Tuesday, March 13, 2007

Chaos and Personality: A Hypothetical Model of the Mind (1991)

[Author's Note: I wrote this paper in 1991 for the Paracollege program at St. Olaf College, where I received my undergraduate degree. I've been wanting to make it available online for some time, not necessarily because I agree with its conclusions almost 16 years later, but because it was my first attempt to assemble a model of how the mind works and because some of the ideas presented are proto-versions of ideas that are important to my operant model of magick. These days, my thoughts on the working of the mind run more along the lines outlined in The End of the Unconscious Mind, and unfortunately the Jungian model that I use in this paper does not stand up well to the elimination of the Freudian unconscious. Still, the model does provide some insight into my thought processes that have been developing over the course of the last twenty years. And yes, it's long. You have been warned.]


The mind has been the object of a great deal of speculation for a very long time. Only recently, chaos theory, a new movement in mathematics, has provided solutions to many diverse problems related to modeling the natural world. It may also hold the answer to unraveling the mysteries of the mind. This paper describes one possible way in which chaos theory can be applied to modeling the mind. The basis of this model begins with the theories of the psychoanalyst Carl Gustav Jung and goes on to incorporate findings from associationism and behaviorism, in addition to some of the mathematical findings of chaos theory. The result is a comprehensive hypothetical model of how the mind operates.

Chaos and Personality: A Hypothetical Model of the Mind

Ever since the beginning of recorded history, human beings have speculated upon the nature of the mind, the tool that has enabled our species to build a great global culture and shape the world to fit our designs. While the study of the physical sciences has progressed at an almost alarming rate in the last two hundred years, formal study of the mind remains in its infancy. While this is in part due to a lack of adequate tools with which to observe the mind's inner workings, it is also due to the fact that while many models of the mind have been proposed, none have been universally accepted as was Newton's Principia Mathematica in physics.

Because of this, Thomas Kuhn, in his famous work, The Structure of Scientific Revolutions, refers to psychology as a preparadigmatic science. A paradigmatic science is a scientific discipline based upon a model or set of principles which are accepted by most if not all of the practicioners of the discipline. Psychology is described as preparadigmatic because while many different schools of psychology exist, no one set of models or principles is universally, or almost universally, accepted (Kuhn, 1962). In this paper I will expound my own theory of personality which I have developed over the last two years, drawing upon several of the various schools of psychological thought. It also draws upon the principles of chaos theory, a fairly new movement in mathematics, and thus may someday contribute to mathematical modeling of the mind.

Around the turn of the century, the psychiatrist Carl Gustav Jung proposed a theory that was to revolutionize psychoanalysis - the theory of the complex. Both Freud and Adler integrated the complex into their own theories of personality. Freud's Oedipus and Elektra complexes are based upon a child's sexual attraction to his or her opposite-sex parent, while Adler's inferiority complex is related to an individual's feelings of helplessness and powerlessness (Marx & Cronan-Hillix, 1987). However, it was Jung who eventually developed this theory to the greatest degree.

To understand the complex, it is first necessary to understand Jung's concept of the association. An association is simply one element of information stored in memory. It can thus be a word, an image, or a simple memory of an event. Associations are linked together into complexes by their feeling-tone, the term Jung used to describe the emotional character of each association (Campbell, 1971). The complex can best be represented spatially. At the center of the complex is the nucleus, composed of a specific association coupled with a strong feeling-tone, usually described as traumatic in Jung's works. This is most likely because Jung was a clinician and dealt primarily with psychiatric patients. Jung also believed that complexes could exist which were not of a traumatic nature. Such complexes, according to Jung, are related to creativity and the appreciation of art and beauty (Singer,1984).

Other associations which are of a similar feeling-tone to that of the nucleus are linked to the complex in such a way that thinking of them evokes the feeling-tone of the nucleus. This feeling tone, if traumatic, is uncomfortable and unpleasant (Singer, 1984). Every so often when I am thinking about things a thought crosses my mind which should be essentially value-neutral, such as the memory of an innocuous object or situation. However, despite the thought's apparently value-neutral character, thinking of it produces a sort of mental twinge. By tracing the images and elements associated with the thought, I can usually trace it back to some situation in which I felt uncomfortable. In this example, the memory of the situation that originally produced the emotion represents the nucleus, while the thought that evokes the original feeling-tone is one of the linked associations.

Obviously, a complex of this nature is not particularly neurotic or debilitating. However, this is because in such cases, the feeling-tone of the nucleus has not been intensified through contact with the collective unconscious. The collective unconscious is the repository of the oldest and most basic set of thought-patterns within the mind. These patterns, or archetypes, are similar to the schemas of modern cognitive psychology, except that they are much more basic and mythological in nature. Examples of archetypes include Mother, Father, the Sun, the Hero, and many other images common to most if not all religions, particularly those practiced in primitive societies. The feeling-tone of an association that touches upon the collective unconscious is magnified in such a way that it takes on a sort of mythic reality of its own. Because of this, individuals often perceive such complexes as possessing an external reality of their own (Singer, 1984).

A traumatic association which has been magnified in this way is usually repressed; the mind denies all knowledge of the association in an effort to protect itself from fully experiencing the magnified impact of the traumatic feeling-tone. Paradoxically, however, it is this repression that prevents the mind from dealing with the traumatic emotion. As the individual goes on living, the association will often act as a sort of magnet, pulling other associations with similar feeling-tones to itself. Thus, the complex grows, becoming larger and stronger. When a complex becomes strong enough, it may become autonomous - in effect, develop a mind of its own. The complex is then capable of producing affects, intrusions into consciousness which seem to possess a reality separate from that of the individual. The conscious mind cannot control such intrusions, and has some difficulty dealing with them. Jung believed that such affects were responsible for the "voices" reported by schizophrenic patients and many other symptoms associated with psychotic disorders. (Campbell, 1971).

The ego, that is, the sense of self that most individuals experience, is dealt with fairly extensively in Jungian psychology. According to Jung, the ego is made up of certain characteristics, or functions. These functions, according to traditional Jungian theory, are thinking, feeling, sensation, and intuition. The thinking function is characterized by rational thought and logic. The feeling function, on the other hand, is characterized by impulsive thoughts based on emotional qualities such as beauty and happiness. These two functions are considered complementary, in that an individual will tend to use one or the other in any given situation. Jung observed that most people tend to use one of these functions more often than the other. Sensation and intuition are also complementary functions. The sensation function makes use of empirical data, such as details, and eventually recognizes patterns by examining and combining their characteristics. The intuition function sees patterns almost immediately and then fills in whatever details it deems necessary (Singer, 1984).

In addition to these functions, Jung also noticed that people tended to be either introverts or extroverts. In modern vernacular, the introvert avoids people and enjoys being alone, while the extrovert prefers social settings and being with other people. While the Jungian definitions are similar, they are not identical. To a Jungian psychologist, the introvert is best at dealing with his or her own ideas and internal world. On the other hand, the extrovert prefers to deal with the external world. While this does produce tendencies similar to those described by the popular definitions, the correlation is not absolute (Campbell, 1971). For example, up until about eighth grade, I was rated as an extrovert according to the Myers-Briggs personality inventory, the test that is most often used to determine the relative strengths of the various functions. However, I was a loner and disliked social situations. Now I am rated as an introvert, and am much more social than I was in seventh and eighth grade.

The Myers-Briggs personality inventory includes one other set of complementary functions, perceiving and judging. While these may be part of the final form of Jung's function model, I have found no reference to them in the works of Jung or in June Singer's much more recent book on Jungian psychology, Boundaries of the Soul (Singer, 1984). However, I will explain the terms nonetheless. Essentially, the perceiving and judging functions describe the speed at which an individual makes judgments. The judging function is characterized by rapid judgments made on the basis of relatively little information. It tends to be fast, but not particularly accurate. On the other hand, the perceiving function tends to obtain as much data as possible before reaching a conclusion. This function is, in the end, more accurate than the judging function, but gathering enough data takes more time.

By measuring the degree to which each of these functions is used, it is possible to determine an individual's personality type. The Myers-Briggs personality inventory yields a combination of four letters which represents the subject's personality type. For example, I am an INTP, which stands for [I]ntrovert, i[N]tuitive (Introvert is represented by I, so to avoid confusion Intuitive is represented by the letter N), [T]hinking, and [P]erceiving. These letters represent the trait from each pair of complementary functions that is dominant. In Jungian psychology, the final goal of development is to balance all of the functions in such a way that they are equally developed (Campbell, 1971). By the Myers-Briggs, such a personality could not be represented as a set of letters.

In addition to this model of the ego, Jungian psychology also theorizes the existence of what is called the shadow. While the ego represents the sense of self possessed by most individuals, the shadow represents that which the individual feels is not him or herself. Dominant functions normally reside in the ego, while those which are not dominant reside in the shadow. According to this model, my shadow would be ESFJ ([E]xtrovert, [S]ensation, [F]eeling, and [J]udging). The shadow is also the repository of repressed material - those characteristics of the individual that his or her mind cannot accept (Singer, 1984).

There are three other important concepts in Jungian psychology that represent facets of the personality. These are the anima, the animus, and the persona. The anima and animus are complementary - the anima is related to the feminine archetype, which is characterized as passive and receptive, while the animus is related to the masculine archetype, characterized as active and dominating. In males, the animus and the ego are usually integrated early on in the development of personality, while in females the anima tends to merge with the ego. However, it is important to keep in mind that the reverse is possible, just more unusual. In males the anima and in females the animus is often denied and separated from the personality and may become the root of neurotic conditions relating to the opposite sex. This is because of the association of the anima and animus with prominant archetypes. Often, the anima or animus becomes associated with a specific person, usually a parent or lover. In the case of parents, complexes similar to the Freudian Oedipus and Elektra complexes may result, while in the case of a lover, severe difficulties often result if the relationship is terminated. In addition, neurotic conditions revolving around the relationship may develop (Singer, 1984).

Most of the Jungian model of personality is internal, in that it describes structures that cannot be directly observed and which are removed from the external world. It is through personas that the mind interacts with its environment. A persona is similar to a complex in that it is a set of associations. However, unlike a complex, it is built around a certain societal role that has been internalized by the ego. The persona which relates to a given situation acts as a sort of filter, preventing impulses which are not appropriate to the situation from being expressed. The persona also guides behavior in such a way that it conforms to the societal norm for whatever role it represents (Campbell, 1971). For example, one of my personas is that of a student, since it is a role I have played for most of my life. This persona dictates the sort of things that I discuss and how I act in situations where I am expected to behave as a student. I also have a persona which is more appropriate to scientific circles. This persona, while not highly developed, will probably be used extensively once I am out of school, since I plan on becoming a scientist. In addition to these two somewhat similar personas, I have a very different artistic persona - I am also a writer and a musician. When I am making use of my artistic persona, my behavior is markedly different. Instead of discussing hypotheses and theories, I speak much more of aesthetics and style. Most people have many personas, suited to many different situations, which allows the ego to adapt more easily to switching roles.

Jung draws a distinction between the ego and the self. While the ego is what we believe ourselves to be, the self is what we actually are. This distinction becomes clear when one examines the difference between the ego and the shadow. While the shadow is actually part of the individual's personality, it represents those things which the ego does not or cannot accept. The shadow is not part of the ego, but it is part of the self. Similarly, while the anima or animus may not be integrated into the ego, it is part of the self because it is an element of the individual's personality. The ego, the conscious mind, is a subset of the self. The self represents everything, conscious and unconscious, accepted and denied, that makes up the individual's personality. In a perfectly developed person, the ego and self are one. All elements of the individual's personality have been integrated, dealt with, and accepted (Singer, 1984).

Needless to say, such people are quite unusual. However, Jung proposed his system of psychotherapy to facilitate this process of development. He terms this process of integration individuation. It is the theory of individuation that leads many to consider Jung the first truly humanistic psychologist. Individuation is similar to the process of self-actualization proposed by Maslow, one of the founders of the humanistic movement in psychology (Maslow, 1970). According to the theory of individuation, the individual must develop all facets of his or her personality in order to integrate them into the self. This includes the functions, the anima, the animus, the shadow, and all unconscious complexes which may produce neurotic symptoms. While self-actualization is more concerned with the development of skills and talents, Jungian theory holds that during the process of individuation new skills must be acquired. For example, the integration of an underdeveloped thinking function is only possible through the development of logical and rational thought processes, while the integration of an underdeveloped feeling function requires the individual to learn to deal with situations emotionally (Campbell, 1971).

While Jung's model of personality is an excellent starting point, it does not adequately explain all of what goes on within the mind and brain. Furthermore, it is not rigorous enough to enable effective mathematical modeling of personality. Jung preferred his clinical practice to laboratory work, and developed his personality theory as a therapeutic tool. My own model of personality is similar to Jungian theory, but alters it in several important ways that allow it to function as a more general system.

The British empiricist and philosopher David Hume presents a view of the organization of the mind that is somewhat different from that of Jung. While according to Jung's model associations are organized by feeling-tone, Hume believes that associations are organized by more rational and logical principles. Hume describes two different types of impressions, the impression and the idea. An impression is a piece of raw information obtained by the senses, and is not modified by the mind in any way. An idea is an association created by the linking of two or more impressions or ideas. Hume's theory of mind also involved the concept of different levels of thought. The impression is the first level of thought, the closest to physical reality. An idea created by the combining of two or more impressions is one level removed from the first, while an idea created by the combining of two or more level one ideas is two levels removed from the first, and so on (Hume, 1748).

According to Hume, the three basic principles by which these associations are combined are similarity, causality, and contiguity. Similarity simply refers to a resemblance between two impressions or ideas. Causality refers to the basic scientific principle of cause and effect, while contiguity refers to temporal or spatial proximity (Turner, 1967). It is interesting to note that all of these principles are present in the magical theories of primitive tribes, which is what one would expect if they are in fact basic and archetypal.

Hume's theory of the mind does not account for the complexes and emotional structures observed by Jung in his clinical practice, or for that matter emotional appreciation of art and music, but it does account for other more day-to-day thought processes. Two things that are similar tend to be thought of together, and our minds are quick to note causal relationships. The power of temporal proximity has been demonstrated by the conditioning experiments of the behaviorists, while spatial proximity is often a useful mnemonic device.

Since it is unclear from introspection which of these two organizational principles is operating in the mind, it may be helpful to examine the findings of empirical research. Research in state-dependent learning seems to support the Jungian position. The principle behind state-dependent learning is simple - information is best remembered when the individual is in the same frame of mind as he or she was in when the information was originally memorized. Research has confirmed this hypothesis fairly clearly, but has discovered one key difference between the process that seems to be going on and Jung's theory of association organization (Levinthal, 1990). According to the Jungian model, information should be best remembered when the individual is in the same emotional state as he or she was in when the information was originally memorized. This is because the information is organized into complexes by feeling-tone, and the elements of complexes will surface more easily if the mind's feeling-tone matches that of the complex. This seems to be true (Levinthal, 1990). However, a more noticeable state-dependent effect is that obtained using alcohol and other drugs.

Most people are familiar with the concept of the alcoholic blackout. While I have heard of people who maintain that the blackout is primarily an excuse used by alcoholics to justify their behavior, it has been widely reported. Alcohol produces a strong state-dependent effect. Information memorized while intoxicated is far more likely to be recalled when the individual is again intoxicated, even if the individual does not actually black out (McKim, 1991). It is this drug-induced state-dependent effect that leads me to my first major modification to Jungian theory. Feeling-tone is not an accurate term for an effect that can be caused by drugs. I have chosen the term mental state to replace feeling-tone, as it is more general. Mental state directly correlates to the biochemical state of the brain, and is experienced in the mind as a shift in mood or thought patterns. Feeling-tone is encompassed by this more biochemical definition, since it is believed that emotions are related to biochemical hormonal shifts produced by the limbic system (Levinthal, 1990).

Under a Jungian model revised to take this into account, then, information is organized into complexes on the basis of overall mental state, not just feeling-tone. Drug-induced states seem to have a greater effect on learning than does emotional state, probably because drugs produce a much more rapid shift in biochemical state than normal emotional processes and because the shift is often much greater (McKim, 1991). While this research supports Jung, Hume is supported by day-to-day experience. It is clear to most who think carefully about their own thought processes that Hume's principles of cognitive organization also make sense. They are, however, overridden by strong emotions. Hume's careful, thought-out processes seem to apply more readily to information that is more neutral in tone.

The simple solution that reconciles these two theories is that both processes are at work simultaneously in the mind. Drawing upon Jung's model of the ego, it is not too great a jump in logic to suggest that one of these processes, Jung's, is mediated by the feeling function and the other, Hume's, is mediated by the thinking function. Making use of fairly basic terminology, I have termed these two organizational principles and their respective functions the feeling system and the thinking system. An individual's personality type determines which of these systems is dominant - in effect, which of them is used more often.

The feeling system is older and more basic in character. Looking at Piaget's stages of development, it would seem that the feeling system develops before the thinking system, in that emotions come about before logic (Hurlock, 1950). All associations have a mental state component, and without this component they cannot be encoded at all. However, the strength of this component is variable. Emotionally charged memories and memories formed while under the influence of drugs possess a strong mental state component, while neutral associations such as a list of the names of famous golfers possess an almost negligible mental state component. Anatomically, a good place to look for the localization of this process of joining mental state components to associations is probably the limbic system, notably the hippocampus and amygdala. It has been shown in case studies that bilateral removal of the hippocampus results in the inability to form new memories (Kolb & Whishaw, 1990). According to this theory of mental state, without the hippocampus the brain cannot assign a mental state component to its associations and thus cannot encode them.

On the other hand, the thinking system is highly symbolic and organized according to logical principles. This is the function that is cultivated by our society, which is organized along lines that thinking types best understand. While it develops later, it is cultivated more thoroughly by our educational system. It is likely that the thinking system is related to the neocortex, particularly the frontal lobe. It may be that information is organized by the thinking system after it is withdrawn from memory, which seems to be more closely affiliated with the feeling system. Whatever the case, the more neutral the emotional tone of the association, the more likely it is that the association will tend to be organized along more logical lines.

It is this definition of the association that will serve as a basis for the chaotic model of personality. The association, made up of a memory coupled with a mental state component, is in effect the basic structural unit of the mind. To reiterate, it is organized by two systems, the thinking system and the feeling system. The thinking system deals with the memories themselves, and links these contents together using the principles of similarity, causality, and contiguity. The feeling system organizes memories by their mental state components. Both systems organize memories into structures resembling the Jungian complex, but it is only the feeling system that produces pathological complexes. The thinking system is too closely related to the conscious mind to deal well with repressed material, and it is the mental state component, not the memory itself, that is amplified by contact with the collective unconscious.

Calling a model of personality based upon the above definition of the association and mental state chaotic may seem like something of a misnomer. However, the term chaotic refers to chaos theory, a fairly new movement in mathematics. Chaos theory was developed to describe complex non-linear systems in which there are many degrees of freedom, too many for classical mathematics to describe without a great deal of difficulty. Much of chaos theory is based upon discoveries concerning the nature of weather systems. Weather is a highly complex, non-linear system that is difficult to predict. Despite the fact that a great deal of high-tech equipment is used by meteorologists today, their accuracy has not improved very much in the last hundred years. In the sixties, however, it was believed that science would soon enable us not only to predict the weather, but control it. It was believed that within weather systems there existed certain critical points at which the course of, for example, a storm front could be altered. The theory was that if these critical points could be worked out, planes could be sent up with special equipment to affect the front at these points. In order to figure out where the critical points were, computer simulations of weather systems were developed and observed. Even with the primitive equipment of the time, it was thought that the computer was the answer to the problem of weather control (Gleick, 1987).

However, a greater problem became apparent as the simulations were more carefully examined. While they produced realistic, albeit simple, weather patterns, a small shift in any of the numbers, such as that produced by roundoff error, produced a large-scale shift in the weather pattern over a long enough period of time. Instead of manifesting critical points or anything of the sort, small number shifts propagated through the system and were amplified in such a way that two simulations with nearly identical starting points would produce totally different weather patterns, regardless of the starting point values (Gleick, 1987).

This is very similar in many ways to how the mind seems to work. As any therapist knows, it is possible for two people with nearly identical personalities to function in such a manner that one may require institutionalization while the other may be quite successful. Also, two people with very similar starting points, such as identical twins, may become very different people over time, even if raised together. Even within the mind of one individual, a single bit of sensory information can produce an extensive cognitive response that completely alters his or her mental state. This effect is produced by what chaos theorists term the butterfly effect. This term comes out of the work on computer weather simulations, and refers to the notion that a butterfly fluttering over China could produce a huge storm in the United States given a period of a few weeks. The butterfly effect is believed to come about because every point of a chaotic system is actually a critical point. A shift anywhere in the system, however slight, can produce a large-scale change in the overall pattern of the system over time (Gleick, 1987).

Obviously, the presence of the butterfly effect within the mind and between individuals does not necessarily point to a chaotic model. The system must be more rigorously defined in numerical terms. This is difficult when dealing with associations and other internal information which cannot be obtained through direct observation. However, it is possible to set up a sort of self-referential coordinate system and a rudimentary structure for these complexes and associations. Jung's notion of the self seems as good a place as any to place the origin of this coordinate system. Of all Jung's definitions, the self is the most inclusive and represents the sum of all mental contents. The self is not really an association, so I will call it 0. One level removed from the self can be found the nucleus of the ego, the nucleus of the shadow, and the nucleus of the anima or animus. These associations I will call 1. The system is fairly simple - each association is given a number representing the distance in associations from the self.

The term level seems to describe this number in an effective manner. The nucleus of the ego has many associations linked to it, all of which are level 2, since they are two associations from the self. For the sake of convenience, the shortest possible path will be used to determine level. For example, a level 2 association linked to the ego may also be linked to an association which is at level 7. However, the association remains level 2. On the other hand, if the link to the nucleus of the ego is somehow broken, the level of this association would become 8. A separate coordinate system must be developed for the thinking system and the feeling system, since their bonds are fundamentally different, but both can make use of this same principle of association level.

These bonds, both thinking and feeling, are being formed all the time. They can also be broken, but this is a much longer process. Classical conditioning is a useful model of bond formation. What Pavlov did when he rang a bell and presented his dogs with food was activate what is essentially a sort of thinking bond related to contiguity; two stimuli are presented close together in time, and thus become associated. Eventually, when the bell is rung the bond is activated and produces the salivation response without the presence of food (Pavlov, 1960). If this is actually what is going on, it may represent evidence that something akin to thinking and feeling processes may be going on in animals.

Classical conditioning has also been examined in humans. With humans, we have a clearer idea of what is happening. For example, patients receiving chemotherapy often associate the nausea that accompanies the presence of the drugs they are given with neutral stimuli, such as the sight of the nurse who administers the injections or the type of hypodermic needle used to inject the drug (Ornstein & Sobel, 1987). While this is essentially a thinking-type bond, it also has a feeling component. Nausea is an unpleasant feeling, and also produces a negative emotional state. The activation of the thinking bond links to a complex relating to such experiences and evokes the mental state of experiencing nausea.

This demonstrates how the thinking system may operate in a similar manner to the feeling-related complexes detailed by Jung. The original association in these cases is probably related to the first time the individual received chemotherapy treatments. Cluster elements relating to the experience join with the complex, simply due to the thinking principle of similarity. There is also most likely a feeling component. I know that when I go to the doctor I feel somewhat similar every time. The feeling is somewhat like apprehension, but different. Assuming that other individuals experience a similar effect, this sort of emotional similarity may serve to strengthen the thinking bond by creating similar feeling bonds around the same associations.

It has been noted that nausea tends to produce a strong classical conditioning effect. In other words, it tends to cause bonds between associations to form very rapidly (Pavlov, 1960). While nausea may not be an archetype in the traditional Jungian sense, the response it produces may be an evolutionary advantage that helps us to avoid poisonous foods. If this is case, the condition of nausea may behave in a similar manner to certain of the archetypes. Since there seems to be a mental state relating to experiencing nausea, it may be that nausea produces a very specific biochemical shift in the brain, much more specific than the other senses. Taste and smell are the senses most likely to evoke memories, despite our usual reliance on vision (Levinthal, 1990). The fact that taste and smell are chemical senses and are linked to an older section of the cortex (Kolb & Whishaw, 1990) may be related to this.

Looking at the way in which classical conditioning works, it is clear that breaking a bond is very difficult and takes a long time. This process is called extinction, and it is hard to say if it is ever really accomplished. Pavlov discovered that it was possible to get his dogs to stop responding to the bell by ringing it many times without presenting food. However, if the bell was again paired with the presentation of food, the dogs would pick up the association very rapidly (Pavlov, 1960). It is clear that even when a bond is extinguished, a recollection of the bond remains. Since most conditioning experiments were done by behaviorists on animals, this recollection was not seen as particularly important. However, with humans it has been found that conditioning acts in a very similar manner. Extinction, whether it is done on humans or animals, takes a long time and is fairly difficult to accomplish, especially using intermittent reinforcement schedules (McKim, 1991).

Chaos theory is closely related to fractal geometry. In mathematics, a fractal is a geometric form with a fractional dimension. In other words, while a line is one-dimensional and a plane is two-dimensional, a fractal might have a dimension between one and two. This type of fractal would appear to be a line that twists around itself in a symmetrical pattern. While the form is actually a line, it also occupies a plane because the line is not completely straight. Thus, the dimension is fractional (Mandelbrot, 1983). Fractals have several important characteristics which apply to the chaotic model of personality. While I will not perform a rigorous fractal analysis of the model here as I am not a mathematician, I will demonstrate how this model can be viewed as a fractal. The most important of these characteristics is self-similarity. What this means is that a fractal has a basic form which will be visible no matter how many times the fractal is magnified (Mandelbrot, 1983).

To demonstrate this, I will construct a simple fractal. In this case, the basic form is that of a triangle. To draw this fractal, begin by drawing an equilateral triangle. The triangle does not have to be equilateral - I wrote a computer simulation that produces this sort of fractal using a triangle of any sort - but an equilateral triangle is the easiest to visualize. Draw a second triangle inside the first by connecting the midpoints of each side of the first triangle. The original triangle should now be divided into four sections. Now draw a triangle inside three of the four sections, the ones at the corners. The middle section should be left alone. Repeat  this process over and over again, drawing smaller and smaller triangles. In fact, repeat it infinitely. This fractal is called the Sierpinski triangle (Barnsley, 1988).

Imagine magnifying the Sierpinski triangle. Since the same pattern is followed infinitely, it should be clear that the base triangle will always be visible, since the triangles that compose the shape become infinitely small. This is a simple example of self-similarity. However, not all fractals return to exactly the same shape. Another famous fractal, the Mandelbrot set, returns a shape similar to the base form but not identical when magnified. Whenever the base form manifests itself under magnification, it appears to be slightly different. The Mandelbrot set describes a more chaotic system than does the Sierpinski triangle simply because the base elements that make it up are not completely identical (Mandelbrot, 1983).

As a fractal, the model of complexes and associations more clearly resembles the Mandelbrot set than the Sierpinski triangle in that it is more chaotic than a simple ordered structure. The base form is that of the complex itself - a nuclear element surrounded by n cluster associations. n is a variable, probably with some sort of range and pattern, though this pattern is difficult to deduce without direct observation of the mind. No matter how much the mental model is magnified, the complex keeps showing up as a structure. Since n is variable, it is unlikely that any two given complexes will be exactly the same.

At first, the shape of this model seems very basic and straightforward. It is a sort of tree which expands outward as the level of association increases. Each complex can be represented as n line segments expanding outward from a common nucleus. At the other end of the line segments are other nuclei with rays expanding outward, and so on. However, this simple representation does not take into account that associations on any level can link to associations on any other level. Whenever the links change, as they do constantly, this already convoluted structure shifts. If these characteristics are taken into account, the shape cannot be drawn well three-dimensionally. If an association at level 100 links to one at level three, spatially the bond should be the same length. In a three-dimensional representation, the level 100 association would have to be drawn as much more distant from level 0.

However, if this is taken into account, the above makes a fairly good structural model of the entire system. It is complicated, especially when the thinking and feeling systems are modeled together, but it seems to work. There is, however, one other point that further complicates it. This is the vector nature of association bonds. Pavlov discovered a rudimentary form of this in his laboratory. Mere temporal contiguity is not enough to cause an association bond to form. Pavlov found that if the bell was rung after the food was presented to the dogs, no association would form. The dog could not be made to salivate to the bell unless the bell was rung prior to presentation of the food (Pavlov, 1960).

The coordinate system of association level provides a convenient way to notate these directions, since the level values follow a linear progression and there are two directions in which an association bond can be formed. I will notate these directions as up and down. A bond with an up direction runs from a high level association to a low-level association. An up bond will not change the level of an association, since the shortest path from 0 is used to determine level. A down bond runs from a low level association to a high-level association and may change the level of the association to which it links.

A structural model of this sort is interesting and useful in some ways, but it is also important to look at the functional or dynamic aspects of the system. Since the system is constantly changing, a static structural model does not adequately describe the processes going on in the mind as we think. To explain a more functional way of looking at this system, it is necessary to invoke another concept related to chaos theory, that of the strange attractor. An attractor in mathematics is a difficult concept to explain without making use of a great deal of mathematical jargon. Instead of attempting to define the general case, I will explain how a certain type of attractor, the type I will be using, works. Imagine two points on a plane, and then imagine a function which "orbits" the two points, similar to the way in which a planet orbits the sun. The two points are said to be the attractor of the function. In effect, they "attract" the values of the function toward themselves. In the case of a strange attractor, the function is chaotic--that is, it does not fall into any repetitive pattern of orbits. The function continues to orbit the points over time, but in a semi-random fashion. It does not leave the orbit, but within the pattern the variation is basically random (Gleick, 1987).

Now imagine that there are more than two points, and that each point represents an association. The function orbiting the points represents mental state over time. Within the thinking system, as the function moves closer to an association, the thoughts that are going through the individual's mind are becoming more similar to that of the association. Depending on the degree of similarity between the thoughts of the individual and the content of the association, there is a chance that the association will be "activated" and thus come to mind as the individual thinks. This chance is directly proportional to the distance from the association. This "distance" is not spatial, but is actually more a quality of the coordinate system that we have imposed upon the mind. When an association is activated, the points change. They are replaced by the points linked to the association that has just been activated, and the function continues to orbit, with a chance of activating each of those associations.

The feeling system is still more complex because there is another characteristic that must be considered - the strength of the association. This means, essentially, that within the function's orbit, there is a greater area from which a strong association will be activated. This strength is related to the intensity of the mental state component, and the number of cluster elements which are linked to the association. In the thinking system, mental state is not considered. However, when dealing with the feeling system, the concept of intensity must be considered. Intensity represents a sort of "radius" - the probability of the association being activated - covers a greater "area" in the context of the spatial model.

Finally, within both systems, the concept of familiarity is important. Essentially, what this means is that the radius of an association is affected by constant activation. If a certain association comes to mind often, it will be strengthened and if it is ignored it will weaken, provided it is not a pathological complex. This is how extinction works. The bond from one association to another is not activated over a long period of time, and thus it begins to fade. However, if after some time it is re-activated, the bond will strengthen rapidly. Familiarity is the only factor that affects intensity of an association in the thinking system.

This functional model demonstrates how the dynamic process of thought operates. However, it still seems largely internal and divorced from the real world. While it is interesting to speculate upon how the mind functions, it is also important to look at how the mind that is being modeled relates to its surroundings. As per Jungian psychology, the ego creates personas, which are thinking-system complexes related to a particular societal role (Campbell, 1971). There is also usually some emotional content to the associations making up a persona, but the dynamic is primarily one of the thinking system. When information enters the mind through the senses, it is processed by the ego, which activates the appropriate persona for the situation. Until the situation changes, the persona remains the same, and only those associations related to the persona are likely to be activated. However, each persona retains a link to the ego so that if the proper sensory information presents itself, the ego can switch personas.

The mental state function is not actually random. It is affected by the ego, the self, and to some degree directed based on the information present in the outside world. However, the function would appear chaotic if mapped because the world is not completely ordered. Also, there is a degree of randomness inherent in the system because of the complexity of its dynamics. The situation discussed above is ideal. In a neurotic patient, other powerful complexes such as the anima, animus, or shadow may gain control of the mental state function. In such a case, the function may defy the wishes of the ego entirely, which can be alarming to the individual (Singer, 1984). This leads to the discussion of autonomous complexes. The autonomous complex, in effect, has a sort of mind of its own. It is capable of acting without the direction of the ego and producing affects (Campbell, 1971). In extreme cases, such as multiple personality disorder, the ego may be virtually destroyed. If this happens, several complexes may struggle for control of the mental state function. These complexes develop separate personalities, and in effect live different lives. In the case of schizophrenia, a complex may become strong enough to make suggestions to the ego in the form of "voices" or other hallucinations (Sarason & Sarason, 1989).

This follows directly from the principle of self-similarity. The ego is a complex and controls the mind by virtue of its size and number of associations. However, if another complex becomes large enough, it too can gain a sort of will and personality. The fact that complexes can operate in this way seems to support the fractal modeling of complex processes. In most cases, only complexes that have been magnified by the collective unconscious can operate in this manner, though multiple personality disorder may be an exception because in many cases of MPD, the ego is destroyed through trauma such as childhood abuse (Sarason & Sarason, 1989).

This dynamic of self-similarity can also be applied to mass psychology. Groupthink is a documented fact in psychology, and describes the interesting phenomenon that occurs when a group of people act with one mind, such as in mob situations (Hartley, 1952). This situation is also very cleanly explained by the chaotic model. Essentially, a group is just a complex on a larger scale, that is, at a different level of magnification. The nucleus of such a complex is whatever is uniting the people in the group, often a common goal or the rhetoric of a persuasive speaker. The reason a mob is clumsy and simple-minded is because even in a very large group there are relatively few associations, or individuals, when compared with the mind of an individual. Information transmission is also important. In the mind, information can travel very rapidly. In a mob, each person can only speak to the people next to them, which leads to slow and clumsy transmission. Furthermore, any message is liable to be corrupted as it travels from person to person.

Other evidence of chaotic processes is found in the basic biological processes of the brain. While the mind and brain are not necessarily one in the same, it is clear that the two are related in some way. PET scans, in which radioactive glucose is injected into the bloodstream and tracked as it is absorbed by the various areas of the brain, do seem to display self-similarity over time. Similar areas of the brain seem to be highlighted during similar activities both within and between individuals, but the pattern is highly chaotic and rarely repeats exactly. A more clear example of this is seem in the interaction between the brain and the immune system, thought to be mediated by the hypothalamus. It has been shown that while the immune system is controlled by the rate of neurons firing in the hypothalamus, the functioning of the immune system increases the rate of fire in the hypothalamus. It would seem that this system would get out of control easily, as in the case of severe allergic reactions. However, such reactions are rare (Ornstein & Sobel, 1987). A simple explanation for this is that within the system, every point is a critical point. While many neurons firing produce a large-scale effect, even a few neurons firing can in a sense swing the system the other way, creating a normally stable pattern within a fairly volatile system. This is very similar to the way in which weather systems operate and is best decribed as fundamentally chaotic in the mathematical sense (Gleick, 1987).

There are always those who, after reading a fairly detailed theory of personality such as this, will ask what good it is. While it is true that this system is largely conceptual, it does have its applications. In artificial intelligence research such a model may help in the simulation of mental processes. Obviously, for this to happen the model must be formalized more completely. However, the concept remains and may one day be used in such a fashion. Such a model, if formalized, would also have its uses in psychotherapy. If, for example, it can be determined that an individual does not produce as many responses to a given association as this model would dictate, the therapist may conclude that somewhere related to the association is repressed material. For this to be possible, it is necessary to examine the patterns formed by the cluster elements. Some sort of relationship for the variable value of n must be determined for the model to be used in this way. These are two applications that leap to mind, though there are undoubtedly others. To understand the mind is to understand ourselves, and such knowledge is usually welcome. This model demonstrates many of the key processes going on within the mind, and shows how they can relate to each other.

Designing this model of personality has been a sort of adventure for me, as I have carefully examined the nature of my own thought processes in addition to those discussed by Jung and those I have read about over the past four years. It has consisted of introspection, observation, and a great deal of library research. It has helped me to organize my thinking concerning the mind, the brain, and its inner workings. I hope that someday this model and its ramifications will contribute to our understanding and investigations of complex psychological processes on both the biochemical and psychological levels, and will enable all of us to see more clearly into that enigmatic structure that we call the mind.


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