Embodied Mathematics and the Origins of Geometry

Dionyssios Lappas; Panayotis Spyrou

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Embodied Mathematics and the Origins of Geometry

Dionyssios Lappas·Panayotis Spyrou

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Abstract

In this paper, we propose that 'embodied mathematics' should be studied not only by reduction to the present individual bodily experience but in an historical context as well, as far as the origins of mathematics are concerned. Some early mathematical results are the Theorems of Geometry and arose as attempts to objectively render the main perceptual categories such as verticality, horizontality, similarity (or its varieties). Inasmuch as these are of a qualitative nature, it was required that they be expressed in a quantitative way in order to be objectified. The first form of this objectification occurred in the case of 'archetypal results', namely the Pythagorean triads and the internal ratio of the legs in the right triangles. In the next stage, a 'scientific' treatment would come from a shift of objectification and descriptions inside an abstract theory, which would constitute the first logicomathematical knowledge. In this theory, the 'archetypal results' were incorporated, generalized and acquired their unquestionable, supertemporal validity. The study presents a particular epistemological analysis of some of the main terms used in the beginnings of Geometrical Thought and Euclid's Elements, utilizing the theoretical apparatus of the theory of 'embodied mathematics'. It also traces models of objectification for the 'archetypal results' and indicates their diffusion in later mathematical developments.

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Dionyssios Lappas, Panayotis Spyrou. 2003-08-01. Embodied Mathematics and the Origins of Geometry. https://arxiv.org/abs/math/0308003

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