I don’t know what there is about the idea of risk and the people who think and write about it. Perhaps it’s that the analysis of risk inevitably leads to an epistemological abyss. Whatever the case, the idea of risk seems to attract the most imaginative, philosophically minded, even humorous writers. Michael R. Powers falls squarely within this group. His Acts of God and Man: Ruminations on Risk and Insurance (Columbia University Press, 2012) is a challenging book but definitely worth the intellectual effort necessary to read it.
In this post I’m going to concentrate on two chapters, “What Is Randomness?” and, more briefly, “Patterns, Real and Imagined.”
Common examples of presumed randomness include stock prices, coin tosses, weather patterns, and industrial accidents. “The most salient aspect of these and similar phenomena is their unpredictability; that is, they are unknown ahead of time and generally cannot be forecast with anything approaching perfect accuracy. There are, however, certain limited circumstances under which such phenomena can be predicted reasonably well: those in which the forecaster possesses what financial traders might call ‘insider’ information.” (p. 178) For example, a magician who is skilled at tossing coins may be reasonably certain that his next coin toss will come up heads.
Powers calls any uncertainty that can be eliminated by means of “insider” information (that is, “any and all information potentially available to the most privileged, persistent, and conscientious observer, whether or not such an observer exists in practice”) as knowable complexity (KC). “Any residual uncertainty, which cannot be dispelled by even the ideal observer, will be called unknowable complexity (UC).” Powers equates UC with true randomness.
It doesn’t take a great leap of faith (indeed, Chaitin’s work on incompressible sequences of integers, specifically his impossibility theorem, takes us most of the way) to show that “no systematic approach to the study of randomness can ever: (1) confirm a source of uncertainty as UC; or (2) confirm some sources of uncertainty as KC without inevitably creating type-2 errors in other contexts. These are the cognitive constraints under which we operate.” (p. 187)
Moving from theory to practice, the author points to one of the empirical problems of randomness traders face every day: trying to separate signals from noise. This problem often manifests itself in the phenomenon of pareidolia, “in which a person believes that he or she sees systematic patterns in disordered and possibly entirely random data.” Powers doesn’t have a workable solution to this problem, and he finds the meta-problem also lacking a satisfactory answer: “Rather ironically, the line between the overidentification and underidentification of patterns is one pattern that tends to be underidentified. In addition to dubious uses of data in pseudoscientific pursuits such as numerology and astrology, there also are various quasi-scientific methods, such as the Elliott wave principle employed by some financial analysts and neurolinguistic programming methods of business managers and communication facilitators that haunt the boundary of the scientific and the fanciful.” (p. 192)
Some reviewers have described Powers’ work as idiosyncratic, which, we know, is a fancy way of saying half-baked or crazy. But how much more satisfying it is to read the so-called idiosyncratic than the mundane.