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Circles DisturbedThe Interplay of Mathematics and Narrative$
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Apostolos Doxiadis and Barry Mazur

Print publication date: 2012

Print ISBN-13: 9780691149042

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691149042.001.0001

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Adventures of the Diagonal: Non-Euclidean Mathematics and Narrative

Adventures of the Diagonal: Non-Euclidean Mathematics and Narrative

(p.407) Chapter 12 Adventures of the Diagonal: Non-Euclidean Mathematics and Narrative
Circles Disturbed

Arkady Plotnitsky

, Apostolos Doxiadis, Barry Mazur
Princeton University Press

This chapter explores the relationship between narrative and non-Euclidean mathematics. It considers how non-Euclidean mathematics and the narratives accompanying it are linked: first, to the question of the potentially uncircumventable limits of thought and knowledge; and second, to the question of a certain heterogeneous and yet interactive multiplicity of concepts and of different fields such as algebra and geometry. The chapter starts with the Pythagoreans' discovery of the concept of “incommensurability,” or the irrationality of certain numbers, specifically the side and the diagonal of the square, and the narrative associated with this discovery. It then examines the transition from non-Euclidean physics to non-Euclidean mathematics by focusing on quantum mechanics and its relation to non-Euclidean epistemology. It also discusses the algebraic aspects of non-Euclidean geometry and concludes with the suggestion that non-Euclidean thinking retains the essential, shaping role of the movement of thought.

Keywords:   narrative, non-Euclidean mathematics, algebra, incommensurability, non-Euclidean physics, quantum mechanics, non-Euclidean epistemology, non-Euclidean geometry, non-Euclidean thinking

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