Locale,Street, Square—a Naive Theory of the City

The paper outline three basic categories of urban phenomenology based upon the simple notion of a trajectory thorough a network of streets. This formal notion gives rise to three different phases of such a trajectory—where the movement stops, when it proceeds unproblematically, and when several possibilities for choosing the further trajectory present themselves; thus, the locale, the street, and the square, as indicated in the title. Based on the Peircean notions of First-, Second-, and Thirdness, the paper makes a first investigation as to which aspects of urban experience are connected to these three categories.     

Interaction between locale and taxon strategies in human spatial learning

Three computer-based experiments which tested human participants in a non-immersive virtual watermaze task sought to determine factors which dictate whether the presence of a visual platform disrupts locale learning and taxon learning. In Experiment 1, the visible platform disrupted locale but not taxon learning based on viewpoint-independent and viewpoint-dependent information, respectively. In Experiment 2, taxon learning based on non-geometric cues providing viewpoint-dependent information was disrupted by the visible platform when the cues required relational information to disambiguate them from other cues. Experiment 3 placed participants in an isosceles triangular pool. The presence of the visible platform did not disrupt the encoding of relational information provided by shape of the pool. These results support the notion that geometric cues are encoded in a separate module which is impenetrable to non-geometric cues not creating the shape of the environment.     

Continuity and geometric logic

This paper is largely a review of known results about various aspects of geometric logic. Following Grothendieckʼs view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers and maps as bundles.