Spatial Dynamics: Some Conceptual and Mathematical Issues

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Abstract
Spatial dynamics—the study of the spatiotemporal dimension of socioeconomic activities—is grounded on highly questionable premises. These are implicit or explicit philosophical theses regarding knowledge (empiricism) and society (methodological individualism). As a consequence of these premises—it is argued—the scientific knowledge of social phenomena becomes problematic if not impossible. It is further demonstrated that the dominant paradigm in the social sciences (based on empiricism and individualism) is not the only possible one. A fairly comprehensive overview of an alternative is presented, which draws upon recent advances in Marxian theory. In this perspective, the constitution and transformation of spatial configurations cannot be understood in terms of observable spatial relations; as social forms, spatial patterns must be explained in terms of the dynamics of the underlying social structure. Accordingly, ‘spatial dynamics’ must be reconstructed as the dynamics of spatial forms: the study of the formation and transformation of spatial configurations as expressions of the expanded reproduction of the capitalist mode of production in capitalist social formations. It is further argued—from the very nature of the capitalist process—that the transformation of spatial forms should be viewed as a process of evolution through instabilities and fluctuations. Accordingly, there is a sound theoretical motivation for experimenting with ‘dissipative structures’ and catastrophe theory. The basic ideas of nonequilibrium thermodynamics and dissipative structures are presented via two simple mathematical models. The latter do not intend to formalize Marx's or Schumpeter's theory. Their only function in the discourse of this paper is to illustrate how the ideas of structural determination, crises, and qualitative change can be captured in rigorous mathematical terms.

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