Monday, January 31, 2011

Darkness at Noon

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

In today's Wall Street Journal , Peter Woit reviews a new book on dark matter and dark energy.

For a more literary approach, see "dark materials" in this  journal.

Before thir eyes in sudden view appear
The secrets of the hoarie deep, a dark
Illimitable Ocean without bound,
Without dimension, where length, breadth, and highth,
And time and place are lost; where eldest Night
And Chaos, Ancestors of Nature, hold
Eternal Anarchie, amidst the noise
Of endless warrs and by confusion stand.
For hot, cold, moist, and dry, four Champions fierce
Strive here for Maistrie, and to Battel bring amidst the noise
Thir embryon Atoms....
                                ... Into this wilde Abyss,
The Womb of nature and perhaps her Grave,
Of neither Sea, nor Shore, nor Air, nor Fire,
But all these in thir pregnant causes mixt
Confus'dly, and which thus must ever fight,
Unless th' Almighty Maker them ordain
His dark materials to create more Worlds,
Into this wilde Abyss the warie fiend
Stood on the brink of Hell and look'd a while,
Pondering his Voyage....

-- John Milton, Paradise Lost , Book II

Related material:

1. The “spider” symbol of Fritz Leiber’s short story “Damnation Morning”—

2. Angels and demons here and in the Catholic Church.

3. The following diagram by one “John Opsopaus”—


Sunday, January 30, 2011

Brightness at Noon, continued…

Filed under: General — m759 @ 12:00 PM

A phrase suggested by last night's New York Times  obituaries

From Milton to Milton  (click to enlarge)


The "green fields" is from Shakespeare.

The above author, Vinton Adams Dearing, died* on April 6, 2005. From this journal on that date, some babbling.

"Have your people call my people." — George Carlin

* See Dearing's page 34



Filed under: General — m759 @ 11:00 AM

Today's sermon, suggested by yesterday's New York midday and evening lottery— "6/18 and 4/18."

Background for 6/18— Go Tigers!


Background for 4/18— Requiem for an Editor*


* See "Sally Menke, Tarantino's Editor, Dies."

Saturday, January 29, 2011

Cold Open

Filed under: General — m759 @ 11:16 PM

Kernel and Moonshine

"The yarns of seamen have a direct simplicity, the whole meaning of which lies within the shell of a cracked nut. But Marlow was not typical (if his propensity to spin yarns be excepted), and to him the meaning of an episode was not inside like a kernel but outside, enveloping the tale which brought it out only as a glow brings out a haze, in the likeness of one of these misty halos that sometimes are made visible by the spectral illumination of moonshine."

— Joseph Conrad in Heart of Darkness

Some background—

Spider and Snake on cover of Fritz Leiber's novel Big Time

An image from yesterday's search
God, TIme, Hopkins

"We got tom-toms over here bigger than a monster
Bla Bla Bla Bla Bla Bla Bla Bla"

— "Massive Attack"

"I'm just checking your math on that. Yes, I got the same thing."

— "The Social Network"

"Live… Uh, check thatFrom New York, it's Saturday Night! "

Friday, January 28, 2011


Filed under: General — m759 @ 8:22 AM

From this morning's New York Times

 "On November 12th and 13th, 2010,
  a meeting of Roman Catholic bishops
  convened to respond to the growing demand
  for exorcism rites."
  — Trailer for the film "The Rite," which opens today


Meanwhile, in this  journal on November 12th and 13th, 2010… Award Show Story.

Related material — God, Time, Hopkins and a Faustian link from November 12th.

Update of 9:57 AM 1/28— The Faustian link suggests readings from
James G. Hart's The Person and the Common Life  (Kluwer Academic, 1992).

See pages 1,  2,  3,  4,  and  5, and note especially the spider metaphor on page 5 —


Thursday, January 27, 2011

Mathematics and Narrative, continued…

Filed under: General,Geometry — m759 @ 10:30 AM

Indiana Jones and the Magical Oracle

Mathematician Ken Ono in the December 2010 American Mathematical Society Notices


The "dying genius" here is Ramanujan, not Galois. The story now continues at the AMS website—


      (Excerpt from Jan. 27 screenshot;
      the partitions story has been the top
      news item at the site all week.)

From a Jan. 20, 2011, Emory University press release —
"Finite formula found for partition numbers" —

"We found a function, that we call P, that is like a magical oracle," Ono says. "I can take any number, plug it into P, and instantly calculate the partitions of that number. P does not return gruesome numbers with infinitely many decimal places. It's the finite, algebraic formula that we have all been looking for."

For an introduction to the magical oracle, see a preprint, "Bruinier-Ono," at the American Institute of Mathematics website.

Ono also discussed the oracle in a video (see minute 25) recorded Jan. 21 and placed online today.

See as well "Exact formulas for the partition function?" at mathoverflow.net.

A Nov. 29, 2010, remark by Thomas Bloom on that page leads to a 2006 preprint by Ono and Kathrin Bringmann, "An Arithmetic Formula for the Partition Function*," that seems not unrelated to Ono's new "magical oracle" formula—

Click to enlarge


The Bruinier-Ono paper does not mention the earlier Bringmann-Ono work.

(Both the 2011 Bruinier-Ono paper and the 2006 Bringmann-Ono paper mention their debt to a 2002 work by Zagier—  Don Zagier, "Traces of singular moduli," in Motives, Polylogarithms and Hodge theory, Part II  (Irvine, CA, 1998), International Press Lecture Series 3 (International Press, Somerville, MA, 2002),   pages 211-244.)

Some background for those who prefer mathematics to narrative
The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and q-Series ,
by Ken Ono, American Mathematical Society CBMS Series, 2004.

* Proc. Amer. Math. Soc. 135 (2007), 3507-3514.

Wednesday, January 26, 2011

All Others Pay Cash

Filed under: General — m759 @ 1:20 PM

Click to enlarge.


Related material: Daniel Bell on the City of Heaven
and the Louvin Brothers' "Cash on the Barrelhead."

Requiem for a Screenwriter*

Filed under: General — m759 @ 1:00 PM

Click for obit.


Hexagram 61

Still Point.

* Notably, of the film "Downfall" (Der Untergang ).
   "Has time rewritten every line?" —Streisand

Bell Toll

Filed under: General — m759 @ 12:00 PM

"The ladder to the City of Heaven can no longer be a 'faith ladder,' but an empirical one," he wrote, "a utopia has to specify where one wants to go, how to get there, the costs of the enterprise, and some realization of, and justification for the determination of who is to pay."

AP on Daniel Bell, Harvard professor of sociology, who died yesterday at 91

Early Nothing

Filed under: General,Geometry — Tags: — m759 @ 11:29 AM

(Continued from yesterday)

Today's New York Times  obituaries —


From Wes Clark's site Web Noir

Scenes from "The Set-Up," a 1949 noir classic by Robert Wise


From Bruce Gordon's obituary in today's New York Times

"Mr. Gordon appeared on Broadway many times. He was in the original cast of the hit comedy 'Arsenic and Old Lace,' which opened in 1941 and starred Boris Karloff. Uncharacteristically, given his later résumé, Mr. Gordon played a policeman." —Margalit Fox

Related material —


(See Savage Solstice in this journal on December 21st, 2010.)

Tuesday, January 25, 2011

For Your Consideration…

Filed under: General — m759 @ 1:20 PM

Early Nothing

Manohla Dargis on film director Fritz Lang in The New York Times  (online Jan. 21, 2011, printed Jan. 23)—

"Hollywood endings can be beautiful fibs, but in Lang’s movies the glossy smiles and fade-outs feel forced. You can almost feel him pulling at them, trying to bring them back into the dark where they belong. The miracle of his Hollywood era is that, even when the screenplays tried to force his work in one direction, he managed to take them into richer, more complex realms with a style that was alternately baroque and stripped down and peopled with characters whose cynicism was earned. Every so often, though, he did strike screenwriting gold, notably in 'The Big Heat,' his 1953 crime masterwork. 'Say, I like this, early nothing,' a mink-swaddled Gloria Grahame says of a hotel room. Everyone really is a critic."

Here comes everyone .

Another Reappearing Number

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

(A sequel to yesterday's reappearing number)

25 —

5x5 ultra super magic square

See "Quine, Newton, logic" in this journal.

Brightness at Noon, continued–

Filed under: General — m759 @ 12:00 PM

Hymn Noir

"This is that 'once in a lifetime,'
this is the thrill divine."

Dorcas Cochran, "Again"


Today's previous post as well as Loretta's Rainbow,
the "hole in the record" theme in The Third Wor*d War,
"Is Nothing Sacred?," and James Joyce's Birthday, 2009.

See also "the name of the story" in this journal.


Filed under: General — m759 @ 4:04 AM

For Brian Rust, "father of modern discography,"
who died on Twelfth Night, 2011—

A song.

IMAGE- Detail of a photo by Richard Newton at flickr.com

Related material— a video of the song—
Ida Lupino in "Road House" (1948) singing "Again."

See also this journal's Twelfth Night posts. (Note particularly the 4/01 link.)

Monday, January 24, 2011

A Reappearing Number, continued

Filed under: General — m759 @ 12:24 PM

"In the work of Ramanujan, the number 24 appears repeatedly.
This is an example of what mathematicians call magic numbers,
which continually appear, where we least expect them,
for reasons that no one understands."

— Michio Kaku, Hyperspace, Oxford U. Press, 1994, p. 173

See also "A Reappearing Number," this journal, July 4, 2010.

Sunday, January 23, 2011


Filed under: General — m759 @ 12:00 PM



Filed under: General — m759 @ 11:29 AM

Yesterday's afternoon post

"'Two distinguished philosophers from the heart of the profession
  offer a meditation on the meaning of life….'"

Paul Newman and Robert Redford in 'The Sting'

Saturday, January 22, 2011

Midnight in the Garden continues…

Filed under: General — m759 @ 11:59 PM

Today's funeral Mass for Sargent Shriver,
tonight's review in the New York TImes  of a singer
from the Kollege of Musical Knowledge,
and today's New York lottery numbers suggest the following links—

8/15 and 9/10.

Ask Not

Filed under: General — m759 @ 1:20 PM

Background— see Natural Hustler in this journal.



    This is from All Things Shining— "Conclusion: Lives Worth Living in a Secular Age"

High School Squares*

Filed under: General,Geometry — Tags: — m759 @ 1:20 AM

The following is from the weblog of a high school mathematics teacher—


This is related to the structure of the figure on the cover of the 1976 monograph Diamond Theory


Each small square pattern on the cover is a Latin square,
with elements that are geometric figures rather than letters or numerals.
All order-four Latin squares are represented.

For a deeper look at the structure of such squares, let the high-school
chart above be labeled with the letters A through X, and apply the
four-color decomposition theorem.  The result is 24 structural diagrams—

    Click to enlarge

IMAGE- The Order-4 (4x4) Latin Squares

Some of the squares are structurally congruent under the group of 8 symmetries of the square.

This can be seen in the following regrouping—

   Click to enlarge

IMAGE- The Order-4 (4x4) Latin Squares, with Congruent Squares Adjacent

      (Image corrected on Jan. 25, 2011– "seven" replaced "eight.")

* Retitled "The Order-4 (i.e., 4×4) Latin Squares" in the copy at finitegeometry.org/sc.

Thursday, January 20, 2011


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

Reynolds Price died today. See Lore of the Manhattan Project in this journal.

In memoriam : Descartes's Twelfth Step and Symmetry and a Trinity.

Brightness at Noon, continued

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

"One wild rhapsody a fake for another."

– Wallace Stevens, "Arrival at the Waldorf," in Parts of a World  (1942)

"Camelot is an illusion.

That doesn't matter, according to Catherine.
Camelot is an artificial construction, a public perception.
The things that matter are closer, deeper, self-generated, unkillable.
You've got to grow up to discover what those things are."

— Dan Zak, Washington Post  movie review on Feb. 27, 2009. See also this journal on that date.

See as well a note on symmetry from Christmas Eve, 1981, and Verbum in this journal.

Some philosophical background— Derrida in the Garden.

Some historical background— A Very Private Woman  and Noland.

Wednesday, January 19, 2011

A Shade Out of Synch

Filed under: General — m759 @ 5:24 PM

Review of a 1968 novel by Wilfrid Sheed, who died today—



Sheed on his boyhood in My Life as a Fan: A Memoir

"So it was back to… tinkering with my batting stance and praying that some one of my aged neighbors would miraculously rear back and give birth, like Sarah in the Bible, to a boy who would even more miraculously emerge at about my own age and not turn out to be a butterfly collector or other form of creep." (Simon & Schuster, 1993; in 2001 edition, page 84)

See also Shadow (September 23rd) —

"I was the shadow of the waxwing slain" — John Shade in Pale Fire , a novel by butterfly collector Vladimir Nabokov

—as well as Intermediate Cubism and Ironic Butterfly.


"This is called the transformation of things."

Intermediate Cubism

Filed under: General,Geometry — Tags: , — m759 @ 2:22 PM

The following is a new illustration for Cubist Geometries

IMAGE- A Galois cube: model of the 27-point affine 3-space

(For elementary cubism, see Pilate Goes to Kindergarten and The Eightfold Cube.
 For advanced, see Solomon's Cube and Geometry of the I Ching .)

Cézanne's Greetings.

Sunday, January 16, 2011

The Empire Room Strikes Back

Filed under: General — m759 @ 5:24 PM

The New York Times  now offers a sequel to its philosophy series "The Stone"

"a sword that heals."

From the Times  City Room this afternoon—

Click to enlarge


"One wild rhapsody a fake for another."

— Wallace Stevens, "Arrival at the Waldorf," in Parts of a World  (1942)

The Mind Spider*

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

On a conference at the New School for Social Research on Friday and Saturday, December 3rd and 4th, 2010—

"This conference is part of the early stages in the formation of a lexicon of political concepts. It will be the 5th in a series of conferences started in Tel Aviv University. The project is guided by one formal principle: we pose the Socratic question "what is x?", and by one theatrical principle: the concepts defined should be relevant to political thought…."

[The conference is not unrelated to the New York Times  philosophy series "The Stone." Connoisseurs of coincidence— or, as Pynchon would have it, "chums of chance"— may read the conclusion of this series, titled "Stoned," in the light of the death on December 26th (St. Stephen's Day) of Matthew Lipman, creator of the "philosophy for children" movement. Many New York Times  readers will, of course, be ignorant of the death by stoning of St. Stephen


   Beloit College Nuremberg Chronicle

commemorated on December 26th. They should study Acts of the ApostlesChapter  6 and Chapter 7.]

Meanwhile, in this  journal—

Click to enlarge


For some background on the Dec. 4th link to "Damnation Morning," see "Why Me?"

For some political background, see "Bright Star"+"Dark Lady" in this journal.

* The title refers to a story by Fritz Leiber.

Endings and Beginnings

Filed under: General — m759 @ 4:07 AM

"Not any or every death is an end, or birth a beginning."

J. M. Bernstein, The Philosophy of the Novel

Some related philosophy in  a novel —


IMAGE- 'The Borrowed Heart' in Prince Ombra

For some background, see "New School for Social Research" and "Orozco" in this journal.

See also the brief biography of Bernstein in a document about a meeting last month
in the Orozco Room at the New School.

Friday, January 14, 2011

Mathematics and Narrative continues…

Filed under: General — m759 @ 11:07 PM

From 6/22, 2010 —


    I would argue that at least sometimes, lottery numbers may be regarded,
    according to Bernstein's definition, as story statements.

From 7/02, 2010 —


Ironic Butterfly

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

David Brooks’s column today quotes Niebuhr. From the same source—
Reinhold Niebuhr, The Irony of American History

Chapter 8: The Significance of Irony

Any interpretation of historical patterns and configurations raises the question whether the patterns, which the observer discerns, are “objectively” true or are imposed upon the vast stuff of history by his imagination. History might be likened to the confusion of spots on the cards used by psychiatrists in a Rorschach test. The patient is asked to report what he sees in these spots; and he may claim to find the outlines of an elephant, butterfly or frog. The psychiatrist draws conclusions from these judgments about the state of the patient’s imagination rather than about the actual configuration of spots on the card. Are historical patterns equally subjective?
The Biblical view of human nature and destiny moves within the framework of irony with remarkable consistency. Adam and Eve are expelled from the Garden of Eden because the first pair allowed “the serpent” to insinuate that, if only they would defy the limits which God had set even for his most unique creature, man, they would be like God. All subsequent human actions are infected with a pretentious denial of human limits. But the actions of those who are particularly wise or mighty or righteous fall under special condemnation. The builders of the Tower of Babel are scattered by a confusion of tongues because they sought to build a tower which would reach into the heavens.

Niebuhr’s ironic butterfly may be seen in the context of last
Tuesday’s post Shining and of last Saturday’s noon post True Grid


The “butterfly” in the above picture is a diagram showing the 12 lines* of the Hesse configuration from True Grid.

It is also a reference to James Hillman’s classical image (see Shining) of the psyche, or soul, as a butterfly.

Fanciful, yes, but this is in exact accordance with Hillman’s remarks on the soul (as opposed to the spirit— see Tuesday evening’s post).

The 12-line butterfly figure may be viewed as related to the discussions of archetypes and universals in Hillman’s Re-Visioning Psychology  and in Charles Williams’s The Place of the Lion . It is a figure intended here to suggest philosophy, not entertainment.

Niebuhr and Williams, if not the more secular Hillman, might agree that those who value entertainment above all else may look forward to a future in Hell (or, if they are lucky, Purgatory). Perhaps such a future might include a medley of Bob Lind’s “Elusive Butterfly” and Iron Butterfly’s “In-a-Gadda-da-Vida.”

* Three horizontal, three vertical, two diagonal, and four arc-shaped.

Tuesday, January 11, 2011

Toy Story Variations

Filed under: General — m759 @ 11:30 PM

Where Entertainment Is God  continues...

New York Lottery today— Midday 710, Evening 563.

This suggeests a scientific note from the date 7/10  (2009) and the page number 563 from Dec. 29

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

For a different perspective on Toy Story , see the Dec. 29 post.

Other entertainments — The novel Infinite Jest  and two versions of "Heeere's Johnny !" —

            From Stanley Kubrick and from today's New York Times :


See also All Things Shining  and the lottery theology of Jorge Luis Borges.

Soul and Spirit

Filed under: General,Geometry — Tags: , — m759 @ 9:29 PM

This morning's post, "Shining," gave James Hillman's 1976 remarks
on the distinction between soul  and spirit .

The following images may help illustrate these concepts.


The distinction as illustrated by Jeff Bridges —





The mirror has two faces (at least).

Postscript from a story, "The Zahir," in the Borges manner,
  by Mark Jason Dominus (programmer of the quilt designs above)—

"I  left that madhouse gratefully."

Dominus is also the author of…


Click for details.


Filed under: General — m759 @ 11:07 AM

(Continued from January 3rd)

Readings from James Hillman's 1976 classic Re-Visioning Psychology

On the "eye of the soul" and on spirit  as clarity


On the distinction between spirit  and soul  (pp. 67-70)—

Click to enlarge.


* Here "Shining" refers to the recent pop-philosophy book All Things Shining , not to Stephen King.  

Monday, January 10, 2011

Big Time*

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

(True Grid continued)

"They're gonna put me in the movies,
They're gonna make a big star out of me…"


“Thus the whirligig of time brings in his revenges.”  
Twelfth Night ,
Act V, Sc. I  [text]

See also this journal on Twelfth Night, 2011.

* Background:

   The Changewar stories of Fritz Leiber, including Big Time  and "Damnation Morning."

   The Shakespearean fool of Dec. 30 is also not without relevance.

Sunday, January 9, 2011

Back to You, Olivia

Filed under: General — m759 @ 7:00 PM

After the Diablo Ballet, the Ballet Blanc .

In Other Entertainment News…

Filed under: General — m759 @ 1:01 PM

The Netflix Prize

An invited address today at the Mathematical Association of America annual meeting —

  (Click to enlarge.)




Filed under: General — Tags: — m759 @ 11:00 AM

Another  topic from today's newspaper —

IMAGE- Nicole Kidman in a Sunday supplement

Commentary —

"We're gonna need more holy water." — "Season of the Witch," a film that opened Friday

See also

This morning's post Inception and the following site:

Image- The Ninefold Favicon

Note the ninefold favicon at the above site. Some background—
The Ninth Gate  in yesterday's post and this image from last September



Filed under: General — m759 @ 10:30 AM


"… a wake-initiated lucid dream occurs when the dreamer goes from a normal
waking state directly into a dream state with no apparent lapse in consciousness."

Not necessarily a good idea.

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


Saturday, January 8, 2011

True Grid (continued)

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

"Rosetta Stone" as a Metaphor
  in Mathematical Narratives

For some backgound, see Mathematics and Narrative from 2005.

Yesterday's posts on mathematics and narrative discussed some properties
of the 3×3 grid (also known as the ninefold square ).

For some other properties, see (at the college-undergraduate, or MAA, level)–
Ezra Brown, 2001, "Magic Squares, Finite Planes, and Points of Inflection on Elliptic Curves."

His conclusion:

When you are done, you will be able to arrange the points into [a] 3×3 magic square,
which resembles the one in the book [5] I was reading on elliptic curves….

This result ties together threads from finite geometry, recreational mathematics,
combinatorics, calculus, algebra, and number theory. Quite a feat!

5. Viktor Prasolov and Yuri Solvyev, Elliptic Functions and Elliptic Integrals ,
    American Mathematical Society, 1997.

Brown fails to give an important clue to the historical background of this topic —
the word Hessian . (See, however, this word in the book on elliptic functions that he cites.)

Investigation of this word yields a related essay at the graduate-student, or AMS, level–
Igor Dolgachev and Michela Artebani, 2009, "The Hesse Pencil of Plane Cubic Curves ."

From the Dolgachev-Artebani introduction–

In this paper we discuss some old and new results about the widely known Hesse
  of 9 points and 12 lines in the projective plane P2(k ): each point lies
on 4 lines and each line contains 3 points, giving an abstract configuration (123, 94).

PlanetMath.org on the Hesse configuration


A picture of the Hesse configuration–

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

(See Visualizing GL(2,p), a note from 1985).

Related notes from this journal —

From last November —

Saturday, November 13, 2010


m759 @ 10:12 PM

From the December 2010 American Mathematical Society Notices


Related material from this  journal—

Mathematics and Narrative and

Consolation Prize (August 19, 2010)

From 2006 —

Sunday December 10, 2006


 m759 @ 9:00 PM

A Miniature Rosetta Stone:

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

“Function defined form, expressed in a pure geometry
that the eye could easily grasp in its entirety.”

– J. G. Ballard on Modernism
(The Guardian , March 20, 2006)

“The greatest obstacle to discovery is not ignorance –
it is the illusion of knowledge.”

— Daniel J. Boorstin,
Librarian of Congress, quoted in Beyond Geometry

Also from 2006 —

Sunday November 26, 2006


m759 @ 7:26 AM

Rosalind Krauss
in "Grids," 1979:

"If we open any tract– Plastic Art and Pure Plastic Art  or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.

Or, to take a more up-to-date example…."

"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
The Club Dumas ,1993

"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
Robert Plant ,1971

The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.

An example of the universal*– or, according to Krauss,
a "staircase" to the universal– is the ninefold square:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo, the field of Reason…."
John Outram, architect    

For more on the field of reason, see
Log24, Oct. 9, 2006.

A reasonable set of "strange correspondences"
in the garden of Apollo has been provided by
Ezra Brown in a mathematical essay (pdf).

Unreason is, of course, more popular.

* The ninefold square is perhaps a "concrete universal" in the sense of Hegel:

"Two determinations found in all philosophy are the concretion of the Idea and the presence of the spirit in the same; my content must at the same time be something concrete, present. This concrete was termed Reason, and for it the more noble of those men contended with the greatest enthusiasm and warmth. Thought was raised like a standard among the nations, liberty of conviction and of conscience in me. They said to mankind, 'In this sign thou shalt conquer,' for they had before their eyes what had been done in the name of the cross alone, what had been made a matter of faith and law and religion– they saw how the sign of the cross had been degraded."

– Hegel, Lectures on the History of Philosophy ,
   "Idea of a Concrete Universal Unity"

"For every kind of vampire,
there is a kind of cross."
– Thomas Pynchon   

And from last October —

Friday, October 8, 2010


m759 @ 12:00 PM

Starting Out in the Evening
… and Finishing Up at Noon

This post was suggested by last evening's post on mathematics and narrative and by Michiko Kakutani on Vargas Llosa in this morning's New York Times .



Above: Frank Langella in
"Starting Out in the Evening"

Right: Johnny Depp in
"The Ninth Gate"


"One must proceed cautiously, for this road— of truth and falsehood in the realm of fiction— is riddled with traps and any enticing oasis is usually a mirage."

– "Is Fiction the Art of Lying?"* by Mario Vargas Llosa,
    New York Times  essay of October 7, 1984

* The Web version's title has a misprint—
   "living" instead of "lying."

"You've got to pick up every stitch…"

Friday, January 7, 2011

Ayn Sof

Filed under: General — Tags: , — m759 @ 7:26 PM

(A continuation of this morning's Coxeter and the Aleph)

"You've got to pick up every stitch… Must be the season of the witch."
Donovan song at the end of Nicole Kidman's "To Die For"

Mathematics and Narrative, Illustrated



"As is well known, the Aleph is the first letter of the Hebrew alphabet.
Its use for the strange sphere in my story may not be accidental.
For the Kabbala, the letter stands for the En Soph ,
the pure and boundless godhead; it is also said that it takes
the shape of a man pointing to both heaven and earth, in order to show
that the lower world is the map and mirror of the higher; for Cantor's
Mengenlehre , it is the symbol of transfinite numbers,
of which any part is as great as the whole."

— Borges, "The Aleph"

From WorldLingo.com

Ein Sof

Ein Soph or Ayn Sof (Hebrew  אין סוף, literally "without end", denoting "boundlessness" and/or "nothingness"), is a Kabbalistic term that usually refers to an abstract state of existence preceding God's Creation of the limited universe. This Ein Sof , typically referred to figuratively as the "light of Ein Sof " ("Or Ein Sof "), is the most fundamental emanation manifested by God. The Ein Sof  is the material basis of Creation that, when focused, restricted, and filtered through the sefirot , results in the created, dynamic universe.

Cultural impact

Mathematician Georg Cantor labeled different sizes of infinity using the Aleph. The smallest size of infinity is aleph-null (0), the second size is aleph-one (1), etc. One theory about why Cantor chose to use the aleph is because it is the first letter of Ein-Sof. (See Aleph number)

"Infinite Jest… now stands as the principal contender
for what serious literature can aspire to
in the late twentieth and early twenty-first centuries."

All Things Shining, a work of pop philosophy published January 4th


"You're gonna need a bigger boat." — Roy Scheider in "Jaws"

"We're gonna need more holy water." — "Season of the Witch," a film opening tonight

See also, with respect to David Foster Wallace, infinity, nihilism,
and the above reading of "Ayn Sof" as "nothingness,"
the quotations compiled as "Is Nothing Sacred?"

Coxeter and the Aleph

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

In a nutshell —

Epigraph to "The Aleph," a 1945 story by Borges:

O God! I could be bounded in a nutshell,
and count myself a King of infinite space…
— Hamlet, II, 2


The story in book form, 1949

A 2006 biography of geometer H.S.M. Coxeter:


The Aleph (implicit in a 1950 article by Coxeter):


The details:

(Click to enlarge)


Related material: Group Actions, 1984-2009.

Thursday, January 6, 2011

Epiphany for Hal

Filed under: General — m759 @ 12:00 PM

IMAGE- 'A Beautiful Mind' on games (from index)

IMAGE- 'War Games' computer- 'How about a nice game of chess?'

See also Nabokov + chess + patterns.

Epiphany Riddle

Filed under: General,Geometry — Tags: — m759 @ 11:32 AM

"Spaces and geometries, those which we perceive,
which we can’t perceive, or which only some of us perceive,
are a recurring theme in Against  the Day ."

Michael White

"大哉大哉  宇宙之谜
 美哉美哉  真理之源"

"Great indeed is the riddle of the universe.
 Beautiful indeed is the source of truth."

— Shing-Tung Yau, Chairman,
Department of Mathematics, Harvard University

"Always keep a diamond in your mind."

King Solomon at the Paradiso

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

Image from stoneship.org

Wednesday, January 5, 2011

True Grid Example

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

See today's earlier posts Ode and True Grid (continued) and, in the latter's
context of tic-tac-toe war games —  Balance, from Halloween 2005 —

IMAGE- The ninefold square

“An asymmetrical balance is sought since it possesses more movement.
This is achieved by the imaginary plotting of the character
upon a nine-fold square, invented by some ingenious writer of the Tang dynasty.
If the square were divided in half or in four, the result would be symmetrical,
but the nine-fold square permits balanced asymmetry."

Paraphrase of a passage in Chiang Yee's Chinese Calligraphy

True Grid (continued)

Filed under: General — m759 @ 7:59 PM

For material related to the Dec. 29, 2010, posts Toy Stories and True Grid

See Theological Points of Tron: Legacy, by the anonymous blogger hilbertthm90.

An excerpt —

Another story told in the movie is how this girl was about to be destroyed by the evil guys only to find “the father” standing over her after she blacked out and he “saved her”. The father’s disk contains all the information about everything in the grid, so in a sense the father is omniscient. Clearly the father is a stand in for the Biblical God since he creates a whole universe and is omniscient (and by some of the actions he performs in the movie, he seems omnipotent as well). I don’t think the Christian parallels are all in my head.

There is some sketchy theology that occurs that might be in my head, though. The “real world” outside of the grid seems to be a symbol for heaven. If this is true, it presents a very interesting theological point.

Compare and contrast —

Woody and Buzz  from Christmas Day, 2010 —


Update of 8:55 PM — Related material from today's  Ghost Light weblog


See also today's New York midday lottery number, 596, as it appears in a search
for "legacy code" in this journal. It is China's code for its first nuclear test.

Today's evening New York number is less alarming — 401, suggesting the date
4/01 — i.e., April Fools' Day.


Filed under: General — m759 @ 7:00 PM
From http://www.douban.com/note/63358774/ —

An Ode to the Unity of Time and Space 

Time, ah, time,
how you go off like this!

Physical things, ah, things,
so abundant you are!

The Ruo’s waters are three thousand,
how can they not have the same source?

Time and space are one body,
mind and things sustain each other.

Time, o time,
does not time come again?

Heaven, o heaven,
how many are the appearances of heaven!

From ancient days constantly shiftling on,
black holes flaring up.

Time and space are one body,
is it without end?

Great indeed
is the riddle of the universe.

Beautiful indeed
is the source of truth.

To quantize space and time
the smartest are nothing.

To measure the Great Universe with a long thin tube
the learning is vast.
                                 By Shing-Tung Yau

时乎时乎 逝何如此
物乎物乎 繁何如斯
弱水三千 岂非同源
时空一体 心物互存
时兮时兮 时不再欤
天兮天兮 天何多容
亘古恒迁 黑洞冥冥
时空一体 其无尽耶
大哉大哉 宇宙之谜
美哉美哉 真理之源
时空量化 智者无何
管测大块 学也洋洋 

Roll Credits

Filed under: General — m759 @ 12:00 PM

IMAGE- Robert Mitchum sings 'Everlasting Arms'

"What a fellowship…"

Happy birthday, Iris.

Riff Design

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

"Leave a space." — Tom Stoppard, in a play about philosophers


The word "riff" at top in the Times  obits is from an ad for Google's Chrome browser.
The white space is artificial, made by deleting last  year's dead.

Scene from 'A Good Year'

A Good Year

For further details, click on the image below.

'The Power Of The Center: A Study of Composition in the Visual Arts,' by Rudolf Arnheim

Tuesday, January 4, 2011

Star Quality

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

A search in memory of Gerry Rafferty,
a talented singer-songwriter who died today at 63.

"Here was finality indeed, and cleavage!"
— Malcolm Lowry, Under the Volcano

The White Itself

Filed under: General — m759 @ 11:02 AM

The Development of Logic 

IMAGE- Kneale and Kneale on Plato's theory of forms and 'the white itself'

A Universal Etymological English Dictionary


Joan Didion —



The above readings are related* to All Things Shining , a work of pop philosophy published today.

For a review of the new book, click on the image below.


* Didion's remarks on James Jones are related to the title  of the new book.
  Jones wrote a novel, The Thin Red Line , on which a film is based that
  contains the phrase "all things shining." The phrase is not in the novel.
  The authors of All Things Shining  credit neither novel nor film.

Monday, January 3, 2011

New Critical Art

Filed under: General — m759 @ 9:00 PM

From a scholar quoted in this morning's post

"Both Vico and Joyce, each in his own way, practice what Vico calls a nuov'arte critica , a 'new critical art'…"

From Hugh Grant's birthday, 2003 (found in a search for whiteness  in this morning's post) —

Tara Fitzgerald and Hugh Grant
in "Sirens" (1994)


At Tara, in this fateful hour,
I place all heaven with its power.
And the sun with its brightness,
And the snow with its whiteness,
And the fire with all the strength it hath,
And the lightning with its rapid wrath,
And the winds with their swiftness along their path,
And the sea with its deepness,
And the rocks with their steepness,
And the earth with its starkness;
All these I place
By God’s almighty help and grace
Between myself and the powers of darkness.

From A Swiftly Tilting Planet
by Madeleine L’Engle

The cover of yesterday's Sunday New York Times Book Review
features stylized letters by artist Leonardo Sonnoli that include black
circles and triangles —

IMAGE- NY Times Book Review cover art by Leonardo Sonnoli

The stylized Sonnoli letters spell out "WORDS ABOUT WORDS ABOUT WORDS."
This phrase is used to introduce essays on criticism by "six accomplished critics."

A less accomplished critic might note that in the picture above, Tara is modeling
a new fashion by Sonnoli — namely, the word OOV.  A search for this word yields…

"OOV in text processing stands for 'out-of-vocabulary,' i.e., a word
 that is not known in the computer's online dictionary."

It should be.

Addendum (from a link in the same search for whiteness ) in memory of a great beauty who died on Sunday —


Filed under: General — m759 @ 11:07 AM

For the authors of the new book All Things Shining

See the discussions of "concrete universals" in James Hillman's Re-Visioning Psychology  and in Donald Phillip Verene's Vico and Joyce

IMAGE- The imaginative universal in Vico and Joyce

The index to All Things Shining  contains no entries for Hillman (or his mentor Jung), Verene, Joyce, Vico, or the word "universal."

It does, however, contain four references to an example  of a universal —

whiteness, 161, 169-173, 175, 178

See also "whiteness" in this  journal.

Sunday, January 2, 2011

A Universal Form

Filed under: General,Geometry — m759 @ 6:40 PM

Simon Critchley today in the New York Times  series "The Stone"—

Philosophy, among other things, is that living activity of critical reflection in a specific context, by which human beings strive to analyze the world in which they find themselves, and to question what passes for common sense or public opinion— what Socrates called doxa— in the particular society in which they live. Philosophy cuts a diagonal through doxa. It does this by raising the most questions of a universal form: “What is X?”

Actually, that's two diagonals. See Kulturkampf at the Times  and Geometry of the I Ching .


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

"Art has to reveal to us ideas, formless spiritual essences."

— A character clearly talking nonsense, from the National Library section of James Joyce's Ulysses

"Unsheathe your dagger definitions. Horseness is the whatness of allhorse."

— A thought of Stephen Dedalus in the same Ulysses  section

For a representation of horseness related to Singer's dagger definitions in Saturday evening's post, see Generating the Octad Generator and Art Wars: Geometry as Conceptual Art.

More seriously, Joyce's "horseness" is related to the problem of universals. For an illuminating approach to universals from a psychological point of view, see James Hillman's Re-Visioning Psychology  (Harper Collins, 1977). (See particularly pages 154-157.)

Saturday, January 1, 2011

For a Dead Philosopher —

Filed under: General — Tags: — m759 @ 7:06 PM

Dagger Definitions

Part I

From 'Ulysses,' 1922 first edition, page 178-- 'dagger definitions'

Click for some background.

Part II


Click for some background.

Update of Jan. 2, 2011

Singer goes on to say that "A finite projective plane, PG (2, p), defined in this way is Pascalian and Desarguesian ; it exists for every prime and positive integer , and there is only one such PG (2, p) for a given p  and n …."

His definitions therefore deliberately exclude non -Desarguesian finite projective planes, which were known to exist at the time he wrote.

Bit by Bit, Putting It Together…

Filed under: General — m759 @ 12:00 PM

This morning's earlier post linked to a 2009 essay by the late Denis Dutton on Damien Hirst and Acheulian Hand Axes.

Related material on hand axes —


Related material on Damien Hirst —


The large stone of the Hirst diamond skull —



Related philosophy — "And that  is the state  of the art ." — Stephen Sondheim

See also this  journal on the date of the above Hirst skull post.

Christchurch Philosophy

Filed under: General — m759 @ 9:48 AM

In memory of Denis Dutton, a professor of philosophy at Canterbury University in Christchurch, New Zealand, who reportedly died in Christchurch on Tuesday, December 28, 2010. (This date presumably refers to New Zealand Daylight Time, 18 hours ahead of Eastern Standard time; both U.S. and New Zealand sources say Dutton died on Dec. 28.)

The New York Times reports his death today —

"A version of this article appeared in print on January 1, 2011, on page A17 of the New York edition."

Dutton's academic specialty was the philosophy of art.

For some remarks on philosophy and on art from the day of Dutton's death, see "Church Diamond" in this journal, 3:09 PM EST December 27 (9:09 AM December 28, New Zealand Daylight Time).

See also Dutton's essay "Has Conceptual Art Jumped the Shark Tank?" that was linked to here on St. Luke's Day, 2009.

For some context, see the recent Log24 posts Dry Bones and Canterbury Tale.

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