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Unformatted text preview: Electronic copy available at: AUBRY Mathieu Metaphors in Mathematics ......................................................................................................... Electronic copy available at: Abstract: Analogies play an essential role in Mathematics. George Lakoff and Rafael E. Nunez have shown in Where Mathemat- ics Comes From that our understanding of basic mathematics is deeply linked to our experience of the world. They claim that we understand mathematics throught Conceptual Metaphors between source domains (for example spa- tial relationships between objects) and target domains (abstract Mathematics). These metaphors are supposed to map certain basic schemata of thought, namely, cross-modal organizational structures. In fact the use of conceptual metaphor is a more general cognitive process, used not only in other sciences (as in physics [6], or Cell Biology and Ecology [7] ) but also in every aspect of our understanding of the world, for example in philosophy [8] and ethics [1]. In this report, I am going to deal with specific cases of metaphors in advanced and abstract mathematics linked to our conception of space. The goal is both to show that conceptual metaphor theory continues to apply with great success in these areas, and to try to understand the theory more deeply. Introduction: Les Analogies ont un r ole essentiel en math ematiques. George Lakoff et Rafael E. Nunez ont montr e dans Where Mathematics Comes From que notre compr ehension des math ematiques el ementaires etait profond ement li ee ` a notre exp erience du monde. Ils affirment que nous comprenons les math ematiques gr ace ` a un ensemble de M etaphores Conceptuelles entre des domaines sources (par exemple des relations spatiales entre objets) et des domaines cibles (des structures math ematiques abstraites). Ces m etaphores conserveraient certains sch emas el ementaires de pen- s ee, appell es structures organisationnelles cross-modales. En fait, lutilisation de m etaphores conceptuelles est un processus cognitif g en eral, utilis e non seulement dans dautres sciences (comme en physique [6] ou en biologie et en ecologie [7]) mais encore dans toute notre compr ehension du monde, par exemple en philosophie [8] et dans le domaine moral [1]. Ce rapport pr esente une etude de cas particuliers de m etaphores en math ematiques, li ees ` a la conception de lespace. Le but est ` a la fois de montrer que la th eorie de la m etaphore conceptuelle est toujours valable dans ce domaine et dessayer de la comprendre plus pr ecis ement....
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This note was uploaded on 10/24/2011 for the course SCIENCE PHY 453 taught by Professor Barnard during the Winter '11 term at BYU.

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