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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.
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, John Nash: game theory, John von Neumann, 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, sealed-bid auction, second-price auction, self-driving car, Silicon Valley, Skype, sorting algorithm, spectrum auction, 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.
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, John von Neumann, Lao Tzu, lone genius, New Journalism, Norbert Wiener, pets.com, Pierre-Simon Laplace, Richard Feynman, 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.
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, 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, Mikhail Gorbachev, Mohammed Bouazizi, Nash equilibrium, Nate Silver, obamacare, pattern recognition, performance metric, Pierre-Simon Laplace, place-making, placebo effect, prediction markets, quantitative easing, random walk, randomized controlled trial, Richard Feynman, Richard Feynman, Richard Thaler, Robert Shiller, Robert Shiller, Ronald Reagan, Saturday Night Live, 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.
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, 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.
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.
airport security, availability heuristic, Bayesian statistics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, big-box store, Black Swan, Broken windows theory, 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, haute cuisine, Henri Poincaré, high batting average, housing crisis, income per capita, index fund, 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, 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.
Albert Einstein, crowdsourcing, dark matter, Edmond Halley, Edward Charles Pickering, en.wikipedia.org, Eratosthenes, gravity well, Isaac Newton, 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, V2 rocket
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.
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, moral hazard, Nash equilibrium, 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.
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, 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.
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, 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.
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, John Conway, Pierre-Simon Laplace, place-making, probability theory / Blaise Pascal / Pierre de Fermat, retrograde motion, Richard Feynman, 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.
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, Pierre-Simon Laplace, RAND corporation, Turing machine, V2 rocket, 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.
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.
Albert Einstein, Albert Michelson, Arthur Eddington, cosmic abundance, dark matter, Donald Davies, Edmond Halley, invention of the telescope, Isaac Newton, 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.
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, 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!)
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, 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, 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, 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.”
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, Jacquard loom, Jaron Lanier, jimmy wales, John von Neumann, Joseph-Marie Jacquard, lifelogging, Louis Daguerre, Marshall McLuhan, Menlo Park, microbiome, Milgram experiment, Network effects, New Journalism, Norbert Wiener, 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, 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
Everything Is Obvious: *Once You Know the Answer by Duncan J. Watts
active measures, affirmative action, Albert Einstein, Amazon Mechanical Turk, Black Swan, butterfly effect, Carmen Reinhart, Cass Sunstein, clockwork universe, cognitive dissonance, 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, 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, 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.
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, 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, 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.
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, 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, Richard Feynman: Challenger O-ring, Richard Thaler, Satyajit Das, Schrödinger's Cat, security theater, selection bias, Silicon Valley, stem cell, Steve Jobs, Steven Pinker, Stewart Brand, the scientific method, Thorstein Veblen, Turing complete, Turing machine, Vilfredo Pareto, Walter Mischel, Whole Earth Catalog, 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.
Albert Einstein, Apple's 1984 Super Bowl advert, Arthur Eddington, clockwork universe, complexity theory, double helix, Edmond Halley, Isaac Newton, lone genius, music of the spheres, Pierre-Simon Laplace, Richard Feynman, Richard Feynman, Saturday Night Live, 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?
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, 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, 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.
The End of Theory: Financial Crises, the Failure of Economics, and the Sweep of Human Interaction by Richard Bookstaber
asset allocation, bank run, bitcoin, butterfly effect, 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, 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.
Gaming the Vote: Why Elections Aren't Fair (And What We Can Do About It) by William Poundstone
affirmative action, Albert Einstein, 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.
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, 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, 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, transatlantic slave trade, 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.
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, 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, 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.
A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation by Richard Bookstaber
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.
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, Myron Scholes, pattern recognition, Paul Erdős, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, random walk, Richard Feynman, 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’.)
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, 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.)
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, Jacquard loom, Jeff Bezos, jimmy wales, John Markoff, John von Neumann, light touch regulation, linked data, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Menlo Park, 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.
The Evolution of Everything: How New Ideas Emerge by Matt Ridley
affirmative action, Affordable Care Act / Obamacare, Albert Einstein, Alfred Russel Wallace, altcoin, anthropic principle, anti-communist, bank run, banking crisis, barriers to entry, bitcoin, blockchain, 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 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, 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, 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’.
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 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, John Markoff, 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, 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, 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.
The Beginning of Infinity: Explanations That Transform the World by David Deutsch
agricultural Revolution, Albert Michelson, anthropic principle, artificial general intelligence, Bonfire of the Vanities, conceptual framework, cosmological principle, dark matter, David Attenborough, discovery of DNA, Douglas Hofstadter, Eratosthenes, Ernest Rutherford, first-past-the-post, Georg Cantor, Gödel, Escher, Bach, illegal immigration, invention of movable type, Isaac Newton, Islamic Golden Age, Jacquard loom, Jacquard loom, John Conway, John von Neumann, Joseph-Marie Jacquard, Kenneth Arrow, Loebner Prize, Louis Pasteur, pattern recognition, Pierre-Simon Laplace, Richard Feynman, Richard Feynman, Search for Extraterrestrial Intelligence, Stephen Hawking, supervolcano, technological singularity, The Coming Technological Singularity, the scientific method, Thomas Malthus, Thorstein Veblen, Turing test, Vernor Vinge, Whole Earth Review, William of Occam, 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.
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, 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, Richard Feynman, risk tolerance, Rubik’s Cube, Saturday Night Live, Schrödinger's Cat, scientific mainstream, 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.