Log24

Tuesday, August 10, 2021

Ex Fano Apollinis

Filed under: General — Tags: — m759 @ 9:41 AM
 

Margaret Atwood on Lewis Hyde's 
Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.


"As a Chinese jar . . . ."
     — Four Quartets

 

Rosalind Krauss
in "Grids," 1979:

"If we open any tract– Plastic Art and Pure Plastic Art  or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.

Or, to take a more up-to-date example…."

"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
– The Club Dumas , 1993

"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
– Robert Plant, 1971

The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.

An example of the universal— or, according to Krauss,
a "staircase" to the universal— is the ninefold square:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo,
  the field of Reason…."
– John Outram, architect    

The "Katz" of the August 7 post Art Angles
is a product of Princeton's
Department of Art and Archaeology.

 

ART —

 

The Lo Shu as a Finite Space
 

ARCHAEOLOGY —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71

Monday, July 12, 2021

Educational Series

Filed under: General — Tags: — m759 @ 11:06 AM

(Continued from St. Luke's Day, 2014)


 

Tablet:

 

The Lo Shu as a Finite Space
 

Cube:

 

IMAGE- A Galois cube: model of the 27-point affine 3-space

Saturday, July 10, 2021

Plan 9 from Ancient China

Filed under: General — Tags: — m759 @ 3:33 PM

The Lo Shu as a Finite Space

Robert A. Wilson on symmetries of the ninefold square —

"All of these ideas have shown promise at some time or other, and some are still under active investigation. But my conclusion after all this work is that the part of algebra that shows the most promise for genuinely useful applications to fundamental physics is the representation theory, real, complex, integral and modular, of the group GL(2, 3). There is, of course, no guarantee that a viable theory can be built on this foundation. But it appears to be the only part of algebra that both has a reasonable chance of success and has not already been exhaustively explored in the physics literature. It is therefore worth serious consideration."

— "Potential applications of modular representation theory to quantum mechanics," arXiv, May 28, 2021, revised June 7, 2021.

See as well GL(2,3) in this  journal .

Related material: Christmas Eve 2012.

Monday, July 5, 2021

Do Hillbillies Dream of Dinner Parties?

Filed under: General — Tags: , , — m759 @ 2:55 AM

The title was suggested by a New Yorker  photo caption
about Yale on June 19, 2021 —

"Amy Chua, a celebrity professor at the top-ranked
law school in the country, is at the center of a
campus-wide fracas known as 'Dinner Party-gate.' "

Other recent Yale material —

Remarks related to New Haven and geometry —

The Lo Shu as a Finite Space

Friday, November 13, 2020

Raiders of the Lost Dorm Room

Filed under: General — Tags: , — m759 @ 11:48 AM

“That really is, really, I think, the Island of the Misfit Toys at that point.
You have crossed the Rubicon, you jumped on the crazy train and
you’re headed into the cliffs that guard the flat earth at that time, brother,”
said Rep. Denver Riggleman, a Republican congressman from Virginia,
in an interview.”

— Jon Ward, political correspondent, Yahoo News , Nov. 12, 2020

The instinct for heaven had its counterpart:
The instinct for earth, for New Haven, for his room,
The gay tournamonde as of a single world

In which he is and as and is are one.

— Wallace Stevens, “An Ordinary Evening in New Haven

 

Related material for comedians

See as well Sallows in this  journal.

“There exists a considerable literature
devoted to the Lo shu , much of it infected
with the kind of crypto-mystic twaddle
met with in Feng Shui.”

— Lee C. F. Sallows, Geometric Magic Squares ,
Dover Publications, 2013, page 121

Thursday, October 19, 2017

Design Grammar***

Filed under: G-Notes,General,Geometry — m759 @ 10:22 PM

The elementary shapes at the top of the figure below mirror
the looking-glass property  of the classical Lo Shu square.

The nine shapes at top left* and their looking-glass reflection
illustrate the looking-glass reflection relating two orthogonal
Latin squares over the three digits of modulo-three arithmetic.

Combining these two orthogonal Latin squares,** we have a
representation in base three of the numbers from 0 to 8.

Adding 1 to each of these numbers yields the Lo Shu square.

Mirror symmetry of the ninefold Lo Shu magic square

* The array at top left is from the cover of
Wonder Years:
Werkplaats Typografie 1998-2008
.

** A well-known construction.

*** For other instances of what might be
called "design grammar" in combinatorics,
see a slide presentation by Robin Wilson.
No reference to the work of Chomsky is
intended.

Tuesday, October 17, 2017

Plan 9 Continues

Filed under: General,Geometry — Tags: , — m759 @ 9:00 PM

See also Holy Field in this journal.

Some related mathematics —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Analysis of the Lo Shu structure —

Structure of the 3×3 magic square:

4  9  2
3  5  7    decreased by 1 is
8  1  6

3  8  1
2  4  6
7  0  5

In base 3 —

10  22  01
02  11  20
21  00  12

As orthogonal Latin squares
(a well-known construction) —

1  2  0     0  2  1
0  1  2     2  1  0
2  0  1     1  0  2 .

— Steven H. Cullinane,
October 17, 2017

Sunday, November 9, 2014

Twaddle

Filed under: General,Geometry — Tags: — m759 @ 1:00 AM

“There exists a considerable literature
devoted to the Lo shu , much of it infected
with the kind of crypto-mystic twaddle
met with in Feng Shui.”

— Lee C. F. Sallows, Geometric Magic Squares ,
Dover Publications, 2013, page 121

Cf. Raiders of the Lost Theorem, Oct. 13, 2014.

See also tonight’s previous post and
“Feng Shui” in this journal.

Tuesday, October 21, 2014

Art as a Tool

Filed under: General,Geometry — m759 @ 12:35 PM

Two news items on art as a tool:

Two Log24 posts related to the 3×3 grid, the underlying structure for China’s
ancient Lo Shu “magic” square:

Finally, leftist art theorist Rosalind Krauss in this journal
on Anti-Christmas, 2010:

Which is the tool here, the grid or Krauss?

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