A 4-Dimensional Bifurcation Map

Editor's Note:

The new sciences of Chaos and Complexity change forever our understandings of the concept of sturcture.  Instead of the solid geometries of Euclid, one must turn to the fractal geometries of Mandelbrot and others developed in the past 60 years.

R.D. Smith has provided an excellent argument for viewing SOCIAL STRUCTURE as a fractal rather than as a solid object.  He focuses upon CLASS, RACE, GENDER and ETHNICITY as case in point.

Marxists and others doing work in class structure, structures of gender, race and or ethnicity would do well to
use this entirely new understanding of Structure as basis of any theoretical statements they might want to make.

For a much more discursive, much less mathematical treatment of the concept of structure, see an article, Chaos and the Concept of Structure, by James Yarbrough and myself at:

Chaos and the Concept of Structure

TR Young, Director, the Red Feather Institute

Smith, R. D. (1998) 'Social Structures and Chaos Theory'
Sociological Research Online, vol. 3, no. 1

Copyright Sociological Research Online, 1998

Abstract

Up to this point many of the social-scientific discussions of the impact of Chaos theory have dealt with using chaos concepts to refine matters of prediction and control. Chaos theory, however, has far more fundamental consequences which must also be considered. The identification of chaotic events arise as consequences of the attempts to model systems mathematically. For social science this means we must not only evaluate the mathematics but also the assumptions underlying the systems themselves. This paper attempts to show that such social-structural concepts as class, race, gender and ethnicity produce analytic difficulties so serious that the concept of structuralism itself must be reconceptualised to make it adequate to the demands of Chaos theory. The most compelling mode of doing this is through the use of Connectionism. The paper will also attempt to show this effectively means the successful inclusion of Chaos theory into social sciences represents both a new paradigm and a new epistemology and not just a refinement to the existing structuralist models. Research using structuralist assumptions may require reconciliation with the new paradigm.

Keywords:

Chaos Theory, Complexity, Connectionism, Consciousness, Memes, Network Theory, Reductionism, Social Change, Soliton, Structuralism, Timelines, Transduction

VIEW the entire article at Sociological Research Online: 

                        http://www.socresonline.org.uk/socresonline/3/1/11.html