204129

Springer, Dordrecht

2018

319 pages

ISBN 978-3-319-98022-5

A conceptual history of space and symmetry

from Plato to the superworld

Pietro Giuseppe Fré

The author argues that symmetry and geometry are inextricably entangled and their current meaning is the result of a long process of abstraction which was determined through history and can be understood within the analytic system of thought of western civilization that started with the Ancient Greeks. The evolution of geometry and symmetry theory in the last forty years has been deeply and constructively influenced by supersymmetry/supergravity and the allied constructions of strings and branes. Further advances in theoretical physicscannot be based simply on the Galilean method of interrogating nature and then formulating a testable theory to explain the observed phenomena. One ought to interrogate human thought, meaning frontier-line mathematics concerned with geometry and symmetry in order to find there the threads of so far unobserved correspondences, reinterpretations and renewed conceptions.

Publication details

Full citation [Harvard style]:

Fré, P. (2018). A conceptual history of space and symmetry: from Plato to the superworld, Springer, Dordrecht.

The episteme

Fré Pietro Giuseppe

1-7

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Symmetry and mathematics

Fré Pietro Giuseppe

9-31

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How group theory came into being

Fré Pietro Giuseppe

33-59

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From crystals to Plato

Fré Pietro Giuseppe

61-88

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The long tale of lie groups

Fré Pietro Giuseppe

89-127

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Hermann Weyl and representation theory

Fré Pietro Giuseppe

129-155

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A short history of differential geometry

Fré Pietro Giuseppe

157-206

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Geometry becomes complex

Fré Pietro Giuseppe

207-239

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Geometry becomes special

Fré Pietro Giuseppe

241-267

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Black holes

Fré Pietro Giuseppe

269-287

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Modern manifolds from ancient polyhedra

Fré Pietro Giuseppe

289-306

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