Log24

Thursday, February 2, 2017

An Object for New Haven

Filed under: General — m759 @ 1:44 PM

The title was suggested by a Wallace Stevens poem.

See "The Thing and I" in this journal. See also

Words and Objects according to Whorf

Page 240 of Language, Thought, and Reality , MIT, 1956,
     in the article "Languages and Logic," reprinted from
    Technol. Rev. , 43: 250-252, 266, 268, 272 (April 1941)

Saturday, June 22, 2013

Stevens and the Rock

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

Passage quoted in A Philosopher's Stone (April 4, 2013)—

This passage from Heidegger suggested the lexicon excerpt on
to hypokeimenon  (the underlying) in yesterday's post Lexicon.

A related passage:

The Eliade passage was quoted in a 1971 Ph.D. thesis
on Wallace Stevens.

Some context— Stevens's Rock in this journal.

Sunday, January 5, 2020

The Vulgate of Experience

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

"The eye’s plain version is a thing apart,
The vulgate of experience."

— Wallace Stevens, opening lines of
"An Ordinary Evening in New Haven"

Real  architectural detail from a New Year's
Netflix fiction

Click for context.

See as well a similar architectural detail in
a Log24 post of June 21, 2010.

Saturday, November 2, 2019

Plan 9 Continues.

Filed under: General — Tags: — m759 @ 9:14 AM

"So, after summer, in the autumn air, 
Comes the cold volume of forgotten ghosts,

But soothingly, with pleasant instruments, 
So that this cold, a children's tale of ice, 
Seems like a sheen of heat romanticized."

— Wallace Stevens,
"An Ordinary Evening in New Haven"

IMAGE- German title of 'The Recruit' is 'Der Einsatz'; the MacGuffin is 'Ice 9.'

The German title of "The Recruit" (released Jan. 31, 2003)
is "Der Einsatz." Its MacGuffin is "'Ice 9."

Wednesday, October 9, 2019

Philosophical Infanticide

Filed under: General — Tags: — m759 @ 5:51 AM

From Wallace Stevens

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
Of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

From The Point  magazine yesterday, October 8, 2019
Parricide:  On Irad Kimhi's Thinking and Being .
Book review by Steven Methven.

The conclusion:

"Parricide is nothing that the philosopher need fear . . . .
What sustains can be no threat. Perhaps what the
unique genesis of this extraordinary work suggests is that
the true threat to philosophy is infanticide."

This remark suggests revisiting a post from Monday

Monday, October 7, 2019

Berlekamp Garden vs. Kinder Garten

Filed under: General — m759 @ 11:00 PM

Stevens's Omega and Alpha (see previous post)
suggest a review.

Omega — The Berlekamp Garden. 
                  See Misère Play (April 8, 2019).
Alpha  —  The Kinder Garten. 
                  See Eighfold Cube.

. . . .

Monday, October 7, 2019

Lenz

Filed under: General — m759 @ 2:56 PM

Or:  Je repars .

From Wallace Stevens

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
Of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

Mathematician Hanfried Lenz reportedly died in Berlin on June 1, 2013.

This journal that weekend

Friday, August 9, 2019

The Next Thing

Filed under: General — m759 @ 10:00 AM

From posts tagged The Next Thing

an apt illustration can be found on the cover of
the 1943 first edition of Hesse's Glasperlenspiel 

http://www.log24.com/log/pix11/110203-Glasperlenspiel1943-Detail.jpg

See also Stevens's use of the phrase "heaven-haven"
in "Notes" (1942), the original plan of New Haven,
and related scholia in this journal.

http://www.log24.com/log/pix11/110203-Scholia.jpg

Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

– Rubén Darío

An academic work from 2003 discusses Stevens's "Notes"
as "a perfect geometric whole."

Note that "perfect" means "complete, finished, done."

 

Monday, November 13, 2017

Plan 9 at Yale

Filed under: General — Tags: — m759 @ 9:00 PM

Yale Professors Race Google and IBM to the First Quantum Computer

"So, after summer, in the autumn air, 
Comes the cold volume*  of forgotten ghosts,

But soothingly, with pleasant instruments, 
So that this cold, a children's tale of ice, 
Seems like a sheen of heat romanticized."

— Wallace Stevens,
"An Ordinary Evening in New Haven"

* Update of 10:20 the same evening:

An alternative to The Snow Queen  
as "the cold volume" of Wallace Stevens

On The King in the Window , by Adam Gopnik —

"The book is dedicated to Adam Gopnik's son,
Luke Auden, and his late, great godfathers,
Kirk Varnedoe and Richard Avedon.

'A fantasy that is as ambitious in theme,
sophisticated in setting, and cosmic in scope
as the works of Madeline L'Engle.

The unlikely eponymous hero is Oliver Parker,
an 11-year-old American boy living in Paris
with his mother and journalist father.
After he finds a prize in his slice of cake on
The Night of Epiphany and dons the customary
gilt-paper crown, the boy is plunged into
a battle over nothing less than control of the universe.

His enemy is the dreaded Master of Mirrors,
who rose to power during the reign of Louis XIV,
when Parisians developed technology for making
sheet glass. This faceless, evil being,
capable of capturing souls
through mirrors and enslaving them
in an alternate world that lies beyond all mirrors,
now seeks to dominate the entire universe by
mounting a quantum computer on the Eiffel Tower.

Oliver's mission is to defeat the Master of Mirrors
and save his father's stolen soul.' "

— Description at https://biblio.co.nz/. . . .

Monday, April 24, 2017

The Trials of Device

Filed under: General,Geometry — Tags: , , — m759 @ 3:28 PM

"A blank underlies the trials of device"
— Wallace Stevens, "An Ordinary Evening in New Haven" (1950)

A possible meaning for the phrase "the trials of device" —

See also Log24 posts mentioning a particular device, the pentagram .

For instance —

Wittgenstein's pentagram and 4x4 'counting-pattern'

Related figures

Pentagon with pentagram    

Tuesday, March 21, 2017

Res Ipsa

Filed under: General,Geometry — Tags: — m759 @ 7:00 PM

From The Poetic Quotidian, a journal of quotations—

See also, in this journal, New Haven + Grid.

The Ninefold Square

Tuesday, July 19, 2016

Interior, Exterior

Filed under: General,Geometry — m759 @ 10:30 AM

The post Outer, Inner of July 16, 2016, contained the following
illustration of a quote from "An Ordinary Evening in New Haven" —

An image from yesterday morning pictured a link to the
Feb. 10, 2014, post Mystery Box III: Inside, Outside.

That post, shown below, offers a deeper interpretation of the
Stevens quote "an interior made exterior."

(Click image below to use the post's links.)

Saturday, July 16, 2016

Outer, Inner

Filed under: General — m759 @ 11:00 PM

A detail from this morning's 6 AM post

An Ordinary Evening in New Haven, XXII

Professor Eucalyptus said, “The search
For reality is as momentous as
The search for god.” It is the philosopher’s search

For an interior made exterior
And the poet’s search for the same exterior made
Interior: breathless things broodingly abreath

With the Inhalations of original cold
And of original earliness. Yet the sense
Of cold and earliness is a daily sense,

Not the predicate of bright origin.
Creation is not renewed by images
Of lone wanderers. To re-create, to use

The cold and earliness and bright origin
Is to search. Likewise to say of the evening star,
The most ancient light in the most ancient sky,

That it is wholly an inner light, that it shines
From the sleepy bosom of the real, re-creates,
Searches a possible for its possibleness.

— Wallace Stevens

See also Bloomsday 2007, "Obituaries in the News."

This morning's 6 AM post linked to a more recent obituary in the news

"… while Jules and Judy were still living in Brooklyn Heights … 
Jules collaborated with his former roommate, Norton Juster,
by illustrating what was to become the children’s classic
The Phantom Tollbooth . Neither author or illustrator had
a clue as to how to get this unlikely work published, and it
was Judy’s idea to take it to a mutual friend . . . ."

Tuesday, August 4, 2015

To Fuse Words with Things

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

A passage suggested by the previous post —

 
   — Catholic Resistance in Elizabethan England :
        Robert Persons's Jesuit Polemic, 1580–1610
        by Victor Houliston (Ashgate Publishing, 2007)

Boundary Value Problem

Filed under: General — Tags: — m759 @ 11:30 AM

"'The Owl in the Sarcophagus,' for all its incantatory
elegiac power, consists almost entirely of 
a self-generated and self-generating rhetoric.
It points up one of the limits of poetic composition itself,
the boundary where technique turns into technology."

— Bart Eeckhout in Wallace Stevens and the Limits
     of Reading and Writing ,
 University of Missouri Press,
     2002, p. 210

See as well this morning's previous post.

Block That Metaphor

Filed under: General — Tags: — m759 @ 11:00 AM

"In theory, a robot could be the cloud-connecting Charon
that ushers us into the Internet of Things." 

Bryan Lufkin at Gizmodo.com, July 29, 2015

Related material —

The death of MIT computability theorist Hartley Rogers, Jr.
at 89 on July 17, and this journal on July 17.

Monday, August 3, 2015

Text and Context*

Filed under: General,Geometry — Tags: — m759 @ 2:00 AM

"The ORCID organization offers an open and
independent registry intended to be the de facto  
standard for contributor identification in research
and academic publishing. On 16 October 2012,
ORCID launched its registry services and
started issuing user identifiers." — Wikipedia

This journal on the above date —

  

A more recent identifier —

Related material —

See also the recent posts Ein Kampf and Symplectic.

* Continued.

Sunday, August 2, 2015

Comedy

Filed under: General — Tags: — m759 @ 4:20 PM

Symplectic

Filed under: General,Geometry — Tags: — m759 @ 7:00 AM

See "Symplectic" in this journal.  Some illustrations —

 

Midrash —

"Adorned with cryptic stones and sliding shines,
An immaculate personage in nothingness,
With the whole spirit sparkling in its cloth,

Generations of the imagination piled
In the manner of its stitchings, of its thread,
In the weaving round the wonder of its need,

And the first flowers upon it, an alphabet
By which to spell out holy doom and end,
A bee for the remembering of happiness."

— Wallace Stevens, "The Owl in the Sarcophagus"

Tuesday, May 12, 2015

Writing Well*

Filed under: General,Geometry — Tags: — m759 @ 11:00 PM

See Stevens + New Haven.

* The above figure may be viewed as
   the Chinese "Holy Field" or as the
   Chinese character for "Well"
   inscribed in a square.

Wednesday, February 11, 2015

Dead Reckoning

Filed under: General — Tags: — m759 @ 5:28 PM

Continued from yesterday evening

IMAGE- Bogart in 'Casablanca' with chessboard

Today's mathematical birthday — 

Claude Chevalley, 11 Feb. 1909 – 28 June 1984.

From MacTutor —

Chevalley's daughter, Catherine Chevalley, wrote about
her father in "Claude Chevalley described by his daughter"
(1988):—

For him it was important to see questions as a whole, to see the necessity of a proof, its global implications. As to rigour, all the members of Bourbaki cared about it: the Bourbaki movement was started essentially because rigour was lacking among French mathematicians, by comparison with the Germans, that is the Hilbertians. Rigour consisted in getting rid of an accretion of superfluous details. Conversely, lack of rigour gave my father an impression of a proof where one was walking in mud, where one had to pick up some sort of filth in order to get ahead. Once that filth was taken away, one could get at the mathematical object, a sort of crystallized body whose essence is its structure. When that structure had been constructed, he would say it was an object which interested him, something to look at, to admire, perhaps to turn around, but certainly not to transform. For him, rigour in mathematics consisted in making a new object which could thereafter remain unchanged.

The way my father worked, it seems that this was what counted most, this production of an object which then became inert— dead, really. It was no longer to be altered or transformed. Not that there was any negative connotation to this. But I must add that my father was probably the only member of Bourbaki who thought of mathematics as a way to put objects to death for aesthetic reasons.

Recent scholarly news suggests a search for Chapel Hill
in this journal. That search leads to Transformative Hermeneutics.
Those who, like Professor Eucalyptus of Wallace Stevens's
New Haven, seek God "in the object itself" may contemplate
yesterday's afternoon post on Eightfold Design in light of the
Transformative post and of yesterday's New Haven remarks and
Chapel Hill events.

Sunday, November 23, 2014

Remarks on Reality

Filed under: General — Tags: — m759 @ 5:09 PM

Wallace Stevens in "An Ordinary Evening in New Haven"
(1950) on "The Ruler of Reality" —

"Again, 'He has thought it out, he thinks it out,
As he has been and is and, with the Queen
Of Fact, lies at his ease beside the sea.'"

One such scene, from 1953 —

Another perspective, from "The Osterman Weekend" (1983) —

Tuesday, October 7, 2014

As Is

Filed under: General — Tags: , — m759 @ 10:05 PM

"That simple operator, 'as,' turns out to carry within its philosophical grammar
a remarkable complex field* of operations…."

Charles Altieri,  Painterly Abstraction in Modernist American Poetry,
Cambridge University Press, 1989, page 343

See also Rota on Heidegger (What "As" Is, July 6, 2010), and Lead Belly
on the Rock Island Line — "You got to ride it like you find it."

* Update of Oct. 10, 2014: See also "Complex + Grid" in this journal.

Friday, February 21, 2014

Night’s Hymn of the Rock

Filed under: General,Geometry — Tags: , , — m759 @ 3:33 AM

One way of interpreting the symbol  IMAGE- Modal Diamond in a square 
at the end of yesterday's post is via
the phrase "necessary possibility."

See that phrase in (for instance) a post
of July 24, 2013, The Broken Tablet .

The Tablet  post may be viewed in light
of a Tom Wolfe passage quoted here on
the preceding day, July 23, 2013—

IMAGE- Tom Wolfe in 'The Painted Word' on conceptual art

On that  day (July 23) another weblog had
a post titled

Wallace Stevens: Night's Hymn of the Rock.

Some related narrative —

IMAGE- The 2001 film 'The Discovery of Heaven'

I prefer the following narrative —

Part I:  Stevens's verse from "The Rock" (1954) —
"That in which space itself is contained"

Part II:  Mystery Box III: Inside, Outside (2014)

Monday, February 10, 2014

Mystery Box III: Inside, Outside

Filed under: General,Geometry — Tags: , , , , — m759 @ 2:28 PM

(Continued from Mystery Box, Feb. 4, and Mystery Box II, Feb. 5.)

The Box

Inside the Box

Outside the Box

For the connection of the inside  notation to the outside  geometry,
see Desargues via Galois.

(For a related connection to curves  and surfaces  in the outside
geometry, see Hudson's classic Kummer's Quartic Surface  and
Rosenhain and Göpel Tetrads in PG(3,2).)

Monday, August 26, 2013

Dark Side Tales

Filed under: General — m759 @ 3:00 PM

"Got to keep the loonies on the path."

Lyrics to Dark Side of the Moon

For those who, like Tom Stoppard, prefer the dark side—

NEW ANGLE:
He runs, panting, until he ends up
in front of a tall, brilliantly lit office building.
As he approaches, the lights in the building
are going off floor by floor.

INT. OFFICE BUILDING – NIGHT
He rushes into
the lobby, running for the elevator.

NIGHT WATCHMAN
Burning the midnight oil, Mr. Smith?
You forgot to sign in.

Bateman wheels around and shoots him.
He runs toward the revolving doors.
As he swings around in the doors, he notices
a JANITOR who has witnessed the shooting.
He revolves back into the lobby and shoots the janitor.

NEW ANGLE:
He runs out of the building
and across the street to an identical office building,
the one that houses Pierce & Pierce.

INT. PIERCE & PIERCE LOBBY – NIGHT
Bateman nods at the Pierce & Pierce NIGHT WATCHMAN
and signs in. He breathes a sigh of relief as
​the elevator doors close behind him.

— AMERICAN PSYCHO
by Mary Harron and Guinevere Turner
(Based on the novel by Bret Easton Ellis, 
Fourth Draft, November 1998)

Not quite so dark—

"And then one day you find ten years have got behind you."

— Lyrics to Dark Side of the Moon

This journal ten years ago, on August 25, 2003

         … We seek

The poem of pure reality, untouched
By trope or deviation, straight to the word,
Straight to the transfixing object, to the object

At the exactest point at which it is itself,
Transfixing by being purely what it is,
A view of New Haven, say, through the certain eye,

The eye made clear of uncertainty, with the sight
Of simple seeing, without reflection. We seek
Nothing beyond reality. Within it,

Everything, the spirit's alchemicana
Included, the spirit that goes roundabout
And through included, not merely the visible,

The solid, but the movable, the moment,
The coming on of feasts and the habits of saints,
The pattern of the heavens and high, night air.

— Wallace Stevens, "An Ordinary Evening
     in New Haven," Canto IX
    (Collected Poems , pp. 471-472)


"A view of New Haven, say…." —

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo,
the field of Reason…."
John Outram, architect 


A similar version of this Apollonian image —

  Detail:

Related material for the loonies:

"the spirit's alchemicana."

Tuesday, June 25, 2013

Big Rock

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

From the LA Times  online obituaries today:

Michael Feran Baigent was born in Nelson, New Zealand,
in 1948. After graduating from New Zealand's University
of Canterbury with a degree in psychology, he worked as a
photographer and magazine editor in Australia, New
Zealand and Spain before taking up research for a
documentary called "The Shadow of the Templars."

From 1998 he lectured on and led tours of the temples and
tombs in Egypt, and from 2001 he was editor of the
magazine "Freemasonry Today."

Elliott Reid

Longtime film, TV actor with a comic touch

Elliott "Ted" Reid, 93, a longtime character actor in films
and on television, stage and radio who played opposite
Marilyn Monroe and Jane Russell in the classic comedy
"Gentlemen Prefer Blondes," died Friday [June 21, 2013]
in Studio City, said his nephew Roger R. Jackson.

From a post last Saturday, June 22, and the earlier
​post last Friday, June 21, that preceded it:

The Eliade passage was quoted in a 1971 Ph.D. thesis
on Wallace Stevens.

Some context— Stevens's Rock in this journal.

Friday, June 21, 2013

Lexicon

Filed under: Uncategorized — m759 @ 1:00 PM

From the final pages of the new novel
Lexicon , by Max Barry: 

"… a fundamental language
of the human mind— 
the tongue in which the human animal 
speaks to itself at the basest level. 
The machine language, in essence…."

"… the questions raised by 
this underlying lexicon
What are its words? 
How many are there? ….
Can we learn to speak them?
What does it sound like 
when who we are is expressed
in its most fundamental form? 
Something to think about."

       R. Lowell

See also, in this journal, Big Rock.

Sunday, April 14, 2013

Space Itself

Filed under: General,Geometry — Tags: — m759 @ 9:25 AM

From The Cambridge Companion to Wallace Stevens ,
John N. Serio, ed., "Stevens's Late Poetry," by B.J. Leggett,
pp. 62-75, an excerpt from page 70:

Click the above image for further details.

See also Nothingness and "The Rock" in this journal.

Further readings along these lines:

IMAGE- Parallel book covers- 'The Mystery of the Quantum World' and (adapted) 'The Stars My Destination'

For pure mathematics, rather than theories of the physical world, 
see the properties of the cube illustrated on the second (altered
book cover above.

Tuesday, January 8, 2013

Vermont Throws Itself Together

Filed under: General — Tags: — m759 @ 7:00 PM

"The way, when we climb a mountain,
  Vermont throws itself together"

— Wallace Stevens, "July Mountain"

For another view of reality in New Haven, see the
brief biography of Vermont poet Frances Frost
at the Yale University Library.  From that biography:

"She was survived by her son, the poet Paul Blackburn,
and by her daughter, Sister Marguerite of the Order
of St. Joseph
."

See also a figure from The New York Times  published
online on Epiphany, 2013:

Monday, November 19, 2012

Poetry and Truth

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

From today's noon post

"In all his poems with all their enchantments
for the poet himself, there is the final enchantment
that they are true. The significance of the poetic act
then is that it is evidence. It is instance and illustration.
It is an illumination of a surface,
the movement of a self in the rock.
Above all it is a new engagement with life.
It is that miracle to which the true faith of the poet
attaches itself."

— Wallace Stevens at Bard College, March 30, 1951

Stevens also said at Bard that

"When Joan of Arc said: 

Have no fear: what I do, I do by command.
My brothers of Paradise tell me what I have to do.

these words were the words of an hallucination.
No matter what her brothers of Paradise drove her to do,
what she did was never a poetic act of faith in reality
because it could not be."

There are those who would dispute this.

Some related material:

"Ageometretos me eisito."—
"Let no one ignorant of geometry enter."—
Said to be a saying of Plato, part of the
seal of the American Mathematical Society—

A poetic approach to geometry—

"A surface" and "the rock," from All Saints' Day, 2012

Spaces as Hypercubes

— and from 1981—

http://www.log24.com/log/pix09/090217-SolidSymmetry.jpg

Some mathematical background for poets in Purgatory—

"… the Klein correspondence underlies Conwell's discussion 
of eight heptads. These play an important role in another
correspondence, illustrated in the Miracle Octad Generator
of R. T. Curtis, that may be used to picture actions
of the large Mathieu group M24."

Wednesday, February 8, 2012

Old Sport

Filed under: General — m759 @ 7:11 PM

From yesterday's Random Walk

IMAGE- Wallace Stevens, Collected Poems, page 474- 'An Ordinary Evening in New Haven,' Canto XIII
Followup—

IMAGE- NY lottery midday Wed., Feb. 8, 2012- 474, 1922

"Oh, hello, old sport."

The Great Gatsby

Tuesday, February 7, 2012

Random Walk

Filed under: General — m759 @ 9:48 AM

New York Lottery, evening of 
Monday, February 6th, 2012:
558 and 0608.

See also posts  558 and 0608.

IMAGE- An Ordinary Evening in New Haven, Canto XIII, by Wallace Stevens

Saturday, October 8, 2011

An Ordinary Evening in Hartford

Filed under: General — Tags: , — m759 @ 7:59 AM

From Rebecca Goldstein's Talks and Appearances page—

• "36 (Bad) Arguments for the Existence of God,"
   Annual Meeting of the Freedom from Religion Foundation,
   Marriot, Hartford, CT, Oct 7 [2011], 7 PM

From Wallace Stevens

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

For those who prefer greater depth on Yom Kippur, yesterday's cinematic link suggests…

"Yo sé de un laberinto griego que es una línea única, recta."
 —Borges, "La Muerte y la Brújula " ("Death and the Compass")

See also Alpha and Omega (Sept. 18, 2011) and some context from 1931.

Thursday, September 1, 2011

Boundary (continued*)

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

It is now midnight. Yesterday was Odin's Day. Today is Thor's Day.

From a weblog post on Captain America and Thor

"While all this [Captain America] is happening an SS officer, Johann Schmidt (Hugo Weaving), has found a religious artefact called the Tesseract which Schmidt describes as 'the jewel of Odin’s treasure room,' linking it in with the Thor storyline."

That's Entertainment  weblog, August 14, 2011

From Wallace Stevens, "An Ordinary Evening in New Haven," Canto III—

The point of vision and desire are the same.
It is to the hero of midnight that we pray
On a hill of stones to make beau mont thereof.

Captain America opened in the United States on Friday, July 22, 2011.

Thor opened in the United States on Friday, May 6, 2011.

"There is  such a thing as a tesseract." —A Wrinkle in Time

* Continued from August 30.

Wednesday, June 29, 2011

The Shattered Mind

Filed under: General,Geometry — Tags: — m759 @ 12:26 AM

For St. Peter's Day

"For Stevens, the poem 'makes meanings of the rock.'
In the mind, 'its barrenness becomes a thousand things/
And so exists no more.' In fact, in a peculiar irony
that only a poet with Stevens's particular notion
of the imagination's function could develop,
the rock becomes the mind itself, shattered
into such diamond-faceted brilliance
that it encompasses all possibilities for human thought…."

—A discussion of Stevens's late poem "The Rock" (1954)
    in Wallace Stevens: A World of Transforming Shapes,
    by Alan D. Perlis, Bucknell University Press, 1976, p. 120

Related material on transforming shapes:

The Diamond 16 Puzzle  and…

IMAGE- The URL for permutationpuzzles.org, with favicon

Wednesday, June 15, 2011

A for Anastasios

Filed under: General,Geometry — m759 @ 7:59 PM

The title was suggested by this evening's 4-digit NY lottery number.

"… the rhetoric might be a bit over the top."

http://www.log24.com/log/pix11A/110615-NYlottery.jpg

According to Amazon.com, 2198 (i.e., 2/1/98) was the publication
date of Geometry of Vector Sheaves , Volume I, by Anastasios Mallios.

Related material—

The question of S.S. Chern quoted here June 10: —
"What is Geometry?"— and the remark by Stevens that
accompanied the quotation—

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."
— Wallace Stevens,
“An Ordinary Evening in New Haven” VI

The work of Mallios in pure mathematics cited above seems
quite respectable (unlike his later remarks on physics).
His Vector Sheaves  appears to be trying to explore new territory;
hence the relevance of Stevens's "Alpha." See also the phrase
"A-Invariance" in an undated preprint by Mallios*.

For the evening 3-digit number, 533, see a Stevens poem—

http://www.log24.com/log/pix11A/110615-RiverOfRivers.jpg

This meditation by Stevens is related to the female form of Mallios's Christian name.

As for the afternoon numbers, see "62" in The Beauty Test (May 23, 2007), Geometry and Death, and "9181" as the date 9/1/81.

* Later published in International Journal of Theoretical Physics , Vol. 47, No. 7, cover date 2008-07-01

Friday, June 10, 2011

Hierophant

Filed under: General — Tags: , , — m759 @ 7:59 PM

Some background for yesterday’s posts:

Midrash for Gnostics and related notes,
as well as yesterday’s New York Lottery.

….    “We seek
The poem of pure reality, untouched
By trope or deviation, straight to the word,
Straight to the transfixing object, to the object
At the exactest point at which it is itself,
Transfixing by being purely what it is….”
— Wallace Stevens (1879-1955),
“An Ordinary Evening in New Haven” IX

“Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals.”
— Wallace Stevens,
“An Ordinary Evening in New Haven” VI

Wikipedia

“A hierophant is a person who brings religious congregants into the presence of that which is deemed holy . The word comes from Ancient Greece, where it was constructed from the combination of ta hiera , ‘the holy,’ and phainein , ‘to show.’ In Attica it was the title of the chief priest at the Eleusinian Mysteries. A hierophant is an interpreter of sacred mysteries and arcane principles.”

Weyl as Alpha, Chern as Omega—

(Click to enlarge.)

http://www.log24.com/log/pix11A/110610-WeylChernSm.jpg

Postscript for Ellen Page, star of “Smart People
and of “X-Men: The Last Stand“— a different  page 679.

Your assignment, should you choose to accept it—

Interpret today’s  NY lottery numbers— Midday 815, Evening 888.

My own bias is toward 815 as 8/15 and 888 as a trinity,
but there may be less obvious and more interesting approaches.

Wednesday, May 11, 2011

Succor

Filed under: General — m759 @ 7:00 AM

This morning's online New York Times  on Paul Simon's latest show

"Here was salvation and succor…."

The review mentions a song from Simon's new album that he did not  play at last night's show—

The Afterlife.

Salvation:

After you climb up the ladder of time
The Lord God is near
Face-to-face in the vastness of space
Your words disappear

Succor:

You got to fill out a form first
And then you wait in the line

Simon is an accomplished poet, but I prefer Wallace Stevens.

                         … A figure like Ecclesiast,
Rugged and luminous, chants in the dark
A text that is an answer, although obscure.

— Wallace Stevens, “An Ordinary Evening in New Haven

For clues about such a text, see yesterday's New York Lottery numbers.

http://www.log24.com/log/pix11A/110511-ny_lottery_header_bg.gif

Thursday, May 5, 2011

Beyond Forgetfulness

Filed under: General,Geometry — Tags: , — m759 @ 10:10 AM

From this journal on July 23, 2007

It is not enough to cover the rock with leaves.
We must be cured of it by a cure of the ground
Or a cure of ourselves, that is equal to a cure

Of the ground, a cure beyond forgetfulness.
And yet the leaves, if they broke into bud,
If they broke into bloom, if they bore fruit
,

And if we ate the incipient colorings
Of their fresh culls might be a cure of the ground.

– Wallace Stevens, "The Rock"

This quotation from Stevens (Harvard class of 1901) was posted here on when Daniel Radcliffe (i.e., Harry Potter) turned 18 in July 2007.

Other material from that post suggests it is time for a review of magic at Harvard.

On September 9, 2007, President Faust of Harvard

"encouraged the incoming class to explore Harvard’s many opportunities.

'Think of it as a treasure room of hidden objects Harry discovers at Hogwarts,' Faust said."

That class is now about to graduate.

It is not clear what "hidden objects" it will take from four years in the Harvard treasure room.

Perhaps the following from a book published in 1985 will help…

http://www.log24.com/log/pix11A/110505-MetamagicalIntro.gif

The March 8, 2011, Harvard Crimson  illustrates a central topic of Metamagical Themas , the Rubik's Cube—

http://www.log24.com/log/pix11A/110427-CrimsonAtlas300w.jpg

Hofstadter in 1985 offered a similar picture—

http://www.log24.com/log/pix11A/110505-RubikGlobe.gif

Hofstadter asks in his Metamagical  introduction, "How can both Rubik's Cube and nuclear Armageddon be discussed at equal length in one book by one author?"

For a different approach to such a discussion, see Paradigms Lost, a post made here a few hours before the March 11, 2011, Japanese earthquake, tsunami, and nuclear disaster—

http://www.log24.com/log/pix11A/110427-ParadigmsLost.jpg

Whether Paradigms Lost is beyond forgetfulness is open to question.

Perhaps a later post, in the lighthearted spirit of Faust, will help. See April 20th's "Ready When You Are, C.B."

Sunday, April 24, 2011

Romancing the Metaphor

Filed under: General — Tags: — m759 @ 2:24 PM

Background —

From a 1990 novel —
http://www.log24.com/log/pix11A/110424-StoneJunction.jpg

Saturday, February 5, 2011

Zen and the Art of Philosophy

Filed under: General,Geometry — m759 @ 12:00 PM

Wallace Stevens Concordance

An Ordinary Evening in New Haven
line 540 (xxx.18): In which hundreds of eyes, in one mind, see at once.

The cover art of a 1976 monograph, "Diamond Theory," was described in this morning's post.

As Madeleine L'Engle noted in 1976, the cover art resembles the character Proginoskes in her novel A Wind in the Door.

A search today for Proginoskes yields a description by Brendan Kidwell

http://www.log24.com/log/pix11/110205-KidwellProginoskesArt.png

A link at Kidwell's site leads to a weblog by Jeff Atwood, a founder of Stack Overflow, a programmers' question-and-answer site.
(Stack Overflow is said to have inspired the similar site for mathematicians, Math Overflow.)

Yesterday Atwood discussed technical writing.

This suggests a look at Robert M. Pirsig on that subject in his 1974 philosophical novel Zen and the Art of Motorcycle Maintenance.

(See also a document on Pirsig's technical-writing background.)

Pirsig describes his novel as "a sort of Chautauqua."

This, together with the Stevens and Proginoskes quotes above, leads back to the Log24 Feb. 1 post The Search.

An image from that post (click to enlarge)—

http://www.log24.com/log/pix11/110201-TwoViews-300w.jpg

Here the apparently fragmented nature of the set of
images imagined as rising above the podium of the
Hall of Philosophy at Chautauqua rather naturally
echoes Stevens's "hundreds of eyes" remark.

Thursday, February 3, 2011

Brightness at Noon (continued)

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

"The predicate of bright origin"

— A phrase of Wallace Stevens from "An Ordinary Evening in New Haven" (1950)

Perhaps the predicate Stevens means is "bright."

If so, an apt illustration can be found on the cover of
the 1943 first edition of Hesse's Glasperlenspiel

http://www.log24.com/log/pix11/110203-Glasperlenspiel1943-Detail.jpg

See also Stevens's use of the phrase "heaven-haven" in "Notes" (1942),
the original plan of New Haven, and related scholia in this journal.

http://www.log24.com/log/pix11/110203-Scholia.jpg

… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

– Rubén Darío

An academic work from 2003 discusses Stevens's "Notes" as
"a perfect geometric whole."

Note that "perfect" means "complete, finished, done."

Tuesday, February 1, 2011

The Search

Filed under: General — m759 @ 10:01 AM

An image suggested by last night's PBS hour "Chautauqua: An American Narrative"—

http://www.log24.com/log/pix11/110201-TwoViews.jpg

Click for larger versions of the image search and of the Hall of Philosophy.

Both the screenshot and the Chautauqua photo (by jbi46 at flickr.com) were taken on July 19th, 2010.

The screenshot appeared in the post "Pediments of Appearance" (which also included two much less complex images).

Some background —  A webpage on  Analytical Cubism and a related search in this journal.

From Wallace Stevens, who appears at top center in the image above—

An Ordinary Evening in New Haven, XXII

Professor Eucalyptus said, “The search
For reality is as momentous as
The search for god.” It is the philosopher’s search

For an interior made exterior
And the poet’s search for the same exterior made
Interior: breathless things broodingly abreath

With the Inhalations of original cold
And of original earliness. Yet the sense
Of cold and earliness is a daily sense,

Not the predicate of bright origin.
Creation is not renewed by images
Of lone wanderers. To re-create, to use

The cold and earliness and bright origin
Is to search. Likewise to say of the evening star,
The most ancient light in the most ancient sky,

That it is wholly an inner light, that it shines
From the sleepy bosom of the real, re-creates,
Searches a possible for its possibleness.

Monday, June 21, 2010

Test

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

From a post by Ivars Peterson, Director
of Publications and Communications at
the Mathematical Association of America,
at 19:19 UTC on June 19, 2010—

Exterior panels and detail of panel,
Michener Gallery at Blanton Museum
in Austin, Texas—

http://www.log24.com/log/pix10A/100621-MichenerGalleryPanel.jpg

Peterson associates the four-diamond figure
with the Pythagorean theorem.

A more relevant association is the
four-diamond view of a tesseract shown here
on June 19 (the same date as Peterson's post)
in the "Imago Creationis" post—

Image-- The Four-Diamond Tesseract

This figure is relevant because of a
tesseract sculpture by Peter Forakis—

http://www.log24.com/log/pix09A/091220-ForakisHypercube.jpg

This sculpture was apparently shown in the above
building— the Blanton Museum's Michener gallery—
as part of the "Reimagining Space" exhibition,
September 28, 2008-January 18, 2009.

The exhibition was organized by
Linda Dalrymple Henderson, Centennial Professor
in Art History at the University of Texas at Austin
and author of The Fourth Dimension and
Non-Euclidean Geometry in Modern Art

(Princeton University Press, 1983;
new ed., MIT Press, 2009).

For the sculptor Forakis in this journal,
see "The Test" (December 20, 2009).

"There is  such a thing
as a tesseract."
A Wrinkle in TIme   

Saturday, June 19, 2010

Imago Creationis

Filed under: General,Geometry — Tags: , , , , — m759 @ 6:00 PM

Image-- The Four-Diamond Tesseract

In the above view, four of the tesseract's 16
vertices are overlaid by other vertices.
For views that are more complete and
moveable, see Smith's tesseract page.

Four-Part Tesseract Divisions

http://www.log24.com/log/pix10A/100619-TesseractAnd4x4.gif

The above figure shows how four-part partitions
of the 16 vertices  of a tesseract in an infinite
Euclidean  space are related to four-part partitions
of the 16 points  in a finite Galois  space

Euclidean spaces versus Galois spaces
in a larger context—

 

 


Infinite versus Finite

The central aim of Western religion —

"Each of us has something to offer the Creator...
the bridging of
                 masculine and feminine,
                      life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist  (1998)

The central aim of Western philosophy —

              Dualities of Pythagoras
              as reconstructed by Aristotle:
                 Limited     Unlimited
                     Odd     Even
                    Male     Female
                   Light      Dark
                Straight    Curved
                  ... and so on ....

"Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy."
— Jamie James in The Music of the Spheres  (1993)

Another picture related to philosophy and religion—

Jung's Four-Diamond Figure from Aion

http://www.log24.com/log/pix10A/100615-JungImago.gif

This figure was devised by Jung
to represent the Self. Compare the
remarks of Paul Valéry on the Self—

Flight from Eden: The Origins of Modern Literary Criticism and Theory, by Steven Cassedy, U. of California Press, 1990, pages 156-157—

 

 

Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. "Every act of understanding is based on a group," he says (C, 1:331). "My specialty— reducing everything to the study of a system closed on itself and finite" (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one "group" undergoes a "transformation" and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: "The S[elf] is invariant, origin, locus or field, it's a functional property of consciousness" (C, 15:170 [2:315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind's momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. "Mathematical science…  reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind" (O, 1:36). "Psychology is a theory of transformations, we just need to isolate the invariants and the groups" (C, 1:915). "Man is a system that transforms itself" (C, 2:896).

Notes:

  Paul Valéry, Oeuvres  (Paris: Pléiade, 1957-60)

C   Valéry, Cahiers, 29 vols. (Paris: Centre National de le Recherche Scientifique, 1957-61)

Note also the remarks of George David Birkhoff at Rice University
in 1940 (pdf) on Galois's theory of groups and the related
"theory of ambiguity" in Galois's testamentary letter—

… metaphysical reasoning always relies on the Principle of Sufficient Reason, and… the true meaning of this Principle is to be found in the “Theory of Ambiguity” and in the associated mathematical “Theory of Groups.”

If I were a Leibnizian mystic, believing in his “preestablished harmony,” and the “best possible world” so satirized by Voltaire in “Candide,” I would say that the metaphysical importance of the Principle of Sufficient Reason and the cognate Theory of Groups arises from the fact that God thinks multi-dimensionally* whereas men can only think in linear syllogistic series, and the Theory of Groups is the appropriate instrument of thought to remedy our deficiency in this respect.

* That is, uses multi-dimensional symbols beyond our grasp.

Related material:

Imago Creationis

A medal designed by Leibniz to show how
binary arithmetic mirrors the creation by God
of something (1) from nothing (0).

http://www.log24.com/log/pix10A/100618-LeibnizMedaille.jpg

Another array of 16 strings of 0's and 1's, this time
regarded as coordinates rather than binary numbers—

Frame of Reference

http://www.log24.com/log/pix10A/100619-ReferenceFrame.gif

The Diamond Theorem

http://www.log24.com/log/pix10A/100619-Dtheorem.gif

Some context by a British mathematician —

http://www.log24.com/log/pix10A/100619-Cameron.gif

Imago

by Wallace Stevens

Who can pick up the weight of Britain, 
Who can move the German load 
Or say to the French here is France again? 
Imago. Imago. Imago. 

It is nothing, no great thing, nor man 
Of ten brilliancies of battered gold 
And fortunate stone. It moves its parade 
Of motions in the mind and heart, 

A gorgeous fortitude. Medium man 
In February hears the imagination's hymns 
And sees its images, its motions 
And multitudes of motions 

And feels the imagination's mercies, 
In a season more than sun and south wind, 
Something returning from a deeper quarter, 
A glacier running through delirium, 

Making this heavy rock a place, 
Which is not of our lives composed . . . 
Lightly and lightly, O my land, 
Move lightly through the air again.

Wednesday, August 26, 2009

Wednesday August 26, 2009

Filed under: General — m759 @ 9:00 AM
A Puritan Settlement
in memory of
Sen. Edward Kennedy

“When New Haven was founded, the city was laid out into a grid of nine squares surrounded by a great wilderness.
    Last year [2000] History of Art Professor Emeritus Vincent Scully said the original town plan reflected a feeling that the new city should be sacred.
    Scully said the colony’s founders thought of their new Puritan settlement as a ‘nine-square paradise on Earth, heaven on earth, New Haven, New Jerusalem.'”

Yale Daily News, Jan. 11, 2001

“Real and unreal are two in one:
    New Haven
 Before and after one arrives….”

 — Wallace Stevens,
    “An Ordinary Evening
     in New Haven,” XXVIII

See also Art and Man at Yale.

Friday, April 17, 2009

Friday April 17, 2009

Filed under: General,Geometry — Tags: — m759 @ 10:31 AM

Begettings of
the Broken Bold

Thanks for the following
quotation (“Non deve…
nella testa“) go to the
weblog writer who signs
himself “Conrad H. Roth.”

Autobiography
of Goethe

(Vol. II, London, Bell & Daldy,
1868, at Google Books):

… Yesterday I took leave of my Captain, with a promise of visiting him at Bologna on my return. He is a true

A PAPAL SOLDIER’S IDEAS OF PROTESTANTS 339

representative of the majority of his countrymen. Here, however, I would record a peculiarity which personally distinguished him. As I often sat quiet and lost in thought he once exclaimed “Che pensa? non deve mai pensar l’uomo, pensando s’invecchia;” which being interpreted is as much as to say, “What are you thinking about: a man ought never to think; thinking makes one old.” And now for another apophthegm of his; “Non deve fermarsi l’uomo in una sola cosa, perche allora divien matto; bisogna aver mille cose, una confusione nella testa;” in plain English, “A man ought not to rivet his thoughts exclusively on any one thing, otherwise he is sure to go mad; he ought to have in his head a thousand things, a regular medley.”

Certainly the good man could not know that the very thing that made me so thoughtful was my having my head mazed by a regular confusion of things, old and new. The following anecdote will serve to elucidate still more clearly the mental character of an Italian of this class. Having soon discovered that I was a Protestant, he observed after some circumlocution, that he hoped I would allow him to ask me a few questions, for he had heard such strange things about us Protestants that he wished to know for a certainty what to think of us.

Notes for Roth:

Roth and Corleone in Havana

The title of this entry,
“Begettings of the Broken Bold,”
is from Wallace Stevens’s
“The Owl in the Sarcophagus”–

This was peace after death, the brother of sleep,
The inhuman brother so much like, so near,
Yet vested in a foreign absolute,

Adorned with cryptic stones and sliding shines,
An immaculate personage in nothingness,
With the whole spirit sparkling in its cloth,

Generations of the imagination piled
In the manner of its stitchings, of its thread,
In the weaving round the wonder of its need,

And the first flowers upon it, an alphabet
By which to spell out holy doom and end,
A bee for the remembering of happiness.

Peace stood with our last blood adorned, last mind,
Damasked in the originals of green,
A thousand begettings of the broken bold.

This is that figure stationed at our end,
Always, in brilliance, fatal, final, formed
Out of our lives to keep us in our death....

Related material:

  • Yesterday’s entry on Giordano Bruno and the Geometry of Language
  • James Joyce and Heraldry
  • “One might say that he [Joyce] invented a non-Euclidean geometry of language; and that he worked over it with doggedness and devotion….” —Unsigned notice in The New Republic, 20 January 1941
  • Joyce’s “collideorscape” (scroll down for a citation)
  • “A Hanukkah Tale” (Log24, Dec. 22, 2008)
  • Stevens’s phrase from “An Ordinary Evening in New Haven(Canto XXV)

Some further context:

Roth’s entry of Nov. 3, 2006–
Why blog, sinners?“–
and Log24 on that date:
First to Illuminate.”

Tuesday, February 24, 2009

Tuesday February 24, 2009

Filed under: General,Geometry — Tags: — m759 @ 1:00 PM
 
Hollywood Nihilism
Meets
Pantheistic Solipsism

Tina Fey to Steve Martin
at the Oscars:
"Oh, Steve, no one wants
 to hear about our religion
… that we made up."

Tina Fey and Steve Martin at the 2009 Oscars

From Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 117:

… in 'The Pediment of Appearance,' a slight narrative poem in Transport to Summer

 A group of young men enter some woods 'Hunting for the great ornament, The pediment of appearance.' Though moving through the natural world, the young men seek the artificial, or pure form, believing that in discovering this pediment, this distillation of the real, they will also discover the 'savage transparence,' the rude source of human life. In Stevens's world, such a search is futile, since it is only through observing nature that one reaches beyond it to pure form. As if to demonstrate the degree to which the young men's search is misaligned, Stevens says of them that 'they go crying/The world is myself, life is myself,' believing that what surrounds them is immaterial. Such a proclamation is a cardinal violation of Stevens's principles of the imagination.


Superficially the young men's philosophy seems to resemble what Wikipedia calls "pantheistic solipsism"– noting, however, that "This article has multiple issues."

As, indeed, does pantheistic solipsism– a philosophy (properly called "eschatological pantheistic multiple-ego solipsism") devised, with tongue in cheek, by science-fiction writer Robert A. Heinlein.

Despite their preoccupation with solipsism, Heinlein and Stevens point, each in his own poetic way, to a highly non-solipsistic topic from pure mathematics that is, unlike the religion of Martin and Fey, not made up– namely, the properties of space.

Heinlein:

"Sharpie, we have condensed six dimensions into four, then we either work by analogy into six, or we have to use math that apparently nobody but Jake and my cousin Ed understands. Unless you can think of some way to project six dimensions into three– you seem to be smart at such projections."
    I closed my eyes and thought hard. "Zebbie, I don't think it can be done. Maybe Escher could have done it."

Stevens:

A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:

For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought:

The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...

The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,

Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.

The rock is the habitation of the whole,
Its strength and measure, that which is near,
     point A
In a perspective that begins again

At B: the origin of the mango's rind.

                    (Collected Poems, 528)

Stevens's rock is associated with empty space, a concept that suggests "nothingness" to one literary critic:

B. J. Leggett, "Stevens's Late Poetry" in The Cambridge Companion to Wallace Stevens— On the poem "The Rock":

"… the barren rock of the title is Stevens's symbol for the nothingness that underlies all existence, 'That in which space itself is contained'….  Its subject is its speaker's sense of nothingness and his need to be cured of it."

This interpretation might appeal to Joan Didion, who, as author of the classic novel Play It As It Lays, is perhaps the world's leading expert on Hollywood nihilism.

More positively…

Space is, of course, also a topic
in pure mathematics…
For instance, the 6-dimensional
affine space
(or the corresponding
5-dimensional projective space)

The 4x4x4 cube

over the two-element Galois field
can be viewed as an illustration of
Stevens's metaphor in "The Rock."

Heinlein should perhaps have had in mind the Klein correspondence when he discussed "some way to project six dimensions into three." While such a projection is of course trivial for anyone who has taken an undergraduate course in linear algebra, the following remarks by Philippe Cara present a much more meaningful mapping, using the Klein correspondence, of structures in six (affine) dimensions to structures in three.

Cara:

Philippe Cara on the Klein correspondence
Here the 6-dimensional affine
space contains the 63 points
of PG(5, 2), plus the origin, and
the 3-dimensional affine
space contains as its 8 points
Conwell's eight "heptads," as in
Generating the Octad Generator.

Tuesday, February 17, 2009

Tuesday February 17, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 1:06 PM

Diamond-Faceted:
Transformations
of the Rock

A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:

For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought:

The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...

The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,

Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.

The rock is the habitation of the whole,
Its strength and measure, that which is near,
     point A
In a perspective that begins again

At B: the origin of the mango's rind.

                    (Collected Poems, 528)

A mathematical version of
this poetic concept appears
in a rather cryptic note
from 1981 written with
Stevens's poem in mind:

http://www.log24.com/log/pix09/090217-SolidSymmetry.jpg

For some explanation of the
groups of 8 and 24
motions referred to in the note,
see an earlier note from 1981.

For the Perlis "diamond facets,"
see the Diamond 16 Puzzle.

For a much larger group
of motions, see
Solomon's Cube.

As for "the mind itself"
and "possibilities for
human thought," see
Geometry of the I Ching.

Friday, March 7, 2008

Friday March 7, 2008

Filed under: General — m759 @ 8:28 PM
Tony Rome, Jill St. John, and NY Lottery for March 7, 2008: Mid-day 162, Evening 323

“We keep coming back
 and coming back
 To the real: to the hotel
            instead of the hymns….”

    — Wallace Stevens,  
    “An Ordinary Evening
   in New Haven

Monday, July 23, 2007

Monday July 23, 2007

Filed under: General,Geometry — Tags: , , , , — m759 @ 8:00 AM
Daniel Radcliffe
is 18 today.
Daniel Radcliffe as Harry Potter

Greetings.

“The greatest sorcerer (writes Novalis memorably)
would be the one who bewitched himself to the point of
taking his own phantasmagorias for autonomous apparitions.
Would not this be true of us?”

Jorge Luis Borges, “Avatars of the Tortoise”

El mayor hechicero (escribe memorablemente Novalis)
sería el que se hechizara hasta el punto de
tomar sus propias fantasmagorías por apariciones autónomas.
¿No sería este nuestro caso?”

Jorge Luis Borges, “Los Avatares de la Tortuga

Autonomous Apparition

At Midsummer Noon:

“In Many Dimensions (1931)
Williams sets before his reader the
mysterious Stone of King Solomon,
an image he probably drew from
a brief description in Waite’s
The Holy Kabbalah (1929) of
a supernatural cubic stone
on which was inscribed
‘the Divine Name.’”
The image “http://www.log24.com/log/pix07/070624-Waite.gif” cannot be displayed, because it contains errors.
Related material:
It is not enough to cover the rock with leaves.
We must be cured of it by a cure of the ground
Or a cure of ourselves, that is equal to a cure 

Of the ground, a cure beyond forgetfulness.
And yet the leaves, if they broke into bud,
If they broke into bloom, if they bore fruit,

And if we ate the incipient colorings
Of their fresh culls might be a cure of the ground.

– Wallace Stevens, “The Rock”

See also
as well as
Hofstadter on
his magnum opus:
“… I realized that to me,
Gödel and Escher and Bach
were only shadows
cast in different directions by
some central solid essence.
I tried to reconstruct
the central object, and
came up with this book.”
Goedel Escher Bach coverHofstadter’s cover.

Here are three patterns,
“shadows” of a sort,
derived from a different
“central object”:
Faces of Solomon's Cube, related to Escher's 'Verbum'

Click on image for details.

Monday, July 2, 2007

Monday July 2, 2007

Filed under: General,Geometry — m759 @ 8:28 PM

A figure like Ecclesiast/
Rugged and luminous,
 chants in the dark/
A text that is an answer,
although obscure.

— Wallace Stevens,
"An Ordinary Evening
in New Haven"

A Text

Time and Chance
today in the
Keystone State:

PA Lottery July 2, 2007: Mid-day 004, Evening 802


From 8/02
in 2005:

50 Years Ago
on this date, poet
Wallace Stevens died.

Memorial: at the
Wallace Stevens
Concordance,
enter center.


Result:

The Man with the Blue Guitar
line 150 (xiii.6): The heraldic center of the world

Human Arrangement
line 13: The center of transformations that

This Solitude of Cataracts
line 18: Breathing his bronzen breath at the azury center of time.

A Primitive Like an Orb
line 1 (i.1): The essential poem at the center of things,
line 87 (xi.7): At the center on the horizon, concentrum, grave

Reply to Papini
line 33 (ii.15): And final. This is the center. The poet is

Study of Images II
line 7: As if the center of images had its

An Ordinary Evening in New Haven
line 291 (xvii.3): It fails. The strength at the center is serious.
line 371 (xxi.11): At the center, the object of the will, this place,

Things of August
line 154 (ix.18): At the center of the unintelligible,

The Hermitage at the Center
Title: The Hermitage at the Center

Owl's Clover, The Old Woman and the Statue (OP)
line 13 (ii.9): At the center of the mass, the haunches low,

The Sail of Ulysses (OP)
line 50 (iv.6): The center of the self, the self

Someone Puts a Pineapple Together (NA)
line 6 (i.6): The angel at the center of this rind,

Of Ideal Time and Choice (NA)
line 29: At last, the center of resemblance, found
line 32: Stand at the center of ideal time,


For a text on today's
mid-day number, see

  Theme and Variations.

Tuesday, February 6, 2007

Tuesday February 6, 2007

Filed under: General,Geometry — Tags: — m759 @ 8:00 AM
The Poetics of Space

The title is from Bachelard.
I prefer Stevens:

The rock is the habitation of the whole,
Its strength and measure, that which is near, point A
In a perspective that begins again

At B:  the origin of the mango's rind.
It is the rock where tranquil must adduce
Its tranquil self, the main of things, the mind,

The starting point of the human and the end,
That in which space itself is contained, the gate
To the enclosure, day, the things illumined

By day, night and that which night illumines,
Night and its midnight-minting fragrances,
Night's hymn of the rock, as in a vivid sleep.

— Wallace Stevens,
   "The Rock," 1954

Joan Ockman in Harvard Design Magazine (Fall 1998):

"'We are far removed from any reference to simple geometrical forms,' Bachelard wrote…."

No, we are not. See Log24, Christmas 2005: 

Compare and contrast:

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

 

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

 

(Click on pictures for details.)

More on Bachelard from Harvard Design Magazine:

"The project of discerning a loi des quatre éléments would preoccupy him until his death…."

For such a loi, see Theme and Variations and…

The image “http://www.log24.com/log/pix07/070206-Elements.gif” cannot be displayed, because it contains errors.

(Click on design for details.)

Thought for Today:
"If you can talk brilliantly
about a problem, it can create
the consoling illusion that
it has been mastered."
— Stanley Kubrick, American
movie director (1928-1999).

(AP, "Today in History,"
February 6, 2007)

Sunday, January 7, 2007

Sunday January 7, 2007

Filed under: General,Geometry — m759 @ 12:00 PM

Thursday, April 7, 2005  7:26 PM

In the Details

Wallace Stevens,
An Ordinary Evening in New Haven:

XXII

Professor Eucalyptus said, “The search
For reality is as momentous as
The search for God.”  It is the philosopher’s search
For an interior made exterior
And the poet’s search for the same exterior made
Interior….

   … Likewise to say of the evening star,
The most ancient light in the most ancient sky,
That it is wholly an inner light, that it shines
From the sleepy bosom of the real, re-creates,
Searches a possible for its possibleness.

Julie Taymor, “Skewed Mirrors” interview:

“… they were performing for God. Now God can mean whatever you want it to mean. But for me, I understood it so totally. The detail….

They did it from the inside to the outside. And from the outside to the in. And that profoundly moved me then. It was…it was the most important thing that I ever experienced.”

“Skewed Mirrors”
illustrated:


Click on the above to enlarge.

Details:

The image “http://www.log24.com/log/pix05/050407-Messick2.png” cannot be displayed, because it contains errors.

The above may be of interest to students
of  iconology — what Dan Brown in
The Da Vinci Code calls “symbology” —
and of redheads.

The artist of Details,
“Brenda Starr” creator
Dale Messick, died on Tuesday,
April 5, 2005, at 98.

The image “http://www.log24.com/log/pix05/050407-Messick.jpg” cannot be displayed, because it contains errors.
AP Photo
Dale Messick in 1982

For further details on
April 5, see
Art History:
The Pope of Hope

Saturday, December 2, 2006

Saturday December 2, 2006

Filed under: General,Geometry — m759 @ 1:29 AM

Venus at
St. Anne's
,
continued

In honor of
the film "Bobby,"
now playing.

("Venus at St. Anne's"
is the title of the final
chapter of
the C. S. Lewis classic
That Hideous Strength.)

Star and Diamond

Symbol of Venus
and
Symbol of Plato

Related symbols:

Marilyn Monroe

Representation of Plato's Academy

Click on pictures
for details related tp
the Feast of St. Anne
(July 26).

"The best theology today,
in its repudiation of a
rhetorical religious idealism,
finds itself in agreement
with a recurrent note
in contemporary poetry….

We keep coming back
and coming back/
To the real: to the hotel
instead of the hymns/
That fall upon it
out of the wind.  We seek/
… Nothing beyond reality.
Within it/
Everything,
the spirit’s alchemicana….

(From 'An Ordinary Evening
in New Haven,'
in The Collected Poems
of Wallace Stevens….
)

… Not grim/
Reality, but reality grimly seen….

(Ibid.)"

— "The Church's
New Concern with the Arts
,"
by Amos N. Wilder,
Hollis Professor
of Divinity, Emeritus,
at Harvard Divinity School,
in Christianity and Crisis,
February 18, 1957.

 

 

 

"All the truth in the world
adds up to one big lie."

— Dylan, "Things Have Changed"
 

Saturday, August 26, 2006

Saturday August 26, 2006

Filed under: General,Geometry — Tags: — m759 @ 8:00 PM
Philosopher's Rock
 
(continued from  

previous entry)

"Alcatraz, Spanish for pelican, was named Isla de los Alcatraces after the birds that were the island's only inhabitants." —Bay City Guide

Related material

Thomas Kuhn's "Pelican Brief":

"… the Philosopher’s Stone was a psychic rather than a physical product.  It symbolized one’s Self…."

Philosopher's Pelican:

"The formula presents a symbol of the self…."

Jung and the Imago Dei:

"… Jung presents a diagram to illustrate the dynamic movements of the self…."

…the movement of
a self in the rock…

Stevens, The Rock, and Piranesi's Prisons

Wallace Stevens:
The Poems of Our Climate
,
by Harold Bloom,
Cornell U. Press, 1977

Sunday, January 29, 2006

Sunday January 29, 2006

Filed under: General — m759 @ 10:00 AM
New Haven

The image “http://www.log24.com/log/pix06/060130-NewHaven11.gif” cannot be displayed, because it contains errors.

The eye’s plain version is a thing apart,
The vulgate of experience.  Of this,
A few words, an and yet, and yet, and yet–

As part of the never-ending meditation,
Part of the question that is a giant himself:
Of what is this house composed if not of the sun,

These houses, these difficult objects, dilapidate
Appearances of what appearances,
Words, lines, not meanings, not communications,

Dark things without a double, after all,
Unless a second giant kills the first–
A recent imagining of reality,

Much like a new resemblance of the sun,
Down-pouring, up-springing and inevitable,
A larger poem for a larger audience,

As if the crude collops came together as one,
A mythological form, a festival sphere,
A great bosom, beard and being, alive with age.

— Wallace Stevens, opening lines of
    “An Ordinary Evening in New Haven

Wednesday, January 11, 2006

Wednesday January 11, 2006

Filed under: General,Geometry — Tags: , — m759 @ 10:30 PM

Time in the Rock

"a world of selves trying to remember the self
before the idea of self is lost–

Walk with me world, upon my right hand walk,
speak to me Babel, that I may strive to assemble
of all these syllables a single word
before the purpose of speech is gone."

— Conrad Aiken, "Prelude" (1932),
    later part of "Time in the Rock,
    or Preludes to Definition, XIX" (1936),
    in Selected Poems, Oxford U. Press
    paperback, 2003, page 156

"The rock is the habitation of the whole,
Its strength and measure, that which is near, point A
In a perspective that begins again

At B: the origin of the mango's rind.
It is the rock where tranquil must adduce
Its tranquil self, the main of things, the mind,

The starting point of the human and the end,
That in which space itself is contained, the gate
To the enclosure, day, the things illumined

By day, night and that which night illumines,
Night and its midnight-minting fragrances,
Night's hymn of the rock, as in a vivid sleep."

— Wallace Stevens in The Rock (1954)

"Poetry is an illumination of a surface,
  the movement of a self in the rock."
— Wallace Stevens, introduction to
    The Necessary Angel, 1951
 

Related material:
Jung's Imago and Solomon's Cube.

 

The following may help illuminate the previous entry:

"I want, as a man of the imagination, to write poetry with all the power of a monster equal in strength to that of the monster about whom I write.  I want man's imagination to be completely adequate in the face of reality."

— Wallace Stevens, 1953 (Letters 790)

The "monster" of the previous entry is of course not Reese Witherspoon, but rather Vox Populi itself.

Sunday, October 2, 2005

Sunday October 2, 2005

Filed under: General — m759 @ 1:06 PM

Happy Birthday, Wallace Stevens

Readings for today:

At the Wallace Stevens online concordance, search for X and for primitive.

In the e-book edition of Bester's  The Deceivers,  search for X.

    "We seek
Nothing beyond reality. Within it,

Everything, the spirit's alchemicana
Included, the spirit that goes roundabout
And through included, not merely the visible,

The solid, but the movable, the moment,
The coming on of feasts and the habits of saints,
The pattern of the heavens and high, night air."

Wallace Stevens,
Oct. 2, 1879 – Aug. 2, 1955,
"An Ordinary Evening in New Haven"
IX.1-18, from The Auroras of Autumn,
Knopf, NY (1950)

Related material:

(Added Monday, Oct. 3, 8:45 AM)

"What if Shakespeare had been born in Teaneck, N.J., in 1973?

He would call himself Spear Daddy. His rap would exhibit a profound, nuanced understanding of the frailty of the human condition, exploring the personality in all its bewildering complexity: pretension, pride, vulnerability, emotional treachery, as well as the enduring triumph of love.

Spear Daddy would disappear from the charts in about six weeks."

Gene Weingarten in the Washington Post,
    Sunday, Oct. 2, 2005

Presenting…

Spear Daddy!

'The Deceivers'— A novel by Alfred Bester, author of 'The Stars My Destination

Continuing Bester's Maori theme,
students from Cullinane College:

The image “http://www.log24.com/log/pix05B/051003-Enlarge.jpg” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix05B/051003-CC2.jpg” cannot be displayed, because it contains errors.

(See Literature and Geography.)
 

Saturday, July 30, 2005

Saturday July 30, 2005

Filed under: General — Tags: , — m759 @ 11:21 AM

Born today: Laurence Fishburne

Matrix

"The nine-fold square has centre, periphery, axes and diagonals. But all are present only in their bare essentials. It is also a sequence of eight triads. Four pass through the centre and four do not. This is the garden of Apollo, the field of Reason, sheltered by the Gate from the turmoil of the Delta, with its endless cycles of erasure and reinscription. This is the Temple of Solomon, as inscribed, for example, by a nine-fold compartmentation to provide the ground plan of Yale…."

— Architects John Outram Associates
    on work at Rice University

Yale Daily News, Jan. 11, 2001:  

    "When New Haven was founded, the city was laid out into a grid of nine squares surrounded by a great wilderness.
    Last year History of Art Professor Emeritus Vincent Scully said the original town plan reflected a feeling that the new city should be sacred.
    Scully said the colony's founders thought of their new Puritan settlement as a 'nine-square paradise on Earth, heaven on earth, New Haven, New Jerusalem.'"

"Real and unreal are two in one:
    New Haven
 Before and after one arrives…."

 — Wallace Stevens,
    "An Ordinary Evening in New Haven,' XXVIII
 

Related material:
 Log24 entries on
St. Peter's Day, 2004

Thursday, April 7, 2005

Thursday April 7, 2005

Filed under: General — m759 @ 7:26 PM

In the Details

Wallace Stevens,
An Ordinary Evening in New Haven:

XXII

Professor Eucalyptus said, “The search
For reality is as momentous as
The search for God.”  It is the philosopher’s search
For an interior made exterior
And the poet’s search for the same exterior made
Interior….

   … Likewise to say of the evening star,
The most ancient light in the most ancient sky,
That it is wholly an inner light, that it shines
From the sleepy bosom of the real, re-creates,
Searches a possible for its possibleness.

Julie Taymor, “Skewed Mirrors” interview:

“… they were performing for God. Now God can mean whatever you want it to mean. But for me, I understood it so totally. The detail….

They did it from the inside to the outside. And from the outside to the in. And that profoundly moved me then. It was…it was the most important thing that I ever experienced.”

“Skewed Mirrors”
illustrated:

Click on the above to enlarge.

Details:

The image “http://www.log24.com/log/pix05/050407-Messick2.png” cannot be displayed, because it contains errors.

The above may be of interest to students
of  iconology — what Dan Brown in
The Da Vinci Code calls “symbology” —
and of redheads.

The artist of Details,
“Brenda Starr” creator
Dale Messick, died on Tuesday,
April 5, 2005, at 98.

The image “http://www.log24.com/log/pix05/050407-Messick.jpg” cannot be displayed, because it contains errors.
AP Photo
Dale Messick in 1982

For further details on
April 5, see
Art History:
The Pope of Hope


Friday, December 10, 2004

Friday December 10, 2004

Filed under: General — Tags: — m759 @ 3:00 AM

Gray Particular
in Hartford

From Wallace Stevens,

"The Rock, Part III:
Forms of the Rock in a Night-Hymn" —

The rock is
   the gray particular of man's life,
The stone from which
   he rises, up–and–ho,
The step to
   the bleaker depths of his descents…

From this morning's
New York Times obituaries

The image “http://log24.com/log/pix03/nytC.gif” cannot be displayed, because it contains errors.leve Gray, a painter admired for his large-scale, vividly colorful and lyrically gestural abstract compositions, died on Wednesday in Hartford. He was 86.

The cause was a massive subdural hematoma suffered after he fell on ice and hit his head on Tuesday outside his home in Warren, Conn., said his wife, the writer Francine du Plessix Gray.

*******************************

Jackson Mac Low, a poet, composer and performance artist whose work reveled in what happens when the process of composition is left to carefully calibrated chance, died on Wednesday….

… in 1999 [he] received the Wallace Stevens Award, which carries a $100,000 prize, from the Academy of American Poets.

A Wallace Stevens Award,
in Seven Parts:

  I.  From a page linked to in
      Tuesday's entry White Christmas:

"A bemused Plato reasoned that nonbeing must in some sense be, otherwise what is it that there is not? In our own day Martin Heidegger ventured that das Nichts nichtet — 'the nothing nothings' — evidently still sensing a problem."
— W. V. Quine in Quiddities

 II.  "As if nothingness
             contained a métier…"
      — Wallace Stevens, "The Rock"

III.  "Massive subdural hematoma"
       — Three-word poem
           performed on Tuesday
           in Connecticut

IV.  mé·tier n.

 

  • An occupation, a trade, or a profession.
  • Work or activity for which a person is particularly suited; one's specialty.

[French, from Old French mestier, from Vulgar Latin misterium, from Latin ministerium. See ministry.]
Source: The American Heritage® Dictionary of the English Language, Fourth Edition

 

  V.  "ho"
        — Wallace Stevens, "The Rock"

 VI.  Francine du Plessix Gray…
       From the
       Archives of the
       New York Review of Books:

July 16, 1992: Splendor and Miseries, review of

Women for Hire: Prostitution and Sexuality in France after 1850 by Alain Corbin, translated by Alan Sheridan

La Vie quotidienne dans les maisons closes, 1830–1930 by Laure Adler

Figures of Ill Repute: Representing Prostitution in Nineteenth-Century France by Charles Bernheimer

Painted Love: Prostitution in French Art of the Impressionist Era by Hollis Clayson

VII.   From an entry of April 29, 2004:

 

"… a 'dead shepherd who brought
tremendous chords from hell
And bade the sheep carouse' "

 

— Wallace Stevens
as quoted by Michael Bryson

 

(p. 227, The Palm
at the End of the Mind:

Selected Poems and a Play.
Ed. Holly Stevens.

New York: Vintage Books, 1990)

 

Sunday, December 5, 2004

Sunday December 5, 2004

Filed under: General — Tags: , , — m759 @ 3:00 PM

Chorus from
The Rock

Author Joan Didion is 70 today.

On Didion’s late husband, John Gregory Dunne:

“His 1989 memoir Harp includes Dunne’s early years in Hartford and his Irish-Catholic family’s resentment of WASP social superiority: ‘Don’t stand out so that the Yanks can see you,’ he wrote, ‘don’t let your pretensions become a focus of Yank merriment and mockery.'”

The Hartford Courant, August 4, 2002

From a Hartford Protestant:

The American Sublime

How does one stand
To behold the sublime,
To confront the mockers,
The mickey mockers
And plated pairs?

When General Jackson
Posed for his statue
He knew how one feels.
Shall a man go barefoot
Blinking and blank?

But how does one feel?
One grows used to the weather,
The landscape and that;
And the sublime comes down
To the spirit itself,

The spirit and space,
The empty spirit
In vacant space.
What wine does one drink?
What bread does one eat?

— Wallace Stevens

A search of the Internet for “Wallace Stevens”  + “The Rock” + “Seventy Years Later” yields only one quotation…

Log24 entries of Aug. 2, 2002:

From “Seventy Years Later,” Section I of “The Rock,” a poem by Wallace Stevens:

A theorem proposed
between the two —
Two figures in a nature
of the sun….

From page 63 of The New Yorker issue dated August 5, 2002:

“Birthday, death-day —
what day is not both?”
— John Updike

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 Play It As It Lays:

I lie here in the sunlight, watch the hummingbird.  This morning I threw the coins in the swimming pool, and they gleamed and turned in the water in such a way that I was almost moved to read them.  I refrained.
— Page 214

And the sublime comes down
To the spirit itself,
The spirit and space,
The empty spirit
In vacant space.

One heart will wear a Valentine.
— Sinatra, 1954

Thursday, December 2, 2004

Thursday December 2, 2004

Filed under: General,Geometry — m759 @ 8:23 PM

The Poem of Pure Reality

                                       “We seek
The poem of pure reality, untouched
By trope or deviation,
    straight to the word,
Straight to the transfixing object,
    to the object
At the exactest point at which it is itself,
Transfixing by being purely what it is….”

Wallace Stevens (1879-1955)
“An Ordinary Evening in New Haven” IX,
from The Auroras of Autumn (1950)
(Collected Poems, pp. 465-489)

I have added new material to Geometry of the 4×4 Square, including links to a new commentary on a paper by Burkard Polster.

“It is a good light, then, for those
That know the ultimate Plato,
Tranquillizing with this jewel
The torments of confusion.”

— Wallace Stevens,
Collected Poetry and Prose, page 21,
The Library of America, 1997

Thursday, August 28, 2003

Thursday August 28, 2003

Filed under: General — Tags: , , — m759 @ 6:35 PM

Spirit

In memory of
 Walter J. Ong, S. J.,
professor emeritus
at St. Louis University,
St. Louis, Missouri

"The Garden of Eden is behind us
and there is no road back to innocence;
we can only go forward."

— Anne Morrow Lindbergh,
Earth Shine, p. xii

  Earth Shine, p. xiii: 

We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.

— T. S. Eliot, Four Quartets.

Eliot was a native of St. Louis.

"Every city has its gates, which need not be of stone. Nor need soldiers be upon them or watchers before them. At first, when cities were jewels in a dark and mysterious world, they tended to be round and they had protective walls. To enter, one had to pass through gates, the reward for which was shelter from the overwhelming forests and seas, the merciless and taxing expanse of greens, whites, and blues–wild and free–that stopped at the city walls.

In time the ramparts became higher and the gates more massive, until they simply disappeared and were replaced by barriers, subtler than stone, that girded every city like a crown and held in its spirit."

Mark Helprin, Winter's Tale

Book Cover,
1954:

"The pattern of the heavens
     and high, night air"
Wallace Stevens,
An Ordinary Evening in New Haven

See also my notes of
Monday, August 25, 2003
(the feast day of Saint Louis,
for whom the city is named).

For a more Eden-like city,
see my note of
October 23, 2002,
on Cuernavaca, Mexico,
where Charles Lindbergh
courted Anne Morrow.
 

Monday, August 25, 2003

Monday August 25, 2003

Filed under: General — Tags: , — m759 @ 4:24 AM

Words Are Events

August 12 was the date of death of Joseph Patrick Kennedy, Jr., and the date I entered some theological remarks in a new Harvard weblog.  It turns out that August 12 was also the feast day of a new saint… Walter Jackson Ong, of St. Louis University, St. Louis, Missouri, a Jesuit institution.

Today, August 25, is the feast day of St. Louis himself, for whom the aforementioned city and university are named.

The New York Times states that Ong was "considered an outstanding postmodern theorist, whose ideas spawned college courses…."

There is, of course, no such thing as a postmodern Jesuit, although James Joyce came close.

From The Walter J. Ong Project:

"Ong's work is often presented alongside the postmodern and deconstruction theories of Claude Levi-Strauss, Jacques Derrida, Michel Foucault, Hélène Cixous, and others. His own work in orality and literacy shows deconstruction to be unnecessary: if you consider language to be fundamentally spoken, as language originally is, it does not consist of signs, but of events. Sound, including the spoken word, is an event. It takes time. The concept of 'sign,' by contrast, derives primarily not from the world of events, but from the world of vision. A sign can be physically carried around, an event cannot: it simply happens. Words are events."

 

From a commonplace book
on the number 911:

"We keep coming back and coming back
To the real: to the hotel
    instead of the hymns
That fall upon it out of the wind.
    We seek

The poem of pure reality, untouched
By trope or deviation,
    straight to the word,
Straight to the transfixing object,
    to the object

At the exactest point at which
    it is itself,
Transfixing by being purely
    what it is,
A view of New Haven, say,
    through the certain eye,

The eye made clear of uncertainty,
    with the sight
Of simple seeing, without reflection.
    We seek
Nothing beyond reality. Within it,

Everything, the spirit's alchemicana
Included, the spirit that goes
    roundabout
And through included,
    not merely the visible,

The solid, but the movable,
    the moment,
The coming on of feasts
     and the habits of saints,
The pattern of the heavens
     and high, night air."

Wallace Stevens (1879-1955)
An Ordinary Evening in New Haven
IX.1-18, from The Auroras of Autumn,
Knopf, NY (1950)
(Collected Poems, pp. 465-489)
NY Times Obituary (8-3-1955)

 

The web page where I found the Stevens quote also has the following:

 

Case 9 of Hekiganroku:
Joshu's Four Gates

A monk asked Joshu,
"What is Joshu?" (Chinese: Chao Chou)

Joshu said,
"East Gate, West Gate,
 North Gate, South Gate."

Setcho's Verse:

Its intention concealed,
    the question came;
The Diamond King's eye was
    as clear as a jewel.
There stood the gates,
    north, south, east, and west,
But the heaviest hammer blow
    could not open them.

Setcho (980-1052),
Hekiganroku, 9 (Blue Cliff Records)
(translated by Katsuki Sekida,
Two Zen Classics, 1977, p. 172)

 

See also my previous entry for today,
"Gates to the City."

Monday, January 20, 2003

Monday January 20, 2003

Filed under: General — Tags: — m759 @ 5:00 PM

Shine On, Robinson Jeffers

"…be in nothing so moderate as in love of man, 
      a clever servant, insufferable master.
There is the trap that catches noblest spirits,
     that caught — they say — God, when he walked on earth."
Shine, Perishing Republic, by Robinson Jeffers

Robinson Jeffers died at Big Sur, California, on January 20, 1962 — a year to the day after Robert Frost spoke at the Kennedy inauguration.

"The poetry of Robinson Jeffers shines with a diamond's brilliance when he depicts Nature's beauty and magnificence.   His verse also flashes with a diamond's hardness when he portrays human pain and folly."
Gary Suttle  

"Praise Him, He hath conferred aesthetic distance
Upon our appetites, and on the bloody
Mess of our birthright, our unseemly need,
Imposed significant form. Through Him the brutes
Enter the pure Euclidean kingdom of number…."
— Howard Nemerov, 
   Grace To Be Said at the Supermarket 

"Across my foundering deck shone 
A beacon, an eternal beam. | Flesh fade, and mortal trash 
Fáll to the resíduary worm; | world's wildfire, leave but ash: 
In a flash, at a trumpet crash, 
I am all at once what Christ is |, since he was what I am, and 
Thís Jack, jóke, poor pótsherd, | patch, matchwood,
    immortal diamond, 
Is immortal diamond."
— Gerard Manley Hopkins,
    That Nature is a Heraclitean Fire and of the Comfort of the Resurrection

"In the last two weeks, I've been returning to Hopkins.  Even in the 'world's wildfire,' he asserts that 'this Jack, joke, poor potsherd, patch, matchwood, immortal diamond,/Is immortal diamond.' A comfort."
— Michael Gerson, head White House speechwriter,
    in Vanity Fair, May 2002, page 162

"There's none but truth can stead you.  Christ is truth."
— Gerard Manley Hopkins

"The rock cannot be broken.  It is the truth."
— Wallace Stevens 

"My ghost you needn't look for; it is probably
Here, but a dark one, deep in the granite…."
— Robinson Jeffers, Tor House

On this date in 1993, the inauguration day of William Jefferson Clinton, Audrey Hepburn died.

"…today, the Rock cries out to us, clearly, forcefully…."
Maya Angelou, January 20, 1993

"So, purposing each moment to retire,
She linger'd still. Meantime, across the moors,
Had come young Porphyro, with heart on fire"
— John Keats, The Eve of St. Agnes (January 20), IX

Top view of
ordinary
diamond

Top view of
Hearts On Fire
diamond

Advertising Copy:

What you see with a Hearts On Fire diamond is an unequalled marriage of math and physics, resulting in the world's most perfectly cut diamond.

 

"Eightpointed symmetrical signs are ancient symbols for the Venus goddess or the planet Venus as either the Morning star or the Evening star."
Symbols.com

"Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave.  Its flashes are flashes of fire, a raging flame."
Song of Solomon

"The last words from the people in the towers and on the planes, over and over again, were 'I love you.'  Over and over again, the message was the same, 'I love you.' …. Perhaps this is the loudest chorus from The Rock:  we are learning just how powerful love really is, even in the face of death."
The Rev. Kenneth E. Kovacs

"Then I'll get on my knees and pray
We don't get fooled again."
The Who 

See also my note, "Bright Star," of October 23, 2002.

 

Wednesday, November 27, 2002

Wednesday November 27, 2002

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

Waiting for Logos

Searching for background on the phrase "logos and logic" in yesterday's "Notes toward a Supreme Fact," I found this passage:

"…a theory of psychology based on the idea of the soul as the dialectical, self-contradictory syzygy of a) soul as anima and b) soul as animus. Jungian and archetypal psychology appear to have taken heed more or less of only one half of the whole syzygy, predominantly serving an anima cut loose from her own Other, the animus as logos and logic (whose first and most extreme phenomenological image is the killer of the anima, Bluebeard). Thus psychology tends to defend the virginal innocence of the anima and her imagination…"

— Wolfgang Giegerich, "Once More the Reality/Irreality Issue: A Reply to Hillman's Reply," website 

The anima and other Jungian concepts are used to analyze Wallace Stevens in an excellent essay by Michael Bryson, "The Quest for the Fiction of an Absolute." Part of Bryson's motivation in this essay is the conflict between the trendy leftist nominalism of postmodern critics and the conservative realism of more traditional critics:

"David Jarraway, in his Stevens and the Question of Belief, writes about a Stevens figured as a proto-deconstructionist, insisting on 'Steven's insistence on dismantling the logocentric models of belief' (311) in 'An Ordinary Evening in New Haven.' In opposition to these readings comes a work like Janet McCann's Wallace Stevens Revisited: 'The Celestial Possible', in which the claim is made (speaking of the post-1940 period of Stevens' life) that 'God preoccupied him for the rest of his career.'"

Here "logocentric" is a buzz word for "Christian." Stevens, unlike the postmodernists, was not anti-Christian. He did, however, see that the old structures of belief could not be maintained indefinitely, and pondered what could be found to replace them. "Notes toward a Supreme Fiction" deals with this problem. In his essay on Stevens' "Notes," Bryson emphasizes the "negative capability" of Keats as a contemplative technique:

"The willingness to exist in a state of negative capability, to accept that sometimes what we are seeking is not that which reason can impose…."

For some related material, see Simone Weil's remarks on Electra waiting for her brother Orestes. Simone Weil's brother was one of the greatest mathematicians of the past century, André Weil.

"Electra did not seek Orestes, she waited for him…"

— Simone Weil

"…at the end, she pulls it all together brilliantly in the story of Electra and Orestes, where the importance of waiting on God rather than seeking is brought home forcefully."

— Tom Hinkle, review of Waiting for God

Compare her remarks on waiting for Orestes with the following passage from Waiting for God:

"We do not obtain the most precious gifts by going in search of them but by waiting for them. Man cannot discover them by his own powers, and if he sets out to seek for them he will find in their place counterfeits of which he will be unable to discern falsity.

The solution of a geometry problem does not in itself constitute a precious gift, but the same law applies to it because it is the image of something precious. Being a little fragment of particular truth, it is a pure image of the unique, eternal, and living Truth, the very Truth that once in a human voice declared: "I am the Truth."

Every school exercise, thought of in this way, is like a sacrament.

In every school exercise there is a special way of waiting upon truth, setting our hearts upon it, yet not allowing ourselves to go out in search of it. There is a way of giving our attention to the data of a problem in geometry without trying to find the solution…."

— Simone Weil, "Reflections on the Right Use of School Studies with a View to the Love of  God"

Weil concludes the preceding essay with the following passage:

"Academic work is one of those fields containing a pearl so precious that it is worth while to sell all of our possessions, keeping nothing for ourselves, in order to be able to acquire it."

This biblical metaphor is also echoed in the work of Pascal, who combined in one person the theological talent of Simone Weil and the mathematical talent of her brother. After discussing how proofs should be written, Pascal says

"The method of not erring is sought by all the world. The logicians profess to guide to it, the geometricians alone attain it, and apart from their science, and the imitations of it, there are no true demonstrations. The whole art is included in the simple precepts that we have given; they alone are sufficient, they alone afford proofs; all other rules are useless or injurious. This I know by long experience of all kinds of books and persons.

And on this point I pass the same judgment as those who say that geometricians give them nothing new by these rules, because they possessed them in reality, but confounded with a multitude of others, either useless or false, from which they could not discriminate them, as those who, seeking a diamond of great price amidst a number of false ones, but from which they know not how to distinguish it, should boast, in holding them all together, of possessing the true one equally with him who without pausing at this mass of rubbish lays his hand upon the costly stone which they are seeking and for which they do not throw away the rest."

— Blaise Pascal, The Art of Persuasion

 

For more diamond metaphors and Jungian analysis, see

The Diamond Archetype.

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