists, who had set the pace in tearing down skyhooks, continued to surprise the world. It fell to Pierre-Simon Laplace (using Emilie du Châtelet’s improvements to cumbersome Newtonian geometry) to take Newtonism to its logical conclusion. Laplace argued that the present state of the universe was ‘the effect of its past and the cause of its future’. If an intellect were powerful enough to calculate every effect of every cause, then ‘nothing would be uncertain and the future just like the past would be present before its eyes’.


pages: 524 words: 120,182

Complexity: A Guided Tour by Melanie Mitchell

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Albert Michelson, Alfred Russel Wallace, anti-communist, Arthur Eddington, Benoit Mandelbrot, bioinformatics, cellular automata, Claude Shannon: information theory, clockwork universe, complexity theory, computer age, conceptual framework, Conway's Game of Life, dark matter, discrete time, double helix, Douglas Hofstadter, en.wikipedia.org, epigenetics, From Mathematics to the Technologies of Life and Death, Geoffrey West, Santa Fe Institute, Gödel, Escher, Bach, Henri Poincaré, invisible hand, Isaac Newton, John Conway, John von Neumann, Long Term Capital Management, mandelbrot fractal, market bubble, Menlo Park, Murray Gell-Mann, Network effects, Norbert Wiener, Norman Macrae, Paul Erdős, peer-to-peer, phenotype, Pierre-Simon Laplace, Ray Kurzweil, reversible computing, scientific worldview, stem cell, The Wealth of Nations by Adam Smith, Thomas Malthus, Turing machine

Newton’s insight—now the backbone of modern science—was that this law applies everywhere in the universe, to falling apples as well as to planets. As he wrote: “nature is exceedingly simple and conformable to herself. Whatever reasoning holds for greater motions, should hold for lesser ones as well.” Newtonian mechanics produced a picture of a “clockwork universe,” one that is wound up with the three laws and then runs its mechanical course. The mathematician Pierre Simon Laplace saw the implication of this clockwork view for prediction: in 1814 he asserted that, given Newton’s laws and the current position and velocity of every particle in the universe, it was possible, in principle, to predict everything for all time. With the invention of electronic computers in the 1940s, the “in principle” might have seemed closer to “in practice.” Revised Views of Prediction However, two major discoveries of the twentieth century showed that Laplace’s dream of complete prediction is not possible, even in principle.


pages: 483 words: 141,836

Red-Blooded Risk: The Secret History of Wall Street by Aaron Brown, Eric Kim

activist fund / activist shareholder / activist investor, Albert Einstein, algorithmic trading, Asian financial crisis, Atul Gawande, backtesting, Basel III, Bayesian statistics, beat the dealer, Benoit Mandelbrot, Bernie Madoff, Black Swan, business cycle, capital asset pricing model, central bank independence, Checklist Manifesto, corporate governance, creative destruction, credit crunch, Credit Default Swap, disintermediation, distributed generation, diversification, diversified portfolio, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, experimental subject, financial innovation, illegal immigration, implied volatility, index fund, Long Term Capital Management, loss aversion, margin call, market clearing, market fundamentalism, market microstructure, money market fund, money: store of value / unit of account / medium of exchange, moral hazard, Myron Scholes, natural language processing, open economy, Pierre-Simon Laplace, pre–internet, quantitative trading / quantitative finance, random walk, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, road to serfdom, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, special drawing rights, statistical arbitrage, stochastic volatility, stocks for the long run, The Myth of the Rational Market, Thomas Bayes, too big to fail, transaction costs, value at risk, yield curve

Second, we know nothing about the accuracy of this statement in particular; we only make a claim about the long-term accuracy of lots of statements. This is how we turn an event that has already happened—drawing nine red marbles out of 10—into a hypothetical coin-flip gambling game that can be repeated indefinitely. The main alternative to frequentist statistics today is the Bayesian view. It is named for Thomas Bayes, an eighteenth-century theorist, but it was Pierre-Simon Laplace who put forth the basic ideas. It was not until the twentieth century, however, that researchers, including Richard Cox and Bruno de Finetti, created the modern formulation. In the Bayesian view of the urn, you must have some prior belief about the number of red marbles in the urn. For example, you might believe that any number from 0 to 100 red marbles is equally likely. Drawing the 10 marbles causes you to update your prior belief into a posterior belief.


pages: 437 words: 132,041

Alex's Adventures in Numberland by Alex Bellos

Andrew Wiles, Antoine Gombaud: Chevalier de Méré, beat the dealer, Black Swan, Black-Scholes formula, Claude Shannon: information theory, computer age, Daniel Kahneman / Amos Tversky, Edward Thorp, family office, forensic accounting, game design, Georg Cantor, Henri Poincaré, Isaac Newton, Johannes Kepler, lateral thinking, Myron Scholes, pattern recognition, Paul Erdős, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, random walk, Richard Feynman, Rubik’s Cube, SETI@home, Steve Jobs, The Bell Curve by Richard Herrnstein and Charles Murray, traveling salesman

Buffon arrived at his equation by studying an eighteenth-century gambling game called ‘clean tile’, in which you throw a coin on to a tiled surface and bet on whether it will touch the cracks between tiles or rest cleanly. Buffon came up with the following alternative scenario: imagine that a floor is marked with parallel lines spaced evenly apart and that a needle is thrown on it. He then correctly calculated that if the length of the needle is l and the distance between lines is d, then the following equation holds: Probability of the needle touching the line = A few years after Buffon died, Pierre Simon Laplace realized that this equation could be used to estimate a value for pi. If you throw lots and lots of needles on the floor, then the ratio of the number of times that the needle hits the line to the total number of throws will be approximately equal to the mathematical probability of the needle touching the line. In other words, after many throws or: (The symbol means ‘is approximately equal to’.)


pages: 532 words: 133,143

To Explain the World: The Discovery of Modern Science by Steven Weinberg

Albert Einstein, Alfred Russel Wallace, Astronomia nova, Brownian motion, Commentariolus, cosmological constant, dark matter, Dava Sobel, double helix, Edmond Halley, Eratosthenes, Ernest Rutherford, fudge factor, invention of movable type, Isaac Newton, James Watt: steam engine, Johannes Kepler, music of the spheres, On the Revolutions of the Heavenly Spheres, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, retrograde motion, Thomas Kuhn: the structure of scientific revolutions

The Newtonian theory certainly provided a common meeting ground for astronomers trying to explain observations that went beyond Kepler’s laws. The methods for applying Newton’s theory to problems involving more than two bodies were developed by many authors in the late eighteenth and early nineteenth centuries. There was one innovation of great future importance that was explored especially by Pierre-Simon Laplace in the early nineteenth century. Instead of adding up the gravitational forces exerted by all the bodies in an ensemble like the solar system, one calculates a “field,” a condition of space that at every point gives the magnitude and direction of the acceleration produced by all the masses in the ensemble. To calculate the field, one solves certain differential equations that it obeys. (These equations set conditions on the way that the field varies when the point at which it is measured is moved in any of three perpendicular directions.)


pages: 790 words: 150,875

Civilization: The West and the Rest by Niall Ferguson

Admiral Zheng, agricultural Revolution, Albert Einstein, Andrei Shleifer, Atahualpa, Ayatollah Khomeini, Berlin Wall, BRICs, British Empire, business cycle, clean water, collective bargaining, colonial rule, conceptual framework, Copley Medal, corporate governance, creative destruction, credit crunch, David Ricardo: comparative advantage, Dean Kamen, delayed gratification, Deng Xiaoping, discovery of the americas, Dissolution of the Soviet Union, European colonialism, Fall of the Berlin Wall, Francisco Pizarro, full employment, Hans Lippershey, haute couture, Hernando de Soto, income inequality, invention of movable type, invisible hand, Isaac Newton, James Hargreaves, James Watt: steam engine, John Harrison: Longitude, joint-stock company, Joseph Schumpeter, Kickstarter, Kitchen Debate, land reform, land tenure, liberal capitalism, Louis Pasteur, Mahatma Gandhi, market bubble, Martin Wolf, mass immigration, means of production, megacity, Mikhail Gorbachev, new economy, Pearl River Delta, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, profit maximization, purchasing power parity, quantitative easing, rent-seeking, reserve currency, road to serfdom, Ronald Reagan, savings glut, Scramble for Africa, Silicon Valley, South China Sea, sovereign wealth fund, special economic zone, spice trade, spinning jenny, Steve Jobs, Steven Pinker, The Great Moderation, the market place, the scientific method, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, Thorstein Veblen, total factor productivity, trade route, transaction costs, transatlantic slave trade, undersea cable, upwardly mobile, uranium enrichment, wage slave, Washington Consensus, women in the workforce, World Values Survey

/ To arms, citizens, / Form in battalions, / March, march! / Let impure blood / Water our furrows! … [Spare] not these bloody despots / … All these tigers who pitilessly / Ripped out their mothers’ wombs!’ † Now Slavkov in the Czech Republic, Austerlitz was the scene of the battle that prompted Napoleon to commission the Arc de Triomphe. * At the Ecole Militaire in Paris, Napoleon had been examined by Pierre-Simon Laplace, one of the pioneers of the mathematics of probability. * Compare Eugène Delacroix’s Liberty Leads the People (1830) with Egide, Baron Wappers’s Episode of the Belgian Revolution of 1830 (1835) and (among many twentieth-century examples) the Mexican Diego Rivera’s The Arsenal (1928). † Wagner had, according to his autobiography, ‘conceive[d] the plan of a tragedy for the ideal stage of the future, entitled Jesus of Nazareth.


pages: 528 words: 146,459

Computer: A History of the Information Machine by Martin Campbell-Kelly, William Aspray, Nathan L. Ensmenger, Jeffrey R. Yost

Ada Lovelace, air freight, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Apple's 1984 Super Bowl advert, barriers to entry, Bill Gates: Altair 8800, borderless world, Buckminster Fuller, Build a better mousetrap, Byte Shop, card file, cashless society, cloud computing, combinatorial explosion, computer age, deskilling, don't be evil, Donald Davies, Douglas Engelbart, Douglas Engelbart, Dynabook, fault tolerance, Fellow of the Royal Society, financial independence, Frederick Winslow Taylor, game design, garden city movement, Grace Hopper, informal economy, interchangeable parts, invention of the wheel, Jacquard loom, Jeff Bezos, jimmy wales, John Markoff, John von Neumann, Kickstarter, light touch regulation, linked data, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Menlo Park, Mitch Kapor, natural language processing, Network effects, New Journalism, Norbert Wiener, Occupy movement, optical character recognition, packet switching, PageRank, pattern recognition, Pierre-Simon Laplace, pirate software, popular electronics, prediction markets, pre–internet, QWERTY keyboard, RAND corporation, Robert X Cringely, Silicon Valley, Silicon Valley startup, Steve Jobs, Steven Levy, Stewart Brand, Ted Nelson, the market place, Turing machine, Vannevar Bush, Von Neumann architecture, Whole Earth Catalog, William Shockley: the traitorous eight, women in the workforce, young professional

His researches were mainly mathematical, and in 1816 his achievements were recognized by his election to the Royal Society, the leading scientific organization in Britain. He was then twenty-five—an enfant terrible with a growing scientific reputation. In 1819 Babbage made the first of several visits to Paris, where he met a number of the leading members of the French Scientific Academy, such as the mathematicians Pierre-Simon Laplace and Joseph Fourier, with whom he formed lasting friendships. It was probably during this visit that Babbage learned of the great French table-making project organized by Baron Gaspard de Prony. This project would show Babbage a vision that would determine the future course of his life. De Prony began the project in 1790, shortly after the French Revolution. The new government planned to reform many of France’s ancient institutions and, in particular, to establish a fair system of property taxation.


pages: 604 words: 165,488

Mr Five Per Cent: The Many Lives of Calouste Gulbenkian, the World's Richest Man by Jonathan Conlin

accounting loophole / creative accounting, anti-communist, banking crisis, British Empire, carried interest, Ernest Rutherford, estate planning, Fellow of the Royal Society, light touch regulation, MITM: man-in-the-middle, Network effects, Pierre-Simon Laplace, rent-seeking, stakhanovite, Yom Kippur War

Instead she contacted the Iranian consul-general in Paris, Abdol Hossein Sardari, who halted proceedings and even got the German Embassy to phone Soulas with an apology.11 Goering was interested in a number of items from Gulbenkian’s collection, but had the courtesy to make offers through Prince Andrei Youssoupoff, offers which Gulbenkian refused.12 Houdon’s Diana did not go to Berlin. In Lisbon, however, restrictions placed on his currency movements by the British and American authorities continued to tie Gulbenkian’s hands, making it difficult to acquire new items for his collection. It took over a year for him to make arrangements to pay Henri de Rothschild for his portrait of the astronomer Pierre-Simon Laplace by Lépicié and for another portrait by Nattier. Henri’s grandmother had formed a renowned collection of works by Chardin and other eighteenth-century French artists, which Gulbenkian had admired at La Muette in Paris thirty years before. At the outbreak of war these paintings were moved to London, where the majority were destroyed in the Blitz. Gulbenkian tried to buy several of Rothschild’s Chardins and add them to all the other paintings he planned to give to the National Gallery, but was again unable to release the funds.


pages: 551 words: 174,280

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, global pandemic, Gödel, Escher, Bach, illegal immigration, invention of movable type, Isaac Newton, Islamic Golden Age, Jacquard loom, Johannes Kepler, John Conway, John von Neumann, Joseph-Marie Jacquard, Kenneth Arrow, Loebner Prize, Louis Pasteur, pattern recognition, Pierre-Simon Laplace, Richard Feynman, Search for Extraterrestrial Intelligence, Stephen Hawking, supervolcano, technological singularity, Thales of Miletus, The Coming Technological Singularity, the scientific method, Thomas Malthus, Thorstein Veblen, Turing test, Vernor Vinge, Whole Earth Review, William of Occam, zero-sum game

But, if Archimedes had been willing to allow his rules to be applied without arbitrary limits, he could have invented a much better universal system just by removing the arbitrary limits from the existing Greek system. A few years later the mathematician Apollonius invented yet another system of numerals which fell short of universality for the same reason. It is as though everyone in the ancient world was avoiding universality on purpose. The mathematician Pierre Simon Laplace (1749–1827) wrote, of the Indian system, ‘We shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity.’ But was this really something that escaped them, or something that they chose to steer clear of? Archimedes must have been aware that his method of extending a number system – which he used twice in succession – could be continued indefinitely.


Blueprint: The Evolutionary Origins of a Good Society by Nicholas A. Christakis

agricultural Revolution, Alfred Russel Wallace, Amazon Mechanical Turk, assortative mating, Cass Sunstein, crowdsourcing, David Attenborough, different worldview, disruptive innovation, double helix, epigenetics, experimental economics, experimental subject, invention of agriculture, invention of gunpowder, invention of writing, iterative process, job satisfaction, Joi Ito, joint-stock company, land tenure, Laplace demon, longitudinal study, Mahatma Gandhi, Marc Andreessen, means of production, mental accounting, meta analysis, meta-analysis, microbiome, out of africa, phenotype, Pierre-Simon Laplace, placebo effect, race to the bottom, Ralph Waldo Emerson, replication crisis, Rubik’s Cube, Silicon Valley, social intelligence, social web, stem cell, Steven Pinker, the scientific method, theory of mind, twin studies, ultimatum game, zero-sum game

From an early age, we categorize objects according to fundamental commonalities, discriminate between these categories, and assign each category a basic essence. P. Bloom, How Pleasure Works: The New Science of Why We Like What We Like (New York: W. W. Norton, 2010); S. A. Gelman, The Essential Child: Origins of Essentialism in Everyday Thought (New York: Oxford University Press, 2010). 40. In the end, we would get Laplace’s Demon. For “such an intellect,” French mathematician Pierre-Simon Laplace argued in 1814, “nothing would be uncertain and the future just like the past would be present before its eyes.” P. S. Laplace, A Philosophical Essay on Probabilities, 6th ed., trans. F. W. Truscott and F. L. Emory (New York: Dover, 1951), p. 4. 41. There is actually much debate about whether the idea that the world obeys natural laws and is predictable can be reconciled with the idea that humans can truly have free will.


pages: 789 words: 207,744

The Patterning Instinct: A Cultural History of Humanity's Search for Meaning by Jeremy Lent

"Robert Solow", Admiral Zheng, agricultural Revolution, Albert Einstein, Alfred Russel Wallace, Atahualpa, Benoit Mandelbrot, Bretton Woods, British Empire, Buckminster Fuller, Capital in the Twenty-First Century by Thomas Piketty, cognitive dissonance, commoditize, complexity theory, conceptual framework, dematerialisation, demographic transition, different worldview, Doomsday Book, en.wikipedia.org, European colonialism, failed state, Firefox, Francisco Pizarro, Georg Cantor, happiness index / gross national happiness, hedonic treadmill, income inequality, Intergovernmental Panel on Climate Change (IPCC), Internet of things, invention of gunpowder, invention of writing, Isaac Newton, Johann Wolfgang von Goethe, Johannes Kepler, Lao Tzu, Law of Accelerating Returns, mandelbrot fractal, mass immigration, megacity, Metcalfe's law, Mikhail Gorbachev, Nicholas Carr, Norbert Wiener, oil shale / tar sands, out of africa, peak oil, Pierre-Simon Laplace, QWERTY keyboard, Ray Kurzweil, Sapir-Whorf hypothesis, Scientific racism, scientific worldview, shareholder value, sharing economy, Silicon Valley, Simon Kuznets, social intelligence, South China Sea, Stephen Hawking, Steven Pinker, technological singularity, the scientific method, theory of mind, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, Thorstein Veblen, Turing test, ultimatum game, urban sprawl, Vernor Vinge, wikimedia commons

It was the winter of 1961, and while another snowstorm was threatening outside, Lorenz was busy constructing his own model of the weather on a state-of-the-art computer installed in his office, replete with vacuum tubes and a spaghetti of wires. Lorenz was on the cutting edge of the scientific endeavor to decipher the hidden mechanisms of nature. Back in the eighteenth century, mathematician Pierre-Simon Laplace had proposed that the universe was completely deterministic and, given enough information, it was theoretically possible to predict the movement of every atom. Scientists ever since had been inspired by this vision, analyzing nature's building blocks with the goal of predicting exactly how they worked. They had been hamstrung primarily by limitations in calculating horsepower, but the recent arrival of computers held the promise of great breakthroughs.


pages: 824 words: 218,333

The Gene: An Intimate History by Siddhartha Mukherjee

Albert Einstein, Alfred Russel Wallace, All science is either physics or stamp collecting, Any sufficiently advanced technology is indistinguishable from magic, Asilomar, Asilomar Conference on Recombinant DNA, Benoit Mandelbrot, butterfly effect, dark matter, discovery of DNA, double helix, Drosophila, epigenetics, Ernest Rutherford, experimental subject, Internet Archive, invisible hand, Isaac Newton, longitudinal study, medical residency, moral hazard, mouse model, New Journalism, out of africa, phenotype, Pierre-Simon Laplace, Ponzi scheme, Ralph Waldo Emerson, Scientific racism, stem cell, The Bell Curve by Richard Herrnstein and Charles Murray, Thomas Malthus, twin studies

Already, the bare outline of an idea was coalescing in his mind—a notion so simple, and yet so deeply radical, that no biologist had dared to explore it fully: What if all the finches had arisen from a common ancestral finch? What if the small armadillos of today had arisen from a giant ancestral armadillo? Lyell had argued that the current landscape of the earth was the consequence of natural forces that had accumulated over millions of years. In 1796, the French physicist Pierre-Simon Laplace had proposed that even the current solar system had arisen from the gradual cooling and condensation of matter over millions of years (when Napoléon had asked Laplace why God was so conspicuously missing from his theory, Laplace had replied with epic cheekiness: “Sire, I had no need for that hypothesis”). What if the current forms of animals were also the consequence of natural forces that had accumulated over millennia?


pages: 1,737 words: 491,616

Rationality: From AI to Zombies by Eliezer Yudkowsky

Albert Einstein, Alfred Russel Wallace, anthropic principle, anti-pattern, anti-work, Arthur Eddington, artificial general intelligence, availability heuristic, Bayesian statistics, Berlin Wall, Build a better mousetrap, Cass Sunstein, cellular automata, cognitive bias, cognitive dissonance, correlation does not imply causation, cosmological constant, creative destruction, Daniel Kahneman / Amos Tversky, dematerialisation, different worldview, discovery of DNA, Douglas Hofstadter, Drosophila, effective altruism, experimental subject, Extropian, friendly AI, fundamental attribution error, Gödel, Escher, Bach, hindsight bias, index card, index fund, Isaac Newton, John Conway, John von Neumann, Long Term Capital Management, Louis Pasteur, mental accounting, meta analysis, meta-analysis, money market fund, Nash equilibrium, Necker cube, NP-complete, P = NP, pattern recognition, Paul Graham, Peter Thiel, Pierre-Simon Laplace, placebo effect, planetary scale, prediction markets, random walk, Ray Kurzweil, reversible computing, Richard Feynman, risk tolerance, Rubik’s Cube, Saturday Night Live, Schrödinger's Cat, scientific mainstream, scientific worldview, sensible shoes, Silicon Valley, Silicon Valley startup, Singularitarianism, Solar eclipse in 1919, speech recognition, statistical model, Steven Pinker, strong AI, technological singularity, The Bell Curve by Richard Herrnstein and Charles Murray, the map is not the territory, the scientific method, Turing complete, Turing machine, ultimatum game, X Prize, Y Combinator, zero-sum game

“He is here,” said the guide in that strange loud whisper. The endless grid of robed figures replied in one voice: perfectly blended, exactly synchronized, so that not a single individual could be singled out from the rest, and betrayed: “Who is absent?” “Jakob Bernoulli,” intoned the guide, and the walls replied: “Is dead but not forgotten.” “Abraham de Moivre,” “Is dead but not forgotten.” “Pierre-Simon Laplace,” “Is dead but not forgotten.” “Edwin Thompson Jaynes,” “Is dead but not forgotten.” “They died,” said the guide, “and they are lost to us; but we still have each other, and the project continues.” In the silence, the guide turned to Brennan, and stretched forth a hand, on which rested a small ring of nearly transparent material. Brennan stepped forward to take the ring— But the hand clenched tightly shut.

This corresponds to multiplying together the probability assigned to the outcome in each experiment, to find the joint probability of all the experiments together. We take the logarithm to simplify our intuitive understanding of the accumulated score, to maintain our grip on the tiny fractions involved, and to ensure we maximize our expected score by stating our honest probabilities rather than placing all our play money on the most probable bet. Bayesianity states that when you die, Pierre-Simon Laplace examines every single event in your life, from finding your shoes next to your bed in the morning to finding your workplace in its accustomed spot. Every losing lottery ticket means you cared enough to play. Laplace assesses the advance probability you assigned to each event. Where you did not assign a precise numerical probability in advance, Laplace examines your degree of anticipation or surprise, extrapolates other possible outcomes and your extrapolated reactions, and renormalizes your extrapolated emotions to a likelihood distribution over possible outcomes.


pages: 903 words: 235,753

The Stack: On Software and Sovereignty by Benjamin H. Bratton

1960s counterculture, 3D printing, 4chan, Ada Lovelace, additive manufacturing, airport security, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, algorithmic trading, Amazon Mechanical Turk, Amazon Web Services, augmented reality, autonomous vehicles, basic income, Benevolent Dictator For Life (BDFL), Berlin Wall, bioinformatics, bitcoin, blockchain, Buckminster Fuller, Burning Man, call centre, carbon footprint, carbon-based life, Cass Sunstein, Celebration, Florida, charter city, clean water, cloud computing, connected car, corporate governance, crowdsourcing, cryptocurrency, dark matter, David Graeber, deglobalization, dematerialisation, disintermediation, distributed generation, don't be evil, Douglas Engelbart, Douglas Engelbart, Edward Snowden, Elon Musk, en.wikipedia.org, Eratosthenes, Ethereum, ethereum blockchain, facts on the ground, Flash crash, Frank Gehry, Frederick Winslow Taylor, future of work, Georg Cantor, gig economy, global supply chain, Google Earth, Google Glasses, Guggenheim Bilbao, High speed trading, Hyperloop, illegal immigration, industrial robot, information retrieval, Intergovernmental Panel on Climate Change (IPCC), intermodal, Internet of things, invisible hand, Jacob Appelbaum, Jaron Lanier, Joan Didion, John Markoff, Joi Ito, Jony Ive, Julian Assange, Khan Academy, liberal capitalism, lifelogging, linked data, Mark Zuckerberg, market fundamentalism, Marshall McLuhan, Masdar, McMansion, means of production, megacity, megastructure, Menlo Park, Minecraft, MITM: man-in-the-middle, Monroe Doctrine, Network effects, new economy, offshore financial centre, oil shale / tar sands, packet switching, PageRank, pattern recognition, peak oil, peer-to-peer, performance metric, personalized medicine, Peter Eisenman, Peter Thiel, phenotype, Philip Mirowski, Pierre-Simon Laplace, place-making, planetary scale, RAND corporation, recommendation engine, reserve currency, RFID, Robert Bork, Sand Hill Road, self-driving car, semantic web, sharing economy, Silicon Valley, Silicon Valley ideology, Slavoj Žižek, smart cities, smart grid, smart meter, social graph, software studies, South China Sea, sovereign wealth fund, special economic zone, spectrum auction, Startup school, statistical arbitrage, Steve Jobs, Steven Levy, Stewart Brand, Stuxnet, Superbowl ad, supply-chain management, supply-chain management software, TaskRabbit, the built environment, The Chicago School, the scientific method, Torches of Freedom, transaction costs, Turing complete, Turing machine, Turing test, undersea cable, universal basic income, urban planning, Vernor Vinge, Washington Consensus, web application, Westphalian system, WikiLeaks, working poor, Y Combinator

In twelfth century Majorca, Ramon Llull described logical machines, influencing Gottfried Leibniz, who developed a predictive calculus and a biliteral alphabet that, drawing on the I Ching, allowed for the formal reduction of any complex symbolic expression to a sequence of discrete binary states (zero and one, on and off). Later, the formalization of logic within the philosophy mathematics (from Pierre-Simon Laplace, to Gottlob Frege, Georg Cantor, David Hilbert, and so many others) helped to introduce, inform, and ultimately disprove a version of the Enlightenment as the expression of universal deterministic processes (of both thought and physics). In 1936, with his now-famous paper, “On Computable Numbers, with an Application to the Entscheidungsproblem,” a very young Alan Turing at once introduced the theoretical basis of modern computing and demonstrated the limits of what could and could not ever be calculated and computed by a universal technology.


Engineering Security by Peter Gutmann

active measures, algorithmic trading, Amazon Web Services, Asperger Syndrome, bank run, barriers to entry, bitcoin, Brian Krebs, business process, call centre, card file, cloud computing, cognitive bias, cognitive dissonance, combinatorial explosion, Credit Default Swap, crowdsourcing, cryptocurrency, Daniel Kahneman / Amos Tversky, Debian, domain-specific language, Donald Davies, Donald Knuth, double helix, en.wikipedia.org, endowment effect, fault tolerance, Firefox, fundamental attribution error, George Akerlof, glass ceiling, GnuPG, Google Chrome, iterative process, Jacob Appelbaum, Jane Jacobs, Jeff Bezos, John Conway, John Markoff, John von Neumann, Kickstarter, lake wobegon effect, Laplace demon, linear programming, litecoin, load shedding, MITM: man-in-the-middle, Network effects, Parkinson's law, pattern recognition, peer-to-peer, Pierre-Simon Laplace, place-making, post-materialism, QR code, race to the bottom, random walk, recommendation engine, RFID, risk tolerance, Robert Metcalfe, Ruby on Rails, Sapir-Whorf hypothesis, Satoshi Nakamoto, security theater, semantic web, Skype, slashdot, smart meter, social intelligence, speech recognition, statistical model, Steve Jobs, Steven Pinker, Stuxnet, telemarketer, text mining, the built environment, The Death and Life of Great American Cities, The Market for Lemons, the payments system, Therac-25, too big to fail, Turing complete, Turing machine, Turing test, web application, web of trust, x509 certificate, Y2K, zero day, Zimmermann PGP

, Guy Politzer and Ira Noveck, Journal of Psycholinguistic Research, Vol.20, No.2 (March 1991), p.83. [232] “Task Understanding”, Vittorio Girotto, in “The Nature of Reasoning”, Cambridge University Press, 2004, p.103. [233] “G.W.Leibniz The Art of Controversies”, Marcelo Dascal, Springer Verlag, 2008. Several variations of this are found in Leibniz’ writings, mostly in Latin, and often as undated notes on loose paper. [234] “A Philosophical Essay on Probabilities”, Pierre-Simon Laplace (transl. Frederick Truscott and Frederick Emory, Dover Publications, 1951. [235] “Why Johnny can’t surf (safely)? Attacks and defenses for web users”, Amir Herzberg, Computers & Security, Vol.28, No.1-2 (February/March 2009), p.63. [236] “Influence: Science and Practice”, Robert Cialdini, Allyn and Bacon, 2001. [237] “Perseverance in self perception and social perception: Biased attributional processes in the debriefing paradigm”, Lee Ross, Mark Lepper and Michael Hubbard, Journal of Personality and Social Psychology, Vol.32, No.5 (November 1975), p.880. [238] “Human Inferences: Strategies and Shortcomings of Social Judgment”, Richard Nisbett and Lee Ross, Prentice-Hall, 1980. [239] “Graphology — a total write-off”, Barry Beyerstein, in “Tall Tales about the Mind and Brain: Separating Fact from Fiction”, p.265. [240] “The Fallacy of Personal Validation: A classroom Demonstration of Gullibility”, Bertram Forer, Journal of Abnormal Psychology, Vol.44 (1949), p.118. [241] “The ‘Barnum Effect’ in Personality Assessment: A Review of the Literature”, D.Dickson and I.Kelly, Psychological Reports.