Happy Walpurgisnacht, continued:

And an especially Faustian
Walpurgis Night to
Harvard University, home of
Robert Langdon, fictional professor
of Religious Symbology --



"That corpse you planted
          last year in your garden,
  Has it begun to sprout?
          Will it bloom this year? 
  Or has the sudden frost
          disturbed its bed?"

-- T. S. Eliot, "The Waste Land"

From Log24 last September:



A man returns a crucifix
to a Huichol village chapel.

Photo by Rachel Cobb
for National Geographic

Wednesday, April 30, 2008  10:30 AM

Happy Walpurgisnacht, Julie:

Wednesday, April 30, 2008  9:00 AM

Annals of Philosophy, continued:

Tuesday, April 29, 2008  11:09 AM

Religious Art, continued...

Sacerdotal Jargon
at Harvard:



Thomas Wolfe
(Harvard M.A., 1922)

versus



Rosalind Krauss
(Harvard M.A., 1964,
Ph.D., 1969)

on

The Kernel of Eternity

"No culture has a pact with eternity."
-- George Steiner, interview in  
The Guardian of April 19

"At that instant he saw,
in one blaze of light, an image
of unutterable conviction....
the core of life, the essential
pattern whence all other things
proceed, the kernel of eternity."

-- Thomas Wolfe, Of Time
and the River, quoted in
Log24 on June 9, 2005

From today's online Harvard Crimson:

"... under the leadership of Faust,
Harvard students should look forward
to an ever-growing opportunity for
international experience
and artistic endeavor."

Pauli as Mephistopheles
in a 1932 parody of
Goethe's Faust at Niels Bohr's
institute in Copenhagen

From a recent book
on Wolfgang Pauli,
The Innermost Kernel:

A belated happy birthday
to the late
Felix Christian Klein
  (born on April 25) --

"The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety, a subtlety in which it was natural for Cézanne to say: 'I see planes bestriding each other and sometimes straight lines seem to me to fall' or 'Planes in color.... The colored area where shimmer the souls of the planes, in the blaze of the kindled prism, the meeting of planes in the sunlight.' The conversion of our Lumpenwelt went far beyond this. It was from the point of view of another subtlety that Klee could write: 'But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space-- which he calls the mind or heart of creation-- determines every function.' Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less."

-- Wallace Stevens, Harvard College Class of 1901, "The Relations between Poetry and Painting" in The Necessary Angel (Knopf, 1951)

Krauss is concerned to present Modernism less in terms of its history than its structure, which she seeks to represent by means of a kind of diagram: "It is more interesting to think of modernism as a graph or table than a history." The "table" is a square with diagonally connected corners, of the kind most likely to be familiar to readers as the Square of Opposition, found in elementary logic texts since the mid-19th century. The square, as Krauss sees it, defines a kind of idealized space "within which to work out unbearable contradictions produced within the real field of history." This she calls, using the inevitable gallicism, "the site of Jameson's Political Unconscious" and then, in art, the optical unconscious, which consists of what Utopian Modernism had to kick downstairs, to repress, to "evacuate... from its field."

-- Arthur C. Danto in ArtForum, Summer 1993

For a presentation of the Klein Group, see Marc Barbut, "On the Meaning of the Word 'Structure' in Mathematics," in Introduction to Structuralism, ed. Michael Lane (New York: Basic Books, 1970). Claude Lévi-Strauss uses the Klein group in his analysis of the relation between Kwakiutl and Salish masks in The Way of the Masks, trans. Sylvia Modelski (Seattle: University of Washington Press, 1982), p. 125; and in relation to the Oedipus myth in "The Structural Analysis of Myth," Structural Anthropology, trans. Claire Jackobson [sic] and Brooke Grundfest Schoepf (New York: Basic Books, 1963). In a transformation of the Klein Group, A. J. Greimas has developed the semiotic square, which he describes as giving "a slightly different formulation to the same structure," in "The Interaction of Semiotic Constraints," On Meaning (Minneapolis: University of Minnesota Press, 1987), p. 50. Jameson uses the semiotic square in The Political Unconscious (see pp. 167, 254, 256, 277) [Fredric Jameson, The Political Unconscious: Narrative as a Socially Symbolic Act (Ithaca: Cornell University Press, 1981)], as does Louis Marin in "Disneyland: A Degenerate Utopia," Glyph, no. 1 (1977), p. 64.

In this representation, V is a normal subgroup of the alternating group A₄ (and also the symmetric group S₄) on 4 letters. In fact, it is the kernel of a surjective map from S₄ to S₃. According to Galois theory, the existence of the Klein four-group (and in particular, this representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals.

For radicals of another sort, see A Logocentric Meditation, A Mass for Lucero, and [update of 7 PM] Steven Erlanger in today's New York Times-- "France Still Divided Over Lessons of 1968 Unrest."

For material related to Klee's phrase mentioned above by Stevens, "the organic center of all movement in time and space," see the following Google search:

Click on the above
 image for details.

See also yesterday's
Religious Art.

Monday, April 28, 2008  7:00 AM

Annals of Aesthetics, continued:

Religious Art

The black monolith of
Kubrick's 2001 is, in
its way, an example
of religious art.



One artistic shortcoming
(or strength-- it is, after
all, monolithic) of
that artifact is its
resistance to being
analyzed as a whole
consisting of parts, as
in a Joycean epiphany.

The following
figure does
allow such
  an epiphany.



One approach to
 the epiphany:

"Transformations play
  a major role in
  modern mathematics."
- A biography of
Felix Christian Klein

The above 2x4 array
(2 columns, 4 rows)
 furnishes an example of
a transformation acting
on the parts of
an organized whole:



For other transformations
acting on the eight parts,
hence on the 35 partitions, see
"Geometry of the 4x4 Square,"
as well as Peter J. Cameron's
"The Klein Quadric
and Triality" (pdf),
and (for added context)
"The Klein Correspondence,
Penrose Space-Time, and
a Finite Model."

For a related structure--
  not rectangle but cube-- 
see Epiphany 2008.

Sunday, April 27, 2008  8:28 AM

Annals of Aesthetics, continued:

Happy Birthday
 
to the late
Gian-Carlo Rota,
mathematician and
scholar of philosophy

Rota* on his favorite philosopher:

"I believe Husserl to be the greatest philosopher of all times....

Intellectual honesty is the striking quality of Husserl's writings. He wrote what he honestly believed to be true, neither more nor less. However, honesty is not clarity; as a matter of fact, honesty and clarity are at opposite ends. Husserl proudly refused to stoop to the demands of showmanship that are indispensable in effective communication."

Related material:
 
The Diamond Theorem
 

* Gian-Carlo Rota, "Ten Remarks on Husserl and Phenomenology," in O.K. Wiegand et al. (eds.), Phenomenology on Kant, German Idealism, Hermeneutics and Logic, pp. 89-97, Kluwer Academic Publishers, 2000

Saturday, April 26, 2008  10:31 AM

Annals of Aesthetics:

Mere Philosophy

In Memory of
Edmund Husserl

"Mereology (from the Greek μερος, 'part')
is the theory of parthood relations:
of the relations of part to whole and the
relations of part to part within a whole.
Its roots can be traced back to
the early days of philosophy...."

-- Stanford Encyclopedia of Philosophy

"Beauty is the proper conformity
of the parts to one another
and to the whole."

-- Classic definition quoted   
by Werner Heisenberg
(Log24, May 18-20, 2005)

"It seems, as one becomes older,
That the past has another pattern,
      and ceases to be a mere sequence...."

-- T. S. Eliot, Four Quartets



See also Time Fold
and Theme and Variations.

Friday, April 25, 2008  8:00 AM

ART WARS continued:

"It is the intention
 of this piece
 to destabilize the locus
  of that authorial act...."

-- Yale art student
    Aliza Shvarts,
quoted today in
The Harvard Crimson

From Log24 on
March 14:

Rite of Spring From the online  Harvard Crimson -- Related material: A figure from   Monday's entry -- -- and   June 30, 2007's Annals of Theology, with a link to a film: The Center of the World. The center referred to in that film is the same generic "center" displayed at Harvard and in the above mandorla: not the Harvard Women's Center, but rather the women's center. See also Yeats -- "the centre cannot hold," Stevens -- "the center of resemblance," and Zelazny -- "center loosens, forms again elsewhere."

Related material
from Google:

JSTOR: Killing Time with Mark Twain's Autobiographies ... frame "writing" within his own writing in order to destabilize the locus of his authorial voice and to promote a textual confusion that doubly displaces ... links.jstor.org/... - Similar pages

Other ways
of killing time:

From Log24 on April 21, the date of Mark Twain's death-- Psychoshop, by Alfred Bester and Roger Zelazny: His manner was all charm and grace; pure cafe society.... He purred a chuckle. "My place. If you want to come, I'll show you." "Love to. The Luogo Nero? The Black Place?" "That's what the locals call it. It's really Buoco Nero, the Black Hole." "Like the Black Hole of Calcutta?" "No. Black Hole as in astronomy. Corpse of a dead star, but also channel between this universe and its next-door neighbor." The Pennsylvania Lottery yesterday, April 24, 2008: Mid-day 923, Evening 765.... and hence Log24, 9/23 (2007), and page 765 of From Here to Eternity (Delta paperback, 1998): He stayed that way for eight days, never what you could really call drunk, but certainly never anywhere near sober, and always with a bottle of Georgette's expensive scotch in one hand and a glass in the other. He did not talk at all except to say "Yes" or "No," mostly "No," when confronted with a direct question, and he never ate anything when they were there. It was like living in the same house with a dead person.

Thursday, April 24, 2008  9:00 AM

Philosophy Wars continued:

"No culture has a pact with eternity," he says. "The conditions which made possible the giants of the western poetic, aesthetic, philosophic tradition no longer really obtain." Steiner doesn't believe "there can be a Hamlet without a ghost, a Missa Solemnis without a missa," and if you say that the questions addressed by religion are "nonsense or baby talk or trivial, I don't believe that certain dimensions will be available to you. Particularly today, when the atheist case is being put, if I may say so, with such vulgarity of mind."

Wednesday, April 23, 2008  9:00 AM

Happy Shakespeare's Birthday:

Upscale Realism

or, "Have some more
wine and cheese, Barack."

(See April 15, 5:01 AM)

  Allyn Jackson on Rebecca Goldstein
in the April 2006 AMS Notices (pdf)

"Rebecca Goldstein’s 1983 novel The Mind-Body Problem has been widely admired among mathematicians for its authentic depiction of academic life, as well as for its exploration of how philosophical issues impinge on everyday life. Her new book, Incompleteness: The Proof and Paradox of Kurt Gödel, is a volume in the 'Great Discoveries' series published by W. W. Norton.... In March 2005 the Mathematical Sciences Research Institute (MSRI) in Berkeley held a public event in which its special projects director, Robert Osserman, talked with Goldstein about her work. The conversation, which took place before an audience of about fifty people at the Commonwealth Club in San Francisco, was taped.... A member of the audience posed a question that has been on the minds of many of Goldstein’s readers: Is The Mind-Body Problem based on her own life? She did indeed study philosophy at Princeton, finishing her Ph.D. in 1976 with a thesis titled 'Reduction, Realism, and the Mind.' She said that while there are correlations between her life and the novel, the book is not autobiographical.... She... talked about the relationship between Gödel and his colleague at the Institute for Advanced Study, Albert Einstein. The two were very different: As Goldstein put it, 'Einstein was a real mensch, and Gödel was very neurotic.' Nevertheless, a friendship sprang up between the two. It was based in part, Goldstein speculated, on their both being exiles-- exiles from Europe and intellectual exiles. Gödel's work was sometimes taken to mean that even mathematical truth is uncertain, she noted, while Einstein's theories of relativity were seen as implying the sweeping view that 'everything is relative.' These misinterpretations irked both men, said Goldstein. 'Einstein and Gödel were realists and did not like it when their work was put to the opposite purpose.'"

Related material:

From Log24 on
March 22 (Tuesday of
Passion Week), 2005:

"'What is this Stone?' Chloe asked.... 'It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'" -- Many Dimensions, by Charles Williams, 1931 For more on this theme appropriate to Passion Week -- Jews playing God -- see Rebecca Goldstein in conversation with Bob Osserman of the Mathematical Sciences Research Institute at the Commonwealth Club, San Francisco, Tuesday, March 22. Wine and cheese reception at 5:15 PM (San Francisco time).

From
UPSCALE,
a website of the
physics department at
the University of Toronto:

Mirror Symmetry "The image [above] is a depiction of the universe as a mirror image of God, drawn by Robert Fludd in the early 17th century. The caption of the upper triangle reads: 'That most divine and beautiful counterpart visible below in the flowing image of the universe.' The caption of the lower triangle is: 'A shadow, likeness, or reflection of the insubstantial* triangle visible in the image of the universe.'" * Sic. The original is incomprehensibilis, a technical theological term. See Dorothy Sayers on the Athanasian Creed and John 1:5.

For further iconology of the
above equilateral triangles,
see Star Wars (May 25, 2003),
Mani Padme (March 10, 2008),
Rite of Sping (March 14, 2008),
and
Art History: The Pope of Hope
(In honor of John Paul II
three days after his death
in April 2005).

Happy Shakespeare's Birthday.

Monday, April 21, 2008  11:07 AM

Final Arrangements, continued:

"Been somewhere interesting? Tell us about it for a chance to win a trip for 2 to Paris."

"Give faith a fighting chance."

"I sit now in a little room off the bar at four-thirty in the morning drinking ochas and then mescal and writing this on some Bella Vista notepaper I filched the other night.... But this is worst of all, to feel your soul dying. I wonder if it is because to-night my soul has really died that I feel at the moment something like peace. Or is it because right through hell there is a path, as Blake well knew, and though I may not take it, sometimes lately in dreams I have been able to see it? ...And this is how I sometimes think of myself, as a great explorer who has discovered some extraordinary land from which he can never return to give his knowledge to the world: but the name of this land is hell. It is not Mexico of course but in the heart."

Gian-Carlo Rota

His manner was all charm and grace; pure cafe society....

He purred a chuckle. "My place. If you want to come, I'll show you."

"Love to. The Luogo Nero? The Black Place?"

"That's what the locals call it. It's really Buoco Nero, the Black Hole."

"Like the Black Hole of Calcutta?"

"No. Black Hole as in astronomy. Corpse of a dead star, but also channel between this universe and its next-door neighbor."

"Here? In Rome?"

"Sure. They drift around in space until they run out of gas and come to a stop. This number happened to park here."

Saturday, April 19, 2008  5:01 AM

Philosophy Wars continued:

Saturday, April 19, 2008  4:30 AM

From the Labyrinth of Solitude:

From "Today in History,"
by the Associated Press--

April 19, 2008--
"On this date....  
Ten years ago....
Mexican poet-philosopher
Octavio Paz died at age 84."

"Mexico is a solar country--
but it is also a black country,
a dark country. This duality
of Mexico has preoccupied
me since I was a child."

-- Octavio Paz, as quoted
   by Homero Aridjis

"And the light shineth in
darkness; and the darkness
comprehended it not."
-- John 1:5  

"Ya la ronda
  llega aquí"

Friday, April 18, 2008  9:00 AM

Annals of Religion, continued:

Thursday, April 17, 2008  8:28 AM

Annals of Religion, continued:

Top Headlines

(at Google News):

Obama, Clinton... Suicide bomber... Pope Benedict XVI...

In other words:

The best lack all conviction while the worst Are full of passionate intensity. Surely some revelation is at hand.... -- William Butler Yeats

Revelation for  
April 16, 2008 --
day of the Pennsylvania
Clinton-Obama debate and
 of the Pope's birthday --

The Pennsylvania Lottery:



Make of this revelation
what you will.

My own interpretations:
the Lichtung of 4/13 and
the Dickung of page 441
of Heidegger's
Basic Writings, where
the terms Lichtung and
Dickung are described.

See also "The Shining of
May 29" (JFK's birthday).

"By groping toward the light
we are made to realize
how deep the darkness is
around us."

-- Arthur Koestler,  
The Call Girls:
A Tragi-Comedy

Wednesday, April 16, 2008  10:10 AM

Annals of Religion, continued...