Spatial–numerical associations (SNAs) are prevalent yet their origin is poorly understood. We first consider the possible prime role of reading habits in shaping SNAs and list three observations that argue against a prominent influence of this role: (1) directional reading habits for numbers may conflict with those for non-numerical symbols, (2) short-term experimental manipulations can overrule the impact of decades of reading experience, (3) SNAs predate the acquisition of reading. As a promising alternative, we discuss behavioral, neuroscientific, and neuropsychological evidence in support of finger counting as the most likely initial determinant of SNAs. Implications of this “manumerical cognition” stance for the distinction between grounded, embodied, and situated cognition are discussed.

Grounded theories assume that there is no central module for cognition. According to this view, all cognitive phenomena, including those considered the province of amodal cognition such as reasoning, numeric, and language processing, are ultimately grounded in (and emerge from) a variety of bodily, affective, perceptual, and motor processes. The development and expression of cognition is constrained by the embodiment of cognitive agents and various contextual factors (physical and social) in which they are immersed. The grounded framework has received numerous empirical confirmations. Still, there are very few explicit computational models that implement grounding in sensory, motor and affective processes as intrinsic to cognition, and demonstrate that grounded theories can mechanistically implement higher cognitive abilities. We propose a new alliance between grounded cognition and computational modeling toward a novel multidisciplinary enterprise: Computational Grounded Cognition. We clarify the defining features of this novel approach and emphasize the importance of using the methodology of Cognitive Robotics, which permits simultaneous consideration of multiple aspects of grounding, embodiment, and situatedness, showing how they constrain the development and expression of cognition.

Embodied theories are increasingly challenging traditional views of cognition by arguing that conceptual representations that constitute our knowledge are grounded in sensory and motor experiences, and processed at this sensorimotor level, rather than being represented and processed abstractly in an amodal conceptual system. Given the established empirical foundation, and the relatively underspecified theories to date, many researchers are extremely interested in embodied cognition but are clamoring for more mechanistic implementations. What is needed at this stage is a push toward explicit computational models that implement sensorimotor grounding as intrinsic to cognitive processes. In this article, six authors from varying backgrounds and approaches address issues concerning the construction of embodied computational models, and illustrate what they view as the critical current and next steps toward mechanistic theories of embodiment. The first part has the form of a dialog between two fictional characters: Ernest, the “experimenter,” and Mary, the “computational modeler.” The dialog consists of an interactive sequence of questions, requests for clarification, challenges, and (tentative) answers, and touches the most important aspects of grounded theories that should inform computational modeling and, conversely, the impact that computational modeling could have on embodied theories. The second part of the article discusses the most important open challenges for embodied computational modeling.