"Presidents who overanalyze fail, while those whooversimplify succeed."

— John Allen Paulos

"A Mathematician Reads the Newspaper"

The Complexity Horizon

Mr. Paulos [author of "Innumeracy"] uses the quotation above onlyas suggestive, not necessarily a truism. Certainly it seems to be the case whenwe consider the popularity of those presidents who oversimplified (Reagan, F. D.Roosevelt) and the lesser popularity of those who overanalyzed (Jimmy Carter).

The quotation was relevant to Paulos' discussion of complexity horizons: aconcept we can all use. What it means is that every subject has a certain degreeof complexity, below which the subject can be understood, but above which thesubject is impossible to comprehend.

Some subjects can be compressed; that is, brought down to a small number offundamental elements, sufficiently to be comprehensible (i.e., how to drive acar). Others can not (i.e., the origin of life). People, as well as subjects,differ in their complexity horizons. You might find quantum theory beyond yourcomplexity horizon, while dog training is not. For some ivory tower thinkers,the reverse could be true. Try to explain economic theory to a native of theAfrican bush who is familiar mostly with barter, and you would find it beyondhis complexity horizon. It can not be compressed to terms he could understand,because its essence would be lost.

A good example of compression sufficient to bring a subject within ourcomplexity horizon is the newspaper story. A journalist must investigate a storywhich may have many complexities, but compress it to terms understandable by theaverage reader. In the process, some subtleties will inevitably be lost, but agood reporter will extract the essentials and make the subject understandable —though not necessarily accurate. [Ask any reporter]

Not all subjects, however well reported, are susceptible to realisticcompression. Here is where the sophistication of the reader comes in. A readermust judge the complexity of a story, the access of the reporter to evidence,the degree to which that evidence is valid, the credibility of the reporter'ssources, and many other factors. Not many do it well. Schools do not train us incritical thinking; today, politically correct "thinking" is in vogue,which subordinates accuracy to results. Part of this comes from our custom ofrelying on the media for information, when in fact, much of what we hear iserroneous and all of it is distorted to some degree.

Then, too, there is personal prejudice, which causes all of us (yes, you andme both) to slant information in a way favorable to our interests.

Many, if not most, of us tend to overestimate our complexity horizon. Wehold strong political views based on certain known bits of information placedinto our own limited experience. Thinking of the names "Clinton" and "Dole"will probably bring a definite opinion as to their presidential capabilities.Which of the two would in fact be a better president has so many complexvariables, no one can really do more than reiterate prejudices. The subject istruly beyond our complexity horizon.

So, in fact, is much of the information given us about risk management. Weread about what firm is a better insurance broker, the extent of self-insurance,the cost of risk for various industries, the causes of workers compensation costchanges, the costs of pollution cleanup, the effects of our tort liabilitysystem, and so on and on. Though the figures issue from sincere and capablepeople with prestigious firms, they have little substance. Though the s. and c.people don't usually know it, the issues are beyond their complexity horizons.

Copyright © 1996 by David Warren
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