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Modelling and Generating Complex Emergent Behaviour

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Modelling and Generating Complex Emergent Behaviour MODELLING AND GENERATING COMPLEX EMERGENT BEHAVIOUR A thesis submitted for the degree of Doctor of Philosophy By Kirsty Kitto B.Sc.(Hons), B.Comp.Sci. The School of Chemistry, Physics and Earth Sciences, The Flinders University of South Australia June 2006 Abstract Despite a general recognition of the importance of complex systems, there is a dearth of general models capable of describing their dynamics. This is attributed to a complexity scale; the models are attempting to describe systems at di®erent parts of the scale and are hence not compatible. We require new models capable of describing complex behaviour at di®erent points of the complexity scale. This work identi¯es, and proceeds to examine systems at the high end of the complexity scale, those which have not to date been well understood by our current modelling methodology. It is shown that many such models exhibit what might be termed contextual dependency, and that it is precisely this feature which is not well understood by our current modelling methodology. A particular problem is discussed; our apparent inability to generate systems which display high end complex- ity, exhibited by for example the general failure of strong ALife. A new model, Process Physics, that has been developed at Flinders University is discussed, and arguments are presented that it exhibits high end complexity. The features of this model that lead to its displaying such behaviour are discussed, and the generalisation of this model to a broader range of complex systems is attempted. Themes: contextuality and complexity; reductive failure; Process Physics; quantum the- ories as models of complexity i I certify that this thesis does not incorporate without acknowledg- ment any material previously submitted for a degree or diploma in any university; and that to the best of my knowledge and belief it does not contain any material previously published or written by another person except where due reference is made in the text. Kirsty Kitto ii Acknowledgements This work has involved a long, very interesting, but often rather torturous journey. What began as an examination of the quantum measurement problem quickly increased in scope to the foundations of quantum mechanics, then again to fundamental physics in general, before shifting its emphasis to complex systems. Before long even biology, ecology, eco- nomics and arti¯cial life came into the scope of this project. As such, this work could not have been possible without the assistance of a large number of people from a wide range of ¯elds, whose conversations, criticisms, witticisms and creativity has challenged and extended my knowledge. A special thanks to my supervisor, Reg Cahill, without whose guidance and support this project would have been inconceivable and probably not allowed. His ideas have shaped more than my approach to physics. The ¯nal thesis itself could not have been possible without the assistance of people from a variety of disciplines and ¯elds; I would like to especially acknowledge discussions with, and often assistance from Daniel Kortschak, Susan Gunner, and Peter Wood. Also my family and friends for their patience and support. Finally, I would like to acknowledge the internet. Without the dramatic explosion of readily accessible ideas, theories, articles, preprints and tutorials that it provides, work such as this, at the boundaries of many substantially di®erent disciplines would be di±cult if not impossible; our theories are now in a position to evolve to new levels of complexity thanks to the creation of this vital resource. May it always remain free. iii Contents Abstract i Declaration ii Acknowledgements iii Chapter 1 Reductionism at its Limits 1 1.1 The Scienti¯c Method . 1 1.1.1 Reductive Analysis . 2 1.2 Complex Systems . 7 1.2.1 Contextual Complexity in Biological Systems . 10 1.2.2 Defying Reduction | Very Complex Systems . 12 1.2.3 Emergence . 15 1.2.4 Complexity and Postmodernism . 16 1.3 Contextuality . 17 1.3.1 Complexity and Contextuality . 17 1.4 Object Based Modelling . 18 1.5 The Complexity Scale . 19 1.5.1 High End Complexity . 20 1.6 Objectivity: Contextuality, Subjectivity and Observer Dependence . 24 Chapter 2 An Example System: Arti¯cial Life 27 2.1 ALife, Complexity and Emergence . 28 2.1.1 Insu±cient Complexity . 29 2.1.2 The Complexity of Development . 31 2.1.3 Measures of ALife Complexity . 32 2.1.4 ALife: Simulations versus Emergence . 37 2.2 Hierarchical Structure . 40 2.2.1 Hyperstructures . 40 2.2.2 The Ansatz for Dynamical Hierarchies (ADH) . 43 2.3 Towards the Generation of Interesting Emergent Behaviour . 46 Chapter 3 Hierarchical Systems 47 v 3.1 Hierarchical Concepts . 48 3.1.1 The Alphabet of a Hierarchy . 48 3.1.2 Span . 49 3.1.3 Dynamical Rates and Strength of Interaction . 50 3.1.4 Nearly-Decomposable Systems . 50 3.1.5 Scalar and Speci¯cation Hierarchies . 53 3.1.6 Structural and Control Hierarchies . 56 3.1.7 Dynamical Hierarchies . 57 3.1.8 Downward Causation . 59 3.1.9 The Context of a Hierarchy . 59 3.1.10 Evolutionary Transitions . 61 3.2 Theories of Hierarchical Behaviour . 62 3.2.1 Hierarchies and Open Dissipative Systems . 63 3.2.2 Hierarchies and Emergence . 64 3.3 Towards the Dynamical Generation of Emergent Hierarchical Structure . 65 Chapter 4 An Example System: Process Physics 67 4.1 Modelling Reality . 67 4.1.1 The Process Model of Fundamental Physics . 69 4.2 A Hierarchical Analysis of the System . 74 4.2.1 Near-decomposability . 74 4.2.2 Baas hierarchy structure . 74 4.3 The Historical Roots of Process Physics . 77 4.3.1 The Nature of Quantum Theories . 77 4.3.2 The Global Colour Model (GCM) and the Functional Integral Cal- culus (FIC) . 84 4.3.3 The Derivation of the Iterator Equation . 87 Chapter 5 Generalising Quantum Theories 90 5.1 Bell's Theorem and Contextuality . 91 5.1.1 The Assumptions Behind Classical Ontologies . 92 5.1.2 Bell's Theorem and Nonlocality . 96 5.1.3 Nonlocality and Relativity . 100 5.1.4 Contextuality . 103 5.1.5 The Relationship Between Nonlocality and Contextuality . 106 5.1.6 The Meaning of Nonlocal and Contextual Behaviour . 107 5.1.7 Observers in Quantum Theory . 111 5.2 Contextuality is Generic . 114 5.3 Symmetry . 121 vi 5.3.1 Symmetry and Conservation Laws . 123 5.3.2 Symmetry and Interaction . 125 5.3.3 Symmetry Breaking . 127 5.3.4 Goldstone's Theorem . 129 5.3.5 Action Sequencing . 134 5.4 Symmetry is Generic . 136 5.4.1 Economics . 137 5.4.2 Self-Organised Criticality and NG-modes . 140 5.4.3 Biological Modelling . 142 5.4.4 Arts, Crafts and Aesthetics . 143 5.4.5 A Generalised Model of Emergent Behaviour? . 143 5.5 The Structure of the Vacuum . 143 5.6 Modelling Quantum Behaviour . 144 5.6.1 Quantum State Di®usion and Spontaneous Localisation Theories . 145 5.6.2 Towards an Operational and Realistic Framework . 153 Chapter 6 Quantum Field Theoretic Descriptions of Emergent Phenomena 156 6.1 Generating Complex Emergent Behaviour . 156 6.1.1 Generating Interaction among Emergent Phenomena . 157 6.1.2 Generating Hierarchical Behaviour . 157 6.2 The Recursive Gauge Principle (RGP) . 158 6.3 An Example System | Solitons in Cellular Automata . 161 6.4 Emergent Behaviour in Process Physics . 165 6.4.1 QSD in Process Physics . 169 6.4.2 The Structure of Space, Time and Matter . 169 6.4.3 Nambu{Goldstone Modes . 170 6.4.4 Relativity in Process Physics . 171 6.4.5 Gravity in Process Physics . 175 6.4.6 Thermodynamics in Process Physics . 177 6.4.7 Observational Emergence in Process Physics . 178 6.5 Proof of Concept | Sympatric Speciation . 179 6.6 Further Work | Biological Development . 184 Chapter 7 Conclusions: An Emergent Methodology 186 7.1 De¯ning Emergence . 186 7.2 De¯ning Complexity . 187 7.2.1 Modelling the Contexts of Emergent Behaviour . 188 7.2.2 Moving Beyond an Object-Based Methodology . 189 7.2.3 Reductive Paradigms? . 191 vii 7.3 Contextuality and Observer Dependence . 191 7.4 In Conclusion . 192 Appendix A Notation 193 A.1 Observational Emergence . 193 A.2 Quantum Mechanics . 193 A.3 Quantum Field Theory . 194 A.4 Process Physics . 194 A.4.1 Low level relational model . 194 A.4.2 Quantum Homotopic Field Theory (QHFT) . 194 A.4.3 Gravity Model . 195 A.4.4 Model of Sympatric Speciation . 195 A.5 Abbreviations used in the text . 195 Appendix B It^o calculus | a brief summary 196 B.1 The Markov property . 196 B.2 Wiener processes . 196 B.3 It^o's theorem . 197 Appendix C Generalized Master Equations 198 C.1 Solution by Generalized Master Equations . 198 C.2 A derivation of the Quantum State Di®usion equation . 202 References 207 viii List of Tables 2.1 The di®erent classes of evolutionary activity. 36 3.1 The di®erences between a scalar and a speci¯cation hierarchy as de¯ned.
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