Some may prefer the Stargate version of a seventh symbol —
“Jackson has identified the seventh symbol.” — Stargate
Some may prefer the Stargate version of a seventh symbol —
“Jackson has identified the seventh symbol.” — Stargate
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
The title refers to Calabi-Yau spaces.
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 —
A related Calabi-Yau "Chinese jar" first described in detail in 1905 —
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
" . . . 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
" . . . 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.
"As McCarthy peers through the screen, or veil,
of technological modernity to reveal the underlying
symbolic structures of human experience,
The Making of Incarnation weaves a set of stories
one inside the other, rings within rings, a perpetual
motion machine." — Amazon.com description
of a novel published on All Souls' Day (Dia de los
Muertos), 2021.
The McCarthy novel is mentioned in The New York Times today —
For a simpler perpetual motion machine, see T. S. Eliot's "Chinese jar."
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
Indeed they can :
“. . . 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. . . .“
These “Chinese jars” (as opposed to their contents)
are as follows:
.
See as well Eliot’s 1922 remarks on “extinction of personality”
and the phrase “ego-extinction” in Weyl’s Philosophy of Mathematics —
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 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.
"… 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.
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):
Related entry: Binary Geometry.
In the box-style I Ching
Hexagram 34,
The Power of the Great,
is represented by
.
Art is represented
by a box
(Hexagram 20,
Contemplation, View)
.
And of course
great art
is represented by
an X in a box.
(Hexagram 2,
The Receptive)
.
“… as a Chinese jar still
Moves perpetually
in its stillness”
“… at the still point,
there the dance is.”
— T. S. Eliot
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.” |
For those who prefer
technology to poetry,
there is the Xbox 360.
(Today is day 360 of 2005.)
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.
Balance
"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"
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.
Related material: Elegance and the following description of Beethoven's last quartet.
Program note by Eric Bromberger:
String Quartet in F major, Op. 135 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. |
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…."
These "Chinese jars"
(as opposed to their contents)
are as follows:
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.
Powered by WordPress