In memory of Yale art historian Vincent Scully, who reportedly
died at 97 last night at his home in Lynchburg, Va., some remarks
from the firm of architect John Outram and from Scully —
Update from the morning of December 2 —
The above 3×3 figure is of course not unrelated to
the 4×4 figure in The Matrix for Quantum Mystics:
.
See as well Tsimtsum in this journal.
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.
For Dan Brown fans …
… and, for fans of The Matrix, another tale
from the above death date: May 16, 2019 —
An illustration from the above
Miracle Octad Generator post:
Related mathematics — Tetrahedron vs. Square.
"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— |
“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)
Born today: Laurence Fishburne
Yale Daily News, Jan. 11, 2001:
“When New Haven was founded, the city was laid out into a grid of nine squares surrounded by a great wilderness.
Last year History of Art Professor Emeritus Vincent Scully said the original town plan reflected a feeling that the new city should be sacred.
Scully said the colony’s founders thought of their new Puritan settlement as a ‘nine-square paradise on Earth, heaven on earth, New Haven, New Jerusalem.'”
“Real and unreal are two in one:
New Haven
Before and after one arrives….”
— Wallace Stevens,
“An Ordinary Evening in New Haven,’ XXVIII
— ART WARS —
Mental Health Month, Day 25:
Matrix of the Death God
Having dealt yesterday with the Death Goddess Sarah, we turn today to the Death God Abraham. (See Jacques Derrida, The Gift of Death, University of Chicago Press, 1996.) For a lengthy list of pictures of this damned homicidal lunatic about to murder his son, see The Text This Week.
See, too, The Matrix of Abraham, illustrated below. This is taken from a book by R. M. Abraham, Diversions and Pastimes, published by Constable and Company, London, in 1933.
The Matrix of Abraham
A summary of the religious import of the above from Princeton University Press:
“Moslems of the Middle Ages were fascinated by pandiagonal squares with 1 in the center…. The Moslems thought of the central 1 as being symbolic of the unity of Allah. Indeed, they were so awed by that symbol that they often left blank the central cell on which the 1 should be positioned.”
— Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton U. Press, 2002, pp. 71-72
Other appearances of this religious icon on the Web:
A less religious approach to the icon may be found on page 393 of R. D. Carmichael’s Introduction to the Theory of Groups of Finite Order (Ginn, Boston, 1937, reprinted by Dover, 1956).
This matrix did not originate with Abraham but, unlike Neo, I have not yet found its Architect.
Story
"How much story do you want?"
— George Balanchine
While researching yesterday's entry on Balanchine, Apollo, and the nine Muses, I came across this architect's remarks, partially quoted yesterday and continued here:
"The icon that I use for this element is the nine-fold square…. This is the garden of Apollo, the field of Reason…. This is the Temple of Solomon, as inscribed, for example, by a nine-fold compartmentation to provide the ground plan of Yale, as described to me by Professor Hersey."
Checking this out yesterday, I came across the following at a Yale University Art Gallery site:
"This exhibition of nine boldly colored, asymmetrically designed quilts selected from a private collection will be displayed in the Matrix Gallery….
With the guidance of Professor Maude Southwell Wahlman, author of 'Signs and Symbols: African Images in African American Quilts,' the collector has explored and gathered examples…."
Exploring and gathering examples myself today, I received a book in the mail — W. M. Spackman's On the Decay of Humanism (Rutgers University Press, 1967) — and picked up a second-hand book at a sale — Barbara Michaels's Stitches in Time (Harper Collins Publishers, 1995).
The Spackman book includes the following poem at the end:
In sandarac etui for sepulchre
lies the cered body of a poisoned queen;
and in her mouth and hair, and at her feet,
and in the grey folds of her winding-sheet,
there sifts a dreamy powder, smooth and green,
the magic of an idle sorcerer,
an ancient spell, cast when the shroud was spun.
In death her hands clasp amourously a bowl
that still contains the fragments of her soul,
a tale of Beauty sought, and Beauty won,
his false lips kissed, and Beauty dead for her.
— Alexander B. Griswold, Princeton '28, in the
Nassau Literary Magazine of December 1925
From a synopsis of Michaels's Stitches in Time:
"Michaels follows Rachel, a graduate student studying women's crafts–weaving, spinning, quilting, embroidery–and the superstitions connected with them. Linking all important rites of passage to the garments created as markers of these occasions leads Rachel to her theory: in societies in which magic was practiced, the garment was meant to protect its wearer. She gains evidence that her theory is valid when an evil antique bridal quilt enters her life."
Although Stitches in Time is about a quilt — stitched, not spun — Griswold's line
"an ancient spell, cast when the shroud was spun"
is very closely related to the evil spell in Michaels's book.
The above events display a certain synchronicity that Wallace Stevens might appreciate, especially in light of the following remark in a review of Stitches in Time:
"…the premise is too outlandish for even the suspension of disbelief…." (Publishers Weekly, 4/24/95)
Stevens might reply,
The very man despising honest quilts
Lies quilted to his poll in his despite.— "The Comedian as the Letter C," Part V
Finally, those who prefer stories to the more formal qualities of pure dance (ballet) pure mathematics (see previous entry), pure (instrumental) music, and pure (abstract, as in quilt designs) art, can consult the oeuvre of Jodie Foster — as in my
Pearl Harbor Day entry on Buddhism.
An art historian named Griswold — perhaps that very same Griswold quoted above — might have a thing or two to say to Jodie on her recent film "Anna and the King." In the April, 1957, issue of The Journal of the Siam Society, Alexander B. Griswold takes issue with Broadway's and Hollywood's "grotesque caricature" of Siamese society, and ultimately with Anna herself:
"The real fault lies in the two books they ultimately spring from — The English Governess at the Court of Siam and The Romance of the Harem — both written by Mrs. Anna Leonowens.''
See also The Diamond 16 Puzzle for some quilt designs.
Powered by WordPress
