Mathematical Blending

54 Pages Posted: 16 May 2009 Last revised: 13 Nov 2009

See all articles by James C. Alexander

James C. Alexander

Case Western Reserve University - Department of Mathematics and Cognitive Science

Date Written: May 14, 2009

Abstract

Mathematics is one of the richest, if often abstruse, areas of higher human cognition. It is a formal system, founded on a minimum of primitive concepts, but involving cognitive mechanisms, such as blending and framing, in an iterative manner, which lead to the rich structure of "higher" mathematics. The use of such cognitive mechanisms is done in a very controlled way, so as to maintain the rigor of the discipline. Indeed, blending and other such mechanisms are incorporated into the formal structure of the discipline. On the other hand, some blends that are obvious, even necessary, in hindsight, have taken long times - sometimes centuries - to be realized. We hypothesis there is a cognitive cost to actualizing blends, which must be overcome. This phenomenon is investigated via the historical record.

Keywords: cognitive science, mathematics, conceptual integration, blending

Suggested Citation

Alexander, James C., Mathematical Blending (May 14, 2009). Available at SSRN: https://ssrn.com/abstract=1404844 or http://dx.doi.org/10.2139/ssrn.1404844

James C. Alexander (Contact Author)

Case Western Reserve University - Department of Mathematics and Cognitive Science ( email )

Cleveland, OH 44106
United States

HOME PAGE: http://www.cwru.edu/artsci/math/alexander/

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