Log24

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 . . .

Saturday, October 14, 2017

Center

Rosalind Krauss in 1978

"To get inside the systems of this work,
whether LeWitt's or Judd's or Morris's,
is precisely to enter
a world without a center,
a world of substitutions and transpositions
nowhere legitimated by the revelations
of a transcendental subject. This is the strength
of this work, its seriousness, and its claim to modernity." 

Wikipedia

"The center of
the quaternion group,
Q8 = {1, −1, i, −i, j, −j, k, −k} ,
is {1, −1}."

Illustration from a post of Feb. 3,  2011

http://www.log24.com/log/pix11/110203-Scholia.jpg.

In Principio:

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

Red October  continues …

See also Molloy in this  journal.

Related art  theory —

Geometry of the 4×4 Square 

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…"

Wednesday, January 6, 2010

Epiphany Revisited

Filed under: General,Geometry — 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.

Saturday, November 28, 2009

Annals of Intelligence:

Filed under: General — m759 @ 1:06 AM

A Cross for the
Goat Men

Cross made from 9 squares of a 25-square matrix

Related material:

Krauss, Malevich, and
Linguistic Creation

Thursday, February 19, 2009

Thursday February 19, 2009

Filed under: General — 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, May 21, 2007

Monday May 21, 2007

Filed under: General — 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
 

Saturday, January 6, 2007

Saturday January 6, 2007

Filed under: General — 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: 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   
 

Wednesday, September 13, 2006

Wednesday September 13, 2006

Filed under: General — 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."

Saturday, July 30, 2005

Saturday July 30, 2005

Filed under: General — 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, May 14, 2005

Saturday May 14, 2005

Filed under: General — Tags: — m759 @ 4:00 PM


Art at Princeton

From Princeton University Press,
A. W. Mellon Lectures in the
Bollingen Series:

The Bollingen Cross
The Bollingen Cross
or “Gnostic wheel
of Princeton U. Press

Paths to the Absolute:
Mondrian, Malevich, Kandinsky,
Pollock, Newman, Rothko, and Still
by John Golding

Cloth | 2000 | $65.00 | ISBN: 0-691-04896-7
240 pp. | 7 x 10 | 63 color plates 109 halftones

This may illuminate Krauss’s remarks on
Mondrian and Malevich at the
conclusion of the previous entry.

Saturday May 14, 2005

Filed under: General — 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.

Tuesday, October 7, 2003

Tuesday October 7, 2003

Filed under: General — 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: General — 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.

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