"Nothing opens up new spaces…."
— Book description from the University of Chicago Press,
shown here on February Ninth, 2020:
See as well the Roman Polanski film "The Ninth Gate" and
an obituary reporting a death on February Ninth.
"… while at the end I didn't yearn for spectacular special effects,
I did wish for spectacular information–something awesome,
not just a fade to white." — Roger Ebert, March 10, 2000
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…." |
|
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
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 . . .
Above: Frank Langella in Right: Johnny Depp in |
 |
“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
For the title plan, see Sisteen in this journal.
I do not follow the Public Library of Science (PLOS), although,
as shown above, I do follow some of the followers.
This post was suggested by Amy Hubbard's recent reference
to a PLOS article on beliefs in Hell.
Pop culture seems more informative. Readers of the PLOS article
should also know about the Dakota, John Lennon, and Rosemary's
Baby, as well as Woody Allen, The Ninth Gate , and Plan 9 from
Outer Space.
(Continued from High White Noon,
Finishing Up at Noon, and A New York Jew.)
Above: Frank Langella in "Starting Out in the Evening"
Below: Frank Langella and Johnny Depp in "The Ninth Gate"
"Not by the hair on your chinny-chin-chin."
Above: Detail from a Wikipedia photo.
For the logo, see Lostpedia.
For some backstory, see Noether.
Those seeking an escape from the eightfold nightmare
represented by the Dharma logo above may consult
the remarks of Heisenberg (the real one, not the
Breaking Bad version) to the Bavarian Academy
of Fine Arts.
Those who prefer Plato's cave to his geometry are
free to continue their Morphean adventures.
(Continued.)
Jaws for Frank
Part I: October 8, 2010
|
Above: Frank Langella in Right: Johnny Depp in |
|
Part II: Noon Today
"The rest is the madness of art."
See also Patterns in the Carpets
and Saturday's Shadows.
Margaret Soltan this morning posted a haiku about a fox in her garden.
Related material— The Ninth Gate* versus The Ninth Configuration.
* For some backstory, see pop physics.
The twin topics of autism and of narrowing definitions
suggested the following remarks.
The mystical number "318" in the pilot episode
of Kiefer Sutherland's new series about autism, "Touch,"
is so small that it can easily apply (as the pilot
illustrated) to many different things: a date, a
time, a bus number, an address, etc.
The last 3/18 Log24 post— Defining Configurations—
led, after a false start and some further research,
to the writing of the webpage Configurations and Squares.
An image from that page—
Interpreting this, in an autistic manner, as the number
287501346 lets us search for more specific items
than those labeled simply 318.
The search yields, among other things, an offer of
Night Magic Cologne (unsold)—
For further mystery and magic, see, from the date
the Night Magic offer closed— May 8, 2010— "A Better Story."
See also the next day's followup, "The Ninth Gate."
"Design is how it works." —Steve Jobs
Website logo—
Screenshot from How Stuff Works—
(Click image for details.)
From "A Device Worthy of a Gothic Novel,"
Chapter XVI of The Club Dumas,
by Arturo Perez-Reverte (1993),
Vintage International, April 1998….
the basis of the 1999 Roman Polanski film
The Ninth Gate —
Aren't you going to give me a document to sign?"
"A document?"
"Yes. It used to be called a pact. Now it would be a contract
with lots of small print, wouldn't it? 'In the event of litigation,
the parties are to submit to the jurisdiction of the courts of…'
That's a funny thing. I wonder which court covers this."
(For the title, see the previous post.)
Compare and contrast—
Background on the film "The Ninth Gate"—
Pop-sci background, courtesy of Fox Searchlight Pictures, for the film
Update of 2:48 PM July 20th—
See Peter Woit's July 19th post "Questions About the Multiverse."
"A New York Jew imitates D. H. Lawrence at his peril."
See also The Ninth Gate and Spider Women.
* For the title, do a search in this journal.
The New Yorker 's review of The Great Escape (Simon & Schuster, $27), by Kati Marton—
"Marton, who fled Hungary as a child in 1957, illuminates Budapest's vertiginous Golden Age and the darkness that followed (a darkness that some of her subjects, notably Arthur Koestler, never shook)."
— Issue dated November 6, 2006
See also The Ninth Gate in this journal and the life of Marton's second husband, Peter Jennings.
This post was suggested by—
The above Sábato novel was translated as The Angel of Darkness .
Its Spanish title was "Abaddón el Exterminador " (Abaddon the Exterminator ).
From a customer review of the novel at Amazon.com—
"Early in the book a drunken outcast will see the vision of the Great Beast of Revelation. Near the end he will tell others of what he has seen. Meanwhile Sábato, who was originally trained as a scientist, seeks out the supernatural and the mystical in order to find an antidote to Stalinism, simple-minded 'Progress' and a superficial positivism."
For a more sophisticated vision of the Beast, see The Ninth Gate.
For Abaddon in a less sophisticated antidote to positivism, see The Chronicle of Abaddon the Destroyer: The War in Heaven .
I prefer Charles Williams's approach to War in Heaven .
If there is an afterlife, perhaps Sábato's experience there will be more lively than his novel's tombstone would imply.
He may, despite his wish for heavenly peace, turn out to be (in a phrase from this morning's post) a badly needed "ghost warrior."
For the fictional Harvard symbologist Robert Langdon,
a commentary on the favicon in today's noon post—
This is from a novel that was filmed as "The Ninth Gate."
The book and film concern a series of nine engravings.
For all nine, see an excellent analysis by Michael S. Howard in
his journal "Gnostic Essays" on November 20, 2006.
A summary of the engravings—
See also this journal on that date.
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— |
A stitch in time…
Related material—
See also "Putting Mental Health on the Map at Harvard"—
Harvard Crimson , Friday, April 8, 2011, 2:09 AM—
They're outside the Science Center with their signs, their cheer, and their smiles. They've been introducing themselves over House lists, and they want you to ask questions. They're here for you. They're the Student Mental Heath Liaisons.
Harvard's SMHL crew—they pronounce it smile—have recently launched a new website and recruited more members in their effort to foster an informed and understanding environment on campus….
Mental Health Services, SMHL said, are not meant for "students who are really 'crazy.'" Everyone is entitled to a little help smiling.
Roberta Smith in today's New York Times —
"… the argument that painting may ultimately be about
little more than the communication of some quality of
light and space, however abstract or indirect."
— Review of "Rooms With a View" at the Met
Lowry —
Malcolm Lowry, author of Under the Volcano
Hollywood —
Related material —
| 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— |
(A sequel to last night's "For Taylor")
On Joan Tewkesbury, who wrote the script for the 1975 film "Nashville"—
She urges writers to continue to generate new ideas
and new material. "Keep writing. The hardest thing
is to sell one script and not have another to follow it with."
One script— Yesterday's link titled "An Ordinary Evening in Tennessee"
Another— "A Point of Central Arrival"
Related material 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— |
"You've got to pick up every stitch…"
* A former governor of Tennessee who died at 80 yesterday in Nashville
Another topic from today's newspaper —
Commentary —
"We're gonna need more holy water." — "Season of the Witch," a film that opened Friday
See also —
This morning's post Inception and the following site:
Note the ninefold favicon at the above site. Some background—
The Ninth Gate in yesterday's post and this image from last September—
"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— |
… 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.
|
Above: Frank Langella in Right: Johnny Depp in |
|
“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
My own adventures in that realm— as reader, not author— may illustrate Llosa’s remark.
A nearby stack of paperbacks I haven’t touched for some months (in order from bottom to top)—
What moral Vargas Llosa might draw from the above stack I do not know.
Generally, I prefer the sorts of books in a different nearby stack. See Sisteen, from May 25. That post the fanciful reader may view as related to number 16 in the above list. The reader may also relate numbers 24 and 22 above (an odd couple) to By Chance, from Thursday, July 22.
* The Web version’s title has a misprint— “living” instead of “lying.”
Friday’s post “Religion at Harvard” continues…
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.
Let No Man
Write My Epigraph
"His graceful accounts of the Bach Suites for Unaccompanied Cello illuminated the works’ structural logic as well as their inner spirituality."
—Allan Kozinn on Mstislav Rostropovich in The New York Times, quoted in Log24 on April 29, 2007
"At that instant he saw, in one blaze of light, an image of unutterable conviction…. the core of life, the essential pattern whence all other things proceed, the kernel of eternity."
— Thomas Wolfe, Of Time and the River, quoted in Log24 on June 9, 2005
"… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)"
— Peter J. Cameron, "The Geometry of the Mathieu Groups" (pdf)
"… donc Dieu existe, réponse!"
(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)
"Pauli as Mephistopheles
in a 1932 parody of
Goethe's Faust at Niels Bohr's
institute in Copenhagen.
The drawing is one of
many by George Gamow
illustrating the script."
— Physics Today
'To meet someone' was his enigmatic answer. 'To search for the stone that the Great Architect rejected, the philosopher's stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso.'"
— The Club Dumas, basis for the Roman Polanski film "The Ninth Gate" (See 12/24/05.)
— The Innermost Kernel
(previous entry)
And from
"Symmetry in Mathematics
and Mathematics of Symmetry"
(pdf), by Peter J. Cameron,
a paper presented at the
International Symmetry Conference,
Edinburgh, Jan. 14-17, 2007,
we have
The Epigraph–
(Here "whatever" should
of course be "whenever.")
Also from the
Cameron paper:
|
Local or global?
Among other (mostly more vague) definitions of symmetry, the dictionary will typically list two, something like this:
• exact correspondence of parts; Mathematicians typically consider the second, global, notion, but what about the first, local, notion, and what is the relationship between them? A structure M is homogeneous if every isomorphism between finite substructures of M can be extended to an automorphism of M; in other words, "any local symmetry is global." |
Some Log24 entries
related to the above politically
(women in mathematics)–
Global and Local:
One Small Step
and mathematically–
Structural Logic continued:
Structure and Logic (4/30/07):
This entry cites
Alice Devillers of Brussels–
"The aim of this thesis
is to classify certain structures
which are, from a certain
point of view, as homogeneous
as possible, that is which have
as many symmetries as possible."
"There is such a thing
as a tesseract."
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:
"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
Temptation
|
|
The Star |
|
In memory of Nina Simone, a singer who died April 21, whose autobiography was titled (after the Screamin’ Jay Hawkins song) I Put a Spell on You, and in honor of Aaron Spelling, producer of “Satan’s School for Girls,” whose birthday is today, I suggest the following three cultural milestones.
First, an accurate, if tasteless, recounting of Scripture at a Christian site that correctly notes that Satan may appear as “an angel of light”… rather like Aaron Spelling? This site also offers, as background music, a lame parody of the evils of Rock ‘n’ Roll in the form of a midi of “Fire” that would hardly tempt even someone Hell-bent on sinning.
Second, a book, The Club Dumas, by Arturo Perez-Reverte, the basis of the Roman Polanski film “The Ninth Gate.” This book is notable for the way it skillfully, and perhaps accurately, depicts Satan as an “angel of light” who does not resemble Aaron Spelling in the least. This Satan could really tempt me.
Finally, my favorite music video of all time: the 1988 Kylie Minogue “Locomotion.” If the Devil could now look, sing, and dance like Kylie in 1988, I would be lost. Fortunately, perhaps, the days when Kylie could make me fall in love with one glance are now over. Still, if I had to fall, I would much rather do it with Kylie than with Spelling. As she herself says,
“It’s better the Devil you know.”
For more on Kylie, trains, and death, see the Jan. 3 entry The Shanghai Gesture.
The locomotive image is courtesy of a website that may, in view of the subject of this entry, prefer to remain anonymous.
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