Information theory of cartography : a framework for entropy-based cartographic communication theory

Abstract

Map is an effective communication means. It carries and transmits spatial information about spatial objects and phenomena, from map makers to map users. Therefore, cartography can be regarded as a communication system. Efforts has been made on the application of Shannon Information theory developed in digital communication to cartography to establish an information theory of cartography, or simply cartographic information theory (or map information theory). There was a boom during the period from later 1960s to early 1980s. Since later 1980s, researcher have almost given up the dream of establishing the information theory of cartography because they met a bottleneck problem. That is, Shannon entropy is only able to characterize the statistical information of map symbols but not capable of characterizing the spatial configuration (patterns) of map symbols. Fortunately, break-through has been made, i.e. the building of entropy models for metric and thematic information as well as a feasible computational model for Boltzmann entropy. This paper will review the evolutional processes, examine the bottleneck problems and the solutions, and finally propose a framework for the information theory of cartography. It is expected that such a theory will become the most fundamental theory of cartography in the big data era.