The previous post’s search for Turing + Dyson yielded a
quotation from Kierkegaard on possibility and necessity.
Further details —
See also . . .
Monday, July 15, 2019
Possibility and Necessity: Kierkegaard Meets Nietzsche
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Thursday, February 20, 2014
Relativity Blues
A review of this date in 2005 —
Modal Theology
“We symbolize logical necessity
with the box (
)
and logical possibility
with the diamond (
).”
— Keith Allen Korcz
And what do we
symbolize by 
?
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Sunday, February 27, 2005
Sunday February 27, 2005
Necessity
Above: Detail from an editor’s necktie
on the New York Times obituary page
of Sunday, Feb. 27, 2005:
“The form, the pattern”
— T. S. Eliot
“We symbolize logical necessity
with the box ()….”
— Keith Allen Korcz
“4 x 4 = 16”
— Anonymous
“Es muss sein!”
— Beethoven
Monday, January 24, 2005
Monday 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
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
and Applications: A Survey”
(pdf), by Jules Desharnais,
Bernhard Möller, and
Georg Struth, March 2004
See also
Galois Correspondence
Galois Correspondence
Evariste Galois
“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.