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The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street
** by
Justin Fox

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Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, bank run, Benoit Mandelbrot, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, card file, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discovery of the americas, diversification, diversified portfolio, Edward Glaeser, endowment effect, Eugene Fama: efficient market hypothesis, experimental economics, financial innovation, Financial Instability Hypothesis, floating exchange rates, George Akerlof, Henri Poincaré, Hyman Minsky, implied volatility, impulse control, index arbitrage, index card, index fund, invisible hand, Isaac Newton, John Nash: game theory, John von Neumann, joint-stock company, Joseph Schumpeter, libertarian paternalism, linear programming, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market design, New Journalism, Nikolai Kondratiev, Paul Lévy, pension reform, performance metric, Ponzi scheme, prediction markets, pushing on a string, quantitative trading / quantitative ﬁnance, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, road to serfdom, Robert Shiller, Robert Shiller, rolodex, Ronald Reagan, shareholder value, Sharpe ratio, short selling, side project, Silicon Valley, South Sea Bubble, statistical model, The Chicago School, The Myth of the Rational Market, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Thomas L Friedman, Thorstein Veblen, Tobin tax, transaction costs, tulip mania, value at risk, Vanguard fund, volatility smile, Yogi Berra

Robert Loring Allen, Irving Fisher: A Biography (Cambridge, Mass., and Oxford: Blackwell, 1993), 95. The preceding story about the theft is taken from Allen’s book and Irving Norton Fisher, My Father Irving Fisher (New York: Comet Press Books, 1956). These two books are the source of all Fisher biographical information in this book, except as otherwise noted. 3. Henri Poincaré, The Value of Science: Essential Writings of Henri Poincaré (New York: The Modern Library, 2001), 402. 4. Louis Bachelier, “Theory of Speculation,” in The Random Character of Stock Prices, trans. A. James Boness, ed. Paul Cootner (Cambridge, Mass.: MIT Press, 1969), 28. 5. Bachelier, “Theory of Speculation,” 17. 6. Poincaré, Value of Science, 419. 7. Bachelier, “Theory of Speculation,” 25–26. 8. This and all other biographical information on Bachelier is from Jean-Michel Courtault et al., “Louis Bachelier on the Centenary of Théorie de la Spéculation,” Mathematical Finance (July 2000): 341–53.

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Bachelier undertook his investigation at a time when scientists had begun to embrace the idea that while there could be no absolute certainty about anything, uncertainty itself could be a powerful tool. Instead of trying to track down the cause of every last jiggling of a molecule or movement of a planet, one could simply assume that the causes were many and randomness the result. “It is thanks to chance—that is to say, thanks to our ignorance, that we can arrive at conclusions,” wrote the great French mathematician and physicist Henri Poincaré in 1908.3 The greatest tool for building knowledge upon such ignorance was what was called the Gaussian distribution (after German stargazer and mathematician Carl Friedrich Gauss), the normal distribution, or simply the bell curve. A Gaussian array of numbers can be adequately described by invoking only the mean (i.e., the top of the bell) and what in the waning years of the nineteenth century came to be known as the standard deviation (the width of the bell).

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His work was so innovative that when Albert Einstein employed similar mathematical tools five years later to describe the random motion of tiny particles suspended in a fluid or a gas—called “Brownian motion,” after the botanist who first noted it—he helped lay the foundations of nuclear physics. But while physicists, building upon Einstein’s work, were putting together atomic bombs by the 1940s, practical application of Bachelier’s insights would not emerge until the 1970s. This is not simply a tale of ignored genius. There was a major limitation to Bachelier’s work, of which he was well aware. His teacher, Henri Poincaré, made sure of that. While he celebrated the use of the bell curve in the physical sciences, Poincaré thought caution needed to be exercised in applying it to human behavior. The Gaussian distribution, or the bell curve, is the product of countless random and independent causes. “When men are brought together,” Poincaré wrote, “they no longer decide by chance and independently of each other, but react upon one another.

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Alex's Adventures in Numberland
** by
Alex Bellos

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

The outcomes cluster symmetrically around a mean value. Of course, a graph of measurements won’t give you a continuous curve – it will give you (as we saw with my baguettes) a jagged landscape of fixed amounts. The bell curve is a theoretical ideal of the pattern produced by random error. The more data we have, the closer the jagged landscape of outcomes will fit the curve. In the late nineteenth century the French mathematician Henri Poincaré knew that the distribution of an outcome that is subject to random measurement error will approximate the bell curve. Poincaré, in fact, conducted the same experiment with baguettes as I did, but for a different reason. He suspected that his local boulangerie was rpping him off by selling underweight loaves, so he decided to exercise mathematics in the interest of justice. Every day for a year he weighed his daily lkg loaf.

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When the normal distribution is found in a set of data, this could simply be because the measurements have been gathered too shambolically. Which brings me back to my baguettes. Were their weights really normally distributed? Was the tail thin or fat? First, a recap. I weighen argued00 baguettes. The distribution of their weights was chapter 10. The graph showed some hopeful trends – there was a mean of somewhere around 400g, and a more or less symmetrical spread between 380 and 420g. If I had been as indefatigable as Henri Poincaré, I would have continued the experiment for a year and had 365 (give or take days of bakery closure) weights to compare. With more data, the distribution would have been clearer. Still, my smaller sample was enough to get an idea of the pattern forming. I used a trick, compressing my results by redrawing the graph with a scale that grouped baguette weights in bounds of 8g rather than 1g. This created the following graph: When I first drew this out I felt relief, as it really looked like my baguette experiment was producing a bell curve.

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The summer heat, I assumed, was drying them out faster. Again, this variation could have had the effect of stretching the curve leftwards. My experiment may have shown that baguette weights approximated a slightly distorted bell curve, yet what I had really learned was that measurement is never so simple. The normal distribution is a theoretical ideal, and one cannot assume that all results will conform to it. I wondered about Henri Poincaré. When he measured his bread did he eliminate bias due to the Parisian weather, or the time of day of his measurements? Perhaps he had not demonstrated that he was being sold a 950g loaf instead of a 1kg loaf at all, but had instead proved that from baking to measuring, a 1kg loaf reduces in weight by 50g. The history of the bell curve, in fact, is a wonderful parable about the curious kinship between pure and applied scientists.

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Surfaces and Essences
** by
Douglas Hofstadter,
Emmanuel Sander

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affirmative action, Albert Einstein, Arthur Eddington, Benoit Mandelbrot, Brownian motion, Chance favours the prepared mind, cognitive dissonance, computer age, computer vision, dematerialisation, Donald Trump, Douglas Hofstadter, Ernest Rutherford, experimental subject, Flynn Effect, Georg Cantor, Gerolamo Cardano, Golden Gate Park, haute couture, haute cuisine, Henri Poincaré, Isaac Newton, l'esprit de l'escalier, Louis Pasteur, Mahatma Gandhi, mandelbrot fractal, Menlo Park, Norbert Wiener, place-making, Silicon Valley, statistical model, Steve Jobs, Steve Wozniak, theory of mind, upwardly mobile, urban sprawl

Another widely held view of analogy (and here we come to the second stereotype) is that when people make analogies, they call on sophisticated reasoning mechanisms that, through intricate machinations, somehow manage to link together far-flung domains of knowledge, sometimes in a conscious fashion; the conclusions reached thereby may be very subtle but will also be very tentative. This vision gives rise to the image of analogies as being the fruit of strokes of genius, or at least of deep and unusual insights. And there are indeed numerous famous cases of this sort that one can cite — great scientific discoveries resulting from sudden inspirations of people who found undreamt-of links between seemingly unrelated domains. Thus the mathematician Henri Poincaré wrote, “One day… the idea came to me very concisely, very suddenly, and with great certainty, that the transformations of indeterminate ternary quadratic forms were identical to those of non-Euclidean geometry.” This flash of inspiration gave rise to much rich new mathematics. One can also admiringly recall various architects, painters, and designers who, thanks to some fresh analogy, were able to transport a concept from one domain to a distant one in such a fruitful way that people were amazed.

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Likewise, the fact that we can easily put our finger on scads of situation-essences by exploiting standard labels that have been handed to us by our culture does not mean that we could do so in a trackless, uncharted wilderness where no one has gone before. Concepts have a special property that distinguishes them from physical tools: as opposed to being just an external device, a concept becomes an integral part of the person who acquires it. The mathematician Henri Poincaré is said to have stated, “When a dog eats the flesh of a goose, it turns into the flesh of a dog.” He was referring to how we internalize knowledge we acquire, and how it differs for that reason from mere tools, which remain separate from us, much as a piton is totally separate from a mountain climber. Merely having a library filled with books about, say, mathematics, fashion, or word origins does not make one a mathematician, a fashion designer, or an etymologist.

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These mental pitons are no longer just inert objects in an external cliff, but become parts of the person using them. They cannot be easily removed in the same way that one can take a piton out of a rock, because to remove a concept is to take away some of the person who owns it. How would Albert Einstein contribute to contemporary physics, were he a young physicist today? What would Alexander Pushkin bring to today’s poetry? What would Shakespeare or Dante write if they were alive today? What would Henri Poincaré give to mathematics, and Sigmund Freud to cognitive science? What analogies would they discover lurking implicitly in today’s concepts? What depths could they perceive in the world around them, by using the tools of their new conceptual universe to interpret the surface appearances that they would encounter all around them? Sailing Off into Outer Conceptual Space In this chapter and the preceding one, we have presented an image of any particular language’s repertoire of lexical items as forming a “lexical galaxy” in conceptual space.

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

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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, Richard Feynman, Richard Feynman, Richard Stallman, Schrödinger's Cat, Slavoj Žižek, Stephen Hawking, stochastic process, the scientific method, wikimedia commons

One of these questions was the “three-body problem”—how three massive objects would move under the influence of their mutual gravitational pull. (For two bodies it’s easy, and Newton had solved it: Planets move in ellipses.) This problem was tackled by Henri Poincaré, who in his early thirties was already recognized as one of the world’s leading mathematicians. He did not solve it, but submitted an essay that seemed to demonstrate a crucial feature: that the orbits of the planets would be stable. Even without knowing the exact solutions, we could be confident that the planets would at least behave predictably. Poincaré’s method was so ingenious that he was awarded the prize, and his paper was prepared for publication in Mittag-Leffler’s new journal, Acta Mathematica.169 Figure 52: Henri Poincaré, pioneer of topology, relativity, and chaos theory, and later president of the Bureau of Longitude. But there was a slight problem: Poincaré had made a mistake.

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Special relativity, which explains how the speed of light can have the same value for all observers, was put together by a number of researchers over the early years of the twentieth century. (Its successor, general relativity, which interpreted gravity as an effect of the curvature of spacetime, was due almost exclusively to Einstein.) One of the major contributors to special relativity was the French mathematician and physicist Henri Poincaré. While Einstein was the one who took the final bold leap into asserting that the “time” as measured by any moving observer was as good as the “time” measured by any other, both he and Poincaré developed very similar formalisms in their research on relativity.55 Historian Peter Galison, in his book Einstein’s Clocks, Poincaré’s Maps: Empires of Time, makes the case that Einstein and Poincaré were as influenced by their earthbound day jobs as they were by esoteric considerations of the architecture of physics.56 Einstein was working at the time as a patent clerk in Bern, Switzer land, where a major concern was the construction of accurate clocks.

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Nietzsche felt that a successful life was one that you would be proud to have repeated in an endless cycle.168 The idea of a cyclic universe, or “eternal return,” was by no means original with Nietzsche. It appears now and again in ancient religions—in Greek myths, Hinduism, Buddhism, and some indigenous American cultures. The Wheel of Life spins, and history repeats itself. But soon after Nietzsche imagined his demon, the idea of eternal recurrence popped up in physics. In 1890 Henri Poincaré proved an intriguing mathematical theorem, showing that certain physical systems would necessarily return to any particular configuration infinitely often, if you just waited long enough. This result was seized upon by a young mathematician named Ernst Zermelo, who claimed that it was incompatible with Boltzmann’s purported derivation of the Second Law of Thermodynamics from underlying reversible rules of atomic motion.

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

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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, 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, 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, pre–internet, Ralph Waldo Emerson, RAND corporation, reversible computing, Richard Feynman, Richard Feynman, 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

(Illustration credit 9.2) (Illustration credit 9.3) (Illustration credit 9.4) (Illustration credit 9.5) Scientists envied the demon’s powers. It became a familiar character in cartoons enlivening physics journals. To be sure, the creature was a fantasy, but the atom itself had seemed fantastic, and the demon had helped tame it. Implacable as the laws of nature now seemed, the demon defied these laws. It was a burglar, picking the lock one molecule at a time. It had “infinitely subtile senses,” wrote Henri Poincaré, and “could turn back the course of the universe.”♦ Was this not just what humans dreamed of doing? Through their ever better microscopes, scientists of the early twentieth century examined the active, sorting processes of biological membranes. They discovered that living cells act as pumps, filters, and factories. Purposeful processes seemed to operate at tiny scales. Who or what was in control?

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Whether the population of France is an even or odd number at any given instant is random, but the population of France itself is surely not random: it is a definite fact, even if not knowable.♦ John Maynard Keynes tackled randomness in terms of its opposites, and he chose three: knowledge, causality, and design.♦ What is known in advance, determined by a cause, or organized according to plan cannot be random. “Chance is only the measure of our ignorance,”♦ Henri Poincaré famously said. “Fortuitous phenomena are by definition those whose laws we do not know.” Immediately he recanted: “Is this definition very satisfactory? When the first Chaldean shepherds watched the movements of the stars, they did not yet know the laws of astronomy, but would they have dreamed of saying that the stars move at random?” For Poincaré, who understood chaos long before it became a science, examples of randomness included such phenomena as the scattering of raindrops, their causes physically determined but so numerous and complex as to be unpredictable.

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♦ “HE DIFFERS FROM REAL LIVING ANIMALS”: Royal Institution Lecture, 28 February 1879, Proceedings of the Royal Institution 9 (1880): 113, in William Thomson, Mathematical and Physical Papers, vol. 5 (Cambridge: Cambridge University Press, 1911), 21. ♦ “INFINITE SWARMS OF ABSURD LITTLE MICROSCOPIC IMPS”: “Editor’s Table,” Popular Science Monthly 15 (1879): 412. ♦ “CLERK MAXWELL’S DEMON”: Henry Adams to Brooks Adams, 2 May 1903, in Henry Adams and His Friends: A Collection of His Unpublished Letters, ed. Harold Cater (Boston: Houghton Mifflin, 1947), 545. ♦ “INFINITELY SUBTILE SENSES”: Henri Poincaré, The Foundations of Science, trans. George Bruce Halsted (New York: Science Press, 1913), 152. ♦ “NOW WE MUST NOT INTRODUCE DEMONOLOGY”: James Johnstone, The Philosophy of Biology (Cambridge: Cambridge University Press, 1914), 118. ♦ “IF WE VIEW THE EXPERIMENTING MAN”: Leó Szilárd, “On the Decrease of Entropy in a Thermodynamic System by the Intervention of Intelligent Beings,” trans. Anatol Rapoport and Mechthilde Knoller, from Leó Szilárd, “Über Die Entropieverminderung in Einem Thermodynamischen System Bei Eingriffen Intelligenter Wesen,” Zeitschrift für Physik 53 (1929): 840–56, in Harvey S.

**
Chaos
** by
James Gleick

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Benoit Mandelbrot, butterfly effect, cellular automata, Claude Shannon: information theory, discrete time, Edward Lorenz: Chaos theory, experimental subject, Georg Cantor, Henri Poincaré, Isaac Newton, iterative process, John von Neumann, Louis Pasteur, mandelbrot fractal, Murray Gell-Mann, Norbert Wiener, pattern recognition, Richard Feynman, Richard Feynman, Stephen Hawking, stochastic process, trade route

It asks, if you don’t know the measurements, what can you say about overall structure. Smale had solved one of the historic, outstanding problems of topology, the Poincaré conjecture, for spaces of five dimensions and higher, and in so doing established a secure standing as one of the great men of the field. In the 1960s, though, he left topology for untried territory. He began studying dynamical systems. Both subjects, topology and dynamical systems, went back to Henri Poincaré, who saw them as two sides of one coin. Poincaré, at the turn of the century, had been the last great mathematician to bring a geometric imagination to bear on the laws of motion in the physical world. He was the first to understand the possibility of chaos; his writings hinted at a sort of unpredictability almost as severe as the sort Lorenz discovered. But after Poincaré’s death, while topology flourished, dynamical systems atrophied.

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“IT WOULD EMBRACE” Pierre Simon de Laplace, A Philosophical Essay on Probabilities (New York: Dover, 1951). “THE BASIC IDEA” Winfree. “THAT’S THE KIND OF RULE” Lorenz. SUDDENLY HE REALIZED “On the Prevalence,” p. 55. SMALL ERRORS PROVED CATASTROPHIC Of all the classical physicists and mathematicians who thought about dynamical systems, the one who best understood the possibility of chaos was Jules Henri Poincaré. Poincaré remarked in Science and Method: “A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still know the situation approximately.

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Is God a Mathematician?
** by
Mario Livio

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Albert Einstein, Antoine Gombaud: Chevalier de Méré, Brownian motion, cellular automata, correlation coefficient, correlation does not imply causation, cosmological constant, Dava Sobel, double helix, Edmond Halley, Eratosthenes, Georg Cantor, Gerolamo Cardano, Gödel, Escher, Bach, Henri Poincaré, Isaac Newton, John von Neumann, music of the spheres, probability theory / Blaise Pascal / Pierre de Fermat, The Design of Experiments, the scientific method, traveling salesman

Recall that Kant asserted that information from our senses is organized exclusively along Euclidean templates before it is recorded in our consciousness. Geometers of the nineteenth century quickly developed intuition in the non-Euclidean geometries and learned to experience the world along those lines. The Euclidean perception of space turned out to be learned after all, rather than intuitive. All of these dramatic developments led the great French mathematician Henri Poincaré (1854–1912) to conclude that the axioms of geometry are “neither synthetic a priori intuitions nor experimental facts. They are conventions [emphasis added]. Our choice among all possible conventions is guided by experimental facts, but it remains free.” In other words, Poincaré regarded the axioms only as “definitions in disguise.” Poincaré’s views were inspired not just by the non-Euclidean geometries described so far, but also by the proliferation of other new geometries, which before the end of the nineteenth century seemed to be almost getting out of hand.

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Most mathematicians regarded the new geometries as amusing curiosities at best. Whereas Euclidean geometry derived much of its historical power from being seen as the description of real space, the non-Euclidean geometries had been perceived initially as not having any connection whatsoever to physical reality. Consequently, the non-Euclidean geometries were treated by many mathematicians as Euclidean geometry’s poor cousins. Henri Poincaré was a bit more accommodating than most, but even he insisted that if humans were to be transported to a world in which the accepted geometry was non-Euclidean, then it was still “certain that we should not find it more convenient to make a change” from Euclidean to non-Euclidean geometry. Two questions therefore loomed large: (1) Could geometry (in particular) and other branches of mathematics (in general) be established on solid axiomatic logical foundations?

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E=mc2: A Biography of the World's Most Famous Equation
** by
David Bodanis

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Albert Einstein, Arthur Eddington, Berlin Wall, British Empire, dark matter, Ernest Rutherford, Erwin Freundlich, Fellow of the Royal Society, Henri Poincaré, Isaac Newton, John von Neumann, Mercator projection, pre–internet, Richard Feynman, Richard Feynman, Silicon Valley, Silicon Valley startup, Stephen Hawking, Thorstein Veblen, V2 rocket

He sent off the relativity article he was so proud of, along with others he’d written. He was rejected. A little later he applied to a high school, again offering his services as a teacher. The equation was sealed in the envelope with the rest of his application forms. There were twenty-one applicants, and three got called in for interviews. Einstein wasn’t one of them. In time a few scientists did begin to hear of his work, and then jealousy set in. Henri Poincaré was one of the glories of Third Republic France, and, along with David Hilbert in Germany, one of the greatest mathematicians in the world. As a young man Poincaré had written up the ﬁrst ideas behind what later became chaos theory; as a student, the story goes, he’d once seen an elderly woman on a street corner knitting, and then, thinking about the geometry of her knitting needles as he walked along the street, he’d hurried back and told her that there was another way she could have done it: he’d independently come up with purling.

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The Château de Cirey ended up shuttered and abandoned during the Revolution, but was later refurbished. Her ﬁrst son never lived to see that, having become ambassador to Britain under Louis XVI, which led, after his return to France, to his arrest and subsequent death by the guillotine. “If I were King,” du Châtelet once wrote, “. . . women would be worth more, and men would gain something new to emulate.” henri poincaré lived for seven years after Einstein’s 1905 publications, still unreconciled to the fact that outside of France he wasn’t recognized as a founder of relativity. In his ﬁnal years he wrote eloquent, thoughtful essays on creativity. He also ensured that no one who wanted to work on Einstein’s theories could be promoted in France. mile va marić-einstein continued looking up to her husband, even as he started an affair and their marriage broke apart.

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The Physics of Wall Street: A Brief History of Predicting the Unpredictable
** by
James Owen Weatherall

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Albert Einstein, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Asian financial crisis, bank run, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, butterfly effect, capital asset pricing model, Carmen Reinhart, Claude Shannon: information theory, collateralized debt obligation, collective bargaining, dark matter, Edward Lorenz: Chaos theory, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial innovation, George Akerlof, Gerolamo Cardano, Henri Poincaré, invisible hand, Isaac Newton, iterative process, John Nash: game theory, Kenneth Rogoff, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, martingale, new economy, Paul Lévy, prediction markets, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative ﬁnance, random walk, Renaissance Technologies, risk-adjusted returns, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Coase, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, statistical arbitrage, statistical model, stochastic process, The Chicago School, The Myth of the Rational Market, tulip mania, V2 rocket, volatility smile

His marks were not the best at the university, but the small handful of students who bested him, classmates like Paul Langevin and Alfred-Marie Liénard, are now at least as famous as Bachelier himself, among mathematicians anyway. It was good company to be in. After finishing his undergraduate degree, Bachelier stayed at the University of Paris for his doctorate. His work attracted the attention of the best minds of the day, and he began to work on a dissertation — the one Samuelson later discovered, on speculation in financial markets — with Henri Poincaré, perhaps the most famous mathematician and physicist in France at the time. Poincaré was an ideal person to mentor Bachelier. He had made substantial contributions to every field he had come in contact with, including pure mathematics, astronomy, physics, and engineering. Although he did attend a grande école as an undergraduate, like Bachelier he had done his graduate work at the University of Paris.

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Thorp, and William T. Ziemba. 2011. The Kelly Capital Growth Investment Criterion. Singapore: World Scientific Publishing. Maddy, Penelope. 1997. Naturalism in Mathematics. New York: Oxford University Press. — — — . 2001. “Naturalism: Friends and Foes.” Philosophical Perspectives 15: 37–67. — — — . 2007. Second Philosophy. New York: Oxford University Press. Mahwin, Jean. 2005. “Henri Poincaré. A Life in the Service of Science.” Notices of the AMS 52 (9): 1036–44. Malaney, Pia. 1996. “The Index Number Problem: A Differential Geometric Approach.” Dissertation defended at Harvard University. Malevergne, Y., and D. Sornette. 2006. Extreme Financial Risks: From Dependence to Risk Management. Berlin: Springer-Verlag. Malkiel, Burton G. 1973. A Random Walk Down Wall Street: The Best Investment Advice for the New Century.

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The Great Convergence: Information Technology and the New Globalization
** by
Richard Baldwin

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3D printing, additive manufacturing, Admiral Zheng, agricultural Revolution, air freight, Amazon Mechanical Turk, Berlin Wall, bilateral investment treaty, Branko Milanovic, buy low sell high, call centre, Columbian Exchange, Commodity Super-Cycle, David Ricardo: comparative advantage, deindustrialization, domestication of the camel, Edward Glaeser, Erik Brynjolfsson, financial intermediation, George Gilder, global supply chain, global value chain, Henri Poincaré, imperial preference, industrial robot, invention of agriculture, invention of the telegraph, investor state dispute settlement, Isaac Newton, Islamic Golden Age, James Dyson, knowledge economy, knowledge worker, Lao Tzu, low skilled workers, market fragmentation, New Economic Geography, out of africa, paper trading, Pax Mongolica, profit motive, rent-seeking, reshoring, Richard Florida, rising living standards, Second Machine Age, Simon Kuznets, Skype, Snapchat, Stephen Hawking, telepresence, telerobotics, The Wealth of Nations by Adam Smith, trade liberalization, trade route, Washington Consensus

PART V Looking Ahead Despite the best efforts of the smartest humans, no one has found a way to know the future. This ineluctable fact has caused many thinkers to shy away from making predictions. As the Confucian poet Lao Tzu put it: “Those who have knowledge, don’t predict. Those who predict, don’t have knowledge.” But this is wrongheaded. We have a duty to think hard about what may be so as to better prepare society for the changes that may come. As Henri Poincaré wrote in The Foundations of Science, “It is far better to foresee even without certainty than not to foresee at all.”1 Following his wise words, this book’s closing chapter puts forth some conjectures about how globalization may change in the years to come. My guess is that the changes will be radical and disruptive. CHAPTER 10 Future Globalization Globalization is, I believe, in for a radical new transformation, but it will only happen if the cost of moving people falls in the future as much as the cost of moving ideas has in the recent past.

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Daria Taglioni and Deborah Winkler, “Making Global Value Chains Work for Development,” Economic Premise No. 143 (Washington, DC: World Bank Group, 2014), http://documents.worldbank.org/curated/en/2014/05/19517206/making-global-value-chains-work-development. 9. Centre for the Promotion of Imports from developing countries (CBI), “How fast can you become part of the global motorcycle supply chain?” CBI Success Story, July 12, 2012, https://www.cbi.eu/success-stories/how-fast-can-you-become-part-of-the-global-motorcycle-supply-chain-/136079/. PART V. LOOKING AHEAD 1. Henri Poincaré, The Foundations of Science, trans. George Bruce Halsted, Cambridge Library Collection (Cambridge: Cambridge University Press, 1902, 1905, 1908/2014). 10. FUTURE GLOBALIZATION 1. For details on this trade shock, see the 2009 eBook, Richard Baldwin, ed., The Great Trade Collapse: Causes, Consequences and Prospects (London: Centre for Economic Policy Research, November 2009). 2. “A Third Industrial Revolution,” The Economist, April 21, 2012, 15. 3.

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Geek Wisdom
** by
Stephen H. Segal

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Ada Lovelace, Albert Einstein, Any sufficiently advanced technology is indistinguishable from magic, battle of ideas, biofilm, fear of failure, Henri Poincaré, Jacquard loom, Jacquard loom, Mark Zuckerberg, mutually assured destruction, Saturday Night Live, Vernor Vinge

In their own way, the storytelling tropes that emerged from Serling’s influence have been as sweeping a cultural revolution as anything Jefferson could have imagined. Sometimes, geekery is of such high quality that it takes over mainstream culture. The Hollywood trade journal Variety called The Twilight Zone (1959) “the best that has ever been accomplished in half-hour filmed television.” “TO DOUBT EVERYTHING OR TO BELIEVE EVERYTHING ARE TWO EQUALLY CONVENIENT SOLUTIONS; BOTH DISPENSE WITH THE NEED FOR THOUGHT.” —HENRI POINCARÉ, SCIENCE AND HYPOTHESIS WHETHER WE’RE TALKING about religious institutions or the news media, there are times when it’s crucially important to doubt the information we’re given and other times when the need to believe in something can be the only thing that offers any respite. Our tendency, however, is to choose one side or the other of that split and stay there. As human beings, we’re fundamentally lazy.

**
A Beautiful Mind
** by
Sylvia Nasar

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Al Roth, Albert Einstein, Andrew Wiles, Brownian motion, cognitive dissonance, Columbine, experimental economics, fear of failure, Henri Poincaré, invisible hand, Isaac Newton, John Conway, John Nash: game theory, John von Neumann, Kenneth Rogoff, linear programming, lone genius, market design, medical residency, Nash equilibrium, Norbert Wiener, Paul Erdős, prisoner's dilemma, RAND corporation, Ronald Coase, second-price auction, Silicon Valley, Simon Singh, spectrum auction, The Wealth of Nations by Adam Smith, Thorstein Veblen, upwardly mobile

We can all run, and some of us can run the mile in less than 4 minutes; but there is nothing that most of us can do that compares with the creation of the Great G-minor Fugue.”4 Nash’s genius was of that mysterious variety more often associated with music and art than with the oldest of all sciences. It wasn’t merely that his mind worked faster, that his memory was more retentive, or that his power of concentration was greater. The flashes of intuition were non-rational. Like other great mathematical intuitionists — Georg Friedrich Bernhard Riemann, Jules Henri Poincaré, Srinivasa Ramanujan — Nash saw the vision first, constructing the laborious proofs long afterward. But even after he’d try to explain some astonishing result, the actual route he had taken remained a mystery to others who tried to follow his reasoning. Donald Newman, a mathematician who knew Nash at MIT in the 1950s, used to say about him that “everyone else would climb a peak by looking for a path somewhere on the mountain.

…

He had been trapped in Princeton for an entire hot and sticky summer, forced to put aside the interesting problems he had been thinking about, to cram for the general examination.6 Luckily, Lefschetz had appointed a friendly trio of examiners: Church, Steenrod, and a visiting professor from Stanford, Donald Spencer.7 The whole nerve-racking event had gone rather well. Many mathematicians, most famously the French genius Henri Poincaré, have testified to the value of leaving a partially solved problem alone for a while and letting the unconscious work behind the scenes. In an oft-quoted passage from a 1908 essay about the genesis of mathematical discovery, Poincaré writes:8 For fifteen days I struggled to prove that no functions analogous to those I have since called Fuchsian functions could exist. I was then very ignorant.

…

The beer party scene was reconstructed from the recollections of Melvin Hausner, 2.6.96, Martin Davis, 2.20.96, and Hartley Rogers, 1.16.96, who attended several such parties in the course of their graduate school careers. 4. Davis, interview. 5. Ibid. Amazingly, Davis was able, forty years later, to recall the entire song, a few lines of which are given here, interview. 6. Kuhn, interview, 4.16.97. 7. Ibid. 8. Henri Poincaré, quoted in E. T. Bell, Men of Mathematics, op. cit., p. 551. 9. John Nash to Robert Leonard, e-mail, 2.20.93. Further details supplied by Harold Kuhn, interview, 4.17.97. 10. “All the graduate students were afraid of him,” according to Donald Spencer, interview, 11.8.95. 11. Von Neumann’s dress and manner are described by George Mowbry in a letter, 4.5.95. Harold Kuhn, interview, 5.2.97. 12.

**
Debunking Economics - Revised, Expanded and Integrated Edition: The Naked Emperor Dethroned?
** by
Steve Keen

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accounting loophole / creative accounting, banking crisis, banks create money, barriers to entry, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black Swan, Bonfire of the Vanities, butterfly effect, capital asset pricing model, cellular automata, central bank independence, citizen journalism, clockwork universe, collective bargaining, complexity theory, correlation coefficient, credit crunch, David Ricardo: comparative advantage, debt deflation, diversification, double entry bookkeeping, en.wikipedia.org, Eugene Fama: efficient market hypothesis, experimental subject, Financial Instability Hypothesis, Fractional reserve banking, full employment, Henri Poincaré, housing crisis, Hyman Minsky, income inequality, invisible hand, iterative process, John von Neumann, laissez-faire capitalism, liquidity trap, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, market clearing, market microstructure, means of production, minimum wage unemployment, open economy, place-making, Ponzi scheme, profit maximization, quantitative easing, RAND corporation, random walk, risk tolerance, risk/return, Robert Shiller, Robert Shiller, Ronald Coase, Schrödinger's Cat, scientific mainstream, seigniorage, six sigma, South Sea Bubble, stochastic process, The Great Moderation, The Wealth of Nations by Adam Smith, Thorstein Veblen, time value of money, total factor productivity, tulip mania, wage slave

For example, the biological processes in living organisms were thought to be merely a surface manifestation of the underlying chemical processes, and they in turn were just surface manifestations of the quantum mechanics that ruled chemical interactions. This attitude, known as ‘strong reductionism,’ argued that, ultimately, all sciences could be reduced to physics. This belief was best put by the man who first showed its true limits, Henri Poincaré: This conception was not without grandeur; it was seductive, and many among us have not finally renounced it; they know that one will attain the ultimate elements of things only by patiently disentangling the complicated skein that our senses give us; that it is necessary to advance step by step, neglecting no intermediary; that our fathers were wrong in wishing to skip stations; but they believe that when one shall have arrived at these ultimate elements, there again will be found the majestic simplicity of celestial mechanics.

…

Complexity theory and Econophysics Complexity theory is not so much a school of thought in economics as a group of economists who apply what is popularly known as ‘chaos theory’ to economic issues. Since the first edition of this book, there has also been an enormous growth in the number of physicists taking an active interest in economics and finance, and this new school of ‘Econophysics’ has largely subsumed the complexity theory approach. The concept of chaos itself was first discovered in 1899 by the French mathematician Henri Poincaré. However, knowledge of it languished until the mid-1960s because it could not be fully explored until after the invention of computers. Chaotic models of necessity cannot be understood simply by writing down the equations which represent them: instead, they must be simulated, and their properties analyzed numerically. This was simply not possible before the advent of computers. An essential aspect of complexity is the existence of nonlinear relationships between elements of a system, and the apparent ability of complex systems to ‘self-organize.’

…

But, whatever the merits of this doubt are, this possibility – i.e. the completeness of the system of (individual) preferences – must be assumed even for the purposes of the “indifference curve method.” But if this property of u>v is assumed, then our use of the much less questionable [probabilistic method] yields the numerical utilities too!’ (von Neumann and Morgenstern 1953: 28–9). 4 Chaos was first ‘discovered’ by Henri Poincaré in 1899, when he tried to find a solution to the ‘many body problem’ – the problem of gravitational attraction between a star and more than just one planet – and instead proved that there was no analytic solution; instead, the bodies would follow complex aperiodic paths (i.e. cycles occur which never exactly repeat themselves, unlike conventional cyclical functions like sine waves, etc.), which were later labelled ‘chaotic.’ 5 More complex data distributions are predicted by some more elaborate versions of the EMH, but the normal distribution is still the overall yardstick. 6 There are a number of econometric analyses that attempt to account for this.

**
The Social Animal: The Hidden Sources of Love, Character, and Achievement
** by
David Brooks

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Albert Einstein, asset allocation, Atul Gawande, Bernie Madoff, business process, Cass Sunstein, choice architecture, clean water, Daniel Kahneman / Amos Tversky, David Brooks, delayed gratification, deliberate practice, disintermediation, Donald Trump, Douglas Hofstadter, Emanuel Derman, en.wikipedia.org, fear of failure, financial deregulation, financial independence, Flynn Effect, George Akerlof, Henri Poincaré, hiring and firing, impulse control, invisible hand, Joseph Schumpeter, labor-force participation, loss aversion, medical residency, meta analysis, meta-analysis, Monroe Doctrine, Richard Thaler, risk tolerance, Robert Shiller, Robert Shiller, school vouchers, six sigma, Steve Jobs, Steven Pinker, the scientific method, The Spirit Level, The Wealth of Nations by Adam Smith, Thorstein Veblen, transaction costs, Walter Mischel, young professional

Taylor had guided Harold through a method that had him surfing in and out of his unconscious, getting the conscious and unconscious processes to work together—first mastering core knowledge, then letting that knowledge marinate playfully in his mind, then willfully trying to impose order on it, then allowing the mind to consolidate and merge the data, then returning and returning until some magical insight popped into his consciousness, and then riding that insight to a finished product. The process was not easy, but each ounce of effort and each moment of frustration and struggle pushed the internal construction project another little step. By the end, he was seeing the world around him in a new way. There was, as the mathematician Henri Poincaré observed, “an unsuspected kinship … between facts, long known, but wrongly believed to be strangers to one another.” Harold no longer had to work to apply qualities like thumos to the world around him; they simply became the automatic categories of his mind, the way he perceived new situations. When he was in kindergarten and first grade, Harold struggled to learn to read, but then it came naturally to him.

…

He wanted to change a section in which a character was dying, because now he knew how it really felt. The muses came and went. After working for a few hours, she felt her brain running dry, as if little carbonated bubbles in her brain had been used up and everything had gone flat. She became clumsy, lazy and stale. Then other times she would awake in the middle of the night, absolutely sure of what she should do to solve a problem. The mathematician Henri Poincaré solved one of the most difficult problems of his life while stepping onto a bus. The answer just came to him. “I went on with the conversation already commenced, but I felt a perfect certainty,” he later wrote. Erica sometimes had little revelations like that, too, while she was parking the car or making a cup of tea. Like all artists and craftsmen, she was a plaything of the muses. Creativity seemed to happen in a hidden world beyond her control.

**
The Music of the Primes
** by
Marcus Du Sautoy

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Ada Lovelace, Andrew Wiles, Arthur Eddington, Augustin-Louis Cauchy, computer age, Dava Sobel, Dmitri Mendeleev, Eratosthenes, Erdős number, four colour theorem, Georg Cantor, German hyperinflation, global village, Henri Poincaré, Isaac Newton, Jacquard loom, Jacquard loom, music of the spheres, New Journalism, Paul Erdős, Richard Feynman, Richard Feynman, Search for Extraterrestrial Intelligence, Simon Singh, Solar eclipse in 1919, Stephen Hawking, Turing machine, William of Occam, Wolfskehl Prize, Y2K

To herald the new century, Hilbert challenged the audience with a list of twenty-three problems that he believed should set the course for the mathematical explorers of the twentieth century. The ensuing decades saw many of the problems answered, and those who discovered the solutions make up an illustrious band of mathematicians known as ‘the honours class’. It includes the likes of Kurt Gödel and Henri Poincaré, along with many other pioneers whose ideas have transformed the mathematical landscape. But there was one problem, the eighth on Hilbert’s list, which looked as if it would survive the century without a champion: the Riemann Hypothesis. Of all the challenges that Hilbert had set, the eighth had a special place in his heart. There is a German myth about Frederick Barbarossa, a much-loved German emperor who died during the Third Crusade.

…

At the centre of mathematics, the pursuit of order, mathematicians could only hear the sound of chaos. Mathematicians can’t bear to admit that there might not be an explanation for the way Nature has picked the primes. If there were no structure to mathematics, no beautiful simplicity, it would not be worth studying. Listening to white noise has never caught on as an enjoyable pastime. As the French mathematician Henri Poincaré wrote, ‘The scientist does not study Nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If Nature were not beautiful, it would not be worth knowing, and if Nature were not worth knowing, life would not be worth living.’ One might hope that the prime-number heartbeat settles down after a jumpy start. Not so – things just seem to get worse the higher you count.

**
Smarter Than You Think: How Technology Is Changing Our Minds for the Better
** by
Clive Thompson

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3D printing, 4chan, A Declaration of the Independence of Cyberspace, augmented reality, barriers to entry, Benjamin Mako Hill, butterfly effect, citizen journalism, Claude Shannon: information theory, conceptual framework, corporate governance, crowdsourcing, Deng Xiaoping, discovery of penicillin, Douglas Engelbart, Edward Glaeser, en.wikipedia.org, experimental subject, Filter Bubble, Freestyle chess, Galaxy Zoo, Google Earth, Google Glasses, Henri Poincaré, hindsight bias, hive mind, Howard Rheingold, information retrieval, iterative process, jimmy wales, Kevin Kelly, Khan Academy, knowledge worker, Mark Zuckerberg, Marshall McLuhan, Menlo Park, Netflix Prize, Nicholas Carr, patent troll, pattern recognition, pre–internet, Richard Feynman, Richard Feynman, Ronald Coase, Ronald Reagan, sentiment analysis, Silicon Valley, Skype, Snapchat, Socratic dialogue, spaced repetition, telepresence, telepresence robot, The Nature of the Firm, the scientific method, The Wisdom of Crowds, theory of mind, transaction costs, Vannevar Bush, Watson beat the top human players on Jeopardy!, WikiLeaks, X Prize, éminence grise

Each person has gravitated to a tool that they understand well and that fits their cognitive style. • • • The subtler risk of living in our Google-drenched world may not be how it affects our factual knowledge. It’s how it affects our creativity. Sure, social knowledge is great. But many big strikes of creative insight really do require Thinker-style interiority, in which we quietly mull over material that we have deeply internalized. In his essay “Mathematical Creation,” Henri Poincaré described the way this sort of breakthrough happens. Poincaré had been working for two weeks at his desk, trying to prove that a set of functions couldn’t exist. One day he overcaffeinated himself, and while he lay in bed trying to sleep, the ideas stirred in his head. A breakthrough emerged: By morning he had realized that “Fuchsian functions”—as he eventually called them—really did exist.

…

Potts, “Information Re-Retrieval: Repeat Queries in Yahoo’s Logs,” in SIGIR ’07: Proceedings of the 30th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval (2007), 151–58. collaborative inhibition: Celia B. Harris, Paul G. Keil, John Sutton, and Amanda J. Barnier, “We Remember, We Forget: Collaborative Remembering in Older Couples,” Discourse Processes 48, no. 4 (2011), 267–303. In his essay “Mathematical Creation”: Henri Poincaré, “Mathematical Creation,” in The Anatomy of Memory: An Anthology (New York: Oxford University Press, 1996), 126–35. I’m grateful to Jim Holt for drawing my attention to Poincaré’s essay in Holt’s essay “Smarter, Happier, More Productive,” London Review of Books 33, no. 5 (March 3, 2011), 9–12, accessed March 24, 2013, www.lrb.co.uk/v33/n05/jim-holt/smarter-happier-more-productive; my analysis here draws on Holt’s writing.

**
Big Bang
** by
Simon Singh

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Albert Einstein, Albert Michelson, All science is either physics or stamp collecting, Andrew Wiles, anthropic principle, Arthur Eddington, Astronomia nova, Brownian motion, carbon-based life, Cepheid variable, Chance favours the prepared mind, Commentariolus, Copley Medal, cosmic abundance, cosmic microwave background, cosmological constant, cosmological principle, dark matter, Dava Sobel, Defenestration of Prague, discovery of penicillin, Dmitri Mendeleev, Edmond Halley, Edward Charles Pickering, Eratosthenes, Ernest Rutherford, Erwin Freundlich, Fellow of the Royal Society, fudge factor, Hans Lippershey, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, Henri Poincaré, horn antenna, if you see hoof prints, think horses—not zebras, Index librorum prohibitorum, invention of the telescope, Isaac Newton, John von Neumann, Karl Jansky, Louis Daguerre, Louis Pasteur, luminiferous ether, Magellanic Cloud, Murray Gell-Mann, music of the spheres, Olbers’ paradox, On the Revolutions of the Heavenly Spheres, Paul Erdős, retrograde motion, Richard Feynman, Richard Feynman, scientific mainstream, Simon Singh, Solar eclipse in 1919, Stephen Hawking, the scientific method, Thomas Kuhn: the structure of scientific revolutions, unbiased observer, V2 rocket, Wilhelm Olbers, William of Occam

It is generally agreed by philosophers and historians of science that the Babylonians were not true scientists, because they were still content with a universe guided by gods and explained with myths. In any case, collecting hundreds of measurements and listing endless stellar and planetary positions was trivial compared with genuine science, which has the glorious ambition of trying to explain such observations by understanding the underlying nature of the universe. As the French mathematician and philosopher of science Henri Poincaré rightly declared: ‘Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.’ Figure 5 It is possible to estimate the size of the Sun, once we know its distance. One approach is to use a total solar eclipse and our knowledge of the Moon’s distance and diameter. A total solar eclipse is visible only from a small patch on the Earth’s surface at any given time, because the Sun and the Moon appear almost the same size when viewed from the Earth.

…

When they brewed beer, they were interested in the technological methods and the results, but not why or how one material was being transformed into another. They had no inkling of the underlying chemical or biochemical mechanisms at work. So, the Egyptians were technologists, not scientists, whereas Eratosthenes and his colleagues were scientists, not technologists. The intentions of the Greek scientists were identical to those described two thousand years later by Henri Poincaré: The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Of course I do not here speak of that beauty that strikes the senses, the beauty of qualities and appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmonious order of the parts, and which a pure intelligence can grasp.

**
Infinite Ascent: A Short History of Mathematics
** by
David Berlinski

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Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Andrew Wiles, Benoit Mandelbrot, Douglas Hofstadter, Eratosthenes, four colour theorem, Georg Cantor, Gödel, Escher, Bach, Henri Poincaré, Isaac Newton, John von Neumann, Murray Gell-Mann, Stephen Hawking, Turing machine, William of Occam

On surfaces of constant negative curvature, Euclidean straight lines undergo a semantic transmogrification; no longer straight and hardly even lines, they are identified with geodesics, which are arcs measuring the shortest distance between two points. FIG. 7.2 Once this adjustment to Euclid’s system is countenanced, Euclid’s parallel postulate unobtrusively recedes. Lines through a point parallel to a given line? There are lots of them. Writing some thirty years after Lobachevsky, Henri Poincaré provided a far more intuitive model of hyperbolic geometry, one known now as the Poincaré disk. Up to a certain point, the disk is what it seems—a flat, circular, bounded, Euclidean expanse, something like a dish with no depth. Points within the disk are Euclidean points. But lines in the Poincaré disk consist of circular arcs intersecting the boundaries at right angles (Figure 7.3). It is the definition of distance that changes the Poincaré disk into a model of hyperbolic geometry.

**
A Brief History of Time
** by
Stephen Hawking

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Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, bet made by Stephen Hawking and Kip Thorne, Brownian motion, cosmic microwave background, cosmological constant, dark matter, Edmond Halley, Ernest Rutherford, Henri Poincaré, Isaac Newton, Magellanic Cloud, Murray Gell-Mann, Richard Feynman, Richard Feynman, Stephen Hawking

Between 1887 and 1905 there were several attempts, most notably by the Dutch physicist Hendrik Lorentz, to explain the result of the Michelson-Morley experiment in terms of objects contracting and clocks slowing down when they moved through the ether. However, in a famous paper in 1905, a hitherto unknown clerk in the Swiss patent office, Albert Einstein, pointed out that the whole idea of an ether was unnecessary, providing one was willing to abandon the idea of absolute time. A similar point was made a few weeks later by a leading French mathematician, Henri Poincaré. Einstein’s arguments were closer to physics than those of Poincaré, who regarded this problem as mathematical. Einstein is usually given the credit for the new theory, but Poincaré is remembered by having his name attached to an important part of it. The fundamental postulate of the theory of relativity, as it was called, was that the laws of science should be the same for all freely moving observers, no matter what their speed.

**
Models. Behaving. Badly.: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life
** by
Emanuel Derman

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Albert Einstein, Asian financial crisis, Augustin-Louis Cauchy, Black-Scholes formula, British Empire, Brownian motion, capital asset pricing model, Cepheid variable, crony capitalism, diversified portfolio, Douglas Hofstadter, Emanuel Derman, Eugene Fama: efficient market hypothesis, Henri Poincaré, Isaac Newton, law of one price, Mikhail Gorbachev, quantitative trading / quantitative ﬁnance, random walk, Richard Feynman, Richard Feynman, riskless arbitrage, savings glut, Schrödinger's Cat, Sharpe ratio, stochastic volatility, the scientific method, washing machines reduced drudgery, yield curve

Ampère’s Law: The magnetic forces that two current elements, I1 of length dl1 and I2 of length dl2, separated by a distance r21 , exert on each other. Each element can point in an arbitrary direction, and they can be separated by an arbitrary distance. Ampère’s formula is shown boxed. A SYMPATHETIC UNDERSTANDING Ampère titled his paper “Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience.” But as Henri Poincaré remarked in 1905 about “Ampère’s immortal work,” Ampère’s laws could not have been deduced from experience, because he had no infinitesimal currents to experiment with. Only what Einstein called intuition or a “sympathetic understanding of experience” could have led him from observations of entire circuits to a law for infinitesimal current elements. In his encyclopedic A Treatise on Electricity and Magnetism, James Clerk Maxwell later wrote: The experimental investigation by which Ampère established the laws of the mechanical action between electric currents is one of the most brilliant achievements in science.

**
Turing's Vision: The Birth of Computer Science
** by
Chris Bernhardt

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Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Andrew Wiles, British Empire, cellular automata, Claude Shannon: information theory, complexity theory, Conway's Game of Life, discrete time, Douglas Hofstadter, Georg Cantor, Gödel, Escher, Bach, Henri Poincaré, Internet Archive, Jacquard loom, Jacquard loom, John Conway, John von Neumann, Joseph-Marie Jacquard, Norbert Wiener, Paul Erdős, Turing complete, Turing machine, Turing test, Von Neumann architecture

He realized that the set of all possible sets caused problems for his theory, but the question was whether there was some slight modification that could be made to fix things, or whether there was some substantial error that would require a major modification of what mathematicians were doing. The quotes at the start of this chapter give some idea of how Cantor’s work was initially received. Some mathematicians thought his work was nonsense. Leopold Kronecker and Henri Poincaré both attacked it. He was even attacked on religious grounds. If God was the infinite, did having different infinities imply an infinite number of gods? Other mathematicians, notably Hilbert, supported Cantor and felt that what he was doing was not only correct, but important for the future of mathematics. In the first chapter, we discussed the foundations of mathematics. There was the formalist approach of Hilbert and the logicist approach of Russell and Whitehead.

**
What Kind of Creatures Are We? (Columbia Themes in Philosophy)
** by
Noam Chomsky

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Affordable Care Act / Obamacare, Albert Einstein, Arthur Eddington, Brownian motion, conceptual framework, en.wikipedia.org, failed state, Henri Poincaré, Isaac Newton, Jacques de Vaucanson, means of production, phenotype, Ronald Reagan, The Wealth of Nations by Adam Smith, theory of mind, Turing test, wage slave

Antoine Lavoisier before him believed that “the number and nature of elements [is] an unsolvable problem, capable of an infinity of solutions none of which probably accord with Nature”; “It seems extremely probable that we know nothing at all about… [the]… indivisible atoms of which matter is composed,” and never will, he believed. Kekulé seems to be saying that there isn’t a problem to be solved; the structural formulas are useful or not, but there is no truth of the matter. Large parts of physics were understood the same way. Henri Poincaré went so far as to say that we adopt the molecular theory of gases only because we are familiar with the game of billiards. Ludwig Boltzmann’s scientific biographer speculates that he committed suicide because of his failure to convince the scientific community to regard his theoretical account of these matters as more than a calculating system—ironically, shortly after Albert Einstein’s work on Brownian motion and broader issues had convinced physicists of the reality of the entities he postulated.

**
Where Good Ideas Come from: The Natural History of Innovation
** by
Steven Johnson

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Ada Lovelace, Albert Einstein, Alfred Russel Wallace, carbon-based life, Cass Sunstein, cleantech, complexity theory, conceptual framework, cosmic microwave background, crowdsourcing, data acquisition, digital Maoism, discovery of DNA, Dmitri Mendeleev, double entry bookkeeping, double helix, Douglas Engelbart, Drosophila, Edmond Halley, Edward Lloyd's coffeehouse, Ernest Rutherford, Geoffrey West, Santa Fe Institute, greed is good, Hans Lippershey, Henri Poincaré, hive mind, Howard Rheingold, hypertext link, invention of air conditioning, invention of movable type, invention of the printing press, invention of the telephone, Isaac Newton, Islamic Golden Age, Jacquard loom, James Hargreaves, James Watt: steam engine, Jane Jacobs, Jaron Lanier, John Snow's cholera map, Joseph Schumpeter, Joseph-Marie Jacquard, Kevin Kelly, lone genius, Louis Daguerre, Louis Pasteur, Mason jar, Mercator projection, On the Revolutions of the Heavenly Spheres, online collectivism, packet switching, PageRank, patent troll, pattern recognition, price mechanism, profit motive, Ray Oldenburg, Richard Florida, Richard Thaler, Ronald Reagan, side project, Silicon Valley, silicon-based life, six sigma, Solar eclipse in 1919, spinning jenny, Steve Jobs, Steve Wozniak, Stewart Brand, The Death and Life of Great American Cities, The Great Good Place, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, transaction costs, urban planning

The shower or stroll removes you from the task-based focus of modern life—paying bills, answering e-mail, helping kids with homework—and deposits you in a more associative state. Given enough time, your mind will often stumble across some old connection that it had long overlooked, and you experience that delightful feeling of private serendipity: Why didn’t I think of that before? In his book The Foundations of Science, the French mathematician and physicist Henri Poincaré devotes an autobiographical chapter to the question of mathematical creativity. The chapter begins with a detailed account of how Poincaré discovered the class of Fuchsian functions, one of the first influential mathematical concepts of his career. He begins by attempting to prove that the functions do not exist; for fifteen days he struggles at his desk with no success. Then one evening he breaks from his ordinary routine and drinks black coffee.

**
The Man Who Invented the Computer
** by
Jane Smiley

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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, RAND corporation, Turing machine, V2 rocket, Vannevar Bush, Von Neumann architecture

He sat in the bar for several hours, thinking through each of his concepts but concentrating particularly upon ideas for how the memory would work and how an electronically based on-off process would calculate. Atanasoff’s experience is interesting on a number of levels. The way in which a state of effort followed by a state of relaxation induced an understanding of the system he wanted to build is reminiscent of what had happened to Turing and also to Henri Poincaré, the mathematician, as quoted in psychiatric researcher Nancy Andreasen’s The Creative Brain: For fifteen days I strove to prove that there could not be any functions like those we have since called Fuchsian functions. I was very ignorant: every day, I seated myself at my work table, stayed an hour or two, tried a great number of combinations and reached no results. One evening, contrary to my custom, I drank black coffee and could not sleep.

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

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Ada Lovelace, butterfly effect, carbon footprint, Clapham omnibus, cognitive dissonance, continuous integration, David Attenborough, decarbonisation, discovery of DNA, Edward Lorenz: Chaos theory, Henri Poincaré, mandelbrot fractal, megacity, Northern Rock, oil shale / tar sands, phenotype, planetary scale, short selling, Stewart Brand, University of East Anglia

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. This was a serious flaw in the concept of determinism, but it was not until 1961 that Lorenz used an early computer to demonstrate the chaotic behaviour of weather and found it to be wholly unpredictable beyond about a week. He was the originator of the ‘butterfly effect’ – the idea that the small eddy made by the flapping of a butterfly’s wings could initiate much later a hurricane; he showed that this was because weather systems are highly sensitive to the initial conditions of their origin.

**
The Rise of the Quants: Marschak, Sharpe, Black, Scholes and Merton
** by
Colin Read

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Albert Einstein, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, collateralized debt obligation, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, David Ricardo: comparative advantage, discovery of penicillin, discrete time, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, floating exchange rates, full employment, Henri Poincaré, implied volatility, index fund, Isaac Newton, John von Neumann, Joseph Schumpeter, Long Term Capital Management, Louis Bachelier, margin call, market clearing, martingale, means of production, moral hazard, naked short selling, price stability, principal–agent problem, quantitative trading / quantitative ﬁnance, RAND corporation, random walk, risk tolerance, risk/return, Ronald Reagan, shareholder value, Sharpe ratio, short selling, stochastic process, The Chicago School, the scientific method, too big to fail, transaction costs, tulip mania, Works Progress Administration, yield curve

When his parents The Times 103 died before he had completed high school, Bachelier was forced to struggle to complete high school while he provided for his younger sister and infant brother and managed the family business. While others went off to college in Paris, he was schooled in life and in financial markets until he was finally able to enter the Sorbonne in Paris in 1892 at the age of 22. Bachelier was a non-traditional student, with more distractions than usual and with less-than-ideal grades. However, he was fortunate to come under the supervision of Jules Henri Poincaré (1854–1912), a highly respected mathematician and physicist, famous for his Poincaré conjecture, a theorem on three-dimensional spheres that took almost a century to prove. Bachelier’s graduation thesis was surprisingly advanced, especially his insights into the Gaussian theory of errors, which earned words of praise from Poincaré: [Bachelier’s treatment is] very original, and all the more interesting in that Fourier’s reasoning can be extended with a few changes to the theory of errors ...

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

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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, Schrödinger's Cat, Search for Extraterrestrial Intelligence, The Present Situation in Quantum Mechanics, Wilhelm Olbers

In 1886 the King of Sweden offered a prize of 2,500 kroner (a tidy sum, more than most Europeans would earn in a year) to whoever could prove (or disprove) the stability of the solar system: that is, say for sure whether the planets would continue to orbit around the Sun forever or if there was a chance that one or more of them might one day spiral into the Sun or escape the pull of its gravity and float away. The French mathematician Henri Poincaré took up the challenge. He began by looking at a simpler problem involving just the Sun, the Earth, and the Moon—what is referred to as a three-body problem. He discovered that even with just three bodies, the problem was mathematically impossible to solve exactly. What’s more, certain arrangements of the three bodies would be so sensitive to initial conditions that the equations pointed to completely irregular and unpredictable behavior.

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The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom
** by
Graham Farmelo

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Albert Einstein, anti-communist, Arthur Eddington, Berlin Wall, cuban missile crisis, double helix, Ernest Rutherford, Fall of the Berlin Wall, Fellow of the Royal Society, financial independence, gravity well, Henri Poincaré, invention of radio, invisible hand, Isaac Newton, John von Neumann, Kevin Kelly, Murray Gell-Mann, Richard Feynman, Richard Feynman, Simon Singh, Solar eclipse in 1919, Stephen Hawking, strikebreaker, University of East Anglia

Although his defence could be regarded as stubborn, he does make it clear that he expected his theory to be superseded; the task in hand was to develop the theory as far as it could be taken. Bohr’s criticisms do not seem to have shaken him in the least – he would need this thick skin during the coming barrage of scepticism and derision. A week after he wrote to Bohr, Dirac gave his first public presentation of the hole theory to an audience in Paris, at the Henri Poincaré Institute. He will not have taken much pleasure from giving the lecture, as he reluctantly agreed to give it in French, bringing back abhorrent memories of meals with his father. When he returned to Bristol for Christmas, he had no choice but to speak French again. After his absence for nine months, his family was desperate to see him and to show him their latest plaything – the ‘Gramaphone’ (sic).32 But Dirac was, as always, downhearted even at the thought of returning to his enervating Bristol routine, his mother endlessly fussing over him, his father still intimidating him simply by his presence.

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H. 1 Heath, Edward 1, 2n51 Heaviside, Oliver 1, 2 Hebblethwaite, Cyril 1 Heckmann, Otto 1n5 Hegel, Georg Wilhelm Friedrich 1n53 Heisenberg, Werner 1, 2, 3, 4, 5, 6, 7, 8, 9, 10n8 personality 1, 2, 3, 4 addresses the Kapitza Club 1, 2n28 quantum theory (1925) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 non-commuting quantities 1, 2 and PD’s first paper on quantum mechanics 1 works with Born and Jordan at Göttingen 1, 2 and Schrödinger’s work on wave mechanics 1 uncertainty principle 1, 2, 3, 4, 5, 6 pianistic skills 1, 2, 3 and PD’s attack on religion 1 appointed full professor in Leipzig 1 and the Dirac equation 1, 2 visits Japan with PD 1 Soviet government’s attitude to his work 1 pleased at Hitler’s coming to power 1, 2 and the positron 1 atomic nucleus structure 1 Nobel Prize for physics 1, 2, 3, 4, 5, 6, 7 celebrations in Copenhagen 1, 2 message to Born from the Nazi Government 1 a ‘White Jew’ 1 meeting with Bohr (1941) 1 attests to Betty’s non-Jewish status 1, 2n34 interned near Cambridge 1 explanation of his wartime conduct 1 PD supports 1, 2 quarrels with Pauli 1 at Lindau 1 interviewed with PD 1 appearance 1 death 1 Heisenberg-Pauli theory 1 Hellman, Bruce 1 Henri Poincaré Institute, Paris 1 Hess, Rudolf 1 Hessen, Boris 1, 2, 3 high-dimensional field theories 1, 2 high-energy particle accelerators 1, 2 high-energy physics 1, 2 Highgate Cemetery, London 1 Hilbert, David 1 Hippodrome theatre, Bristol 1, 2, 3 Hiroshima, bombing of (1945) 1, 2 Histon, Cambridgeshire 1 Hitler, Adolf 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 Hofer, Kurt 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11n18 Hoffman, Dustin 1 Holborn Registry Office, central London 1 Holcomb, Dorothy 1 hole theory 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21n7 Holiday Inn, Tallahassee 1 Holmes, Sherlock 1, 2, 3n7, see also 4 Holten, Beatrice (Flo’s sister) 1n16 Holten, Fred (Flo’s brother) 1 Holten, Nell (Flo’s sister) 1, 2, 3 Holten, Richard (PD’s maternal grandfather) 1, 2 Hong Kong 1 Hoover, Herbert 1 Hoover, J.

**
The Fabric of the Cosmos
** by
Brian Greene

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airport security, Albert Einstein, Albert Michelson, Arthur Eddington, Brownian motion, clockwork universe, conceptual framework, cosmic microwave background, cosmological constant, dark matter, dematerialisation, Hans Lippershey, Henri Poincaré, invisible hand, Isaac Newton, Murray Gell-Mann, Richard Feynman, Richard Feynman, Stephen Hawking, urban renewal

In turn, the second law has provided us with an intuitive distinction between what we call past and what we call future. It has given us a practical explanation for why things in daily life, things that are typically composed of huge numbers of constituents, start like this and end like that, while we never see them start like that and end like this. But over the course of many years— and thanks to important contributions by physicists like Lord Kelvin, Josef Loschmidt, Henri Poincaré, S. H. Burbury, Ernst Zermelo, and Willard Gibbs—Ludwig Boltzmann came to appreciate that the full story of time’s arrow is more surprising. Boltzmann realized that although entropy had illuminated important aspects of the puzzle, it had not answered the question of why the past and the future seem so different. Instead, entropy had redefined the question in an important way, one that leads to an unexpected conclusion.

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If those molecular motions were to take place in reverse, the molecules would join back together, re-fusing the shell into its previous form. 4. To keep the focus on modern ways of thinking about these ideas, I am skipping over some very interesting history. Boltzmann’s own thinking on the subject of entropy went through significant refinements during the 1870s and 1880s, during which time interactions and communications with physicists such as James Clerk Maxwell, Lord Kelvin, Josef Loschmidt, Josiah Willard Gibbs, Henri Poincaré, S. H. Burbury, and Ernest Zermelo were instrumental. In fact, Boltzmann initially thought he could prove that entropy would always and absolutely be nondecreasing for an isolated physical system, and not that it was merely highly unlikely for such entropy reduction to take place. But objections raised by these and other physicists subsequently led Boltzmann to emphasize the statistical/probabilistic approach to the subject, the one that is still in use today. 5.

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The Misbehavior of Markets
** by
Benoit Mandelbrot

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Albert Einstein, asset allocation, Augustin-Louis Cauchy, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black-Scholes formula, British Empire, Brownian motion, buy low sell high, capital asset pricing model, carbon-based life, discounted cash flows, diversification, double helix, Edward Lorenz: Chaos theory, Elliott wave, equity premium, Eugene Fama: efficient market hypothesis, Fellow of the Royal Society, full employment, Georg Cantor, Henri Poincaré, implied volatility, index fund, informal economy, invisible hand, John von Neumann, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market microstructure, new economy, paper trading, passive investing, Paul Lévy, Plutocrats, plutocrats, price mechanism, quantitative trading / quantitative ﬁnance, Ralph Nelson Elliott, RAND corporation, random walk, risk tolerance, Robert Shiller, Robert Shiller, short selling, statistical arbitrage, statistical model, Steve Ballmer, stochastic volatility, transfer pricing, value at risk, volatility smile

In such a wild world, an imaginary investor participating in this econometric simulation could be wiped out overnight. Alas, this is not a computer fantasy. Hitherto, standard financial theory has followed the first, mild path. How it got on that mistaken path, and how it can get off it, will be seen in subsequent chapters. CHAPTER III Bachelier and His Legacy IN MARCH 1900, the academic equivalent of a trial by fire was convened at the University of Paris. The judges included Henri Poincaré, one of the most celebrated mathematicians of all time. He was a genius whose restless energy had led him across virtually every field of mathematical inquiry and beyond: probability, function theory, topology, geometry, optics, and, above all, celestial mechanics. He was a widely read popularizer of math and science, and his collected columns fill several books read to this day. He was, however, a living paradox, both establishment figure and academic maverick.

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The Drunkard's Walk: How Randomness Rules Our Lives
** by
Leonard Mlodinow

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Albert Einstein, Alfred Russel Wallace, Antoine Gombaud: Chevalier de Méré, Atul Gawande, Brownian motion, butterfly effect, correlation coefficient, Daniel Kahneman / Amos Tversky, Donald Trump, feminist movement, forensic accounting, Gerolamo Cardano, Henri Poincaré, index fund, Isaac Newton, law of one price, pattern recognition, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, Richard Feynman, Richard Feynman, Ronald Reagan, Stephen Hawking, Steve Jobs, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, V2 rocket, Watson beat the top human players on Jeopardy!

In that data, when the number of conscripts was plotted against their height, the bell-shaped curve was distorted: too few prospects were just above five feet two and a compensating surplus was just below that height. Quételet argued that the difference—about 2,200 extra “short men”—was due to fraud or, you might say friendly fudging, as those below five feet two were excused from service. Decades later the great French mathematician Jules-Henri Poincaré employed Quételet’s method to nab a baker who was shortchanging his customers. At first, Poincaré, who made a habit of picking up a loaf of bread each day, noticed after weighing his loaves that they averaged about 950 grams instead of the 1,000 grams advertised. He complained to the authorities and afterward received bigger loaves. Still he had a hunch that something about his bread wasn’t kosher.

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The Infinite Book: A Short Guide to the Boundless, Timeless and Endless
** by
John D. Barrow

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Albert Einstein, Andrew Wiles, anthropic principle, Arthur Eddington, cosmological principle, dark matter, Edmond Halley, Fellow of the Royal Society, Georg Cantor, Henri Poincaré, Isaac Newton, mutually assured destruction, Olbers’ paradox, prisoner's dilemma, Ray Kurzweil, short selling, Stephen Hawking, Turing machine

Unfortunately for Cantor, that call never came and he spent the whole of his career in the minor mathematical department in Halle – where there were few visitors and no mathematicians of Cantor’s calibre – living comfortably in a big house with his close family following his marriage in 1875 to his sister’s friend, Vally Guttmann. Things were to become more exciting for Cantor, but not in ways that he could have wished. THE CHRONICLE OF KRONECKER ‘Logic sometimes makes monsters’ Henri Poincaré3 The year 1871 was a watershed in Cantor’s career as a mathematician. Until that time, his former professor in Berlin, Leopold Kronecker, had been on good terms with him, sympathetic to his work and helpful in getting him established in Halle. He even provided some important mathematical suggestions which helped Cantor to complete some of his first research papers. Then something changed. Cantor began to work on infinities, and in Kronecker’s eyes he had suddenly become ‘a corrupter of youth’.4 Kronecker was the son of a wealthy Prussian businessman and was in no need of a university salary to support his mathematical career (Figure 5.1).

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Rush Hour
** by
Iain Gately

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Albert Einstein, autonomous vehicles, Beeching cuts, blue-collar work, British Empire, business intelligence, business process, business process outsourcing, call centre, car-free, Clapham omnibus, cognitive dissonance, congestion charging, connected car, DARPA: Urban Challenge, Dean Kamen, decarbonisation, Deng Xiaoping, Detroit bankruptcy, don't be evil, Elon Musk, extreme commuting, Google bus, Henri Poincaré, Hyperloop, Jeff Bezos, low skilled workers, postnationalism / post nation state, Ralph Waldo Emerson, remote working, self-driving car, Silicon Valley, stakhanovite, Steve Jobs, telepresence, Tesla Model S, urban planning, éminence grise

In France each was called the horloge mère, or ‘mother clock’, in Germany it was the primäre Normaluhr (‘primary reference clock’). Leipzig was the first town to have an electronically distributed system, followed by Frankfurt and Bern in Switzerland ‘where a hundred clock faces began marching together in 1890’. European governments, meanwhile, encouraged research into perfect time and competed with each other, as a matter of national pride, as to whose was the most precise. Henri Poincaré put France in the lead with The Measure of Time (1898), a masterpiece of theoretical physics, which gave anyone curious about the matter both barrels. Time was a memory, but did we form memories at the speed of light, or faster? Albert Einstein also linked railway time to physics. He was inspired to wonder whether time might be constant – or not – when commuting to work as a patent clerk in Bern.

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Mindware: Tools for Smart Thinking
** by
Richard E. Nisbett

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affirmative action, Albert Einstein, availability heuristic, big-box store, Cass Sunstein, choice architecture, cognitive dissonance, correlation coefficient, correlation does not imply causation, cosmological constant, Daniel Kahneman / Amos Tversky, dark matter, endowment effect, experimental subject, feminist movement, fundamental attribution error, glass ceiling, Henri Poincaré, Isaac Newton, job satisfaction, lake wobegon effect, libertarian paternalism, loss aversion, low skilled workers, Menlo Park, meta analysis, meta-analysis, quantitative easing, Richard Thaler, Ronald Reagan, Socratic dialogue, Steve Jobs, Steven Levy, the scientific method, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, William of Occam, Zipcar

Ghiselin’s essayists insist that (a) they had little or no idea what factors prompted the solution, and (b) even the fact that thought of any kind about the problem was taking place is sometimes unknown. The mathematician Jacques Hadamard reports that “on being very abruptly awakened by an external noise, a solution long searched for appeared to me at once without the slightest instant of reflection on my part … and in a quite different direction from any of those which I previously tried to follow.” The mathematician Henri Poincaré records that “the changes of travel made me forget my mathematical work … At the moment when I put my foot on the step [of the omnibus] the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry.” The philosopher and mathematician Alfred North Whitehead wrote of “the state of imaginative muddled suspense which precedes successful inductive generalization.”

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Erwin Schrodinger and the Quantum Revolution
** by
John Gribbin

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Albert Einstein, Albert Michelson, All science is either physics or stamp collecting, Arthur Eddington, British Empire, Brownian motion, double helix, Drosophila, Edmond Halley, Ernest Rutherford, Fellow of the Royal Society, Henri Poincaré, Isaac Newton, John von Neumann, Richard Feynman, Richard Feynman, Schrödinger's Cat, Solar eclipse in 1919, The Present Situation in Quantum Mechanics, the scientific method, trade route, upwardly mobile

It will never move back into one half of the box, giving us a chance to slide the partition back and keep it there. Or will it? The puzzle is that, according to Newton’s laws of mechanics, every collision between atoms is reversible. If we made a movie showing the gas spreading out to fill the box, then ran the movie backwards, it might look bizarre, but there would be nothing going on in the time-reversed version of events that conflicted with Newton’s laws. In 1890, the French physicist Henri Poincaré (1854–1912) established that in a box of gas like this, every possible arrangement of the atoms in the box must occur sooner or later. Boltzmann’s resolution to the puzzle was to point out that although there is nothing in Newton’s laws to prevent all the gas gathering in one half of the box, the statistical likelihood of this happening is very, very small. If you wait long enough the gas will all gather in one end of the box; if you wait longer still, the wine glass will reconstruct itself.

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Priceless: The Myth of Fair Value (And How to Take Advantage of It)
** by
William Poundstone

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availability heuristic, Cass Sunstein, collective bargaining, Daniel Kahneman / Amos Tversky, delayed gratification, Donald Trump, East Village, en.wikipedia.org, endowment effect, equal pay for equal work, experimental economics, experimental subject, feminist movement, game design, German hyperinflation, Henri Poincaré, high net worth, index card, invisible hand, John von Neumann, laissez-faire capitalism, loss aversion, market bubble, mental accounting, meta analysis, meta-analysis, Nash equilibrium, new economy, payday loans, Potemkin village, price anchoring, price discrimination, psychological pricing, Ralph Waldo Emerson, RAND corporation, random walk, RFID, Richard Thaler, risk tolerance, Robert Shiller, Robert Shiller, rolodex, Steve Jobs, The Chicago School, The Wealth of Nations by Adam Smith, ultimatum game, working poor

Allais did not limit himself to disproving wrong ideas in economics. He was just then embarking on a grand quest to disprove Einstein’s theory of relativity. Allais devised a special pendulum that would one day show Einstein’s error, or so he believed. He would spend much of the 1950s attempting to demonstrate that Einstein had cribbed relativity (for what it’s worth) from that great Frenchman Henri Poincaré. Proving that Savage’s theory was wrong was much simpler. Like a troll in a fairy tale, Allais posed three riddles. I will use a streamlined version of the questions Allais published the following year, putting the money amounts in dollars. Though not identical to the riddles Allais posed to Savage, they will give you the flavor of his argument. Riddle one: Which of the following would you rather have?

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Physics in Mind: A Quantum View of the Brain
** by
Werner Loewenstein

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Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, complexity theory, dematerialisation, discovery of DNA, Gödel, Escher, Bach, Henri Poincaré, informal economy, information trail, Isaac Newton, Murray Gell-Mann, Necker cube, Norbert Wiener, Richard Feynman, Richard Feynman, stem cell, trade route, Turing machine

But between the lines, there is something that may, even a hundred years after Boltzmann, strike one as mind-bogglingly surreal: Evolution can, in principle, also go the other way round. Indeed, that point, namely full time reversibility, is implicit in Boltzmann’s derivation, as it started from Newton’s time-reversible laws. But the proof is in the pudding—a theorem in this case. And that came not long after Boltzmann’s coup, when the mathematician Henri Poincaré incontrovertibly showed that any system obeying Newton’s laws must, in due time, return to its original state (or to a state near it). So the Queen’s declarations on page 5, strange as they may seem, are really not so far out. They are certainly coherent and quite in line with physics theory. Indeed, they are in accord with the precept every physicist holds dear: that the universe is symmetrical.

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Fermat’s Last Theorem
** by
Simon Singh

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Albert Einstein, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, Augustin-Louis Cauchy, Fellow of the Royal Society, Georg Cantor, Henri Poincaré, Isaac Newton, John Conway, John von Neumann, kremlinology, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, Simon Singh, Wolfskehl Prize

While the fascinating thing about Penrose’s tiled surfaces is their restricted symmetry, the interesting property of modular forms is that they exhibit infinite symmetry. The modular forms studied by Taniyama and Shimura can be shifted, switched, swapped, reflected and rotated in an infinite number of ways and still they remain unchanged, making them the most symmetrical of mathematical objects. When the French polymath Henri Poincaré studied modular forms in the nineteenth century, he had great difficulty coming to terms with their immense symmetry. After working on a particular type of modular form, he described to his colleagues how every day for two weeks he would wake up and try and find an error in his calculations. On the fifteenth day he realised and accepted that modular forms were indeed symmetrical in the extreme.

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Lonely Planet France
** by
Lonely Planet Publications

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banking crisis, bike sharing scheme, British Empire, car-free, carbon footprint, centre right, Columbine, double helix, Frank Gehry, glass ceiling, haute couture, haute cuisine, Henri Poincaré, Honoré de Balzac, illegal immigration, Jacquard loom, Jacquard loom, Joseph-Marie Jacquard, Louis Blériot, Louis Pasteur, low cost carrier, Mahatma Gandhi, Murano, Venice glass, ride hailing / ride sharing, sensible shoes, Silicon Valley, supervolcano, trade route, urban renewal, urban sprawl, V2 rocket

Banks, villas, pharmacies, brasseries – wherever you wander in Nancy, you are bound to stumble across their handiwork, from sinuous grillwork to curvaceous stained-glass windows and doorways that are a profusion of naturalistic ornament. Slip back to this genteel era by picking up the free Art Nouveau Itineraries brochure and map at the tourist office, covering four city strolls. Lucien Weissenburger’s 1910 Brasserie Excelsior (Click here ) and the 1908 Chambre de Commerce Offline map Google map with wrought iron by Louis Majorelle, both located on rue Henri Poincaré, are central standouts. Close to the Musée de l’École de Nancy lies the whimsical Villa Majorelle (1 rue Louis-Majorelle; adult/child €3.50/2.50; guided tours 2.30pm & 3.45pm Sat & Sun May-Oct) , built by Henri Sauvage in 1901 and bearing the hallmark of Majorelle (furniture) and Gruber (stained glass). The centrepiece is the dining room Les Blés with its vinelike stone fireplace. Festivals & Events Get your groove on to live jazz, blues and Latin at the 10-day Jazz Pulsations (www.nancyjazzpulsations.com) in October.

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Gentilhommiere FRENCH €€ Offline map Google map ( 03 83 32 26 44; 29 rue des Maréchaux; menus €23-38; lunch Mon-Fri, dinner Mon-Sat) Warm-hued, subtly lit Gentilhommiere stands head and shoulders above most of the restaurants on rue des Maréchaux. Presentation is key in specialities like scallop tartlet with Lorraine black truffles and braised lamb with spiced couscous. Brasserie Excelsior BRASSERIE €€ Offline map Google map ( 03 83 35 24 57; 50 rue Henri Poincaré; menus €26-45; 8am-12.30am Mon-Sat, 8am-11pm Sun) As opulent as a Fabergé egg with its stucco and stained glass, Excelsior whisks you back to the decadent era of art nouveau. Brusquely efficient waiters bring brasserie classics such as oysters (September through April), juicy steaks and banquet-like seafood platters to the table. La Bouche á L’Oreille BISTRO € Offline map Google map ( 03 83 35 17 17; 42 rue des Carmes; menus 11.95-23.95; lunch Tue-Fri, dinner Mon-Sat) Resembling an overgrown doll’s house, this bistro filled with knick-knacks specialises in cheese-based dishes like raclette and fondue.

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Maison des Sœurs Macarons CONFECTIONERY Offline map Google map (www.macaron-de-nancy.com; 21 rue Gambetta; closed Mon morning, Sun) When Nancy’s Benedictine nuns hit hard times during the French Revolution, they saw the light in heavenly macarons. They’re still made to the original recipe (egg whites, sugar, Provençal almonds) at this old-world confectioner. A dozen box (€7.50) makes a great gift. Lefèvre-Lemoine CONFECTIONERY Offline map Google map (47 rue Henri Poincaré; daily) They don’t make sweetshops like this 1840s treasure any more, where a bird chirps a welcome as you enter. One of the old-fashioned sweet tins made a cameo appearance in the film Amélie . Bergamotes de Nancy (bergamot boiled sweets), caramels, nougat, gingerbread, glazed mirabelles (plums) – how ever will you choose? Baccarat CRYSTAL Offline map Google map (www.baccarat.fr; 2 rue des Dominicains; closed Mon morning, Sun) Shop like royalty (or window -shop like mere mortals) for exquisite crystal and jewellery here, where the simplest ring – impossibly delicate – goes for €150.

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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

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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, John Nash: game theory, John von Neumann, linear programming, meta analysis, meta-analysis, Nate Silver, p-value, placebo effect, prediction markets, RAND corporation, recommendation engine, Renaissance Technologies, Richard Feynman, Richard Feynman, Richard Feynman: Challenger O-ring, Ronald Reagan, speech recognition, statistical model, stochastic process, Thomas Kuhn: the structure of scientific revolutions, traveling salesman, Turing machine, Turing test, uranium enrichment, Yom Kippur War

Bertillon’s notions of probability were mathematical gibberish, and he developed ever more fantastical arguments. As conservative antirepublicans, Roman Catholics, and anti-Semites supported Dreyfus’s conviction, a campaign to exonerate him was organized by his family, anticlericals, Jews, and left-wing politicians and intellectuals led by the novelist Émile Zola. At Dreyfus’s military trial in 1899, his lawyer called on France’s most illustrious mathematician and physicist, Henri Poincaré, who had taught probability at the Sorbonne for more than ten years. Poincaré believed in frequency-based statistics. But when asked whether Bertillon’s document was written by Dreyfus or someone else, he invoked Bayes’ rule. Poincaré considered it the only sensible way for a court of law to update a prior hypothesis with new evidence, and he regarded the forgery as a typical problem in Bayesian hypothesis testing.

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Pathfinders: The Golden Age of Arabic Science
** by
Jim Al-Khalili

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agricultural Revolution, Albert Einstein, Andrew Wiles, Book of Ingenious Devices, colonial rule, Commentariolus, Dmitri Mendeleev, Eratosthenes, Henri Poincaré, invention of the printing press, invention of the telescope, invention of the wheel, Isaac Newton, Islamic Golden Age, Joseph Schumpeter, retrograde motion, Silicon Valley, Simon Singh, stem cell, Stephen Hawking, the scientific method, Thomas Malthus, trade route, William of Occam

I have already described, in considering the achievements of Copernicus, how Einstein’s papers on the Special Theory of Relativity in 1905 heralded a revolution in physics. It was his breakthrough that brought about the paradigm shift in our understanding of reality, and not the preparatory work of those who came before him. But it is also true that there would not have been a theory of relativity without the work of Jules Henri Poincaré and Lorentz, a few years earlier. Similarly, much is made of the conflict between Newton and his contemporary, the German mathematician Gottfried Leibniz, over who most deserves credit for the invention of calculus. The truth is that they arrived at their discoveries independently. But neither man started from scratch; and indeed much of the groundwork had been laid down half a century earlier by the great French mathematician Fermat, not forgetting the contributions of such men as Thābit ibn Qurra, Ibn al-Haytham and al-Bīrūni, or indeed Greeks such as Archimedes, and Chinese and Indian mathematicians (notably Āryabhata in the sixth century CE).

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Investment: A History
** by
Norton Reamer,
Jesse Downing

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Albert Einstein, algorithmic trading, asset allocation, backtesting, banking crisis, Berlin Wall, Bernie Madoff, Brownian motion, buttonwood tree, California gold rush, capital asset pricing model, Carmen Reinhart, carried interest, colonial rule, credit crunch, Credit Default Swap, Daniel Kahneman / Amos Tversky, debt deflation, discounted cash flows, diversified portfolio, equity premium, estate planning, Eugene Fama: efficient market hypothesis, Fall of the Berlin Wall, family office, Fellow of the Royal Society, financial innovation, fixed income, Gordon Gekko, Henri Poincaré, high net worth, index fund, interest rate swap, invention of the telegraph, James Hargreaves, James Watt: steam engine, joint-stock company, Kenneth Rogoff, labor-force participation, land tenure, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, margin call, means of production, Menlo Park, merger arbitrage, moral hazard, mortgage debt, Network effects, new economy, Nick Leeson, Own Your Own Home, pension reform, Ponzi scheme, price mechanism, principal–agent problem, profit maximization, quantitative easing, RAND corporation, random walk, Renaissance Technologies, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, Sand Hill Road, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, spinning jenny, statistical arbitrage, technology bubble, The Wealth of Nations by Adam Smith, time value of money, too big to fail, transaction costs, underbanked, Vanguard fund, working poor, yield curve

The Father of Mathematical Finance It has been said that mathematical ﬁnance emerged largely out of Louis Bachelier’s work on the theory of derivatives pricing at the turn of the twentieth century. Bachelier’s father was a vendor of wine who also dabbled in science as a hobby. When Louis’s parents died abruptly after he achieved his bachelor’s degree, he found himself thrust into the position of steward of his family’s business. He became quite ﬂuent in ﬁnance as a result of this experience, and soon Bachelier found himself back in academia working under the polymath Henri Poincaré.1 He defended the ﬁrst portion of his thesis, entitled “Theory of Speculation,” in March 1900. In it, he showed how to value complicated French derivatives using advanced mathematics. In fact, his approach bore some similarity to that of Fischer Black and Myron Scholes many years later. Bachelier’s work was the ﬁrst use of formal models of randomness to describe and evaluate markets. In his paper, Bachelier used a form of what is called Brownian motion.2 Brownian motion was named after Robert Brown, who studied the random motions of pollen in water.

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Black Box Thinking: Why Most People Never Learn From Their Mistakes--But Some Do
** by
Matthew Syed

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Alfred Russel Wallace, Arthur Eddington, Atul Gawande, Black Swan, British Empire, call centre, Captain Sullenberger Hudson, Checklist Manifesto, cognitive bias, cognitive dissonance, conceptual framework, corporate governance, credit crunch, deliberate practice, double helix, epigenetics, fear of failure, fundamental attribution error, Henri Poincaré, hindsight bias, Isaac Newton, iterative process, James Dyson, James Hargreaves, James Watt: steam engine, Joseph Schumpeter, Lean Startup, meta analysis, meta-analysis, minimum viable product, quantitative easing, randomized controlled trial, Silicon Valley, six sigma, spinning jenny, Steve Jobs, the scientific method, Thomas Kuhn: the structure of scientific revolutions, too big to fail, Toyota Production System, Wall-E, Yom Kippur War

The theory of evolution through natural selection was proposed independently by Charles Darwin and Alfred Russel Wallace (an extraordinary, unsung polymath) in the mid-nineteenth century.11 S. Korschinsky in 1889 and Hugo de Vries in 1901 independently established the significance of genetic mutation. Even Einstein’s pioneering work has echoes in the work of his contemporaries. The French mathematician Henri Poincaré wrote about the “Principle of Relativity” in 1904, a year before Einstein published his landmark paper on the Special Theory. In the 1920s William Ogburn and Dorothy Thomas, two academics from Columbia University, found as many as 148 examples of independent innovation. Multiples are the norm; not the exception. They entitled their paper “Are Inventions Inevitable?”* The reason harks back to the “responsive” nature of creativity.

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The Three-Body Problem (Remembrance of Earth's Past)
** by
Cixin Liu

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back-to-the-land, cosmic microwave background, Deng Xiaoping, game design, Henri Poincaré, horn antenna, invisible hand, Isaac Newton, Norbert Wiener, Panamax, RAND corporation, Search for Extraterrestrial Intelligence, Von Neumann architecture

Now I could be at peace in a bustling city. Even in the midst of a noisy crowd, my heart would be completely tranquil. For the first time, I enjoyed math. I felt like a libertine who has always fluttered carelessly from one woman to another suddenly finding himself in love. The physics principles behind the three-body problem28 are very simple. It’s mainly a math problem. “Didn’t you know about Henri Poincaré?” Wang Miao interrupted Wei to ask.29 At the time, I didn’t. Yes, I know that someone studying math should know about a master like Poincaré, but I didn’t worship masters and I didn’t want to become one, so I didn’t know his work. But even if I had, I would have continued to pursue the three-body problem. Everyone seems to believe that Poincaré proved that the three-body problem couldn’t be solved, but I think they’re mistaken.

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

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4chan, Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, algorithmic trading, anthropic principle, asset allocation, autonomous vehicles, Berlin Wall, Bill Duvall, bitcoin, Community Supported Agriculture, complexity theory, constrained optimization, cosmological principle, cryptocurrency, Danny Hillis, delayed gratification, dematerialisation, diversification, 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, linear programming, martingale, Nash equilibrium, natural language processing, NP-complete, P = NP, packet switching, 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 Malthus, traveling salesman, Turing machine, urban planning, Vickrey auction, Walter Mischel, Y Combinator

And like James he was inspired by evolution, thinking about creative innovation as the outcome of new ideas being generated randomly and astute human minds retaining the best of those ideas. Campbell supported his argument liberally with quotes from other scientists and mathematicians about the processes behind their own discoveries. The nineteenth-century physicists and philosophers Ernst Mach and Henri Poincaré both seemed to offer an account similar to Campbell’s, with Mach going so far as to declare that “thus are to be explained the statements of Newton, Mozart, Richard Wagner, and others, when they say that thought, melodies, and harmonies had poured in upon them, and that they had simply retained the right ones.” When it comes to stimulating creativity, a common technique is introducing a random element, such as a word that people have to form associations with.

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The Better Angels of Our Nature: Why Violence Has Declined
** by
Steven Pinker

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1960s counterculture, affirmative action, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, availability heuristic, Berlin Wall, Bonfire of the Vanities, British Empire, Broken windows theory, California gold rush, Cass Sunstein, citation needed, clean water, cognitive dissonance, colonial rule, Columbine, computer age, conceptual framework, correlation coefficient, correlation does not imply causation, crack epidemic, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Brooks, delayed gratification, demographic transition, desegregation, Doomsday Clock, Douglas Hofstadter, Edward Glaeser, en.wikipedia.org, European colonialism, experimental subject, facts on the ground, failed state, first-past-the-post, Flynn Effect, food miles, Francis Fukuyama: the end of history, fudge factor, full employment, ghettoisation, Gini coefficient, global village, Henri Poincaré, impulse control, income inequality, informal economy, invention of the printing press, Isaac Newton, lake wobegon effect, libertarian paternalism, loss aversion, Marshall McLuhan, McMansion, means of production, mental accounting, meta analysis, meta-analysis, Mikhail Gorbachev, mutually assured destruction, open economy, Peace of Westphalia, Peter Singer: altruism, QWERTY keyboard, race to the bottom, Ralph Waldo Emerson, random walk, Republic of Letters, Richard Thaler, Ronald Reagan, Rosa Parks, Saturday Night Live, security theater, Skype, Slavoj Žižek, South China Sea, statistical model, stem cell, Steven Levy, Steven Pinker, The Bell Curve by Richard Herrnstein and Charles Murray, The Wealth of Nations by Adam Smith, theory of mind, transatlantic slave trade, transatlantic slave trade, Turing machine, ultimatum game, uranium enrichment, V2 rocket, Walter Mischel, WikiLeaks, women in the workforce

Even a coin flip can be predicted from the starting conditions and the laws of physics, and a skilled magician can exploit those laws to throw heads every time.46 Yet when we zoom out to take a wide-angle view of a large number of these events, we are seeing the sum of a vast number of causes that sometimes cancel each other out and sometimes align in the same direction. The physicist and philosopher Henri Poincaré explained that we see the operation of chance in a deterministic world either when a large number of puny causes add up to a formidable effect, or when a small cause that escapes our notice determines a large effect that we cannot miss.47 In the case of organized violence, someone may want to start a war; he waits for the opportune moment, which may or may not come; his enemy decides to engage or retreat; bullets fly; bombs burst; people die.

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No Hitler, no World War II: Mueller, 2004a, p. 54. 45. No Hitler, no Holocaust: Goldhagen, 2009; Himmelfarb, 1984, p. 81; Fischer, 1998, p. 288; Valentino, 2004. 46. Probability of heads: Keller, 1986. Persi Diaconis, a statistician and magician, can throw heads ten times in a row; see E. Landuis, “Lifelong debunker takes on arbiter of neutral choices,” Stanford Report, Jun. 7, 2004. 47. Henri Poincaré: Science and method, quoted in Richardson, 1960, p. 131. 48. “mankind has become less warlike”: Richardson, 1960, p. 167. 49. Other datasets point to same conclusion: Sorokin, 1957, p. 564: “As in the data presented here is nothing to support the claim of disappearance of war in the past, so is there nothing to support the claim, in spite of the exceptionally high figures for the twentieth century, that there has been (or will be) any steady trend toward increase of war.

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Antifragile: Things That Gain From Disorder
** by
Nassim Nicholas Taleb

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Air France Flight 447, Andrei Shleifer, banking crisis, Benoit Mandelbrot, Berlin Wall, Black Swan, credit crunch, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discrete time, double entry bookkeeping, Emanuel Derman, epigenetics, financial independence, Flash crash, Gary Taubes, Gini coefficient, Henri Poincaré, high net worth, Ignaz Semmelweis: hand washing, informal economy, invention of the wheel, invisible hand, Isaac Newton, James Hargreaves, Jane Jacobs, joint-stock company, joint-stock limited liability company, Joseph Schumpeter, knowledge economy, Lao Tzu, Long Term Capital Management, loss aversion, Louis Pasteur, mandelbrot fractal, meta analysis, meta-analysis, microbiome, moral hazard, mouse model, Norbert Wiener, pattern recognition, placebo effect, Ponzi scheme, principal–agent problem, purchasing power parity, quantitative trading / quantitative ﬁnance, Ralph Nader, random walk, Ray Kurzweil, rent control, Republic of Letters, Ronald Reagan, Rory Sutherland, Silicon Valley, six sigma, spinning jenny, statistical model, Steve Jobs, Steven Pinker, Stewart Brand, stochastic process, stochastic volatility, The Great Moderation, The Wealth of Nations by Adam Smith, Thomas Malthus, too big to fail, transaction costs, urban planning, Yogi Berra, Zipf's Law

., 2010, “Black Swans and Knight’s Epistemological Uncertainty: Are These Concepts Also Underlying Behavioral and Post-Walrasian Theory?” Journal of Post Keynesian Economics 32(4): 567–570. Davis, Devra, 2007, The Secret History of the War on Cancer. Basic Books. Dawes, Robyn M., 2001, Everyday Irrationality: How Pseudo-Scientists, Lunatics, and the Rest of Us Systematically Fail to Think Rationally. Westview. De Finetti, B., 1937, La prévision: ses lois logiques, ses sources subjectives. Institut Henri Poincaré. De Finetti, B., 1974, Theory of Probability, Vol. 1. London: John. De Finetti, B., 1989, “Probabilism.” Erkenntnis 31(2): 169–223. De la Hunty, A., S. Gibson, and M. Ashwell, 2006, “A Review of the Effectiveness of Aspartame in Helping with Weight Control.” Nutrition Bulletin 31(2):115–128. De Long, J. Bradford, and Andrei Shleifer, 1993, “Princes and Merchants: European City Growth Before the Industrial Revolution.”

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

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airport security, availability heuristic, 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, 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, new economy, Norbert Wiener, PageRank, pattern recognition, pets.com, 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 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

Adrianne Jeffries, “High-Frequency Trading Approaches the Speed of Light,” BetaBeat.com, February 17, 2012. http://www.betabeat.com/2012/02/17/high-frequency-trading-approaches-the-speed-of-light/. 5. Terrance Odean, “Do Investors Trade Too Much?” American Economic Review, 89, no. 5 (December 1999), pp. 1279–1298. http://web.ku.edu/~finpko/myssi/FIN938/Odean_Do%20Investors%20Trade%20Too%20Much_AER_1999.pdf. 6. Bruno de Finetti, “La Prévision: Ses Lois Logiques, Ses Sources Subjectives,” Annales de l’Institut Henri Poincaré, 7 (1937). 7. Markets provide us with valuable information whether or not we participate in them directly. An economist might hate bananas, refusing to buy bananas at the supermarket at any price, but she still might be interested in knowing what they cost, to help her calculate the inflation rate. Or an orchard might be interested to know what the price was to decide whether it should plant more banana trees.

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Types and Programming Languages
** by
Benjamin C. Pierce

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Albert Einstein, combinatorial explosion, experimental subject, finite state, Henri Poincaré, recommendation engine, sorting algorithm, Turing complete, Turing machine, type inference, Y Combinator

For example, in System F, the type variable X in the type T = ∀X.X→X ranges over all types, including T itself (so that, for example, we can instantiate a term of type T at type T, yielding a function from T to T). The polymorphism found in ML, on the other hand, is often called predicative (or stratified), because the range of type variables is restricted to monotypes, which do not contain quantifiers. The terms “predicative” and “impredicative” originate in logic. Quine (1987) offers a lucid summary of their history: 23.11 Notes 361 In exchanges with Henri Poincaré . . . Russell attributed [Russell’s] paradox tentatively to what he called a vicious-circle fallacy. The “fallacy” consisted in specifying a class by a membership condition that makes reference directly or indirectly to a range of classes one of which is the very class that is being specified. For instance the membership condition behind Russell’s Paradox is non-self-membership: x not a member of x.

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Coming of Age in the Milky Way
** by
Timothy Ferris

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Albert Einstein, Albert Michelson, Alfred Russel Wallace, anthropic principle, Arthur Eddington, Atahualpa, Cepheid variable, Chance favours the prepared mind, Commentariolus, cosmic abundance, cosmic microwave background, cosmological constant, cosmological principle, dark matter, delayed gratification, Edmond Halley, Eratosthenes, Ernest Rutherford, Gary Taubes, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, Henri Poincaré, invention of writing, Isaac Newton, John Harrison: Longitude, Karl Jansky, Lao Tzu, Louis Pasteur, Magellanic Cloud, mandelbrot fractal, Menlo Park, Murray Gell-Mann, music of the spheres, planetary scale, retrograde motion, Richard Feynman, Richard Feynman, Search for Extraterrestrial Intelligence, Searching for Interstellar Communications, Solar eclipse in 1919, Stephen Hawking, Thomas Kuhn: the structure of scientific revolutions, Thomas Malthus, Wilhelm Olbers

As FitzGerald put it, “The block of stone [holding the apparatus] must be distorted, put out of shape by its motion … the stone would have to shorten in the direction of motion and swell out in the other two directions.”5 The Dutch physicist Hendrik Antoon Lorentz independently arrived at the same hypothesis, and worked it out in mathematical detail. This, the “Lorentz contraction,” was to emerge in a different form as a key element in the special theory of relativity. The French physicist Henri Poincaré, one of the few leading scientists to take the Lorentz contraction seriously, came close to developing it into a form that was mathematically equivalent to Einstein’s theory; Poincaré spoke presciently of “a principle of relativity” that would prescribe that no object could exceed the velocity of light.6 But most researchers found it odd to the point of desperation to suggest that the velocity of the earth causes the entire planet to contract, like an orange squashed between a titan’s hands, and Lorentz himself soon set the idea aside.

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The Age of Radiance: The Epic Rise and Dramatic Fall of the Atomic Era
** by
Craig Nelson

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Albert Einstein, Brownian motion, cognitive dissonance, Columbine, corporate governance, cuban missile crisis, dark matter, Doomsday Clock, El Camino Real, Ernest Rutherford, failed state, Henri Poincaré, hive mind, Isaac Newton, John von Neumann, Louis Pasteur, Menlo Park, Mikhail Gorbachev, music of the spheres, mutually assured destruction, nuclear winter, oil shale / tar sands, Project Plowshare, Ralph Nader, Richard Feynman, Richard Feynman, Ronald Reagan, Skype, Stuxnet, technoutopianism, too big to fail, uranium enrichment, V2 rocket, éminence grise

Wilhelm Röntgen, with his unruly beard and hair, wild and untamed, would become the world’s image of a mad genius. When Röntgen sent preprints of his article announcing X-rays out to fellow scientists at the end of 1895, his discovery was the dramatic breakthrough in an investigation of the mysterious relationship between matter and energy that had been building long before he’d ever charged a tube. One of the recipients was French mathematician Henri Poincaré, who shared Röntgen’s X-ray photographs with the fellow members of Paris’s Académie des Sciences on January 20, 1896. In that audience was Antoine Henri Becquerel, who, inspired by the fact that the X-rays seemed to emanate from the area of the vacuum tube that glowed, immediately began experimenting with fluorescent materials and their emissions. Henri’s grandfather, Antoine César Becquerel, was a Parisian celebrity for having discovered the use of electrolytes to refine metal and was one of the first graduates of the École Polytechnique, which became so central to the military, scientific, and engineering cultures of France that anyone wanting a career in those fields needed to be a polytechnicien.

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France (Lonely Planet, 8th Edition)
** by
Nicola Williams

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active transport: walking or cycling, back-to-the-land, bike sharing scheme, British Empire, car-free, carbon footprint, centre right, Columbine, double helix, Guggenheim Bilbao, haute couture, haute cuisine, Henri Poincaré, Honoré de Balzac, illegal immigration, industrial robot, information trail, Jacquard loom, Jacquard loom, Joseph-Marie Jacquard, Louis Blériot, Louis Pasteur, low cost carrier, Mahatma Gandhi, means of production, Murano, Venice glass, pension reform, QWERTY keyboard, ride hailing / ride sharing, Saturday Night Live, Silicon Valley, Skype, supervolcano, trade route, urban renewal, urban sprawl, V2 rocket

Aux Délices du Palais ( 03 83 30 44 19; 69 Grande Rue; starters €5, mains €9, desserts €4; Mon-Fri & dinner Sat) Billing itself as bistronomique (whatever that means), this informal place serves whatever the jovial chef’s muse inspires him to make – everything from chicken tajine (North African–style stew) to beef fajitas to endive tartes. Great value, so it’s no surprise it’s got an enthusiastic local following. Brasserie Excelsior ( 03 83 35 24 57; 50 rue Henri Poincaré; Nancy Gare; after-10pm menu €18.90, other menus €30.50; 8am-12.30am Mon-Sat, 8am-11pm Sun, meals served noon-3pm & 7pm–closing time) Built in 1910, this sparkling brasserie’s art-nouveau decor makes every glance at the ceiling memorable – and the food’s excellent too. The sauerkraut options include choucroute à trois poissons (sauerkraut with salmon, haddock and monkfish). Le Gastrolâtre (Chez Tanésy; 03 83 35 51 94; 23 Grande Rue; lunch menu €25, other menus €42; Tue-Sat) A 16th- and 17th-century town house has been transformed into a homey, intimate bistro specialising in mouth-watering Lorraine- and Provence-inspired cuisine, including fowl.

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Daum factory outlet ( 03 83 32 14 55; www.daum.fr; 17 rue des Cristalleries; Cristalleries; 9.30am-12.30pm & 2-6pm Mon-Sat, closed Mon Jul & Aug) About 1km northeast of place Stanislas, this place sells discontinued Daum designs and unsigned seconds. Bergamotes de Nancy, the local confectionery speciality, are hard candies made with bergamot, a citrus fruit (used to flavour Earl Grey tea) that grows on Mt Etna. Selling Bergamottes (with two t’s) is Lefèvre-Lemoine (Au Duché de Lorraine; 03 83 30 13 83; 47 rue Henri Poincaré; Nancy Gare; 8.30am-7pm Mon-Sat, 9.30am-12.30pm Sun), founded in 1840 and last redecorated – with Gilded Age panache – back in 1928. One of its old-fashioned red sweets tins made a cameo appearance in the film Amélie. Getting There & Away CAR Rental options: ADA ( 03 83 36 53 09; 138 rue St-Dizier) Europcar ( 03 83 37 57 24; 18 rue de Serre) National-Citer ( 03 83 37 38 59; train station departure hall; Nancy Gare) TRAIN The train station (place Thiers; Nancy Gare), spiffed up for the arrival of the TGV Est Européen in 2007, is on the line linking Paris’ Gare de l’Est (€50.50 by TGV, 1½ hours, eight to 10 direct daily) with Strasbourg (€20.70, 1½ hours, seven to 12 daily).