Fundamental to spatial knowledge in all species are the representations underlying object recognition, object search, and navigation through space. But what sets humans apart from other species is our ability to express spatial experience through language. This target article explores the language ofobjectsandplaces, asking what geometric properties are preserved in the representations underlying object nouns and spatial prepositions in English. Evidence from these two aspects of language suggests there are significant differences in the geometric richness with which objects and places (...) are encoded. When an object is named (i.e., with count nouns), detailed geometric properties – principally the object's shape (axes, solid and hollow volumes, surfaces, and parts) – are represented. In contrast, when an object plays the role of either “figure” (located object) or “ground” (reference object) in a locational expression, only very coarse geometric object properties are represented, primarily the main axes. In addition, the spatial functions encoded by spatial prepositions tend to be nonmetric and relatively coarse, for example, “containment,” “contact,” “relative distance,” and “relative direction.” These properties are representative of other languages as well. The striking differences in the way language encodes objects versus places lead us to suggest two explanations: First, there is a tendency for languages to level out geometric detail from both object and place representations. Second, a nonlinguistic disparity between the representations of “what” and “where” underlies how language represents objects and places. The language of objects and places converges with and enriches our understanding of corresponding spatial representations. (shrink)

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that (...) are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. (shrink)

In this article, I revisit Landau and Jackendoff's () paper, “What and where in spatial language and spatial cognition,” proposing a friendly amendment and reformulation. The original paper emphasized the distinct geometries that are engaged when objects are represented as members of object kinds, versus when they are represented as figure and ground in spatial expressions. We provided empirical and theoretical arguments for the link between these distinct representations in spatial language and their accompanying nonlinguistic neural representations, emphasizing the “what” (...) and “where” systems of the visual system. In the present paper, I propose a second division of labor between two classes of spatial prepositions in English that appear to be quite distinct. One class includes prepositions such as in and on, whose core meanings engage force-dynamic, functional relationships between objects, with geometry only a marginal player. The second class includes prepositions such as above/below and right/left, whose core meanings engage geometry, with force-dynamic relationships a passing or irrelevant variable. The insight that objects’ force-dynamic relationships matter to spatial terms’ uses is not new; but thinking of these terms as a distinct set within spatial language has theoretical and empirical consequences that are new. I propose three such consequences, rooted in the fact that geometric knowledge is highly constrained and early-emerging in life, while force-dynamic knowledge of objects and their interactions is relatively unconstrained and needs to be learned piecemeal over a lengthy timeline. First, the two classes will engage different learning problems, with different developmental trajectories for both first and second language learners; second, the classes will naturally lead to different degrees of cross-linguistic variation; and third, they may be rooted in different neural representations. (shrink)