Friday, May 1, 2009

Exploring Complexity

This book is an introduction to the science of complexity. Although written at a fairly elementary level, the chemistry, physics and mathematics are detailed. Therefore it is probably not a good book for some who is not interested in learning the basic mathematics.

Never the less, for those wishing to do the work, this is a very insightful book. It outlines and describes observations and understanding that are very revolutionary. The concepts of complexity science are no less fundamental than other well know advances in science and will have profound impact on our society.

As an example, the authors describe a simple experiment observed in 1900 whose results were not understood. Imagine two parallel plates with the space between them being filled with a liquid. If the temperature of the two plates and the liquid are all at the same temperature, the system is in equilibrium and nothing is moving or changing (at least at the macro level). However, if the temperature of one plate is raised, convection patterns begin to form patterns as shown in the drawing below. This was discovered by Benard in 1900. The flow patterns alternate – one clockwise and the next one counter clockwise.

These patterns emerge with no intelligence in fluid or a design. And, they are repeatable. If the temperature difference is increased, at some pint the patterns break down and chaos, or turbulence, is created that has a high degree of randomness.

I’m sure that you will note that these patterns look similar to what we observe in weather system. High pressure systems and low pressure system alternate directions of rotation.

Imagine yourself an observer in the liquid between the two plates. When the system is in equilibrium and nothing is changing, you would have no perception of time or space as everything would look the same. However, when the patterns emerge, time and space now have meaning. And, those meanings change again when it becomes chaotic.

For a summary of the book, I have chosen the authors’ words in the Preface:

“Our physical world is no longer symbolized by the stable and periodic planetary motions that are at the heart of classical mechanics. It is a world of instabilities and fluctuations, which are ultimately responsible for the amazing variety and richness of the forms and structures we see in nature around us. New concepts and new tools are clearly necessary to describe nature, in which evolution and pluralism become the key words. This book provides a short introduction to the methods devised over recent decades to explore complexity, be it at the level of molecules, of biological systems, or even of social systems.

We stress the role of two disciplines that have dramatically modified our outlook on complexity. The first is non-equilibrium physics. In this discipline the most unexpected outcome is the discovery of fundamental new properties of matter in far-from-equilibrium conditions. The second discipline is the modern theory of dynamical systems. Here, the central discovery is the prevalence of instability. Briefly, this means that small changes in initial conditions may lead to large amplifications of the effects of the changes.

The new methods developed in this context lead to a better understanding of the environment in which we live. In this environment we find both unexpected regularities as well as equally unexpected large-scale fluctuations. As evidence of regularity: matter is associated with an overwhelming dominance of particles over antiparticles, and life with a dominance of chiral (Note: Chirality, or "handedness", (Greek, χειρ, kheir: "hand") is a property of asymmetry important in several branches of science., asymmetric biomolecules over their symmetrical opposites. What could have been the selection mechanism giving rise to such large-scale regularities? Conversely, we could have expected uniformity and stability of our climatic conditions. However, contrary to such expectations, climate has fluctuated violently over periods quite short as compared to the characteristic time of the evolution of the sun. How is this possible? We now begin to have methods to address these questions.

The first chapter of this book presents selected examples of complex phenomena arising in the framework of physico-chemical and biological systems, as well environment at large. This description brings out a number of concepts that deal with mechanisms that are encountered repeatedly throughout the different phenomena; they are nonequilibrium, stability, bifurcation and symmetry breaking, and long-range order. In Chapter 2 these concepts are taken up and analyzed in more detail. They become the basic elements of what we believe to be a new scientific vocabulary, the vocabulary of complexity.

Following these two purely descriptive chapters, Chapter 3 addresses the problem of complexity from the standpoint of the modern theory of dynamical systems. We discuss some mechanisms by which nonlinear systems driven away from equilibrium can generate instabilities that lead to bifurcations and symmetry breaking. Special emphasis is placed in our analysis on the emergence of chaotic dynamics, the natural tendency of large classes of systems to evolve to states displaying both deterministic behavior and unpredictability.

Chapter 4 attempts a more detailed description of complex phenomena, going beyond the purely phenomenological level of the preceding chapters. We present the basic elements of probabilistic analysis of nonlinear nonequilibrium systems and construct a microscopic model of bifurcation and evolution. We also discuss some ways by which the concept of information can be integrated in the description of dynamical systems.

In the classical view, there was a sharp distinction between chance and necessity, between stochastic and deterministic behavior. The analysis in Chapters 3 and 4 shows that the situation is much more subtle. There are various forms of randomness, some of which are associated with the chaotic behavior of the solutions of simple deterministic equations. Chapter 5 addresses the question of the origin of randomness and irreversibility. We also discuss the closely related problem of understanding entropy and, in fact, the very concept of time. We believe that we begin to decipher the message of the celebrated second law of thermodynamics. We are living in a world of unstable processes, and this allows us to define an entropy function. Moreover, we live in a world in which the symmetry between past and future is broken; a world in which irreversible processes lead to equilibrium in our future. This universal prevalence of the breaking of time symmetry is at the heart of the second law.

We have expressed our conviction that science is bound to play an increasingly important role in our effort to understand our global environment. The ability to break the disciplinary barriers and to try new ways of looking at sometimes long standing problems is therefore one of the essential goals of the methods of analysis of complex phenomena set forth in this book. Chapter 6 demonstrates how this transfer of knowledge from one field to another can be envisaged. We devote much of this final chapter to questions that are beyond the realm of traditional concern in the physical sciences, such as the dynamics of climatic change, and the behavior of social insects and human populations. Obviously, each of these problems has its own specificities, and the possibility of a broad generalization should in no way be anticipated. Still, the role of nonlinearities and of fluctuations appears very clearly. It strongly suggests that the modeling of such systems should benefit from the new perspectives that the study of complex phenomena in nonlinear dynamical systems has provided to science.”

Exploring Complexity: An Introduction
Gregoire Nicolis and Ilya Prigogine
Freeman, 1989, 313 p

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