Tutorial on Embodiment
5.2.3. Where mathematics comes from?*
At this point, you may agree that embodiment plays a key part in low-level tasks such as moving around or grasping, and also in slightly higher-level tasks such as object categorization. However, could it possibly play a role in mental processes that we consider purely abstract, such as mathematical thinking? Suprisingly, George Lakoff and Rafael Nunez argue in their provocative book, entitled Where Mathematics Comes From (2000), that even abstract mathematical notions such as the concepts of a real number or a set have their origins in our specific embodiment and could not have been construed differently. Mathematical concepts, according to Lakoff and Nunez, are based on metaphors (e.g., a point "moving" toward infinity) and these metaphors are in turn grounded in, or based on, our embodiment. Empirically they demonstrate some of their insights by discussing the gestures mathematicians typically use to explain their ideas. Therefore, not only categorization is grounded in (shaped by) the body, but so is cognition in general, including spatial and social cognition, problem solving and reasoning, and natural language.
Artificial Intelligence Laboratory
Department of Informatics, University of Zurich
Development and learning (12 November 2009)
In this lecture (in particular in minutes 30-36), Rolf Pfeifer talks about embodied categorization, building grounded cognition and the Lakoff-Nunez hypothesis.
*This section has been adapted from Pfeifer & Bongard (2007), pg. 2-3.
Lakoff, G. & Nunez, R. (2000), Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
Pfeifer, R. & Bongard, J. C. (2007), How the body shapes the way we think: a new view of intelligence, MIT Press, Cambridge, MA.