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1 A Galilean Dialogue on the Levels of Reality |
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1 | (20) |
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18 | (3) |
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2 A Random Journey from Monism to the (Dream of) Unity of Science |
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21 | (24) |
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21 | (3) |
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2.2 Reductionism: The Philosophical Point of View |
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24 | (6) |
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2.2.1 General Introduction |
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24 | (3) |
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2.2.2 Philosophical Model of Theory-Reduction |
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27 | (3) |
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2.3 Reduction in Physics and Philosophy |
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30 | (4) |
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34 | (11) |
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34 | (1) |
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2.4.2 Reduction Versus Emergence |
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35 | (2) |
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2.4.3 Emergence and Reduction in Natural Sciences |
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37 | (1) |
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2.4.4 Emergence and Reduction in Special Sciences |
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38 | (4) |
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42 | (3) |
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3 A First Attempt to Tame Complexity: Statistical Mechanics |
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45 | (26) |
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3.1 A Short History of Statistical Mechanics |
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47 | (3) |
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3.2 Towards a Systematic Theory |
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50 | (7) |
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3.2.1 Boltzmann's Grand Vision |
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52 | (3) |
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3.2.2 Beyond the Mathematical Limitations of Ergodic Theory |
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55 | (2) |
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57 | (1) |
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3.3 The Paradigmatic Brownian Motion |
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57 | (5) |
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62 | (5) |
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67 | (4) |
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68 | (3) |
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4 From Microscopic Reversibility to Macroscopic Irreversibility |
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71 | (28) |
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4.1 The Problem of Irreversibility |
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71 | (7) |
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4.1.1 Boltzmann and Irreversibility |
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74 | (2) |
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4.1.2 Different Ideas About Irreversibility |
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76 | (2) |
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4.2 Irreversibility and Emergence |
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78 | (6) |
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4.3 From Microscopic to Macroscopic Equations |
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84 | (7) |
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4.3.1 Continuous Media and Thermodynamics |
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84 | (2) |
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4.3.2 In Boltzmann's Footsteps |
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86 | (3) |
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4.3.3 The Emergence of a Dissipative Phenomenon: Friction in a Reversible World |
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89 | (1) |
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4.3.4 Hydrodynamics in an Artificial World: Cellular Automata |
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90 | (1) |
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4.4 From Atoms to Cold Fronts: A Random Walk Through Hydrodynamics and Meteorology |
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91 | (3) |
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94 | (5) |
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96 | (3) |
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5 Determinism, Chaos and Reductionism |
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99 | (22) |
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5.1 General Remarks on Determinism |
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99 | (6) |
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5.1.1 Determinism and Predictability |
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101 | (4) |
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105 | (2) |
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107 | (3) |
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5.4 Chaos and Probability |
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110 | (2) |
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5.5 Quarrels on Chaos and Determinism: Chaos and Probability Revisited |
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112 | (3) |
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115 | (6) |
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119 | (2) |
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6 Quantum Mechanics, Its Classical Limit and Its Relation to Chemistry |
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121 | (20) |
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6.1 Classical Versus Quantum Mechanics |
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122 | (8) |
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6.1.1 Is Classical Mechanics Nothing but a Limit of Quantum Mechanics? |
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124 | (2) |
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6.1.2 Quantum Mechanics, Classical Chaos and Planetary Dynamics |
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126 | (2) |
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6.1.3 An Interlude: Discrete Versus Continuous Descriptions and the Semiclassical Limit |
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128 | (2) |
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6.2 Chemistry Is Not Just Applied Quantum Mechanics |
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130 | (8) |
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6.2.1 Quantum Mechanics Does Not Explain Chemistry |
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131 | (1) |
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6.2.2 Why Does the Born-Oppenheimer Approximation Fail to Predict the Shape of Molecules? |
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132 | (2) |
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6.2.3 A Look at a Specific Problem: The Pyramidal Molecules |
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134 | (3) |
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6.2.4 Beyond the Born-Oppenheimer Method |
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137 | (1) |
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6.3 Summary and Conclusions |
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138 | (3) |
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139 | (2) |
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7 Some Conclusions and Random Thoughts |
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141 | |
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7.1 Unity of Science Beyond Reductionism |
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141 | (6) |
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7.1.1 Common Practice in Statistical Mechanics |
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141 | (2) |
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7.1.2 From Boltzmann's Disputes with Zermelo to Models Built from Data |
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143 | (3) |
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146 | (1) |
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147 | (5) |
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7.2.1 Statistical Mechanics as Statistical Inference? |
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147 | (2) |
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7.2.2 Algorithmic Complexity: A Key to Understanding Nature? |
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149 | (3) |
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152 | |
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154 | |