# Book Review Probability Fractals and the Physical World Chaos and Complexity. By B

код для вставкиСкачатьBOOKS Probability, Fractals and the Physical World Chaos and Complexity. By B. K a y . VCH Verlagsgesellschaft, Weinheim/VCH Publishers, New York, 1993. XXII, 593 pp., paperback DM 78.00.-ISBN 3-527-29007-9/ 1-56081-798-4 This book is intended as a popular introduction to some modern interdisciplinary ideas of chaos, fracBRIAN KAYE tals. and scaling. It is addressed m&ly CHAOS to a readership of high-school students COMpihITY and university beginners. The main content of the book is well described by its subtitle: “Discovering the Surprising Patterns of Science and Technology”. The main goal of the book is stated in the last paragraph of the author’s introduction : its readers should “gain a new appreciation of the physical significance of the theorems of probability theory and also grasp the significance of fractal structures manifest in the physical world around us”. This is the main idea of the book, and therefore its title “Chaos & Complexity” is misleading. Starting from some preliminary explanations of the concepts of dynamical chaos. the author switches to a very necessary introductory discussion of classical probability problems, including Buffon’s needle and the Poisson distribution (although there are mistakes in both equations representing the Poisson distribution, on pp. 209 and 210) and others of a less classical nature, such as hyperbolic (scaling) probability distributions. This introduction is very interesting and motivating, and also provides young readers ‘ This section contains book reviews and a list of new book, received by theeditor. Book reviews are written by invitation from the editor. Suggestions for books to bc reviewed and for book reviewers i r e welcome. Publihhers should send brochures or (better) books to Dr. Ralf Baumann. Redaktion Angewaiidte Cheinie. Postfach 10 11 61, D-69451 Weinheim. Federal Republic of Germany. The editor rescrves the right of selecting which books will be reviewed [Jninvited books not chosen, for review will not be returned. \ with ideas for simple experiments they can d o by themselves in order to become familiar with the concepts and methods of probability theory and applied statistics, and to appreciate their relevance in science and everyday life. According to the classification adopted on page 7, all the cases described here are random rather then chaotic. The greater part of the book is devoted t o consideration of different fractal sets and objects. The concepts of fractal geometry leading to the notion of fractal dimension(s) form an important part of modern material and geological sciences and engineering, and also find applications in other fields, such as biology and social science. This notion gives us an important and experimentally measurable characteristic of rough lines and surfaces, such as coastlines and landscapes, catalyst surfaces, dusts, etc. The author is an expert in this field of characterization of fractal objects, and therefore the chapters devoted to the properties and characterization of real systems, such as aerosols, powders, aggregates, and mixtures are not only brilliantly written but also very interesting, even for a specialist. Here I would like to stress once more that these topics are mostly classified by the scientific community as belonging to the fields of random (or stochastic) processes, fractals, scaling, growth or roughening phenomena, etc., which normally implies an “external” source of randomness, such as thermal Brownian motion, quenched disorder, and so on. This can be easily seen by comparing the titles of numerous conferences on these topics. Therefore, the greater part of the book is devoted to something other than the subject of its title. Only a small part of the book treats what scientists normally refer to as dynamical chaos. The only problems that can be considered as such are the logistic map (May’s equation) discussed in Chapter 12 and parts of Chapters 2 and 14 on iteration of maps and the form of basins of attractors. The main questions of stability, sensitivity to initial conditions, and predictability are only briefly mentioned in the introductory Chapter 1 (see the discussion of the butterfly effect). Although the author has a good habit of using a dictionary to explain the ety- mology and meanings of terms he uses and provides us with much interesting information in many other cases, the word “complex” is an unfortunate exception, being used more o r less as a synonym for the word “complicated“. The notion of complexity is not even analyzed (for a deeper discussion see, e.g., Applied C1~ao.s Theory. A Paradigm ,jbr Cotnpkexirj~,by A. B. Cambel, Academic Press, 1993). and consequently many interesting points, such as hierarchical and algorithmic definitions of complexity, or problems of evolution of complex systems, which can be useful for an introductory text, remain unexplained. Unfortunately some statements are unclear o r vague, and some citations are inaccurate: e.g., the attribution ofthe uncertainty principle to Karl Heisenberg instead of Werner Heisenberg (p. 4). a reference to “Peratoe” (instead of V. Pareto) on page 442, and the three times erroneously transcribed name of N. Ya. Vilenkin. Overall, the book is a very interesting introductory text which is more suitable for inspiration than for learning. It can serve as a source of additional material and fresh jokes and anecdotes concerning the whole field of probability and fractal geometry, and as a brilliant advertisement for this new field of science and new way of thinking. If this advertisement works. the reader will then turn to other texts that are more accurate and precise (see the discussion of these two concepts on p. 134). Igor ,M.Sokolol~ Institut fur Theoretische Polymerphysik der UniversitBt Freiburg (FRG) Too chaotic, too complex! In the book review section in issue 12 the cover of the book “Chaos and Complexity” was incorrectly depicted with the review of the book “Chemistry Imagined. Reflections on Science.” The correct picture is shown here.

1/--страниц