CHAOS THEORY: INTERFACE WITH JUNGIAN PSYCHOLOGY

by Gerald Schueler, Ph.D. © 1997

Introduction.

Peat (1988) acknowledges one of today's foremost problems. He says that science has developed an increasing tendency to fragment knowledge and experience into various areas of specialization. This situation of fragmenting knowledge extends today into the areas of economics, sociology, psychology, practical government, and human relationships. Many of our current problems, especially in the areas of health care, agriculture, nuclear energy, and mass communications, are primarily the result of professionals lacking expertise in other areas, and thus failing to see overall patterns which could lead to significant solutions. "It is almost as if the twentieth century had lost its ability to perceive the larger patterns of nature and the broad contexts in which events happen. A particularly significant area of concern is that of the meaning of life and of personal values, subjects that science finds particularly difficult to measure, analyze, and quantify" (Peat, 1988, p 114). Here we see what could be called a significant problem today: if we can't measure it or analyze it in a laboratory, we tend to ignore it or pretend it doesn't exist. This is one result of the domination of science on our assumptions and attitudes today and according to Peat this chaotic fragmentation of knowledge extends into all fields, including economics, sociology, psychology, practical government, and virtually all human relationships. Peat (1988) proposes that the Jungian concept of synchronicity, C. G. Jung's acausal principle of meaningful coincidences, be used to counter this fragmentation because synchronicity "always deals in the widest context and seeks its patterns across boundaries and categories" (p 114).

Fragmentation is not only found in science, but also in psychology. As early as 1970, Royce (1970) addressed the need for a systems approach to psychology. Along this line, Frank (1968) asserted that any study of human and animal behavior must take into account what he called "organized complexities" by which he equates living beings with open complex systems. He describes six interrelated processes that regulate and control every organized complexity: growth, organization, communication, stability, direction, and creation. He also states that while people must interrelate with others, each has their own private "life space" which contains their own private world view and self image.

Somewhat in opposition to Peat's negativism, Ross (1991) says there is currently a great deal of interdisciplinary work going on in the social sciences and in all the humanistic disciplines. Philosophers now analyze novels and poems, for example. Critics historicize the texts they study, and social historians now employ social science theories and methods. The historical fact of the fragmentation of knowledge in our society has been recognized, and interdisciplinary studies have been established to counteract this trend.

Lyon (1992) agrees that we are seeing more and more interdisciplinary knowledge today. Typical university text books, for example, now often contain discourses from other disciplines. She complains, however, that there is no clear understanding of what "interdisciplinary" means. Furthermore, she points out that the gendered language of our culture has identified hard facts and sciences as masculine with sentiment, idealism, and imaginative insight as feminine. While "gender constraints," as she calls them, are more relaxed today, they still exist and must be appropriately dealt with in any true interdisciplinary study. Keller (1985) notes that the pioneers of modern science referred to objectivity, reason, and mind as male, and subjectivity, feeling, and nature as female. She calls this a "deeply rooted popular mythology" that has no basis in fact. She convincingly postulates that this false association, when applied to the concept of science as a form of human reason over nature, has inevitably led to a deep gender gap in which the equivalent argument of male over female is a natural albeit unspoken fallout, effecting all aspects of our culture.

Probably the highest hurdle to surmount, according to Lyon (1992), is the "specialized isolated disciplinary structures" that still currently exist, where those in power see interdisciplinary study as a personal attack upon their authority. Bias is one reason for disciplinary study, and bias can come in many different forms. Most researchers in the US, for example, work on the premise that the bulk of knowledge is generated in this country and eventually flows into other countries. While this assertion, which we could call a national bias, was probably true in some disciplines following World War II, it is not true today and researchers can no longer ignore the work done in foreign countries (Chaudhari, 1992).

Locker (1994) reveals the lack of an interdisciplinary perspective of research in today's world of business communication. She complains that business communication tends to ignore concepts and methods from other disciplines. This "negative attitude toward interdisciplinary research" is caused

by several factors such as the lack of needed time and effort, and the possibility of mistaken interpretations. She proposes several steps that can be taken to make business communication research more interdisciplinary. Her premise and proposed solutions are echoed by Kent (1994). However, Kent adds the existence of a "political barrier" to Locker's causes, stating that researchers have a narrow-minded view that knowledge is the property of specialists. He advises researchers to rise above politics and to expand into other fields. Smeltzer (1994) adds that most researchers have "individual biases" that keep them from an interdisciplinary perspective. One very real problem is the tendency to evaluate articles whose subject matter lies outside of one's area of expertise without first studying that discipline. But interdisciplinary study can pay off, as noted by Lafer (1994) whose 'Truckee River Community Project' involves a successful interdisciplinary hands-on exploration of the Truckee River in Nevada.

The recent success of chaos theory with mathematical repeatable systems has led to many attempts to apply those theories in other disciplines. While some good has come from this, Ruelle (1994) points out that results are not always up to expectations. He notes that the results of scientific or mathematical research must have relevance to our everyday world. The results of modeling real-world systems, for example, are only as good as the models themselves. The mathematical models investigated in chaos theory, for example, cannot be used to explain human behavior because human beings are too complex, and cannot be defined by a set of differential equations.

History.

Shortly after World War II, the US Navy realized the growing fragmentation of knowledge witHin its ranks. To counteract this problem, the Navy gave birth to operations research or what would later be called systems analysis: the concept of a temporary team of experts from various fields working together to solve problems that require expertise in various disciplines. This was so successful, other Defense Department agencies as well as the business and industrial communities that contracted to them soon adopted it and gave birth to the matrix structure of management, which is found throughout the technical world today (Hodge and Anthony, 1991, pp 333-337).

But the idea of interdisciplinary study did not originate with the Navy. According to Klein (1990), the idea is as old as Plato and Aristotle. She points out that the ancient Romans used to argue about the dangers of overspecialization in their educational systems. She gives a detailed account of the evolution of interdisciplinarity throughout this century and notes that the real problem lies in striking the right balance between specialization and integration. She describes a strong momentum building towards interdisciplinarity throughout this century in the United States. Literature on interdisciplinary problem-focused research, for example, began with a single paper in 1951 and grew significantly through the following decades. Today topics include the dynamics of interdisciplinarity and the nature of interdisciplinary theory and method.

Definition.

Although no formal definition of interdisciplinary study has been widely accepted, if it is anything at all, it is a counter to the current fragmentation of knowledge that prevails in virtually all levels of our society today. Unlike the systems analysis approach of a team of experts, interdisciplinary study is an attempt to broaden the perspective of the individual scientist, researcher, educator, engineer, or social worker. Kleig (1990) gives four ways of defining interdisciplinarity: (1) by example, to describe the forms that it can take, (2) by motivation, to explain why it occurs, (3) by principles of interaction, to demonstrate the process of how various disciplines can interact, and (4) by terminological hierarchy, to use labels to distinguish various levels of integration. She acknowledges that these are all legitimate strategies.

According to Kleig (1990), interdisciplinarity implies an integration that can change or enrich each discipline. When disciplines are simply brought together in an additive fashion without integration or enrichment, it is called multidisciplinarity. She lists four kinds of interaction that can occur in the interdisciplinary process: (1) borrowing, (2) solving problems, (3) increased consistency of subjects or methods, and (4) the emergence of a new interdiscipline. At least one of these should be present.

Mathematics.

Mathematics and mathematical modeling are important tools used in many avenues of today's society. Fowkes and Mahony (1994) predict that the trend toward the increased use of mathematical modeling in other disciplines will continue to grow in the future. American industry, for example, has discovered that mathematical modeling is cheaper than experimentation for understanding many industrial processes.

According to Schwartz (1992), Galileo started the rush to mathematics in physics. He discovered that he could get the Church to accept his writings only if he couched his findings in terms of a mathematical theory rather than a direct representation of reality (p 14). Others quickly followed his example. Later, Newton deliberately couched his Principia in mathematics primarily to keep from being pestered by novices (p 20). Whatever their motivations, these forefathers of modern science began a trend toward the use of mathematics that has continued unabated. Today, a scientific paper without mathematics would be unthinkable.

Modern economics, biology, psychology, sociology, geology, and other disciplines such as politics and history all employ mathematical models and embrace statistical analyses. The problem, according to Schwartz, is that there is now so much math, that few can understand what is really being said. He quotes Einstein as lamenting, "Ever since the mathematicians have gotten hold of relativity I myself no longer understand it" (p 30).

Schwartz (1992) points out that mathematics is a language intended to show relationships and was never before used for itself alone as it is today. Mathematics has limitations (most mathematical models, for example, assume simplicity and linearity although our world is complex and nonlinear) and these have been underemphasized and poorly understood (Schwartz, 1992, p 31). Mathematicians have lost sight of practical application or even of usefulness and their "obscurantist mathematical argument" (Schwartz, 1992, p 34) is putting science at too far a distance from the layman; which Schwartz (1992) calls "the inaccessibility of science" (p 38). He argues, "The world is not a machine. It is a complex, historically evolved network of physical, biological, and cultural structures. And the sooner we liberate ourselves from the then liberating, now oppressive mechanical framework of the seventeenth century the better off we will be" (Schwartz, 1992,

p 141). He points out that systems with complex developmental histories are explained very well without mathematics, such as the geological theory of plate tectonics, molecular genetics, and the process of viral replication in bacteria.

Like many others, Schwartz (1992) poses the issue that science is too compartmentalized, and that there is not enough communication between disciplines. Each discipline has "secrets" and they use obscure language which helps to maintain those secrets (Schwartz, 1992, p 178). A very large part of this obscure language is mathematical. Echoing Keeler (1985), he concludes that "by finding out about our science we find out about ourselves" (Schwartz, 1992, p xix).

Interdisciplinary study, on the other hand, can pay off in many ways, not the least being financial. Two physicists while working at the Sante Fe Institute, for an example, learned about economics and how complexity theory could demonstrate financial trends in the market place. They quit their jobs as physicists with the institute and went into economics on their own. They use the techniques derived from the theory of deterministic chaos and of nearly chaotic systems to find regularities in financial markets' fluctuations, and they invest accordingly. So far, they have been very successful (Gell-Mann, 1994, p 48).

We have to remember that mathematics is a language. It expresses relationships between parameters, and nothing more. It is not hocus pocus. It is not infallible. Mathematics per se holds no secret keys to the universe. While the potential of mathematical modeling is obvious for many disciplines, the results of mathematical modeling must be translatable to the real world in which we live. They must make sense. They must have meaning to us. Fowles and Mahony (1994) point out that mathematical ingenuity is not enough because the results must be interpreted correctly and interpretation is generally more important than the mathematics used. Furthermore, the "solution technique" that a scientist will use with a particular mathematical model will often depend on exactly how the problem itself is defined.

Interdisciplinary Education.

Everett (1992) says that rather than expecting the student to adjust to the school, the school should adjust to the individual needs of the student. She points out that this is exactly what is done in interdisciplinary schools.

Holt (1976) calls interdisciplinary schools that help students explore the world as they choose s-chools (the letter s is separated by a hyphen), as opposed to schools that hold students by the threat of jail or poverty, which he calls S-chools (same, but with a capital S). He points out that S-chools cannot be made to get better, and will probably get worse. He also distinguishes between t-eachers (sympathetic teachers who gives children liberty and choices) and T-eachers (teachers who force education according to what others have decided children should know). His argument is that S-chools should be made to become s-chools.

In 1985, a group of Appalachian teachers in Ohio began the Institute for Democracy in Education. The institute promotes school practices that give students experiences in democracy and also supports teachers who give their students democracy in the classrooms (Wood, 1992, p 10). The idea is to let students choose which subjects they want to learn and which materials they want to use. This empowers the students and gives them a sense of control over their lives (Wood, 1992, p 11).

The Graduate School of America operates as a s-chool and it empowers students to direct their own education and to move at their own pace. It has an interdisciplinary studies cirriculum in which the student is encouraged to integrate disciplines of their choice.

Translations from Physics to Social Sciences

The 1977 physics Nobel Prize winner Ilya Prigogine points out that the traditional gap between the "soft" and "hard" sciences is no longer as wide as it was (Nicolis and Prigogine, 1989). "There was a sharp distinction between simple systems, such as studied by physics or chemistry, and complex systems, such as studied in biology and the human sciences" (p 3). This distinction is narrowing, and he suggests that scientists begin studying more complex systems using "new knowledge" such as that recently discovered in chaos theory and complexity theory. He says, "Parallel developments in the thermodynamic theory of irreversible phenomena, in the theory of dynamical systems, and in classical mechanics have converged to show in a compelling way that the gap between 'simple' and 'complex' between 'disorder' and 'order,' is much narrower than previously thought" (Nicolis and Prigogine, 1989 p 8).

Iberall and Soodak (1987) argue that physics should look at living systems. They believe that the basic theories of physics should be extended to link with theories of organization and self-organization. As an example of how this can be accomplished, the authors use the classical hydrodynamic Reynolds number in terms of matter moving through a field which they give as:

Re = V/(/L)

where V is the velocity in a flow field, is the kinematic viscosity of the fluid, and L is a dimensional parameter (usually length) of the field. The classical dimensionless number represents the ratio of inertial forces (external) to viscous forces (internal) for flowing liquids. When Re < 1, the flow is laminar (orderly). When Re > 1, the flow becomes turbulent (chaotic). Mathematically, a bifurcation occurs in the solutions to the governing equations. At Re = 1, a crisis point, the situation is uncertain and unstable.

The concept of Re is extended by the authors who show that the numerator represents a convective velocity, those forces that sweep matter into and through the field (environmental influences) while the denominator is a diffusional velocity such as the rate of transport of momentum or rate of heat flow (internal influences). The classical equation is extended as:

Re = V(convection) / V(diffusion)

This form of the equation addresses whether or not the energy associated with the global convection velocity can be absorbed into the internal energy at the atomic level by some diffusive process. If not, the field becomes unstable and a new structured form or pattern emerges. The authors point out that convective field processes compete with local diffusion transports. Furthermore, a diffusive process may be momentum diffusivity or some other dominant mode of diffusion such as electrical, thermal, or chemical. In this way, the idea of Re can be transferred into other areas besides fluid flow, such as chemical patterns and even social patterns. "The generalized Reynolds number criterion for emergence can even be applied to the nucleation of people into urban settlements in the post-Neolithic period" (Iberall and Soodak, 1987, p 508).

In psychology, this equation can be reworded as:

Re = sensory data / data assimilation

Unfortunately, psychological data are usually qualitative rather than quantitative, and thus numerical generation is difficult or impossible. However, the equation can be used to address a qualitative analysis because it suggests that Re will be greater than 1 whenever a person's sensory data overloads the ability for assimilation. This is to say, whenever data are presented to us that cannot be assimilated into our world view or belief system. A psychological name for this occurrence (i.e., for Re > 1) is a significant emotional event. Such events will either result in a breakdown of the psyche (e.g., cognitive dissonance) or to a change in the psyche's world view. They usually cannot be ignored with impunity.

Synchronicity.

The psychologist Carl Jung and the physicist Wolfgang Pauli together devised the concept of synchronicity, which can be seen as a marriage between physics and psychology (Peat, 1987). A synchronicity is defined as a meaningful coincidence, but the theory devised by Jung and Pauli has very wide implications. It suggests, for example, that the inner world of the psyche (subjectivity) and the outer world of matter (objectivity) are a syzygy (Jung borrowed this term from the Gnostic concept of a duality, or two complementary entities or forces whose natures are polar opposites of each other). Jung's collective unconscious, which lies 'below' the levels of our individual or personal unconscious contains only collective contents and is objective to the individual psyche perceiving it. Thus, in Jung's psychology, the subjective ego (which is a component of the psyche) looks outward at the physical objective world of matter, at the spacetime continuum of relativity physics, while the psyche looks inward at another external world, a psychic spacetime continuum. In this regard, Jung mentions "the psychically relative space-time continuum that is characteristic of the unconscious as such" (Jung, 1959, p 24). We cannot view this psychic continuum directly, but rather see it only through its projections in the form of images, dreams, fantasies, and myths. when something is observed in both continuums (related objective events) and is considered to be meaningful in some way by the observer (a purely subjective call) we have a synchronicity that can be considered as a temporary local merger of the two continuums. The concept of synchronicity, developed by a physicist and a

psychologist, can therefore be used as a vehicle through which the two disciplines can be interrelated (this interpretation of synchronicity is not universally accepted today by Jungian psychologists).

A Personal View of Interdisciplinarity.

I am interested in the interdisciplinary study of chaos theory and Jungian psychology. Kellert (1993) defines chaos theory as

"the qualitative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems" (p 2). He defines a dynamical system as one that varies over time. Aperiodic behavior occurs when defining variables do not have repeating values. Systems that are deterministic have behavior that can generally be mathematically simulated by five or less differential equations. Chaos theory also looks at complex systems, which can be defined as dynamic systems with a large number of interacting parts. From the foregoing, we can conclude that chaos theory uses mathematics to address the behavior of complex changing systems.

According to Jung (1959), the ego is not simple, but complex and "cannot be described exhaustively" (p 3). Furthermore, the ego rests on both a somatic and psychic basis and establishes itself as a component of the psyche. It develops from the friction that is generated between the body and its environment shortly after birth, and grows throughout one's lifetime because "once established as a subject, it goes on developing from further collisions with the outer world and the inner." (Jung, 1959, p 5). Jung defines the ego as a part of the psyche (that part which is conscious) which, in turn, is part of the self which he defines as the "total personality."

If we make the assumption that the psyche is a complex system, many of the principles in chaos theory relating to complex systems should be applicable to the psyche. However, the mathematics of chaos theory will certainly not be transportable because of the complexity of the psyche relative to those simpler systems described through mathematical relationships. The behavior of the human psyche, or ego for that matter, has yet to be defined in terms of differential equations. However, we could expect some qualitative comparisons to be transported in a useful manner.

As a personal approach to this subject of study, I will look for areas of similarity while avoiding direct mathematical translations. For example, at the outset it appears that the strange attractors described in chaos theory could relate to Jung's archetypes of the collective unconscious in several important ways. Chaos theory describes a strange attractor as something that can attract a stable system into regions of instable functioning. Jung says that archetypes can approach the psyche, giving us strange dreams for instance, and unless assimilated by the ego they can attract us into various kinds of neurotic behaviors. There could also be a relationship between the 'life space' of psychology (the personal state or condition of a human being) and the 'phase space' of chaos theory (the state or condition of a complex system). I will also be concerned about gender differences in that the psyche and unconscious are usually depicted as feminine while the ego and the conscious are usually seen as masculine. Lastly, I will attempt to be truly interdisciplinary (integrative) rather than multidisciplinary (additive).

References.

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Chaudhari, P. (1992). Complexity and materials research. Physics Today. Oct. 22-23.

Everett, M. (1992). Interdisciplinary schools for the 21st century. Education Digest. v57. n7. 57-60.

Fowles, N.D., & Mahony, J.J. (1994). An introduction to mathematical modeling. Chinchester, England: John Wiley & Sons.

Frank, L.K. (1968). Organized Complexities, in Royce, J. R. (Ed.) (1970). Toward Unification in Psychology: The First Banff Conference on Theoretical Psychology. Toronto: University of Toronto Press.

Gell-Mann, M. (1994). The quark and the jaguar: Adventures in the simple and the complex. New York: W.H. Freeman and Co.

Hodge, B.J., & Anthony, W.P. (1991). Organizational theory: A strategic approach. Fourth Edition. Boston: Allyn and Bacon.

Iberall, A. S., & Soodak, H. "A physics for complex systems." in Yates, F. E. (Ed.) (1987). Self-organizing systems: The emergence of order. New York: Plenum Press.

Jung, C.G. (1959). Aion: Researches into the phenomenology of the self. Hull, R.F.C. (Trans). Bollingen Series XX, Vol 9, Part 2. Princeton, NJ: Princeton University Press.

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Kellert, S. H. (1993). In the wake of chaos: Unpredictable order in dynamical systems. Chicago: The University of Chicago Press.

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Lafer, S. (1994). The familiar made curious: A case for hometown interdisciplinary studies. English Journal. v83. n1. 14-21.

Lyon, A. (1992). Interdisciplinarity: giving up territory. College English. v54. n6. 681-694.

Nicolis G., & Prigogine, I. (1989). Exploring complexity: An introduction. New York: W.H. Freeman and Co.

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Ruelle, D. (1994). Where can one hope to profitably apply the ideas of chaos? Physics Today. July 94 pp 24-30.

Ross, D. (1991). Against canons: Liberating the social sciences. Society. v29. n1. 10-15.

Royce, J.R. (Ed.) (1970). Toward Unification in Psychology: The First Banff Conference on Theoretical Psychology. Toronto: University of Toronto Press.

Schwartz, J. (1992). The creative moment: How science made itself alien to modern culture. New York: HarperCollins.

Smeltzer, L.R. (1994). Confessions of a researcher: A reply to Kitty Locker. Journal of Business Communication. v31. n2. 157-160.

Wood, G.H. (1992). Schools that work: America's most innovative public education programs. New York: Dutton.

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