Month: April 2004

  • 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.

  • Minimalism


    "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:


     
    Form,
    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


    Geometry
    of the 4x4 square


    The Grid of Time


    ART WARS:
    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 


    GENERAL AUDIENCE OF JOHN PAUL II
    Wednesday 15 January 2003
    :


    "The invocation of the Lord is relentless...."


    and


    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."

  • Inscape



    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:


    Skylark,
    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.


  • Hatched


    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

  • 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?"


    Answer:


    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!"

  • 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.

  • 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."

  • 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.




  • 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

  • President Queeg,
    continued


    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.