Log24

Sunday, February 12, 2017

Colorful Tales

Filed under: General — Tags: — m759 @ 1:23 pm

“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”

— Hermann Weyl, Philosophy of  Mathematics and
    Natural Science 
, Princeton, 1949, p. 237

Harvard University Press on the late Angus Fletcher, author of
The Topological Imagination  and Colors of the Mind

From the Harvard webpage for Colors of the Mind

Angus Fletcher is one of our finest theorists of the arts,
the heir to I. A. Richards, Erich Auerbach, Northrop Frye.
This… book…  aims to open another field of study:
how thought— the act, the experience of thinking—
is represented in literature.

. . . .

Fletcher’s resources are large, and his step is sure.
The reader samples his piercing vision of Milton’s

Satan, the original Thinker,
leaving the pain of thinking
as his legacy for mankind.

A 1992 review by Vinay Dharwadker of Colors of the Mind —

See also the above word "dianoia" in The Echo in Plato's Cave.
Some context 

This post was suggested by a memorial piece today in
the Los Angeles Review of Books

A Florilegium for Angus Fletcher

By Kenneth Gross, Lindsay Waters, V. N. Alexander,
Paul Auster, Harold Bloom, Stanley Fish, K. J. Knoespel,
Mitchell Meltzer, Victoria Nelson, Joan Richardson,
Dorian Sagan, Susan Stewart, Eric Wilson, Michael Wood

Fletcher reportedly died on November 28, 2016.

"I learned from Fletcher how to apprehend
the daemonic element in poetic imagination."

— Harold Bloom in today's Los Angeles florilegium

For more on Bloom and the daemonic, see a Log24 post,
"Interpenetration," from the date of Fletcher's death.

Some backstory:  Dharwadker in this journal.

Wednesday, February 8, 2017

Damning

Filed under: General — m759 @ 9:42 pm

BuzzFeed, Tuesday, January 10, 2017, on "the damning letter"—

From the Jan. 10 BuzzFeed story

At the time of the hearing, Judiciary Committee Chairman Strom Thurmond never put the letter into the congressional record, and its contents remained largely unknown. In the only line that was made public at the time — published in June 1986 by Knight Ridder reporter Aaron Epstein — King made clear her opposition to Sessions’ nomination.

“For a century, the racial practices that characterized our region were established and enforced by men who, like Mr. Sessions, protested that they, too, were not personally hostile to blacks,” King’s letter said, according to Epstein’s dispatch.

A searchable text of the alleged 1986 letter, along with the
alleged attached statement, is now available at
https://www.aol.com/article/news/2017/02/08/
coretta-scott-kings-letter-opposing-jeff-sessions-1986-full-text/21709762/
.

A search of the letter and statement at that webpage yields
no instances of the phrases "racial practices," "established and enforced,"
or "personally hostile."

Hence the word "alleged" above.

Update of 1:44 PM ET on Feb. 9, 2017:

A relevant Wikipedia article —
Questioned document examination.

Tuesday, February 7, 2017

Authority Figure

Filed under: General — m759 @ 3:09 pm

Accepting for Professor Corey Thomas Pynchon.

Saturday, January 28, 2017

Cranking It Up

Filed under: General — m759 @ 12:17 pm

From "Core," a post of St. Lucia's Day, Dec. 13, 2016 —

'We are rooted in yoga and love the magic that happens when that practice is cranked up to eleven.'

In related news yesterday —

California yoga mogul’s mysterious death:
Trevor Tice’s drunken last hours detailed

"Police found Tice dead on the floor in his home office,
blood puddled around his head. They also found blood
on walls, furniture, on a sofa and on sheets in a nearby
bedroom, where there was a large bottle of Grey Goose
vodka under several blood-stained pillows on the floor."

See as well an image from "The Stone," a post of March 18, 2016 —

Some backstory —

“Lord Arglay had a suspicion that the Stone would be
purely logical.  Yes, he thought, but what, in that sense,
were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams

Sunday, January 15, 2017

Career Event

Filed under: General — m759 @ 1:29 pm

See also related remarks.

Sunday, January 8, 2017

A Theory of Everything

Filed under: General,Geometry — Tags: , — m759 @ 7:11 pm

The title refers to the Chinese book the I Ching ,
the Classic of Changes .

The 64 hexagrams of the I Ching  may be arranged
naturally in a 4x4x4 cube. The natural form of transformations
("changes") of this cube is given by the diamond theorem.

A related post —

The Eightfold Cube, core structure of the I Ching

Monday, September 5, 2016

Space Case

Filed under: General — m759 @ 2:00 pm

The New York Times  yesterday evening —

Michel Butor dies at 89

Butor reportedly died on August 24.

This journal on that date —

From Butor's obituary —

"He studied philosophy at the Sorbonne
under the phenomenologist
Gaston Bachelard, writing a thesis on
mathematics and the idea of necessity."

"In 2013 the Académie Française awarded
Mr. Butor its Grand Prix for his life’s work.

Explaining his philosophy in an interview
with the critic and television producer
Georges Charbonnier in 1965, Mr. Butor said,
'Every written word is a victory over death.' "

A search for Bachelard in this journal yields remarks
related to Bachelard's Poetics of Space  and to the above
phrase by Wallace Stevens.

Thursday, August 25, 2016

Diamond on the Map

Filed under: General — Tags: — m759 @ 4:38 pm

A check of Cora Diamond, editor of the 1976 Wittgenstein
book shown in the previous post, yields …

The date of the above talk was April 3, 2015.

For this journal on that date,  see a link, "by Steven H. Cullinane,"
in yesterday's post Core Statements.

Monday, August 8, 2016

A Point of Identity

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

For a  Monkey Grammarian  (Viennese Version)

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by Helen Lane 

A logo that may be interpreted as one-eighth of a 2x2x2 array
of cubes —

The figure in white above may be viewed as a subcube representing,
when the eight-cube array is coordinatized, the identity (i.e., (0, 0, 0)).

Shown below are a few variations on the figure by VCQ,
the Vienna Center for Quantum Science and Technology —
 

(Click image to enlarge.)

Thursday, August 4, 2016

Routine

Filed under: General — Tags: — m759 @ 10:30 pm

Peter Gelzinis in the Boston Herald  today

"What has become painfully clear this week
is that there is no Republican campaign for
the presidency. There is only The Donald,
his 
reflex tweets, the folded pieces of paper
he pulls out of his coat pocket and a crazy
stand-up routine that is part Lenny Bruce
and part professor Irwin Corey."

APPLAUSE

Tuesday, July 5, 2016

For the Children in the Apple Tree (continued)

Filed under: General — Tags: , — m759 @ 6:00 am

(See previous posts now tagged Apple Tree Children.)

See as well the comic book in "Midnight Special" —

(Image previously posted in "Common Core vs. Central Structure")

Sunday, July 3, 2016

Another 48 Hours

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

The Onion  on Friday, July 1, 2016 —

Investigators: First 48 Hours Most Critical
In Locating Missing Children Who Entered
Portal To Fantastical World

From Friday afternoon —

Friday, May 27, 2016

Peer Review

Filed under: General — Tags: , — m759 @ 7:00 am

A review of the phrase "Innermost Kernel" in this journal
suggests the following meditation

"Who am I?" — Existential cry
in "Zoolander" and "Zoolander 2."

A similar question occurs in "Peer Gynt" —

Ben Brantley in yesterday morning's print New York Times *
expressed a nihilistic view of Peer as an onion-peeler —

"Toward the end of Ibsen’s 'Peer Gynt,' a saga of self
under siege, the title character is discovered peeling
an onion, finding in the layers of that humble vegetable
a symbol for the chapters of an eventful life . . . .

[the director’s] approach is the same one that Peer
applies to the onion: Keep stripping until you find the core.
Of course in Peer’s case what is finally found is
plenty of nothing, an apt conclusion for a man
for whom a solid self remains elusive."

I prefer a view from what Fitzgerald called
"the dark fields of the republic" — the Dordt College view —

* The Times — "A version of this review appears in print on May 26, 2016, 
on page C3 of the New York edition with the headline:
'A Saga of Self-Identity, Stripped to Its Core, Still Provokes.' "

Wednesday, March 23, 2016

Requiem for an Actress

Filed under: General — Tags: — m759 @ 10:15 pm

The New York Times  this evening on the late Rita Gam:

"After generally being typecast in supporting roles
in two dozen films for what Life described as
'her sultry face and insinuating voice,' she recalled
in 1992, 'I looked into the black pit at 40 and
wondered, what do I do for an encore?' "

See also Sidney Lumet in this journal as well as
"Some cartoon graveyards are better than others."

Friday, March 4, 2016

Chess by Other Means

Filed under: General — m759 @ 7:22 pm

On film director Stanley Kubrick:

From "Kubrick," by Michael Herr, Vanity Fair , August 1999—

"He disliked the usual references to his having been a 'chess hustler' in his Greenwich Village days, as though this impugned the gravity and beauty of the exercise, the suggestion that his game wasn’t pour le sport  or, more correctly, pour l’art . To win the game was important, to win the money was irresistible, but it was nothing compared with his game, with the searching, endless action of working on his game. But of course he was hustling, he was always hustling; as he grew older and moved beyond still photography, chess became movies, and movies became chess by other means. I doubt that he ever thought of chess as just a game, or even as a game at all. I do imagine that a lot of people sitting across the board from him got melted, fried, and fragmented when Stanley let that cool ray come streaming down out of his eyes— talk about penetrating looks and piercing intelligence; here they’d sat down to a nice game of chess, and all of a sudden he was doing the thinking for both of them."

On physics writer Peter Woit:

From Part II of an interview with Peter Woit by Gerald Alper
in Smashpipe  published March 1, 2016:

"For just a moment, he allows himself to become self reflective: 'I was always a smart kid. A very smart kid. I suppose if I ever took a standardized test I would do very well, especially, in the area of abstract reasoning.'

Peter Woit says this as matter-of-factly as if he said, 'When I was a kid my father drove a Chevrolet.' He says it as Kareem Abdul-Jabbar, if asked to describe how he became the person he is, might have said 'I was always a tall kid. A very tall kid. In school, short kids bored me.'

I felt I had to say, 'but there must be a few million people in the United States who would also score very high in abstract thinking in the standardized tests and none of them have your interests.'

'The people around here all do. And there are thousands of us all around the world.'

'But there are 7 billion people in the world.'

Peter Woit had to concede the mathematical point, but I don't think he appreciated the psychological distinction I was alluding to. There is an astonishing divide between the culture of science and the culture of humanities that C.P. Snow famously alluded to. There is even a greater divide between the culture of pure mathematics and the culture of the earthbound evolutionarily programmed biological world into which we are born.

There is a celebrated quip by Dick Cavett that encapsulates this. Reflecting on his famous interview of the then reigning world chess champion, Bobby Fischer, he observed:

'Throughout the interview I could feel the force of his IQ.'

Paraphrasing this I could say that throughout the interview, which was at times exhilarating, at times daunting, I could feel the force of his two hundred QMIQ (quantum mechanics IQ). Norman Mailer once commented that the immediacy of television— the fact that most influential people in the world can be brought into your living room— creates the illusion that you have thereby been included in their inner power circle, and to that extent vicariously empowered. But you are no closer to the corridors of power then you were before. Analogously, you can sit just a few feet away from a world-class expert, close enough to reach out and touch them, but you are no closer to their accumulated wisdom— unless you are willing to go home and put in ten thousand hours of hard work trying to raise the level of your understanding."

http://www.log24.com/log/pix09A/091109-Nicole.jpg

Illustration from a post of
Schicksalstag  2009

Monday, February 15, 2016

Global and Local

Filed under: General — m759 @ 12:36 pm

Track listing

  1. "Dirty Laundry" (Henley, Danny Kortchmar) – 5:36
  2. "The Boys of Summer" (Mike Campbell, Henley) – 4:45
  3. "All She Wants to Do Is Dance" (Kortchmar) – 4:28
  4. "Not Enough Love in the World" (Henley, Kortchmar, Benmont Tench) – 3:54
  5. "Sunset Grill" (Henley, Kortchmar, Tench) – 6:22
  6. "The End of the Innocence" (Henley, Bruce Hornsby) – 5:14
  7. "The Last Worthless Evening" (John Corey, Henley, Stan Lynch) – 6:05
  8. "New York Minute" (Henley, Kortchmar, Jai Winding) – 6:34
  9. "I Will Not Go Quietly" (Henley, Kortchmar) – 5:41
  10. "The Heart of the Matter" (Campbell, Henley, J.D. Souther) – 5:21
  11. "The Garden of Allah" (Corey, Paul Gurian, Henley, Lynch) – 7:02
  12. "You Don't Know Me at All" (Corey, Henley, Lynch) – 5:36
  13. "Everybody Knows" (Leonard CohenSharon Robinson) – 6:10

Thursday, June 4, 2015

Molly Bloom on Education

Filed under: General — m759 @ 10:18 am

Two pieces by NPR education writer Molly Bloom:

See also yesterday's post on another NPR / Princeton education figure,
Keith Devlin:

An illustration (click for larger view with context):

Friday, May 8, 2015

Spielraum

Filed under: General,Geometry — Tags: , — m759 @ 9:30 am

Review:

Illustrating the Spiegel-Spiel des Gevierts

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth. 
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by
Helen Lane 

 

Friday December 5, 2008

m759 @ 1:06 PM
 
Mirror-Play of
the Fourfold

For an excellent commentary
 on this concept of Heidegger,

View selected pages
from the book

Dionysus Reborn:

Play and the Aesthetic Dimension
in Modern Philosophical and
Scientific Discourse

(Mihai I. Spariosu,
Cornell U. Press, 1989)

Related material:
the logo for a
web page

Logo for 'Elements of Finite Geometry'

– and Theme and Variations.

Tuesday, May 5, 2015

Paz

Filed under: General — Tags: — m759 @ 11:35 am

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth. 
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by
Helen Lane 

Thursday, April 23, 2015

Colorful Tale

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

(A sequel to yesterday's ART WARS and this
morning's De Colores )

“Perhaps the philosophically most relevant feature
of modern science is the emergence of abstract
symbolic structures as the hard core of objectivity
behind– as Eddington puts it– the colorful tale
of the subjective storyteller mind.” — Hermann Weyl
(Philosophy of  Mathematics and Natural Science ,
Princeton, 1949, p. 237)

See also Deathly Hallows.

Thursday, April 9, 2015

Translation

Filed under: General — m759 @ 6:27 pm

From an informative April 7 essay in The Nation —

In his marvelous book Is That a Fish in Your Ear?: Translation and the Meaning of Everything , David Bellos demonstrates many of the ways that translation is not only possible but ubiquitous, so thoroughly woven into the fabric of our daily lives—from classrooms to international financial markets, from instruction manuals to poems—that if translation were somehow to become impossible, the world would descend into the zombie apocalypse faster than you can say “je ne sais quoi ."

— "Forensic Translation," by Benjamin Paloff

See also searches in this  journal for Core and for Kernel.
See as well Fabric Design and Symplectic.

Tuesday, February 24, 2015

Amy’s After-Party

Filed under: General — m759 @ 2:21 pm

Continued from Putting the A in VANITY,
Putting the AI in FAIR, and Core Problem:

Tuesday, December 2, 2014

Colorful Tale

Filed under: General — Tags: — m759 @ 9:45 am

Continued.

"Perhaps the philosophically most relevant feature
of modern science is the emergence of abstract
symbolic structures as the hard core of objectivity
behind— as Eddington puts it— the colorful tale
of the subjective storyteller mind."

— Hermann Weyl in Philosophy of Mathematics
     and Natural Science
 , Princeton, 1949, p. 237

Tom Wolfe on art theorists in The Painted Word  (1975) :

"It is important to repeat that Greenberg and Rosenberg
did not create their theories in a vacuum or simply turn up
with them one day like tablets brought down from atop
Green Mountain or Red Mountain (as B. H. Friedman once
called the two men). As tout le monde  understood, they
were not only theories but … hot news,
straight from the studios, from the scene."

The Weyl quote is a continuing theme in this journal.
The Wolfe quote appeared here on Nov. 18, 2014,
the reported date of death of Yale graduate student 
Natasha Chichilnisky-Heal.

Directions to her burial (see yesterday evening) include
a mention of "Paul Robson Street" (actually Paul
Robeson Place) near "the historic Princeton Cemetery."

This, together with the remarks by Tom Wolfe posted
here on the reported day of her death, suggests a search
for "red green black" —

The late Chichilnisky-Heal was a student of political economy.

The search colors may be interpreted, if one likes, as referring
to politics (red), economics (green), and Robeson (black).

See also Robeson in this journal.

Thursday, September 25, 2014

Mystery

Filed under: General,Geometry — m759 @ 11:00 am

"Welcome to America." — Harrison Ford in "The Devil's Own"

America  (current issue):

On readings at Mass on Sunday, Sept. 21, 2014 —

"Isaiah 55:8-9: 'For my thoughts are not your thoughts,
neither are your ways my ways, says the Lord.
For as the heavens are higher than the earth,
so are my ways higher than your ways
and my thoughts than your thoughts.'

The Gospel reading… was a perfect complement to
the passage from Isaiah…."

The America  piece quoting Isaiah was titled "The Mystery of God."

The author "currently works at Xavier College Preparatory
in Palm Desert, CA, where he teaches theology…."

Related material: This  journal that Sunday morning:

See also "The Mystery of God, Part II" —

Other secular stand-ins for "the thing one doesn't know"—
The mysteries of the late Joseph D. McNamara.

Sunday, September 21, 2014

Sermon

Filed under: General,Geometry — m759 @ 11:00 am

The previous post discussed the anatomy of the sum 9 + 6.

A different approach:  “A” and “The 6 spreads in A” below —

Thursday, September 18, 2014

Them Apples

Filed under: General — m759 @ 12:00 pm

John Baez at Google+ has an interesting post on crackpots,
dated September 13, 2014.

Related recent material from this  journal:

Sense (Sept. 13) and Sensibility (Sept. 14 and later).

See also a New York Times  piece from 2009:

Related material:

An Apple for Devlin and

“You don’t need to eat a whole apple to know it’s rotten.”
Warren Siegel

Thursday, September 11, 2014

Oh, Moon of Alabama

Filed under: General — Tags: — m759 @ 11:09 am

The mention of Gauss in today's previous post, along with
recent news, suggested this post.

"How do you  get young people excited about space?"

— Megan Garber in The Atlantic , Aug. 16, 2012

Further details:  Child Buyers (July 16, 2013).

Thursday, September 4, 2014

Halloween Manifestos, 2013:

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

Here and at Catholics for Classical Education.

See also Tom Wolfe on manifestos —

Wolfe on manifestos in 'From Bauhaus to Our House'

— and part of an interesting Sept. 2, 2014, manifesto by
Common Core supporter Keith Devlin:

“Graduate students of mathematics are introduced to further
assumptions (about handling the infinite, and various other issues),
equally reasonable and useful, and in accord both with our everyday
intuitions (insofar as they are relevant) and with the rest of
mainstream mathematics. And on the basis of those assumptions,
you can prove that

1 + 2 + 3 + … = –1/12.

That’s right, the sum of all the natural numbers equals –1/12.

This result is so much in-your-face, that people whose mathematics
education stopped at the undergraduate level (if they got that far)
typically say it is wrong. It’s not. Just as with the 0.999… example,
where we had to construct a proper meaning for an infinite decimal
expansion before we could determine what its value is, so to we
have to define what that infinite sum means. ….”

For a correction to Devlin’s remarks, see a physics professor’s weblog post —

“From a strictly mathematical point of view,
the equation 1+2+3+4+ … = -1/12 is incorrect,
and involves confusing the Dirichlet series with
the zeta function.”  — Greg Gbur, May 25, 2010

Sunday, July 13, 2014

Numbers

Filed under: General — m759 @ 7:00 pm

Friday, July 4, 2014

Knockout

Filed under: General,Geometry — m759 @ 9:29 am

(Continued from yesterday’s noon post, from  “Block That Metaphor,”
and from “Mystery Box III: Inside, Outside“)

“In one corner are the advocates of the Common Core,
led by the Bill and Melinda Gates Foundation, which
helped develop the standards and has defended them
against efforts by some states to roll them back. In the
challengers’ corner, a lineup of foundations and
philanthropists…. Other funders in the opponents’ corner
read like a ‘who’s who’ of well-heeled conservative
philanthropists, including Pittsburgh media magnate
Richard Mellon Scaife….”

— “Meet the Funders Fighting the Common Core,”
from Inside Philanthropy , Feb. 10, 2014

Scaife reportedly died this morning.

Thursday, July 3, 2014

Gates and Windows:

Filed under: General — m759 @ 12:00 pm

The Los Alamos Vision

“Gates said his foundation is an advocate for the Common Core State Standards
that are part of the national curriculum and focus on mathematics and language
arts. He said learning ‘needs to be on the edge’ where it is challenging but not
too challenging, and that students receive the basics through Common Core.

‘It’s great to teach other things, but you need that foundation,’ he said.”

— T. S. Last in the Albuquerque Journal , 12:05 AM Tuesday, July 1, 2014

See also the previous post (Core Mathematics: Arrays) and, elsewhere
in this journal,

“Eight is a Gate.” — Mnemonic rhyme:

Wednesday, July 2, 2014

An Apple for Devlin

Filed under: General — Tags: — m759 @ 2:56 pm

A columnist for the Mathematical Association of America,
Keith Devlin, yesterday posted an essay on Common Core
math education. A response:

IMAGE- Sign: 'Rotten to the Common Core'

Screenshot from a June 14, 2014, New York Times  video.

Friday, March 14, 2014

Quotation

Filed under: General — Tags: , , — m759 @ 1:09 pm

Edward Frenkel in a vulgar and stupid
LA Times  opinion piece, March 2, 2014 —

"In the words of the great mathematician Henri Poincare, mathematics is valuable because 'in binding together elements long-known but heretofore scattered and appearing unrelated to one another, it suddenly brings order where there reigned apparent chaos.' "

My attempts to find the source of these alleged words of Poincaré were fruitless.* Others may have better luck.

The search for Poincaré's words did, however, yield the following passage —

HENRI POINCARÉ
THE FUTURE OF MATHEMATICS

If a new result is to have any value, it must unite elements long since known, but till then scattered and seemingly foreign to each other, and suddenly introduce order where the appearance of disorder reigned. Then it enables us to see at a glance each of these elements in the place it occupies in the whole. Not only is the new fact valuable on its own account, but it alone gives a value to the old facts it unites. Our mind is frail as our senses are; it would lose itself in the complexity of the world if that complexity were not harmonious; like the short-sighted, it would only see the details, and would be obliged to forget each of these details before examining the next, because it would- be incapable of taking in the whole. The only facts worthy of our attention are those which introduce order into this complexity and so make it accessible to us.

Mathematicians attach a great importance to the elegance of their methods and of their results, and this is not mere dilettantism. What is it that gives us the feeling of elegance in a solution or a demonstration? It is the harmony of the different parts, their symmetry, and their happy adjustment; it is, in a word, all that introduces order, all that gives them unity, that enables us to obtain a clear comprehension of the whole as well as of the parts. But that is also precisely what causes it to give a large return; and in fact the more we see this whole clearly and at a single glance, the better we shall perceive the analogies with other neighbouring objects, and consequently the better chance we shall have of guessing the possible generalizations. Elegance may result from the feeling of surprise caused by the unlooked-for occurrence together of objects not habitually associated. In this, again, it is fruitful, since it thus discloses relations till then unrecognized. It is also fruitful even when it only results from the contrast between the simplicity of the means and the complexity of the problem presented, for it then causes us to reflect on the reason for this contrast, and generally shows us that this reason is not chance, but is to be found in some unsuspected law. ….

HENRI POINCARÉ
L'AVENIR DES MATHÉMATIQUES

Si un résultat nouveau a du prix, c'est quand en reliant des éléments connus depuis longtemps, mais jusque-là épars et paraissant étrangers les uns aux autres, il introduit subitement l'ordre là où régnait l'apparence du désordre. Il nous permet alors de voir d'un coup d'œil chacun de ces éléments et la place qu'il occupe dans l'ensemble. Ce fait nouveau non-seulement est précieux par lui-même, mais lui seul donne leur valeur à tous les faits anciens qu'il relie. Notre esprit est infirme comme le sont nos sens; il se perdrait dans la complexité du monde si cette complexité n'était harmonieuse, il n'en verrait que les détails à la façon d'un myope et il serait forcé d'oublier chacun de ces détails avant d'examiner le suivant, parce qu'il serait incapable de tout embrasser. Les seuls faits dignes de notre attention sont ceux qui introduisent de l'ordre dans cette complexité et la rendent ainsi accessible.

Les mathématiciens attachent une grande importance à l'élégance de leurs mé-thodes et de leurs résultats; ce n'est pas là du pur dilettantisme. Qu'est ce qui nous donne en effet dans une solution, dans une démonstration, le sentiment de l'élégance? C'est l'harmonie des diverses parties, leur symétrie, leur heureux balancement; c'est en un mot tout ce qui y met de l'ordre, tout ce qui leur donne de l'unité, ce qui nous permet par conséquent d'y voir clair et d'en comprendre l'ensemble en même temps que les détails. Mais précisément, c'est là en même temps ce qui lui donne un grand rendement ; en effet, plus nous verrons cet ensemble clairement et d'un seul coup d'œil, mieux nous apercevrons ses analogies avec d'autres objets voisins, plus par conséquent nous aurons de chances de deviner les généralisations possibles. L'élé-gance peut provenir du sentiment de l'imprévu par la rencontre inattendue d'objets qu'on n'est pas accoutumé à rapprocher; là encore elle est féconde, puisqu'elle nous dévoile ainsi des parentés jusque-là méconnues; elle est féconde même quand elle ne résulte que du contraste entre la simplicité des moyens et la complexité du problème posé ; elle nous fait alors réfléchir à la raison de ce contraste et le plus souvent elle nous fait voir que cette raison n'est pas le hasard et qu'elle se trouve dans quelque loi insoupçonnée. ….

* Update of 1:44 PM ET March 14 — A further search, for "it suddenly brings order," brought order. Words very close to Frenkel's quotation appear in a version of Poincaré's "Future of Mathematics" from a 1909 Smithsonian report

"If a new result has value it is when, by binding together long-known elements, until now scattered and appearing unrelated to each other, it suddenly brings order where there reigned apparent disorder."

Friday, February 28, 2014

Code

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

From Northrop Frye's The Great Code: The Bible and Literature , Ch. 3: Metaphor I —

"In the preceding chapter we considered words in sequence, where they form narratives and provide the basis for a literary theory of myth. Reading words in sequence, however, is the first of two critical operations. Once a verbal structure is read, and reread often enough to be possessed, it 'freezes.' It turns into a unity in which all parts exist at once, without regard to the specific movement of the narrative. We may compare it to the study of a music score, where we can turn to any part without regard to sequential performance. The term 'structure,' which we have used so often, is a metaphor from architecture, and may be misleading when we are speaking of narrative, which is not a simultaneous structure but a movement in time. The term 'structure' comes into its proper context in the second stage, which is where all discussion of 'spatial form' and kindred critical topics take their origin."

Related material: 

"The Great Code does not end with a triumphant conclusion or the apocalypse that readers may feel is owed them or even with a clear summary of Frye’s position, but instead trails off with a series of verbal winks and nudges. This is not so great a fault as it would be in another book, because long before this it has been obvious that the forward motion of Frye’s exposition was illusory, and that in fact the book was devoted to a constant re-examination of the same basic data from various closely related perspectives: in short, the method of the kaleidoscope. Each shake of the machine produces a new symmetry, each symmetry as beautiful as the last, and none of them in any sense exclusive of the others. And there is always room for one more shake."

— Charles Wheeler, "Professor Frye and the Bible," South Atlantic Quarterly  82 (Spring 1983), pp. 154-164, reprinted in a collection of reviews of the book.
 

For code  in a different sense, but related to the first passage above,
see Diamond Theory Roullete, a webpage by Radamés Ajna.

For "the method of the kaleidoscope" mentioned in the second
passage above, see both the Ajna page and a webpage of my own,
Kaleidoscope Puzzle.

Thursday, February 6, 2014

The Representation of Minus One

Filed under: General,Geometry — Tags: , , — m759 @ 6:24 am

For the late mathematics educator Zoltan Dienes.

“There comes a time when the learner has identified
the abstract content of a number of different games
and is practically crying out for some sort of picture
by means of which to represent that which has been
gleaned as the common core of the various activities.”

— Article by “Melanie” at Zoltan Dienes’s website

Dienes reportedly died at 97 on Jan. 11, 2014.

From this journal on that date —

http://www.log24.com/log/pix11/110219-SquareRootQuaternion.jpg

A star figure and the Galois quaternion.

The square root of the former is the latter.

Update of 5:01 PM ET Feb. 6, 2014 —

An illustration by Dienes related to the diamond theorem —

See also the above 15 images in

http://www.log24.com/log/pix11/110220-relativprob.jpg

and versions of the 4×4 coordinatization in  The 4×4 Relativity Problem
(Jan. 17, 2014).

Monday, August 19, 2013

Tale

Filed under: General — Tags: — m759 @ 8:00 pm

IMAGE- NY Times online front page with caption- 'Thereby hangs a tale.'

The tale is not Thomas Nagel's remarks on philosophy
summarized above, but rather the late John Hollander's
remarks on Nowhere:

"We all know where it is they've gone, the dead:
Beyond Noplace, far into wide Nowhere."

See also Nagel's book The View from Nowhere .

Sunday, June 30, 2013

Book Award

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

"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.

In the spirit of the late Thomas Guinzburg

See also "Concrete Universal" in this journal.

Related material— From a Bloomsday reply
to a Diamond Theory  reader's comment, an excerpt—

The reader's comment suggests the following passages from
the book by Stirling quoted above—

 

Here Stirling plays a role analogous to that of Professor Irwin Corey
accepting the National Book Award for Gravity's Rainbow  in 1974.

Monday, May 13, 2013

Game Show

Filed under: General — m759 @ 10:00 pm

For the late Bob Stewart:

"She was a panelist on many game shows, including
'What’s My Line?' and 'The Hollywood Squares.'"

Translation Studies Continued:

See Cameron's Kernel and

Image-- The Three-Point Line: A Finite Projective Space
 (Click image for some background.)

Sunday, April 28, 2013

C’mon Baby…

Filed under: General — Tags: — m759 @ 3:13 am
 

Let's do the twist.

The image at left
is from a poster
for a film released
on March 28, 2003.

See this journal
on that date.

A phrase from yesterday's noon post:

Sinking the Magic 8-Ball .

A scene from the above film is related to this phrase.
Another image from the film poster:

A review of the film:

"The final 'twist' seems to negate the entire story,
like a bad shaggy-dog joke."

Such a joke:

“Words and numbers are of equal value,
  for, in the cloak of knowledge,
  one is warp and the other woof.”

— The princesses Rhyme and Reason
      in The Phantom Tollbooth

"A core component in the construction
is a 3-dimensional vector space over F."

—  Page 29 of "A twist in the M24 moonshine story,"
      by Anne Taormina and Katrin Wendland.
      (Submitted to the arXiv on 13 Mar 2013.)

The number of points in such a space is, of course, 8.

Friday, April 5, 2013

Reflections (continued)

Filed under: General — m759 @ 4:30 pm

From a search for Mirror-Play in this journal:

That search was suggested by a much lengthier
search, for Core, that itself was suggested
by yesterday's post (on Katherine Neville's birthday)
titled A Philosopher's Stone.

See, too, Tom Hanks (shown above as symbologist
Robert Langdon) in "Lucky Guy" (reviewed by TIME
yesterday), and a related poem:

Yes, you! You’re the Lucky One

Prospective purchasers of the poet's work
may consult a press release from LSU Press
dated 4/4/2013. The poet died, apparently*
unlamented by his publisher, on 3/30.

* But only  apparently.

Thursday, April 4, 2013

A Philosopher’s Stone

Filed under: General — m759 @ 4:00 pm

"Core" (in the original, Kern ) is perhaps
not the best translation of hypokeimenon :

IMAGE- Hypokeimenon in Liddell and Scott's Greek-English Lexicon

See also Heidegger's original German:

Related material: In this journal, "underlie" and "underlying."

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'

Sunday, December 23, 2012

Digital Recreation

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

Denzel Washington in Deja Vu  (2006), directed by Tony Scott—

Click to enlarge.

IMAGE- Denzel Washington in 'Deja Vu' (2006)

See also Tony Scott and four and a half days ago* —

  
Japanese character
       for "field"

Related material from five  days ago

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth. 
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by 
Helen Lane (Kindle edition of 
2011-11-07, Kindle locations 
1207-1210).

* More precisely, what will be 4.5 days ago at 3:09 AM ET.

Tuesday, December 18, 2012

Monkey Grammar

Filed under: General,Geometry — Tags: , , — m759 @ 2:29 am

For a modern Adam and Eve—

W. Tecumseh Fitch and Gesche Westphal Fitch,
editors of a new four-volume collection titled
Language Evolution  (Feb. 2, 2012, $1,360)—

Related material—

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth. 
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by
Helen Lane (Kindle edition of
2011-11-07, Kindle locations
1207-1210).

The "play of mirrors" link above is my own.

Click on W. Tecumseh Fitch for links to some
examples of mirror-play in graphic design—
from, say, my own work in a version of 1977, not from
the Fitches' related work published online last June—

See also Log24 posts from the publication date
of the Fitches' Language Evolution

Groundhog Day, 2012.

Happy birthday to the late Alfred Bester.

Sunday, November 18, 2012

Kernel

Filed under: General — m759 @ 5:24 am

(Continued)

Rachel Dodes in The Wall Street Journal
on All Souls' Day, 2012

"In one of the first lines uttered by Daniel Day-Lewis, playing Abraham Lincoln in the new Steven Spielberg film opening Nov. 9, he says, 'I could be bounded in a nutshell, and count myself a king of infinite space— were it not that I have bad dreams.'

The line was ripped straight from 'Hamlet,' by Lincoln's favorite writer, William Shakespeare. Tony Kushner, the Pulitzer Prize-winning playwright ('Angels in America') who wrote the script for the film, says that Shakespeare, much like Lincoln, 'had extraordinary mastery over the darkest parts of the human spirit.'"

The above quotation omits Shakespeare's words prefacing the nutshell part— "O God."

These same words in a different tongue—  "Hey Ram"— have often been quoted as the last words of Gandhi. (See yesterday's noon post.)

"… for the Highest Essence (brahman ),
which is the core of the world, is identical
with the Highest Self (ātman ), the kernel
of man's existence."

— Heinrich Zimmer, Myths and Symbols
in Indian Art and Civilization
, Pantheon
Books, 1946, page 142 

Related material: A post linked to here on Friday night
that itself links to a different Shakespeare speech.

Sunday, November 4, 2012

Shakespeare’s Rhyme

Filed under: General — m759 @ 5:01 am

From Saturday Night Live  last night—

IMAGE- Louis C. K. as Shakespeare on SNL

Related material from the Log24 post "Now Lens"
(March 11, 2011)—

Errol Morris in The New York Times  on March 9, 2011

"If everything is incommensurable, then everything
is seen through the lens of the present, the lens of now ."

"Borges concluded by quoting Chesterton, 'there is nothing
more frightening than a labyrinth that has no center.' [72]"

See also Borges on Shakespeare, everything, and nothing 
in a note from September 7, 2006.

Everything and nothing in Peter J. Cameron's weblog yesterday—

The existence of everything entails the existence of nothing;
indeed, the existence of anything (any set A) entails
the existence of the empty set (the set {x∈A:x≠x}).
But not the other way round.

Right, I had better put on my anorak and go out now …

Illustration added by m759—

How many miles to Babylon?*
Three score miles and ten.
Can I get there by candle-light?**
Yes, and back again.

* Suggested by the Pindar link in this journal yesterday.

** Quoted in the "Seven is Heaven" post on All Souls' Day.

Sunday, September 23, 2012

Plan 9 (continued)–

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

In Like Flynn

From the Wall Street Journal  site Friday evening—

ESSAY September 21, 2012, 9:10 p.m. ET

Are We Really Getting Smarter?

Americans’ IQ scores have risen steadily over the past century.
James R. Flynn examines why.

IMAGE- Raven's Progressive Matrices problem with ninth configuration a four-diamonds grid

No, thank you. I prefer the ninth configuration as is—

IMAGE- Four-diamonds grid, the ninth configuration in a Raven's Progressive Matrices problem

Why? See Josefine Lyche’s art installation “Grids, you say?

Her reference there to “High White Noon” is perhaps
related to the use of that phrase in this journal.

The phrase is from a 2010 novel by Don DeLillo.
See “Point Omega,” as well as Lyche’s “Omega Point,”
in this journal.

The Wall Street Journal  author above, James R. Flynn (born in 1934),
“is famous for his discovery of the Flynn effect, the continued
year-after-year increase of IQ scores in all parts of the world.”
Wikipedia

His son Eugene Victor Flynn is a mathematician, co-author
of the following chapter on the Kummer surface— 

For use of the Kummer surface in Buddhist metaphysics, see last night’s
post “Occupy Space (continued)” and the letters of Nanavira Thera from the
late 1950s at nanavira.blogspot.com.

These letters, together with Lyche’s use of the phrase “high white noon,”
suggest a further quotation

You know that it would be untrue
You know that I would be a liar
If I was to say to you
Girl, we couldn’t get much higher

See also the Kummer surface at the web page Configurations and Squares.

Friday, June 29, 2012

The Uploading (continued)*

Filed under: General — m759 @ 9:29 pm

It Must Be Abstract
It Must Change
It Must Give Pleasure

Parts of a poem by Wallace Stevens

“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”

– Thomas Wolfe, Of Time and the River

      Of Time and the River and the Frogs —

Video uploaded on Jan. 26, 2008, of talk, 'The Lively Kernel,' on object-oriented software

* This post's title refers to the above uploading date—  Jan. 26, 2008.

Friday, April 20, 2012

Complex Reflection

Filed under: General — Tags: — m759 @ 11:32 am

Yesterday's post in memory of Octavio Paz

… the free-standing, two-sided “Life-Death Figure,”
carved from stone in Mexico some time between
A.D. 900 and 1250, 
has multiple personalities.

Holland Cotter,  New York Times 

An earlier post yesterday, Fashion Notes, linked to a Sting video—

IMAGE- Sting meets his own reflection in a mirror in 'We'll Be Together' video

From "Loo Ree," by Zenna Henderson

"It's so hard to explain–"

"Oh, foof!" I cried defiantly, taking off my glasses and, smearing the tears across both lenses with a tattered Kleenex. "So I'm a dope, a moron! If I can explain protective coloration to my six-year-olds and the interdependence of man and animals, you can tell me something of what the score is!" I scrubbed the back of my hand across my blurry eyes. "If you have to, start out 'Once upon a time."' I sat down– hard.  

Loo Ree smiled and sat down, too. "Don't cry, teacher. Teachers aren't supposed to have tears."  

"I know it," I sniffed. "A little less than human-that's us."

"A little more than human, sometimes." Loo Ree corrected gently. "Well then, you must understand that I'll have to simplify. You will have to dress the bare bones of the explanation according to your capabilities.  

"Once upon a time there was a classroom. Oh, cosmic in size, but so like yours that you would smile in recognition if you could see it all. And somewhere in the classroom something was wrong. Not the whispering and murmuring– that's usual. Not the pinching and poking and tattling that goes on until you get so you don't even hear it." I nodded. How well I knew.  

"It wasn't even the sudden blow across the aisle or the unexpected wrestling match in the back of the room. That happens often, too. But something else was wrong. It was an undercurrent, a stealthy, sly sort of thing that has to be caught early or it disrupts the whole classroom and tarnishes the children with a darkness that will never quite rub off.  

"The teacher could feel it –as all good teachers can– and she spoke to the principal. He, being a good principal, immediately saw the urgency of the matter and also saw that it was beyond him, so he called in an Expert." "You?" I asked, feeling quite bright because I had followed the analogy so far.  

Loo Ree smiled. "Well, I'm part of the Expert."  

"If you have to, start out 'Once upon a time.'"

Yesterday's Paz post was at 6:48 PM EDT.

For the autistic, here is some related mathematics.

Yesterday's Fashion Notes post was at 1:06 PM  EDT.

A related chronological note from Rolling Stone  yesterday—

"Levon Helm, singer and drummer for the Band,
 died on April 19th in New York of throat cancer.
 He was 71. 

"He passed away peacefully at 1:30 this afternoon…."

Helm and The Band performing "The Weight"—

"I pulled into Nazareth, I was a-feelin' 'bout half past dead…"

Tuesday, November 1, 2011

For All Hallows Day

Filed under: General,Geometry — Tags: — m759 @ 11:07 am

The following was suggested by the Sermon
of October 30 (the day preceding Devil's Night)
and by yesterday's Beauty, Truth, Halloween.

"The German language has itself been influenced by Goethe's Faust , particularly by the first part. One example of this is the phrase 'des Pudels Kern ,' which means the real nature or deeper meaning of something (that was not evident before). The literal translation of 'des Pudels Kern ' is 'the core of the poodle,' and it originates from Faust's exclamation upon seeing the poodle (which followed him home) turn into Mephistopheles." —Wikipedia

See also the following readings (click to enlarge)—

Hans Primas on Pauli's 'des Pudels Kern'

Suzanne Gieser on Pauli's 'des Pudels Kern'

Note particularly…

"The main enigma of any description of a patternless
unus mundus  is to find appropriate partitions which
create relevant patterns." —Hans Primas, above

"In general, the partition of into right cosets
can differ from its partition into left cosets. Galois
was the first to recognize the importance of when
these partitions agree. This happens when the
subgroup is normal." — David A. Cox,
Galois Theory , Wiley, 2004, p. 510

Saturday, September 17, 2011

The Uploading

Filed under: General — Tags: — m759 @ 11:32 am

(Continued from March 9.)

A detail from "Feist Sings 1, 2, 3, 4"—

"Uploaded by SesameStreet on Jul 18, 2008"

Those who prefer, as Weyl put it,
"
the hard core of objectivity"
to, as Eddington put it,
"the colorful tale of the subjective storyteller mind"
may consult this journal on the same day… July 18, 2008.

Friday, September 16, 2011

Icons

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

Background: Jung's Aion in this journal discusses this
figure from finite geometry's diamond theorem

http://www.log24.com/log/pix11B/110915-FourDiamondsIcon.gif

Fig. A

This resembles a figure that served Jung
as a schema of the Self

http://www.log24.com/log/pix11B/110915-Jung-FourDiamonds.gif

Fig. B

Fig. A, with color variations, serves as the core
of many automatically generated Identicons
a different sort of self-symbol.

Examples from Sept. 6 at MathOverflow

http://www.log24.com/log/pix11B/110915-ChuangGravatar.png     http://www.log24.com/log/pix11B/110915-JacobLurieGravatar.png

A user wanting to custom-tailor his self-symbol should consider
the following from the identicon service Gravatar

1. User Submissions.  " you hereby do and shall grant to Automattic a worldwide, perpetual, irrevocable, royalty-free and fully-paid, transferable (including rights to sublicense) right to perform the Services (e.g., to use, modify, reproduce, distribute, prepare derivative works of, display, perform, and otherwise fully exercise and exploit all intellectual property, publicity, and moral rights with respect to any User Submissions, and to allow others to do so)."

Sounds rather Faustian.

Thursday, July 21, 2011

The Race

Filed under: General — Tags: — m759 @ 7:14 am
 
IMAGE- From Esther Dyson- Boats on the Charles- 'Race you to the bridge!'

An image related to
the Flesh obituary below—

See "As It Lays" in this journal.

Vegas background for 'Play It As It Lays'

(Not as it lies .)

New York Times 
obituaries today—

 

Click to enlarge.

http://www.log24.com/log/pix11B/110721-NYT-Gayler-240w.jpg

http://www.log24.com/log/pix11B/110721-NYT-Flesh-240w.jpg

     "That's GUY-ler, not GAY-ler."

      See also Time and the River, Number of the Beast, and Story Theory.

Monday, July 11, 2011

And/Or Problem

Filed under: General,Geometry — Tags: — m759 @ 11:59 pm

"It was the simultaneous emergence
and mutual determination
of probability and logic
that von Neumann found intriguing
and not at all well understood."

Miklós Rédei

Context:

Update of 7 AM ET July 12, 2011—

Freeman Dyson on John von Neumann's
Sept. 2, 1954, address to the International
Congress of Mathematicians on
"Unsolved Problems in Mathematics"—

                                     …."The hall was packed with
mathematicians, all expecting to hear a brilliant
lecture worthy of such a historic occasion. The
lecture was a huge disappointment. Von Neumann
had probably agreed several years earlier to give
a lecture about unsolved problems and had then
forgotten about it. Being busy with many other
things, he had neglected to prepare the lecture.
Then, at the last moment, when he remembered
that he had to travel to Amsterdam and say something
about mathematics, he pulled an old lecture
from the 1930s out of a drawer and dusted it off.
The lecture was about rings of operators, a subject
that was new and fashionable in the 1930s. Nothing
about unsolved problems.
Nothing about the
future."

Notices of the American Mathematical Society ,
February 2009, page 220

For a different account, see Giovanni Valente's
2009 PhD thesis from the University of Maryland,
Chapter 2, "John von Neumann's Mathematical
'Utopia' in Quantum Theory"—

"During his lecture von Neumann discussed operator theory and its con-
nections with quantum mechanics and noncommutative probability theory,
pinpointing a number of unsolved problems. In his view geometry was so tied
to logic that he ultimately outlined a logical interpretation of quantum prob-
abilities. The core idea of his program is that probability is invariant under
the symmetries of the logical structure of the theory. This is tantamount to
a formal calculus in which logic and probability arise simultaneously. The
problem that exercised von Neumann then was to construct a geometrical
characterization of the whole theory of logic, probability and quantum me-
chanics, which could be derived from a suitable set of axioms…. As he
himself finally admitted, he never managed to set down the sought-after
axiomatic formulation in a way that he felt satisfactory."

Sunday, June 19, 2011

Friday, November 19, 2010

Absolute Ambition

Filed under: General — Tags: , — m759 @ 10:30 am

"It's my absolute ambition that you are touched to the core of your being with the content…."

— Julie Taymor on Spider-Man: Turn Off the Dark  (Playbill video, undated)

Another ambitious comic-book promotion —

"What Logicomix  does that few works in any medium do is to make intellectual passion palpable. That is its greatest strength. And it’s here that its form becomes its substance."

— Judith Roitman, review (pdf, 3.7 MB) of Logicomix: An Epic Search for Truth , in …

http://www.log24.com/log/pix10B/101119-AMSnoticesSm.jpg

 The December 2010 AMS Notices  cover has excerpts from Logicomix.

Related material:

"In the classical grammarians’ sense of the power of form over 'content' and style over 'substance,' he originated the phrase, 'the medium is the message.'"

— Joseph P. Duggan on Marshall McLuhan at The University Bookman

See also, in this  journal, The Medium is the Message, Wechsler, and Blockheads .

Saturday, September 18, 2010

Yom Kippur Special

Filed under: General — m759 @ 9:29 am

John Hooper in The Guardian  quotes the Pope in Westminster Cathedral this morning—

"Here too I think of the immense suffering caused by the abuse of children, especially within the church and by her ministers. Above all, I express my deep sorrow to the innocent victims of these unspeakable crimes.

"I also acknowledge, with you, the shame and humiliation which all of us have suffered because of these sins; and I invite you to offer it to the Lord with trust that this chastisement will contribute to the healing of the victims and the purification of the church and the renewal of her age-old commitment to the education and care of young people."

The pope made his comments at a service that was the occasion for religious pageantry of a sort rarely seen in Britain. He was preceded into the cathedral by more than 100 scarlet-robed priests and a constellation of bishops and cardinals. To a volley of applause from the congregation, he appeared at the climax of a musical build-up that could have come from the score for a sci-fi movie epic.

Related material— Childhood's Rear End.

Sunday, August 15, 2010

The Game

Filed under: General — Tags: , , — m759 @ 11:07 pm
'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse

We shall now give a brief summary of the beginnings of the Glass Bead Game. It appears to have arisen simultaneously in Germany and in England. In both countries, moreover, it was originally a kind of exercise employed by those small groups of musicologists and musicians who worked and studied in the new seminaries of musical theory. If we compare the original state of the Game with its subsequent developments and its present form, it is much like comparing a musical score of the period before 1500, with its primitive notes and absence of bar lines, with an eighteenth-century score, let alone with one from the nineteenth with its confusing excess of symbols for dynamics, tempi, phrasing, and so on, which often made the printing of such scores a complex technical problem.

The Game was at first nothing more than a witty method for developing memory and ingenuity among students and musicians. And as we have said, it was played both in England and Germany before it was ‘invented’ here in the Musical Academy of Cologne, and was given the name it bears to this day, after so many generations, although it has long ceased to have anything to do with glass beads.

The inventor, Bastian Perrot of Calw, a rather eccentric but clever, sociable, and humane musicologist, used glass beads instead of letters, numerals, notes, or other graphic symbols. Perrot, who incidentally has also bequeathed to us a treatise on the Apogee and Decline of Counterpoint, found that the pupils at the Cologne Seminary had a rather elaborate game they used to play. One would call out, in the standardized abbreviations of their science, motifs or initial bars of classical compositions, whereupon the other had to respond with the continuation of the piece, or better still with a higher or lower voice, a contrasting theme, and so forth. It was an exercise in memory and improvisation quite similar to the sort of thing probably in vogue among ardent pupils of counterpoint in the days of Schütz, Pachelbel, and Bach — although it would then not have been done in theoretical formulas, but in practice on the cembalo, lute, or flute, or with the voice.

Bastian Perrot in all probability was a member of the Journeyers to the East. He was partial to handicrafts and had himself built several pianos and clavichords in the ancient style. Legend has it that he was adept at playing the violin in the old way, forgotten since 1800, with a high-arched bow and hand-regulated tension of the bow hairs. Given these interests, it was perhaps only natural that he should have constructed a frame, modeled on a child’s abacus, a frame with several dozen wires on which could be strung glass beads of various sizes, shapes, and colors. The wires corresponded to the lines of the musical staff, the beads to the time-values of the notes, and so on. In this way he could represent with beads musical quotations or invented themes, could alter, transpose, and develop them, change them and set them in counterpoint to one another. In technical terms this was a mere plaything, but the pupils liked it; it was imitated and became fashionable in England too. For a time the game of musical exercises was played in this charmingly primitive manner. And as is so often the case, an enduring and significant institution received its name from a passing and incidental circumstance. For what later evolved out of that students’ sport and Perrot’s bead-strung wires bears to this day the name by which it became popularly known, the Glass Bead Game.

Hermann Hesse

“For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.”

— “Albertus Secundus,” epigraph to The Glass Bead Game

From DownloadThat.com

(Click to enlarge.)

http://www.log24.com/log/pix10B/100815-ThePaletteSm.jpg

Monday, June 14, 2010

Birkhoff on the Galois “Theory of Ambiguity”

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

The Principle of Sufficient Reason

by George David Birkhoff

from "Three Public Lectures on Scientific Subjects,"
delivered at the Rice Institute, March 6, 7, and 8, 1940

EXCERPT 1—

My primary purpose will be to show how a properly formulated
Principle of Sufficient Reason plays a fundamental
role in scientific thought and, furthermore, is to be regarded
as of the greatest suggestiveness from the philosophic point
of view.2

In the preceding lecture I pointed out that three branches
of philosophy, namely Logic, Aesthetics, and Ethics, fall
more and more under the sway of mathematical methods.
Today I would make a similar claim that the other great
branch of philosophy, Metaphysics, in so far as it possesses
a substantial core, is likely to undergo a similar fate. My
basis for this claim will be that metaphysical reasoning always
relies on the Principle of Sufficient Reason, and that
the true meaning of this Principle is to be found in the
Theory of Ambiguity” and in the associated mathematical
“Theory of Groups.”

If I were a Leibnizian mystic, believing in his “preestablished
harmony,” and the “best possible world” so
satirized by Voltaire in “Candide,” I would say that the
metaphysical importance of the Principle of Sufficient Reason
and the cognate Theory of Groups arises from the fact that
God thinks multi-dimensionally3 whereas men can only
think in linear syllogistic series, and the Theory of Groups is

2 As far as I am aware, only Scholastic Philosophy has fully recognized and ex-
ploited this principle as one of basic importance for philosophic thought

3 That is, uses multi-dimensional symbols beyond our grasp.
______________________________________________________________________

the appropriate instrument of thought to remedy our deficiency
in this respect.

The founder of the Theory of Groups was the mathematician
Evariste Galois. At the end of a long letter written in
1832 on the eve of a fatal duel, to his friend Auguste
Chevalier, the youthful Galois said in summarizing his
mathematical work,4 “You know, my dear Auguste, that
these subjects are not the only ones which I have explored.
My chief meditations for a considerable time have been
directed towards the application to transcendental Analysis
of the theory of ambiguity. . . . But I have not the time, and
my ideas are not yet well developed in this field, which is
immense.” This passage shows how in Galois’s mind the
Theory of Groups and the Theory of Ambiguity were
interrelated.5

Unfortunately later students of the Theory of Groups
have all too frequently forgotten that, philosophically
speaking, the subject remains neither more nor less than the
Theory of Ambiguity. In the limits of this lecture it is only
possible to elucidate by an elementary example the idea of a
group and of the associated ambiguity.

Consider a uniform square tile which is placed over a
marked equal square on a table. Evidently it is then impossible
to determine without further inspection which one
of four positions the tile occupies. In fact, if we designate
its vertices in order by A, B, C, D, and mark the corresponding
positions on the table, the four possibilities are for the
corners A, B, C, D of the tile to appear respectively in the
positions A, B, C, D;  B, C, D, A;  C, D, A, B; and D, A, B, C.
These are obtained respectively from the first position by a

4 My translation.
5 It is of interest to recall that Leibniz was interested in ambiguity to the extent
of using a special notation v (Latin, vel ) for “or.” Thus the ambiguously defined
roots 1, 5 of x2-6x+5=0 would be written x = l v 5 by him.
______________________________________________________________________

null rotation ( I ), by a rotation through 90° (R), by a rotation
through 180° (S), and by a rotation through 270° (T).
Furthermore the combination of any two of these rotations
in succession gives another such rotation. Thus a rotation R
through 90° followed by a rotation S through 180° is equivalent
to a single rotation T through 270°, Le., RS = T. Consequently,
the "group" of four operations I, R, S, T has
the "multiplication table" shown here:

http://www.log24.com/log/pix10A/100614-BirkhoffTable.jpg
This table fully characterizes the group, and shows the exact
nature of the underlying ambiguity of position.
More generally, any collection of operations such that
the resultant of any two performed in succession is one of
them, while there is always some operation which undoes
what any operation does, forms a "group."
__________________________________________________

EXCERPT 2—

Up to the present point my aim has been to consider a
variety of applications of the Principle of Sufficient Reason,
without attempting any precise formulation of the Principle
itself. With these applications in mind I will venture to
formulate the Principle and a related Heuristic Conjecture
in quasi-mathematical form as follows:

PRINCIPLE OF SUFFICIENT REASON. If there appears
in any theory T a set of ambiguously determined ( i e .
symmetrically entering) variables, then these variables can themselves
be determined only to the extent allowed by the corresponding
group G. Consequently any problem concerning these variables
which has a uniquely determined solution, must itself be
formulated so as to be unchanged by the operations of the group
G ( i e . must involve the variables symmetrically).

HEURISTIC CONJECTURE. The final form of any
scientific theory T is: (1) based on a few simple postulates; and
(2) contains an extensive ambiguity, associated symmetry, and
underlying group G, in such wise that, if the language and laws
of the theory of groups be taken for granted, the whole theory T
appears as nearly self-evident in virtue of the above Principle.

The Principle of Sufficient Reason and the Heuristic Conjecture,
as just formulated, have the advantage of not involving
excessively subjective ideas, while at the same time
retaining the essential kernel of the matter.

In my opinion it is essentially this principle and this
conjecture which are destined always to operate as the basic
criteria for the scientist in extending our knowledge and
understanding of the world.

It is also my belief that, in so far as there is anything
definite in the realm of Metaphysics, it will consist in further
applications of the same general type. This general conclu-
sion may be given the following suggestive symbolic form:

Image-- Birkhoff diagram relating Galois's theory of ambiguity to metaphysics

While the skillful metaphysical use of the Principle must
always be regarded as of dubious logical status, nevertheless
I believe it will remain the most important weapon of the
philosopher.

___________________________________________________________________________

A more recent lecture on the same subject —

"From Leibniz to Quantum World:
Symmetries, Principle of Sufficient Reason
and Ambiguity in the Sense of Galois
"

by Jean-Pierre Ramis (Johann Bernoulli Lecture at U. of Groningen, March 2005)

Theory of Ambiguity

Filed under: General,Geometry — m759 @ 5:01 pm

Théorie de l'Ambiguité

According to a 2008 paper by Yves André of the École Normale Supérieure  of Paris—

"Ambiguity theory was the name which Galois used
 when he referred to his own theory and its future developments."

The phrase "the theory of ambiguity" occurs in the testamentary letter Galois wrote to a friend, Auguste Chevalier, on the night before Galois was shot in a duel.

Hermann Weyl in Symmetry, Princeton University Press, 1952—

"This letter, if judged by the novelty and profundity of ideas it contains, is perhaps
  the most substantial piece of writing in the whole literature of mankind."

Conclusion of the Galois testamentary letter, according to
the 1897 Paris edition of Galois's collected works—

Image-- Galois on his theory of ambiguity, from Collected Works, Paris, 1897

The original—

Image-- Concluding paragraphs, Galois's 'last testament' letter to Chevalier, May 29, 1832

A transcription—

Évariste GALOIS, Lettre-testament, adressée à Auguste Chevalier—

Tu sais mon cher Auguste, que ces sujets ne sont pas les seuls que j'aie
explorés. Mes principales méditations, depuis quelques temps,
étaient dirigées sur l'application à l'analyse transcendante de la théorie de
l'ambiguité. Il s'agissait de voir a priori, dans une relation entre des quantités
ou fonctions transcendantes, quels échanges on pouvait faire, quelles
quantités on pouvait substituer aux quantités données, sans que la relation
put cesser d'avoir lieu. Cela fait reconnaitre de suite l'impossibilité de beaucoup
d'expressions que l'on pourrait chercher. Mais je n'ai pas le temps, et mes idées
ne sont pas encore bien développées sur ce terrain, qui est
immense.

Tu feras imprimer cette lettre dans la Revue encyclopédique.

Je me suis souvent hasardé dans ma vie à avancer des propositions dont je n'étais
pas sûr. Mais tout ce que j'ai écrit là est depuis bientôt un an dans ma
tête, et il est trop de mon intérêt de ne pas me tromper pour qu'on
me soupconne d'avoir énoncé des théorèmes dont je n'aurais pas la démonstration
complète.

Tu prieras publiquement Jacobi et Gauss de donner leur avis,
non sur la vérité, mais sur l'importance des théorèmes.

Après cela, il y aura, j'espère, des gens qui trouveront leur profit
à déchiffrer tout ce gachis.

Je t'embrasse avec effusion.

                                               E. Galois   Le 29 Mai 1832

A translation by Dr. Louis Weisner, Hunter College of the City of New York, from A Source Book in Mathematics, by David Eugene Smith, Dover Publications, 1959–

You know, my dear Auguste, that these subjects are not the only ones I have explored. My reflections, for some time, have been directed principally to the application of the theory of ambiguity to transcendental analysis. It is desired see a priori  in a relation among quantities or transcendental functions, what transformations one may make, what quantities one may substitute for the given quantities, without the relation ceasing to be valid. This enables us to recognize at once the impossibility of many expressions which we might seek. But I have no time, and my ideas are not developed in this field, which is immense.

Print this letter in the Revue Encyclopédique.

I have often in my life ventured to advance propositions of which I was uncertain; but all that I have written here has been in my head nearly a year, and it is too much to my interest not to deceive myself that I have been suspected of announcing theorems of which I had not the complete demonstration.

Ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the importance of the theorems.

Subsequently there will be, I hope, some people who will find it to their profit to decipher all this mess.

J t'embrasse avec effusion.
                        
                                                     E. Galois.   May 29, 1832.

Translation, in part, in The Unravelers: Mathematical Snapshots, by Jean Francois Dars, Annick Lesne, and Anne Papillaut (A.K. Peters, 2008)–

"You know, dear Auguste, that these subjects are not the only ones I have explored. For some time my main meditations have been directed on the application to transcendental analysis of the theory of ambiguity. The aim was to see in a relation between quantities or transcendental functions, what exchanges we could make, what quantities could be substituted to the given quantities without the relation ceasing to take place. In that way we see immediately that many expressions that we might look for are impossible. But I don't have the time and my ideas are not yet developed enough in this vast field."

Another translation, by James Dolan at the n-Category Café

"My principal meditations for some time have been directed towards the application of the theory of ambiguity to transcendental analysis. It was a question of seeing a priori in a relation between quantities or transcendent functions, what exchanges one could make, which quantities one could substitute for the given quantities without the original relation ceasing to hold. That immediately made clear the impossibility of finding many expressions that one could look for. But I do not have time and my ideas are not yet well developed on this ground which is immense."

Related material

"Renormalisation et Ambiguité Galoisienne," by Alain Connes, 2004

"La Théorie de l’Ambiguïté : De Galois aux Systèmes Dynamiques," by Jean-Pierre Ramis, 2006

"Ambiguity Theory, Old and New," preprint by Yves André, May 16, 2008,

"Ambiguity Theory," post by David Corfield at the n-Category Café, May 19, 2008

"Measuring Ambiguity," inaugural lecture at Utrecht University by Gunther Cornelissen, Jan. 16, 2009

Sunday, April 18, 2010

For Trevanian

Filed under: General — Tags: — m759 @ 8:00 pm

Where Entertainment Is God
(continued)

Google News at about 7:37 PM —

Image -- Google News, 'Dragon' Edges Out 'Kick-Ass' At Box Office

The Eiger Sanction, by Trevanian –

"Because CII men worked in foreign countries without invitation, and often to the detriment of the established governments, they had no recourse to official protection. Organization men to the core, the CII heads decided that another Division must be established to combat the problem. They relied on their computers to find the ideal man to head the new arm, and the card that survived the final sorting bore the name Yurasis Dragon. In order to bring Mr. Dragon to the United States, it was necessary to absolve him of accusations lodged at the War Crimes Tribunal concerning certain genocidal peccadillos, but CII considered him worth the effort."

Thursday, August 6, 2009

Thursday August 6, 2009

Filed under: General — Tags: , — m759 @ 6:00 am

The Running

"Budd Schulberg, who wrote the award-winning screenplay for 'On the Waterfront' and created a classic American archetype of naked ambition, Sammy Glick, in his novel What Makes Sammy Run?, died on Wednesday. He was 95…."

Running man with blue background on the cover of 'Eye of Cat,' by Roger Zelazny

Log24, Dec. 16, 2003:

See, too, Blue Matrices, and
a link for Beethoven's birthday:

Juliette Binoche with musical score from Kieslowski's 'Blue'

Song for the
Unification of Europe

Tuesday, March 10, 2009

Tuesday March 10, 2009

Filed under: General,Geometry — Tags: — m759 @ 9:26 am
Language Game

“Music, mathematics, and chess are in vital respects dynamic acts of location. Symbolic counters are arranged in significant rows. Solutions, be they of a discord, of an algebraic equation, or of a positional impasse, are achieved by a regrouping, by a sequential reordering of individual units and unit-clusters (notes, integers, rooks or pawns). The child-master, like his adult counterpart, is able to visualize in an instantaneous yet preternaturally confident way how the thing should look several moves hence. He sees the logical, the necessary harmonic and melodic argument as it arises out of an initial key relation or the preliminary fragments of a theme. He knows the order, the appropriate dimension, of the sum or geometric figure before he has performed the intervening steps. He announces mate in six because the victorious end position, the maximally efficient configuration of his pieces on the board, lies somehow ‘out there’ in graphic, inexplicably clear sight of his mind….”

“… in some autistic enchantment, pure as one of Bach’s inverted canons or Euler’s formula for polyhedra.”

— George Steiner, “A Death of Kings,” in The New Yorker, issue dated Sept. 7, 1968

Related material:

“Classrooms are filled with discussions not of the Bible and Jesus but of 10 ‘core values’– perseverance and curiosity, for instance– that are woven into the curriculum.”

— “Secular Education, Catholic Values,” by Javier C. Hernandez, The New York Times, Sunday, March 8, 2009

“… There was a problem laid out on the board, a six-mover. I couldn’t solve it, like a lot of my problems. I reached down and moved a knight…. I looked down at the chessboard. The move with the knight was wrong. I put it back where I had moved it from. Knights had no meaning in this game. It wasn’t a game for knights.”


— Raymond Chandler, The Big Sleep

The Chandler quotation appears in “Language Game,” an entry in this journal on April 7, 2008.

Some say the “Language Game” date, April 7, is the true date (fixed, permanent) of the Crucifixion– by analogy, Eliot’s “still point” and Jung’s “centre.” (See yesterday, noon.)

Friday, October 3, 2008

Friday October 3, 2008

Filed under: General — m759 @ 4:30 pm
The Prize

Paul Newman and Elke Sommer in 'The Prize'

“The secret to life, and
to love, is getting started,
keeping going, and then
getting started again.”

Nobel Laureate
Seamus Heaney
at Sanders Theatre,
Harvard College,
September 30, 2008

On Elke Sommer:

“…Young Elke… studied
in the prestigious
Gymnasium School
in Erlangen….”

Film Fatales

Erlangen Prize Lecture:

Variations on a Theme of
Plato, Goethe, and Klein

(Background:
Christmas Knot, Sept. 26,
and Hard Core, July 17-18.)

Saturday, July 19, 2008

Saturday July 19, 2008

Filed under: General,Geometry — Tags: , , — m759 @ 2:00 pm
Hard Core

(continued from yesterday)

Bertram Kostant, Professor Emeritus of Mathematics at MIT, on an object discussed in this week's New Yorker:

"A word about E(8). In my opinion, and shared by others, E(8) is the most magnificent 'object' in all of mathematics. It is like a diamond with thousands of facets. Each facet offering a different view of its unbelievable intricate internal structure."

Hermann Weyl on the hard core of objectivity:

"Perhaps the philosophically most relevant feature of modern science is the emergence of abstract symbolic structures as the hard core of objectivity behind– as Eddington puts it– the colorful tale of the subjective storyteller mind." (Philosophy of Mathematics and Natural Science, Princeton, 1949, p. 237)


Steven H. Cullinane on the symmetries of a 4×4 array of points:

A Structure-Endowed Entity

"A guiding principle in modern mathematics is this lesson: Whenever you have to do with a structure-endowed entity S, try to determine its group of automorphisms, the group of those element-wise transformations which leave all structural relations undisturbed.  You can expect to gain a deep insight into the constitution of S in this way."

— Hermann Weyl in Symmetry

Let us apply Weyl's lesson to the following "structure-endowed entity."

4x4 array of dots

What is the order of the resulting group of automorphisms?

The above group of
automorphisms plays
a role in what Weyl,
following Eddington,
  called a "colorful tale"–

The Diamond 16 Puzzle

The Diamond 16 Puzzle

This puzzle shows
that the 4×4 array can
also be viewed in
thousands of ways.

"You can make 322,560
pairs of patterns. Each
 pair pictures a different
symmetry of the underlying
16-point space."

— Steven H. Cullinane,
July 17, 2008

For other parts of the tale,
see Ashay Dharwadker,
the Four-Color Theorem,
and Usenet Postings
.

Friday, July 18, 2008

Friday July 18, 2008

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

Hard Core

David Corfield quotes Weyl in a weblog entry, "Hierarchy and Emergence," at the n-Category Cafe this morning:

"Perhaps the philosophically most relevant feature of modern science is the emergence of abstract symbolic structures as the hard core of objectivity behind– as Eddington puts it– the colorful tale of the subjective storyteller mind." (Philosophy of Mathematics and Natural Science [Princeton, 1949], p. 237)

For the same quotation in a combinatorial context, see the foreword by A. W. Tucker, "Combinatorial Problems," to a special issue of the IBM Journal of Research and Development, November 1960 (1-page pdf).

See also yesterday's Log24 entry.

Thursday, July 3, 2008

Thursday July 3, 2008

Filed under: General — m759 @ 7:11 pm
De Haut en Bas

“… this hard prize,
Fully made, fully apparent,
     fully found”

— Wallace Stevens,
“Credences of Summer”

Marlon Brando and Robert De Niro in 'The Score'

Marlon Brando and Robert De Niro
in “The Score

The Prize:

Billie Holiday, 'On the Sentimental Side' 3-CD set

Friday, June 6, 2008

Friday June 6, 2008

Filed under: General — Tags: , — m759 @ 1:00 pm
Order and Disorder

Robin Williams observes the Keystone State lottery of June 5, 2008: Mid-day 025, Evening 761
Midrash:
The Dance of Chance

Associated Press
"Today in History"
 Thought for Today:

"Two dangers constantly threaten
the world: order and disorder."
— Paul Valery, French poet
(1871-1945).
[La Crise de l'Esprit]

Also from Valéry:

«Notre esprit est fait d'un désordre,
plus un besoin de mettre en ordre
.»
(Mauvaises Pensées et Autres)

«L’ordre pèse toujours à l’individu. Le désordre lui fait désirer la police ou la mort. Ce sont deux circonstances extrêmes où la nature humaine n’est pas à l’aise. L’individu recherche une époque tout agréable, où il soit le plus libre et le plus aidé. Il la trouve vers le commencement de la fin d’un système social. Alors, entre l’ordre et le désordre, règne un moment délicieux. Tout le bien possible que procure l’arrangement des pouvoirs et des devoirs étant acquis, c’est maintenant que l’on peut jouir des premiers relâchements de ce système. Les institutions tiennent encore. Elles sont grandes et imposantes. Mais sans que rien de visible soit altéré en elles, elles n’ont guère plus que cette belle présence; leurs vertus se sont toutes produites; leur avenir est secrètement épuisé; leur caractère n’est plus sacré, ou bien il n’est plus que sacré; la critique et le mépris les exténuent et les vident de toute valeur prochaine. Le corps social perd doucement son lendemain. C’est l’heure de la jouissance et de la consommation générale.»

Paul Valéry, Préface aux Lettres Persanes (1926), recueillie dans Variété, II, 1930

Sunday, May 25, 2008

Sunday May 25, 2008

Filed under: General,Geometry — Tags: , , , — m759 @ 9:00 am
 
Wechsler Cubes
"Confusion is nothing new."
— Song lyric, Cyndi Lauper
 
Part I:
Magister Ludi

Hermann Hesse's 1943 The Glass Bead Game (Picador paperback, Dec. 6, 2002, pp. 139-140)–

"For the present, the Master showed him a bulky memorandum, a proposal he had received from an organist– one of the innumerable proposals which the directorate of the Game regularly had to examine. Usually these were suggestions for the admission of new material to the Archives. One man, for example, had made a meticulous study of the history of the madrigal and discovered in the development of the style a curved that he had expressed both musically and mathematically, so that it could be included in the vocabulary of the Game. Another had examined the rhythmic structure of Julius Caesar's Latin and discovered the most striking congruences with the results of well-known studies of the intervals in Byzantine hymns. Or again some fanatic had once more unearthed some new cabala hidden in the musical notation of the fifteenth century. Then there were the tempestuous letters from abstruse experimenters who could arrive at the most astounding conclusions from, say, a comparison of the horoscopes of Goethe and Spinoza; such letters often included pretty and seemingly enlightening geometric drawings in several colors."

Part II:
A Bulky Memorandum

From Siri Hustvedt, author of Mysteries of the Rectangle: Essays on Painting (Princeton Architectural Press, 2005)– What I Loved: A Novel (Picador paperback, March 1, 2004, page 168)–

A description of the work of Bill Wechsler, a fictional artist:

"Bill worked long hours on a series of autonomous pieces about numbers. Like O's Journey, the works took place inside glass cubes, but these were twice as large– about two feet square. He drew his inspiration from sources as varied as the Cabbala, physics, baseball box scores, and stock market reports. He painted, cut, sculpted, distorted, and broke the numerical signs in each work until they became unrecognizable. He included figures, objects, books, windows, and always the written word for the number. It was rambunctious art, thick with allusion– to voids, blanks, holes, to monotheism and the individual, the the dialectic and yin-yang, to the Trinity, the three fates, and three wishes, to the golden rectangle, to seven heavens, the seven lower orders of the sephiroth, the nine Muses, the nine circles of Hell, the nine worlds of Norse mythology, but also to popular references like A Better Marriage in Five Easy Lessons and Thinner Thighs in Seven Days. Twelve-step programs were referred to in both cube one and cube two. A miniature copy of a book called The Six Mistakes Parents Make Most Often lay at the bottom of cube six. Puns appeared, usually well disguised– one, won; two, too, and Tuesday; four, for, forth; ate, eight. Bill was partial to rhymes as well, both in images and words. In cube nine, the geometric figure for a line had been painted on one glass wall. In cube three, a tiny man wearing the black-and-white prison garb of cartoons and dragging a leg iron has

— End of page 168 —

opened the door to his cell. The hidden rhyme is "free." Looking closely through the walls of the cube, one can see the parallel rhyme in another language: the German word drei is scratched into one glass wall. Lying at the bottom of the same box is a tiny black-and-white photograph cut from a book that shows the entrance to Auschwitz: ARBEIT MACHT FREI. With every number, the arbitrary dance of associations worked togethere to create a tiny mental landscape that ranged in tone from wish-fulfillment dream to nightmare. Although dense, the effect of the cubes wasn't visually disorienting. Each object, painting, drawing, bit of text, or sculpted figure found its rightful place under the glass according to the necessary, if mad, logic of numerical, pictorial, and verbal connection– and the colors of each were startling. Every number had been given a thematic hue. Bill had been interested in Goethe's color wheel and in Alfred Jensen's use of it in his thick, hallucinatory paintings of numbers. He had assigned each number a color. Like Goethe, he included black and white, although he didn't bother with the poet's meanings. Zero and one were white. Two was blue. Three was red, four was yellow, and he mixed colors: pale blue for five, purples in six, oranges in seven, greens in eight, and blacks and grays in nine. Although other colors and omnipresent newsprint always intruded on the basic scheme, the myriad shades of a single color dominated each cube.

The number pieces were the work of a man at the top of his form. An organic extension of everything Bill had done before, these knots of symbols had an explosive effect. The longer I looked at them, the more the miniature constructions seemed on the brink of bursting from internal pressure. They were tightly orchestrated semantic bombs through which Bill laid bare the arbitrary roots of meaning itself– that peculiar social contract generated by little squiggles, dashes, lines, and loops on a page."

Part III:
Wechsler Cubes
(named not for
Bill Wechsler, the
fictional artist above,
but for the non-fictional
David Wechsler) –

 

From 2002:

 

Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest.

 
Part IV:
A Magic Gallery
Log24, March 4, 2004
 

ZZ
WW

Figures from the
Kaleidoscope Puzzle
of Steven H. Cullinane:


Poem by Eugen Jost:
Zahlen und Zeichen,
Wörter und Worte

Mit Zeichen und Zahlen
vermessen wir Himmel und Erde
schwarz
auf weiss
schaffen wir neue Welten
oder gar Universen

 Numbers and Names,
Wording and Words

With numbers and names
we measure heaven and earth
black
on white
we create new worlds
and universes

English translation
by Catherine Schelbert

A related poem:

Alphabets
by Hermann Hesse

From time to time
we take our pen in hand
and scribble symbols
on a blank white sheet
Their meaning is
at everyone's command;
it is a game whose rules
are nice and neat.

But if a savage
or a moon-man came
and found a page,
a furrowed runic field,
and curiously studied
lines and frame:
How strange would be
the world that they revealed.
a magic gallery of oddities.
He would see A and B
as man and beast,
as moving tongues or
arms or legs or eyes,
now slow, now rushing,
all constraint released,
like prints of ravens'
feet upon the snow.
He'd hop about with them,
fly to and fro,
and see a thousand worlds
of might-have-been
hidden within the black
and frozen symbols,
beneath the ornate strokes,
the thick and thin.
He'd see the way love burns
and anguish trembles,
He'd wonder, laugh,
shake with fear and weep
because beyond this cipher's
cross-barred keep
he'd see the world
in all its aimless passion,
diminished, dwarfed, and
spellbound in the symbols,
and rigorously marching
prisoner-fashion.
He'd think: each sign
all others so resembles
that love of life and death,
or lust and anguish,
are simply twins whom
no one can distinguish…
until at last the savage
with a sound
of mortal terror
lights and stirs a fire,
chants and beats his brow
against the ground
and consecrates the writing
to his pyre.
Perhaps before his
consciousness is drowned
in slumber there will come
to him some sense
of how this world
of magic fraudulence,
this horror utterly
behind endurance,
has vanished as if
it had never been.
He'll sigh, and smile,
and feel all right again.

— Hermann Hesse (1943),
"Buchstaben," from
Das Glasperlenspiel,
translated by
Richard and Clara Winston

Tuesday, April 29, 2008

Tuesday April 29, 2008

Sacerdotal Jargon
at Harvard:

Thomas Wolfe

Thomas Wolfe
(Harvard M.A., 1922)

versus

Rosalind Krauss

Rosalind Krauss
(Harvard M.A., 1964,
Ph.D., 1969)

on

The Kernel of Eternity

"No culture has a pact with eternity."
George Steiner, interview in  
The Guardian of April 19

"At that instant he saw,
in one blaze of light, an image
of unutterable conviction….
the core of life, the essential
pattern whence all other things
proceed, the kernel of eternity."

— Thomas Wolfe, Of Time
and the River, quoted in
Log24 on June 9, 2005

 

From today's online Harvard Crimson:

"… under the leadership of Faust,
Harvard students should look forward
to an ever-growing opportunity for
international experience
and artistic endeavor."

 

Wolfgang Pauli as Mephistopheles

Pauli as Mephistopheles
in a 1932 parody of
Goethe's
Faust at Niels Bohr's
institute in Copenhagen

From a recent book
on Wolfgang Pauli,
The Innermost Kernel:

Pauli's Dream Square (square plus the two diagonals)

A belated happy birthday
to the late
Felix Christian Klein
  (born on April 25) —

The Klein Group: The four elements in four colors, with black points representing the identity

Another Harvard figure quoted here on Dec. 5, 2002:

"The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety, a subtlety in which it was natural for Cézanne to say: 'I see planes bestriding each other and sometimes straight lines seem to me to fall' or 'Planes in color…. The colored area where shimmer the souls of the planes, in the blaze of the kindled prism, the meeting of planes in the sunlight.' The conversion of our Lumpenwelt went far beyond this. It was from the point of view of another subtlety that Klee could write: 'But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space– which he calls the mind or heart of creation– determines every function.' Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less."

— Wallace Stevens, Harvard College Class of 1901, "The Relations between Poetry and Painting" in The Necessary Angel (Knopf, 1951)

From a review of Rosalind Krauss's The Optical Unconscious  (MIT Press hardcover, 1993):

Krauss is concerned to present Modernism less in terms of its history than its structure, which she seeks to represent by means of a kind of diagram: "It is more interesting to think of modernism as a graph or table than a history." The "table" is a square with diagonally connected corners, of the kind most likely to be familiar to readers as the Square of Opposition, found in elementary logic texts since the mid-19th century. The square, as Krauss sees it, defines a kind of idealized space "within which to work out unbearable contradictions produced within the real field of history." This she calls, using the inevitable gallicism, "the site of Jameson's Political Unconscious" and then, in art, the optical unconscious, which consists of what Utopian Modernism had to kick downstairs, to repress, to "evacuate… from its field."

— Arthur C. Danto in ArtForum, Summer 1993

Rosalind Krauss in The Optical Unconscious (MIT Press paperback, 1994):

For a presentation of the Klein Group, see Marc Barbut, "On the Meaning of the Word 'Structure' in Mathematics," in Introduction to Structuralism, ed. Michael Lane (New York: Basic Books, 1970). Claude Lévi-Strauss uses the Klein group in his analysis of the relation between Kwakiutl and Salish masks in The Way of the Masks, trans. Sylvia Modelski (Seattle: University of Washington Press, 1982), p. 125; and in relation to the Oedipus myth in "The Structural Analysis of Myth," Structural Anthropology, trans. Claire Jackobson [sic] and Brooke Grundfest Schoepf (New York: Basic Books, 1963). In a transformation of the Klein Group, A. J. Greimas has developed the semiotic square, which he describes as giving "a slightly different formulation to the same structure," in "The Interaction of Semiotic Constraints," On Meaning (Minneapolis: University of Minnesota Press, 1987), p. 50. Jameson uses the semiotic square in The Political Unconscious (see pp. 167, 254, 256, 277) [Fredric Jameson, The Political Unconscious: Narrative as a Socially Symbolic Act (Ithaca: Cornell University Press, 1981)], as does Louis Marin in "Disneyland: A Degenerate Utopia," Glyph, no. 1 (1977), p. 64.

For related non-sacerdotal jargon, see…
 

Wikipedia on the Klein group (denoted V, for Vierergruppe):

In this representation, V is a normal subgroup of the alternating group A4 (and also the symmetric group S4) on 4 letters. In fact, it is the kernel of a surjective map from S4 to S3. According to Galois theory, the existence of the Klein four-group (and in particular, this representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals.

For radicals of another sort, see A Logocentric Meditation, A Mass for Lucero, and [update of 7 PM] Steven Erlanger in today's New York Times— "France Still Divided Over Lessons of 1968 Unrest."

For material related to Klee's phrase mentioned above by Stevens, "the organic center of all movement in time and space," see the following Google search:

April 29, 2008, Google search on 'penrose space time'

Click on the above
 image for details.

See also yesterday's
Religious Art.

Thursday, March 27, 2008

Thursday March 27, 2008

Filed under: General,Geometry — Tags: — m759 @ 3:29 pm

Back to the Garden

Film star Richard Widmark
died on Monday, March 24.

From Log24 on that date:

"Hanging from the highest limb
of the apple tree are
     the three God's Eyes…"

    — Ken Kesey  

Related material:

The Beauty Test, 5/23/07–
 
H.S.M. Coxeter's classic
Introduction to Geometry (2nd ed.):

The image “http://www.log24.com/log/pix07/070523-Coxeter62.jpg” cannot be displayed, because it contains errors.

Note the resemblance of
the central part to
a magical counterpart–
the Ojo de Dios
of Mexico's Sierra Madre.

From a Richard Widmark film festival:

GARDEN OF EVIL
Henry Hathaway, 1954

"A severely underrated Scope western, shot in breathtaking mountain locations near Cuernavaca. Widmark, Gary Cooper and Cameron Mitchell are a trio of fortune hunters stranded in Mexico, when they are approached by Susan Hayward to rescue her husband (Hugh Marlowe) from a caved-in gold mine in Indian country. When they arrive at the 'Garden of Evil,' they must first battle with one another before they have to stave off their bloodthirsty Indian attackers. Widmark gives a tough, moving performance as Fiske, the one who sacrifices himself to save his friends. 'Every day it goes, and somebody goes with it,' he says as he watches the setting sun. 'Today it's me.' This was one of the best of Hollywood veteran Henry Hathaway's later films. With a brilliant score by Bernard Herrmann."

See also
the apple-tree
entries from Monday
(the date of Widmark's death)
and Tuesday, as well as
today's previous entry and
previous Log24
entries on Cuernavaca
.

Thursday, June 21, 2007

Thursday June 21, 2007

Filed under: General,Geometry — Tags: , , , , — m759 @ 12:07 pm

Let No Man
Write My Epigraph

(See entries of June 19th.)

"His graceful accounts of the Bach Suites for Unaccompanied Cello illuminated the works’ structural logic as well as their inner spirituality."

Allan Kozinn on Mstislav Rostropovich in The New York Times, quoted in Log24 on April 29, 2007

"At that instant he saw, in one blaze of light, an image of unutterable conviction…. the core of life, the essential pattern whence all other things proceed, the kernel of eternity."

— Thomas Wolfe, Of Time and the River, quoted in Log24 on June 9, 2005

"… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)"

— Peter J. Cameron, "The Geometry of the Mathieu Groups" (pdf)

"… donc Dieu existe, réponse!"

— Attributed, some say falsely,
to Leonhard Euler
 
"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"

(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)

 

Wolfgang Pauli as Mephistopheles

"Pauli as Mephistopheles
in a 1932 parody of
Goethe's Faust at Niels Bohr's
institute in Copenhagen.
The drawing is one of
many by George Gamow
illustrating the script."
Physics Today

 

"Borja dropped the mutilated book on the floor with the others. He was looking at the nine engravings and at the circle, checking strange correspondences between them.

'To meet someone' was his enigmatic answer. 'To search for the stone that the Great Architect rejected, the philosopher's stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso.'"

The Club Dumas, basis for the Roman Polanski film "The Ninth Gate" (See 12/24/05.)


"Pauli linked this symbolism
with the concept of automorphism."

The Innermost Kernel
 (previous entry)

And from
"Symmetry in Mathematics
and Mathematics of Symmetry
"
(pdf), by Peter J. Cameron,
a paper presented at the
International Symmetry Conference,
Edinburgh, Jan. 14-17, 2007,
we have

The Epigraph–

Weyl on automorphisms
(Here "whatever" should
of course be "whenever.")

Also from the
Cameron paper:

Local or global?

Among other (mostly more vague) definitions of symmetry, the dictionary will typically list two, something like this:

• exact correspondence of parts;
• remaining unchanged by transformation.

Mathematicians typically consider the second, global, notion, but what about the first, local, notion, and what is the relationship between them?  A structure M is homogeneous if every isomorphism between finite substructures of M can be extended to an automorphism of M; in other words, "any local symmetry is global."

Some Log24 entries
related to the above politically
(women in mathematics)–

Global and Local:
One Small Step

and mathematically–

Structural Logic continued:
Structure and Logic
(4/30/07):

This entry cites
Alice Devillers of Brussels–

Alice Devillers

"The aim of this thesis
is to classify certain structures
which are, from a certain
point of view, as homogeneous
as possible, that is which have
  as many symmetries as possible."

"There is such a thing
as a tesseract."

Madeleine L'Engle 

Saturday, March 24, 2007

Saturday March 24, 2007

Filed under: General — m759 @ 2:12 am
Today’s New York Times:
 

Herman Stein, 91,
Composer of Moody
Horror and Science-
Fiction Scores, Dies

The image “Herman Stein, film composer

Stein died on March 15.
It is not known whether he
  wrote the musical theme
for Log24 on that day,
Boink, Boink.”

Friday, February 9, 2007

Friday February 9, 2007

Filed under: General,Geometry — m759 @ 3:24 pm
The Romance
of Mathematics

The image “http://www.log24.com/log/pix07/070209-Cupid2.gif” cannot be displayed, because it contains errors.

On teachers of “core mathematics classes for non-majors, mathematics appreciation courses, and other lower level courses”:

“We are accustomed to being marginalized by society, our political leaders, and even our college and university administrations who often fail to see the scholarship involved in teaching. But how dare the Notices ignore us?”

— Complaint in the March 2007 Notices of the American Mathematical Society by “Julian F. Fleron, Ph.D., Professor of Mathematics, Westfield State College”

Let us examine Fleron’s alleged scholarship:

“Before each of my classes I put a quote on the board. The quote is either related to the mathematics we are studying, related to mathematics more generally, or related to learning and education. Student response has been tremendous, and I have found it to be very beneficial.” —Julian Fleron

Fleron offers us, without specifying an exact source, the following quotation:

“Mighty is geometry; joined with art, resistless. Euripides.

A search for the source leads us to a quotation from 1914, a time when teaching did sometimes involve scholarship:

“1568. Mighty are numbers, joined with art resistless. EURIPIDES. Hecuba, Line 884.”

Memorabilia Mathematica, by Robert Edouard Moritz, The Macmillan Company, 1914

But even in 1914, the scholarship, if one can call it that, was misleading. The 1914 quotation (which at least refers accurately to numbers, not geometry) is blatantly taken out of context to imply a connection with the mathematical art of number theory (as practiced by, say, G. H. Hardy) that is certainly not found in Euripides. The details:

HECUBA Sheltered beneath these tents is a host of Trojan women.

AGAMEMNON Dost mean the captives, the booty of the Hellenes?

HECUBA With their help will I punish my murderous foe.

AGAMEMNON How are women to master men?

HECUBA Numbers are a fearful thing, and joined to craft a desperate foe.

AGAMEMNON True; still I have a mean opinion of the female race.

This dialogue may have some relevance to today’s rumored selection at Harvard of a woman (Drew Gilpin Faust as Hecuba) to replace a man (Larry Summers as Agamemnon) in the president’s office. The dialogue’s only relevance to mathematics is in its reference to the perennial conflict between the sexes. Perhaps that conflict will serve to illustrate the title given by the Notices to Fleron’s complaint: “Teaching the Romance of Mathematics.”

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,
2005:

Multispeech

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,”

and
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.

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

 

Score:

"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

Perhaps.
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.
 

Monday, June 19, 2006

Monday June 19, 2006

Filed under: General — m759 @ 4:00 pm

Snippets:
A Reply to John Updike

See Updike on digitized snippets.

The following four snippets were pirated from the end of MathPages Quotations, compiled by Kevin Brown.

They are of synchronistic interest in view of the previous two Log24 entries, which referred (implicitly) to a Poe story and (explicitly) to Pascal.

"That is another of your odd notions,"
said the Prefect, who had the fashion
of calling everything 'odd' that was
beyond his comprehension, and thus
lived amid an absolute legion of 'oddities.'
Edgar Allan Poe

I knew when seven justices could not
take up a quarrel, but when the parties
were met themselves, one of them
thought but of an If, as, 'If you said so,
then I said so'; and they shook hands
and swore brothers. Your If is the only
peacemaker; much virtue in If.
Shakespeare

I have made this letter longer than usual
because I lack the time to make it shorter.
Blaise Pascal

S'io credessi che mia risposta fosse
a persona che mai tornasse al mondo,
questa fiamma staria senza piu scosse.
Ma per cio che giammai di questo fondo
non torno vivo alcun, s'i'odo il vero,
senza tema d'infamia ti rispondo.
Dante, 1302

For translations of the Dante (including one by Dorothy Sayers), see everything2.com.

An anonymous author there notes that Dante describes a flame in which is encased a damned soul. The flame vibrates as the soul speaks:

If I thought that I were making
Answer to one that might return to view
The world, this flame should evermore
cease shaking.

But since from this abyss, if I hear true,
None ever came alive, I have no fear
Of infamy, but give thee answer due.

-- Dante, Inferno, Canto 27, lines 61-66,
translated by Dorothy Sayers

Updike says,

“Yes, there is a ton of information on the web but much of it is grievously inaccurate, unedited, unattributed and juvenile. The electronic marvels that abound around us serve, I have the impression, to inflame what is most informally and non-critically human about us. Our computer screens stare back at us with a kind of giant, instant aw-shucks, disarming in its modesty.”

Note Updike’s use of “inflame.”

For an aw-shucks version of “what is most informally and non-critically human about us,” as well as a theological flame, see both the previous entry and the above report from Hell.

Note that the web serves also to correct material that is inaccurate, unedited, unattributed, and juvenile. For examples, see Mathematics and Narrative. The combination of today’s entry for Pascal’s birthday with that web page serves both to light one candle and to curse the darkness.

Friday, April 28, 2006

Friday April 28, 2006

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

Exercise

Review the concepts of integritas, consonantia,  and claritas in Aquinas:

"For in respect to beauty three things are essential: first of all, integrity or completeness, since beings deprived of wholeness are on this score ugly; and [secondly] a certain required design, or patterned structure; and finally a certain splendor, inasmuch as things are called beautiful which have a certain 'blaze of being' about them…."

Summa Theologiae Sancti Thomae Aquinatis, I, q. 39, a. 8, as translated by William T. Noon, S.J., in Joyce and Aquinas, Yale University Press, 1957

Review the following three publications cited in a note of April 28, 1985 (21 years ago today):

(1) Cameron, P. J.,
     Parallelisms of Complete Designs,
     Cambridge University Press, 1976.

(2) Conwell, G. M.,
     The 3-space PG(3,2) and its group,
     Ann. of Math. 11 (1910) 60-76.

(3) Curtis, R. T.,
     A new combinatorial approach to M24,
     Math. Proc. Camb. Phil. Soc.
    
79 (1976) 25-42.

Discuss how the sextet parallelism in (1) illustrates integritas, how the Conwell correspondence in (2) illustrates consonantia, and how the Miracle Octad Generator in (3) illustrates claritas.
 

Monday, March 13, 2006

Monday March 13, 2006

Filed under: General — Tags: , , — m759 @ 1:01 pm
Christ at the
Lapin Agile

The image “http://www.log24.com/log/pix06/060313-WasleyChrist1.jpg” cannot be displayed, because it contains errors.

The Christ by Wasley,
on wall under his right arm
the Picasso painting.”

Le Républicain Lorrain du 14 janvier 2001

Le Lapin Agile veille sur la Butte (par Michel Genson)

24 décembre 1900. Dans son atelier glacial du Bateau Lavoir, à  flanc de la colline de Montmartre, Picasso se frotte les yeux. C’est bien Wasley, son ami Wasley, qu’il aperçoit traversant la place Ravignan, courbé sous le poids d’un grand Christ en croix. Le sculpteur titube et s’en va gravissant un à un les escaliers qui mènent au sommet de la Butte, direction la rue des Saules. Car l’œuvre est destinée aux murs du petit estaminet où la bande a trouvé asile, pour y échanger chaque soir des refrains, bocks et vaticinations les plus folles. La bande, c’est à dire Utrillo, Max Jacob, Modigliani et les autres… Un siècle et un souffle de légende plus tard, le même Christ blanc occupe toujours la même place, sous les lumières tamisées du Lapin Agile. À l’abri sous son aisselle droite, l’autoportrait de Picasso en Arlequin a été authentique en son temps. Jusqu’au jour où le grand Frédé, tenancier mythique du lieu, s’est gratté la barbe avant de le céder à un amateur suédois de passage. Depuis l’original a fait le voyage du MAM (Modern Art Museum) de New-York, et la Butte se contente d’une copie.

Pour le reste, rien a changé ou presque pour le doyen des cabarets parisiens. Ni le décor, ni l’esprit. L’incroyable patine noire des murs, posée là par des lustres de tabagies rigolardes ou inspirées, rappelle au générique les voix des habituées de jadis, Apollinaire, Carco, Dullin, Couté, puis Pierre Brasseur, et plus proches de nous encore d’autres débutants, Caussimon, Brassens, François Billetdoux… La liste exhaustive serait impossible à dresser de tous ceux qui ont émargé au livre d’or du Lapin Agile.
 
« En haut de la rue Saint-Vincent… » La goualante roule sa rime chaotique sur le pavé de la Butte. Au carrefour de la rue des Saules, la façade est avenante, sans apprêts, avec son acacia dans la cour, et cette étrange dénomination, née des amours burlesques entre l’imagination d’un dessinateur et les facéties des usagers. En 1875, André Gill, caricaturiste ami de Rimbaud, croque en effet, pour l’enseigne de l’ancien Cabaret des Assassins, un lapin facétieux sautant d’une marmite. Le temps d’un jeu de mots et le Lapin à Gill gagne son brevet d’agilité. L’épopée commence, que perpétue Yves Mathieu, aujourd’hui propriétaire, mémoire et continuateur d’une histoire somme toute unique. Histoire, qui, pour l’anecdote, faillit se terminer prématurément, sous la pioche des démolisseurs. Vers 1900, les bicoques du maquis montmartrois doivent laisser place à un grand projet immobilier. C’est Aristide Bruant qui sauvera in extremis le cabaret. Il achète l’établissement, laisse Frédé dans les murs qu’il revendra pour « un prix amical » à Paulo, le fils du même Frédé. Lequel Paulo n’est autre que le beau-père de l’actuel patron : « C’est un truc de famille. J’ai commencé à chanter ici en 48, égrène Yves Mathieu. Ensuite j’ai fait de l’opérette à la Gaîté Lyrique, de la revue aux Folies Bergères, je suis parti en Amérique… En revenant j’ai repris le cabaret, ma femme y chante, mes fils sont là, ils apprennent le métier… C’est comme le cirque, c’est le même esprit. »

Malgré les tempêtes et les modes, le Lapin Agile dure et perdure donc. Et sa silhouette pour carte postale inspire toujours les peintres venus de partout. Comme si la halte faisait partie d’un parcours initiatique immuable. Deux pièces pour un minuscule rez-de-chaussée, dans la première, mi-loge, mi-vestiaire, une guitare attend son tour de projecteur. En l’occurrence un faisceau unique clouant le chanteur (l’humoriste ou le diseur) au rideau rouge de la seconde salle. Là où le spectacle se déroule depuis toujours, là où l’on s’accoude sans vergogne à la table d’Apollinaire, sous les lampes toujours drapées de rouge, pour écouter Ferré, Aragon, Mac Orlan ou les rengaines du Folklore populaire montmartrois. Yves Mathieu reste ferme, « ici, pas de sonorisation, pas de haut-parleur. Les gens découvrent la voix humaine. » Un refrain de Piaf glisse jusqu’au « laboratoire », le réduit où les autres artistes du programme dissertent sur l’état du monde. Les meubles de Bruant sont encore là, au hasard d’un coffre breton, un autre de marine, la façade d’un lit clos… « Des trucs d’origine » pour Yves Mathieu, qui malgré les vicissitudes du temps – il s’ingénie toute l’année durant à entretenir un établissement qui ne bénéficie d’aucun classement officiel, ni d’aucun subside – prêche haut et fort sa confiance, « parce qu’on aura plus que jamais besoin de racines, de repères, et qu’ici, c’est tout un pan de patrimoine qu’on défend à travers la chanson française, celle qu’on chante tous ensemble… » Le même secoue sa longue carcasse et se fend d’un sourire entendu : « Quand je descends à Paris, c’est pas pareil. Ici, le jour, c’est comme dans une église. Il y a le silence, et l’impression de ressentir les ondes laissées pare les cerveaux de ces types, là… » Aux murs, dessins ou tableaux laissés par Mac Orlan, Maclet ou Suzanne Valadon jouent avec l’ombre amicale.

Le Lapin Agile, 22 rue des Saules, 75018 Paris. Tel : 01 46 06 85 87

Source:
http://www.au-lapin-agile.com/info4.htm

Note the above description
of Christmas Eve 1900,
and the remark that
“Ici, le jour, c’est comme
dans une église.”

A search for more material on
the Wasley Christ leads to
Princeton’s Nassau Church:

The fullness of time. I don’t have to call on the physicists among us to conclude that this fullness was not meant to be the end of the time line. That Paul must not have been talking about time in a linear way. Fullness. Complete. Almost perfect. Overflowing with grace. Just right. Fullness. As in “the earth is the Lord’s and the fullness thereof.” Fullness. As in “I pray that you may have the power to comprehend with all of the saints, what is the breadth, and length, and height and depth, and to know the love of Christ that surpasses all knowledge, so that you may be filled with all the fullness of God.” Fullness. As in “For in Christ, all the fullness of God was pleased to dwell.” “When the fullness of time had come, God sent his Son, born of a woman.”

I can remember Christmas Eve as a child….

— Christmas Eve, 2004,
    Sermon at Nassau Church by
    The Rev. Dr. David A. Davis

Related material from Log24:

Religious Symbolism at Princeton,
on the Nassau Church,

Counting Crows on
the Feast of St. Luke
(“Fullness… Multitude”),

The Quality of Diamond,
in memory of
Saint Hans-Georg Gadamer,
who died at 102
four years ago on this date,

and

Diamonds Are Forever.

Thursday, November 10, 2005

Thursday November 10, 2005

Filed under: General — m759 @ 4:00 pm
The Rhetoric of
Scientism

Kansas, Where “Ignorant”
is the New “Educated”:

“… the Board of Education went as far as to redefine what science is: it’s no longer just a search for natural explanations for natural phenomena. Now it’s a search for… well, that’s a bit hard to say. Any sort of explanation, apparently. Pixies, ghosts, telekinesis, auras, ancient astronauts, excesses of choleric humor, they all seem to be fair game in the interest of ‘academic freedom.'”

John Rennie, editor in chief of
  Scientific American, Nov. 8, 2005

The shocking redefinition
(with changes highlighted):
Kansas Definition of Science
Adopted Feb. 14, 2001

Science is the human activity of seeking natural explanations for what we observe in the world around us.  Science does so through the use of observation, experimentation, and logical argument while maintaining strict empirical standards and healthy skepticism. Scientific explanations are built on observations, hypotheses, and theories. A hypothesis is a testable statement about the natural world that can be used to build more complex inferences and explanations. A theory is a well-substantiated explanation of some aspect of the natural world that can incorporate observations, inferences, and tested hypotheses

Kansas Definition of Science
Approved Nov. 8, 2005

Science is a systematic method of continuing investigation that uses observations, hypothesis testing, measurement, experimentation, logical argument and theory building to lead to more adequate explanations of natural phenomena. Science does so while maintaining strict empirical standards and healthy skepticism. Scientific explanations are built on observations, hypotheses, and theories. A hypothesis is a testable statement about the natural world that can be used to build more complex inferences and explanations. A theory is a well-substantiated explanation of some aspect of the natural world that can incorporate observations, inferences, and tested hypotheses.

Scientific explanations must meet certain criteria. Scientific explanations are consistent with experimental and/or observational data and testable by scientists through additional experimentation and/or observation. Scientific explanation must meet criteria that govern the repeatability of observations and experiments. The effect of these criteria is to insure that scientific explanations about the world are open to criticism and that they will be modified or abandoned in favor of new explanations if empirical evidence so warrants. Because all scientific explanations depend on observational and experimental confirmation, all scientific knowledge is, in principle, subject to change as new evidence becomes available. The core theories of science have been subjected to a wide variety of confirmations and have a high degree of reliability within the limits to which they have been tested. In areas where data or understanding are incomplete, new data may lead to changes in current theories or resolve current conflicts. In situations where information is still fragmentary, it is normal for scientific ideas to be incomplete, but this is also where the opportunity for making advances may be greatest. Science has flourished in different regions during different time periods, and in history, diverse cultures have contributed scientific knowledge and technological inventions. Changes in scientific knowledge usually occur as gradual modifications, but the scientific enterprise also experiences periods of rapid advancement. The daily work of science and technology results in incremental advances in our understanding of the world about us.” Scientific explanations must meet certain criteria. Scientific explanations are consistent with experimental and/or observational data and testable by scientists through additional experimentation and/or observation. Scientific explanation must meet criteria that govern the repeatability of observations and experiments. The effect of these criteria is to insure that scientific explanations about the world are open to criticism and that they will be modified or abandoned in favor of new explanations if empirical evidence so warrants. Because all scientific explanations depend on observational and experimental confirmation, all scientific knowledge is, in principle, subject to change as new evidence becomes available. The core theories of science have been subjected to a wide variety of confirmations and have a high degree of reliability within the limits to which they have been tested. In areas where data or understanding is incomplete, new data may lead to changes in current theories or resolve current conflicts. In situations where information is still fragmentary, it is normal for scientific ideas to be incomplete, but this is also where the opportunity for making advances may be greatest. Science has flourished in different regions during different time periods, and in history, diverse cultures have contributed scientific knowledge and technological inventions. Changes in scientific knowledge usually occur as gradual modifications, but the scientific enterprise also experiences periods of rapid advancement. The daily work of science and technology results in incremental advances in understanding the world.”

From both old (2001) and
new (2005) Kansas standards:


Teaching With Tolerance and Respect

“A teacher is an important role model for  demonstrating respect, sensitivity, and civility. Teachers should not ridicule, belittle or embarrass a student for expressing an alternative view or belief.”

It’s a very ancient saying,
But a true and honest thought,
That if you become a teacher,
By your pupils you’ll be taught.

— Oscar Hammerstein,
“Getting to Know You”

Scientism and Civility:

A Google blog search for
fucking kansas evolution standards -fuck
yields “about 47” entries.

A search for
fuck kansas evolution standards -fucking
yields  “about 34” entries.

A search for
fuck fucking kansas evolution standards
yields “about 42” entries.

Saturday, June 11, 2005

Saturday June 11, 2005

Filed under: General — m759 @ 3:11 am

The Last Word

Beethoven Week on the BBC ended at midnight June 10.

“With Beethoven, music did not grow up, it regressed to adolescence. He was a hooligan who could reduce Schiller’s Ode to Joy to madness, bloodlust, and megalomania.”

Arts and Letters Daily, lead-in to an opinion piece in The Guardian of Tuesday, June 7, 2005:

Beethoven Was a Narcissistic Hooligan

“If Beethoven had dedicated his obvious talents to serving the noble Pythagorean view of music, he might well have gone on to compose music even greater than that of Mozart. You can hear this potential in his early string quartets, where the movements often have neat conclusions and there is a playfulness reminiscent of Mozart or Haydn. If only Beethoven had nourished these tender shoots instead of the darker elements that one can also hear. For the darkness is already evident in the early quartets too, in their sombre harmonies and sudden key changes. As it was, however, his darker side won out; compare, for example, the late string quartets. Here the youthful humour has completely vanished; the occasional signs of optimism quickly die out moments after they appear and the movements sometimes end in uncomfortably inconclusive cadences….

In A Clockwork Orange it is the fourth movement of Beethoven’s Ninth Symphony that echoes in the mind of Alex whenever he indulges in one of his orgies of violence. Alex’s reaction may be rather extreme, but he is responding to something that is already there in this dark and frenzied setting of Schiller’s Ode to Joy; the joy it invites one to feel is the joy of madness, bloodlust and megalomania. It is glorious music, and seductive, but the passions it stirs up are dark and menacing.”

The image “http://www.log24.com/log/pix05A/050611-Clock.jpg” cannot be displayed, because it contains errors.

Dylan Evans, former Lacanian psychotherapist (pdf) and now head of the undergraduate robotics program at the University of the West of England.

Speak for yourself, Dylan.

“Evil did not have the last word.”

—  Richard John Neuhaus, April 4, 2005

Evil may have had the last word in Tuesday’s Guardian, but now that Beethoven Week has ended, it seems time for another word.

For another view of Beethoven, in particular the late quartets, see the Log24 Beethoven’s Birthday entry of December 16, 2002:

Beethoven’s Birthday

“Ludwig van Beethoven’s String Quartet in A Minor, Opus 132, is one of the transcendent masterworks of the Western classical tradition. It is built around its luminous third movement, titled ‘Holy song of thanksgiving by one recovering from an illness.’

In this third movement, the aging Beethoven speaks, clearly and distinctly, in a voice seemingly meant both for all the world and for each individual who listens to it. The music, written in the ancient Lydian mode, is slow and grave and somehow both a struggle and a celebration at the same time.

This is music written by a supreme master at the height of his art, saying that through all illness, tribulation and sorrow there is a strength, there is a light, there is a hope.”

—  Andrew Lindemann Malone

“Eliot’s final poetic achievement—and, for many, his greatest—is the set of four poems published together in 1943 as Four Quartets…. Structurally—though the analogy is a loose one—Eliot modeled the Quartets on the late string quartets of Beethoven, especially… the A Minor Quartet; as early as 1931 he had written the poet Stephen Spender, ‘I have the A Minor Quartet on the gramophone, and I find it quite inexhaustible to study. There is a sort of heavenly or at least more than human gaiety about some of his later things which one imagines might come to oneself as the fruit of reconciliation and relief after immense suffering; I should like to get something of that into verse before I die.'”

— Anonymous author at a
Longman Publishers website

“Each of the late quartets has a unique structure, and the structure of the Quartet in A Minor is one of the most striking of all. Its five movements form an arch. At the center is a stunning slow movement that lasts nearly half the length of the entire quartet…

The third movement (Molto adagio) has a remarkable heading: in the score Beethoven titles it ‘Hymn of Thanksgiving to the Godhead from an Invalid,’ a clear reflection of the illness he had just come through. This is a variation movement, and Beethoven lays out the slow opening section, full of heartfelt music. But suddenly the music switches to D major and leaps ahead brightly; Beethoven marks this section ‘Feeling New Strength.’ These two sections alternate through this movement (the form is A-B-A-B-A), and the opening section is so varied on each reappearance that it seems to take on an entirely different character each time: each section is distinct, and each is moving in its own way (Beethoven marks the third ‘With the greatest feeling’). This movement has seemed to many listeners the greatest music Beethoven ever wrote. and perhaps the problem of all who try to write about this music is precisely that it cannot be described in words and should be experienced simply as music.”

—  Eric Bromberger,
Borromeo Quartet program notes 

In accordance with these passages, here is a web page with excellent transcriptions for piano by Steven Edwards of Beethoven’s late quartets:

The 16 String Quartets.

Our site music for today, Beethoven’s String Quartet No. 15 in A Minor, Opus 132, Movement 3 (1825), is taken from this web page.

See also the previous entry.
 

Thursday, June 9, 2005

Thursday June 9, 2005

Filed under: General,Geometry — Tags: , — m759 @ 7:45 pm
Kernel of Eternity

continued

"At that instant he saw,
in one blaze of light,
an image of unutterable conviction….
the core of life, the essential pattern
whence all other things proceed,
the kernel of eternity."

— Thomas Wolfe,
Of Time and the River

From "The Relations between
Poetry and Painting," by Wallace Stevens:

"The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety…. It was from the point of view of… [such a] subtlety that Klee could write: 'But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space—which he calls the mind or heart of creation— determines every function.' Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less."

As yesterday's entry "Kernel of Eternity" indicated, the word "kernel" has a definite meaning in mathematics.  The Klein four-group, beloved of structural anthropologists and art theorists, is a particularly apt example of a kernel. (See PlanetMath for details.)

Diagrams of this group may have influenced Giovanni Sambin, professor of mathematical logic at the University of Padua; the following impressive-looking diagram is from Sambin's

The image “http://www.log24.com/theory/images/SambinBP1Pic2A.jpg” cannot be displayed, because it contains errors.

Sambin argues that this diagram reflects some of the basic structures of thought itself… making it perhaps one way to describe what  Klee called the "mind or heart of creation." 

But this verges on what Stevens called the sacerdotal.  It seems that a simple picture of the "kernel of eternity" as the four-group, a picture without reference to logic or philosophy, and without distracting letters and labels, is required.  The following is my attempt to supply such a picture:

Klein four-group

This is a picture of the four-group
as a permutation group on four points.
Pairs of colored arrows indicate the three
transformations other than the identity,
which may be regarded either as
invisible or as rendered by
the four black points themselves.

Update of 7:45 PM Thursday:

Review of the above (see comments)
by a typical Xanga reader:

"Ur a FUCKIN' LOSER!!!!!  LMFAO!!!!"

For more merriment, see
The Optical Unconscious
and
The Painted Word.

A recent Xangan movie review:

"Annakin's an idiot, but he's not an idiot because that's the way the character works, he's an idiot because George Lucas was too lazy to make him anything else. He has to descend to the Daaaahk Side, but the dark side never really seems all that dark. He kills children, but offscreen. We never get to see the transformation. One minute he cares about the republic, the next he's killing his friends, and then for some reason he's duelling with Obi Wan on a lava flow. Who cares? Not me….

So a big ol' fuck you to George Lucas. Fuck you, George!"

Both Xangans seem to be fluent in what Tom Wolfe has called the "fuck patois."

A related suggestion from Google:

Give Dad a photo gift

These remarks from Xangans and Google
 suggest the following photo gift,
based on a 2003 journal entry:

The image “http://www.log24.com/log/pix05A/050609-Fahne.jpg” cannot be displayed, because it contains errors.

Wednesday, June 8, 2005

Wednesday June 8, 2005

Filed under: General,Geometry — Tags: , , — m759 @ 4:00 pm

Kernel of Eternity

Today is the feast day of Saint Gerard Manley Hopkins, “immortal diamond.”

“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”

— Thomas Wolfe, Of Time and the River

“… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)”

— Peter J. Cameron,
The Geometry of the Mathieu Groups (pdf)

“… donc Dieu existe, réponse!

— attributed, some say falsely, to Leonhard Euler

Monday, May 23, 2005

Monday May 23, 2005

Filed under: General — m759 @ 2:56 am

Final Arrangements
continued:

The image “http://www.log24.com/log/pix05/050523-522Obits2.jpg” cannot be displayed, because it contains errors.

Elements:

 
  PIERO DORAZIO

  (1927 – 2005) 

  The image “http://www.log24.com/log/pix05/050523-Dorazio1.jpg” cannot be displayed, because it contains errors.

  Aquatint, 1982
  Plate 9.5 x 9 cm | Sheet 24 x 16 cm
  99 copies signed and numbered
  from 1/99 to 99/99,
  15 from I/XV to XV/XV
  Copy 11/99
  Printed by Renzo Romero, Rome.
  This artwork accompanies the book
 
Staras by Guido Ballo,
  edition Galleria Rizzardi, Milan (1982).
 
  Edizioni l’Obliquo, Galleria di Grafica

Elegant.” — The Daily Telegraph

Wednesday, March 2, 2005

Wednesday March 2, 2005

Filed under: General — Tags: — m759 @ 2:22 pm

White Stone

"I have stolen more quotes and thoughts and purely elegant little starbursts of writing from the Book of Revelation than anything else in the English language– and it is not because I am a biblical scholar, or because of any religious faith, but because I love the wild power of the language and the purity of the madness that governs it and makes it music."

— Hunter S. Thompson, Author's Note, Generation of Swine

In memory of Peter Foy,
who died in Las Vegas
on 2/17

The image “http://log24.com/log/pix05/050302-Peter2.jpg” cannot be displayed, because it contains errors.

Revelation 2:17:

"And I will give him a white stone…."

The image “http://log24.com/log/pix05/050302-Diamond1.jpg” cannot be displayed, because it contains errors.

Related material:

2003 2/17: "immortal diamond"
2004 2/17:  "hard core"           
2005 2/17:  "the diamond"       

For an "elegant starburst," see

"Starflight," from 10/10, 2004

The image “http://www.log24.com/log/pix05/050302-S.jpg” cannot be displayed, because it contains errors.

the date of
Christopher Reeve's death.

See also
Revelation 10:10

"And I took the little book
out of the angel's hand,
and ate it up; and it was in my mouth
sweet as honey: and as soon as I had
eaten it, my belly was bitter."

For the relationship of this verse to
the style of Hunter Thompson, see

The image “http://www.log24.com/log/pix05/050302-Apo.jpg” cannot be displayed, because it contains errors.

From the Department of Justice:
"LSD generally is taken by mouth.
The drug is colorless and odorless
but has a slightly bitter taste."
Among the street terms for LSD
is "Superman."

Sunday, February 13, 2005

Sunday February 13, 2005

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

Eight is a Gate

“The old men know
when an old man dies.”
— Ogden Nash

“Heaven is a state,
a sort of metaphysical state.”
— John O’Hara, Hope of Heaven, 1938

The image “http://www.log24.com/log/pix05/050213-Three.jpg” cannot be displayed, because it contains errors.

But in a larger sense…

Mais il y a un autre sens dans la dédicace que je trouve plus profond encore. Il s’agit de se dédier soi-même. Le terme que l’on traduit par dédicace est en japonais ekô, littéralement “se tourner vers”. Il est composé de deux idéogrammes, e qui signifie “tourner le dos, se tourner, revenir en arrière” et , “faire face, s’adresser à”.

Dans l’école Tendai, on explique que ce terme possède trois sens:

– tourner le dos (e) aux phénomènes et faire face () au principe;
– tourner le dos (e) au soi et faire face () aux autres;
– tourner le dos (e) aux causes et faire face () aux effets.

On pourrait dire regarder l’essentiel, regarder autrui et regarder le futur. Le terme évoque un retournement. Il s’agit d’aller à rebours de nos fonctionnements habituels, de bouleverser nos attitudes, se détourner de l’égocentrisme pour aller dans le sens de l’ouverture, ne plus se fourvoyer dans l’erreur mais s’ouvrir à la clarté.

Ekô a bien dans les textes bouddhistes un double sens, c’est à la fois dédier quelque chose comme la récitation d’un texte mais également se dédier soi-même. Dans cette deuxième attitude, c’est soi-même, tout entier, corps et esprit, qui est l’objet de la dédicace. Plus qu’on donne, on se donne. On trouve les deux sens chez Dôgen qui n’ignore pas le “transfert des mérites” mais qui sait que ekô se confond avec la voie de l’éveil. Il y a par exemple ce passage dans le Shôbôgenzô Zuimonki:

“Dans le bouddhisme, il y a ceux qui sont foncièrement doués d’amour et de compassion, de connaissance et de sagesse. Pour peu qu’ils étudient, ceux qui en sont dépourvus les réaliseront. Ils n’ont qu’à abandonner le corps et l’esprit, se dédier (ekô) dans le grand océan du bouddhisme, se reposer sur les enseignements du bouddhisme et ne pas rester dans les préjugés personnels.”
[Buppô ni wa, jihi chie mo yori sonawaru hito mo ari. Tatoi naki hito mo gaku sureba uru nari. Tada shinjin o tomoni hôge shite, buppô no daikai ni ekô shite, buppô no kyô ni makasete, shikiyoku o son zuru koto nakare.]
(Shôbôgenzô zuimonki, Edition populaire, cinquième cahier, première causerie)

Le français ne peut véritablement rendre la subtilité du choix des mots de Dôgen qui utilise des figures de style typiquement chinoises comme le chiasme, l’opposition et l’appariement. Il emploie des verbes d’état d’une part : se reposer, rester, de l’autre des verbes d’action, abandonner (hôge su, lit. “laisser choir”), se dédier (ekô su, lit. “se tourner vers”, qui a presque ici le sens de “se jeter”). Réaliser l’amour, la compassion, la connaissance et la sagesse nécessite une transformation, une conversion, un saut dans l’ailleurs. Ce dynamisme permet de quitter le soi égocentré pour entrer dans la dimension de l’éveil, ce que Dôgen appelle ici le bouddhisme.

Ce retournement, ekô, possède une double dimension, à la fois interne et externe. D’un point de vue intérieur, nous nous dédions à l’éveil, d’un point de vue extérieur, nous nous dédions aux autres. Mais l’intérieur et l’extérieur sont comme les deux faces d’une même feuille de papier.

La dédicace universelle:
une causerie d’Eric Rommeluère

Thursday, September 30, 2004

Thursday September 30, 2004

Filed under: General — m759 @ 6:25 pm

Out for Blood
____________________

Dedication added on
Oct. 4, 2004, 2:10 PM:
To Jacques Levy,
who died on Sept. 30, 2004.
Levy directed “Red Cross,”
a Sam Shepard play that is
said to be about
the vampire quality
of language
.”
_____________________

Kerry “shouldn’t be looking to score
technical points like this is
Harvard-Yale debate society.”

— Chris Lehane, quoted in
today’s Washington Post

From today’s Harvard Crimson:

Ben and Jerry:

Affleck

Bruckheimer

“I know I’m in the minority,
but I like Bush.”

Jerry Bruckheimer,
quoted in the
New York Daily News
of April 11, 2004

Wednesday, September 15, 2004

Wednesday September 15, 2004

Filed under: General — m759 @ 2:56 pm

On Translation

From Illuminations, by Walter Benjamin, translated by Harry Zohn:

“If there is such a thing as a language of truth, the tensionless and even silent depository of the ultimate truth which all thought strives for, then this language of truth is– the true language.  And this very language, whose divination and description is the only perfection a philosopher can hope for, is concealed in concentrated fashion in translations.  There is no muse of philosophy, nor is there one of translation.  But despite the claims of sentimental artists, these two are not banausic.  For there is a philosophical genius that is characterized by a yearning for that language which manifests itself in translations: ‘Les langues imparfaites en cela que plusieurs, manque la suprême: penser étant écrire sans accessoires, ni chuchotement mais tacite encore l’immortelle parole, la diversité, sur terre, des idiomes empêche personne de proférer les mots qui, sinon se trouveraient, par une frappe unique, elle-même matériellement la vérité.’*  If what Mallarmé evokes here is fully fathomable to a philosopher, translation, with its rudiments of such a language, is midway between poetry and doctrine.  Its products are less sharply defined, but it leaves no less of a mark on history.”

* “The imperfection of languages consists in their plurality, the supreme one is lacking: thinking is writing without accessories or even whispering, the immortal word still remains silent; the diversity of idioms on earth prevents everybody from uttering the words which otherwise, at one single stroke, would materialize as truth.’

Stéphane Mallarmé / Crise de vers

(The Benjamin is from a copy of Illuminations I purchased exactly 12 years ago, on Sept. 15, 1992.)

Thursday, August 19, 2004

Thursday August 19, 2004

Filed under: General — m759 @ 3:09 am

Angel of the
First Degree

June 24, 2002, at 8:22:21 PM:

A few words for M.C.C.

Honey Blonde
She’s as sweet as
  tupelo honey
She’s an angel
  of the first degree.
She’s as sweet as
  tupelo honey
Just like honey, baby,
  from the bee.
— Van Morrison, 1971

Elmer Bernstein, Film Composer, Dies at 82

By THE ASSOCIATED PRESS
Filed at 1:22 a.m. ET
Thursday, Aug. 19, 2004

LOS ANGELES (AP)– Elmer Bernstein, the versatile, Oscar-winning composer who scored such movie classics as “The Ten Commandments,” “The Magnificent Seven,”‘ “To Kill a Mockingbird,”‘ “The Great Escape” and “True Grit,” died Wednesday. He was 82.

Bernstein died in his sleep at his Ojai home.

That, M.C.C., is what
Fritz Leiber means by

The Big Time.

Tuesday, August 10, 2004

Tuesday August 10, 2004

Filed under: General,Geometry — Tags: , , — m759 @ 3:01 pm

Battle of Gods and Giants

In checking the quotations from Dante in the previous entry, I came across the intriguing site Gigantomachia:

"A gigantomachia or primordial battle between the gods has been retold in myth, cult, art and theory for thousands of years, from the Egyptians to Heidegger. This site will present the history of the theme. But it will do so in an attempt to raise the question of the contemporary relevance of it. Does the gigantomachia take place today? Where? When? In what relation to you and me?"

Perhaps atop the Empire State Building?

(See An Affair to Remember and  Empire State Building to Honor Fay Wray.)

Perhaps in relation to what the late poet Donald Justice called "the wood within"?

Perhaps in relation to T. S. Eliot's "The Waste Land" and the Feast of the Metamorphosis?

Or perhaps not.

Perhaps at Pergamon:

Perhaps at Pergamon Press:

Invariants 

"What modern painters are trying to do,
if they only knew it, is paint invariants."

— James J. Gibson in Leonardo
(Vol. 11, pp. 227-235.
Pergamon Press Ltd., 1978)

An example of invariant structure:

The three line diagrams above result from the three partitions, into pairs of 2-element sets, of the 4-element set from which the entries of the bottom colored figure are drawn.  Taken as a set, these three line diagrams describe the structure of the bottom colored figure.  After coordinatizing the figure in a suitable manner, we find that this set of three line diagrams is invariant under the group of 16 binary translations acting on the colored figure.

A more remarkable invariance — that of symmetry itself — is observed if we arbitrarily and repeatedly permute rows and/or columns and/or 2×2 quadrants of the colored figure above. Each resulting figure has some ordinary or color-interchange symmetry.

This sort of mathematics illustrates the invisible "form" or "idea" behind the visible two-color pattern.  Hence it exemplifies, in a way, the conflict described by Plato between those who say that "real existence belongs only to that which can be handled" and those who say that "true reality consists in certain intelligible and bodiless forms."

For further details, see a section on Plato in the Gigantomachia site.

Friday, July 9, 2004

Friday July 9, 2004

Filed under: General — m759 @ 7:11 pm

Scoop

This afternoon I came across, in a briefcase I seldom use, two books I had not looked at since I bought them last month:

  • The Footprints of God, a recently published paperback by Greg Iles, a writer who graduated from Trinity High School, Natchez, Mississippi, in 1979, and from the University of Mississippi in Oxford in 1983.
  • Sanctuary, by the better-known Mississippi writer William Faulkner.

At the time I purchased the books, indeed until I looked up Iles on the Web today, I was not aware of the Mississippi connection.  Their physical connection, lying together today in my briefcase, is, of course, purely coincidental.  My view of coincidence is close to that of Arthur Koestler, who wrote The Challenge of Chance and The Roots of Coincidence, and to that of Loren Eiseley, who wrote of a dice game and of "the Other Player" in his autobiography, All the Strange Hours.

A Log24 entry yesterday referred to a comedic novel on the role of chance in physics, Cosmic Banditos.  Today's New York Times quotes an entertainer who referred to President Bush yesterday, at a political fund-raiser, as a bandito.  Another coincidence… this one related directly to the philosophy of coincidences expounded jokingly in Cosmic Banditos.

I draw no conclusions from such coincidences, but they do inspire me to look a little deeper into life's details — where, some say, God is.  Free association on these details, together with a passage in Sanctuary, inspired the following collage:

The image “http://www.log24.com/log/pix04A/040709-FritoReba.jpg” cannot be displayed, because it contains errors.


Related Texts

Faulkner on a trinity of women
in Sanctuary (Ch. 25):

"Miss Reba emerged from behind the screen with three glasses of gin. 'This'll put some heart into us,' she said. 'We're setting here like three old sick cats.'  They bowed formally and drank, patting their lips.  Then they began to talk.  They were all talking at once,* again in half-completed sentences, but without pauses for agreement or affirmation."


"In Defense of the Brand":

"When I was helping Frito corn chips expand its core user group in the mid-'90s, we didn't ask Frito-Lay to just wave the Fritos banner. The brand was elevated to a place where it could address its core users in a way that was relevant to their lifestyle. We took the profile of the audience and created a campaign starring Reba McEntire. It captured the brand's essence, and set Frito eaters amidst good music, good people, and good fun."

Song lyric, Reba McEntire:
 
"I might have been born
just plain white trash,
but Fancy was my name."

Loren Eiseley, 
Notes of an Alchemist:

I never found
the hole in the wall;
I never found
Pancho Villa country
where you see the enemy first.
— "The Invisible Horseman"

Sunday, April 25, 2004

Sunday April 25, 2004

Filed under: General,Geometry — m759 @ 3:31 pm

Small World

Added a note to 4×4 Geometry:

The 4×4 square model  lets us visualize the projective space PG(3,2) as well as the affine space AG(4,2).  For tetrahedral and circular models of PG(3,2), see the work of Burkard Polster.  The following is from an advertisement of a talk by Polster on PG(3,2).

The Smallest Perfect Universe

“After a short introduction to finite geometries, I’ll take you on a… guided tour of the smallest perfect universe — a complex universe of breathtaking abstract beauty, consisting of only 15 points, 35 lines and 15 planes — a space whose overall design incorporates and improves many of the standard features of the three-dimensional Euclidean space we live in….

Among mathematicians our perfect universe is known as PG(3,2) — the smallest three-dimensional projective space. It plays an important role in many core mathematical disciplines such as combinatorics, group theory, and geometry.”

— Burkard Polster, May 2001

Monday, April 5, 2004

Monday April 5, 2004

Filed under: General,Geometry — Tags: , , — m759 @ 4:03 am

Ideas and Art

 
Motto of
Plato's Academy

 

From Minimalist Fantasies,
by Roger Kimball, May 2003:

All I want anyone to get out of my paintings, and all I ever get out of them, is the fact that you can see the whole idea without any confusion. … What you see is what you see.
—Frank Stella, 1966

Minimal Art remains too much a feat of ideation, and not enough anything else. Its idea remains an idea, something deduced instead of felt and discovered.
— Clement Greenberg, 1967

The artists even questioned whether art needed to be a tangible object. Minimalism … Conceptualism — suddenly art could be nothing more than an idea, a thought on a piece of paper….
— Michael Kimmelman, 2003

There was a period, a decade or two ago, when you could hardly open an art journal without encountering the quotation from Frank Stella I used as an epigraph. The bit about “what you see is what you see” was reproduced ad nauseam. It was thought by some to be very deep. In fact, Stella’s remarks—from a joint interview with him and Donald Judd—serve chiefly to underscore the artistic emptiness of the whole project of minimalism. No one can argue with the proposition that “what you see is what you see,” but there’s a lot to argue with in what he calls “the fact that you can see the whole idea without any confusion.” We do not, of course, see ideas. Stella’s assertion to the contrary might be an instance of verbal carelessness, but it is not merely verbal carelessness. At the center of minimalism, as Clement Greenberg noted, is the triumph of ideation over feeling and perception, over aesthetics.
— Roger Kimball, 2003

 

 

From How Not Much Is a Whole World,
by Michael Kimmelman, April 2, 2004

Decades on, it's curious how much Minimalism, the last great high modern movement, still troubles people who just can't see why … a plain white canvas with a line painted across it


"William Clark,"
by Patricia Johanson, 1967

should be considered art. That line might as well be in the sand: on this side is art, it implies. Go ahead. Cross it.

….

The tug of an art that unapologetically sees itself as on a par with science and religion is not to be underestimated, either. Philosophical ambition and formal modesty still constitute Minimalism's bottom line.

If what results can sometimes be more fodder for the brain than exciting to look at, it can also have a serene and exalted eloquence….

That line in the sand doesn't separate good art from bad, or art from nonart, but a wide world from an even wider one.

 

I maintain that of course
we can see ideas.

Example: the idea of
invariant structure.

"What modern painters
are trying to do,
if they only knew it,
is paint invariants."

— James J. Gibson, Leonardo,
    Vol. 11, pp. 227-235.
    Pergamon Press Ltd., 1978

For a discussion
of how this works, see
Block Designs,
4×4 Geometry, and
Diamond Theory.

Incidentally, structures like the one shown above are invariant under an important subgroup of the affine group AGL(4,2)…  That is to say, they are not lost in translation.  (See previous entry.)

Wednesday, February 18, 2004

Wednesday February 18, 2004

Filed under: General — m759 @ 11:11 am

Hard Core, Part II:
Star of Africa

In memory of St. Katharine Hepburn,
who died on St. Peter’s Day, 2003:
“Although the greater saints
are more acceptable to God
than the lesser,
it is sometimes profitable
to pray to the lesser.”
St. Thomas Aquinas  

From The Times, UK, Feb. 18, 2004:

Straw denies
a big-three takeover
at EU summit
 

Britain’s Foreign Secretary “said that there were no plans to set up a small body within the EU to take control of its affairs.

However, he told a news conference at the Foreign Office that it made sense for the three biggest economies to work ‘collaboratively’ on matters of common interest….

At tonight’s summit Mr Blair, Gerhard Schröder, the German Chancellor, and President Chirac of France will discuss initiatives to co-ordinate and strengthen the EU’s industrial policy….

German commentators regard the summit as a sea-change in British policy towards Europe — a signal that London’s main aim is no longer to split Paris and Berlin.”

Tuesday, February 17, 2004

Tuesday February 17, 2004

Filed under: General — m759 @ 4:35 pm

Hard Core

From USATODAY.com,
Posted 2/16/2004 11:16 PM

Diamond at heart of star
outweighs any on Earth

Astronomers announced Friday that a white dwarf star they’ve been studying is a chunk of crystallized carbon that weighs 5 million trillion trillion pounds. That’s the same as a diamond that is approximately 10 billion trillion trillion carats, or a one followed by 34 zeros.

Twinkle-twinkle indeed: An artist’s conception of the diamond core of a dead white-dwarf star.

Harvard-Smithsonian
Center for Astrophysics.

“It’s the mother of all diamonds,” said astronomer Travis Metcalfe, Harvard-Smithsonian Center for Astrophysics….

The biggest diamond on Earth is the 530-carat Star of Africa, part of the Crown Jewels of England. It was cut from a 3,100-carat gem*, the biggest ever found.

* The Cullinan diamond

Friday, December 5, 2003

Friday December 5, 2003

Filed under: General — Tags: — m759 @ 1:06 pm
Number 61    Hexagram 61: Inner Truth

For Joan Didion on her birthday

From “On Keeping a Notebook” (1966)
in Slouching Towards Bethlehem:

How it felt to me: that is getting closer to the truth about a notebook. I sometimes delude myself about why I keep a notebook, imagine that some thrifty virtue derives from preserving everything observed.  See enough and write it down, I tell myself, and then some morning when the world seems drained of wonder, some day when I am only going through the motions of doing what I am supposed to do, which is write- on that bankrupt morning I will simply open my notebook and there it will all be, a forgotten account with accumulated interest, paid passage back to the world out there: dialogue overheard in hotels and elevators and at the hatcheck counter in Pavillon (one middle-aged man shows his hat check to another and says, “That’s my old football number”)….

I imagine, in other words, that the notebook is about other people. But of course it is not. I have no real business with what one stranger said to another at the hat-check counter in Pavillon; in fact I suspect that the line “That’s my old football number” touched not my own imagination at all, but merely some memory of something once read, probably “The Eighty-Yard Run.”

From a 1994 interview with Tommy Lee Jones by Bryant Gumbel:

Gumbel: While majoring in English, Jones was also an offensive guard on the Harvard football team. Number 61 in your program, his last game, against Yale, proved to be one of the most famous games every played. Harvard scored 16 points in the last 42 seconds to gain a 29-all tie. (Photo of Jones in football uniform, footage of 1968 football game.)

Mr. J: It couldn’t have been a more spectacular way to leave the game that had been so important to me all my life. The grass had never looked that green, nor the sky that blue.

Gumbel: That lucky game was for Jones a precursor of good fortune to come. It seems Harvard´s team doctor, Thomas Quigley, had caught some of Tommy Lee’s off the field plays and come away impressed. (Photo of Jones at rehearsal)

Mr. J: And when I was about to graduate, he asked if I had thought about going to New York, and I said I didn’t know. He said, “Well, if you do, take this letter and give it to my daughter, she’s doing a play.”

Ms. Jane Alexander (Actress): And I opened it. It was from my father, and it said: “This young man excels at Harvard. He is a good football player, but he wants to be an actor. Take care of him.” So I introduced him to a few agents, and right away he got a job.

Mr. J: And I had one line…. The line was five words long.

Gumbel: Were this a fairy tale, it would be….

Joan Didion: “That’s my old football number.”

Sunday, November 23, 2003

Sunday November 23, 2003

Filed under: General — m759 @ 1:06 pm

Epiphany

Yesterday, to give thanks for the winning score in the Harvard-Yale game (Harvard won, 37 to 19), I browsed the Net to find the religious significance, if any, of the number “37.” I encountered the picture at left below, of a burning bush.  (It was frame 37 in a sequence of frames from an episode of The Simpsons.)  The finger of flame did not seem to lead to anything meaningful, so I ignored it.  (Frame 38 in the sequence seems to be a Simpsons version of Edward G. Robinson in “The Ten Commandments.”) Then today, lo and behold, the Commandments themselves appeared before my very eyes, as yet another cartoon… this time, on the editorial page of my local paper (reprinted from McKee in the Augusta Chronicle).  Combining the two cartoons, we see the Flaming Finger of God in action.

The above thought process is, of course, less than mentally healthy, but may be of anecdotal interest to some.  Several other examples of religious insanity seem relevant:

  • Jesus Christ: The Number of His Name, by Bonnie Gaunt, which contains a riff on the number “37” that John Nash at his looniest would be proud of.
  • Mel Gibson on his new film,
    “The Passion” —

    When Gibson was in Rome shooting the film, he told an Italian interviewer that he had felt moved by God’s spirit to undertake the project. I asked him what he’d meant by that. How did he know that God wanted him to make “The Passion”?

    “There are signals,” he said. “You get signals. Signs. ‘Signal graces,’ they’re called. It’s like traffic lights. It’s as clear as a traffic light. Bing! I mean, it just grabs you and you know you have to listen to that and you have to follow it.”

    Peter J. Boyer in The New Yorker

  • Finally, for religious enthusiasts who, like our President, have a Yale background, an article on the mystical properties of Yale’s score yesterday in the big game —

    19th Nervous Breakdown

Monday, November 17, 2003

Monday November 17, 2003

Filed under: General — Tags: — m759 @ 10:49 am

Total Recall:

in which Philip K. Dick
meets Joan Didion yet again

From Joan Didion’s new work on California history, Where I Was From:

“There was never just the golden dream of riches and bountiful nature, but always a scene of exploitation and false promises, indifference and ruthlessness, a kind of hollow core.”

Hollow no more.      

Friday, September 12, 2003

Friday September 12, 2003

Filed under: General — Tags: — m759 @ 3:06 pm

Commentary
on the two previous entries

On 4:04:08:

“Je ne connais que deux sortes d’êtres immuables sur la terre: les géomètres et les animaux; ils sont conduits par deux règles invariables la démonstration et l’instinct; et encore les géomètres ont-ils eu quelques disputes, mais les animaux n’ont jamais varié.”

— Voltaire, Dictionnaire Philosophique, “Des Contradictions dans les Affaires et dans les Hommes

A Singer 7-cycle

 On 4:04:08
and on
Particularity:

“El pan que se come no es pan.”

— Voltaire quoting Montesquieu
on the Pope’s declarations,
Spanish translation

Thursday, September 4, 2003

Thursday September 4, 2003

Filed under: General — m759 @ 2:42 am

Monolith

“Music can name the unnameable
and communicate the unknowable.”

— Quotation attributed to Leonard Bernstein

“Finally we get to Kubrick’s ultimate trick….  His secret is in plain sight…. The film is the monolith. In a secret that seems to never have been seen by anyone: the monolith in the film has the same exact dimensions as the movie screen on which 2001 was projected.”

—  Alchemical Kubrick 2001, by Jay Weidner 

My entry of Saturday, August 30,
included the following illustration:

My entry of Monday, September 1,
concluded with the black monolith.

“There is little doubt that the black monolith
in 2001 is the Philosopher’s Stone.”

—  Alchemical Kubrick 2001, by Jay Weidner 

 The philosopher Donald Davidson
died on Saturday, August 30.

The New York Times says that as an undergraduate, Davidson “persuaded Harvard to let him put on ‘The Birds’ by Aristophanes and played the lead, Peisthetairos, which meant memorizing 700 lines of Greek. His friend and classmate Leonard Bernstein, with whom he played four-handed piano, wrote an original score for the production.”

Perhaps they are still making music together.

Monday, August 18, 2003

Monday August 18, 2003

Filed under: General,Geometry — Tags: , — m759 @ 3:09 pm

Entries since Xanga’s
August 10 Failure:


Sunday, August 17, 2003  2:00 PM

A Thorny Crown of…

West Wing's Toby Ziegler

From the first episode of
the television series
The West Wing“:

 

Original airdate: Sept. 22, 1999
Written by Aaron Sorkin

MARY MARSH
That New York sense of humor. It always–

CALDWELL
Mary, there’s absolutely no need…

MARY MARSH
Please, Reverend, they think they’re so much smarter. They think it’s smart talk. But nobody else does.

JOSH
I’m actually from Connecticut, but that’s neither here nor there. The point is that I hope…

TOBY
She meant Jewish.

[A stunned silence. Everyone stares at Toby.]

TOBY (CONT.)
When she said “New York sense of humor,” she was talking about you and me.

JOSH
You know what, Toby, let’s just not even go there.

 

Going There, Part I

 

Crown of Ideas

Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003.

From his New York Times obituary:

” ‘He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,’ said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe’s first big show at the Modern, ‘High & Low.’ ‘Art was always material first — it was never, ever bound by a thorny crown of ideas.’ ”

For a mini-exhibit of ideas in honor of Varnedoe, see

Fahne Hoch.

Verlyn Klinkenborg on Varnedoe:

“I was always struck by the tangibility of the words he used….  It was as if he were laying words down on the table one by one as he used them, like brushes in an artist’s studio. That was why students crowded into his classes and why the National Gallery of Art had overflow audiences for his Mellon Lectures earlier this year. Something synaptic happened when you listened to Kirk Varnedoe, and, remarkably, something synaptic happened when he listened to you. You never knew what you might discover together.”

Perhaps even a “thorny crown of ideas“?

“Crown of Thorns”
Cathedral, Brasilia

Varnedoe’s death coincided with
the Great Blackout of 2003.

“To what extent does this idea of a civic life produced by sense of adversity correspond to actual life in Brasília? I wonder if it is something which the city actually cultivates. Consider, for example the cathedral, on the monumental axis, a circular, concrete framed building whose sixteen ribs are both structural and symbolic, making a structure that reads unambiguously as a crown of thorns; other symbolic elements include the subterranean entrance, the visitor passing through a subterranean passage before emerging in the light of the body of the cathedral. And it is light, shockingly so….”

Modernist Civic Space: The Case of Brasilia, by Richard J. Williams, Department of History of Art, University of Edinburgh, Scotland

 

Going There, Part II

Simple, Bold, Clear

Art historian Kirk Varnedoe was, of course, not the only one to die on the day of the Great Blackout.

Claude Martel, 34, a senior art director of The New York Times Magazine, also died on Thursday, August 14, 2003.

Janet Froelich, the magazine’s art director, describes below a sample of work that she and Martel did together:

“A new world of ideas”

Froelich notes that “the elements are simple, bold, and clear.”

For another example of elements with these qualities, see my journal entry

Fahne Hoch.

The flag design in that entry
might appeal to Aaron Sorkin’s
Christian antisemite:

 

Fahne,
S. H. Cullinane,
Aug. 15, 2003

Dr. Mengele,
according to
Hollywood

 

Note that the elements of the flag design have the qualities described so aptly by Froelich– simplicity, boldness, clarity:

They share these qualities with the Elements of Euclid, a treatise on geometrical ideas.

For the manner in which such concepts might serve as, in Gopnik’s memorable phrase, a “thorny crown of ideas,” see

“Geometry for Jews” in

ART WARS: Geometry as Conceptual Art.

See also the discussion of ideas in my journal entry on theology and art titled

Understanding: On Death and Truth

and the discussion of the wordidea” (as well as the word, and the concept, “Aryan”) in the following classic (introduced by poet W. H. Auden):

 

 

Saturday, August 16, 2003  6:00 AM

Varnedoe’s Crown

Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003.

From his New York Times obituary:

” ‘He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,’ said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe’s first big show at the Modern, ‘High & Low.’ ‘Art was always material first — it was never, ever bound by a thorny crown of ideas.’ “

For a mini-exhibit of ideas in honor of Varnedoe, see

Fahne Hoch. 

Verlyn Klinkenborg on Varnedoe:

“I was always struck by the tangibility of the words he used….  It was as if he were laying words down on the table one by one as he used them, like brushes in an artist’s studio. That was why students crowded into his classes and why the National Gallery of Art had overflow audiences for his Mellon Lectures earlier this year. Something synaptic happened when you listened to Kirk Varnedoe, and, remarkably, something synaptic happened when he listened to you. You never knew what you might discover together.”

Perhaps even a “thorny crown of ideas”?

“Crown of Thorns”
Cathedral, Brasilia

Varnedoe’s death coincided with
the Great Blackout of 2003.

“To what extent does this idea of a civic life produced by sense of adversity correspond to actual life in Brasília? I wonder if it is something which the city actually cultivates. Consider, for example the cathedral, on the monumental axis, a circular, concrete framed building whose sixteen ribs are both structural and symbolic, making a structure that reads unambiguously as a crown of thorns; other symbolic elements include the subterranean entrance, the visitor passing through a subterranean passage before emerging in the light of the body of the cathedral. And it is light, shockingly so….”

Modernist Civic Space: The Case of Brasilia, by Richard J. Williams, Department of History of Art, University of Edinburgh, Scotland


Friday, August 15, 2003  3:30 PM

ART WARS:

The Boys from Brazil

It turns out that the elementary half-square designs used in Diamond Theory

 

also appear in the work of artist Nicole Sigaud.

Sigaud’s website The ANACOM Project  has a page that leads to the artist Athos Bulcão, famous for his work in Brasilia.

From the document

Conceptual Art in an
Authoritarian Political Context:
Brasilia, Brazil
,

by Angélica Madeira:

“Athos created unique visual plans, tiles of high poetic significance, icons inseparable from the city.”

As Sigaud notes, two-color diagonally-divided squares play a large part in the art of Bulcão.

The title of Madeira’s article, and the remarks of Anna Chave on the relationship of conceptual/minimalist art to fascist rhetoric (see my May 9, 2003, entries), suggest possible illustrations for a more politicized version of Diamond Theory:

 

Fahne,
S. H. Cullinane,
Aug. 15, 2003

Dr. Mengele,
according to
Hollywood

 

Is it safe?

These illustrations were suggested in part by the fact that today is the anniversary of the death of Macbeth, King of Scotland, and in part by the following illustrations from my journal entries of July 13, 2003 comparing a MOMA curator to Lady Macbeth:

 

Die Fahne Hoch,
Frank Stella,
1959


Dorothy Miller,
MOMA curator,
died at 99 on
July 11, 2003
.

 


Thursday, August 14, 2003  3:45 AM

Famous Last Words

The ending of an Aug. 14 Salon.com article on Mel Gibson’s new film, “The Passion”:

” ‘The Passion’ will most likely offer up the familiar puerile, stereotypical view of the evil Jew calling for Jesus’ blood and the clueless Pilate begging him to reconsider. It is a view guaranteed to stir anew the passions of the rabid Christian, and one that will send the Jews scurrying back to the dark corners of history.”

— Christopher Orlet

“Scurrying”?!  The ghost of Joseph Goebbels, who famously portrayed Jews as sewer rats doing just that, must be laughing — perhaps along with the ghost of Lady Diana Mosley (née Mitford), who died Monday.

This goes well with a story that Orlet tells at his website:

“… to me, the most genuine last words are those that arise naturally from the moment, such as

 

Joseph Goebbels

 

Voltaire’s response to a request that he foreswear Satan: ‘This is no time to make new enemies.’ ”

For a view of Satan as an old, familiar, acquaintance, see the link to Prince Ombra in my entry last October 29 for Goebbels’s birthday.


Wednesday, August 13, 2003  3:00 PM

Best Picture

For some reflections inspired in part by

click here.


Tuesday, August 12, 2003  4:44 PM

Atonement:

A sequel to my entry “Catholic Tastes” of July 27, 2003.

Some remarks of Wallace Stevens that seem appropriate on this date:

“It may be that one life is a punishment
For another, as the son’s life for the father’s.”

—  Esthétique du Mal, Wallace Stevens

Joseph Patrick Kennedy, Jr.

“Unless we believe in the hero, what is there
To believe? ….
Devise, devise, and make him of winter’s
Iciest core, a north star, central
In our oblivion, of summer’s
Imagination, the golden rescue:
The bread and wine of the mind….”

Examination of the Hero in a Time of War, Wallace Stevens

Etymology of “Atonement”:

Middle English atonen, to be reconciled, from at one, in agreement

At One

“… We found,
If we found the central evil, the central good….
… we and the diamond globe at last were one.”

Asides on the Oboe, Wallace Stevens


Tuesday, August 12, 2003  1:52 PM

Franken & ‘Stein,
Attorneys at Law

Tue August 12, 2003 04:10 AM ET
NEW YORK (Reuters) – Fox News Network is suing humor writer Al Franken for trademark infringement over the phrase ‘fair and balanced’ on the cover of his upcoming book, saying it has been ‘a signature slogan’ of the network since 1996.”

Franken:
Fair?

‘Stein:
Balanced?

For answers, click on the pictures
of Franken and ‘Stein.


Sunday, June 8, 2003

Sunday June 8, 2003

Filed under: General — m759 @ 3:04 am

Of Time and the River

Today is the feast day of Saint Gerard Manley Hopkins, “immortal diamond.”

“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”

Thomas Wolfe, Of Time and the River

Thomas Wolfe

“entered the university at Chapel Hill at fifteen ‘an awkward, unhappy misfit.’ By the time he graduated, he was editor of the college newspaper….”

Jeff MacNelly, who died on this date in the Year of Our Lord 2000,

“in 1977 started drawing the comic strip ‘Shoe‘…. The strip was named in honor of the legendary Jim Shumaker, for whom MacNelly worked at the Chapel Hill Weekly.” 

From my Monday, June 2, 2003 entry:

Two quotations from “The Diamond Project“:

“We all know that something is eternal,” the Stage Manager says. “And it ain’t houses and it ain’t names, and it ain’t earth, and it ain’t even stars—everybody knows in their bones that something is eternal, and that something has to do with human beings.”
— John Lahr, review of “Our Town 

“Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave.  Its flashes are flashes of fire, a raging flame.”
Song of Solomon

Here are some other thoughts from the same date, but a different time, fictional time, Faulkner time:

June Second, 1910

Where the shadow of the bridge fell I could see down for a long way, but not as far as the bottom. When you leave a leaf in water a long time after a while the tissue will be gone and the delicate fibers waving slow as the motion of sleep. They dont touch one another, no matter how knotted up they once were, no matter how close they lay once to the bones. And maybe when He says Rise the eyes will come floating up too, out of the deep quiet and the sleep, to look on glory.

— William Faulkner, The Sound and the Fury

The concluding link from my June 2, 2003, entry furnishes a clue to the timelessness of Quentin Compson‘s thoughts above:

Glory… Song of Songs 8. 7-8

From the King James Bible‘s rendition of the Song of Songs:

8:7  Many waters cannot quench love, neither can the floods drown it: if a man would give all the substance of his house for love, it would utterly be contemned.
8:8  We have a little sister, and she hath no breasts: what shall we do for our sister in the day when she shall be spoken for?

For Quentin Compson’s thoughts on his little sister Caddy, consult the online hypertext edition of

Friday, April 25, 2003

Friday April 25, 2003

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

Mark

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

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

From a site titled Meaning of the Twentieth Century —

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

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

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

Some fruits of the "162 theory" —

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

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

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

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

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

Smooth Between Sea and Land

by A. E. Housman

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

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

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

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

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

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

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

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

 


The rune known as
"Dagaz"

Represents
the balance point or "still point."


The Nike Bastion

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

From Rune Meanings:

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

Also known as "the rune of transformation."

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

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

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

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

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

Saturday, December 28, 2002

Saturday December 28, 2002

Filed under: General — m759 @ 11:59 pm

Solace from Hell’s Kitchen

State of Grace

The Sting

This midnight’s site music is “Solace: A Mexican Serenade,” part of which was used in the film “The Sting.” George Roy Hill, the film’s director, died Friday, Dec. 27. He turned 81 on Friday, Dec. 20. See my note of that date,

Last-Minute Shopping.”

Saturday, December 21, 2002

Saturday December 21, 2002

Filed under: General — m759 @ 11:59 pm

For the Green Lady
of
Perelandra,
from the City of Angels

“The oral history of Los Angeles
is written in piano bars.” 
— Joan Didion in Slouching Towards Bethlehem

Tonight’s midnight music in the garden of good and evil is a shamelessly romantic classic from a site titled simply Piano Bar.

De Rêve En Rêverie
(Lyrics by Eddy Marnay)

Tu es le pianiste
Et moi je suis ton encore.
Un feu de joie pour deux
Tombe sur nous d’un ciel amoureux.
Toi, toi qui m’as tout appris
Moi, dans l’ombre de ta vie
Je vis,
Je vis de rêve
En rêverie. 

 Washington Square Press paperback, 1981, page 222 

Monday, December 16, 2002

Monday December 16, 2002

Filed under: General — m759 @ 2:22 am

Beethoven’s Birthday

“Ludwig van Beethoven’s String Quartet in A Minor, Opus 132, is one of the transcendent masterworks of the Western classical tradition. It is built around its luminous third movement, titled ‘Holy song of thanksgiving by one recovering from an illness.’

In this third movement, the aging Beethoven speaks, clearly and distinctly, in a voice seemingly meant both for all the world and for each individual who listens to it. The music, written in the ancient Lydian mode, is slow and grave and somehow both a struggle and a celebration at the same time.

This is music written by a supreme master at the height of his art, saying that through all illness, tribulation and sorrow there is a strength, there is a light, there is a hope.”

—  Andrew Lindemann Malone

“Eliot’s final poetic achievement—and, for many, his greatest—is the set of four poems published together in 1943 as Four Quartets…. Structurally—though the analogy is a loose one—Eliot modeled the Quartets on the late string quartets of Beethoven, especially… the A Minor Quartet; as early as 1931 he had written the poet Stephen Spender, ‘I have the A Minor Quartet on the gramophone, and I find it quite inexhaustible to study. There is a sort of heavenly or at least more than human gaiety about some of his later things which one imagines might come to oneself as the fruit of reconciliation and relief after immense suffering; I should like to get something of that into verse before I die.'”

— Anonymous author at a
Longman Publishers website

“Each of the late quartets has a unique structure, and the structure of the Quartet in A Minor is one of the most striking of all. Its five movements form an arch. At the center is a stunning slow movement that lasts nearly half the length of the entire quartet…

The third movement (Molto adagio) has a remarkable heading: in the score Beethoven titles it ‘Hymn of Thanksgiving to the Godhead from an Invalid,’ a clear reflection of the illness he had just come through. This is a variation movement, and Beethoven lays out the slow opening section, full of heartfelt music. But suddenly the music switches to D major and leaps ahead brightly; Beethoven marks this section ‘Feeling New Strength.’ These two sections alternate through this movement (the form is A-B-A-B-A), and the opening section is so varied on each reappearance that it seems to take on an entirely different character each time: each section is distinct, and each is moving in its own way (Beethoven marks the third ‘With the greatest feeling’). This movement has seemed to many listeners the greatest music Beethoven ever wrote. and perhaps the problem of all who try to write about this music is precisely that it cannot be described in words and should be experienced simply as music.”

—  Eric Bromberger,
Borromeo Quartet program notes 

In accordance with these passages, here is a web page with excellent transcriptions for piano by Steven Edwards of Beethoven’s late quartets:

The 16 String Quartets.

Our site music for today, Beethoven’s String Quartet No. 15 in A Minor, Opus 132, Movement 3 (1825), is taken from this web page.

Friday, November 22, 2002

Friday November 22, 2002

Filed under: General — m759 @ 11:00 pm

MAYA

Jack London died on this date.  On the other hand, Hoagy Carmichael, Jamie Lee Curtis, and Mariel Hemingway were born.

Friday, November 8, 2002

Friday November 8, 2002

Filed under: General,Geometry — m759 @ 3:33 am

Religious Symbolism
at Princeton

In memory of Steve McQueen (“The Great Escape” and “The Thomas Crown Affair”… see preceding entry) and of Rudolf Augstein (publisher of Der Spiegel), both of whom died on November 7 (in 1980 and 2002, respectively), in memory of the following residents of

The Princeton Cemetery
of the Nassau Presbyterian Church
Established 1757

SYLVIA BEACH (1887-1962), whose father was pastor of the First Presbyterian Church, founded Shakespeare & Company, a Paris bookshop which became a focus for struggling expatriate writers. In 1922 she published James Joyce’s Ulysses when others considered it obscene, and she defiantly closed her shop in 1941 in protest against the Nazi occupation.

KURT GÖDEL (1906-1978), a world-class mathematician famous for a vast array of major contributions to logic, was a longtime professor at the Institute for Advanced Study, founded in 1930. He was a corecipient of the Einstein Award in 1951.

JOHN (HENRY) O’HARA (1905-1970) was a voluminous and much-honored writer. His novels, Appointment in Samarra (1934) and Ten North Frederick (1955), and his collection of short stories, Pal Joey (1940), are among his best-known works.

and of the long and powerful association of Princeton University with the Presbyterian Church, as well as the theological perspective of Carl Jung in Man and His Symbols, I offer the following “windmill,” taken from the Presbyterian Creedal Standards website, as a memorial:

The background music Les Moulins de Mon Coeur, selected yesterday morning in memory of Steve McQueen, continues to be appropriate.

“A is for Anna.”
— James Joyce

Saturday, October 12, 2002

Saturday October 12, 2002

Filed under: General — Tags: — m759 @ 3:26 pm

She's a…
Twentieth Century Fox

Columbus Day
Dinner Dance

Date: Sat Oct 12, 2002
Time: 6:30pm-???
Italian American Club
of Southern Nevada

2333 East Sahara Ave.,
Las Vegas, NV 89104
Live music by Boyd Culter's 5-Piece band, prime rib dinner, and dancing at the Italian-American Club of Southern Nevada. All are welcome to attend. Tickets are only $25 and must be purchased in advance.
Cost: $25.00
For More information
Call 457-3866  or visit  
Web Site

In honor of this dance, of Columbus, and of Joan Didion, this site's music for the weekend is "Spinning Wheel."  For the relevance of this music, see Chapter 65 (set in Las Vegas) of Didion's 1970 novel Play It As It Lays, which, taken by itself, is one of the greatest short stories of the twentieth century.

The photograph of Didion on the back cover of Play It (taken when she was about 36) is one of the most striking combinations of beauty and intelligence that I have ever seen.

She's the queen of cool
And she's the lady who waits.
The Doors, "Twentieth Century Fox," Jan. 1967

Play It As It Lays is of philosophical as well as socio-literary interest; it tells of a young actress's struggles with Hollywood nihilism.  For related material, see The Studio by Didion's husband, John Gregory Dunne.  A review of Dunne's book:

"Not since F. Scott Fitzgerald and Nathanael West has anyone done Hollywood better."

High praise indeed.

Thursday, August 29, 2002

Thursday August 29, 2002

Filed under: General — m759 @ 4:40 pm

For the feast day of

St. Ingrid Bergman:

Like Shakespeare, Ingrid Bergman was born and died on the same date… In her case, August 29.

To honor her performance in “Spellbound,” here is a copy of the first crossword puzzle ever published.

The Reversible Diamond Puzzle

“This puzzle appeared in the November 1874 number of ‘St. Nicholas.’

ACROSS, from top to bottom:

1. A consonant. 2. A number. 3. Measures of distance. 4. An abyss. 5. A consonant.

DOWN, from right to left:

1. A consonant. 2. A snare. 3. A name. 4. The point of anything small. 5. A consonant.

S
T E N
M I L E S
P I T
M

The across words are different from the down words, but there is a direct relation between them: one is the reversible form of the other.”

One might also compare an eerie sound clip from the  Oscar-winning score of “Spellbound” with a weird clip from “Selim,” by the World Saxophone Quartet.  The latter is from the album “Selim Sivad” (Miles Davis backwards). One reviewer claims that this album displays “astonishing, telepathic group interplay.” This may or may not be true; if the services of a psychiatrist are required to help decide the issue, let us hope she is as attractive as Saint Ingrid.

The above remarks are, of course, intended as a partial antidote to the music inevitably associated with Bergman… “As Time Goes By.”  (Please do not play it again, Sam.)  Of course, the World Saxophone Quartet may be too powerful an antidote… It reminds one, as does the greatly superior weird music from the “Forbidden Planet” soundtrack, of Monsters from the Id.  From such monsters, let us pray to Saint Ingrid for deliverance.

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