Thoughts raised by a BBC program on Chaos Theory

A while back I posted links to the YouTube copies of a BBC program titled The Secret Life of Chaos. I did like the program in that it was beautiful to watch and it cited a number of research results that are indeed important. I didn't like what it did with that material.

For example, the idea of self organizing systems with feedback producing behavior which appears regular but is inherently hard to predict seems to me to go back at least to Adam Smith and his recognition of the "hidden hand" in market behavior. Yet the program attributes such concepts only to Allan Turing in the latter part of the last century.

The program also suggested that we can not solve very large systems of equations, while in fact computers can do that very thing. Chaos theory is applied to systems in which small variations in original conditions eventually (rapidly) lead to large changes in system behavior. Indeed, the term is applied specifically, as I understand its use, to systems in which there are simple equations that capture the physics of the system, and indeed the exciting thing is to infer the simple equations that underly the complex behavior.

I would also point out that the concept of self-organizing systems seems to me to have developed in areas such as neurobiology and automata theory, where there are networks of discrete computational elements, and the concepts were specifically useful for computer simulation. This is the field I think of as "Complexity Theory", in which the key outcome (similar to that of Chaos theory) is that very simple decision rules applied uniformly to a network can result in unexpected emergent properties.

Evolution can be used, I suppose, both on the decision rules in networks of decision making nodes and in the parameters of equations governing behaviors of fields or volumes.

The human brain has evolved to seek patterns in stimulus, I suppose because there is survival value in the perception of such patterns. As we view galaxies in telescopes or waves on the water or clouds in the sky we perceive patterns. Indeed, we have evolved with the tendency to attribute meaning to the patterns. I would suggest that usually the meanings we attribute are wrong, at least until generations of original thinkers find deeper understanding. Any child can see animal shapes in the clouds as if they had been designed by some celestial artist, but a more adult understanding attributes to shapes of the clouds to the effect of simple rules of atmospheric physics.

Cloud photo by Ian Britton via freephoto.com