Log24

Thursday, August 7, 2025

Points

Filed under: General — Tags: — m759 @ 2:49 am

"What do you get with that card?"

"Big Top points."
 

Cicero, In Verrem  II. 1. 46 —

He reached Delos. There one night he secretly   46 
carried off, from the much-revered sanctuary of 
Apollo, several ancient and beautiful statues, and 
had them put on board his own transport. Next 
day, when the inhabitants of Delos saw their sanc- 
tuary stripped of its treasures, they were much 
distressed . . . .
Delum venit. Ibi ex fano Apollinis religiosissimo 
noctu clam sustulit signa pulcherrima atque anti- 
quissima, eaque in onerariam navem suam conicienda 
curavit. Postridie cum fanum spoliatum viderent ii 


 

Ex Fano 

Saturday, November 2, 2024

For Julia Cicero:  Ex Fano Apollinis

Filed under: General — Tags: — m759 @ 11:56 pm

Cicero, In Verrem  II. 1. 46 —

He reached Delos. There one night he secretly   46 
carried off, from the much-revered sanctuary of 
Apollo, several ancient and beautiful statues, and 
had them put on board his own transport. Next 
day, when the inhabitants of Delos saw their sanc- 
tuary stripped of its treasures, they were much 
distressed . . . .
Delum venit. Ibi ex fano Apollinis religiosissimo 
noctu clam sustulit signa pulcherrima atque anti- 
quissima, eaque in onerariam navem suam conicienda 
curavit. Postridie cum fanum spoliatum viderent ii 

See also "Ex Fano" in this  journal.

For more crazed gravitas, vide . . .

Latin Square Triangles .


Addendum:

The above New Yorker  passage is dated Sept. 26, 2024.
Also on that date . . .

Sunday, September 8, 2024

Sunday Morning Koppel

Filed under: General — m759 @ 9:25 am

Today's host for a special political edition of CBS Sunday Morning
is Ted Koppel. Vocabulary review:

Koppel's appearance today was backed by the usual CBS Sunday Morning
sun-disk Apollo symbol. An Apollo symbol that some may prefer —

The Ninefold Square

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    

Wednesday, June 5, 2024

For a future Michael Crichton*—  The Tachikawa Hint

Filed under: General — Tags: — m759 @ 9:22 am

Hat tip to Peter Woit for quoting the above  yesterday.

* See Crichton in this  weblog and the solar Apollo symbols
of CBS Sunday Morning, which this week featured Crichton.

As an Apollo symbol, I prefer the Chinese "holy field" —
a ninefold square.

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, February 17, 2020

RIP Charles Portis

Filed under: General — Tags: , — m759 @ 4:04 pm

     See also "True Grid " in this  journal.

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    

See as well . . .

Wednesday, December 12, 2018

An Inscape for Douthat

Some images, and a definition, suggested by my remarks here last night
on Apollo and Ross Douthat's remarks today on "The Return of Paganism" —

Detail of Feb. 20, 1986, note by Steven H. Cullinane on Weyl's 'relativity problem'

Kibler's 2008 'Variations on a theme' illustrated.

In finite geometry and combinatorics,
an inscape  is a 4×4 array of square figures,
each figure picturing a subset of the overall 4×4 array:


 

Related material — the phrase
"Quantum Tesseract Theorem" and  

A.  An image from the recent
      film "A Wrinkle in Time" — 

B.  A quote from the 1962 book —

"There's something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz."

Sunday, March 19, 2017

Delos Incorporated* Sunday School

Filed under: General,Geometry — m759 @ 9:00 am

The 3x3 square

Click image for a search.

* Parent company of Westworld.
  See also Delos  in this journal.

Wednesday, May 13, 2015

Space

Filed under: General,Geometry — Tags: , , — m759 @ 2:00 pm

Notes on space for day 13 of May, 2015 —

The 13 symmetry axes of the cube may be viewed as
the 13 points of the Galois projective space PG(2,3).
This space (a plane) may also be viewed as the nine points
of the Galois affine space AG(2,3) plus the four points on
an added "line at infinity."

Related poetic material:

The ninefold square and Apollo, as well as 

http://www.log24.com/log/pix11A/110426-ApolloAndDionysus.jpg

Sunday, April 1, 2012

The Palpatine Dimension

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

A physics quote relayed at Peter Woit's weblog today—

"The relation between 4D N=4 SYM and the 6D (2, 0) theory
is just like that between Darth Vader and the Emperor.
You see Darth Vader and you think 'Isn’t he just great?
How can anyone be greater than that? No way.'
Then you meet the Emperor."

— Arkani-Hamed

Some related material from this  weblog—

(See Big Apple and Columbia Film Theory)

http://www.log24.com/log/pix12/120108-Space_Time_Penrose_Hawking.jpg

The Meno Embedding:

Plato's Diamond embedded in The Matrix

Some related material from the Web—

IMAGE- The Penrose diamond and the Klein quadric

See also uses of the word triality  in mathematics. For instance…

A discussion of triality by Edward Witten

Triality is in some sense the last of the exceptional isomorphisms,
and the role of triality for n = 6  thus makes it plausible that n = 6
is the maximum dimension for superconformal symmetry,
though I will not give a proof here.

— "Conformal Field Theory in Four and Six Dimensions"

and a discussion by Peter J. Cameron

There are exactly two non-isomorphic ways
to partition the 4-subsets of a 9-set
into nine copies of AG( 3,2).
Both admit 2-transitive groups.

— "The Klein Quadric and Triality"

Exercise: Is Witten's triality related to Cameron's?
(For some historical background, see the triality  link from above
and Cameron's Klein Correspondence and Triality.)

Cameron applies his  triality to the pure geometry of a 9-set.
For a 9-set viewed in the context of physics, see A Beginning

From MIT Commencement Day, 2011—

A symbol related to Apollo, to nine, and to "nothing"

A minimalist favicon—

IMAGE- Generic 3x3 square as favicon

This miniature 3×3 square— http://log24.com/log/pix11A/110518-3x3favicon.ico — may, if one likes,
be viewed as the "nothing" present at the Creation. 
See Feb. 19, 2011, and Jim Holt on physics.

Happy April 1.

Wednesday, October 12, 2011

High White Noon

Filed under: General,Geometry — Tags: — m759 @ 12:00 pm

Grid from a post linked to in yesterday's 24 Hour DeLillo

The 3x3 square

A Study in Art Education

For an example of this grid as slow art , consider the following—

"One can show that the binary tetrahedral group
is isomorphic to the special linear group SL(2,3)—
the group of all 2×2 matrices over the finite field F3
with unit determinant." —Wikipedia

As John Baez has noted, these two groups have the same structure as the geometric 24-cell.

For the connection of the grid to the groups and the 24-cell, see Visualizing GL(2,p).

Related material—

The 3×3 grid has been called a symbol of Apollo (Greek god of reason and of the sun).

"This is where we sat through his hushed hour,
a torchlit sky, the closeness of hills barely visible
at high white noon." — Don DeLillo, Point Omega

Friday, September 9, 2011

A Beginning

Filed under: General — Tags: , — m759 @ 5:29 am
 

From MIT Commencement Day, 2011—

A symbol related to Apollo, to nine, and to "nothing"

A minimalist favicon—

IMAGE- Generic 3x3 square as favicon

This miniature 3×3 square— http://log24.com/log/pix11A/110518-3x3favicon.ico — may, if one likes,
be viewed as the "nothing" present at the Creation. 
See Feb. 19, 2011, and Jim Holt on physics.

Saturday, January 8, 2011

True Grid (continued)

Filed under: General,Geometry — Tags: , — m759 @ 12:00 pm

"Rosetta Stone" as a Metaphor
  in Mathematical Narratives

For some backgound, see Mathematics and Narrative from 2005.

Yesterday's posts on mathematics and narrative discussed some properties
of the 3×3 grid (also known as the ninefold square ).

For some other properties, see (at the college-undergraduate, or MAA, level)–
Ezra Brown, 2001, "Magic Squares, Finite Planes, and Points of Inflection on Elliptic Curves."

His conclusion:

When you are done, you will be able to arrange the points into [a] 3×3 magic square,
which resembles the one in the book [5] I was reading on elliptic curves….

This result ties together threads from finite geometry, recreational mathematics,
combinatorics, calculus, algebra, and number theory. Quite a feat!

5. Viktor Prasolov and Yuri Solvyev, Elliptic Functions and Elliptic Integrals ,
    American Mathematical Society, 1997.

Brown fails to give an important clue to the historical background of this topic —
the word Hessian . (See, however, this word in the book on elliptic functions that he cites.)

Investigation of this word yields a related essay at the graduate-student, or AMS, level–
Igor Dolgachev and Michela Artebani, 2009, "The Hesse Pencil of Plane Cubic Curves ."

From the Dolgachev-Artebani introduction–

In this paper we discuss some old and new results about the widely known Hesse
configuration
  of 9 points and 12 lines in the projective plane P2(k ): each point lies
on 4 lines and each line contains 3 points, giving an abstract configuration (123, 94).

PlanetMath.org on the Hesse configuration

http://www.log24.com/log/pix11/110108-PlanetMath.jpg

A picture of the Hesse configuration–

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

(See Visualizing GL(2,p), a note from 1985).

Related notes from this journal —

From last November —

Saturday, November 13, 2010

Story

m759 @ 10:12 PM

From the December 2010 American Mathematical Society Notices

http://www.log24.com/log/pix10B/101113-Ono.gif

Related material from this  journal—

Mathematics and Narrative and

Consolation Prize (August 19, 2010)

From 2006 —

Sunday December 10, 2006

 

 m759 @ 9:00 PM

A Miniature Rosetta Stone:

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

“Function defined form, expressed in a pure geometry
that the eye could easily grasp in its entirety.”

– J. G. Ballard on Modernism
(The Guardian , March 20, 2006)

“The greatest obstacle to discovery is not ignorance –
it is the illusion of knowledge.”

— Daniel J. Boorstin,
Librarian of Congress, quoted in Beyond Geometry

Also from 2006 —

Sunday November 26, 2006

 

m759 @ 7:26 AM

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    

For more on the field of reason, see
Log24, Oct. 9, 2006.

A reasonable set of "strange correspondences"
in the garden of Apollo has been provided by
Ezra Brown in a mathematical essay (pdf).

Unreason is, of course, more popular.

* The ninefold square is perhaps a "concrete universal" in the sense of Hegel:

"Two determinations found in all philosophy are the concretion of the Idea and the presence of the spirit in the same; my content must at the same time be something concrete, present. This concrete was termed Reason, and for it the more noble of those men contended with the greatest enthusiasm and warmth. Thought was raised like a standard among the nations, liberty of conviction and of conscience in me. They said to mankind, 'In this sign thou shalt conquer,' for they had before their eyes what had been done in the name of the cross alone, what had been made a matter of faith and law and religion– they saw how the sign of the cross had been degraded."

– Hegel, Lectures on the History of Philosophy ,
   "Idea of a Concrete Universal Unity"

"For every kind of vampire,
there is a kind of cross."
– Thomas Pynchon   

And from last October —

Friday, October 8, 2010

 

m759 @ 12:00 PM
 

Starting Out in the Evening
… and Finishing Up at Noon

This post was suggested by last evening's post on mathematics and narrative and by Michiko Kakutani on Vargas Llosa in this morning's New York Times .

http://www.log24.com/log/pix10B/101008-StartingOut.jpg

 

Above: Frank Langella in
"Starting Out in the Evening"

Right: Johnny Depp in
"The Ninth Gate"

http://www.log24.com/log/pix10B/101008-NinthGate.jpg

"One must proceed cautiously, for this road— of truth and falsehood in the realm of fiction— is riddled with traps and any enticing oasis is usually a mirage."

– "Is Fiction the Art of Lying?"* by Mario Vargas Llosa,
    New York Times  essay of October 7, 1984

* The Web version's title has a misprint—
   "living" instead of "lying."

"You've got to pick up every stitch…"

Monday, December 13, 2010

Plan 9 Revisited

Filed under: General,Geometry — m759 @ 9:00 am

Leading today's New York Times  obituaries —

http://www.log24.com/log/pix10B/101213-NYTobits.jpg

— is that of Nassos Daphnis, a painter of geometric abstractions
who in 1995 had an exhibition at a Leo Castelli gallery
titled "Energies in Outer Space." (See pictures here.)

Daphnis died, according to the Times, on November 23.
See Art Object, a post in this journal on that date—

There is more than one way
to look at a cube.

http://www.log24.com/log/pix10B/101123-plain_cube_200x227.gif

Some context— this morning's previous post (Apollo's 13,
on the geometry of the 3×3×3 cube), yesterday's noon post
featuring the 3×3 square grid (said to be a symbol of Apollo),

The 3x3 square

and, for connoisseurs of the Ed Wood school of cinematic art,
a search in this journal for the phrase "Plan 9."

You can't make this stuff up.

Sunday, December 12, 2010

Brightness at Noon continued…

Filed under: General — Tags: , — m759 @ 12:00 pm

A picture one might view as
related to the novel An Object of Beauty
and the film "The Object of Beauty" —

The 3x3 square

Click for some background.

"If it's a seamless whole you want,
 pray to Apollo." — Margaret Atwood

Friday, October 15, 2010

Mathematics and Narrative, continued

Filed under: General — Tags: — m759 @ 6:29 am
 

The Story of N

http://www.log24.com/log/pix09/090109-Stories.jpg

Roberta Smith in the New York Times  of July 7, 2006

Art Review

Endgame Art? It's Borrow, Sample and Multiply in an Exhibition at Bard College

"… The show has an endgame, end-time mood, as if we are looking at the end of the end of the end of Pop, hyperrealism and appropriation art. The techniques of replication and copying have become so meticulous that they are beside the point. This is truly magic realism: the kind you can't see, that has to be explained. It is also a time when artists cultivate hybridism and multiplicity and disdain stylistic coherence, in keeping with the fashionable interest in collectivity, lack of ego, the fluidity of individual identity. But too often these avoidance tactics eliminate the thread of a personal sensibility or focus.

I would call all these strategies fear of form, which can be parsed as fear of materials, of working with the hands in an overt way and of originality. Most of all originality. Can we just say it? This far from Andy Warhol and Duchamp, the dismissal of originality is perhaps the oldest ploy in the postmodern playbook. To call yourself an artist at all is by definition to announce a faith, however unacknowledged, in some form of originality, first for yourself, second, perhaps, for the rest of us.

Fear of form above all means fear of compression— of an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible. With a few exceptions, forms of collage and assemblage dominate this show: the putting together (or simply putting side by side) of existing images and objects prevails. The consistency of this technique in two and three dimensions should have been a red flag for the curators. Collage has driven much art since the late 1970's. Lately, and especially in this exhibition, it often seems to have become so distended and pulled apart that its components have become virtually autonomous and unrelated, which brings us back to square one. This is most obvious in the large installations of graphic works whose individual parts gain impact and meaning from juxtaposition but are in fact considered distinct artworks."

Margaret Atwood on art and the trickster

"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.'  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."

* Lewis Hyde, Trickster Makes This World: Mischief, Myth, and Art,  Farrar Straus & Giroux, January 1998

Smith mentions "an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible."

Atwood mentions "a seamless whole."

For some related remarks, see "A Study in Art Education" and the central figure pictured above. (There "N" can stand for "number," "nine," or "narrative.")

Sunday, June 13, 2010

Sunday School

Filed under: General — m759 @ 9:00 am

What on earth is a 'concrete universal'?"
Said to be an annotation (undated)
by Robert M. Pirsig of A History of Philosophy,
by Frederick Copleston, Society of Jesus.

From Aaron Urbanczyk's 2005 review of Christ and Apollo  by William Lynch, S.J., a book first published in 1960—

"Lynch's use of analogy vis-a-vis literature provides, in a sense, a philosophical basis to the theoretical paradox popularized by W. K. Wimsatt (1907-1975), which contends that literature is a sort of 'concrete universal.'"

The following figure has often been
offered in this journal as a symbol of Apollo

Image-- 3x3 array of white squares

Arguments that it is, rather, a symbol of Christ
may be left to the Society of Jesus.

One possible approach—
Urbanczyk's review says that
"Christianity offers the critic
   a privileged ontological window…."

"The world was warm and white when I was born:
Beyond the windowpane the world was white,
A glaring whiteness in a leaded frame,
Yet warm as in the hearth and heart of light."

Delmore Schwartz

Sunday, May 9, 2010

For Miss Prothero (and Dylan Thomas)

Filed under: General — Tags: , — m759 @ 4:23 am

 

The Ninth Gate

Friday’s post “Religion at Harvard” continues…

Image-- List of nine religions in the chapters of Prothero's 'God is Not One'

This list may be of some use to
Rebecca Newberger Goldstein, who, like Prothero,
spoke recently at Harvard Book Store.

See also Rosalind Krauss on Grids,
An Education, and Plan 9 from Outer Space.

Readers more advanced than Harvard audiences
may wish to compare yesterday’s linked-to story
Loo Ree” with the works of Alison Lurie
in particular, Imaginary Friends and Familiar Spirits.

Wednesday, April 7, 2010

Veritas

Filed under: General — Tags: — m759 @ 9:00 am

Some historians consider today's date, April 7, to be the date of the Crucifixion in the Roman calendar (a solar calendar, as opposed to the Jewish lunar scheme).

Since the ninefold square has been called both a symbol of Apollo and the matrix of a cross, it will serve as an icon for today–

The 3x3 square

The image “http://www.log24.com/log/pix05B/051202-Cross.gif” cannot be displayed, because it contains errors.
Adapted from
Ad Reinhardt

Wednesday, September 30, 2009

Wednesday September 30, 2009

Filed under: General,Geometry — Tags: — m759 @ 9:48 am

Midnight in the Garden, Autumn 2009

 

Review:

Der Einsatz
 
Motto of Plato's Academy: 'Let no one ignorant of geometry enter'
The Ninefold Square (a 3x3 grid)

The New York Times Magazine on Sunday, Sept. 20, 2009:
 
'The Holy Grail of the Unconscious' at The New York Times

From this journal on the following day, Sept. 21:

Pearl Jam 'Backspacer' album released Sept. 20, 2009

Happy birthday, Stephen King.

Today's previous entry is based on a song, "Unthought Known,"
from the above album; the cover of the album uses the 3×3 grid
shown in Sept. 20's midnight review. For related material
on the unconscious, see June 13-15, 2005.

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

Tom O'Bedlam's Song

Thursday, February 19, 2009

Thursday February 19, 2009

Filed under: General — Tags: — m759 @ 7:07 am

A Sunrise
for Sunrise

“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.”

Rosalind Krauss, “Grids”

Yesterday’s entry featured a rather simple-minded example from Krauss of how the ninefold square (said to be a symbol of Apollo)

The 3x3 grid

may be used to create a graphic design– a Greek cross, which appears also in crossword puzzles:

Crossword-puzzle design that includes Greek-cross elements

Illustration by
Paul Rand
(born Peretz Rosenbaum)

A more sophisticated example
of the ninefold square
in graphic design:

“That old Jew
gave me this here.”

— A Flag for Sunrise  

The 3x3 grid as an organizing frame for Chinese calligraphy. Example-- the character for 'sunrise'
From Paul-Rand.com

Wednesday, December 10, 2008

Wednesday December 10, 2008

Filed under: General,Geometry — m759 @ 3:26 pm
Symbol

“If it’s a seamless whole you want,
 pray to Apollo, who sets the limits
  within which such a work can exist.”

Margaret Atwood,
quoted here on
November 17, 2008

The 3x3 square

A symbol of Apollo

Related material:

A web page by
Nick Wedd at Oxford

with a neater version
of pictures I drew on
March 26, 1985

(Recall that Apollo is the god
   of, among other things, reason.)

Monday, November 17, 2008

Monday November 17, 2008

Filed under: General,Geometry — m759 @ 9:00 am
Limits

From the previous entry:

“If it’s a seamless whole you want,
 pray to Apollo, who sets the limits
  within which such a work can exist.”

— Margaret Atwood,
author of Cat’s Eye

The 3x3 square

Happy birthday
to the late
Eugene Wigner

… and a belated
Merry Christmas
 to Paul Newman:

Elke Sommer, former Erlangen Gymnasium student, in 'The Prize' with Paul Newman, released Christmas Day, 1963

“The laws of nature permit us to foresee events on the basis of the knowledge of other events; the principles of invariance should permit us to establish new correlations between events, on the basis of the knowledge of established correlations between events. This is exactly what they do.”

— Eugene Wigner, Nobel Prize Lecture, December 12, 1963

Saturday, August 2, 2008

Saturday August 2, 2008

Filed under: General,Geometry — m759 @ 2:02 pm
Geometry and Death

(continued from
June 15, 2007)

Today is the anniversary
of the 1955 death of poet
Wallace Stevens.

Related material:

A poem by Stevens,

an essay on  the
relationships between
poets and philosophers —
“Bad Blood,” by
Leonard Michaels

and

The ninefold square, a symbol of Apollo

the Log24 entries
of June 14-15, 2007
.

Sunday, November 26, 2006

Sunday November 26, 2006

Filed under: General — m759 @ 7:26 am

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    

For more on the field
of reason, see
Log24, Oct. 9, 2006.

A reasonable set of
"strange correspondences"
in the garden of Apollo
has been provided by Ezra Brown
in a mathematical essay (pdf).

Unreason is, of course,
more popular.

* The ninefold square is perhaps a "concrete universal" in the sense of Hegel:

"Two determinations found in all philosophy are the concretion of the Idea and the presence of the spirit in the same; my content must at the same time be something concrete, present. This concrete was termed Reason, and for it the more noble of those men contended with the greatest enthusiasm and warmth. Thought was raised like a standard among the nations, liberty of conviction and of conscience in me. They said to mankind, 'In this sign thou shalt conquer,' for they had before their eyes what had been done in the name of the cross alone, what had been made a matter of faith and law and religion– they saw how the sign of the cross had been degraded."

— Hegel, Lectures on the History of Philosophy, "Idea of a Concrete Universal Unity"

"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon   
 

Saturday, September 16, 2006

Saturday September 16, 2006

Filed under: General — Tags: , — m759 @ 11:07 am

Pandora's Box

Part I:
The Pandora Cross

"There is no painter in the West who can be unaware of the symbolic power of the cruciform shape and the Pandora's box of spiritual reference that is opened once one uses it."

— Rosalind Krauss in "Grids"


The image “http://www.log24.com/log/pix06A/060916-Art.jpg” cannot be displayed, because it contains errors.

(See Log24, Sept. 13)

Part II:
The Opening

Remarks by the Pope on Sept. 12,
as reported by the Vatican:

Faith, Reason, and the University:
Memories and Reflections

For the result of
the Pope's remarks, see
a transcript of
 yesterday's Google News
and the following
from BBC today:

The image “http://www.log24.com/log/pix06A/060916-Benedict16.jpg” cannot be displayed, because it contains errors.
Click to enlarge the screenshot.

Part III:
Hope

The New Yorker (issue of June 5, 2006) on the late Oriana Fallaci:

"In September [2005], she had a private audience with Pope Benedict XVI at Castel Gandolfo, his summer residence outside Rome. She had criticized John Paul II for making overtures to Muslims, and for not condemning terrorism heartily enough, but she has hopes for Joseph Ratzinger."

For further details, see yesterday's Log24.


Part IV:
The Sibyl's Song

The image “http://www.log24.com/log/pix06A/060916-MC7.GIF” cannot be displayed, because it contains errors.

— From The Magic Circle,
 a spiritual narrative
 by Katherine Neville

For more on "the long-mute voice
of the past," on "darkness beneath
the volcano," and on uncorking,
see Glory Season and Harrowing.

Related material from
Log24 on Dec. 2, 2005:

Benedict XVI, before he became Pope:

"… a purely harmonious concept of beauty is not enough…. Apollo, who for Plato's Socrates was 'the God' and the guarantor of unruffled beauty as 'the truly divine' is absolutely no longer sufficient."

A symbol of Apollo:

IMAGE- The ninefold square

and a related
Christian symbol,

The image �http://www.log24.com/log/pix05B/051202-Cross.gif� cannot be displayed, because it contains errors.

the Greek Cross
(adapted from
Ad Reinhardt).

Moral of the Pandora Cross:

"Nine is a very powerful Nordic number."
— Katherine Neville in The Magic Circle…

quoted in The Nine, a Log24 entry
for Hermann Weyl's birthday,
November 9, 2004.
 

Friday, August 4, 2006

Friday August 4, 2006

Filed under: General — Tags: , — m759 @ 2:56 am

ART WARS
continued from
previous entry

In memory of
Elisabeth Schwarzkopf:

"Who is the fairest of them all?"

This question might
well be posed by…

The image “http://www.log24.com/log/pix05/050501-Krauss.jpg” cannot be displayed, because it contains errors.

Rosalind Krauss,
Meyer Schapiro Professor
of Modern Art and Theory
at Columbia University
(Ph.D., Harvard U., 1969).

"The grid is a staircase to the Universal….
We could think about Ad Reinhardt, who,
despite his repeated insistence that
'Art is art,'
ended up by painting a series of…
nine-square grids in which the motif
that inescapably emerges is
a Greek cross.

The image “http://www.log24.com/log/pix05B/051202-Cross.gif” cannot be displayed, because it contains errors.
Adapted from
Ad Reinhardt

There is no painter in the West
who can be unaware of
the symbolic power
of the cruciform shape and the
Pandora's box of spiritual reference
that is opened once one uses it."

— Rosalind Krauss in "Grids"

"Nine is a very powerful Nordic number."
— Katherine Neville, author of The Eight

Related material:

Balanchine's Birthday,

Apollo and Christ.
 

Sunday, February 5, 2006

Sunday February 5, 2006

Filed under: General — m759 @ 9:00 pm
The Logic of Apollo

“The icon that I use… is the nine-fold square…. This is the garden of Apollo, the field of Reason….”

Architect’s notes on the design of a college campus

“Binary image morphological operations are well suited to a large class of basic image processing applications. These operations include image analysis tasks such as shape recognition, image segmentation, noise reduction, and feature extraction.”

The image “http://www.log24.com/theory/images/060206-Masks.gif” cannot be displayed, because it contains errors.

A Programmable Logic-based Implementation of Ultra-fast Parallel Binary Image Morphological Operations (pdf), by Kenneth G. Ricks et al., ISCA 18th International Conference on Computers and Their Applications (March 2003)

Saturday, July 30, 2005

Saturday July 30, 2005

Filed under: General — Tags: , , — m759 @ 11:21 am

Born today: Laurence Fishburne

Matrix

“The nine-fold square has centre, periphery, axes and diagonals. But all are present only in their bare essentials. It is also a sequence of eight triads. Four pass through the centre and four do not. This is the garden of Apollo, the field of Reason, sheltered by the Gate from the turmoil of the Delta, with its endless cycles of erasure and reinscription. This is the Temple of Solomon, as inscribed, for example, by a nine-fold compartmentation to provide the ground plan of Yale….”– Architects John Outram Associates
on work at Rice University

Yale Daily News, Jan. 11, 2001:  

“When New Haven was founded, the city was laid out into a grid of nine squares surrounded by a great wilderness.
Last year History of Art Professor Emeritus Vincent Scully said the original town plan reflected a feeling that the new city should be sacred.
Scully said the colony’s founders thought of their new Puritan settlement as a ‘nine-square paradise on Earth, heaven on earth, New Haven, New Jerusalem.'”

“Real and unreal are two in one:
New Haven
Before and after one arrives….”

— Wallace Stevens,
An Ordinary Evening in New Haven,’ XXVIII

Related material:
Log24 entries on
St. Peter’s Day, 2004

Thursday, April 22, 2004

Thursday April 22, 2004

Filed under: General,Geometry — Tags: , , — m759 @ 10:07 pm

Minimalism

"It's become our form of modern classicism."

— Nancy Spector in 
   the New York Times of April 23, 2004

Part I: Aesthetics

In honor of the current Guggenheim exhibition, "Singular Forms" — A quotation from the Guggenheim's own website

"Minimalism refers to painting or sculpture

  1. made with an extreme economy of means
  2. and reduced to the essentials of geometric abstraction….
  3. Minimalist art is generally characterized by precise, hard-edged, unitary geometric forms….
  4. mathematically regular compositions, often based on a grid….
  5. the reduction to pure self-referential form, emptied of all external references….
  6. In Minimal art what is important is the phenomenological basis of the viewer’s experience, how he or she perceives the internal relationships among the parts of the work and of the parts to the whole….
  7. The repetition of forms in Minimalist sculpture serves to emphasize the subtle differences in the perception of those forms in space and time as the spectator’s viewpoint shifts in time and space."

Discuss these seven points
in relation to the following:

 
Form,
by S. H. Cullinane

Logos and Logic

Mark Rothko's reference
to geometry as a "swamp"
and his talk of "the idea" in art

Michael Kimmelman's
remarks on ideas in art 

Notes on ideas and art

Geometry
of the 4×4 square

The Grid of Time

ART WARS:
Judgment Day
(2003, 10/07)

Part II: Theology

Today's previous entry, "Skylark," concluded with an invocation of the Lord.   Of course, the Lord one expects may not be the Lord that appears.


 John Barth on minimalism:

"… the idea that, in art at least, less is more.

It is an idea surely as old, as enduringly attractive and as ubiquitous as its opposite. In the beginning was the Word: only later came the Bible, not to mention the three-decker Victorian novel. The oracle at Delphi did not say, 'Exhaustive analysis and comprehension of one's own psyche may be prerequisite to an understanding of one's behavior and of the world at large'; it said, 'Know thyself.' Such inherently minimalist genres as oracles (from the Delphic shrine of Apollo to the modern fortune cookie), proverbs, maxims, aphorisms, epigrams, pensees, mottoes, slogans and quips are popular in every human century and culture–especially in oral cultures and subcultures, where mnemonic staying power has high priority–and many specimens of them are self-reflexive or self-demonstrative: minimalism about minimalism. 'Brevity is the soul of wit.' "


Another form of the oracle at Delphi, in minimalist prose that might make Hemingway proud:

"He would think about Bert.  Bert was an interesting man.  Bert had said something about the way a gambler wants to lose.  That did not make sense.  Anyway, he did not want to think about it.  It was dark now, but the air was still hot.  He realized that he was sweating, forced himself to slow down the walking.  Some children were playing a game with a ball, in the street, hitting it against the side of a building.  He wanted to see Sarah.

When he came in, she was reading a book, a tumbler of dark whiskey beside her on the end table.  She did not seem to see him and he sat down before he spoke, looking at her and, at first, hardly seeing her.  The room was hot; she had opened the windows, but the air was still.  The street noises from outside seemed almost to be in the room with them, as if the shifting of gears were being done in the closet, the children playing in the bathroom.  The only light in the room was from the lamp over the couch where she was reading.

He looked at her face.  She was very drunk.  Her eyes were swollen, pink at the corners.  'What's the book,' he said, trying to make his voice conversational.  But it sounded loud in the room, and hard.

She blinked up at him, smiled sleepily, and said nothing.

'What's the book?'  His voice had an edge now.

'Oh,' she said.  'It's Kierkegaard.  Soren Kierkegaard.' She pushed her legs out straight on the couch, stretching her feet.  Her skirt fell back a few inches from her knees.  He looked away.

'What's that?' he said.

'Well, I don't exactly know, myself."  Her voice was soft and thick.

He turned his face away from her again, not knowing what he was angry with.  'What does that mean, you don't know, yourself?'

She blinked at him.  'It means, Eddie, that I don't exactly know what the book is about.  Somebody told me to read it once, and that's what I'm doing.  Reading it.'

He looked at her, tried to grin at her — the old, meaningless, automatic grin, the grin that made everbody like him — but he could not.  'That's great,' he said, and it came out with more irritation than he had intended.

She closed the book, tucked it beside her on the couch.  She folded her arms around her, hugging herself, smiling at him.  'I guess this isn't your night, Eddie.  Why don't we have a drink?'

'No.'  He did not like that, did not want her being nice to him, forgiving.  Nor did he want a drink.

Her smile, her drunk, amused smile, did not change.  'Then let's talk about something else,' she said.  'What about that case you have?  What's in it?'  Her voice was not prying, only friendly, 'Pencils?'

'That's it,' he said.  'Pencils.'

She raised her eyebrows slightly.  Her voice seemed thick.  'What's in it, Eddie?'

'Figure it out yourself.'  He tossed the case on the couch."

— Walter Tevis, The Hustler, 1959,
    Chapter 11


See, too, the invocation of Apollo in

A Mass for Lucero, as well as 

GENERAL AUDIENCE OF JOHN PAUL II
Wednesday 15 January 2003
:

"The invocation of the Lord is relentless…."

and

JOURNAL ENTRY OF S. H. CULLINANE
Wednesday 15 January 2003
:

Karl Cullinane —
"I will fear no evil, for I am the
meanest son of a bitch in the valley."

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