Beginning with one of the most remarkable ecological collapses of recent times, that of the passenger pigeon, this book surveys collapse processes across the entire spectrum of the natural and man-made world. The reader is taken through extreme weather events, crashing financial markets and companies, the chaotic nature of Earth's orbit, revolutionary political change, the spread of disease and many other fascinating cases. The author's key observation is the consistent occurrence of one or more of six fundamental dynamics ('six sources of collapse'), all of which can be best described and investigated using fundamental mathematical concepts which include low probability events, group dynamics, evolutionary games, instability, nonlinearity and network effects. The exposition assumes a minimal mathematical background, but even professional mathematicians are likely to get rich insights from the range of examples. This book will also be of interest to readers in business and finance, engineering, ecology and political science.
Beginning with one of the most remarkable ecological collapses of recent times, that of the passenger pigeon, this book surveys collapse processes across the entire spectrum of the natural and man-made world. The reader is taken through extreme weather events, crashing financial markets and companies, the chaotic nature of Earth's orbit, revolutionary political change, the spread of disease and many other fascinating cases. The author's key observation is the consistent occurrence of one or more of six fundamental dynamics ('six sources of collapse'), all of which can be best described and investigated using fundamental mathematical concepts which include low probability events, group dynamics, evolutionary games, instability, nonlinearity and network effects. The exposition assumes a minimal mathematical background, but even professional mathematicians are likely to get rich insights from the range of examples. This book will also be of interest to readers in business and finance, engineering, ecology and political science.
1. Introduction; 2. Predicting unpredictable events; 3. Group behavior: crowds, herds, and video games; 4. Evolution and collapse: game playing in a changing world; 5. Instability, oscillation, and feedback; 6. Nonlinearity: invitation to chaos and catastrophe; 7. It's all about networks; 8. Putting it all together: looking at collapse phenomena in '6-D'; 9. Endnotes.
An accessible investigation into the mathematics behind collapse processes, ranging from crashing financial markets to extreme weather to ecological disasters.
Charles Hadlock has worked as a risk consultant in the chemical, power, transportation and mining industries. As the dean of a business school, he witnessed collapses of corporations, currencies and markets. Combined with his scientific background, interdisciplinary collaborative work and extensive management experience at the top levels of corporations and governments, he has a uniquely broad perspective on collapse processes. He has previously authored an award-winning monograph on field theory and an acclaimed text on mathematical modelling in environmental management.
Based on his experience as a risk consultant, manager, and
professor of finance and mathematics, Hadlock examines the
phenomenon of collapse from six different technical points of view,
namely low probability events, group behavior, evolutionary
processes, instability, nonlinear dynamics, and network effects. In
each case, we are offered a high-level, accessible presentation of
the underlying mathematical notions. … all chapters are rife with
real-world instances of collapse that can be explained, or at least
analysed, under one or more of the six approaches. Readers are
likely to find such examples one of the most compelling
contributions of the book." - Marco Faella, Mathematical
Reviews
"Hadlock's writing is invariably clear and concise, yet informal
and appealing, as befits a mathematical memoirist. The book is by
no means a textbook, although it could be regarded as a compendium
of modules suitable for presentation to undergraduates at various
stages of development by instructors seeking to enhance their
lectures with a smattering of genuine applications. For that reason
alone, every teaching mathematician should own a copy of this
book!" - James Case, SIAM News
"… The book is organized into chapters that can be read
independently, but taken as whole it provides a very broad overview
of the mathematical ideas behind complexity theory. Readers need
some knowledge of calculus, differential equations, and probability
to fully understand the material, but this book requires less
mathematical background than many other books on this topic. It
would be suitable for undergraduate students in science and
engineering as well as students in the social sciences and
management." - B. Borchers, CHOICE
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