Квантовая география: задачи типизации, классификации и районирования

Abstract

The possibility of using the mathematical apparatus of the quantum theory of computer science for modeling geographical phenomena in solving problems of typification, classification and zoning to explain the reasons for the integrity of territorial objects is discussed. The methods of trivial and principal bundles of differential geometry and functional analysis of virtual internal spaces of geosystems (geomers and geochores) are used. The advantage of the quantum description lies in the linear simplicity of equations and formulas reflecting both the typical functions of discrete quantum states of geosystems and the superposition of these states realized in the observed spatial patterns in nature and society. This approach is the result of the ascent from a simple understanding of geographical objects as systems of continuous connection of elements to the allocation of independent discrete layers of independent functioning (geomers), their polysystem equivalence in geochores and holysystem integrity in region. The integrity of objects is described by general equations that do not take into account the influence of the geographical environment, therefore they allow creating models of different geosystems in the same way. For quantitative analysis of cartographic data, methods of reliability theory are used, based on the identification of frequency distributions of geomer areas by height, calculation of reliability and safety indicators. The application of the ideas of quantum geoinformatics is demonstrated by the example of assessing the factorial influence on the habitus of landscapes based on the signs of territorial manifestation of facies of different factorial series (facies classes) of the localities of the Maly Khamar-Daban ridge and the altitude distribution of the geomes of the Transbaikalia.