Non‐Euclidean Geographic Spaces: Mapping Functional Distances

Abstract

Many geographers have stated that the world living space is changing.Under improved technology of transportation, planners often speak of a shrinking world.This observation is not unique to the transportation system, however, and one could find many other areas of communication, via mail, telephone, financial trading, or cultural exchanges where the concept of spatial distance must be revised.Recent research in map transformation reflects a need for understanding the spatial structure of those many "invisible" layers of space which make up our environment (Hagerstrand 1957;Tobler 1961Tobler , 1977;;Angel and Hyman 1972;Clark 1977;Muller 1978).The cartography of functional spaces raises unusual mathematical problems and disturbs the long-established landform tradition of geographical thinking.This may explain the reluctance of some cartographers to cross the border between conventional planimetric mapping and functional maps which destroy the universal geographical reference framework.Furthermore, the effectiveness and practicability of functional maps are not known.Other geographers such as Muehrcke (1978), for example, claim that conventional planimetric mapping is alien to our everyday conception of the environment.Human mobility, for example, is essentially restricted; and the "crow's flight"concept of the topographic map may violate the map use logic: the map user must mentally transform the physical distancespace in order to find a way to move around.Physical distances provide few clues regarding such factors as traffic, road conditions, mode of travel, comfort, energy, time, and cost.Falk and Abler (1980) have emphasized the need for a better understanding of the spatial interactions created by modern intercommunications media such as telephone, telex, and advanced computer-mediated channels.*I wish to thank the staff of the Bundesforschungsanstalt fur Landeskunde and Raumordnung (BFLR), Bonn, West Germany, for their collaboration and logistic support.Financial support was provided by the Alexander

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