Friday, April 30, 2004 5:24 PM
On "Notes Toward a Supreme Fiction," by Wallace Stevens:
"This third section continues its play of opposing forces, introducing in the second canto a 'blue woman,' arguably a goddess- or muse-figure, who stands apart from images of fecundity and sexuality...."
-- Michael Bryson
From a Beethoven's Birthday entry:
within unalterable structure...
-- Roger Zelazny, Eye of Cat
See, too, Blue Matrices, and
a link for Beethoven's birthday:
Song for the
Unification of Europe
From today's news:
PRAGUE, Czech Republic (AP) - Ushering in a bold new era, hundreds of thousands of people packed streets and city squares across Europe on Friday for festivals and fireworks marking the European Union's historic enlargement to 25 countries from 15.
The expanded EU, which takes in a broad swath of the former Soviet bloc - a region separated for decades from the West by barbed wire and Cold War ideology - was widening to 450 million citizens at midnight (6 p.m.EDT) to create a collective superpower rivalling the United States.
"All these worlds are yours
Attempt no landing there."
Friday, April 30, 2004 6:24 AM
These are the folios of April,
All the library of spring
— Christopher Morley
The above quotation is dedicated to Quay A. McCune, M.D., whose copy of Bartlett's Familiar Quotations I purchased for two dollars at a Friends of the Library sale on July 2, 1999. Dr. McCune's copy of Bartlett was the twelfth edition, of November 1948, in a February 1952 reprint. It was edited by Christopher Morley.
Incidentally, Morley's father Frank, a professor of mathematics, is the discoverer of Morley's theorem, which says that the angle trisectors of any triangle, of whatever shape, determine an equilateral "Morley triangle" hidden within the original triangle.
Those familiar with Dorothy Sayers's explication of the Trinity, The Mind of the Maker, will recognize that this figure represents a triumph over the heresies she so skillfully describes in the chapter "Scalene Trinities." From another chapter:
"... this is the Idea that is put forward for our response. There is nothing mythological about Christian Trinitarian doctrine: it is analogical. It offers itself freely for meditation and discussion; but it is desirable that we should avoid the bewildered frame of mind of the apocryphal Japanese gentleman who complained:
'Honourable Father, very good;
Honourable Son, very good; but
I do not understand at all.'
'Honourable Bird,' however, has certain advantages as a pictorial symbol, since, besides reminding us of those realities which it does symbolise, it also reminds us that the whole picture is a symbol and no more."
In the Morley family trinity, if Frank is the Father and Christopher is the Son, we must conclude that the Holy Spirit is Christopher's mother — whose maiden name was, appropriately, Bird.
Thursday, April 29, 2004 5:12 PM
Tonight on PBS:
The Jesus Factor
From Good Friday:
For an explanation
From Holy Saturday:
"There is a suggestion of Christ descending into the abyss for the harrowing of Hell. But it is the Consul whom we think of here, rather than of Christ. The Consul is hurled into this abyss at the end of the novel."
-- Introduction to
On the former:
On the latter:
"...a 'dead shepherd who brought
tremendous chords from hell
And bade the sheep carouse' "
(p. 227, The Palm at the End of the Mind: Selected Poems and a Play. Ed. Holly Stevens. New York: Vintage Books, 1990)
— Wallace Stevens
as quoted by Michael Bryson
See also the entries of 5/12.
Wednesday, April 28, 2004 7:00 AM
"...the source of all great mathematics is the special case, the concrete example. It is frequent in mathematics that every instance of a concept of seemingly great generality is in essence the same as a small and concrete special case."
— Paul Halmos in
I Want To Be a Mathematician
Tuesday, April 27, 2004 5:31 PM
A Meditation for Poetry Month
Click on the picture below for details.
Notes on the compiling of Only the Dead:
Today's obituary of the author of Last Exit to Brooklyn suggested I look up Wolfe's short story, "Only the Dead Know Brooklyn." That story contained, near its end, a reference to drowning. Thoughts of drowning and of Brooklyn suggested (this being poetry month) Hart Crane's classic The Bridge. When I looked for material on Crane on the Web, I found, to my considerable surprise, that today is the anniversary of Crane's death.
As Wolfe says, apropos of Selby and Brooklyn,
"Red Hook! Jesus!"
As Crane says, apropos of Wolfe and the Brooklyn Bridge,
"Terrific threshold of the prophet's pledge,
Prayer of pariah, and the lover's cry...."
Unfortunately, the bridge is not for sale. However....
Tuesday, April 27, 2004 2:45 AM
Two interviews by Rebecca Murray —
Interview with Sofia Coppola, who won an Oscar for the screenplay of Lost in Translation:
Did you write that character with Bill Murray in mind?
I did. I was definitely picturing him and I definitely wrote it for him. I couldn't really think of anyone else.
Interview with Bill Murray, costar — with Scarlett Johansson — of Lost in Translation:
Your character whispers something to Scarlett’s character in a crucial scene. Can we know what you said?
You never will.
True. But we can imagine.
Hint 1: The publication date for
Kierkegaard's Works of Love
in a sixties paperback edition:
November 7, 1964
(See Directions Out)
Hint 2: The above photo
of Scarlett Johansson
just walking down the street
Hint 3: The top 10 songs
of November 7, 1964
Final hint: It's a song title.
Monday, April 26, 2004 5:24 PM
Outside the World
(A sequel to the previous entry)
Title: The Point Outside the World:
Kierkegaard and Wittgenstein
on Nonsense, Paradox, and Religion
Author: M. Jamie Ferreira
(Love's Grateful Striving)
(U. of Va., Charlottesville)
Appeared in: Wittgenstein Studies 2/97,
also in Religious Studies,
Vol. 30, March 1994,
See particularly the following passage:
The second rationale for the indirection of communication of the religious is also antitheoretical and a practical re-orientation (to acquire new skills, "to be able") rather than the reception of information.
This appreciative understanding of the speaker distinguishes the austere view from that which rejects religious language, but the austere view also reveals an understanding of religious utterances as grammatical remarks, meaningful as rules of linguistic usage. Wittgenstein points to "Theology as grammar" when he writes that "Grammar tells us what kind of object anything is" and that "The way you use the word 'God' does not show whom you mean -- but rather what you mean." 30
He illustrates: "God's essence is supposed to guarantee his existence -- but what this really means is that what is here at issue is not the existence of something." 31
Grammatical remarks are rules for use; they are neither empirical conclusions nor attempts to offer a perspective from "outside the world."
30 Philosophical Investigations, no. 373;
Culture and Value, p. 50.
31 Culture and Value, p. 82.
As noted in the previous entry, the number 373 does seem to point, whether Wittgenstein meant it to or not, to "a point outside the world."
Of course, the pointing is in the eye of the beholder... As, for instance, the time of this entry, 5:24, "points" to Kali, the Dark Lady, as played (yet again -- see previous entry) by Linda Hamilton.
Monday, April 26, 2004 4:00 PM
Part I: Indirections
"By indirections, find directions out."
-- Polonius in Hamlet: II, i
"Foremost among the structural similarities between Kierkegaard and Wittgenstein... is the use of indirect communication: as paradoxical as it may sound, both authors deliberately obfuscate their philosophy for the purposes of clarifying it.... let us examine more closely particular instances of indirect communication from both of the philosophers with the intention of finding similarity. 'By indirections, find directions out.' – Polonius in Hamlet: II, i"
On religious numerology (indirections)...
For the page number "373" as indicating "eternity," see
Zen and Language Games (5/2/03), which features Wittgenstein,
Language Game (1/14/04), also featuring Wittgenstein, and
Note 31, page 373, in Kierkegaard's Works of Love (1964 Harper Torchbook paperback, tr. by Howard and Edna Hong),
which says "Compare I John 4:17."
4:17 Herein is our love made perfect, that we may have boldness in the day of judgment: because as he is, so are we in this world.
The reference to Judgment Day leads us back to Linda Hamilton, who appears (some say, as noted in Zen and Language Games, as the Mother of God) in Terminator 2: Judgment Day, and to Part II of our meditation....
Part II: Directions Out
"This Way to the Egress"
-- Sign supposedly written by P. T. Barnum
A Google search on this phrase leads to the excellent website
The Summoning of Everyman.
A link from Part I of a log24 entry for Thursday, April 22:
to the following --
Frame not included in
Terminator 2: Judgment Day
Dr. Silberman: You broke my arm!
Sarah Connor: There are
in the human body,
This suggests, in light of the above-mentioned religious interpretation of Terminator 2, in light of the 2003 10/07 entry, and in light of the April 22 10:07 PM log24 invocation, the following words from the day after the death of Sgt. Pat Tillman:
Doonesbury April 23, 2004
A more traditional farewell, written by a soldier, for a soldier, may be found at The Summoning of Everyman site mentioned above:
A Few Noteworthy Words
From an American Soldier.
Monday, April 26, 2004 4:01 AM
From today's New York Times:
"Philip Hamburger, a writer for The New Yorker for more than six decades whose meticulously calibrated inflections — sober, droll and everything in between — helped create and nurture the magazine's reputation for urbanity, died on Friday [April 23, Shakespeare's birthday] at Columbia Presbyterian Center in Manhattan. He was 89....
Although he had a light touch, reflecting his own affability, there were times when he did not seek to amuse."
From Friday's rather unamusing log24 entry on the philosophy of mathematical proof, a link to a site listed in the Open Directory under
Society: Philosophy: Philosophy of Logic: Truth Definitions --
"See also The Story Theory of Truth."
From the weekend edition (April 24-25) of aldaily.com, a Jew's answer to Pilate's question:
With a philosophy degree you can ask such difficult questions as “What is truth?”, “Can we know the good?”, and “Do you want fries with that?”... more»
Whether Hamburger's last Friday was in any sense a "good" Friday, I do not know.
Related religious meditations....
From Holy Thursday, April 8, 2004:
The Triple Crown of Philosophy,
which links to a Hamburger song, and
from Good Friday, April 9, 2004,
an unorthodox portrait of a New Yorker as St. Peter — from Scorsese's "The Last Temptation of Christ."
The many connoisseurs of death who admire Mel Gibson's latest film can skip the final meditation, from the admirable Carol Iannone:
The Last Temptation Reconsidered.
They, as someone once said, have their reward.
Sunday, April 25, 2004 3:31 PM
Added a note to 4x4 Geometry:
The 4x4 square model lets us visualize the projective space PG(3,2) as well as the affine space AG(4,2). For tetrahedral and circular models of PG(3,2), see the work of Burkard Polster. The following is from an advertisement of a talk by Polster on PG(3,2).
The Smallest Perfect Universe
"After a short introduction to finite geometries, I'll take you on a... guided tour of the smallest perfect universe -- a complex universe of breathtaking abstract beauty, consisting of only 15 points, 35 lines and 15 planes -- a space whose overall design incorporates and improves many of the standard features of the three-dimensional Euclidean space we live in....
Among mathematicians our perfect universe is known as
-- Burkard Polster, May 2001
Friday, April 23, 2004 10:00 PM
Proof by Osmosis
by Kenneth Chang in the
New York Times of April 6, 2004
"A rigorous proof, a notion first set forth by Euclid around 300 B.C., is a progression of logic, starting from assumptions and arriving at a conclusion. If the chain is correct, the proof is true. If not, it is wrong.
But a proof is sometimes a fuzzy concept, subject to whim and personality. Almost no published proof contains every step; there are just too many....
.... reviewers rarely check every step, instead focusing mostly on the major points. In the end, they either believe the proof or not.
'It's like osmosis,' said Dr. Akihiro Kanamori, a mathematics professor at Boston University who writes about the history of mathematics. 'More and more people say it's a proof and you believe them.'...."
See also The Story Theory of Truth.
Thursday, April 22, 2004 10:07 PM
"It's become our form of modern classicism."
-- Nancy Spector in
the New York Times of April 23, 2004
Part I: Aesthetics
In honor of the current Guggenheim exhibition, "Singular Forms" — A quotation from the Guggenheim's own website:
"Minimalism refers to painting or sculpture
Discuss these seven points
in relation to the following:
by S. H. Cullinane
Logos and Logic
Mark Rothko's reference
to geometry as a "swamp"
and his talk of "the idea" in art
remarks on ideas in art
Notes on ideas and art
of the 4x4 square
The Grid of Time
Part II: Theology
Today's previous entry, "Skylark," concluded with an invocation of the Lord. Of course, the Lord one expects may not be the Lord that appears.
John Barth on minimalism:
"... the idea that, in art at least, less is more.
It is an idea surely as old, as enduringly attractive and as ubiquitous as its opposite. In the beginning was the Word: only later came the Bible, not to mention the three-decker Victorian novel. The oracle at Delphi did not say, 'Exhaustive analysis and comprehension of one's own psyche may be prerequisite to an understanding of one's behavior and of the world at large'; it said, 'Know thyself.' Such inherently minimalist genres as oracles (from the Delphic shrine of Apollo to the modern fortune cookie), proverbs, maxims, aphorisms, epigrams, pensees, mottoes, slogans and quips are popular in every human century and culture--especially in oral cultures and subcultures, where mnemonic staying power has high priority--and many specimens of them are self-reflexive or self-demonstrative: minimalism about minimalism. 'Brevity is the soul of wit.' "
Another form of the oracle at Delphi, in minimalist prose that might make Hemingway proud:
"He would think about Bert. Bert was an interesting man. Bert had said something about the way a gambler wants to lose. That did not make sense. Anyway, he did not want to think about it. It was dark now, but the air was still hot. He realized that he was sweating, forced himself to slow down the walking. Some children were playing a game with a ball, in the street, hitting it against the side of a building. He wanted to see Sarah.
When he came in, she was reading a book, a tumbler of dark whiskey beside her on the end table. She did not seem to see him and he sat down before he spoke, looking at her and, at first, hardly seeing her. The room was hot; she had opened the windows, but the air was still. The street noises from outside seemed almost to be in the room with them, as if the shifting of gears were being done in the closet, the children playing in the bathroom. The only light in the room was from the lamp over the couch where she was reading.
He looked at her face. She was very drunk. Her eyes were swollen, pink at the corners. 'What's the book,' he said, trying to make his voice conversational. But it sounded loud in the room, and hard.
She blinked up at him, smiled sleepily, and said nothing.
'What's the book?' His voice had an edge now.
'Oh,' she said. 'It's Kierkegaard. Soren Kierkegaard.' She pushed her legs out straight on the couch, stretching her feet. Her skirt fell back a few inches from her knees. He looked away.
'What's that?' he said.
'Well, I don't exactly know, myself." Her voice was soft and thick.
He turned his face away from her again, not knowing what he was angry with. 'What does that mean, you don't know, yourself?'
She blinked at him. 'It means, Eddie, that I don't exactly know what the book is about. Somebody told me to read it once, and that's what I'm doing. Reading it.'
He looked at her, tried to grin at her — the old, meaningless, automatic grin, the grin that made everbody like him — but he could not. 'That's great,' he said, and it came out with more irritation than he had intended.
She closed the book, tucked it beside her on the couch. She folded her arms around her, hugging herself, smiling at him. 'I guess this isn't your night, Eddie. Why don't we have a drink?'
'No.' He did not like that, did not want her being nice to him, forgiving. Nor did he want a drink.
Her smile, her drunk, amused smile, did not change. 'Then let's talk about something else,' she said. 'What about that case you have? What's in it?' Her voice was not prying, only friendly, 'Pencils?'
'That's it,' he said. 'Pencils.'
She raised her eyebrows slightly. Her voice seemed thick. 'What's in it, Eddie?'
'Figure it out yourself.' He tossed the case on the couch."
— Walter Tevis, The Hustler, 1959,
See, too, the invocation of Apollo in
A Mass for Lucero, as well as
GENERAL AUDIENCE OF JOHN PAUL II
Wednesday 15 January 2003:
"The invocation of the Lord is relentless...."
JOURNAL ENTRY OF S. H. CULLINANE
Wednesday 15 January 2003:
Karl Cullinane —
"I will fear no evil, for I am the
meanest son of a bitch in the valley."
Thursday, April 22, 2004 2:14 PM
Picture said to be of
a Japanese Skylark,
Hibari or Alauda japonica.
Photo: 05/2002, Nagano, Japan.
A false definition of "inscape":
Brad Leithauser, New York Review of Books, April 29, 2004:
"Not surprisingly, most Hopkins criticism is secular at heart, though without always acknowledging just how distorted—how weirdly misguided— Hopkins himself would find all interpretations of a spiritual life that were drawn purely from the outside. For him, a failure to see how divine promptings informed his shaping internal life—his 'inscape,' his own term for it—was to miss everything of his life that mattered."
"By 'inscape' he [Hopkins] means the unified complex of characteristics that give each thing its uniqueness and that differentiate it from other things."
A false invocation of the Lord:
Brad Leithauser, New York Review of Books, Sept. 26, 2002:
"I'd always thought 'Skylark' quite appealing, but it wasn't until I heard Helen Forrest singing it, in a 1942 recording with Harry James and his Orchestra, that it became for me something far more: one of the greatest popular songs anybody ever wrote. With her modest delivery, a voice coaxing and plaintive, Forrest is a Little Girl Lost who always finds herself coming down on exactly the right note—no easy thing with a song of such unexpected chromatic turns. On paper, the Johnny Mercer lyric looks unpromising—antiquated and clunky:
But in Helen Forrest's performance, 'Skylark' turns out to be a perfect blend of pokiness and urgency, folksiness and ethereality—and all so convincing that it isn't until the song is finished that you step back and say, 'Good Lord, she's singing to a bird!' "
For Hopkins at midnight in the garden of good and evil, a truer invocation:
Saint Hoagy's Day
Today is the feast day of St. Hoagy Carmichael, who was born on the feast day of Cecelia, patron saint of music. This midnight's site music is "Stardust," by Carmichael (lyrics by Mitchell Parish). See also "Dead Poets Society" — my entry of Friday, December 13, on the Carmichael song "Skylark" — and the entry "Rhyme Scheme" of later that same day.
Wednesday, April 21, 2004 2:09 PM
Today is the birthday of Teiji Takagi.
"Kronecker's youthful dream had to wait for Takagi's development of class field theory to be stated and proved properly."
-- The Honors Class:
Hilbert's Problems and Their Solvers,
by Ben Yandell
(A. K. Peters, Ltd., 2003 paperback,
Tuesday, April 20, 2004 3:00 PM
Yesterday's Cartesian theatre continues....
Robert Osserman, a professor emeritus of mathematics at Stanford University, is special-projects director at the Mathematical Sciences Research Institute, in Berkeley, Calif.
Osserman at aldaily.com today:
"The past decade has been an exciting one in the world of mathematics and a fabulous one (in the literal sense) for mathematicians, who saw themselves transformed from the frogs of fairy tales -- regarded with a who-would-want-to-kiss-that aversion, when they were noticed at all -- into fascinating royalty, portrayed on stage and screen....
Who bestowed the magic kiss on the mathematical frog?"
William Randolph Hearst III.
"Trained as a mathematician at Harvard, he now likes to hang out with Ken Ribet and the other gurus at the University of California, Berkeley's prestigious Mathematical Sciences Research Institute. Two years ago, he moderated a panel of math professors discussing Princeton professor Andrew Wiles's historic proof of Fermat's Last Theorem."
-- Wired magazine, June 1995
Hearst Gift Spurs Math Center Expansion and
Review of Rational Points on Elliptic Curves by Joseph H. Silverman and John T. Tate (pdf), Bull. Amer. Math. Soc. (N.S.) 30 (1994), no. 2, 248--252,
by William Randolph Hearst III
and Kenneth A. Ribet.
"And that's the secret of frog kissin', and you can do it too if you'll just listen.
Just slow down, turn around, bend down and kiss you a frog! Ribet! Ribet!"
Monday, April 19, 2004 7:59 PM
From aldaily.com today:
"If my mind is a tiny theatre I watch in my brain, then there is a tinier mind and theatre inside that mind to see it, and so on forever... more»"
This leads to the dream (or nightmare) of the Cartesian theatre, as pictured by Daniel Dennett.
From websurfing yesterday and today...
The tiny theatre of Ivor Grattan-Guinness:
"... mathematicians often treat history with contempt (unsullied by any practice or even knowledge of it, of course)."
-- The Rainbow of Mathematics
The contempt for history of the Harvard mathematics department (see previous entry) suggests a phrase....
A search on "Harvard sneer" yields, as the first page found, a memorial to an expert practitioner of the Harvard sneer... Robert Harris Chapman, Professor of English Literature, playwright, theatrical consultant, and founding Director of the Loeb Drama Center from 1960 to 1980.
Continuing the Grattan-Guinness rainbow theme in a tinier theatre, we may picture Chapman's reaction to the current Irish Repertory Theatre production of Finian's Rainbow. Let us hope it is not a Harvard sneer.
In a yet tinier theatre, we may envision a mathematical version of Finian's Rainbow, with Og the leprechaun played by Andrew P. Ogg. Ogg would, of course, perform a musical version of his remarks on the Jugendtraum:
"Follow the fellow who follows a dream."
in Finian's Rainbow
"Give her a song like.... 'Look to the Rainbow,' and her gleaming soprano effortlessly flies it into the stratosphere where such numbers belong. This is the voice of enchantment...."
-- Ben Brantley, today's NY Times
For related philosophical remarks on rainbows, infinite regress, and redheads, see
Loretta's Rainbow and
The Leonardo Code.
Sunday, April 18, 2004 2:00 AM
Dream of Youth Revisited
For some material related to the entry Dream of Youth of last Dec. 8 (the feast day of St. Hermann Weyl), see the recently updated A Mathematical Lie.
See, too, a "comedy of errors" from
7 rue René Descartes in Strasbourg (pdf)
on what Hilbert reportedly called "the most beautiful part of mathematics."
Friday, April 16, 2004 10:00 AM
Mistakes Were Made
By Al Kamen, Washington Post
Friday, April 16, 2004
"... Bush, in his news conference Tuesday.... found a way to make not one, not two, but three factual errors in a single 15-word sentence, which must be something of a world indoor record. Bush said it is still possible that inspectors will find weapons of mass destruction in Iraq.
'They could still be there. They could be hidden, like the 50 tons of mustard gas in a turkey farm,' he said, referring to Libya's WMD disclosures last month.
The White House, according to Reuters, said the accurate figure was 23.6 metric tons or 26 tons, not 50. The stuff was found at various locations, not at a turkey farm. And there was no mustard gas on the farm at all, but unfilled chemical munitions.
Other than that, the sentence was spot on."
Other mistakes ...
"It's not at all like CIA Director George J. Tenet to forget not one, but two, conversations with President Bush in the critical month [August] before Sept. 11, 2001. But there's one possible explanation for his distraction when he testified Wednesday morning to the Sept. 11 commission: He was thinking about his luncheon plans.
Tenet was spotted around 12:30 at the Hay-Adams, sitting at a window table for two with none other than Jack Valenti, outgoing head of the Motion Picture Association of America...."
Hey, that's why
they make erasers.