Journal of Economic Dynamics and Control 17 (1993) 519-522. North-Holland

Searching for certainty

Book review

Richard H. Day Cifliw.@v of Southern Cal(fornia. Los Angeles, CA 90089, (ISA

John L. Casti, Searching for Certainty: What Scientists Can Know about the Future (William Marrow and Company, New York, NY, 1990).

Judging by the flow of books, the substantial displays in bookstores, and the flow of quality television specials devoted to it, popular science is a major business. Some of the greatest contributors to science have engaged in it. Einstein’s Relativity, for example, carried on its jacket the assertion: ‘A clear statement anyone can understand.’ Henri Poincare, Arthur Eddington, Max Planck, Erwin Schrodinger, John von Neuman, James Jeans, Jacques Monod, Charles Sherrington, Niko Tinbergen, and Konrad Lorenz, among others, wrote splendid nontechnical statements about science and its implications for human understanding. Their masterpieces are profoundly thoughtful reflections by great thinkers and, as such, they are probably too intense, too poetic, too deeply aesthetic, too spiritual even, to be truly popular in the literal sense of the term.

For that broad mission the genre of ‘pop science’ has emerged. Usually undertaken by journalists, such as Gleich on Chaos, or professional writers, such as the dramatist Ardrey in his series of engagingly provocative books on animal ethology, these writers have mastered at some level the technicalities of the subject at hand, and attempt to make their understanding accessible. Such work can be of high order and must be motivated by a strong desire to communicate, to share one’s knowledge, spurred on, perhaps, by the commercial possibilities that have now, no doubt, reached substantial proportions. It is for the latter reason that the term ‘pop science’ carries a somewhat pejorative connotation.

John Casti’s book, perhaps surprisingly, is an unabashed contribution in this latter vein. ‘Perhaps surprisingly’ because he was trained as a mathematician and the author of scholarly papers in the technical areas about which he writes.

01651889/93/$05.00 c 1993-Elsevier Science Publishers B.V. All rights reserved

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Nonetheless, the present book is real ‘pop science’ as a scan of the contents quickly reveals: ‘Polishing the Crystal Ball’, ‘The Good, The Bad and the Probable’, ‘From Blobs to Barbie’, ‘A Bull is a Bowl’, ‘Wargasms as Catas- trophes’ (pp. 15-17) etc., and it exemplifies a hallmark of pop science in the personalization of a technical topic by brief biographical synopses intended to humanize the discussion. Thus, ‘. . the time honored, socially acceptable way for conscientious objectors to discharge their duty to God and Country during war is to serve in the medical core . . . Richardson was a Quaker who studied physics at Cambridge. ’ (p. 93). Another hallmark is assurances that what was worked out in arcane terms by those rather odd ducks that actually do science, can really be understood in common terms and ‘for those masochistically oriented readers . . the mathematical transliteration of these relationships can be found in the ‘To Dig Deeper Section’. But, of course, that is the whole point of pop science. It is for those who can’t, won’t, or don’t have time and energy to ‘dig deeper’.

But let’s talk about the book itself. What Casti has done is pull together several rather different and to some extent independently developed strands of mathematical science that share implications concerning the predictability of phenomena: weather forecasting, biomorphology, stock market forecasting, and war science, finishing with the predictability of logic itself. These five chapters are preceded by an introduction to scientific method. His unifying theme is the extent to which logic can lead to certain knowledge (p. 23) and the analysis of one of the primary causes of uncertainty, randomness. He begins with a highly readable account of the mathematician Edward 0. Thorp’s triumphantly practi- cal analysis of the game of black jack. Poincart’s description of randomness (Science and Hypothesis, Chapter XI) is more profound and elegant ~ but it should be. Poincare was not doing pop science, as I said before. As for Casti, he does leave his willing reader with what for many - even in science today in spite of Poincare et al. - is a startling fact: that deterministic causality does not imply predictability! It is explicated with the help of brief accounts of instability, catastrophes, chaos, and strange attractors. Given Casti’s own work, it is not surprising that these passages contain some of the more successful attempts to simplify the complexity of complex dynamics using ingenious examples from number theory.

Weather forecasting provides an especially appropriate and appealing terri- tory to illustrate the relevance of these ideas, for here it is that Newtonian laws are found to lead to the kind of instabilities that appear to make forecasting weather beyond relatively short periods essentially impossible. Next comes morphogenesis or self organization: how a succession of forms develop struc- turally distinct architectures, yet each emerging somehow from its predecessor. Various theories, some rather exotic ones, in biological processes are reviewed.

‘Meanwhile, over at the casino’, Casti asks, ‘can we predict/explain the behavior of stock market prices?’ This part of the book comes closest to my own

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area of research, that of complex economic dynamics. Not surprisingly, I found this least convincing of the discussions, for almost immediately the author misunderstands certain basic ideas in the field. Thus ‘the fundamentalist view of the world sees a price as only a reflection of an underlying value’ (p. 193). Actually, the fundamentalist view is nothing of the kind, but rather the belief that investments should be made by comparing current prices, which reflect many forces including random ‘news’ and investor band wagon and panic effects, with estimates of a company’s intrinsic value based on profitability, its debt-equity position, the quality of its management, the success of its research and development activities, and other fundamental measures of performance quite independent of the market’s current valuation. But Casti is not entirely at fault. His interpretation has been the most influential one in the recent academic finance literature.

This example reveals a major pitfall in all efforts to encapsulate and synthesize diverse fields. The author is seldom an expert in all of them and, indeed, is usually a layman himself in some of them. There is always the danger that he will march off on a misguided tangent like that of the scholastic gurus that he unwittingly takes as the supreme authorities.

Then comes war science, the efforts to understand how violent conflict breaks out of a preceding interaction among nations. It is here especially that formal reasoning by means of mathematical thinking seems especially limited when stacked up against a great mind’s power to synthesize a myriad of facts into a coherent and prescient understanding. Casti does not go into this aspect of cognition, having specifically limited himself in the beginning from such consid- erations, but the lesson does stand out: there was far more twixt Keynes and Churchill than dreamt of in scientific methodology alone, for both, in remark- able essays shortly after the close of World War I, predicted World War II, and both without the benefit of the theory of differential games.

Finally, comes still another pop scientific effort to explain Godel’s theorem in a chapter entitled ‘Proof or Consequences’, which contains the inevitable de- scriptions of Turing’s Machine, computability, random numbers, and so on. This is really deep water and I suspect most readers will be left floundering in spite of the author’s ingenious effort to make common sense of the profound paradoxes of pure logic. He is in good company here, for I believe the same can be said for related efforts from Hofstadter to Penrose.

Scientists are usually annoyed by books like this, especially by those sections that cover their areas of expertise. The synthesizers inevitably and of necessity gloss over significant details and fail to express the essence of matters that just are impenetrable without unusual intelligence, extensive training, and prodi- gious mental exercise. Nonetheless, commercial pop science does a great deal of good, for it exposes people to the work of specialists that does or may or will or should influence their lives in significant ways. And after all, the scientific enterprise depends on the willingness of governments and the people who

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support them to allocate resources to their mysterious undertakings, to tolerate activities that seem (and truly may often be) impractical and even useless. Engaging their sympathies is a matter of survival!

There will be a number of guardians of scientific integrity who will be more worried about the dangers of encouraging fads, of exaggerating the importance of what may turn out upon further research to be unimportant or even incorrect ideas. Such charges are often made against those of us in the social sciences that employ nonlinear dynamics. But science itself, as Casti rightly explains, is a dialectical process. I use the term here in the Socratic sense of the confronta- tion of hypotheses with argument, persuasion, and debate, out of which emerges new understanding that may serve for a time until further experience reveals new conflicts, new paradoxes, new conundrums that command explanation. Skepti- cal criticism is therefore an integral part of the search for truth and Casti need not feel chagrined by such reactions.

All in all, I think Casti succeeds rather well in his mission, as such. It is an extremely challenging one because scientific ideas begin their articulation in a language of specialized symbols and vocabulary unknown in ordinary dis- course. The popular interpreter must transform this language into common parlance that will evoke the appropriate images and mobilize the scientifically unaided intuition. It seems to me that for the majority of people, visual media _ the TV documentary - is best suited for this purpose because it can display imagery directly in a more ‘natural’ way than does prose. But for those who like to read, perhaps because it provokes the thinking process itself, books such as this provide a useful and entertaining introduction to important works of the mind.