Among the basic ideas explored by GERG members are dynamical versions of the fundamental tenets of general systems theory, especially those pertaining to evolution of course, such as morphogenesis, pattern formation, self-organization, autopoesis, autocatalysis, and so on. In this view, culture is in a process of self-organization. This process of social morphogenesis, also known as world cultural history, has smooth phases punctuated by bifurcations, like any dynamical process. According to the dynamical way of thinking we have learned from chaos theory and the new mathematics, these occasional bifurcations are the hinges of history, the special times of social meltdown when small intentional actions may produce major results. This perspective is what we mean by the bifurcation paradigm. In short, we are now in the midst of a major bifurcation of history, and as well, a fabulous window of opportunity. Thus the bifurcation paradigm is equal to the creative posture multiplied by a mathematically informed optimism.