Log24

Saturday, June 13, 2015

The Holy Field

Filed under: General,Geometry — m759 @ 7:45 pm

( A Chinese designation for the 3×3 square )

Friday, March 7, 2014

Field Dream

Filed under: General — m759 @ 7:11 pm

A field in China —

IMAGE- Chinese field from opening of TV series 'Resurrection'

The following link was suggested by today’s previous post
and by the ABC TV series “Resurrection” scheduled to start
at 9 PM ET Sunday, March 9, 2014 —

Field Dream

Tuesday, March 27, 2012

Literary Field

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

An image suggested by Google's observance today
of Mies van der Rohe's 126th birthday—

Related material:

See also yesterday's Chapter and Verse  by Stanley Fish,
and today's Arts & Letters Daily .

Monday, March 19, 2012

Field

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

IMAGE- Two versions of 'field'

— Illustration by Neill Cameron for his father, combinatorialist Peter J. Cameron

Illustration by Nao of the Japanese (and Chinese) character for "field"—

IMAGE- Japanese character for 'field'

Related material—

Finitegeometry.org favicon from February 24, 2012

Wednesday, June 30, 2010

Field Dream

Filed under: General,Geometry — Tags: , , , , — m759 @ 10:23 am

In memory of Wu Guanzhong, Chinese artist who died in Beijing on Friday

Image-- The Dream of the Expanded Field

"Once Knecht confessed to his teacher that he wished to learn enough to be able to incorporate the system of the I Ching into the Glass Bead Game.  Elder Brother laughed.  'Go ahead and try,' he exclaimed.  'You'll see how it turns out.  Anyone can create a pretty little bamboo garden in the world.  But I doubt that the gardener would succeed in incorporating the world in his bamboo grove.'"

— Hermann Hesse, The Glass Bead Game, translated by Richard and Clara Winston

"The Chinese painter Wu Tao-tzu was famous because he could paint nature in a unique realistic way that was able to deceive all who viewed the picture. At the end of his life he painted his last work and invited all his friends and admirers to its presentation. They saw a wonderful landscape with a romantic path, starting in the foreground between flowers and moving through meadows to high mountains in the background, where it disappeared in an evening fog. He explained that this picture summed up all his life’s work and at the end of his short talk he jumped into the painting and onto the path, walked to the background and disappeared forever."

Jürgen Teichmann. Teichmann notes that "the German poet Hermann Hesse tells a variation of this anecdote, according to his own personal view, as found in his 'Kurzgefasster Lebenslauf,' 1925."

Sunday, November 10, 2013

Abstraction

Filed under: General — Tags: — m759 @ 5:24 pm

(Continued from Dec. 6, 2012)

Context:
Chinese Field  and Modal Diamond .

(See also today’s previous post.)

Saturday, February 24, 2024

Li

Filed under: General — Tags: , , , — m759 @ 2:36 am

The Chinese concept of li  in yesterday's post "Logos" is related,
if only by metaphor, to the underlying form (sets of "line diagrams")
of patterns in the Cullinane diamond theorem:

"But very possibly the earliest use of li  is the one instance that
it appears in the Classic of Poetry  (Ode 210) where it refers to
the borders or boundary lines marking off areas in a field.
Here it appears in conjunction with chiang  and is explained
as 'to divide into lots (or parcels of land)' (fen-ti )."

P. 33 of "Li Revisited and Other Explorations"
by Allen Wittenborn, Bulletin of Sung and Yüan Studies
No. 17 (1981), pp. 32-48 (17 pages),
https://www.jstor.org/stable/23497457.

Sunday, September 17, 2023

Logo

Filed under: General — m759 @ 9:57 am

From posts tagged Field Theology

Illustration of the Japanese (and Chinese) character for "field"—

IMAGE- Japanese character for 'field'

From an Instagram ad today —

Tuesday, December 7, 2021

Tortoise Variations

Filed under: General — Tags: , — m759 @ 2:42 am

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Fanciful version —

Less fanciful versions . . . 

Unmagic Squares

Consecutive positive integers:

1   2   3
4   5   6
7   8   9

Consecutive nonnegative integers:

0   1   2
3   4   5
6   7   8

Consecutive nonnegative integers
written in base 3:

00  01  02
10  11  12
20  21  22

This last square may be viewed as
coordinates, in the 3-element Galois
field GF(3), of the ninefold square.

Note that the ninefold square so viewed
embodies the 12 lines of the two-dimensional
affine space over GF(3)

As does, similarly, the ancient Chinese
"magic" square known as the "Lo Shu."

These squares are therefore equivalent under
affine transformations.

This method generalizes.

— Steven H. Cullinane, Nov. 20, 2021

 

The Lo Shu as a Finite Space

Saturday, November 20, 2021

The Unmagicking

Filed under: General — Tags: — m759 @ 11:51 am
 

Unmagic Squares

Consecutive positive integers:

1   2   3
4   5   6
7   8   9

Consecutive nonnegative integers:

0   1   2
3   4   5
6   7   8

Consecutive nonnegative integers
written in base 3:

00  01  02
10  11  12
20  21  22

This last square may be viewed as
coordinates, in the 3-element Galois
field GF(3), of the ninefold square.

Note that the ninefold square so viewed
embodies the 12 lines of the two-dimensional
affine space over GF(3)

As does, similarly, the ancient Chinese
"magic" square known as the "Lo Shu."

These squares are therefore equivalent under
affine transformations.

This method generalizes.

— Steven H. Cullinane, Nov. 20, 2021

Tuesday, August 10, 2021

Ex Fano Apollinis

Filed under: General — Tags: , , , , — m759 @ 9:41 am
 

Margaret Atwood on Lewis Hyde's 
Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.


"As a Chinese jar . . . ."
     — Four Quartets

 

Rosalind Krauss
in "Grids," 1979:

"If we open any tract– Plastic Art and Pure Plastic Art  or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.

Or, to take a more up-to-date example…."

"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
– The Club Dumas , 1993

"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
– Robert Plant, 1971

The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.

An example of the universal— or, according to Krauss,
a "staircase" to the universal— is the ninefold square:

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    

The "Katz" of the August 7 post Art Angles
is a product of Princeton's
Department of Art and Archaeology.

 

ART —

 

The Lo Shu as a Finite Space
 

ARCHAEOLOGY —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71

Saturday, July 3, 2021

Here, There, and Chicago

Filed under: General — Tags: , — m759 @ 9:07 pm

The above phrase "the intersection of storytelling and visual arts"
suggests a review . . .

Storytelling —

Visual arts —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71

A Midrash for Michener —

IMAGE- Marie-Louise von Franz on the 'field' that represents 'the structural outlines of the collective unconscious'

For a connection of the above "Holy Field"
with pure mathematics, see Coxeter's Aleph.

Wednesday, November 11, 2020

The Work of a Comedian

Filed under: General — Tags: , — m759 @ 10:57 am

Flashback to Sept. 7, 2008

Change for Washington:

'The Laws of Change: I Ching and the Philosophy of Life,' by Jack M. Balkin

For the details, see yale.edu/lawweb:

“As important to Chinese civilization as the Bible is to Western culture,
the I Ching  or Book of Changes  is one of the oldest treasures of
world literature. Yet despite many commentaries written over the years,
it is still not well understood in the English-speaking world. In this
masterful [sic ] new interpretation, Jack Balkin returns the I Ching  to
its rightful place….

Jack M. Balkin

Jack M. Balkin

Jack M. Balkin is Knight Professor of Constitutional Law
and the First Amendment at Yale Law School, and
the founder and director of Yale’s Information Society Project.
His books and articles range over many different fields….”

Wallace Stevens on 'the work of a comedian'

Sunday, July 1, 2018

The Perpetual Motion of T. S. Eliot

Filed under: General — Tags: — m759 @ 10:28 am

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman

Sunday, October 18, 2015

Coordinatization Problem

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

There are various ways to coordinatize a 3×3 array
(the Chinese "Holy Field'). Here are some —

See  Cullinane,  Coxeter,  and  Knight tour.

Sunday, July 12, 2015

Characteristica Universalis

Filed under: General — m759 @ 7:00 pm

From Wikipedia —

"Many Leibniz scholars… seem to agree that he intended
his characteristica universalis  … to be a form of … 
ideographic language. This was to be based on a
rationalised version of the 'principles' of Chinese characters…."

See as well O Nine,  Chinese Calligraphy, and Holy Field.

Friday, July 10, 2015

Without Border

Filed under: General — Tags: , — m759 @ 3:18 pm

The previous post's Holy Field symbol, 
with border removed, becomes the
Chinese character for "well."

See also The Lost Well.

Thursday, July 9, 2015

Man and His Symbols

Filed under: General,Geometry — m759 @ 2:24 pm

(Continued)

A post of July 7, Haiku for DeLillo, had a link to posts tagged "Holy Field GF(3)."

As the smallest Galois field based on an odd prime, this structure 
clearly is of fundamental importance.  

The Galois field GF(3)

It is, however, perhaps too  small  to be visually impressive.

A larger, closely related, field, GF(9), may be pictured as a 3×3 array

hence as the traditional Chinese  Holy Field.

Marketing the Holy Field

IMAGE- The Ninefold Square, in China 'The Holy Field'

The above illustration of China's  Holy Field occurred in the context of
Log24 posts on Child Buyers.   For more on child buyers, see an excellent
condemnation today by Diane Ravitch of the U. S. Secretary of Education.

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.

Thursday, February 19, 2015

The Bluebird of Happiness

Filed under: General — m759 @ 12:48 pm

(Chinese style)

Tuesday, November 18, 2014

The Abacus Conundrum…

Filed under: General — Tags: — m759 @ 1:44 am

Continues.

http://www.log24.com/log/pix10B/101206-AbacusConundrum.jpg

Prequel from 1961 (click image for context):

Detail that may be interpreted as the Chinese
3×3 "Holy Field" and a Chinese temple bell—

"Ting-a-ling." — Kurt Vonnegut.

Tuesday, January 21, 2014

Walls

Filed under: General — m759 @ 7:59 pm

Click images for related material.

IMAGE- Chrles Grigg, undated Korky the Cat 'Grand Obstacle Race' drawing

IMAGE- 'In Cold Mud: The Obstacle-Racing Craze Gets Serious' - Lizzie Widdicombe

"Oh, I've got a field!
  I can build walls!"

Thursday, June 13, 2013

Gate

Filed under: General,Geometry — Tags: , , , — m759 @ 2:13 pm

"Eight is a Gate." — Mnemonic rhyme

Today's previous post, Window, showed a version
of the Chinese character for "field"—

This suggests a related image

The related image in turn suggests

Unlike linear perspective, axonometry has no vanishing point,
and hence it does not assume a fixed position by the viewer.
This makes axonometry 'scrollable'. Art historians often speak of
the 'moving' or 'shifting' perspective in Chinese paintings.

Axonometry was introduced to Europe in the 17th century by
Jesuits returning from China.

Jan Krikke

As was the I Ching.  A related structure:

Window

Filed under: General — Tags: — m759 @ 6:48 am

From Jim Holt’s Aug. 29, 2008, review of
The Same Man:
George Orwell and Evelyn Waugh in Love and War

by David Lebedoff

“Orwell thought ‘good prose is like a window pane,’
forceful and direct. Waugh was an elaborate stylist
whose prose ranged from the dryly ironical to the
richly ornamented and rhetorical. Orwell was solitary
and fiercely earnest. Waugh was convivial and
brutally funny. And, perhaps most important, Orwell
was a secularist whose greatest fear was the
emergence of Big Brother in this world. Waugh was
a Roman Catholic convert whose greatest hope lay
with God in the next.”

The Orwell quote is from “Why I Write.”
A search for the original yields

IMAGE- Heading data for Orwell's 'Why I Write' in Chinese weblog 'Acquisition of Sunshine'

Detail:

IMAGE- Date of a Chinese weblog post: 2009-06-04

Synchronicity:

Log24 posts of 2009-06-04.

See, too, in this journal the
Chinese character for “field”

Sunday, October 21, 2012

Multispeech

Filed under: General — m759 @ 9:00 pm

IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

     Click image above
     for some background.

IMAGE- Snow White Imprisoned- An image for the Snow Queen

IMAGE- Charlize Theron as Ravenna: 'She drifted.'

Thursday, September 27, 2012

Kummer and the Cube

Filed under: General,Geometry — Tags: , , — m759 @ 7:11 pm

Denote the d-dimensional hypercube by  γd .

"… after coloring the sixty-four vertices of  γ6
alternately red and blue, we can say that
the sixteen pairs of opposite red vertices represent
the sixteen nodes of Kummer's surface, while
the sixteen pairs of opposite blue vertices
represent the sixteen tropes."

— From "Kummer's 16," section 12 of Coxeter's 1950
    "Self-dual Configurations and Regular Graphs"

Just as the 4×4 square represents the 4-dimensional
hypercube  γ4  over the two-element Galois field GF(2),
so the 4x4x4 cube represents the 6-dimensional
hypercube  γ6  over GF(2).

For religious interpretations, see
Nanavira Thera (Indian) and
I Ching  geometry (Chinese).

See also two professors in The New York Times
discussing images of the sacred in an op-ed piece
dated Sept. 26 (Yom Kippur).

Saturday, March 24, 2012

The David Waltz…

Filed under: General,Geometry — m759 @ 9:00 am

In Turing's Cathedral

"At the still point…" — T. S. Eliot

In memory of David L. Waltz, artificial-intelligence pioneer,
who died Thursday, March 22, 2012—

  1. The Log24 post of March 22 on the square-triangle theorem
  2. The March 18 post, Square-Triangle Diamond
  3. Remarks from the BBC on linguistic embedding
    that begin as follows—
         "If we draw a large triangle and embed smaller triangles in it,
          how does it look?"—
    and include discussion of a South American "tribe called Piranha" [sic ]
  4. The result of a Cartoon Bank search suggested by no. 3 above—
    (Click image for some related material.)
  5. A suggestion from the Cartoon Bank—
    IMAGE- 'Try our new grid view.'
  6. The following from the First of May, 2010

    The Nine Divisions of Heaven–

    Image-- Routledge Encyclopedia of Taoism, Vol. I, on the Nine Heavens, 'jiutian,' ed. by Fabrizio Pregadio

    Some context–

    IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

    "This pattern is a square divided into nine equal parts.
    It has been called the 'Holy Field' division and
    was used throughout Chinese history for many
    different purposes, most of which were connected
    with things religious, political, or philosophical."

    – The Magic Square: Cities in Ancient China,
    by Alfred Schinz, Edition Axel Menges, 1996, p. 71

  7. The phrase "embedding the stone" —

Tuesday, November 23, 2010

Art Object

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

There is more than one way
to look at a cube.

http://www.log24.com/log/pix10B/101123-plain_cube_200x227.gif

 From Cambridge U. Press on Feb. 20, 2006 —

IMAGE- 'Cambridge Tracts in Mathematics 168: The Cube'

and from this journal on June 30, 2010 —

In memory of Wu Guanzhong, Chinese artist
who died in Beijing on June 25, 2010

Image-- The Dream of the Expanded Field

See also this journal on Feb. 20, 2006
(the day The Cube  was published).

Wednesday, June 16, 2010

Geometry of Language

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

(Continued from April 23, 2009, and February 13, 2010.)

Paul Valéry as quoted in yesterday’s post:

“The S[elf] is invariant, origin, locus or field, it’s a functional property of consciousness” (Cahiers, 15:170 [2: 315])

The geometric example discussed here yesterday as a Self symbol may seem too small to be really impressive. Here is a larger example from the Chinese, rather than European, tradition. It may be regarded as a way of representing the Galois field GF(64). (“Field” is a rather ambiguous term; here it does not, of course, mean what it did in the Valéry quotation.)

From Geometry of the I Ching

Image-- The 64 hexagrams of the I Ching

The above 64 hexagrams may also be regarded as
the finite affine space AG(6,2)— a larger version
of the finite affine space AG(4,2) in yesterday’s post.
That smaller space has a group of 322,560 symmetries.
The larger hexagram  space has a group of
1,290,157,424,640 affine symmetries.

From a paper on GL(6,2), the symmetry group
of the corresponding projective  space PG(5,2),*
which has 1/64 as many symmetries—

(Click to enlarge.)

Image-- Classes of the Group GL(6,)

For some narrative in the European  tradition
related to this geometry, see Solomon’s Cube.

* Update of July 29, 2011: The “PG(5,2)” above is a correction from an earlier error.

Saturday, May 1, 2010

An Education

Filed under: General,Geometry — Tags: — m759 @ 9:00 am
 

天鈞

 

Made famous by Ursula K. Le Guin
as the book title "Lathe of Heaven,"
this Chinese phrase, tianjun, apparently
means something more like "Scales of Heaven"–
an appropriate image for Law Day 2010.

Image--Scales (the legal symbol)

An anonymous forum user says that

"…if you switch the two characters around,
you get: 鈞天, which is one of
the nine heavens, more specifically,
the middle heaven."

This is supported by a
non-anonymous source:

"I follow A.C. Graham’s translation of
Juntian as 'Level Heaven (the innermost
of the nine divisions of heaven)';
he renders Juntian guangyue as
'the mighty music of the innermost heaven.'"

— "Music in the World of Su Shi (1037-1101):
Terminology
," by Stuart H. Sargent,
Colorado State University,
Journal of Sung-Yuan Studies 32 (2002), 39-81

The Nine Divisions of Heaven–

Image-- Routledge Encyclopedia of Taoism, Vol. I, on the Nine Heavens, 'jiutian,' ed. by Fabrizio Pregadio

Some context–

The 3x3 ('ninefold') square

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71

Wednesday, May 6, 2009

Wednesday May 6, 2009

Filed under: General,Geometry — Tags: , — m759 @ 11:07 am
Joke

“My pursuits are a joke
in that the universe is a joke.
One has to reflect
the universe faithfully.”

John Frederick Michell
Feb. 9, 1933 –
April 24, 2009 

“I laugh because I dare not cry.
This is a crazy world and
the only way to enjoy it
is to treat it as a joke.”

— Robert A. Heinlein,
The Number of the Beast

For Marisa Tomei
  (born Dec. 4, 1964) —
on the day that
   Bob Seger turns 64 —

A Joke:
Points All Her Own

Points All Her Own,
Part I:

(For the backstory, see
the Log24 entries and links
on Marisa Tomei’s birthday
last year.)

Ad for a movie of the book 'Flatland'


Points All Her Own,

Part II:

(For the backstory, see
Galois Geometry:
The Simplest Examples
.)

Galois geometry: the simplest examples

Points All Her Own,

Part III:

(For the backstory, see
Geometry of the I Ching
and the history of
Chinese philosophy.)

Galois space of six dimensions represented in Euclidean spaces of three and of two dimensions

In simpler terms:

Smackdown!

Garfield on May 6, 2009: Smackdown!

Sunday, September 7, 2008

Sunday September 7, 2008

Filed under: General — Tags: — m759 @ 7:09 am
Bringing Change
to Washington

'Only I can bring change to Washington'-- LA Times, Sept. 7, 2008

First in War,
   First in Peace…

Quotations for
Chairman George

on February 22, 1999
(Washington’s Birthday)

I Ching Hexagram 49: The Image of Revolution

Fire in
the lake:
the image of Revolution

Thus the
superior man
Sets the calendar
in order
And makes the seasons clear.


Change for Washington:

'The Laws of Change: I Ching and the Philosophy of Life,' by Jack M. Balkin

For the details, see
yale.edu/lawweb:

“As important to Chinese civilization as the Bible is to Western culture, the I Ching or Book of Changes is one of the oldest treasures of world literature. Yet despite many commentaries written over the years, it is still not well understood in the English-speaking world. In this masterful [sic] new interpretation, Jack Balkin returns the I Ching to its rightful place….

Jack M. Balkin\

Jack M. Balkin

Jack M. Balkin is Knight Professor of Constitutional Law and the First Amendment at Yale Law School, and the founder and director of Yale’s Information Society Project. His books and articles range over many different fields….”

Wallace Stevens on 'the work of a comedian'

Friday, January 19, 2007

Friday January 19, 2007

Filed under: General — m759 @ 11:07 pm
Triple Kiss

The image “http://www.log24.com/log/pix07/070119-TripleKiss.gif” cannot be displayed, because it contains errors.

I bent to kiss the lovely Maid,
And found a threefold kiss return’d.
— “The Crystal Cabinet

The above illustration of a classic Blake verse is for Anthony Daniels, a critic of Ezra Pound. The illustration may appeal to Daniels, since it is, like the persona presented by Daniels himself, petit-bourgeois and vulgar.

It was inspired by today’s two previous entries and by Daniels’s remarks, in this month’s New Criterion magazine, on Ezra Pound:

“Of his poetry I shall say nothing: not being fluent in Greek, Chinese, Italian, Farsi, and so forth, I do not feel much qualified to comment on it…. I shall merely confess to a petit-bourgeois partiality for comprehensibility and to what Pound himself called, in the nearest he ever came to a mea culpa with regard to his own ferocious anti-Semitism at a time of genocide, ‘a vulgar suburban prejudice’ against those who suppose that their thoughts are so profound that they justify a lifetime of exegesis if ever their meaning is to be even so much as glimpsed through a glass darkly.”

— “Pound’s Depreciation

Daniels, here posing as a vulgar suburban petit-bourgeois, is unwilling to examine Pound’s poetry even “through a glass darkly.”  This echoes the petit-bourgeois, but not vulgar,  “confession” of today’s previous entry:

“I didn’t expect much–didn’t look out the window
At school more diligent than able–docile stable”

— “A Life,” by Zbigniew Herbert

Pound, editor of T. S. Eliot’s “The Waste Land”– published in the first issue of the original Criterion magazine in 1922– might refer Daniels to the ghost of Guy Davenport:

“‘The architectonics of a narrative,’ Davenport says, ‘are emphasized and given a role to play in dramatic effect when novelists become Cubists; that is, when they see the possibilities of making a hieroglyph, a coherent symbol, an ideogram of the total work. A symbol comes into being when an artist sees that it is the only way to get all the meaning in.’….

In his study of The Cantos, Davenport defines the Poundian ideogram as ‘a grammar of images, emblems, and symbols, rather than a grammar of logical sequence…. An idea unifies, dominates, and controls the particulars that make the ideogram’…. He insists on the intelligibility of this method: ‘The components of an ideogram cohere as particles in a magnetic field, independent of each other but not of the pattern in which they figure.'”

— Andre Furlani, “‘When Novelists Become Cubists’: The Prose Ideograms of Guy Davenport

Related material:

A remark
on form and pattern
by T. S. Eliot
(friend of Pound
and founder of
the original
Criterion magazine)

Wednesday, August 30, 2006

Wednesday August 30, 2006

Filed under: General,Geometry — Tags: , — m759 @ 10:07 am
The Seventh Symbol:

A Multicultural Farewell

to a winner of the
Nobel Prize for Literature,
the Egyptian author of
The Seventh Heaven:
Supernatural Stories
 —

The image “http://www.log24.com/theory/images/GF64-63cycleA495.gif” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix06A/060830-SeventhSymbol.jpg” cannot be displayed, because it contains errors.

"Jackson has identified
the seventh symbol."
Stargate

Other versions of
the seventh symbol —

Chinese version:

The image “http://www.log24.com/log/pix06A/060830-hexagram20.gif” cannot be displayed, because it contains errors.

pictorial version:

The image “http://www.log24.com/log/pix06A/060830-Box.jpg” cannot be displayed, because it contains errors.

algebraic version:

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"… Max Black, the Cornell philosopher, and others have pointed out how 'perhaps every science must start with metaphor and end with algebra, and perhaps without the metaphor there would never have been any algebra' …."

— Max Black, Models and Metaphors, Cornell U. Press, 1962, page 242, as quoted in Dramas, Fields, and Metaphors, by Victor Witter Turner, Cornell U. Press, paperback, 1975, page 25

Friday, February 25, 2005

Friday February 25, 2005

Filed under: General — Tags: — m759 @ 10:53 am

Mr. Holland’s Week,
continued

“Philosophers ponder the idea of identity: what it is to give something a name on Monday and have it respond to that name on Friday regardless of what might have changed in the interim. Medical science tells us that the body’s cells replace themselves wholesale within every seven years, yet we tell ourselves that we are what we were.

The question is widened and elongated in the case of the Juilliard String Quartet.”

Bernard Holland in the New York Times,
    Monday, May 20, 1996

“Robert Koff, a founding member of the Juilliard String Quartet and a concert violinist who performed on modern and Baroque instruments, died on Tuesday at his home in Lexington, Mass. He was 86….

Mr. Koff, along with the violinist Robert Mann, the violist Raphael Hillyer and the cellist Arthur Winograd, formed the Juilliard String Quartet in 1946….”

Allan Kozinn in the New York Times,
    Friday, February 25, 2005

“One listened, for example, to the dazed, hymnlike beauty of the F Major’s Lento assai, and then to the acid that Beethoven sprinkles all around it. It is a wrestling match, awesome but also poignant. Schubert at the end of his life had already passed on to another level of spirit. Beethoven went back and forth between the temporal world and the world beyond right up to his dying day.”

Bernard Holland in the New York Times,
    Monday, May 20, 1996

Words move, music moves
Only in time; but that which is only living
Can only die. Words, after speech, reach
Into the silence. Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.
Not the stillness of the violin, while the note lasts,
Not that only, but the co-existence,
Or say that the end precedes the beginning,
And the end and the beginning were always there
Before the beginning and after the end.
And all is always now.

T. S. Eliot, Four Quartets

Related material: Elegance and the following description of Beethoven’s last quartet.

Program note by Eric Bromberger:

String Quartet in F major, Op. 135
LUDWIG VAN BEETHOVEN

Born December 16, 1770, Bonn
Died March 26, 1827, Vienna

This quartet – Beethoven’s last complete composition – comes from the fall of 1826, one of the blackest moments in his life. During the previous two years, Beethoven had written three string quartets on commission from Prince Nikolas Galitzin, and another, the Quartet in C-sharp minor, Op. 131, composed between January and June 1826. Even then Beethoven was not done with the possibilities of the string quartet: he pressed on with yet another, making sketches for the Quartet in F major during the summer of 1826.

At that point his world collapsed. His twenty-year-old nephew Karl, who had become Beethoven’s ward after a bitter court fight with the boy’s mother, attempted suicide. The composer was shattered: friends reported that he suddenly looked seventy years old. When the young man had recovered enough to travel, Beethoven took him – and the sketches for the new quartet – to the country home of Beethoven’s brother Johann in Gneixendorf, a village about thirty miles west of Vienna. Here, as he nursed Karl back to health, Beethoven’s own health began to fail. He would get up and compose at dawn, spend his days walking through the fields, and then resume composing in the evening. In Gneixendorf he completed the Quartet in F major in October and wrote a new finale to his earlier Quartet in B-flat major, Op. 130. These were his final works. When Beethoven return to Vienna in December, he took almost immediately to bed and died the following March.

One would expect music composed under such turbulent circumstances to be anguished, but the Quartet in F major is radiant music, full of sunlight – it is as if Beethoven achieved in this quartet the peace unavailable to him in life. This is the shortest of the late quartets, and many critics have noted that while this music remains very much in Beethoven’s late style, it returns to the classical proportions (and mood) of the Haydn quartets.

The opening movement, significantly marked Allegretto rather than the expected Allegro, is the one most often cited as Haydnesque. It is in sonata form – though a sonata form without overt conflict – and Beethoven builds it on brief thematic fragments rather than long melodies. This is poised, relaxed music, and the finale cadence – on the falling figure that has run throughout the movement – is remarkable for its understatement. By contrast, the Vivace bristles with energy. Its outer sections rocket along on a sharply-syncopated main idea, while the vigorous trio sends the first violin sailing high above the other voices. The very ending is impressive: the music grows quiet, comes to a moment of stasis, and then Beethoven wrenches it to a stop with a sudden, stinging surprise.

The slow movement – Beethoven carefully marks it Lento assai, cantante e tranquillo – is built on the first violin’s heartfelt opening melody; the even slower middle section, full of halting rhythms, spans only ten measures before the return of the opening material, now elaborately decorated. The final movement has occasioned the most comment. In the manuscript, Beethoven noted two three-note mottoes at its beginning under the heading Der schwer gefasste Entschluss: “The Difficult Resolution.” The first, solemnly intoned by viola and cello, asks the question: “Muss es sein?” (“Must it be?”). The violins’ inverted answer, which comes at the Allegro, is set to the words “Es muss sein!” (“It must be!”). Coupled with the fact that this quartet is virtually Beethoven’s last composition, these mottoes have given rise to a great deal of pretentious nonsense from certain commentators, mainly to the effect that they must represent Beethoven’s last thoughts, a stirring philosophical affirmation of life’s possibilities. The actual origins of this motto are a great deal less imposing, for they arose from a dispute over an unpaid bill, and as a private joke for friends Beethoven wrote a humorous canon on the dispute, the theme of which he then later adapted for this quartet movement. In any case, the mottoes furnish material for what turns out to be a powerful but essentially cheerful movement. The coda, which begins pizzicato, gradually gives way to bowed notes and a cadence on the “Es muss sein!” motto.

Tuesday, April 6, 2004

Tuesday April 6, 2004

Filed under: General — Tags: , , , — m759 @ 10:00 pm

Ideas and Art, Part III

The first idea was not our own.  Adam
In Eden was the father of Descartes…

— Wallace Stevens, from
Notes Toward a Supreme Fiction

"Quaedam ex his tanquam rerum imagines sunt, quibus solis proprie convenit ideae nomen: ut cùm hominem, vel Chimaeram, vel Coelum, vel Angelum, vel Deum cogito."

Descartes, Meditationes III, 5

"Of my thoughts some are, as it were, images of things, and to these alone properly belongs the name idea; as when I think [represent to my mind] a man, a chimera, the sky, an angel or God."

Descartes, Meditations III, 5

Begin, ephebe, by perceiving the idea
Of this invention, this invented world,
The inconceivable idea of the sun.

You must become an ignorant man again
And see the sun again with an ignorant eye
And see it clearly in the idea of it.

— Wallace Stevens, from
Notes Toward a Supreme Fiction

"… Quinimo in multis saepe magnum discrimen videor deprehendisse: ut, exempli causâ, duas diversas solis ideas apud me invenio, unam tanquam a sensibus haustam, & quae maxime inter illas quas adventitias existimo est recensenda, per quam mihi valde parvus apparet, aliam verò ex rationibus Astronomiae desumptam, hoc est ex notionibus quibusdam mihi innatis elicitam, vel quocumque alio modo a me factam, per quam aliquoties major quàm terra exhibetur; utraque profecto similis eidem soli extra me existenti esse non potest, & ratio persuadet illam ei maxime esse dissimilem, quae quàm proxime ab ipso videtur emanasse."

Descartes, Meditationes III, 11

"… I have observed, in a number of instances, that there was a great difference between the object and its idea. Thus, for example, I find in my mind two wholly diverse ideas of the sun; the one, by which it appears to me extremely small draws its origin from the senses, and should be placed in the class of adventitious ideas; the other, by which it seems to be many times larger than the whole earth, is taken up on astronomical grounds, that is, elicited from certain notions born with me, or is framed by myself in some other manner. These two ideas cannot certainly both resemble the same sun; and reason teaches me that the one which seems to have immediately emanated from it is the most unlike."

Descartes, Meditations III, 11

"Et quamvis forte una idea ex aliâ nasci possit, non tamen hîc datur progressus in infinitum, sed tandem ad aliquam primam debet deveniri, cujus causa sit in star archetypi, in quo omnis realitas formaliter contineatur, quae est in ideâ tantùm objective."

Descartes, Meditationes III, 15

"And although an idea may give rise to another idea, this regress cannot, nevertheless, be infinite; we must in the end reach a first idea, the cause of which is, as it were, the archetype in which all the reality [or perfection] that is found objectively [or by representation] in these ideas is contained formally [and in act]."

Descartes, Meditations III, 15

Michael Bryson in an essay on Stevens's "Notes Toward a Supreme Fiction,"

The Quest for the Fiction of the Absolute:

"Canto nine considers the movement of the poem between the particular and the general, the immanent and the transcendent: "The poem goes from the poet's gibberish to / The gibberish of the vulgate and back again. / Does it move to and fro or is it of both / At once?" The poet, the creator-figure, the shadowy god-figure, is elided, evading us, "as in a senseless element."  The poet seeks to find the transcendent in the immanent, the general in the particular, trying "by a peculiar speech to speak / The peculiar potency of the general." In playing on the senses of "peculiar" as particular and strange or uncanny, these lines play on the mystical relation of one and many, of concrete and abstract."

Brian Cronin in Foundations of Philosophy:

"The insight is constituted precisely by 'seeing' the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight."

— From Ch. 2, Identifying Direct Insights

Michael Bryson in an essay on Stevens's "Notes Toward a Supreme Fiction":

"The fourth canto returns to the theme of opposites. 'Two things of opposite natures seem to depend / On one another . . . . / This is the origin of change.'  Change resulting from a meeting of opposities is at the root of Taoism: 'Tao produced the One. / The One produced the two. / The two produced the three. / And the three produced the ten thousand things' (Tao Te Ching 42) …."

From an entry of March 7, 2004

 

From the web page

Introduction to the I Ching–
By Richard Wilhelm
:

"He who has perceived the meaning of change fixes his attention no longer on transitory individual things but on the immutable, eternal law at work in all change. This law is the tao of Lao-tse, the course of things, the principle of the one in the many. That it may become manifest, a decision, a postulate, is necessary. This fundamental postulate is the 'great primal beginning' of all that exists, t'ai chi — in its original meaning, the 'ridgepole.' Later Chinese philosophers devoted much thought to this idea of a primal beginning. A still earlier beginning, wu chi, was represented by the symbol of a circle. Under this conception, t'ai chi was represented by the circle divided into the light and the dark, yang and yin,

.

This symbol has also played a significant part in India and Europe. However, speculations of a gnostic-dualistic character are foreign to the original thought of the I Ching; what it posits is simply the ridgepole, the line. With this line, which in itself represents oneness, duality comes into the world, for the line at the same time posits an above and a below, a right and left, front and back-in a word, the world of the opposites."

The t'ai chi symbol is also illustrated on the web page Cognitive Iconology, which says that

"W.J.T. Mitchell calls 'iconology'
a study of the 'logos'
(the words, ideas, discourse, or 'science')
of 'icons' (images, pictures, or likenesses).
It is thus a 'rhetoric of images'
(Iconology: Image, Text, Ideology, p. 1)."

A variation on the t'ai chi symbol appears in a log24.net entry for March 5:

The Line,
by S. H. Cullinane

See too my web page Logos and Logic, which has the following:

"The beautiful in mathematics resides in contradiction. Incommensurability, logoi alogoi, was the first splendor in mathematics."

— Simone Weil, Oeuvres Choisies, ed. Quarto, Gallimard, 1999, p. 100

 Logos Alogos,
by S. H. Cullinane 

In the conclusion of Section 3, Canto X, of "Notes," Stevens says

"They will get it straight one day
at the Sorbonne.
We shall return at twilight
from the lecture
Pleased that
the irrational is rational…."

This is the logoi alogoi of Simone Weil.

In "Notes toward a Supreme Fiction,"
Wallace Stevens lists three criteria
for a work of the imagination:

It Must Be Abstract

The Line,
by S.H. Cullinane 

It Must Change

 The 24,
by S. H. Cullinane

It Must Give Pleasure

Puzzle,
by S. H. Cullinane

Related material:

Logos and Logic.

 

Sunday, September 22, 2002

Sunday September 22, 2002

Filed under: General,Geometry — Tags: , , , , — m759 @ 8:02 pm

Force Field of Dreams

Metaphysics and chess in today’s New York Times Magazine:

  • From “Must-See Metaphysics,” by Emily Nussbaum:

    Joss Whedon, creator of a new TV series —

    “I’m a very hard-line, angry atheist” and
    “I want to invade people’s dreams.”

  • From “Check This,” by Wm. Ferguson:

    Garry Kasparov on chess —

    “When the computer sees forced lines,
    it plays like God.”

Putting these quotations together, one is tempted to imagine God having a little game of chess with Whedon, along the lines suggested by C. S. Lewis:

As Lewis tells it the time had come for his “Adversary [as he was wont to speak of the God he had so earnestly sought to avoid] to make His final moves.” (C. S. Lewis, Surprised by Joy, Harcourt, Brace, and World, Inc., 1955, p. 216) Lewis called them “moves” because his life seemed like a chess match in which his pieces were spread all over the board in the most disadvantageous positions. The board was set for a checkmate….

For those who would like to imagine such a game (God vs. Whedon), the following may be helpful.

George Steiner has observed that

The common bond between chess, music, and mathematics may, finally, be the absence of language.

This quotation is apparently from

Fields of Force:
Fischer and Spassky at Reykjavik
. by George Steiner, Viking hardcover, June 1974.

George Steiner as quoted in a review of his book Grammars of Creation:

“I put forward the intuition, provisional and qualified, that the ‘language-animal’ we have been since ancient Greece so designated us, is undergoing mutation.”

The phrase “language-animal” is telling.  A Google search reveals that it is by no means a common phrase, and that Steiner may have taken it from Heidegger.  From another review, by Roger Kimball:

In ”Grammars of Creation,” for example, he tells us that ”the classical and Judaic ideal of man as ‘language animal,’ as uniquely defined by the dignity of speech . . . came to an end in the antilanguage of the death camps.”

This use of the Holocaust not only gives the appearance of establishing one’s credentials as a person of great moral gravity; it also stymies criticism. Who wants to risk the charge of insensitivity by objecting that the Holocaust had nothing to do with the ”ideal of man as ‘language animal’ ”?

Steiner has about as clear an idea of the difference between “classical” and “Judaic” ideals of man as did Michael Dukakis. (See my notes of September 9, 2002.)

Clearly what music, mathematics, and chess have in common is that they are activities based on pure form, not on language. Steiner is correct to that extent. The Greeks had, of course, an extremely strong sense of form, and, indeed, the foremost philosopher of the West, Plato, based his teachings on the notion of Forms. Jews, on the other hand, have based their culture mainly on stories… that is, on language rather than on form. The phrase “language-animal” sounds much more Jewish than Greek. Steiner is himself rather adept at the manipulation of language (and of people by means of language), but, while admiring form-based disciplines, is not particularly adept at them.

I would argue that developing a strong sense of form — of the sort required to, as Lewis would have it, play chess with God — does not require any “mutation,” but merely learning two very powerful non-Jewish approaches to thought and life: the Forms of Plato and the “archetypes” of Jung as exemplified by the 64 hexagrams of the 3,000-year-old Chinese classic, the I Ching.

For a picture of how these 64 Forms, or Hexagrams, might function as a chessboard,

click here.

Other relevant links:

“As you read, watch for patterns. Pay special attention to imagery that is geometric…”

and


from Shakhmatnaia goriachka

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