Log24

Thursday, January 26, 2006

Thursday January 26, 2006

Filed under: General,Geometry — m759 @ 9:00 am
In honor of Paul Newman’s age today, 81:

On Beauty

Elaine Scarry, On Beauty (pdf), page 21:

“Something beautiful fills the mind yet invites the search for something beyond itself, something larger or something of the same scale with which it needs to be brought into relation. Beauty, according to its critics, causes us to gape and suspend all thought. This complaint is manifestly true: Odysseus does stand marveling before the palm; Odysseus is similarly incapacitated in front of Nausicaa; and Odysseus will soon, in Book 7, stand ‘gazing,’ in much the same way, at the season-immune orchards of King Alcinous, the pears, apples, and figs that bud on one branch while ripening on another, so that never during the cycling year do they cease to be in flower and in fruit. But simultaneously what is beautiful prompts the mind to move chronologically back in the search for precedents and parallels, to move forward into new acts of creation, to move conceptually over, to bring things into relation, and does all this with a kind of urgency as though one’s life depended on it.”

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

The above symbol of Apollo suggests, in accordance with Scarry’s remarks, larger structures.   Two obvious structures are the affine 4-space over GF(3), with 81 points, and the affine plane over GF(32), also with 81 points.  Less obvious are some related projective structures.  Joseph Malkevitch has discussed the standard method of constructing GF(32) and the affine plane over that field, with 81 points, then constructing the related Desarguesian projective plane of order 9, with 92 + 9 + 1 = 91 points and 91 lines.  There are other, non-Desarguesian, projective planes of order 9.  See Visualizing GL(2,p), which discusses a spreadset construction of the non-Desarguesian translation plane of order 9.  This plane may be viewed as illustrating deeper properties of the 3×3 array shown above. To view the plane in a wider context, see The Non-Desarguesian Translation Plane of Order 9 and a paper on Affine and Projective Planes (pdf). (Click to enlarge the excerpt beow).

The image “http://www.log24.com/theory/images/060126-planes2.jpg” cannot be displayed, because it contains errors.

See also Miniquaternion Geometry: The Four Projective Planes of Order 9 (pdf), by Katie Gorder (Dec. 5, 2003), and a book she cites:

Miniquaternion geometry: An introduction to the study of projective planes, by T. G. Room and P. B. Kirkpatrick. Cambridge Tracts in Mathematics and Mathematical Physics, No. 60. Cambridge University Press, London, 1971. viii+176 pp.

For “miniquaternions” of a different sort, see my entry on Visible Mathematics for Hamilton’s birthday last year:

The image “http://www.log24.com/theory/images/Quaternions2.jpg” cannot be displayed, because it contains errors.

 

Saturday, December 24, 2005

Saturday December 24, 2005

Filed under: General — Tags: — m759 @ 9:00 pm
Nine is a Vine
(continued)

The image “http://www.log24.com/log/pix05B/051224-Stars.jpg” cannot be displayed, because it contains errors.

The figures are:
 
A symbol of Apollo from
Balanchine's Birthday and
A Minature Rosetta Stone,

a symbol of pure reason from
Visible Mathematics and
Analogical Train of Thought,

a symbol of Venus from
Why Me? and
To Graves at the Winter Solstice,

and, finally, a more
down-to-earth symbol,
adapted from a snowflake in

The image “http://www.log24.com/log/pix05B/051224-RebaCard2.jpg” cannot be displayed, because it contains errors.

an online Christmas card.

Those who prefer their
theological art on the scary side
may enjoy the
Christian Snowflake
link in the comments on
the "Logos" entry of
Orthodox Easter (May 1), 2005.

Monday, December 5, 2005

Monday December 5, 2005

Filed under: General — Tags: — m759 @ 1:00 pm
Magical Thinking
 
for Joan Didion
on Her Birthday

The Associated Press on the Kennedy Center honors yesterday:

"Dancer Suzanne Farrell was feted by her former colleague at the New York City Ballet, Jacques d'Amboise. The company, led by George Balanchine, 'was the center of American ballet and she was the diamond in its crown,' d'Amboise said."

Log24 on Balanchine

As Sir Arthur Quiller-Couch, paraphrasing Horace, remarks in his Whitsun, 1939, preface to the new edition of the Oxford Book of English Verse, "tamen usque recurret Apollo."
 

The New York Lottery yesterday:

The mid-day number was 926;
the evening number was 373.

For the significance of 926,
see 9/26 2002 and
Balanchine's Birthday.

For the significance of 373, see

  Art Wars,
May 2, 2003,

 White, Geometric, and Eternal,
Dec. 20, 2003,

 Directions Out,
April 26, 2004,

 Outside the World,
April 26, 2004,

 The Last Minute,
Sept. 15, 2004,

and

Diamonds Are Forever,
Jan. 25, 2005.

See also the link
at the end of
  yesterday's entry.

For related material that is
more personally linked to
Joan Didion, see
Log24, June 1-16, 2004.
 

Friday, December 2, 2005

Friday December 2, 2005

Filed under: General — m759 @ 8:05 pm
For St. Robertson Davies,
whose feast is today:

Apollo and Christ

Benedict XVI, before he became Pope:

“… 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.”

Discuss the following
symbol of Apollo

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as the source of
a Christian symbol–

The image “http://www.log24.com/log/pix05B/051202-Cross.gif” cannot be displayed, because it contains errors.

the Greek Cross.

Related material:

The play
now then again

(Time-Bending Love Story
Comes Home to Fermilab
)

The image “http://www.log24.com/log/pix05B/051202-NowThen2.jpg” cannot be displayed, because it contains errors.

with cover art by Roz Francis

illustrating the time 8:05:19,

Hexagram 19 in the
Cullinane series

The image “http://www.log24.com/log/pix05B/051202-Hex19.jpg” cannot be displayed, because it contains errors.

(“A dance results”
— Marie-Louise von Franz),

and

Paul Preuss on Apollo,
quantum physics, and
the isle of Delos.

Saturday, July 30, 2005

Saturday July 30, 2005

Filed under: General — Tags: , , — m759 @ 11:21 am

Born today: Laurence Fishburne

Matrix

“The nine-fold square has centre, periphery, axes and diagonals. But all are present only in their bare essentials. It is also a sequence of eight triads. Four pass through the centre and four do not. This is the garden of Apollo, the field of Reason, sheltered by the Gate from the turmoil of the Delta, with its endless cycles of erasure and reinscription. This is the Temple of Solomon, as inscribed, for example, by a nine-fold compartmentation to provide the ground plan of Yale….”– Architects John Outram Associates
on work at Rice University

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

Related material:
Log24 entries on
St. Peter’s Day, 2004

Wednesday, July 20, 2005

Wednesday July 20, 2005

Filed under: General — m759 @ 7:20 pm
Moon Day
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.”

Another rhetorical contrast,
from a different date —

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.”

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.

Monday, June 13, 2005

Monday June 13, 2005

Filed under: General — m759 @ 9:00 pm

STAR WARS
continued 

The image “http://www.log24.com/log/pix05A/050613-Crowe.jpg” cannot be displayed, because it contains errors.

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

Friday, May 20, 2005

Friday May 20, 2005

Filed under: General — Tags: , — m759 @ 1:20 pm

The Shining of Apollo

"Plato's most significant passage may be found in Phaedrus 265b: 'And we made four divisions of the divine madness, ascribing them to four gods, saying that prophecy was inspired by Apollo, the mystic madness by Dionysos, the poetic by the Muses, and the madness of love […] by Aphrodite and Eros' (trans. by H.N. Fowler, in the Loeb Classical Library)."

Saverio Marchignoli, note on section 20, paragraphs 115-119, of the Discourse on the Dignity of Man (Oratio de hominis dignitate) (1486) by Pico della Mirandola, considered the "Manifesto of the Renaissance."

Related material:
A Mass for Lucero,
The Shining of May 29,
Shining Forth,
Sermon for St. Patrick's Day, and the phrase
Diamond Struck by the Sun.

Friday, June 4, 2004

Friday June 4, 2004

Filed under: General — m759 @ 11:22 am

Feel lucky?
Well, do you?

The image “http://www.log24.com/log/pix04A/040604-Sting.gif” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix04A/040604-Lucky.jpg” cannot be displayed, because it contains errors.  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:

The image “http://www.log24.com/log/pix04A/040604-Feeling.jpg” cannot be displayed, because it contains errors.

5.  The fact that the “day” to be seized in Language Games is numbered 22, and that on day 22 of November 1963,  the  following died:

C. S. Lewis
John F. Kennedy
  Aldous Huxley.

6. The fact that November 22 is the feast of  Cecilia, patron saint of music.

7. Yesterday’s entry about the alignment of stars, combined with the alignment of Venus with Apollo (i. e., the sun) scheduled for June 8.

All of the above suggest the following readings from unholy scripture:

A.  The “long twilight struggle” speech of JFK

B.  “The Platters were singing ‘Each day I pray for evening just to be with you,’ and then it started to happen.  The pump turns on in ecstasy.  I closed my eyes, I held her with my eyes closed and went into her that way, that way you do, shaking all over, hearing the heel of my shoe drumming against the driver’s-side door in a spastic tattoo, thinking that I could do this even if I was dying, even if I was dying, even if I was dying; thinking also that it was information.  The pump turns on in ecstasy, the cards fall where they fall, the world never misses a beat, the queen hides, the queen is found, and it was all information.”

— Stephen King, Hearts in Atlantis, August 2000 Pocket Books paperback, page 437

C.  “I will show you, he thought, the war for us to die in, lady.  Sully your kind suffering child’s eyes with it.  Live burials beside slow rivers.  A pile of ears for a pile of arms.  The crisps of North Vietnamese drivers chained to their burned trucks…. Why, he wondered, is she smiling at me?”

— Robert Stone, A Flag for Sunrise,  Knopf hardcover, 1981, page 299

Thursday, April 22, 2004

Thursday April 22, 2004

Filed under: General,Geometry — Tags: , — m759 @ 10:07 pm

Minimalism

"It's become our form of modern classicism."

— Nancy Spector in 
   the New York Times of April 23, 2004

Part I: Aesthetics

In honor of the current Guggenheim exhibition, "Singular Forms" — A quotation from the Guggenheim's own website

"Minimalism refers to painting or sculpture

  1. made with an extreme economy of means
  2. and reduced to the essentials of geometric abstraction….
  3. Minimalist art is generally characterized by precise, hard-edged, unitary geometric forms….
  4. mathematically regular compositions, often based on a grid….
  5. the reduction to pure self-referential form, emptied of all external references….
  6. In Minimal art what is important is the phenomenological basis of the viewer’s experience, how he or she perceives the internal relationships among the parts of the work and of the parts to the whole….
  7. The repetition of forms in Minimalist sculpture serves to emphasize the subtle differences in the perception of those forms in space and time as the spectator’s viewpoint shifts in time and space."

Discuss these seven points
in relation to the following:

 
Form,
by S. H. Cullinane

Logos and Logic

Mark Rothko's reference
to geometry as a "swamp"
and his talk of "the idea" in art

Michael Kimmelman's
remarks on ideas in art 

Notes on ideas and art

Geometry
of the 4×4 square

The Grid of Time

ART WARS:
Judgment Day
(2003, 10/07)

Part II: Theology

Today's previous entry, "Skylark," concluded with an invocation of the Lord.   Of course, the Lord one expects may not be the Lord that appears.


 John Barth on minimalism:

"… the idea that, in art at least, less is more.

It is an idea surely as old, as enduringly attractive and as ubiquitous as its opposite. In the beginning was the Word: only later came the Bible, not to mention the three-decker Victorian novel. The oracle at Delphi did not say, 'Exhaustive analysis and comprehension of one's own psyche may be prerequisite to an understanding of one's behavior and of the world at large'; it said, 'Know thyself.' Such inherently minimalist genres as oracles (from the Delphic shrine of Apollo to the modern fortune cookie), proverbs, maxims, aphorisms, epigrams, pensees, mottoes, slogans and quips are popular in every human century and culture–especially in oral cultures and subcultures, where mnemonic staying power has high priority–and many specimens of them are self-reflexive or self-demonstrative: minimalism about minimalism. 'Brevity is the soul of wit.' "


Another form of the oracle at Delphi, in minimalist prose that might make Hemingway proud:

"He would think about Bert.  Bert was an interesting man.  Bert had said something about the way a gambler wants to lose.  That did not make sense.  Anyway, he did not want to think about it.  It was dark now, but the air was still hot.  He realized that he was sweating, forced himself to slow down the walking.  Some children were playing a game with a ball, in the street, hitting it against the side of a building.  He wanted to see Sarah.

When he came in, she was reading a book, a tumbler of dark whiskey beside her on the end table.  She did not seem to see him and he sat down before he spoke, looking at her and, at first, hardly seeing her.  The room was hot; she had opened the windows, but the air was still.  The street noises from outside seemed almost to be in the room with them, as if the shifting of gears were being done in the closet, the children playing in the bathroom.  The only light in the room was from the lamp over the couch where she was reading.

He looked at her face.  She was very drunk.  Her eyes were swollen, pink at the corners.  'What's the book,' he said, trying to make his voice conversational.  But it sounded loud in the room, and hard.

She blinked up at him, smiled sleepily, and said nothing.

'What's the book?'  His voice had an edge now.

'Oh,' she said.  'It's Kierkegaard.  Soren Kierkegaard.' She pushed her legs out straight on the couch, stretching her feet.  Her skirt fell back a few inches from her knees.  He looked away.

'What's that?' he said.

'Well, I don't exactly know, myself."  Her voice was soft and thick.

He turned his face away from her again, not knowing what he was angry with.  'What does that mean, you don't know, yourself?'

She blinked at him.  'It means, Eddie, that I don't exactly know what the book is about.  Somebody told me to read it once, and that's what I'm doing.  Reading it.'

He looked at her, tried to grin at her — the old, meaningless, automatic grin, the grin that made everbody like him — but he could not.  'That's great,' he said, and it came out with more irritation than he had intended.

She closed the book, tucked it beside her on the couch.  She folded her arms around her, hugging herself, smiling at him.  'I guess this isn't your night, Eddie.  Why don't we have a drink?'

'No.'  He did not like that, did not want her being nice to him, forgiving.  Nor did he want a drink.

Her smile, her drunk, amused smile, did not change.  'Then let's talk about something else,' she said.  'What about that case you have?  What's in it?'  Her voice was not prying, only friendly, 'Pencils?'

'That's it,' he said.  'Pencils.'

She raised her eyebrows slightly.  Her voice seemed thick.  'What's in it, Eddie?'

'Figure it out yourself.'  He tossed the case on the couch."

— Walter Tevis, The Hustler, 1959,
    Chapter 11


See, too, the invocation of Apollo in

A Mass for Lucero, as well as 

GENERAL AUDIENCE OF JOHN PAUL II
Wednesday 15 January 2003
:

"The invocation of the Lord is relentless…."

and

JOURNAL ENTRY OF S. H. CULLINANE
Wednesday 15 January 2003
:

Karl Cullinane —
"I will fear no evil, for I am the
meanest son of a bitch in the valley."

Saturday, December 20, 2003

Saturday December 20, 2003

Filed under: General,Geometry — m759 @ 1:09 am

For St. Emil’s Day

On this date in 1962, Emil Artin died.

He was, in his way, a priest of Apollo, god of music, light, and reason.

The previous entry dealt with permutation groups, in the context of a Jan. 2004 AMS Notices review of a book on the mathematics of juggling.

It turns out that juggling is, in fact, related to Artin’s theory of “braid groups.”  For details, see Juggling Braids.

For more on Apollo, see my entry of

1/09.

Monday, November 17, 2003

Monday November 17, 2003

Filed under: General — m759 @ 9:25 am

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.

Sunday, April 27, 2003

Sunday April 27, 2003

Filed under: General,Geometry — m759 @ 3:24 pm

ART WARS:

Graphical Password

From a summary of “The Design and Analysis of Graphical Passwords“:

“Results from cognitive science show that people can remember pictures much better than words….

The 5×5 grid creates a good balance between security and memorability.”

 Ian Jermyn, New York University; Alain Mayer, Fabian Monrose, Michael K. Reiter, Bell Labs, Lucent Technologies; Aviel Rubin, AT&T Labs — Research

Illustration — Warren Beatty as
a graphical password:

Town & Country,”
released April 27, 2001

Those who prefer the simplicity of a 3×3 grid are referred to my entry of Jan. 9, 2003, Balanchine’s Birthday.  For material related to the “Town & Country” theme and to Balanchine, see Leadbelly Under the Volcano (Jan. 27, 2003). (“Sometimes I live in the country, sometimes I live in town…” – Huddie Ledbetter).  Those with more sophisticated tastes may prefer the work of Stephen Ledbetter on Gershwin’s piano preludes or, in view of Warren Beatty’s architectural work in “Town & Country,” the work of Stephen R. Ledbetter on window architecture.

As noted in Balanchine’s Birthday, Apollo (of the Balanchine ballet) has been associated by an architect with the 3×3, or “ninefold” grid.  The reader who wishes a deeper meditation on the number nine, related to the “Town & Country” theme and more suited to the fact that April is Poetry Month, is referred to my note of April 27 two years ago, Nine Gates to the Temple of Poetry.

Intermediate between the simplicity of the 3×3 square and the (apparent) complexity of the 5×5 square, the 4×4 square offers an introduction to geometrical concepts that appears deceptively simple, but is in reality fiendishly complex.  See Geometry for Jews.  The moral of this megilla?

32 + 42 = 52.

But that is another story.

Friday, April 25, 2003

Friday April 25, 2003

Filed under: General,Geometry — Tags: , , — m759 @ 7:59 pm

Mark

Today is the feast of Saint Mark.  It seems an appropriate day to thank Dr. Gerald McDaniel for his online cultural calendar, which is invaluable for suggesting blog topics.

Yesterday's entry "Cross-Referenced" referred to a bizarre meditation of mine titled "The Matthias Defense," which combines some thoughts of Nabokov on lunacy with some of my own thoughts on the Judeo-Christian tradition (i.e., also on lunacy).  In this connection, the following is of interest:

From a site titled Meaning of the Twentieth Century —

"Freeman Dyson has expressed some thoughts on craziness. In a Scientific American article called 'Innovation in Physics,' he began by quoting Niels Bohr. Bohr had been in attendance at a lecture in which Wolfgang Pauli proposed a new theory of elementary particles. Pauli came under heavy criticism, which Bohr summed up for him: 'We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that is not crazy enough.' To that Freeman added: 'When a great innovation appears, it will almost certainly be in a muddled, incomplete and confusing form. To the discoverer, himself, it will be only half understood; to everyone else, it will be a mystery. For any speculation which does not at first glance look crazy, there is no hope!' "

Kenneth Brower, The Starship and the Canoe, 1979, pp. 146, 147

It is my hope that the speculation, implied in The Matthias Defense, that the number 162 has astonishing mystical properties (as a page number, article number, etc.) is sufficiently crazy to satisfy Pauli and his friend Jung as well as the more conventional thinkers Bohr and Dyson.  It is no less crazy than Christianity, and has a certain mad simplicity that perhaps improves on some of that religion's lunatic doctrines. 

Some fruits of the "162 theory" —

Searching on Google for muses 162, we find the following Orphic Hymn to Apollo and a footnote of interest:

27 Tis thine all Nature's music to inspire,
28 With various-sounding, harmonising lyre;
29 Now the last string thou tun'ft to sweet accord,
30 Divinely warbling now the highest chord….

"Page 162 Verse 29…. Now the last string…. Gesner well observes, in his notes to this Hymn, that the comparison and conjunction of the musical and astronomical elements are most ancient; being derived from Orpheus and Pythagoras, to Plato. Now, according to the Orphic and Pythagoric doctrine, the lyre of Apollo is an image of the celestial harmony…."

For the "highest chord" in a metaphorical sense, see selection 162 of the 1919 edition of The Oxford Book of English Verse (whose editor apparently had a strong religious belief in the Muses (led by Apollo)).  This selection contains the phrase "an ever-fixèd mark" — appropriately enough for this saint's day.  The word "mark," in turn, suggests a Google search for the phrase "runes to grave" Hardy, after a poem quoted in G. H. Hardy's A Mathematician's Apology.

Such a search yields a website that quotes Housman as the source of the "runes" phrase, and a further search yields what is apparently the entire poem:

Smooth Between Sea and Land

by A. E. Housman

Smooth between sea and land
Is laid the yellow sand,
And here through summer days
The seed of Adam plays.

Here the child comes to found
His unremaining mound,
And the grown lad to score
Two names upon the shore.

Here, on the level sand,
Between the sea and land,
What shall I build or write
Against the fall of night?

Tell me of runes to grave
That hold the bursting wave,
Or bastions to design
For longer date than mine.

Shall it be Troy or Rome
I fence against the foam
Or my own name, to stay
When I depart for aye?

Nothing: too near at hand
Planing the figured sand,
Effacing clean and fast
Cities not built to last
And charms devised in vain,
Pours the confounding main.

(Said to be from More Poems (Knopf, 1936), p. 64)

Housman asks the reader to tell him of runes to grave or bastions to design.  Here, as examples, are one rune and one bastion.

 


The rune known as
"Dagaz"

Represents
the balance point or "still point."


The Nike Bastion

 Dagaz: (Pronounced thaw-gauze, but with the "th" voiced as in "the," not unvoiced as in "thick") (Day or dawn.)

From Rune Meanings:

 Dagaz means "breakthrough, awakening, awareness. Daylight clarity as opposed to nighttime uncertainty. A time to plan or embark upon an enterprise. The power of change directed by your own will, transformation. Hope/happiness, the ideal. Security and certainty. Growth and release. Balance point, the place where opposites meet."

Also known as "the rune of transformation."

For the Dagaz rune in another context, see Geometry of the I Ching.  The geometry discussed there does, in a sense, "hold the bursting wave," through its connection with Walsh functions, hence with harmonic analysis.

 Temple of Athena Nike on the Nike Bastion, the Acropolis, Athens.  Here is a relevant passage from Paul Valéry's Eupalinos ou L'Architecte about another temple of four columns:

Et puis… Écoute, Phèdre (me disait-il encore), ce petit temple que j'ai bâti pour Hermès, à quelques pas d'ici, si tu savais ce qu'il est pour moi ! — Où le passant ne voit qu'une élégante chapelle, — c'est peu de chose: quatre colonnes, un style très simple, — j'ai mis le souvenir d'un clair jour de ma vie. Ô douce métamorphose ! Ce temple délicat, nul ne le sait, est l'image mathématique d'une fille de Corinthe que j'ai heureusement aimée. Il en reproduit fidèlement les proportions particulières. Il vit pour moi !

Four columns, in a sense more suited to Hardy's interests, are also a recurrent theme in The Diamond 16 Puzzle and Diamond Theory.

Apart from the word "mark" in The Oxford Book of English Verse, as noted above, neither the rune nor the bastion discussed has any apparent connection with the number 162… but seek and ye shall find.
 

Sunday, April 13, 2003

Sunday April 13, 2003

Filed under: General — m759 @ 11:59 pm

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

Friday, January 10, 2003

Friday January 10, 2003

Filed under: General,Geometry — Tags: — m759 @ 8:15 pm

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."

Duncanology Part 3

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.''

Is a puzzlement.

See also The Diamond 16 Puzzle for some quilt designs.

Thursday, January 9, 2003

Thursday January 9, 2003

Filed under: General — Tags: , , , , — m759 @ 4:48 pm

Balanchine's Birthday

Today seems an appropriate day to celebrate Apollo and the nine Muses.

From a website on Balanchine's and Stravinsky's ballet, "Apollon Musagete":

In his Poetics of Music (1942) Stravinsky says: "Summing up: What is important for the lucid ordering of the work– for its crystallization– is that all the Dionysian elements which set the imagination of the artist in motion and make the life-sap rise must be properly subjugated before they intoxicate us, and must finally be made to submit to the law: Apollo demands it."  Stravinsky conceived Apollo as a ballet blanc– a "white ballet" with classical choreography and monochromatic attire. Envisioning the work in his mind's eye, he found that "the absence of many-colored hues and of all superfluities produced a wonderful freshness." Upon first hearing Apollo, Diaghilev found it "music somehow not of this world, but from somewhere else above." The ballet closes with an Apotheosis in which Apollo leads the Muses towards Parnassus. Here, the gravely beautiful music with which the work began is truly recapitulated "on high"– ceaselessly recycled, frozen in time.

— Joseph Horowitz

 

Another website invoking Apollo:

The icon that I use… is the nine-fold square…. The nine-fold square has centre, periphery, axes and diagonals.  But all are present only in their bare essentials.  It is also a sequence of eight triads.  Four pass through the centre and four do not.  This is the garden of Apollo, the field of Reason…. 

In accordance with these remarks, here is the underlying structure for a ballet blanc:

A version of 'grid3x3.gif.'

This structure may seem too simple to support movements of interest, but consider the following (click to enlarge):

As Sir Arthur Quiller-Couch, paraphrasing Horace, remarks in his Whitsun, 1939, preface to the new edition of the Oxford Book of English Verse, "tamen usque recurret Apollo."

The alert reader will note that in the above diagrams, only eight of the positions move.

Which muse remains at the center?

Consider the remark of T. S. Eliot, "At the still point, there the dance is," and the fact that on the day Eliot turned 60, Olivia Newton-John was born.  How, indeed, in the words of another "sixty-year-old smiling public man," can we know the dancer from the dance?

Tuesday, December 10, 2002

Tuesday December 10, 2002

Filed under: General — Tags: — m759 @ 1:06 am

Three Coins in the Fountain

Mars

Victory

Sol Invictus

The reverse of three bronze coins
minted during Constantine’s early years

"Constantine like many of his predecessors had worshipped the Greek and Roman gods, particularly Apollo, Mars and Victory. This fact is evident in the portrayal of these gods on the earliest of Constantine’s coins. Yet surprisingly, even after his dream experience, and subsequent victory over Maxentius, it is recorded that he continued to worship these gods. Although the images of Apollo, Mars and Victory quickly disappeared from his coinage, later coins minted under Constantine shows that he likely continued to worship the sol invicta [sic] or ‘Unconquered Sun’ for 10 years or more after his dream experience. Yet, over a period of years, the experience of the sign, and the victory at the Milvian bridge, eventually led Constantine to favour and later to convert to the Christian faith."

— Ross Nightingale, "The 'Sign' that Changed the Course of History," in Ancient Coin Forum

"Three coins in the fountain,
Each one seeking happiness.
Thrown by three hopeful lovers,
Which one will the fountain bless?

Three hearts in the fountain,
Each heart longing for its home.
There they lie in the fountain
Somewhere in the heart of Rome."

Sinatra's version of the 1954 song
(Lyrics by Sammy Cahn,
 music by Jule Styne)

Which one will the fountain bless?

In order to answer this theological conundrum, we need to know more about the unfamiliar god Sol Invictus.

A quick web search reveals that some fanatical Protestants believe that the Roman deities Sol Invictus and Mithra were virtually the same.  Of course, it is unwise to take the paranoid ravings of Protestants too seriously, but in this case they may be on to something.

The Catholic Church itself seems to identify Sol Invictus with Mithra:

"Sunday was kept holy in honour of Mithra…. The 25 December was observed as his birthday, the natalis invicti, the rebirth of the winter-sun, unconquered by the rigours of the season. A Mithraic community was not merely a religious congregation…"

The Catholic Encyclopedia, 1911 edition.

Nihil Obstat, October 1, 1911. Remy Lafort, S.T.D., Censor
Imprimatur. +John Cardinal Farley, Archbishop of New York

It would seem, therefore, that as December 25 approaches we are preparing to celebrate the festival of Sol Invictus. This perhaps answers the theological riddle posed by Sammy Cahn.

From "Things Change," starring Don Ameche:
"A big man knows the value of a small coin."

Today's site music celebrates
Cahn, Styne, Sinatra, and the spirit of the 1950's.
Many thanks to
Loyd's Piano Music Page
for this excellent rendition of a Styne classic
.

Wednesday, October 9, 2002

Wednesday October 9, 2002

Filed under: General — m759 @ 11:36 pm

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.

Wednesday October 9, 2002

Filed under: General — Tags: — m759 @ 5:01 pm

ART WARS:

Apollo and Dionysus

From the New York Times of October 9, 2002:

Daniel Deverell Perry, a Long Island architect who created the marble temple of art housing the Sterling and Francine Clark Art Institute in Williamstown, Mass., died Oct. 2 in Woodstock, N.Y…. He was 97.

Apollo

Clark Art Institute

Nymphs and Satyr

Elvis

From The Birth of Tragedy, by Friedrich Nietzsche (tr. by Shaun Whiteside):

Chapter 1….

To the two gods of art, Apollo and Dionysus, we owe our recognition that in the Greek world 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.

Chapter 25….

From the foundation of all existence, the Dionysiac substratum of the world, no more can enter the consciousness of the human individual than can be overcome once more by that Apolline power of transfiguration, so that both of these artistic impulses are forced to unfold in strict proportion to one another, according to the law of eternal justice.  Where the Dionysiac powers have risen as impetuously as we now experience them, Apollo, enveloped in a cloud, must also have descended to us; some future generation will behold his most luxuriant effects of beauty.

Notes: 

  • On the Clark Art Institute, from Perry’s obituary in the Times:

    “When it opened in 1955, overlooking 140 acres of fields and ponds, Arts News celebrated its elegant galleries as the ‘best organized and most highly functional museum erected anywhere.'”

  • The “Nymphs and Satyr” illustration above is on the cover of “CAI: Journal of the Clark Art Institute,” Volume 3, 2002.  It is a detail from the larger work of the same title by William Bouguereau.
  • Today, October 9, is the anniversary of the dedication in 28 B.C. of the Temple to Apollo on the Palatine Hill in Rome.  See the journal entry below, which emphasizes the point that Apollo and Dionysus are not as greatly opposed as one might think.

Wednesday October 9, 2002

Filed under: General — Tags: — m759 @ 2:40 am
 
To Apollo

On this date in 28 B.C. the Temple of Apollo
was dedicated on the Palatine Hill in Rome.

Horace, Odes, XXXI

Frui paratis et valido mihi,
Latoe, dones et precor integra
Cum mente nec turpem senectam
Degere nec cithara carentem.

O grant me, Phoebus, calm content,
Strength unimpaird, a mind entire,
Old age without dishonour spent,
Nor unbefriended by the lyre!

— The Odes and Carmen Saeculare of Horace,
John Conington, translator.
London, George Bell and Sons, 1882.

Representations of Apollo: 

 

1

2

3

See also
The Angel in the Stone

"Everything is found 
and lost and buried 
and then found again"

— Tanya Wendling

Tuesday, September 24, 2002

Tuesday September 24, 2002

Filed under: General — m759 @ 11:33 pm

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….”

From my journal note, “A Mass for Lucero“:

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.”

Monday, September 9, 2002

Monday September 9, 2002

Filed under: General — m759 @ 3:33 pm

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.

Sunday, September 8, 2002

Sunday September 8, 2002

Filed under: General — Tags: — m759 @ 2:00 am

In honor of the September 8 birthdays of

From a website on Donna Tartt‘s novel The Secret History… 

“It is like a storyteller looking up suddenly into the eyes of his audience across the embers of a once blazing fire…

…the reader feels privy to the secrets of human experience by their passage down through the ages; the telling and re-telling. A phrase from the ghost in Hamlet comes to mind:

‘I could a tale unfold whose lightest word /
Would harrow up thy soul…..’ “

This work of literature seems especially relevant at the start of a new school year, and in light of my remarks below about ancient Greek religion. One should, when praising Apollo, never forget that Dionysus is also a powerful god.

For those who prefer film to the written word, I recommend “Barton Fink” as especially appropriate viewing for the High Holy Days. Judy Davis (my favorite actress) plays a Faulkner-figure’s “secretary” who actually writes most of his scripts.

Tartt is herself from Faulkner country.  For her next book, see this page from Square Books, 160 Courthouse Square, Oxford, Misssissippi.

Let us pray that Tartt fares better in real life than Davis did in the movie.

As music for the High Holy Days, I recommend Don Henley’s “The Garden of Allah.” For some background on the actual Garden of Allah Hotel at 8080 Sunset Boulevard (where “Barton Fink” might have taken place), see

NAZIMOVA AND THE GARDEN OF ALLA.

Saturday, September 7, 2002

Saturday September 7, 2002

Filed under: General — m759 @ 4:44 pm

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. 

Monday, September 2, 2002

Monday September 2, 2002

Filed under: General — m759 @ 5:25 am

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.

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