Wednesday, February 1, 2023
Thursday, September 20, 2018
Thursday, July 12, 2018
The Bell
Three hidden keys open three secret gates
Wherein the errant will be tested for worthy traits
And those with the skill to survive these straits
Will reach The End where the prize awaits
— Ready Player One , by Ernest Cline
“Look, my favorite expression is,
‘When you go up to the bell, ring it,
or don’t go up to the bell.’ …
We’ve gone too far. We have to ring the bell.”
— Mel Brooks on “The Producers”
in The New York Times today.
A 2016 Scribner edition of Stephen King’s IT —
Related material —
Mystery box merchandise from the 2011 J. J. Abrams film Super 8
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Wednesday, July 11, 2018
Titans
July 10, 2018
The private jets have begun clogging the jetways
in Sun Valley, Idaho, which can only mean one thing:
'Billionaire summer camp’' has begun.
The annual Allen & Company conference, the investment
firm’s invite-only gathering of some of the world’s most
powerful corporate titans, officially begins on Wednesday."
In other news —
Get ready to see the Titans in training camp."
See also another post now tagged "Clash of the Titans."
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Wednesday, November 30, 2016
Tuesday, September 27, 2016
Chomsky and Lévi-Strauss in China
Or: Philosophy for Jews
From a New Yorker weblog post dated Dec. 6, 2012 —
"Happy Birthday, Noam Chomsky" by Gary Marcus—
"… two titans facing off, with Chomsky, as ever,
defining the contest"
"Chomsky sees himself, correctly, as continuing
a conversation that goes back to Plato, especially
the Meno dialogue, in which a slave boy is
revealed by Socrates to know truths about
geometry that he hadn’t realized he knew."
Socrates and the slave boy discussed a rather elementary "truth
about geometry" — A diamond inscribed in a square has area 2
(and side the square root of 2) if the square itself has area 4
(and side 2).
Consider that not-particularly-deep structure from the Meno dialogue
in the light of the following…
The following analysis of the Meno diagram from yesterday's
post "The Embedding" contradicts the Lévi-Strauss dictum on
the impossibility of going beyond a simple binary opposition.
(The Chinese word taiji denotes the fundamental concept in
Chinese philosophy that such a going-beyond is both useful
and possible.)
The matrix at left below represents the feminine yin principle
and the diamond at right represents the masculine yang .
From a post of Sept. 22,
"Binary Opposition Illustrated" —
A symbol of the unity of yin and yang —
Related material:
A much more sophisticated approach to the "deep structure" of the
Meno diagram —
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Monday, September 12, 2016
The Kummer Lattice
The previous post quoted Tom Wolfe on Chomsky's use of
the word "array."
An example of particular interest is the 4×4 array
(whether of dots or of unit squares) —
.
Some context for the 4×4 array —
The following definition indicates that the 4×4 array, when
suitably coordinatized, underlies the Kummer lattice .
Further background on the Kummer lattice:
Alice Garbagnati and Alessandra Sarti,
"Kummer Surfaces and K3 surfaces
with $(Z/2Z)^4$ symplectic action."
To appear in Rocky Mountain J. Math. —
The above article is written from the viewpoint of traditional
algebraic geometry. For a less traditional view of the underlying
affine 4-space from finite geometry, see the website
Finite Geometry of the Square and Cube.
Some further context …
"To our knowledge, the relation of the Golay code
to the Kummer lattice … is a new observation."
— Anne Taormina and Katrin Wendland,
"The overarching finite symmetry group of
Kummer surfaces in the Mathieu group M24 "
As noted earlier, Taormina and Wendland seem not to be aware of
R. W. H. T. Hudson's use of the (uncoordinatized*) 4×4 array in his
1905 book Kummer's Quartic Surface. The array was coordinatized,
i.e. given a "vector space structure," by Cullinane eight years prior to
the cited remarks of Curtis.
* Update of Sept. 14: "Uncoordinatized," but parametrized by 0 and
the 15 two-subsets of a six-set. See the post of Sept. 13.
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Thursday, September 1, 2016
Bedtime Story
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Friday, August 26, 2016
Wolfe vs. Chomsky
1. Tom Wolfe has a new book on Chomsky, "The Kingdom of Speech."
2. This suggests a review of a post of Aug. 11, 2014, Syntactic/Symplectic.
To paraphrase Wittgenstein, sentence 1 above is about "correlating in real life"
(cf. Crooked House and Wolfe's From Bauhaus to Our House ), and may be
compared to sentence 2 above, which links to a sort of "correlating in
mathematics" that is a particular example of the more general sort of
mathematical correlating mentioned by Wittgenstein in 1939.
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