Friday, April 30, 2004

Friday April 30, 2004

Filed under: General,Geometry — m759 @ 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:

Moulin Bleu


Kaleidoscope turning…
Shifting pattern
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
(Blue 1)

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
except Europa.
Attempt no landing there.”

Friday April 30, 2004

Filed under: General — Tags: — m759 @ 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
 Honourable Bird
     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

Thursday April 29, 2004

Filed under: General — m759 @ 5:12 PM


Tonight on PBS:
The Jesus Factor

From Good Friday:

3 PM

For an explanation
of this icon, see

Art Wars
To Be.

From Eternity:

Red Hook! Jesus!

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
Under the Volcano


In memory of
René Descartes
(born March 31)
René Gruau
(died March 31)

On the former:

“The predominant use
of the letter

to represent
an unknown value
came about in
an interesting way.”

On the latter:

“The women he drew
often seemed
to come alive.”

“…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

Wednesday April 28, 2004

Filed under: General — m759 @ 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

Tuesday April 27, 2004

Filed under: General — m759 @ 5:31 PM

Last Exit:
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

Filed under: General — m759 @ 2:45 AM

The Whisper

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

Monday April 26, 2004

Filed under: General — m759 @ 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,
                    pp. 29-44.

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

Filed under: General — m759 @ 4:00 PM

Directions Out

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 number373” 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),  

  • Publisher: Perennial (Nov. 7, 1964)
  • ISBN: 0061301221

    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.

    Related thoughts….

    A link from Part I of a log24 entry for Thursday, April 22:

    Judgment Day
    (2003, 10/07)

    to the following —


    Frame not included in
    Terminator 2: Judgment Day

    Dr. Silberman: You broke my arm!

    Sarah Connor: There are
    two-hundred-fifteen bones
    in the human body,
    [expletive deleted].
    That’s one.

    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

    Filed under: General — m759 @ 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

    Sunday April 25, 2004

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

    Small World

    Added a note to 4×4 Geometry:

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

    The Smallest Perfect Universe

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

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

    — Burkard Polster, May 2001

    Friday, April 23, 2004

    Friday April 23, 2004

    Filed under: General — m759 @ 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

    Thursday April 22, 2004

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


    "It's become our form of modern classicism."

    — Nancy Spector in 
       the New York Times of April 23, 2004

    Part I: Aesthetics

    In honor of the current Guggenheim exhibition, "Singular Forms" — A quotation from the Guggenheim's own website

    "Minimalism refers to painting or sculpture

    1. made with an extreme economy of means
    2. and reduced to the essentials of geometric abstraction….
    3. Minimalist art is generally characterized by precise, hard-edged, unitary geometric forms….
    4. mathematically regular compositions, often based on a grid….
    5. the reduction to pure self-referential form, emptied of all external references….
    6. In Minimal art what is important is the phenomenological basis of the viewer’s experience, how he or she perceives the internal relationships among the parts of the work and of the parts to the whole….
    7. The repetition of forms in Minimalist sculpture serves to emphasize the subtle differences in the perception of those forms in space and time as the spectator’s viewpoint shifts in time and space."

    Discuss these seven points
    in relation to the following:

    by S. H. Cullinane

    Logos and Logic

    Mark Rothko's reference
    to geometry as a "swamp"
    and his talk of "the idea" in art

    Michael Kimmelman's
    remarks on ideas in art 

    Notes on ideas and art

    of the 4×4 square

    The Grid of Time

    Judgment Day
    (2003, 10/07)

    Part II: Theology

    Today's previous entry, "Skylark," concluded with an invocation of the Lord.   Of course, the Lord one expects may not be the Lord that appears.

     John Barth on minimalism:

    "… the idea that, in art at least, less is more.

    It is an idea surely as old, as enduringly attractive and as ubiquitous as its opposite. In the beginning was the Word: only later came the Bible, not to mention the three-decker Victorian novel. The oracle at Delphi did not say, 'Exhaustive analysis and comprehension of one's own psyche may be prerequisite to an understanding of one's behavior and of the world at large'; it said, 'Know thyself.' Such inherently minimalist genres as oracles (from the Delphic shrine of Apollo to the modern fortune cookie), proverbs, maxims, aphorisms, epigrams, pensees, mottoes, slogans and quips are popular in every human century and culture–especially in oral cultures and subcultures, where mnemonic staying power has high priority–and many specimens of them are self-reflexive or self-demonstrative: minimalism about minimalism. 'Brevity is the soul of wit.' "

    Another form of the oracle at Delphi, in minimalist prose that might make Hemingway proud:

    "He would think about Bert.  Bert was an interesting man.  Bert had said something about the way a gambler wants to lose.  That did not make sense.  Anyway, he did not want to think about it.  It was dark now, but the air was still hot.  He realized that he was sweating, forced himself to slow down the walking.  Some children were playing a game with a ball, in the street, hitting it against the side of a building.  He wanted to see Sarah.

    When he came in, she was reading a book, a tumbler of dark whiskey beside her on the end table.  She did not seem to see him and he sat down before he spoke, looking at her and, at first, hardly seeing her.  The room was hot; she had opened the windows, but the air was still.  The street noises from outside seemed almost to be in the room with them, as if the shifting of gears were being done in the closet, the children playing in the bathroom.  The only light in the room was from the lamp over the couch where she was reading.

    He looked at her face.  She was very drunk.  Her eyes were swollen, pink at the corners.  'What's the book,' he said, trying to make his voice conversational.  But it sounded loud in the room, and hard.

    She blinked up at him, smiled sleepily, and said nothing.

    'What's the book?'  His voice had an edge now.

    'Oh,' she said.  'It's Kierkegaard.  Soren Kierkegaard.' She pushed her legs out straight on the couch, stretching her feet.  Her skirt fell back a few inches from her knees.  He looked away.

    'What's that?' he said.

    'Well, I don't exactly know, myself."  Her voice was soft and thick.

    He turned his face away from her again, not knowing what he was angry with.  'What does that mean, you don't know, yourself?'

    She blinked at him.  'It means, Eddie, that I don't exactly know what the book is about.  Somebody told me to read it once, and that's what I'm doing.  Reading it.'

    He looked at her, tried to grin at her — the old, meaningless, automatic grin, the grin that made everbody like him — but he could not.  'That's great,' he said, and it came out with more irritation than he had intended.

    She closed the book, tucked it beside her on the couch.  She folded her arms around her, hugging herself, smiling at him.  'I guess this isn't your night, Eddie.  Why don't we have a drink?'

    'No.'  He did not like that, did not want her being nice to him, forgiving.  Nor did he want a drink.

    Her smile, her drunk, amused smile, did not change.  'Then let's talk about something else,' she said.  'What about that case you have?  What's in it?'  Her voice was not prying, only friendly, 'Pencils?'

    'That's it,' he said.  'Pencils.'

    She raised her eyebrows slightly.  Her voice seemed thick.  'What's in it, Eddie?'

    'Figure it out yourself.'  He tossed the case on the couch."

    — Walter Tevis, The Hustler, 1959,
        Chapter 11

    See, too, the invocation of Apollo in

    A Mass for Lucero, as well as 

    Wednesday 15 January 2003

    "The invocation of the Lord is relentless…."


    Wednesday 15 January 2003

    Karl Cullinane —
    "I will fear no evil, for I am the
    meanest son of a bitch in the valley."

    Thursday April 22, 2004

    Filed under: General — m759 @ 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.”

    A truer definition:

    “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:

    Have you seen a valley green with Spring
    Where my heart can go a-journeying,
    Over the shadows and the rain
    To a blossom-covered lane?

    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:

    Friday, December 27, 2002
    12:00 AM

    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

    Wednesday April 21, 2004

    Filed under: General — m759 @ 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,
    page 256)

    Kazuya Takahashi,
    Kumoi IV

    Tuesday, April 20, 2004

    Tuesday April 20, 2004

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

    Rhetorical Question

    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

    See also

    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.


    Chet Atkins summarizes:

    "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

    Monday April 19, 2004

    Filed under: General — m759 @ 7:59 PM

    Cartesian Theatre

    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."

    Melissa Errico
    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

    Sunday April 18, 2004

    Filed under: General — m759 @ 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

    Friday April 16, 2004

    Filed under: General — m759 @ 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.

    Thursday, April 15, 2004

    Thursday April 15, 2004

    Filed under: General — m759 @ 12:30 PM

    Today’s Kerry Misery Index

    70%: Karl Rove is smiling today.

    “The Sharon-Bush partnership creates a ticklish tactical problem for John Kerry. The Democrats (like the GOP) have traditionally regarded Jewish settlements in the West Bank as ‘obstacles to peace.’

    Now that Bush has ruled that some of them are kosher, Kerry is in an awkward position.

    If he follows President Bush’s new policy direction he will bump up hard against the Jimmy Carter-NPR wing of his own party, not to mention polite European society. If, on the other hand, he decides to stand pat he will, much to his dismay, find himself running for commander in chief as the favorite son of Arafat and Hamas.”

    — Zev Chafets, columnist for the New York Daily News, April 15, 2004

    Wednesday, April 14, 2004

    Wednesday April 14, 2004

    Filed under: General — m759 @ 3:14 AM

    President Queeg,

    Compare and contrast:

    The President of the United States
    and Captain Queeg.

    From last night’s press conference:

    “….you never admit a mistake. Is that a fair criticism…. ?”


    From The Caine Mutiny:

    “… Naturally, I can only cover these things from memory…  If I’ve left anything out, why, just ask me specific questions and I’ll be glad to answer them… one-by-one…”

    For further details, see

    The Bush Mutiny.

    Tuesday, April 13, 2004

    Tuesday April 13, 2004

    Filed under: General — m759 @ 1:26 PM

    Lies, Damned Lies, and Statistics

    The previous entry dealt with politicians’ lies and clergymen’s damned lies.  This entry deals with statistics (often grouped with the former two sins).

    Group: Kerry’s Misery Index
    Selective, Makes Bush Look Bad

    Tuesday, April 13, 2004 11:40 AM ET

    WASHINGTON -(Dow Jones)- U.S. Sen. John Kerry, D-Mass., claims middle-class Americans are miserable under the economic stewardship of President George W. Bush. A new report released Tuesday says Kerry’s campaign selectively designed a “misery index” to make Bush look bad.

    Sunday, April 11, 2004

    Sunday April 11, 2004

    Filed under: General — m759 @ 11:59 PM

    Easter Politics

    At Fort Hood, Texas, a sermon for the President of the United States:

    ” ‘Christianity is based on one historic event– it happened Easter morning.’ Members of the congregation responded with cries of ‘Amen!’.”

    Scott Lindlaw, The Associated Press

    This, of course, is a damned lie.  Christianity is, in fact, based on damned lies, not on Easter or any other alleged historic events.

    Meanwhile, in Boston, the President’s political rival John Kerry received communion at a Catholic Easter service, implying his endorsement of the Catholic dogma of transubstantiation — one of the blackest of Christianity’s many damned lies.

    So voters have a choice this year between a damned Protestant liar and a damned Catholic liar… just as in 1960.  Plus ça change, plus c’est la même chose.

    For my own Easter sermon, see the previous entry.

    Sunday April 11, 2004

    Filed under: General,Geometry — m759 @ 3:28 PM

    Good Friday and
    Descartes’s Easter Egg

    “The use of z, y, x . . . to represent unknowns is due to René Descartes, in his La géometrie (1637)…. In a paper on Cartesian ovals, prepared before 1629, x alone occurs as unknown…. This is the earliest place in which Descartes used one of the last letters of the alphabet to represent an unknown.”

    — Florian Cajori, A History of Mathematical Notations. 2 volumes. Lasalle, Illinois: The Open Court Publishing Co., 1928-1929. (Vol. 1, page 381)

    This is from


    Descartes’s Easter Egg is found at

    EggMath: The Shape of an Egg —
    Cartesian Ovals

    An Easter Meditation
    on Humpty Dumpty

    The following is excerpted from a web page headed “Catholic Way.”  It is one of a series of vicious and stupid Roman Catholic attacks on Descartes.  Such attacks have been encouraged by the present Pope, who today said “may the culture of life and love render vain the logic of death.”

    The culture of life and love is that of the geometry (if not the philosophy) of Descartes.  The logic of death is that of Karol Wojtyla, as was made very clear in the past century by the National Socialist Party, which had its roots in Roman Catholicism.

    Humpty Dumpty sat on a wall.
    Humpty Dumpty had a great fall

    “In the century just completed, the human race found itself in a position not unlike the scrambled mess at the base of an imaginary English wall….

    … we are heirs to a humanity that is broken, fractured, confused, unsure of what to make of itself….

     … ‘postmodernism’ is merely the articulation of the fractured, dissipated state of the human being…. 

    Without relating a history of modern philosophy, our unfortunate human shell has suffered a continual fragmentation for a period of roughly 500 years. (You philosophers out there will recognize immediately that I am referring to the legacy of René Descartes.) And this fragmentation has been a one-way street: one assault after another on the integrity and dignity of the human person until you have, well, the 20th Century.

    But now it’s the 21st Century.

    The beauty … the marvel … the miracle of our time is the possibility that gravity will reverse itself: Humpty Dumpty may be able, once again, to assume his perch.”

    —  Ted Papa,
    Raising Humpty Dumpty


    The upper part
    of the above icon
    is from EggMath.
    For the lower part,
    see Good Friday.

    Saturday, April 10, 2004

    Saturday April 10, 2004

    Filed under: General — m759 @ 3:19 PM


    In memory of
    René Descartes
    (born March 31)
    René Gruau
    (died March 31)

    On the former:

    “The predominant use of the letter x
    to represent an unknown value
    came about in an interesting way.”

    On the latter:

    “The women he drew
    often seemed to come alive.”

    Saturday April 10, 2004

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


    “The Ferris wheel came into view again, just the top, silently burning high on the hill, almost directly in front of him, then the trees rose up over it.  The road, which was terrible and full of potholes, went steeply downhill here; he was approaching the little bridge over the barranca, the deep ravine.  Halfway across the bridge he stopped; he lit a new cigarette from the one he’d been smoking, and leaned over the parapet, looking down.  It was too dark to see the bottom, but: here was finality indeed, and cleavage!  Quauhnahuac was like the times in this respect, wherever you turned the abyss was waiting for you round the corner. Dormitory for vultures and city of Moloch! When Christ was being crucified, so ran the sea-borne, hieratic legend, the earth had opened all through this country …”

    — Malcolm Lowry, Under the Volcano, 1947. (Harper & Row reissue, 1984, p. 15)

    Comment by Stephen Spender:

    “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 Under the Volcano

     Edward Gibbon, Decline and Fall of the Roman Empire, Chapter XXI

    Gibbon, discussing the theology of the Trinity, defines perichoresis as

    “… the internal connection and spiritual penetration which indissolubly unites the divine persons59 ….

    59 … The perichoresis  or ‘circumincessio,’ is perhaps the deepest and darkest corner of the whole theological abyss.”

     “Whoever fights monsters should see to it that in the process he does not become a monster.  And when you look long into an abyss, the abyss also looks into you.”

    — Friedrich Nietzsche, Beyond Good and Evil, section 146, translated by Walter Kaufmann

    William Golding:

     “Simon’s head was tilted slightly up.  His eyes could not break away and the Lord of the Flies hung in space before him. 

    ‘What are you doing out here all alone?  Aren’t you afraid of me?’

    Simon shook.

    ‘There isn’t anyone to help you.  Only me.  And I’m the Beast.’

    Simon’s mouth labored, brought forth audible words.

    ‘Pig’s head on a stick.’

    ‘Fancy thinking the Beast was something you could hunt and kill!’ said the head.  For a moment or two the forest and all the other dimly appreciated places echoed with the parody of laughter.  ‘You knew, didn’t you?  I’m part of you?  Close, close, close!’ “

    “Thought of the day:
    You can catch more flies with honey than vinegar… if you’re into catchin’ flies.”

    Alice Woodrome, Good Friday, 2004

    Anne Francis,
    also known as
    Honey West:

    “Here was finality indeed,
    and cleavage!”

    Under the Volcano

    From the official
         Anne Francis Web Site:   

       Come into my parlor….

    For some background,
    see the use of the word
    “spider” in Under the Volcano:


    by Patrick A. McCarthy.

    See, too, Why Me?

    Friday, April 9, 2004

    Friday April 9, 2004

    Filed under: General — m759 @ 5:36 PM

    Lost in Translation?

    In memory of

    Murray L. Bob:

    A lecture,

    A picture,

    A song.

    Friday April 9, 2004

    Filed under: General — m759 @ 4:35 PM

    Meanwhile, back at the ranch…

    Bush Seeks to Shore Up
    Support for Iraq

    Fri Apr 9, 2004 03:49 PM ET

    By Jeremy Pelofsky

    CRAWFORD, Texas (Reuters) – President Bush on Friday won renewed pledges of support for U.S. efforts in Iraq from allies Italy, Poland and El Salvador, the White House said, as casualties and kidnappings mounted.

    Viva El Salvador!

    — Jim Carrey at
     the 1996 Academy Awards

    Friday April 9, 2004

    Filed under: General — m759 @ 3:00 PM

    3 PM

    For an explanation
    of this icon, see
    Art Wars
     To Be.

    Friday April 9, 2004

    Filed under: General — m759 @ 2:45 PM


    Kylie sings

    In memory of Victor Argo,
    who died Tuesday, April 6, 2004.
    Today's New York Times
    says Mr. Argo was cast
    "somewhat against type"
    by Martin Scorsese as

    The Apostle Peter in
    "The Last Temptation of Christ."

    Friday April 9, 2004

    Filed under: General — m759 @ 2:29 PM

    Odd Massing

    “An odd massing of consciousness takes place.”

    — David Kalstone,
       On “Lost in Translation”

    Friday April 9, 2004

    Filed under: General — m759 @ 1:44 PM

    We Call This Friday Good

    — T. S. Eliot

    Welcome to our imaginative and inspiring toy catalog!
    Today is Friday 9-April 2004.
    On this day in 1914
    1st full color film shown
    “The World, The Flesh & the Devil”
    What you will discover in this site is what we have been able to find in our everlasting search for the most original, innovative, amusing and mind bending toys from around the world.

    Have Fun.  

    Friday April 9, 2004

    Filed under: General — m759 @ 1:00 AM

    Triple Crown, Part II

    (See previous entry.)

    The winner is Mike Sullivan, far and away.

    An essay, by Sullivan’s son,
    from Harper’s magazine, Oct. 2002 —

    Horseman, Pass By:
    Glory, Grief, and the Race for
    the Triple Crown

    by John Jeremiah Sullivan

    Far back, far back in our dark soul
    the horse prances.

    — D. H. Lawrence  

    “As opposed to the typical sportswriter, who has a passion for the subject and can put together a sentence, my father’s ambition had been to Write (poetry, no less), and sports were what he knew, so he sort of stumbled onto making his living that way….

    Two years ago, in May, I sat with him in his hospital room at Riverside Methodist, in Columbus….

    I asked him to tell me what he remembered from all those years of writing about sports, for he had seen some things in his time…. This is what he told me:

    I was at Secretariat’s Derby, in ’73, the year before you were born — I don’t guess you were even conceived yet. That was … just beauty, you know?  He started in last place, which he tended to do. I was covering the second-place horse, which wound up being Sham. It looked like Sham’s race going into the last turn, I think. The thing you have to understand is that Sham was fast, a beautiful horse. He would have had the Triple Crown in another year. And it just didn’t seem like there could be anything faster than that. Everybody was watching him. It was over, more or less. And all of a sudden there was this … like, just a disruption in the corner of your eye, in your peripheral vision. And then before you could make out what it was, here Secretariat came. And then Secretariat had passed him. No one had ever seen anything run like that–a lot of the old guys said the same thing. It was like he was some other animal out there …

    I wrote that down when I got back to my father’s apartment, where my younger sister and I were staying the night. He lived two more months, but that was the last time I saw him alive.”

    Thanks to the New York Times for today’s review of John Jeremiah Sullivan’s new book, which includes the above.

    See, too,

    Words Are Events.

    Thursday, April 8, 2004

    Thursday April 8, 2004

    Filed under: General — m759 @ 12:00 AM

    Triple Crown

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

    Michael Kimmelman, April 2, 2004 


    From Hans Reichenbach‘s

    The Rise of Scientific Philosophy:

    Ch. 18 – The Old and the New Philosophy

    “The speculative philosophers allotted to art a dignified position by putting art on a par with science and morality: truth, beauty and the good were for them the triple crown of human searching and longing.”

    Ch. 15 – Interlude: Hamlet’s Soliloquy

    “I have good evidence.  The ghost was very conclusive in his arguments.  But he is only a ghost.  Does he exist?  I could not very well ask him.  Maybe I dreamed him.  But there is other evidence….

    It is really a good idea: that show I shall put on.  It will be a crucial experiment.  If they murdered him they will be unable to hide their emotions.  That is good psychology.  If the test is positive I shall know the whole story for certain.  See what I mean?  There are more things in heaven and earth than are dreamt of in your philosophy, my dear logician.
        I shall know it for certain?  I see your ironical smile.  There is no certainty….
       There I am, the eternal Hamlet.  What does it help me to ask the logician….?  His advice confirms my doubt rather than giving me the courage I need for my action.  One has to have more courage than Hamlet to be always guided by logic.”


    On this Holy Thursday, the day of Christ’s Last Supper, let us reflect on Quine’s very pertinent question in Quiddities (under “Communication”):

    “What transubstantiation?”

    “It is easiest to tell what transubstantiation is by saying this: little children should be taught about it as early as possible. Not of course using the word…because it is not a little child’s word. But the thing can be taught… by whispering…”Look! Look what the priest is doing…He’s saying Jesus’ words that change the bread into Jesus’ body. Now he’s lifting it up. Look!”

    From “On Transubstantiation” by Gertrude Elizabeth Margaret Anscombe, Collected Philosophical Papers, V.III: Ethics, Religion, and Politics, 1981, Univ. of Minnesota Press, as quoted in the weblog of William Luse, Sept, 28, 2003

    A perhaps more credible instance of transubstantiation may be found in this account of Anscombe on the Feast of Corpus Christi:

    “In her first year at Oxford, she converted to Catholicism. In 1938, after mass at Blackfriars on the Feast of Corpus Christi, she met Peter Geach, a young man three years her senior who was also a recent convert to Catholicism. Like her, Geach was destined to achieve eminence in philosophy, but philosophy played no role in bringing about the romance that blossomed. Smitten by Miss Anscombe’s beauty and voice, Geach immediately inquired of mutual friends whether she was ‘reliably Catholic.’ Upon learning that she was, he pursued her and, swiftly, their hearts were entangled.”

    — John M. Dolan, Living the Truth

    Christ plays in ten thousand places,
    Lovely in limbs, and
        lovely in eyes not his
    To the Father through
        the features of men’s faces.

    — Gerard Manley Hopkins

    Concluding reflections for Holy Thursday:

    Truth, Beauty, and The Good

    Art is magic delivered from
    the lie of being truth.
     — Theodor Adorno, Minima moralia,
    London, New Left Books, 1974, p. 222
    (First published in German in 1951.)

    The director, Carol Reed, makes…
     impeccable use of the beauty of black….
    V. B. Daniel on The Third Man 

    I see your ironical smile.
    Hans Reichenbach (see above)

    Adorno, The Third Man, and Reichenbach
    are illustrated below (l. to r.) above the names of cities with which they are associated. 


    In keeping with our transubstantiation theme, these three cities may be regarded as illustrating the remarks of Jimmy Buffett

    on culinary theology.

    Wednesday, April 7, 2004

    Wednesday April 7, 2004

    Filed under: General — m759 @ 2:00 PM

    As a Little Child

    Today’s birthdays:

    Francis Ford Coppola and
    Russell Crowe.

    From MindfulGroup.com:

    Welcome to our imaginative and inspiring toy catalog!

    Today is Wednesday 7-April 2004. On this day in 30 Jesus crucified by Roman troops in Jerusalem (scholars’ estimate)

    What you will discover in this site is what we have been able to find in our everlasting search for the most original, innovative, amusing and mind bending toys from around the world.

    Have Fun.    

    Coliseum Tell me more
    Coliseum The Coliseum Builder Block System can be used to recreate the Roman Coliseum. Reenact ancient Gladiator matches and bring Ancient Rome into your home.

    Wednesday April 7, 2004

    Filed under: General — m759 @ 3:30 AM

    Mother of Beauty

    In memory of architect Pierre Koenig

    Mother of Beauty: A Note on Modernism.

    “… Case Study House #22 … was high drama — one in which the entire city becomes part of the architect’s composition. Approached along a winding street set high in the Hollywood Hills, the house first appears as a blank concrete screen. From here, the visitor steps out onto a concrete deck that overlooks a swimming pool. Just beyond it, the house’s living room — enclosed in a glass-and steel-frame — cantilevers out from the edge of the hill toward the horizon.

    The house was immortalized in a now famous image taken by the architectural photographer Julius Shulman. In it, two women, clad in immaculate white cocktail dresses, are perched on the edge of their seats in the glass-enclosed living room, their pose suggesting a kind of sanitized suburban bliss. A night view of the city spreads out beneath them, an endless grid of twinkling lights that perfectly captures the infinite hopes of the postwar American dream….

        “My blue dream…”  
    — F. Scott Fitzgerald

    Perhaps no house, in fact, better sums up the mix of outward confidence and psychic unease that defined Cold War America….”

    Los Angeles Times, Nicolai Ouroussoff

    Tuesday, April 6, 2004

    Tuesday April 6, 2004

    Filed under: General — Tags: , — m759 @ 10:00 PM

    Ideas and Art, Part III

    The first idea was not our own.  Adam
    In Eden was the father of Descartes…

    — Wallace Stevens, from
    Notes Toward a Supreme Fiction

    “Quaedam ex his tanquam rerum imagines sunt, quibus solis proprie convenit ideae nomen: ut cùm hominem, vel Chimaeram, vel Coelum, vel Angelum, vel Deum cogito.”

    Descartes, Meditationes III, 5

    “Of my thoughts some are, as it were, images of things, and to these alone properly belongs the name idea; as when I think [represent to my mind] a man, a chimera, the sky, an angel or God.”

    Descartes, Meditations III, 5

    Begin, ephebe, by perceiving the idea
    Of this invention, this invented world,
    The inconceivable idea of the sun.

    You must become an ignorant man again
    And see the sun again with an ignorant eye
    And see it clearly in the idea of it.

    — Wallace Stevens, from
    Notes Toward a Supreme Fiction

    “… Quinimo in multis saepe magnum discrimen videor deprehendisse: ut, exempli causâ, duas diversas solis ideas apud me invenio, unam tanquam a sensibus haustam, & quae maxime inter illas quas adventitias existimo est recensenda, per quam mihi valde parvus apparet, aliam verò ex rationibus Astronomiae desumptam, hoc est ex notionibus quibusdam mihi innatis elicitam, vel quocumque alio modo a me factam, per quam aliquoties major quàm terra exhibetur; utraque profecto similis eidem soli extra me existenti esse non potest, & ratio persuadet illam ei maxime esse dissimilem, quae quàm proxime ab ipso videtur emanasse.”

    Descartes, Meditationes III, 11

    “… I have observed, in a number of instances, that there was a great difference between the object and its idea. Thus, for example, I find in my mind two wholly diverse ideas of the sun; the one, by which it appears to me extremely small draws its origin from the senses, and should be placed in the class of adventitious ideas; the other, by which it seems to be many times larger than the whole earth, is taken up on astronomical grounds, that is, elicited from certain notions born with me, or is framed by myself in some other manner. These two ideas cannot certainly both resemble the same sun; and reason teaches me that the one which seems to have immediately emanated from it is the most unlike.”

    Descartes, Meditations III, 11

    “Et quamvis forte una idea ex aliâ nasci possit, non tamen hîc datur progressus in infinitum, sed tandem ad aliquam primam debet deveniri, cujus causa sit in star archetypi, in quo omnis realitas formaliter contineatur, quae est in ideâ tantùm objective.”

    Descartes, Meditationes III, 15

    “And although an idea may give rise to another idea, this regress cannot, nevertheless, be infinite; we must in the end reach a first idea, the cause of which is, as it were, the archetype in which all the reality [or perfection] that is found objectively [or by representation] in these ideas is contained formally [and in act].”

    Descartes, Meditations III, 15

    Michael Bryson in an essay on Stevens’s “Notes Toward a Supreme Fiction,”

    The Quest for the Fiction of the Absolute:

    “Canto nine considers the movement of the poem between the particular and the general, the immanent and the transcendent: “The poem goes from the poet’s gibberish to / The gibberish of the vulgate and back again. / Does it move to and fro or is it of both / At once?” The poet, the creator-figure, the shadowy god-figure, is elided, evading us, “as in a senseless element.”  The poet seeks to find the transcendent in the immanent, the general in the particular, trying “by a peculiar speech to speak / The peculiar potency of the general.” In playing on the senses of “peculiar” as particular and strange or uncanny, these lines play on the mystical relation of one and many, of concrete and abstract.”

    Brian Cronin in Foundations of Philosophy:

    “The insight is constituted precisely by ‘seeing’ the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight.”

    — From Ch. 2, Identifying Direct Insights

    Michael Bryson in an essay on Stevens’s “Notes Toward a Supreme Fiction“:

    “The fourth canto returns to the theme of opposites. ‘Two things of opposite natures seem to depend / On one another . . . . / This is the origin of change.’  Change resulting from a meeting of opposities is at the root of Taoism: ‘Tao produced the One. / The One produced the two. / The two produced the three. / And the three produced the ten thousand things’ (Tao Te Ching 42) ….”

    From an entry of March 7, 2004

    From the web page

    Introduction to the I Ching–
    By Richard Wilhelm

    “He who has perceived the meaning of change fixes his attention no longer on transitory individual things but on the immutable, eternal law at work in all change. This law is the tao of Lao-tse, the course of things, the principle of the one in the many. That it may become manifest, a decision, a postulate, is necessary. This fundamental postulate is the ‘great primal beginning’ of all that exists, t’ai chi — in its original meaning, the ‘ridgepole.’ Later Chinese philosophers devoted much thought to this idea of a primal beginning. A still earlier beginning, wu chi, was represented by the symbol of a circle. Under this conception, t’ai chi was represented by the circle divided into the light and the dark, yang and yin,


    This symbol has also played a significant part in India and Europe. However, speculations of a gnostic-dualistic character are foreign to the original thought of the I Ching; what it posits is simply the ridgepole, the line. With this line, which in itself represents oneness, duality comes into the world, for the line at the same time posits an above and a below, a right and left, front and back-in a word, the world of the opposites.”

    The t’ai chi symbol is also illustrated on the web page Cognitive Iconology, which says that

    “W.J.T. Mitchell calls ‘iconology’
    a study of the ‘logos’
    (the words, ideas, discourse, or ‘science’)
    of ‘icons’ (images, pictures, or likenesses).
    It is thus a ‘rhetoric of images’
    (Iconology: Image, Text, Ideology, p. 1).”

    A variation on the t’ai chi symbol appears in a log24.net entry for March 5:

    The Line,
    by S. H. Cullinane

    See too my web page Logos and Logic, which has the following:

    “The beautiful in mathematics resides in contradiction. Incommensurability, logoi alogoi, was the first splendor in mathematics.”

    — Simone Weil, Oeuvres Choisies, ed. Quarto, Gallimard, 1999, p. 100

     Logos Alogos,
    by S. H. Cullinane 

    In the conclusion of Section 3, Canto X, of “Notes,” Stevens says

    “They will get it straight one day
    at the Sorbonne.
    We shall return at twilight
    from the lecture
    Pleased that
    the irrational is rational….”

    This is the logoi alogoi of Simone Weil.

    In “Notes toward a Supreme Fiction,”
    Wallace Stevens lists three criteria
    for a work of the imagination:

    It Must Be Abstract

    The Line,
    by S.H. Cullinane 

    It Must Change

     The 24,
    by S. H. Cullinane

    It Must Give Pleasure

    by S. H. Cullinane

    Related material:

    Logos and Logic.


    Tuesday April 6, 2004

    Filed under: General — m759 @ 2:45 AM

    Ideas and Art, Part II

    "We do not, of course, see  ideas."

    — Roger Kimball, Minimalist Fantasies, 2003

    "Idea (Lat. idea , forma , species ; Gk. idea , eidos , from idein , to see; Fr. idée ; Ger. Bild ; Begriff )

    Probably to no other philosophical term have there been attached so many different shades of meaning as to the word idea. Yet what this word signifies is of much importance. Its sense in the minds of some philosophers is the key to their entire system. But from Descartes onwards usage has become confused and inconstant. Locke, in particular, ruined the term altogether in English philosophical literature…."

    The Catholic Encylopedia, 1910  

    James Hillman, A Blue Fire , p. 53:

    "For us ideas are ways of regarding things (modi res considerandi ), perspectives.  Ideas give us eyes, let us see …. Ideas are ways of seeing and knowing….

    Our word idea  comes from the Greek eidos , which meant originally in early Greek thought, and as Plato used it, both that which one sees — an appearance or shape in a concrete sense — and that by means of which one sees.  We see them, and by means of them.  Ideas are both the shape of events, their constellation in this or that archetypal pattern, and the modes that make possible our ability to see through events into their pattern.  By means of an idea we can see the idea cloaked in the passing parade.  The implicit connection between having ideas to see with  and seeing ideas themselves suggests that the more ideas we have, the more we see, and the deeper the ideas we have, the deeper we see.  It also suggests that ideas engender other ideas, breeding new perspectives for viewing ourselves and world.

    Moreover, without them we cannot 'see' even what we sense with the eyes in our heads, for our perceptions are shaped according to particular ideas …. And our ideas change as changes take place in the soul, for as Plato said, soul and idea refer to each other, in that an idea is the 'eye of the soul,' opening us through its insight and vision."

    Hillman does not say where in Plato this extraordinary saying, that an idea is the eye of the soul, occurs.  He is probably wrong.

    Both Kimball and Hillman seem confused.

    A more sensible approach to these matters is available in Brian Cronin's Foundations of Philosophy:

    "3.4 An Insight Pivots between the Abstract and the Concrete

    On the one hand, an insight is dealing with data and images which are concrete and particular: Archimedes had one chalice, one King, and one particular problem to solve. On the other hand, what the insight grasps is an idea, a relation, a universal, a law; and that is abstract. The laws that Archimedes eventually formulated were universal, referring not only to this chalice but also to any other material body immersed in any other liquid at any time or any place. The insight is constituted precisely by 'seeing' the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight. First let us now clarify the difference between images, ideas and concepts…."

    — From Ch. 2, Identifying Direct Insights

    Monday, April 5, 2004

    Monday April 5, 2004

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

    Ideas and Art

    Motto of
    Plato's Academy


    From Minimalist Fantasies,
    by Roger Kimball, May 2003:

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

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

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

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



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

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

    "William Clark,"
    by Patricia Johanson, 1967

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


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

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

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


    I maintain that of course
    we can see ideas.

    Example: the idea of
    invariant structure.

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

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

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

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

    Sunday, April 4, 2004

    Sunday April 4, 2004

    Filed under: General — m759 @ 3:48 PM

    Links for Palm Sunday

    Google’s “sunlit paradigm” and

    my own “Lost in Translation.”

    Friday, April 2, 2004

    Friday April 2, 2004

    Filed under: General — m759 @ 2:29 PM

    ART WARS Update

    Two New York Times reviews today are relevant to the themes of ART WARS:

    Minimal Art, by Michael Kimmelman

    Hannah and Martin, by Margo Jefferson.

    The themes of these reviews
    — a minimalist dividing line,
    and polar opposites —
    are combined in my March 15 page,

    The Line.

    Thursday, April 1, 2004

    Thursday April 1, 2004

    Filed under: General — Tags: — m759 @ 9:17 PM

    Loretta’s Rainbow

    AMC April 1, 2004:

    8:00 PM Coal Miner’s Daughter
    10:30 PM Love with the Proper Stranger

    From an interview
    with Iris Dement

    (b. 5 January, 1961, Paragould, Arkansas)

    Your songs are filled with hints of a very complicated, difficult life.

    ID:  Well, I turned 36 this year, and I feel like I’ve been through some difficult things in my life. By far the most difficult thing was leaving the church. My whole life revolved around the church, all through growing up and even as an adult. I didn’t leave it out of rebelliousness, because I loved the feeling of being in the church, with the music and the preaching. But there was an awakening one day, a realization that I didn’t believe in a large part of this stuff, and I could either go on and pretend to be a part of the group or acknowledge that it was not me or something I could live with.

    What’s your first musical memory?

    ID:  The first music that I consciously remember, no doubt about it, was a Loretta Lynn record. I was very young, maybe four, and it was the middle of the day when my mom and dad brought it home from the store. It was a Loretta Lynn gospel record and on the cover she was wearing a lacy yellow dress and she had pretty red hair. I immediately liked it before even hearing it, she was so pretty.

    My parents’s first record player was one of those suitcase types with the lid that flipped up and I listened to it over and over again and probably had that whole album memorized in a week. We didn’t have a lot of records so I played the same ones over and over, and I think there’s something really neat about not having too much coming at you so you really absorb just one or two things. Because something really gets into your bones when you don’t have a lot of choices. You get to know things inside out.

    So now with all the choices out there, are you listening to more stuff?

    ID:  No, I don’t really listen to a whole lot of music. I never did. I had a few things I really liked like the Loretta Lynn record that I listened to constantly. I’m kind of embarrassed to say this, but I still listen to those same records. When I’m out on the road, I take them with me. I put on my Merle, my Johnny, my Loretta.

    eBay item 4004170928:

    Loretta Lynn, Hymns, 1965

    And the rain’s comrade,
    the bow of Iris
    wove her many colours
    into a rounded track.”
    Dionysiaca 2.200

    Thursday April 1, 2004

    Filed under: General — Tags: — m759 @ 6:23 PM

    The Leonardo Code


    Thursday April 1, 2004

    Filed under: General — Tags: — m759 @ 3:33 PM

    Thirty-Three and Three

    “Continue a search for thirty-three and three.
    Veiled forever is the secret door.”

    — Katherine Neville, aka Cat Velis, in The Eight,
    Ballantine Books, January 1989, page 140

    (Today is April 1.)

    Thursday April 1, 2004

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

    Poetry Month:

    Stevens as a Riviera Presbyterian

    He never supposed
    That he might be truth, himself, or part of it,
    That the things that he rejected might be part
    And the irregular turquoise, part, the perceptible blue
    Grown denser, part, the eye so touched, so played
    Upon by clouds, the ear so magnified
    By thunder, parts, and all these things together,
    Parts, and more things, parts. He never supposed divine
    Things might not look divine, nor that if nothing
    Was divine then all things were, the world itself,
    And that if nothing was the the truth, then all
    Things were the truth, the world itself was the truth.

    Had he been better able to suppose:
    He might sit on a sofa on a balcony
    Above the Mediterranean, emerald
    Becoming emeralds. He might watch the palms
    Flap green ears in the heat. He might observe
    A yellow wine and follow a steamer’s track
    And say, “The thing I hum appears to be
    The rhythm of this celestial pantomime.”

    — from Wallace Stevens, “Landscape with Boat”

    (See the previous entry, which mentions Stevens and Jeffers as poets with a Presbyterian background, and also an essay by Justin Quinn that compares Stevens with Jeffers in the context of the poem quoted above.)

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