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: From the official promotional material for the Chicago event:
Also from the official Chicago Christkindl website:
In its English version, the Nuremberg website calls the alleged "Christmas Fairy" an angel:
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--
Here is the banner for the Nuremberg site:
Maybe. Posted 11/28/2006 at 9:00 AM |
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. Posted 11/27/2006 at 2:45 AM |
Rosalind Krauss "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 of An example of the universal*--
For more on the field A reasonable set of Unreason is, of course, * The ninefold square is perhaps a "concrete universal" in the sense of Hegel: "For every kind of vampire, Posted 11/26/2006 at 7:26 AM |
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 Posted 11/26/2006 at 12:25 AM |
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.) Posted 11/25/2006 at 1:25 PM |
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 -- Paul Halmos in 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:
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 Halmos's advice, select as "a small and concrete special case" the 4-point affine plane, which we may call 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 4x4 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. Posted 11/24/2006 at 1:06 PM |
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...." 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 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.) Posted 11/22/2006 at 9:00 PM |
Windmill and Diamond From "Today in History," by The Associated Press: On this date: Hiller directed the 1972 film A quotation from that film: "When life itself seems lunatic, 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."
"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 Posted 11/22/2006 at 12:00 PM |
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 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. Posted 11/21/2006 at 7:07 AM |
Triumphs Yesterday's link to a Log24 entry for the Feast of the Triumph of the Cross led to the following figure: 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."
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 This instance of the number 945 as an "artists' signature" is perhaps
more impressive than the instances cited in yesterday's Log24 entry, Signature. Posted 11/20/2006 at 7:20 PM |
Signature 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. Posted 11/19/2006 at 2:02 PM |
Copyright © 2006 Steven H. Cullinane Posted 11/18/2006 at 4:09 AM |
Posted 11/16/2006 at 9:29 PM |
"Let all thy words be counted." Dante, Inf., canto X. Words for G. Robert Crowningshield, a developer of the International Diamond Grading System™ According to a press release, Crowningshield died on November 8. See Grave Matters, an entry of that date, and its links to Geometry's Tombstones, Birth, Death, and Symmetry, and Religious Symbolism at Princeton.
Perhaps Crowningshield's 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 Religious Symbolism at Princeton (...that lay in the house that Jack built). Posted 11/16/2006 at 12:00 PM |
G. Robert Crowningshield, 87, Posted 11/16/2006 at 2:00 AM |
"Many modern Grail stories have a root in the early romances of von Eschenbach....
For an interpretation of 588, see Guy Fawkes Day: Twilight Kingdom, Grail: The Hermeneutics of Chance, Camelot: The Legend Continues, A Case for Indiana Jones, Spots of Time Revisited. For an interpretation of 715, see 7/15, Ein Bild: "Und was fur ein Bild des Christentums ist dabei herausgekommen?" The number 588 above is clearly a MacGuffin. Whether it represents any deeper reality is an open question. "It is a very difficult Posted 11/15/2006 at 3:10 AM |
Cognitive Blend: Casino Royale and Time in the Rock In today's cognitive blend, the role of Casino Royale is played by the Pennsylvania Lottery, which points to 7/26, Venus at St. Anne's (title of the closing chapter of That Hideous Strength). The role of Time in the Rock is played by a Log24 entry of 3/29, Diamond Theory in 1937. "There is such a thing as a tesseract." Posted 11/13/2006 at 8:23 PM |
Prime Suspect: 007 Left: An ad from a page on the new Bond film Right: From PBS last night, "Prime Suspect 7" Posted 11/13/2006 at 11:07 AM |
Time in the Rock Posted 11/12/2006 at 8:00 PM |
Grace Today in History, by The Associated Press On this date: "In 1929, Grace Kelly-- the future movie star and Princess of Monaco-- was born in Philadelphia." Today's mid-day lottery in the State of Grace: 361 Happy birthday. No se puede vivir sin amar. Posted 11/12/2006 at 3:10 PM |
The Height of Folly An interpretation: 762 feet is the height of Honolulu's Diamond Head. 2/06 is the date of a Log24 entry quoting Indiana Jones: "Legend says that when the stones are brought together the diamonds inside of them will glow." Related material: "... in search of a well-needed vacation, he is unprepared for this zany package tour from Hell...." -- Library Journal review of the David Lodge novel Paradise News Posted 11/12/2006 at 2:00 PM |
Instance Log24, Feb. 25, 2004: From a review by Adam White Scoville of Iain Pears's novel titled An Instance of the Fingerpost: "Perhaps we are meant to see the story as a cubist
retelling of the crucifixion, as Pilate, Barabbas, Caiaphas, and Mary
Magdalene might have told it. If so, it is sublimely done so that the
realization gradually and unexpectedly dawns upon the reader. The
title, taken from Sir Francis Bacon, suggests that at certain times,
'understanding stands suspended' and in that moment of clarity
(somewhat like Wordsworth's 'spots of time,' I think), the answer will become apparent as if a fingerpost were pointing at the way." Another instance: The film "Barabbas" (1962) shown on Turner Classic Movies at 8 PM Friday, Nov. 10. Compare and contrast--
The Lagerkvist novel may be of more enduring interest than Stone 588, but, as Friday's lottery numbers indicate, even lesser stories have their place. Posted 11/12/2006 at 12:25 AM |
Today's numbers: Today is the day that Stanley found Livingstone. Click on picture for details. "Stone 588, I presume?" Related material: This afternoon's entry on color symmetry and Click on picture for details. See, too, the following from a Log24 entry of last Monday--
"To von Eschenbach, the Grail
was never really a material cup, but a jewel like the jewel in the lotus, a symbol of enlightenment, of something intangible and always beyond reach." -- Arcadian Functor -- in this context:
"Philosophers ponder the idea
of identity: what it is to give
something a name on Monday and have it respond to that name on Friday...." -- Bernard Holland in The New York Times Monday, May 20, 1996 Posted 11/10/2006 at 11:20 PM |
Veterans Jack Palance as Jesus Raza, Lee Marvin as Henry "Rico" Fardan in "The Professionals" (1966). Both Palance and Marvin were World War II veterans. Palance died today. Posted 11/10/2006 at 7:00 PM |
Livingstone On this date: In 1871, journalist-explorer Henry M. Stanley
found Scottish missionary David Livingstone, who had not been heard
from for years, near Lake Tanganyika in central Africa. Related material:
The history of Princeton's Witherspoon Street Presbyterian Church 1 Peter 2, on the "living stone." -- NIV Bible "Counter-change is
Posted 11/10/2006 at 3:31 PM |
"A victory should be celebrated
with funeral ceremonies." (BEGIN VIDEO CLIP) ED BRADLEY: "... Only a few fishermen help the boat people ashore. We joined in...." (END VIDEO CLIP) Posted 11/9/2006 at 7:20 PM |
Hour of the Wolf Today is Schicksalstag, the "day of fate" in German history. This entry's time slot, 3:00 AM ET-- which some say is the beginning of "the hour of the wolf*"-- was reserved earlier for some entry appropriate to the day. (Actual time of this entry: about 12:48 PM ET).
Related material from Aug. 6, 2006:
* "Wolf" -- See the etymological notes Posted 11/9/2006 at 3:00 AM |
Grave Matters See Log24 four years ago on this date: Religious Symbolism at Princeton. Compare and contrast with last month's entries related to a Princeton Coxeter colloquium: Geometry's Tombstones and Birth, Death, and Symmetry. Posted 11/8/2006 at 8:00 PM |
may constitute winning in another game." -- Ludwig Wittgenstein, Appendix III, paragraph 8, said to have been written on September 23, 1937 For clues to interpreting today's Keystone State mid-day lottery number, 023, see The Prime Cut Gospel. For clues to interpreting today's Keystone State evening lottery number, 666, see the "Apocalypse Now" quotations on All Saints' Day, 2006. Posted 11/7/2006 at 9:00 PM |
A Game of Chess "And these chessmen are men and women as they appear to themselves
and to one another in this world. And the silver table is Time. And
those who stand and watch are the immortal souls of these same men and
women."
-- C. S. Lewis,
The Great Divorce I Ching chessboard Related material: "At the still point, there the dance is" and Posted 11/7/2006 at 12:00 AM |
Today's Birthdays:
Mike Nichols, director of "Spamalot," and Maria Shriver Yesterday evening's entry, "Grail," continued: "To von Eschenbach, the Grail was never really a material cup, but a jewel like the jewel in the lotus, a symbol of enlightenment, of something intangible and always beyond reach. I must confess that the reason I know this is because I'm a bit of an opera fan. The work of von Eschenbach was a source for Wagner...." -- From the weblog Arcadian Functor, Nov. 6, 2006 West Coast Story: A musical adaptation of Romeo and Juliet Featuring "A Girl Named Maria" and "Bring Us Together" (Official inaugural ball theme of Richard M. Nixon) Posted 11/6/2006 at 11:00 AM |
Grail: The Hermeneutics of Chance "... as Genevieve W. Foster has shown in her Jungian analysis, the eyes, the rose,
and the star are equivalent to the 'Grail' of The Waste Land."
-- Grover Smith, T.S. Eliot’s Poetry and Plays: A Study in Sources and Meaning. Chicago: University of Chicago Press, 1956 The Grail also appears in legend as a stone-- From a Nov. 6, 2006, entry in the New Zealand weblog Arcadian Functor: "Many modern Grail stories have a root in the early romances of von Eschenbach....
They live from a Stone whose essence is most pure. If you have never heard of it I shall name it for you here. It is called Lapsit exillis.A search on "lapsit exillis" leads to "Cubic Stones from the Sky"... These stones are often seen as the Holy Grail.... For 804, see 8/04 -- The Presbyterian Exorcist (in part a tribute to Wallace Stevens). For 008 and a "cubic stone," see Christmas 2005. A poetic connection between the star of "The Hollow Men" and Christmas is furnished by the remarks of Wallace Stevens linked to in the previous entry from the word "information." Posted 11/5/2006 at 8:00 PM |
Twilight Kingdom "What he cannot contemplate is the reproach of when at length he may meet the eyes...." -- On "The Hollow Men" " ... unless The eyes reappear As the perpetual star Multifoliate rose Of death's twilight kingdom" Related readings from unholy scripture: A. The "long twilight struggle" speech of JFK B. "The Platters were singing 'Each day I pray for evening just to be with you,' and then it started to happen. The pump turns on in ecstasy. I closed my eyes, I held her with my eyes closed and went into her that way, that way you do, shaking all over, hearing the heel of my shoe drumming against the driver's-side door in a spastic tattoo, thinking that I could do this even if I was dying, even if I was dying, even if I was dying; thinking also that it was information. The pump turns on in ecstasy, the cards fall where they fall, the world never misses a beat, the queen hides, the queen is found, and it was all information." -- Stephen King, Hearts in Atlantis, August 2000 Pocket Books paperback, page 437 C. "I will show you, he thought, the war for us to die in, lady. Sully your kind suffering child's eyes with it. Live burials beside slow rivers. A pile of ears for a pile of arms. The crisps of North Vietnamese drivers chained to their burned trucks.... Why, he wondered, is she smiling at me?" -- Robert Stone, A Flag for Sunrise, Knopf hardcover, 1981, page 299 The image and A, B, C are from Log24 on June 4, 2004. Posted 11/5/2006 at 12:00 PM |
Links to some applications of finite geometry to quantum information theory have been added to finitegeometry.org. Posted 11/4/2006 at 2:15 PM |
First to Illuminate "From the History of a Simple Group" (pdf), by Jeremy Gray: "The American mathematician A. B. Coble [1908; 1913]* seems to have been the first to illuminate the 27 lines and 28 bitangents with the elementary theory of geometries over finite fields. The combinatorial aspects of all this are pleasant, but the mathematics is certainly not easy." * [Coble 1908] A. Coble, "A configuration in finite geometry isomorphic with that of the 27 lines on a cubic surface," Johns Hopkins University Circular 7:80-88 (1908), 736-744. [Coble 1913] A. Coble, "An application of finite geometry to the characteristic theory of the odd and even theta functions," Trans. Amer. Math. Soc. 14 (1913), 241-276. Posted 11/3/2006 at 9:00 AM |
Posted 11/2/2006 at 4:28 PM |
The Method Bush ... "What did they tell you?" Kerry "They told me that you had gone totally insane and that your methods were unsound." Bush "Are my methods unsound?" Kerry "I don't see any method at all, sir." Karl Rove "Perfect, genuine, complete, crystalline, pure." Posted 11/1/2006 at 9:48 PM |
Professor Emeritus, Savage Logic "Savage logic works like a kaleidoscope whose chips can fall into a variety of patterns while remaining unchanged in quantity, form, or color. The number of patterns producible in this way may be large if the chips are numerous and varied enough, but it is not infinite. The patterns consist in the disposition of the chips vis-a-vis one another (that is, they are a function of the relationships among the chips rather than their individual properties considered separately). And their range of possible transformations is strictly determined by the construction of the kaleidoscope, the inner law which governs its operation. And so it is too with savage thought. Both anecdotal and geometric, it builds coherent structures out of 'the odds and ends left over from psychological or historical process.' These odds and ends, the chips of the kaleidoscope, are images drawn from myth, ritual, magic, and empirical lore. (How, precisely, they have come into being in the first place is one of the points on which Levi-Strauss is not too explicit, referring to them vaguely as the 'residue of events... fossil remains of the history of an individual or a society.') Such images are inevitably embodied in larger structures-- in myths, ceremonies, folk taxonomies, and so on-- for, as in a kaleidoscope, one always sees the chips distributed in some pattern, however ill-formed or irregular. But, as in a kaleidoscope, they are detachable from these structures and arrangeable into different ones of a similar sort. Quoting Franz Boas that 'it would seem that mythological worlds have been built up, only to be shattered again, and that new worlds were built from the fragments,' Levi-Strauss generalizes this permutational view of thinking to savage thought in general." -- Clifford Geertz, "The Cerebral Savage: the Structural Anthropology of Claude Levi-Strauss," in Encounter, Vol. 28 No. 4 (April 1967), pp. 25-32. Today's New York Times
Amen. Posted 11/1/2006 at 8:24 AM |