Gray's Epicyclical Evolution

Abstract

KROEBER] Gray's Epicyclical Evolution 2 An appendix provides the name lists on which this curve is based, with a description of my premises and procedures in constructing them. For much of the format of this graph and my sym­ bolism, as for criticism and encouragement in general, I am indebted to A. L. Kroeber of the Uni­ versity of California. In his pioneering Configurations of Culture Growth, Kroeber failed to discern any pattern in the arts and sciences studied separately, whereas my study indicates a pattern when they are taken as a whole. When and in which of the arts and sciences genius would emerge appeared random, but the totality of genius in any particular time appeared not random but de­ termined. REFERENCES CITED B. FARRINGTON 1949 Greek Science, 2 vols. New York, Penguin Books. M. ROSTOVTZEFF 1927 Social and Economic History of the Roman Empire. Oxford, Clarendon Press. 1941 Social and Economic History of the Hellenistic Age, 3 vols. Oxford Clarendon Press. Gray's Epicydical Evolu.tion A. L. KROEBER University of California, Berkeley that his I SUGGESTED to Gray Evolution style was overcompact for his subject mat­ ter in The Epicyclical of Graeco-Roman Civilization, and that his manuscript might find easier and wider comprehension if he could make it more redundant. He answered that he did not know how; perhaps if he became polemical in a future article, he might be able to amplify. My function in this comment on or complement to his paper is first to sup­ ply the needed redundancy, and second to point out certain relations of Gray's thought to that of others and to the basic problems involved. Epicyclical here has nothing to do with mathematics. There is nothing more mathematical in Gray's paper than counting. In astronomy an epicycle is the path of a circle that spins on an axle which rotates around the circumference of another circle. A point in the peripheral or epicyclic circle is therefore sometimes outside and sometimes inside the basic circle. This is not a picture of what Gray is formulating. A related meaning is that of cycle or cyclic, which denotes not com­ plete revolutions around a fixed center or the perimeter of a circle, but repeti­ tive waves, like the up-and-down recurrent cycloid curves traced by a point on a wheel rolling on a plane. From this seems to come the derivative meaning of cycle as the recurrent period of cycloid or other curves. These two mean­ ings of wave and period are often confused with each other and can be confused with epicycle. This' fact has led to many ambiguities, like cycles of history. Gray's epicycles I think would technically be epicycloids, that is, cycloid or near-cycloid curves superimposed on a circle or part of its perimeter instead of on a straight line. The epicycloid starts in contact with the basic circle or