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—


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

Related geometry—


 (See Štefan Porubský: Pythagorean Theorem .)

A proof with  diamond-blazons—


(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


"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


Dream —



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)


Playing with Blocks



Playing with Blocks

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

"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 — 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.


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 — 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)—


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


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

Junco died on Bastille Day.


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.


Filed under: General — 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


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


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 

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


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."

Happy Birthday, Harrison Ford

Filed under: General — m759 @ 10:01 AM

A link from the Temple of Doom.

See also this morning's previous entry.

Mathematics and Narrative, continued

Filed under: General — m759 @ 9:29 AM

Image-- 'A Story to End All Stories,' by Ramanujan

     Friday, January 9, 2009

Monday, July 12, 2010

Special FX…

Filed under: General — m759 @ 11:30 PM

For fans of the story theory of truth

A date from the FX channel tonight
at the end of the film "Man on Fire"—

December 16, 2003— 

Material linked to here on that dateBlue Matrices.

From the "Man on Fire" soundtrack
Title: Una Palabra  (Carlos Varela)

Una palabra no dice nada
y al mismo tiempo lo esconde todo

The 2004 film, set in Mexico, was based on a 1981 novel set in Italy.

The author of that novel reportedly died in Malta on July 10, 2005.

Eyes on the Prize

Filed under: General,Geometry — m759 @ 6:29 PM

Google Logo July 11, 2010

Image-- Google logo featuring World Cup Soccer field with the 'oog' from 'Google' on the field

"Oog" is Dutch (and Afrikaans) for "eye."

Strong Emergence Illustrated
(May 23, 2007 — Figures from Coxeter)—

The image 
“http://www.log24.com/log/pix07/070523-Coxeter62.jpg” cannot be 
displayed, because it contains errors.

The 2007 "strong emergence" post compares the
center figure to an "Ojo de Dios."

Through Phenomenology to Thought

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

Part I: Phenomenology

Image-- 'Heidegger: Through Phenomenology to Thought,' page 501, on a 'simple middle [-point]'

Part II: Thought

Geometry Simplified

Lying Forth

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


Related material:

Heidegger and Aristotle: The Twofoldness of Being,
by Walter A. Brogan, (SUNY Press, 2005)—

Pages 96-97

Heidegger: Through Phenomenology to Thought,
by William J. Richardson, S.J., (Springer, 1974)—

Pages  492493494495,  and  501

Sunday, July 11, 2010


Filed under: General — m759 @ 6:08 PM


Happy St. Benedict's Day.

Language Lab

Filed under: General — Tags: — m759 @ 11:02 AM

From a search in this journal for "Krell"—

Dialogue from an American adaptation of Shakespeare's Tempest

“… Which makes it a gilt-edged priority that one  of us
 gets into that Krell lab and takes that brain boost.”

– Taken from a video, Forbidden Planet Monster Attack


From yesterday's A Manifold Showing

"Propriation gathers the rift-design of the saying and unfolds it
in such a way that it becomes the well-joined structure of a manifold showing."
(p. 415 of Heidegger's Basic Writings, edited by David Farrell Krell,
HarperCollins paperback, 1993)

German versions found on the Web—

„Das Ereignis versammelt den Aufriß der Sage und entfaltet ihn zum Gefüge des vielfältigen Zeigens.“ 323

323 Heidegger, Weg zur Sprache, S. 259.

"Das Regende im Zeigen der Sage ist das Eignen. Es erbringt das An- und Abwesen in sein jeweilig Eigenes, aus dem dieses sich an ihm selbst zeigt und nach seiner Art verweilt. Das erbringende Eignen, das die Sage als die Zeige in ihrem Zeigen regt, heiße das Ereignen. Es er-gibt das Freie der Lichtung, in die Anwesendes anwähren, aus der Abwesendes entgehen und im Entzug sein Währen behalten kann. Was das Ereignen durch die Sage ergibt, ist nie Wirkung einer Ursache, nicht die Folge eines Grundes. Das erbringende Eignen, das Ereignen, ist gewährender als jedes Wirken, Machen und Gründen. Das Ereignende ist das Ereignis selbst – und nichts außerdem. Das Ereignis, im Zeigen der Sage erblickt, läßt sich weder als ein Vorkommnis noch als ein Geschehen vorstellen, sondern nur im Zeigen der Sage als das Gewährende erfahren. Es gibt nichts anderes, worauf das Ereignis noch zurückführt, woraus es gar erklärt werden könnte. Das Ereignen ist kein Ergebnis (Resultat) aus anderem, aber die Er-gebnis, deren reichendes Geben erst dergleichen wie ein `Es gibt' gewährt, dessen auch noch `das Sein' bedarf, um als Anwesen in sein Eigenes zu gelangen. Das Ereignis versammelt den Aufriß der Sage und entfaltet ihn zum Gefüge des Vielfältigen Zeigens. Das Ereignis ist das Unscheinbarste des Unscheinbaren, das Einfachste des Einfachen, das Nächste des Nahen und das Fernste des Fernen, darin wir Sterbliche uns zeitlebens aufhalten." 8

8 M. Heidegger: Unterwegs zur Sprache. S. 258 f.

From Google Translate:

"The event brings together the outline of the legend and unfolds it to the structure of the manifold showing."

Philosophers’ Keystone

Filed under: General — Tags: , — m759 @ 2:02 AM

(Background— Yesterday's Quarter to Three,
A Manifold Showing, Class of 64, and Child's Play.)

Image-- Notes on Lowry's arrival in Mexico on the ship 'Pennsylvania'

Image-- PA Lottery Saturday, July 10, 2010-- Midday 017, Evening 673


Fans of Gregory Chaitin and Harry Potter
may consult Writings for Yom Kippur
for the meaning of yesterday's evening 673.

(See also Lowry and Cabbala.)

Fans of Elizabeth Taylor, Ava Gardner,
and the Dark Lady may consult Prime Suspect
for the meaning of yesterday's midday 17.

For some more serious background, see Dante—

"….mirando il punto 
a cui tutti li tempi son presenti

– Dante, Paradiso, XVII, 17-18

The symbol    is used throughout the entire book
in place of such phrases as ‘Q.E.D.’  or
‘This completes the proof of the theorem’
to signal the end of a proof.”

Measure Theory, by Paul R. Halmos, Van Nostrand, 1950      

Halmos died on the date of Yom Kippur —  
October 2, 2006.            

Saturday, July 10, 2010

Child’s Play

Filed under: General — m759 @ 6:00 PM

Image-- 'Aion pais esti paizon....'

… twó flocks, twó folds—black, white; ' right, wrong; reckon but, reck but, mind
But thése two; wáre of a wórld where bút these ' twó tell, each off the óther….

— "Spelt from Sibyl's Leaves," by Gerard Manley Hopkins


Related material:

Max Black — "Beginners are taught that a set having three members is a single thing, wholly constituted by its members but distinct from them. After this, the theological doctrine of the Trinity as 'three in one' should be child's play." ("The Elusiveness of Sets," Review of Metaphysics, June 1971, p. 615– as quoted by Bill Vallicella)

 Edward Gibbon, Decline and Fall of the Roman Empire, Chapter XXI

Gibbon, discussing the theology of the Trinity, defines perichoresis as

“… the internal connection and spiritual penetration which indissolubly unites the divine persons59 ….

59 … The perichoresis  or ‘circumincessio,’ is perhaps the deepest and darkest corner of the whole theological abyss.”

 ”Whoever fights monsters should see to it that in the process he does not become a monster.  And when you look long into an abyss, the abyss also looks into you.”

– Friedrich Nietzsche, Beyond Good and Evil, section 146, translated by Walter Kaufmann

Class of 64

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

Samuel Beckett on Dante and Joyce:

"Another point of comparison is the preoccupation
  with the significance of numbers."

"If I'd been out 'til quarter to three
Would you lock the door,
Will you still need me, will you still feed me,
When I'm sixty-four?"


Happy birthday to Sue Lyon (Night of the Iguana, 1964)

A Manifold Showing

Filed under: General — m759 @ 7:11 AM

"Heidegger suggests that we experience the saying of language as a shining forth:

'It lets what is coming to presence shine forth, lets what is withdrawing into absence vanish.  The saying is by no means the supplemental linguistic expression of what shines forth; rather, all shining and fading depend on the saying that shows.' (pp. 413-414).

But what is the basis and origin of this possibility of saying?  The happening of saying in the clearing, its allowing things to shine forth, can also be called an 'owning.' Owning is the event of a thing’s coming into its own, of its showing itself as itself. Heidegger also calls it 'propriating,' 'en-owning,' or Ereignis:

'Propriation gathers the rift-design of the saying and unfolds it in such a way that it becomes the well-joined structure of a manifold showing. (p. 415)'"

— "Heidegger: On the Way to Language," by Paul Livingston

Page references are apparently to Heidegger's Basic Writings, edited by David Farrell Krell, HarperCollins paperback, 1993.

See also Shining Forth.

Quarter to Three, continued

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

In memory of an historian of Mexico
who died on Tuesday, July 6, 2010


Related material—

Image-- 'The Unfolding'-- A review of Anne Carson's 'Nox'


Time Fold.

In the latter, click on
the link Eleven.

Thursday, July 8, 2010

Toronto vs. Rome

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

or: Catullus vs. Ovid

(Today's previous post, "Coxeter vs. Fano,"
might also have been titled "Toronto vs. Rome.")

ut te postremo donarem munere mortis

Catullus 101



Image by Christopher Thomas at Wikipedia
Unfolding of a hypercube and of a cube —


Image--Chess game from 'The 
Seventh Seal'

The metaphor for metamorphosis no keys unlock.
— Steven H. Cullinane, "Endgame"

The current New Yorker  has a translation of
  the above line of Catullus by poet Anne Carson.
According to poets.org, Carson "attended St. Michael's College
at the University of Toronto and, despite leaving twice,
received her B.A. in 1974, her M.A. in 1975 and her Ph.D. in 1981."

Carson's translation is given in a review of her new book Nox.

The title, "The Unfolding," of the current review echoes an earlier
New Yorker  piece on another poet, Madeleine L'Engle—

Cynthia Zarin in The New Yorker, issue dated April 12, 2004–

“Time, for L’Engle, is accordion-pleated. She elaborated,
‘When you bring a sheet off the line, you can’t handle it
until it’s folded, and in a sense, I think, the universe can’t
exist until it’s folded– or it’s a story without a book.’”

(See also the "harrow up" + Hamlet  link in yesterday's 6:29 AM post.)

Coxeter vs. Fano

Filed under: General,Geometry — m759 @ 11:07 AM

The following excerpts from Coxeter's Projective Geometry
sketch his attitude toward geometry in characteristic two.
"… we develop a self-contained account… made
more 'modern' by allowing the field to be general
(though not of characteristic 2) instead of real or complex."

The "modern" in quotation marks may have been an oblique
reference to Segre's Lectures on Modern Geometry  (1948, 1961).
(See Coxeter's reference 15 below.)

Click to enlarge.

Image-- Coxeter on the Fano Plane

"It is interesting to see what happens…."

Another thing that happens if 1 + 1 = 0 —

It is no longer true that every finite reflection group
is a Coxeter group (provided we use Chevalley's
fixed-hyperplane definition of "reflection").

Wednesday, July 7, 2010

07 Book

Filed under: General — m759 @ 6:29 AM


A Talent for Writing, and Falling Into Things


The above headline from this morning's New York Times  is a rather strong reminder of a post linked to here last night—  a post from April 10, 2004 (Holy Saturday), titled "Harrowing."

The book under review is a biography of William Golding, also quoted here in "Harrowing."

From that post—

“There is a suggestion of Christ descending into the abyss for the harrowing of Hell.  But it is the Consul whom we think of here, rather than of Christ.  The Consul is hurled into this abyss at the end of the novel.”

– Stephen Spender, introduction to Malcolm Lowry's Under the Volcano

Related material:

Theater of Truth

 rift-design— Definition by Deborah Levitt

"Rift.  The stroke or rending by which a world worlds, opening both the 'old' world and the self-concealing earth to the possibility of a new world. As well as being this stroke, the rift is the site— the furrow or crack— created by the stroke. As the 'rift design' it is the particular characteristics or traits of this furrow."

– "Heidegger and the Theater of Truth," in Tympanum: A Journal of Comparative Literary Studies, Vol. 1, 1998

See also "harrow up" + Hamlet  in this journal.

Tuesday, July 6, 2010

Bright Star

Filed under: General — m759 @ 10:30 PM

"Ya la ronda llega aquí."

A room by the architect Luis Barragán.

A Serious Artist

Filed under: General — m759 @ 10:00 PM

Today's Google logo
honors a serious artist:

Image-- Frida Kahlo in Google logo July 6, 2010

Related material:

Holy Saturday, 2004

That post quotes the words of another serious artist,
Malcolm Lowry, on a barranca, or deep ravine.
(See also Heidegger's "rift" concept.)

For a less serious rift, see the art of Kylie Minogue.

What “As” Is

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

or:  Combinatorics (Rota) as Philosophy (Heidegger) as Geometry (Me)

“Dasein’s full existential structure is constituted by
the ‘as-structure’ or ‘well-joined structure’ of the rift-design*…”

— Gary Williams, post of January 22, 2010


Gian-Carlo Rota on Heidegger…

“… The universal as  is given various names in Heidegger’s writings….

The discovery of the universal as  is Heidegger’s contribution to philosophy….

The universal ‘as‘ is the surgence of sense in Man, the shepherd of Being.

The disclosure of the primordial as  is the end of a search that began with Plato….
This search comes to its conclusion with Heidegger.”

— “Three Senses of ‘A is B’ in Heideggger,” Ch. 17 in Indiscrete Thoughts

… and projective points as separating rifts

Image-- The Three-Point Line: A Finite Projective Space

    Click image for details.

* rift-design— Definition by Deborah Levitt

Rift.  The stroke or rending by which a world worlds, opening both the ‘old’ world and the self-concealing earth to the possibility of a new world. As well as being this stroke, the rift is the site— the furrow or crack— created by the stroke. As the ‘rift design‘ it is the particular characteristics or traits of this furrow.”

— “Heidegger and the Theater of Truth,” in Tympanum: A Journal of Comparative Literary Studies, Vol. 1, 1998

Thoreau on Group Theory

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

"Instead of a million count half a dozen." —Walden

"Of all the symmetric groups, S6 is perhaps the most remarkable."
Notes 2 (Autumn 2008), apparently by Robert A. Wilson,
   for Group Theory, MTH714U

For a connection of MTH714U with Walden, see "Window, continued."

For a connection of "Window" with the remarkable S6, see Inscapes.

For some deeper background, see Wilson's "Exceptional Simplicity."

Window, continued

“Simplicity, simplicity, simplicity!
I say, let your affairs be as two or three,
and not a hundred or a thousand;
instead of a million count half a dozen,
and keep your accounts on your thumb-nail.”
— Henry David Thoreau, Walden

This quotation is the epigraph to
Section 1.1 of Alexandre V. Borovik’s
Mathematics Under the Microscope:
Notes on Cognitive Aspects of Mathematical Practice
(American Mathematical Society,
Jan. 15, 2010, 317 pages).

From Peter J. Cameron’s review notes for
his new course in group theory


From Log24 on June 24

Geometry Simplified

Image-- The Four-Point Plane: A Finite Affine Space
(an affine  space with subsquares as points
and sets  of subsquares as hyperplanes)

Image-- The Three-Point Line: A Finite Projective Space
(a projective  space with, as points, sets
of line segments that separate subsquares)


Show that the above geometry is a model
for the algebra discussed by Cameron.

Monday, July 5, 2010


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

“Examples are the stained-glass
windows of knowledge.” — Nabokov

Image-- Example of group actions on the set Omega of three partitions of a 4-set into two 2-sets

Related material:

Thomas Wolfe and the
Kernel of Eternity

Sunday, July 4, 2010

Brightness at Noon (continued)

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

Today's sermon mentioned the phrase "Omega number."

Other sorts of Omega numbers— 24 and 759— occur
in connection with the set named Ω by R. T. Curtis in 1976—

Image-- In a 1976 paper, R.T. Curtis names the 24-set of his Miracle Octad Generator 'Omega.'

— R. T. Curtis, "A New Combinatorial Approach to M24,"
Math. Proc. Camb. Phil. Soc. (1976), 79, 25-42

Sermon for July 4

Filed under: General — m759 @ 11:00 AM

"Throughout history mystics and philosophers have sought a compact key to universal wisdom…."

Charles H. Bennett, "On Random and Hard-to-Describe Numbers," 1979.

Bennett was writing about Gregory Chaitin's concept of an "Omega number."

(See Thursday's "Omega at Eight" and Friday's "The Girl Who Fixed the Omega.")

Here is a different Omega number — Alt 234.

Related material:

Image-- Google Calculator-- '1776+234=2010'

A Reappearing Number*

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


Part 1
Part 2
Part 3

*See also the theater section
of today's New York Times.

Saturday, July 3, 2010

Beyond the Limits

Filed under: General,Geometry — Tags: — m759 @ 7:29 PM

"Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation…."

– Don DeLillo, Point Omega

Capitalized, the letter omega figures in the theology of two Jesuits, Teilhard de Chardin and Gerard Manley Hopkins. For the former, see a review of DeLillo. For the latter, see James Finn Cotter's Inscape  and "Hopkins and Augustine."

The lower-case omega is found in the standard symbolic representation of the Galois field GF(4)—

GF(4) = {0, 1, ω, ω2}

A representation of GF(4) that goes beyond the standard representation—


Here the four diagonally-divided two-color squares represent the four elements of GF(4).

The graphic properties of these design elements are closely related to the algebraic properties of GF(4).

This is demonstrated by a decomposition theorem used in the proof of the diamond theorem.

To what extent these theorems are part of "a saga of created reality" may be debated.

I prefer the Platonist's "discovered, not created" side of the debate.

Devising Entities

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

or, Darkness and Brightness at Noon

"Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation…. We tried to create new realities overnight, careful sets of words that resemble advertising slogans in memorability and repeatability. These were words that would yield pictures eventually and then become three-dimensional."

— Don DeLillo, Point Omega

GF(4) = {0, 1, ω, ω2}

Symbolic representation of a Galois field

"One two three  four,
  who are we  for?"

— Cheerleaders' chant

Friday, July 2, 2010

The Girl Who Fixed the Omega

Filed under: General — m759 @ 7:29 PM

Thanks to Nora Ephron for "The Girl Who Fixed the Umlaut"
(New Yorker  of July 5, 2010).

How to type a capital Omega—

Number Lock on, Alt key down, then numeric keypad
(or, on laptop, fn-style numbers on letter keys) 234.
Alt key up. Result: Ω.  Number Lock off.

Related poetic flight of fancy—

The most recent occurrence of 234 in the New York Lottery was on
August 6, 2008, the Feast of the Transfiguration.

Clicking on the Transfiguration link in this journal's post
for that date leads to an article on poet Paul Mariani.

Tracing a quotation in that article leads to…


The date of Mariani's poem, 24 August 2002, leads to a post in this journal
related to Mariani's "Loyola's Company" and to "that language only
light and diamonds know."

Related material: last night's Omega at Eight.

Thursday, July 1, 2010

Sibyl at Nine

Filed under: General — m759 @ 9:00 PM

By W. S. Merwin, the new Poet Laureate of the United States—

Image-- 'Prophecy,' by W.S. Merwin

Some context— This journal on September 29, 2003.

Omega at Eight

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

The "compact key to universal wisdom" passage in the previous post seemed
too well written to be the work of an anonymous webforum author.

Here is a slightly expanded version—

Throughout history mystics and philosophers have sought
a compact key to universal wisdom, a finite formula or text
that would provide the answer to every question. The use of
the Bible, the Koran and the I Ching for divination and the
tradition of the secret books of Hermes Trismegistus and the
medieval Jewish Cabala exemplify this belief or hope.  Such
sources of universal wisdom are traditionally protected from
casual use by being difficult to find as well as difficult to un-
derstand and dangerous to use, tending to answer more quest-
ions and deeper ones than the searcher wishes to ask. The
esoteric book is, like God, simple yet undescribable. It is om-
niscient, and it transforms all who know it. The use of clas-
sical texts to foretell mundane events is considered supersti-
tious nowadays, yet in another sense science is in quest of its
own Cabala, a concise set of natural laws that would explain
all phenomena. In mathematics, where no set of axioms can
hope to prove all true statements, the goal might be a concise
axiomatization of all "interesting" true statements.
      Ω is in many senses a Cabalistic number. It can be known
of through human reason, but not known. To know it in detail
one must accept its uncomputable sequence of digits on faith,
like words of a sacred text.   

This is Martin Gardner's* and Charles H. Bennett's
revised version of a passage from Bennett's  paper
"On Random and Hard-to-Describe Numbers," 1979.

The original passage from Bennett's paper—

Throughout history mystics and philosophers have sought a compact key to
universal wisdom, a finite formula or text which, when known and understood,
would provide the answer to every question. The Bible, the Koran, the mythical
secret books of Hermes Trismegistus, and the medieval Jewish Cabala have
been so regarded. Sources of universal wisdom are traditionally protected from
casual use by being hard to find, hard to understand when found, and dangerous
to use, tending to answer more and deeper questions than the user wishes to
ask. Like God the esoteric book is simple yet undescribable, omniscient, and
transforms all who know It. The use of classical texts to fortell [sic] mundane events
is considered superstitious nowadays, yet, in another sense, science is in quest of
its own Cabala, a concise set of natural laws which would explain all phenomena.
In mathematics, where no set of axioms can hope to prove all true statements,
the goal might be a concise axiomatization of all "interesting" true statements.
      Ω is in many senses a Cabalistic number. It can be known of, but not known,
through human reason. To know it in detail, one would have to accept its un-
computable digit sequence on faith, like words of a sacred text.

The Bennett paper deals with Gregory Chaitin's concept of an "Omega Number."

I prefer the Omega of Josefine Lyche—

Image-- Uncertified copy of 1986 figures by Cullinane in a 2009 art exhibit in Oslo

Click for further details.

See also All Hallows' Eve, 2002.

* Martin Gardner's Mathematical Games  column
"The Random Number Omega Bids Fair to Hold the Mysteries of the Universe,"
Scientific American, November 1979, 241(5), pp. 20–34.
The column is reprinted as "Chaitin's Omega," Ch. 21, pp. 307-319 in the
collection of Gardner's columns titled Fractal Music, Hypercards and More,
W.H. Freeman & Co., 1991

Darkness at Seven

Filed under: General,Geometry — m759 @ 7:00 PM

Hoax and Hype 
Four Years Ago Today—

Image-- Fanfiction-- Harry Potter and Plato's Diamond

There is Plato's diamond—

Image-- Plato's Diamond

and there is diamond theory

Google Search result for 'Diamond Theory'

… but there is no "Plato's Diamond Theory."

See, however, today's noon entry, "Plato's Code."

"You gotta be true to your code…" —Sinatra

Plato’s Code

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

John Allen Paulos yesterday at Twitter

"Plato's code cracked? http://bit.ly/ad6k1S
Fascinating if not a hoax or hype."

The story that Paulos linked to is about a British
academic who claims to have found some
symbolism hidden in Plato's writings by
splitting each into 12 parts and correlating
the 12 parts with semitones of a musical scale.

I prefer a different approach to Plato that is
related to the following hoax and hype—


From Dan Brown's novel Angels & Demons  (2000)

IMAGE- Illuminati Diamond, pp. 359-360 in 'Angels & Demons,' Simon & Schuster Pocket Books 2005, 448 pages, ISBN 0743412397


Image-- From 'Alchemy,' by Holmyard, the diamond of Aristotle's 4 elements and 4 qualities

This  four-elements diamond summarizes the classical
four elements and four qualities neatly, but some scholars
might call the figure "hype" since it deals with an academically
disreputable subject, alchemy, and since its origin is unclear.

For the four elements' role in some literature more respectable
than Dan Brown's, see Poetry's Bones.

Although an author like Brown might spin the remarks
below into a narrative—  The Plato Code — they are
neither  hoax nor hype.


Image-- From the Diamond in Plato's Meno to Modern Finite Geometry



For related non-hoax, non-hype remarks, see
The Rational Enterprise: Logos in Plato's Theaetetus,
by Rosemary Desjardins.

Those who prefer  hoax and hype in their philosophy may consult
the writings of, say, Barbara Johnson, Rosalind Krauss, and—
in yesterday's NY Times's  "The Stone" columnNancy Bauer.

Image-- The Philosophers' Stone according to The New York Times

— The New York Times

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