Chaos and Complexity

Article excerpt


THE BIRTH OF MODERN SCIENCE has been attributed to a variety of circumstances, events, and people, [1] but unquestionably one of the key figures in its development was Rene Descartes, the French philosopher who first articulated the fundamentals of the modem scientific method of inquiry. [2] A major tenet of Descartes' approach was the idea that complex systems can be understood by analyzing one part at a time, and then putting things back together to yield a comprehensive picture. This reductionism has been at the core of some of the most spectacular successes of the scientific endeavor, from particle physics to molecular biology. But what if some natural phenomena simply cannot be so conveniently partitioned to facilitate our comprehension? What if breaking the components apart alters their properties so much that what we learn from the separate pieces of the puzzle gives us a different and misleading idea of the system as a whole? In other words, can reductionist science study emergent properties which, by definition, are the result of complex interactions?

There has been much talk of emergent properties, especially in describing the complexity of biological development and evolution. Yet, it is hard to put a finger on what even sophisticated researchers mean when they say, for example, that human consciousness is an emergent property of the physical structure of the brain and of its interactions with the environment Perhaps the simplest way to understand emergent properties is to consider the relation between hydrogen, oxygen, and water. Although the combination of two atoms of hydrogen and one of oxygen yields water, the complex properties of water (e.g., the temperatures at which it undergoes state transitions to steam or ice) are not derivable from the individual properties of hydrogen and oxygen. In other words, knowing all we know about the structure and behavior of the atoms composing water, allows us to predict the structure but not the behavior of water. This means that complexity produces new properties specific to the new level of organization (in thi s case, molecular vs. atomic) that are due not to the sum of the parts, but to their interaction. This, it would seem, is enough to stop the Cartesian research program dead in its tracks.

Scientists from several disciplines, from astronomy to meteorology, from evolutionary biology to the social sciences, have been struggling with interactions and emergent properties without a good paradigm to guide them. That is, until Chaos Theory and its more recent derivative, Complexity Theory appeared on the scene. These novel conceptual and mathematical approaches to the study of complex systems promised to provide a way out of the thicket of emergent properties. Science, it seems, had finally cracked the next level of analysis, one that will replace the Cartesian approach and substitute a new, scientific holism for the old reductionism. More than 35 years after the publication of the first study on chaos, with an entire institute devoted to the study of complexity ( headed by Nobel laureate Murray Gell-Mann and with technical journals and thousands of published papers in the offing, it is time for a skeptical evaluation of the new holism. Has chaos/complexity ("chaoplexity" as it i s sometimes called) delivered on its initial promise? Or has it fallen much short of its original goal? Does it provide a truly new set of tools and answers, or is it just a passing fad in the academic world?


What is chaos? In the vernacular, the word is a synonym for randomness, completely non-deterministic and irregular phenomena. Typically it carries a negative connotation--a chaotic situation is one that we would like to avoid. In mathematical theory, however, chaos refers to a deterministic (i.e., non-random) phenomenon characterized by special properties that make the predictability of outcomes very difficult. …