Panagis Liossatos

Spatial Dynamics: Some Conceptual and Mathematical Issues

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 Marxs or Schumpeters 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.

A Formal Model of Big Step Disarmament and Domino Effects

In a book manuscript recently completed, the authors have presented a general systems approach to the study of situations involving many regions interacting in physical space. However, we indicated that at many places it is also possible to extend the analysis to situations involving many nations interacting in policy space. We also began to develop a theory of major discontinuous change (transition) in the behavioral structure of a multi-nation system and hinted that gravity-like interactions in policy space might be useful in this connection. In this paper we wish to develop a specific application of such a theory.

Social Injustice and Optimal Space-Time Development

Some young, Nordic scholars have recently criticized social science research as it is conducted in the United States and other industrialized, big power nations. These scholars have been critical of the so-called value-free, objective investigations. Many, if not most such investigations do have value judgments implicit in the sense that they ignore the distribution variable and the problems generated by the uneven distribution of goods and resources. By conducting research contributing to an effective attack on other problems of the industrialized, big power nations, many scholars in these nations indirectly lend considerable support to a social system which perpetuates or intensifies the unequal distribution of wealth. During a visit by the senior author to Oslo in the summer of 1972, many Nordic scholars insisted that we in the big power nations make explicit the features of social justice or injustice that are deeply rooted in our investigations. The senior author had this critique in mind when he participated in the meetings of the South Asia Section of the Peace Science Society (International) in Delhi. He could not help but observe that social injustice, in terms of unequal command of goods and wealth and resources, was on the increase in India, despite the idealistic, democratic principles of social justice which have been widely proclaimed in its recent history of independence. He also came to recognize that thus far every one of the models of optimal space-time development which we have constructed in the last several years seems to have embedded in it increasing social injustice-increasing discrepancies over time in the spatial distribution of productive capital and the consumption of goods-findings consistent with the historical record and with current life. Hence, in this paper we examine carefully the properties of optimal space-time development models. We seek to identify those which lead to the increasing discrepancies noted above. Further, we ask: are there

Socio-Economic Dimensions of the Arms Race

The most interesting idea in L.F. Richardson’s work’ is the conception of an arms race as a world-dynamic process driven by a multi-nation interaction mechanism and intranational forces. Unfortunately, this positive aspect of the Richardson tradition is overshadowed by the absence of social science theory that would guide us in deciphering interaction mechanisms and intranational forces. This paper is a first step in the direction of embedding Richardson’s system into an adequate theoretical frame. The Richardson model is reviewed in Section 2. We point out the problematic nature of the traditional ideas that underly Richardson-type schemes; and focus on the intranational economic force. It is argued that the latter cannot be the same for different socio-economic formations, such as the United States and the Soviet Union. This leads us to the construction of a modified Richardson model, which is thoroughly analyzed in Section 3. This simple model allows us to illustrate how an arms race can be formalized not as a purely deterministic process but rather as an evolutionary process that is effected by instabilites and f luc t~a t ions .~ Thus one can very well start with a deterministic formalism (as Richardson did), provided that this formalism be appropriately interpreted and embedded in a stochastic framework. Linear causality is replaced by the concept of structural determination: A given structural setting determines a spectrum of possibilities for system behavior. It is through random fluctuations, effected by the action of micro forces, that a specific alternative is ultimately selected. Finally, Section 4 is devoted to some concluding remarks about the arms race.

Commodity Production and Interregional Transfers of Value

This chapter is concerned with the question of uneven appropriation of the net social product by regionally based fractions of capital. We therefore propose to examine just a moment in the process of uneven regional development. Unfortunately, we shall not offer any direct integration of uneven regional development with capitalist accumulation. We intend to work out only some of the theoretical preconditions for doing so. Specifically, we shall elaborate a concept of regional inequalities at a level of abstraction at which accumulation is absent and the capital-labor relation is reproduced on the same scale from year to year (simple reproduction). This is an abstraction that provides the minimum theoretical structure required for the analysis of value-price relationships and for the introduction of the concept of unequal interregional relations. This method of investigation emanates from Marx (1977, Ch. 23) and Sraffa (1960).

Social Justice and Economic Development Revisited

This paper extends a space-time development model that parallels basic physical systems, providing additional insights into social processes. Forces for spatial diffusion of capital are examined and utility stemming from the consumption of “c-power” and other non-economic goods is incorporated. The social justice implications of these extensions are derived.