Tuesday, December 14, 2010

Types of Ambiguity —

Filed under: General,Geometry — m759 @ 9:48 PM

Galois Meets Doctor Faustus

Galois's theory of mathematical  ambiguity (see June 14) —

  My principal meditations for some time have been directed towards
  the application of the theory of ambiguity to transcendental
  analysis.  It was a question of seeing a priori in a relation
  between quantities or transcendent functions, what exchanges one
  could make, which quantities one could substitute for the given
  quantities without the original relation ceasing to hold.  That
  immediately made clear the impossibility of finding many expressions
  that one could look for.  But I do not have time and my ideas are
  not yet well developed on this ground which is immense.

 — Evariste Galois, testamentary letter, translated by James Dolan

Thomas Mann on musical  ambiguity in his novel Doctor Faustus


Related material — Some context for the above and some remarks on the German original.

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