… For the Harvard Arts Weekend:
"Grids, You Say?" by Josefine Lyche, with
Lyche's quotation from Rosalind Krauss in October
(Vol. 9, Summer 1979) —
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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
From AntiChristmas 2010—
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.
"In the master's bedroom, they gathered for the feast…."
— Suggested by the current film Hotel Transylvania
"For every kind of vampire, there is a kind of cross."
– Thomas Pynchon, Gravity's Rainbow
Related material— the Feast of Saint Patrick in 2009.
"We have named this journal in celebration of that moment in our century when revolutionary practice, theoretical inquiry and artistic innovation were joined in a manner exemplary and unique." — Rosalind Krauss and Annette Michelson, "About October," October (Spring, 1976, MIT Press) 1: pp. 3–5
“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)
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.
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:
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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”…
ART WARS:
Time and the Grid
Art theorist Rosalind Krauss and poet T. S. Eliot on time, timelessness, and the grid.
Earlier . . .
A Riddler Wannabe —
Related material — The Krauss passage quoted as above
by Shechtman in The New Yorker in December 2021 appears
also in a Log24 post of October 18, 2017: "Three Small Grids."
"If the window is this matrix of ambi- or multivalence,
and the bars of the windows-the grid-are what help us
to see, to focus on, this matrix, they are themselves
the symbol of the symbolist work of art. They function as
the multilevel representation through which the work of art
can allude, and even reconstitute, the forms of Being."
— Page 59, Rosalind Krauss, "Grids," MIT Press,
October , Vol. 9 (Summer, 1979), pp. 50-64
Related material —
Click the above image for a related Log24 post of 15 years ago today.
A related literary remark —
"Imagine Raiders of the Lost Ark set in 20th-century London, and then
imagine it written by a man steeped not in Hollywood movies but in Dante
and the things of the spirit, and you might begin to get a picture…."
— Doug Thorpe in an Amazon.com book review, not of Dark Materials.
Grids
Author: Rosalind Krauss
Source: October , Vol. 9 (Summer, 1979), pp. 50-64
Published by: The MIT Press
Stable URL: http://www.jstor.org/stable/778321
From page 59:
"Flowing and freezing; glace in French means glass, mirror, and ice;
transparency, opacity, and water. In the associative system
of symbolist thought this liquidity points in two directions.
First, towards the flow of birth-the amniotic fluid, the 'source'-
but then, towards the freezing into stasis or death-
the unfecund immobility of the mirror. For Mallarmé, particularly,
the window functioned as this complex, polysemic sign by which
he could also project the 'crystallization of reality into art.' 5
Mallarmé's Les Fenêtres dates from 1863;
Redon's most evocative window, Le Jour , appeared in 1891
in the volume Songes . If the window is this matrix of
ambi- or multivalence, and the bars of the windows-the grid-
are what help us to see, to focus on, this matrix, they are
themselves the symbol of the symbolist work of art.
They function as the multilevel representation through which
the work of art can allude, and even reconstitute, the forms of Being."
5 Robert G. Cohn, "Mallarmé's Windows," Yale French Studies ,
no. 54 (1977), 23-31.
Another evocative example — See Galois Window in this journal.
Last year on this date:
A Riddler Wannabe —
Related material — The Krauss passage quoted as above
by Shechtman in The New Yorker in December 2021 appears
also in a Log24 post of October 18, 2017: "Three Small Grids."
This post was suggested by a New York Times obituary this evening —
"Tom Mathews, Promoter of Liberal Causes and Candidates, Dies at 96."
Mathews reportedly died on October 14, 2017.
"Mr. Mathews and his business partner Roger Craver 'dreamed for years
of finding the perfect citizen-candidate,' the authors wrote, 'a man or
woman of the center-left with a feel for issues, a history of independence,
a winning television manner and, most important of all, a center — a core
of beliefs more important to him or her than getting elected.'
Dream on.
From the date of Mathews's death:
Posts now tagged A Center for Krauss —
An earlier post today, now tagged "Three Small Magic Squares,"
suggests a review of a post from October 25 three years ago
that contains the following figure —
Fans of the October Revolution may enjoy a passage
by Rosalind Krauss on grids:
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.
Barron's Educational Series (click to enlarge):
The Tablet of Ahkmenrah:
"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):
Art theorist Rosalind Krauss and The Ninefold Square
Click image for some background.
Context:
and the following post from last October:
* Who is Kearney? See, for instance, this book.
(The title is a nod to Peter Woit's recent post "Nothingness Smackdown.")
"To wrestle new mediums to the mat of specificity has been a preoccupation of mine since the inception of October , the magazine I founded in 1976 with Annette Michelson, the first issue of which carried my essay 'Video and Narcissism' which attempts to tie the essence of video to the spectacular nature of mirrors."
— Rosalind Krauss, 2008, introduction to Perpetual Inventory (MIT Press, 2010)
Related material— The video art and mirror art of Josefine Lyche.
See also Krauss's essay on video in Perpetual Inventory— "Video: The Aesthetics of Narcissism" (first published as "Video and Narcissism," October , no. 1 (Spring 1976))—
"In The Language of the Self , Lacan begins by characterizing the space of the therapeutic transaction as an extraordinary void created by the silence of the analyst. Into this void the patient projects the monologue of his own recitation, which Lacan calls 'the monumental construct of his narcissism.'"
— and related remarks on October and the void quoted here March 10 in "Boo Boo Boo."
"… 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 Ninefold Square
See Coxeter and the Aleph and Ayn Sof—
| Mathematics and Narrative, Illustrated |
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 Mathematics |
 Narrative |
"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—
A picture of the Hesse configuration–
(See Visualizing GL(2,p), a note from 1985).
Related notes from this journal —
From last November —
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From the December 2010 American Mathematical Society Notices—
Related material from this journal— Consolation Prize (August 19, 2010) |
From 2006 —
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Sunday December 10, 2006
“Function defined form, expressed in a pure geometry
– J. G. Ballard on Modernism
“The greatest obstacle to discovery is not ignorance –
— Daniel J. Boorstin, |
Also from 2006 —
|
Sunday November 26, 2006
Rosalind Krauss "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,
"And it's whispered that soon if we all call the tune
The nine engravings of The Club Dumas
An example of the universal*– or, according to Krauss,
"This is the garden of Apollo, the field of Reason…."
For more on the field of reason, see
A reasonable set of "strange correspondences" 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 ,
"For every kind of vampire, |
And from last October —
|
Friday, October 8, 2010
Starting Out in the Evening 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 .
"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,
* The Web version's title has a misprint— |
The Hunt for Exemplary October
October 25 was the date of Russia's October Revolution (Old Style). The New Style date is November 7.
Nien Cheng, dead on All Souls' Day 2009:
For details of Mrs. Cheng's life, see a Washington Post obituary by Patricia Sullivan dated Nov. 5. Mrs. Cheng died on Nov. 2 (All Souls' Day, Dia de Los Muertos).
— 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.
The Krauss Cross
"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."
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