PRINCIPLES

Chaos: A Very Short Introduction by Leonard Smith



Chaos: A Very Short Introduction by Leonard Smith

Introduction

The chaos by Leonard A. Smith's book explains the phenomena in mathematics and science, in which small differences in initial conditions have a major impact on the future state of affairs. These rule three simple principles that produce a remarkable variety of chaotic systems: a sensitive dependence on initial conditions, determinism and nonlinearity. All of these words (and many more) are clearly explained in this book. Although it deals quite a bit of mathematics, but the author manages to dispense with complicated equations. Presumably, according to Smith, the difference is that the basic premise of chaos theory - small change, big impact - all of us had already known, albeit without precise mathematical formulation. The book is in spite of the difficult (and sometimes abstract) issue written of course, richly illustrated and with a glossary provided, which allows easy look up key terms (Brocker et al. 2007).

In this essay, we will be discussing principles used by Leonard Smith in his book. In addition, we will be discussing the relation of these principles with mathematics and science.

Discussion

In many ways, the book becomes a companion handbook easily read with access to references conveniently listed. For the non-mathematician, the explanations of important concepts are particularly useful. Few books could better Smith's definition at the beginning of his book of what is meant by chaos. Other concepts, involved are also explained with simplicity that will be envied by most academics that have to teach them. A popular discussion of such important terms as “uncertainty”, “Olbers' paradox”, etc. are explained and defined in brief, simple terms. These definitions form a glossary at the end of the book where a full index and recommended future reading is included (Brocker et al. 2007).

The first principle that is mentioned in the book is that Chaos exists in systems all around us. Even the simplest system of cause and effect can be subject to chaos, denying us accurate predictions of its behavior, and sometimes giving rise to astonishing structures of large-scale order. The growing understanding of Chaos Theory has fascinating applications in the real world - from technology to global warming, politics, human behavior, and even gambling on the stock market (Khare et al. 2011).

Leonard Smith shows that we all have an intuitive understanding of chaotic systems. He uses accessible mathematics and physics (replacing complex equations with simple examples like pendulums, railway lines, and tossing coins) to explain the theory, and points to numerous examples in philosophy and literature (Edgar Allen Poe, Chang-Tzu, Arthur Conan Doyle) that illuminate the problems. The beauty of fractal patterns and their relation to chaos, as well as the history of chaos, and its uses in the real world and implications for the philosophy of science are all discussed in this Very Short Introduction (Ghil et al. 2010).

The second principle related to the "butterfly effect" that has now become a popular slogan of ...