PART I

Introduction

            The Swiss psychologist, Carl G. Jung, occasionally lamented that psychological parameters were not measurable and that mathematics was not used in psychology. He was very interdisciplinary and combined science and psychology where he could. However, Jung (1981) noted that the human mind has an inherent numerical capability; number, he said, was archetypal. This paradox implies, that while the human mind has devised sophisticated mathematics for use with external objects, it has not yet devised a mathematical system for itself. Because of this, psychology is usually referred to as a soft science, as opposed to physics, for example, which is called a hard science because it is measurable and uses mathematics. 

            Today, the lack of a scientific method in psychology is being addressed by a new scientific discipline called chaos theory. Chaos theory is being used to address all kinds of interdisciplinary avenues. Basically it is a science of self-organizing or living systems and these complex systems do not have to be entirely physical.  Today, chaos theory is successfully being applied to psychology (Blackerby, 1993; Butz, 1997; Kelso, 1999; Robertson & Combs, 1995; Walker, 2000)

            The essential finding of chaos theory is that order can come out of chaos. The theory, which is highly mathematical, tries to find potential or hidden order in what often appears to be chaotic or random data. For example, chaos theory has been used, with varying degrees of success, to address the stock market, population, history, biology, and many other areas outside of the physics laboratory. More recently, it has been used to consider the human mind as a complex system, which is also our goal here (Blackerby, 1993; van Eenwyk, 1997; Wieland-Burstan, 1992; Walker, 2000).

             Chaos theory appears to be the most promising method to bring science and psychology together. Once the human mind, or psyche as Jung preferred to call it, is seen to be an open, complex system, then some of the mathematics and principles of chaos theory can be applied to the psyche.

             This work is an attempt to define Jung's psyche as a complex dynamic system and transpose to it some of the basic principles of chaos theory. When we do this, we find that the psyche is very similar to the physical body. It builds up entropy and then dissipates it. It is sensitive to initial conditions, has sensitive decision points, and can be drawn into unstable conditions. Furthermore, the psyche is fundamentally unpredictable because part of its functioning is probabilistic in nature. Consciousness, which Jung equates to the ego as a component of the psyche, is also a complex.

            With the descriptions in hand, of Jung’s psyche and the findings of chaos theory, we can develop a two-dimensional mathematical construct called a phase space for the ego which leads us to several basic psychological ordering parameters which then can be related by the use of suitable mathematical equations. In this way a framework for at least some rudimentary mathematics can be developed for the psyche.