parallelisms “still point” « Search Results

Sunday, September 14, 2014

Sermon

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

Epigraphs from Parallelisms of Complete Designs
by Peter J. Cameron (Cambridge University Press, 1976)

Introduction
Through the unknown, remembered gate
When the last of earth left to discover
Is that which was the beginning
(T. S. Eliot: Little Gidding)

I The existence theorem
Here the impossible union
Of spheres of existence is actual
(T. S. Eliot: The Dry Salvages)

II The parallelogram property
A condition of complete simplicity
(Costing not less than everything)
(T. S. Eliot: Little Gidding)

III Steiner points and Veblen points
You say I am repeating
Something I have said before. I shall say it again.
Shall I say it again?
(T. S. Eliot: East Coker)

IV Edge-colourings of complete graphs
And hollyhocks that aim too high
Red into grey and tumble down
(T. S. Eliot: East Coker)

V Biplanes and metric regularity
Two and two, necessarye conjunction,
Holding eche other by the hand or the arm
Whiche betokeneth concorde.
(T. S. Eliot: East Coker)

VI Automorphism groups
At the still point of the turning world. Neither flesh nor fleshless;
Neither from nor towards; at the still point, there the dance is,
But neither arrest nor movement.
(T. S. Eliot: Burnt Norton)

VII Resolutions and partition systems
… fiddle with pentagrams
Or barbituric acids, or dissect
The recurrent image into pre-conscious terrors .. .
(T. S. Eliot: The Dry Salvages)

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Saturday, August 20, 2011

Castle Rock

Filed under: General,Geometry — Tags: 2x4 — m759 @ 6:29 pm

Happy birthday to Amy Adams
(actress from Castle Rock, Colorado)

"The metaphor for metamorphosis…" —Endgame

Related material:

"The idea that reality consists of multiple 'levels,' each mirroring all others in some fashion, is a diagnostic feature of premodern cosmologies in general…."

— Scholarly paper on "Correlative Cosmologies"

"How many layers are there to human thought? Sometimes in art, just as in people’s conversations, we’re aware of only one at a time. On other occasions, though, we realize just how many layers can be in simultaneous action, and we’re given a sense of both revelation and mystery. When a choreographer responds to music— when one artist reacts in detail to another— the sensation of multilayering can affect us as an insight not just into dance but into the regions of the mind.

The triple bill by the Mark Morris Dance Group at the Rose Theater, presented on Thursday night as part of the Mostly Mozart Festival, moves from simple to complex, and from plain entertainment to an astonishingly beautiful and intricate demonstration of genius….

'Socrates' (2010), which closed the program, is a calm and objective work that has no special dance excitement and whips up no vehement audience reaction. Its beauty, however, is extraordinary. It’s possible to trace in it terms of arithmetic, geometry, dualism, epistemology and ontology, and it acts as a demonstration of art and as a reflection of life, philosophy and death."

— Alastair Macaulay in today's New York Times

SOCRATES: Let us turn off the road a little….

— Libretto for Mark Morris's 'Socrates'

See also Amy Adams's new film "On the Road"
in a story from Aug. 5, 2010 as well as a different story,
Eightgate, from that same date:

A 2x4 array of squares

The above reference to "metamorphosis" may be seen,
if one likes, as a reference to the group of all projectivities
and correlations in the finite projective space PG(3,2)—
a group isomorphic to the 40,320 transformations of S₈
acting on the above eight-part figure.

See also The Moore Correspondence from last year
on today's date, August 20.

For some background, see a book by Peter J. Cameron,
who has figured in several recent Log24 posts—

"At the still point, there the dance is."
— Four Quartets

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Tuesday, February 16, 2010

Mysteries of Faith

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

From today's NY Times—

Obituaries for mystery authors
Ralph McInerny and Dick Francis

From the date (Jan. 29) of McInerny's death–

"…although a work of art 'is formed around something missing,' this 'void is its vanishing point, not its essence.'"

– Harvard University Press on Persons and Things (Walpurgisnacht, 2008), by Barbara Johnson

From the date (Feb. 14) of Francis's death–

2x2x2 cube

The EIghtfold Cube

The "something missing" in the above figure is an eighth cube, hidden behind the others pictured.

This eighth cube is not, as Johnson would have it, a void and "vanishing point," but is instead the "still point" of T.S. Eliot. (See the epigraph to the chapter on automorphism groups in Parallelisms of Complete Designs, by Peter J. Cameron. See also related material in this journal.) The automorphism group here is of course the order-168 simple group of Felix Christian Klein.

For a connection to horses, see
a March 31, 2004, post
commemorating the birth of Descartes
and the death of Coxeter–

Putting Descartes Before Dehors

Binary coordinates for a 4x2 array Chess knight formed by a Singer 7-cycle

For a more Protestant meditation,
see The Cross of Descartes—

Descartes

"I've been the front end of a horse
and the rear end. The front end is better."
— Old vaudeville joke

For further details, click on
the image below–

Notre Dame Philosophical Reviews

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Friday, February 5, 2010

The Great Brown

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

Today's New York Times on a current theatrical presentation of The Great Gatsby—

"Throughout the show, the relationship between what is read and its context keeps shifting, with the real world finally giving way entirely to the fictive one."

Owl Eyes in The Great Gatsby—

"This fella's a regular Belasco."

David Brown, producer. Brown died on Monday.

From The Diamond as Big as the Monster in this journal on Dec. 21, 2005–

"At the still point, there the dance is.” –T. S. Eliot, Four Quartets

Eliot was quoted in the epigraph to the chapter on automorphism groups in Parallelisms of Complete Designs, by Peter J. Cameron, published when Cameron was at Merton College, Oxford.

“As Gatsby closed the door of ‘the Merton College Library’ I could have sworn I heard the owl-eyed man break into ghostly laughter.” –F. Scott Fitzgerald

Related material: Yesterday's posts and the jewel in Venn's lotus.

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Wednesday, December 21, 2005

Wednesday December 21, 2005

Filed under: General,Geometry — Tags: The Hawkline Diamonds — m759 @ 4:07 pm

For the feast of
St. Francis Scott Key Fitzgerald

The Diamond
as Big as
the Monster

From Fitzgerald’s The Diamond as Big as the Ritz:

“Now,” said John eagerly, “turn out your pocket and let’s see what jewels you brought along. If you made a good selection we three ought to live comfortably all the rest of our lives.”
Obediently Kismine put her hand in her pocket and tossed two handfuls of glittering stones before him.
“Not so bad,” cried John, enthusiastically. “They aren’t very big, but– Hello!” His expression changed as he held one of them up to the declining sun. “Why, these aren’t diamonds! There’s something the matter!”
“By golly!” exclaimed Kismine, with a startled look. “What an idiot I am!”
“Why, these are rhinestones!” cried John.

From The Hawkline Monster, by Richard Brautigan:

“What are we going to do now?” Susan Hawkline said, surveying the lake that had once been their house.
Cameron counted the diamonds in his hand. There were thirty-five diamonds and they were all that was left of the Hawkline Monster.
“We’ll think of something,” Cameron said.

Related material:

“A disciple of Ezra Pound, he adapts to the short story the ideogrammatic method of The Cantos, where a grammar of images, emblems, and symbols replaces that of logical sequence. This grammar allows for the grafting of particulars into a congeries of implied relation without subordination. In contrast to postmodernists, Davenport does not omit causal connection and linear narrative continuity for the sake of an aleatory play of signification but in order to intimate by combinational logic kinships and correspondences among eras, ideas and forces.”

— When Novelists Become Cubists:
The Prose Ideograms of Guy Davenport,
by Andre Furlani

“T.S. Eliot’s experiments in ideogrammatic method are equally germane to Davenport, who shares with the poet an avant-garde aesthetic and a conservative temperament. Davenport’s text reverberates with echoes of Four Quartets.”

— Andre Furlani

“At the still point,
there the dance is.”

— T. S. Eliot, Four Quartets,
quoted in the epigraph to
the chapter on automorphism groups
in Parallelisms of Complete Designs,
by Peter J. Cameron,
published when Cameron was at
Merton College, Oxford.

“As Gatsby closed the door of
‘the Merton College Library’
I could have sworn I heard
the owl-eyed man
break into ghostly laughter.”

— F. Scott Fitzgerald

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Friday, January 7, 2005

Friday January 7, 2005

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

In Memory of
Guy Davenport

From the day Davenport died:

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“At Merton College, Oxford,
he wrote the first thesis on Joyce
to be accepted by the university.”

— Today’s New York Times

From a very informative essay
on Davenport’s aesthetics:

“T.S. Eliot’s experiments
in ideogrammatic method
are equally germane to Davenport,
who shares with the poet
an avant-garde aesthetic and
a conservative temperament.
Davenport’s text reverberates
with echoes of Four Quartets.”

— Andre Furlani

“At the still point, there the dance is.”