Steven Postrel
In print, at least, what might seem arrogant
comes across as a kind of innocent, childlike enthusiasm, a lack
of concern for anything but the sheer joy of figuring things out.
His ruthless simplifications of geology, evolution, and neurology
pay off because, as Bak notes, his models describe behavior that
is common across these domains. This universality means that
trampling across others' turf is not only acceptable, but almost
mandatory, if the underlying principles are to be exposed.
Finally, for the most part, Bak wants the reader to grasp the
basic logic of his arguments; only rarely does he try to persuade
with flights of poetic language or brute intellectual authority.
Synopsis A professor of physics
offers a stunning new theory of complex systems, from earthquakes
to stock markets. This book, written by the discoverer of
self-organized criticality, describes for general readers a
concept that has become increasingly important in science. Many
seemingly disparate aspects of the world, from the formation of
the landscape to the process of evolution, all share a set of
simple, easily described properties-- which may be explained as
manifestations of a single principle.
A reader from Boston, MA, November 3, 1999
Per Bak's ideas (and ideas of others that are
occasionally presented without quoting the original sources) are
remarkably interesting, but the book itself seems to be a product
of an uncontrolled avalanche in author's brain. Too low rigor and
signal-to-noise to be interesting scientifically, too poorly
written to be read as fiction - sorry, two stars. A 10-page
summary could have done much better. --This text refers to the
paperback edition of this title
Universality classes for sandpile models (and
complex adaptable systems) have never been defined. Without
universality classes one cannot claim that an arbitrary
mathematical model (like a sandpile model or a 'complex adaptable
system') describes or explains anything in nature. One or a few
scaling exponents do not define a universality class for systems
away from criticality. There is no evidence, to date, that
turbulence, economics, and most other phewnomena that occur in
nature or society are critical phenomena. Furthermore, there is
good reason to expect that socio-economic phenomena are not
mathematical phenomena at all.
Per Bak has made a glitzy try at explaining a
number of natural phenomena. The idea of "self-organized
criticality" is one that many disciplines grom geology to
taxonomy to economics have had as a "dance partner."
Unfortunately, the idea of spontaneous order requires rigorous
argument, not just clever analogy. For an elegant statement of
the relations among the processes and components of the Universe
that interact to give us stability and instability, basic
arguments and a history of ideas can be found in Prigogine and
Stengers' "Order Out of Chaos: Man's New Dialog with
Nature." In collaboration with Stengers, Prigogine has
updated his arguments for the role of the structures and
behaviors in Nature in "The End of Certainty: Time, Chaos
and the New Laws of Nature." Incidentally, the Nobel
Laureate work of Ilya Prigogine seems not to have been discussed
in Bak's cute little book. Even though this book is clearly
written, there are enough omissions and errors to make a reader
nervous. For two instances of many problems. 1-Many examples are
drawn from paleontological and evolutionary phenomena. Data on
life spans of fossil genera (a Sepkowski compilation of data) are
the source for one of histograms and are incorrectly transferred
to Bak's book as a "kill curve." Kill curves are an
important part of evolutionary/extinction theory. Bak might also
have cited Van Valen's mechanism for disappearance by predation:
the Red Queen's Hypothesis (roughly put, predators snarf up the
most convenient meal, not always the slowest member of a
species). This is an interesting variation on natural selection
and one which Bak's cleverness could discuss to good effect.
2-Linear log-log plots appear without error bars and might have
been done by the old Mark One Eyeball Method. How is a reader to
know if the data reflected in the points were sloppy or tight
fits? This is a crucial point in pattern matching. A shaky
pattern makes a less convincing argument than a reliable one. Why
aren't major intellectual contributions to the idea of self
organization and critical conditions from Van Valen (1973), G. U.
Yule (1987), D. Raup (1991) and Prigogine (1984, 1996) given some
discussion? I mention the above examples because argument by
analogy is centered on Pattern Matching. Pattern can be defined
for mathematical purposes as "a template, motif, design
which may be repeated" (see Gr'fcnbaum and Shephard,
"Tilings and Patterns"). But Bak does not say WHY
pattern in mathematics (created by mathematical rules) should
match pattern in Nature (created by rules which we are still
working out). A quick answer would be that the pattern/analogy is
only as good as the elements of the items being compared are
comparable. Clearly, mechanisms of creation of the compared
patterns are different. Use of analogy is a creative, useful way
to probe the unknown by the known, but Bak does not lay even this
foundation for the arguments in the book. Because mathematical
pattern (as survival curves, radioactive decay and the like
appears in nature does not mean that the pattern match alone is
"proof" for general a natural process as explanation
for diverse observations. Bak's "avalanche behavior in
sandpiles" is only as good as a master pattern if the
transfer of data and mathematical information from other sources
is impeccable. For an example of careful argument using
understandable mathematics to understand processes in nature I
recommend David Raup's witty "Extinction: Bad Luck or Bad
Genes?." In closing, I cannot recommend this book in spite
of its occasional cleverness and clear writing. In the spirit of
the Red Queen's Hypothesis, it is not quite quick enough to avoid
the predator/critic.
sdekey@natinst.com
from Austin, Texas, February 1, 1998
If you believe in Occam's razor, you will
probably like the idea of self-organized criticality (SOC). It is
simple enough to be understood and appreciated by
non-mathematicians, yet profound enough to make us look at
phenomenons in nature and society in a different way. Per Bak
presented SOC in a highly readable fashion. It is not the
difficulty of the subject or the writing that makes the reader
stop and ruminate, as is the case with many science writings, but
the simple yet intriguing nature of the idea itself. Is the
author overreaching in some of his assertions and conclusions (as
some people took exception to his choice of title)? Perhaps. But
this book is short and highly enjoyable, and I think it is worth
spending a few hours of one's time reading it.
A reader from Pound Ridge, New York, November
2, 1997
In spite of its many faults: failure to
acknowledge Prigogine's conclusions that foreshadowed most of
Bak's; petty sniping at others, incredibly hit and miss editing,
and some outright silly passages (such as the idea that people
living somewhere where there haven't been earthquakes for a long
time would want to buy earthquake insurance), Bak has something
important to say, and at times says it well and eloquently.The
fact that he has found a substantial number of natural systems
that create a spoor of commmon properties, and has nailed some of
them is important. But: he says he insisted on the title of his
book, not the editors (permit me to doubt this)and then says not
one word about how he came to the conclusion that power curves,
fractals, 1/f distributions and Zipf's law apply to ALL of
nature. Has he any evidence of natural processes that don't? Is
anyone working this side of the problem? He has a refreshing view
of what good science consists of, but does not display a
scientist's attitude of disinterested pursuit of truth. This may
be editorial inspiration to avoid qualifications in order to make
stronger statements. I hope so, because I genuinely like the way
he thinks, and find his ideas stimulating. But his claim to be
the "discoverer" of self-organized criticality is close
to fatuous.