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Transformations
Mathematical Approaches to Culture Change
- 1st Edition - May 10, 2014
- Editors: Colin Renfrew, Kenneth L. Cooke
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 5 2 2 - 5
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 7 5 2 - 3
Transformations: Mathematical Approaches to Culture Change focuses on the application of contemporary mathematical techniques to the study of culture change and formulates problems… Read more
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Request a sales quoteTransformations: 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.
List of Contributors
Foreword
Preface
Acknowledgments
I 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
References
II 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
Inteφretations and Results
Summary
References
III 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
References
IV 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
Initial Trial Runs
Range of Behavior of the Iterates
Extensions and Alterations of the Model
Further Outlook
References
V The Decision Nexus and Early Economies
15 A Preliminary Consideration of Behavioral Change
Behavioral Systems and Behavioral Change
Decision-Making Processes
The Study of Change
Conclusion
References
16 Economic Optimization Models and the Study of Hunter-Gatherer Subsistence Settlement Systems
Introduction
Assumptions
Mathematical Programming Models
The Netsilik Models—Matrix Setup
Dynamic Applications
Model of Postrifle Economy
Archaeological Application
Evaluation
References
17 A Formal Mathematical Model for the Operation of Consensus-Based Hunting-Gathering Bands
Introduction
Hunter-Gatherer Information Processing
Some Preliminaries—The Modeled Environment
The Group Theoretic Framework
The Decision Function
Individual Capabilities
Recognition Capabilities of Voting Groups
Group-Directional Decision Making
Decision Capabilities of Groups with Central Decision Maker
Predictions and Open Questions
References
VI Holistic Behavior and Catastrophe Theory
18 The Elements of Catastrophe Theory or The Honing of Occam's Razor
19 Discontinuities in the Endogenous Change of Settlement Pattern
Introduction
Settlement Discontinuity
Nucleated and Dispersed Settlement
Factors Regulating Settlement Size
The Dynamics of Change: Catastrophe Theory
Variation in the Perceived Benefits of Aggregation
Constraint Catastrophes
Settlement Location and Catastrophe Cascades
Cascades
References
20 A Geometrical Model of Ideologies
Introduction
Basic Aims
Conflict Lines
The Opinion Space X
The Surface Μ
The Shape of Μ
Ideological Interpretation of Μ
Embedding Μ in Three Dimensions
Experimental Testing
Dynamics of the Opinions of Individuals
Dynamics of Governmental Change
Dynamics of Ideologies
References
21 Systems Collapse as Social Transformation: Catastrophe and Anastrophe in Early State Societies
Introduction
General Features of System Collapse
Stability and the Growth of Systems
The Cusp Catastrophe
Acephalous and Centered Societies: Anastrophe
Chiefdoms and the Butterfly Catastrophe
Transformations
References
Index
- No. of pages: 538
- Language: English
- Edition: 1
- Published: May 10, 2014
- Imprint: Academic Press
- Paperback ISBN: 9781483245225
- eBook ISBN: 9781483277523
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