Central Place Theory after Christaller and Lösch. Some further Explorations. In Memory of August Lösch, 15 October 1906 - 30 May 1945 - Michael Sonis (European Regional Science Association (ERSA), 2005)
This paper presents the critical reevaluation of the methodology of classical Christaller- Central Place Theory.First of all the reconstruction of Central Place Geometry on the basis of the Barycentric Calculus was considered. On this basis the novel superpositional model of the actual Central Place System is constructed. Building blocks of this model are the Beckman-McPherson models representing the main tendencies of optimal organizations of space acting simultaneously in the actual Central Place system. The weights of these building blocks represent the level of realization of the specific extreme tendency in the real system. Next the (jumping) catastrophic dynamics of the Central Place hierarchies presented with the help of geometrical scheme of the movement of the point representing actual Central Place system in the polyhedron of all admissible Central Place systems. Three main applications of the new conceptual framework are elaborated in detail: 1. The Superposition Principle: elaboration of the algorithm of decomposition of an actual Central place system into the weighted sum of the Beckmann-McPherson building blocks. 2. The Enumeration of all structurally stable optimal (minimal cost) transportation flows in the hierarchical Central Place system and 3. The Merger of two major theories in the Regional Science: the classical Input-Output theory of Leontief and the classical Christaller- Central Place theory.
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