All geographical distances are optimal
L'HOSTIS
Type de document
NOTE INTERNE OU DE TRAVAIL
Langue
anglais
Auteur
L'HOSTIS
Résumé / Abstract
L'Hostis (2015) has demonstrated that triangle inequality which is one of the four mathematical properties of distances, and whose role is to ensure the optimal character of distances, reveals some key aspects of distances and of geographical spaces. We elaborate from this demonstration by investigating the optimality of distances in empirical approaches and in spatial theories. The first part of paper explores the consequences of considering that the mathematical property of triangle inequality is always respected. Indeed, violations of triangle inequality are not observed in geographical spaces. The study of optimality of distances in empirical approaches confirms its role as a key property. The general principle of least-effort applies to most movements and spacings. But in addition, trajectories with lots of detours, as those of shoppers, runners and nomads, are optimal from a particular point of view. It is also the case for the theme of excess travel which is based on a disjunction between an optimum by a driver and an optimum by an external observer. Any movement, any spacing in cities or in geographical space in general exhibits some kind of optimality.The place of distance in spatial theories reveals a contrasted position. In general, spatial theories do not place a great emphasis on distances. Several authors need to complement the idea of distance with an additional concept, like accessibility, in order to introduce a value for individuals and society. Conversely, for others including Brunet, distance embodies behaviours and intentions of actors. The discussion highlights the fact that optimum is relative to the actors involved. We observe that no consensus about the optimal nature of distances can be found in spatial theories, but strong arguments exist to support the idea.
