In Conclusion

            The mathematics presented here are purely theoretical; a series of mathematical statements based on the definition of Jung’s psyche as a complex dissipative system.  Someday they may be verified by experiment and the ordering parameters of the psyche may be measurable. Until then we must remember that the interface of chaos theory and psychology is still in its infancy. Jungian psychology is especially susceptible to this interface because Jung himself considered the joining of science and psychology to be of paramount importance and he deliberately formed many of his definitions and ideas with this interface in mind. Unfortunately he was not aware of modern chaos theory, which was just coming onto the scene at the time of his death. 

            Because Jung defined the psyche as a complex interfacing of ego consciousness, personal unconscious, and collective unconscious we are able to create a two-dimensional phase space for the ego trajectory as it goes through life. We then equate archetypes with chaotic attractors and developmental tasks and other sensitive decision points with bifurcations.

            Jung tried to fit energy and entropy into his definitions using the scientific terminology at the time. Today we can go a few steps further because we now have Prigogine’s entropy and uncertainty. By applying chaos theory to Jung’s psyche we can conclude that the ego has four primary states in which entropy can increase and decrease thus maintaining the ego as a dissipative system.

            The ego goes through life attracted and repelled by the archetypes, undergoes developmental and other bifurcations, is subject to a wide range of perturbations that could lead to instability, and spends most of its time in far-from-equilibrium conditions.  Our conscious awareness continually oscillates outward into the world and inward into the personal unconscious in an attempt to assimilate both domains.

            Life, according to Jungian psychology, is not without meaning. In fact, meaning or intensity is an integral part of what we define here as psychic mass. The ego is alive or self-aware in direct proportion to its sense of meaning. The primary meaning or purpose of the ego trajectory through life is the individuation process. As we have seen, this encompasses a sense of individuality together with the development of psychic balance.  It also includes the sharpening of a strong self-image and the maintenance of a meaningful worldview, both of which must be flexible enough to assimilate new experiences.

            Jung was disappointed that psychology seemed to be completely unsuitable for mathematics. This book represents a preliminary attempt to rectify this situation, at least in a perfunctory fashion. Mathematics, after all, is little more than a language of symbols; a symbolic way of demonstrating relationships. Once we have defined our psychological ordering parameters, we can use mathematics to describe their relationships even though we currently lack the means to quantify these parameters. We have used Jung’s ordering parameters whenever possible, and have invented new ones only where necessary. It is our hope that the introductory material presented here will inspire others to further this effort.