Month: November 2006

  • Judgment at Nuremberg:

    Christkindl

    “Christmas markets have been part of this festive
    time for centuries in Germany. They were usually held in front of
    churches and were looked at as part of a church visit. The oldest
    recorded market dates to 1310 in Munich, Germany. It was called Nikolausdult
    and was very different from the markets of today. It was an opportunity
    for farmers to come to town, do some shopping and at the same time,
    offer their wares.

    The reformation of the church in the 16th century brought changes to the Christmas markets. Nikolaus was replaced by the Christkindl
    (Christchild) as the gift giver and the Nikolaus markets became
    Christkindl markets. This custom began in the Protestant areas of
    Bavaria with Nuremberg being the first city to call its market Christkindlesmarkt. Munich, a Catholic city, changed its Nikolausdult to Christkindlmarkt in 1805.”

    Background for Christkindl Market in Kitchener, Ontario

    This will also serve as background for today’s New York Times story on Chicago’s Christkindlmarkt:

    “The Christkindl, the Christmas Fairy, is a cherished
    highlight during the Holiday Tree Lighting. The Christmas Fairy
    proclaims the opening of Christkindlmarket Chicago.”

    Also from the official Chicago Christkindl website:

    On the “Christkindl,” the Christmas Fairy & our sister-market visit
    • www.christkindlesmarkt.de

      The
      famous “Christkindl,” the Christmas Fairy, is the trademark of
      Christkindlmarket Chicago and its sister-market Christkindlesmarket
      Nürnberg, Germany

    In its English version, the Nuremberg website calls the alleged “Christmas Fairy” an angel:

    “The Nuremberg Christmas Angel with her white and
    golden dress, long blond curls and her golden crown, has been the
    symbol for the Christmas Market for many decades. During Advent time,
    the Christmas Angel is the most important representative of the city
    and of the traditional Christmas Market.

    Every year, on the
    Friday before the first Advent Sunday, the Nuremberg Christmas Angel
    opens the Nuremberg Christmas Market by reciting a solemn prologue.”

    The German version of the Nuremberg site calls the Christmas Angel the Christkind
    (Christ Child).  This confusion of the Christ Child with a
    supernatural bringer of gifts– hence, later, an angel, and, in Chicago,
    a fairy– is said to have originated with Martin Luther.

    From a Radio Deutsche Welle website–

    Nuremberg, City of Angels

    The making of a myth

     

    The Christkind
    was originally introduced in the 16th century by religious reformer
    Martin Luther.  Until then, it was always Saint Nicholas who
    brought gifts on Dec. 6.  But as Protestants can’t have saints,
    Luther needed a new Christmas tradition for his followers. “Luther
    wanted to move the gift-giving away from the Catholic holiday on Dec.
    6,” said Nuremberg tourism manager Michael Weber. “So he reinvented the
    tradition for Protestants by moving it to Christmas Eve and making the Christkind– really, the baby Jesus– the person who brought the gifts.”

     

    It was under the rule of the National Socialists that the image of today’s Christkind
    was ultimately anchored in the collective German mind.  They built
    on Nuremberg’s tradition of producing tinsel angels, and in 1933, had a
    young girl in an angel costume open the city’s Christmas Market for the
    first time.  After the second World War, Nuremberg’s tinsel angels
    became simply the Nuremberg Christkind, and the figures were sold
    nation-wide. 

    Here is the banner for the Nuremberg site:

    The image “http://www.log24.com/log/pix06B/061128-Nuremberg2.jpg” cannot be displayed, because it contains errors.

      The banner reads:
    Nuremberg Christkindlesmarkt–
    Where the Christ Child
    is at home

    Maybe.

  • Concrete Universal:

    The Poetry
    of Philosophy

    “What
    on earth is
       a ‘concrete universal’?”

    Said to be an annotation
    (undated)
    by Robert M. Pirsig of
    A History of Philosophy,
    by Frederick Copleston,
    Society of Jesus
    .


    For an answer, see
    The Structure of the

    ‘Concrete Universal’

    in Literature,”
    by W. K. Wimsatt, Jr.,

    PMLA,
    Vol. 62,
    No. 1
    (March, 1947),

    pp. 262-280.

    This is reprinted in Wimsatt’s
    The Verbal Icon:
    Studies in the
    Meaning of Poetry
    .

    The final chapter of
    The Verbal Icon
    is titled
    “Poetry and Christian Thinking.”
    For more on Wimsatt
    and this topic, see
    Reclaiming the Bible
    as Literature,”
    by Louis A. Markos.

  • Today’s Sermon

    Rosalind Krauss
    in “Grids,” 1979:

    “If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World,
    for instance– we will find that Mondrian and Malevich are not
    discussing canvas or pigment or graphite or any other form of
    matter.  They are talking about Being or Mind or Spirit. 
    From their point of view, the grid is a staircase to the Universal, and
    they are not interested in what happens below in the Concrete.

    Or, to take a more up-to-date example….”

    “He was looking at
    the nine engravings
    and at the circle,
    checking strange
    correspondences
    between them.”
    The Club Dumas,  
     1993 

    “And it’s whispered that soon
    if we all call the tune
    Then the piper will lead us
    to reason.”
    Robert Plant,   
    1971

    The nine engravings of
    The Club Dumas
    (filmed as “The Ninth Gate“)
    are perhaps more an example
    of the concrete than of the
    universal.

    An example of the universal*–
    or, according to Krauss, a
    staircase” to the universal–
    is the ninefold square:

    The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

    “This is the garden of Apollo,
    the field of Reason….”
    John Outram, architect    

    For more on the field
    of reason, see
    Log24, Oct. 9, 2006.

    A reasonable set of
    “strange correspondences”
    in the garden of Apollo
    has been provided by Ezra Brown
    in a mathematical essay (pdf).

    Unreason is, of course,
    more popular.

    * The ninefold square is perhaps a “concrete universal” in the sense of Hegel:

    “Two
    determinations found in all philosophy are the concretion of the Idea
    and the presence of the spirit in the same; my content must at the same
    time be something concrete, present. This concrete was termed Reason,
    and for it the more noble of those men contended with the greatest
    enthusiasm and warmth. Thought was raised like a standard among the
    nations, liberty of conviction and of conscience in me. They said to
    mankind, ‘In this sign thou shalt conquer,’ for they had before their
    eyes what had been done in the name of the cross alone, what had been
    made a matter of faith and law and religion– they saw how the sign of
    the cross had been degraded.”

    – Hegel, Lectures on the History of Philosophy, “Idea of a Concrete Universal Unity”

    “For every kind of vampire,
    there is a kind of cross.”
    – Thomas Pynchon   

  • Galois’s Window

    The image “http://www.log24.com/theory/images/SmallSpaces.gif” cannot be displayed, because it contains errors.

    Related material from March 2004:
    Anschaulichkeit (3/16) and
    Readings for St. Patrick’s Day.

    “For every kind of vampire,
    there is a kind of cross.”
    – Thomas Pynchon,
    Gravity’s Rainbow

  • The Concert from Hell

    Today’s birthdays:

    Bob Lind, composer of “Elusive Butterfly,” and General Augusto Pinochet.

    Also today:

    Stones tour rolls into Vancouver.

    These events prompt fond memories of a Log24 entry from the Feast of the Transfiguration in 2002 and of more recent entries from this date last year– Buckley and Pinochet and Rehearsing Hell.

    Perhaps the afterlife will include, for some, a Mick Jagger rendition
    of the Lind tune (along with the Percy Faith rendition of
    “Satisfaction” mentioned in The Last Samurai.)

  • “Simplify, simplify…”

    Galois’s Window:

    Geometry
    from Point
    to Hyperspace


    by Steven H. Cullinane

     
    Euclid is “the most famous
    geometer ever known
    and for good reason:
     
    for millennia it has been
    his window
     
    that people first look through
    when they view geometry.”

     
    Euclid’s Window:
    The Story of Geometry
    from Parallel Lines
    to Hyperspace
    ,

    by Leonard Mlodinow

    “…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

    Euclid’s geometry deals with affine
    spaces of 1, 2, and 3 dimensions
    definable over the field
    of real numbers.

    Each of these spaces
    has infinitely many points.

    Some simpler spaces are those
    defined over a finite field–
    i.e., a “Galois” field–
    for
    instance, the field
    which has only two
    elements, 0 and 1, with
    addition and multiplication
    as follows:

    + 0 1
    0 0 1
    1 1 0
    * 0 1
    0 0 0
    1 0 1
    We may picture the smallest
    affine spaces over this simplest
    field by using square or cubic
    cells as “points”:

    Galois affine spaces

    From these five finite spaces,
    we may, in accordance with
    Halmos’s advice,

    select as “a small and
    concrete special case”
    the 4-point affine plane,
    which we may call

    Galois's Window

    Galois’s Window.

    The interior lines of the picture

    are by no means irrelevant to
    the space’s structure, as may be
    seen by examining the cases of
    the above Galois affine 3-space
    and Galois affine hyperplane

    in greater detail.

    For more on these cases, see

    The Eightfold Cube,

    Finite Relativity,

    The Smallest Projective Space
    ,

    Latin-Square Geometry, and

    Geometry of the 4×4 Square.

    (These documents assume that
    the reader is familar with the
    distinction between affine and
    projective geometry.)

    These 8- and 16-point spaces
    may be used to
    illustrate the action of Klein’s
    simple group of order 168
    and the action of
    a subgroup of 322,560 elements

    within the large Mathieu group.

    The view from Galois’s window

    also includes aspects of

    quantum information theory.

    For links to some papers
    in this area, see
      Elements of Finite Geometry.

  • Time and the…

    Rock of Ages

    “Who knows where madness lies?”
    – Rhetorical question
    in “Man of La Mancha”
    (See previous entry.)

    Using madness to
    seek out madness, let us
      consult today’s numbers…

    Pennsylvania Lottery
    Nov. 22, 2006:

    Mid-day 487
    Evening 814

    The number 487 leads us to
    page 487 in the
    May 1977 PMLA,
    The Form of Carnival

    in Under the Volcano“:

    “The printing presses’ flywheel
    marks the whirl of time*
        that will split La Despedida….”

    The image “http://www.log24.com/log/pix06B/061122-Flywheel.gif” cannot be displayed, because it contains errors.

    Flywheel

    From Dana Grove,
    A Rhetorical Analysis of
    Under the Volcano
    ,
    page 92:

    “… In this way, mystical as well as psychological
    dimensions are established.  Later on, the two pass by a printer’s shop
    window and curiously stop to inspect, amidst wedding portraits and well
    in front of the revolving flywheel of the printing machines, ‘a
    photographic enlargement purporting to show the disintegration of a
    glacial deposit in the Sierra Madre, of a great rock split by forest
    fires.’  Significantly the picture is called ‘La Despedida,’ the
    Parting.  Yvonne cannot help but see the symbolic significance of the
    photograph and wishes with all of her might ‘to heal the cleft rock’
    just as she wishes to heal the divorce….”

    Some method in this madness
    is revealed by the evening
    lottery number, 814, which
    leads to an entry of 8/14:

    Cleavage Term


    “… a point of common understanding
    between the classic and romantic worlds.
    Quality, the cleavage term
    between
    hip and square, seemed to be it.”
    Robert M. Pirsig 

    The image “http://www.log24.com/log/pix06B/061122-Goldstein.jpg” cannot be displayed, because it contains errors.

    Rebecca Goldstein

    The 8/14 entry also deals with
    Rebecca Goldstein, who
    seems to understand
    such cleavage
    very well.

    (See also today’s previous entry.)

    * Cf. Shakespeare’s “whirligig of time
    linked to in the previous entry.)

  • Joyce’s nightmare continues…

    Windmill and Diamond

    From “Today in History,”
    by The Associated Press:

    On this date:

    In 1965, the musical
    “Man of La Mancha”
    opened in New York.

    In 1975, Juan Carlos
    was proclaimed
    King of Spain.

    Today’s birthdays:

    … Movie director
    Arthur Hiller is 83….

    Hiller directed the 1972 film
    of “Man of La Mancha.”

    A quotation from that film:

    “When life itself seems lunatic,
    who knows where madness lies?”

    Adapted from Log24 entries of
    Jan. 5, 2003, and Feb. 1, 2003:

    The image “http://www.log24.com/log/pix06B/061122-TimeEternity.gif” cannot be displayed, because it contains errors.

    One can approach these symbols in either a
    mathematical or a literary fashion. For a mathematical
    discussion of the symbols’ structure, see Theme and Variations. Those who prefer literary discussions may make up their own stories.

     
    “Plato is wary of all forms of rapture other than
    reason’s. He is most deeply leery of, because himself so susceptible
    to, the literary imagination. He speaks of it as a kind of holy madness
    or intoxication and goes on to link it to Eros, another derangement
    that joins us, but very dangerously, with the gods.”
     
    Rebecca Goldstein in
        The New York Times,
        December 16, 2002 
     
    “It’s all in Plato, all in Plato;
    bless me, what do they
    teach them at these schools?”
     
    – C. S. Lewis in

    The Narnia Chronicles

  • ART WARS (cont. from Halloween)

    The Great Beyond

    “Beyond Belief”:

    This was the name of a

    Nov. 5-7
    conference on
    the religion of Scientism

    described in today’s

    New York Times
    .

    Beyond Despair:

    Doonesbury 11/21/06

     

    Doonesbury 11/21/06

    For some, art serves as
    an alternative to both
    traditional religion and
    the religion of Scientism.

    See, for instance, the Log24
    entries on All Hallows’ Eve
    in both 2005 and 2006.

  • ART WARS continued

    Triumphs

    Yesterday’s link to a Log24 entry for the Feast of the Triumph of the Cross led to the following figure:

    Primitive roots modulo 17
    (Based on Weyl’s Symmetry)

    Today, an entry in the The New Criterion‘s weblog tells of Hilton Kramer’s new collection of essays on art, The Triumph of Modernism.

    From a Booklist review:

    Kramer “celebrates the revelations of modern art, defining
    modernism as nothing less than ‘the discipline of truthfulness, the
    rigor of honesty.’”

    Further background: Kramer opposes

    “willed frivolity and politicized vulgarization as fashionable enemies
    of high culture as represented in the recent past by the integrity of
    modernism.”

    – “25 Years of The New Criterion

    Perhaps Kramer would agree that such integrity is exemplified by “Two Giants” of modernism described by Roberta Smith in The New York Times recently (Nov. 3– birthdate of A. B. Coble, an artist of a different kind). She is reviewing an exhibit,

    ”Albers and Moholy-Nagy: From the
    Bauhaus to the New World,” that continues through Jan. 21 at the Whitney Museum of American Art,

    945 Madison Avenue

     945
    Madison Avenue.

    This instance of the number 945 as an “artists’ signature” is perhaps
    more impressive than the instances cited in yesterday’s Log24 entry, Signature.