Chaos

James Gleick

ISBN 0-670-81178-5

Read January 27, 2000 to March 27, 2000.

Reviewed April 3, 2000.

I remember when I was 16 or 17 riding in the truck with dad from Hubbard to Hillsboro one day and talking endlessly about the capabilities of prediction given our knowledge of physics and increasing computer power. Maybe not the whole universe, but every pebble in the gravel could be modeled and, using known laws of motion and chemistry, etc. the whole future of the system could be predicted. Then came along the chaotic moon of Saturn, Hyperion, whose motions cannot be predicted for more than a few hours hence. I was confused.

I was, and am, pretty ignorant.

Even then, in the early 70s philosophy had moved away from this. Bertrand Russell was wrong. There was no boredom of a totally predictable universe on which his work was based. Within the decade following that truck ride, similar mathematical behaviors were found in a surprising range of varied disciplines from simple laws-of-motion physics to weather to fluid flow. Higher order terms, once neglected for simplicity, or ignored for lack of computing power, began to be seen as drivers to a type of randomness called Chaos. A whole field of pragmatic mathematics was born around this and sub-fields like population studies and epidemiology with troublesome outlier data sets could be re-opened in light of the resulting new modes of thought.

My favorite quote was from the physicist who, on his death bed, said he had two questions for God: “Why relativity?” and “Why turbulence?” He suspected that God might have an answer for the first.

The basic ideas may be demonstrated in fluid flow. At the beginning it is laminar, then, under a certain driving force, eddies will form. At some additional force level, these will double, then with more force, redouble again and again, until turbulence occurs. The force level at which turbulence occurs is 4.609 of something not clearly defined in the book (of the original eddy level? dimensions? the doubling power?).

What is remarkable is the universality of this phenomena. It occurs not only in fluid flow and turbulence but all sorts of other phenomena, even pendulum motion and sleep habits. In classical physics, it is often possible to neglect higher order terms, and this was often done in the development of Newtonian basics, but chaos analysis allows these to be seen and studied. Patterns form under all conditions, not just the "clean" ones.

Other important concepts are strange attractors, hyper sensitivity, and scaling. Chaotic patterns still follow patterns in phase space (an analytical technique) that fill predictable volumes but consume none themselves and, when analyzed at various scales do not give hints as to what the scale is. Indeed, it is possible to have small volumes with enormous surface area and enormous line lengths in tiny areas through the concept of scaling which says that the patterns appear the same regardless of scale, as in the Mandelbrot set. Erosion, clouds, lungs and kidneys, and trees scale over at least some range, for example. Sometimes a phenomena will have multiple strange attractors, or states that it favors and often the switch from one to another is ultra sensitive to initial conditions. This was discovered through the use of analog computers to solve differential equations with at least three variables (the minimum complexity in which chaos can occur and the maximum complexity that mathematicians and scientists before powerful computers would consider tackling). The outcomes could not be predicted and were ultra sensitive to the initial settings, sometimes changing without a physical change of the settings. Outliers which previously were ignored in data turned out to be just scaled manifestations of the same chaotic sense.

The book contains pictures and examples and the history of and main players in the study back to Mandelbrot Set, the Lorenz Attractor, the Great Red Spot of Jupiter, scaled doubling of phase space paths, frequency plots of chaotic processes, frequency responses, river paths (scaleable), lightning paths (scaleable) the Helium cell, Birkhoff's Bagel, the pendulum at rest, under driven, critically driven, and over driven, coastlines, the Sierpinski carpet (infinite edge in finite area), the Menger sponge (infinite surface in finite volume), and even the chaos taffy machines.

I find it amazingly helpful to think of all sorts of processes, physical ones that I've studied and pondered and now, even sociological ones and economic ones, car repairs and relationships, the flow of history, and the spread and eddies of capitalism in these terms. Work is still being done to strictly prove the concepts mathematically, but the discoverers and analyzers of chaotic behavior, whether they are civil engineers or meteorologists, physicists, mathematicians, or computer designers, are really on to something powerful here. They have a lot to gain from admitting that chaos reigns.

The book is well written for the layman with high school level math. Gleick even goes to quite a bit of trouble to explain the complex number system (and the complex plane in which all this phase analysis occurs) to such readers. I only wish that I had taken the time to absorb this material about 15 years ago when the book first came out.

So, one might ask God, "why, then, chaos?" Well, it makes life quite interesting, quite unpredictable, quite beautiful in many places, and it certainly leaves Him a great deal of room to act without tipping His Hand. Why He needs to act without tipping His Hand is another question.