Renfrew / Cooke Transformations

Mathematical Approaches to Culture Change
1. Auflage 2014
ISBN: 978-1-4832-7752-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 538 Seiten, Web PDF

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.

Autoren/Hrsg.

Renfrew, Colin

Cooke, Kenneth L.

Inhaltsverzeichnis

1;Front Cover;1
2;Transformation: Mathematical Approaches to Culture Change;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;List of Contributors;16
7;Foreword;18
8;Preface;20
9;Acknowledgments;22
10;PART I: .......TICS AND CULTURE CHANGE;26
10.1;Chapter
1. Transformations;28
10.1.1;Levels of Analysis;32
10.1.2;The Tyranny of Darwin;34
10.1.3;Comparative Archaeology;41
10.1.4;Modeling the Past;55
10.1.5;La Comédie Humaine;62
10.1.6;Acknowledgments;66
10.1.7;References;66
10.2;Chapter 2. Mathematical Approaches to Culture Change;70
10.2.1;Dynamic Models and Difference Equations;71
10.2.2;Differential Equations;74
10.2.3;Stability and Qualitative Behavior;77
10.2.4;Graphical Representations;83
10.2.5;Cultural Models and Dynamic Simulations;86
10.2.6;Randomness and Stochastic Processes;94
10.2.7;Optimization and the Mathematical Theory of Games;100
10.2.8;Acknowledgments;104
10.2.9;References;105
10.3;Chapter
3. Mathematics in the Field of History;108
10.3.1;Introduction;108
10.3.2;Mathematics;109
10.3.3;Classical Use of Mathematics;109
10.3.4;Basic Abilities of the Computer;110
10.3.5;Symbol Manipulation;110
10.3.6;Chance Effects;111
10.3.7;Complexity;112
10.3.8;Music Generation;112
10.3.9;Simulation;113
10.3.10;A Simple Process;113
10.3.11;Fuzzy Systems;114
10.3.12;Kladistics;114
10.3.13;Conclusion;115
10.3.14;References;115
10.4;Chapter
4. Morphogenesis in Biological and Social Systems;116
10.4.1;Introduction;116
10.4.2;Population Distributions in Space;118
10.4.3;Cultural Differentiation;127
10.4.4;Discussion;133
10.4.5;References;135
11;PART
II: HIERARCHY AND SOCIAL SPACE;138
11.1;References;140
11.2;Chapter 5. Simulating the Growth of Hierarchies;142
11.2.1;Introduction;142
11.2.2;Rank-Size Relationships;143
11.2.3;The Data;147
11.2.4;The Processes;151
11.2.5;Discussion of the Results;164
11.2.6;Conclusion;167
11.2.7;References;168
11.3;Chapter
6. Exploring Dominance: Predicting Polities from Centers;170
11.3.1;Problems in Reconstructing the Territories of Polities;172
11.3.2;The XTENT Model;174
11.3.3;The XTENT Model as a Framework of Comparison;190
11.3.4;Acknowledgments;191
11.3.5;References;191
11.4;Chapter 7. A Reconstruction of Toltec Period Political Units in the Valley of Mexico;194
11.4.1;Specifying the Interaction Model;196
11.4.2;Testing the Interaction Model;197
11.4.3;Previous Discussions of Toltec Political Organization;216
11.4.4;Interpretations and Results;217
11.4.5;Summary;223
11.4.6;Acknowledgments;224
11.4.7;References;224
12;PART
Ill: SIMULATON AND THE MEASUREMENT OF CHANGE;226
12.1;References;228
12.2;Chapter
8. Logistic Trends in Southwest Population Growth;230
12.2.1;Depicting Prehistoric Population Trends;231
12.2.2;Method of Analysis;233
12.2.3;Results;235
12.2.4;Discussion;238
12.2.5;Summary;243
12.2.6;Acknowledgments;243
12.2.7;References;244
12.3;Chapter
9. Alternative Models of Prehistoric Change;246
12.3.1;Empirical Problems;246
12.3.2;Methodological Problems;247
12.3.3;Theoretical Problems;248
12.3.4;An Alternative Approach;249
12.3.5;Observational Adequacy;250
12.3.6;Assumed Linearity;252
12.3.7;The Locus of Patterning;254
12.3.8;Theory;255
12.3.9;Interpretation;256
12.3.10;References;260
12.4;Chapter
10. Settlement Simulation;262
12.4.1;Empirical and Theoretical Background;264
12.4.2;Model Building;270
12.4.3;Development;274
12.4.4;References;280
12.5;Chapter
11. Occupation Frequency Simulation on a Broad Ecotone;282
12.5.1;Introduction;282
12.5.2;Environment;284
12.5.3;Cultural Variability and Processes;288
12.5.4;Operationalization;292
12.5.5;Conclusion;297
12.5.6;Acknowledgments;298
12.5.7;References;298
12.6;Chapter
12. The Wave of Advance Model for the Spread of Agriculture in Europe;300
12.6.1;The Original Problem;301
12.6.2;The Model;303
12.6.3;Population Growth;306
12.6.4;Diffusionary Processes and Settlement Patterns;310
12.6.5;Simulation Studies;313
12.6.6;Acknowledgments;316
12.6.7;References;316
13;PART
IV: SYSTEMS AND SUBSYSTEM INTERAOTON;320
13.1;References;323
13.2;Chapter
13. A Structural Model of Industrialized Societies: Evolutions, Stability, Policies, Govemability;324
13.2.1;Societies as a Complex System;324
13.2.2;Characteristics of Structural Modeling;326
13.2.3;From Graph to Weighted Digraph;329
13.2.4;Associated Graphic Presentation;332
13.2.5;Pulse and Value Evolutions;335
13.2.6;The Search for Intrinsic Stability;338
13.2.7;Governability and the Search for Strategies;341
13.2.8;Internal Tensions and Conflicts at Work;344
13.2.9;Conclusion;347
13.2.10;Note;349
13.2.11;Acknowledgments;349
13.2.12;References;349
13.3;Chapter 14. An Experiment on the Simulation of Culture Changes;352
13.3.1;The Interaction Model;353
13.3.2;The Simulation: Objectives and Technique;354
13.3.3;Initial Trial Runs;360
13.3.4;Range of Behavior of the Iterates;365
13.3.5;Extensions and Alterations of the Model;368
13.3.6;Further Outlook;371
13.3.7;Acknowledgment;372
13.3.8;References;372
14;PART
V: THE DECISION NEXUS AND EARLY ECONOMIES;374
14.1;Chapter
15. A Preliminary Consideration of Behavioral Change;378
14.1.1;Behavioral Systems and Behavioral Change;378
14.1.2;Decision-Making Processes;385
14.1.3;The Study of Change;387
14.1.4;Conclusion;391
14.1.5;Acknowledgments;392
14.1.6;References;392
14.2;Chapter
16. Economic Optimization Models and the Study of Hunter-Gatherer Subsistence Settlement Systems;394
14.2.1;Introduction;394
14.2.2;Assumptions;395
14.2.3;Mathematical Programming Models;395
14.2.4;The Netsilik Models—Matrix Setup;400
14.2.5;Dynamic Applications;417
14.2.6;Model of Postrifle Economy;419
14.2.7;Archaeological Application;419
14.2.8;Evaluation;425
14.2.9;Acknowledgments;426
14.2.10;References;426
14.3;Chapter 17. A Formal Mathematical Model for the Operation of Consensus-Based Hunting-Gathering Bands;430
14.3.1;Introduction;430
14.3.2;Hunter-Gatherer Information Processing;431
14.3.3;Some Preliminaries—The Modeled Environment;432
14.3.4;The Group Theoretic Framework;434
14.3.5;The Decision Function;435
14.3.6;Individual Capabilities;435
14.3.7;Recognition Capabilities of Voting Groups;436
14.3.8;Group-Directional Decision Making;438
14.3.9;Decision Capabilities of Groups with Central Decision Maker;440
14.3.10;Predictions and Open Questions;442
14.3.11;References;443
14.4;References;376
15;PART
VI: .OLISTIC BEHAVIOR AND CATASTROPHE THEORY;444
15.1;References;447
15.2;Chapter
18. The Elements of Catastrophe Theory or The Honing of Occam's Razor;450
15.2.1;References;460
15.3;Chapter
19. Discontinuities in the Endogenous Change of Settlement Pattern;462
15.3.1;Introduction;462
15.3.2;Settlement Discontinuity;463
15.3.3;Nucleated and Dispersed Settlement;465
15.3.4;Factors Regulating Settlement Size;467
15.3.5;The Dynamics of Change: Catastrophe Theory;472
15.3.6;Variation in the Perceived Benefits of Aggregation;476
15.3.7;Constraint Catastrophes;480
15.3.8;Settlement Location and Catastrophe Cascades;482
15.3.9;Cascades;484
15.3.10;References;485
15.4;Chapter
20. A Geometrical Model of Ideologies;488
15.4.1;Introduction;488
15.4.2;Basic Aims;489
15.4.3;Conflict Lines;490
15.4.4;The Opinion Space X;491
15.4.5;The Surface .;492
15.4.6;The Shape of .;493
15.4.7;Ideological Interpretation of .;495
15.4.8;Embedding . in Three Dimensions;497
15.4.9;Experimental Testing;498
15.4.10;Dynamics of the Opinions of Individuals;499
15.4.11;Dynamics of Governmental Change;500
15.4.12;Dynamics of Ideologies;501
15.4.13;References;504
15.5;Chapter
21. Systems Collapse as Social Transforaiation: Catastrophe and Anastrophe in Early State Societies;506
15.5.1;Introduction;506
15.5.2;General Features of System Collapse;507
15.5.3;Stability and the Growth of Systems;512
15.5.4;The Cusp Catastrophe;515
15.5.5;Acephalous and Centered Societies: Anastrophe;519
15.5.6;Chiefdoms and the Butterfly Catastrophe;524
15.5.7;Transformations;528
15.5.8;References;530
16;Index;532