Results and Prospects of the use of Mathematical Methods in Economic Geography

A review of the use of mathematical techniques in Soviet geography finds that the new methods are an essential tool in the application of systems theory to geographical problems. Mathematical techniques are held to have the greatest promise in the investigation of space (topology), the study of large systems (set theory, general systems theory) and research on complex relationships between phenomena with a certain randomness (linear algebra, polylinear algebra, probability theory). The use of mathematical techniques should be combined with traditional methods in geography, and instead of replacing the traditional geographical methodology, mathematics may be expected to strengthen that methodology. A real need is seen for a set of basic axioms in geography, and mathematics is expected to play a significant role in this connection. Mathematical models have proved useful in the investigation of particular spatial structures, such as population density within cities and the location of service establishments. But problems have been encountered in the modeling of territorial production systems.     

Quantitative Methods in Physical-Geography Research

The use of quantitative techniques in physical geography is discussed with reference to three particular disciplines—climatology, glaciology and geomorphology. Although significant advances have been made in these and other particular disciplines, there is increasing need for applying quantitative methods to the composite of geographical processes, related to various forms of the exchange of matter and energy. A quantitative approach to integrated physical-geography research is needed for a resolution of the general problem of a quantitative explanation of the physical-geographic process and the formulation of a quantitative theory of physical geography. Aside from inherent difficulties in applying quantitative techniques to physical geography, particularly the biogeographic disciplines, there are additional problems of an organizational nature in the Soviet Union, where specialists in various disciplines tend to be associated with different institutes.     

On the Significance of Lenin's Ideas for Soviet Geography

The president of the Geographical Society USSR reviews the present state of Soviet geographic theory in the light of Leninist philosophy. The objective existence of natural regions with definite boundaries is affirmed. The approach of “social physics,” applying natural laws to social phenomena, is rejected. The use of mathematical techniques is welcomed, but not to the extent of giving rise to a separate discipline of “theoretical geography” that would deal with whatever is common to both physical and economic geography. The geographical environment is defined as that part of the earth's natural environment in which nature and society are in direct interaction. Both geographical determinism and social determinism (geographical nihilism) are rejected. The definition of geography as a system of scientific disciplines is affirmed, and a proposed redefinition of geography as dealing with the evolution and control of dynamic spatial systems is rejected.     

Present Problems in Theoretical Geography

The need for a distinctive discipline of theoretical geography is enhanced by three current research trends in geography related to the scientific and technical revolution. They are remote sensing, resource use and economic location. Theoretical geography is concerned with the automated processing of the growing body of geographical data, the study of complex geosystems and their multidimensional geospaces and the development of a set of geographical axioms. The development of theoretical geography is closely related to the growing use of mathematical methods in geography by formulating geographical problems in a form amenable to mathematical analysis. Theoretical geography helps to formalize geographical concepts and facilitates the building of models in geography. Models, in turn, provide a better understanding of a system than can be expressed in words.     

The Role and Significance of Objective (Mathematical) Methods in Geographic Research

A staff member of Leningrad University's Cartography Department reviews the introduction of quantitative methods into geography and offers a classification of physical and mathematical models used in geography. The increasing use of objective methods, including physical and chemical techniques, is expected inevitably to affect the nature of geography as a scientific discipline, just as the use of aerial photography changed the theory and practice of topographic mapping.     

A Selected Bibliography of Mathematical Articles in Soviet Economic Geography (1960–1968)

Advocates of a new discipline of theoretical geography seek to bolster their argument for establishment of the discipline with quotations from Lenin. Theoretical geography, conceived more broadly than Bunge's mathematical geography, would seek to generalize the findings of all the particular geographical disciplines, to formulate general geographical laws, develop a common geographic method and common approaches to the formalization and modeling of geographic phenomena. Its objects of study are so-called geosystems, which are conceptualized as totalities of the autonomous spatial systems of the environment, population and the economy. Each geosystem is viewed as being associated with its geospace, defined as the “eigenspace of geographical objects, of geographically whole formations”. Geosystems are regarded as possessing a certain degree of freedom in contrast to the view that cause-and-effect relations within such systems are rigidly predetermined. The outlines of a number of general geographic laws are suggested. They include the law of growing contrast in spatial systems of all types and the law of asynchronism in the development of spatial systems. Theoretical geography is presented as having significant practical application in the analysis and prediction of the effect of man's development of spatial systems, in setting of development priorities and determining optimal types of development.     

Mathematical education for geographers

Abstract

The mathematical topics which are of use to geography students are outlined, as are the methods used for teaching mathematical techniques in geography courses at Leeds over the last few years. The concluding section relates practice to goals, and the problems of providing the student with a framework into which he can fit all the pieces of knowledge he has acquired. Possible future developments are reviewed briefly in the light of the development of new mathematical techniques on the one hand, and criticisms of the existing state of the art on the other. The subject matter of the paper is limited to mathematical education, and there is only indirect and brief concern with statistics.     

系统论信息论方法在旅游地理研究中的应用

系统论信息论控制论是全面研究各种现象的相互关系的相互作用的综合性基础科学,广泛应用于各种不同性质的系统的模拟,预测和控制任务,旅游系统也不例外。本文重点讨论系统和信息论方法在旅游地理研究中的应用,其中包括从系统论角度对旅游综合体的系统结构分析的从信息论角度的地域旅游评价。最后讨论了有关上述方法在旅游地理学中实际应用的一些原则性部题。     

A New Work on Theoretical Geography (a review of David Harvey,Explanation in Geography)

A discussion of Harvey's book, with particular reference to the landscape concept, classification principles, modeling, the map as an information channel, the systems paradigm and the organization of geography as a science. In the reviewer's view, Harvey's book represents a useful introduction to the strategy of geography because it seeks to formulate a sort of metatheory of geography as a whole, instead of dealing with particular geographical disciplines. Sochava regards geography not as a simple collection of particular disciplines that sometimes exchange information and join in the solution of interdisciplinary problems. He views geography rather as a vast area of human knowledge that seeks to integrate within itself those elements from various disciplines that relate to the basic function of geography, leaving all that is nongeographical to such sciences as geology, biology and economics.     

Editorial: Geography and the ‘European Year of Citizenship through Education’

The paper introduces a library of video podcasts (vodcasts) used to support the learning and teaching of geographical methods and techniques relating to physical geography and GIScience in particular. While the notion of video learning is not new, the accessibility of the multimedia snippets via lightweight mp4 players in a field context allows a geographical freedom to learning that goes beyond previous classroom-based work. Evaluation, conducted through the use of reflective diaries and focus groups, identified that all students thought the podcast reference library was a valuable learning resource, of particular appeal to students with a visual approach to learning.     

Applied spatial modelling in the twenty-first century: the Wilson legacy. Looking back and looking forward

ABSTRACT

In this paper, we review the contributions of Alan Wilson to geography and regional science over a period of more than 50 years. Beginning from theoretical insights, mathematical models and spatial analytics methods for cities, the research becomes somewhat more applied in the 1980s. The notable impact of this work in a business and commercial setting is in marked contrast to a relative lack of traction in a public policy environment. Reasons for this are explored. In more recent times, the advent of big data has started to generate transformational approaches to geographical problems. We argue that years of accumulated experience from the study of more abstract problems within less well-instrumented systems was a precursor to this. Finally, we argue that through working with a ‘family’ of modellers, the skills available to meet these challenges is significantly more extensive than could have been the case in the absence of such a programme. It is a legacy which is at once inspiring, durable and hugely significant.     

Study of the History of Geographical Ideas

Two recent books on the history of geographical ideas, by A. G. Isachenko of Leningrad University, and by Preston James of Syracuse University, are reviewed in the general context of the need for a textbook for courses now being taught at Soviet universities. The Isachenko book is criticized on the ground that it reduces the history of geographical ideas to a history of physical geography, ignoring the impact of human activity. James, who deals with the history of geographical ideas as a whole, is praised for having included a chapter on the new geography in the Soviet Union and on the innovative aspects of theoretical geography, such as systems theory, spatial systems, diffusion on studies, etc. In the reviewer's opinion, the two books need to be examined critically in connection with preparation of a text for a Soviet university course on the history and methodology of geography.     

Problems in the Building of Mathematical Models for Geographic Systems

Some basic concepts and principles of general systems theory applicable to geographical systems are formulated. A geosystem is viewed from the point of view of the controllable processes that convert it from one state to another and insure its self-regulation and stability. Since geographical systems derive energy from the surrounding environment and use it for their physical-chemical and biological functions, the structural elements of such systems behave thermodynamically like automata performing irreversible processes, and the laws of thermodynamics can therefore be applied to the functioning of such systems. A mathematical apparatus is demonstrated for the study migratory flows of mass and energy in geographical systems.     

Mathematical Training of Students in the Economic-Geography Department of Moscow University's Geography Faculty

Courses offered in the mathematics training of economic geographers at Moscow University are reviewed. A total of 350 hours, stretching over the first four years of the five-year course of study, includes two courses in mathematical principles (higher mathematics and statistics) followed by two courses that deal with particular applications in economic geography (including one on location models). A need is seen for revising the present program with a view to expanding the total number of hours to 500–600, providing more rigorous training in mathematical techniques and computer programing at an earlier stage, and leaving the actual applications to courses in economic geography proper.     

THE STUDY OF SPATIAL DIFFERENCES IN CULTURAL ENLIGHTENMENT SERVICES

The study of cultural enlightenment services, comprising entertainment (movies, theaters), information (museums, libraries) and healthful activities (athletics, rest homes), is found to have been neglected by Soviet geographers. A variety of techniques are proposed to investigate spatial differences in this research area; the methods range from comparing the level of services in a particular place or area with a standard place (say, Moscow) to the use of information theory to measure the amount of information imparted in the provision of cultural services. In addition to the study of cultural services, there is need for a broader geography of culture in general, which would also examine the production and flows of cultural goods and the movements of population associated with the satisfaction of cultural needs.     

20世纪80年代以来人文地理研究进展及趋向分析

20世纪80年代以来,人文地理研究逐步走向多元化,从不同视角、不同技术手段进行不同区域、不同问题的理论与实践研究。指出在研究中存在的主要问题：①微观研究有待加强;②人文地理基础理论研究薄弱;③人文地理地位不高,且仍在下降;④人文地理研究方法增多,但运用力度不够;⑤人文地理研究风气尚需要斧正。21世纪以来,人文地理研究出现新的研究趋向：研究成果更具综合性、边缘性、可操作性、可视性,与实际应用结合更加紧密,且理论研究有所深入。根据问题,建议：①做扎扎实实的工作,克服浮躁情绪,潜心钻研;②加大相关学科研究方法借用力度;③加强人文地理研究成果的可操作性;④加强人文地理学中的研究创新;⑤适时开展人文地理理论建设。     

西方舞蹈地理研究进展：从非表征争议到创意地理实践

作为早期非表征理论构建的主要场景,舞蹈是特定想法—行为的表达与实践,有助于探察身体动作在理解和创造表达上的潜能,而舞蹈正式进入文化地理学视域的时期也正好是非表征理论对传统文化地理学的挑战接近成熟的关键时期。随着展演的身体成为分析对象以及编舞成为地理研究中新的非表征方法概念,舞蹈作为社会跨学科实践和工具受到越来越多关注。本文以非表征理论引发的诸多争议为基本背景,力求全面呈现如下两个转变过程：①舞蹈如何从关于身体、展演性、认同等地理学话题,逐渐演变为检测动作节奏、感觉、生成空间的地理实践和方法;②舞蹈地理研究经历如何从批判的舞蹈文化政治学,逐渐转向实践性的展演艺术与创意地理学。文章认为,非表征思想有望用于解决表征之外可能存在的开放性实践难题,丰富调节实践的情感维度,并拓展分析情感交缠的物质主义话语,而转变后的西方舞蹈地理研究对于理解我国现当代文化政治经济的情感属性、思考艺术影响下城市公共社区的差异化也就具有明确的启发价值。     

THINGS THAT ARE ALMOST BUT NOT QUITE WELL KNOWN IN PHYSICAL GEOGRAPHY

The author, a physical geographer, sees no need to despair about the present state of the discipline and the future of geography. He places geography in context among the sciences and finds a need for a synthesizing discipline that pulls together the findings of the particular disciplines. Such a function might be performed by landscape science and regional geography. In general, geographers are found to go too far afield in their research and there is a need to define the focus of the disciplines to eliminate the present centrifugal tendencies. Such a unifying focus might be found in geographical prediction. Geographers should be aware of the limits and capabilities of their discipline; geography is most effective in fostering solutions in conjunction with other disciplines. Fieldwork per se is criticized; some geographers make a fetish of fieldwork, spending their life in the field without ever writing up the results as a contribution to science. The language of geographical exposition must be cleansed of pseudoscientific jargon; too much geographical writing is incomprehensible. The use of mathematics in geography should be placed in historical perspective; it is not the panacea for all that ails geography.     

An Approach to the Substantiation of Stochastic Conceptions in Geography

The penetration of stochastic-statistical conceptions into geography is viewed as a natural process in the history of development of science, as is seen from the history of physics and biology. Without denying the importance and the need for theoretical models constructed in geography on the basis of strict determinism, the authors stress the heuristic value that the stochastic-statistical methods have for an explanation of geographical phenomena. The authors suggest that Soviet geographers still have a preference for deterministic models based on the classic mathematical notions of exactly predictable relationships.