Clarification on chaos and complexity

In his review of my book Chaos and Complexity in Astrophysics (Physics Today, September 2007, page 71 ), Mario Livio correctly points out that “chaos theory actually has had a limited impact on most areas of astrophysical research.” That was indeed the main reason for my writing the book.

Many astrophysical systems are genuinely very complicated, as Livio says, but nowhere in the book did I “pretend that those systems are governed by a simple, underlying mechanism described by a limited set of nonlinear equations.” Likewise, I did not complain about “astrophysicists resorting too quickly to … computer simulations.” I merely wished to stress that numerical simulations alone cannot be the key to physical understanding and that modern approaches of nonlinear dynamics and pattern theory may be very useful, at least as complementary tools, in the pursuit of that understanding.

It seems to me that atmospheric and oceanic geophysicists—and even research engineers in various fields—have been rather successful in using such combined approaches, even though the systems they have been dealing with are also very complicated.

I think these points should be made, to set the record straight.

I decided not to include any detailed discussion of convection theory in the book, save the Lorentz and Moore–Spiegel models that were among the early paradigms of deterministic chaos. Turbulence in general and convection in particular are vast and complex subjects, and many books have been devoted to their various aspects. I apologize again, as I did in the book, for not including many important contributions and thus disappointing some readers.