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xi | |
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1 | (6) |
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2 Still Life As A Model Of Spacetime |
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7 | (34) |
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8 | (12) |
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20 | (14) |
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A.1 Guide to Still Life and the Artistic Movements |
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34 | (3) |
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A.2 Guide to the Science of Space and Time |
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37 | (4) |
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3 The Notion Of Space In Mathematics Through The Lens Of Modern Art |
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41 | (66) |
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41 | (5) |
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46 | (5) |
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51 | (11) |
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62 | (16) |
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78 | (4) |
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82 | (4) |
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3.7 What Kind of Space Is Space? |
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86 | (2) |
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88 | (1) |
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3.9 Measure Spaces and Fractals |
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89 | (6) |
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95 | (3) |
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3.11 Why Do We Need So Many Notions of Space? |
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98 | (1) |
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A.1 Guide to the Art and Artists |
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99 | (1) |
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A.2 Guide to Space and Symmetry in Mathematics |
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100 | (1) |
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A.3 Guide to Linear Spaces |
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101 | (1) |
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A.4 Guide to Projective Geometry |
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101 | (1) |
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101 | (2) |
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A.6 Guide to Smooth Geometry |
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103 | (1) |
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A.7 Guide to Metric and Riemannian Geometry |
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104 | (1) |
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A.8 Guide to Algebraic Geometry and Singularities |
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104 | (1) |
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A.9 Guide to Fractal Geometry and Measure Theory |
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104 | (1) |
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A.10 Guide to Mathematical Quasicrystals |
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105 | (2) |
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4 Entropy And Art: The View Beyond Arnheim |
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107 | (30) |
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4.1 Thermodynamic Entropy |
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107 | (9) |
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4.2 Entropy and Cosmology |
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116 | (3) |
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4.3 Entropy and Information |
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119 | (5) |
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4.4 Quantum Information and Entanglement |
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124 | (4) |
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4.5 Entropy versus Complexity |
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128 | (2) |
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4.6 The Problem with Arnheim |
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130 | (2) |
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A.1 Guide to the Art Theory and the Artists |
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132 | (2) |
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A.2 Guide to the Science of Entropy and Information |
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134 | (3) |
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5 Structures Of Randomness |
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137 | (28) |
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138 | (3) |
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5.2 Randomness and the Cosmos |
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141 | (2) |
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143 | (8) |
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151 | (3) |
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5.5 All the Colors of Noise |
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154 | (2) |
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5.6 Chaos versus Randomness |
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156 | (5) |
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161 | (2) |
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A.2 Guide to the Theory of Randomness |
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163 | (2) |
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6 Plentiful Nothingness: The Void In Modern Art And Modern Science |
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165 | (38) |
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165 | (4) |
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6.2 Gravity and the Geometry of Empty Space |
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169 | (9) |
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6.3 The Void in Quantum Physics |
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178 | (5) |
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6.4 The Void in Quantum Gravity |
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183 | (3) |
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186 | (3) |
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6.6 False Vacua: The Higgs Field |
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189 | (2) |
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6.7 A Proliferation of Vacua: The Multiverse Landscape |
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191 | (7) |
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A.1 Guide to the Artists and Artistic Movements |
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198 | (2) |
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A.2 Guide to the Void in Modern Science |
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200 | (3) |
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7 The Geometry And Physics Of Numbers |
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203 | (24) |
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203 | (2) |
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7.2 The von Neumann Construction of Natural Numbers |
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205 | (2) |
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7.3 The Mystery of Prime Numbers |
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207 | (8) |
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7.4 Primes as Elementary Particles of Arithmetic |
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215 | (8) |
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223 | (1) |
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A.2 Guide to Number Theory and Physics |
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224 | (3) |
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227 | (20) |
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8.1 The Standard Model of Particle Physics |
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227 | (5) |
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8.2 The Geometrization of Physics |
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232 | (7) |
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8.3 What Is a Good Mathematical Model? |
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239 | (2) |
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8.4 Abstraction and Representation |
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241 | (2) |
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243 | (1) |
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A.2 Guide to the Geometry of Particle Physics |
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244 | (3) |
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9 Can You Hear The Shape Of The Cosmos? |
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247 | (20) |
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9.1 The Geometry of the Cosmos |
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247 | (10) |
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257 | (4) |
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9.3 The Universe Like a Drum |
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261 | (3) |
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264 | (1) |
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A.2 Guide to the History of Cosmology |
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264 | (1) |
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A.3 Guide to the Geometry of the Cosmos |
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264 | (3) |
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10 The Train And The Cosmos: Visionary Modernity |
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267 | (50) |
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10.1 Mythopoesis and Modernity |
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267 | (1) |
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268 | (9) |
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277 | (17) |
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10.4 The City and the Stars |
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294 | (15) |
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10.5 The Modern Destiny of Visionary Modernity |
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309 | (2) |
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A.1 Guide to the Artists and the Artistic and Philosophical Movements |
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311 | (2) |
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A.2 Guide to Anarchism and Modernism |
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313 | (1) |
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A.3 Guide to Trains and Electrification as Symbols of Modernity |
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314 | (1) |
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A.4 Guide to the Mechanical Body in the Avant-Garde |
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314 | (1) |
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A.5 Guide to Cosmism, Automata, and Cybernetics |
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315 | (1) |
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A.6 Guide to Transhumanism and Posthumanism |
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316 | (1) |
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11 Mathematical Illuminations |
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317 | (20) |
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11.1 Between Meditation and Scientific Illustration |
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317 | (10) |
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11.2 Illuminated Mathematical Notebooks |
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327 | (6) |
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11.3 Some Further Readings |
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333 | (1) |
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A.1 Guide to the Art and the Artists |
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334 | (1) |
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A.2 Guide to Graphical Language in Science |
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335 | (1) |
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A.3 Guide to the Mathematical Results Mentioned in This Chapter |
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335 | (1) |
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A.4 Guide to Further General Readings |
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336 | (1) |
Acknowledgments |
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337 | (1) |
Individuals and Institutions |
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337 | (1) |
Funding Agencies |
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338 | (1) |
Images Sources |
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338 | (17) |
Index |
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355 | |