The biggest advances in understanding the dynamics of bubbles have come from Didier Sornette, Professor of Entrepreneurial Risks and Finance at ETH Zurich. Sornette has developed mathematical models to explain earthquake activity, Amazon book sales, herding behavior in social networks like Facebook, and, yes, even stock market bubbles and crashes. He wrote a book titled Why Stockmarkets Crash. He found that most traditional theories do a very poor job of explaining bubbles. The only explanation that makes sense involves cooperative self-organization, very much like that seen in the schools of fish and flocks of birds. As Sornette wrote, “A central property of a complex system is the possible occurrence of coherent large-scale collective behaviors with a very rich structure, resulting from the repeated nonlinear interactions among its constituents: the whole turns out to be much more than the sum of its parts.”

Prof. Sornette recently sent an interesting paper to me and my Endgame co-author, Jonathan Tepper. In his note to us, Sornette says that we may find the paper "useful both in helping generating a complete overview of the economic and financial world through the roots in 30 years of massive bubbles, as well as via new examples of bubbles and their graphic depictions."

The paper is appended.