Thursday, June 30, 2005

Thursday June 30, 2005

Filed under: General — m759 @ 2:56 AM
On This Date:

In 1936, Gone with the Wind
was published.

In 1971, Monica Potter
was born.

The image “http://www.log24.com/log/pix05A/050630-Potter2A.jpg” cannot be displayed, because it contains errors.

Amazon.com and
Tall Tall Trees

Related material:

There is one story and one story only
That will prove worth your telling,
Whether as learned bard or gifted child;
To it all lines or lesser gauds belong
That startle with their shining
Such common stories as they stray into.

Is it of trees you tell, their months and virtues,
Or strange beasts that beset you,
Of birds that croak at you the Triple will?
Or of the Zodiac and how slow it turns
Below the Boreal Crown,
Prison to all true kings that ever reigned?

Water to water, ark again to ark,
From woman back to woman:
So each new victim treads unfalteringly
The never altered circuit of his fate,
Bringing twelve peers as witness
Both to his starry rise and starry fall.

Or is it of the Virgin’s silver beauty,
All fish below the thighs?
She in her left hand bears a leafy quince;
When, with her right hand she crooks a finger, smiling,
How may the King hold back?
Royally then he barters life for love.

Or of the undying snake from chaos hatched,
Whose coils contain the ocean,
Into whose chops with naked sword he springs,
Then in black water, tangled by the reeds,
Battles three days and nights,
To be spewed up beside her scalloped shore?

Much snow is falling, winds roar hollowly,
The owl hoots from the elder,
Fear in your heart cries to the loving-cup:
Sorrow to sorrow as the sparks fly upward.
The log groans and confesses:
There is one story and one story only.

Dwell on her graciousness,
dwell on her smiling,
Do not forget what flowers
The great boar trampled down in ivy time.
Her brow was creamy as the crested wave,
Her sea-blue eyes were wild
But nothing promised that is not performed.

— Robert Graves,
To Juan at the Winter Solstice

Wednesday, June 29, 2005

Wednesday June 29, 2005

Filed under: General — m759 @ 7:00 PM

Meditation for St. Peter’s Day

“Religious activists fool themselves if they believe public displays of the Ten Commandments reflect a more moral and less corrupt nation. One needs only to watch television to discern the level of our depravity.”

Cal Thomas, June 28, 2005

For further details, see

Reality TV and The Magic Christian,
by Peter Carlson.

Wednesday June 29, 2005

Filed under: General — m759 @ 12:00 PM
Reading for St. Peter’s Day:

The image “http://www.log24.com/log/pix05A/050629-Gate240.jpg” cannot be displayed, because it contains errors.

Click on picture for details.

Wednesday June 29, 2005

Filed under: General — m759 @ 10:45 AM
A Link for St. Peter’s Day:


Monday, June 27, 2005

Monday June 27, 2005

Filed under: General — m759 @ 1:09 PM

  “Res ipsa loquitur, baby.”

— Maureen Dowd in
    “Quid Pro Quack

Cross Window

Royal Palm Student

Dream of Heaven

  March 21, 2004

Monday June 27, 2005

Filed under: General — m759 @ 3:26 AM
For of Such is the
Kingdom of Heaven

From today’s online New York Times,
with a slight embellishment:

The image “http://www.log24.com/log/pix05A/050627-NYTobits3.jpg” cannot be displayed, because it contains errors.

Monday June 27, 2005

Filed under: General — m759 @ 12:00 AM

Into the Dark

O dark dark dark. They all go into the dark,
The vacant interstellar spaces, the vacant into the vacant
And we all go with them, into the silent funeral,
Nobody’s funeral, for there is no one to bury.
I said to my soul, be still, and let the dark come upon you
Which shall be the darkness of God. As, in a theatre,
The lights are extinguished, for the scene to be changed
With a hollow rumble of wings, with a movement of
    darkness on darkness….

— T. S. Eliot, Four Quartets

“I’m well past eighty now and fairly certain I won’t see ninety but I’d like more of a choice than Hell or Paradise when I leave. Now that we know the Bible was created by a vote of Emperor Constantine’s clergy, wouldn’t we all be better off if other options were offered? Or is the fear of what happens after death the glue that holds Religion together? I hope not because I believe better of God.

As a Deist, I have no fear or doubts of the way that life ends. I can bravely face the reality of ceasing to exist because the God of my heart comforts me by promising to provide a dark, starless night of nothingness when my visit is over.”

Paul Winchell (pdf) (See previous entry.)

Paul Winchell was born at the winter solstice — the longest night — December 21, 1922.

For another view of the longest night, see the five Log24 entries ending on the day after the longest night of 2003.   Summary of those entries:

After the Long Night

“My God, it’s full of stars!”

Sunday, June 26, 2005

Sunday June 26, 2005

Filed under: General,Geometry — Tags: , — m759 @ 7:26 PM

Thanks for the Memory

As I write, Susannah McCorkle is singing "Thanks for the Memory."

Below are some photos from the website of Paul Winchell, ventriloquist, inventor, theologian.  Winchell died in his sleep at 82 early on Friday, June 24, 2005.

The image “http://www.log24.com/log/pix05A/050626-LucyAndHope.jpg” cannot be displayed, because it contains errors.
Paul Winchell seems to have
posted a topic for discussion:
"God is a mathematical equation
   beyond our understanding."

Related material:

From Friday's entry
Cross by Sol LeWitt
(Fifteen Etchings, 1973):

The image “http://www.log24.com/log/pix05A/050626-Cross.jpg” cannot be displayed, because it contains errors.

"No bridge reaches God, except one…
God's Bridge: The Cross."
— Billy Graham Evangelistic Association,
quoted in Friday's entry.

This cross may, of course, also
be interpreted as panes of a window
  — see Lucy photo above —
or as a plus sign — see "a mathematical
equation beyond our understanding"
in, for instance, Algebraic Geometry,
by Robin Hartshorne. For a theological
citation of Hartshorne's work, see
Midsummer Eve's Dream
(June 23, 1995).

Saturday, June 25, 2005

Saturday June 25, 2005

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

Religious Symbolism
at Midnight:

The image “http://www.log24.com/log/pix05A/050625-Star.jpg” cannot be displayed, because it contains errors.

Related material:

Star Wars 6/13/05,
Dark City 6/14/05,
and De Arco, as well
as the following from
July 26, 2003:

Bright Star and Dark Lady

"Mexico is a solar country — but it is also a black country, a dark country. This duality of Mexico has preoccupied me since I was a child."

Octavio Paz,
quoted by Homero Aridjis

Bright Star



Dark Lady

Friday, June 24, 2005

Friday June 24, 2005

Filed under: General,Geometry — Tags: — m759 @ 4:07 PM
Geometry for Jews

The image “http://www.log24.com/log/pix05A/050624-Cross.jpg” cannot be displayed, because it contains errors.

People have tried in many ways
to bridge the gap
between themselves and God….
No bridge reaches God, except one…
God's Bridge: The Cross

— Billy Graham Evangelistic Association,
according to messiahpage.com

"… just as God defeats the devil:
this bridge exists;
it is the theory of the field
of algebraic functions over
a finite field of constants
(that is to say, a finite number
of elements: also said to be a Galois
field, or earlier 'Galois imaginaries'
because Galois first defined them
and studied them….)"

André Weil, 1940 letter to his sister,
Simone Weil, alias Simone Galois
(see previous entry)

Related material:

Billy Graham and the City:
A Later Look at His Words

— New York Times, June 24, 2005

Geometry for Jews
and other art notes

Galois Geometry

Mathematics and Narrative

Thursday, June 23, 2005

Thursday June 23, 2005

Filed under: General,Geometry — m759 @ 3:00 PM

Mathematics and Metaphor

The current (June/July) issue of the Notices of the American Mathematical Society has two feature articles.  The first, on the vulgarizer Martin Gardner, was dealt with here in a June 19 entry, Darkness Visible.  The second is related to a letter of André Weil (pdf) that is in turn related to mathematician Barry Mazur’s attempt to rewrite mathematical history  and to vulgarize other people’s research by using metaphors drawn, it would seem, from the Weil letter.
A Mathematical Lie conjectures that Mazur’s revising of history was motivated by a desire to dramatize some arcane mathematics, the Taniyama conjecture, that deals with elliptic curves and modular forms, two areas of mathematics that have been known since the nineteenth century to be closely related.

Mazur led author Simon Singh to believe that these two areas of mathematics were, before Taniyama’s conjecture of 1955, completely unrelated — 

“Modular forms and elliptic equations live in completely different regions of the mathematical cosmos, and nobody would ever have believed that there was the remotest link between the two subjects.” — Simon Singh, Fermat’s Enigma, 1998 paperback, p. 182

This is false.  See Robert P. Langlands, review of Elliptic Curves, by Anthony W. Knapp, Bulletin of the American Mathematical Society, January 1994.

It now appears that Mazur’s claim was in part motivated by a desire to emulate the great mathematician André Weil’s manner of speaking; Mazur parrots Weil’s “bridge” and “Rosetta stone” metaphors —

From Peter Woit’s weblog, Feb. 10, 2005:

“The focus of Weil’s letter is the analogy between number fields and the field of algebraic functions of a complex variable. He describes his ideas about studying this analogy using a third, intermediate subject, that of function fields over a finite field, which he thinks of as a ‘bridge‘ or ‘Rosetta stone.'” 

In “A 1940 Letter of André Weil on Analogy in Mathematics,” (pdf), translated by Martin H. Krieger, Notices of the A.M.S., March 2005, Weil writes that

“The purely algebraic theory of algebraic functions in any arbitrary field of constants is not rich enough so that one might draw useful lessons from it. The ‘classical’ theory (that is, Riemannian) of algebraic functions over the field of constants of the complex numbers is infinitely richer; but on the one hand it is too much so, and in the mass of facts some real analogies become lost; and above all, it is too far from the theory of numbers. One would be totally obstructed if there were not a bridge between the two.  And just as God defeats the devil: this bridge exists; it is the theory of the field of algebraic functions over a finite field of constants….

On the other hand, between the function fields and the ‘Riemannian’ fields, the distance is not so large that a patient study would not teach us the art of passing from one to the other, and to profit in the study of the first from knowledge acquired about the second, and of the extremely powerful means offered to us, in the study of the latter, from the integral calculus and the theory of analytic functions. That is not to say that at best all will be easy; but one ends up by learning to see something there, although it is still somewhat confused. Intuition makes much of it; I mean by this the faculty of seeing a connection between things that in appearance are completely different; it does not fail to lead us astray quite often. Be that as it may, my work consists in deciphering a trilingual text {[cf. the Rosetta Stone]}; of each of the three columns I have only disparate fragments; I have some ideas about each of the three languages: but I know as well there are great differences in meaning from one column to another, for which nothing has prepared me in advance. In the several years I have worked at it, I have found little pieces of the dictionary. Sometimes I worked on one column, sometimes under another.”

Here is another statement of the Rosetta-stone metaphor, from Weil’s translator, Martin H.  Krieger, in the A.M.S. Notices of November 2004,  “Some of What Mathematicians Do” (pdf):

“Weil refers to three columns, in analogy with the Rosetta Stone’s three languages and their arrangement, and the task is to ‘learn to read Riemannian.’  Given an ability to read one column, can you find its translation in the other columns?  In the first column are Riemann’s transcendental results and, more generally, work in analysis and geometry.  In the second column is algebra, say polynomials with coefficients in the complex numbers or in a finite field. And in the third column is arithmetic or number theory and combinatorial properties.”

For greater clarity, see  Armand Borel (pdf) on Weil’s Rosetta stone, where the three columns are referred to as Riemannian (transcendental), Italian (“algebraico-geometric,” over finite fields), and arithmetic (i.e., number-theoretic).
From Fermat’s Enigma, by Simon Singh, Anchor paperback, Sept. 1998, pp. 190-191:

Barry Mazur: “On the one hand you have the elliptic world, and on the other you have the modular world.  Both these branches of mathematics had been studied intensively but separately…. Than along comes the Taniyama-Shimura conjecture, which is the grand surmise that there’s a bridge between these two completely different worlds.  Mathematicians love to build bridges.”

Simon Singh: “The value of mathematical bridges is enormous.  They enable communities of mathematicians who have been living on separate islands to exchange ideas and explore each other’s  creations…. The great potential of the Taniyama-Shimura conjecture was that it would connect two islands and allow them to speak to each other for the first time.  Barry Mazur thinks of the Taniyama-Shimura conjecture as a translating device similar to the Rosetta stone…. ‘It’s as if you know one language and this Rosetta stone is going to give you an intense understanding of the other language,’ says Mazur.  ‘But the Taniyama-Shimura conjecture is a Rosetta stone with a certain magical power.'”

If Mazur, who is scheduled to speak at a conference on Mathematics and Narrative this July, wants more material on stones with magical powers, he might consult The Blue Matrix and The Diamond Archetype.

Tuesday, June 21, 2005

Tuesday June 21, 2005

Filed under: General — m759 @ 4:24 PM

Art History

“I studied with Reinhardt and I found that a fantastic course. I think he was really very stimulating….

Art history was very personal through the eyes of Ad Reinhardt.”

— Robert Morris,
    Smithsonian Archives of American Art

Related material:

“The Road to Simplicity Followed by Merton’s Friends: Ad Reinhardt and Robert Lax” in The Merton Annual 13 (2000) 245-256, by Paul J. Spaeth, library director at St. Bonaventure University

The Merton here is Trappist monk Thomas Merton.  Here is Merton in a letter to poet Robert Lax on the death of their friend Ad Reinhardt, sometimes called the “black monk” of abstract art:

“Make Mass beautiful silence like big black picture speaking requiem. Tears in the shadows of hermit hatch requiems blue black tone. Sorrows for Ad in the oblation quiet peace request rest. Tomorrow is solemns in the hermit hatch for old lutheran reinhardt commie paintblack… Tomorrow is the eternal solemns and the barefoots and the ashes and the masses, oldstyle liturgy masses without the colonels… Just old black quiet requiems in hermit hatch with decent sorrows good by college chum.”

— from J. S. Porter, “Farewell to a Monk,”
    Antigonish Review, Winter 1997

Sunday, June 19, 2005

Sunday June 19, 2005

Filed under: General,Geometry — Tags: — m759 @ 4:00 AM
Darkness Visible
“No light, but rather darkness visible
 Serv’d only to discover sights of woe”
John Milton, Paradise Lost,
Book I,  lines 63-64

From the cover article (pdf) in the
June/July 2005 Notices of the
American Mathematical Society–

Martin Gardner

A famed vulgarizer, Martin Gardner,
summarizes the art of Ad Reinhardt
(Adolph Dietrich Friedrich Reinhardt,
  Dec. 24, 1913 – Aug. 30, 1967):

“Ed Rinehart [sic] made a fortune painting canvases that were just one solid color.  He had his black period in which the canvas was totally black.  And then he had a blue period in which he was painting the canvas blue.  He was exhibited in top shows in New York, and his pictures wound up in museums.  I did a column in Scientific American on minimal art, and I reproduced one of Ed Rinehart’s black paintings.  Of course, it was just a solid square of pure black.  The publisher insisted on getting permission from the gallery to reproduce it.”

Related material
from Log24.net,
Nov. 9-12, 2004:

Fade to Black

“…that ineffable constellation of talents that makes the player of rank: a gift for conceiving abstract schematic possibilities; a sense of mathematical poetry in the light of which the infinite chaos of probability and permutation is crystallized under the pressure of intense concentration into geometric blossoms; the ruthless focus of force on the subtlest weakness of an opponent.”

— Trevanian, Shibumi

“‘Haven’t there been splendidly elegant colors in Japan since ancient times?’

‘Even black has various subtle shades,’ Sosuke nodded.”

— Yasunari Kawabata, The Old Capital

An Ad Reinhardt painting
described in the entry of
noon, November 9, 2004
is illustrated below.

Ad Reinhardt,  Greek Cross

Ad Reinhardt,
Abstract Painting,
Oil on canvas, 60 x 60 inches.
Solomon R. Guggenheim Museum

The viewer may need to tilt
the screen to see that this
painting is not uniformly black,
but is instead a picture of a
Greek cross, as described below.

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

Greek Cross

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

— Rosalind Krauss,
Meyer Schapiro Professor
of Modern Art and Theory
at Columbia University

(Ph.D., Harvard U., 1969),
in “Grids”

The image “http://www.log24.com/log/pix04B/041109-Krauss.jpg” cannot be displayed, because it contains errors.


In memory of
St. William Golding
(Sept. 19, 1911 – June 19, 1993)

Friday, June 17, 2005

Friday June 17, 2005

Filed under: General — m759 @ 4:01 PM
The Quality of Diamond,

From Log 24.net on
Thursday, February 19, 2004:

Five Easy Pieces
for Lee Marvin’s Birthday


“EVERYTHING’S a story.
You are a story– I am a story.”
— Frances Hodgson Burnett,
A Little Princess


“You see that sign, sir?”
[Pointing to a notice demanding
courtesy from customers]



“You see this sign?”


“Aquarians are
extremely independent.”

Lorna Thayer, 85,
the waitress in Five Easy Pieces,
who was once someone’s little princess,
died on June 4, 2005.

Lorna Thayer, 1954
Lorna Thayer,

The 2 PM June 4 Log24 entry
has a link to
The Quality of Diamond,
where more of the Lorna Thayer
story may be found.

Thursday, June 16, 2005

Thursday June 16, 2005

Filed under: General — Tags: — m759 @ 2:02 PM
Final Arrangements, continued:

"Joe Strauss to
Joe Six-Pack"

(Editor's sneering headline
for a David Brooks essay
in today's New York Times)
and Back Again

"I was emptying some boxes in my basement the other day and I came across an essay somebody had clipped on Ernest Hemingway from the July 14, 1961, issue of Time magazine. The essay was outstanding. Over three pages of tightly packed prose, with just a few photos, the anonymous author performed the sort of high-toned but accessible literary analysis that would be much harder to find in a mass market magazine today….

The sad thing is that this type of essay was not unusual in that era….

The magazines would devote pages to the work of theologians like Abraham Joshua Heschel* or Reinhold Niebuhr. They devoted as much space to opera as to movies because an educated person was expected to know something about opera, even if that person had no prospect of actually seeing one….

Back in the late 1950's and early 1960's, middlebrow culture, which is really high-toned popular culture, was thriving in America. There was still a sense that culture is good for your character, and that a respectable person should spend time absorbing the best that has been thought and said."

— David Brooks,
   The New York Times,
   June 16, 2005

The Time essay begins by quoting Hemingway himself:

"All stories,
 if continued far enough,
 end in death,
 and he is no true storyteller
 who would keep that from you."

Here is the top section of today's
New York Times obituaries.
The image “http://www.log24.com/log/pix05A/050616-NYTobits.jpg” cannot be displayed, because it contains errors.

Here is the
middlebrow part —

The image “http://www.log24.com/log/pix05A/050616-NYTbrow.jpg” cannot be displayed, because it contains errors.
Esteemed Conductor
Dies at 91

— and here is a link that returns,
as promised in this entry's headline,
to "Joe Strauss"
complete with polkas.

*  "Judaism is a religion of time, not space."
    — Wikipedia on Heschel.
    See the recent Log24 entries
    Star Wars continued,
    Dark City, and
    Cross-Referenced, and last year's
    Bloomsday at 100.

Wednesday, June 15, 2005

Wednesday June 15, 2005

Filed under: General — m759 @ 1:44 AM


From today’s New York Times,
a review of a Werner Herzog film,
“Wheel of Time,” that opens
today in Manhattan:

The image “http://www.log24.com/log/pix05A/050615-Mandala.jpg” cannot be displayed, because it contains errors.

From the June 13-14
midnight Log24 entry:

The image “http://www.log24.com/log/pix05A/050614-DarkCity.jpg” cannot be displayed, because it contains errors.

“With a little effort, anything can be
shown to connect with anything else:
existence is infinitely cross-referenced.”

— Opening sentence of
Martha Cooley’s The Archivist

These images suggest
a Google search on the phrase
crucified on the wheel of time,”

which yields the following.

Click to go to DARK CITYDARK CITY (1998)
Crucified on the Wheel Of Time.
A visual feast.

From Dark City: A Hollywood Jesus Movie Review

“There is something mesmerizing about this important film. It flows in the same vein as The Truman Show, The Game, and Pleasantville.  Something isn’t real with the world around John Murdoch. Some group is trying to control things and it isn’t God.”


Related material:
Skewed Mirrors and
The Graces of Paranoia

Tuesday, June 14, 2005

Tuesday June 14, 2005

Filed under: General — m759 @ 12:00 PM

Darkness at Noon

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I stood out in the open cold
To see the essence of the eclipse
Which was its perfect darkness.

I stood in the cold on the porch
And could not think of anything so perfect
As man’s hope of light in the face of darkness.

— Richard Eberhart,
“The Eclipse”

See also March 11.

Tuesday June 14, 2005

Filed under: General — m759 @ 12:00 AM

Dark City

Jennifer Connelly at
premiere of “Cinderella Man” —

The image “http://www.log24.com/log/pix05A/050614-Connelly.jpg” cannot be displayed, because it contains errors.

In memory of Martin Buber,
author of Good and Evil,
who died on June 13, 1965:

The image “http://www.log24.com/log/pix05A/050614-DarkCity.jpg” cannot be displayed, because it contains errors.

“With a little effort, anything can be
shown to connect with anything else:
existence is infinitely cross-referenced.”

— Opening sentence of
Martha Cooley’s The Archivist

Woe unto
them that
call evil
good, and
good evil;
that put
for light,
and light
for darkness

Isaiah 5:20


As she spoke
about the Trees
of Life and Death,
I watched her…. 
The Archivist

The world
has gone
mad today
And good’s
bad today,

And black’s
white today,
And day’s
night today

Cole Porter

Jennifer Connelly in “Dark City”

(from journal note of June 19, 2002) —

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And, one might add for Flag Day,
“you sons of bitches.”

The image “http://www.log24.com/log/pix05A/050614-Flag.jpg” cannot be displayed, because it contains errors.

Monday, June 13, 2005

Monday June 13, 2005

Filed under: General — m759 @ 9:00 PM


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

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

For John Nash on his birthday:

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

Tom O’Bedlam’s Song

Monday June 13, 2005

Filed under: General — m759 @ 2:00 PM

Cliffs of Moher

My father’s father,
    his father’s father, his —
Shadows like winds

Go back to a parent before thought,
    before speech,
At the head of the past.

They go to the cliffs of Moher
    rising out of the mist….

— Wallace Stevens,
   “The Irish Cliffs of Moher”

A Portrait of the Artist
 as a Young Man
James Joyce, Chapter 5:

As he came back to the hearth, limping slightly but with a brisk step, Stephen saw the silent soul of a jesuit look out at him from the pale loveless eyes. Like Ignatius he was lame but in his eyes burned no spark of Ignatius’s enthusiasm. Even the legendary craft of the company, a craft subtler and more secret than its fabled books of secret subtle wisdom, had not fired his soul with the energy of apostleship. It seemed as if he used the shifts and lore and cunning of the world, as bidden to do, for the greater glory of God, without joy in their handling or hatred of that in them which was evil but turning them, with a firm gesture of obedience back upon themselves and for all this silent service it seemed as if he loved not at all the master and little, if at all, the ends he served. SIMILITER ATQUE SENIS BACULUS, he was, as the founder would have had him, like a staff in an old man’s hand, to be leaned on in the road at nightfall or in stress of weather, to lie with a lady’s nosegay on a garden seat, to be raised in menace.

The dean returned to the hearth and began to stroke his chin.

–When may we expect to have something from you on the esthetic question? he asked.

–From me! said Stephen in astonishment. I stumble on an idea once a fortnight if I am lucky.

–These questions are very profound, Mr Dedalus, said the dean. It is like looking down from the cliffs of Moher into the depths. Many go down into the depths and never come up. Only the trained diver can go down into those depths and explore them and come to the surface again.

See also Kahn’s The Art and Thought of Heraclitus and the references to a “Delian diver” in Chitwood’s Death by Philosophy.

Death by Philosophy:

“Although fragments examined earlier may enable Heraclitus’ reader to believe that the stylistic devices arose directly from his dislike of humanity, I think rather that Heraclitus deliberately perfected the mysterious, gnomic style he praises in the following  fragment.

31. The lord whose oracle is at Delphi neither speaks nor hides, but  indicates. (fr. 93)

Heraclitus not only admires the oracular style of delivery, but recommends it; this studied ambiguity is, I think, celebrated and alluded to in the Delian diver comment. For just as the prophecies of the Delian or Delphic god are at once obscure and darkly clear, so too are the workings of the Logos and Heraclitus’ remarks on it.”

Related material:
A Mass for Lucero.

That web page concludes with a reference to esthetics and a Delian palm, and was written three years ago on this date.

Today is also the date of death for Martin Buber, philosophical Jew.

Here is a Delphic saying in memory of Buber:

“It is the female date that is considered holy, and that bears fruit.”

—  Steven Erlanger,
    New York Times story,
    dateline Jerusalem, June 11

Sunday, June 12, 2005

Sunday June 12, 2005

Filed under: General — m759 @ 5:01 PM
Fathers’ Day Meditation

Who is my father in this world,
in this house,
At the spirit’s base?

— Wallace Stevens,
“The Irish Cliffs of Moher”

The image “http://www.log24.com/log/pix05A/050612-Imago2.jpg” cannot be displayed, because it contains errors.

Il Miglior Fabbro:

Sunday June 12, 2005

Filed under: General — m759 @ 2:29 PM
Bedlam Songs

By a knight of ghosts and shadows
I summoned am to tourney…

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The image “http://www.log24.com/log/pix05A/AmericaAlbum2.jpg” cannot be displayed, because it contains errors.

In the desert you can
remember your name
‘Cause there ain’t no one
for to give you no pain.

Sunday June 12, 2005

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

From The New Yorker of June 6, 2005:

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Recommended geometry:

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Click on picture to enlarge.

Related material:


Geometry for Jews

Mathematics and Narrative.

Saturday, June 11, 2005

Saturday June 11, 2005

Filed under: General — m759 @ 7:10 PM
Picture This

In memory of film producer Fernando Ghia:

“Among Ghia’s solo credits as a producer is

The image “http://www.log24.com/log/pix05A/050611-Lamb3.jpg” cannot be displayed, because it contains errors.

Lady Caroline Lamb,’ a 1972 period drama
written and directed by Robert Bolt.”

Today’s LA Times

Ghia died on June 1, 2005
(the date of the Dutch “No” vote).
In the spirit of Pale Fire, here is an excerpt
from a Log24 entry of that date:

The Road to Brussels

“History is not, of course, a cookbook offering pretested recipes. It teaches by analogy, not by maxims. It can illuminate the consequences of actions in comparable situations, yet each generation must discover for itself what situations are in fact comparable.”

 — Henry Kissinger, quoted in
     Drama of the Diagonal, Part Deux

Les livres d’histoire et la vie
racontent la même comédie….

Alain Boublil

“Along the road from Ohain to Braine-l’Alleud that hemmed in the plain of Mont-St-Jean and cut at right angles the road to Brussels, which the Emperor wished to take, he [Wellington] had placed 67,000 men and 184 cannons.” Fr. Libert, Waterloo

In researching this entry, I thought of
Wellington’s statement
in “Lady Caroline Lamb” —
These are the Scots Greys.”

The image “http://www.log24.com/log/pix05A/050601-Forever.jpg” cannot be displayed, because it contains errors.

and found the above picture.

Related material:

Women’s History Month.

Saturday June 11, 2005

Filed under: General — Tags: — m759 @ 2:25 PM


Some academics may feel that a denunciation of an essay by one of their fellow academics as "evil" (see this morning's entry The Last Word) goes too far.

Here is a followup to that entry.

From the Riviera Presbyterian Church, a sermon quoting Madeleine L’Engle's classic A Wrinkle in Time:

For a moment there was the darkness of space, then another planet. The outlines of this planet were not clean and clear. It seemed to be covered with a smoky haze. Through the haze Meg thought she could make out the familiar outlines of continents like pictures in her Social Studies books. "Is it because of our atmosphere that we can't see properly?" she asked anxiously. "No, Meg, yyou know thattt itt iss nnott tthee attmosspheeere," Mrs. Which said. "Yyou mmusstt bee brrave."

"It's the Thing!" Charles Wallace cried. "It's the Dark Thing we saw… when we were riding on Mrs. Whatsit's back!" "Did it just come?" Meg asked in agony, unable to take her eyes from the sickness of the shadow which darkened the beauty of the earth. Mrs. Whatsit sighed. "No, Meg. It hasn't just come. It has been there for a great many years. That is why your planet is such a troubled one." "I hate it!" Charles Wallace cried passionately. "I hate the Dark Thing!" Mrs. Whatsit nodded. "Yes, Charles dear. We all do." "But what is it?" Calvin demanded. "We know that it's evil, but what is it?" "Yyouu hhave ssaidd itt!" Mrs. Which's voice rang out. "Itt iss Eevill. Itt iss thee Ppowers of Ddarrkknessss!" "But what's going to happen?" Meg's voice trembled. "Oh, please, Mrs. Which, tell us what's going to happen!" "We will continue tto ffight!" Something in Mrs. Which's voice made all three of the children stand straighter, throwing back their shoulders with determination, looking at the glimmer that was Mrs. Which with pride and confidence. "And we're not alone, you know, children," came Mrs. Whatsit, the comforter. "All through the universe it's being fought, all through the cosmos… and some of our very best fighters have come right from your own planet, and it's a little planet, dears, out on the edge of a little galaxy." 

"Who have some of our fighters been?" Calvin asked. "Oh, you must know them dear," Mrs. Whatsit said. Mrs. Who's spectacles shone out at them triumphantly, "And the light shineth in darkness, and the darkness comprehended it not." "Jesus!" Charles Wallace said. "Why, of course, Jesus!" "Go on, Charles, love. There were others. All your great artists. They've been lights for us to see by." "Leonardo da Vinci?" Calvin suggested tentatively. "And Michelangelo?" "And Shakespeare," Charles Wallace called out, "and Bach! And Pasteur and Madame Curie and Einstein!" Now Calvin's voice rang with confidence. "And Schweitzer and Gandhi and Buddha and Beethoven and Rembrandt and St. Francis!" "Watch!" the Medium told them. The earth with its fearful covering of dark shadow swam out of view and they moved rapidly through the Milky Way. And there was the Thing again. Suddenly there was a great burst of light through the Darkness. The light spread out and where it touched the Darkness the Darkness disappeared. The light spread until the patch of Dark Thing had vanished, and there was only a gentle shining, and through the shining came the stars, clear and pure. No shadows. No fear. Only the stars and the clear darkness of space, quite different from the fearful darkness of the Thing. "You see!" the Medium cried, smiling happily. "It can be overcome! It is being overcome all the time!"

And it is. Lift up your hearts, lift up your heads, catch the ball, practice Advent, see in the dark. You are a city set on a hill, whose light cannot be hid. said Jesus, and he believed it.



Saturday June 11, 2005

Filed under: General — m759 @ 12:48 PM

Birthday Links

Today’s birthdays:
Gene Wilder and Adrienne Barbeau.

For Gene:
A discussion of Frankenstein as
The Modern Prometheus at
Mathematics and Narrative.

For Adrienne:
Chinese Arithmetic.

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.”

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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.

Friday, June 10, 2005

Friday June 10, 2005

Filed under: General — m759 @ 5:01 AM
All in the Timing

Posted in USA TODAY
6/9/2005 11:40 PM:

Schwarzenegger Timeline

A look at the job approval rating
of California Governor
Arnold Schwarzenegger
since his election in Oct. 2003.

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What’s YOUR opinion?

Update of 2:29 PM:

Austrian Wins
Kyoto Prize

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From today’s New York Times:

Austrian conductor Nikolaus Harnoncourt, 75,
was recognized for his ”exceptional creativity.”


For a sample of Harnoncourt conducting
Beethoven’s “Ode to Joy,”  from the film
A Clockwork Orange,” see
The CMT Shop,
Simply the Best Movie Themes.

Peter Bates, Audiophile Audition:
“Harnoncourt’s sense of drama is intense.”

Friday June 10, 2005

Filed under: General — m759 @ 3:57 AM


This entry is in memory of Howard Eavenson Boyer, Jr., who, today’s New York Times informs us, was born in Philadelphia on Oct. 26, 1943, and in his youth studied the 17th-century metaphysical poets.

Later in life, Boyer worked for Harvard University Press, where he edited science books, including Mind Children: The Future of Robot and Human Intelligence (1988), by Hans Moravec.

Boyer died at 61 on May 4, 2005.

From Log24.net on Sept. 9, 2003,

Reply to Lucifer:

January 9, 1989, is the date of The New Yorker’s review of Hans Moravec’s Mind Children: The Future of Robot and Human Intelligence (Harvard University Press).

Brad Leithauser, reviewing Mind Children, says that if Moravec “is correct in supposing that human minds will be transferred into or otherwise fused with machines, it seems likely that traditional religious questions — and traditional religions themselves — will either melt away or suffer wholesale metamorphosis. Debates about Heaven or Hell — to take but one example — would hold little relevance for an immortal creature.”

Au contraire.  Immortal creatures– such as, according to Christianity, human beings– are the only creatures for whom such debates hold relevance.

For an example of such a debate, see

The Contrasting Worldviews of
Sigmund Freud and C.S. Lewis,

by Harvard psychiatrist Armand Nicholi.

For more on Nicholi, see my entry
of August 19, 2003,

Intelligence Test.

Friday June 10, 2005

Filed under: General — m759 @ 1:25 AM

From Andrew Cusack’s weblog:

April 21, 2005

‘For Christ and Liberty’

Though [it is] a purely Protestant institution (literally), I am rather fond of Patrick Henry College. Indeed, it takes some courage in this day and age to only admit students willing to sign a ten-point profession of Protestant Reformed faith. They also happen to have an old-fashioned ball featuring ‘English country dancing, delicacies such as cream puffs and truffles and leisurely strolls about the scenic grounds of the historic Selma Plantation’.

Anyhow, the college, whose motto is ‘For Christ and Liberty’, was visited [by] Anthony Esolen, a contributing editor to Touchstone magazine, who makes these comments:

Today I received a request to write a short article on Pope Benedict XVI from a club called the De Tocqueville Society, in a small college in Northern Virginia.

That such a request came was no surprise. Its provenance is, and cheeringly so. For this De Tocqueville Society is made up of a group of students at the new Patrick Henry College, founded by Mike Farris, the President of the Home School Legal Defense Association. More than ninety percent of the college’s students were homeschooled. If there’s a Roman Catholic in the bunch, I’ve yet to hear about it, and I’ve been to that campus twice to give lectures. [Note: Esolen does not seem to be aware that PHC requires its students to be Protestant.]

More on that in a moment. I could spend all evening singing the praises of PHC (as the students fondly call it), but let me share one discovery I made that should gratify Touchstone readers. The first time I spoke there, two years ago, I was stunned to meet young men and women who—who were young men and women. I am not stretching the truth; go to Purcellville and see it for yourselves if you doubt it; I believe my wife took a couple of pictures, just to quiet the naysayers. The young men stand tall and look you in the eye—they don’t skulk, they don’t scowl and squirm uncomfortably in the back chairs as they listen to yet another analysis of Rebecca of Sunnybrook Farm, or one of the healthier poems of Sylvia Plath. They’re frank and generous and respectful, but they hold their own in an argument, and they are eager to engage you in those. They are comfortable in their skins; they wear their manhood easily. And the young ladies are beautiful. They don’t wither away in class, far from it; but they wear skirts, they are modest in their voices and their smiles, they clearly admire the young men and are esteemed in turn; they are like creatures from a faraway planet, one sweeter and saner than ours.

Two years ago I spoke to them about medieval Catholic drama. They are evangelicals, half of them majors in Government, the rest, majors in Liberal Arts. They kept me and my wife in that room for nearly three hours after the talk was over. “Doctor Esolen, what you say about the habits of everyday life—to what extent is it like what Jean Pierre de Coussade calls ‘the sacrament of the present moment’?” “Doctor Esolen, do you see any connections between the bodiliness of this drama and the theology of Aleksandr Schmemann?” “Doctor Esolen, you have spoken a great deal about our recovery of a sense of beauty, but don’t you think that artists can also use the grotesque as a means of bringing people to the truth?” “You’ve suggested to us that Christians need to reclaim the Renaissance as our heritage, yet we are told that that was an age of the worship of man for his own sake. To what extent is the art of that period ours to reclaim?” And on and on, until nearly midnight.

The questions were superior to any that I have ever heard from a gathering of professors—and alas, I’ve been to many of those. I mean not only superior in their enthusiasm and their insistence, but in their penetrating to the heart of the problem, their willingness to make connections apparently far afield but really quite apropos, and their sheer beauty—I can think of no better word for it.

A few weeks ago I was in town for another talk, on the resurrection of the body. The Holy Father had passed away. At supper, ten or fifteen of the students packed our table, to ask questions before the talk. They were reverent and extraordinarily well informed; most especially they were interested in the Theology of the Body. The questions on that topic continued after the lecture, and I had the same experience I’d had before, but now without the surprise.

And these are the young people who are devoting an entire issue of their journal to the thought of Cardinal Ratzinger, now the new head of the Roman Catholic Church. They are hungry to know about him; in the next week or two they will do what our slatternly tarts and knaves, I mean our journalists, have never done and will not trouble themselves to do, and that is to read what Benedict XVI has said, read it with due appreciation for their differences with him, and due deference to a holy and humble man called by Christ to be a light not only to Roman Catholics but to all the nations.

These students don’t know it, but in their devotion to their new school (they are themselves the guards, the groundskeepers, the janitors; they ‘own’ the school in a way that is hard to explain to outsiders), they live the community life extolled by Leo XIII in Rerum Novarum; in their steadfastness to the truth they are stalwart participators in the quest set out by John Paul II in Fides et Ratio; in their welcoming of me and, God bless them, of the good Benedict XVI, they live in the true spirit of Lumen Gentium, that greathearted document of the council so often invoked for the lame tolerance of every betrayal of the ancient faith. And for what it’s worth, they are readers of Touchstone Magazine.

Be silent, Greeleys and Dowds of the world. These young people have you whipped, if for no other reason than that they believe in the One who is Truth, and who sets us free. How can I praise these my young brothers and sisters any more highly? God bless them and Patrick Henry College. And the rest of us, let’s keep an eye on them. We’ll be seeing quite a harvest from that seedbed!

Many of the points Esolen commends are things I hope will be found in the colleges of my university when I get around to starting it. I particularly admire that Patrick Henry College’s young men and women are just that, according to Esolen. This is all too often hard to achieve in modern American higher education, where students are quite often just elderly adolescents. (Though I suspect this has more to do with parents and family than education).

The absurdist drinking age that the Federal government underhandedly coerced each state into passing hinders maturity as well. Indeed, when I start the first college or colleges of the university I’m planning, each will have a private college bar which will serve anyone over the age of 16 or so. (Probably at the barman or barmaid’s discretion). Civil disobedience is the only solution.

Though the graduates Patrick Henry College provides will be Protestant (at least at the time of their graduation), I have no doubt that they will act as leaven to raise up the social and political life of our United States. I’m not particularly fond that they proudly advertise their commendation as “One of America’s Top Ten Conservative Colleges”. I’m not of the view that colleges ought to be ‘conservative’ or ‘liberal’ per se. They ought to be seen more as communities of inquisitive, curious, intelligent people united in the quest for truth. Labels like ‘conservative’ and ‘liberal’ are far too narrow and allow the simple-minded to pidgeon-hole things which are too complex for such monikers.

But anyhow, cheers for Patrick Henry College.

Posted by Andrew Cusack at April 21, 2005 05:25 PM

Thursday, June 9, 2005

Thursday June 9, 2005

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


"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

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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
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:

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Wednesday, June 8, 2005

Wednesday June 8, 2005

Filed under: General — m759 @ 6:26 PM
The Power of Myth

“Myths have no life of their own. They wait for us to give them flesh.”

— Albert Camus, Prometheus in the Underworld

“Prometheus — One of the Titans of Greek myth, famous as a benefactor of man”

Log24 yesterday, 9:39 PM

The New York Times on today’s maiden speech of the new prime minister of France:

“PARIS, June 8 —  … In replying to his critics, Mr. De Villepin quoted from Albert Camus’s description of Prometheus, saying, ‘He is harder than his rock and more patient than his vulture.'”

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

Wednesday June 8, 2005

Filed under: General — m759 @ 11:11 AM

“Mike Nichols, who oversaw Monty Python’s Spamalot, picked up the prize for directing a musical.

A somewhat flustered Nichols told the audience he had forgotten what he intended to say, but then went on to thank his company and Eric Idle, ‘from whom all blessings flow.'”

The Age, Monday, June 6

One of my
favorite books:

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Excerpt from the chapter
“All Blessings Flow (Very Large Array)”–

“I started to cry.  My search was over.
In a home for the deranged I had found
the last of the holy Thirty-Six….

‘Beam me up, Scotty.'”

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Related material:

In memory of Anne Bancroft
and her work in
84 Charing Cross Road

entries of Dec. 11-13, 2002,
and entries of
All Souls’ Day, 2004,
and of June 8, 2003.

Tuesday, June 7, 2005

Tuesday June 7, 2005

Filed under: General — m759 @ 9:39 PM
939, or
Too Clever by Half

On the new
Prime Minister of France:

In Praise of Those Who Stole the Fire, M. de Villepin’s grandest literary effort to date…. will enhance his reputation within a small Paris set, but not in Washington, where he is already regarded as too clever by half.”

— Philip Delves Broughton,
    “De Villepin bares soul
     as France’s politician poet
    The Telegraph, May 23, 2003

From a Study Guide to
Frankenstein, or The Modern Prometheus:

The Titan Prometheus was “‘… chained to Mount Caucasus where an eagle preyed on his liver’ (Bullfinch [sic] 939).”  The study guide does not say whether 939 is a page number or paragraph number, nor does it name which edition of Bulfinch’s Mythology is meant.

The rest of the story:

From the Web-Guide to Thomas Pynchon’s V:

“Prometheus —  One of the Titans of Greek myth, famous as a benefactor of man. Zeus had him make men out of mud and water; however, pitying mankind, he stole fire from heaven and gave it to them. As punishment, Zeus chained him to Mount Caucasus where an eagle preyed on his liver all day, the liver being renewed at night. Hercules eventually released him and killed the eagle. Zeus sent Pandora to Earth with her box of evils to balance the gift of fire.”

Related material:

Pandora’s Box

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The Barest Vocabulary

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Postscript for John Nash:

  Why 939 signifies
“too clever by half” —
see 6:26 and 313.

See also

Joke #939
Date: Thu, 13 Nov 1997
From: Rainybow
Q: Do you know why God created woman second?
A: Because he didn’t want all the advice.

Tuesday June 7, 2005

Filed under: General — m759 @ 6:26 PM

Blair Insists
EU Treaty Not Dead

From BBC News:

Is it me or have we all been locked in a Monty Python sketch this week? …

Dutch Voter: Hello, I wish to complain about this treaty what I voted for not half an hour ago.

Eurocrat: Oh yes, the EU Constitution. What, uh… what’s wrong with it?

DV: I’ll tell you what’s wrong with it, my lad. Its dead, that’s what’s wrong with it!

E: No, no, uh… what we need now is a period of reflection.

DV: Look matey, I know a dead treaty when I see one, and I’m looking at one right now.

E: No, no it’s not dead, it’s being ratified. Remarkable treaty, the EU Constitution, innit, eh? 300 pages!

DV: The verbosity don’t enter into it, my lad. It’s stone dead. It’s passed on! This treaty is no more! It has ceased to be! It’s expired and gone to meet its maker! It’s a stiff! Bereft of life, it rests in peace! If the senior politicians hadn’t been ramming it down our throats, it’d be pushing up daisies! It’s off the table. It’s kicked the waste paper basket. It’s in the shredder. It’s shuffled off its mortal coil, run down the curtain and joined the bleedin’ choir invisible! THIS IS AN EX-TREATY!

E: Well, I’d better replace it then. [takes a quick peek around Brussels]

E: Sorry squire, I’ve had a look around Brussels, and uh, we’re right out of treaties.

DV: I see. I see, I get the picture.

E: I’ve got a Charter of Fundamental Rights.

DV: Pray, does it lead us to an increasingly united federation of nation states?

E: Not really.


Jonathan Rowles, Fleet

Tuesday June 7, 2005

Filed under: General,Geometry — Tags: — m759 @ 1:01 PM
The Sequel to Rhetoric 101:

101 101

“A SINGLE VERSE by Rimbaud,”
writes Dominique de Villepin,
the new French Prime Minister,
“shines like a powder trail
on a day’s horizon.
It sets it ablaze all at once,
explodes all limits,
draws the eyes
to other heavens.”

— Ben Macintyre,
The London Times, June 4:

When Rimbaud Meets Rambo

“Room 101 was the place where
your worst fears were realised
in George Orwell’s classic
 Nineteen Eighty-Four.

[101 was also]
Professor Nash’s office number
  in the movie ‘A Beautiful Mind.'”

Prime Curios

Classics Illustrated —

The image “http://www.log24.com/log/pix05A/050607-Nightmare.jpg” cannot be displayed, because it contains errors.

Click on picture for details.

(For some mathematics that is actually
from 1984, see Block Designs
and the 2005 followup
The Eightfold Cube.)

Monday, June 6, 2005

Monday June 6, 2005

Filed under: General — m759 @ 9:00 PM
Rhetoric 101:
Poetry and Reason

"La voix de la pensée
est-elle plus qu'un rêve?"

"Is the language of thought
 any more than a dream?"

— Rimbaud


Related material:

When Rimbaud Meets Rambo

Monday June 6, 2005

Filed under: General — m759 @ 6:01 PM

It was the best of times,
it was the worst of times.

One Bound

With one bound,
the Prime Minister is free.”

Times of London,
    June 7, 2005


Monday June 6, 2005

Filed under: General — m759 @ 1:00 PM

Order and Disorder

From “Connoisseur of Chaos,”
by Wallace Stevens, in
Parts of a World, 1942:


A.  A violent order is a disorder; and
B.  A great disorder is an order.
    These Two things are one. (Pages of illustrations.)               


A.  Well, an old order is a violent one. This proves nothing.
    Just one more truth, one more
    Element in the immense disorder of truths.

B.  It is April as I write. The wind
    Is blowing after days of constant rain.
    All this, of course, will come to summer soon.
    But suppose the disorder of truths should ever come
    To an order, most Plantagenet, most fixed. . . .
    A great disorder is an order.
    Now, A And B are not like statuary, posed
    For a vista in the Louvre. They are things chalked
    On the sidewalk so that the pensive man may see.


    The pensive man . . . He sees that eagle float
    For which the intricate Alps are a single nest.

Related material:
“Derrida on Plato on writing says ‘In order for these contrary values (good/evil, true/false, essence/appearance, inside/outside, etc.) to be in opposition, each of the terms must be simply EXTERNAL to the other, which means that one of these oppositions (the opposition between inside and outside) must already be accredited as the matrix of all possible opposition.’ “

Peter J. Leithart

See also

Skewed Mirrors,
Sept. 14, 2003

“Evil did not  have the last word.”
Richard John Neuhaus, April 4, 2005

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


“There is never any ending to Paris.”
— Ernest Hemingway

Monday June 6, 2005

Filed under: General — m759 @ 3:35 AM

Mot Juste?

From today’s New York Times, on the effort of Paris to be chosen as the host of the 2012 Olympics:

“‘To have the games would bring a little fun, as you say, a breath of fresh air,’ said Benoît Génuini, president of the French operation of Accenture, a global consulting company, on a balcony of the Louvre last week during an event to highlight the city’s cultural attractions as an Olympic host. He remarked that the country was morose and that the city itself had become a sort of museum. ‘The games would put Paris back in the saddle and lead it into the 21st century,’ he said, ‘get it out of its stupor.'”

Attributed to Dominique de Villepin, the new Prime Minister of France: words about his book on poetry–

“It tries to penetrate the heart of the poetic ferment, this secret place where words are made and unmade, where language is fashioned.”
The image “http://www.log24.com/log/pix05A/050604-VillepinChirac.jpg” cannot be displayed, because it contains errors.
Villepin (l.) with President Chirac

Saturday, June 4, 2005

Saturday June 4, 2005

Filed under: General,Geometry — m759 @ 7:00 PM
  Drama of the Diagonal
   The 4×4 Square:
  French Perspectives

The image “http://www.log24.com/log/pix05A/050604-Fuite1.jpg” cannot be displayed, because it contains errors.
   Les Anamorphoses:
   The image “http://www.log24.com/log/pix05A/050604-DesertSquare.jpg” cannot be displayed, because it contains errors.
  “Pour construire un dessin en perspective,
   le peintre trace sur sa toile des repères:
   la ligne d’horizon (1),
   le point de fuite principal (2)
   où se rencontre les lignes de fuite (3)
   et le point de fuite des diagonales (4).”
  Serge Mehl,
   Perspective &
  Géométrie Projective:
   “… la géométrie projective était souvent
   synonyme de géométrie supérieure.
   Elle s’opposait à la géométrie
   euclidienne: élémentaire
  La géométrie projective, certes supérieure
   car assez ardue, permet d’établir
   de façon élégante des résultats de
   la géométrie élémentaire.”
  Finite projective geometry
  (in particular, Galois geometry)
   is certainly superior to
   the elementary geometry of
  quilt-pattern symmetry
  and allows us to establish
   de façon élégante
   some results of that
   elementary geometry.
  Other Related Material…
   from algebra rather than
   geometry, and from a German
   rather than from the French:  

This is the relativity problem:
to fix objectively a class of
equivalent coordinatizations
and to ascertain
the group of transformations S
mediating between them.”
— Hermann Weyl,
The Classical Groups,
Princeton U. Press, 1946

The image “http://www.log24.com/log/pix05/050124-galois12s.jpg” cannot be displayed, because it contains errors.

Evariste Galois

 Weyl also says that the profound branch
of mathematics known as Galois theory

   “… is nothing else but the
   relativity theory for the set Sigma,
   a set which, by its discrete and
    finite character, is conceptually
   so much simpler than the
   infinite set of points in space
   or space-time dealt with
   by ordinary relativity theory.”
  — Weyl, Symmetry,
   Princeton U. Press, 1952
   Metaphor and Algebra…  

“Perhaps every science must
start with metaphor
and end with algebra;
and perhaps without metaphor
there would never have been
any algebra.” 

   — attributed, in varying forms, to
   Max Black, Models and Metaphors, 1962

For metaphor and
algebra combined, see  

  “Symmetry invariance
  in a diamond ring,”

  A.M.S. abstract 79T-A37,
Notices of the
American Mathematical Society,
February 1979, pages A-193, 194 —
the original version of the 4×4 case
of the diamond theorem.

More on Max Black…

“When approaching unfamiliar territory, we often, as observed earlier, try to describe or frame the novel situation using metaphors based on relations perceived in a familiar domain, and by using our powers of association, and our ability to exploit the structural similarity, we go on to conjecture new features for consideration, often not noticed at the outset. The metaphor works, according to Max Black, by transferring the associated ideas and implications of the secondary to the primary system, and by selecting, emphasising and suppressing features of the primary in such a way that new slants on it are illuminated.”

— Paul Thompson, University College, Oxford,
    The Nature and Role of Intuition
     in Mathematical Epistemology

  A New Slant…  

That intuition, metaphor (i.e., analogy), and association may lead us astray is well known.  The examples of French perspective above show what might happen if someone ignorant of finite geometry were to associate the phrase “4×4 square” with the phrase “projective geometry.”  The results are ridiculously inappropriate, but at least the second example does, literally, illuminate “new slants”– i.e., diagonals– within the perspective drawing of the 4×4 square.

Similarly, analogy led the ancient Greeks to believe that the diagonal of a square is commensurate with the side… until someone gave them a new slant on the subject.

Saturday June 4, 2005

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

Drama of the Diagonal,

“I could name other writers
who share this sense of a world
larger than ourselves; their writing provides
a field in which something like
a sacramental imagination is clearly at play.”

Paul Mariani,
God and the Imagination


“… the horizon is not the limit of meaning,
but that which extends meaning
from what is directly given
to the whole context in which it is given,
including a sense of a world.”

David Vessey,
Gadamer and the Fusion of Horizons


From Wallace Stevens,
A Primitive Like an Orb“:
It is a giant, always, that is evolved,
To be in scale, unless virtue cuts him, snips
Both size and solitude or thinks it does,
As in a signed photograph on a mantelpiece.
But the virtuoso never leaves his shape,
Still on the horizon elongates his cuts,
And still angelic and still plenteous,
Imposes power by the power of his form.
Here, then, is an abstraction given head,
A giant on the horizon, given arms,
A massive body and long legs, stretched out,
A definition with an illustration, not
Too exactly labeled, a large among the smalls
Of it, a close, parental magnitude,
At the center of the horizon, concentrum, grave
And prodigious person, patron of origins.
That's it. The lover writes, the believer hears,
The poet mumbles and the painter sees,
Each one, his fated eccentricity,
As a part, but part, but tenacious particle,
Of the skeleton of the ether, the total
Of letters, prophecies, perceptions, clods
Of color, the giant of nothingness, each one
And the giant ever changing, living in change.


Related material
(Click on pictures
for details.)

Logos Alogos
by S. H. Cullinane

The image “http://www.log24.com/log/pix05/021126-diagonH2.jpg” cannot be displayed, because it contains errors.

Logos Alogos II:

See also
Subject and Predicates and
The Quality of Diamond.

Thursday, June 2, 2005

Thursday June 2, 2005

Filed under: General — m759 @ 2:00 PM
The Barest Vocabulary
at the Altar of Facts

From Log24,
April 28, 2005:

The image “http://www.log24.com/log/pix05/050310-hex.jpg” cannot be displayed, because it contains errors.

(See also Log24,
April 5, 2005.)
Compare this diagram with that of
Samuel Beckett in Quad (1981):
The image “http://www.log24.com/log/pix05/050428-Quad.jpg” cannot be displayed, because it contains errors.

Related quotation:

Barry Mazur on a seminal paper of algebraist Saunders Mac Lane:

The paper was rejected “because the editor thought that it was ‘more devoid of content’ than any other he had read.  ‘Saunders wrote back and said, “That’s the point,”‘ Mazur said.  ‘And in some ways that’s the genius of it. It’s the barest, most Beckett-like vocabulary that incorporates the theory and nothing else.'”

Other related material:

The image “http://www.log24.com/log/pix05A/050602-Duif.jpg” cannot be displayed, because it contains errors.

From Reuters:

“Members of the ballot commission manually count EU referendum votes in the Duifkerk in Amsterdam June 1st, 2005. Dutch voters soundly rejected the European Union constitution in a referendum on June 1…..  Photo by… Ronald Fleurbaaij”

Background reading on the new
Prime Minister of France:

“M. de Villepin positively worships Napoleon, and models himself after his hero. In a 600-page biography, Villepin wrote admiringly about the difference between great men like Napoleon and the ‘common run’ of men. It is worth reading every word carefully.

‘Here we touch on that particular essence of great men, on what distinguishes Napoleon or Alexander, Caesar or de Gaulle, from the common run. It is excess, exaltation, and a taste for risk that forms their genius. It is why they are often better understood in their élan by writers and poets, who are possessed of the same thirst for the absolute, than by those who pray at the altar of facts.’
(New Republic)

And in praise of French nationalism, de Villepin wrote,

‘The Gaullist adventure renewed the élan of [Napoleon’s] Consulate through the restoration of a strong executive and the authority of the State, the same scorn for political parties and for compromise, a common taste for action, and an obsession with the general interest and the grandeur of France.’

Those words come straight from 1800. Napoleon’s ‘genius,’ his ‘thirst for the absolute,’ ‘excess, exaltation, and a taste for risk,’ ‘a strong executive and the authority of the State,’ ‘his ‘scorn for political parties and for compromise,’ and ‘an obsession with the grandeur of France’ — it is all classic national hero worship. But today that kind of thinking is used to promote a new vision of destiny, the European Union.”

James Lewis at The American Thinker,
   Jan. 4, 2005

Wednesday, June 1, 2005

Wednesday June 1, 2005

Filed under: General — m759 @ 7:20 PM
The Road to Brussels

“History is not, of course, a cookbook offering pretested recipes. It teaches by analogy, not by maxims. It can illuminate the consequences of actions in comparable situations, yet each generation must discover for itself what situations are in fact comparable.”

 — Henry Kissinger, quoted in
     Drama of the Diagonal, Part Deux

Les livres d’histoire et la vie
racontent la même comédie….

Alain Boublil

Wellington at Waterloo

The image “http://www.log24.com/log/pix05/050601-Map.jpg” cannot be displayed, because it contains errors.


“Along the road from Ohain to Braine-l’Alleud that hemmed in the plain of Mont-St-Jean and cut at right angles the road to Brussels, which the Emperor wished to take, he [Wellington] had placed 67,000 men and 184 cannons.” Fr. Libert, Waterloo

The Emperor’s Welcome

From Expatriate Online:
Your Bookmark to Belgium

The image “http://www.log24.com/log/pix05/050601-Waterloo.jpg” cannot be displayed, because it contains errors.

Wednesday June 1, 2005

Filed under: General — m759 @ 3:57 AM
Just Say Nee

The image “http://www.log24.com/log/pix05/050601-Nee.jpg” cannot be displayed, because it contains errors.

Click on picture
for details.

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