Boundary conditions of conceptual spaces

The topographic structure underlying conceptual knowledge representations remains vividly debated. Two major accounts can be distinguished: spatial vs. non-spatial accounts. Attempts to adjudicate between these accounts have been unsuccessful. We hypothesize that boundary conditions during acquisition and performance determine the topographic structure at the cognitive and neural level. This proposal aims at delineating the boundary conditions that define the topography of conceptual knowledge. Two major questions will be addressed:
1. What is the impact of context factors on the architecture of conceptual knowledge and its behavioral and neural expression? The transitive nature of numbers, for example, lends itself for spatially projecting numerical magnitude onto a one-dimensional manifold. For more complex (e.g. two-dimensional) concepts, the representation may take a map-like topography. For non-transitive series and other memory contents such as arithmetic facts, however, a spatial architecture appears less suited and graph-like, semantic networks have been proposed. Hence, transitivity and dimensionality of the conceptual knowledge may call for different topographies and may hence represent potential boundary factors that define the topography. Other unresolved issues that will be addressed include the question how two previously unrelated transitive series are projected onto a common metric and how two-dimensional conceptual spaces translate into manual and ocular behavior.
2. What role do other potential boundary factors such as expertise and familiarity with concepts play in the construction of conceptual representations? The way in which newly acquired concepts are linked with existing knowledge influences behavior. We investigate how signature effects of the innate numerical magnitude representation (distance and size effects) emerge during the acquisition of numerical symbols in children. Hence we investigate the impact of developmental dependencies on the shape of conceptual knowledge.
Using a common set of experiments, the project combines complementary behavioral measures to delineate the topographical structure (reaction times, pointing positions on a touchscreen, ocular parameters from eye tracking) and neurofunctional functional magnetic resonance imaging data from adults and elementary school children. To elucidate the role of pre-existing knowledge, the project combines a training approach in which participants will be taught new conceptual spaces with the investigation of existing concepts such as number knowledge.
Delineating neural and cognitive principles underlying the acquisition and adaptation of conceptual content will advance our understanding of conceptual knowledge representation. By shifting the focus from the question whether all concepts are spatially represented toward the more fruitful question of how contextual variables shape the observed performance, this project enables a more productive debate.