Tuesday, January 24, 2012

The Screwing

Filed under: General,Geometry — Tags: , — m759 @ 7:59 AM

"Debates about canonicity have been raging in my field
(literary studies) for as long as the field has been
around. Who's in? Who's out? How do we decide?"

— Stephen Ramsay, "The Hermeneutics of Screwing Around"

An example of canonicity in geometry—

"There are eight heptads of 7 mutually azygetic screws, each consisting of the screws having a fixed subscript (from 0 to 7) in common. The transformations of LF(4,2) correspond in a one-to-one manner with the even permutations on these heptads, and this establishes the isomorphism of LF(4,2) and A8. The 35 lines in S3 correspond uniquely to the separations of the eight heptads into two complementary sets of 4…."

 — J.S. Frame, 1955 review of a 1954 paper by W.L. Edge,
"The Geometry of the Linear Fractional Group LF(4,2)"

Thanks for the Ramsay link are due to Stanley Fish
(last evening's online New York Times ).

For further details, see The Galois Tesseract.

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