Bacelar Valente, Mario (2022) Geometric cognition: a hub-and-spoke model of geometric concepts. [Preprint]

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Abstract

Geometric cognition is still poorly understood. Concerning pure geometry, it is basically terra incognita. In the present paper, we develop a tentative model of the neural representation of geometric concepts; for that we adopt an interdisciplinary approach bringing together elements of the history of geometry and the cognitive neuroscience of semantic cognition. Our interest is to develop a model of the neural representation of abstract geometric objects in the Euclidean practice. To arrive at a coherent model, it is necessary to consider earlier forms of geometry. For that, we address the change from practical to pure geometry, proposing models of the neural representations of geometric concepts for each of these practices. This will enable us to have an understanding of geometric objects in terms of a neural model and in relation to neural models of geometric figures. Our models are based on the hub-and-spoke theory. We will present a tentative model of the neural representation of geometric figures in ancient Greek practical geometry. We then propose a related model for the earliest form of pure geometry – that of Hippocrates of Chios. Finally, we develop the model of the neural representation of geometric objects in Euclidean geometry.

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Item Type:	Preprint
Creators:	Creators Email ORCID Bacelar Valente, Mario
Keywords:	geometric cognition; geometric concept; geometric figure; geometric object
Subjects:	Specific Sciences > Cognitive Science Specific Sciences > Mathematics
Depositing User:	mario bacelar valente
Date Deposited:	06 Mar 2022 20:27
Last Modified:	06 Mar 2022 20:27
Item ID:	20240
Subjects:	Specific Sciences > Cognitive Science Specific Sciences > Mathematics
Date:	20 February 2022
URI:	https://philsci-archive.pitt.edu/id/eprint/20240

Available Versions of this Item

• Pure geometry and geometric cognition. (deposited 11 Mar 2021 16:33)
  • Geometric cognition: a hub-and-spoke model of geometric concepts. (deposited 06 Mar 2022 20:27) [Currently Displayed]

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