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1st Edition - January 28, 1979

**Editors:** Colin Renfrew, Kenneth L. Cooke

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… Read more

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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.

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
- Published: January 28, 1979
- Imprint: Academic Press
- eBook ISBN: 9781483277523