Old School Tie
"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.' "
"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...."
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 4x4 case
of the diamond theorem.
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