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Oscar Dementiev
Oscar Dementiev

The Essence Of Chaos

As a meteorologist, Lorenz initially became interested in the field of chaos because of its implications for weather forecasting. In a chapter ranging through the history of weather prediction and meteorology to a brief picture of our current understanding of climate, he introduces many of the researchers who conceived the experiments and theories, and he describes his own initial encounter with chaos.

The Essence of Chaos

For the personal glimpses of chaos theory development alone, this book is worthwhile; for a clear, sharp development of the subject, the book is excellent; and for tying humanistic and scientific considerations together so well, there is a major debt owed to Lorenz.

In giving a nontechnical but careful account of the field of dynamical systems and 'chaos,' and setting it in a broader scientific context, Lorenz has .. communicate[d] the nature of the mathematical sciences and how mathematics contributes to society.

Chaos surrounds us. Seemingly random events -- the flapping of a flag, a storm-driven wave striking the shore, a pinball's path -- often appear to have no order, no rational pattern. Explicating the theory of chaos and the consequences of its principal findings -- that actual, precise rules may govern such apparently random behavior -- has been a major part of the work of Edward N. Lorenz. In The Essence of Chaos, Lorenz presents to the general reader the features of this "new science," with its far-reaching implications for much of modern life, from weather prediction to philosophy, and he describes its considerable impact on emerging scientific fields.

A further discussion invites readers to make their own chaos. Still others debate the nature of randomness and its relationship to chaotic systems, and describe three related fields of scientific thought: nonlinearity, complexity, and fractality. Appendixes present the first publication of Lorenz's seminal paper "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?"; the mathematical equations from which the copious illustrations were derived; and a glossary.

The essence of Chaos and Corruption is a special attribute unique to a number of artifacts in ADOM. The nature of these artifacts is so strongly connected to the forces of Chaos that they radiate corruption on their own. Prolonged contact with such artifacts can therefore significantly affect the PC.

Each carried artifact containing the essence has a 50% chance to increase the PC's corruption by 1 corruption point (adjusted by Appearance and other factors). Equipped artifacts containing the essence have an additional chance to cause corruption.

The PC will receive an alignment boost if (s)he sacrifices an artifact containing the essence. The magnitude of the effect is not substantial (especially considering the level of the PC at which (s)he will usually obtain the artifacts) but may be enough to achieve L+ alignment or turn into a fallen champion of Chaos or Balance.

Many of us whom, we hope, Virginia Woolf meant to include in her definition of "the common reader" have heard by now of "chaos theory," which seems to have burst suddenly like a new sun on our intellectual horizons. Some of us may listen with wonderment as others discuss the subject, perhaps venturing a few observations of our own. To most of us, however, the subject is remote and possibly daunting. Yet knowledgeable people tell us that chaos theory is implicated in such vital matters in our daily lives as weather forecasting and cardiac arrhythmias. Our crops are washed out unexpectedly; cities never flooded before are inundated; winter snows fail to accumulate in the mountains; friends or relatives are seized by renegade heart rhythms and carried away. Can these effects which we previously attributed to Fate or God be explained by chaos theory?

James Gleick's popular Chaos: Making a New Science (1987) gave us an interesting story of the emergence of chaos theory. But Gleick gave yet another account that heroicized and masculinized science as the drama of man against the universe and its secrets. N. Katherine Hayles re-told the story of chaos theory in her Chaos Bound: Orderly Disorder in Contemporary Literature and Science (1990). There she argued convincingly that "different disciplines base the theories they construct on similar presuppositions because these are the assumptions that guide the constitution of knowledge in a given episteme" (xi). Holding degrees in chemistry (B.S., M.S.) and a doctorate in English, she attempted to redress some of the effects of Gleick's popularization of the "new science" and to initiate a deserved feminist critique of his narrative methodology. In 1992, M. Mitchell Waldrop brought us a critically acclaimed and engagingly readable Complexity: The Emerging Science at the Edge of Order and Chaos. But his chapter titles alone suggest how he continues the note struck by Gleick: "The Irish Idea of Hero," "The Revolt of the Old Turks," "Secrets of the Old One," "'You Guys Really Believe That?'" and so on.

With the arrival of Edward Lorenz's The Essence of Chaos, however, we have the voice of someone who wishes to tell us clearly and simply about chaos and not to perpetuate any myths about either science or its personalities. Throughout the book, he is genial and straightforward, speaking with the voice of a major participant in the development of chaos theory who wants to share with the reader its history and the names of the many others who contributed to the project. He speaks even-handedly about his predecessors, his postdocs his colleagues, his competitors in the search for solutions, and the people who suggested he needed a computer (and then a larger one). Without melodrama, we travel with him from conference to conference where he is presenter or auditor. The reader leaves the text as one would leave an absorbing visit with a magnanimous teacher.

Although Lorenz wants to be clear and simple, one of the great virtues of his book is that he refuses to oversimplify or to blur distinctions. Thus much of the beginning of the book tells us how the subject of chaos is large and complicated. "Glimpses of Chaos" is an admirably apt chapter title which signals the quiet wit and good humor that characterize the book. Consider, too, the subsections within the chapter: "It Only Looks Random," "Pinballs and Butterflies," "It Ain't Got Rhythm," and "Zeroing in on Chaos." Lorenz carefully prepares the reader with respect to what is chaos and what is limited chaos, to what is randomness and what is apparent randomness. "I shall use the term chaos to refer collectively to processes of this sort," Lorenz writes, "ones that appear to proceed according to chance even though their behavior is in fact determined by precise laws" (4). The problem of defining chaos is complicated, he tells us, "because several other terms, notably nonlinearity, complexity, and fractality, are often used more or less synonymously with chaos in one or several of its senses" (4). For example, a narrow definition of randomness: "a random sequence of events is one in which anything that can ever happen can happen next" (6). A somewhat broader definition, however, is "a random sequence is simply one in which any one of several things can happen next, even though not necessarily anything that can ever happen can happen next" (7).

For Lorenz, sensitive dependence on initial conditions is central to an acceptable definition of chaos. He moves methodically, in this fashion, to describe a chaotic system "as one that is sensitively dependent on interior changes in initial conditions. Sensitivity to exterior changes will not by itself imply chaos. Concurrently, we may wish to modify our idea as to what constitutes a single dynamical system, and decide that, if we have altered the value of any virtual constant, we have replaced our system by another system. In that case chaos, as just redefined, will be equivalent to sensitive dependence on changes that are made within one and the same system" (24).

Many people who are scarcely familiar with chaos theory have seen the familiar butterfly-like pattern that Lorenz's computer printed out when he left it unattended one day to fetch a cup of coffee. The pattern is a graphical representation of what is variously known as "hidden" or "strange" attractors. Lorenz explains: "The states of any system that do occur again and again, or are approximated again and again, more and more closely, therefore belong to a rather restricted set. This is the set of attractors" (41). Although they appear to be structures emerging from chaos, Lorenz cautions that we should regard what we see as "a graphical representation of an attractor" (41). How this figure came to be the "butterfly" image of chaos is not entirely clear, but Lorenz speculates that it has something to do with his early, seminal paper "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?" at the meeting of the American Association for the Advancement of Science, in December 1972. Although the paper and the printout are his and suggest the butterfly connection, the full title reminds us of his focus on sensitivity to initial conditions.

In his fascinating fifth chapter, "Encounters with Chaos," Lorenz reviews events leading up to the development of chaos as a science. The story goes back to the discovery of the planet Neptune in the nineteenth century. Eighteenth-century astronomers had developed solutions to the two-body problem of planets handily enough, but observations of Neptune suggested that astronomers needed to attempt a three-body equation which was vastly more complicated. It was Henri Poincaré (1854-1912) in his work on the three-body equation who seems to have come closest to first identifying chaos as it is now understood. Lorenz notes, "To [Poincaré, chaos] was the phenomenon that rendered the three-body equations too complex to be solved, rather than the principal subject of a future field of investigation" (121). Nevertheless, until the advent of computers, most mathematicians focused on the less challenging linear equations; the nonlinear equations required more computational time than they could profitably spend on them. Today's powerful computers, however, enable mathematicians to do routinely what Poincaré could envision, but could not bring to reality. 041b061a72


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