World Systems, the Eonic Effect, and "Attractors"

The following passage is from Paul Ziolo’s essay “Chaos, Catastrophe, and Psychohistory.”  It's about CDSR, “attractors”, and the geometries + visual metaphors that are part and parcel of such.   Ziolo’s discussion in this passage is a very fascinating one, a set of ideas pertinent I think to both discussions of World Systems Theory (in its structures/processes) and the Eonic effect.  The question that needs asking is: how does CDSR illuminate notions of World(-)Systems analysis and, in turn, how can a world(-)systems approach help us to understand the framing of complex dynamic systems models in human affairs? 

The same question goes for the Eonic model (albeit with a slight variation):  Does the MACRO historic process that we know as the “Eonic effect” (a real world process in which we are only beginning to put our finger on, grasp, & understand) operate through the instrumentality of CDS or might CDS be the larger natural principle at work here [operating through what we see as the Eonic pattern in world history]?

Where stands WST and the Eonic Effect in respect to such ideas about “point”, “limit-cycle”, and “chaotic” attractors?  And,can these help us better understand how macro-social and historic phenomena operate in human experience over time? (For instance on the world-systems end of things, can they shed better light on Core/Periphery & Hegemony/Rivalry relationships? Can they shed better light on how trade/ communications networks function in a world systemic framework? )(Or, in regard to the Eonic Effect, can an understanding of attractors help us to better fathom such concepts as “fast action periods”, “fields of diffusion”, etc.?  Can they help us to more fully understand why certain places and certain times are hot spots/hot points in world history and, therefore, centers around which the rest of human events seems to revolve?) …

Your thoughts?

Luke R.

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“An order parameter is a collective phenomenon. It is emergent beyond the obvious other structures of organisations and societies …”

                                Kenyon B. De Greene - “Field Theoretic Framework for the Interpretation of the Evolution, Instability, Structural Change and Management of Complex Systems” - in Chaos Theory in the Social Sciences: Foundations and Applications edited by L. Douglas Kiel and Euel Elliott, University of Michigan Press, Ann Arbor, 2000, p. 280.                                         

                … extensive field of complex dynamic systems research (CDSR) or, to put it more generally, nonlinear science. As a basis for the integration of exogenous (objectively-oriented) and endogenous (subjectively-oriented) epistemologies, CDSR has a long, if fractured, history. Some of its more fundamental ideas can be traced back to the time of Heraclitus of Ephesus (fl. c. 500 b.c.e.), but in the more concise mathematical sense, the roots of CDSR grew out of the multidimensional calculus, algebraic and dynamic topology, fluid dynamics, applied systems theory and nonlinear problems in chemistry, biology, meteorology and experimental physics - to name but a few. As the name implies, CDSR arose from studies of sudden discontinuous change and shifting patterns of complexity in dynamic, co-evolving systems, whether they are physical, chemical, biological, psychological, social or environmental. In many ways, the more abstract, generalised concepts behind CDSR or ‘nonlinear science’ represent a kind of Kuhnian paradigm transform in scientific thinking and as such, are still embroiled in controversy.

... Contemporary science reveals that matter is much richer, more complex in its behaviour and its capacities for self-organisation than earlier thinkers were aware of. Moreover, recent research in neurobiology, exemplified in such studies as those of Schore (1994) and Siegel (1999), are beginning to vindicate many of the earlier intuitive concepts of psychoanalysis, tracing their etiologies within a more concise, neurobiological framework ... Such research reveals that psychic life itself is an emergent property of organic life. By ‘emergent property’ we mean that it is synergetic - something greater than simply the sum of its parts. Emergent properties or synergetic phenomena are self-organising and do indeed possess a distinct level of autonomy as far as analysis is concerned, but discourse at this level will aways be limited. Simple reductionism does not work in such cases however, and solutions must be found that adequately explain both continuities and differences at small and large levels. … as DeMause correctly points out - many aspects of psychological evolution, especially at the level of social behaviour, are in fact Lamarckian - i.e. they are epigenetically determined through the transmission of shifting emotional and cognitive patterns across generations in both families and societies. Many CDSR-derived models were developed explicitly to deal with discontinuities of this type. Before we focus on explicit types of model, I will offer a very brief history of CDSR and describe the basic concepts.

                Dynamic models for social systems …René Thom’s Stabilité Structurelle et Morphogénèse,

“In the situation where man is deprived of all possibilities of intellectualization, that is, pf interpreting geometrically a given process, either he will seek to create, despite anything, through suitable interpretations, an intuitive justification of the process…  In other words, geometrization precedes verbalization. Thom goes on to point out that through failure to adequately geometrize the theory of gravitation, little advance has been made in this field, and that moreover, such a lack of advance is ignored - i.e. ‘resigned incomprehension’. It should be borne in mind that by ‘geometry’, Thom does not mean ‘Euclidean’ geometry, but rather dynamic topology.

                Put simply, chaos and catastrophe are words that refer to the properties of attractors - dynamic ‘wells’ or vortices that pull individual evolutionary paths or trajectories towards themselves. If we were to imagine a mountain landscape with very smooth ground on which a very large ball was rolling about, the valleys would be attractors - places the ball would be most likely to end up, and from which it would require applied and consistent effort to dislodge it. Mountain peaks are ‘repellors’ where the ball could never rest, but would roll down any direction at random, while the ridges (or saddle-points) connecting the peaks are places where the ball is unstable (it won’t remain where it is) but has a choice between two equally steep slopes, each of which leads down to a neighboring attractor of greater or lesser depth. These geographical metaphors are still common in the language of CDSR and Thom employs it frequently to dicuss models in ultrastructure and morphogenesis - the growth and transformation of living patterns and forms.

                An attractor can basically be of three types - a point attractor, a limit-cycle attractor and a ‘strange’ attractor (one that is verging on or exhibiting chaos, sometimes called a ‘chaotic’ attractor - these often bizarre entities comprise what is called the ‘zoo’ of CDSR!). In a point attractor, all trajectories converge to a single point. In a limit-cycle attractor, trajectories constantly tend to converge to some definite orbit or cycle of values. A chaotic attractor is easily visualized - imagine a hurricane with its clearly-visible vortex and virtually incalculable number of violently swirling molecules of air (trajectories). This example is apt since what is called ‘chaos theory’ has its origins in meteorology - one type of ‘monster’ from the CDSR zoo is the Lorentz Attractor, discovered by Edward Lorentz while researching atmospheric turbulence and described in his classic paper of 1963[[i][v]]. An attractor exhibits ‘chaos’ when the behaviour of trajectories on the small scale is unrepeated and unpredictable. ‘Chaos’ does not mean lack of order however, since attractors of this type can exhibit quite definable properties on the large scale. Catastrophes on the other hand are manifolds or ‘deformed surfaces’ like crumpled sheets of paper -  kinds of topological map, whose properties represent structurally stable patterns of shifts between two or more attractors. After a sceptical reception during the late 70’s, catastrophe theory has advanced, and become more fully integrated into the overall pattern of CDSR research as issues governing dimensionality and phase transition (attractor shift) become clearer and more quantifiable.

                In psychology, moods, desires, emotional or behaviour patterns and modes of cognition or communication are all types of attractor. The emergence of a stable personal identity is also the emergence of a particularly complex (but stable) ‘chaotic’ attractor and illustrates a fundamental fact in CDSR that should be compared to to a similar fact in psychohistory. The behaviour of a complex attractor is highly sensitive to initial conditions. In psychohistory, we may also say that the human being is an evolving process whose psychodynamics and manifest behaviours are also crucially dependent on initial conditions - conditions experienced during the perinatal and early childhood periods. On the historical level, as DeGreene’s quote illustrates, socioeconomic systems and processes, revolutions, wars, alliances, etc. are all examples of attractors and attractor shifts - DeGreene’s ‘macropsychological parameters’ are the very processes of psychospeciation and psychoclass conflict studied in psychohistory. Phenomena at both the social (macro) and the psychological (micro) level have been successfully modelled using both chaos and catastrophe-theoretic models. These models can be either qualitative or quantative, depending on types of question being asked, and their formulation. In psychohistory, apart from straightforward data-gathering and the application of normal statistical methods (such as SPSS) in very specific, localized studies, larger-scale modelling is still at the qualitative stage and is likely to remain so until more efficient research strategies are developed on the basis of algorithms derived from these initial models.

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