Spatial Entropy

A major problem in information theory concerns the derivation of a continuous measure of entropy from the discrete measure. Many analysts have shown that Shannon's treatment of this problem is incomplete, but few have gone on to rework his analysis. In this paper, it is suggested that a new measure of discrete entropy which incorporates interval size explicitly is required; such a measure is fundamental to geography and this statistic has been called spatial entropy. The use of the measure is first illustrated by application to one-and two-dimensional aggregation problems, and then the implications of this statistic for Wilson's entropy-maximizing method are traced. Theil's aggregation statistic is reinterpreted in spatial terms, and finally, some heuristics are suggested for the design of real and idealized spatial systems in which entropy is at a maximum.