SENSITIVE DEPENDENCE ON INITIAL CONDITIONS


Gerald J. Schueler, Ph.D


The behaviors of all dynamic systems are dependent upon their initial conditions. In classical mechanics, the initial conditions of systems are usually known. A very simple example, of a small ball dropped onto the edge of a razor blade, as shown in the illustration below, how important initial conditions can be to a dynamic system:



----BALL STRIKING RAZOR BLADE


The ball can strike the blade in such a way that it can go off to the left (center of Figure) or to the right (right of Figure). The initial condition that will determine whether the ball goes to the left or right is minute. If the ball were initially held centered over the blade (left of Figure), a prediction of which direction the ball will bounce would be impossible to make with certainty.

Dynamic systems, that are highly dependent on their initial conditions, are the main subjects of investigation in modern chaos theory. Kellert (1993) points out that: “A dynamical system that exhibits sensitive dependence on initial conditions will produce markedly different solutions for two specifications of initial states that are initially very close together." The ball falling on a razor blade is a good example of such a dynamic system because a very slight change in the initial conditions of the ball can result in falling to the right or left of the blade.

According to Rosen (1991):

The natural evolution of quasi-isolated systems should be analyzed by considering the evolution process as a sequence of states in time. A state is the condition of the system at any time, and this can be either discrete or continuous. At any time, we can consider the system's state as the initial conditions for whatever processes follow.

The initial conditions of a complex system can therefore be found by making observations, at selected times, of the system’s state space. Theoretically, this can even be done for the universe at large. Ruelle (1991) says:

Newtonian mechanics gives a completely deterministic picture of the world: if we know the state of the universe at some initial time, we should be able to determine its state at any other time.

This ability is called determinism and it holds true for all dynamic systems. However, the initial conditions of many complex systems cannot be accurately determined. When systems exhibit sensitive dependence on initial conditions, they are no longer predictable, and determinism no longer holds. One complex system that is often used as a typical example, is the weather. Ruelle (1991) says:

It is conceivable that the presence of Venus, or any other planet, modifies the evolution of the weather, with consequences that we cannot disregard. The evidence is that whether we have rain or not this afternoon depends upon, among many other things, the gravitational influence of Venus a few weeks ago!

The state or condition of a complex system, over time, depends on its initial conditions. This phenomenon has been labeled the Butterfly Effect because it suggests that a butterfly, that beats its wings in Peking today, can transform a storm system next month in New York. This is now known to have some validity, especially with weather prediction.

In 1961, Edward Lorenz discovered that his computer gave him a different answer when he started at the beginning of his calculations than when he took a "short-cut" and started near the midpoint. Intuitively it should not have mattered, because the differences were so very small they should have been negligible. But the final result, he discovered, was highly dependent on the starting conditions.

In one computer run, he started with the number .506127. The short-cut run began with the number .506, a rounded-off number. The rounding off made all the difference. The calculations had to do with the weather, and the rounding off error should not have made the difference of a small puff of wind, yet the results of the two calculations were totally different.

One of the practical conclusions from his discovery is that long-range weather forecasting is doomed to failure. This is not because we can't measure good enough; but rather, like the uncertainty principle of quantum mechanics, there are distinct limits to how far we can predict future events with certainty, even in our everyday macroscopic world.

For every event that occurs, small uncertainties multiply over time, cascading upward into unpredictability (Briggs & Peat, 1989; Cohen & Stewart, 1994; Gleick, 1987). Every human being is a complex system, both physically and mentally. Our birth, and early development as a child, will largely determine how we find ourselves as adults. This is because we do not enter life as a "blank slate;" we enter life with pre-established desires and traits (Darley, Glucksberg & Kinchla, 1981).

The early part of our lives can effect us in our later life. Psychoanalysis argues that we must remember our early childhood, if we are to find maturity in our adult life. Jung (1989) notes “the enormous influence which childhood has on the later development of character” (p. 136). He also points out that “most neuroses are misdevelopments that have been built up over many years” (1985, p. 24).

We must come to grips with our childhood. The Butterfly Effect strongly suggests the importance of remembering our past and assimilating all of our childhood experiences in order to see clearly why we behave as we do today.

Jung (1978) taught that the ego rises up from the psyche shortly after birth from friction between the body and the external environment. Jung (1954) wrote that “the child’s psyche, prior to the stage of ego-consciousness, is very far from being empty and devoid of content” (p. 44). How humans develop and learn depends upon the interplay between genetic (nature) and environmental (nurture) factors (Rubiner, 1997).

Our brain is not a tabula rasa on which anything can be imprinted. The central nervous system has tendencies that are reflected in a gravitation toward particular behaviors partly expressed in our rituals, mythologies, religions, and social structures. Superimposed on this biological backdrop is an equally inherited ability to reason. Reason appears to be possible because built-in feedback loops create a hierarchical progression with the capacity to always look back at previous levels of integration (Showbris, 1994, p. 386).

Once the ego has established itself as an individual identity, it goes on developing by virtue of continuous friction with the outer world as well as internal friction due to the need for assimilation of experiences. Furthermore, the ego’s “stability is relative, because far-reaching changes of personality can sometimes occur” (Jung, 1978, p. 6). Mental instability is as much the cause of growth as it is of illness or pathological behavior.

Jung (1989) recognized three primary phases of life as: (1) the first few years of life, called the presexual stage; (2) the later years of childhood up to puberty, called the prepubertal stage; and (3) the adult period from puberty on, called the period of maturity. He also taught that the ego develops from the Self (the central archetype of the psyche) within the psyche during the first half of life, and then returns to the Self by assimilating it during the second half of life in what he calls the individuation process (Edinger, 1974).

Jacobi (1973) says that: “Unless it is inhibited, obstructed, or distorted by some specific disturbance, [the individuation process] is a process of maturation or unfolding, the psychic parallel to the physical process of growth and aging” (p. 107). How far the Self of any person matures by means of the individuation process, during the second half of life, largely depends on how well the ego develops during the first half of life. Thus, according to Jung, the state of the psyche of any individual is highly dependent on its initial conditions.


THE ABOVE FROM:

THE CHAOS OF JUNG'S PSYCHE

An on-line book by Gerald J. Schueler, Ph.D. and Betty J. Schueler, Ph.D that for whatever reason no longer be found in an internet search.


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