some reviews of How Nature Works: The Science of Self-Organising Criticality by Per Bak (Oxford University Press, 1997)

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 from Houston, January 20, 1999

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. from Ohio, USA, June 22, 1998

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. 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.


1/f noise and signal processing
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