Log24

Saturday, May 4, 2019

The Chinese Jars of Shing-Tung Yau

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

The title refers to Calabi-Yau spaces.

T. S. Eliot —

Four Quartets

. . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.

A less "cosmic" but still noteworthy code — The Golay code.

This resides in a 12-dimensional space over GF(2).

Related material from Plato and R. T. Curtis

Counting symmetries with the orbit-stabilizer theorem

A related Calabi-Yau "Chinese jarfirst described in detail in 1905

Illustration of K3 surface related to Mathieu moonshine

A figure that may or may not be related to the 4x4x4 cube that
holds the classical  Chinese "cosmic code" — the I Ching

ftp://ftp.cs.indiana.edu/pub/hanson/forSha/AK3/old/K3-pix.pdf

Friday, May 3, 2019

“As a Chinese jar” — T. S. Eliot

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

 

Thursday, January 4, 2018

Perspectives from a Chinese Jar

Filed under: General,Geometry — Tags: , — m759 @ 4:40 PM

" . . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness."

— T. S. Eliot, Four Quartets

"The Grand Valley spirit never dies."

— Adapted from the Tao Te Ching

Monday, April 13, 2020

Tribute

Filed under: General — m759 @ 2:46 PM

The May 2020 Notices of the American Mathematical Society  has a
memorial tribute article on Goro Shimura, who died on May 3, 2019.

See also this  journal on May 3, 2019 in posts now tagged Wondertale.

Related ethnic remark:  “As a Chinese jar…” — T. S.  Eliot

 

“Things can get muddled further….”

— Webpage on the Japanese word

manji.

Indeed they can :

Sunday, June 16, 2019

Eliot’s Perpetual Motion Structure*

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

From a date described by Peter Woit in his post
"Not So Spooky Action at a Distance" (June 11) —

See also The Lost Well.

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

Monday, June 3, 2019

Jar Story

Filed under: General — Tags: , — m759 @ 3:41 PM

(Continued)

  ". . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.”

— T. S. Eliot, Four Quartets

From Writing Chinese Characters:

“It is practical to think of a character centered
within an imaginary square grid . . . .
The grid can be subdivided, usually to
9 or 16 squares. . . ."

The image “http://www.log24.com/log/pix04B/041119-ZhongGuo.jpg” cannot be displayed, because it contains errors.

These “Chinese jars” (as opposed to their contents)
are as follows:    

Grids, 3x3 and 4x4 .

See as well Eliot's 1922 remarks on "extinction of personality"
and the phrase "ego-extinction" in Weyl's Philosophy of Mathematics

Monday, May 6, 2019

Possibilities

Filed under: General — Tags: — m759 @ 12:25 PM

Related material — The last three posts —

The Crimson Abyss,
Transgressive Politics at Harvard, and
"Thousand" Rhetoric

— as well as Saturday's The Chinese Jars of Shing-Tung Yau.

Friday, May 3, 2019

The Structure of Story Space

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

T. S. Eliot

Four Quartets

. . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.

Lévi-Strauss

A Permanent Order of Wondertale Elements

In Vol. I of Structural Anthropology , p. 209, I have shown that this analysis alone can account for the double aspect of time representation in all mythical systems: the narrative is both “in time” (it consists of a succession of events) and “beyond” (its value is permanent). With regard to Propp’s theories my analysis offers another advantage: I can reconcile much better than Propp himself  his principle of a permanent order of wondertale elements with the fact that certain functions or groups of functions are shifted from one tale to the next (pp. 97-98. p. 108). If my view is accepted, the chronological succession will come to be absorbed into an atemporal matrix structure whose form is indeed constant. The shifting of functions is then no more than a mode of permutation (by vertical columns or fractions of columns).

Or by congruent quarter-sections.

Friday, July 6, 2018

Something

Filed under: General,Geometry — Tags: , — m759 @ 9:48 AM

"… Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness."

— T. S. Eliot, "Burnt Norton," 1936

"Read something that means something."

Advertising slogan for The New Yorker

The previous post quoted some mystic meditations of Octavio Paz
from 1974. I prefer some less mystic remarks of Eddington from
1938 (the Tanner Lectures) published by Cambridge U. Press in 1939 —

"… we have sixteen elements with which to form a group-structure" —

See as well posts tagged Dirac and Geometry.

Tuesday, September 26, 2017

Happy Birthday, T. S. Eliot

Filed under: General — m759 @ 2:56 AM

" . . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness."

Four Quartets

See posts now tagged Myspace China.

Thursday, March 8, 2007

Thursday March 8, 2007

Filed under: General,Geometry — m759 @ 1:00 PM
Day Without
Logic

The image “http://www.log24.com/log/pix06A/060804-DWA2.gif” cannot be displayed, because it contains errors.

Symbol of the Dec. 1
Day Without Art

This resembles the following symbol,
due to logician Charles Sanders Peirce,
of the logic of binary opposition:

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

(For futher details on the role
of this symbol in logic, see
Chinese Jar Revisited.)

On this, International Women’s Day,
we might also consider the
widely quoted thoughts on logic of
Harvard professor Barbara Johnson:

Nothing Fails Like Success, by Barbara Johnson

Detail:

Barbara Johnson, Nothing Fails Like Success, detail

“Instead of a simple ‘either/or’ structure,
deconstruction attempts to elaborate a discourse
that says neither “either/or”, nor “both/and”
nor even “neither/nor”, while at the same time
not totally abandoning these logics either.”

It may also be of interest on
International Women’s Day
that in the “box style” I Ching
(suggested by a remark of
Jungian analyst
Marie-Louise von Franz)
the symbol

The image “http://www.log24.com/theory/images/PeirceBox.bmp” cannot be displayed, because it contains errors.
 
denotes
Hexagram 2,
The Receptive.

Friday, August 4, 2006

Friday August 4, 2006

Filed under: General — m759 @ 2:00 PM
The Double Cross

The following symbol
has been associated
with the date
December 1:

The image “http://www.log24.com/log/pix06A/060804-DWA2.gif” cannot be displayed, because it contains errors.

Click on the symbol
for details.

That date is connected
to today’s date since
Dec. 1 is the feast
i.e., the deathday– of
a saint of mathematics:
G. H. Hardy, author of
the classic
A Mathematician’s Apology
(online, pdf, 52 pp. ),
while today is the birthday
of three less saintly
mathematical figures:
Sir William Rowan Hamilton,

For these birthdays, here is
a more cheerful version of
the above symbol:

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

For the significance of
this version, see
Chinese Jar Revisited
(Log24, June 27, 2006),
a memorial to mathematician
Irving Kaplansky
(student of Mac Lane).

This version may be regarded
as a box containing the
cross of St. Andrew.
If we add a Greek cross
(equal-armed) to the box,
we obtain the “spider,”
or “double cross,” figure

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

of my favorite mythology:
Fritz Leiber’s Changewar.

Tuesday, June 27, 2006

Tuesday June 27, 2006

Filed under: General,Geometry — m759 @ 10:31 AM
Chinese Jar
Revisited

In memory of
Irving Kaplansky,
who died on
Sunday, June 25, 2006

“Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.”

T. S. Eliot


Kaplansky received his doctorate in mathematics at Harvard in 1941 as the first Ph.D. student of Saunders Mac Lane.

From the April 25, 2005, Harvard Crimson:

Ex-Math Prof Mac Lane, 95, Dies

Gade University Professor of Mathematics Barry Mazur, a friend of the late Mac Lane, recalled that [a Mac Lane paper of 1945] had at first been rejected from a lower-caliber mathematical journal because the editor thought that it was “more devoid of content” than any other he had read.

“Saunders wrote back and said, ‘That’s the point,'” Mazur said. “And in some ways that’s the genius of it. It’s the barest, most Beckett-like vocabulary that incorporates the theory and nothing else.”

He likened it to a sparse grammar of nouns and verbs and a limited vocabulary that is presented “in such a deft way that it will help you understand any language you wish to understand and any language will fit into it.”

A sparse grammar of lines from Charles Sanders Peirce (Harvard College, class of 1859):

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

The image “http://www.log24.com/theory/images/PeirceSymbols1.jpg” cannot be displayed, because it contains errors.

It is true of this set of binary connectives, as it is true of logic generally, that (as alleged above of Mac Lane’s category theory) “it will help you understand any language you wish to understand and any language will fit into it.” Of course, a great deal of questionable material has been written about these connectives. (See, for instance, Piaget and De Giacomo.) For remarks on the connectives that are not questionable, see Wittgenstein’s Tractatus Logico-Philosophicus (English version, 1922), section 5.101, and Knuth’s “Boolean Basics” (draft, 2006).

Related entry: Binary Geometry.

Monday, December 26, 2005

Monday December 26, 2005

Filed under: General — Tags: — m759 @ 7:00 PM
Language Game on
Boxing Day

In the box-style I Ching
Hexagram 34,
The Power of the Great,
is represented by

  The image “http://www.log24.com/theory/images/Box34.gif” cannot be displayed, because it contains errors. .

Art is represented
by a box
(Hexagram 20,
Contemplation, View)

  The image “http://www.log24.com/theory/images/Box20.gif” cannot be displayed, because it contains errors. .

  And of course 
great art
is represented by
an X in a box.
(Hexagram 2,
The Receptive)

  The image “http://www.log24.com/theory/images/Box02.gif” cannot be displayed, because it contains errors. .

“… as a Chinese jar still   
Moves perpetually
 in its stillness”

“… at the still point,  
there the dance is.”

— T. S. Eliot 

The image “http://www.log24.com/log/pix05/050501-Quad.jpg” cannot be displayed, because it contains errors.

A Jungian on this six-line figure:

“They are the same six lines that exist in the I Ching…. Now observe the square more closely: four of the lines are of equal length, the other two are longer…. For this reason symmetry cannot be statically produced and a dance results.”
 
— Marie-Louise von Franz,
   Number and Time


For those who prefer
technology to poetry,
there is the Xbox 360.

(Today is day 360 of 2005.)

Monday December 26, 2005

Filed under: General — m759 @ 3:00 PM

Wren Day

St. Stephen’s Day [Dec. 26] is a national holiday in Ireland, but the celebrations have little connection to the Saint.”

This day in Ireland is instead devoted to a barbaric ritual, “the hunting of the wren.”

Let us therefore recall a more civilized figure– St. Christopher Wren— whose feast day is Feb. 25.

From Log24 on that date in 2005:

… 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

Monday, October 31, 2005

Monday October 31, 2005

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

The image “http://log24.com/log/pix03/030109-gridsmall.gif” cannot be displayed, because it contains errors.

"An asymmetrical balance is sought since it possesses more movement. This is achieved by the imaginary plotting of the character upon a nine-fold square, invented by some ingenious writer of the Tang dynasty. If the square were divided in half or in four, the result would be symmetrical, but the nine-fold square permits balanced asymmetry."

— Chiang Yee, Chinese Calligraphy,
   
quoted in Aspen no. 10, item 8

"'Burnt Norton' opens as a meditation on time. Many comparable and contrasting views are introduced. The lines are drenched with reminiscences of Heraclitus' fragments on flux and movement….  the chief contrast around which Eliot constructs this poem is that between the view of time as a mere continuum, and the difficult paradoxical Christian view of how man lives both 'in and out of time,' how he is immersed in the flux and yet can penetrate to the eternal by apprehending timeless existence within time and above it. But even for the Christian the moments of release from the pressures of the flux are rare, though they alone redeem the sad wastage of otherwise unillumined existence. Eliot recalls one such moment of peculiar poignance, a childhood moment in the rose-garden– a symbol he has previously used, in many variants, for the birth of desire. Its implications are intricate and even ambiguous, since they raise the whole problem of how to discriminate between supernatural vision and mere illusion. Other variations here on the theme of how time is conquered are more directly apprehensible. In dwelling on the extension of time into movement, Eliot takes up an image he had used in 'Triumphal March': 'at the still point of the turning world.' This notion of 'a mathematically pure point' (as Philip Wheelwright has called it) seems to be Eliot's poetic equivalent in our cosmology for Dante's 'unmoved Mover,' another way of symbolising a timeless release from the 'outer compulsions' of the world. Still another variation is the passage on the Chinese jar in the final section. Here Eliot, in a conception comparable to Wallace Stevens' 'Anecdote of the Jar,' has suggested how art conquers time:

       Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness."

— F. O. Matthiessen,
   The Achievement of T.S. Eliot,
   Oxford University Press, 1958,
   as quoted in On "Burnt Norton"

Friday, February 25, 2005

Friday February 25, 2005

Filed under: General — 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.

Friday, November 19, 2004

Friday November 19, 2004

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

From Tate to Plato

In honor of Allen Tate‘s birthday (today)
and of the MoMA re-opening (tomorrow)

“For Allen Tate the concept of tension was the most useful formal tool at the critic’s disposal, as irony and paradox were for Brooks. The principle of tension sustains the whole structure of meaning, and, as Tate declares in Tension in Poetry (1938), he derives it from lopping the prefixes off the logical terms extension and intension (which define the abstract and denotative aspect of the poetic language and, respectively, the concrete and connotative one). The meaning of the poem is ‘the full organized body of all the extension and intension that we can find in it.’  There is an infinite line between extreme extension and extreme intension and the readers select the meaning at the point they wish along that line, according to their personal drives, interests or approaches. Thus the Platonist will tend to stay near the extension end, for he is more interested in deriving an abstraction of the object into a universal….”

— from Form, Structure, and Structurality,
   by Radu Surdulescu

“Eliot, in a conception comparable to Wallace Stevens’ ‘Anecdote of the Jar,’ has suggested how art conquers time:

        Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.”

F. O. Matthiessen
   in The Achievement of T.S. Eliot,
   Oxford University Press, 1958

From Writing Chinese Characters:

“It is practical to think of a character centered within an imaginary square grid…. The grid can… be… subdivided, usually to 9 or 16 squares….”

The image “http://www.log24.com/log/pix04B/041119-ZhongGuo.jpg” cannot be displayed, because it contains errors.

These “Chinese jars
(as opposed to their contents)
are as follows:

The image “http://www.log24.com/log/pix04B/041119-Grids.gif” cannot be displayed, because it contains errors.

Various previous Log24.net entries have
dealt with the 3×3 “form” or “pattern”
(to use the terms of T. S. Eliot).

For the 4×4 form, see Poetry’s Bones
and Geometry of the 4×4 Square.

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