Information Theory of Cartography: An Information-theoretic Framework for Cartographic Communication

Abstract

Map is one of the communication means created by human being. Cartographers have been making efforts on the comparison of maps to natural languages so as to establish a “cartographic language” or “map language”. One of such efforts is to adopt the Shannon’s Information Theory originated in digital communication into cartography so as to establish an entropy-based cartographic communication theory. However, success has been very limited although research work had started as early as the mid-1960s. It is then found that the bottleneck problem was the lack of appropriate measures for the spatial (configurational) information of (graphic and image) maps, as the classic Shannon entropy is only capable of characterizing statistical information but fails to capture the configurational information of (graphic and image) maps. Fortunately, after over 40-year development, some bottleneck problems have been solved. More precisely, generalized Shannon entropies for metric and thematic information of (graphic) maps have been developed and the first feasible solution for computing the Boltzmann entropy of image maps has been invented, which is capable of measuring the spatial information of not only numerical images but also categorical maps. With such progress, it is now feasible to build the “Information Theory of Cartography”. In this paper, a framework for such a theory is proposed and some key issues are identified. For these issues, some have already been tackled while others still need efforts. As a result, a research agenda is set for future action. After all these issues are tackled, the theory will become matured so as to become a theoretic basis of cartography. It is expected that the Information Theory of Cartography will play an increasingly important role in the discipline of cartography because more and more researchers have advocated that information is more fundamental than matter and energy.

Keywords

• |information theory of cartography|cartographic communication|spatial information of maps|generalized shannon entropy|boltzmann entropy