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.Dr Arthur L. Loeb is Senior Lecturer on Visual and Environmental Studies, Curator of the Teaching Collection in the Carpenter Centre for the Visual Arts, and Acting Master of Dudley House, Harvard University. He was born in The Netherlands and educated in the United States at the University of Pennsylvania and Harvard University. His doctorate is in Chemical Physics, but through his research contact with Gyorgy Kepes, M. C. Escher and R. Buckminster Fuller, he has been able to embrace the whole spectrum of design. His 40 or so publications show his expertize as well as his exceptional ability in combining the compatible aspects of the arts and the sciences. Prior to his appointment at Harvard University he has been an Associate Professor of Electrical Engineering at the Massachusetts Institute of Technology and Staff Scientist at the Kennecott Copper Company.