Log24

Wednesday, July 28, 2010

Without Diamond-Blazons

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

Excerpt from Wallace Stevens's
"The Pediment of Appearance"—

Young men go walking in the woods,
Hunting for the great ornament,
The pediment* of appearance.

They hunt for a form which by its form alone,
Without diamond—blazons or flashing or
Chains of circumstance,

By its form alone, by being right,
By being high, is the stone
For which they are looking:

The savage transparence.

* Pediments, triangular and curved—

http://www.log24.com/log/pix10B/100728-Pediments.jpg

— From "Stones and Their Stories," an article written
and illustrated by E.M. Barlow, copyright 1913.

Related geometry—

http://www.log24.com/log/pix10B/100728-SimplifiedPeds.gif

 (See Štefan Porubský: Pythagorean Theorem .)

A proof with  diamond-blazons—

http://www.log24.com/log/pix10B/100728-DiamondProof.gif

(See Ivars Peterson's "Square of the Hypotenuse," Nov. 27, 2000.)

Monday, July 26, 2010

Brightness at Noon continued

Filed under: General — m759 @ 12:00 pm

Riddle

"Midnight in the Garden continued," a post of 12:00 AM July 20, posed the riddle of what the previous day's NY Lottery midday "440" might mean.

A jocular answer was given. Some background for a more serious answer—

Paul Newall, “Kieślowski’s Three Colours Trilogy”

“Julie recognises the music of the busker outside playing a recorder as that of her husband’s. When she asks him where he heard it, he replies that he makes up all sorts of things. This is an instance of a theory of Kieślowski’s that ‘different people, in different places, are thinking the same thing but for different reasons.’ With regard to music in particular, he held what might be characterised as a Platonic view according to which notes pre-exist and are picked out and assembled by people. That these can accord with one another is a sign of what connects people, or so he believed.”

In honor of Wye Jamison Allanbrook, author of Rhythmic Gesture in Mozart, we note that 440 is Concert A.

Allanbrook died on July 15. See this journal on that date—

Angels in the Architecture,
Happy Birthday, and
Brightness at Noon.

A Dream for Molnar

Filed under: General — Tags: , , — m759 @ 4:00 am

Thomas Steven Molnar, Catholic philosopher

http://www.log24.com/log/pix10B/100726-Molnar.jpg

Dream —

http://www.log24.com/log/pix10B/100726-InceptionCup.jpg

http://www.log24.com/log/pix10B/100726-Dream.jpg

See also Binoche in “Bleu and Du Sucre

Image-- Sugar cube in coffee, from 'Bleu'

Saturday, July 24, 2010

The Leonardo Code

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

"If you’re the kind of geek who yearns for detailed schematics
 of the technology behind all of this, you’ll be disappointed—
 there are none."

— "7 Reasons Why Techies Love 'Inception'," by John Hagel

"Show me all  the blueprints"
 — Leonardo DiCaprio in "The Aviator" (2004)

http://www.log24.com/log/pix10B/100724-InceptionBlocks.jpg

Playing with Blocks

http://www.log24.com/log/pix10B/100724-InceptionPoster.jpg

Rotation

Playing with Blocks

"Many of the finite simple groups can be described as symmetries of finite geometries, and it remains a hot topic in group theory to expand our knowledge of the Classification of Finite Simple Groups using finite geometry."

Finite geometry page at the Centre for the Mathematics of
   Symmetry and Computation at the University of Western Australia
   (Alice Devillers, John Bamberg, Gordon Royle)

For such symmetries, see Robert A. WIlson's recent book The Finite Simple Groups.

The finite simple groups are often described as the "building blocks" of finite group theory.

At least some of these building blocks have their own building blocks. See Non-Euclidean Blocks.

For instance, a set of 24 such blocks (or, more simply, 24 unit squares) appears in the Miracle Octad Generator (MOG) of R.T. Curtis, used in the study of the finite simple group M24.

(The octads  of the MOG illustrate yet another sort of mathematical blocks— those of a block design.)

Thursday, July 22, 2010

Pilate Goes to Kindergarten, continued

Filed under: General,Geometry — Tags: , , — m759 @ 2:02 pm

Barnes & Noble has an informative new review today of the recent Galois book Duel at Dawn.

It begins…

"In 1820, the Hungarian noble Farkas Bolyai wrote an impassioned cautionary letter to his son Janos:

'I know this way to the very end. I have traversed this bottomless night, which extinguished all light and joy in my life… It can deprive you of your leisure, your health, your peace of mind, and your entire happiness… I turned back when I saw that no man can reach the bottom of this night. I turned back unconsoled, pitying myself and all mankind. Learn from my example…'

Bolyai wasn't warning his son off gambling, or poetry, or a poorly chosen love affair. He was trying to keep him away from non-Euclidean geometry."

For a less dark view (obtained by simply redefining "non-Euclidean" in a more logical way*) see Non-Euclidean Blocks and Finite Geometry and Physical Space.

* Finite  geometry is not  Euclidean geometry— and is, therefore, non-Euclidean
  in the strictest sense (though not according to popular usage), simply because
  Euclidean  geometry has infinitely many points, and a finite  geometry does not.
  (This more logical definition of "non-Euclidean" seems to be shared by
  at least one other person.)

  And some  finite geometries are non-Euclidean in the popular-usage sense,
  related to Euclid's parallel postulate.

  The seven-point Fano plane has, for instance, been called
  "a non-Euclidean geometry" not because it is finite
  (though that reason would suffice), but because it has no parallel lines.

  (See the finite geometry page at the Centre for the Mathematics
   of Symmetry and Computation at the University of Western Australia.)

By Chance

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

PA Lottery 7/21— Midday 312, Evening 357.

Related material:

This journal on 3/12

Image-- Group Characters, from 'Symmetry,' Pergamon Press, 1963

and a .357—

Image-- MTV star spotting-- Lindsay Lohan, Nun with a Gun

Related philosophy—

"Character is fate." — Heraclitus

"Pray for the grace of accuracy." — Robert Lowell

Oh, and a belated happy 7/21 birthday to Ernest Hemingway and Robin Williams.

Soul Riff

Filed under: General — m759 @ 3:33 am

A link in the previous post to the Harvard Foundation led to a screenshot
of a long-neglected Harvard web page. That page stated yesterday that
"the Harvard Foundation 2008 Artist of the Year has not yet been announced."

It turns out to be jazz artist Herbie Hancock, who was honored at
Harvard's Sanders Theatre on Saturday, March 1, 2008.

Related material from this journal—

Call and Response

Doonesbury 2/29/08-- Assignment: Identify Sources

For a response from the next day,
March 1, click on the professor
.

Wednesday, July 21, 2010

Dream Names continued

Filed under: General — m759 @ 6:29 pm

From the 7/20 Harvard Crimson

"The scholarly expeditions undertaken by modern-day explorer and Harvard Foundation Director S. Allen Counter will be featured in a biopic produced by actor Will Smith.

…. Debbie Allen is also producing the film, and Farhad Safinia will be penning the script, Variety  magazine reported.

…. Counter said that Debbie Allen described his character as 'a mixture of Indiana Jones and Robert Langdon,' the fictional Harvard professor of symbology in Dan Brown’s novels."

Farhad Safinia is co-writer and co-producer, with Mel Gibson, of "Apocalypto."

From "The Envelope: The Awards Insider" at the LA Times, a review of the film based on Dan Brown's "Angels & Demons"—

"The script tips its hand too early, and can't quite turn Langdon into Indiana Langdon on his Last Crusade."

—  , Orlando Sentinel  movie critic, May 15, 2009

Related material:

The Robert Jones Code

Masonic pyramid in 
'Being There' (co-writer of screenplay-- Robert Jones)

(Click for video.)

Tuesday, July 20, 2010

Dream Names

Filed under: General — m759 @ 12:00 pm

The protagonist of the new film Inception  is named Dom Cobb.

The name Dom may come from "Dominic." (I have not yet seen the film.)
If it does not, see Wiktionary for other possible meanings.

(See also the 1958 Polish short film "Dom.")

The name "Cobb" may have come from a previous film, Following,
by Inception director Christopher Nolan.

My own preference is for Rachel  Cobb.

The Corpse Express

Filed under: General,Geometry — m759 @ 2:02 am

See Malcolm Lowry's "A corpse will be transported by express!" in this journal.

From June 23

"When Plato regards geometry as the prerequisite to
philosophical knowledge, it is because geometry alone
renders accessible the realm of things eternal;
tou gar aei ontos he geometrike gnosis estin."

— Ernst Cassirer, Philosophy and Phenomenological Research,
   Volume V, Number 1, September, 1944.

Maybe.

June 23, Midsummer Eve, was the date of death for Colonel Michael Cobb.

Cobb, who died aged 93, was "a regular Army officer who in retirement produced
the definitive historical atlas of the railways of Great Britain." — Telegraph.co.uk, July 19

As for geometry, railways, and things eternal, see parallel lines converging
in Tequila Mockingbird and Bedlam Songs.

Station of the Rock Island Line

The Rock Island Line’s namesake depot 
in Rock Island, Illinois

See also Wallace Stevens on "the giant of nothingness"
in "A Primitive Like an Orb" and in Midsummer Eve's Dream

At the center on the horizon, concentrum, grave
And prodigious person, patron of origins.

Midnight in the Garden continued

Filed under: General — m759 @ 12:00 am

Lottery hermeneutics for yesterday's numbers—

PA— Midday 711, Evening 039.

NY— Midday 440, Evening 704.

Simple interpretive methods— numbers as dates and as hexagram numbers— yield 7/11, hexagram 39, and 7/04.

The reader may supply his own interpretations of 7/11 and 7/04; for hexagram 39, see Wilhelm's commentary

"The hexagram pictures a dangerous abyss lying before us
  and a steep, inaccessible mountain rising behind us."

— and the cover of Cold Mountain

The image 
“http://www.log24.com/log/pix05A/050703-Cold.jpg” cannot be displayed, 
because it contains errors.

Adapted from cover of
German edition of Cold Mountain

This suggests revisiting The Edge of Eternity (July 5, 2005).

The hermeneutics of the NY midday 440 is more difficult. A Google search suggests that a Log24 post for Epiphany 2004, "720 in the Book," might yield a clue to the 440 riddle.

Image-- 'What is a closed-form number?'

By all means, let us 440.

Monday, July 19, 2010

White, Blue, and Red

Filed under: General — m759 @ 11:29 pm

Ross Douthat in The New York Times of July 19—

"The Roots of White Anxiety"—

"…while most extracurricular activities increase your odds of admission to an elite school, holding a leadership role or winning awards in organizations like high school R.O.T.C., 4-H clubs and Future Farmers of America actually works against your chances. Consciously or unconsciously, the gatekeepers of elite education seem to incline against candidates who seem too stereotypically rural or right-wing or 'Red America.'"

So much the worse for the elite schools.

Reba on the 4-H Network

For a more adult approach to the 2008 ACM Awards,
see "Happy May 18, Reba."

Pediments of Appearance

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

Part I —

A search for images of Wallace Stevens's "Pediment of Appearance"—

(Click to enlarge.)

Image-- A version of Stevens's 'pediment of appearance'

Part II —

A geometric analogue of the pediment—

Image-- A version of Stevens's 'pediment of appearance'

Note that the above cross also appears in
Euclid's proof of the Pythagorean theorem.

Part III —

An echo of the above geometry—

Image-- Fuentiduena chapel at the Cloisters

Sunday, July 18, 2010

Darkness at Noon

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

The New York Times, July 17

"'A Disappearing Number'… is lucid, dynamic and continuously engaging."

"'All beautiful theorems require a very high degree of economy, unexpectedness and inevitability,' the string-theory* specialist Aninda tells us after elucidating one of Ramanujan’s formulas. That’s not a bad recipe for beautiful theater either…."

Related material:

Image-- 'Deus ex Machina and the Aesthetics of Proof'

Hardy is also the play's (apparently uncredited) source of "economy."

"… a very high degree of unexpectedness, combined with inevitability  and economy."

A Mathematician's Apology, §18, by G. H. Hardy, 1940

* For more on string theory and a deus, see Not Even Wrong, July 7, 2010.

Today’s Sermon

Filed under: General — m759 @ 11:00 am

New York Lottery on Saturday, July 17, 2010—

Midday 049, Evening 613.

Related material:

Hexagram 49 and 6/13.

A quotation from this journal on 6/13

"Christianity offers the critic a privileged ontological window…."

Aaron Urbanczyk's 2005 review of Christ and Apollo 
   
by William Lynch, S.J., a book first published in 1960

Picture from today's New York Times  (page ST1 in New York edition)—

http://www.log24.com/log/pix10B/100718-LamWindow.jpg

Du Sucre

Filed under: General,Geometry — m759 @ 4:19 am

http://passionforcinema.com/sapphire/ on "Bleu" —  Jan. 9, 2010 —

"An extremely long lens on an insert of a sugar cube, dipped just enough, in a small cup of coffee, so that it gradually seeps in the dark beverage. Four and a half seconds of unadulterated cinematic bliss."

Image-- Sugar cube in coffee, from 'Bleu'

Related material from this journal:

The Dream of
the Expanded Field

Image-- 4x4 square and 4x4x4 cube

A Tale of Two Cities

Filed under: General — m759 @ 2:22 am

Madrid

Image-- Eduardo Sanchez Junco, dead on Bastille Day, 2010

Junco died on Bastille Day.

Paris

An artist's view —

Image-- Artist's view of Paris by Gracia Lam

The above Gracia Lam illustration was suggested
 by her work in a New York Times  piece on the Sabbath
(Sunday, July 18, 2010, on page ST1 of the New York edition).

"Accentuate the Positive." — Clint Eastwood

Saturday, July 17, 2010

Mathematics and Narrative continued

Filed under: General — m759 @ 12:00 pm

"List, list, O, list!"
Hamlet's father's ghost

"Ordering and patterning are not wholly narrative activities."
James E. Giles, 1986

"See also… the true  story 0, 1, 2, 3…" 
Log24, January 9, 2009

  For some non-narrative patterning of this list, see (for instance)
         Apostol's Modular Functions and Dirichlet Series in Number Theory.

Friday, July 16, 2010

Language Game continued…

Filed under: General — m759 @ 11:30 pm

In the Details

This afternoon's post, Point Omega continued, concerned the New York Lottery numbers for yesterday evening and midday today.

A footnote to that post—

Today's evening New York Lottery number was 664.

In the spirit of the theological content of this afternoon's post—

Today's evening NY number 664 may or may not refer to the year of the Synod of Whitby.

That Synod was about reconciling the customs of Rome with the customs of Iona.

A somewhat relevant link from the Language Game post referred to in this afternoon's post was on the word "selving." This link, now broken, referred to a paper hosted by, as it happens, Iona College. The following is a link to a cached copy of that paper—

"The Story of the Self: The Self of the Story," by James E. Giles (Religion and Intellectual Life, Fall 1986— Volume 4, Number 1, pages 105-112)

Point Omega continued

Filed under: General — m759 @ 1:26 pm

"We tried to create new realities overnight…."
Point Omega, quoted here in the post
Devising Entities (July 3, 2010)

Image-- NY Lottery, evening  July 15=000, midday July 16=911

See also last night's Meditation as well as the earlier posts
Language Game and The Subject Par Excellence.

Meditation

Filed under: General — Tags: — m759 @ 2:15 am

From a religious meditation on St. Peter's Day, 2008, "Big Rock"—

An academic quotes Wallace Stevens:
"Professor Eucalyptus in 'Ordinary Evening' XIV, for example, 'seeks/ God in the object itself'…."

My reaction:
"I have more confidence that God is to be found in the Ping Pong balls of the New York Lottery."

From today's New York Lottery— Midday 215, Evening 000.

The latter number seems to speak with a certain authority.

The former may or may not mean something. See a search for "2/15" in this journal.

Thursday, July 15, 2010

Brightness at Noon, continued

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

"What exactly was Point Omega?"

This is Robert Wright in Nonzero: The Logic of Human Destiny.

Wright is discussing not the novel Point Omega  by Don DeLillo,
but rather a (related) concept of  the Jesuit philosopher Pierre Teilhard de Chardin.

My own idiosyncratic version of a personal "point omega"—

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

Click for further details.

The circular sculpture in the foreground
is called by the artist "The Omega Point."
This has been described as
"a portal that leads in or out of time and space."

For some other sorts of points, see the drawings
on the wall and Geometry Simplified

Image-- The trivial two-point affine space and the trivial one-point projective space, visualized

The two points of the trivial affine space are represented by squares,
and the one point of the trivial projective space is represented by
a line segment separating the affine-space squares.

For related darkness  at noon, see Derrida on différance
as a version of Plato's khôra

(Click to enlarge.)

Image-- Fordham University Press on Derrida, differance, and khora

The above excerpts are from a work on and by Derrida
published in 1997 by Fordham University,
a Jesuit institutionDeconstruction in a Nutshell

Image-- A Catholic view of Derrida

For an alternative to the Villanova view of Derrida,
see Angels in the Architecture.

Happy Birthday…

Filed under: General — m759 @ 3:33 am

Linda Ronstadt.

Angels in the Architecture

Filed under: General — Tags: — m759 @ 3:12 am

"Things fall apart;
the centre cannot hold
"

http://www.log24.com/log/pix10A/100715-AugustineCenter.jpg

The above building is home to the Derridean leftists
of the Villanova philosophy department.

center loosens,
forms again elsewhere

"The most obvious problem with Derrida's argument in The Gift of Death is his misconception of Christianity. In his description of Christian mystery, the crucified figure of Jesus is strikingly absent, having been replaced by a mysterious 'infinite other.' In this respect, Derrida's understanding of Christianity is essentially gnostic; the humanity of Jesus is displaced by gnostic mystery. Although Derrida claims to describe historical Christianity, in fact, his argument is based on a serious distortion of Christian practice and theology. Although the title might seem an obvious reference to Christ's atoning death, Derrida's book can only be characterized as an overt and unacknowledged displacement of the Crucifixion and its central place in Christian worship."

 

— Peter Goldman, now at Westminster College in Salt Lake City

See also Highway 1 Revisited (August 1, 2006).

Wednesday, July 14, 2010

Derechos Reservados

Filed under: General — m759 @ 8:16 pm

http://www.log24.com/log/pix10A/100714-DerechosSm.jpg

Related material— Today's previous posts
Happy Bastille Day, The Lotus Gate, and Only Connect.

"Every city has its gates…." —Winter's Tale

Only Connect

Filed under: General — m759 @ 7:00 pm

Janet Maslin, book review of One Day  in today's online New York Times

"Emma is demonstrably the smarter of the two in ways that Dexter finds intimidating. While he roams the world, she sends him books that he doesn’t enjoy or understand. Dexter on Howards End : 'It’s like they’ve been drinking the same cup of tea for 200 pages, and I keep waiting for someone to pull a knife or an alien invasion or something, but that’s not going to happen is it?'"

Related material: LiLo in "Machete."

The Lotus Gate*

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

Image-- The Jewel in Venn's Lotus (Zen in Cuernavaca)
The Jewel
in Venn's Lotus

See also a prequel to
Ramanujan's Flowering Tree

Flowering Judas.

* “Every city has its gates, which need not be of stone. Nor need soldiers be upon them or watchers before them. At first, when cities were jewels in a dark and mysterious world, they tended to be round and they had protective walls. To enter, one had to pass through gates, the reward for which was shelter from the overwhelming forests and seas, the merciless and taxing expanse of greens, whites, and blues–wild and free–that stopped at the city walls.

In time the ramparts became higher and the gates more massive, until they simply disappeared and were replaced by barriers, subtler than stone, that girded every city like a crown and held in its spirit.”

Mark Helprin, Winter’s Tale

Happy Bastille Day…

Filed under: General — m759 @ 11:00 am

To the leftist philosophers of Villanova

From "Make a Différance"
(Women's History Month, 2005)—

Frida Saal's 

Lacan The image 
“http://www.log24.com/log/pix05/050322-Diamond.gif” cannot be displayed,
 because it contains errors. Derrida:

"Our proposal includes the lozenge (diamond) in between the names, because in the relationship / non-relationship that is established among them, a tension is created that implies simultaneously a union and a disjunction, in the perspective of a theoretical encounter that is at the same time necessary and impossible. That is the meaning of the lozenge that joins and separates the two proper names….  What prevails between both of them is the différance, the Derridean signifier that will become one of the main issues in this presentation."

Football-mandorla (vesica piscis) with link to 'Heaven Can 
Wait'

“He pointed at the football
  on his desk. ‘There it is.’”
Glory Road
    

Quodlibet* 

Compare and contrast
the diamond in the football
with the jewel in the lotus.

* "A scholastic argumentation upon a subject chosen at will, but almost always theological. These are generally the most elaborate and subtle of the works of the scholastic doctors." —Century Dictionary

Tuesday, July 13, 2010

Quest for the Lost Origin…

Filed under: General — Tags: — m759 @ 6:12 pm

Project Management at Villanova

Image-- NY Times review of 'Sorcerer's Apprentice' with ad for Project Management Institute program at Villanova University

Yesterday's noon post, "Lying Forth," linked to a passage by Walter A. Brogan, Professor of Philosophy at Villanova University.

A related Brogan remark for Harrison Ford's birthday—

"The last few pages of the text 'Différance' [an essay by Derrida] are a refutation of the nostalgia and hope involved in Heidegger's ontology, a rejection of the quest for the lost origin and final word."

Walter A. Brogan, "The Original Difference," pp. 31-40 in Derrida and Différance, ed. by David C. Wood and Robert Bernasconi (Northwestern University Press, 1988), p. 32

See, too, "Make a Différance."

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