Wednesday, January 23, 2019


Filed under: General,Geometry — Tags: , — m759 @ 10:00 AM

For those who prefer more elaborate decorations —

1.  A Facebook image from last August … 

2.  The Facebook glider suggests a tune from "The Thomas Crown Affair"
     (1968) that appeared in a Dec. 16, 2018 post on Christianity and
     "interlocking names"—

'The Eddington Song'

The revised lyrics describe a square space.

3.  An even more  elaborate square space:
     the Dance of the Snowflakes from
     Balanchine's version of The Nutcracker —

Tuesday, April 24, 2018

Dance, Music, Space

Filed under: General,Geometry — m759 @ 10:00 PM

". . . dance, fueled by music, opens up space."

—  Alastair Macaulay in the online New York Times  today

Putting aside the unfortunate fuel metaphor, this suggests a review —

A video published on the above date —

The video has six-plus-two dancers, a more concise arrangement
than the eight-plus-two discussed by Macaulay.

Another approach to six plus two:  the diamond-theorem correlation.

Tuesday, January 9, 2018

Unpleasantly Discursive

Filed under: General — m759 @ 10:12 PM

Background for the remarks of Koen Thas in the previous post —
Schumacher and Westmoreland, "Modal Quantum Theory" (2010).

Related material —

" There is a pleasantly discursive treatment 
of Pontius Pilate’s unanswered question
‘What is truth?’ "

— Coxeter, 1987, introduction to Trudeau’s
     The Non-Euclidean Revolution

The whole  truth may require an unpleasantly  discursive treatment.

Example —

1. The reported death on Friday, Jan. 5, 2018, of a dancer
     closely associated with George Balanchine

2. This journal on Friday, Jan. 5, 2018:

3. Illustration from a search related to the above dancer:

4. "Per Mare Per Terras" — Clan slogan above, illustrated with
     what looks like a cross-dagger.

    "Unsheathe your dagger definitions." — James Joyce.

5. Discursive remarks on quantum theory by the above
    Schumacher and Westmoreland:

6. "How much story do you want?" — George Balanchine

Sunday, November 19, 2017


Filed under: General,Geometry — m759 @ 12:00 AM

"New to the series are the Trials of the Gods events
that pit players against Ancient Egyptian gods."

Review of the new game  Assassin's Creed: Origins 

"How much story do you want?" — George Balanchine

Geometry of the I Ching (Box Style)

Thursday, April 13, 2017

Making Space

Filed under: General — m759 @ 6:00 PM

The New York Times  online today:

At MoMA, Women at Play in the Fields of Abstraction

" The famous flowchart of Modern art's evolution simply doesn't apply
in 'Making Space: Women Artists and Postwar Abstraction.' "

Monday, June 20, 2016

Plan 9 Continues

Filed under: General — Tags: — m759 @ 11:00 AM

See …

At the Still Point … (February 12, 2008)

For Balanchine's Birthday (January 9, 2007)

Go Set a Structure (Various dates)

and …

Monday, September 22, 2014

A Holy Cross for Brooklyn

Filed under: General — m759 @ 12:00 PM

Saturday night’s 9  PM post:

“Once again, Harvard defeats Holy Cross.”

That post quoted Joseph Campbell describing a

“… matrix of the cosmic process, whether in the macrocosm
or in a microcosmic field of manifestation.”

Related material —


Microcosmic field of manifestation:

Saturday, February 9, 2013

Snow Dance

Filed under: General,Geometry — m759 @ 2:09 PM

The Snow White dance from last Nov. 14
features an ad that was originally embedded
in an American Mathematical Society Notices
review describing three books of vulgarized
mathematics. These books all use "great
equations" as a framing device.

This literary strategy leads to a more abstract
snow dance. See the ballet blanc  in this journal
on Balanchine's birthday (old style) in 2003.
That dance involves equation (C) below.

Recall that in a unit ring ,
"0" denotes the additive identity,
"1" the multiplicative identity, and "-1" the
additive inverse of the multiplicative identity.

Three classic equations:

(A)  1 + 1 = 2    (Characteristic 0, ordinary arithmetic)

(B)  1 + 1 = 0   (Characteristic 2 arithmetic, in which 2 = 0)

(C)  1 + 1 = -1 (Characteristic 3 arithmetic, in which 2 = -1)

Cases (B) and (C), in which the characteristic is prime,
occur in Galois geometry.

For a more elaborate snow dance, see Master Class.

Wednesday, September 19, 2012

Art Wars (continued)

Filed under: General,Geometry — m759 @ 8:00 PM

Today's previous post, "For Odin's Day," discussed 
a mathematical object, the tesseract, from a strictly
narrative point of view.

In honor of George Balanchine, Odin might yield the
floor this evening to Apollo.

From a piece in today's online New York Times  titled
"How a God Finds Art (the Abridged Version)"—

"… the newness at the heart of this story,
in which art is happening for the first time…."

Some related art

IMAGE- Figure from Plato's Meno in version by Benjamin Jowett, Master of Balliol College, Oxford

and, more recently

This more recent figure is from Ian Stewart's 1996 revision 
of a 1941 classic, What Is Mathematics? , by Richard Courant
and Herbert Robbins.

Apollo might discuss with Socrates how the confused slave boy
of Plato's Meno  would react to Stewart's remark that

"The number of copies required to double an
 object's size depends on its dimension."

Apollo might also note an application of Socrates' Meno  diagram
to the tesseract of this afternoon's Odin post


Wednesday, September 12, 2012

Where Madness Lies

Filed under: General — m759 @ 5:24 AM

IMAGE- NYT obituaries-- psychiatrist Thomas Szasz and Broadway director Albert Marre-- with Stravinsky/Balanchine ad

    "Who knows where madness lies?" —Man of La Mancha

    "Hum a few bars and I'll fake it." —Stravinsky

Wednesday, May 4, 2011

Unity and Multiplicity

Filed under: General — Tags: — m759 @ 9:00 AM

Continued from Crimson Walpurgisnacht.

EpigraphsTwo quotations from  
Shakespeare's Birthday last year

Rebecca Goldstein
   on first encountering Plato

"I was reading Durant's section on Plato, struggling to understand his theory of the ideal Forms that lay in inviolable perfection out beyond the phantasmagoria. (That was the first, and I think the last, time that I encountered that word.)"

Screenwriter Joan Didion

"We tell ourselves stories in order to live….

We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the 'ideas' with which we have learned to freeze the shifting phantasmagoria which is our actual experience."

From Thomas Mann, "Schopenhauer," 1938, in Essays of Three Decades , translated by H. T. Lowe-Porter, Alfred A. Knopf, 1947, pp. 372-410—

Page 372: THE PLEASURE we take in a metaphysical system, the gratification purveyed by the intellectual organization of the world into a closely reasoned, complete, and balanced structure of thought, is always of a pre-eminently aesthetic kind. It flows from the same source as the joy, the high and ever happy satisfaction we get from art, with its power to shape and order its material, to sort out life's manifold confusions so as to give us a clear and general view.

Truth and beauty must always be referred the one to the other. Each by itself, without the support given by the other, remains a very fluctuating value. Beauty that has not truth on its side and cannot have reference to it, does not live in it and through it, would be an empty chimera— and "What is truth?"


Page 376: … the life of Plato was a very great event in the history of the human spirit; and first of all it was a scientific and a moral event. Everyone feels that something profoundly moral attaches to this elevation of the ideal as the only actual, above the ephemeralness and multiplicity of the phenomenal, this devaluation  of the senses to the advantage of the spirit, of the temporal to the advantage of the eternal— quite in the spirit of the Christianity that came after it. For in a way the transitory phenomenon, and the sensual attaching to it, are put thereby into a state of sin: he alone finds truth and salvation who turns his face to the eternal. From this point of view Plato's philosophy exhibits the connection between science and ascetic morality.

But it exhibits another relationship: that with the world of art. According to such a philosophy time itself is merely the partial and piecemeal view which an individual holds of ideas— the latter, being outside time, are thus eternal. "Time"— so runs a beautiful phrase of Plato— "is the moving image of eternity." And so this pre-Christian, already Christian doctrine, with all its ascetic wisdom, possesses on the other hand extraordinary charm of a sensuous and creative kind; for a conception of the world as a colourful and moving phantasmagoria of pictures, which are transparencies for the ideal and the spiritual, eminently savours of the world of art, and through it the artist, as it were, first comes into his own.

From last night's online NY Times  obituaries index—


"How much story do you want?" — George Balanchine

Thursday, October 21, 2010


Filed under: General — Tags: — m759 @ 3:57 AM

The NY Times recently discussed "Longing for the Lines That Had Us at Hello"

and  “We land in Albuquerque at 4 a.m. That’s strictly a 9 o’clock town.”

And so…


Click to enlarge.

"How much story do you want?" — George Balanchine

Thursday, December 31, 2009

All About Eve

Filed under: General — Tags: — m759 @ 9:57 AM

NY Times obituaries on New Year's Eve, 2009-- Carlene Hatcher Polite and David Levine

Genesis 3:24
So he drove out the man; and he placed
at the east of the garden of Eden Cherubims,
and a flaming sword which turned every way,
to keep the way of the tree of life.

"The links are direct between the tautology out of the Burning Bush, that 'I am' which accords to language the privilege of phrasing the identity of God, on the one hand, and the presumptions of concordance, of equivalence, of translatability, which, though imperfect, empower our dictionaries, our syntax, our rhetoric, on the other. That 'I am' has, as it were, at an overwhelming distance, informed all predication. It has spanned the arc between noun and verb, a leap primary to creation and the exercise of creative consciousness in metaphor. Where that fire in the branches has gone out or has been exposed as an optical illusion, the textuality of the world, the agency of the Logos in logic—be it Mosaic, Heraclitean, or Johannine—becomes 'a dead letter.'"

George Steiner, Grammars of Creation

Carlene Hatcher Polite–
"Shall I help you?" asked a bass voice.
"If you can," answered a contralto.
"Trace down this tree. Let me show you
men in its stead. Leaf through this bush,
extinguish the burning fire…"
The Flagellants, page 8

"How much story do you want?"
George Balanchine

Thursday, May 10, 2007

Thursday May 10, 2007

Filed under: General — m759 @ 10:31 AM
Thanks to Xangan JadedFey
for the following


on the previous entry:

Wikipedia entry - Green

Related material:

All Hallows’ Eve, 2005

Tesseract on the cover of The Gameplayers of Zan

— as well as
Balanchine’s Birthday
and the color worn by
Jean Butler in
Women of the Sidhe
(Wednesday’s entry).

Wednesday, March 7, 2007

Wednesday March 7, 2007

Filed under: General,Geometry — m759 @ 8:24 AM
In the Labyrinth
of Time:


Related material–


The image “http://www.log24.com/log/pix07/070307-Symbols.gif” cannot be displayed, because it contains errors.


The False Artaxerxes:
Borges and the
Dream of Chess

This entry was inspired by
Xanga footprints yesterday
from Virginia:

1. Virginia
Time and the Grid
9:48 AM
2. Virginia
11:38 AM
3. Virginia
Games and Truth
1:25 PM
4. Virginia
The Transcendent Signified
5:15 PM
5. Virginia
Zen and Language Games
5:16 PM
6. Virginia
Balanchine’s Birthday
6:12 PM
7. Virginia
The Agony and the Ya-Ya
6:12 PM
8. Virginia
Directions Out
6:13 PM
9. Virginia
The Four Last Things
6:13 PM

Tuesday, January 9, 2007

Tuesday January 9, 2007

Filed under: General — Tags: — m759 @ 12:00 PM
For Balanchine's Birthday

(continued from
January 9, 2003)

George Balanchine

Encyclopædia Britannica Article

born January 22
[January 9, Old Style], 1904,
St. Petersburg, Russia
died April 30, 1983, New York,
New York, U.S.

Photograph:George Balanchine.
George Balanchine.
©1983 Martha Swope

original name 
Georgy Melitonovich Balanchivadze

most influential choreographer of classical ballet in the United States in the 20th century.  His works, characterized by a cool neoclassicism, include The Nutcracker (1954) and Don Quixote (1965), both pieces choreographed for the New York City Ballet, of which he was a founder (1948), the artistic director, and the…

Balanchine,  George… (75 of 1212 words)

"What on earth is
a concrete universal?"
— Robert M. Pirsig


From Wikipedia's
"Upper Ontology"
Epiphany 2007:

"There is no neutral ground
that can serve as
a means of translating between
specialized (lower) ontologies."

There is, however,
"the field of reason"–

the 3×3 grid:

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

Click on grid
for details.

As Rosalind Krauss
has noted, some artists
regard the grid as

"a staircase to
  the Universal."

Other artists regard
Epiphany itself as an
approach to
the Universal:

"Epiphany signals the traversal
of the finite by the infinite,
of the particular by the universal,
of the mundane by the mystical,
of time by eternity.

Richard Kearney, 2005,
in The New Arcadia Review

The image “http://www.log24.com/log/pix07/070109-Kearney2.jpg” cannot be displayed, because it contains errors.

Kearney (right) with
Martin Scorsese (left)
and Gregory Peck
in 1997.

"… one of the things that worried me about traditional metaphysics, at least as I imbibed it in a very Scholastic manner at University College Dublin in the seventies, is that philosophy was realism and realism was truth. What disturbed me about that was that everything was already acquired; truth was always a systematic given and it was there to be learned from Creation onwards; it was spoken by Jesus Christ and then published by St. Thomas Aquinas: the system as perfect synthesis. Hence, my philosophy grew out of a hunger for the 'possible' and it was definitely a reaction to my own philosophical formation. Yet that wasn't my only reaction. I was also reacting to what I considered to be the deep pessimism, and even at times 'nihilism' of the postmodern turn."

— Richard Kearney, interview (pdf) in The Leuven Philosophy Newsletter, Vol. 14, 2005-2006

For more on "the possible," see Kearney's The God Who May Be, Diamonds Are Forever, and the conclusion of Mathematics and Narrative:


"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."


Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity,
Christ Church College, Oxford
(the home of Lewis Carroll)

Wednesday, December 13, 2006

Wednesday December 13, 2006

Filed under: General — m759 @ 9:29 AM

 Best Wishes for a
C. S. Lewis


 C.S. Lewis

Image of Lewis from
Into the Wardrobe

What on earth
  is a concrete

— Robert M. Pirsig, author of Zen and the Art of Motorcyle Maintenance

For one approach to an answer, click on the picture at left.

Update of 4:23 PM:

The Lewis link above deals with the separation of Heaven from Hell.  The emphasis is on Heaven.  A mysterious visitor to this website, “United States,” seems to be seeking equal time for Hell.  And so…


Based on Xanga footprints of Dec. 13, 2006
from m759’s site-visitor “United States”
(possibly a robot; if so, a robot with strange tastes).

TIME OF     DATE OF             PAGE VISITED   

1217 040520  Parable
1218 060606  The Omen
1220 051205  Don’t Know Much About History
1225 030822  Mr. Holland’s Week (And in Three Days…)
1233 030114  Remarks on Day 14 (What is Truth?)
1238 040818  Train of Thought (Oh, My Lolita)
1244 020929  Angel Night (Ellis Larkins)
1249 040715  Identity Crisis (Bourne and Treadstone)
1252 050322  Make a Differance (Lacan, Derrida, Reba)
1255 050221  Quarter to Three on Night of HST’s death
1256 040408  Triple Crown on Holy Thursday
1258 040714  Welcome to Mr. Motley’s Neighborhood
1258 030221  All About Lilith
0103 040808  Quartet (for Alexander Hammid)
0104 030106  Dead Poet in the City of Angels
0109 030914  Skewed Mirrors (Readings on Aesthetics)
0110 050126  A Theorem in Musical Form
0125 021007  Music for R. D. Laing
0138 020806  Butterflies & Popes (Transfiguration)
0140 060606  The Omen (again)
0156 030313  ART WARS: Perennial Tutti-Frutti
0202 030112  Ask Not (A Bee Gees Requiem)
0202 050527  Drama of the Diagonal, Part Deux
0202 060514  STAR WARS continued (Eclipse and Venus)
0207 030112  Ask Not (again… Victory of the Goddess)
0207 030221  All About Lilith (again… Roll credits.)

“How much story do you want?”
— George Balanchine

Monday, October 9, 2006

Monday October 9, 2006

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM
To Apollo

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

“This is the garden of Apollo,
the field of Reason….”
John Outram, architect

To Apollo (10/09/02)
Art Wars: Apollo and Dionysus
Balanchine’s Birthday
Art Theory for Yom Kippur
A Form
A Form, continued
Deep Game
Gameplayers of Zen
And So To Bed
Translation Plane for Rosh Hashanah
Derrida Dead
The Nine
From Tate to Plato
Art History
A Miniature Rosetta Stone
High Concept
High Concept, Continued
Analogical Train of Thought
Today’s Sermon: Magical Thinking
Seven is Heaven, Eight is a Gate
Nine is a Vine
Apollo and Christ
Hamilton’s Whirligig
On Beauty
Sunday Morning
New Haven
Washington Ballet
Catholic Schools Sermon
The Logic of Apollo
Game Boy
Art Wars Continued: The Krauss Cross
Art Wars Continued: Pandora’s Box
The Pope in Plato’s Cave
Today’s Birthdays
Symbology 101

Tuesday, August 22, 2006

Tuesday August 22, 2006

Filed under: General,Geometry — m759 @ 9:00 AM


In talks at Valencia, Spain, in May through August of 2004, Alexander Borisenko, of Kharkov National University in the Ukraine, provided a detailed introduction to the topic of today’s opening lecture at ICM 2006 in Madrid:

An Introduction to Hamilton and Perelman’s Work on the Conjectures of Poincare and Thurston (pdf, 155 pages).

For a less detailed introduction, see an ICM 2006 press release (pdf, 3 pages) on Fields Medal winner Grigory Perelman.

Related material: The previous entry, “Beginnings,” and an introduction to the second-simplest two-dimensional geometry (Balanchine’s Birthday, 2003).

“How much story do you want?”
George Balanchine

Sunday, August 6, 2006

Sunday August 6, 2006

Filed under: General — Tags: — m759 @ 7:00 PM
Game Boy
The image “http://www.log24.com/log/pix06A/060806-Einsatz.jpg” cannot be displayed, because it contains errors.
Click on picture for details.
"Nine is a very
powerful Nordic number
— Katherine Neville


to put one's back
into something
bei etwas
Einsatz zeigen
to up the ante
den Einsatz erhöhen
to debrief den Einsatz
nachher besprechen
to be on duty
im Einsatz sein
mil.to be in action im Einsatz sein
to play for
high stakes
mit hohem
Einsatz spielen



"His music had of course come from Russian folk sources and from Rimsky-Korsakov and from other predecessors, in the way that all radical art has roots. But to be a true modernist, a cosmopolitan in the twentieth century, it was necessary to seem to disdain nationalism, to be perpetually, heroically novel– the more aloof, the better. 'Cold and transparent, like an "extra dry" champagne, which gives no sensation of sweetness, and does not enervate, like other varieties of that drink, but burns,' Stravinsky said about his own Octet, Piano Concerto, and Piano Sonata. The description might be applied to works by Picasso or Duchamp."

— Michael Kimmelman in
  The New York Review of Books,
issue dated Aug. 10, 2006

But the description
certainly applies to
Bridget Moynahan:

The image “http://www.log24.com/log/pix06A/060806-Recruit2.jpg” cannot be displayed, because it contains errors.

"… like an 'extra dry' champagne,
which gives no sensation of
sweetness, and does not enervate."

For more on the
"Ice 9" figure, see
Balanchine's Birthday.

Friday, August 4, 2006

Friday August 4, 2006

Filed under: General — m759 @ 2:56 AM

continued from
previous entry

In memory of
Elisabeth Schwarzkopf:

"Who is the fairest of them all?"

This question might
well be posed by…

The image “http://www.log24.com/log/pix05/050501-Krauss.jpg” cannot be displayed, because it contains errors.

Rosalind Krauss,
Meyer Schapiro Professor
of Modern Art and Theory
at Columbia University
(Ph.D., Harvard U., 1969).

"The grid is a staircase to the Universal….
We could think about Ad Reinhardt, who,
despite his repeated insistence that
'Art is art,'
ended up by painting a series of…
nine-square grids in which the motif
that inescapably emerges is
a Greek cross.

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

There is no painter in the West
who can be unaware of
the symbolic power
of the cruciform shape and the
Pandora's box of spiritual reference
that is opened once one uses it."

— Rosalind Krauss in "Grids"

"Nine is a very powerful Nordic number."
— Katherine Neville, author of The Eight

Related material:

Balanchine's Birthday,

Apollo and Christ.

Monday, May 22, 2006

Monday May 22, 2006

Filed under: General — m759 @ 2:45 AM

The image “http://www.log24.com/log/pix06A/060522-BalanchineDuhham.jpg” cannot be displayed, because it contains errors.

Balanchine, Dunham

In memory of
Katherine Dunham,
who died Sunday at 96

“How much story do you want?”
— George Balanchine

From pbs.org:

“In 1940 Dunham and her company appeared in the black Broadway musical, ‘Cabin in the Sky,’ staged by George Balanchine, in which Dunham played the sultry siren Georgia Brown….”

From the Library of Congress:

“George Balanchine and Katherine Dunham were, in effect, co-choreographers of the dances in the show, at least for those in which she and her dancers appeared. When choreographing for dancers trained in techniques other than classical ballet, Balanchine’s habit was to respect their expertise and their personal style, to allow them as much creative input as they wished to make, and then to arrange their steps, combinations, and movements into a unified choreographic composition. Dunham found this method of collaboration quite agreeable, and she and Balanchine enjoyed a particularly amicable working relationship.

The story of Cabin in the Sky centers on Little Joe, a kindhearted but morally ambivalent Everyman, who is stabbed in a dispute over a crap game, dies and is bound for Hell, but is saved by his good wife’s prayers and given extra time on earth to qualify for admission to Heaven. Dooley Wilson played Little Joe….”

The image “http://www.log24.com/log/pix06A/060522-Wilson.jpg” cannot be displayed, because it contains errors.

“It’s still the  
   same old story….”

Friday, May 19, 2006

Friday May 19, 2006

Filed under: General — m759 @ 1:00 AM
Star and Diamond

” ‘I know what it is you last saw,’ she said; ‘for that is also in my mind. Do not be afraid! But do not think that only by singing amid the trees, nor even by the slender arrows of elvenbows, is this land of Lothlórien maintained and defended against the Enemy. I say to you, Frodo, that even as I speak to you, I perceive the Dark Lord and know his mind, or all his mind that concerns the Elves. And he gropes ever to see me and my thought. But still the door is closed!’
      She lifted up her white arms, and spread out her hands towards the East in a gesture of rejection and denial. Eärendil, the Evening Star, most beloved of the Elves, shone clear above. So bright was it that the figure of the Elven-lady cast a dim shadow on the ground. Its ray glanced upon a ring about her finger; it glittered like polished gold overlaid with silver light, and a white stone in it twinkled as if the Even-star had come to rest upon her hand. Frodo gazed at the ring with awe; for suddenly it seemed to him that he understood.
      ‘Yes,’ she said, divining his thought, ‘it is not permitted to speak of it, and Elrond could not do so. But it cannot be hidden from the Ring-Bearer, and one who has seen the Eye. Verily it is in the land of Lórien upon the finger of Galadriel that one of the Three remains. This is Nenya, the Ring of Adamant, and I am its keeper.’ ”

— J. R. R. Tolkien, The Lord of the Rings

Related material:

The last 3 entries,
as well as
Mathematics and Narrative

“How much story
do you want?”
— George Balanchine  

Sunday, January 29, 2006

Sunday January 29, 2006

Filed under: General — m759 @ 9:00 AM

In the punctual centre of all circles white
     Stands truly….

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

… and Bloom with his vast accumulation
Stands and regards and repeats the primitive lines.

— Wallace Stevens,
“From the Packet of Anacharsis”

Related material:
Balanchine’s Birthday.

Saturday, December 24, 2005

Saturday December 24, 2005

Filed under: General — m759 @ 9:00 PM
Nine is a Vine

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?
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.

Friday, December 16, 2005

Friday December 16, 2005

Filed under: General,Geometry — m759 @ 2:00 PM
Jesus vs. the Goddess:
A Brief Chronology

In 1946, Robert Graves published King Jesus, an historical novel based on the theory and Graves’ own historical conjecture that Jesus was, in fact, the rightful heir to the Israelite throne… written while he was researching and developing his ideas for The White Goddess.”

In 1948, C. S. Lewis finished the first draft of The Lion, The Witch, and The Wardrobe, a novel in which one of the main characters is “the White Witch.”

In 1948, Robert Graves published The White Goddess.

In 1949, Robert Graves published Seven Days in New Crete [also titled Watch the North Wind Rise], “a novel about a social distopia in which Goddess worship is (once again?) the dominant religion.”

Lewis died on November 22, 1963, the day John F. Kennedy was killed.

Related material:
Log24, December 10, 2005

Graves died on December 7 (Pearl Harbor Day), 1985.

Related material:
Log24, December 7, 2005, and
Log24, December 11, 2005

Jesus died, some say, on April 7 in the year 30 A.D.

Related material:

Art Wars, April 7, 2003:
Geometry and Conceptual Art,

Eight is a Gate, and

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Plato’s Diamond

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— Motto of
Plato’s Academy

“Plato is wary of all forms of rapture other than reason’s. He is most deeply leery of, because himself so susceptible to, the literary imagination. He speaks of it as a kind of holy madness or intoxication and goes on to link it to Eros, another derangement that joins us, but very dangerously, with the gods.”
Rebecca Goldstein in
    The New York Times,
    three years ago today
    (December 16, 2002) 
“It’s all in Plato, all in Plato;
 bless me, what do they
teach them at these schools?”
— C. S. Lewis in
the Narnia Chronicles

“How much story do you want?”
— George Balanchine

Tuesday, December 6, 2005

Tuesday December 6, 2005

Filed under: General — m759 @ 3:33 AM
  In memory of…

– Spanish singer Gloria Lasso, who made her name recording romantic ballads in Latin America and Paris, died in her sleep on Sunday at her home in Cuernavaca. She was 83.

Today’s Harvard Crimson–

Pudding Show Features
Wild West Theme

From yesterday’s entry,
a tribute to Olivia Newton-John:

“At the still point,
there the dance is.”
— T. S. Eliot

Xanadu (1980)

For related material, see

Balanchine’s Birthday (1/9/03)
and Deep Game (6/26/04).

 For more on Balanchine,
Olivia Newton-John, Sunday,
 and Eliot’s “still point,”
see the previous entry.

For more Harvard humor,
see The Crimson Passion.

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,


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.

Wednesday, May 25, 2005

Wednesday May 25, 2005

Filed under: General,Geometry — m759 @ 2:22 PM

The Turning

Readers who have an Amazon.com account may view book pages relevant to the previous entry.  See page 77 of The Way We Think, by Fauconnier and Turner (Amazon search term = Meno).  This page discusses both the Pythagorean theorem and Plato's diamond figure in the Meno, but fails to "blend" these two topics.  See also page 53 of The History of Mathematics, by Roger Cooke (first edition), where these two topics are in fact blended (Amazon search term = Pythagorean).  The illustration below is drawn from the Cooke book.

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Cooke demonstrates how the Pythagorean theorem might have been derived by "blending" Plato's diamond (left) with the idea of moving the diamond's corners (right).

The previous entry dealt with a conference on mathematics and narrative.  Above is an example I like of mathematics…. Here is an example I like of narrative:

Kate felt quite dizzy. She didn't know exactly what it was
that had just happened, but she felt pretty damn  certain  that
it  was  the  sort of experience that her mother would not have
approved of on a first date.
     "Is this all part of what we have to do to go to  Asgard?"
she said. "Or are you just fooling around?"
     "We will go to Asgard...now," he said.
     At that moment he raised his hand as if to pluck an apple,
but instead of plucking he made a tiny, sharp turning movement.
The effect  was as if he had twisted the entire world through a
billionth part of a billionth  part  of  a  degree.  Everything
shifted,  was  for  a  moment  minutely  out of focus, and then
snapped back again as a suddenly different world.

— Douglas Adams, The Long Dark Tea-Time of the Soul

And here is a blend of the concepts "Asgard" and "conference":

    During the Interuniverse Society conference,
    a bridge was opened to Valhalla…."

     In Norse myth, the rainbow bridge
     that connected Earth to Asgard,
     home of the gods.  It was extended
     to Tellus Tertius during the
     Interuniverse Society conference"

— From A Heinlein Concordance

The image “http://www.log24.com/log/pix05/050525-Rainbow.jpg” cannot be displayed, because it contains errors.

— Front page picture from a
local morning newspaper published
today, Wednesday, May 25, 2005

As George Balanchine once asked,
"How much story do you want?"

Friday, December 17, 2004

Friday December 17, 2004

Filed under: General — Tags: — m759 @ 9:00 PM
Christmas Dance at Taos

One grows used to the weather,
The landscape and that;
And the sublime comes down
To the spirit itself,

The spirit and space,
The empty spirit
In vacant space.

— Wallace Stevens,
"The American Sublime"

The Times Online on the artist Agnes Martin,
who died Dec. 16 in Taos, New Mexico:

"At a glance, or from a distance, her work looks like nothing at all. Square canvases are so palely touched with colour they might almost be blank. Considered slowly and carefully and close-up, however, the whole surface comes alive."

"The restraint and formal regularity of Martin’s work has led her often to be grouped with the Minimalists. She shares something of their self-effacing rigour and their concern with the material qualities of art, but she herself preferred to be seen in the context of the Abstract Expressionist painters who were her own contemporaries and early artistic models. Like them she may have seen abstract art as the means to a distinctively American sublime…."

"Taos had been a magnet for artists since the last years of the 19th century. D. H. Lawrence famously spent time there in the 1920s. 'Never shall I forget the Christmas dances at Taos,' he wrote, 'twilight, snow, the darkness coming over the great wintry mountains and the lonely pueblo.'"

Related material:

Pictures of Nothing,

Balanchine's Birthday.

Monday, September 27, 2004

Monday September 27, 2004

Filed under: General — m759 @ 3:00 PM

Romantic Interaction

(See previous entry.)

From today’s Harvard Crimson:

Pudding Show Features
Wild West Theme

From yesterday’s entry,
a tribute to Olivia Newton-John:

“At the still point,
there the dance is.”
— T. S. Eliot

Xanadu (1980)

For related material, see

Balanchine’s Birthday (1/9/03)
and Deep Game (6/26/04).

Monday, August 30, 2004

Monday August 30, 2004

Filed under: General — Tags: — m759 @ 4:01 PM


for Penelope Doob,
Radcliffe '64:

"How much story do you want?"
— George Balanchine

Tuesday, June 29, 2004

Tuesday June 29, 2004

Filed under: General,Geometry — m759 @ 2:22 PM
And So To Bed

Advanced Study (6/26/04), continued…

Part I: Ulysses


Going to dark bed there was a square round Sinbad the Sailor roc’s auk’s egg in the night of the bed of all the auks of the rocs of Darkinbad the Brightdayler.


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Ulysses, conclusion of Ch. 17

Part II: Badcoc

A Visual Meditation for
the Feast of St. Peter

The image “http://www.log24.com/log/pix04A/040629-Badcoc.gif” cannot be displayed, because it contains errors.

For further details on this structure, see

Magic Squares, Finite Planes,
and Points of Inflection
on Elliptic Curves
by Ezra Brown, and

Visualizing GL(2, p)
by Steven H. Cullinane.

For a more literary approach
to this structure, see

Balanchine’s Birthday (Jan. 9, 2003),
Art Theory for Yom Kippur (Oct. 5, 2003),
A Form (May 22, 2004),
Ineluctable (May 27, 2004),
A Form, continued (June 5, 2004),
Parallelisms (June 6, 2004),
Deep Game (June 26, 2004), and
Gameplayers of Zen (June 27, 2004).

The image “http://www.log24.com/log/pix04A/040629-Players.jpg” cannot be displayed, because it contains errors.

To appreciate fully this last entry
on Gameplayers,
one must understand
the concept of “suicide”
in the game of Go

and be reminded
by the fatuous phrase of the
Institute of Contemporary Art
quoted in Gameplayers
encompassed by ‘nothing’ ” —
of John 1:5.

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Saturday, June 26, 2004

Saturday June 26, 2004

Filed under: General — m759 @ 3:03 AM
Deep Game

The entry Ado of June 25, 2004 contains a link to an earlier entry, A Form, continued, of June 5, 2004.  This in turn contains a link to a site by Wolfgang Wildgen which contains the following:

“Historically, we may say that the consequence of Bruno’s parallel work on cosmology and artificial memory is a new model of semantic fields which was so radical in its time that the first modern followers (although ignorant of this tradition) are the Von-Neumann automata and the neural net systems of the 1980s (cf. Wildgen 1998: 39, 237f).”

Wildgen, W. 1998. Das kosmische Gedächtnis. Kosmologie, Semiotik und Gedächtniskunst im Werke von Giordano Bruno. Frankfurt/Bern: Lang.

For an applet illustrating
the above remarks, see


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Figure A

Neighborhood in a
Cellular Automaton
by Adam Campbell

For more of the Gedächtnis
in this Kunst, see the following
Google search on shc759:

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Figure B

Note that the reference to “forerunners” in fig. B occurs in a journal entry of June 12, 2002. See also the reference to a journal entry of the following day, June 13, 2002, in last Tuesday’s Dirty Trick.

Those who have viewed Campbell’s applet (see  fig. A) may appreciate the following observation of poet and Dante translator Robert Pinsky:

“… a grid, and a flow–
that is the essence of terza rima….”

Poetry, Computers, and Dante’s Inferno

For some related remarks
on the muses and epic poetry,
see a paper on Walter Benjamin:

“Here the memory (Gedächtnis) means
‘the epic faculty par excellence.’ “
(Benjamin, Der Erzähler, 1936: in
Gesammelte Schriften, 1991, II.2, 453)

Benjamin on Experience,
Narrative, and History

One possible connection to the muses is, as noted in a link in yesterday’s Ado, via George Balanchine.

An apt link to epic poetry (aside from the reference to Dante above) is, via the June 12, 2002, entry, to the epic The Gameplayers of Zan (the third reference in fig. B above).

The applet linked below fig. A very nicely illustrates the “structured chaos” of a space described by automata theory.  For a literary approach to such a space, see the Gameplayers entry.

For the benefit of art critic Robert Hughes, who recently made a distinction between “fast art” and “slow art,” the Campbell applet has a convenient speed control.

Friday, June 25, 2004

Friday June 25, 2004

Filed under: General — m759 @ 2:00 PM


Picture at ICA Big Nothing exhibit

Click on above picture
for some background.

Click on above picture
for some background.

Related material:

A Form (May 22, 2004),
A Form, continued (June 5, 2004),
Balanchine’s Birthday (Jan. 9, 2003),
Pictures of Nothing (Aug. 23, 2003)

Saturday, May 22, 2004

Saturday May 22, 2004

Filed under: General — Tags: — m759 @ 3:00 PM

A Form

John Leonard in the June 10, 2004, New York Review of Books, on E. L. Doctorow:

"… he's got urgent things to say and seeks some form to say them in, or a form that will tease and torture secret meanings out of what he thinks he already knows, or a form, like a wishing well, down which to dream, scream, or drown."

48. The Well

The Judgment

The Well. The town may be changed,
But the well cannot be changed.
It neither decreases nor increases.
They come and go and draw from the well.
If one gets down almost to the water
And the rope does not go all the way,
Or the jug breaks, it brings misfortune.

From the Book of Ecclesiastes 12:6

or ever the silver cord be loosed, or the golden bowl be broken, or the pitcher be broken at the fountain, or the wheel broken at the cistern

From Chuck Polisher's I Ching Lexicon:

See also the following form, discussed in

Balanchine's Birthday
(1/9/03) and in

Art Theory
for Yom Kippur


Wednesday, January 21, 2004

Wednesday January 21, 2004

Filed under: General — m759 @ 8:28 AM


This is the first anniversary of the death of Irene Diamond, patron of the arts, for whom the New York City Ballet’s Diamond Project is named.  (See last year’s entries for January 20-23.)

Since tomorrow is the 100th anniversary of the birth of George Balanchine (according to the Gregorian, or “new style,” calendar), it seems appropriate to recall his ballet Diamonds, though it has no apparent connection with Irene.

Diamonds is the conclusion of a three-part work titled Jewels. (The first two parts are Emeralds, with music by Fauré, and Rubies, with music by Stravinsky.)

” ‘And then for the finale, Diamonds, I move to Tchaikovsky-always Tchaikovsky for dancing.’

Balanchine chose to use Tchaikovsky’s Symphony No. 3 in D major, gracefully cutting the first movement of the piece (by some accounts because it was too long, and by others because he felt it just wasn’t suitable for dancing).”

Jeannine Potter, notes on Jewels 

In other words, Balanchine “cut” Diamonds. For another use of this metaphor, see The Diamond Project.  The following remark on the first movement seems appropriate on this, the anniversary of Irene Diamond’s death.

“The introduction to the first movement of the symphony is marked Moderato assai, Tempo di marcia funebre, the funeral march proceeding with increased pace….”

—  Symphony No. 3 in D Major

The following link to a part of Irene’s year-long funeral march seems appropriate:

Longtime Juilliard Benefactor Dies.

Whether her good deeds made her, like Christ and Gerard Manley Hopkins, an immortal Diamond, I do not know.  Let us hope so.

Sunday, November 2, 2003

Sunday November 2, 2003

Filed under: General,Geometry — Tags: — m759 @ 11:11 AM

All Souls' Day
at the Still Point

From remarks on Denis Donoghue's Speaking of Beauty in the New York Review of Books, issue dated Nov. 20, 2003, page 48:

"The Russian theorist Bakhtin lends his august authority to what Donoghue's lively conversation has been saying, or implying, all along.  'Beauty does not know itself; it cannot found and validate itself — it simply is.' "

From The Bakhtin Circle:

"Goethe's imagination was fundamentally chronotopic, he visualised time in space:

Time and space merge … into an inseparable unity … a definite and absolutely concrete locality serves at the starting point for the creative imagination… this is a piece of human history, historical time condensed into space….

Dostoevskii… sought to present the voices of his era in a 'pure simultaneity' unrivalled since Dante. In contradistinction to that of Goethe this chronotope was one of visualising relations in terms of space not time and this leads to a philosophical bent that is distinctly messianic:

Only such things as can conceivably be linked at a single point in time are essential and are incorporated into Dostoevskii's world; such things can be carried over into eternity, for in eternity, according to Dostoevskii, all is simultaneous, everything coexists…. "

Bakhtin's notion of a "chronotope" was rather poorly defined.  For a geometric structure that might well be called by this name, see Poetry's Bones and Time Fold.  For a similar, but somewhat simpler, structure, see Balanchine's Birthday.

From Four Quartets:

"At the still point, there the dance is."

From an essay by William H. Gass on Malcolm Lowry's classic novel Under the Volcano:

"There is no o'clock in a cantina."

Sunday, April 27, 2003

Sunday April 27, 2003

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


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.

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…

Later the Same Day
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 — m759 @ 8:15 PM


“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?

Saturday, December 7, 2002

Saturday December 7, 2002

Filed under: General — m759 @ 9:30 PM


Shall we read?

From Contact, by Carl Sagan:

  “You mean you could decode a picture hiding in pi
and it would be a mess of Hebrew letters?”
  “Sure.  Big black letters, carved in stone.”
  He looked at her quizzically.
  “Forgive me, Eleanor, but don’t you think
you’re being a mite too… indirect? 
You don’t belong to a silent order of Buddhist nuns. 
Why don’t you just tell your

From The Nation – Thailand
Sat Dec 7 19:36:00 EST 2002:

New Jataka books
blend ethics and art

Published on Dec 8, 2002

“The Ten Jataka, or 10 incarnations of the Lord Buddha before his enlightenment, are among the most fascinating religious stories….

His Majesty the King wrote a marvellous book on the second incarnation of the Lord Buddha…. It has become a classic, with the underlying aim of encouraging Thais to pursue the virtue of perseverance.

For her master’s degree at Chulalongkorn University’s Faculty of Arts, Her Royal Highness Princess Maha Chakri Sirindhorn wrote a dissertation related to the Ten Jataka of the Buddha. Now with the 4th Cycle Birthday of Princess Sirindhorn approaching on April 2, 2003, a group of artists, led by prominent painter Theeraphan Lorpaiboon, has produced a 10-volume set, the “Ten Jataka of Virtues”, as a gift to the Princess.

Once launched on December 25, the “Ten Jataka of Virtues” will rival any masterpiece produced in book form….”

“How much story do you want?” 
— George Balanchine

Tuesday, July 30, 2002

Tuesday July 30, 2002

Filed under: General — Tags: — m759 @ 12:12 AM

Aesthetics of Madness

Admirers of the film "A Beautiful Mind" may be interested in the thoughts of psychotherapist Eric Olson on what he calls the "collage method" of therapy.  The fictional protagonist of "A Beautiful Mind," very loosely based on the real-life mathematician John Nash, displays his madness in a visually striking manner (as required by cinematic art).  He makes enormous collages of published matter in which he believes he has found hidden patterns. 

This fictional character is in some ways more like the real-life therapist Olson than like the real-life schizophrenic Nash.  For an excellent introduction to Olson's world, see the New York Times Magazine article of April 1, 2001, on Olson and on the mysterious death of Olson's father Frank, who worked for the CIA.  Here the plot thickens… the title of the article is "What Did the C.I.A. Do to Eric Olson's Father?

For Olson's own website, see The Frank Olson Legacy Project, which has links to Olson's work on collage therapy.   Viewed in the context of this website, the resemblance of Olson's collages to the collages of "A Beautiful Mind" is, to borrow Freud's expression, uncanny.  Olson's own introduction to his collage method is found on the web page "Theory and therapy."

All of the above resulted from a Google search to see if Arlene Croce's 1993 New Yorker article on Balanchine and Stravinsky, "The Spelling of Agon," could be found online.   I did not find Arlene, but I did find the following, from a collage of quotations assembled by Eric Olson —

"There might be a game in which paper figures were put together to form a story, or at any rate were somehow assembled. The materials might be collected and stored in a scrap-book, full of pictures and anecdotes. The child might then take various bits from the scrap-book to put into the construction; and he might take a considerable picture because it had something in it which he wanted and he might just include the rest because it was there.”

— Ludwig Wittgenstein,
Lectures and Conversations on Aesthetics, Psychology and Religious Belief, 1943/1978

“Not games. Puzzles. Big difference. That’s a whole other matter. All art — symphonies, architecture, novels — it’s all puzzles. The fitting together of notes, the fitting together of words have by their very nature a puzzle aspect. It’s the creation of form out of chaos. And I believe in form.”

Stephen Sondheim
in Stephen Schiff, “Deconstructing Sondheim,”
The New Yorker, March 8, 1993, p. 76.

“God creates, I assemble.”

— George Balenchine [sic]
in Arlene Croce, “The Spelling of Agon,”
The New Yorker, July 12, 1993, p. 91

The aesthetics of collage is, of course, not without its relevance to the creation (or assembly) of weblogs.

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