Tuesday, September 30, 2003

Tuesday September 30, 2003

Filed under: General — m759 @ 4:38 PM

Project for the
New Century

“A bully can be stopped, and so can a mob. It takes one person with the courage and a resolute voice.”

Tim Robbins, speech to National Press Club, April 15, 2003

Resoluteness is a necessary, but not sufficient, condition for such a voice.  Also needed is eloquence.  Here is such a voice:

William Rivers Pitt.


I wrote the above at 3:38 PM today, thinking I had finally found someone to admire whom my left-leaning friends might also admire.

Perhaps resoluteness and eloquence suffice to stop a mob; they are not, however, sufficient to impress professional journalists, who, to be much impressed, require a third quality– truthfulness.

Since today’s major Washington and New York papers indicate that a presidential scandal of Water- or Monica-gate proportions may be in the offing, some minimal fact-checking seems in order.  Hence, at 3:40 PM today, I did a Google search on names Pitt discusses:

“karl rove”  
“robert mosbacher”  

That search indicates that unfortunately, mob-stopper Pitt seems, like many leftists, to be a liar.

Here is an excerpt from Pitt on Karl Rove dated Tuesday, Sept. 30, 2003:

The Most Insidious of Traitors

“Karl Rove, senior political advisor to George W. Bush, is a very powerful man. That is not to say he has never been in trouble. Rove was fired from the 1992 Bush Sr. campaign for trashing Robert Mosbacher, Jr., who was the chief fundraiser for the campaign and an avowed Bush loyalist. Rove accomplished this trashing of Mosbacher by planting a negative story with columnist Bob Novak. The campaign figured out that Karl had done the dirty deed, and he was given his walking papers.

Demonstrably, Rove is back in the saddle again. The January 2003 edition of Esquire magazine carried an article by Ron Suskind…. “

Here is an excerpt from columnist Robert Novak dated December 5, 2002:

Low Political Intrigue

“The article in Esquire’s January edition by Pulitzer Prize-winning journalist Ron Suskind is actually about Karl Rove, Bush’s powerful political adviser…. 

Unfortunately, I did not escape Suskind’s article, which includes these sentences: ‘Sources close to the former president say Rove was fired from the 1992 Bush presidential campaign after he planted a negative story with columnist Robert Novak about dissatisfaction with campaign fund-raising chief and Bush loyalist Robert Mosbacher Jr. It was smoked out, and he was summarily ousted.’  I was called by no fact-checker, who would have learned of multiple errors.

Suskind has confused former Secretary of Commerce Robert Mosbacher Sr., Bush’s 1992 chief fund-raiser, with his son Rob, who headed the Bush campaign in Texas (Victory ’92). Criticism of the younger Mosbacher, a frequent unsuccessful candidate in Texas, was not ‘planted’ with me by Rove but was passed to me by a Bush aide whom I interviewed. Rove was indeed fired by Mosbacher from Victory ’92 but continued as a national Bush-for-president operative.

Three mistakes in two sentences lend credence to claims by White House aides that they were misrepresented in Suskind’s July article…”

I say Pitt seems to be lying because in today’s editorial he never even mentions Novak’s column of December 5, 2002, which is, as noted above, readily available. 

It is, of course, possible that Pitt and Suskind are right and Novak is wrong.  It is also possible that Orwell was wrong, that Stalin was a great man, and that Communism is the wave of the future.

Tuesday September 30, 2003

Filed under: General — Tags: — m759 @ 3:16 AM

On the Beach

On this date in 1954, the first nuclear submarine, the USS Nautilus, was commissioned.

Related reading in today’s New York Times:

  1. Obituary of Marshall N. Rosenbluth, physicist who helped develop the H-bomb.  He died Sunday in San Diego, California.
  2. Quotation from a Fermilab physicist:
    “There are a bunch of things that nothing can turn them around. Death is one.”

Related reading from yesterday’s entries:

Related reading from the Song of Songs:

“Love is strong as death.”

Related viewing:

From Here to Eternity

 Today’s birthday: Deborah Kerr.

Monday, September 29, 2003

Monday September 29, 2003

Filed under: General — m759 @ 3:03 PM

Magic Hawaii

Today, the birthday of singer Jerry Lee Lewis, is also the feast of St. Michael and All Angels.

In honor of Lewis:

Killer Radio, an entry of July 31, 2003, that contains the following…

“When the light came she was sitting on the bed beside an open suitcase, toying with her diamond rings.  She saw the light first in the depths of the largest stone.”

— Paul Preuss, Broken Symmetries,
    scene at Diamond Head, Oahu,

In honor of the angels:

Mathematics as an Adequate Language,
by Israel Gelfand, Sept. 2, 2003, which contains the following…

“Many people consider mathematics to be a boring and formal science.  However, any really good work in mathematics always has in it: beauty, simplicity, exactness, and crazy ideas.  This is a strange combination.  I understood earlier that this combination is essential on the example of classical music and poetry.  But it is also typical in mathematics.  It is not by chance that many mathematicians enjoy serious music.

This combination of beauty, simplicity, exactness, and crazy ideas is, I think, common to both mathematics and music.”

These qualities seem also to be sought by practitioners of religion and physics… for example, by the spiritually-minded physicist in Preuss’s Broken Symmetries.  Skeptics might prefer, to the word “religion,” the word (pronounced with a sneer) “magic.”

What do we find if, following in the footsteps of Gelfand and Preuss, we do a Google search on the following words…

beauty simplicity exactness
 crazy magic Hawaii

The search yields two results:

  1. The Pupil: Poems by W. S. Merwin.
    The above link is to a poem, “Prophecy,” that seems suitable for these, the High Holy Days at the end of one year and the beginning of another.

    For a follow-up to the poem, see
    The Shining of Lucero.

  2. Striking Through the Mask, or
     The Allegorical Meanings
     in Moby Dick

These two selections, both on the theme of light and darkness, offer a language that is perhaps more adequate than mathematics for dealing with the nature of the High Holy Days.  For a more lighthearted approach to these concerns, also with a Hawaiian theme, see

The Aloha Mass.

Monday September 29, 2003

Filed under: General — m759 @ 1:15 AM

Declaring Victory
and Going Home

Elia Kazan

Sunday, September 28, 2003

Sunday September 28, 2003

Filed under: General — Tags: — m759 @ 4:13 PM

Spirit of East St. Louis

On Miles Davis and Philly Joe Jones:

Miles said to Jones, "I think this is it." Jones agreed having said of the group, "The first time we played together…we just looked around at each other and said, ‘hum here it is right here. We’ve got musical telepathy here. We have five people who always know what’s going to happen next.’" And those five people became legendary as the classic Miles Davis Quintet was baptized for its first time.

From The American Art Form:

While singing work songs, a leader would call out a phrase, and the rest of the people would answer. This is known as call and response. In Cindy Blackman's "Telepathy" , the lead saxophone who is playing the melody calls out a phrase, and another horn responds. In some jazz music, there is what is known as "trading 4's". This is when one instrument plays 4 measures, and then another plays 4 measures off what the first person played, and so on. This is a modern rendition of call and response.


Trading Fours

See also

Miles Davis, E. S. P.,

Bill Stewart, Telepathy,

Desmond and Mulligan, Two of a Mind,

Google search, "musical telepathy,"

and a novel dealing with East St. Louis (where Miles Davis grew up) and telepathy,

The Hollow Man, by Dan Simmons.

From the jacket of The Hollow Man:

Jeremy Bremen has a secret. All his life he has been cursed with the unwanted ability to read minds. He can hear the secret thoughts behind the placid expressions of strangers, colleagues, and friends. Their dreams, their fears, their most secret desires are as intimate to him as his own. For years his wife, Gail, has served as a shield between Jeremy and the intrusive thoughts of those around him. Her presence has protected him from the outside world and allowed him to continue his work as one of the world's leading mathematicians. But now Gail is dying, her mind slipping slowly away, and Jeremy comes face-to-face with the horror of his own omniscience. Vulnerable and alone, he is suddenly exposed to a chaotic flood of others' thoughts, threatening to fill him with the world's pain and longing, to sweep away his very sanity. His mathematical studies have taken him to the threshold of knowledge and enabled him to map uncharted regions of the mind, to recognize the mind itself as a mirror of the universe…and to see in that mirror the fleeting reflection of the creator himself. But his studies taught him nothing at all about the death of the mind, about the loss of love and trust, and about the terrible loneliness of mortality. Now Jeremy is on the run – from his mind, from his past, from himself – hoping to find peace in isolation. Instead he witnesses an act of brutality that sends him on a treacherous odyssey across America, from a fantasy theme park to the mean streets of an uncaring city, from the lair of a killer to the gaudy casinos of Las Vegas, and at last to a sterile hospital room in St. Louis in search of the voice that is calling him to the secret of existence itself.

Friday, September 26, 2003

Friday September 26, 2003

Filed under: General — m759 @ 9:26 PM

Time is a Weapon

“Time is a weapon, it’s cold and it’s cruel.”

— Max D. Barnes song lyric,
sung by Ray Price
(See Aug. 1, 2003, entry.)


was the time of yesterday afternoon’s entry,


The Friday,
Sept. 26, 2003,
Mid-Day Lottery
Number for
(State of Grace)

“Only through time time is conquered.”
— T. S. Eliot, Four Quartets

Friday September 26, 2003

Filed under: General — m759 @ 3:28 PM

A Mass for
Rosh Hashanah

In memory of playwright Herb Gardner, who died on Wednesday, Sept. 24, 2003, in honor of the Jewish New Year, Rosh Hashanah, which begins at sunset today, and in celebration of T. S. Eliot’s birthday, which is today, here is an illustrated Mass from the Catholic News Service dated Sept. 24 (Saint Herb’s Day):

Proposed Vatican document on liturgy returned to drafting committee

By Cindy Wooden
Catholic News Service

ROME (CNS) — A proposed Vatican document on liturgical norms was sent back to its drafting committee after cardinals and bishops raised some objections and encouraged some changes.

Among other things, the draft presented to consulting prelates in June reportedly discouraged the distribution of Communion under the forms of both bread and wine and said altar girls were permissible only for a good reason.

 cards of unparalleled fabulosity

See also the two previous entries,
and “Max’s Hawaiian Ecstasies” in
Gardner’s play “The Goodbye People.”

For a musical accompaniment to this
requiem for Gardner,
 the “Aloha Mass,”
click here.

at the

The Mass, at Max’s Hawaiian Ecstasies
in Paradise, will conclude with
Simply Irresistible,” sung by
Saint Robert Palmer and performed by…

Irresistible Grace.

The role of the congregation will, as usual,
be performed by George Plimpton.
Payment for our sins will be made by
Johnny Cash.

Thursday, September 25, 2003

Thursday September 25, 2003

Filed under: General — m759 @ 3:57 PM

In Memory of Playwright
 Herb Gardner

eBay item 3243620848:

“Up for auction is a Hawaiian hula girl music box. It plays ‘Tiny Bubbles’ and spins around. It is approx. 12″ tall and the top part of the body is made of hard plastic. It is in great condition.”


Wednesday, September 24, 2003

Wednesday September 24, 2003

Filed under: General — m759 @ 10:01 PM

Bel Canto

The conclusion of tonight’s season-
opening episode of “The West Wing”
was a picture of President Bartlet  
 receiving the Host at Mass.

Related material:

The Source:

Tips On Popular Singing
by Frank Sinatra
in collaboration with
his vocal teacher John Quinlan

What prompted me to find this
booklet on the Web
(at about 8:45 PM tonight) was

40,000 Years of Music
by Jacques Chailley
(Farrar, Straus & Giroux, 1964),
page 162,
on the bel canto style of singing.

I picked up this book this afternoon
at a sale for $1.

See also Sinatra’s remarks on bel canto
(various places on the Web).

For the religious significance of
the page number 162, see my
entry of 9/11 2003,


Added at 3:20 AM Sept. 25…

In Related News:

Source: Google News, about 3:15 AM 9/25/03

Tuesday, September 23, 2003

Tuesday September 23, 2003

Filed under: General — m759 @ 1:15 PM

Intelligence Test

At left:
IQ Test

Today’s British Intelligence Award
goes to Reuters news agency:

Key Phrase Was Dropped
from UK Iraq Dossier

Tue September 23, 2003 12:33 PM ET
By Katherine Baldwin and Janet McBride

LONDON (Reuters) – The British intelligence chief responsible for a pre-war dossier on Iraq’s weapons dropped a key sentence from it days before publication after prompting from Downing Street, an inquiry heard Tuesday.

He did it at the suggestion of Jonathan Powell, chief of staff to Prime Minister Tony Blair, the inquiry heard.

The offending sentence stated that former Iraqi President Saddam Hussein was prepared to use chemical and biological weapons “if he believes his regime is under threat.”

Powell argued that phrase suggested Iraq was only a threat if attacked.

The revelation that Powell ordered the sentence to be omitted raises fresh doubts over the intervention of Blair’s office in the compilation of the September dossier.

Today’s British Stupidity Award goes,
of course, to Jonathan Powell.

Monday, September 22, 2003

Monday September 22, 2003

Filed under: General — Tags: — m759 @ 4:23 AM

What Is Poetry?

Sunday, September 21, 2003

Sunday September 21, 2003

Filed under: General — m759 @ 4:11 PM

Today in History

Happy birthday, Ronna.

Saturday, September 20, 2003

Saturday September 20, 2003

Filed under: General — m759 @ 11:59 PM

Contrapuntal Structure

Click here for a web page based on my Sept. 16 entry The Form, the Pattern.

Friday, September 19, 2003

Friday September 19, 2003

Filed under: General — m759 @ 3:57 AM

The Mysteries of 26

My entry of May 26, 2003 —

Many Dimensions — Why 26? 

dealt with the question of whether this number, said to be of significance (as a number of dimensions) in theoretical physics, has any purely mathematical properties of interest.

That entry contained the above figure, a so-called Levi graph illustrating point/line incidence in the finite projective plane with 13 points and 13 lines, PG(2,3).

It turns out that in a paper of April 7, 2000, John H. Conway and Christopher S. Simons discussed a close connection between this plane and the Monster group.  See

26 Implies the Bimonster 

(Journal of Algebra. Vol. 235, no. 2.
MR 2001k:20028).

Conway had written about such a connection as early as 1985.

I apologize for not knowing about this sooner, and so misleading any mathematical readers about the number 26, which it seems does have considerable purely mathematical significance.

Thursday, September 18, 2003

Thursday September 18, 2003

Filed under: General — m759 @ 2:45 AM

Happy Ending

From yesterday morning:

“At three o’clock in the morning
Eurydice is bound to come into it.”
—Russell Hoban,
The Medusa Frequency

For June Carter Cash as Eurydice,
see The Circle is Unbroken.

Let us pray that Jesus College
will help this production,
with Johnny Cash as Orpheus,
to have a happy ending

From Jesus College, Oxford
Not the Jesus I had in mind, but it will do:

“… Filled with despair, Orpheus dragged himself back to earth with only his music left to him…. In death Orpheus once more entered the Underworld, still playing the lyre. He and Eurydice were permanently reunited. Many scholars see Orpheus as another pagan prototype of Christ.”


Wednesday, September 17, 2003

Wednesday September 17, 2003

Filed under: General — m759 @ 3:00 AM

Time’s Breakdown

“… even if we can break down time into component Walsh functions, what would it achieve?”

— The Professor, in “Passing in Silence,”
    by Oliver Humpage

“Being is not a steady state but an occulting one: we are all of us a succession of stillness blurring into motion on the wheel of action, and it is in those spaces of black between the pictures that we find the heart of mystery in which we are never allowed to rest. The flickering of a film interrupts the intolerable continuity of apparent world; subliminally it gives us those in-between spaces of black that we crave.”

Gösta Kraken, Perception Perceived: an Unfinished Memoir (p. 9 in Fremder, a novel by Russell Hoban)

“The Underground’s ‘flicker’ is a mechanical reconciliation of light and darkness, the two alternately exhibited very rapidly.”

Hugh Kenner on T. S. Eliot’s “Burnt Norton” in Four Quartets

From last year’s entries:

ART WARS September 12, 2002


For some further reflections on flickering time,
see an essay by Nicholson Baker on

the Geneva mechanism
in movie projectors

“At three o’clock in the morning
Eurydice is bound to come into it.”
—Russell Hoban,
The Medusa Frequency

For June Carter Cash as Eurydice,
see The Circle is Unbroken.

Let us pray that Jesus College
will help this production,
with Johnny Cash as Orpheus,
to have a happy ending.

Tuesday, September 16, 2003

Tuesday September 16, 2003

Filed under: General,Geometry — Tags: — m759 @ 2:56 PM

The Form, the Pattern

"…the sort of organization that Eliot later called musical, in his lecture 'The Music of Poetry', delivered in 1942, just as he was completing Four Quartets: 'The use of recurrent themes is as natural to poetry as to music,' Eliot says:

There are possibilities for verse which bear some analogy to the development of a theme by different groups of instruments [‘different voices’, we might say]; there are possibilities of transitions in a poem comparable to the different movements of a symphony or a quartet; there are possibilities of contrapuntal arrangement of subject-matter."

— Louis L. Martz, from
"Origins of Form in Four Quartets,"
in Words in Time: New Essays on Eliot’s Four Quartets, ed. Edward Lobb, University of Michigan Press, 1993

"…  Only by the form, the pattern,     
Can words or music reach
The stillness…."

— T. S. Eliot,
Four Quartets

Four Quartets

For a discussion of the above
form, or pattern, click here.

Tuesday September 16, 2003

Filed under: General — m759 @ 2:56 AM


Words move, music moves
Only in time….

— T. S. Eliot, Four Quartets

It is time that beats in the breast and it is time
That batters against the mind, silent and proud,
The mind that knows it is destroyed by time.

Time is a horse that runs in the heart, a horse
Without a rider on a road at night.
The mind sits listening and hears it pass.

— Wallace Stevens, “The Pure Good of Theory”

Only through time time is conquered.

— T. S. Eliot, Four Quartets

Monday, September 15, 2003

Monday September 15, 2003

Filed under: General — m759 @ 4:15 PM

All the King's Horses

Johnny Cash's funeral was today.

Today is also the feast day of the Protestant saint Robert Penn Warren.

Here is how Stanley Kubrick might
make a memorial stone for Cash.


"He is
the outlaw
the people
the hero
in black."


Hex Witch
of Seldom

The title of this entry, "All the King's Horses," is of course a slightly altered version of the title of Robert Penn Warren's famous novel.  For the connection with horses, see my entries of

September 12, 2003, and of

September 5, 2002.

See also 

The Journey Westward and

Into the West,

as well as the beginning of Mark Helprin's novel

Winter's Tale:

"There was a white horse, on a quiet winter morning when snow covered the streets gently…." 

Monday September 15, 2003

Filed under: General — m759 @ 4:44 AM

Two More Skewed Mirrors

Background: Previous three entries and
The Crucifixion of John O’Hara.

  1. From The New Yorker,
    issue dated Sept. 22, 2003…

    John Updike on John O’Hara

    And yet the ultimate units of society, the human individuals lost within the crushing agglomeration of hostility, rivalry, snobbery, exclusion, and defeat that O’Hara felt in his bones, have aspirations and hopes and passions, and can be regarded with tenderness by a writer whose bleak and swift style seems at first not to care. A small story from “Files on Parade” (1939) titled “By Way of Yonkers” sticks in my mind as especially moving. Its two principals, the young woman unnamed and the man named only in the last sentence, exist on the lower levels of Depression survival. She, with her gunmetal stockings and Cossack hat and “neat, short nose with jigsaw nostrils,” seems to be a hooker. She arrives at the man’s shabby apartment so late that he tells her she must have come by way of Yonkers, and when he asks “How’d you do?” of the engagement that delayed her she not quite evades the question:

    “Oh—” she said it very high. Then: “All right. Financially. But do we have to talk about it? You and me?”

    She talks instead about her fading appetite for liquor, and the expense of dental care. He, lying inert and fully dressed on his bed, talks of being broke, of not wanting to take money from her, of how he can’t seem “to make a connection in this town.” The town is New York, and he is a minor gangster thrown out of work by the repeal of Prohibition. But he has met a man who offered him a connection in Milwaukee, and he is going to go there for a long time. The concluding words are unspectacular and unexpectedly sweeping:

    [She asks,] “Any chance you being back in town soon?”
    “Well, not right away, honey. First I have to build up my connection again.”
    “Well, I don’t have to tell you, I’m glad for you. It’s about time you got a good break.” She resumed rubbing his ankle. He put his hand on the top of her head.
    “Yeah? You’re as good a break as I ever got.”
    “Ah, Christ, Bill,” she said, and fell face down in tears.

    One is moved not only by their plight of presumably eternal separation but by the dignity that O’Hara, in a literary time of programmatic pro-proletarian advocacy (Odets and Steinbeck and Mike Gold), instinctively brings to his two specimens of lowlife. He does not view them politically, from above; he is there in the room with them, and one is moved by the unspoken presence of an author so knowing, so unjudgmental, so nearly an outcast himself.

  2. Johnny Cash singing “Hurt” —

    The video can be seen here.

Ah, Christ, Johnny.

Sunday, September 14, 2003

Sunday September 14, 2003

Filed under: General,Geometry — m759 @ 9:12 PM

Skewed Mirrors

Readings on Aesthetics
for the
Feast of the Triumph of the Cross

Part I

Bill Moyers and Julie Taymor

Director Taymor on her own passion play (see previous entry), “Frida“: 

“We always write stories of tragedies because that’s how we reach our human depth. How we get to the other side of it. We look at the cruelty, the darkness and horrific events that happened in our life whether it be a miscarriage or a husband who is not faithful. Then you find this ability to transcend. And that is called the passion, like the passion of Christ. You could call this the passion of Frida Kahlo, in a way.”

— 10/25/02 interview with Bill Moyers

From transcript
of 10/25/02

MOYERS: What happened to you in Indonesia.

TAYMOR: This is probably it for me. This is the story that moves me the most…. 

I went to Bali to a remote village by a volcanic mountain on the lake. They were having a ceremony that only happens only every 10 years for the young men. I wanted to be alone.

I was listening to this music and all of a sudden out of the darkness I could see glints of mirrors and 30 or 40 old men in full warrior costume– there was nobody in this village square. I was alone. They couldn’t see me in the shadows. They came out with these spears and they started to dance. They did, I don’t know, it felt like an eternity but probably a half hour dance. With these voices coming out of them. And they danced to nobody. Right after that, they and I went oh, my God. The first man came out and they were performing for God. Now God can mean whatever you want it to mean. But for me, I understood it so totally. The detail on the costumes. They didn’t care if someone was paying tickets, writing reviews. They didn’t care if an audience was watching. They did it from the inside to the outside. And from the outside to the in. And that profoundly moved me then.

MOYERS: How did you see the world differently after you were in Indonesia?

From transcript
of 11/29/02

….They did it from the inside to the outside. And from the outside to the in. And that profoundly moved me then. It was…it was the most important thing that I ever experienced. … 


MOYERS: Now that you are so popular, now that your work is…


MOYERS: No, I’m serious.

 Now that you’re popular, now that your work is celebrated and people are seeking you, do you feel your creativity is threatened by that popularity or liberated by it?

TAYMOR: No, I think it’s neither one. I don’t do things any differently now than I would before.

And you think that sometimes perhaps if I get a bigger budget for a movie, then it will just be the same thing…

MOYERS: Ruination. Ruination.

TAYMOR: No, because LION KING is a combination of high tech and low tech.

There are things up on that stage that cost 30 cents, like a little shadow puppet and a lamp, and it couldn’t be any better than that. It just couldn’t.

Sometimes you are forced to become more creative because you have limitations. ….

TAYMOR: Well I understood really the power of art to transform.

I think transformation become the main word in my life.

Transformation because you don’t want to just put a mirror in front of people and say, here, look at yourself. What do you see?

 You want to have a skewed mirror. You want a mirror that says you didn’t know you could see the back of your head. You didn’t know that you could amount cubistic see almost all the same aspects at the same time.

It allows human beings to step out of their lives and to revisit it and maybe find something different about it.

It’s not about the technology. It’s about the power of art to transform.

I think transformation becomes the main word in my life, transformation.

Because you don’t want to just put a mirror in front of people and say, here, look at yourself. What do you see?

You want to have a skewed mirror. You want a mirror that says, you didn’t know you could see the back of your head. You didn’t know that you could…almost cubistic, see all aspects at the same time.

And what that does for human beings is it allows them to step out of their lives and to revisit it and maybe find something different about it.

Part II

 Inside and Outside: Transformation

(Research note, July 11, 1986)

Click on the above typewritten note to enlarge.

Summary of
Parts I and II:

See also
Geometry for Jews.

“We’re not here to stick a mirror on you. Anybody can do that, We’re here to give you a more cubist or skewed mirror, where you get to see yourself with fresh eyes. That’s what an artist does. When you paint the Crucifixion, you’re not painting an exact reproduction.”

Julie Taymor on “Frida” (AP, 10/22/02)

“She made ‘real’ an oxymoron, 
         she made mirrors, she made smoke.
She had a curve ball
          that wouldn’t quit,
                              a girlfriend for a joke.”

— “Arizona Star,” Guy Clark / Rich Alves

Sunday September 14, 2003

Filed under: General — m759 @ 2:56 PM

The Graces of Paranoia

The New Yorker on Mel Gibson’s filmed passion play:

How did he know that God wanted him to make “The Passion“?

Gibson in “Signs

“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….” 

— “The Jesus War: Mel Gibson’s Obsession,” by Peter J. Boyer, The New Yorker, September 15, 2003, p. 70

On the later plays of August Strindberg:

In some plays, when the central character notices things in the everyday world that start to take on unearthly significance (the masts of a half-sunken ship begin to resemble the three crosses on Calvary; someone takes sick just when one wishes the person dead), it usually indicates that the character is starting to experience a life-changing paranoid-schizophrenic episode, not unlike the one Strindberg himself experienced in his so-called “inferno” crisis in the 1890s.

— Cary M. Mazer, “A Strindberg Christmas

For the Grace that I prefer to Gibson’s looney ravings, see my entries for this date last year.

Saturday, September 13, 2003

Saturday September 13, 2003

Filed under: General — m759 @ 1:44 AM

For the Man in Black

Lyrics:  Arizona Star

“Shinin’ like a diamond
 she had tombstones in her eyes.”

A picture: Salma Hayek and Julie Taymor

A book:  Dark Ladies, by Fritz Leiber

This offers a gentler form of the alcoholic experience than Malcolm Lowry’s classic Under the Volcano:

“I’ve had hallucinations from alcohol, too…. But only during withdrawal oddly, the first three days.  In closets and dark corners and under tables — never in very bright light — I’d see these black and sometimes red wires, about the thickness of telephone cords, vibrating, whipping around.  Made me think of giant spiders’ legs and such.  I’d know they were hallucinations — they were manageable, thank God.  Bright light would always wipe them out.”

— Fritz Leiber, “Our Lady of Darkness,” in Dark Ladies

Related entries:

The Feast of Kali, the Dark Lady, and

Architecture of Eternity,
my own “Once Upon a Time in Mexico.”

For a more serious Dark Lady portrait, see the site of artist John de la Vega.

Friday, September 12, 2003

Friday September 12, 2003

Filed under: General — m759 @ 3:33 PM

Into the Sunset

I just learned of Johnny’s Cash’s death.  On Google News, the headline was  Johnny Cash rides into sunset.  The source was the Bangkok Post.

“Don’t you know that
when you play at this level
there’s no ordinary venue.”

One Night in Bangkok (midi)

No Ordinary Venue

“They are the horses of a dream.
 They are not what they seem.”

The Hex Witch of Seldom, page 16

A Singer 7-Cycle
A Singer

The Magnificent Seven:


“the adventures of filming this epic
on location in Cuernavaca, Mexico.”

“He is the outlaw the people love,
the hero dressed in black.”

The Hex Witch of Seldom,
by Nancy Springer, page 15

“Words are events.”

Walter J. Ong, Society of Jesus 

“…search for thirty-three and three…”
The Black Queen in The Eight

Friday September 12, 2003

Filed under: General — m759 @ 3:06 PM

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

“El pan que se come no es pan.”

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

Thursday, September 11, 2003

Thursday September 11, 2003

Filed under: General — Tags: , — m759 @ 6:25 PM


Walter J. Ong


Upon learning of the recent death of Walter J. Ong, S. J., philosopher of language, I ordered a copy of his book

Hopkins, the Self, and God
University of Toronto Press, 1986.

As the reader of my previous entry will discover, I have a very low opinion of the literary skills of the first Christians.   This sect’s writing has, however, improved in the past two millennia.

Despite my low opinion of the early Christians, I am still not convinced their religion is totally unfounded.  Hence my ordering of the Ong book.  Since then, I have also ordered two other books, reflecting my interests in philosophical fiction (see previous entry) and in philosophy itself:

Philosophical fiction —

The Hex Witch of Seldom,
by Nancy Springer,
Penguin Putnam Inc., 2002
(See 1 Corinthians 1:26-29)

Philosophy —

by Richard Robinson,
Fellow of Oriel College, Oxford,
Oxford U. Press, 1954, reprinted 1962.

Following the scientific advice of Niels Bohr and Freeman Dyson, I articulated on April 25, 2003, a mad theory of the mystical significance of the number 162.

Here is that theory applied to the three works named above, all three of which I received, synchronistically, today.

Page 162 of Hopkins, the Self, and God is part of the long list of references at the back of the book.  Undiscouraged by the seeming insignificance (vide my note Dogma) of this page, I looked more closely.  Behold, there was Christ…  Carol T. Christ, that is, author of The Finer Optic: The Aesthetic of Particularity in Victorian Poetry, Yale University Press, 1975. “Particularity” seemed an apt description of my “162” approach to literature, so I consulted Christ’s remarks as described in the main body of Ong’s book.

Particularity according to Christ —

“Victorian particularist aesthetics has prospered to the present time, and not only in novels.  The isolated, particularized, unique ‘good moment’ [Christ, 105], the flash of awareness at one particular instant in just the right setting, which Hopkins celebrates….”

— Ong, Hopkins, the Self, and God, p. 14

I highly recommend the rest of Ong’s remarks on particularity.

Turning to the other two of the literary trinity of books I received today….

Page 162 of The Hex Witch of Seldom has the following:

“There was a loaf of Stroehmann’s Sunbeam Bread in the grocery sack also; she and Witchie each had several slices.  Bobbi folded and compressed hers into little squares and popped each slice into her mouth all at once.”

The religious significance of this passage seems, in Ong’s Jesuit context, quite clear.

Page 162 of Definition has the following:

“Real Definition as the Search for a Key.  Mr. Santayana, in his book on The Sense of Beauty, made the following extremely large demands on real definition:

‘A definition <of beauty> that should really define must be nothing less than the exposition of the origin, place, and elements of beauty as an object of human experience.  We must learn from it, as far as possible, why, when, and how beauty appears, what conditions an object must fulfil to be beautiful, what elements of our nature make us sensible of beauty, and what the relation is between the constitution of the object and the excitement of our sensibility.  Nothing less will really define beauty or make us understand what aesthetic appreciation is.  The definition of beauty in this sense will be the task of this whole book, a task that can be only very imperfectly accomplished within its limits.’ ”

Here is a rhetorical exercise for Jesuits that James Joyce might appreciate:

Discuss Bobbi’s “little squares” of bread as the Body of Christ.  Formulate, using Santayana’s criteria, a definition of beauty that includes this sacrament.

Refer, if necessary, to
the log24.net entries
Mr. Holland’s Week and Elegance.

Refrain from using the phrase
“scandal of particularity”
unless you can use it as well as
Annie Dillard.

Wednesday, September 10, 2003

Wednesday September 10, 2003

Filed under: General — Tags: — m759 @ 4:04 PM


The title refers to my entry of last April 4,

The Eight,

and to the time of this entry.

From D. H. Lawrence and the Dialogical Principle:

“Plato’s Dialogues…are queer little novels….[I]t was the greatest pity in the world, when philosophy and fiction got split.  They used to be one, right from the days of myth.  Then they went and parted, like a nagging married couple, with Aristotle and Thomas Aquinas and that beastly Kant.  So the novel went sloppy, and philosophy went abstract-dry.  The two should come together again, in the novel.”

— pp. 154-5 in D. H. Lawrence, “The Future of the Novel,” in Study of Thomas Hardy and Other Essays. Ed.  Bruce Steele.  Cambridge: Cambridge University Press,1983. 149-55.



“The wild, brilliant, alert head of St. Mawr seemed to look at her out of another world… the large, brilliant eyes of that horse looked at her with demonish question…. ‘Meet him half way,’ Lewis [the groom] said.  But halfway across from our human world to that terrific equine twilight was not a small step.”    

— pp. 30, 35 in D. H. Lawrence, “St. Mawr.” 1925.  St. Mawr and Other Stories.  Ed. Brian Finney.  Cambridge: Cambridge University Press, 1983.

See also

Plato, Pegasus, and the Evening Star.

Katherine Neville’s novel The Eight, referred to in my note of April 4, is an excellent example of how not to combine philosophy with fiction.  Lest this be thought too harsh, let me say that the New Testament offers a similarly ludicrous mixture.

On the other hand, there do exist successful combinations of philosophy with fiction… For example, The Glass Bead Game, Zen and The Art of Motorcycle Maintenance, Under the Volcano, the novels of Charles Williams, and the C. S. Lewis classic That Hideous Strength.

This entry was prompted by the appearance of the god Pan in my entry on this date last year, by Hugh Grant’s comedic encounters with Pan in “Sirens,” by Lawrence’s remarks on Pan in “St. Mawr,” and by the classic film “Picnic at Hanging Rock.”

Wednesday September 10, 2003

Filed under: General — m759 @ 4:00 AM

Now for the grand finale…

Edward Teller Is Dead at 95;
Fierce Architect of H-Bomb

Two links…

Patrick’s Rune
             at Shane Ross’s Caltech site

Patrick’s Rune
             at S. H. Cullinane’s Harvard site

…and a quote from Ross’s home page:

The truth shall make you free.

— The Caltech motto and John 8:32

Wednesday September 10, 2003

Filed under: General — m759 @ 1:09 AM

Sept. 9, 2003,
NY Times Screenshot

the Hits
Just Keep
On Coming


  “Clean. Fast.

“Dr. Jose Barchilon, a psychoanalyst and educator who studied the unconscious roots of creativity and mental illness, died on

August 6

at his home in New Rochelle, N.Y. He was 90.

In addition to training and teaching in New York and Denver, Dr. Barchilon wrote extensively, including early studies of psychosomatic illness and psychoanalytic studies of novels by Jane Austen, Albert Camus, Mark Twain and others.

He also trained a generation of psychiatrists and psychoanalysts….”

The New York Times, Sept. 9, 2003

NYT Store

Photo: Sigmund Freud, 1922.

Photo: Sigmund Freud, 1922.
Framed, 16×20.
Price: $540. Learn More.

Tuesday, September 9, 2003

Tuesday September 9, 2003

Filed under: General — m759 @ 11:19 PM

“Words are Events”

Walter J. Ong, S. J.

Gisele Marie Louise Marguerite La Fleche,

better known as Gisele MacKenzie, star of “Your Hit Parade,” died on

Friday, September 5, 2003.

The American Heritage® Dictionary of the English Language, Fourth Edition, 2000:


NOUN: A slender spire, especially one on a church above the intersection of the nave and transepts

ETYMOLOGY: French, arrow, flèche, from Old French, arrow, of Germanic origin.


NOUN: The hub of a wheel

ETYMOLOGY: Middle English, from Old English nafu.

From my entry of Saturday, Sept. 6, 2003:

‘That person who is to be known,
he in whom these parts rest,
like spokes in the nave of a wheel,
you know him,
lest death should hurt you.’

Prasna Upanishad

La Fleche

Cover illustration for
The Spirit of Zen

The Spirit is Willing…

Tuesday September 9, 2003

Filed under: General — m759 @ 9:37 PM

Olympic Style

For Dr. Mary McClintock Dusenbury,
Radcliffe College Class of 1964,
who shares an August 22 birthday with
the late Leni Riefenstahl —

Three occurrences of the same
sangaku (temple tablet):

August 19, 2003,

August 22, 2003,

September 6, 2003.

Tuesday September 9, 2003

Filed under: General — m759 @ 6:23 PM

Reply to Lucifer

The New York State Lottery evening number for Saturday, September 6, 2003, was


See last year’s entries for Mary Shelley’s birthday,

The Number of the Beast and

A Chain of Links. 

These were written partly in response to the New York State Lottery midday number for Monday, August 26, 2002, which was also


In reply to that occurrence, I commented on the website

Lucifer Media Corporation.

In reply to last Saturday’s return of the beastly lottery number, I recommend the following links on software guru Bill Joy:

Sept. 9 – Sun Co-founder Joy Steps Down:

“Joy co-founded Sun, originally an acronym for Stanford University Network, with McNealy in 1982. Before that, Joy was the designer of the Berkeley version of the Unix operating system and helped pioneer the concept of open source.
   More recently, Joy found himself at the center of controversy after he wrote a Wired magazine article on the challenges posed to mankind by new technologies such as nanotechnology, robotics and genetic engineering.”


Joy’s April 2000 Wired article, titled

Why the future doesn’t need us:

Our most powerful 21st-century technologies – robotics, genetic engineering, and nanotech – are threatening to make humans an endangered species.

Joy says

“I can date the onset of my unease to the day I met Ray Kurzweil….”

I, too, can date, at least approximately, an encounter with the philosophy of

transhumanism (a Lucifer Media link)

that Kurzweil embraces…  It was sometime in the first half of January, 1989… I know this because 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.

For the temple tablet associated with Nicholi in that entry, see my entry of September 6, 2003 (the NY Lottery “666” date),

Pictures for Kurosawa.

To sum up this entry, a phrase of C. S. Lewis seems appropriate:

Surprised by Joy.

Tuesday September 9, 2003

Filed under: General — m759 @ 4:04 PM

Story Theory

The conflict between the Euclidean, or “diamond” theory of truth, and the Trudeau, or “story” theory of truth, continues.

On this, Hugh Grant’s birthday, let us recall last year’s log24 entry for this date. On Roger Ebert’s review of the Hugh Grant film “Sirens” about the artist Norman Lindsay:

Ebert gets Pan wrong in this film; he says, “the bearded Lindsay is a Pan of sorts.” No. The “Pan of sorts” is in fact the girl who romps joyfully with the local boys and who later, with great amusement, uses her divine x-ray vision to view Tara Fitzgerald naked in church.

This year’s offering for Grant’s birthday is an illustrated prayer by a great defender of the religious, or “story,” theory of truth, Madeleine L’Engle:

Tara Fitzgerald


At Tara, in this fateful hour,
I place all heaven with its power.
And the sun with its brightness,
And the snow with its whiteness,
And the fire with all the strength it hath,
And the lightning with its rapid wrath,
And the winds with their swiftness along their path,
And the sea with its deepness,
And the rocks with their steepness,
And the earth with its starkness;
All these I place
By God’s almighty help and grace
Between myself and the powers of darkness.

From A Swiftly Tilting Planet
by Madeleine L’Engle

For an uncensored view, see my Harvard weblog.

Monday, September 8, 2003

Monday September 8, 2003

Filed under: General — m759 @ 4:07 PM

Goodbye and Hello

Larry Rodgers
The Arizona Republic
Aug. 24, 2003 12:00 AM:

“If any musician can look death in the eye and smile, it’s California-based songwriter extraordinaire Warren Zevon.”

From April 7, 2003:

April is Math Awareness Month.
This year’s theme is “mathematics and art.”

From an entry yesterday on looking death in the eye and smiling:

Such serenity “is indestructible and only increases with age and nearness to death. It is the secret of beauty and the real substance of all art.”

Warren Zevon died yesterday.

From an entry earlier today on a circle of souls in the sun:

“they lovingly welcome two more into their company.”

Sun Tree
Terry Frost

Frost died on September 1.
The above picture by Frost is from

Modern British Artists.

Monday September 8, 2003

Filed under: General — m759 @ 1:25 PM

Pre- and Post-Cognition

Majority Report:


A Matter of Life and Death,

an entry from Sept. 13, 2002, linked to in last night’s ART WARS notes:

“In the sun, Dante and Beatrice find themselves surrounded by a circle of souls famous for their wisdom on earth. They appear as splendid lights and precious jewels who dance and sing as they lovingly welcome two more into their company.”

Minority Report:

Doonesbury, Monday morning, Sept. 8, 2003:

©2003 G.B. Trudeau

For more chanting,
click here.

Monday September 8, 2003

Filed under: General — m759 @ 4:24 AM

ART WARS Sept. 1, 2003:

Sir Terry Frost Dies

A noted English abstract painter died at 87 on Monday, September 1.  From a memorial essay on Sir Terry Frost, born in 1915, in The Daily Telegraph: 

“He was educated at Leamington Spa Central School where he edited the art magazine, but left at 15 to work….” His first jobs included, the Telegraph says, painting “the red, white and blue targets on to fighter planes.”

The “target” the Telegraph refers to
is known as the Royal Air Force Roundel.

It may indeed have functioned as a target, but it was originally intended only as a distinctive identifying mark.

Some of Frost’s later work may be viewed at the British Government Art Collection.  For some of Frost’s work more closely related to his early “target” theme, see the Badcock’s Gallery site.

An example:


For related religious
and cinematic material, see

Pilate, Truth, and Friday the Thirteenth,

a meditation for Good Friday of 2001,

A Matter of Life and Death,

a meditation for Friday the Thirteenth
of September, 2002,


The Unity of Mathematics,

from the day Frost died, which concludes
with links related to the religious symbol of


Monolithic Form

Sunday, September 7, 2003

Sunday September 7, 2003

Filed under: General — Tags: , , — m759 @ 11:11 PM

Horse Sense

Mathematicians are familiar with the emblem of Springer Verlag, the principal publisher of higher mathematics.

Ferdinand Springer, son of Julius Springer, founder of Springer Verlag, “was a passionate chess player and published a number of books on the subject. In 1881 this personal hobby and the name Springer led the company to adopt the knight in chess (in German, Springer) as its colophon.”

Hermann Hesse on a certain sort of serenity:

“I would like to say something more to you about cheerful serenity, the serenity of the stars and of the mind…. neither frivolity nor complacency; it is supreme insight and love, affirmation of all reality, alertness on the brink of all depths and abysses; it is a virtue of saints and of knights; it is indestructible and only increases with age and nearness to death. It is the secret of beauty and the real substance of all art.”

— From The Glass Bead Game

A saint and a knight, Jeanne d’Arc, was memorably portrayed by Milla Jovovich in The Messenger.

(Jovovich seems fated to play more-than-human characters in religious epics; see The Fifth Element.)

Another Springer, related to horses and to the accusation of witchcraft faced by Jeanne d’Arc, is Nancy Springer, the author of

The Hex Witch of Seldom.

Springer has written a number of books about horses, as well as other topics.

All of the above…. especially the parts having to do with mathematics and horses… was prompted by my redrawing today of a horse-shape within mathematics.  See my entry The Eight of April 4, 2003, and the horse-figure redrawn at right below.





Believers in the story theory of truth may wish to relate the gifts of Jeanne d’Arc and of the girl in The Hex Witch of Seldom to the legend of Pegasus.  See, for instance,

Plato, Pegasus, and the Evening Star.

For another connection between mathematics and horses, see Sangaku.

Saturday, September 6, 2003

Saturday September 6, 2003

Filed under: General — m759 @ 2:56 PM

Pictures for Kurosawa

Five years ago on this day, director Akira Kurosawa died.

The above pictures are offered as a remembrance of Kurosawa and also of Charlotte Selver, who died on August 22, 2003.

The picture at right is from an entry of August 22.  As one obituary of Selver says, “She was very sharp and very precise.”

The picture at left is the cover of Alan Watts’s book The Spirit of Zen (a religion that is also very sharp and very precise).

A New Seeing,
by Mary Alice Roche

The connection with Alan Watts was a fateful one. As Charlotte recalls it, “My aunt wrote me from San Francisco, ‘last night I heard a man lecture about what you do.’ And she sent me Alan Watts’s first little book, The Spirit of Zen. I had never heard of Zen, was amazed and fascinated, and decided to visit the author.” She did so in August of 1953, and that was the beginning of a long relationship with Zen Buddhism – and also the beginning of a long series of joint seminars with Alan Watts, first in New York, and later, on Watts’s ferryboat in Sausalito, California. Some of the titles of their seminars were “Moving Stillness,” “The Unity of Opposites,” “Our Instantaneous Life,” “The Mystery of Perception,” “The Tao in Rest and Motion.” (Watts always said that Charlotte Selver taught a Western equivalent of Taoism.)

The picture at right above is intended as a sangaku, or Japanese temple tablet.

The picture at left above on the cover of Watts’s book may be regarded as illustrating the following:

“As these flowing rivers that go towards the ocean, when they have reached the ocean, sink into it, their name and form are broken, and people speak of the ocean only, exactly thus these sixteen parts of the spectator that go towards the person (purusha), when they have reached the person, sink into him, their name and form are broken, and people speak of the person only, and he becomes without parts and immortal. On this there is this verse:

‘That person who is to be known, he in whom these parts rest, like spokes in the nave of a wheel, you know him, lest death should hurt you.’ “

Prasna Upanishad

Saturday September 6, 2003

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

The Tempest

IMAGE- 'Wind over Water,' i.e. 'Feng Shui'

A tropical storm over Florida (lower left)
and a hurricane at Bermuda (upper right)
at 3:15 p.m. EDT on Friday, Sept. 5, 2003:

Wind over Water

as described by William Shakespeare in 1611.

“Wind over Water” in the I Ching,
the Classic of Transformations,
signifies huan, “dissolving.”


Our revels now are ended. These our actors, as I foretold you, were all spirits and are melted into air, into thin air: and, like the baseless fabric of this vision, the cloud-capp’d towers, the gorgeous palaces, the solemn temples, the great globe itself, yea, all which it inherit, shall dissolve and, like this insubstantial pageant faded, leave not a rack behind. We are such stuff as dreams are made on, and our little life is rounded with a sleep. (Prospero, IV.i)

Friday, September 5, 2003

Friday September 5, 2003

Filed under: General — Tags: — m759 @ 11:59 PM

For Grace Paley:
An Enormous Change
at the Last Minute
(of September 5)

Hexagram 59 of the I Ching comprises the trigrams for wind and water (as in the environmental art of Feng Shui).

The name of the hexagram, Huan, means dispersion or dissolution.

The character Huan may be written as shown at right above.  The picture of the character Huan is taken from

The LiSe Heyboer I Ching.

Essentially the same picture is shown at

The Dan Stackhouse I Ching,

where it is explained as follows:

“At the top is a person or people , a flattened version of the more familiar . In the center an eye looks out from a cave or cavern. At the bottom a hand holds a stick or club as though ready to strike something. represents flowing water.”

The creature in the cave holding a club is reminiscent of my previous entry for today, on the “bone people,” or ancestors, of mankind.

For a transition, in the Kubrick 2001 style, to a more modern scene, see my next entry.

Friday September 5, 2003

Filed under: General — Tags: — m759 @ 8:23 PM

Da Capo

“The story bent and climbed and went into weird areas. For instance, at one time Simon Peter was a cave-dweller; at another, he only appeared in other characters’ dreams….”

Keri Hulme on The Bone People

“Words are events.”

The Walter J. Ong Project

In East Asian traditions, “Rocks are seen as events–rather slow-moving events–but as events….”

Graham Parkes, professor of philosophy at the University of Hawaii

Parkes is working on a translation of Nietzsche’s Thus Spake Zarathustra and is the author of “The Overflowing Soul: Images of Transformation in Nietzsche’s Zarathustra.”

He is also the translator, with David Pellauer, of Nietzsche and Music, by Georges Liébert (Chicago: University of Chicago Press, 2003).

Friday September 5, 2003

Filed under: General — Tags: — m759 @ 3:28 PM

Recommended Reading

       for Cullinane College:

“The Talented form their own society and that’s as it should be: birds of a feather.  No, not birds.  Winged horses!  Ha!  Yes, indeed. Pegasus… the poetic winged horse of flights of fancy.  A bloody good symbol for us.  You’d see a lot from the back of a winged horse…”

To Ride Pegasus, by Anne McCaffrey.

“Born in Cambridge, MA, on April Fool’s Day 1926 (‘I’ve tried very hard to live up to being an April-firster,’ she quips), McCaffrey graduated from Radcliffe College in 1947.”

 — School Library Journal

Born on March 9, 1947, in Christchurch, Keri Hulme won the Pegasus Prize for her Maori novel, The Bone People.

Thursday, September 4, 2003

Thursday September 4, 2003

Filed under: General — Tags: — m759 @ 4:23 PM


The late philosopher Donald Davidson (see previous entry) had a gift for titles. For example:

“The Folly of Trying to Define Truth”
(Journal of Philosophy June 1996, pp. 263-278)  and

“A Nice Derangement of Epitaphs”
(In R. Grandy and R. Warner (eds.), Philosophical Grounds of Rationality, Oxford: Oxford University Press, 1986).

For my thoughts on the former, see 

Pilate, Truth, and Friday the Thirteenth,

The Diamond Theory of Truth, and

Sept. 2, 2002 (Laurindo Almeida’s Birthday).

For my thoughts on the latter, see

Happy Birthday, Mary Shelley (2003),

For Mary Shelley’s Birthday (2002),

and, in honor of J. R. R. Tolkien, who died on the date September 2,

The Article on Epitaphs

at Wikipedia Encyclopedia, which contains the following:

J. R. R. Tolkien is buried next to his wife, and on their tombstone the names ‘Beren’ and ‘Luthien’ are engraved, a fact that sheds light on the love story of Beren and Luthien which is recorded in several versions in his works.”  

A nice derangement, indeed.

Thursday September 4, 2003

Filed under: General — m759 @ 2:42 AM


“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.

Wednesday, September 3, 2003

Wednesday September 3, 2003

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


From my entry of Sept. 1, 2003:

"…the principle of taking and giving, of learning and teaching, of listening and storytelling, in a word: of reciprocity….

… E. M. Forster famously advised his readers, 'Only connect.' 'Reciprocity' would be Michael Kruger's succinct philosophy, with all that the word implies."

— William Boyd, review of Himmelfarb, New York Times Book Review, October 30, 1994

Last year's entry on this date: 

Today's birthday:
James Joseph Sylvester

"Mathematics is the music of reason."
— J. J. Sylvester

Sylvester, a nineteenth-century mathematician, coined the phrase "synthematic totals" to describe some structures based on 6-element sets that R. T. Curtis has called "rather unwieldy objects." See Curtis's abstract, Symmetric Generation of Finite Groups, John Baez's essay, Some Thoughts on the Number 6, and my website, Diamond Theory.

The picture above is of the complete graph K6  Six points with an edge connecting every pair of points… Fifteen edges in all.

Diamond theory describes how the 15 two-element subsets of a six-element set (represented by edges in the picture above) may be arranged as 15 of the 16 parts of a 4×4 array, and how such an array relates to group-theoretic concepts, including Sylvester's synthematic totals as they relate to constructions of the Mathieu group M24.

If diamond theory illustrates any general philosophical principle, it is probably the interplay of opposites….  "Reciprocity" in the sense of Lao Tzu.  See

Reciprocity and Reversal in Lao Tzu.

For a sense of "reciprocity" more closely related to Michael Kruger's alleged philosophy, see the Confucian concept of Shu (Analects 15:23 or 24) described in

Shu: Reciprocity.

Kruger's novel is in part about a Jew: the quintessential Jewish symbol, the star of David, embedded in the K6 graph above, expresses the reciprocity of male and female, as my May 2003 archives illustrate.  The star of David also appears as part of a graphic design for cubes that illustrate the concepts of diamond theory:

Click on the design for details.

Those who prefer a Jewish approach to physics can find the star of David, in the form of K6, applied to the sixteen 4×4 Dirac matrices, in

A Graphical Representation
of the Dirac Algebra

The star of David also appears, if only as a heuristic arrangement, in a note that shows generating partitions of the affine group on 64 points arranged in two opposing triplets.

Having thus, as the New York Times advises, paid tribute to a Jewish symbol, we may note, in closing, a much more sophisticated and subtle concept of reciprocity due to Euler, Legendre, and Gauss.  See

The Jewel of Arithmetic and

The Golden Theorem.

Tuesday, September 2, 2003

Tuesday September 2, 2003

Filed under: General,Geometry — Tags: — m759 @ 1:11 PM

One Ring to Rule Them All

In memory of J. R. R. Tolkien, who died on this date, and in honor of Israel Gelfand, who was born on this date.

Leonard Gillman on his collaboration with Meyer Jerison and Melvin Henriksen in studying rings of continuous functions:

“The triple papers that Mel and I wrote deserve comment. Jerry had conjectured a characterization of beta X (the Stone-Cech compactification of X) and the three of us had proved that it was true. Then he dug up a 1939 paper by Gelfand and Kolmogoroff that Hewitt, in his big paper, had referred to but apparently not appreciated, and there we found Jerry’s characterization. The three of us sat around to decide what to do; we called it the ‘wake.’  Since the authors had not furnished a proof, we decided to publish ours. When the referee expressed himself strongly that a title should be informative, we came up with On a theorem of Gelfand and Kolmogoroff concerning maximal ideals in rings of continuous functions. (This proved to be my second-longest title, and a nuisance to refer to.) Kolmogoroff died many years ago, but Gelfand is still living, a vigorous octogenarian now at Rutgers. A year or so ago, I met him at a dinner party in Austin and mentioned the 1939 paper. He remembered it very well and proceeded to complain that the only contribution Kolmogoroff had made was to point out that a certain result was valid for the complex case as well. I was intrigued to see how the giants grouse about each other just as we do.”

Leonard Gillman: An Interview

This clears up a question I asked earlier in this journal….

Wednesday, May 14, 2003

Common Sense

On the mathematician Kolmogorov:

“It turns out that he DID prove one basic theorem that I take for granted, that a compact hausdorff space is determined by its ring of continuous functions (this ring being considered without any topology) — basic discoveries like this are the ones most likely to have their origins obscured, for they eventually come to be seen as mere common sense, and not even a theorem.”

Richard Cudney, Harvard ’03, writing at Xanga.com as rcudney on May 14, 2003

That this theorem is Kolmogorov’s is news to me.


The above references establish that Gelfand is usually cited as the source of the theorem Cudney discusses.  Gelfand was a student of Kolmogorov’s in the 1930’s, so who discovered what when may be a touchy question in this case.  A reference that seems relevant: I. M. Gelfand and A. Kolmogoroff, “On rings of continuous functions on topological spaces,” Doklady Akad. Nauk SSSR 22 (1939), 11-15.  This is cited by Gillman and Jerison in the classic Rings of Continuous Functions.

There ARE some references that indicate Kolmogorov may have done some work of his own in this area.  See here (“quite a few duality theorems… including those of Banaschewski, Morita, Gel’fand-Kolmogorov and Gel’fand-Naimark”) and here  (“the classical theorems of M. H. Stone, Gelfand & Kolmogorov”).

Any other references to Kolmogorov’s work in this area would be of interest.

Naturally, any discussion of this area should include a reference to the pioneering work of M. H. Stone.  I recommend the autobiographical article on Stone in McGraw-Hill Modern Men of Science, Volume II, 1968.

A response by Richard Cudney:

“In regard to your entry, it is largely correct.  The paper by Kolmogorov and Gelfand that you refer to is the one that I just read in his collected works.  So, I suppose my entry was unfair to Gelfand.  You’re right, the issue of credit is a bit touchy since Gelfand was his student.  In a somewhat recent essay, Arnol’d makes the claim that this whole thread of early work by Gelfand may have been properly due to Kolmogorov, however he has no concrete proof, having been but a child at the time, and makes this inference based only on his own later experience as Kolmogorov’s student.  At any rate, I had known about Gelfand’s representation theorem, but had not known that Kolmogorov had done any work of this sort, or that this theorem in particular was due to either of them. 

And to clarify-where I speak of the credit for this theorem being obscured, I speak of my own experience as an algebraic geometer and not a functional analyst.  In the textbooks on algebraic geometry, one sees no explanation of why we use Spec A to denote the scheme corresponding to a ring A.  That question was answered when I took functional analysis and learned about Gelfand’s theorem, but even there, Kolmogorov’s name did not come up.

This result is different from the Gelfand representation theorem that you mention-this result concerns algebras considered without any topology(or norm)-whereas his representation theorem is a result on Banach algebras.  In historical terms, this result precedes Gelfand’s theorem and is the foundation for it-he starts with a general commutative Banach algebra and reconstructs a space from it-thus establishing in what sense that the space to algebra correspondence is surjective, and hence by the aforementioned theorem, bi-unique.  That is to say, this whole vein of Gelfand’s work started in this joint paper.

Of course, to be even more fair, I should say that Stone was the very first to prove a theorem like this, a debt which Kolmogorov and Gelfand acknowledge.  Stone’s paper is the true starting point of these ideas, but this paper of Kolmogorov and Gelfand is the second landmark on the path that led to Grothendieck’s concept of a scheme(with Gelfand’s representation theorem probably as the third).

As an aside, this paper was not Kolmogorov’s first foray into topological algebra-earlier he conjectured the possibility of a classification of locally compact fields, a problem which was solved by Pontryagin.  The point of all this is that I had been making use of ideas due to Kolmogorov for many years without having had any inkling of it.”

Posted 5/14/2003 at 8:44 PM by rcudney

Monday, September 1, 2003

Monday September 1, 2003

Filed under: General — m759 @ 3:33 PM

The Unity of Mathematics,

or “Shema, Israel”

A conference to honor the 90th birthday (Sept. 2) of Israel Gelfand is currently underway in Cambridge, Massachusetts.

The following note from 2001 gives one view of the conference’s title topic, “The Unity of Mathematics.”

Reciprocity in 2001

by Steven H. Cullinane
(May 30, 2001)

From 2001: A Space Odyssey, by Arthur C. Clarke, New American Library, 1968:

The glimmering rectangular shape that had once seemed no more than a slab of crystal still floated before him….  It encapsulated yet unfathomed secrets of space and time, but some at least he now understood and was able to command.

How obvious — how necessary — was that mathematical ratio of its sides, the quadratic sequence 1: 4: 9!  And how naive to have imagined that the series ended at this point, in only three dimensions!

— Chapter 46, “Transformation”

From a review of Himmelfarb, by Michael Krüger, New York, George Braziller, 1994:

As a diffident, unsure young man, an inexperienced ethnologist, Richard was unable to travel through the Amazonian jungles unaided. His professor at Leipzig, a Nazi Party member (a bigot and a fool), suggested he recruit an experienced guide and companion, but warned him against collaborating with any Communists or Jews, since the objectivity of research would inevitably be tainted by such contact. Unfortunately, the only potential associate Richard can find in Sao Paulo is a man called Leo Himmelfarb, both a Communist (who fought in the Spanish Civil War) and a self-exiled Jew from Galicia, but someone who knows the forests intimately and can speak several of the native dialects.

“… Leo followed the principle of taking and giving, of learning and teaching, of listening and storytelling, in a word: of reciprocity, which I could not even imitate.”

… E. M. Forster famously advised his readers, “Only connect.” “Reciprocity” would be Michael Kruger’s succinct philosophy, with all that the word implies.

— William Boyd, New York Times Book Review, October 30, 1994

Reciprocity and Euler

Applying the above philosophy of reciprocity to the Arthur C. Clarke sequence

1, 4, 9, ….

we obtain the rather more interesting sequence
1/1, 1/4, 1/9, …..

This leads to the following problem (adapted from the St. Andrews biography of Euler):

Perhaps the result that brought Euler the most fame in his young days was his solution of what had become known as the Basel problem. This was to find a closed form for the sum of the infinite series

1/1 + 1/4 + 1/9 + 1/16 + 1/25 + …

— a problem which had defeated many of the top mathematicians including Jacob Bernoulli, Johann Bernoulli and Daniel Bernoulli. The problem had also been studied unsuccessfully by Leibniz, Stirling, de Moivre and others. Euler showed in 1735 that the series sums to (pi squared)/6. He generalized this series, now called zeta(2), to zeta functions of even numbers larger than two.

Related Reading

For four different proofs of Euler’s result, see the inexpensive paperback classic by Konrad Knopp, Theory and Application of Infinite Series (Dover Publications).

Related Websites

Evaluating Zeta(2), by Robin Chapman (PDF article) Fourteen proofs!

Zeta Functions for Undergraduates

The Riemann Zeta Function

Reciprocity Laws
Reciprocity Laws II

The Langlands Program

Recent Progress on the Langlands Conjectures

For more on
the theme of unity,

Monolithic Form

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