Chaos Theory in the Social Sciences: Foundations and Applications

Front Cover
......Page 1
Chaos Theory in the Social Sciences: Foundations and Applications......Page 4
Contents......Page 8
Euel Elliott and L. Douglas Kiel: Introduction......Page 10
The Mathematics and Behavior of Chaos......Page 13
Graphical Analysis in Chaos Research......Page 15
Organization of the Book......Page 16
Chaotic Dynamics in the Social Sciences: Exploration and Method......Page 17
Chaos Theory and Political Science......Page 19
Chaos Theory and Economics......Page 21
Chaos Theory Implications for Social Systems Management and Social Science......Page 22
Conclusion......Page 23
Part 1: Chaotic Dynamics in Social Science Data......Page 26
1. L. Douglas Kiel and Euel Elliott: Exploring Nonlinear Dynamics with a Spreadsheet: A Graphical View of Chaos for Beginners......Page 28
Stable Equilibrium......Page 30
Periodic Behavior......Page 31
Chaos......Page 32
Sensitivity to Initial Conditions......Page 33
Attractors......Page 35
Conclusion......Page 37
2. Michael McBurnett: Probing the Underlying Structure in Dynamical Systems: An Introduction to Spectral Analysis......Page 40
Mathematical Background......Page 41
The Spectral Density and Spectral Distribution Functions......Page 43
Investigation of Selected Time Series......Page 46
Spectra of Selected Time Series......Page 47
A Periodic Function......Page 49
The Lorenz and Rossler Equations and Their Spectra......Page 51
Spectrum for the Public Opinion Series......Page 55
Conclusions......Page 59
NOTES......Page 60
Chaos......Page 62
An Attractor......Page 63
Chaotic Attractor......Page 64
K Entropy......Page 65
Lyapunov Characteristic Exponents......Page 66
Conclusion......Page 73
Notes......Page 74
4. Ted Jaditz: The Prediction Test for Nonlinear Determinism......Page 76
Preliminaries: What Is the Chaos Hypothesis?......Page 77
An Introduction to the Prediction Test......Page 83
The Problem of Forecast Evaluation......Page 86
An Illustrative Example: The Inflation Rate......Page 90
Discussion......Page 95
Notes......Page 97
5. Diana Richards: From Individuals to Groups: The Aggregationof Votes and Chaotic Dynamics......Page 98
From Individuals to Groups......Page 99
Chaotic Dynamics......Page 101
Symbolic Dynamics......Page 102
Multidimensional Spatial Voting......Page 105
The Importance of Cycles......Page 107
The Iterated Inverse Image of the Social Choice Function......Page 109
Chaotic Dynamics......Page 112
Simple Voting......Page 113
Market Mechanisms......Page 114
The Constraints on Outcomes and Paths......Page 115
The Structure of Outcomes......Page 117
View 1: Incoherent Social Choices......Page 121
View 2: Instability Fosters Political Stability......Page 122
Notes......Page 124
Part 2: Chaos Theory and Political Science......Page 126
Deterministic Chaos......Page 128
Nonlinear Political Interactions......Page 130
Strategic Interaction......Page 138
Axiomatic Theory......Page 140
Chaos as Allegory......Page 143
Beyond Chaos......Page 145
Notes......Page 146
7. Alvin M. Saperstein: The Prediction of Unpredictability: Applications of the New Paradigm of Chaos in Dynamical Systems to the Old Problem of the Stability of a System of Hostile Nations......Page 148
Science (Understanding) and Technology (Control)......Page 150
The Science of International Relations......Page 155
The Prediction of Chaos and the Outbreak of War......Page 158
Which Is More War-Prone—A Bipolar or a Tripolar World?......Page 162
Are Democracies More or Less Prone to War?......Page 164
Which is More War-Prone: A System of Shifting Alliances or a Collection of Go-lt-Alone States?......Page 166
Conclusion......Page 171
8. Michael McBurnett: Complexity in the Evolution of Public Opinion......Page 174
The Emergence of Opinion Cycles in Competitive Nominations......Page 175
Analyzing Deterministic Data......Page 179
Analyzing Noisy Data......Page 180
Construction of the Time Series from Public Opinion Data......Page 184
Measuring the Dimension of a Strange Attractor......Page 188
The Correlation Dimension and the Effects of Noise......Page 192
A Test of an Alternative Model......Page 194
Lyapunov Exponents and the Presence of Chaotic Dynamics......Page 196
Application to the Constructed Time Series......Page 200
Conclusions......Page 201
Notes......Page 203
Part 3: Chaos Theory and Economics......Page 206
9. J. Barkley Rosser, Jr.: Chaos Theory and Rationality in Economics......Page 208
Chaotic Preference Cycles......Page 209
Interpersonal Utility Effects and Chaotic Dynamics......Page 210
Chaotic Cobwebs......Page 211
Overlapping Generations Models......Page 212
Discounting and Chaos in Infinite Horizon Models......Page 215
Nonseparable Utility and Chaos in Infinite Horizon Models......Page 216
Empirical Evidence......Page 217
The Problem for Rational Expectations......Page 219
Conclusion......Page 220
Notes......Page 221
10. Brian J. L. Berry and Heja Kim: Long Waves 1790-1990: Intermittency, Chaos, and Control......Page 224
Long Waves of Prices......Page 225
Long Cycles of Economic Growth......Page 238
Discussion......Page 242
11. Dimitrios S. Dendrinos: Cities as Spatial Chaotic Attractors......Page 246
New Dynamical Features......Page 247
A New Type of Explanation......Page 248
Frequent Perturbations......Page 249
Unresolved Issues......Page 250
The Universal Map of Discrete Relative Dynamics......Page 251
The Single-Stock Case......Page 252
The Universal Map and Physical Space......Page 256
The Alternative: Dynamics......Page 258
Periodic, Quasi-Periodic, and Chaotic Spatial Settlements......Page 264
Efficient Versions of the Map......Page 265
Nonefficient Specifications......Page 268
Conclusions......Page 270
APPENDIX A: THE GEOMETRY OF LOCATION IN R2......Page 275
APPENDIX B: THE REPULSION TRIANGLE AND ITS ATTRACTION ANTITRIANGLE......Page 277
Part 4: Implications for Social Systems Management and Social Science......Page 280
12. Kenyon B. De Greene: Field-Theoretic Framework for the Interpretation of the Evolution, Instability, Structural Change, and Management of Complex Systems......Page 282
Evolution, Instability, and Structure of Complex Systems......Page 284
Dissipative-Structure Theoretical Interpretations......Page 285
Order Parameter as Macropsychological Structure......Page 286
The Study of Phase Transitions......Page 287
Societal and Macropsychological Order Parameters......Page 288
The Kondratiev Cycle/Structure in Recent Societal Evolution......Page 289
The Phases of the Kondratievs......Page 290
Features of a Kondratiev Phase of Depression......Page 291
Explanation of the Kondratiev Cycle/Structure......Page 292
Deterministic Chaos and Other Nonlinear Behaviors......Page 293
On Paradigm Change......Page 294
The Growth of Exhaustion of Information/Knowledge at the End of the Kondratiev Cycle/Structure......Page 296
Systems Management at a Time of Transformational Change......Page 299
Concluding Remarks and Recommendations......Page 301
13. David L. Harvey and Michael Reed: Social Science as the Study of Complex Systems......Page 304
Philosophical Assumptions......Page 307
Implications of Critical Realism for Social Scientific Method......Page 310
Dissipative Social Systems......Page 311
Social Ontology: The Structure of Dissipative Social Systems......Page 314
Strategies of Modeling and Their Ontological Limits......Page 316
Modeling Strategies and Levels of Abstraction......Page 318
Promise and Paradox: The Future of the Paradigmin the Social Sciences......Page 323
Predictive Modeling......Page 324
Statistical Modeling......Page 326
Iconological Modeling......Page 327
Structural Modeling......Page 328
Ideal Typical Modeling......Page 329
Historical Narratives......Page 330
Summary and Conclusions......Page 331
Notes......Page 332
References......Page 334
Contributors......Page 356
Back Cover......Page 360