Talk:Fuzzy sphere

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Mathematics rating:
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 Field:  Geometry

Does the "fuzzy sphere" have anything to do with the "fuzzy logic" proposed by L.Zadeh in 1965? The article should be placed in a more general context, like which branch of physics is the fuzzy sphere used in?

No, the fuzzy sphere is not related to 'fuzzy logic'. The fuzzy sphere is an example of a Noncommutative geometry. Noncommutative geometries are an active area of research in theoretical physics, as these provide a means for regularising quantum field theories. Effectively, the noncommutativity generates an uncertainty relation (akin to heisenberg's uncertainty relationship) that creates a 'fuzziness' of the geometry which 'smears out' divergences. Proponents like Alain Connes claim that a quantum spacetime based on noncommutative geometries will be at the heart of a (still to be developed) all-encompassing theory of quantum gravity.
And yes, the article falls short of placing this abstract mathematical concept in context. JocK (talk) 02:52, 8 December 2008 (UTC)