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Blending in mathematics

Blending in mathematics Mathematics is one of the richest, if more 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. It is suggested that blending and other such mechanisms are incorporated into the formal structure of the discipline. This thesis is examined via a number of examples. This has the effect that blends are easy to make in mathematics. On the other hand, before blends and other processes were incorporated into mathematics, some blends that are obvious, even necessary, in hindsight, have taken a long time — 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Semiotica - Journal of the International Association for Semiotic Studies / Revue de l'Association Internationale de Sémiotique de Gruyter

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Publisher
de Gruyter
Copyright
© 2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
ISSN
0037-1998
eISSN
1613-3692
DOI
10.1515/semi.2011.063
Publisher site
See Article on Publisher Site

Abstract

Mathematics is one of the richest, if more 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. It is suggested that blending and other such mechanisms are incorporated into the formal structure of the discipline. This thesis is examined via a number of examples. This has the effect that blends are easy to make in mathematics. On the other hand, before blends and other processes were incorporated into mathematics, some blends that are obvious, even necessary, in hindsight, have taken a long time — 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.

Journal

Semiotica - Journal of the International Association for Semiotic Studies / Revue de l'Association Internationale de Sémiotiquede Gruyter

Published: Oct 1, 2011

Keywords: blending ; framing ; conceptual integration ; mathematics ; structure ; arrested blend

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