Edward Lorenz: Chaos theory Concepts

Chaos: Making a New Science

by James Gleick · 18 Oct 2011 · 396pp · 112,748 words

CHAOS Making a New Science James Gleick To Cynthia human was the music, natural was the static… —JOHN UPDIKE Contents Prologue The Butterfly Effect Edward Lorenz and his toy weather. The computer misbehaves. Long-range forecasting is doomed. Order masquerading as randomness. A world of nonlinearity. “We completely missed the point.”

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swept across an earth as smooth as glass. Night never came, and autumn never gave way to winter. It never rained. The simulated weather in Edward Lorenz’s new electronic computer changed slowly but certainly, drifting through a permanent dry midday midseason, as if the world had turned into Camelot, or some

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the weather. Yet in Lorenz’s particular system of equations, small errors proved catastrophic. HOW TWO WEATHER PATTERNS DIVERGE. From nearly the same starting point, Edward Lorenz saw his computer weather produce patterns that grew farther and farther apart until all resemblance disappeared. (From Lorenz’s 1961 printouts.) He decided to look

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system, proposing such causes as meteorite strikes. Yet perhaps the geodynamo contains its own chaos. THE LORENZIAN WATERWHEEL. The first, famous chaotic system discovered by Edward Lorenz corresponds exactly to a mechanical device: a waterwheel. This simple device proves capable of surprisingly complicated behavior. The rotation of the waterwheel shares some of

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ideas to science in the 1960s and 1970s became an intellectual current that made itself felt simultaneously in many places. Self-similarity was implicit in Edward Lorenz’s work. It was part of his intuitive understanding of the fine structure of the maps made by his system of equations, a structure he

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. ACTUALLY, BY 1971 the scientific literature already contained one small line drawing of the unimaginable beast that Ruelle and Takens were trying to bring alive. Edward Lorenz had attached it to his 1963 paper on deterministic chaos, a picture with just two curves on the right, one inside the other, and five

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characteristic diffidence, Lorenz made the occasion a social one, and they went with their wives to an art museum. THE FIRST STRANGE ATTRACTOR. In 1963 Edward Lorenz could compute only the first few strands of the attractor for his simple system of equations. But he could see that the interleaving of the

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successive states in the flash of an imaginary strobe light. Either way, such pictures finally began to reveal the fine fractal structure guessed at by Edward Lorenz. EXPOSING AN ATTRACTOR’S STRUCTURE. The strange attractor above—first one orbit, then ten, then one hundred—depicts the chaotic behavior of a rotor, a

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of scattered points. Hénon went on to other problems, but fourteen years later, when finally he heard about the strange attractors of David Ruelle and Edward Lorenz, he was prepared to listen. By 1976 he had moved to the Observatory of Nice, perched high above the Mediterranean Sea on the Grande Corniche

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in 1982. Wilson’s great contribution to physics, along with work by two other physicists, Leo Kadanoff and Michael Fisher, was an important ancestor of chaos theory. These men, working independently, were all thinking in different ways about what happened in phase transitions. They were studying the behavior of matter near the

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to create convection in the liquid helium by making the bottom plate warmer than the top plate. It was exactly the convection model described by Edward Lorenz, the classic system known as Rayleigh-Bénard convection. Libchaber was not aware of Lorenz—not yet. Nor had he any idea of Mitchell Feigenbaum’s

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despised guesses, approximations, half-truths based on intuition rather than proof. He was the kind of mathematician who would continue to insist, twenty years after Edward Lorenz’s attractor entered the literature, that no one really knew whether those equations gave rise to a strange attractor. It was unproved conjecture. The familiar

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imprecision and not-quite–repeatability of the analog computer worked to Shaw’s advantage. He quickly saw the sensitive dependence on initial conditions that persuaded Edward Lorenz of the futility of longterm weather forecasting. He would set the initial conditions, push the go button, and off the attractor would go. Then he

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folder away with him. Later, when his friends begged him for details, he told them the high point had been a dinner in honor of Edward Lorenz, who was finally receiving the recognition that had eluded him for so many years. When Lorenz walked into the room, shyly holding his wife’s

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tools exist. Chaos and Beyond “The classification of the constituents of a chaos, nothing less here is essayed.” —HERMAN MELVILLE, Moby-Dick TWO DECADES AGO Edward Lorenz was thinking about the atmosphere, Michel Hénon the stars, Robert May the balance of nature. Benoit Mandelbrot was an unknown IBM mathematician, Mitchell Feigenbaum an

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. Bees hovered and darted in a dynamical buzz. Clouds skidded across the sky. He could not work the old way any more. Afterword EVEN NOW, CHAOS THEORY sounds like a bit of an oxymoron. In the 1980s, “chaos” and “theory” were words that didn’t seem to belong in the same room

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least no longer the exception. By and large, the pioneers of chaos came in from the wilderness and took their places in the scientific establishment. Edward Lorenz, as a much-honored professor emeritus at M.I.T., was still seen coming to work in his nineties and watching the weather from his

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only mathematician to seriously follow Poincaré’s lead in the twenties and thirties was George D. Birkhoff, who, as it happened, briefly taught a young Edward Lorenz at M.I.T. THAT FIRST DAY Lorenz; also, “On the Prevalence,” p. 56. “WE CERTAINLY HADN’T” Lorenz. YEARS OF UNREAL OPTIMISM Woods, Schneider

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(Cambridge, Mass.: The M.I.T. Press, 1967), p. 57. DAVID RUELLE SUSPECTED Ruelle. THE REACTION OF THE SCIENTIFIC PUBLIC “Turbulent Dynamical Systems,” p. 275. EDWARD LORENZ HAD ATTACHED “Deterministic Nonperiodic Flow,” p. 137. “IT IS DIFFICULT TO RECONCILE Ibid., p. 140. HE WENT TO VISIT LORENZ Ruelle. “DON’T FORM A

The Physics of Wall Street: A Brief History of Predicting the Unpredictable

by James Owen Weatherall · 2 Jan 2013 · 338pp · 106,936 words

would change science, and finance, forever. The ideas at the heart of Farmer’s and Packard’s work were first developed by a man named Edward Lorenz. As a young boy, Lorenz thought he wanted to be a mathematician. He had a clear talent for mathematics, and when it came time to

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computers to solve the differential equations necessary to predict roulette had unwittingly put Farmer and Packard at the cutting edge of the newest research in chaos theory. Farmer’s advisor was right that there was a dissertation in the roulette calculations. What he didn’t know was that the dissertation would be

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Collective and the Chaos Cabal. Shaw threw out a nearly finished dissertation to start working on chaos theory full-time; Farmer officially switched away from astrophysics. By the late 1970s, a great deal had been done on chaos theory. Lorenz had discovered many of the basic principles and had then come up with simple

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settle down into one of these states. But for other systems, the attractors can be much more complicated. A major contribution to the study of chaos theory was the realization that if a system is chaotic, these attractors have a highly intricate fractal structure. But despite these foundations, the subject was still

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and starts, without any real research center. Normally, graduate work in physics is a collaboration among graduate students, young postdoctoral researchers, and a professor. But chaos theory was still so new that these kinds of research groups didn’t yet exist. You couldn’t go to graduate school to study

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chaos theory. The Dynamical Systems Collective was an attempt to fix this, by pulling its members through graduate school by their bootstraps. Some of the faculty at

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new and open to novel ideas, and enough professors were supportive that the four initial members were permitted to guide themselves, collectively, to PhDs in chaos theory. From the very start, prompted perhaps by the roulette experience, the Dynamical Systems Collective was interested in prediction. It was a novel way of thinking

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empirically, by looking at how the system actually behaved. The Dynamical Systems Collective lasted for four years, during which time it made seminal advances in chaos theory and managed to turn years of thinking about roulette into respectable science. But the Eudaemons couldn’t stay in graduate school forever. Farmer graduated in

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, in March 1992, the pressure was on to find a deal. It is tempting to say that Farmer, Packard, and their Prediction Company collaborators “used chaos theory to predict the markets” or something along those lines. In fact, this is how their enterprise is usually characterized. But that isn’t quite right

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. Farmer and Packard didn’t use chaos theory as a meteorologist or a physicist might. They didn’t do things such as attempt to find the fractal geometry underlying markets, or derive the

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deterministic laws that govern financial systems. Instead, the fifteen years that Farmer and Packard spent working on chaos theory gave them an unprecedented (by 1991 standards) understanding of how complex systems work, and the ability to use computers and mathematics in ways that someone

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trained in economics (or even in most areas of physics) would never have imagined possible. Their experience with chaos theory helped them appreciate how regular patterns — patterns with real predictive power — could be masked by the appearance of randomness. Their experience also showed them how

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-Sintra (keeping his academic position all the while). It was during this period, working on research for the military, that Sornette first began to study chaos theory and complex systems, subjects that would later provide much of the foundation for his interdisciplinary work. In June 1986, Sornette married a young geophysicist named

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a paradigm Western mining town”: This background on Silver City is from Wallis (2007). “. . . first developed by a man named Edward Lorenz”: The biographical and historical details concerning Lorenz and the history of chaos theory are from Gleick (1987) and Lorenz (1993). “. . . the work of two physicists named James Yorke and Tien-Yien Li

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(1999); likewise, Broad (1992) writes that Farmer and Packard are “private entrepreneurs using world-class skills in chaos theory to predict the rise and fall of stocks and bonds.” “Farmer and Packard didn’t use chaos theory . . .”: This section in particular is based on an interview with Farmer. The closest thing from Farmer’s

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Theory. Singapore: World Scientific Publishing. Bass, Thomas A. 1985. The Eudaemonic Pie. Boston: Houghton Mifflin. — — — . 1999. The Predictors: How a Band of Maverick Physicists Used Chaos Theory to Trade Their Way to a Fortune on Wall Street. New York: Henry Holt. Batterman, Robert. 2002. The Devil in the Details: Asymptotic Reasoning in

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Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?” In The Chaos Avant-Garde: Memories of the Early Days of Chaos Theory, ed. Ralph Abraham and Yoshisuke Ueda. Singapore: World Scientific Publishing. Lowenstein, Roger. 2000. When Genius Failed: The Rise and Fall of Long-Term Capital Management

Making Sense of Chaos: A Better Economics for a Better World

by J. Doyne Farmer · 24 Apr 2024 · 406pp · 114,438 words

fellow physics graduate student at Santa Cruz, appeared at our usual communal dinner in a state of excitement. He had just been introduced to meteorologist Edward Lorenz’s mathematical model, which featured a system of three simple equations and contained something called a strange attractor.17 Rob had programmed the equations on

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that era, such as Stanislaw Ulam and Nicholas Metropolis, were still there. I had regular conversations with the mathematical physicist Mitchell Feigenbaum, a pioneer of chaos theory. Los Alamos was perhaps the only place in the United States where working on chaos was considered a perfectly normal thing to do, and with

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bigger, and their motion becomes more and more irregular – the motion becomes turbulent. In a hurricane this becomes what is called fully developed turbulence. As Edward Lorenz realized, turbulence is due to chaotic dynamics. As soon as the movement of the ripples becomes irregular, the motion is chaotic. Turbulence corresponds to complicated

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research on chaotic dynamics. I had the good fortune to be asked to intern at the National Center for Atmospheric Research (NCAR) with Edward Lorenz, the pioneer of chaos theory and one of the leading meteorologists of his day. Since my internship was unpaid, to save money I camped illegally on the spectacular mesa

What We Cannot Know: Explorations at the Edge of Knowledge

by Marcus Du Sautoy · 18 May 2016

to small changes was not very well known for decades into the twentieth century. Indeed, it really took the rediscovery of the phenomenon by scientist Edward Lorenz, when he, like Poincaré, thought he’d made some mistake, before the ideas of chaos became more widely known. While working as a meteorologist at

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small variations in the initial circumstances produce only small variations in the final state of the system.’ It is this maxim that the discovery of chaos theory in the twentieth century revealed as false. This sensitivity to small changes in initial conditions has the potential to sabotage my attempts to use the

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isn’t opinionated and prepared to give his own views on the subject at hand. I was curious how governments deal with the problems that chaos theory creates for anyone trying to make policy decisions. How do politicians cope with the challenges of predicting or manipulating the future, given that we can

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knew the equations and we could make more realistic models of the Earth.’ But May is cautious not to let the climate change deniers use chaos theory as a way to undermine the debate. ‘Not believing in climate change because you can’t trust weather reports is a bit like saying that

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Tom Stoppard’s play Arcadia to illustrate the strange tension that exists between the power of science to know some things with extraordinary accuracy and chaos theory, which denies us knowledge of many parts of the natural world. One of the protagonists, Valentine, declares: We’re better at predicting events at the

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cake and plunged back into the chaos of the select committees and petty politics of Westminster. May’s last point relates to the challenge that chaos theory poses for knowing something about the past as much as the future. At least with the future we can wait and see what the outcome

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. This is in part due to lack of data from that period. Can we ever recover that data, or could this always remain a mystery? Chaos theory is usually a limiting factor in what we can know about the future. But it can also imply limits on what we can know about

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of probability that is at work in evolution. The evolutionary tree itself has an interesting quality that is similar to the shapes that appear in chaos theory, a quality known as fractal. The fractal evolutionary tree. The evolutionary tree is a picture of the evolution of life on Earth. Making your way

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to know these with 100% accuracy. So each time they run the simulation they make small changes to the data. Because of the effects of chaos theory, just a small change could result in a large deviation in the outcomes. For example, astronomers know the dimensions of the ellipse of Mercury’s

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recedes back into the hands of the gods. DOES GOD PLAY DICE? What of the challenge to define God as the things we cannot know? Chaos theory asserts that I cannot know the future of certain systems of equations because they are too sensitive to small inaccuracies. In the past gods weren

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lay. Twentieth-century mathematics has revealed that these ancient gods are still with us. There are natural phenomena that will never be tamed and known. Chaos theory implies that our futures are often beyond knowledge because of their dependence on the fine-tuning of how things are set up in the present

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. Because we can never have complete knowledge of the present, chaos theory denies us access to the future. At least until that future becomes the present. That’s not to say that all futures are unknowable. Very

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unknowability inherent in his own scientific field of quantum physics. But he has also been interested in the gap in knowledge that the mathematics of chaos theory provides as an opportunity for his God to influence the future course of humanity. Polkinghorne has proposed that it is via the indeterminacies implicit in

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chaos theory that a supernatural intelligence can still act without violating the laws of physics. Chaos theory says that we can never know the set-up precisely enough to be able to run deterministic equations, and

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change requires a complete holistic top-down intervention. This is not a God in the detail but by necessity an all-knowing God. Given that chaos theory means that even the location of an electron on the other side of the universe could influence the whole system, we need to have complete

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predictions based on that part. So it would require knowledge of the whole to act via this chink in that which is unknown to us. Chaos theory is deterministic, so this isn’t an attempt to use the randomness of something like quantum physics as a way to have influence. Polkinghorne’s

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the chance to intervene and shift the system between any of these scenarios without us being aware of the shift. But, as we have seen, chaos theory means that these small shifts can still have hugely different outcomes. Polkinghorne is careful to assert that you allow shifts between systems where there is

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of mathematics should lead to complete knowledge of the future, I will never have access to that complete knowledge. The shocking revelation of twentieth-century chaos theory is that even an approximation to that knowledge won’t help. The divergent paths of the chaotic billiard table mean that since we can never

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know which path we are on, our future is not predictable. Chaos theory implies that there are things we can never know. The mathematics in which I had placed so much faith to give me complete knowledge has

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made up of similar certainties, even if we as humans might not ultimately have access to them. I throw my dice and the mathematics of chaos theory I recognize means I may never be able to calculate the final outcome of the throw of the dice. But at least the mathematics says

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quantum physics stops us zooming in beyond the Planck length. Are the fractals of the First Edge only in my mathematical mind? Quantum physics and chaos theory appear to be incompatible with each other. It is possible that quantum physics has the effect of suppressing chaotic systems. It should be said that

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the paradoxes of quantum theory is that here we are 80 years later and we still don’t understand it.’ In the First Edge, exploring chaos theory, I’d read how Polkinghorne believed that God might get involved with the decimal places we can’t know. I wondered why he had chosen

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chaos theory, rather than his home territory of quantum physics, as the unknown through which his God might act. ‘There was a period of about ten years

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appeared to me just a little too slick. To counterbalance that I lurched a bit too far in the other direction. I don’t think chaos theory is the whole solution. It’s really just the suggestion that the physical universe is orderly but looser in its order than Newton would have

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enterprise.’ Looking back at the Edges I’ve visited so far, nothing seems quite as unanswerable as the question of whether the universe is infinite. Chaos theory told me that the future is unknowable, but I can just wait until it becomes the present and then I’ll know. As I slice

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of the system. If the universe is described by a quantum wave function, does there need to be something outside the system to observe it? Chaos theory implies that we can’t understand part of the system as an isolated problem, because an electron on the other side of the universe may

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, I expect to get 100 6s. But I just want to throw it once and know something about how it will fall. The equations of chaos theory tell us that so much of the future is dependent on extremely fine-tuning of the decimal places that control the input of the equations

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reading this book might have a profound effect on the way you lead your life, even if you will never know whether it’s true. Chaos theory implies that not only my casino dice but humans too are in some ways part of the unknowable. Although we are physical systems, no amount

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–6, 387, 388, 397–8, 400, 401, 402, 403, 404, 413 Babylonians 83, 251, 366, 368, 417 Bach 77, 121, 304 Bacon, Francis 399 banking, chaos theory and 54 Barbour, Julian: The End of Time 299–300 Barrow, Professor John 236–40, 242 baryons 107, 108, 109, 110, 115, 119 Beit Guvrin

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, 304, 305, 308, 313, 314, 315 celluloid 91 Cepheid star 202–3, 204 Chadwick, James 100–1 Chalmers, David 347 Chandrasekhar, Subrahmanyan 275 Chaos 67 chaos theory 39–41, 43–53, 54, 55, 56, 58–9, 60, 61, 62–4, 68–72, 157, 168, 178, 179, 242, 402–3, 408, 419 charm

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, Alexis 29 Cleverbot (app) 303, 313, 317, 332 climate change 6, 53 cloud chambers 100, 104–6 Cohen, Paul 401–2 Compton wavelength 167 computers: chaos theory modelling on 61–2, 64; consciousness/artificial intelligence and 8, 281, 303–4, 313, 317, 322, 325, 336, 337–9, 345–6, 349, 351, 352

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’s theorem and 171; black holes and 285, 289; calculus and 30–2, 33, 34, 88; Cantor set and 65–6; Cardano and 23–4; chaos theory and 41, 43, 44, 48, 54–5, 66–8, 157, 408, 419; consciousness and 304, 308–9, 321, 325, 338, 343; evolution and 56–7

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, Thomson’s experiments to understand 95–6, 140 electromagnetic force 107, 108, 274 electromagnetism 34, 104, 107, 108, 136, 138–43, 417 electron 48, 407; chaos theory and 70, 402; discovery of 95, 96, 97, 98, 99, 100, 101; electromagnetic force and 107; hydrogen atom and 274; mass of 126, 127, 230

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tree of life and 60–2; God and 230, 411; mismanaged ecosystems and 55; origin of life and 56–66; pattern spotting and 20; probability/chaos theory and 54–5, 56–66; random mutation and 8, 56–62; solar system/universe 32–41, 43, 55, 133, 155, 177, 206, 220, 223, 234

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112, 113, 114, 116, 125; vacuum and 183 Gettier, Edmund 412 God: aeon theory and 296; author and 13–14; Barrow and 236–40, 242; chaos theory and 69–71, 178–9; collapsing wave function and 178–9; consciousness and 319–20, 348–9, 355; cosmology and 235–7, 406; creation of

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’ 298 see also individual area of mathematics Maxwell, James Clerk 34, 136, 142, 143, 419; Matter and Motion 47 May, Robert M. 51–3, 72; chaos theory and 48–54, 55, 56, 57, 72; ‘Simple Mathematical Models with Very Complicated Dynamics’ 48–51, 56 McCabe, Herbert 15, 181 McGurk effect 328 Mendeleev

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, 228–9, 231, 241, 274, 284, 288, 289, 297, 338, 354, 355, 402, 407, 408–9; black holes and 274, 284, 288, 289, 355; chaos theory and see chaos theory; Copenhagen interpretation of 178; counterintuitive nature of 132, 159, 164, 284; density of electron and 126; double-slit light experiment 134–6, 143, 144

Fluke: Chance, Chaos, and Why Everything We Do Matters

by Brian Klaas · 23 Jan 2024 · 250pp · 96,870 words

the butterfly effect, the notion that a butterfly flapping its wings in Brazil could trigger a tornado in Texas. Lorenz had inadvertently given birth to chaos theory. The lesson was clear: if Laplace’s demon could exist, its measurements would need to be flawless. If the creature was off by even one

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lead to big changes. Sherlock Holmes once quipped, “It has long been an axiom of mine that the little things are infinitely the most important.” Chaos theory proved Holmes right. Because small changes can make such a big difference, the universe will always appear uncertain, even random, to us. No matter the

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never become Laplace’s demon. If there is a clockwork universe ticking away behind everything we see and experience, we will never fully understand it. Chaos theory meant that even those predictable billiard balls had to be reclassified as unpredictable. Even the slightly different pull created by the gravitational mass of human

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charlatans and fools. Or, as the theologian Pema Chödrön put it, “If you’re invested in security and certainty, you are on the wrong planet.” Chaos theory changed how we understand the world. But Lorenz’s discovery also leads to some unsettling questions about our own existence. If an infinitesimal change in

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. This definition comes from the complex-systems scholar Scott E. Page of the University of Michigan. V. These are loose analogies. All these concepts from chaos theory and complex systems are mathematically precise terms with more specific definitions in dynamical systems theory, so please forgive any imprecision, for the sake of ease

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and lots of repeated predictions. But who’s to say that today’s physical conditions are comparable to those in the future? After all, as chaos theory has demonstrated, tiny variations in physical systems that produce the weather can produce big changes. What if we’re comparing apples to oranges? These questions

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comparing the bin Laden raid to another raid in Somalia. But now for the problem: weather patterns are contingent. As we know from Edward Lorenz, the meteorological founding father of chaos theory, initial conditions matter enormously, so weather patterns will diverge more and more over time based on the smallest imaginable changes. The weather

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for weather forecasting to be useful, and because infinitesimal shifts in initial conditions create wildly different results, all bets are off after about ten days. Chaos theory takes over. We might call this chaotic uncertainty. With weather, we’ve recognized the limits of our understanding; nobody tries to forecast whether it will

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supreme because the idiosyncratic behavior of a single person can reroute us all onto a different path. The logical extension of that viewpoint—rooted in chaos theory—means that every individual isn’t just capable of changing history. Rather, we are each changing history constantly, with every action—even every thought. Who

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Hitler question is more profound than a thorny moral dilemma. The right answer pivots on our view of how history works and why change happens. Chaos theory proves that small changes can produce enormous impacts, so any manipulation of the past would risk drastic change, making the thought experiment even more uncertain

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meteorology, founding the precursor to Britain’s modern weather service, the Meteorological Office, and producing the foundational work that inspired Lorenz, the meteorologist who discovered chaos theory a century later. In his work, FitzRoy coined the word forecast, a term central to prediction. FitzRoy’s story, alas, doesn’t have a happy

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past, but somehow seem immune to the same deterministic logic when it’s our present. Determinism doesn’t mean that we can predict the future. Chaos theory shows that seemingly insignificant tweaks to the initial conditions in a deterministic system can produce wildly different results over time. Our lives could therefore be

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weather a few days in advance. After two weeks or so, all bets are off, even for the world’s best supercomputer. Determinism combined with chaos theory says that we can’t change the script, but if we could, then even one microscopic change to the plot or the characters—even a

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letting go just a little, we may liberate not only ourselves, but our best ideas. Poincaré, fittingly, is the mathematician who paved the way for chaos theory, which would later become known by the image of an intertwined world, in which hurricanes could be swirled into existence by a single butterfly flapping

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Bulletin 45 (2) (April 1996). LGP-30 computer: James Gleick, Chaos: Making a New Science (New York: Viking Books, 1987). chaos theory: Edward Lorenz, The Essence of Chaos (Seattle: University of Washington Press, 1995). “infinitely the most important”: Arthur Conan Doyle, The Adventures of Sherlock Holmes: Collins Classics (Glasgow,

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change, 5, 7, 28, 37, 247 accumulation of small changes, 28 ascribed to machinations of the gods, 22 chance and chaos as drivers of, 13 chaos theory and, 26 in contingency versus convergence, 15–16 interconnectedness and, 28 Laplace’s demon and, 23 time travel and, 6 uncertainty and, 12 chaos, 11

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of the swarm and, 83, 84, 87 chaos, edge of, 92, 93, 252 financial crises and, 95 swarms and, 83. See also cascades tipping points chaos theory, 26, 116, 123, 178 determinism and, 224 history and, 161, 162 cheetahs, genetic bottleneck of, 59n chemistry, 88, 207 Chen Jing, 188 Chilton, R. H

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Beats Truth theorem, 65–66, 67, 232 FitzRoy, Robert, 175, 177, 178–79 fluctuations, random, 13, 16, 31 brain development in utero and, 45–46 chaos theory and, 26 unexpected opportunities or disaster from, 42, 61 Forster, E. M., 73 founder effects, 60 Four Pests campaign, in China, 97, 252 Fragile Families

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

by Nate Silver · 31 Aug 2012 · 829pp · 186,976 words

Brazil can set off a tornado in Texas. It comes from the title of a paper19 delivered in 1972 by MIT’s Edward Lorenz, who began his career as a meteorologist. Chaos theory applies to systems in which each of two properties hold: The systems are dynamic, meaning that the behavior of the system

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example, it might instead read 29.517. Surely this couldn’t make that much difference? Lorenz realized that it could. The most basic tenet of chaos theory is that a small change in initial conditions—a butterfly flapping its wings in Brazil—can produce a large and unexpected divergence in outcomes—a

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tornado in Texas. This does not mean that the behavior of the system is random, as the term “chaos” might seem to imply. Nor is chaos theory some modern recitation of Murphy’s Law (“whatever can go wrong will go wrong”). It just means that certain types of systems are very hard

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is the epitome of a dynamic system, and the equations that govern the movement of atmospheric gases and fluids are nonlinear—mostly differential equations.23 Chaos theory therefore most definitely applies to weather forecasting, making the forecasts highly vulnerable to inaccuracies in our data. Sometimes these inaccuracies arise as the result of

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the Platonic ideal they were hoping to represent. The forecasters know the flaws in the computer models. These inevitably arise because—as a consequence of chaos theory—even the most trivial bug in the model can have potentially profound effects. Perhaps the computer tends to be too conservative on forecasting nighttime rainfalls

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were actually a bit worse than climatology. FIGURE 4-6: COMPARISON OF HIGH-TEMPERATURE FORECASTS40 After a little more than a week, Loft told me, chaos theory completely takes over, and the dynamic memory of the atmopshere erases itself. Although the following analogy is somewhat imprecise, it may help to think of

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formulate predictions from there. In fact, he wanted to understand how stress was changing and evolving throughout the entire system; his approach was motivated by chaos theory. Chaos theory is a demon that can be tamed—weather forecasters did so, at least in part. But weather forecasters have a much better theoretical understanding of

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of earthquakes. Earthquakes may be an inherently complex process. The theory of complexity that the late physicist Per Bak and others developed is different from chaos theory, although the two are often lumped together. Instead, the theory suggests that very simple things can behave in strange and mysterious ways when they interact

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system: everything affects everything else and the systems are perpetually in motion. In meteorology, this problem is quite literal, since the weather is subject to chaos theory—a butterfly flapping its wings in Brazil can theoretically cause a tornado in Texas. But in loosely the same way, a tsunami in Japan or

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, the problem is that meteorologists assume they have imprecise measurements of what the initial conditions were like, and weather patterns (because they are subject to chaos theory) are extremely sensitive to changes in the initial conditions. In economic forecasting, likewise, the quality of the initial data is frequently quite poor. Weather prediction

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perhaps interested in whether it will be rainier on average throughout the Northern Hemisphere. Meteorologists, nevertheless, have to wrestle with complexity:* the entire discipline of chaos theory developed out of what were essentially frustrated attempts to make weather forecasts. Climatologists have to deal with complexity as well: clouds, for instance, are small

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(CSIS), 425–27 Centers for Disease Control (CDC), 205, 206–7, 211 Central Park, 391, 391 CFOs, 359 Chadwick, Henry, 95 chaos, cone of, 139 chaos theory, 118–22, 124, 132, 162, 172, 195, 386 complexity theory vs., 386n Charleston, S.C., 150 chartists, 339–40, 341 Chavez, Eric, 99 chemistry, 114

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forecasting, 127–28, 131–37, 132 competitive advantage, 313–14 competitiveness, 97 complexity, of global warming forecasting, 382 complexity theory, 172–73, 368–69, 386 chaos theory vs., 386ncomputer age, 7–8 computers: chess played by, 261–62, 287–88; see also Deep Blue; Deep Thought; Fritz poker played by, 324 predictions

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this chapter meaning that complex is largely synonymous with complicated. There is also a particular scientific domain called complexity theory, which some scientists distinguish from chaos theory. We explore these very interesting ideas in chapter 5. * If you scale back their warming estimates to reflect the smaller-than-assumed rate of CO2

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

by Adam Kucharski · 23 Feb 2016 · 360pp · 85,321 words

to insure it. Over the following chapters, we will find out how gambling has continued to influence scientific thinking, from game theory and statistics to chaos theory and artificial intelligence. Perhaps it shouldn’t be surprising that science and gambling are so intertwined. After all, wagers are windows into the world of

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oversight could have dramatic consequences. Seventy years before mathematician Edward Lorenz gave a talk asking “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” Poincaré had outlined the “butterfly effect.” Lorenz’s work, which grew into chaos theory, focused chiefly on prediction. He was motivated by a

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people. Evidently, Shannon’s fears were well founded. TOWARD THE END OF 1977, the New York Academy of Sciences hosted the first major conference on chaos theory. They invited a diverse mix of researchers, including James Yorke, the mathematician who first coined the term “chaotic” to describe ordered yet unpredictable phenomena like

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was a way to illustrate his idea that simple physical processes could descend into what seems like randomness. This idea formed a crucial part of chaos theory, which emerged as a new academic field in the 1970s. During this period, roulette was always lurking in the background. In fact, many of the

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real-life examples of a “chaotic transition” whereby a process switches from a regular pattern to one that is as good as random. Interest in chaos theory and roulette does not appear to have dampened over the years. The topics can still capture the public imagination, as shown by the extensive media

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easiest to test the predictions against the racing data the team had just analyzed. Yet this would be an unwise approach. Before he worked on chaos theory, Edward Lorenz spent the Second World War as a forecaster for the US Air Corps in the Pacific. One autumn in 1944, his team made a series

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1991, he founded a hedge fund with fellow ex-Eudaemon Norman Packard. It was named Prediction Company, and the plan was to apply concepts from chaos theory to the financial world. Mixing physics and finance was to prove extremely successful, and Farmer spent eight years with the company before deciding to return

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time,” he said, “and instead, an ultrafast ecology of robots rises up to take control.” WHEN PEOPLE TALK ABOUT chaos theory, they often focus on the physics side of things. They might mention Edward Lorenz and his work on forecasting and the butterfly effect: the unpredictability of the weather, and the tornado caused by

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might recall the story of the Eudaemons and roulette prediction, and how the trajectory of a billiard ball can be sensitive to initial conditions. Yet chaos theory has reached beyond the physical sciences. While the Eudaemons were preparing to take their roulette strategy to Las Vegas, on the other side of the

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.2. With a medium growth rate, the population density oscillates. FIGURE 5.3. High growth rates lead to highly variable population dynamics. May found that chaos theory could explain what was going on. The fluctuations in density were the result of the population being sensitive to initial conditions. Just as Poincaré had

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human knowledge.” Cards and casinos since have inspired many other scientific ideas. We have seen how roulette helped Henri Poincaré develop the early ideas of chaos theory and allowed Karl Pearson to test his new statistical techniques. We also met Stanislaw Ulam, whose card games led to the Monte Carlo method, now

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blackjack; poker; roulette causation and correlation, issue of, 206–207 Centaur, 100 Cepheus poker bot, 188 Chadwick, Henry, 80 Champions League, 93 Chaos (journal), 15 chaos theory, 9, 13, 22, 120, 124, 127, 217 chaotic decision making, 162 Chapin, R. M., 211 Chapman, Randall, 46, 49, 50–52, 54, 55, 68, 69

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

by James Rickards · 15 Nov 2016 · 354pp · 105,322 words

the continued dominance of obsolete equilibrium models in central bank policymaking and private risk management. Modern complexity theory began in 1960 with the work of Edward Lorenz, an MIT mathematician and meteorologist. Lorenz was modeling atmospheric flows and discovered that minute changes in initial conditions resulted in wildly different outcomes in flow

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can. Regulators who dismiss these insights ignore hurricane warnings while residing in soon-to-be-inundated low-lying bungalows. Complexity and the related field of chaos theory are two branches of the broader sciences of nonlinear mathematics and critical state systems analysis. Los Alamos has been on the cutting edge of these

The Butterfly Defect: How Globalization Creates Systemic Risks, and What to Do About It

by Ian Goldin and Mike Mariathasan · 15 Mar 2014 · 414pp · 101,285 words

name of the effect has origins in the work of Edward Lorenz, who illustrated how a hurricane’s formation may be contingent on whether a distant butterfly had, days or weeks before, flapped its wings.1 The effect was subsequently taken up in chaos theory, which draws on a long tradition of examining the

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CDSs. See credit default swaps central banks: European, 56, 59–60, 63; Icelandic, 37, 38–39; research at, 63; systemic risk measurements by, 59–60 chaos theory, xiii chemical weapons, 194, 254n80 Chen, Lincoln C., 159, 163–64 Chicago, Burnham Plan, 105 China: air pollution in, 137; domestic air travel in, 15

The Vanishing Face of Gaia: A Final Warning

by James E. Lovelock · 1 Jan 2009 · 239pp · 68,598 words

presence as the model evolves. Scientists of these separated disciplines should have realized that they were on the wrong track when quite independently the geophysicist Edward Lorenz, in 1961, and the neo‐Darwinist biologist Robert May, in 1973, made the remarkable discovery that deterministic chaos was an inherent part of the computer

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. Biosphere is now mainly used, in Vernadsky’s sense, as an imprecise word that acknowledges the power of life on Earth without surrendering human sovereignty. CHAOS THEORY Certainty and confidence in science marked its development in the nineteenth and much of the twentieth centuries, but now it carries on unaware that the

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scientists to explore the world of dynamics – the mathematics of moving, flowing and living systems. The insights from the numerical analysis of fluid dynamics by Edward Lorenz and of population biology by Robert May revealed what is called ‘deterministic chaos’. Systems like the weather, the motion of more than two astronomical bodies