Mathematical Cognition as Embodied Simulation

Mathematical Cognition as Embodied Simulation Firat Soylu (fsoylu@indiana.edu) Department of Instructional Systems Technology, Cognitive Science Program, Indiana University, Bloomington W. W. Wright Education Building, Room 2276, 201 North Rose Avenue, Bloomington, IN 47405, USA Abstract Based on behavioral, neuroimaging and neuropsychological data, I argue that a key to understanding mathematical cognition is the sharing of neural resources between sensorimotor and mathematical processes. Mathematical cognition is embodied in the sense that it is grounded in simulations of sensorimotor processes through the use of neural resources that are also active in bodily perception and action. There are two approaches to the study of embodied mathematical cognition: Behavioral, neuroimaging and neuropsychological investigations providing empirical evidence, and the study of conceptual metaphors, focusing on how inferences from physical domains are used to understand abstract mathematical ideas. The first approach suffers from not providing a unified explanation, while the second approach is criticized for not having empirical validation. I discuss the possible implications of approaching to mathematical cognition as embodied simulation in relating disparate findings to provide a more connected picture of how mathematics emerges from the embodied mind. Keywords: embodiment; embodied cognition; mathematical cognition; simulation theories Embodied cognition is a theoretical stance that argues that cognitive processes are grounded in the body’s interaction with the world. Different approaches in embodied cognition propose varying levels for bodily involvement in higher cognition. Clark (1999) has distinguished between simple versus radical embodiment. Simple embodiment focuses on how the body and environment places constraints on a theory of inner organization and processing. Radical embodiment, however, asserts that all cognitive processes are grounded in the sensorimotor system, proposing a profound change in the subject matter and theoretical framework of cognitive science” (p. 348). The fundamental difference between these two approaches is that simple embodiment still relies on internal representations, especially in explaining higher level thinking, whereas radical embodiment entirely rejects the idea of an internal realm and provides a representation free account of cognitive phenomena. I use the term simulation theories of cognition to refer to theories positing that all cognitive processes are simulations of sensorimotor processes. Note that the term simulation theories is also used to refer to a theory of mind asserting that humans understand other people’s mental states by adopting their perspective (Davies & Stone, 1995), which is different than the usage here. Simulation theories posit a decoupling of sensorimotor functions from their original physical inputs and outputs. For example, consider the case of counting on one’s fingers. In its initial form counting can be done through explicit motor behavior where an observer can see the fingers moving. However, the motor movement of fingers can become gradually more subtle, where at some point it might merely seem like twitching to the observer. We can push the activity inward even further allowing the use of motor programs without any overt behavior. At this point finger counting is a motor simulation. This situation exemplifies how a motor function, without overt behavior, can be the underlying neural mechanism for off-line thinking in the very simple case of counting (Wilson, 2002). Previous theories focused on how conceptual content is represented in the sensorimotor system. Gallese & Lakoff (2005) proposed that embodied simulations are the source of both structural and semantic content in conceptual knowledge. Embodied simulations take place in multimodal sensorimotor networks. Unlike the conventional idea of distinct sensory and motor areas communicating through association areas, multimodality refers to the integration of sensory modalities with one another and also with motor modalities. Barsalou (1999) argued that during perceptual experience association areas in the brain capture bottom-up sensory-motor patterns. Later, during the use of perceptual symbols association areas facilitate some of the same sensory-motor areas in a top down manner. Through experience, memories of the same component are stored in a schematic manner. The memories implement simulators of the perceptual experiences they represent. Simulators can be perceptual, proprioceptive, or introspective. Abstract concepts are grounded in the combinatorial and recursive integration of simulators. Mathematics is often characterized as a challenge to embodiment (Nunez, 2008). Although it is relatively difficult to apply the idea of embodied simulations to explain mathematical cognition due to abstract nature of mathematics, there is accumulating evidence for how basic mathematical processes are grounded in the sensorimotor system. In this paper I review different studies on mathematical cognition and discuss some of the challenges in interpreting findings to create a meaningful image of how mathematics can emerge from the embodied mind. Embodiment of Mathematical Thinking Research on embodiment of mathematics is still in its infancy. Mathematical cognition is a big puzzle with many pieces, each piece requiring us to draw knowledge from a