January 24, 2005

• Old School Tie

  From a review of A Beautiful Mind:

  “We are introduced to John Nash, fuddling
  flat-footed about the Princeton courtyard, uninterested in
  his classmates’ yammering about their various accolades. One
  chap has a rather unfortunate sense of style, but rather than
  tritely insult him, Nash holds a patterned glass to the sun,
  [director Ron] Howard shows us refracted patterns of light that take shape
  in a punch bowl, which Nash then displaces onto the neckwear,
  replying, ‘There must be a formula for how ugly your
  tie is.’ “

  

  “Three readings of diamond and box
  have been extremely influential.”

  – Draft of
  Computing with Modal Logics
  (pdf), by Carlos Areces
  and Maarten de Rijke

  “Algebra in general is particularly suited for structuring and
  abstracting. Here, structure is imposed via symmetries and
  dualities, for instance in terms of Galois connections….

  … diamonds and boxes are upper and lower adjoints of Galois connections….”

  – “Modal Kleene Algebra
  and Applications: A Survey“
  (pdf), by Jules Desharnais,
  Bernhard Möller, and
  Georg Struth, March 2004

  See also
  Galois Correspondence

  

  
  Evariste Galois

  and Log24.net, May 20, 2004:

  “Perhaps every science must
  start with metaphor
  and end with algebra;
  and perhaps without metaphor
  there would never
  have been
  any algebra.”

  – attributed, in varying forms
  (1, 2, 3), to Max Black,
  Models and Metaphors, 1962

  For metaphor and
  algebra combined, see

  

  “Symmetry invariance
  in a diamond ring,”

  A.M.S. abstract 79T-A37,
  Notices of the Amer. Math. Soc.,
  February 1979, pages A-193, 194 —
  the original version of the 4×4 case
  of the diamond theorem.

  • 2:45 pm
  • 3 Comments