Dependence on Initial Conditions
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 Figure 4, illustrates how
important initial conditions can be to a dynamic system
Figure 4. 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 4) or to the right (right of Figure 4). 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
4), 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” (p.
12). 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. (p. 78).
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 )
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. (p. 29)
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! (p 23)
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
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