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

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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/
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
to a readership of
high-school students
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
incorrectly depicted
with the review of
the book “Chemistry Imagined. Reflections on Science.” The correct
picture is shown
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