Complexification: Explaining a Paradoxical World Through the Science of SurpriseWhy does time seem to fly on some occasions and drag on others? Why do some societies seem more prone to totalitarianism than others? Why does atonal music sound "worse" to most of us than traditional music? How can a butterfly in Brazil affect the weather in Alaska? The set of ingenious interdisciplinary approaches that are, together, called the science of complexity offers answers to these and dozens of other questions that beg the larger question of why our universe seems so paradoxical. John L. Casti, renowned mathematician and science writer, argues that a complexity that defies human logic is only natural, and he shows directly, engagingly, and with a wealth of illustrations how complexity arises and how it works. Casti explores several types of phenomena that have, until now, consistently eluded science's attempts to understand them: the catastrophic, where a tiny change in a system produces a huge effect (as happens in earthquakes or political revolutions); the chaotic, which includes odd correlations like the ones that make predicting the weather or the stock market so difficu |
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Page 232
... fractal . Fractals are curves that are irregular all over . Moreover , they have exactly the same degree of irregularity at all scales of measurement . So it doesn't matter whether you look at a fractal from far away or up close with a ...
... fractal . Fractals are curves that are irregular all over . Moreover , they have exactly the same degree of irregularity at all scales of measurement . So it doesn't matter whether you look at a fractal from far away or up close with a ...
Page 257
... fractal structure . These high estimates for H provide strong support for the claim that the stock market is not a random walk , but rather is a fractal with trend - reinforcing behavior . This conclusion is in direct contradiction to ...
... fractal structure . These high estimates for H provide strong support for the claim that the stock market is not a random walk , but rather is a fractal with trend - reinforcing behavior . This conclusion is in direct contradiction to ...
Page 303
... Fractal Geometry of Nature . San Francisco : W. H. Freeman , 1982 . Peitgen , H.-O. , D. H. Jürgens and D. Saupe . Fractals for the Classroom . Parts 1 & 2. New York : Springer , 1992 . △ Schroeder , M. Fractals , Chaos , Power Laws ...
... Fractal Geometry of Nature . San Francisco : W. H. Freeman , 1982 . Peitgen , H.-O. , D. H. Jürgens and D. Saupe . Fractals for the Classroom . Parts 1 & 2. New York : Springer , 1992 . △ Schroeder , M. Fractals , Chaos , Power Laws ...
Contents
Rules of Reality | 11 |
Its All in the Motion | 25 |
THE CATASTROPHIC | 43 |
Copyright | |
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argument basic behavior Busy Beaver butterfly called Casti catastrophe theory cell Cellular Automata Chaitin's chaos chaotic chapter colors complex connection consider correlation dimension curve cusp Deeper section dimension dynamical system elements example fact finite fixed point formal system fractal function geometry given Gödel's Theorem Halting Problem human Hurst exponent idea initial input interaction involves Julia set kind leads logical look Mandelbrot set mathematical mathematician measure move natural Newtonian notion objects observer output paradox parameters pattern physical play players possible predict problem quantity question random real-world relation represent result scientific sequence set of rules shown in Figure shows simple simplicial complex single situation space square stable statement strange attractor string strong AI structure surprise symbols teams termed trajectory truth Turing machine Turing test Turing's turn uncomputable University unstable vertices what's York