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Levin, F.M. (1996). British Journal of Medical Psychology. LXVII, 1994. On Psychoanalysis and Non-Linear Dynamics: The Paradigm of Bifurcation. Beatrice Priel and Gabriel Schreiber. Pp. 209-218.. Psychoanal Q., 65:843-845.
Psychoanalytic Electronic Publishing: British Journal of Medical Psychology. LXVII, 1994. On Psychoanalysis and Non-Linear Dynamics: The Paradigm of Bifurcation. Beatrice Priel and Gabriel Schreiber. Pp. 209-218.

(1996). Psychoanalytic Quarterly, 65:843-845

British Journal of Medical Psychology. LXVII, 1994. On Psychoanalysis and Non-Linear Dynamics: The Paradigm of Bifurcation. Beatrice Priel and Gabriel Schreiber. Pp. 209-218.

Fred M. Levin

Priel and Schreiber's concise article invites one to consider several complex psychological variables in relation to non-linear dynamics (catastrophe theory, chaos theory), a branch of mathematics that covers phenomena that appear random but are actually deterministic. When the equations which describe the behavior can be discovered, they can be modeled. This kind of modeling is made possible through the advances of modern computers. Consequently, much of the terminology and imagery presented in the article deals in part with geometric diagrams, a subject not commonly seen in psychological articles.

The authors begin with “bifurcation points” which they define as those points which “designate the emergence of several new and stable solutions.” They introduce a Feigenbaum diagram which demonstrates bifurcation points; the diagram expresses how the frequency of some oscillatory phenomenon is rapidly doubling, and the system is shifting into chaos. The authors highlight this critical time period (or so-called phase state shift) because this “moment” involving the evolution of chaos is something about which experts in chaos theory generally agree: from a strictly mathematical perspective “universal” principles and mathematical constants characterize the changes, apparently independently of the nature of the system involved (whether laser, heart, electronic circuit, weather, or whatever). Although the subject of chaos (and its graphical representation) can indeed be esthetically beautiful, the subject nevertheless remains dauntingly difficult, and finding mathematical solutions to chaos-related functions is at present sometimes impossible. Also, there will be questions about whether and how to apply this specialty knowledge to psychoanalysis.

Within chaotic systems in general initial conditions can prove decisive, making a difference, for example, in which direction is taken at each point of bifurcation. This is called the “butterfly effect” according to the example in which the presence or absence of a single butterfly can allegedly determine whether or not a hurricane ultimately develops at a particular time and place.

The authors assert the applicability of chaos theory to psychoanalysis for a variety of reasons. They point out that Freud's historical description of logical chains of

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associations involving “two or more threads of associations meet[ing] and thereafter proceed[ing] as one” can be seen as neatly overlapping the mathematical perspective of a bifurcation point topographically, but one, according to the authors, “where one of the ramifications has been suppressed.” They also make a number of assertions which support their claims about both the utility of chaos theory as a metaphor and its specific relevance beyond mere metaphor.

One advantage of chaos theory for them is that it smoothly takes into account the surprise and complexity that invariably play a crucial role in clinical psychoanalysis proper. A second advantage is that such moments of surprise, from the perspective of chaos theory, would seem isomorphic to or representative of “a process of destabilization —a transition to a non-linear, far-from-equilibrium stage—that allows for bifurcation points to occur.” In other words, chaos theory appears robust in capturing psychological change in development, based upon its “enhanced sensitivity in perceiving the [local] environment” as well as its ability to formally express “a multiplicity of solutions” to a complex equation.

The authors suggest that variables such as the psychoanalytic transference phenomenon itself might be illuminated when seen in relation to the behavior of the “attractors” of chaos theory. In a nutshell (in terms of chaos theory) transferences might be considered “transitions from [nonchaotic] ‘limit cycles’ to strange [chaotic] attractors through bifurcation. …”

The authors define attractors as “geometric forms that describe the long-term behavior of a [complex] system.” That is, “an attractor is what the behaviour of the system settles down to, or is attracted to,” such as a pendulum's movement over time toward a fixed point of rest. This rest point is described as an attractor because it is as though the point attracts the pendulum. Strange attractors describe still more complex patterns; they also represent the inception of chaotic patterns, and are one of four basic kinds of attractor classifications. The authors can only provide tidbits or hints regarding the many details of chaos theory.

If the reader begins to doubt the relevance of the subject to psychoanalysis, it should be noted that a number of scholarly United States psychoanalysts, notably David Forrest, Robert Galatzer-Levy, and Vann Spruiell, have made similar valuable efforts to alert the psychoanalytic community to chaos theory. Although none of this American work is cited by the authors, this is not surprising, given how rarely American authors cite British scholars.

The authors have condensed their article so much that there is only a bare minimum of illustrations of their ideas or documentation of previous work in their own interdisciplinary field. Also, although a few diagrams do appear (such as the classical Feigenbaum diagram), they are generally inadequate to the task. Some readers might have benefited from more detailed explanations.

The writing of the American psychoanalysts cited above might be useful for readers who wish a better understanding of what is being bravely asserted by Priel and Schreiber. For example, Vann Spruiell helps with verbal explanations of the nature of non-linear dynamics and its specific application to psychoanalysis; Galatzer-Levy provides some helpful visual metaphors (of topological folding) as means of making the subject more comprehensible, while Forrest provides the best general overview of integrating psychological and mathematical approaches that I am aware of.

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Despite the above-noted deficiencies. Priel and Schreiber's article is an important and unique contribution to the application of chaos theory to specific psychological complexities.

We have a great interest in understanding mind and brain, surely the most complex subject ever examined by humankind, and any technology that might organize or simplify this study would be valuable. Moreover, other medical sciences have attempted to exploit chaos theory, so psychoanalysis is entitled to test out its utility.

In my opinion the best part of the paper deals with the application of chaos theory specifically to transference. The idea is basically as follows: (1) certain transferential moments represent, on the one hand, possibilities of structural change in the mind/ brain and, on the other hand, bifurcation points with creative potential; (2) “bifurcation potentially creates information … [,that is,] … space-symmetry breaking is the necessary prerequisite without which the possibility of constructing an information processor simply would not exist” (according to Nicolis and Prigogine, cited in the article); and (3) chaos can be useful to communicate or carry information (as in Shannon's theory of communication, viz., the amount of information conveyed by any communication varies indirectly with our ability to predict what will be said).

The authors are asserting that it is possible that the mind/brain of the transference -experiencing subject in psychoanalysis may at times be undergoing specific states that involve learning readiness (“windows”), and these states would seem to coincide with the onset of chaos. What the chaos involves is a kind of “freedom” to form bifurcation points in one's thinking and through analyzing, thus reorganizing critical data bases of mind and brain.

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Article Citation

Levin, F.M. (1996). British Journal of Medical Psychology. LXVII, 1994.. Psychoanal. Q., 65:843-845

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