Drawing space: mathematicians’ kinetic conceptions of eigenvectors
Drawing space: mathematicians’ kinetic conceptions of eigenvectors
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绘图空间：数学家的特征向量动力学概念
DOI：
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发表时间：
2010
期刊：
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通讯作者：
Shiva Gol Tabaghi
中科院分区：
文献类型：
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作者：
N. Sinclair;Shiva Gol Tabaghi
本文探讨了数学家如何通过包括谈话、手势和图表在内的交际活动来建立意义。在描述数学概念的过程中，数学家使用这些符号资源的方式模糊了数学和物理世界之间的区别。我们将论证，本征向量的数学意义强烈地依赖于时间和运动，因此，依赖于数学抽象的物理解释，这是思维的维度，通常故意缺席正式的，书面的概念定义。我们还将展示手势和谈话如何以不同的方式和独特的方式对数学概念化做出贡献，并进一步阐述图表在两者之间发挥重要中介作用的主张。
This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of eigenvectors depends strongly on both time and motion—hence, on physical interpretations of mathematical abstractions—which are dimensions of thinking that are typically deliberately absent from formal, written definition of the concept. We shall also show how gesture and talk contribute differently and uniquely to mathematical conceptualisation and further elaborate the claim that diagrams provide an essential mediating role between the two.