Log24

Saturday, January 16, 2016

The Strands of History…

Filed under: General,Geometry — m759 @ 8:00 pm

… Meet the Threads of Fiction

"… where the threads of fiction and the strands of history shuttle
back and forth in the great loom of the artist's imagination"

Saturday, November 29, 2014

Mark Strand

Filed under: General — m759 @ 2:14 pm

Friday, September 15, 2023

For the Players

Filed under: General — Tags: — m759 @ 9:08 am
 

From "Knight to Move," by Fritz Leiber

"… You were talking about basic games. Well, the chessboard is clearly a spider’s web with crisscross strands—in Go you even put the pieces on the intersections. The object of the game is to hunt down and immobilize the enemy King, just as a spider paralyzes its victim and sometimes wraps it in its silk. But here’s the clincher: the Knight, the piece most characteristic of chess, has exactly eight crooked moves when it stands in the clear—the number of a spider’s crooked legs, and eyes too! This suggests that all chess-playing planets are Spider-infiltrated from way back. It also suggests that all the chessplayers here for the tournament are Spiders—your shock battalion to take over 61 Cygni 5.”

Colonel von Hohenwald sighed. “I was afraid you’d catch on, dear,” he said softly. “Now you’ve signed your abduction warrant at the very least. You may still be able to warn your HQ, but before they can come to your aid, this planet will be in our hands.”

He frowned. “But why did you spill this to me, Erica? If you had played dumb—”

“I spilled it to you,” she said, “because I wanted you to know that your plot’s been blown––and that my side has already taken countermeasures! We’ve made a crooked Knight’s move too. Has the significance of track games never occurred to you, Colonel? The one-dimensional track, sinuously turning, obviously symbolizes the snake. The pieces are the little bugs and animals the snake has swallowed. As for the dice, well, one of the throws is called Snake Eyes. So be assured that all the k’ta’hra players here are Snakes, ready to counter any Spider grab at 61 Cygni 5.”

The Colonel’s mouth almost gaped. 

Sunday, September 10, 2023

Games Theory

Filed under: General — Tags: , — m759 @ 11:32 pm
 

From "Knight to Move," by Fritz Leiber

"… You were talking about basic games. Well, the chessboard is clearly a spider’s web with crisscross strands—in Go you even put the pieces on the intersections. The object of the game is to hunt down and immobilize the enemy King, just as a spider paralyzes its victim and sometimes wraps it in its silk. But here’s the clincher: the Knight, the piece most characteristic of chess, has exactly eight crooked moves when it stands in the clear—the number of a spider’s crooked legs, and eyes too! This suggests that all chess-playing planets are Spider-infiltrated from way back. It also suggests that all the chessplayers here for the tournament are Spiders—your shock battalion to take over 61 Cygni 5.”

Colonel von Hohenwald sighed. “I was afraid you’d catch on, dear,” he said softly. “Now you’ve signed your abduction warrant at the very least. You may still be able to warn your HQ, but before they can come to your aid, this planet will be in our hands.”

He frowned. “But why did you spill this to me, Erica? If you had played dumb—”

“I spilled it to you,” she said, “because I wanted you to know that your plot’s been blown––and that my side has already taken countermeasures! We’ve made a crooked Knight’s move too. Has the significance of track games never occurred to you, Colonel? The one-dimensional track, sinuously turning, obviously symbolizes the snake. The pieces are the little bugs and animals the snake has swallowed. As for the dice, well, one of the throws is called Snake Eyes. So be assured that all the k’ta’hra players here are Snakes, ready to counter any Spider grab at 61 Cygni 5.”

The Colonel’s mouth almost gaped. 

Friday, December 31, 2021

Fiction for Enola

Filed under: General — m759 @ 8:44 am

From a Log24 search for "Strand" —

Related literary remarks —

From Didion’s Play It As It Lays :

Everything goes.  I am working very hard at
not thinking about how everything goes. 
I watch a hummingbird, throw the I Ching
but never read the coins, keep my mind in the now.
— Page 8

From Joni Mitchell

"Don't it always seem to go . . . ."

From Wallace Stevens:

"Let be be finale of seem."

Sunday, March 8, 2020

Joyce and Einstein on the Beach

Filed under: General — m759 @ 12:49 am

"Hello! Kinch here. Put me on to Edenville.
Aleph, alpha: nought, nought, one." 

"A very short space of time through very short times of space….
Am I walking into eternity along Sandymount strand?"

— James Joyce, Ulysses , Proteus chapter

See also the previous post and Masks of the Illuminati .

Monday, September 2, 2019

For Fans of the “Story Theory of Truth”*

Filed under: General — m759 @ 3:03 am

* See that title in this journal.

Wednesday, March 27, 2019

7-Up

Filed under: General — Tags: — m759 @ 1:00 pm

"Don't want to end up a cartoon
In a cartoon graveyard" 
— Paul Simon

Sunday, July 15, 2018

Jewish Oases

Filed under: General,Geometry — Tags: , — m759 @ 10:06 pm

"… Lincoln Plaza Cinemas, the Juilliard String Quartet,
and the Strand Book Store remained  oases
for cultural and intellectual stimulation."

John S. Friedman in The Forward , Jan. 21, 2018

Read more: 

https://forward.com/culture/392483/
how-fred-bass-dan-talbot-robert-mann
-shaped-new-york-culture/

From  the Oasis  in Steven Spielberg's "Ready Player One" (2018) —

I prefer, from a Log24 search for Flux Capacitor

Symbologist Robert Langdon views a corner of Solomon's Cube

From "Raiders of the Lost Images" —

"The cube shape of the lost Mother Box,
also known as the Change Engine,
is shared by the Stone in a novel by
Charles Williams, Many Dimensions .
See the Solomon's Cube webpage."

Tuesday, August 9, 2016

Snowflake

Filed under: General — m759 @ 1:00 pm

From "A Piece of the Storm,"
by the late poet Mark Strand —

"A snowflake, a blizzard of one…."

Tuesday, December 2, 2014

Models

Filed under: General,Geometry — m759 @ 6:45 pm

Continued from November 30, 2014

"Number right Everything right." — Burkard Polster. 

See also the six  posts of November 30, St. Andrew's Day.

Related material —

Peter J. Cameron today discussing Julia Kristeva on poetry

"This seems to be saying that the Kolmogorov
complexity of poetry is very low: the entire poem
can be generated from a small amount of information."

… and this  journal on St. Andrew's day :

From "A Piece of the Storm,"
by the late poet Mark Strand —

A snowflake, a blizzard of one….

Monday, December 1, 2014

Child Buyer

Filed under: General — Tags: — m759 @ 4:02 am

Sunday, November 30, 2014

Back to the Real

Filed under: General — Tags: — m759 @ 4:30 am

Continued from June 17, 2009 —

"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…."

— Malcolm Lowry, Under the Volcano 

See too a search for Snowflake in this journal.
This word may serve as Mark Strand's "Rosebud."

Investments

Filed under: General,Geometry — Tags: — m759 @ 4:00 am

From "A Piece of the Storm," by the late poet Mark Strand —

A snowflake, a blizzard of one….

From notes to Malcolm Lowry's "La Mordida" —

he had invested, in the Valley of the Shadow of Death….

See also Weyl's Symmetry  in this journal.

Saturday, October 22, 2011

Lunch at the Y

Filed under: General — Tags: — m759 @ 12:00 pm

Or: Starting Out in the Evening, continued from noon yesterday

Yesterday evening's New York Lottery numbers were 510 and 5256.

For the former, see post  510, Music for Patricias.

For the latter, see Richard Feynman at the Caltech YMCA Lunch Forum on 5/2/56—

"The Relation of Science and Religion."

Some background….

The Aleph

"As is well known, the Aleph is the first letter of the Hebrew alphabet.
Its use for the strange sphere in my story may not be accidental.
For the Kabbala, the letter stands for the En Soph ,
the pure and boundless godhead; it is also said that it takes
the shape of a man pointing to both heaven and earth…."

— Borges, "The Aleph," quoted in Ayn Sof (January 7th, 2011)

The Y

See "Pythagorean Letter" in this journal.

Edenville

"Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one." 

"A very short space of time through very short times of space…. Am I walking into eternity along Sandymount strand?"

James Joyce, Ulysses , Proteus chapter

Sunday, March 13, 2011

Twenty-Four

Filed under: General — Tags: — m759 @ 7:59 pm

"Poetry never left me stranded, and as an atheist most of my life, I presumed its mojo was a highbrow, intellectual version of what religion did for those more gullible believers in my midst— dumb bunnies to a one, the faithful seemed to me, till I became one.

In the Texas oil town where I grew up, fierceness won fights, but I was thin-skinned— an unfashionably bookish kid whose brain wattage was sapped by a consuming inner life others didn’t seem to bear the burden of. I just seemed to have more frames per second than other kids."

— "Facing Altars: Poetry and Prayer," by Mary Karr

"The original movie had been slowed to a running time of twenty-four hours.
What he was watching seemed pure film, pure time.
The broad horror of the old gothic movie was subsumed in time."

Point Omega , by Don DeLillo

Sunday, July 11, 2010

Philosophers’ Keystone

Filed under: General — Tags: , — m759 @ 2:02 am

(Background— Yesterday's Quarter to Three,
A Manifold Showing, Class of 64, and Child's Play.)

Image-- Notes on Lowry's arrival in Mexico on the ship 'Pennsylvania'

Image-- PA Lottery Saturday, July 10, 2010-- Midday 017, Evening 673

Hermeneutics

Fans of Gregory Chaitin and Harry Potter
may consult Writings for Yom Kippur
for the meaning of yesterday's evening 673.

(See also Lowry and Cabbala.)

Fans of Elizabeth Taylor, Ava Gardner,
and the Dark Lady may consult Prime Suspect
for the meaning of yesterday's midday 17.

For some more serious background, see Dante—

"….mirando il punto 
a cui tutti li tempi son presenti
"

– Dante, Paradiso, XVII, 17-18

The symbol    is used throughout the entire book
in place of such phrases as ‘Q.E.D.’  or
‘This completes the proof of the theorem’
to signal the end of a proof.”

Measure Theory, by Paul R. Halmos, Van Nostrand, 1950      

           
Halmos died on the date of Yom Kippur —  
October 2, 2006.            

Tuesday, January 5, 2010

Artifice of Eternity

Filed under: General,Geometry — Tags: — m759 @ 7:59 am

A Medal

In memory of Byzantine scholar Ihor Sevcenko,
who died at 87 on St. Stephen's Day, 2009–

The image “http://www.log24.com/log/pix06A/060915-Roots.gif” cannot be displayed, because it contains errors.

William Grimes on Sevcenko in this morning's New York Times:

"Perhaps his most fascinating, if uncharacteristic, literary contribution came shortly after World War II, when he worked with Ukrainians stranded in camps in Germany for displaced persons.

In April 1946 he sent a letter to Orwell, asking his permission to translate 'Animal Farm' into Ukrainian for distribution in the camps. The idea instantly appealed to Orwell, who not only refused to accept any royalties but later agreed to write a preface for the edition. It remains his most detailed, searching discussion of the book."

See also a rather different medal discussed
here in the context of an Orwellian headline from
The New York Times on Christmas morning,
the day before Sevcenko died.
That headline, at the top of the online front page,
was "Arthur Koestler, Man of Darkness."

Leibniz, design for medallion showing binary numbers as an 'imago creationis'

The medal, offered as an example of brightness
to counteract the darkness of the Times, was designed
by Leibniz in honor of his discovery of binary arithmetic.
See Brightness at Noon and Brightness continued.

"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,
Random House, 1973, page 118

Wednesday, August 5, 2009

Wednesday August 5, 2009

Filed under: General,Geometry — Tags: , — m759 @ 11:30 am

 

Word and Image

NYT obituary summaries for Charles Gwathmey and Edward Hall, morning of Aug. 5, 2009

From Hall's obituary
:

"Edward T. Hall, a cultural anthropologist
who pioneered the study of nonverbal
 communication and interactions between
members of different ethnic groups,
 died July 20 at his home in
 Santa Fe, N.M. He was 95."

NY Times piece quoted here on
 the date of Hall's death:
 

"July 20, 1969, was the moment NASA needed, more than anything else in this world, the Word. But that was something NASA's engineers had no specifications for. At this moment, that remains the only solution to recovering NASA's true destiny, which is, of course, to build that bridge to the stars."

— Tom Wolfe, author of The Right Stuff, an account of the Mercury Seven astronauts.

Commentary
The Word according to St. John:

Jill St. John, star of 'Diamonds are Forever'

 

From Hall's obituary:

"Mr. Hall first became interested in
space and time as forms of cultural
 expression while working on
Navajo and Hopi reservations
 in the 1930s."

Log24, July 29
:

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  

"We are the key."
Eye of Cat  

Update of about 4:45 PM 8/5:

Paul Newall, "Kieślowski's Three Colours Trilogy"

"Julie recognises the music of the busker outside playing a recorder as that of her husband's. When she asks him where he heard it, he replies that he makes up all sorts of things. This is an instance of a theory of Kieślowski's that 'different people, in different places, are thinking the same thing but for different reasons.' With regard to music in particular, he held what might be characterised as a Platonic view according to which notes pre-exist and are picked out and assembled by people. That these can accord with one another is a sign of what connects people, or so he believed."

The above photo of Juliette Binoche in Blue accompanying the quotations from Zelazny illustrates Kieślowski's concept, with graphic designs instead of musical notes. Some of the same designs are discussed in Abstraction and the Holocaust (Mark Godfrey, Yale University Press, 2007). (See the Log24 entries of June 11, 2009.)

Related material:

"Jeffrey Overstreet, in his book Through a Screen Darkly, comments extensively on Blue. He says these stones 'are like strands of suspended crystalline tears, pieces of sharp-edged grief that Julie has not been able to express.'….

Throughout the film the color blue crops up, highlighting the mood of Julie's grief. A blue light occurs frequently, when Julie is caught by some fleeting memory. Accompanied by strains of an orchestral composition, possibly her husband's, these blue screen shots hold for several seconds while Julie is clearly processing something. The meaning of this blue light is unexplained. For Overstreet, it is the spirit of reunification of broken things."

Martin Baggs at Mosaic Movie Connect Group on Sunday, March 15, 2009. (Cf. Log24 on that date.)

For such a spirit, compare Binoche's blue mobile in Blue with Binoche's gathered shards in Bee Season.

Monday, March 16, 2009

Monday March 16, 2009

Filed under: General — m759 @ 8:00 pm
Damnation Morning
continued

Annals of Prose Style

  Film Review

“No offense to either of them, but ‘Georgia Rule’ suggests an Ingmar Bergman script as directed by Jerry Lewis. The subject matter is grim, the relationships are gnarled, the worldview is bleak, and, at any given moment, you suspect someone’s going to be hit with a pie.” –John Anderson at Variety.com, May 8, 2007

Sounds perfect to me.


Through a Glass Darkly

“Preserving a strict unity of time and place, this stark tale of a young woman’s decline into insanity is set in a summer home on a holiday island. It is the first part of the trilogy that comprises Winter Light and The Silence, films which are generally seen as addressing Bergman’s increasing disillusionment with the emotional coldness of his inherited Lutheran religion. In particular here, Bergman focuses on the absence of familial love which might perhaps have pulled Karin (Andersson) back from the brink; while Karin’s mental disintegration manifests itself in the belief that God is a spider. As she slips inexorably into madness, she is observed with terrifying objectivity by her emotionally paralyzed father (Björnstrand) and seemingly helpless husband (von Sydow).”

— Nigel Floyd, Time Out, quoted at Bergmanorama

Related material:

1. The “spider” symbol of Fritz Leiber’s short story “Damnation Morning”–

2. Hollywood’s “Angels & Demons” (to open May 15), and

3. The following diagram by one “John Opsopaus”–

http://www.log24.com/log/pix09/090312-OpsopausSquare.jpg

Monday March 16, 2009

Filed under: General — m759 @ 8:00 pm
Damnation Morning
continued

Annals of Prose Style

  Film Review

“No offense to either of them, but ‘Georgia Rule’ suggests an Ingmar Bergman script as directed by Jerry Lewis. The subject matter is grim, the relationships are gnarled, the worldview is bleak, and, at any given moment, you suspect someone’s going to be hit with a pie.” –John Anderson at Variety.com, May 8, 2007

Sounds perfect to me.


Through a Glass Darkly

“Preserving a strict unity of time and place, this stark tale of a young woman’s decline into insanity is set in a summer home on a holiday island. It is the first part of the trilogy

Bergman's trilogy including 'Through a Glass Darkly'

that comprises Winter Light and The Silence, films which are generally seen as addressing Bergman’s increasing disillusionment with the emotional coldness of his inherited Lutheran religion. In particular here, Bergman focuses on the absence of familial love which might perhaps have pulled Karin (Andersson) back from the brink; while Karin’s mental disintegration manifests itself in the belief that God is a spider. As she slips inexorably into madness, she is observed with terrifying objectivity by her emotionally paralyzed father (Björnstrand) and seemingly helpless husband (von Sydow).”

— Nigel Floyd, Time Out, quoted at Bergmanorama

Related material:

1. The “spider” symbol of Fritz Leiber’s short story “Damnation Morning“–

Fritz Leiber's 'spider' figure

2. The Illuminati Diamond of Hollywood’s “Angels & Demons” (to open May 15), and

3. The following diagram by one “John Opsopaus“–

Elemental square by John Opsopaus from 'The Rotation of the Elements'

Thursday, March 27, 2008

Thursday March 27, 2008

Filed under: General,Geometry — Tags: — m759 @ 3:29 pm

Back to the Garden

Film star Richard Widmark
died on Monday, March 24.

From Log24 on that date:

"Hanging from the highest limb
of the apple tree are
     the three God's Eyes…"

    — Ken Kesey  

Related material:

The Beauty Test, 5/23/07–
 
H.S.M. Coxeter's classic
Introduction to Geometry (2nd ed.):

The image “http://www.log24.com/log/pix07/070523-Coxeter62.jpg” cannot be displayed, because it contains errors.

Note the resemblance of
the central part to
a magical counterpart–
the Ojo de Dios
of Mexico's Sierra Madre.

From a Richard Widmark film festival:

GARDEN OF EVIL
Henry Hathaway, 1954

"A severely underrated Scope western, shot in breathtaking mountain locations near Cuernavaca. Widmark, Gary Cooper and Cameron Mitchell are a trio of fortune hunters stranded in Mexico, when they are approached by Susan Hayward to rescue her husband (Hugh Marlowe) from a caved-in gold mine in Indian country. When they arrive at the 'Garden of Evil,' they must first battle with one another before they have to stave off their bloodthirsty Indian attackers. Widmark gives a tough, moving performance as Fiske, the one who sacrifices himself to save his friends. 'Every day it goes, and somebody goes with it,' he says as he watches the setting sun. 'Today it's me.' This was one of the best of Hollywood veteran Henry Hathaway's later films. With a brilliant score by Bernard Herrmann."

See also
the apple-tree
entries from Monday
(the date of Widmark's death)
and Tuesday, as well as
today's previous entry and
previous Log24
entries on Cuernavaca
.

Thursday, November 29, 2007

Thursday November 29, 2007

Filed under: General — Tags: — m759 @ 12:00 pm
A Long Story

 
From today's online NY Times:
Obituaries in the News
By THE ASSOCIATED PRESS

 

Published: [Wednesday]
November 28, 2007
Filed at 11:10 p.m. ET

Gennie DeWeese

 

BOZEMAN, Mont. (AP) — Gennie DeWeese, an artist known for her landscape paintings and woodblock prints whose works are displayed at museums across the Northwest, died Monday [November 26, 2007]. She was 86.

 

DeWeese died at her studio south of Bozeman. Dahl Funeral Chapel confirmed her death.

 

Her first oil painting was of her dog, done when she was 12 years old.

 

In 1995, DeWeese received an honorary doctorate of fine arts from Montana State University, and she received the Montana Governor's Award for the Arts.

Robert M. Pirsig in
Zen and the Art of Motorcycle Maintenance

(April 1974) —

"The rhetoricians of ancient Greece were the first teachers in the history of the Western world. Plato vilified them in all his works to grind an axe of his own and since what we know about them is almost entirely from Plato they’re unique in that they’ve stood condemned throughout history without ever having their side of the story told. The Church of Reason that I talked about was founded on their graves. It’s supported today by their graves. And when you dig deep into its foundations you come across ghosts."

I look at my watch. It’s after two. "It’s a long story," I say.

"You should write all this down," Gennie says.


Quod erat
demonstrandum.

Star and Diamond: A Tombstone for Plato

For more information,
click on the black monolith.

Related material:

In the Details
and
Deep Beauty.

Saturday, August 19, 2006

Saturday August 19, 2006

Filed under: General — Tags: — m759 @ 4:28 pm
Metaphysical
Wonderlands

"With no means to verify its truth, superstring theory, in the words of Burton Richter, director emeritus of the Stanford Linear Accelerator Center, may turn out to be 'a kind of metaphysical wonderland.' Yet it is being pursued as vigorously as ever, its critics complain, treated as the only game in town."

— "The Inelegant Universe," by George Johnson, in the Sept. 2006 Scientific American

Some may prefer metaphysics of a different sort:

"To enter Cervantes’s world, we cross a threshold that is Shakespearean and quixotic into a metaphysical wonderland where time expands to become space and vast vaulted distances bend back on themselves, where the threads of fiction and the strands of history shuttle back and forth in the great loom of the artist’s imagination."

As wonderlands go, I personally prefer Clive Barker's Weaveworld.
 

Monday, August 29, 2005

Monday August 29, 2005

Filed under: General — Tags: — m759 @ 4:00 pm
VALE

The image “http://www.log24.com/log/pix05B/050829-GeorgeAndEsther2.jpg” cannot be displayed, because it contains errors.

George and Esther Szekeres

From the weblog of
David Michael Brown, Jr.:
 

Date:     Sun, 28 Aug 2005
             12:30:40 -0400
From:    Alf van der Poorten AM
           
Subject: Vale George Szekeres and
             Esther Klein Szekeres

Members of the Number Theory List will be sad to learn that George and Esther Szekeres both died this morning.  George, 94, had been quite ill for the last 2-3 days, barely conscious, and died first at 06:30.  Esther, 95, died a half hour later.

Both George Szekeres and Esther Klein will be recalled by number theorists as members of the group of young Hungarian mathematicians of the 1930s including Turan and Erdos.  George and Esther's coming to Australia in the late 40s played an important role in the invigoration of Australian Mathematics.  George was also an expert in group theory and relativity; he was my PhD supervisor.

Emeritus Professor
Alf van der Poorten AM
Centre for Number Theory Research
1 Bimbil Place, Killara NSW

 

Related material:

AVE

3:09 PM EDT Thursday, Aug. 25, 2005:
 

  "Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one." 

 

  "A very short space of time through very short times of space….
   Am I walking into eternity along Sandymount strand?"

   — James Joyce, Ulysses, Proteus chapter

A very short space of time through very short times of space….

   "It is demonstrated that space-time should possess a discrete structure on Planck scales."

   — Peter Szekeres, abstract of Discrete Space-Time

Peter Szekeres is the son of George and Esther Szekeres.
 

ATQUE

"At present, such relationships can at best be heuristically described in terms that invoke some notion of an 'intelligent user standing outside the system.'"

Gian-Carlo Rota in Indiscrete Thoughts, p. 152
 

Related material:
High Concept and
Nothing Nothings (Again).

Thursday, August 25, 2005

Thursday August 25, 2005

Filed under: General,Geometry — m759 @ 3:09 pm
Analogical
Train of Thought

Part I: The 24-Cell

From S. H. Cullinane,
 Visualizing GL(2,p),
 March 26, 1985–

Visualizing the
binary tetrahedral group
(the 24-cell):

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

Another representation of
the 24-cell
:

The image “http://www.log24.com/theory/images/24-cell.jpg” cannot be displayed, because it contains errors.

 From John Baez,
This Week’s Finds in
Mathematical Physics (Week 198)
,”
September 6, 2003: 

Noam Elkies writes to John Baez:

Hello again,

You write:

[…]

“I’d like to wrap up with a few small comments about last Week.  There I said a bit about a 24-element group called the ‘binary tetrahedral group’, a 24-element group called SL(2,Z/3), and the vertices of a regular polytope in 4 dimensions called the ’24-cell’.  The most important fact is that these are all the same thing! And I’ve learned a bit more about this thing from here:”

[…]

Here’s yet another way to see this: the 24-cell is the subgroup of the unit quaternions (a.k.a. SU(2)) consisting of the elements of norm 1 in the Hurwitz quaternions – the ring of quaternions obtained from the Z-span of {1,i,j,k} by plugging up the holes at (1+i+j+k)/2 and its <1,i,j,k> translates. Call this ring A. Then this group maps injectively to A/3A, because for any g,g’ in the group |g-g’| is at most 2 so g-g’ is not in 3A unless g=g’. But for any odd prime p the (Z/pZ)-algebra A/pA is isomorphic with the algebra of 2*2 matrices with entries in Z/pZ, with the quaternion norm identified with the determinant. So our 24-element group injects into SL2(Z/3Z) – which is barely large enough to accommodate it. So the injection must be an isomorphism.

Continuing a bit longer in this vein: this 24-element group then injects into SL2(Z/pZ) for any odd prime p, but this injection is not an isomorphism once p>3. For instance, when p=5 the image has index 5 – which, however, does give us a map from SL2(Z/5Z) to the symmetric group of order 5, using the action of SL2(Z/5Z) by conjugation on the 5 conjugates of the 24-element group. This turns out to be one way to see the isomorphism of PSL2(Z/5Z) with the alternating group A5.

Likewise the octahedral and icosahedral groups S4 and A5 can be found in PSL2(Z/7Z) and PSL2(Z/11Z), which gives the permutation representations of those two groups on 7 and 11 letters respectively; and A5 is also an index-6 subgroup of PSL2(F9), which yields the identification of that group with A6.

NDE


The enrapturing discoveries of our field systematically conceal, like footprints erased in the sand, the analogical train of thought that is the authentic life of mathematics – Gian-Carlo Rota

Like footprints erased in the sand….

Part II: Discrete Space

The James Joyce School
 of Theoretical Physics
:


Log24, May 27, 2004

  “Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one.” 

  “A very short space of time through very short times of space….
   Am I walking into eternity along Sandymount strand?”

   — James Joyce, Ulysses, Proteus chapter

A very short space of time through very short times of space….

   “It is demonstrated that space-time should possess a discrete structure on Planck scales.”

   — Peter Szekeres, abstract of Discrete Space-Time

   “A theory…. predicts that space and time are indeed made of discrete pieces.”

   — Lee Smolin in Atoms of Space and Time (pdf), Scientific American, Jan. 2004

   “… a fundamental discreteness of spacetime seems to be a prediction of the theory….”

   — Thomas Thiemann, abstract of Introduction to Modern Canonical Quantum General Relativity

   “Theories of discrete space-time structure are being studied from a variety of perspectives.”

   — Quantum Gravity and the Foundations of Quantum Mechanics at Imperial College, London

Disclaimer:

The above speculations by physicists
are offered as curiosities.
I have no idea whether
 any of them are correct.

Related material:

Stephen Wolfram offers a brief
History of Discrete Space.

For a discussion of space as discrete
by a non-physicist, see John Bigelow‘s
Space and Timaeus.

Part III: Quaternions
in a Discrete Space

Apart from any considerations of
physics, there are of course many
purely mathematical discrete spaces.
See Visible Mathematics, continued
 (Aug. 4, 2005):

The image “http://www.log24.com/theory/images/Quaternions2.jpg” cannot be displayed, because it contains errors.

Thursday, May 27, 2004

Thursday May 27, 2004

Filed under: General — Tags: , — m759 @ 10:10 am

Ineluctable

On the poetry of Geoffrey Hill:

"… why read him? Because of the things he writes about—war and peace and sacrifice, and the search for meaning and the truths of the heart, and for that haunting sense that, in spite of war and terror and the indifferences that make up our daily hells, there really is some grander reality, some ineluctable presence we keep touching. There remains in Hill the daunting possibility that it may actually all cohere in the end, or at least enough of it to keep us searching for more.

There is a hard edge to Hill, a strong Calvinist streak in him, and an intelligence that reminds one of Milton….."

— Paul Mariani, review in America of Geoffrey Hill's The Orchards of Syon

"Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one." 

"A very short space of time through very short times of space…. Am I walking into eternity along Sandymount strand?"

James Joyce, Ulysses, Proteus chapter

"Time has been unfolded into space."

James O. Coplien, Bell Labs

"Pattern and symmetry are closely related."

James O. Coplien on Symmetry Breaking

"… as the critic S. L. Goldberg puts it, 'the chapter explores the Protean transformations of matter in time . . . apprehensible only in the condition of flux . . . as object . . . and Stephen himself, as subject. In the one aspect Stephen is seeking the principles of change and the underlying substance of sensory experience; in the other, he is seeking his self among its temporal manifestations'….

— Goldberg, S.L. 'Homer and the Nightmare of History.' Modern Critical Views: James Joyce. Ed. Harold Bloom. New York: Chelsea House, 1986. 21-38."

from the Choate site of David M. Loeb

In summary:

 

James Joyce
Joyce

Aleph,
alpha:
nought,
nought,
one
:

See also Time Fold.

(By the way, Jorn Barger seems
to have emerged from seclusion.)

 

Saturday, July 5, 2003

Saturday July 5, 2003

Filed under: General,Geometry — m759 @ 7:21 pm

Elementary,
My Dear Gropius

“What is space, how can it be understood and given a form?”
— Walter Gropius

Stoicheia:

Stoicheia,” Elements, is the title of
Euclid’s treatise on geometry.

Stoicheia is apparently also related to a Greek verb meaning “march” or “walk.”

According to a website on St. Paul’s phrase ta stoicheia tou kosmou,” which might be translated

The Elements of the Cosmos,

“… the verbal form of the root stoicheo was used to mean, ‘to be in a line,’ ‘to march in rank and file.’ … The general meaning of the noun form (stoicheion) was ‘what belongs to a series.’ “

As noted in my previous entry, St. Paul used a form of stoicheo to say “let us also walk (stoichomen) by the Spirit.” (Galatians 5:25) The lunatic ravings* of Saul of Tarsus aside, the concepts of walking, of a spirit, and of elements may be combined if we imagine the ghost of Gropius strolling with the ghosts of Plato, Aristotle, and Euclid, and posing his question about space.  Their reply might be along the following lines:

Combining stoicheia with a peripatetic peripateia (i.e., Aristotelian plot twist), we have the following diagram of Aristotle’s four stoicheia (elements),

which in turn is related, by the “Plato’s diamond” figure in the monograph Diamond Theory, to the Stoicheia, or Elements, of Euclid.

Quod erat demonstrandum.

* A phrase in memory of the Paulist Norman J. O’Connor, the “jazz priest” who died on St. Peter’s day, Sunday, June 29, 2003.  Paulists are not, of course, entirely mad; the classic The Other Side of Silence: A Guide to Christian Meditation, by the Episcopal priest Morton Kelsey, was published by the Paulist Press.

Its cover (above), a different version of the four-elements theme, emphasizes the important Jungian concept of quaternity.  Jung is perhaps the best guide to the bizarre world of Christian symbolism.  It is perhaps ironic, although just, that the Paulist Fathers should distribute a picture of “ta stoicheia tou kosmou,” the concept that St. Paul himself railed against.

The above book by Kelsey should not be confused with another The Other Side of Silence, a work on gay history, although confusion would be understandable in light of recent ecclesiastical revelations.

Let us pray that if there is a heaven, Father O’Connor encounters there his fellow music enthusiast Cole Porter rather than the obnoxious Saul of Tarsus.

Saturday, April 5, 2003

Saturday April 5, 2003

Filed under: General,Geometry — Tags: — m759 @ 9:49 am

Art Wars:
Mathematics and the
Emperor's New Art

From Maureen Dowd's New York Times column of June 9, 2002: 

"The shape of the government is not as important as the policy of the government. If he makes the policy aggressive and pre-emptive, the president can conduct the war on terror from the National Gallery of Art."

 

NY Times, April 5, 2003:
U.S. Tanks Move Into Center of Baghdad
See also today's op-ed piece
by Patton's grandson.

Meanwhile, at the Washington Post, another example of great determination and strength of character:

 

Donald Coxeter Dies: Leader in Geometry

By Martin Weil
Washington Post Staff Writer
Saturday, April 5, 2003

"Donald Coxeter, 96, a mathematician who was one of the 20th century's foremost specialists in geometry and a man of great determination and strength of character as well, died March 31 at his home in Toronto."

From another Coxeter obituary:

In the Second World War, Coxeter was asked by the American government to work in Washington as a code-breaker. He accepted, but then backed out, partly because of his pacifist views and partly for aesthetic reasons: "The work didn't really appeal to me," he explained; "it was a different sort of mathematics."

For a differing account of how geometry is related to code-breaking, see the "Singer 7-cycle" link in yesterday's entry, "The Eight," of 3:33 PM.  This leads to a site titled

An Introduction to the
Applications of Geometry in Cryptography
.

"Now I have precisely the right instrument, at precisely the right moment of history, in exactly the right place."

 — "Patton,"
the film

Quod erat
demonstrandum
.


 

Added Sunday, April 6, 2003, 3:17 PM:

The New York Times Magazine of April 6
continues this Art Wars theme.


                 (Cover typography revised)

The military nature of our Art Wars theme appears in the Times's choice of words for its cover headline: "The Greatest Generation." (This headline appears in the paper, but not the Internet, version.)

Some remarks in today's Times Magazine article seem especially relevant to my journal entry for Michelangelo's birthday, March 6.

"…Conceptualism — suddenly art could be nothing more than an idea….

LeWitt moved between his syntax of geometric sculptures and mental propositions for images: concepts he wrote on paper that could be realized by him or someone else or not at all.  Physical things are perishable.  Ideas need not be."

— Michael Kimmelman, chief art critic of the New York Times, April 6, 2003

Compare this with a mathematician's aesthetics:

"A mathematician, like a painter or a poet, is a maker of patterns.  If his patterns are more permanent than theirs, it is because they are made with ideas."

— G. H. Hardy, A Mathematician's Apology (1940), reprinted 1969, Cambridge U. Press, p. 84 

It seems clear from these two quotations that the real conceptual art is mathematics and that Kimmelman is peddling the emperor's new clothes.

Friday, March 7, 2003

Friday March 7, 2003

Filed under: General — Tags: , — m759 @ 4:00 am

Lovely, Dark and Deep

On this date in 1923, "Stopping by Woods on a Snowy Evening," by Robert Frost, was published.  On this date in 1999, director Stanley Kubrick died.  On this date in 1872, Piet Mondrian was born.

"….mirando il punto
a cui tutti li tempi son presenti"

— Dante, Paradiso, XVII, 17-18 

Chez Mondrian
Kertész, Paris, 1926 

6:23 PM Friday, March 7:

From Measure Theory, by Paul R. Halmos, Van Nostrand, 1950:

"The symbol is used throughout the entire book in place of such phrases as 'Q.E.D.' or 'This completes the proof of the theorem' to signal the end of a proof."
 

Tuesday, February 11, 2003

Tuesday February 11, 2003

Filed under: General — Tags: , , — m759 @ 5:10 pm

St. John von Neumann's Song

The mathematician John von Neumann, a heavy drinker and party animal, advocated a nuclear first strike on Moscow.*  Confined to a wheelchair before his death, he was, some say, the inspiration for Kubrick's Dr. Strangelove.  He was a Jew converted to Catholicism.  His saint's day was February 8.  Here is an excerpt from a book titled Abstract Harmonic Analysis**, just one of the fields illuminated by von Neumann's brilliance:

"…von Neumann showed that an intrinsic definition can be given for the mean M(f) of an almost periodic function…. Von Neumann proved the existence and properties of M(f) by completely elementary methods…."

Should W. B. Yeats wander into the Catholic Anticommunists' section of Paradise, he might encounter, as in "Sailing to Byzantium," an unexpected set of "singing-masters" there: the Platonic archetypes of the Hollywood Argyles.

The Argyles' attire is in keeping with Yeats's desire for gold in his "artifice of eternity"… In this case, gold lamé, but hey, it's Hollywood.  The Argyles' lyrics will no doubt be somewhat more explicit in heaven.  For instance, in "Alley Oop," the line

"He's a mean motor scooter and a bad go-getter"

will in its purer heavenly version be rendered

"He's a mean M(f)er and…"

in keeping with von Neumann's artifice of eternity described above.

This theological meditation was suggested by previous entries on Yeats, music and Catholicism (see Feb. 8, von Neumann's saint's day) and by the following recent weblog entries of a Harvard senior majoring in mathematics:

"I changed my profile picture to Oedipus last night because I felt cursed by fate…."

"It's not rational for me to believe that I am cursed, that the gods are set against me.  Because I don't even believe in any gods!"

The spiritual benefits of a Harvard education are summarized by this student's new profile picture:

The image “http://log24.com/log/pix03/030211-oedipus.gif” cannot be displayed, because it contains errors.

M(f)

*Source: Von Neumann and the Development of Game Theory

**by Harvard professor Lynn H. Loomis, Van Nostrand, 1953, p. 169.

Wednesday, November 6, 2002

Wednesday November 6, 2002

Filed under: General — m759 @ 2:22 pm

Today's birthdays: Mike Nichols and Sally Field.

Who is Sylvia?
What is she? 

 

From A Beautiful Mind, by Sylvia Nasar:

Prologue

Where the statue stood
Of Newton with his prism and silent face,
The marble index of a mind for ever
Voyaging through strange seas of Thought, alone.
— WILLIAM WORDSWORTH

John Forbes Nash, Jr. — mathematical genius, inventor of a theory of rational behavior, visionary of the thinking machine — had been sitting with his visitor, also a mathematician, for nearly half an hour. It was late on a weekday afternoon in the spring of 1959, and, though it was only May, uncomfortably warm. Nash was slumped in an armchair in one corner of the hospital lounge, carelessly dressed in a nylon shirt that hung limply over his unbelted trousers. His powerful frame was slack as a rag doll's, his finely molded features expressionless. He had been staring dully at a spot immediately in front of the left foot of Harvard professor George Mackey, hardly moving except to brush his long dark hair away from his forehead in a fitful, repetitive motion. His visitor sat upright, oppressed by the silence, acutely conscious that the doors to the room were locked. Mackey finally could contain himself no longer. His voice was slightly querulous, but he strained to be gentle. "How could you," began Mackey, "how could you, a mathematician, a man devoted to reason and logical proof…how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you…?"

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. "Because," Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, "the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously."

What I  take seriously:

Introduction to Topology and Modern Analysis, by George F. Simmons, McGraw-Hill, New York, 1963 

An Introduction to Abstract Harmonic Analysis, by Lynn H. Loomis, Van Nostrand, Princeton, 1953

"Harmonic Analysis as the Exploitation of Symmetry — A Historical Survey," by George W. Mackey, pp. 543-698, Bulletin of the American Mathematical Society, July 1980

Walsh Functions and Their Applications, by K. G. Beauchamp, Academic Press, New York, 1975

Walsh Series: An Introduction to Dyadic Harmonic Analysis, by F. Schipp, P. Simon, W. R. Wade, and J. Pal, Adam Hilger Ltd., 1990

The review, by W. R. Wade, of Walsh Series and Transforms (Golubov, Efimov, and Skvortsov, publ. by Kluwer, Netherlands, 1991) in the Bulletin of the American Mathematical Society, April 1992, pp. 348-359

Music courtesy of Franz Schubert.

Saturday, October 19, 2002

Saturday October 19, 2002

Filed under: General — m759 @ 9:47 am

What is Truth?

My state of mind
before reading the
New York Times

My state of mind
after reading the
New York Times

In light of the entry below (“Mass Confusion,” Oct. 19, 2002), some further literary reflections seem called for. Since this is, after all, a personal journal, allow me some personal details…

Yesterday I picked up some packages, delivered earlier, that included four books I had ordered. I opened these packages this morning before writing the entry below; their contents may indicate my frame of mind when I later read this morning’s New York Times story that prompted my remarks. The books are, in the order I encountered them as I opened packages,

  • Prince Ombra, by Roderick MacLeish (1982, reprinted in August 2002 as a Tom Doherty Associates Starscape paperback)
  • Truth, edited by Simon Blackburn and Keith Simmons, from the Oxford Readings in Philosophy series (Oxford University Press, 1999, reprinted as a paperback, 2000)
  • The Savage and Beautiful Country, by Alan McGlashan (1967, reprinted in a revised and expanded edition in 1988 as a Daimon Verlag paperback)
  • Abstract Harmonic Analysis, by Lynn H. Loomis (Van Nostrand, 1953… a used copy)

Taken as a whole, this quartet of books supplies a rather powerful answer to the catechism question of Pontius Pilate, “What is truth?”…

The answer, which I pray will some day be delivered at heaven’s gate to all who have lied in the name of religion, is, in Jack Nicholson’s classic words,

You can’t handle the truth!  

Thursday, September 5, 2002

Thursday September 5, 2002

Filed under: General — m759 @ 11:59 pm

Arrow in the Blue

A description by Arthur Koestler (born Sept. 5, 1905) of a

close encounter with the divine:

“…a wordless essence, a fragrance of eternity, a quiver of the arrow in the blue.”

Koestler also mentions the “blue Andalusian sky.” 

Some thoughts suggested by the above and by the Sept. 5, 2002, New York Times story on the first anniversary of the murder of the Mexican lawyer

María de los Angeles Tames….

1. The blue of the Andalusian sky is essentially the same as the blue of the sky above Baja California.  See photographs of the last Jesuit mission in Mexico,

Santa María de los Angeles

2.  A Google search for “blue Andalusian sky” yielded two results: the Koestler page quoted above, and a page on the Gypsy film “Vengo.”  For a reasonable likeness of St. Sara, patron saint of the Gypsies, also known as The Dark Lady, also known as Kali, see the poster of dancer

Sara Baras at Flamenco-world.com

“MONCHO ELCHE, ALICANTE, ESPAÑA
ARTE, DUENDE, MAJESTAD Y GRANDEZA
Es imposible resumir el Flamenco en cuatro palabras, pero al mirar el poster Sara Baras por Paco Sanchez, son esas las palabras que me vienen a la mente.  Gracias, Paco Sanchez.”

For the music Sara dances to, composed and played by Jesús de Rosario, listen to audio clips at

Juana la Loca: Vivir por Amor.

3. For an American version of The Dark Lady, see an homage from Catalonia to

Emmy Lou Harris

For a Harris song that seems appropriate to the blue-sky theme above, see

Thanks to You.

Saturday, August 3, 2002

Saturday August 3, 2002

Filed under: General — m759 @ 10:42 pm

Miss Sauvé

Homily on Flannery O’Connor

for the Sunday following Corpus Christi Day, 2002:

The part of her fiction that most fascinates me, then and now, is what many critics referred to as “the grotesque,” but what she herself called “the reasonable use of the unreasonable.” [Flannery O’Connor, Mystery and Manners: Occasional Prose, Robert and Sally Fitzgerald, eds. (New York: Farrar, Straus, 1969)] 

 A modest example comes to mind. In a short story  ….  the setting sun appears like a great red ball, but she sees it as “an elevated Host drenched in blood” leaving a “line like a red clay road in the sky.” [Flannery O’Connor, “A Temple of the Holy Ghost” from A Good Man is Hard to Find (New York: Harcourt, Brace & World, 1971)] 

In a letter to a friend of hers, O’Connor would later write, “…like the child, I believe the Host is actually the body and blood of Christ, not just a symbol. If the story grows for you it is because of the mystery of the Eucharist in it.” In that same correspondence, O’Connor relates this awkward experience:

I was once, five or six years ago, taken by [Robert Lowell and Elizabeth Hardwick] to have dinner with Mary McCarthy…. She departed the Church at the age of 15 and is a Big Intellectual. We went and eight and at one, I hadn’t opened my mouth once, there being nothing for me in such company to say…. Having me there was like having a dog present who had been trained to say a few words but overcome with inadequacy had forgotten them. Well, toward morning the conversation turned on the Eucharist, which I, being the Catholic, was obviously supposed to defend. [McCarthy] said that when she was a child and received the Host, she thought of it as the Holy Ghost, He being the “most portable” person of the Trinity; now she thought of it as a symbol and implied that it was a pretty good one. I then said, in a very shaky voice, “Well, if it’s a symbol, to hell with it.” That was all the defense I was capable of but I realize now that this is all I will ever be able to say about it, outside of a story, except that it is the center of existence for me; all the rest of life is expendable. [Sally Fitzgerald, ed., The Habit of Being: The Letters of Flannery O’Connor (Vintage: New York, 1979) 124-125] 

….There is, of course, something entirely preposterous and, well, unreasonable, almost grotesque, about the Catholic doctrine of the Real Presence. We claim, with a perfectly straight face, to eat the body and drink the blood of the Eternal Word of God, the second person of the Most Holy Trinity who, according to some, shouldn’t even have a body to begin with. But therein lies precisely the most outlandish feature of the Eucharist: namely, that it embodies the essential scandal of the Incarnation itself.  

             — Friar Francisco Nahoe, OFM Conv.

From James Joyce

A Portrait Of The Artist As A Young Man

Chapter 3 :

Why was the sacrament of the eucharist instituted under the two species of bread and wine if Jesus Christ be present body and blood, soul and divinity, in the bread alone and in the wine alone? Does a tiny particle of the consecrated bread contain all the body and blood of Jesus Christ or a part only of the body and blood? If the wine change into vinegar and the host crumble into corruption after they have been consecrated, is Jesus Christ still present under their species as God and as man?

— Here he is! Here he is!

From The Gazette, Montreal,

of Sunday, August 20, 1995, page C4:

“Summer of ’69,” a memoir by Judy Lapalme on the death by accidental drowning of her 15-year-old younger brother:

“I had never tasted pizza until Jeff died.  Our family, of staunch Irish Catholic stock with more offspring than money, couldn’t cope with the luxury or the spice.

The Hallidays, neighbors from across the street, sent it over to us the day after the funeral, from Miss Sauvé’s Pizzeria, on Sauvé St., just east of Lajeunesse St. in Ahuntsic.  An all-dressed pizza with the hard hat in the centre….

I was 17 that summer and had just completed Grade 12 at Holy Names High School in Rosemont….

…. Jeff was almost 16, a handsome football star, a rebellious, headstrong, sturdy young man who was forever locking horns with my father…. On Friday, Aug. 1, Jeff went out on the boat… and never came back….    

The day after the funeral, a white Volkswagen from Miss Sauvé’s Pizzeria delivered a jumbo, all-dressed pizza to us. The Hallidays’ daughter,  Diane, had been smitten with Jeff and wanted to do something special.

My father assured us that we wouldn’t like it, too spicy and probably too garlicky. There could not be a worse indictment of a person to my father than to declare them reeking of garlic. 

The rest of us tore into the cardboard and began tasting this exotic offering — melted strands of creamy, rubbery, burn-your-palate mozzarrella that wasn’t Velveeta, crisp, dry, and earthy mushrooms, spicy and salty pepperoni sliding off the crust with each bite, green peppers…. Bread crust both crisp and soggy with tomato sauce laden with garlic and oregano. 

It was an all-dressed pizza, tasted for the first time, the day after we buried Jeff….

The fall of 1969, I went to McGill…. I never had another pizza from Miss Sauvé’s.  It’s gone now — like so many things.”

     Ten thousand places

AS kingfishers catch fire, dragonflies dráw fláme;
As tumbled over rim in roundy wells
Stones ring; like each tucked string tells, each hung bell’s
Bow swung finds tongue to fling out broad its name;
Each mortal thing does one thing and the same:         
Deals out that being indoors each one dwells;
Selves—goes itself; myself it speaks and spells,
Crying Whát I do is me: for that I came.
 
Í say móre: the just man justices;
Kéeps gráce: thát keeps all his goings graces;         
Acts in God’s eye what in God’s eye he is—
Chríst—for Christ plays in ten thousand places,
Lovely in limbs, and lovely in eyes not his
To the Father through the features of men’s faces.

   — Gerard Manley Hopkins, 1844-1889

American Literature Web Resources:

Flannery O’Connor

She died on August 3, 1964 at the age of 39.

In almost all of her works the characters were led to a place where they had to deal with God’s presence in the world.

She once said “in the long run, a people is known, not by its statements or statistics, but by the stories it tells. Fiction is the most impure and the most modest and the most human of the arts.”

Encounter – 02/17/2002:

Flannery OConnor – Southern Prophet:

When a woman wrote to Flannery O’Connor saying that one of her stories “left a bad taste in my mouth,” Flannery wrote back: “You weren’t supposed to eat it.”

Etes-vous sauvé? 

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