"The bride hath paced into the hall,
Red as a rose is she;
Nodding their heads before her goes
The merry minstrelsy."
Wednesday, May 8, 2024
Art Grid: A Fulcrum for Pullman
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Tuesday, December 21, 2021
Grid Language, Grid Logic
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Thursday, April 15, 2021
Grid View and List View
From AntiChristmas 2010 —
Above: Art Theorist Rosalind Krauss and The Ninefold Square
For Krauss:
Grid View List View
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Wednesday, October 18, 2017
Three Small Grids
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:
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Wednesday, March 26, 2014
Saturday, January 8, 2011
True Grid (continued)
"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 —
|
From the December 2010 American Mathematical Society Notices—
Related material from this journal— Consolation Prize (August 19, 2010) |
From 2006 —
|
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— |
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Thursday, September 25, 2025
Wednesday, August 27, 2025
Semitism for St. Cecilia
Time in Venice, Italy: 10:44 AM Wednesday, August 27, 2025 (GMT+2)
|
Cover illustration:
Spies returning from the land of
Colored woodcut from |
The AllSpark as Agent 13 —
Springsteen to a possible Agent 13 —
"Is that you baby or just a brilliant disguise?"
Updates the same day . . .
Time in Venice, Italy: 8:35 PM Wednesday, August 27, 2025 (GMT+2)
Related art from the dies natalis of Rudolf Arnheim —
Time in Venice, Italy: 10:10 PM Wednesday, August 27, 2025 (GMT+2)
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Saturday, August 9, 2025
Sunday, September 8, 2024
Sunday Morning Koppel
Today's host for a special political edition of CBS Sunday Morning
is Ted Koppel. Vocabulary review:
Koppel's appearance today was backed by the usual CBS Sunday Morning
sun-disk Apollo symbol. An Apollo symbol that some may prefer —
The Ninefold Square
|
Rosalind Krauss "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…." |
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Wednesday, May 15, 2024
Passage for a Merry Minstrel: The Script Page*
"The bride hath paced into the hall,
Red as a rose is she;
Nodding their heads before her goes
The merry minstrelsy."
* The title is from the following passage . . .
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Tuesday, April 2, 2024
For Harlan Kane: The Rothfeld Explanation
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."
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Tuesday, December 27, 2022
The Forms of Being
"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.
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Saturday, December 24, 2022
Window as Matrix
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.
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Friday, December 23, 2022
“Was ist Raum?” — Bauhaus Founder Walter Gropius
"Was ist Raum, wie können wir ihn
erfassen und gestalten?"
The Theory and
Organization of the
Bauhaus (1923)
A relevant illustration:
At math.stackexchange.com on March 1-12, 2013:
“Is there a geometric realization of the Quaternion group?” —
The above illustration, though neatly drawn, appeared under the
cloak of anonymity. No source was given for the illustrated group actions.
Possibly they stem from my Log24 posts or notes such as the Jan. 4, 2012,
note on quaternion actions at finitegeometry.org/sc (hence ultimately
from my note “GL(2,3) actions on a cube” of April 5, 1985).
These references will not appeal to those who enjoy modernism as a religion.
(For such a view, see Rosalind Krauss on grids and another writer's remarks
on the religion's 100th anniversary this year.)
Some related nihilist philosophy from Cormac McCarthy —
"Forms turning in a nameless void."
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Thursday, December 22, 2022
For “Dark Materials” Fans: The Monkey Trial
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Wednesday, December 21, 2022
The Unmagic Square
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."
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Tuesday, November 9, 2021
Gestalt für Schicksalstag
"… thinking starts with a problem, a difficulty, a contradiction."
— The late Arthur Mattuck of MIT in last night's post Gestalt .
"The 'technical support' is an underlying ground for aesthetic practice
that supports the work of art as canvas supported oil paint."
— MIT Press on the book by Rosalind Krauss titled Under Blue Cup .
From Grid View and List View (Log24, 15 April 2021) —
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Tuesday, August 10, 2021
Ex Fano Apollinis
|
Margaret Atwood on Lewis Hyde's "Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159) What is "the next world"? It might be the Underworld…. The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254) If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart. |
"As a Chinese jar . . . ."
— Four Quartets
|
Rosalind Krauss "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 "Katz" of the August 7 post Art Angles
is a product of Princeton's
Department of Art and Archaeology.
ART —
.jpg)
ARCHAEOLOGY —
"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."
– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71
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Thursday, March 4, 2021
Teaching the Academy to See
“Art bears the same relationship to society
that the dream bears to mental life. . . .
Like art, the dream mediates between order
and chaos. So, it is half chaos. That is why
it is not comprehensible. It is a vision, not
a fully fledged articulated production.
Those who actualize those half-born visions
into artistic productions are those who begin
to transform what we do not understand into
what we can at least start to see.”
— A book published on March 2, 2021:
Beyond Order , by Jordan Peterson
The inarticulate, in this case, is Rosalind Krauss:
A “raid on the inarticulate” published in Notices of the
American Mathematical Society in the February 1979 issue —
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Wednesday, March 3, 2021
Ink
From this journal on 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  Ad Reinhardt An Ad Reinhardt painting described in the entry of
Ad Reinhardt, Abstract Painting, 1960-66. The viewer may need to tilt the screen to see that “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.” — “Grids,” by Rosalind Krauss, |
Related material from The New York Times today —
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Monday, February 17, 2020
RIP Charles Portis
See also "True Grid " in this journal.
|
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…." |
See as well . . .
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Sunday, July 9, 2017
Sunday School Lesson
"The Occult Roots of Modernism," by Alex Ross,
in the June 26, 2017, issue of The New Yorker .
A related illustration —
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Wednesday, January 4, 2017
A Drama of Many Forms
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.
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Tuesday, January 3, 2017
Cultist Space
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.
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Ein Eck…
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.
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Wednesday, January 7, 2015
Gitterkrieg
(Continued from Jan. 3 and Jan. 5.)
Introduction: "Grids, You Say?" by Josefine Lyche,
and AntiChristmas 2010:
Related material:
Chapter 42 in
A History of Graphic Design ,
by Guity Novin.
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Tuesday, October 21, 2014
Art as a Tool
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 AntiChristmas, 2010:
Which is the tool here, the grid or Krauss?
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Saturday, October 18, 2014
Educational Series
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
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Thursday, August 14, 2014
Full Frontal Aesthetics
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" —
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