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   
 

From A Mass for Lucero:

“To the two gods of art, Apollo and Dionysus, we owe our recognition that… there is a tremendous opposition, as regards both origins and aims, between the Apolline art of the sculptor and the non-visual, Dionysiac art of music.”
— The Birth of Tragedy, by Friedrich Nietzsche, Penguin, 1993, page 14

“Melody, then, is both primary and universal.” (Author’s italics)
— Nietzsche, op. cit., page 33

“…in so far as he interprets music in images, he himself lies amidst the peaceful waves of Apolline contemplation….”
— Nietzsche, op. cit., page 35

Apolline Contemplation

From The Miracle of the Bells, by Russell Janney, Prentice-Hall, 1946, page 333–

“He was singing softly:
‘A pretty girl–
 is like a melody—- !‘
 But that was always
 Bill Dunnigan’s
 Song of Victory….
 Thus thought the…
 press agent for
‘The Garden of the Soul.'”

“The icon that I use… is the nine-fold square…. This is the garden of Apollo, the field of Reason….”

— Architect’s notes on the design of a college campus

“Binary image morphological operations are well suited to a large class of basic image processing applications. These operations include image analysis tasks such as shape recognition, image segmentation, noise reduction, and feature extraction.”

— A Programmable Logic-based Implementation of Ultra-fast Parallel Binary Image Morphological Operations (pdf), by Kenneth G. Ricks et al., ISCA 18th International Conference on Computers and Their Applications (March 2003)

“… a purely harmonious concept of beauty is not enough…. Apollo, who for Plato’s Socrates was ‘the God’ and the guarantor of unruffled beauty as ‘the truly divine’ is absolutely no longer sufficient.”

Words that may or may not have been said on July 20, 1969: “That’s one small step for a man; one giant leap for mankind.”

One small step for me:

Sunday, November 03, 2002

	Music to Read By In honor of Roger Cooke’s review of Helson’s Harmonic Analysis, 2nd Edition, today’s site music is “Moonlight in Vermont.”
	12:00 AM – 5 comments

One giant leap for mankind:

Date Posted: 11/03/02 Sun

---

“The ‘Diamond Theory’ website of Steven Cullinane shows a man who is incapable of telling the truth: a pathological liar who hates and despises the mathematical community; a sociopath caught between the conflicting desires to earn the admiration of mathematicians, and his desire to insult those who ignore him and refuse him his self-perceived due measure of honor and reverie. As such, Steven Cullinane is constantly trying to purchase recognition when he has the funds to advertise on google.com, or steal that recognition by lying and deceiving dmoz.org when money isn’t enough. As you can see from the correspondence below, Jed Pack has clearly pointed out serious errors in Steven Cullinane’s calculations. Now, instead of admitting that he has been caught with his pants down, Steven Cullinane is questioning Jed Pack’s education! Surely, Jed Pack is a more competent mathematician than Steven Cullinane.”

For further details, see Crankbuster.

STAR WARS
continued 

Picture from Feb. 8
(Martin Buber’s birthday)

For John Nash on his birthday:

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

— Tom O’Bedlam’s Song

Feel lucky?
Well, do you?

  This entry was inspired by the following…
1.  A British blogger’s comment today.  This man, feeling like a miserable failure himself, was cheered up by the following practical joke: “If really fed up you could try putting in, miserable failure, (no quote marks) into Google and pressing the ‘I’m feeling lucky’ button.”

2. The page, excerpts from which are shown  above, that you get if you put lucky (no quote marks) into Google and press the “I’m feeling lucky” button.

3. My own entries of May 31 on Language Games and of June 1 on language and history,  Seize the Day and One Brief  Shining Moment.

4.  The related June 1 entry of Loren Webster, Carpe Diem, on the Marilyn Monroe rose.  Images from Carpe and Shining are combined below:

Inaugural Poem for California:

Archaischer Torso Apollos

by Rainer Maria Rilke

Wir kannten nicht sein unerhörtes Haupt,
darin die Augenäpfel reiften. Aber
sein Torso glüht noch wie ein Kandelaber,
in dem sein Schauen, nur zurückgeschraubt,

sich hält und glänzt. Sonst könnte nicht der Bug
der Brust dich blenden, und im leisen Drehen
der Lenden könnte nicht ein Lächeln gehen
zu jener Mitte, die die Zeugung trug.

Sonst stünde dieser Stein entstellt und kurz
unter der Schultern durchsichtigem Sturz
und flimmerte nicht so wie Raubtierfelle;

und bräche nicht aus allen seinen Rändern
aus wie ein Stern: denn da ist keine Stelle,
die dich nicht sieht. Du musst dein Leben ändern.

Illustration:

See also

Philip K. Dick Meets Joan Didion,

Aes Triplex,

From the Empty Center,

The Empty Center, and

Translation of Rilke by Stephen Mitchell:

Archaic Torso of Apollo

We cannot know his legendary head
with eyes like ripening fruit. And yet his torso
is still suffused with brilliance from inside,
like a lamp, in which his gaze, now turned to low,

gleams in all its power. Otherwise
the curved breast could not dazzle you so, nor could
a smile run through the placid hips and thighs
to that dark center where procreation flared.

Otherwise this stone would seem defaced
beneath the translucent cascade of the shoulders
and would not glisten like a wild beast’s fur:

would not, from all the borders of itself,
burst like a star: for here there is no place
that does not see you. You must change your life.

Palm Sunday, Part II:

Cold Mountain

From the notes to the CD of Songs From the Mountain (John Herrmann, Dirk Powell, Tim O’Brien):

“John [Herrmann, banjo player] would like to dedicate his work on this recording to Philip Kapleau Roshi, Kalu Rimpoche, and Harada Tangen Roshi, who all know the way to Cold Mountain….”

 See Buddha’s Birthday (April 8) and The Diamond Project.

“What are you thinking of? What thinking? What? 
  I never know what you are thinking. Think.”

— Tom Eliot, The Waste Land 

“I am thinking…
… of the midnight picnic
Once upon a time….”

— Suzanne Vega, “Tom’s Diner“

Once upon a time… See Later the Same Day and Enormous Changes At the Last Minute

Grace Paley

“De donde crece la palma” — Song lyric 

From On Beauty, by Elaine Scarry, Princeton University Press, 1999, a quotation from Homer —

“in Delos, beside Apollo’s altar —
the young slip of a palm-tree
springing into the light.”

See also A Mass for Lucero and The Shining of Lucero.  

“How much story do you want?”

— George Balanchine

Annie’s Song

In honor of Apollo (see entries below) and of the Red Mass celebrated tonight on the TV drama “The West Wing,” this site’s music is, for the time being, Bach’s

Mass in B minor  (BWV.232) 
   § 17. Et in spiritum sanctum (10k) (arr. for 2 guitars by Richard Yates) (David Lovell)

from the Classical Guitar Midi Archives.

The Shining of Lucero

From my journal note, “Shining Forth“:

The Spanish for “Bright Star” is “Lucero.”

The Eye of the Beholder:

When you stand in the dark and look at a star a hundred light years away, not only have the retarded light waves from the star been travelling for a hundred years toward your eyes, but also advanced waves from your eyes have reached a hundred years into the past to encourage the star to shine in your direction.

— John Cramer, “The Quantum Handshake“

From Broken Symmetries, by Paul Preuss, 1983:

He’d toyed with “psi” himself…. The reason he and so many other theoretical physicists were suckers for the stuff was easy to understand — for two-thirds of a century an enigma had rested at the heart of theoretical physics, a contradiction, a hard kernel of paradox….   

Peter [Slater] had never thirsted after “hidden variables” to explain what could not be pictured.  Mathematical relationships were enough to satisfy him, mere formal relationships which existed at all times, everywhere, at once.  It was a thin nectar, but he was convinced it was the nectar of the gods.

………………

Those so-called crazy psychics were too sane, that was their problem — they were too stubborn to admit that the universe was already more bizarre than anything they could imagine in their wildest dreams of wizardry. (Ch. 16)

From Secret Passages, by Paul Preuss, 1997:

Minakis caught up and walked beside him in silence, moving with easy strides over the bare ground, listening as Peter [Slater] spoke. “Delos One was ten years ago — quantum theory seemed as natural as water to me then; I could play in it without a care. If I’d had any sense of history, I would have recognized that I’d swallowed the Copenhagen interpretation whole.”

“Back then, you insisted that the quantum world is not a world at all,” Minakis prompted him. “No microworld, only mathematical descriptions.”

“Yes, I was adamant. Those who protested were naive — one has to be willing to tolerate ambiguity, even to be crazy.”

“Bohr’s words?”

“The party line. Of course Bohr did say, ‘It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.’ Meaning that when we start to talk what sounds like philosophy, our colleagues should rip us to pieces.” Peter smiled. “They smell my blood already.”

………………  Peter glanced at Minakis. “Let’s say there are indications — I have personal indications — not convincing, perhaps, but suggestive, that the quantum world penetrates the classical world deeply.” He was silent for a moment, then waved his hand at the ruins. “The world of classical physics, I mean. I suppose I’ve come to realize that the world is more than a laboratory.”

“We are standing where Apollo was born,” Minakis said. “Leto squatted just there, holding fast to a palm tree, and after nine days of labor gave birth to the god of light and music….”

To Lucero, in memory of
1962 in Cuernavaca

From On Beauty, by Elaine Scarry,
Princeton University Press, 1999 —

“Homer sings of the beauty of particular things. Odysseus, washed up on shore, covered with brine, having nearly drowned, comes upon a human community and one person in particular, Nausicaa, whose beauty simply astonishes him. He has never anywhere seen a face so lovely; he has never anywhere seen any thing so lovely….

I have never laid eyes on anyone like you,
neither man nor woman…
I look at you and a sense of wonder takes me.

Wait, once I saw the like —
in Delos, beside Apollo’s altar —
the young slip of a palm-tree
springing into the light.”

From Secret Passages, by Paul Preuss, 1997:

“When we try to look inside atoms,” Peter said, “not only can we not see what’s going on, we cannot even construct a coherent picture of what’s going on.”

“If you will forgive me, Peter,” Minakis said, turning to the others. “He means that we can construct several pictures — that light and matter are waves, for example, or that light and matter are particles — but that all these pictures are inadequate. What’s left to us is the bare mathematics of quantum theory.”

…. “Whatever the really real world is like, my friend, it is not what you might imagine.”

………………

 

Talking physics, Peter tended to bluntness. “Tell me more about this real world you imagine but can’t describe.”

Minakis turned away from the view of the sunset. “Are you familiar with John Cramer’s transactional interpretation of quantum mechanics?”

“No I’m not.”

………………

“Read Cramer. I’ll give you his papers. Then we can talk.” 

 From John Cramer, “The Quantum Handshake“:

Advanced waves could perhaps, under the right circumstances, lead to “ansible-type” FTL communication favored by Le Guin and Card…. 

For more on Le Guin and Card, see my journal notes below.

For more on the meaning of “lucero,” see the Wallace Stevens poem “Martial Cadenza.”

On this, his birthday, actor Hugh Grant
is hereby named an

Honorary Waco Wacko.

By the authority vested in me by the possession of

1. Knowledge of Vivienne Browning’s My Browning Family Album, a work dedicated to Dr. Joseph Armstrong, “founder of the Armstrong Browning Library, Baylor University, Waco, Texas,”
2. Knowledge that today is the date of the Battle of Marathon, and of the claim that
   

   “The spread of Pan’s worship beyond his home pastures of Arcadia was said to have arisen around the 5th Century BCE. Pan asked why the Athenians neglected him, and promised them victory over the Persians if they would worship him. At Marathon, the Persians were routed and fled in Panic; so, the Athenians built a temple for him on the Acropolis, and his worship soon extended to all Greece.”

   2a. (including subsidiary knowledge of the ridiculous falseness of all political statements, including the following contemptible lie by Michael Dukakis in his 1988 Democratic National Convention acceptance speech:

   “And as I accept your nomination tonight, I can’t help recalling that the first marathon was run in ancient Greece, and that on important occasions like this one, the citizens of Athens would complete their ceremonies by taking a pledge. That pledge, that covenant, is as eloquent and timely today as it was 2000 years ago.  

   ‘We will never bring disgrace to this, our country, by any act of dishonesty or cowardice. We will fight for the ideals of this, our country. We will revere and obey the laws. We will strive to quicken our sense of civic duty. Thus, in all these ways, we will transmit this country greater, better, stronger, prouder and more beautiful than it was transmitted to us.’ “)

   (None of the Harvard intellects associated with Dukakis saw fit to point out that there never was any such pledge. As a consequence, both Harvard University and the Democratic Party remain cursed to this day.),

3. Knowledge (both intellectual and carnal) of the female form of the god Pan, as seen in the classic and great movie “Sirens” (starring, among others, Hugh Grant) and on the cover of the 1977 Olivia Newton-John album “Making a Good Thing Better,”

   

4. Knowledge that even the best critics can be wrong, as exemplified by Roger Ebert’s remarks in his review of “Sirens”…
   
   

   “Although they are often charged with being emotionally distant, the British have produced more than their share of sexual outlaws, from Oscar Wilde to Aleister Crowley to D.H. Lawrence to Francis Bacon, to balance the ledger. The central figure in ‘Sirens’ is perhaps vaguely inspired by another legendary British bohemian, Augustus John, an artist whose models and mistresses were interchangeable, and who delighted in scandal.

   Named Norman Lindsay, the film’s hero is played by Sam Neill as a notorious painter who lives on an estate in Australia where his art coexists side-by-side with an experiment in living.”

   (Actually, the central figure is not “vaguely inspired” by anyone. He is precisely inspired by an artist named exactly Norman Lindsay, as Roger will learn if he searches the Web. Roger also gets Pan wrong in this film; he says, “the bearded Lindsay is a Pan of sorts.” No. The “Pan of sorts” is in fact the girl who romps joyfully with the local boys and who later, with great amusement, uses her divine x-ray vision to view Tara Fitzgerald naked in church.),

   and, finally,

5. Knowledge that, as the Greeks well knew,  there is a dark side to all this Pan business (Vivienne Browning’s book reveals that her father was a friend, not only of the bohemian artist Norman Lindsay, but also of the black mage Aleister Crowley. Let us pray that Hugh Grant’s performance as a clergyman in “Sirens” and as a defender of the faith in “The Lair of the White Worm” have prepared him to cope with the dark (or, sometimes, “Brown”) side of the divine.),

I hereby declare Hugh Grant an honorary Waco (home of the Dr. Pepper Museum, the Texas Ranger Hall of Fame, and the Armstrong Browning Library) Wacko.

The Boys from Uruguay

If one were to write a “secret history” of the twentieth century, one possible organizing theme might be the religious struggle between worshippers of the Semitic deity (variously known as Yahweh, God, and Allah) and worshippers of the Aryan deities… notably, the Aryan god of music, light, and reason, Apollo.

(See my jounal notes of Monday, Sept. 2, 2002, below.)

In perhaps the best academic website I have ever seen, Karey L. Perkins quotes Walker Percy:

“The truth is that man’s capacity for symbol-mongering in general and language in particular is…intimately part and parcel of his being human, of his perceiving and knowing, of his very consciousness…”

The greatest symbol-monger of the twentieth century was, of course, Adolf Hitler. His use of the Aryan sun-wheel symbol rose to the level of genius. Of course, it ultimately failed to win the approval of the sun god himself, Apollo, who is also the god of reason.

Since symbol-mongering cannot be avoided, let us hope that it can be done in a somewhat more reasonable way than that of the National Socialist movement. Two examples suggest themselves.

1. From Peggy Noonan’s column of Friday, Sept. 6:

   The cross, the heart, and the flag.

2. From Karey Perkins’s website:

   A brain, a heart, and courage. 

On this Rosh Hashanah, the cross as a symbol of intelligence may be offensive to some worshippers of Yahweh. Let them read The Archivist, a novel by Martha Cooley, and then my journal note The Matthias Defense.

They might also contemplate the biblical quotation in the musical “Contact” broadcast from Lincoln Center on September 1, 2002: “Let there be light!”

Three Jews named Paul have been associated with light…

1. Saul of Tarsus, who later assumed an alias.

2. Paul Newman, whose performance in “The Verdict” continues, indirectly, to trouble Cardinal Law of Boston.

3. Paul R. Halmos, a personal hero of mine ever since I saw his Finite Dimensional Vector Spaces and Measure Theory as an ignorant young undergraduate browsing the bookstores of Harvard Square.

In accordance with the “secret history” theme mentioned above, the struggle between Aryan and Semitic religions may also be viewed in the light of the struggle between Christianity and Communism. Hitler exploited this viewpoint very successfully, pretending to be the champion of the Christians against the godless Reds. Peggy Noonan also successfully uses this strategy. Both Hitler and Noonan manage to ignore the fact that Christianity is itself one of the Semitic religions, and that at least two of its three deities are Jewish.

As for me, I rather identify with the young Hitler clone at the end of the film “The Boys from Brazil.” Forced to decide between Gregory Peck and Sir Laurence Olivier, he sides with Olivier. His reason? Peck lied.

In a similar situation, forced to decide between Peggy Noonan and the Jew Halmos, I would probably side with Halmos. Halmos, who should, if not a saint, be at least dubbed a knight, does not, unlike the great majority of the damned human race, lie.

See Halmos’s memoir, I Want to Be a Mathematician. In particular, see the single index entry “communist by allegation” and the 29 entries under “Uruguay.”

Happy birthday to Elia Kazan and Peggy Noonan, and a happy and prosperous New Year to should-be-Sir Paul R. Halmos. 

Elevation of the Host

Some religious fanatics may be offended by my account, in the note below, of a theatrical bartender-priest at Lincoln Center who last night held a CD aloft in what may seem a parody or satire of the elevation of the host in the Mass. They should consider the following account of how a medieval nun viewed the host:

…she saw a great brightness between the priest’s hands, so vivid and so bright and of such wonderful beauty that in her opinion it could not be compared to anything the human spirit could imagine. And it seemed to her that this brightness had a circular shape….

For another appearance of a priest associated, if only by synchronicity, with Lincoln Center, see the photographs below, both from the New York Times obituaries section of Friday, August 30, 2002.

	Richard Lippold, a sculptor known for radiant, expansive abstractions in metal, died on Aug. 22…. Richard Lippold’s ‘‘Orpheus and Apollo’’ at Avery Fisher Hall in 1996. Jack Manning/The New York Times
	Bill Wassmuth, a former Roman Catholic priest who opposed the Aryan Nations group in northern Idaho, died on Tuesday, Aug. 27.

In this little drama of August 30, played out in the obituary section of the New York Times, it is not clear from the Lippold sculpture who is to play the role of Orpheus and who the role of Apollo. One might interpret the note below, written two days later, as implying that Orpheus is to be played by Lionel Hampton and Apollo by Christ himself.  Such a drama is neither parody nor satire.  It is, on the contrary, deadly serious. 

“A great brightness,” as seen by the medieval nun described above, is traditionally associated with the Aryan sun god Apollo.  For more on this theme in Roman Catholic art, see

Sun-Worship and Catholicism,

The Monstrance and the Wafer God, and

A Catholic rebuttal.

For a less dogmatic approach to these matters, see my journal note of June 13, 2002,

 A Mass for Lucero.