The Universe in a Grain of Sand: Self-Organized Criticality, 23 Jun 1998

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 rel! iable 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 Grünbaum 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.

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Simple, lucid presentation of a beautiful theory., 2 Feb 1998

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.

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