Running head: CHAOS THEORY AND COUNSELING PSYCHOLOGY
Chaos Theory and Its Implications for Counseling Psychology
Department of Educational and Counseling Psychology
University of Kentucky
February 20, 2003
Individuals and groups are dynamical systems that generate patterns of behaviors, thoughts, feelings, and interactions. Chaos Theory (ChT), based on a mathematical approach to the non-linear, non-independent modeling, concerns these patterns. ChT has important insights to offer Counseling Psychologists, and implications for the conduct of psychology as a whole. Counseling Psychologists should have a basic, working knowledge of ChT--its impact and implications. In the present exposition I give a mathematical and conceptual overview of ChT and relate it to the definition and mission of Counseling Psychology. Using these bases, implications for theory, research, practice and training are discussed and problems of and suggestions for incorporation of ChT in the conduct of Counseling Psychology addressed.
Chaos Theory and Its Implications for Counseling Psychology
People, individuals and groups, are dynamical systems. Their actions and their interactions generate patterns. Chaos Theory (ChT) 1 concerns the patterns generated by dynamical systems. It is based on a mathematical approach to the non-linear, non-independent modeling of patterns of behavior. ChT has important insights to offer Counseling Psychologists, and more important, implications for the conduct of psychology as a whole.
ChT is not, per se, a philosophical system or paradigm. In fact, it is as non-biased as any mathematical approach can be—which is not to say that it is without its assumptions. While ChT is not biased, I am. My bias will come into play more because I am applying the insights derived from ChT as I see them than actually applying ChT—or dynamical systems modeling--itself. This type of application is not without precedent. Even the Vatican is interested in the ramifications of ChT for religious doctrine (Russell, Murphy, & Peacocke, 1995).
Personally, I think everyone—professional psychologists, other social and physical scientists, and even lay-people--should have a basic, working knowledge of ChT and its impact and implications. My contention is that that background is essential to understanding and effectively functioning in the world--and certainly to helping people, if not also just being one. In fact, these implications are so far-reaching they go even to the core of how we approach psychology. I will attempt, and I trust succeed, in convincing you likewise.
Many, if not all, the concepts that constitute chaos theory are not new. They have been around for quite some time in one form or another. In fact, you would recognize them in sayings, adages, and the like. For example, “for want of a nail the shoe was lost, for want…” Their juxtaposition and connection, the development of concise, scientific language and terms to define their related constructs, and, most important, the application of concrete, systematic, logical mathematical procedures to substantiate them lend them new validity, credibility, and clout—or should.
Let’s start with a most basic question, “Why do I believe ChT applies to psychology at all?” Mathematical models as applied in other disciplines focus on the modeling of patterns of behavior, with the subsequent goal of predicting, if not controlling them. That description would seem to fit much of psychology rather well. However, psychology in general, and Counseling Psychology in particular, is not limited to patterns of behavior. We also deal with patterns of feelings, thoughts, and interpersonal interactions. These phenomena are more challenging to address because the data available to do so are usually, if not always, both difficult to produce and of a less than optimal, solid, ratio-scale type. This situation leads to asking whether ChT does and can apply. And that argument is grounded more in logic than in empirical evidence, at least for those latter three areas.
To start we need to look at what ChT is mathematically. We also need to look at the assumptions about patterns of behaviors, thoughts, feelings, and interactions, on which psychology is founded. Then we must look at the match—briefly.
Context: Explanation, Limitations, and Apology
Before we start I want to talk briefly about our parameters and assumptions concerning this presentation. In particular, the assumptions regarding what is being offered need to be clear, so we are operating in the same mode. Otherwise this experience will be frustrating for all involved.
First, space is limited. To do a complete job, addressing many of the questions and mathematical background needed, would take a book, if not books. In fact, it already has (e.g., Devaney, 1989; Gregersen & Sailer, 1993; Kiel & Elliott, 1997; Nagashima & Baba, 1999). No extensive attempt is made to provide a mathematical derivation, although some mathematical notation is included. Rather, this exposition is a “translation” to the psychological context, and a limited one at that. Books are available to take you as deep as you want to or can go into the mathematics. Some will be referenced and noted along the way.
Second, you likely are not a mathematician. If not you cannot and do not want to get into those types of details—trust me. For some that will mean being unsatisfied with the level or detail of the explanations presented; for others it will mean being lost with what is. For most, hopefully, you will catch the gist and be satisfied—having some further curiosity and some relief with the information provided. For this end to attain, some “translation” is necessary, almost to the point of the explanation seeming more metaphorical than concrete at times. Take my word as a former almost mathematician, you do not want to—and cannot—go into the full mathematics process. It goes on forever. That is what mathematicians are for.
Third, I am not a mathematician. I have a degree in mathematics and likely know more mathematics than 99.9% of the population and 99% of those of you reading. But I do not spend my time doing mathematics as a mathematician does—pushing the understandings and abstractions deeper and deeper. Like a prescribing psychologist, who is not a physician, who is not a pharmocologist, who is not a chemist… I think I know enough to convey what is needed at the level you need it presented to understand and use.
Frankly, I do not know the mathematics as well as do others. Nor as well as I might. I keep learning more, which is why I study the area and call myself a chaotician, not a mathematician. I was trained as a mathematician. I am not talking about arithmetic, or statistics, but mathematics. Few people really grasp what true, theoretical mathematicians do—or want that experience. It was beyond my capabilities, and definitely beyond my desire to develop them. I suspect even more so for you. I stopped being a mathematician, but I do have more in-depth training than many, if not most, people in general and psychologists in particular. Much of the mathematics related to ChT--fractal geometry, complex analysis, even true mathematical probability theory--is beyond me, despite having read the texts. Sometimes, when I say something to you, you are going to ask “why.” At times, honestly, I will not know while others, even at my or our level, may. We all know bits and pieces others do not. Such is the nature of explanation and the dialectical process, from a ChT perspective among others (e.g., Remer, 2002a, 2003a). At other times I may “know,” but will not have the time or space to explain fully here. But I am a Counseling Psychologist—not even a quantitative psychologist--interpreting and using the works and understandings of others, in my discipline—or sub-discipline. I think I know “enough for now” to offer relevant and helpful links to the schemata you possess, and that is education. After this introduction, I hope you will want to steep yourself in ChT and related areas.
The bottom line is that for these, and perhaps other, reasons this exposition is not a mathematical text. It is “close enough.” As ChT implies, and we shall see, “close enough” is all we can expect in our basin of attraction. Having digressed and said what I needed to say, back to the task at hand.