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1 - Space and geometry

Published online by Cambridge University Press:  05 May 2013

Felipe Cucker
Affiliation:
City University of Hong Kong
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Summary

O God! I could be bounded in a nut-shell, and count myself a king of infinite space […]

W. Shakespeare, Hamlet, II, 2

The nature of space

The engraving in Figure 1.1 shows the edge of the world as it was conceived in ancient times. The known land was surrounded by a vast expanse of sea close to whose end waters were inhabited by sea serpents, dragons and other fearsome creatures.

Monsters aside, a fact at odds with our contemporary perception of the world is that the surface of the world was – waves, mountains and other accidents of this surface ignored – flat. This feature is inconsistent with the images of the Earth that satellites bring daily to us but was perfectly consistent with the information available to, say, the ancient Greeks. Indeed, moving north one was led to an increasingly cold landscape and moving south to an increasingly hot one. And at both east and west boundaries of the known land mass, oceans extended which were navigable only close to the land (and hence whose end could neither be seen nor refuted). In addition, it was not possible to distance oneself enough from the surface of the Earth to appreciate its curvature. All these enclosures created a confinement within which the flatness of the Earth was as likely as its spherical curvature.

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Manifold Mirrors
The Crossing Paths of the Arts and Mathematics
, pp. 11 - 26
Publisher: Cambridge University Press
Print publication year: 2013

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  • Space and geometry
  • Felipe Cucker, City University of Hong Kong
  • Book: Manifold Mirrors
  • Online publication: 05 May 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139014632.003
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  • Space and geometry
  • Felipe Cucker, City University of Hong Kong
  • Book: Manifold Mirrors
  • Online publication: 05 May 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139014632.003
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Space and geometry
  • Felipe Cucker, City University of Hong Kong
  • Book: Manifold Mirrors
  • Online publication: 05 May 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139014632.003
Available formats
×