Growth of Western Civilization: Epicyclical or Exponential?

REPORTS AND COMMENTS Growth of Western Civilization: Epicyclical or Exponential? REIN TAAGEPERA BENJAMIN N. COLBY University of Calqornia, Irvine In a series of papers inspired by Kroeber’s Configurations of Culture Growth (1944), Ed- ward Gray presents some quantified indices of creativity that he relates to the rise and decline of Graeco-Roman and more recent European civilizations. Creativity is measured by grading philosophers, painters, sculptors, poets, drama- tists, and other writers on an evaluational scale derived from the commentaries of historians and classical scholars. He also presents an epicyclical model with different economic and political cycles moving in concord or discord. Thus, one cycle might decline while another rises, or all cycles might rise or decline in har- mony. For example the “developed’ and “flores- cent” stages of all the Graeco-Roman cycles coincide twice. These are the Periclean and Alexandrian Museum periods, both generally considered high points of Greek creative civiliza- tion. Gray then examines the course of modern Western civilization with the same type of epicy- clical model. His overall economic cycle begins with a guild system, moves into a mercantile, in- dustrial, and finally a monopolistic economic system. Superimposed on this cycle are two social cycles and four political cycles. Creativity for the political period that he calls the Developed Imperialist State is somewhat higher than would have been “predicted” by the regularity of his model, but the other peaks of empirical data seem to fit his model. Though a number of negative comments have been published in the A A (Di Pietro 1973; Winfree 1974) concerning Gray’s attempt to quantify creativity, they have been directed at the issue of whether creativity is measurable and, if so, whether Gray’s measuring techniques are suitable. We tentatively accept Gray’s ad- mittedly crude measure of creativity (with qualifications that need not be mentioned here), but raise a more fundamental question. The neatly cyclical creativity curve that Gray (1966) presents for Western civilization is an ar- tifact resulting from improper plotting tech- nique. Gray uses unequal time intervals for counting creative persons; then he plots the histogram of periods (which now are shown to be equal) with- out correcting for inequality of periods. Not sur- prisingly, relatively short periods show relatively few creative persons. It so happens that Gray tends to pick shorter periods when he expects little creativity, and longer periods when he ex- pects a peak (see Table I). By subdividing his peak periods and lumping his valley periods, one could obtain any pattern one wants. The proper (i.e.. unarbitrary) way to plot Gray’s interesting data is, of course, first to calculate the average creativity per year, by dividing the number of creativity points by the number of years in the interval. When these values (also shown in Table I) are plotted against time (see Figure l), they show not cycles but an accelerating increase. In order to test whether this increase tends to follow the ex- ponential pattern, the same data are reylotted on semilog paper where exponential curves ap- pear as straight lines (see Figure 2). The pat- tern, indeed, can be approximated by a straight line (on semilog paper), corresponding to the equation c = 0.7 ,0.006 (t - 1000) where C is creativity (number per year of creative persons of classes 1 to 7, weighted by relative importance), t is time in years A.D., and e is the basis of natural logarithms. The “rate constant” of 0.006 per year expresses the relative rate of increase in creativity over time: on the average, Gray’s creativity index has grown by 0.6% per year since 850 A.D. The constants are purposely given with one-place precision only, because data reproducibility is not likely to warrant more precision. Linear cor- relation P is visibly over .90, a feature that is common (and thus of little interest) in time se- ries (in contrast to a set of mutually indepen- dent data points). Once the general exponential trend has been accounted for, we can start looking for possible systematic deviations of the actual curve from the trend line. The only peaks clearly above the trend line (in Figure 2) occur around1400- 1620, and possibly 1850-70 and 1890-1910; the latter are questionable because it is often hard to bracket the creative period of a genius with 20 years’ precision. The only valleys clearly below the trend line occur in 1150-1400, 1650- 1790, and possibly 1870-90 (again with reserva- tions regarding 20 years’ precision). The peaks and valleys hypothesized (and found) by Gray are shown respectively by up- ward and downward arrows in Figure 2. The ex- pected 850-1000 valley is actually seen to be a