An example of a constraint between topology and metrics that may arise in some setting is “ objects are connected if and only if they have zero distance from each other.” In the perception of spatial-temporal entities, connectivity and disconnectivity compositionally characterize more complex features such as being “before,” “after,” “in front,” “behind,” “having holes,” “discreteness,” etc.Ī more complex, computationally dense and higher up layer might construct metric spaces and Euclidean structure. We take the most primitive layers to be topological, which refers to whether objects and events are “connected.” Topology does not distinguish between the types of the lines (e.g., curved or straight) only connectedness-however defined-and its absence, disconnectedness, need be perceived. Toward an answer, the present paper proposes that cognitive models are hierarchical, where lower layers encode structurally simpler data than higher ones, and the structure of spacetime emerges from mutual constraints between layers. Therefore, the natural question is how we establish coherent models of spacetime. The proposed hierarchy acknowledges that neither space nor time can be accessed directly we can only glean their structures by observing and interacting with objects among events. The foundations of the layer-cake structure are derived from physical accounts of causality, supported by a brief mathematical background. This article posits a hierarchy in the cognition of spacetime, analogous to a “layer cake” structure, where layers correspond to different aspects of causality. The existing evidence in the available literature is reviewed to end with some testable consequences of our proposal at the brain and behavioral level. Secondly, we discuss the compositional structure within and between layers. Firstly, we explore the interplay between the objective physical properties of space-time and the subjective compositional modes of relational representations within the reasoner. In this paper, we propose an analogous hierarchy in the cognition of spacetime. In physics, the analysis of the space representing states of physical systems often takes the form of a layer-cake of increasingly rich structure. 3Center for Educational Neuroscience/Department of Psychology and Human Development, University College London, London, United Kingdom.2Cognitive Neuroimaging Unit, INSERM U992, NeuroSpin, Gif-sur-Yvette, France.1Department of Computer Science, University of Oxford, Oxford, United Kingdom.Camilo Miguel Signorelli 1,2 *, Selma Dündar-Coecke 3, Vincent Wang 1 and Bob Coecke 1
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