The Nonlinear World Conceptual Analysis and Phenomenology
The most important characteristic of the “world filled with nonlinearity” is the existence of scale interference: disparate space–time scales interfere with each other. Thus, the effects of unknowable scales invade the world that we can observe directly.
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abduction, 191, 207 absolutely continuous measure, 78 abstract, 17, 102 abstract concept, 17, 102, 133, 136, 137 abstract Lebesgue measure, 69 adaptive landscape, 271 adaptive sweep, 273 adaptor, 67, 100, 197, 198, 255 additive group, 52 additivity, 2 algorithmic randomness, 95, 239 algorithmic randomness and chaos, 92 amplitude equation, 163, 168 Andronov, A. A. (1901-1952), 140 anomalous dimension, 148 applied mathematics, 267 Archaea, 24, 275 Archimedes (287-212 BCE), 70 area, 67 artificial intelligence, 243 artificial language, 243 atonal, 137 attention, 238 attractor, 62 autopoiesis, 268 auxiliary condition, 134, 242, 250–254, 262 averaging method, 184 Avicenna (980-1037), 23 axiom of choice, 28, 110 axiom of randomness, 110 Bacteria, 24, 275 Banach-Tarski’s theorem, 69 bare perturbation series, 163 Barenblatt equation, 158 Barenblatt, G. I., 158
basin, basin of attraction, 62 Belousov-Zhabotinsky reaction, 196 Bernoulli, D. (1700-1782), 9 Bernoulli measure, 66 Bernoulli process, 66 Bilateria, 275 bit, 74 black box, 99, 196 block copolymer, 223 Bohr, N. (1885-1962), 36, 129, 156 Bohr’s atomic theory, 156 Boltzmann equation, 125 Boltzmann, L. (1844-1906), 28, 78, 125, 138 Borel, E. (1871-1956), 70, 109 Borel family of sets, 70 Borel measure, 70 Bridgeman’s Π-theorem, 155 Brin-Katok’s theorem, 88 Burgess fauna, 269 Cahn-Hilliard equation, 213 Cantor, G. (1845-1918), 27 Carath´eodory, C. (1873-1950), 137 catastrophe theory, 267 category theory, 25 Cauchy, A. L. (1789-1857), 10 Cauchy’s equation, 75 cell, 256 cell dynamical system CDS, 208 cell theory, 256 cell wall, 256 Champollion, J.-F. (1790-1832), 7 chaos, 11, 49, 59, 109 chaos, history, 48 chaos, various definitions, 62 chaotic dynamical system, 59
Y. Oono, The Nonlinear World: Conceptual Analysis and Phenomenology, Springer Series in Synergetics 109, DOI 10.1007/978-4-431-54029-8, © Springer Japan 2013
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294 chaotic itinerancy, 110 chaperone, 283 characteristic curve, 160 Chiba, H., 174 choice, 238 chondrogenesis, 226 Church, A. (1903-1995), 96, 98 Church’s thesis, 98 classical mechanics, 134 Clausius’ principle, 5 Clausius, R. (1822-1888), 5 coarse-graining, 144 coding, 49, 58 coin-tossing process, 55 collective variables, 252 commutative or Abelian group, 52 comparative studies, 141 competition, 260 complete isomorphism invariant, 90 completion, 69 complex, 235 complex system, 137, 244, 254, 260 complex system, wrong characterization, 281 complex systems studies, 236, 242, 286 complexification, 271, 272 complexity, 111, 240, 266 complexity, misunderstanding of, 112 composition of partitions, 84 computable function, 98 computation, 96 computer, 49, 204, 207, 229, 267 conceptual analysis, 37 conservation law, 191, 209, 212, 230, 231 correlation function, 126 correlation length, 126, 153 countable, 29 countable infinity, 27 critical index, 127 critical phenomenon, 12, 125 critical point, 125 curve-fitting, 202 cylinder set, 65 d’Alembert, J. (1717-1783), 26 Darwin, C. R. (1809-1882), 245 Darwin process, 245 death, 248, 255 Debye, P. (1884-1966), 131 definiti
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