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..:: Chaos Revisited ::..


Alan Schneider


- Chaos Basics -

            Perhaps the most significant principal of chaos theory is represented by the butterfly effect, one of the initial discoveries that helped to launch the science, made by Edward Lorentz in 1961 (Schueler, 1997, p. 2). Lorentz was involved in ongoing experiments designed to develop efficient long range weather forecasts. On one occasion, he was faced with the need to rerun a long series of computations to verify certain data. Rather than reenter the data comprehensively, he decided to simply reenter key values in the sequences, and executed the computer run. 

            Lorentz was surprised to discover that the results of the second run were very different from the initial attempt. He then closely examined the values used in the second run, and again compared them to the initial run. He noticed that certain numbers had been slightly rounded off in the process of entry into the second program. The impact of this apparently insignificant oversight was amplified through the parameters of the computer program, and resulted in the observed shift in the outcome.  

            The butterfly effect refers to the tendency of chaotic systems to be influenced, or perturbed, by even the slightest change in initial system conditions. Something like the beating of a butterfly’s wings, taken into account as an initial condition, can and does influence an apparently distant phenomenon, such as the state of the entire atmosphere, across a complex bridge of subsequent relationships. If these relationships are sensitive enough, the impact on the atmosphere could conceivably even be notably catastrophic in character, e.g. the occurrence of tornados in Indonesia (Seeger, 2002, p. 331). This was clearly the effect of the slight rounding of the data values seen in Lorentz’s second computer run. He eventually came to the conclusion that the sensitivity of the weather to initial conditions at any given time made the long term prediction of meteorological trends impossible.  

            Initial sensitivity accounts for the ongoing manifestation of another cornerstone concept of chaos theory, non-linearity. Most, if not all, systems seen in the phenomenal world (the world we literally experience) are more or less non-linear in function and form. Non-linear is the chaos theory term describing a process that does not behave consistently across time, but rather fluctuates unpredictably in response to variables that are difficult, if not impossible, to directly observe. Human beings agree, based on observed statistical consistencies, to treat the phenomenal world as though it is present in a stable configuration, although it is always subject to, and demonstrating, perturbation. Non-linear systems are also referred to in the literature as complex systems. 

            The specific mode of change in complex systems is bifurcation. This phenomenon occurs when the system can no longer maintain stability under a given set of initial conditions, and breaks down into a set of more relatively stable conditions. The new conditions may or may not be initially more comfortable from the viewpoint of a human observer, but nonetheless represent the emergence of self-organization – the movement of the system process  into a new, more stable  form (Seeger, 2002, p. 332). Bifurcation and subsequent self-organization are key processes of social and organizational change and renewal in the chaos paradigm. This is in contrast to the view of traditional social science that any chaos-related event is necessarily negative in character. 

            The causative agent driving the mechanism of bifurcation is the strange attractor. There are many forms of attractors seen in the natural world. Static attractors, such as gravity – which simply exists as a mass-related consistent force – and dynamic attractors – represented by the sinusoidal form of alternating current electricity – are easily identified everywhere. Attractors are the underlying principals that maintain order in the world. Chaotic strange attractors are a particular case in which a fixed point of manifestation, and predictable operation, have given way to a general conceptual region of action which can produce unpredictable outcomes. All that can be said with certainty regarding strange attractors is that there is an apparent force present tending to shape events as they become manifest in real time and real space. (Seeger, 2002, p. 334). 

            Strange attractors are specifically postulated as being unobservable, but still present in phase space, the mathematical construct used to describe their characteristics. Phase space can be thought of as a snapshot of a complex system’s possibilities at a given point in time, where each special “dimension” corresponds to a variable in the system (Schueler, 1997, p. 3). Although these possibilities cannot be observed, since they occur in the future, they can be inferred from the performance of past observations of many different systems, which are a matter of concrete record. Hence, the presence of strange attractors can be inferred as being potentially manifest in all systems, regardless of their levels of functioning. When a system becomes significantly unstable, they become active and begin exerting their influence on outcomes. 

            In addition to the chaotic strange attractor and the static attractor, there are three varieties of dynamic or linear attractor: fixed point, limit cycle, and toridal. A brief discussion of these more logical, consistent governing principles readily identifiable in relatively stable systems may be useful here as an aid to fully understanding the influence of strange attractors. The fixed point attractor is illustrated by the center of a system of circular motion, such as the axel to which a wheel is mounted. The limit cycle attractor is seen in the presence of two or more limiting conditions or processes that determine the outcome of some sinusoidal dynamic process – such as the swinging of a clock pendulum, where gravity and the clock driver mechanism (e.g. spring, battery, etc.) are the attractors at work. The toridal attractor is the result of multiple frequencies present in the limit cycle attractor network. The shifting of the Earth’s axis accounting for the Astrological Precession of the Equinoxes is such a toridal attractor system – the limit cycle attractors are the Sun’s gravitational field and the Earth’s mass. But certain variations in the magnetic fields of both the Earth and the Sun cause the constellations to appear to “move backwards” (i.e. counterclockwise) around the North Star, completing one complete cycle every 24,000 years. As a comprehensive example here, turbulence can be characterized as the strange attractor that draws water into chaotic conditions of flow as velocity increases in an enclosure, such as a pipe. The extent of the phenomenon can eventually reach cavitation, where flow effectively ceases, resulting in the “transition” of the turbulent strange attractor into a linear fixed point attractor – cavitation – accompanied by the bifurcation of the system into a more stable, predictable configuration characterized by the absence of fluidic movement. (Schueler, 1997, p. 7).


- The Spiritual Implications of Chaos Theory -

             The forms of the strange attractor operating in the mental systems studied by psychological and spiritual students are the archetypes of the collective unconscious mind. Archetypes conform to the description of strange attractors with great consistency. They are located in a “region” that is unobservable, tend to emerge into conscious recognition under conditions of systemic stress, and generate unpredictable outcomes for the individual’s mental state. All collective archetypes display these characteristics, regardless of the specific behavioral trends they define. And the Psyche is a phenomenon that lends itself quite well to the conception of phase space, particularly in the unconscious regions (Schueler, 1997, pp. 8,9). 

            As the archetypes emerge into conscious expression (rendering them susceptible to observation), they take the form of recognizable cultural images called archetypal symbols. There are hundreds (perhaps thousands) of known archetypal symbols, demonstrated in variations across cultures throughout history, including the Shadow, a repository of all that has been willfully rejected from conscious recognition, the Hero, a figure of salvation and redemption, the Couple, symbols of relationship and involvement, and so on (Schueler, 1997, pp. 9,10).  

            When chaotic events manifest in social systems, the results can be intra personally, interpersonally, and individually traumatic in the extreme, particularly in the case of relatively long term episodes.  One of the results of such long term chaotic manifestations is the cosmology episode (Sellnow & Seeger, 2001, p. 170), characterized by the breakdown of the habitual routines and expectations taken for granted under the pre-chaotic condition. The individuals experiencing cosmology events frequently have a sense of the unreality of their circumstances caused by significant personal and social displacement associated with the chaotic occurrence. They may tend to question their most basic assumptions regarding life, truth, and propriety, and seek new comprehensive spiritual explanations for their circumstances outside what had been their previously dominant cultural paradigm. The rise and fall of cultures and social systems demonstrated throughout history guarantees that the cosmology event will occur with regularity in human affairs and human consciousness.  

            The focus of conscious deliberation on the Physical Plane of expression is the ego, and this primitive form of sentient awareness does not respond well to chaotic conditions, a most unfortunate circumstance, since chaos is the birthplace of all manifestation and all consciousness.  This places human observers on the Physical Plane in more or less permanent conflict with Creation and the Creator, a conflict which we must all either lose, or eventually acquiesce to in spiritual surrender – the distinction resides in the voluntary or resistive nature of our response. And, ultimately, we are all reabsorbed as physical organisms into the chaos that created us, do what we will to postpone this event. The only real hope of existence lies in the access to total consciousness – the Psyche – and its probable links to extended manifestations beyond the physical. This is the realm of the archetypes and archetypal symbols, of the collective level of consciousness, and of all higher modes of human spiritual expression.  It is here that we must go, and here that we can succeed in our spiritual quest as spiritual beings, Created in Love and Light by the Source of Love and Light. We need only take a leap of faith...



Schueler, G.  (1997). Chaos  theory: Interface with Jungian psychology. Retrieved March 12, 2004, from  Internet Website:  http://www.schuelers.com/chaos/chaos1.htm.         

Seeger, M.  (2002). Chaos and crisis: Propositions for a general theory of crisis communication. Public Relations Review, 28, 329-337.

Sellnow, T., & Seeger, M.  (2001). Exploring the boundaries of crisis communication: The case of the 1997 Red River Valley flood. Communication Studies, 52, 153-176. 


                                                                               - With Love, Alan -

                                                                        (CR2008, Alan Schneider)


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