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Axiomatic Foundation of Central Place Theory: Revision from the Standpoint of the Russian School

  • THEORETICAL AND METHODOLOGICAL FRAMEWORK OF SOCIAL GEOGRAPHY
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Abstract—

The article refines the axiomatic foundation of central place theory (CPT) and identifies the possibilities and limitations of a logical transition in research from real settlement systems to central place (CP) systems. The necessity of relying on the CPT axioms in the following form is determined: (1) the space of a CP system is not infinite, but finite: the basis of each system is formed by an isolated lattice; the theory deals with physical space, not mathematical or geographical; (2) the space is homogeneous and isotropic in all respects, except for the distribution of not only the urban, but also the rural population; (3) a hexagonal lattice corresponds to the equilibrium state of an isolated CP system as an attractor; deviations from a hexagonal shape result only from external impact on the system; (4) CP systems are polymorphic: they can exist in modifications with both the same and different values for all levels of the hierarchy and not necessarily an integer value K ∈ (1, 7]. The axiom about a consumer’s “rational” behavior is accepted when establishing the CP hierarchy in terms of the volume of functions performed; when establishing their hierarchy in terms of population, it is redundant. In contrast to the foreign approach to CPT, which presupposes the transfer of properties of an ideal CP system to a real settlement system, in the approach of the Russian school, they are compared. The possibility of the latter is due to the equivalence principle in the relativistic version of the theory, according to which settlement systems form in the geographic space similarly to how CP systems form in the physical space. In both cases, if the gravitational effects are compensated, it is impossible to distinguish a settlement system from a CP system; i.e., a heterogeneous and anisotropic geographical space cannot be distinguished from a homogeneous and isotropic physical one. The immediate consequence of this is equivalence, on the one hand, of the population of settlements and CP, and, on the other, the distances between them in real settlement systems and CP systems.

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Notes

  1. In 1990, the following theorem was “proved”: “The best shape of the influence area among triangles, squares, and hexagons is a triangle” (Drezner, 1990). In 1992, this theorem was refuted and the superiority of the hexagonal shape was proved (Gusein-Zade, 1992).

  2. Cited from: Lösch, A., Prostranstvennaya organizatsiya khozyaistva (Spatial Organization of the Economy), Moscow: Nauka, 2007, p. 174.

  3. Despite possible differences, in the case of CPT, these concepts are essentially synonymous.

  4. This clarification is completely unnecessary, since in this case, ideal and real structures will not be compared with each other, but the ideal and, in some way, transformed real structures, with distances reduced to ideal. Such a reduction deprives the comparison of any meaning.

  5. The graphic representation of such a structure corresponds to K = 7 for each level (Fig. 1). Thus, systems corresponding to different K values will be depicted as parts of the structure corresponding to completion of the last stage of evolution, a kind of stencil, the loci of which occupy the CP as they arise in the evolution of the systems.

  6. Although in the Russian tradition, geographic space is most often simulatneously endowed with the properties of continuity and discreteness at (Baklanov, 2013).

  7. In the second case (for the traditional Christaller lattice), this condition is always true; in the first case, if the changes in the population of settlements in relation to the predicted CPT are completely balanced by the corresponding change in the distance from them to the largest settlement in the system.

  8. According to this, “all physical phenomena proceed in similarly in the inertial reference frame Kg having homogeneous gravitational field with acceleration of gravity g and in the uniformly accelerated system Ka which moves with acceleration g relative to an inertial system without gravitational field” (cited from (Logunov et al., 1996, p. 73)).

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Funding

The study was carried out at the Institute of Geography, Russian Academy of Sciences, topic of the state task of IG RAS AAAA-A19-119022190170-1 (FMGE-2019-0008).

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  1. Institute for African Studies, Russian Academy of Sciences, 123001, Moscow, Russia

    R. V. Dmitriev

  2. Institute of Geography, Russian Academy of Sciences, 119017, Moscow, Russia

    R. V. Dmitriev & V. A. Shuper

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Correspondence to R. V. Dmitriev or V. A. Shuper.

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Dmitriev, R.V., Shuper, V.A. Axiomatic Foundation of Central Place Theory: Revision from the Standpoint of the Russian School. Reg. Res. Russ. 13, 751–757 (2023). https://doi.org/10.1134/S2079970523700983

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