Dimensions and their poles: A metric and topological approach to opposites

Abstract

We explored the nature of 37 spatial dimensions in Italian, such as lungo–corto (long–short), inizio–fine (beginning–end), and convergente–divergente (convergent–divergent). In Study 1 we investigated their metric structure. We asked: (1) Are the extensions of the two poles (P 1 and P 2) the same? (2) What proportion of each dimension can be said to be neither P 1 nor P 2? and (3) Is the extension of P 1 that can be called neither P 1 nor P 2, the same as the extension of P 2 that can be called neither P 1 nor P 2? In Study 2 we investigated the topological structure of the dimensions. We asked: (1) Are the poles, points or ranges? (2) Do intermediates (neither P 1 nor P 2) exist? and (3) If they do, are they points or ranges? Two metric properties explained a considerable proportion of the variation in the responses in the first task: (1) the asymmetry of the extension of the two poles and (2) the extension of the “neither–nor” region between them. The results of the topological task further refined the two-dimensional structure obtained in Study 1 to produce a map of spatial opposites. Our methods and the resulting maps provide a point of departure from which two questions can be investigated: (1) If these methods were used in other languages to study spatial opposites, to what extent would they produce similar maps of opposites? and (2) If these methods were applied to nonspatial opposites and maps analogous to our spatial maps were generated, would any dense regions in the nonspatial maps coincide with sparse regions in the spatial maps? We discuss the potential importance of these questions.

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