Friday, March 29, 2013

Where Credit Is Due

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

Ape to Affleck:

Score by Boston Pops.

Backstory credit— Boston Moms:

IMAGE- Christopher Ann Boldt and Patricia Collinge in 'A Liberal Education'

The Dreaming Jewels (continued)

Filed under: General — Tags: , — m759 @ 8:00 AM

In Memoriam

"In the late ’60s, Williams became a friend and confidant
of science fiction writer Philip K. Dick and wrote about
the iconoclastic author in Rolling Stone  in 1974.
Williams eventually completed a biography on Dick
and became his literary executor after the writer’s death
in 1982. He also edited The Complete Stories of
Theodore Sturgeon, Vol. I-XII 

— Yesterday in the Hollywood Reporter —
Pioneering Rock Journalist Paul S. Williams Dies at 64
4:06 PM PDT 3/28/2013 by Mitch Myers

See also Crawdaddy Story and The Dreaming Jewels
in this journal.

Related reading: Yesterday's noon post and Puzzles.

Update of 8:20 AM Good Friday, 2013:

IMAGE- Daily Princetonian, Good Friday, 2013: James Diamond, rabbi and retired director of Princeton's University's Center for Jewish Life. Diamond was killed in a Princeton auto accident Thursday morning at about 9:42 AM ET.

Monday, March 25, 2013

Einsatz für Pessach

Filed under: General — Tags: — m759 @ 6:00 PM

Today's New York Times :

"… potential recruits with the right skills
have too often been heading for business,
and those who do choose government work
often go to the National Security Agency…."

Review: Einsatz in this journal—

IMAGE- German title of 'The Recruit' is 'Der Einsatz'; the MacGuffin is 'Ice 9.'

The German title of "The Recruit" (released Jan. 31, 2003)
is "Der Einsatz." Its MacGuffin is "'Ice 9."

Brightness at Noon

Filed under: General — Tags: — m759 @ 12:00 PM

The two symbols on the monolith from yesterday

Images of time and eternity in a 1x4x9 black monolith

— may, if one likes, be interpreted as standing for
Damnation Morning and for the Windmill of Time
(alternately, as motifs for a ukara cloth).

The above explanation may help those confused by
knight's-move discourse like that described by
Jemima in The Eiger Sanction .

Art Wars:

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

Monolith for Maggie, continued from yesterday

"The young woman counted—
'Otu, abua, ato, ano, ise, isii, asaa'—
using what remained to her of
the secret language…."

— Opening sentence of the prologue to The Choir Boats,
a 2009 novel by Daniel A. Rabuzzi

The piano link in today's previous post suggests a review
of a post from Feb. 11, 2008. That post suggests in turn
a passage from the Trevanian classic The Eiger Sanction
that says, in part…

"Often it was unnecessary to finish a sentence…."

The Dante Prize

Filed under: General — Tags: — m759 @ 7:59 AM

(Damnation Morning, continued)

For the late, great Bebo Valdés, who
reportedly died on Friday in Stockholm:

Trailers from Hell: Joe Dante on 'The Prize'

"Mr. Valdés never returned to Cuba. He played piano
in Stockholm hotel lounges for more than three decades."

— Ben Ratliff in this morning's New York Times

"Heaven for climate, Hell for company."

Tuesday, March 12, 2013

Michael Porter: The Great and Powerful

Filed under: General — Tags: — m759 @ 12:00 PM

Thanks to University Diaries for her link today to an
excellent Forbes  article on management guru Michael Porter.

Related searches (click images to enlarge)—

For some background, see Diamond model in Wikipedia.

The Stewart quoted in Forbes  is Matthew Stewart, author of The Management Myth .

Smoke and Mirrors

Filed under: General,Geometry — Tags: , — m759 @ 7:00 AM

Sistine Chapel Smoke

Tromso Kunsthall Mirrors

Background for the smoke  image:
A remark by Michelangelo in a 2007 post,  High Concept.

Background for the mirrors  image:
Note the publication date— Mar. 10, 2013.

See that date in this journal and related material.


Filed under: General — Tags: — m759 @ 12:00 AM

For the Garden of Good and Evil

(Click image for some backstory.)

Tim Robbins in 'Mystic River'

On Cambridge, Massachusetts:

"By all means accept the invitation to hell,
should it come. It will not take you far—
from Cambridge to hell is only a step;
or at most a hop, skip, and jump.
But now you are evading— you are
dodging the issue… after all,
Cambridge is hell enough."

— Great Circle , a 1933 novel by Conrad Aiken
(father of Joan Aiken, who wrote The Shadow Guests )

Thursday, February 14, 2013

Chapman’s Homer

Filed under: General — Tags: — m759 @ 12:00 PM

(Continued from August 23, 2012)

“Good is a noun. That was it.
That was what Phaedrus had been looking for.
That was the homer over the fence
that ended the ballgame.”

Robert M. Pirsig

But perhaps not a proper  noun.
See the link to Good's Singularity
at the end of today's previous post.

Annals of Quantum Hype

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

Yesterday's link to Aaronson and Turing suggests a review
of events on August 16, 2012 in the light of Log24 on that date.

Exhibit A: New Institute for Quantum Studies at Chapman University—

Exhibit B: The Aug. 16, 2012, death of Chapman University's Indiana Jones—

Whether this Indiana Jones successfully transgressed
the boundaries of space and time, I do not know.

Exhibit C: Related quantum hype— 

Chapman Professor Lands Discover  Cover Story,
Chapman University Happenings, March 18, 2010

See also Good's Singularity.

Tuesday, January 29, 2013

Clash of the Caped Crusaders

Filed under: General — Tags: — m759 @ 2:29 PM

The New Yorker , quoted here yesterday, on a meeting in 1638 of Galileo and Milton—

"… it’s like those comic-book specials in which Superman meets Batman…."

Related news yesterday from The Hollywood Reporter

IMAGE- Producer Lloyd Phillips dies at 63

      Phillips's upcoming Superman film stars Amy Adams.

      Other entertainment:

      Log24 posts from the day of Phillips's death—


Filed under: General — Tags: , — m759 @ 12:00 PM

A sequel to last midnight's post

IMAGE- Inauguration 2013: Schumer, Binder, Beyoncé

See also Midnight Politics and On the Cusp.

Midnight in the Garden

Filed under: General — Tags: — m759 @ 12:00 AM


     For a related essay, click on the image below.


Thursday, January 24, 2013


Filed under: General,Geometry — Tags: — m759 @ 9:01 PM

The title was suggested by an ad for a film that opens
at 10 PM EST today: "Hansel & Gretel: Witch Hunters."

Related material: Grimm Day 2012, as well as
Amy Adams in Raiders of the Lost Tesseract
and in a Film School Rejects page today.

See also some Norwegian art in
Trish Mayo's Photostream today and in
Omega Point (Log24, Oct. 15, 2012)—

Monday, October 15, 2012

Omega Point

m759 @ 2:00 PM 

For Sergeant-Major America—

IMAGE- Art exhibition with 'Omega Point' and geometric figures related to tesseract, along with movie 'Captain America' figure

The image is from posts of Feb. 20, 2011,
and Jan. 27, 2012.

This instance of the omega point is for 
a sergeant major who died at 92 on Wednesday,
October 10, 2012.

See also posts on that date in this journal—

Midnight,  Ambiguation,  Subtitle for Odin's Day,
 and Melancholia, Depression, Ambiguity.

Object Lesson

Filed under: General — Tags: , — m759 @ 7:59 PM

Suggested by yesterday's Garden Path

Commentary by Trish Mayo on a photo at Flickr:

Gazing Globe

These beautiful garden ornaments have a long history, beginning in the 13th century when they were made in Venice, Italy of hand-blown glass. They have been called by many names: Gazing Globe, Garden Globe, Witch Ball, Butler Globe and Globe of Happiness.

Legends formed about the mysterious powers of the globes. They were said to bring happiness, good luck and prosperity to those who owned it, known to ward off evil spirits, misfortune, illness and witches!

Some say the ball should be placed near the entrance to a house so that if a witch came by she would not be able to get past her reflection as she cannot tear herself away from her own image. Other accounts say a witch cannot bear to see her own reflection so she will not come near a "witch’s ball". A witch cannot sneak up on a person gazing into a globe as he can see if a witch approaches from behind. The smaller ball made of colored glass as opposed to the reflective kind was believed to attract and trap evil spirits.

Spiritually speaking, as one peers into the globe he can experience "oneness" with the universe.

The gazing globes practical purposes included being strategically placed on a path near the front entrance so that you could see when someone was coming for a visit. In Victorian times, the "Butler Ball" served as a mirror for servants to see when guests were needing assistance without staring at them throughout the meal. Another practical use was in the foyer of the home. Parents could keep a close eye on their daughter and her date as he bid her goodnight.

Today the globe is used ornamentally, allowing the whole garden, including the sky, to be viewed with one glance.

Under Covers

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

For Amy Adams and Trudie Styler:


Click each cover for some background. See also

Cube Space

Filed under: General — Tags: , — m759 @ 12:24 PM

For the late Cardinal Glemp of Poland,
who died yesterday, some links:

Wednesday, January 9, 2013

Bad Idea

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

For the 2013 Joint Mathematics Meetings in San Diego,
which start today, a cartoon by Andrew Spann—

(Click for larger image.) 

Related remarks:

This journal on the Feast of Epiphany, 2013

"The Tesseract is where it belongs: out of our reach."

The Avengers'  Nick Fury, played by Samuel L. Jackson

Today's New York Times —

"You never know what could happen.
If you have Sam, you’re going to be cool."

— The late David R. Ellis, film director

If anyone in San Diego cares about the relationship
of Spann's plane to Fury's Tesseract, he or she may
consult Finite Geometry of the Square and Cube.

Eve and Cleavage

Filed under: General — Tags: — m759 @ 11:01 AM

From a poem by Frances Frost—

"The upper peak, the shattered rock that cleaves the northward sky
remains alone untaken by the darkness"

— "From a Mountain-Top," The North American Review ,
December 1939 (Vol. 248, No. 2, page 301)

For some material related to the Frost poem,
if only by verbal coincidence, see shattered + rock in this journal.

See also rock + cleavage.

For the relationship to Eve, see New Year's Eve, 2012
and the following image by Karolin Schnoor, who also
illustrated the New York Times  op-ed piece "Catholic
Education, in Need of Salvation
" published online on
Epiphany 2013 (see last evening's Log24 post)—

For some context, see Establishment of the Talented.


Filed under: General — Tags: — m759 @ 4:07 AM

"Catherine, Duchess of Cambridge, is 31."

— The Associated Press this morning, Jan. 9.

See also, in honor of the date of the Duchess's birth—
1982 Jan. 9— Django in this journal.

Tuesday, January 8, 2013

Vermont Throws Itself Together

Filed under: General — Tags: — m759 @ 7:00 PM

"The way, when we climb a mountain,
  Vermont throws itself together"

— Wallace Stevens, "July Mountain"

For another view of reality in New Haven, see the
brief biography of Vermont poet Frances Frost
at the Yale University Library.  From that biography:

"She was survived by her son, the poet Paul Blackburn,
and by her daughter, Sister Marguerite of the Order
of St. Joseph

See also a figure from The New York Times  published
online on Epiphany, 2013:

Star Wars (continued)

Filed under: General — Tags: — m759 @ 12:00 PM

The New York Times  today has an
obituary of poet Harvey Shapiro

See also the following image

'King's Moves' (eight-pointed star, viewed through bars)

  elsewhere in this journal.

Necessary Angel

Filed under: General — Tags: — m759 @ 9:29 AM

Old Stone-Cutter

His gravestones are his everlasting children.
He loves to get his cramped left hand around
the solid faithful feeling of his chisel
and dig the names of those below the ground

or the family names of provident ones above
who cross their fingers and defy the fates
and acknowledge death their enemy and master
by ordering headstones with their birthing dates.

He carves his holy head, a solemn cherub
with granite wings and childish eyes cast down.
Those who prefer a willowed urn, disliking
angels, can go and die in another town.


(From The North American Review , Vol. 248, No. 2,
1939, page 301)

Solemn cherub by Albrecht Dürer in 1514


Filed under: General — Tags: — m759 @ 8:09 AM

IMAGE- Ada Louise Huxtable quotes Arthur Danto on 'tempular space'

Temporal note: The time  of this post, 8:09 AM ET, may be regarded
as a reference to the date  8/09 in the year of our Lord 2010. See also,
in this journal on that date, "Angels in the Architecture (continued)."

Friday, July 13, 2012


Filed under: General — Tags: — m759 @ 5:48 PM

Oscar-winning producer
Richard Zanuck dies at 77

See also today's previous post,
Vanity Fair 's 1996 "Remains of the Dia,"
and english-for-students.com/dia.html.

Click to enlarge


Filed under: General — Tags: — m759 @ 10:25 AM

1940 —

2003 —

"… Conceptualism — suddenly art
could be nothing more than an idea,
a thought on a piece of paper
that played in your head."

— Michael Kimmelman,
    "The Dia Generation,"
    The New York Times Magazine ,
    Sunday, April 6, 2003


Sunday, April 1, 2012

The Palpatine Dimension

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

A physics quote relayed at Peter Woit's weblog today—

"The relation between 4D N=4 SYM and the 6D (2, 0) theory
is just like that between Darth Vader and the Emperor.
You see Darth Vader and you think 'Isn’t he just great?
How can anyone be greater than that? No way.'
Then you meet the Emperor."

— Arkani-Hamed

Some related material from this  weblog—

(See Big Apple and Columbia Film Theory)


The Meno Embedding:


Some related material from the Web—

IMAGE- The Penrose diamond and the Klein quadric

See also uses of the word triality  in mathematics. For instance…

A discussion of triality by Edward Witten

Triality is in some sense the last of the exceptional isomorphisms,
and the role of triality for n = 6  thus makes it plausible that n = 6
is the maximum dimension for superconformal symmetry,
though I will not give a proof here.

— "Conformal Field Theory in Four and Six Dimensions"

and a discussion by Peter J. Cameron

There are exactly two non-isomorphic ways
to partition the 4-subsets of a 9-set
into nine copies of AG( 3,2).
Both admit 2-transitive groups.

— "The Klein Quadric and Triality"

Exercise: Is Witten's triality related to Cameron's?
(For some historical background, see the triality  link from above
and Cameron's Klein Correspondence and Triality.)

Cameron applies his  triality to the pure geometry of a 9-set.
For a 9-set viewed in the context of physics, see A Beginning

From MIT Commencement Day, 2011—

A symbol related to Apollo, to nine, and to "nothing"

A minimalist favicon—

IMAGE- Generic 3x3 square as favicon

This miniature 3×3 square— http://log24.com/log/pix11A/110518-3x3favicon.ico — may, if one likes,
be viewed as the "nothing" present at the Creation. 
See Feb. 19, 2011, and Jim Holt on physics.

Happy April 1.

Monday, March 5, 2012

For the Nine Muses

Filed under: General — m759 @ 1:00 PM

From "The Talented," a post of April 26, 2011—


And for Josefine Lyche

Unity in Multiplicity —

Pink  in Wikipedia

Wednesday, October 12, 2011

High White Noon

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

Grid from a post linked to in yesterday's 24 Hour DeLillo

The 3x3 square

A Study in Art Education

For an example of this grid as slow art , consider the following—

"One can show that the binary tetrahedral group
is isomorphic to the special linear group SL(2,3)—
the group of all 2×2 matrices over the finite field F3
with unit determinant." —Wikipedia

As John Baez has noted, these two groups have the same structure as the geometric 24-cell.

For the connection of the grid to the groups and the 24-cell, see Visualizing GL(2,p).

Related material—

The 3×3 grid has been called a symbol of Apollo (Greek god of reason and of the sun).

"This is where we sat through his hushed hour,
a torchlit sky, the closeness of hills barely visible
at high white noon." — Don DeLillo, Point Omega

Friday, September 9, 2011

A Beginning

Filed under: General — Tags: , — m759 @ 5:29 AM

From MIT Commencement Day, 2011—

A symbol related to Apollo, to nine, and to "nothing"

A minimalist favicon—

IMAGE- Generic 3x3 square as favicon

This miniature 3×3 square— http://log24.com/log/pix11A/110518-3x3favicon.ico — may, if one likes,
be viewed as the "nothing" present at the Creation. 
See Feb. 19, 2011, and Jim Holt on physics.

Saturday, June 18, 2011

Midnight in the Garden (continued)–

Filed under: General — m759 @ 12:00 AM

Tracking Shot

IMAGE- Cinema column dated Oct. 1, 2009

Related material—

IMAGE- Quote from Hoyle's 'October the First is Too Late'

See also this journal's September 2009 posts.

This  post was suggested by today's previous post and by today's NY Lottery.
For some background to the ioncinema.com post numbered 4210 above,
see, in conjunction with the page headed "Azazel" linked to here earlier today,
the ioncinema.com post numbered 5601.

“Stranger, dreams verily are baffling and unclear of meaning,
and in no wise do they find fulfillment in all things for men.

For two are the gates of shadowy dreams,
and one is fashioned of horn and one of ivory.
Those dreams that pass through the gate of sawn ivory
deceive men, bringing words that find no fulfillment.
But those that come forth through the gate of polished horn
bring true issues to pass, when any mortal sees them.

But in my case it was not from thence, methinks,
that my strange dream came.”

Homer, Odyssey , Book 19

Translation by A.T. Murray, in two volumes.
Harvard University Press, 1919

Quoted in a press release for the film "Two Gates of Sleep."

From the post numbered 460 in this  journal—

At the still point… from the film "Absolute Power" :

IMAGE- Gene Hackman and Judy Davis dance in 'Absolute Power'
Photo credit – Graham Kuhn

I’ve heard of affairs that are strictly plutonic,
But diamonds are a girl’s best friend!

Marilyn Monroe, modeling a Freudian slip

Friday, June 3, 2011


Filed under: General — m759 @ 7:59 AM

Today is Commencement Day at MIT.

“To measure the changes
     of time and space
the smartest are nothing.”

— Shing-Tung Yau,
 The Emperor of Math
and Harvard philosopher

To measure the changes:

The image “http://www.log24.com/log/pix06A/061017-Yellowbook3.jpg” cannot be displayed, because it contains errors.

The smartest are nothing:

The image “http://www.log24.com/log/pix06A/061017-Gump2A.jpg” cannot be displayed, because it contains errors.

Well, perhaps not quite nothing.

The above pictures were posted here on the day the following book was published—


The lives of the nine Jews in the above book amount to more than Yau's "nothing."

Note, however, that claims by Jews (see Jill Abramson yesterday
that their secular publications constitute a substitute for religion
and contain only "absolute truth" should be viewed with at least one
raised eyebrow.

Abramson's remark yesterday that her promotion to New York Times  executive editor
was like "ascending to Valhalla" had a religious flavor worthy of yesterday's
Feast of the Ascension.

In related news from yesterday's Times

IMAGE- 'Fearless Ascent, as a God or a Jet' -NYT

See also a symbol related to Apollo, to nine, and to "nothing"

A minimalist 3×3 matrix favicon—


This may, if one likes, be viewed as the "nothing"
present at the Creation.  See Jim Holt on physics.

Tuesday, April 26, 2011

The Talented

Filed under: General — m759 @ 3:00 AM

"It's going to be accomplished in steps, this establishment of the Talented in the scheme of things."
— Anne McCaffrey, Radcliffe ’47, To Ride Pegasus

"Character, as we have stated, is revealed through action.
We are not yet telepathic; we must embody even the most intellectual traits
and express them physically."
The Craftsmen of Dionysus: An Approach to Acting  by Jerome Rockwood


Dionysus Meets Apollo
in "Thirty Two Short Films About Glenn Gould"—

Step I — Tiny Dancer in My Hand (0.48.46)


Step II — The Bridge (0.52.46)


Step III — Liftoff (1.27.37)


Sunday, April 17, 2011

Sunday School

Filed under: General,Geometry — Tags: — m759 @ 7:00 AM

Apollo and the Tricksters

From The Story of N (Oct. 15, 2010)—

Roberta Smith on what she calls "endgame art"—

"Fear of form above all means fear of compression— of an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible."

Margaret Atwood on tricksters and art—

"If it’s a seamless whole you want, pray to Apollo."

Here is some related material In memory of CIA officer Clare Edward Petty, who died at 90 on March 18—

A review of a sort of storyteller's MacGuffin — the 3×3 grid. This is, in Smith's terms, an "artistic focus" that appears  to be visually comprehensible but is not as simple as it seems.

The Hesse configuration can serve as more than a sort of Dan Brown MacGuffin. As a post of January 14th notes, it can (rather fancifullly) illustrate the soul—


" … I feel I understand
Existence, or at least a minute part
Of my existence, only through my art,
In terms of combinational delight…."

— Vladimir Nabokov, Pale Fire

Saturday, January 8, 2011

True Grid (continued)

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM

"Rosetta Stone" as a Metaphor
  in Mathematical Narratives

For some backgound, see Mathematics and Narrative from 2005.

Yesterday's posts on mathematics and narrative discussed some properties
of the 3×3 grid (also known as the ninefold square ).

For some other properties, see (at the college-undergraduate, or MAA, level)–
Ezra Brown, 2001, "Magic Squares, Finite Planes, and Points of Inflection on Elliptic Curves."

His conclusion:

When you are done, you will be able to arrange the points into [a] 3×3 magic square,
which resembles the one in the book [5] I was reading on elliptic curves….

This result ties together threads from finite geometry, recreational mathematics,
combinatorics, calculus, algebra, and number theory. Quite a feat!

5. Viktor Prasolov and Yuri Solvyev, Elliptic Functions and Elliptic Integrals ,
    American Mathematical Society, 1997.

Brown fails to give an important clue to the historical background of this topic —
the word Hessian . (See, however, this word in the book on elliptic functions that he cites.)

Investigation of this word yields a related essay at the graduate-student, or AMS, level–
Igor Dolgachev and Michela Artebani, 2009, "The Hesse Pencil of Plane Cubic Curves ."

From the Dolgachev-Artebani introduction–

In this paper we discuss some old and new results about the widely known Hesse
  of 9 points and 12 lines in the projective plane P2(k ): each point lies
on 4 lines and each line contains 3 points, giving an abstract configuration (123, 94).

PlanetMath.org on the Hesse configuration


A picture of the Hesse configuration–

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

(See Visualizing GL(2,p), a note from 1985).

Related notes from this journal —

From last November —

Saturday, November 13, 2010


m759 @ 10:12 PM

From the December 2010 American Mathematical Society Notices


Related material from this  journal—

Mathematics and Narrative and

Consolation Prize (August 19, 2010)

From 2006 —

Sunday December 10, 2006


 m759 @ 9:00 PM

A Miniature Rosetta Stone:

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

“Function defined form, expressed in a pure geometry
that the eye could easily grasp in its entirety.”

– J. G. Ballard on Modernism
(The Guardian , March 20, 2006)

“The greatest obstacle to discovery is not ignorance –
it is the illusion of knowledge.”

— Daniel J. Boorstin,
Librarian of Congress, quoted in Beyond Geometry

Also from 2006 —

Sunday November 26, 2006


m759 @ 7:26 AM

Rosalind Krauss
in "Grids," 1979:

"If we open any tract– Plastic Art and Pure Plastic Art  or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.

Or, to take a more up-to-date example…."

"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
The Club Dumas ,1993

"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
Robert Plant ,1971

The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.

An example of the universal*– or, according to Krauss,
a "staircase" to the universal– is the ninefold square:

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    

For more on the field of reason, see
Log24, Oct. 9, 2006.

A reasonable set of "strange correspondences"
in the garden of Apollo has been provided by
Ezra Brown in a mathematical essay (pdf).

Unreason is, of course, more popular.

* The ninefold square is perhaps a "concrete universal" in the sense of Hegel:

"Two determinations found in all philosophy are the concretion of the Idea and the presence of the spirit in the same; my content must at the same time be something concrete, present. This concrete was termed Reason, and for it the more noble of those men contended with the greatest enthusiasm and warmth. Thought was raised like a standard among the nations, liberty of conviction and of conscience in me. They said to mankind, 'In this sign thou shalt conquer,' for they had before their eyes what had been done in the name of the cross alone, what had been made a matter of faith and law and religion– they saw how the sign of the cross had been degraded."

– Hegel, Lectures on the History of Philosophy ,
   "Idea of a Concrete Universal Unity"

"For every kind of vampire,
there is a kind of cross."
– Thomas Pynchon   

And from last October —

Friday, October 8, 2010


m759 @ 12:00 PM

Starting Out in the Evening
… and Finishing Up at Noon

This post was suggested by last evening's post on mathematics and narrative and by Michiko Kakutani on Vargas Llosa in this morning's New York Times .



Above: Frank Langella in
"Starting Out in the Evening"

Right: Johnny Depp in
"The Ninth Gate"


"One must proceed cautiously, for this road— of truth and falsehood in the realm of fiction— is riddled with traps and any enticing oasis is usually a mirage."

– "Is Fiction the Art of Lying?"* by Mario Vargas Llosa,
    New York Times  essay of October 7, 1984

* The Web version's title has a misprint—
   "living" instead of "lying."

"You've got to pick up every stitch…"

Monday, December 13, 2010

Plan 9 Revisited

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

Leading today's New York Times  obituaries —


— is that of Nassos Daphnis, a painter of geometric abstractions
who in 1995 had an exhibition at a Leo Castelli gallery
titled "Energies in Outer Space." (See pictures here.)

Daphnis died, according to the Times, on November 23.
See Art Object, a post in this journal on that date—

There is more than one way
to look at a cube.


Some context— this morning's previous post (Apollo's 13,
on the geometry of the 3×3×3 cube), yesterday's noon post
featuring the 3×3 square grid (said to be a symbol of Apollo),

The 3x3 square

and, for connoisseurs of the Ed Wood school of cinematic art,
a search in this journal for the phrase "Plan 9."

You can't make this stuff up.

Mathematics and Narrative continued…

Filed under: General,Geometry — m759 @ 7:20 AM

Apollo's 13: A Group Theory Narrative —

I. At Wikipedia —


II. Here —

See Cube Spaces and Cubist Geometries.

The 13 symmetry axes of the (Euclidean) cube–
exactly one axis for each pair of opposite
subcubes in the 27-part (Galois) 3×3×3 cube–

The 13 symmetry axes of the cube

A note from 1985 describing group actions on a 3×3 plane array—


Undated software by Ed Pegg Jr. displays
group actions on a 3×3×3 cube that extend the
3×3 group actions from 1985 described above—

Ed Pegg Jr.'s program at Wolfram demonstrating concepts of a 1985<br />
note by Cullinane

Pegg gives no reference to the 1985 work on group actions.

Thursday, August 19, 2010

Consolation Prize

Filed under: General,Geometry — Tags: — m759 @ 9:04 AM

For Kathrin Bringmann, who has been mentioned as a possible candidate for a Fields Medal.

The four Fields medal winners were announced today at the International Congress of Mathematicians in Hyderabad, India. Bringmann was not among them.

Bringmann was, however, the winner of the 2009 SASTRA Ramanujan Prize

See The Hindu  of September 30, 2009 and this journal on that date

Motto of Plato's Academy: 'Let no one ignorant of geometry enter'

The 3x3 grid

A Symbol of Apollo

For more about Bringmann's work, see an article on what has been called Ramanujan's "final problem."

For another problem with a claim to this title, see "Mathematician Untangles Legendary Problem" and search in this journal for Dyson + crank.

Sunday, July 18, 2010

Today’s Sermon

Filed under: General — m759 @ 11:00 AM

New York Lottery on Saturday, July 17, 2010—

Midday 049, Evening 613.

Related material:

Hexagram 49 and 6/13.

A quotation from this journal on 6/13

"Christianity offers the critic a privileged ontological window…."

Aaron Urbanczyk's 2005 review of Christ and Apollo 
by William Lynch, S.J., a book first published in 1960

Picture from today's New York Times  (page ST1 in New York edition)—


Sunday, June 13, 2010

Sunday School

Filed under: General — m759 @ 9:00 AM

What on earth is a 'concrete universal'?"
Said to be an annotation (undated)
by Robert M. Pirsig of A History of Philosophy,
by Frederick Copleston, Society of Jesus.

From Aaron Urbanczyk's 2005 review of Christ and Apollo  by William Lynch, S.J., a book first published in 1960—

"Lynch's use of analogy vis-a-vis literature provides, in a sense, a philosophical basis to the theoretical paradox popularized by W. K. Wimsatt (1907-1975), which contends that literature is a sort of 'concrete universal.'"

The following figure has often been
offered in this journal as a symbol of Apollo

Image-- 3x3 array of white squares

Arguments that it is, rather, a symbol of Christ
may be left to the Society of Jesus.

One possible approach—
Urbanczyk's review says that
"Christianity offers the critic
   a privileged ontological window…."

"The world was warm and white when I was born:
Beyond the windowpane the world was white,
A glaring whiteness in a leaded frame,
Yet warm as in the hearth and heart of light."

Delmore Schwartz

Saturday, March 13, 2010

Space Cowboy

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

From yesterday's Seattle Times

According to police, employees of a Second Avenue mission said the suspect, clad in black and covered in duct tape, had come into the mission "and threatened to blow the place up." He then told staffers "that he was a vampire and wanted to eat people."

The man… also called himself "a space cowboy"….

This suggests two film titles…

Plan 9 from Outer Space

Rebecca Goldstein and a Cullinane quaternion

and Apollo's 13

The 13 symmetry axes of the (Euclidean) cube–
exactly one axis for each pair of opposite
  subcubes in the (Galois) 3×3×3 cube–

The 13 symmetry axes of the cube

Wednesday, September 30, 2009

Wednesday September 30, 2009

Filed under: General,Geometry — m759 @ 9:48 AM

Midnight in the Garden, Autumn 2009



Der Einsatz

Motto of Plato's Academy: 'Let no one ignorant of geometry enter'

The Ninefold Square (a 3x3 grid)

The New York Times Magazine
on Sunday, Sept. 20, 2009:

From this journal on the following day, Sept. 21:

Pearl Jam 'Backspacer' album released Sept. 20, 2009

Happy birthday, Stephen King.

Today's previous entry is based on a song, "Unthought Known,"
from the above album; the cover of the album uses the 3×3 grid
shown in Sept. 20's midnight review. For related material
on the unconscious, see June 13-15, 2005.

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

Thursday, February 19, 2009

Thursday February 19, 2009

Filed under: General — m759 @ 7:07 AM

A Sunrise
for Sunrise

"If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World, for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete."

Rosalind Krauss, "Grids"

Yesterday's entry featured a rather simple-minded example from Krauss of how the ninefold square (said to be a symbol of Apollo)

The 3x3 grid

may be used to create a graphic design– a Greek cross, which appears also in crossword puzzles:

Crossword-puzzle design that includes Greek-cross elements

Illustration by
Paul Rand
(born Peretz Rosenbaum)

A more sophisticated example
of the ninefold square
in graphic design:

"That old Jew
gave me this here."

— A Flag for Sunrise  

The 3x3 grid as an organizing frame for Chinese calligraphy. Example-- the character for 'sunrise'
From Paul-Rand.com

Wednesday, January 21, 2009

Wednesday January 21, 2009

Filed under: General — m759 @ 12:00 PM

Harvard Divinity School logo

“… while some are elected,
others not elect are
passed by….”

A commentary on the
Calvinist doctrine of preterition

Gravity’s Rainbow, Penguin Classics, 1995, page 742:

“… knowing his Tarot, we would expect to look among the Humility, among the gray and preterite souls, to look for him adrift in the hostile light of the sky, the darkness of the sea….

Now there’s only a long cat’s-eye of bleak sunset left over the plain tonight, bright gray against a purple ceiling of clouds, with an iris of


“God is the original
conspiracy theory.”

Pynchon’s Paranoid History

“We remain a young nation, but in the words of Scripture, the time has come to set aside childish things.”

— President Obama yesterday

It is not entirely clear what these “childish things” are. Perhaps the young nation’s “childish things” that the new President refers to are part of what Robert Stone memorably called “our secret culture.” Stone was referring to Puritanism, which some advocates of the new religion of Scientism might call “childish.” I do not. Lunatic, perhaps, but not childish.

Related meditations:

A year ago yesterday, on Sunday, Jan. 20, 2008, the mid-day lottery for New York State was 605.

A midrash in the Judeo-Christian tradition of paranoia a year ago today suggested that 605 might be a veiled reference to “God, the Devil, and a Bridge,” a weblog entry on mathematician André Weil.

Continuing in this vein a year later, we are confronted with the mid-day New York lottery for yesterday:


Taking a hint from another
entry on Weil, this may be
regarded as a reference to
The Oxford Book of
English Verse
(1919 edition):

Selection 742 in that book
comports well with this
jounal’s recent meditations
on death and Brooklyn:

742: The Imprisoned Soul

“Let me glide noiselessly forth;  
With the key of softness
     unlock the locks….”

— Walt Whitman

Applying this method of
exegesis to last year’s
lottery, we have

605: Hymn of Pan

“And all that did then
    attend and follow,
Were silent with love,
    as you now, Apollo,
With envy of
    my sweet pipings.”

“In time, his carefree lifestyle began to upset the early Christians, who saw his earthy temptations as a manifestation of the Devil. Who would’ve thought that the horny old goat would become the blueprint for popular conceptions of Satan– cloven hooves, horns and all?”

Pan: God of Shepherds, Flocks, and Fornication

Hymn 605 thus supplies a reference to the devil mentioned by Weil in the entry of 6/05.

It, together with Hymn 742 of a year later, may be regarded as a divine response to a weblog entry yesterday from the Greater Wasilla Area on listening to the inauguration:

“… thus far, I have not heard any priests of Apollo, nor of any other God, issuing any auguries.”

Neither have I, but hearing is only one of the senses.

“Heard melodies are sweet,
    but those unheard
Are sweeter.”

— John Keats

Wednesday, December 10, 2008

Wednesday December 10, 2008

Filed under: General — m759 @ 9:00 PM

ho anax, hou to manteion esti
to en Delphois, oute legei oute
alla sêmainei

Heraclitus, DK 22 B 93,

The lord whose oracle is
at Delphi neither reveals nor
 conceals, but gives a sign.

A sign, perhaps of the sort
given by Apollo’s oracle:

Road sign with double arrow pointing both left and right

Click on the sign for further details.

Related material:

This week’s New Yorker

Cartoon sign-- enlightenment one way, sandals the other

… as well as   
  today’s previous entry —
Symbol,” discussing Apollo
and a web page
by Nick Wedd —
and Wedd’s home page,
which states that
“I have now found a
  source of Polish sandals.”

Saturday, November 8, 2008

Saturday November 8, 2008

Filed under: General — m759 @ 10:30 AM
Roman Religion

Pope Benedict XVI, formerly the modern equivalent of The Grand Inquisitor


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.”

Tom O’Bedlam:

I know more than Apollo….


“The lapis manalis (Latin: ‘stone of the Manes‘) was a name given to two sacred stones used in the Roman religion. One covered a gate to Hades, abode of the dead….

One such stone covered the mundus Cereris, a pit thought to contain an entrance to the underworld….

The… mundus was located in the Comitium, on the Palatine Hill. This stone was ceremonially opened three times a year, during which spirits of the blessed dead (the Manes) were able to commune with the living. The three days upon which the mundus was opened were August 24, October 5, and November 8. Fruits of the harvest were offered to the dead at this time.”

Related material:

Log24 on      
August 24,     
October 5, and
November 8.  

Sunday, October 5, 2008

Sunday October 5, 2008

Filed under: General — Tags: — m759 @ 4:23 PM
Nash Equilibrium or:
To Make a Short Story Long

Last night's entry presented a
short story summarized by
four lottery numbers.

Today's mid-day lotteries
and associated material:

Pennsylvania, 201– i.e., 2/01:
Kindergarten Theology

Theologian James Edwin Loder:

"In a game of chess, the knight's move is unique because it alone goes around corners. In this way, it combines the continuity of a set sequence with the discontinuity of an unpredictable turn in the middle. This meaningful combination of continuity and discontinuity in an otherwise linear set of possibilities has led some to refer to the creative act of discovery in any field of research as a 'knight's move' in intelligence."

New York, 229– i.e., 2/29:
I Have a Dreamtime

"One must join forces with friends of like mind"

Related material:

Terence McKenna:

"Schizophrenia is not a psychological disorder peculiar to human beings. Schizophrenia is not a disease at all but rather a localized traveling discontinuity of the space time matrix itself. It is like a travelling whirl-wind of radical understanding that haunts time. It haunts time in the same way that Alfred North Whitehead said that the color dove grey 'haunts time like a ghost.'"

Anonymous author:

"'Knight's move thinking' is a psychiatric term describing a thought disorder where in speech the usual logical sequence of ideas is lost, the sufferer jumping from one idea to another with no apparent connection. It is most commonly found in schizophrenia."

Star Wars:
John Nash, as portrayed by Russell Crowe

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

For more on the sleep of Apollo,
see the front page of today's
New York Times Book Review.

Garrison Keillor's piece there,
"Dying of the Light," is
about the fear of death felt
by an agnostic British twit.

For relevant remarks by
a British non-twit, see
William Dunbar–

Timor Mortis conturbat me.

Saturday, March 10, 2007

Saturday March 10, 2007

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

The Logic of Dreams

From A Beautiful Mind–

“How could you,” began Mackey, “how could you, a mathematician, a man devoted to reason and logical proof…how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you…?”

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. “Because,” Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, “the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”


The image “http://www.log24.com/log/pix07/070309-NYlottery.jpg” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix07/070309-PAlottery.jpg” cannot be displayed, because it contains errors.

These numbers may, in the mad way so well portrayed by Sylvia Nasar in the above book, be regarded as telling a story… a story that should, of course, not be taken too seriously.

Friday’s New York numbers (midday 214, evening 711) suggest the dates 2/14 and 7/11.  Clicking on these dates will lead the reader to Log24 entries featuring, among others, T. S. Eliot and Stephen King– two authors not unacquainted with the bizarre logic of dreams.

A link in the 7/11 entry leads to a remark of Noel Gray on Plato’s Meno and “graphic austerity as the tool to bring to the surface, literally and figuratively, the inherent presence of geometry in the mind of the slave.”

Also Friday: an example of graphic austerity– indeed, Gray graphic austerity– in Log24:

Chessboard (Detail)

This illustration refers to chess rather than to geometry, and to the mind of an addict rather than to that of a slave, but chess and geometry, like addiction and slavery, are not unrelated.

Friday’s Pennsylvania numbers, midday 429 and evening 038, suggest that the story includes, appropriately enough in view of the above Beautiful Mind excerpt, Mackey himself.  The midday number suggests the date 4/29, which at Log24 leads to an entry in memory of Mackey.

(Related material: the Harvard Gazette of April 6, 2006, “Mathematician George W. Mackey, 90: Obituary“–  “A memorial service will be held at Harvard’s Memorial Church on April 29 at 2 p.m.“)

Friday’s Pennsylvania evening number 038 tells two other parts of the story involving Mackey…

As Mackey himself might hope, the number may be regarded as a reference to the 38 impressive pages of Varadarajan’s “Mackey Memorial Lecture” (pdf).

More in the spirit of Nash, 38 may also be taken as a reference to Harvard’s old postal address, Cambridge 38, and to the year, 1938, that Mackey entered graduate study at Harvard, having completed his undergraduate studies at what is now Rice University.

Returning to the concept of graphic austerity, we may further simplify the already abstract chessboard figure above to obtain an illustration that has been called both “the field of reason” and “the Garden of Apollo” by an architect, John Outram, discussing his work at Mackey’s undergraduate alma mater:

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

Let us hope that Mackey,
a devotee of reason,
is now enjoying the company
of Apollo rather than that of
Tom O’Bedlam:

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

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

Sunday, December 10, 2006

Sunday December 10, 2006

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

"Like all men of the Library,
I have traveled in my youth."
— Jorge Luis Borges,
The Library of Babel

"Papá me mandó un artículo
de J. G. Ballard en el que
se refiere a cómo el lugar
de la muerte es central en
nuestra cultura contemporánea

— Sonya Walger,
interview dated September 14
(Feast of the Triumph of the Cross),
Anno Domini 2006

The image “http://www.log24.com/log/pix06B/061210-Quest.gif” cannot be displayed, because it contains errors.

Sonya Walger,
said to have been
born on D-Day,
the sixth of June,
in 1974


Walger's father is, like Borges,
from Argentina.
She "studied English Literature
at Christ Church College, Oxford,
where she received
    a First Class degree…. "


"… un artículo de J. G. Ballard…."–

A Handful of Dust
, by J. G. Ballard

(The Guardian, March 20, 2006):

"… The Atlantic wall was only part of a huge system of German fortifications that included the Siegfried line, submarine pens and huge flak towers that threatened the surrounding land like lines of Teutonic knights. Almost all had survived the war and seemed to be waiting for the next one, left behind by a race of warrior scientists obsessed with geometry and death.

Death was what the Atlantic wall and Siegfried line were all about….

… modernism of the heroic period, from 1920 to 1939, is dead, and it died first in the blockhouses of Utah beach and the Siegfried line…

Modernism's attempt to build a better world with the aid of science and technology now seems almost heroic. Bertolt Brecht, no fan of modernism, remarked that the mud, blood and carnage of the first world war trenches left its survivors longing for a future that resembled a white-tiled bathroom.  Architects were in the vanguard of the new movement, led by Le Corbusier and the Bauhaus design school. The old models were thrown out. Function defined form, expressed in a pure geometry that the eye could easily grasp in its entirety."

The image “http://www.log24.com/theory/images/motto2.jpg” cannot be displayed, because it contains errors.
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 

(Click on picture for details.)

The image “http://www.log24.com/log/pix06B/061210-Holl.gif” cannot be displayed, because it contains errors.
The Left Hand of God, by Adolf Holl

Related material:

The Lottery of Babylon
the previous entry.

Monday, December 4, 2006

Monday December 4, 2006

Filed under: General — m759 @ 11:01 AM
Descent of the God

The image “http://www.log24.com/log/pix06B/061204-Theo2.gif” cannot be displayed, because it contains errors.

Related material:

All Hallows’ Eve,


The image “http://www.log24.com/log/pix05B/Gameplayers12.jpg” cannot be displayed, because it contains errors.

as well as

C. S. Lewis,
That Hideous Strength,
Chapter 15,
“The Descent of the Gods,”

Charles Williams,
The Carol of Amen House“:

Beauty arose of old
And dreamed of a perfect thing,
Where none shall be angry or cold
Or armed with an evil sting;

Where the world shall be made anew,
For the gods shall breathe its air,
And Phoebus Apollo there-through
Shall move on a golden stair.

(For the musical score, see
The Masques of Amen House.)

See also
A Mass for Lucero.

Monday, October 9, 2006

Monday October 9, 2006

Filed under: General,Geometry — 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

Saturday, September 16, 2006

Saturday September 16, 2006

Filed under: General — m759 @ 11:07 AM

Pandora's Box

Part I:
The Pandora Cross

"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"

The image “http://www.log24.com/log/pix06A/060916-Art.jpg” cannot be displayed, because it contains errors.

(See Log24, Sept. 13)

Part II:
The Opening

Remarks by the Pope on Sept. 12,
as reported by the Vatican:

Faith, Reason, and the University:
Memories and Reflections

For the result of
the Pope's remarks, see
a transcript of
 yesterday's Google News
and the following
from BBC today:

The image “http://www.log24.com/log/pix06A/060916-Benedict16.jpg” cannot be displayed, because it contains errors.
Click to enlarge the screenshot.

Part III:

The New Yorker (issue of June 5, 2006) on the late Oriana Fallaci:

"In September [2005], she had a private audience with Pope Benedict XVI at Castel Gandolfo, his summer residence outside Rome. She had criticized John Paul II for making overtures to Muslims, and for not condemning terrorism heartily enough, but she has hopes for Joseph Ratzinger."

For further details, see yesterday's Log24.

Part IV:
The Sibyl's Song

The image “http://www.log24.com/log/pix06A/060916-MC7.GIF” cannot be displayed, because it contains errors.

— From The Magic Circle,
 a spiritual narrative
 by Katherine Neville

For more on "the long-mute voice
of the past," on "darkness beneath
the volcano," and on uncorking,
see Glory Season and Harrowing.

Related material from
Log24 on Dec. 2, 2005:

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."

A symbol of Apollo:

IMAGE- The ninefold square

and a related
Christian symbol,

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

the Greek Cross
(adapted from
Ad Reinhardt).

Moral of the Pandora Cross:

"Nine is a very powerful Nordic number."
— Katherine Neville in The Magic Circle…

quoted in The Nine, a Log24 entry
for Hermann Weyl's birthday,
November 9, 2004.

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.

Wednesday, February 8, 2006

Wednesday February 8, 2006

Filed under: General — m759 @ 5:11 PM
For Grammy Night

From A Mass for Lucero:

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

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

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

The image “http://www.log24.com/log/pix06/060208-Scarlett.jpg” cannot be displayed, because it contains errors.

Apolline Contemplation

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

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

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.

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

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

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),


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


"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

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.

Thursday, April 22, 2004

Thursday April 22, 2004

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


"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:

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

of the 4×4 square

The Grid of Time

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 

Wednesday 15 January 2003

"The invocation of the Lord is relentless…."


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


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.

Friday, April 25, 2003

Friday April 25, 2003

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


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

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.

Friday, January 31, 2003

Friday January 31, 2003

Filed under: General — Tags: , — m759 @ 6:20 PM

Irish Fourplay

"…something I once heard Charles M. Schulz say, 'Don't worry about the world coming to an end today. It's already tomorrow in Australia.'"

 — William F. House

"Forewarned is four-armed."

— Folk saying


The painting at left is by Mary B. Kelly, a 1958 graduate of Saint Mary-of-the-Woods College.

Kelly is an expert on portrayals of Goddess figures in art

Today in Australia is February First, the feast of St. Bridget.  As several websites note, St. Bridget is a combination of Christian saint and Goddess figure… rather like St. Sara (patron saint of Gypsies, also known as Kali) or like Sara Pezzini in the classic TV series "Witchblade."

"Aww… Irish foreplay."

— Sara Pezzini in Witchblade, Episode 6

"Mighty in the gift of purity
She was pleasing unto the Bridegroom on high."

Song of St. Bridget

"Brace yourself, Bridget."

— Definition of Irish foreplay


Saint Bridget's Cross:

Four people can form this cross by joining hands as shown.  Of course, a Goddess like Kali (shown above) or Sara Pezzini could do it all by herself.


For futher details, see The Swastika Goddess,  the history of Jews and the Roman Catholic Church, and the history of Irish neutrality in World War II.

Postscript  of 11 PM

The Goddess Bridget in Literature

The Goddess Bridget (or Brigid) is incarnated in two classic works of American literature —

  • The American patriot and Communist Party supporter Dashiell Hammett gave an unflattering portrayal of Brigid (O'Shaughnessy) in The Maltese Falcon.  For a Jungian analysis of the relationship between Sam Spade and Brigid, see the perceptive remarks of Ryan Benedetti:

"In Jungian terms, Brigid becomes a projection of Spade's anima, a contrasexual replica of his own face as expressed in someone of the opposite sex.

Spade wears a variety of masks in his work. Masking allows him to get underneath the scam most clients lay on him. He is closer to the darker side of his unconscious than any of the other characters in the book, and he is so, because of his role as shamus. His function in his society is to expose all of the underlying darkness of the human psyche."

One way of looking at animus and anima is through the following archetypes:

A diamond and its dual "whirl" figure —
or a "jewel-box and its mate"

  • Mark Twain, in Life on the Mississippi, describes the way Goddess Bridget (again, O'Shaughnessy) arranged the conveyance of her late husband to the next world:

 "D'ye mane to soy that Bridget O'Shaughnessy bought the mate to that joo-ul box to ship that dhrunken divil to Purgatory in?"

"Yes, madam."

"Then Pat shall go to heaven in the twin to it, if it takes the last rap the O'Flaherties can raise!"

Friday January 31, 2003

Filed under: General — Tags: — m759 @ 6:20 AM

John O'Hara's Birthday

"We stopped at the Trocadero and there was hardly anyone there.  We had Lanson 1926.  'Drink up, sweet.  You gotta go some.  How I love music.  Frère Jacques, Cuernavaca, ach du lieber August.  All languages.  A walking Berlitz.  Berlitz sounds like you with that champagne, my sweet, or how you're gonna sound.'"

— John O'Hara, Hope of Heaven, Chapter 11, 1938

"And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance."

Acts, Chapter 2, Verse 4

"Lps. The keys to. Given! A way a lone a last a loved a long the


— James Joyce, conclusion of Finnegans Wake

"Using illustrative material from religion, myth, and culture, he starts with the descent of the dove on Jesus and ends with the poetic ramblings of James Joyce."

Review of a biography of the Holy Spirit

Illustration added at 3:21 AM Feb. 3, 2003:


Available for $220 from
 Worship Banners

Wednesday, October 9, 2002

Wednesday October 9, 2002

Filed under: General — m759 @ 5:01 PM


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.


Clark Art Institute

Nymphs and Satyr


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.


  • 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.

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.

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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