Log24

Sunday, July 9, 2017

Sunday School Lesson

Filed under: Uncategorized — m759 @ 9:00 AM

"The Occult Roots of Modernism," by Alex Ross,
in the June 26, 2017, issue of The New Yorker .

A related illustration

Wednesday, January 4, 2017

A Drama of Many Forms

Filed under: Uncategorized — m759 @ 1:24 PM

According to art historian Rosalind Krauss in 1979,
the grid's earliest employers

"can be seen to be participating in a drama
that extended well beyond the domain of art.
That drama, which took many forms, was staged
in many places. One of them was a courtroom,
where early in this century, science did battle with God,
and, reversing all earlier precedents, won."

The previous post discussed the 3×3 grid in the context of
Krauss's drama. In memory of T. S. Eliot, who died on this date
in 1965, an image of the next-largest square grid, the 4×4 array:

 

See instances of the above image.

Tuesday, January 3, 2017

Cultist Space

Filed under: Uncategorized — m759 @ 6:29 PM

The image of art historian Rosalind Krauss in the previous post
suggests a review of a page from her 1979 essay "Grids" —

The previous post illustrated a 3×3 grid. That  cultist space does
provide a place for a few "vestiges of the nineteenth century" —
namely, the elements of the Galois field GF(9) — to hide.
See Coxeter's Aleph in this journal.

Ein Eck…

Filed under: Uncategorized — m759 @ 10:19 AM

Continued

By a disciple of the late John Berger

For further ideological remarks from this source, see the now-defunct
web journal Everyday Analysis: An International Collective.

For further remarks from the date of the above post, October 9, 2013,
see this  journal on that date.

Wednesday, January 7, 2015

Gitterkrieg

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

(Continued from Jan. 3 and Jan. 5.) 

Introduction: "Grids, You Say?" by Josefine Lyche,
and Anti-Christmas 2010:

Related material:
Chapter 42 in
A History of Graphic Design ,
by Guity Novin.

Tuesday, October 21, 2014

Art as a Tool

Filed under: Uncategorized — 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?

Saturday, October 18, 2014

Educational Series

Filed under: Uncategorized — m759 @ 1:01 PM

Barron’s Educational Series (click to enlarge):

The Tablet of Ahkmenrah:

IMAGE- The Tablet of Ahkmenrah, from 'Night at the Museum'

 “With the Tablet of Ahkmenrah and the Cube of Rubik,
my power will know no bounds!”
— Kahmunrah in a novelization of Night at the Museum:
Battle of the Smithsonian , Barron’s Educational Series

Another educational series (this journal):

Image-- Rosalind Krauss and The Ninefold Square

Art theorist Rosalind Krauss and The Ninefold Square

IMAGE- Elementary Galois Geometry over GF(3)

Thursday, August 14, 2014

Full Frontal Aesthetics

Filed under: Uncategorized — m759 @ 7:59 PM

A prequel to today’s noon post

Rosalind Krauss in “Grids” —

“The physical qualities of the surface, we could say,
are mapped onto the aesthetic dimensions of
the same surface. And those two planes—
the physical and the aesthetic— are demonstrated
to be the same plane…. the bottom line of the grid is
a naked and determined materialism.”

A writer I prefer:

Barsotti’s classic illustrated:

The naked and determined Annette Bening in “The Grifters” —

Bottom Line

Filed under: Uncategorized — m759 @ 12:00 PM

“. . . the bottom line of the grid is a naked and determined materialism.”

— Rosalind Krauss, quoted by Josefine Lyche

See also http://www.dailymotion.com/video/
x164rmi_britt-ekland-nude-wicker-man-1973_people.

Wednesday, March 26, 2014

Grid

Filed under: Uncategorized — m759 @ 12:00 PM

For some context, see Holy Field
and Krauss Grid.

Wednesday, October 9, 2013

To Apollo*

Filed under: Uncategorized — Tags: — m759 @ 1:06 PM

From Log24

From Josefine Lyche's website —

* For the title, see Apollo + Outram in this journal.

 

Sunday, April 28, 2013

Red October’s Sermon

Filed under: Uncategorized — Tags: — m759 @ 10:30 AM

For the Harvard Arts Weekend:

"Grids, You Say?" by Josefine Lyche, with
Lyche's quotation from Rosalind Krauss in October
(Vol. 9, Summer 1979) —

IMAGE- 'Grids, You Say?' by Josefine Lyche, with Lyche's quotation of Rosalind Krauss

See also last evening's Elevation of the Host, with Vampire Weekend.

"For every kind of vampire, there is a kind of cross." — Gravity's Rainbow

Tuesday, October 30, 2012

Black October

Filed under: Uncategorized — m759 @ 9:00 AM

From AntiChristmas 2010

Image-- Rosalind Krauss and The Ninefold Square

Art theorist Rosalind Krauss and The Ninefold Square

Krauss is a co-founder of the art journal October .
For some backgound, see the overlapping searches
Krauss October and Matrix Architect.

Sunday, January 1, 2012

Sunday Shul

Filed under: Uncategorized — m759 @ 9:00 AM

"… myths are stories, and like all narratives
they unravel through time, whereas grids
are not only spatial to start with,
they are visual structures that explicitly reject
a narrative or sequential reading of any kind."

— Rosalind Krauss in "Grids,"
October  (Summer 1979), 9: 50-64.

Counterexample—

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

The Ninefold Square

See Coxeter and the Aleph and Ayn Sof

Mathematics and Narrative, Illustrated
http://www.log24.com/log/pix11/110107-The1950Aleph-Sm.jpg

Mathematics
http://www.log24.com/log/pix11/110107-ScriptAlephSm.jpg
Narrative

Saturday, January 8, 2011

True Grid (continued)

Filed under: Uncategorized — 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…"

Sunday, September 12, 2010

A Fragment of Time*

Filed under: Uncategorized — m759 @ 4:30 AM

Between midnight and dawn, when the past is all deception,
The future futureless, before the morning watch
When time stops and time is never ending….

Four Quartets

June 25, 2010

Image-- Rosalind Krauss and The Ninefold Square

Art Theorist Rosalind Krauss and The Ninefold Square

* Title from a quotation in the Sunday New York Times  today
  (in a story about a June 25 death beginning on page MB1 of the New York edition)

Friday, June 25, 2010

How Deep the Darkness

Filed under: Uncategorized — m759 @ 12:25 PM

Image-- Rosalind Krauss and The Ninefold Square

Art Theorist Rosalind Krauss and The Ninefold Square

Sunday, May 9, 2010

For Miss Prothero (and Dylan Thomas)

Filed under: Uncategorized — 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, January 6, 2010

Epiphany Revisited

Filed under: Uncategorized — Tags: — m759 @ 9:00 AM

January 06, 2007
ART WARS: Epiphany

Picture of Nothing
On Kirk Varnedoe’s
2003 Mellon Lectures,
Pictures of Nothing“–

“Varnedoe’s lectures were ultimately about faith, about his faith in the power of abstraction, and abstraction as a kind of anti-religious faith in itself….”

Related material:

The more industrious scholars will derive considerable pleasure from describing how the art-history professors and journalists of the period 1945-75, along with so many students, intellectuals, and art tourists of every sort, actually struggled to see the paintings directly, in the old pre-World War II way, like Plato’s cave dwellers watching the shadows, without knowing what had projected them, which was the Word.”

— Tom Wolfe, The Painted Word

Log24, Aug. 23, 2005:

“Concept (scholastics’ verbum mentis)–  theological analogy of Son’s procession  as Verbum Patris, 111-12″ — Index to Joyce and Aquinas, by William T. Noon, S.J., Yale University Press 1957,  second printing 1963, page 162

“So did God cause the big bang? Overcome by metaphysical lassitude, I finally reach over to my bookshelf for The Devil’s Bible. Turning to Genesis I read: ‘In the beginning there was nothing. And God said, ‘Let there be light!’ And there was still nothing, but now you could see it.'”
— Jim Holt, Big-Bang Theology, from Slate‘s “High Concept” department

'In the beginning' according to Jim Holt

“Bang.”

“…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….”

For properties of the “nothing” represented by the 3×3 grid, see The Field of Reason. For religious material related to the above and to Epiphany, a holy day observed by some, see Plato, Pegasus, and the Evening Star and Shining Forth.


Some Context:

Quaternions in Finite Geometry

Click to enlarge.

See also Nativity.

Friday, February 20, 2009

Friday February 20, 2009

Filed under: Uncategorized — Tags: , , — m759 @ 11:01 PM

The Cross
of Constantine

mentioned in
this afternoon's entry
"Emblematizing the Modern"
was the object of a recent
cinematic chase sequence
(successful and inspiring)
starring Mira Sorvino
at the Metropolitan
Museum of Art.

In memory of
Dr. Hunter S. Thompson,
dead by his own hand
on this date
four years ago

Rolling Stone memorial to Dr. Hunter S. Thompson

Click for details.

There is
another sort of object
we may associate with a
different museum and with
a modern Constantine
See "Art Wars for MoMA"
(Dec. 14, 2008).

This object, modern
rather than medieval,
is the ninefold square:

The ninefold square

It may suit those who,
like Rosalind Krauss
(see "Emblematizing"),
admire the grids of modern art
but view any sort of Christian
cross with fear and loathing.

For some background that
Dr. Thompson might appreciate,
see notes on Geometry and Death
in this journal, June 1-15, 2007,
and the five Log24 entries
 ending at 9 AM Dec. 10. 2006,
which include this astute
observation by J. G. Ballard:

"Modernism's attempt to build a better world with the aid of science and technology now seems almost heroic. Bertolt Brecht, no fan of modernism, remarked that the mud, blood and carnage of the first world war trenches left its survivors longing for a future that resembled a white-tiled bathroom."

Selah.

Friday February 20, 2009

Filed under: Uncategorized — Tags: , — m759 @ 2:01 PM
Emblematizing
 the Modern
 

The following meditation was
inspired by the recent fictional
recovery, by Mira Sorvino
in "The Last Templar,"

of a Greek Cross —
"the Cross of Constantine"–
and by the discovery, by
art historian Rosalind Krauss,
of a Greek Cross in the
art of Ad Reinhardt.

http://www.log24.com/log/pix09/090220-CrossOfDescartes.jpg

The Cross of Descartes  

Note that in applications, the vertical axis
of the Cross of Descartes often symbolizes
the timeless (money, temperature, etc.)
while the horizontal axis often symbolizes time.


T.S. Eliot:

"Men’s curiosity searches past and future
And clings to that dimension. But to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint…."


There is a reason, apart from her ethnic origins, that Rosalind Krauss (cf. 9/13/06) rejects, with a shudder, the cross as a key to "the Pandora's box of spiritual reference that is opened once one uses it." The rejection occurs in the context of her attempt to establish not the cross, but the grid, as a religious symbol:
 

"In suggesting that the success [1] of the grid
is somehow connected to its structure as myth,
I may of course be accused of stretching a point
beyond the limits of common sense, since myths
are stories, and like all narratives they unravel
through time, whereas grids are not only spatial
to start with, they are visual structures
that explicitly reject a narrative
or sequential reading of any kind.

[1] Success here refers to
three things at once:
a sheerly quantitative success,
involving the number of artists
in this century who have used grids;
a qualitative success through which
the grid has become the medium
for some of the greatest works
of modernism; and an ideological
success, in that the grid is able–
in a work of whatever quality–
to emblematize the Modern."

— Rosalind Krauss, "Grids" (1979)

Related material:

Time Fold and Weyl on
objectivity and frames of reference.

See also Stambaugh on
The Formless Self
as well as
A Study in Art Education
and
Jung and the Imago Dei.

Thursday, February 19, 2009

Thursday February 19, 2009

Filed under: Uncategorized — 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

Monday, December 15, 2008

Monday December 15, 2008

Filed under: Uncategorized — Tags: — m759 @ 3:09 PM
Happy Birthday,
Julie Taymor

The image “http://www.log24.com/log/pix05B/Gameplayers12.jpg” cannot be displayed, because it contains errors.

"Julie Taymor… will be directing Helen Mirren in a big-screen adaptation of The Tempest. Dame Helen, in a gender-switch from the original, will be playing Prospera, the usurped Duchess possessed of a vast library and magical powers."

— John Murphy at Bardolatry.com on November 21, 2008

A vast library…

On searching for Garden of Eden patterns (GEP's):

"The grid is a staircase to the Universal…."

— Rosalind Krauss, quoted here on Weyl's birthday, 2004

"I find the whole topic of GEPs a deeply interesting one, from many viewpoints: mathematical, philosophical, physical….

… the obvious problem is, that the required computational time is growing rapidly with the size of the grid, and even for a small grid, like 4×4 (=16 cells) there are 216=65536 possible patterns…."

cateye at RichardDawkins.net

… and magical powers

The date of cateye's post was Sunday, October 21, 2007.

For related material see Log24 on Sunday, October 21, 2007.
 

Monday, May 21, 2007

Monday May 21, 2007

Filed under: Uncategorized — Tags: — m759 @ 4:48 AM
Down the
Up Staircase

Commentary on a
Jonathan Borofsky
painting in the
May 21 New Yorker:

IMAGE- Borofsky's 'Four Gods' and related structures
 
Commentary

"… Mondrian and Malevich
are not discussing canvas
or pigment or graphite
or any other form of matter.
They are talking about about
Being or Mind or Spirit.
From their point of view,
the grid is a staircase
to the Universal…."

Rosalind Krauss
 

Tuesday, January 9, 2007

Tuesday January 9, 2007

Filed under: Uncategorized — m759 @ 12:00 PM
For Balanchine’s Birthday

(continued from
January 9, 2003)

George Balanchine

Encyclopædia Britannica Article

born January 22
[January 9, Old Style], 1904,
St. Petersburg, Russia
died April 30, 1983, New York,
New York, U.S.

Photograph:George Balanchine.
George Balanchine.
©1983 Martha Swope

original name 
Georgy Melitonovich Balanchivadze
most influential choreographer of classical ballet in the United States in the 20th century.  His works, characterized by a cool neoclassicism, include The Nutcracker (1954) and Don Quixote (1965), both pieces choreographed for the New York City Ballet, of which he was a founder (1948), the artistic director, and the…

Balanchine,  George… (75 of 1212 words)

“What on earth is
a concrete universal?”
— Robert M. Pirsig

Review:

From Wikipedia’s
“Upper Ontology”
and
Epiphany 2007:

“There is no neutral ground
that can serve as
a means of translating between
specialized (lower) ontologies.”

There is, however,
“the field of reason”–
the 3×3 grid:

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

Click on grid
for details.

As Rosalind Krauss
has noted, some artists
regard the grid as
“a staircase to
  the Universal.”

Other artists regard
Epiphany itself as an
approach to
the Universal:

Epiphany signals the traversal
of the finite by the infinite,
of the particular by the universal,
of the mundane by the mystical,
of time by eternity.

Richard Kearney, 2005,
in The New Arcadia Review

The image “http://www.log24.com/log/pix07/070109-Kearney2.jpg” cannot be displayed, because it contains errors.

Kearney (right) with
Martin Scorsese (left)
and Gregory Peck
in 1997.

“… one of the things that worried me about traditional metaphysics, at least as I imbibed it in a very Scholastic manner at University College Dublin in the seventies, is that philosophy was realism and realism was truth. What disturbed me about that was that everything was already acquired; truth was always a systematic given and it was there to be learned from Creation onwards; it was spoken by Jesus Christ and then published by St. Thomas Aquinas: the system as perfect synthesis. Hence, my philosophy grew out of a hunger for the ‘possible’ and it was definitely a reaction to my own philosophical formation. Yet that wasn’t my only reaction. I was also reacting to what I considered to be the deep pessimism, and even at times ‘nihilism’ of the postmodern turn.”

— Richard Kearney, interview (pdf) in The Leuven Philosophy Newsletter, Vol. 14, 2005-2006

For more on “the possible,” see Kearney’s The God Who May Be, Diamonds Are Forever, and the conclusion of Mathematics and Narrative:

“We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes)).”

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

“The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being….”

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity,
Christ Church College, Oxford
(the home of Lewis Carroll)

Saturday, January 6, 2007

Saturday January 6, 2007

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM


Picture of Nothing

On Kirk Varnedoe’s
2003 Mellon Lectures,
Pictures of Nothing“–

“Varnedoe’s lectures were ultimately
about faith, about his faith in
the power of abstraction,
and abstraction as a kind of
anti-religious faith in itself….”

The Washington Post

Related material:

The more industrious scholars
will derive considerable pleasure
from describing how the art-history
professors and journalists of the period
1945-75, along with so many students,
intellectuals, and art tourists of every
sort, actually struggled to see the
paintings directly, in the old
pre-World War II way,
like Plato’s cave dwellers
watching the shadows, without
knowing what had projected them,
which was the Word.”

— Tom Wolfe, The Painted Word

Log24, Aug. 23, 2005:

“Concept (scholastics’ verbum mentis)–
theological analogy of Son’s procession
as Verbum Patris, 111-12″

— Index to Joyce and Aquinas,
by William T. Noon, S.J.,
Yale University Press 1957,
second printing 1963, page 162

“So did God cause the big bang?
Overcome by metaphysical lassitude,
I finally reach over to my bookshelf
for The Devil’s Bible.
Turning to Genesis I read:
‘In the beginning
there was nothing.
And God said,
‘Let there be light!’
And there was still nothing,
but now you could see it.'”

— Jim Holt, Big-Bang Theology,
Slate‘s “High Concept” department

The image “http://www.log24.com/log/pix07/070106-Bang.jpg” cannot be displayed, because it contains errors.


“Bang.”

“…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….”

Rosalind Krauss, “Grids”

For properties of the
“nothing” represented
by the 3×3 grid, see
The Field of Reason.

For religious material related
to the above and to Epiphany,
a holy day observed by some,
see Plato, Pegasus, and the
Evening Star
and Shining Forth.

Sunday, November 26, 2006

Sunday November 26, 2006

Filed under: Uncategorized — 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   
 

Monday, October 9, 2006

Monday October 9, 2006

Filed under: Uncategorized — m759 @ 9:00 AM
 
ART WARS:
To Apollo
 
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

To Apollo (10/09/02)
Art Wars: Apollo and Dionysus
(10/09/02)
Balanchine's Birthday
(01/09/03)

Art Theory for Yom Kippur
(10/05/03)

A Form
(05/22/04)
Ineluctable
(05/27/04)

A Form, continued
(06/05/04)
Parallelisms
(06/06/04)
Ado
(06/25/04)

Deep Game
(06/26/04)
Gameplayers of Zen
(06/27/04)
And So To Bed
(06/29/04)
Translation Plane for Rosh Hashanah
(09/15/04)
Derrida Dead
(10/09/04)
The Nine
(11/09/04)
From Tate to Plato
(11/19/04)
Art History
(05/11/05)
A Miniature Rosetta Stone
(08/06/05)
High Concept
(8/23/05) 
High Concept, Continued
(8/24/05)
Analogical Train of Thought
(8/25/05)
Today's Sermon: Magical Thinking
(10/09/05)
Balance
(10/31/05)
Matrix
(11/01/05)
Seven is Heaven, Eight is a Gate
(11/12/05)
Nine is a Vine
(11/12/05)
Apollo and Christ
(12/02/05)
Hamilton's Whirligig
(01/05/06)
Cross
(01/06/06)
On Beauty
(01/26/06)
Sunday Morning
(01/29/06)
Centre
(01/29/06)
New Haven
(01/29/06) 
Washington Ballet
(02/05/06)
Catholic Schools Sermon
(02/05/06)
The Logic of Apollo
(02/05/06)
Game Boy
(08/06/06)
Art Wars Continued: The Krauss Cross
(09/13/06)
Art Wars Continued: Pandora's Box
(09/16/06)
The Pope in Plato's Cave
(09/16/06)
Today's Birthdays
(09/26/06)
Symbology 101
(09/26/06)

Saturday, September 16, 2006

Saturday September 16, 2006

Filed under: Uncategorized — 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.
 

Wednesday, September 13, 2006

Wednesday September 13, 2006

Filed under: Uncategorized — m759 @ 9:28 PM

ART WARS continued:

The Krauss Cross

The image “http://www.log24.com/log/pix06A/060913-Art.jpg” cannot be displayed, because it contains errors.

Rosalind Krauss in "Grids":

"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, we could think about Ad Reinhardt who, despite his repeated insistence that 'Art is art,' ended up by painting a series of black nine-square grids in which the motif that inescapably emerges is a Greek 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."

Rebecca Goldstein on
Mathematics and Narrative
:

"I don't write exclusively on Jewish themes or about Jewish characters. My collection of short stories, Strange Attractors, contained nine pieces, five of which were, to some degree, Jewish, and this ratio has provided me with a precise mathematical answer (for me, still the best kind of answer) to the question of whether I am a Jewish writer. I am five-ninths a Jewish writer."

Jacques Maritain,
October 1941
:

"The passion of Israel
today is taking on
more and more distinctly
the form of the Cross."

E. L. Doctorow,
City of God:

"In the garden of Adding,
Live Even and Odd."

Friday, August 4, 2006

Friday August 4, 2006

Filed under: Uncategorized — 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.
 

Saturday, July 30, 2005

Saturday July 30, 2005

Filed under: Uncategorized — Tags: — m759 @ 11:07 AM

Born today: Arnold Schwarzenegger

Staircase

 

Frame not included in
 Terminator 2: Judgment Day

From Log24, Oct. 7, 2003:

"…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…."

 

— Rosalind Krauss, "Grids"
 

Saturday July 30, 2005

Filed under: Uncategorized — Tags: — m759 @ 10:18 AM

Born today: Hilary Swank

  E is for Everlast

  The image “http://www.log24.com/log/pix05A/050730-Everlast2.jpg” cannot be displayed, because it contains errors.

"The grid is a staircase to the Universal."
— Rosalind Krauss

"To live is to defend a form."
— attributed to Hölderlin
 

Sunday, June 19, 2005

Sunday June 19, 2005

Filed under: Uncategorized — m759 @ 4:00 AM
ART WARS:
Darkness Visible
“No light, but rather darkness visible
 Serv’d only to discover sights of woe”
John Milton, Paradise Lost,
Book I,  lines 63-64

From the cover article (pdf) in the
June/July 2005 Notices of the
American Mathematical Society–

Martin Gardner


A famed vulgarizer, Martin Gardner,
summarizes the art of Ad Reinhardt
(Adolph Dietrich Friedrich Reinhardt,
  Dec. 24, 1913 – Aug. 30, 1967):

“Ed Rinehart [sic] made a fortune painting canvases that were just one solid color.  He had his black period in which the canvas was totally black.  And then he had a blue period in which he was painting the canvas blue.  He was exhibited in top shows in New York, and his pictures wound up in museums.  I did a column in Scientific American on minimal art, and I reproduced one of Ed Rinehart’s black paintings.  Of course, it was just a solid square of pure black.  The publisher insisted on getting permission from the gallery to reproduce it.”

Related material
from Log24.net,
Nov. 9-12, 2004:

Fade to Black

“…that ineffable constellation of talents that makes the player of rank: a gift for conceiving abstract schematic possibilities; a sense of mathematical poetry in the light of which the infinite chaos of probability and permutation is crystallized under the pressure of intense concentration into geometric blossoms; the ruthless focus of force on the subtlest weakness of an opponent.”

— Trevanian, Shibumi

“‘Haven’t there been splendidly elegant colors in Japan since ancient times?’

‘Even black has various subtle shades,’ Sosuke nodded.”

— Yasunari Kawabata, The Old Capital

An Ad Reinhardt painting
described in the entry of
noon, November 9, 2004
is illustrated below.

Ad Reinhardt,  Greek Cross

Ad Reinhardt,
Abstract Painting,
1960-66.
Oil on canvas, 60 x 60 inches.
Solomon R. Guggenheim Museum

The viewer may need to tilt
the screen to see that this
painting is not uniformly black,
but is instead a picture of a
Greek cross, as described below.

“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.

Greek 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,
Meyer Schapiro Professor
of Modern Art and Theory
at Columbia University

(Ph.D., Harvard U., 1969),
in “Grids”

The image “http://www.log24.com/log/pix04B/041109-Krauss.jpg” cannot be displayed, because it contains errors.

Krauss

 
In memory of
St. William Golding
(Sept. 19, 1911 – June 19, 1993)

Saturday, May 14, 2005

Saturday May 14, 2005

Filed under: Uncategorized — m759 @ 1:00 PM
Powers,
continued

Today’s New York Times:

“Horton Marlais Davies, Putnam professor emeritus of religion at Princeton and an author of many books about church history, died on Wednesday at his home in Princeton, N.J. He was 89…. Dr. Davies specialized in the impact of Christianity on the arts.”

The image “http://www.log24.com/log/pix05/050514-Cover2.jpg” cannot be displayed, because it contains errors.

A book edited by Horton Davies,
apparently first published by Eerdmans
at Grand Rapids, Michigan, in 1990

The Catholic Encyclopedia (1908) on the communion of saints:

“One cannot read the parables of the kingdom (Matt., xiii) without perceiving its corporate nature and the continuity which links together the kingdom in our midst and the kingdom to come. The nature of that communion, called by St. John a fellowship with one another (‘a fellowship with us’ — I John, i, 3) because it is a fellowship with the Father, and with his Son, and compared by him to the organic and vital union of the vine and its branches (John, xv), stands out….”
 
Related material:

Religious art in the entry Art History of 11 AM Wednesday, May 11, the date of Davies’s death.  See also the following direct and indirect links from that entry:

To a cruciform artifact from the current film Kingdom of Heaven, to an entry quoting John xv, Nine is a Vine, and to Art Theory for Yom Kippur.

For less-religious material on the number nine, see the entries and links in the Log24 archive for June 17-30, 2004.

From Rosalind Krauss, “Grids”:

“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.”

Amen.

Sunday, May 1, 2005

Sunday May 1, 2005

Filed under: Uncategorized — m759 @ 1:11 PM
Logos

Harvard’s Barry Mazur on
one mathematical style:

“It’s the barest, most Beckett-like vocabulary
that incorporates the theory and nothing else.”

Samuel Beckett, Quad (1981):

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

A Jungian on this six-line logo:

“They are the same six lines
that exist in the I Ching….
Now observe the square more closely:
four of the lines are of equal length,
the other two are longer….
For this reason symmetry
cannot be statically produced
and a dance results.”
 
— Marie-Louise von Franz,
Number and Time (1970),
Northwestern U. Press
paperback, 1979, p. 108

A related logo from
Columbia University’s
Department of Art History
and Archaeology
:

The image “http://www.log24.com/log/pix05/050501-ArtHist2.gif” cannot be displayed, because it contains errors.
 
Also from that department:

Rosalind Krauss,

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

Meyer Schapiro Professor
of Modern Art and Theory:

“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.”

“In the garden of Adding
live Even and Odd…”
— The Midrash Jazz Quartet in
City of God
, by E. L. Doctorow


THE GREEK CROSS

A cross in which all the arms
are the same length.

Here, for reference, is a Greek cross
within a nine-square grid:

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

 Related religious meditation for
    Doctorow’s “Garden of Adding”…

 4 + 5 = 9.

Types of Greek cross
illustrated in Wikipedia
under “cross“:

The image “http://www.log24.com/log/pix05/GrCross.gif” cannot be displayed, because it contains errors.

From designboom.com:

THE BAPTISMAL CROSS

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

is a cross with eight arms:
a Greek cross, which is superimposed
on a Greek ‘chi,’ the first letter
of the Greek word for ‘Christ.’
Since the number eight is symbolic
of rebirth or regeneration,
this cross is often used
as a baptismal cross.

Related material:

The image “http://www.log24.com/theory/images/Symm-axes.jpg” cannot be displayed, because it contains errors.

Fritz Leiber’s “spider”
or “double cross” logo.
See Why Me? and
A Shot at Redemption.

Happy Orthodox Easter.

Tuesday, November 9, 2004

Tuesday November 9, 2004

Filed under: Uncategorized — m759 @ 12:00 PM

The Nine
(Readings for
Weyl’s birthday)

“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.


Greek 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,
Meyer Schapiro Professor
of Modern Art and Theory
at Columbia University

(Ph.D., Harvard U., 1969),
in “Grids”

The image “http://www.log24.com/log/pix04B/041109-Krauss.jpg” cannot be displayed, because it contains errors.

Krauss

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

The image “http://www.log24.com/log/pix04B/041109-Magic.jpg” cannot be displayed, because it contains errors.

in The Magic Circle,
Ballantine paperback,
1999, p. 339

The image “http://www.log24.com/log/pix04B/041109-Neville.jpg” cannot be displayed, because it contains errors.

Neville

“To live is to defend a form.”

(“Leben, das heisst eine Form verteidigen“)
attributed to Hölderlin

For details on the above picture,
which deals with properties of the
nine-square grid, see

Translation Plane.

For more on the defense
of this form,


see the Log24.net entry of
June 5, 2004, A Form,
and the Art Wars entries
for St. Peter’s Day, 2004.

Tuesday, October 7, 2003

Tuesday October 7, 2003

Filed under: Uncategorized — m759 @ 5:09 PM

ART WARS:
Judgment Day

“…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….”

— Rosalind Krauss, “Grids”

Krauss is the Meyer Schapiro Professor of Modern Art and Theory at Columbia University.

For more on Meyer Schapiro, see the link on the phrase “art historian” in my March 10, 2003, entry.

To view that entry in a larger context, see the web page Art at the Vanishing Point, which includes a picture of Mondrian’s own Paris staircase.  The picture below might be thought of as illustrating Krauss’s “grid is a staircase”… a staircase to, in fact, a vanishing point.

 

Frame not included in
 Terminator 2: Judgment Day

For a different view of what the New York Times Book Review has characterized as “high culture,” see the link on that phrase also in my March 10, 2003, entry.  This leads to a work by T. S. Eliot titled Christianity and Culture.   See too the remarks of the Meyer Schapiro Professor in my Oct. 5, 2003, entry, “Art Theory for Yom Kippur,”  in which she likens the Cross to Pandora’s box.

Eliot’s attitude toward this Jewish approach to high culture might be summarized by the following remarks of Sarah Connor in Terminator 2: Judgment Day

Dr. Silberman: You broke my arm!

Sarah Connor: There are two-hundred-fifteen bones in the human body, [expletive deleted]. That’s one.

Sunday, October 5, 2003

Sunday October 5, 2003

Filed under: Uncategorized — Tags: — m759 @ 5:09 AM

At Mount Sinai:
Art Theory for Yom Kippur

From the New York Times of Sunday, October 5, 2003 (the day that Yom Kippur begins at sunset):

"Rabbi Ephraim Oshry, whose interpretations of religious law helped sustain Lithuanian Jews during Nazi occupation…. died on Sept. 28 at Mount Sinai Hospital in Manhattan. He was 89."

For a fictional portrait of Lithuanian Jews during Nazi occupation, see the E. L. Doctorow novel City of God.

For meditations on the spiritual in art, see the Rosalind Krauss essay "Grids."   As a memorial to Rabbi Oshry, here is a grid-based version of the Hebrew letter aleph:


Rabbi Oshry


Aleph

Click on the aleph for details.

"In the garden of Adding,
 Live Even and Odd…."   
— The Midrash Jazz Quartet in
       City of God, by E. L. Doctorow

Here are two meditations
on Even and Odd for Yom Kippur:

Meditation I

From Rosalind Krauss, "Grids":

"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, we could think about Ad Reinhardt who, despite his repeated insistence that 'Art is art,' ended up by painting a series of black nine-square grids in which the motif that inescapably emerges is a Greek 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."

Meditation II

Here, for reference, is a Greek cross
within a nine-square grid:

 Related religious meditation for
    Doctorow's "Garden of Adding"…

 4 + 5 = 9.

Friday, October 3, 2003

Friday October 3, 2003

Filed under: Uncategorized — m759 @ 8:23 PM

ART WARS:
Time and the Grid

Art theorist Rosalind Krauss and poet T. S. Eliot on time, timelessness, and the grid.

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