# Book Review: Chaos Theory Has Filtered Down

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Chaos Theory has filtered down to the public through such short discussions of the issue as are found in films like Jurassic Park or on television documentaries. The issue are more complex than can be indicated in such media depictions, and two authors who have set out to explain chaos theory more thoroughly, though still in a popular vein, are James Gleick with his book Chaos: Making a New Science from 1987 and Ian Stewart with his book Does God Play Dice?: The Mathematics of Chaos from 1989.

Chaos theory is often explained by means of what is called the Butterfly Effect, as described by Gleick in his first chapter, with specific reference to weather forecasting. Everyone who watches TV every night to see what the weather will be tomorrow knows how unreliable weather forecasting can be. It might be assumed that this is because of a lack of data on measurable events such as wind currents, precipitation, and even the effects of topology, but in additon, there is the butterfly effect which is based on computer simulations and which shows that a small change somewhere, such as the movement of a butterfly, could have cascading effects that would alter the weather. Small fluctuations can produce errors which are then multiplied again and again on a global scale, producing a different effect. While small changes can produce big changes, there is no way to predict what those larger changes will be and no way to know what the outcome would have been if those small changes had not occurred. This is the essence of chaos theory.

This would also be why Stewart raises the question once denied as possible by Einstein, who stated that God does not play dice with the universe. Chaos theory says that the universe is decided on the basis of chance to a great degree and that the aggregate of those chances cannot be predicted or even discerned for a clear cause-and-effect assessment. Chaos theory says that a small change in a system can produce more and more changes until something much greater and unforeseen has occurred. Such changes take place all the time, and they as well cannot be tracked or even relied upon. If they could, the aggregate effect would become absorbed into the system over time so that prediction would be possible. The analyst might not know what these small changes were, but he or she would know they always occurred and that the outcome was thus predictable because the causes would always be the same. In fact, they are not always the same.

Gleick examines the issue in a way that holds chaos theory to be a revolution in thinking, a major shift from the ordered universe of Newton and even the less mechanical universe of Einstein. The concept was first explained by Edward Lorenz, though his paper was largely ignored at the time. Others wrote about chaos theory in a more concrete manner, while Lorenz wrote a theoretical treatise that applied to an abstract physical model with broad application. Gleick tells the story of chaos theory in a conversational style that uses many concrete examples from everyday life to show the meaning of the concepts he describes. He also tells much of the story in terms of the actions of people examining the question, describing their discoveries, their experiments, their method of analysis, and so on. The way Gleick tells the story also informs the reader about many of the procedures of science, the starts and stops that constitute scientific investigation, with some dead ends reached even as others find their way to the correct answer, which in scientific terms only means the solution that addresses all of the known data and explains it. Any theory can be challenged later when new data is developed requiring a different theory as an explanation of the entirety.

Gleick tells the story of Stephen Smale and the way he made a leap to a new way of "conceiving the full complexity of dynamical systems" (Gleick 49).

Gleick shows some of the practical applications of chaos theory, one of the more interesting being the way this concept was applied to finding an explanation for a centuries old mystery, the Great Red Spot on Jupiter. A number of explanations had been offered over the years, such as lava flow, a new moon, a body floating on liquid, and a column of gas. Different types of scientist would see some reflection of their area of study in the Great Red Spot. Philip Marcus identified the spot as "a self-organizing system, created and regulated by the same nonlinear twists that create the unpredictable turmoil around it. It is stable chaos" (Gleick 55). Marcus was able to make this leap where others could not because of "an understanding that a complex system can give rise to turbulence and coherence at the same time" (Gleick 56).

Gleick tells the story of many other scientists who have benefited from applications of chaos theory to everything from quantum physics to computer design. Gleick also raises the issue of whether god plays dice with the universe, citing Joseph Ford to the effect that God does but that he uses loaded dice.

Ian Stewart is trained as a mathematician, while Gleick writes about science for the New York Times. Stewart is British, and Gleick American. They write about the same subject from different points-of-view. Stewart begins his book noting that the direction for creation has been first from chaos into order, and that physics has now found that order is something of an illusion masking the continuing chaos of reality. He also cites Newton and the Newtonian era as affirming that nature has laws and man can discover what these laws are. The world described by Newton was a clockwork world which operated like a machine, and Stewart discusses the nature of that world and world-view much more directly than does Gleick. Stewart's discussion includes more about the history of mathematics in particular, showing how different levels of mathematics were created to analyze and describe the physical world and to provide equations for the mechanical processes of an ordered universe. These old view were challenged by certain data, such as the odd behavior of one of the moons of Saturn, Hyperion. The idea of chaos was offered to help explain such fluctuations, and chaos theory does not imply chaos in the normal sense but a way of discovering a hidden pattern. For Stewart, order can chaos are intertwined, and understanding the universe requires understanding and accounting for both order and chaos. More than this, says Stewart, mathematicians now see order and chaos as "two distinct manifestations of an underlying determinism" involving a "continuous spectrum" forming an exemplar of "mathematical beauty" (Stewart 22).

For Stewart, mathematics is capable of explaining everything and even of incorporating the element of chaos into its equations. He analyzes this idea in terms of different real-world situations, from various mathematical and scientific issues to the behavior of human beings in social settings. He discusses much of the history of mathematics as part of his analysis. Where Gleick discusses physicists, Stewart discusses mathematicians. Even when he discusses physics and concepts of physics, Stewart does so in terms of the mathematics that explain what they find and cites mathematicians as to how ideas were developed.

He finds various clues as to the operation of chaos in the idea of attractors, in maps, in Poincare solutions. He also describes the important work of Edward Lorenz and the way it has become key in chaos theory. Part of the chaos leading to order seen by Stewart is in terms of ideas and the way an individual may be studying one thing and discover something about other fields as a by-product, a shift in thinking…
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