Synergy, sigmoids and the seventh-year trifurcation

Summary

Whereas linear and exponential growth have become relatively familiar metaphors, second-order growth processes, as exemplified by autocatalytic chemical reactions, have not yet entered the vernacular. Derek J. de Solla Price has discussed sigmoid growth, but described it as a three-phase process. It is shown here that these three phases are more apparent than real, with initial slow growth, intermediate rapid growth and ultimate saturation all characteristic of the same second-order process. A model, arrived at by the superposition of several sigmoid curves, is proposed for the periodic critical decision points which occur during the course of a career or the life time of an organization. These decision points correspond to a trifurcation, leading to renewed sigmoidal growth, saturation, or a rapid phase-out.