Wednesday, November 21, 2012

And I was right about the curved light rays.

"He asked his readers to imagine some ex- periment in which a seemingly decisive result had been obtained, for example the construc- tion of a figure with light rays marking out four equal sides meeting at four equal angles for which the sum of the angles was less than 2π . This would seem to suggest that space was non-Euclidean,but,said,Poincare ́,thereis another interpretation, which was that space was Euclidean and light rays were curved. There could be no way of deciding logically between these two interpretations, and all we could do would be to settle for the geometry we found most convenient, which, indeed, he said would be the Euclidean one. His reasons were, however, unexpected, and will be con- sidered shortly." (Poincare ́ and the idea of a group, Gray)

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