Transformations
Mathematical Approaches to Culture Change
Published on 10. May 2014
538 pages
978-1-4832-7752-3 (ISBN)
Description
Transformations: Mathematical Approaches to Culture Change focuses on the application of contemporary mathematical techniques to the study of culture change and formulates problems in archaeology, anthropology, and historiography in such a way that they are susceptible to treatment of a mathematical kind. Mathematical models, extending from the almost purely quantitative methods of physics to the purely verbal conceptual explanations, are described. Emphasis is placed on catastrophe theoretic models that exemplify the use of soft mathematics in situations in which the use of hard quantitative models is not possible. Comprised of 21 chapters, this book begins with an overview of the role of mathematics in theoretical archaeology, followed by a discussion on two general categories of mathematical methods that seem to be suitable for modeling cultural transformations: methods of dynamical systems theory and methods that give greater emphasis on discrete entities and the structural relations or patterns among them. Subsequent chapters deal with the use of mathematics in history; morphogenesis in biological and social systems; simulation of the growth of hierarchies; and logistic trends in Southwest population growth. A reconstruction of political units in the Valley of Mexico during the Toltec period is also presented. This monograph will be of interest to archaeologists, anthropologists, historians, biologists, sociologists, and mathematicians.
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Content
List of ContributorsForewordPrefaceAcknowledgmentsI Mathematics and Culture Change 1 Transformations Levels of Analysis The Tyranny of Darwin Comparative Archaeology Modeling the Past La Comédie Humaine References 2 Mathematical Approaches to Culture Change Dynamic Models and Difference Equations Differential Equation Stability and Qualitative Behavior Graphical Representations Cultural Models and Dynamic Simulations Randomness and Stochastic Processes Optimization and the Mathematical Theory of Games References 3 Mathematics in the Field of History Introduction Mathematics Classical Use of Mathematics Basic Abilities of the Computer Symbol Manipulation Chance Effects Complexity Music Generation Simulation A Simple Process Fuzzy Systems Kladistics Conclusion References 4 Morphogenesis in Biological and Social Systems Introduction Population Distributions in Space Cultural Differentiation Discussion ReferencesII Hierarchy and Social Space 5 Simulating the Growth of Hierarchies Introduction Rank-Size Relationships The Data The Process Discussion of the Results Conclusion References 6 Exploring Dominance: Predicting Polities from Centers Problems in Reconstructing the Territories of Polities The XTENT Model The Computer Program and Display Experiment 1: Malta Experiment 2: Cities of Europe Experiment 3: Late Uruk Settlement The XTENT Model as a Framework of Comparison References 7 A Reconstruction of Toltec Period Political Units in the Valley of Mexico Specifying the Interaction Model Testing the Interaction Model Previous Discussions of Toltec Political Organization Intefretations and Results Summary ReferencesIII Simulation and the Measurement Of Change 8 Logistic Trends in Southwest Population Growth Depicting Prehistoric Population Trends Method of Analysis Results Discussion Summary References 9 Alternative Models of Prehistoric Change Empirical Problems Methodological Problems Theoretical Problems An Alternative Approach Observational Adequacy Assumed Linearity The Locus of Patterning Theory Interpretation References 10 Settlement Simulation Empirical and Theoretical Background Model Building Development References 11 Occupation Frequency Simulation on a Broad Ecotone Introduction Environment Cultural Variability and Processes Operationalization Conclusion References 12 The Wave of Advance Model for the Spread of Agriculture in Europe The Original Problem The Model Population Growth Diffusionary Processes and Settlement Patterns Simulation Studies ReferencesIV Systems and Subsystem Interaction 13 A Structural Model of Industrialized Societies: Evolutions, Stability, Policies, Governability Societies as a Complex System Characteristics of Structural Modeling From Graph to Weighted Digraph Associated Graphic Presentation Pulse and Value Evolutions The Search for Intrinsic Stability Governability and the Search for Strategies Internal Tensions and Conflicts at Work Conclusion References 14 An Experiment on the Simulation of Culture Changes The Interaction Model The Simulation: Objectives and Technique
