Chaos: A Very Short IntroductionOUP Oxford, 22/02/2007 - 200 páginas Chaos exists in systems all around us. Even the simplest system of cause and effect can be subject to chaos, denying us accurate predictions of its behaviour, and sometimes giving rise to astonishing structures of large-scale order. Our growing understanding of Chaos Theory is having fascinating applications in the real world - from technology to global warming, politics, human behaviour, and even gambling on the stock market. Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible maths and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable. |
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... mathematics and the sciences, systems where (without cheating) small differences in the way things are now have huge consequences in the way things will be in the future. It would be cheating, of course, if things just happened randomly ...
... mathematics and the sciences, systems where (without cheating) small differences in the way things are now have huge consequences in the way things will be in the future. It would be cheating, of course, if things just happened randomly ...
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... mathematical version of this concept is known as sensitive dependence. Chaotic systems not only exhibit sensitive dependence, but two other properties as well: they are deterministic, and they are nonlinear. In this chapter, we'll see ...
... mathematical version of this concept is known as sensitive dependence. Chaotic systems not only exhibit sensitive dependence, but two other properties as well: they are deterministic, and they are nonlinear. In this chapter, we'll see ...
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Leonard Smith. unstable systems by improving our ability to describe, to understand, perhaps ... mathematical models. The image of chaos amplifying uncertainty and ... systems by considering the impact of slightly different situations. The ...
Leonard Smith. unstable systems by improving our ability to describe, to understand, perhaps ... mathematical models. The image of chaos amplifying uncertainty and ... systems by considering the impact of slightly different situations. The ...
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... mathematical models with the reality they aim to describe muddles the discussion of both. Second, looking more deeply, it may be that some ecosystems evolve as if they were chaotic systems ... mathematics or literature, since we have access ...
... mathematical models with the reality they aim to describe muddles the discussion of both. Second, looking more deeply, it may be that some ecosystems evolve as if they were chaotic systems ... mathematics or literature, since we have access ...
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... mathematical line actually divided continents, as well as the other adventures the molecule of water might have ... systems always respond proportionately. Nonlinear systems need not, giving nonlinearity a critical role in the origin of ...
... mathematical line actually divided continents, as well as the other adventures the molecule of water might have ... systems always respond proportionately. Nonlinear systems need not, giving nonlinearity a critical role in the origin of ...
Índice
1 | |
2 Exponential growth nonlinearity common sense | 22 |
determinism randomness and noise | 33 |
4 Chaos in mathematical models | 58 |
5 Fractals strange attractors and dimensions | 76 |
6 Quantifying the dynamics of uncertainty | 87 |
7 Real numbers real observations and computers | 104 |
statistics and chaos | 112 |
does chaos constrain our forecasts? | 123 |
can we see through our models? | 132 |
11 Philosophy in chaos | 154 |
Glossary | 163 |
Further reading | 169 |
Index | 173 |
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Palavras e frases frequentes
21st-century demon Apprentice Map attractor average Baker’s Map behaviour bell-shaped distribution best models bits butterfly effect chaotic systems climate models components computer simulations Day storm decision support define digital computer dimension dynamical system Earth’s ECMWF ensemble forecast ensemble members equations error exponential growth fact fractal Full Logistic Map future Galton Board golf balls Hénon Hénon Map impact infinitesimal initial condition insight iteration least squares look Lorenz Lyapunov exponent mathematical chaos mathematical map mathematical models mathematical systems mathematicians mature pair measure model inadequacy Moore-Spiegel NAG Board nonlinear systems number of rabbits observational noise panel parameter values perfect model periodic loop physical systems physicist population predictability probability forecasts quantify question random number real world reflect scientists self-similar sensitive dependence shadow solar space statistician statistics stochastic study of chaos temperature Tent Map Theorem things today’s trajectory voles weather forecasting weather model zero