Friday, December 31, 2010

“All Things Shining”

Filed under: General — m759 @ 9:00 AM

David Brooks's column in today's New York Times  suggests a search for the origin of the phrase used as the title of a book Brooks is reviewing— All Things Shining , by philosophy professors Hubert Dreyfus and Sean Dorrance Kelly.


The phrase occurred, notably, in Terrence Malick's 1998 film "The Thin Red Line." I have not yet found an earlier usage.

(A search within  the book for "title" yielded no relevant results, and such searches for "Malick" and for "Thin Red Line" yielded no  results.)

For some background, see an August 20 weblog post by Kelly, Shining in Homer.

For some other background, see an August 20 post in this  weblog.

Update: The phrase occurs in Stephen Mitchell's 1989 translation from the Odes of Solomon

And you have made all things new;
you have showed me all things shining.

Thursday, December 30, 2010

The Sound of Music*

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

From Tuesday at the Stephen King Kindergarten

"They had sung that song all together at the Jack and Jill Nursery School…."

— Stephen King, The Shining

A link introducing Tuesday's kindergarten

Fare Thee Well

Images from Fare Thee Well


Click for Julie Andrews in the full video.



Shakespearean Fool

© 2004 Natasha Wescoat

Dear God, I am not a son of a bitch. Please.

Jack Torrance in The Shining

* For Agathe von Trapp

Wednesday, December 29, 2010

Canterbury Tale

Filed under: General — m759 @ 7:20 PM

For today's Feast of St. Thomas Becket


See also the dedication following the remark by another Ishmael quoted here this morning.

True Grid

Filed under: General,Geometry — m759 @ 5:24 PM

Part I: True

Bulletin of the American Mathematical Society , October 2002, page 563

“…  the study of symmetries of patterns led to… finite geometries….”

– David W. Henderson, Cornell University

This statement may be misleading, if not (see Part II below) actually false. In truth, finite geometries appear to have first arisen from Fano's research on axiom systems. See The Axioms of Projective Geometry  by Alfred North Whitehead, Cambridge University Press, 1906, page 13.

Part II: Grid

For the story of how symmetries of patterns later did  lead to finite geometries, see the diamond theorem.

Toy Stories

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

From the Bulletin of the American Mathematical Society , October 2002, p. 563:

“To produce decorations for their weaving, pottery, and other objects, early artists experimented with symmetries and repeating patterns.  Later the study of symmetries of patterns led to tilings, group theory, crystallography, finite geometries, and in modern times to security codes and digital picture compactifications.  Early artists also explored various methods of representing existing objects and living things.  These explorations led to… [among other things] computer-generated movies (for example, Toy Story ).”

– David W. Henderson, Cornell University



From the weblog The Ghost Light on Christmas Day, 2010 —


For Rachel and her children.

Tuesday, December 28, 2010

Dry Bones

Filed under: General — m759 @ 7:59 PM

The webpage of Cullinane College — "For Love of God…."


Related material —

From a post for the opening of Cullinane College on January 29, 2003:

"Young man sings 'Dry Bones'"




What prompted the above meditation —


From an obituary of Bill White (who reportedly died at 66 on November 14)—

"During his career, he was consulted by, among others,
the crime writer Patricia Cornwell, and the artist Damien Hirst
(who used his expertise when working on his 2007 piece
For the Love of God, a platinum cast of a skull, encrusted with diamonds)."

Insane Symmetry

Filed under: General,Geometry — m759 @ 11:02 AM

Continued from yesterday's Church Diamond and from Dec. 17's Fare Thee Well —

The San Francisco Examiner  last year
on New Year's Eve —

Discover the modern art of Amish quilts

By: Leslie Katz 12/31/09 1:00 AM

Arts editor


Quilts made by Amish women in Pennsylvania,
such as this traditional center diamond,
reveal the makers’ keen sense of color and design.

Household handicrafts and heirlooms made by American women seen as precursors to modern art is one underlying thesis of “Amish Abstractions: Quilts from the Collection of Faith and Stephen Brown,” a provocative exhibit on view at the de Young Museum through June.

Curated by Jill D’Alessandro of the Fine Arts Museums of San Francisco, the show features about 50 full-size and crib quilts made between 1880 and 1940 in Pennsylvania and the Midwest during what experts consider the apex of Amish quilt-making production.

Faith and Stephen Brown, Bay Area residents who began collecting quilts in the 1970s after seeing one in a shop window in Chicago and being bowled over by its bold design, say their continued passion for the quilts as art is in part because they’re so reminiscent of paintings by modern masters like Mark Rothko, Josef Albers, Sol LeWitt and Ellsworth Kelly — but the fabric masterpieces came first.

“A happy visual coincidence” is how the Browns and D’Alessandro define the connection, pointing to the brilliance in color theory, sophisticated palettes and complex geometry that characterize both the quilts and paintings.

“There’s an insane symmetry  to these quilts,” says D’Alessandro….

Read more at the San Francisco Examiner .

The festive nature of the date of the above item, New Year's Eve, suggests Stephen King's

All work and no play makes Jack a dull boy.

and also a (mis)quotation from a photographer's weblog— 

"Art, being bartender, is never drunk."

— Quotation from Peter Viereck misattributed to Randall Jarrell in
   Art as Bartender and the Golden Gate.

By a different photographer —


See also…


We may imagine the bartender above played by Louis Sullivan.

Monday, December 27, 2010

Church Diamond

Filed under: General,Geometry — Tags: — m759 @ 3:09 PM

IMAGE- The diamond property

Also known, roughly speaking, as confluence  or the Church-Rosser property.

From “NYU Lambda Seminar, Week 2” —

[See also the parent page Seminar in Semantics / Philosophy of Language or:
What Philosophers and Linguists Can Learn From Theoretical Computer Science But Didn’t Know To Ask)

A computational system is said to be confluent, or to have the Church-Rosser or diamond property, if, whenever there are multiple possible evaluation paths, those that terminate always terminate in the same value. In such a system, the choice of which sub-expressions to evaluate first will only matter if some of them but not others might lead down a non-terminating path.

The untyped lambda calculus is confluent. So long as a computation terminates, it always terminates in the same way. It doesn’t matter which order the sub-expressions are evaluated in.

A computational system is said to be strongly normalizing if every permitted evaluation path is guaranteed to terminate. The untyped lambda calculus is not strongly normalizing: ω ω doesn’t terminate by any evaluation path; and (\x. y) (ω ω) terminates only by some evaluation paths but not by others.

But the untyped lambda calculus enjoys some compensation for this weakness. It’s Turing complete! It can represent any computation we know how to describe. (That’s the cash value of being Turing complete, not the rigorous definition. There is a rigorous definition. However, we don’t know how to rigorously define “any computation we know how to describe.”) And in fact, it’s been proven that you can’t have both. If a computational system is Turing complete, it cannot be strongly normalizing.

There is no connection, apart from the common reference to an elementary geometric shape, between the use of “diamond” in the above Church-Rosser sense and the use of “diamond” in the mathematics of (Cullinane’s) Diamond Theory.

Any attempt to establish such a connection would, it seems, lead quickly into logically dubious territory.

Nevertheless, in the synchronistic spirit of Carl Jung and Arthur Koestler, here are some links to such a territory —

 Link One — “Insane Symmetry”  (Click image for further details)—


See also the quilt symmetry in this  journal on Christmas Day.

Link Two — Divine Symmetry

(George Steiner on the Name in this journal on Dec. 31 last year (“All about Eve“)) —

“The links are direct between the tautology out of the Burning Bush, that ‘I am’ which accords to language the privilege of phrasing the identity of God, on the one hand, and the presumptions of concordance, of equivalence, of translatability, which, though imperfect, empower our dictionaries, our syntax, our rhetoric, on the other. That ‘I am’ has, as it were, at an overwhelming distance, informed all predication. It has spanned the arc between noun and verb, a leap primary to creation and the exercise of creative consciousness in metaphor. Where that fire in the branches has gone out or has been exposed as an optical illusion, the textuality of the world, the agency of the Logos in logic—be it Mosaic, Heraclitean, or Johannine—becomes ‘a dead letter.'”

George Steiner, Grammars of Creation

(See also, from Hanukkah this year,  A Geometric Merkabah and The Dreidel is Cast.)

Link Three – Spanning the Arc —

Part A — Architect Louis Sullivan on “span” (see also Kindergarten at Stonehenge)

Part B — “Span” in category theory at nLab —


Also from nLab — Completing Spans to Diamonds

“It is often interesting whether a given span in some partial ordered set can be completed into a diamond. The property of a collection of spans to consist of spans which are expandable into diamonds is very useful in the theory of rewriting systems and producing normal forms in algebra. There are classical results e.g. Newman’s diamond lemma, Širšov-Bergman’s diamond lemma (Širšov is also sometimes spelled as Shirshov), and Church-Rosser theorem (and the corresponding Church-Rosser confluence property).”

The concepts in this last paragraph may or may not have influenced the diamond theory of Rudolf Kaehr (apparently dating from 2007).

They certainly have nothing to do with the Diamond Theory of Steven H. Cullinane (dating from 1976).

For more on what the above San Francisco art curator is pleased to call “insane symmetry,” see this journal on Christmas Day.

For related philosophical lucubrations (more in the spirit of Kaehr than of Steiner), see the New York Times  “The Stone” essay “Span: A Remembrance,” from December 22—

“To understand ourselves well,” [architect Louis] Sullivan writes, “we must arrive first at a simple basis: then build up from it.”

Around 300 BC, Euclid arrived at this: “A point is that which has no part. A line is breadthless length.”

See also the link from Christmas Day to remarks on Euclid and “architectonic” in Mere Geometry.

Saturday, December 25, 2010

Not-So-Fearful Symmetry

Filed under: General,Geometry — m759 @ 12:25 AM

From a Mennonite homeschooling family


It's a start. For more advanced remarks from the same date, see Mere Geometry.

Friday, December 24, 2010

Worst Christmas Pageant Ever

Filed under: General — Tags: — m759 @ 10:30 AM

Starring the White Witch of Narnia —

Click to enlarge


Some background —

Kindergarten at Stonehenge, by Louis Sullivan, and
Underneath the Lintel, by Glen Berger

Hollywood vs. Heidegger

Filed under: General — m759 @ 12:00 AM

The Silver ChaliceHollywood version and Heidegger version

Thursday, December 23, 2010

Kindergarten at Stonehenge

Filed under: General — m759 @ 1:44 PM

From "The Stone" (a philosophy series) in today's New York Times

Louis Sullivan, in his Kindergarten Chats , on the pier and lintel as basic elements of architecture:

… [Sullivan says that the pier] embodies “the simplest physical beginnings"….
    Add the lintel and “presto!” …. 
    But he has a question: what is this sudden coming-into-being of a way of being?

  “We have no true name for it in the language. But if you fix the phenomenon well in your thought,
   the absence of an exact word for it need not matter much.”

The source —

(Click for clearer image)


A related passage —

"Crucial here is the concept of emergence , the sudden coming into being of something that is greater than its component parts (like water is greater than its component parts, hydrogen and oxygen; therefore, water is an emergent property)."

Article on Bakhtin in The Cervantes Encyclopedia , by Howard Mancing (Greenwood Publishing Group, 2004)

See also "strong emergence" in this journal.

Wednesday, December 22, 2010


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

Published on November 10, 2009

IMAGE- Borovik and Borovik, 'Mirrors and Reflections: The Geometry of Finite Reflection Groups'

The above book may be regarded as an ironic answer to a question posed here on that date

“Public commentators assumed the air of kindergarten teachers who had to protect their children from thinking certain impermissible and intolerant thoughts.”

– David Brooks in the Nov. 10, 2009, New York Times

What else is new?

For related kindergarten thoughts, see Finite Geometry and Physical Space.

For the connection of the kindergarten thoughts to reflections, see A Simple Reflection Group of Order 168.

Tuesday, December 21, 2010

Savage Solstice

Filed under: General,Geometry — Tags: — m759 @ 7:20 PM

In memory of kaleidoscope enthusiast Cozy Baker, who died at 86, according to Saturday's Washington Post , on October 19th.


This journal on that date — Savage Logic and Savage Logic continued.

See this journal on All Saints' Day 2006 for some background to those posts—

“Savage logic works like a kaleidoscope whose chips can fall into a variety of patterns while remaining unchanged in quantity, form, or color. The number of patterns producible in this way may be large if the chips are numerous and varied enough, but it is not infinite. The patterns consist in the disposition of the chips vis-a-vis one another (that is, they are a function of the relationships among the chips rather than their individual properties considered separately). And their range of possible transformations is strictly determined by the construction of the kaleidoscope, the inner law which governs its operation. And so it is too with savage thought. Both anecdotal and geometric, it builds coherent structures out of ‘the odds and ends left over from psychological or historical process.’

These odds and ends, the chips of the kaleidoscope, are images drawn from myth, ritual, magic, and empirical lore. (How, precisely, they have come into being in the first place is one of the points on which Levi-Strauss is not too explicit, referring to them vaguely as the ‘residue of events… fossil remains of the history of an individual or a society.’) Such images are inevitably embodied in larger structures– in myths, ceremonies, folk taxonomies, and so on– for, as in a kaleidoscope, one always sees the chips distributed in some pattern, however ill-formed or irregular. But, as in a kaleidoscope, they are detachable from these structures and arrangeable into different ones of a similar sort. Quoting Franz Boas that ‘it would seem that mythological worlds have been built up, only to be shattered again, and that new worlds were built from the fragments,’ Levi-Strauss generalizes this permutational view of thinking to savage thought in general.”

– Clifford Geertz, “The Cerebral Savage: the Structural Anthropology of Claude Levi-Strauss,” in Encounter, Vol. 28 No. 4 (April 1967), pp. 25-32.

Related material  —


See also "Levi-Strauss" in this journal and "At Play in the Field."

Monday, December 20, 2010


Filed under: General — Tags: , — m759 @ 7:27 PM

Happy birthday to noir queen Audrey Totter. She starred in “The Set-Up,” a 1949 fight film.


“You sure know how to show a girl a good time.”
— Renée Zellweger in “New in Town” (2009)

Enter a Messenger

Filed under: General — Tags: — m759 @ 9:29 AM

The title is from the Leap Day, 2004, post for Academy Awards day.

Two items from December 16, 2007 —

From a photographer's journal — Kofel, Oberammergau, 12/16/07

From this  journal — Mad Phaedrus Meets Mad Ezra, 12/16/07

See also yesterday's Rosetta and the Stone and Ross Douthat in today's New York Times

"Thanks in part to this bunker mentality, American Christianity has become what Hunter calls a 'weak culture'— one that mobilizes but doesn’t convert, alienates rather than seduces, and looks backward toward a lost past instead of forward to a vibrant future. In spite of their numerical strength and reserves of social capital, he argues, the Christian churches are mainly influential only in the 'peripheral areas' of our common life. In the commanding heights of culture, Christianity punches way below its weight."

"Ready when you are, C.B."

Sunday, December 19, 2010

Rosetta and the Stone

Filed under: General — Tags: , — m759 @ 2:29 PM

"Brightest and Best of the Stars of the Morning"

— Title of a Christian propaganda* song


Rosetta Jacobs (alias Piper Laurie) as the wife of Joseph Goebbels ("The Bunker," 1981)

For the Stone of the title, see Caesarian, The Tiffany Puzzle, and Willkommen .

For Rosetta, see Three in One and a sequel, Stella.

* See an article on Oberammergau and a pastor's weblog with the song in that setting (but with place-name suppressed).


Filed under: General,Geometry — Tags: , — m759 @ 8:00 AM

In the spirit of last night's SNL Hanukkah version of "It's a Wonderful Life" —

A Geometric Merkabah for Hanukkah from December 1, and…

"The Homepage of Contemporary Structuralism" (click to enlarge) —


Detail —


Summary —

IMAGE- Stella Octangula and Claude Levi-Strauss

Saturday, December 18, 2010

Meanwhile, back in 1955…

Filed under: General — m759 @ 9:48 PM

"And this is what the seventh day before Christmas looked like…"

Jean Ritchie at Kentucky Family Reunion, Seventh Day Before Christmas, 1955

George Pickow, Artist Who Chronicled Musical Life, Is Dead at 88

Some Say.

(In the spirit of the season, let us forgive this Ghost of Christmas Past his historical inaccuracy.)

Logic Tale

Filed under: General,Geometry — m759 @ 2:45 PM

Tale (Nov. 23)

Graham Priest (Nov. 28)

A Geometric Merkabah (Dec. 1)

John Baez (Dec. 15, UTC)

Logica Universalis  (journal)


Universal Logic at Neuchatel

Moretti homepage

Moretti thesis, summary

Moretti thesis (pdf, 5.05 MB)

Church Logic

Church Narrative


Friday, December 17, 2010

Time and Chance

Filed under: General,Geometry — m759 @ 1:13 PM

New York Lottery yesterday, December 16, 2010— midday 282, evening 297.

Suggested by a Jesuit commentary that mentions the midday number —

Page 282 of Encyclopaedia of Religion and Ethics , Volume 2,
edited by James Hastings, John Alexander Selbie, and Louis Herbert Gray,
New York, Charles Scribner's Sons, 1910 —

"Philosophy seeks not absolute first principles, nor yet purely immediate insights,
but the self-mediation of the system of truth, and an insight into this self-mediation.
Axioms, in the language of modern theory, are best defined, neither as certainties
nor as absolutely first principles, but as those principles which are used as the first
in a special theory.

LITERATURE — A complete view of the literature of the problems
regarding axioms is impossible, since the topic is connected with all
the fundamental philosophical issues….  JOSIAH ROYCE"

Suggested by the evening number, 297, and by Amy Adams (see previous post) —

Dream of Heaven

See also a cartoon version of Russell and Whitehead discussing axioms.


Filed under: General — m759 @ 12:00 PM

"The film-within-the-film represents no movie ever made by anyone at any time."

Vincent Canby on a Blake Edwards production

IMAGE- Amy Adams, from high school to 'The Fighter'

Dabo claves regni caelorum.  By silent shore
Ripples spread from castle rock.  The metaphor
For metamorphosis no keys unlock.

"Endgame," November 7, 1986

Fare Thee Well

Filed under: General,Geometry — Tags: , — m759 @ 4:01 AM

Excerpt from a post of 8 AM May 26, 2006

A Living Church
continued from March 27, 2006

"The man who lives in contact with what he believes to be a living Church is a man always expecting to meet Plato and Shakespeare to-morrow at breakfast."

– G. K. Chesterton

The Eightfold Cube

Platonic Solid

The image “http://www.log24.com/log/pix06A/060526-JackInTheBox.jpg” cannot be displayed, because it contains errors.

Shakespearean Fool
© 2004 Natasha Wescoat

A related scene from the opening of Blake Edwards's "S.O.B." —


Click for Julie Andrews in the full video.

Thursday, December 16, 2010

Punch Line

Filed under: General — m759 @ 6:00 PM

From a post on December 4th —


The above theater was the venue of "The Front Page" in 1928-1929.

This afternoon's New York Times  front page (click to enlarge) —


"The son of a bitch stole my watch."

Related philosophy —
"Eventually it all works out."

Vincent Canby on a Blake Edwards production

Curtain Call

Filed under: General — m759 @ 2:02 PM

Julie Taymor in an interview published Dec. 12 —

“I’ve got two Broadway shows, a feature film, and Mozart,’’ she said.
“It’s a very interesting place to be and to be able to move back and forth,
but at a certain point you have to be able to step outside and see,’’
and here she dropped her voice to a tranquil whisper, “it’s just theater.
It’s all theater. It’s all theater. The whole thing is theater.’’

Google News this afternoon (Blake Edwards obituary) —



Filed under: General — m759 @ 1:00 PM

Finale of Beethoven's String Quartet No. 16, Opus 135

        Related material — Posts in this journal on The King and the Corpse .

Wednesday, December 15, 2010


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

David Corfield discusses the philosophy of mathematics (Dec. 14) —

"It’s very tricky choosing a rich and interesting case study which is philosophically salient. To encourage the reader or listener to follow up the mathematics to understand what you’re saying, there must be a decent pay-off. An intricate twentieth century case study had better pack plenty of meta-mathematical punch."

Steve Martin discusses the philosophy of art (Dec. 5) —

http://www.log24.com/log/pix10B/101215-BraverMartin.jpg http://www.log24.com/log/pix10B/101215-WallPower.jpg

CBS News interviews Martin at the Whitney Museum —

"We paused to consider the impact of a George Bellows fight scene. Martin said it has 'wall power.'

What does that phrase mean? 'How it holds the wall. How it feels when you're ten or 20 feet away from it. It really takes hold of the room.'"

See also Halloween 2010

IMAGE- The 2x2 case of the diamond theorem as illustrated by Josefine Lyche, Oct. 2010

Tuesday, December 14, 2010

Types of Ambiguity —

Filed under: General,Geometry — m759 @ 9:48 PM

Galois Meets Doctor Faustus

Galois's theory of mathematical  ambiguity (see June 14) —

  My principal meditations for some time have been directed towards
  the application of the theory of ambiguity to transcendental
  analysis.  It was a question of seeing a priori in a relation
  between quantities or transcendent functions, what exchanges one
  could make, which quantities one could substitute for the given
  quantities without the original relation ceasing to hold.  That
  immediately made clear the impossibility of finding many expressions
  that one could look for.  But I do not have time and my ideas are
  not yet well developed on this ground which is immense.

 — Evariste Galois, testamentary letter, translated by James Dolan

Thomas Mann on musical  ambiguity in his novel Doctor Faustus


Related material — Some context for the above and some remarks on the German original.

Play and Interplay

Filed under: General,Geometry — m759 @ 4:23 AM

Julie Taymor in an interview published Dec. 12 —

“I’ve got two Broadway shows, a feature film, and Mozart,’’ she said. “It’s a very interesting place to be and to be able to move back and forth, but at a certain point you have to be able to step outside and see,’’ and here she dropped her voice to a tranquil whisper, “it’s just theater. It’s all theater. It’s all theater. The whole thing is theater.’’

Non-theater —

"The interplay between Euclidean and Galois  geometry" and
related remarks on interplay — Keats's Laws of Aesthetics.

Part theater, part non-theater —

Cubist crucifixion.

Monday, December 13, 2010

Plan 9 Revisited

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

Leading today's New York Times  obituaries —


— is that of Nassos Daphnis, a painter of geometric abstractions
who in 1995 had an exhibition at a Leo Castelli gallery
titled "Energies in Outer Space." (See pictures here.)

Daphnis died, according to the Times, on November 23.
See Art Object, a post in this journal on that date—

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


Some context— this morning's previous post (Apollo's 13,
on the geometry of the 3×3×3 cube), yesterday's noon post
featuring the 3×3 square grid (said to be a symbol of Apollo),

The 3x3 square

and, for connoisseurs of the Ed Wood school of cinematic art,
a search in this journal for the phrase "Plan 9."

You can't make this stuff up.

Mathematics and Narrative continued…

Filed under: General,Geometry — m759 @ 7:20 AM

Apollo's 13: A Group Theory Narrative —

I. At Wikipedia —


II. Here —

See Cube Spaces and Cubist Geometries.

The 13 symmetry axes of the (Euclidean) cube–
exactly one axis for each pair of opposite
subcubes in the 27-part (Galois) 3×3×3 cube–

The 13 symmetry axes of the cube

A note from 1985 describing group actions on a 3×3 plane array—


Undated software by Ed Pegg Jr. displays
group actions on a 3×3×3 cube that extend the
3×3 group actions from 1985 described above—

Ed Pegg Jr.'s program at Wolfram demonstrating concepts of a 1985<br />
note by Cullinane

Pegg gives no reference to the 1985 work on group actions.

Sunday, December 12, 2010

Brightness at Noon continued…

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

A picture one might view as
related to the novel An Object of Beauty
and the film "The Object of Beauty" —

The 3x3 square

Click for some background.

"If it's a seamless whole you want,
 pray to Apollo." — Margaret Atwood

Trip Trap

Filed under: General — m759 @ 11:30 AM

Where Entertainment Is God, continued…

IMAGE-- LA Times on Julie Taymor, Wonderland, and Johnny Depp

Click to enlarge.

Sunday Painting

Filed under: General — m759 @ 10:18 AM

"Blue Eyes took his Sunday painting seriously."


Click on image for further details.

Art Wars continued…

Filed under: General — m759 @ 1:44 AM


Click for higher quality.


Saturday, December 11, 2010

Dual Duel

Filed under: General,Geometry — m759 @ 7:20 AM

"Shifting Amid, and Asserting, His Own Cinema"

— Headline of an essay on Bertolucci in tormorrow's Sunday New York Times

This, together with yesterday's post on the Paris "Symmetry, Duality, and Cinema" conference last June, suggests a review of the phrase "blue diamond" in this journal. The search shows a link to the French art film "Duelle."

Some background for the word and concept from a French dictionary

  adjectif masculin singulier
1 relatif à la dualité, à ce qui est double, constitué de deux éléments distincts
  nom masculin singulier
2 combat opposant deux personnes, à l'arme blanche ou au pistolet, afin de chercher réparation d'un dommage ou d'une injure de l'un des combattants
3 par extension compétition, conflit
4  (linguistique) dans certaines langues, cas de nombre distinct du singulier et du pluriel, correspondant à une action effectuée par deux personnes

  adjectif féminin singulier
relative à la dualité, à ce qui est double, constitué de deux éléments distincts

For examples of  duel  and duelle  see Evariste Galois
and Helen Mirren (the latter in The Tempest  and in 2010 ).

IMAGE-- Imaginary movie poster- 'The Galois Connection'- from stoneship.org

Image from stoneship.org

Friday, December 10, 2010

Cruel Star, Part II

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

Symmetry, Duality, and Cinema

— Title of a Paris conference held June 17, 2010

From that conference, Edward Frenkel on symmetry and duality

"Symmetry plays an important role in geometry, number theory, and quantum physics. I will discuss the links between these areas from the vantage point of the Langlands Program. In this context 'duality' means that the same theory, or category, may be described in two radically different ways. This leads to many surprising consequences."

Related material —


See also  "Black Swan" in this journal, Ingmar Bergman's production of Yukio Mishima's "Madame de Sade," and Duality and Symmetry, 2001.

This journal on the date of the Paris conference
had a post, "Nighttown," with some remarks about
the duality of darkness and light. Its conclusion—

"By groping toward the light we are made to realize
 how deep the darkness is around us."
  — Arthur Koestler, The Call Girls: A Tragi-Comedy,
      Random House, 1973, page 118

Thursday, December 9, 2010

Cruel Star

Filed under: General — Tags: — m759 @ 4:23 AM

This morning's New York Times  obituaries describe a memoir titled "Under a Cruel Star."

This is not  the story of Kayshonne Insixieng May, who appears with mathematics professor Edward Frenkel in his recent homage to Yukio Mishima, "Rites of Love and Math." (See press kit pdf.)


Mathematics Professor Edward Frenkel

For further details, see yesterday's East Bay Express

Erotica, Intrigue, and Arithmetic in 'Rites of Love and Math'
Berkeley professor Edward Frenkel brings his passion for math
to the masses — by starring in an erotic film.

Professor Frenkel also appears in last Saturday's post "Forgive Us Our Transgressions."

Related material —

“I carry the past inside me like an accordion, like a book of picture postcards that people bring home as souvenirs from foreign cities, small and neat,” she wrote in her memoir. “But all it takes is to lift one corner of the top card for an endless snake to escape, zigzag joined to zigzag, the sign of the viper, and instantly all the pictures line up before my eyes.”

Today's New York Times  on Heda Kovaly, author of Under a Cruel Star

See also the endless snake in a post from last Sunday, the day of Kovaly's death.

Wednesday, December 8, 2010


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

The late Hillard Elkins, producer of the erotic review "Oh! Calcutta!" —


The Well Dressed Man with a Beard

After the final no there comes a yes
And on that yes the future world depends.
No was the night. Yes is this present sun.
If the rejected things, the things denied,
Slid over the western cataract, yet one,
One only, one thing that was firm, even
No greater than a cricket's horn, no more
Than a thought to be rehearsed all day, a speech
Of the self that must sustain itself on speech,
One thing remaining, infallible, would be
Enough. Ah! douce campagna of that thing!
Ah! douce campagna, honey in the heart,
Green in the body, out of a petty phrase,
Out of a thing believed, a thing affirmed:
The form on the pillow humming while one sleeps,
The aureole above the humming house . . .

It can never be satisfied, the mind, never.

— Wallace Stevens, from Parts of a World , 1942

Elkins died on Wednesday, December 1, 2010.

From this journal on that date


Tuesday, December 7, 2010

The Lottery

Filed under: General — m759 @ 9:00 PM



A Date for Mel

Filed under: General — m759 @ 11:00 AM


Mel Gibson in "The Beaver"

Adults who prefer more serious fare may search for…

Tora Tora Platinum Vol. 44:
Aimi Nakatani, Miho Hashimoto

Studio: Tora-Tora-Tora


Filed under: General — m759 @ 9:48 AM

(A sequel to The Tiffany Puzzle )

Home page of Sam Wasson, author of
Fifth Avenue, 5 A.M.: Audrey Hepburn, Breakfast at Tiffany's,
and the Dawn of the Modern Woman


See also related posts in this journal

The image “http://www.log24.com/log/pix05B/051019-TwoSides.jpg” cannot be displayed, because it contains errors.

The Tiffany Puzzle

Filed under: General,Geometry — Tags: — m759 @ 5:00 AM

Suggested by Dan Brown's remarks in today's Science Times  special section on puzzles—


For a fanciful linkage of the dreidel 's concept of chance
to The Stone 's concept of invariant law, note that the
New York Lottery evening number on Dec. 1 (the
beginning of Hanukkah) was 840. See also the number
840 in the final post (July 20, 2002) of a search for
Solomon's Cube.


Cold Comfort

Filed under: General — Tags: — m759 @ 4:01 AM

Dan Brown, quoted in today's New York Times

“The human mind is comforted by the notion that a greater power has all the answers. A world in which secret messages swirl around us is exciting because it helps reinforce our belief that true enlightenment is within our reach.”

Monday, December 6, 2010

Out of Black Mountain

Filed under: General — m759 @ 9:14 PM

Robin Hartshorne, AMS Notices , April 2000, p. 464

"Whenever one approaches a subject from two different directions, there is bound to be an interesting theorem expressing their relation." 

From "When Novelists Become Cubists," by Andre Furlani—

With a nod to film-maker Stan Brakhage, Davenport calls his compositional principle "architectonic form." (2) In the essay "Narrative Tone and Form," he identifies in twentieth century literature "a movement from assuming the world to be transparent, and available to lucid thoughts and language, to assuming (having to assume, the artists involved would say) that the world is opaque" (Geography  311). Architectonic form derives from modernist experiments in disrupted perspective (as, for example, in collage and vorticism). "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. Genius always proceeds by faith" (312). The unparaphrasable architectonic text "differs from other narrative in that the meaning shapes into a web, or globe, rather than along a line" (318). The essence of such art "is that it conceals what it most wishes to show; first, because it charges word, image and sense to the fullest, fusing matter and manner; secondly, to allow meaning to be searched out" (57-58).

In architectonic form, meaning may be generated more in the interstices between images, citation, and passages of dialogue than in the content of these elements. "It is the conjunction, not the elements, that creates a new light," Davenport says in an essay on poet Ronald Johnson (194). This is the Poundian aesthetic Charles Olson attempted to translate into practical pedagogical terms as rector of Black Mountain College, a school organized, as Olson explained in a 1952 letter, on the "principle that the real existence of knowledge lies between things & is not confined to labeled areas" (quoted in Duberman 341).


(2) Brakhage has written admiringly of Davenport. In "Ice is for Coffee and for Wine" he speaks of the joy to have "at last met such a man as Pound describes Remy de Goncourt to have been…i.e. one whose intelligence was a way of feeling" (7).


Brakhage, Stan. "Ice is for Coffee and for Wine." Margins  30 (Aug.-Sept. 1974): 6-7.

Davenport, Guy. The Geography of the Imagination . San Francisco, North Point Press, 1981. Reprint: New York, Pantheon, 1992.

Duberman, Martin. Black Mountain . New York, Dutton, 1972

In Hoc Signo

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

Saturday Night Live  on December 4, 2010 —

'The Abacus Conundrum' from SNL

If you liked Harlan Kane's THE ABACUS CONUNDRUM, you'll love…



                                 New York Lottery on Sunday, December 5, 2010

Related links— For 076, yesterday's entry on "Independence Day."
 For 915, see 9/15, "Holy Cross Day Revisited," and its prequel,
 linked to on 9/15 as "Ready When You Are, C.B."

See also "Citizen Harlan" and "The Beaver."

Sunday, December 5, 2010

Hanukkah Continues —

Filed under: General,Geometry — m759 @ 9:29 AM

Dan Brown Meets
The Exorcist

The 973 Code


Baphomet with Ouroboros Pendant

$140  Code: 973


Meanwhile, our hero…


goes to the movies.

In this production, Jeff Goldblum is played by
David Ben-Zvi of the University of Texas at Austin
Geometry Research Group


Click Ben-Zvi for further narrative.

Saturday, December 4, 2010

Forgive Us Our Transgressions

Filed under: General — m759 @ 4:15 PM

Bulletin of the American Mathematical Society

"Recent Advances in the Langlands Program"

Author(s):  Edward Frenkel
Journal:     Bull. Amer. Math. Soc. 41 (2004), 151-184.
Posted:     January 8, 2004

Item in the references:

[La5] G. Laumon, La correspondance de Langlands sur les corps de fonctions  (d'après Laurent
La fforgue), Séminaire Bourbaki, Exp. No. 973, Preprint math.AG/0003131.



Related material— Peter Woit 's post on Frenkel today—

"Math Research Institute, Art, Politics, Transgressive Sex and Geometric Langlands."

See also an item from a Google search on " 'nit-picking' + Bourbaki "—

White Cube — Jake & Dinos Chapman 

Fucking Hell is not, evidently, a realistic (much less nit-picking ) account of the ….
The following link enables you to pan virtually around the Bourbaki
www.whitecube.com/artists/chapman/texts/154/ – Cached

— as well as a search for "White Cube" in this journal.

Damnation on 42nd Street

Filed under: General — m759 @ 5:24 AM

Yesterday's New York Lottery— Midday 042, Evening 919.

Here 042 may be seen as referring to New York's 42nd Street…

Below, West 42nd St., facing north, from yesterday's New York Times


Related material —

That story is part of the Change War  saga by Fritz Leiber, notably represented by Leiber's 1957 novel The Big Time.

See also Comic Book Resources on the new comic-book  series Spider-Man: Big Time

CBR: “Big Time” is this title of this new era of “Amazing Spider-Man.” Why choose that title? What exactly is it referring to?

DAN SLOTT: “Big Time” refers to more than “Amazing Spider-Man,” it also refers to other Spider-Projects: “Astonishing Spider-Man/Iron Man,” the new Norman Osborn mini, and the all-new “Spider-Girl!” With “Amazing,” “Big Time” takes on a lot of meanings. In this book, everything is bigger: bigger stakes for Peter Parker, bigger threats for Spider-Man, and a much bigger comic. We are expanding to 30 pages of material, twice a month!

As for yesterday's evening NY lottery number 919, see 9/19.

Friday, December 3, 2010

Black Swan

Filed under: General — m759 @ 12:06 PM

Click for video.


Background: Greek Orthodox in Lebanon.


The Star
of Venus

Venus Herself


For greater philosophical depth, see an ad for "Tree of Life," an upcoming film by Terrence Malick, by clicking the "Venus Herself" link above.

The trailer for "Tree of Life" is said to be opening with the film "Black Swan" today.

See also articles on Malick at Wikipedia and at Senses of Cinema, and Malick's translation of Heidegger's 1929 essay "Vom Wesen des Grundes " into English. It was published under the title The Essence of Reasons  (Evanston: Northwestern University Press,1969, bilingual edition).

Thursday, December 2, 2010


Filed under: General,Geometry — m759 @ 8:00 AM

The Dreidel Is Cast

The Nietzschean phrase "ruling and Caesarian spirits" occurred in yesterday morning's post "Novel Ending."

That post was followed yesterday morning by a post marking, instead, a beginning— that of Hanukkah 2010. That Jewish holiday, whose name means "dedication," commemorates the (re)dedication of the Temple in Jerusalem in 165 BC.

The holiday is celebrated with, among other things, the Jewish version of a die—  the dreidel . Note the similarity of the dreidel  to an illustration of The Stone*  on the cover of the 2001 Eerdmans edition of  Charles Williams's 1931 novel Many Dimensions


For mathematics related to the dreidel , see Ivars Peterson's column on this date fourteen years ago.
For mathematics related (if only poetically) to The Stone , see "Solomon's Cube" in this journal.

Here is the opening of Many Dimensions


For a fanciful linkage of the dreidel 's concept of chance to The Stone 's concept of invariant law, note that the New York Lottery yesterday evening (the beginning of Hanukkah) was 840. See also the number 840 in the final post (July 20, 2002) of the "Solomon's Cube" search.

Some further holiday meditations on a beginning—

Today, on the first full day of Hanukkah, we may or may not choose to mark another beginning— that of George Frederick James Temple, who was born in London on this date in 1901. Temple, a mathematician, was President of the London Mathematical Society in 1951-1953. From his MacTutor biography

"In 1981 (at the age of 80) he published a book on the history of mathematics. This book 100 years of mathematics (1981) took him ten years to write and deals with, in his own words:-

those branches of mathematics in which I had been personally involved.

He declared that it was his last mathematics book, and entered the Benedictine Order as a monk. He was ordained in 1983 and entered Quarr Abbey on the Isle of Wight. However he could not stop doing mathematics and when he died he left a manuscript on the foundations of mathematics. He claims:-

The purpose of this investigation is to carry out the primary part of Hilbert's programme, i.e. to establish the consistency of set theory, abstract arithmetic and propositional logic and the method used is to construct a new and fundamental theory from which these theories can be deduced."

For a brief review of Temple's last work, see the note by Martin Hyland in "Fundamental Mathematical Theories," by George Temple, Philosophical Transactions of the Royal Society, A, Vol. 354, No. 1714 (Aug. 15, 1996), pp. 1941-1967.

The following remarks by Hyland are of more general interest—

"… one might crudely distinguish between philosophical and mathematical motivation. In the first case one tries to convince with a telling conceptual story; in the second one relies more on the elegance of some emergent mathematical structure. If there is a tradition in logic it favours the former, but I have a sneaking affection for the latter. Of course the distinction is not so clear cut. Elegant mathematics will of itself tell a tale, and one with the merit of simplicity. This may carry philosophical weight. But that cannot be guaranteed: in the end one cannot escape the need to form a judgement of significance."

— J. M. E. Hyland. "Proof Theory in the Abstract." (pdf)
Annals of Pure and Applied Logic 114, 2002, 43-78.

Here Hyland appears to be discussing semantic ("philosophical," or conceptual) and syntactic ("mathematical," or structural) approaches to proof theory. Some other remarks along these lines, from the late Gian-Carlo Rota


    (Click to enlarge.)

See also "Galois Connections" at alpheccar.org and "The Galois Connection Between Syntax and Semantics" at logicmatters.net.

* Williams's novel says the letters of The Stone  are those of the Tetragrammaton— i.e., Yod, He, Vau, He  (cf. p. 26 of the 2001 Eerdmans edition). But the letters on the 2001 edition's cover Stone  include the three-pronged letter Shin , also found on the dreidel .  What esoteric religious meaning is implied by this, I do not know.

Wednesday, December 1, 2010

Novel Ending

Filed under: General — m759 @ 4:01 AM

November was National Novel Writing Month.

Yesterday, at the end of that month, the New York Lottery numbers were—

Midday 962, Evening 954.

Related material—


Wagner star Peter Hofmann died yesterday, November 30. The above obituary,
together with the NY Lottery numbers for the end of November and
the remarks on Nietzsche in this journal Sunday morning, suggest
the following readings from Nietzsche's The Will to Power

Introduction (for National Novel Writing Month)—

"He [Nietzsche's "great man"] would rather lie than tell the truth,
because lying requires more spirit and will."

Details (according to the lottery numbers)—


For deeper background, see the life of the Will to Power  translator, Anthony Ludovici.

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