Minimum-Cost Distances in Spatial Analysis

An axiomatic approach to distance is developed which focuses on those behavioral concepts of distance related to movement in space. In particular, spatial movement by behaving units is postulated to involve a choice from among some set of abstract trips in space, and implicitly, to involve the minimization of some relevant notion of trip costs. In this context, the relevant behavioral notion of distance in space is taken to be the minimum-cost distance generated by this choice process. These trip-cost concepts extend the classical notions of paths, path lengths, and shortest paths in metric spaces. Hence many of the analytical results of the paper involve extensions of classical shortest-path distance properties to minimum-cost distances. In addition to these extensions, a characterization theorem is given which specifies the possible functional relationships between trip costs and their associated path lengths. These relationships include most functional forms which are commonly employed in the literature.     

STRUCTURES OF LANGUAGE AND MYTH: AN ANALYSIS OF A GOONIYANDI TEXT

In this paper we analyse a text in Gooniyandi (southern Kimberley, Western Australia), a myth about the acquisition of fire. Our analysis, broadly structuralist-functionalist in orientation, uses a number of complementary modes of myth analysis, including a variety of structuralism which draws on Lévi-Strauss. Our main point, however, differs from his concerns. It is that the analysis of a myth (indeed, of any text) cannot be pursued independently of its language, and of the linguistic choices implemented by the narrator. Relevant choices include not just lexical, but also grammatical ones, selections of grammatical construction (and patterns in them), not, of course, in the language of translation (English), but in the language of the text. We suggest that our method should be generally applicable to myths in any language.