Mathematical imagination and embodied cognition

Mathematical imagination and embodied cognition

The goal of this paper is to explore qualities of mathematical imagination in light of a classroom episode. It is based on the analysis of a classroom interaction in a high school Algebra class. We examine a sequence of nine utterances enacted by one of the students whom we call Carlene. Through these utterances Carlene illustrates, in our view, two phenomena: (1) juxtaposing displacements, and...

Mathematical Cognition as Embodied Simulation

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 ...

Material-Based Imagination: Embodied Cognition in Animated Images

Drawing upon cognitive science theories of conceptual blending [1] and material anchors [2], as well as recent neuroscience results regarding mirror neurons [3], we argue that animated visual graphics, as embodied images whose understanding relies on our perceptual and motor apparati, connect both material and mental notions of images. Animated visual images mobilize a reflective process in whi...

kant on the embodied cognition

Mathematical Model of Embodied Symbols: Cognition and Perceptual Symbol System

A mathematical model of perceptual symbol system is developed. This development requires new mathematical methods of dynamic logic (DL), which have overcome limitations of classical artificial intelligence and connectionist approaches. The paper discusses these past limitations, relates them to combinatorial complexity (exponential explosion) of algorithms in the past, and relates it further to...