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Steven H. Cullinane
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2008

2008 Apr 16-30

2008 Apr 01-15

2008 Mar 01-31

2008 Feb 16-29

2008 Feb 01-15

2008 Jan 01-31

2007

2007 Dec 01-31

2007 Nov 01-30

2007 Oct 16-31

2007 Oct 01-15

2007 Sep 16-30

2007 Sep 01-15

2007 Aug 16-31

2007 Aug 01-15

2007 Jul 16-31

2007 Jul 01-15

2007 Jun 16-30

2007 Jun 01-15

2007 May 16-31

2007 May 01-15

2007 Apr 16-30

2007 Apr 01-15

2007 Mar 16-31

2007 Mar 01-15

2007 Feb 16-28

2007 Feb 01-15

2007 Jan 16-31

2007 Jan 01-15

2006

2006 Dec 16-31

2006 Dec 01-15

2006 Nov 16-30

2006 Nov 01-15

2006 Oct 16-31

2006 Oct 01-15

2006 Sep 16-30

2006 Sep 01-15

2006 Aug 16-31

2006 Aug 01-15

2006 Jul 16-31

2006 Jul 01-15

2006 Jun 16-30

2006 Jun 01-15

2006 May 01-31

2006 Apr 16-30

2006 Apr 01-15

2006 Mar 16-31

2006 Mar 01-15

2006 Feb 16-28

2006 Feb 01-15

2006 Jan 16-31

2006 Jan 01-15

2005

2005 Dec 16-31

2005 Dec 01-15

2005 Nov 16-30

2005 Nov 01-15

2005 Oct 01-31

2005 Sep 01-30

2005 Aug 16-31

2005 Aug 1-15

2005 Jul 16-31

2005 Jul 1-15

2005 Jun 16-30

2005 Jun 10-15

2005 Jun 1-9

2005 May 16-31

2005 May 1-15

2005 Apr 16-30

2005 Apr 1-15

2005 Mar 1-31

2005 Feb 1-28

2005 Jan 1-31

2004

2004 Dec 1-31

2004 Nov 1-30

2004 Oct 16-31

2004 Oct 1-15

2004 Sep 16-30

2004 Sep 1-15

2004 Aug 16-31

2004 Aug 1-15

2004 Jul 16-31

2004 Jul 1-15

2004 Jun 17-30

2004 Jun 01-16

2004 May 16-31

2004 May 01-15

2004 Apr 16-30

2004 Apr 01-15

2004 Mar 16-31

2004 Mar 01-15

2004 Feb 16-28

2004 Feb 01-15

2004 Jan 16-31

2004 Jan 01-15

2003

2003 Dec 16-31

2003 Dec 01-15

2003 Nov 16-30

2003 Nov 01-15

2003 Oct 16-31

2003 Oct 01-15

2003 Sep 16-30

2003 Sep 01-15

2003 Aug 16-31

2003 Aug 08-15

2003 Aug 01-07

2003 Jul 24-31

2003 Jul 16-23

2003 Jul 01-15

2003 Jun 16-30

2003 Jun 01-15

2003 May 16-31

2003 May 01-15

2003 Apr 16-30

2003 Apr 01-15

2003 Mar 16-31

2003 Mar 01-15

2003 Feb 16-28

2003 Feb 01-15

2003 Jan 16-31

2003 Jan 08-15

2003 Jan 01-07

2002

2002 Dec 16-31

2002 Dec 01-15

2002 Nov 16-30

2002 Nov 01-15

2002 Oct 16-31

2002 Oct 01-15

2002 Sep 16-30

2002 Sep 01-15

2002 Aug 16-31

2002 Aug 01-15

2002 Jul 16-31

June-July 2002

Before
June 2002


Related Sites

Three Days
of the
Saint, 2002

12/6:
Santa vs.
the Volcano


12/7:
Satori at
Pearl Harbor


12/8:
Architecture
of Eternity


Some may feel that the Saint in question is Philip Berrigan, who joined Saburo Ienaga and Ivan Illich on Dec. 6, 2002.

Others may feel that the Saint is Don Ameche, who died on Dec. 6, 1993.

"Things change."

-- SHC 12/9/02

Sequel

Stan Rice died on Dec. 9, 2002. A poem of his tells what happened next.

Eight is a Gate

Hollywood producer dies Dec. 14, meets Bach at Heaven's Gate. Realistic comedy.

The Diamond Project

Notes on dance, mortality, and "the still point" on the date of Irene Diamond's death.

Immortal Diamond,
or
NASA Meets Jesus

Thoughts on John O'Hara and G. M. Hopkins for James Joyce's birthday.

Blackbird Singing

The Fred Rogers memorial koan.

Art Wars

LeWitt vs. Witt

Stone, not Wood

best describes St. Peter

The Word

in the Desert

O'Hara's Crucifixion


Art Wars:

Fahne Hoch

and

Thorny Crown


Unity and Reciprocity

in mathematics

The Quality of Diamond


Da Vinci Code ,

Crimson Passion,

Cubist Crucifixion.

Truth and Style


The Line


Bush Mutiny


Symmetry and Change


A Shot at Redemption


Mathematics and Narrative


The Judas Seat


My other sites

Finitegeometry.org

Finitegeometry.org/sc

The Diamond 16 Puzzle

Notes on Finite Geometry

The Diamond Theorem

The Geometry of Qubits

Diamond Theory

Diamond Theory
in 1937


Galois Geometry

A Four-Color Theorem

Latin-Square Geometry

Walsh Functions

The Fano Plane Revisualized

The MOG

Inscapes

The Diamond Theory of Truth

Logos and Logic

Literary-Philosophical
Puzzle Notes


A Mathematician's Aesthetics

Reflection Groups in Finite Geometry

A Reflection Group of Order 168

Reflection Groups: The Missing Link

Geometry of
the I Ching


The Diamond Archetype

Modal Theology

The Eightfold Way and Solomon's Seal

Crystal and Dragon in Diamond Theory

Poetry's Bones

Time Fold

War of Ideas

The Proof
and the Lie


Lemniscate
to Langlands


Symmetry Groups

Block Designs

Finite Relativity

Cognitive Blending

Geometry of the 4x4 Square

Visualizing GL(2,p)

Pattern Groups

Ideas and Art

Jung's Imago

Theme and Variations

The Geometry of Logic

Space-Time and a Finite Model

Quilt Geometry

Duality and Symmetry

Polster on Pictures

Kaleidoscope

The Dharwadker Files

Certified Crank


Favorite Books

The Practical Cogitator

Style

The Reader Over Your Shoulder

The Oxford Book of English Prose

Fancies and Goodnights


Other Online Commonplace Books

David Lavery

Peter J. Cameron

A. M. Kuchling

Constant Reader

Identity Theory

J. Jacobs

M. Magnus

Anonymous


Sites I Read:

Bloglines list

Some Recent Entries

(These may not be the most recent entries. If there are more recent entries, they may be found here or here.)

Thursday, May 8, 2008  4:48 PM

ART WARS continued:

Synchronicity,
Part Deux


Footprints at Log24 on the afternoon of May 8, 2008, including two from France

From
"On the Holy Trinity,"
the entry in the 3:20 PM
French footprint:

"...while the scientist sees
everything that happens
in one point of space,
the poet feels
everything that happens
in one point of time...
all forming an
instantaneous and transparent
organism of events...."

-- Vladimir Nabokov

From
"Angel in the Details,"
 the entry in the 3:59 PM
French footprint:

"I dwell in Possibility -
A fairer House than Prose"

-- Emily Dickinson


These, along with this afternoon's
earlier entry, suggest a review
of a third Log24 item, Windmills,
with an actress from France as...

Changing Woman:

"Kaleidoscope turning...

Juliette Binoche in 'Blue'  The 24 2x2 Cullinane Kaleidoscope animated images

Shifting pattern
within unalterable structure..."
-- Roger Zelazny, Eye of Cat  

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

-- For the source, see 
Joyce's Nightmare Continues.


Thursday, May 8, 2008  1:00 PM

Annals of Religion, continued:

Synchronicity

Today is the feast of
Saint Robert A. Heinlein.

Time of the above: 1:00 PM.
Update of 2:07 PM --

On the local Charlie Rose broadcast today at about 1:48 PM, Paola Antonelli, the organizer of an exhibit at MoMA, "Design and the Elastic Mind," talked about science fiction's influence (or non-influence) on the exhibit. She used the metaphor "the day after tomorrow." As I had just written a link relating design, science fiction, and May 10 (the date of the literal day after tomorrow-- click on "feast" above), I found her remarks of interest. Here is a related passage from a web page.

Paola Antonelli, curator of 'Design and the Elastic Mind' at MoMA

Paola Antonelli
Photo Credit: Andrea Ciotti

Antonelli on scientists as designers who do not call themselves designers:

"So they all try to reach out. They have that in common. Then what they have in common is this attempt to... propose something for the real future. I don't really like science fiction, but I like to think of tomorrow and the day after tomorrow."

Amen.


Thursday, May 8, 2008  12:00 PM

Annals of Religion:

Star Wars

"JERUSALEM, May 7 (Reuters) -
 Fireworks and military fanfare
 launched Israel's 60th anniversary
 celebrations on Wednesday..."

Related material
from Tuesday:

Mailer's 'The Time of Our Time' May 5, 1998, cover with fireworks starburst


"... someone was down sixty,
   someone was up...."

-- Play It As It Lays   



Wednesday, May 7, 2008  7:00 AM

Review:

Forms of the Rock

Tuesday, May 6, 2008  11:07 AM

Mailer's Wake:

In the Dreamtime
the Point Was Ten

From Play It As It Lays,
the paperback edition of 1990
  (Farrar, Straus and Giroux) --

Page 170:

                                             "... In her half sleep
the point was ten, the jackpot was on eighteen, the
only man that could ever reach her was the son of a
preacher man
, someone was down sixty, someone was
up, Daddy wants a popper and she rode a painted
pony let the spinning wheel spin
.

By the end of a week she was thinking constantly
about where her body stopped and the air began,
about the exact point in space and time that was the
difference between Maria and other. She had the sense
that if she could get that in her mind and hold it for

170    

even one micro-second she would have what she had
come to get."

For further details
see yesterday's entries.

"In her half sleep  
     the point was ten...."
-- Play It As It Lays 

The Random House

Random House logo (color-reversed image)

signed first edition
of Norman Mailer's
The Time of Our Time
(4 pounds, 1286 pages)
was published
  ten years ago yesterday --

May 5, 1998:
Fireworks starburst
on the cover of
The Time of Our Time


Mailer's 'The Time of Our Time' May 5, 1998, cover with fireworks starburst

Also from May 5, 1998:
  File Photo in Mailer's obituary --

(Photo by Bebeto Matthews
with Mailer obituary in

Toronto Globe and Mail)

with excerpt from the obituary,
by Richard Pyle


(Associated Press
Saturday, Nov. 10, 2007
at 8:20 AM EDT)

Norman Mailer, May 5, 1998 (with notes)

Related material:


Yesterday's entries and
the time of this entry:
11:07:51 AM ET

CHANGE WE MAY BELIEVE IN sign, adapted from a current political campaign

I Ching hexagram 51: The Arousing (Shock, Thunder)

51
THE JUDGMENT

SHOCK brings success.
Shock comes - oh, oh!
Laughing words - ha, ha!

in light of...
 
A:  Mailer's fireworks starburst
   
   on his book cover from
      ten years ago yesterday
     
B:  A real starburst in a story
     from ten years ago today.
 

Monday, May 5, 2008  11:07 PM

Short Story:

Time and the River

"At the edge of the meadow
flowed the river.

Nick was glad
to get to the river.

He walked upstream
through the meadow."

-- Ernest Hemingway

Pennsylvania Lottery
May 5, 2008:


PA Lottery May 5, 2008: mid-day 216, evening 725

Related material:

2/167/25

"In the swamp the banks were bare, the big cedars came together overhead, the sun did not come through, except in patches; in the fast deep water, in the half light, the fishing would be tragic. In the swamp fishing was a tragic adventure. Nick did not want it. He did not want to go down the stream any further today."

-- Ernest Hemingway,
Big Two-Hearted River


Monday, May 5, 2008  9:00 PM

Annals of Fear and Loathing:

"All our words from loose using
have lost their edge."
 -- Ernest Hemingway    


Look Homeward, Norman

New York Lottery
May 5, 2008:

NY Lottery May 5, 2008: mid-day 098, evening 411

The evening number,
411, may be interpreted
as 4/11. From Log24
on that date:

NYT obituaries, morning of Friday, April 11, 2008-- Carousel designer and family tribute to Norman Mailer

Click on image for further details.

Ride a painted pony
let the spinning
wheel spin.

As for the mid-day number
098, a Google search
(with the aid of, in retrospect,
the above family tribute)
 on "98 'Norman Mailer'"
yields

Amazon.com:
The Time of Our Time
(Modern Library Paperbacks ...
With The Time of Our Time (1998) Norman Mailer has archetypalized himself and in the seven years since publication, within which films Fear and Loathing in ...

From an unattributed
"editorial review" of
  The Time of Our Time
at Amazon.com:

"Surely this sense of himself
as the republic's recording angel
accounts for the structure
of Mailer's anthology...."

Related material:

From Play It As It Lays,
the paperback edition of 1990
  (Farrar, Straus and Giroux) --

Page 170:

                                             "... In her half sleep
the point was ten, the jackpot was on eighteen, the
only man that could ever reach her was the son of a
preacher man
, someone was down sixty, someone was
up, Daddy wants a popper and she rode a painted
pony let the spinning wheel spin
.

By the end of a week she was thinking constantly
about where her body stopped and the air began,
about the exact point in space and time that was the
difference between Maria and other. She had the sense
that if she could get that in her mind and hold it for

170    

even one micro-second she would have what she had
come to get."

The number 411 from
this evening's New York Lottery
may thus be regarded as naming the
"exact point in space and time"
sought in the above passage.

For a related midrash
on the meaning of the
passage's page number,
see the previous entry.

For a more plausible
recording angel,
see Sinatra's birthday,
December 12, 2002.


Monday, May 5, 2008  11:07 AM

Mathematics and Narrative, continued:

Lottery Sermon

"And take upon's
the mystery of things
 as if we were God's spies"
-- King Lear  

PA Lottery Sunday, May 4, 2008: mid-day 170, evening 144

From Log24 on Aug. 19, 2003
and on Ash Wednesday, 2004:
a reviewer on
An Instance of the Fingerpost::

"Perhaps we are meant to
see the story as a cubist
   retelling of the crucifixion."

From Log24 on
Michaelmas 2007:


Kate Beckinsale (in 'Pearl Harbor') pointing to an instance of the number 144

Google searches suggested by
Sunday's PA lottery numbers
(mid-day 170, evening 144)
and by the above
figure of Kate Beckinsale
pointing to an instance of
the number 144 --

Click to enlarge:

Search for the meaning of 170 and 144, the PA lottery numbers of Sunday, May 4, 2008

Related material:

Beckinsale in another film
(See At the Crossroads,
Log24, Dec. 8, 2006):

"For every kind of vampire,
there is a kind of cross."
-- Gravity's Rainbow  
 
Kate Beckinsale in Underworld: Evolution

Kate Beckinsale, adapted from
poster for Underworld: Evolution
(DVD release date 6/6/6)
 
There is such a thing
as a tesseract.

"It was only in retrospect
that the silliness
became profound."

-- Review of  
Faust in Copenhagen

From the conclusion of
Joan Didion's 1970 novel
  Play It As It Lays --

Cover of 'Play It As It Lays'

"I know what 'nothing' means,
and keep on playing."

From Play It As It Lays,
the paperback edition of 1990
  (Farrar, Straus and Giroux) --

Page 170:

"By the end of a week she was thinking constantly
about where her body stopped and the air began,
about the exact point in space and time that was the
difference between Maria and other. She had the sense
that if she could get that in her mind and hold it for

170  

even one micro-second she would have what she had
come to get."


"The page numbers
are generally reliable."

-- Michaelmas 2007   


Sunday, May 4, 2008  10:12 AM

A Diploma for Frank from...

The Old School

Sinatra on cover of USA Weekend, Sunday, May 4, 2008
 
The Old School
at Tidioute:

The old Tidioute High School, now Tidioute Community Charter School

A product of
the old school
:

Tidioute girl

These little town blues...

"... all good things -- trout as well as
  eternal salvation -- come by grace
and grace comes by art
  and art does not come easy."

-- A River Runs Through It


Saturday, May 3, 2008  11:07 PM

Annals of Theology, continued:

"Teach us to
 number our days."


-- Psalm 90, verse 12 

The New Yorker,
issue dated Oct. 1, 2007 --

James Wood on Robert Alter's new translation of the Psalms:

"At any time, God can cancel a life. 'So teach us to number our days,' as the King James Version has it, 'that we may apply our hearts unto wisdom.'....

The ancient Hebrew word for the shadowy underworld where the dead go, Sheol, was Christianized as 'Hell,' even though there is no such concept in the Hebrew Bible. Alter prefers the words 'victory' and 'rescue' as translations of yeshu'ah, and eschews the Christian version, which is the heavily loaded 'salvation.' And so on. Stripping his English of these artificial cleansers, Alter takes us back to the essence of the meaning. Suddenly, in a world without Heaven, Hell, the soul, and eternal salvation or redemption, the theological stakes seem more local and temporal: 'So teach us to number our days.'"

Today's numbers from the
Pennsylvania Lottery:

PA Lottery Saturday, May 3, 2008: Mid-day 510, Evening 724

which, being interpreted,
is 5/10 and 7/24.

Selah.


Friday, May 2, 2008  12:00 PM

Mr. Holland's Week, continued:

A Balliol Star

In memory of
mathematician
Graham Higman of
 Balliol College and
Magdalen College,
Oxford,
  Jan. 19, 1917 -
April 8, 2008

From a biography of an earlier Balliol student, Gerard Manley Hopkins (1844-1889):

"In 1867 he won First-Class degrees in Classics and 'Greats' (a rare 'double-first') and was considered by Jowett to be the star of Balliol."

Gerard Manley Hopkins in 1888

Hopkins, a poet who coined the term "inscape," was a member of the Society of Jesus.

According to a biography, Higman was the founder of Oxford's Invariant Society.

From a publication of that society, The Invariant, Issue 15-- undated but (according to Issue 16, of 2005) from 1996 (pdf):

Taking the square root
  of a function

 by Ian Collier

"David Singmaster once gave a talk at the Invariants and afterwards asked this question:

What is the square root of the exponential function? In other words, can you define a function f such that for all xf 2(x) -- that is, f ( f (x)) -- is equal to e x ? He did not give the answer straight away so I attempted it...."

Another approach to the expression f(f(x)), by myself in 1982:

Inscapes II by Steven H. Cullinane: f(f(x)) and power sets

For further details,
see Inscapes.

For more about Higman, see an interview in the September 2001 newsletter of the European Mathematical Society (pdf).

"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 


Thursday, May 1, 2008  12:00 PM

For the First of May:

Back from
the Shadows


C. G. Jung on cover of 'Memories, Dreams, Reflections'

                        "I sat upon the shore 
Fishing, with the arid plain behind me"

-- The Waste Land, lines 423-424

Eliot's note on line 424 --

"V. Weston, From Ritual to Romance;
chapter on the Fisher King."

From Ritual to Romance,
by Jessie L. Weston,
Cambridge University Press, 1920,
 Chapter IX, "The Fisher King"--

"So far as the present state of our knowledge goes we can affirm with certainty that the Fish is a Life symbol of immemorial antiquity, and the title of Fisher has, from the earliest ages, been associated with Deities who were held to be specially connected with the origin and preservation of Life."

Weston quotes a writer she does not name* who says that "the Fish was sacred to those deities who were supposed to lead men back from the shadows of death to life."

* The Open Court, June and July 1911, p. 168

Today's Doonesbury
   (a flashback) --


Doonesbury of May 1, 2008: Flashback to Uncle Duke on the leader of Berzerkistan

"Some days it went so well that you could make the country so that you could walk into it through the timber to come out into the clearing and work up onto the high ground and see the hills beyond the arm of the lake."

-- Ernest Hemingway,
 A Moveable Feast

Hemingway on the cover of LIFE magazine, 1961


Wednesday, April 30, 2008  11:07 PM

Happy Walpurgisnacht, continued:

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

http://www.log24.com/log/pix08/080430-Langdon489.jpg

"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:

Rachel Cobb photo of man returning a crucifix to Huichol village chapel

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:

Lucy in the Sky
with Diamonds
and Sacred Heart

PARIS -- Albert Hofmann, the mystical Swiss chemist who gave the world LSD, the most powerful psychotropic substance known, died Tuesday at his hilltop home near Basel, Switzerland. He was 102.

Related material:

Star and Diamond: A Tombstone for Plato

and
a film by Julie Taymor,
Across the Universe:

Across the Universe DVD

Detail of the
Strawberry Fields Forever
Sacred Heart:

Strawberry Fields Sacred Heart from 'Across the Universe'


A song:


Julie Taymor

Julie Taymor


"Shinin' like a diamond,
she had tombstones
in her eyes.
"

-- Album "The Dark,"
by Guy Clark

For related tombstones,
see May 16-19, 2006,
and April 19, 2008.

 Further background:
Art Wars for
Red October.

Wednesday, April 30, 2008  9:00 AM

Annals of Philosophy, continued:

Calendar Catechism

Q: If the opposite of Christmas (December 25) is Anti-Christmas (June 25), and the opposite of Halloween (October 31) is May Day (May 1), then what is the opposite of April 30?

A: October 30... Devil's Night!


Tuesday, April 29, 2008  11:09 AM

Religious Art, continued...

Sacerdotal Jargon
at Harvard:

Thomas Wolfe

Thomas Wolfe
(Harvard M.A., 1922)


versus

Rosalind Krauss

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."


Wolfgang Pauli as Mephistopheles

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:

Pauli's Dream Square (square plus the two diagonals)

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

The Klein Group: The four elements in four colors, with black points representing the identity

Another Harvard figure quoted here on Dec. 5, 2002:
"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)
From a review of Rosalind Krauss's The Optical Unconscious  (MIT Press hardcover, 1993):
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
Rosalind Kraus in The Optical Unconscious (MIT Press paperback, 1994):
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.
For related non-sacerdotal jargon, see...

Wikipedia on the Klein group (denoted V, for Vierergruppe):
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:

April 29, 2008, Google search on 'penrose space time'

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.

Black monolith, proportions 4x9

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.

A 2x4 array of squares

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:

The 35 partitions of an 8-set into two 4-sets

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."

B.C. by Hart, April 27, 2008:  Discovery of the Wheel and of the Diamond

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



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