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Everywhere and EverywhenAdventures in Physics and Philosophy$
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Nick Huggett

Print publication date: 2010

Print ISBN-13: 9780195379518

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780195379518.001.0001

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Looking for Geometry

Looking for Geometry

(p.75) 8 Looking for Geometry
Everywhere and Everywhen

Nick Huggett (Contributor Webpage)

Oxford University Press

One can readily imagine a curved surface, but the very idea of a curved 3‐dimensional space may seem impossible; indeed, until ‘non‐Euclidean’ geometry was developed in the nineteenth century, such was the dominant view. The topic is philosophically rich because geometry is both a branch of mathematics and describes the world, and is studied by physics; what can we learn by logic and what from experience? These chapters explain non‐Euclidean geometry in simple terms, and what it would be like to live in such spaces; they explain how geometry is more of an experimental science than philosophers, such as Kant, supposed. However, Poincaré argued that geometry is not experimental: the physical objects used to measure space may be systematically misleading. He argued that experiment reveals what trajectories lead to the same point, the ‘group’ of the space, and that the geometry is true by definition, or ‘convention’.

Keywords:   geometry, convention, euclidean, non‐euclidean, group, Kant, Poincaré

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