Seven years ago, I enrolled in a college math class at UNC Asheville. I had been unable to crack the code and learn Fractal Geometry on my own (click on this link for a fascinating page on Fractals). Twice each week for an entire semester I scheduled myself out of my office and trekked to the campus of my in order to immerse myself in the study of this quirky field of mathematics.
A short list of some of the topics the course covered (and some images that illustrate the topic) provide a good segue to at least one of the presenters for the Asheville Jung Center’s conference “Jung and Neuroscience”.
Attractor (a set towards which a variable evolves in a dynamical system)
Fractal Dimension (a measure of detail in a pattern [strictly speaking, a fractal pattern] that changes with the scale at which it is measured
Self-similar sets (sets that look the same up close and from far away)
Stable Attractors (points of equilibrium into which systems settle until disrupted)
Strange Attractors (points in a system where the graphic display of equations bifurcate)
Chaotic Attractors (in chaos theory an attractor that displays marked sensitivity to initial conditions)
Julia Sets (consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values and thereby the graph)
Self Organizing System (denotes a system of synergistically cooperative elements whose patterns of global behavior are distributed (i.e., no single element coordinates the activity) and self-limiting in nature)
DNA self replicates and self assembles (electron microscope on the right)
Social self orgainizing in international drug routes
Consider several broad phenomena we all engage in our work as therapists.
- There are motifs that seem to recur in some people’s lives whose particular manifestations evolve depending in the phase of the person’s life.
- Consciousness arises as a complex, emergent phenomenon out of the prima materia of an organ weighing about 3 lbs, the physical body that sustains it, and the soical/interpersonal milieu in which these dynamical systems are nurtured.
- When we sleep, self-organizing phenomenon emerge using the stuff of our daily lives. The intricacy of such phenomena seem to demonstrate exquisite sensitivity to the set of initial conditions (think about Chaos Theory).
- Therapy and analysis involves two complex systems interacting. The language of transference and countertransference could be overlaid upon certain ideas related to dynamical systems.
- The nodes of electronic communication that permit a conference like “Jung and Neuroscience” to weave together a half dozen presenters and hundreds of attendees from dozens of countries.
There is an eerie beauty to the images and ideas mentioned above. I find myself contemplating the ageless ideas proposed by Hermes Trismegistus, ideas like “As above, so below”. That is for me the linguistic representation of self similarity. What does it mean to propose that God made man in His own image? What do we find so intriguing in movies like “Sliding Doors” or “Crash” in which we recognize the power of certain initial conditions.
“Jung and Neuroscience” is an exploration of the interface between the burgeoning field of neuroscience and the field of Jungian psychology. It is too easy to approach these as though they are divergent paths but we are likely to be better served to make our approach like the particle physicists have done when contending with light’s dual, complementary nature as both a wave and a particle.
The mathematics that undergirds the fields of dynamical systems, fractal geometry, and chaotic theory emerged from the work of Henri Poincaré, a late 19th century mathematician. With the advent of modern computing capacity that permitted “iterative” functions to be calculated ( and plotted) after hundreds or thousands of cycles. (an iterative function takes the output or solutions of a system of equations and uses them as the inputs for the next cycle of computation.) The beauty and elegance of the images appearing above can be produced because of the insights Poincaré introduced and the ability to use today’s computational capacity to graphically display the results of thousands of iterative calculations.
Poincaré’s Recurrence Theorem is one of the many intriguing things he posited. He stated that certain systems (nonlinear dynamical systems) will, after a sufficiently long time, return to a state very close to its initial conditions. The notion that a system of equations can “forget” for very long times yet somehow return to its initial conditions, is a profoundly attractive idea. This evokes reminiscences of a sphinx like journey of exodus and return.
Dr. Murray Stein quoted from CW 10 para 318 in his effort to characterize the lunar mind “It is not our ego-consciousness reflecting on itself, rather it turns its attention to the objective actuality of the dream as a communication or message from the unconscious, unitary soul of humanity. It reflects not on the ego but on the self, it recollects that that self, alien to the ego which was ours from the beginning, the trunk from which the go grew.” The lunar mind knows things that the solar mind does not know or does not yet know, or that have not been taken into consideration. Our solar mind can be fast but in its speed it may miss certain vital dimensions. The solar mind and the lunar mind conceived as strange attractors of the dynamical system that comprises our psyche. Consider the idea of personal and collective unconscious as strange attractors of the dynamical system we know as unus mundus.
Dr. Margaret Wilkinson explores the rich metaphoric realm of the dream. Dream analysis is a co-constructive process. As implicit speaks to implicit in the analysis, dreams are a shared, emergent process. Emergent phenomenon, the appearance of patterns that arise from relatively simple interactions, cannot be predicted from the simple rules of interactions. Just as analysis, a process that at some level involves simple rules (appointments, rituals like engaging dreams, active imagination, etc) produces unpredictable results.
In part, the dream may function in part to assemble dissociated self states that are disconnected. The voice of these self states can be discerned in the dream and its images. Through metaphor, unconscious states of the mind are exposed to conscious. Dr. Wilkinson’s comments about the dream images being organized around affective patterns, these patterns that are born of our personal experience provide the elements from which we assemble and organize our selves.
There is no destination to these musings. Instead, I hope this blog serves as an invitation to the reader to further exploration. I intentionally posted this blog during the Asheville Jung Center’s conference “Jung and Neuroscience”. There was an aspect of this post that was experimental, testing if my hypothesis about how the small amount of information I have about Dr. Kahn might have presaged some of his contributions. If these ideas do not emerge during the conference, so be it.
There is something about posting these reflections and the possibility that they might resonate with or evoke in another some useful effect that redeems anew the countless hours I offered to the project of learning fractal geometry. The cycles of life, the iterations involved in remembering my fractal geometry class, the sharing of these thoughts as a blog resemble an iterative function. First I enrolled and completed a class in fractal geometry as a way of answering a deep call within. Anticipating the “Jung and Neuroscience” conference, I take the results of that class from seven years ago and plug it back in like entering results of an iterative equation back into the original equation again and again. The posting of this blog like the plotting of solutions to an iterative function, is a display of the working and reworking of psychic material. My sense about such processes and the emergent results is that given enough time, the process of my psychic unfolding might eventually prove consistent with Poincaré’s Recurrence Theorem so that I may find myself returning to something very close to my original state.
By Len Cruz, MD
“The psychic is a phenomenal world which can be reduced neither to the brain or metaphysics.” Jung, Mysterium Coniunctionis, CW 14, par. 667