Tuesday, November 28, 2006
Judgment at Nuremberg:
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:
Christkindl, the Christmas Fairy, is a cherished highlight during the
Holiday Tree Lighting. The Christmas Fairy proclaims the opening of
Also from the official Chicago Christkindl website:
|On the "Christkindl," the Christmas Fairy & our sister-market visit |
famous "Christkindl," the Christmas Fairy, is the trademark of
Christkindlmarket Chicago and its sister-market Christkindlesmarket
In its English version, the Nuremberg website calls the alleged "Christmas Fairy" an angel:
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
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
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 banner reads:
Where the Christ Child
is at home"
Monday, November 27, 2006
"What on earth is
a 'concrete universal'?"
-- Said to be an annotation
by Robert M. Pirsig of
A History of Philosophy,
by Frederick Copleston,
Society of Jesus.
For an answer, see
"The Structure of the
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
"Poetry and Christian Thinking."
For more on Wimsatt
and this topic, see
"Reclaiming the Bible
by Louis A. Markos.
Sunday, November 26, 2006
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,
-- The Club Dumas,
"And it's whispered that soon
if we all call the tune
Then the piper will lead us
-- Robert Plant,
The nine engravings of
The Club Dumas
(filmed as "The Ninth Gate")
are perhaps more an example
of the concrete than of the
An example of the universal*--
or, according to Krauss, a
"staircase" to the universal--
is the ninefold square:
"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
in the garden of Apollo
has been provided by Ezra Brown
in a mathematical essay (pdf).
Unreason is, of course,
* The ninefold square is perhaps a "concrete universal" in the sense of Hegel:
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
Sunday, November 26, 2006
Saturday, November 25, 2006
The Concert from Hell
Bob Lind, composer of "Elusive Butterfly," and General Augusto Pinochet.
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.)
Friday, November 24, 2006
by Steven H. Cullinane
Euclid is "the most famous
geometer ever known
and for good reason:
for millennia it has been
that people first look through
when they view geometry."
-- Euclid's Window:
The Story of Geometry
from Parallel Lines
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
-- 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
We may picture the smallest
affine spaces over this simplest
field by using square or cubic
cells as "points":
From these five finite spaces,
we may, in accordance with
select as "a small and
concrete special case"
the 4-point affine plane,
which we may call
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,
The Smallest Projective Space,
Latin-Square Geometry, and
Geometry of the 4x4 Square.
(These documents assume that
the reader is familar with the
distinction between affine and
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.
Wednesday, November 22, 2006
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...
Nov. 22, 2006:
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...."
From Dana Grove,
A Rhetorical Analysis of
Under the Volcano,
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...."
Wednesday, November 22, 2006
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
King of Spain.
... 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?"
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.
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."
"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
Tuesday, November 21, 2006
ART WARS (cont. from Halloween)
The Great Beyond
This was the name of a
Nov. 5-7 conference on
the religion of Scientism
described in today's
New York Times.
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.
Monday, November 20, 2006
ART WARS continued
Yesterday's link to a Log24 entry for the Feast of the Triumph of the Cross led to the following figure:
(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:
"celebrates the revelations of modern art, defining modernism as
nothing less than 'the discipline of truthfulness, the rigor of
Further background: Kramer opposes
frivolity and politicized vulgarization as fashionable enemies of high
culture as represented in the recent past by the integrity of
-- "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,
This instance of the number 945 as an "artists' signature" is perhaps more impressive than the instances cited in yesterday's Log24 entry, Signature.
Sunday, November 19, 2006
Morley vs. Sagan:
From AP's "Today in History," Nov. 19, 2006:
Today's birthdays: ... Actress-director Jodie Foster is 44....
Thought for Today: "My theology, briefly, is that the universe was
dictated but not signed." --[Attributed to] Christopher Morley,
American author and journalist (1890-1957).
A different story: Carl Sagan, Contact, Chapter 24-- "The Artist's Signature."
Yet another story: The Pennsylvania lottery yesterday, November 18, 2006-- mid-day 914, evening 945. For interpretations, see 9/14 (Feast of the Triumph of the Cross) and also the following "signature" (i.e., "denominator"):
Number theorists may prefer to
think of 945 as the smallest
odd abundant number
(Al-Baghdadi, ca. 980-1037).
Neither of these occurrences
of 945 in mathematics seems
particularly divine; perhaps there
are some other properties of
this number that make it more
credible as a divine signature--
other, that is, than its occurrence
in a lottery just in time for
Jodie Foster's birthday.
Saturday, November 18, 2006
Animated diamond theorem
Copyright © 2006 Steven H. Cullinane
Thursday, November 16, 2006
Among the Tombstones
"Let all thy words be counted."
Dante, Inf., canto X.
G. Robert Crowningshield,
a developer of the
According to a
See Grave Matters,
an entry of that date,
and its links to
Birth, Death, and Symmetry,
| Dante, Inferno, Canto X, 37-39:|
E l'animose man del duca e pronte
mi spinser tra le sepulture a lui,
dicendo: "Le parole tue sien conte."
And the bold and ready hands
of my Leader
pushed me between the tombs to him,
saying: "Let thy words be fitting".
"Make your words count,"
Virgil instructs Dante:
"Speak aptly, make what you say
appropriate to the situation."
Leader will be...
Niemoller is noted for his role in
the movement that led to the
Barmen Declaration, discussed in
Presbyterian Creedal Standards--
linked to in the above-cited
(...that lay in the house
that Jack built).
Thursday, November 16, 2006
Today's New York Times:
G. Robert Crowningshield, 87,
Who Set Diamond Grading System, Dies