Ralph Abraham's Blog

Demystifying the Akasha

2009-06-29T10:01:00.000-07:00

Sorry or the lapse of eight months. My winter visit to Kolkata resulted in a book project, "Demystifying the Akasha: Consciousness and the Quantum Vacuum", joint with Sisir Roy, Professor of Physics and Applied Math at the Indian Statistical Institute. Yesterday we completed a second draft of the manuscript, and are now seeking a publisher. Meanwhile, I plan to rethink aloud some of our material, one chapter at a time. Also, the front matter will be posted on my website

More Crash Thoughts

2008-10-23T12:02:00.000-07:00

Today Alan Greenspan spoke to the US Congress about the current stock crash. He called it the storm-of-the-century, and predicted it would last for decades. But as we have no recorded data on storms-of-the-century, what is the basis of his prediction ??? We hope it is not a complex dynamical model !!! The teachings of our five-year research on financial bubbles and crashes using agent-based modeling suggest that this crash is largely psychological, involving the effect of investors' memories of prior losses, which is longer lasting that their memories of prior gains. These memories both decay in time, and this is the basis of my expectation that the stock markets will recover within six months --- all depending, of course, on the outcome of the November 4th election.

Dynamical Systems as Models for Long Term Behavior

2008-10-07T16:23:00.000-07:00

Dynamical systems, also known as systems of ordinary differential equations, form the backbone of the mathematical sciences -- physical, biological, or social. They have been formed into spectacular tools for short-term predictions of natural systems. But they generally cannot predict long-term behavior reliably. This fact -- well-known to dynamical systems theorists in the pure math community -- seems unknown to many practitioners in the modeling community. The math behind this fact is known as bifurcation theory, and more information may be found in my MS#127, The Misuse of Mathematics, at the bottom of my article list (click the title of this blog).

Bubbles and Crashes

2008-10-05T21:09:00.000-07:00

For five years or so I have been engaged in a joint research project with Dan Friedman, Professor of Economics at UC Santa Cruz. Sponsored by the National Science Foundation, the project aimed to explore the psychological forces producing bubbles and crashes in financial markets, using agent based modeling as the primary tool. While our models probably could not have predicted the sub-prime mortgage crisis, it surely helps to understand these recent events.
The project website is: Landscape Dynamics