The Mathematical Association of America | 2012 | 222 páginas | rar - pdf |4 Mb
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Beginning with one of the most remarkable ecological collapses of recent time, that of the passenger pigeon, Hadlock goes on to survey collapse processes across the entire spectrum of the natural and man-made world. He takes us through extreme weather events, technological disasters, evolutionary processes, crashing markets and companies, the chaotic nature of Earth's orbit, revolutionary political change, the spread and elimination of disease, and many other fascinating cases.
His key thesis is that one or more of six fundamental dynamics consistently show up across this wide range. These "six sources of collapse" can all be best described and investigated using fundamental mathematical concepts. They include low probability events, group dynamics, evolutionary games, instability, nonlinearity, and network effects, all of which are explained in readily understandable terms. Almost the entirety of the book can be understood by readers with a minimal mathematical background, but even professional mathematicians are likely to get rich insights from the range of examples. The author tells his story with a warmly personal tone and weaves in many of his own experiences, whether from his consulting career of racing around the world trying to head off industrial disasters to his story of watching collapse after collapse in the evolution of an ecosystem on his New Hampshire farm.
Creative teachers could use this book for anything from a liberal arts math course to a senior capstone seminar, and one reviewer suggested that it should be required reading for any mathematics graduate student heading off into a teaching career. This book will also be of interest to readers in the fields under discussion, such as business, engineering, ecology, political science, and others.
Contents
Preface ix
Acknowledgements xi
1 Introduction 1
1.1 What is a collapse?. . 1
1.2 Shades of Hitchcock, and other tales . . 2
1.3 What might tomorrow bring? . . 6
1.4 What this book aims to do . . 13
2 Predicting Unpredictable Events 15
2.1 Like a thief in the night?. . 15
2.2 Chance and regularity. . 17
2.3 A quick statistics primer . . 18
2.4 Normal regularity: the good, the bad, and the miraculous. . 22
2.5 Abnormal regularity: extreme value statistics . . 25
2.6 Getting things right with heavy-tailed distributions . . 31
2.7 The dangers from getting your probabilities wrong . . 35
3 Group Behavior: Crowds, Herds, and Video Games 41
3.1 Fire! . . 41
3.2 Birds, boids, and bicycles . . 44
3.3 The Monte Carlo world. . 48
3.4 Models with probabilities . . 50
3.5 People, properties, and political systems . . 54
3.6 Connections to other chapters . . . 59
4 Evolution and Collapse: Game Playing in a ChangingWorld 61
4.1 My New Hampshire. . 61
4.2 Strategies and games. . 63
4.3 Iterated and evolutionary game playing .. . 68
4.4 Modeling the evolution of species and cultures . . 74
4.5 Implications for understanding collapse. . 80
5 Instability, Oscillation, and Feedback 85
5.1 Sharing an electric blanket and other challenges. . . 85
5.2 Primer on differential equations . . 91
5.3 Stable and unstable equilibriumpoints and related concepts . 97
5.4 The dynamics of interacting populations. . 100
5.5 Structural collapses and related processes. . 106
5.6 The science of trying to maintain control . . 112
5.7 The Chernobyl disaster . . 115
6 Nonlinearity: Invitation to Chaos and Catastrophe 121
6.1 The elephant’s toenail . . 121
6.2 Local linearity . . 122
6.3 Bifurcations, tipping points, and catastrophes . . . 127
6.4 Hysteresis: where there may be no simple turning back . . 134
6.5 Chaos: beginning with a butterfly . . 138
7 It’s All About Networks 145
7.1 How’s your networking? . . 145
7.2 Network fundamentals . . 147
7.3 Important variations in network macrostructure . . 152
7.4 Unexpected network crashes. . 157
7.5 Interactive dynamics across networks . . 161
7.6 Spreading processes through networks . . 165
7.7 A surprising game on a network . . 167
7.8 Networks in an evolutionary context . . 169
8 Putting It All Together: Looking at Collapse Phenomena in “6-D” 173
8.1 A quick review . . 173
8.2 The utility of multiple perspectives in understanding the risk of collapse . 175
8.3 Where to go from here: the modern field of complexity theory . . 186
References 189
Index 201
About the Author 207
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