Any recommendations for learning the fundamentals and applications of chaos theory?

June 5, 2007 3:06 PM

Does anyone have any recommendations for books, textbooks, or blogs that discuss the conceptual development of chaos theory? I'd be very interested in its use in applied mathematics over abstract mathematical theory.

I originally became interested in using fractals in finance, that is that markets seem to display global determinism but local randomness. There have been a few papers and books written on fractals/chaos theory and its applications to finance. These have not been very satisfying to me for a variety of reasons.

I'd prefer a book that is along the lines of another book I picked up awhile ago, "Calculus and its Conceptual Development" which as the title implied, followed the development of calculus through history and its eventual acceptance. It was helpful in that pure mathematics in many textbooks don't always relay the conceptual ideas behind it.

I recently read Poincare and the 3-body Problem which seems to be the beginning of what is later called chaos theory. Something with a more applied mathematics bent would be better.

posted by geoff. to science & nature (11 comments total)

NB: The finance texts that I've read recently that I'm referring to are Fractal Market Analysis by Edgar E. Peters and Fractals and Scaling in Finance by Mandelbrot. Also a handful of papers, but I don't wnat to be deluded by not understanding the fundamental mathematics and philosophy behind chaos theory.
posted by geoff. at 3:15 PM on June 5, 2007

Chaos: Making a New Science is pretty much all about the development of chaos theory, and especially within applied mathematics. For example, the book starts off with chaos theory's genesis in Lorenz's work in weather forecasting models.
posted by marionnette en chaussette at 3:31 PM on June 5, 2007

The main reason you may not have found a satisfying book about using non-linear dynamics in finance is that there's a lots of guesswork and nobody is even sure it can be done. To imply there's global determinism in the markets is to say it has attractors but nobody has found any.

This Review of The Predictors by someone who worked there may be helpful to you, including the linked articles at the bottom.

Oddly enough, I have Peters Fractal Market Analysis and am surprised I do. It was from a short period over 10 years ago when I thought this all had more potential than it did. The book has huge mathematical gaps. I tried to develop a predictive time-series analysis model but found that it was an under-specified problem. It's all fantasy.

The better books today are on using non-linear dynamics to model turbulence and fluid mechanics and optics - perhaps not as sexy as you imagined?
posted by vacapinta at 5:38 PM on June 5, 2007

I also liked `Chaos: Making a New Science'. The author, James Gleick, is a great writer. I recall reading it long before I could undestand the math and still enjoying it, which means it's probably not very technical.
posted by PercussivePaul at 6:26 PM on June 5, 2007

Do you actually want to be able to do anything practical with chaos theory?

While I know very little about that specific sub-discipline, you have to realize that if you want to actually use this math, you might have to get your hands dirty and do a little theory. The great majority of pop-science books about math tell you the history, and are a good read... but you won't walk away actually knowing any of the math, or being able to use it.

Honestly, if you want to learn to use this stuff practically, get a real textbook on it. Grab a motivational pop-science one on the side if you like to learn about the motivations... but if you want to learn chaos theory? Find a good textbook.

(Unfortunately, I can't recommend any, as that's not my field of study)
posted by vernondalhart at 7:09 PM on June 5, 2007

I have no interest with motivational pop-science. I am sure that Chaos: Making a New Science book is great, and I may pick it up, but it was not really want I was looking for.

I hate to keep bringing up finance topics, but that's the academic discipline which I'm most acquainted. For example, Louis Bachelier's Theory of Speculation: The Origins of Modern Finance is a great book. It not only includes his original paper (with the math cleaned up), it includes amazing commentary. It was very much like picking up a Norton Classics Edition.

The reason I haven't picked up Chaos Theory 101 is that I'm familiar with the basics on non-linear dynamic systems and the various mathematics involved. Vacapinta illustrated my point rather well, in that I fully understand attractors, it is how to find them and how you know they are attractors (as oppose to say, random data) and how far you can go when claiming something is an attractor (that is if there are no specific attractors do attractors have specific stochastic properties which may be applied to find them).

I have found great use in going back and reading early research and compiled commentary which often answers a lot of questions that probably don't pop up in established sciences, but the very fundamental problems encountered early on in the science.

Anyway the textbooks I've seen on Chaos theory, at least at the small graduate level section at the local college bookstore, were of no paticular interest. I was hoping to find something perhaps a little more esoteric.
posted by geoff. at 7:33 PM on June 5, 2007

I can't help you, but maybe you should try sending your question on to Cosma Shalizi, who maintains a blog focused on statistics/information theory.

http://www.cscs.umich.edu/~crshalizi/weblog/
posted by Maxwell_Smart at 9:29 PM on June 5, 2007

Yes, Cosma Shalizi has read a lot of books on chaos, dynamical systems, and related topics, and has some book reviews on his website. He also has his Notebooks, which are notes on various topics with lists of readings.
posted by euphotic at 10:49 PM on June 5, 2007

You might try Steven Strogatz's book Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering. You can dowload some of his papers here. He doesn't work on finance, though.
posted by lukemeister at 2:07 PM on June 6, 2007

Shalizi's website is great. I think I may make it into a front page post.
posted by geoff. at 5:50 PM on June 6, 2007

Shalizi's been around forever. And y2karl's already been there.
posted by vacapinta at 6:44 PM on June 6, 2007