By John L. Casti. New York: William Morrow, 1990. 496.
A good scientific theory must not only explain phenomena but also make valid predictions; General relativity, Newtonian mechanics, and Quantum mechanics (QM), all within their own realms, satisfy both conditions. Based on such “success stories” the rationality of the natural world might be concluded (for even “God’s dice playing” in QM, bound by the laws of probability, allows levels of prediction); rather, one should turn matters around and realize that the rationality of the world is an assumption, one that makes normal science possible. Hume posited causality, for example, as a subjective heuristic based upon experience; Kant instead explained it, as well as time and space, as an a priori category, one necessary to human perception and experience, yet not necessarily an accurate portrayal of the world as it is.
Thus human projects of all sorts endeavor to seek patterns and to find hidden order in the world; order is natural and chaos degenerate: we have mysticism, astrology, comparisons of the macro- and microcosm, classical aesthetics, most mythologies and religions, and even most scientific theories. LaPlace has gone down in history for his remark to the effect that if a being were to know the starting conditions of the universe, by applying deterministic scientific laws, “nothing would be uncertain, and the future as the past would be present to its eyes.” That is to say, an inability to predict the future lies merely with either our faulty theories or with our faulty faculties of reason and perception.
In a highly readable fashion John L. Casti’s Searching for Certainty employs numerous practical case studies that both explode the notions of our current potential to explain and predict as well as demonstrate systemic limits to obtaining perfect knowledge. Casti first provides an overview to the topics of chance, causality, and chaos, and then applies these to the weather, biological forms and evolution, the stock market, wars, and mathematics. He avoids the sensationalism that often accompanies “chaos theory” and “catastrophy theory” (sensationalistic titles that garner more attention than bland “non-linear dynamics”), and handily navigates concrete examples and theoretical rigor in a way that reasonably ties together such seemingly disparate case studies. And like Heinz Pagels in The Cosmic Code Casti uses a “definition” of randomness that is really a heuristic: true randomness cannot be beat.
While the author’s wit lightens dense passages in the prose, at times the chapters (of which there are only six) seem to go on forever; the detail with which Casti delves into theories about the outbreak of war is stifling. Similarly, his somewhat top-down (or at least, not bottom-up) explanation of Gödel’s Incompleteness Theorem is far less accessible than that in the book to which any book like Casti’s must be compared: Hofstadter’s Gödel, Escher, Bach (GEB).
Casti described GEB as “an entire humanistic education between the covers of a single book”—more importantly, it is a synthetic work, one that describes how order is to be found in complex systems, and how recursion, a specific type of order, plays such an important role in art, music, math, and perhaps even intelligence. Casti’s goal is not quite so grandiose, and his topic is not recursion, but chaos, something that is a misnomer of sorts, since the mathematics of chaotic systems is anything but chaotic, being instead deterministic in a non-linear, non-continuous fashion. At the same time, while Hofstadter touches upon chaotic systems in GEB when dealing with recursion, dealing with chaos theory necessitates dealing with certain levels of recursion. This is most beautifully illustrated, quite literally, in the chapter on biological forms. The strength of the chapter on stock market prediction is not mathematical formalism, but rather the historical anecdotes that inform the analysis and open the reader’s eyes to how things work.
Many books have a single narrative or theme that develops bit-by-bit from the beginning until the end; others are eclectic collections of fascinating tid-bits, little chests of curiosities; others, such as GEB, weave these two methods together seemlessly. While not as elegant as its “predecessor,” Searching for Certainty is also the third sort of book, and the author’s wit, erudition, and honesty make up for any faults—it is truly delightful and worth reading.