Log24

Monday, May 31, 2010

Memorial for Galois

Filed under: Uncategorized — m759 @ 7:16 PM

… and for Louise Bourgeois

Image-- Louise Bourgeois, sculptor of giant spiders, dies at 98

"The épateurs  were as boring as the bourgeois,
two halves of one dreariness."

— D. H. Lawrence, The Plumed Serpent

Image-- Google 5/31/2010 search for 'eightfold geometry' yields page on mother goddess as spider figure, also pages on some actual geometry

Sunday, May 30, 2010

A Post for Galois

Filed under: Uncategorized — m759 @ 2:00 PM

Evariste Galois, 1811-1832 (Vita Mathematica, V. 11)

  • Paperback: 168 pages
  • Publisher: Birkhäuser Basel; 1 edition (December 6, 1996)
  • Language: English
  • ISBN-10: 3764354100
  • ISBN-13: 978-3764354107
  • Product Dimensions: 9.1 x 6 x 0.4 inches
  • Shipping Weight: 9.1 ounces
  • Average Customer Review: 5.0 out of 5 stars  (1 customer review)
  • Amazon Bestsellers Rank: #933,939 in Books

Awarded 5 stars by Christopher G. Robinson (Cambridge, MA USA).
See also other reviews by Robinson.

Galois was shot in a duel on today's date, May 30, in 1832. Related material for those who prefer entertainment to scholarship—

"It is a melancholy pleasure that what may be [Martin] Gardner’s last published piece, a review of Amir Alexander’s Duel at Dawn: Heroes, Martyrs & the Rise of Modern Mathematics, will appear next week in our June issue." —Roger Kimball of The New Criterion, May 23, 2010.

Today is, incidentally, the feast day of St. Joan of Arc, Die Jungfrau von Orleans. (See "against stupidity" in this journal.)

720 in the Book

Filed under: Uncategorized — Tags: — m759 @ 7:20 AM

"Princeton's Baccalaureate service is an end-of-the-year ceremony focused on members of the senior class. It includes prayers and readings from various religious and philosophical traditions."

One such tradition— the TV series "Lost."

Another— the Pennsylvania Lottery—

Image-- PA lottery, May 5, 2010-- Midday 720, Evening 666

For some context,
see May 6, 2010.

See also this journal's post
"The Omen" on the date 6/6/6.

Today’s Sermon

Filed under: Uncategorized — m759 @ 6:06 AM

Image- Google Book Search results for Robert Stone's 'A Flag for Sunrise' plus 'our secret culture'

Trilateral

Filed under: Uncategorized — m759 @ 5:01 AM

Image-- 'Greater East Asia' characters

"Greater East Asia" (大東亜 Dai-tō-a)
was a Japanese term
(banned during the post-war Occupation)
referring to Far East Asia. —Wikipedia

Image-- East Asia trilateral trade talks

Related historical remarks from Wikipedia

"From the Japanese point of view, one common principal reason stood behind both forming the Greater East Asia Co-Prosperity Sphere and initiating war with the Allies: Chinese markets. Japan wanted their 'paramount relations' in regard to Chinese markets acknowledged by the U.S. government. The U.S., recognizing the abundance of potential wealth in these markets, refused to let the Japanese have an advantage in selling to China."

"Shine on, shine on,
there is work to be done
in the dark before the dawn."

Daisy May Erlewine

Image-- trilateral corner piece 'White Light (Grey)' by Josefine Lyche, 2009

"The exhibition title Theme and Variations
hints at the analytical-intellectual undertone
Josefine Lyche takes this time, but
not without humorous touches."

Saturday, May 29, 2010

An Icon for Hopper

Filed under: Uncategorized — m759 @ 2:56 PM

Image-- Dennis Hopper, who 'helped put the icon in iconoclastic,' dies at 74

Image-- Apocalypse Now, The Cage

"Perfect, genuine,
complete, crystalline, pure."

Image-- Martin Sheen and Dennis Hopper in 'Apocalypse Now'

See also The Cruciatus Curse.

Packed

Filed under: Uncategorized — m759 @ 7:11 AM

Significant Passage:
On the Writing Style of Visual Thinkers

"The words are filled with unstated meaning.
They are (the term is Ricoeur's) 'packed'
and need unpacking." —Gerald Grow

From the date of Ricoeur's death,
May 20, 2005

“Plato’s most significant passage
    may be found in Phaedrus  265b…."

From Sept. 30, 2004

With a little effort,
anything can be shown
to connect with anything else:
existence is infinitely

cross-referenced."Image-- 8-rayed asterisk

— Opening sentence
of Martha Cooley's
The Archivist

Image-- 8-rayed asterisk Example:
Mozart's K 265,
the page number 265,
and a story by George MacDonald.

Mozart's K 265 is variations on the theme
now known as "Twinkle, Twinkle, Little Star."

For darker variations on the Twinkle theme,
see the film "Joshua" and Martin Gardner's
Annotated Alice  (Norton, 2000, pp. 73-75).

Image-- From the film 'Joshua,' Joshua with the Alice statue in Central Park

Joshua

For darker variations on the asterisk theme,
see Darkness Visible (May 25)
and Vonnegut's Asterisk.

Friday, May 28, 2010

Multispeech for Oxford

Filed under: Uncategorized — m759 @ 7:00 PM

Happy Birthday,
Carey Mulligan

http://www.log24.com/log/pix10A/100528-Mulligan.jpg

Star of "An Education"

In "An Education," Mulligan's character
applies for admission to Oxford.

Today's New York Times:

Education »

Oxford Tradition
Comes to This:
‘Death’ (Expound)

Related material:

Such words arrive on the page like suitcases at the baggage claim: You know there is something in them and they have travelled far, but you cannot tell what the writer means. The words are filled with unstated meaning. They are (the term is Ricoeur's) "packed" and need unpacking.

This method of using language, however, is not always a defect; radiantly evocative words have long been the language of myth, mysticism, and love. Also, in earlier centuries, educated readers expected to interpret writing on several different levels at once (e.g., literal, allegorical, moral, and anagogical or spiritual), so that multiple meanings were the norm. This was before the era of clear, expository, fully-explicit prose.

Visual thinkers are accustomed to their own kind of interpreting; the very act of visual perception, as Gregory (1966, 1970) and Gombrich (1959) have shown, is interpretive. When oral thinkers leave you to guess at something they have written, it is usually something that would have been obvious had the writing been a conversation. Such is not the case with visual thinkers, even whose spoken words can be mysterious references to visual thoughts invisible to anyone but the thinker.

Writing done in this "packed" manner makes more sense when read as poetry than when read as prose.

References:

Gombrich, E. H. (1959). Art and Illusion: A Study in the Psychology of Pictorial Representation. London: Phaidon.

Gregory, R. L. (1966). Eye and Brain: The Psychology of Seeing. New York: McGraw-Hill.

Gregory, R. L. (1970). The Intelligent Eye. New York: McGraw-Hill.

"Stacking, Packing, and Enfolding Words," by Gerald Grow in "The Writing Problems of Visual Thinkers"

Those wishing to emulate Mulligan's
character in "An Education" might,
having read the Times article above,
consult this journal's post of May 17,
"Rolling the Stone."

That post contains the following
image from the Times

http://www.log24.com/log/pix10A/100517-NYT-Stone.jpg

May 17 was, by the way, the day
that R. L. Gregory, author of
The Intelligent Eyedied.

Multispeech

Filed under: Uncategorized — m759 @ 9:00 AM

For Memorial Day Weekend:

Finn, again!

See also Time and Chance: Log24 Posts of Oct. 24, 2006*, which include a link to the work of Msgr. Robert Sokolowski of the Catholic University of America.

* For the connection between Finnegans Wake  and the date October 24, 2006, see Polyglot Joyce, p. 223, and Phrase Finder.

From the posts of Saturday, May 22— "The Lyche Gate was the covered gateway at the entrance of the church yard, where the corpse was rested until the priest issued from the church to meet the procession."

Ancient English Ecclesiastical Architecture, by Frank Wills, published by Stanford and Swords, 1850

Thursday, May 27, 2010

Masks

Filed under: Uncategorized — m759 @ 3:33 PM

Masks of comedy and tragedy

Charles Isherwood on the death last Saturday of a fellow theater critic—

"...as it happened, I heard about his death just as I was entering the Lunt-Fontanne to see 'The Addams Family.' For a second time. By myself.

Now, there are happier ways to spend a Saturday night than attending a show you didn’t particularly like for the second time, by yourself. (Long story.) But then there’s no happy way to spend the night a friend dies."

For what it's worth—  night thoughts from this journal, Saturday night to Sunday morning—

From "Sunday School"—

"Nine tailors make a man."
– Dorothy Sayers

A Gathering for Gardner

Filed under: Uncategorized — Tags: — m759 @ 6:00 AM

"You ain't been blue; no, no, no.
 You ain't been blue,
 Till you've had that mood indigo."
 — Song lyrics, authorship disputed

 

Indigo (web color) (#4B0082)

"Pigment indigo (web color indigo) represents
 the way the color indigo was always reproduced
 in pigments, paints, or colored pencils in the 1950s."

Related mythology:

Indigo Children and the classic
1964 film Children of the Damned

Image-- Children of the Damned take sanctuary in St. Dunstan's Church.

Related non-mythology:

Colored pencils

Image-- Diamond-shaped face of Durer's 'Melencolia I' solid, with four colored pencils from Diane Robertson Design

Wednesday, May 26, 2010

To Be Awake

Filed under: Uncategorized — m759 @ 8:28 AM

For a former editor of Humpty Dumpty

American Mathematical Society meets Eliot and Joyce

Click to enlarge.

Tuesday, May 25, 2010

Sisteen

Filed under: Uncategorized — Tags: , — m759 @ 9:57 AM

“Nuvoletta in her lightdress, spunn of sisteen shimmers,
was looking down on them, leaning over the bannistars….

Fuvver, that Skand, he was up in Norwood’s sokaparlour….”

Finnegans Wake

To counteract the darkness of today’s 2:01 AM entry—

Part I— Artist Josefine Lyche describes her methods

A “Internet and hard work”
B “Books, both fiction and theory”

Part II I, too, now rely mostly on the Internet for material. However, like Lyche, I have Plan B— books.

Where I happen to be now, there are piles of them. Here is the pile nearest to hand, from top to bottom.

(The books are in no particular order, and put in the same pile for no particular reason.)

  1. Philip Rieff— Sacred Order/Social Order, Vol. I: My Life Among the Deathworks
  2. Dennis L. Weeks— Steps Toward Salvation: An Examination of Coinherence and Substitution in the Seven Novels of Charles Williams
  3. Erwin Panofsky— Idea: A Concept in Art Theory
  4. Max Picard— The World of Silence
  5. Walter J. Ong, S. J.— Hopkins, the Self, and God
  6. Richard Robinson— Definition
  7. X. J. Kennedy and Dana Gioia, eds.— An Introduction to Poetry
  8. Richard J. Trudeau— The Non-Euclidean Revolution
  9. William T. Noon, S. J.— Joyce and Aquinas
  10. Munro Leaf— Four-and-Twenty Watchbirds
  11. Jane Scovell— Oona: Living in the Shadows
  12. Charles Williams— The Figure of Beatrice
  13. Francis L. Fennell, ed.— The Fine Delight: Centenary Essays on the Poetry of Gerard Manley Hopkins
  14. Hilary Putnam— Renewing Philosophy
  15. Paul Tillich— On the Boundary
  16. C. S. Lewis— George MacDonald

Lyche probably could easily make her own list of what Joyce might call “sisteen shimmers.”

ART WARS continued

Filed under: Uncategorized — Tags: — m759 @ 2:01 AM

Darkness Visible

The inevitable tribute to Martin Gardner
has now appeared at the AMS website—

Image-- American Mathematical Society (AMS) tribute to Martin Gardner, May 25, 2010

Related Imagery—

The following is an image from Saturday morning—

Image-- 'Darkness Visible,' a picture from Log24 on Saturday, May 22, 2010

See also Art Wars and
Mathematics and Narrative.

Monday, May 24, 2010

Finale

Filed under: Uncategorized — m759 @ 4:16 PM

The weekend's posts in this journal coincided,
more or less, with the finale of the TV series "Lost."
Recalling each story brings to mind
the subtitle of Heinrich Zimmer's classic
  The King and the Corpse

Tales of the Soul's Conquest of Evil.

Here, in the spirit of "The Fifth Element," is a
brief graphic summary of such a conquest—

The Soul

(Click for details)

Image-- Josefine Lyche as Diamond Girl, representing the soul's triumph over evil

Evil

(from Saturday morning)

Image-- The Asterisk of Evil

Sunday, May 23, 2010

Death Story

Filed under: Uncategorized — m759 @ 9:40 PM

Image-- Arts & Letters Daily, news item on Bloglines first posted at 12 AM Sunday, May 23, 2010

For Your Consideration —

Filed under: Uncategorized — m759 @ 10:10 AM

Cannes Festival Readies for Awards Night

Uncertified Copy

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

The pictures in the detail are copies of
figures created by S. H. Cullinane in 1986.
They illustrate his model of hyperplanes
and points in the finite projective space
known as PG(3,2) that underlies
Cullinane's diamond theorem.

The title of the pictures in the detail
is that of a film by Burkard Polster
that portrays a rival model of PG(3,2).

The artist credits neither Cullinane nor Polster.

Sunday School

Filed under: Uncategorized — m759 @ 9:00 AM

"Mathematics is forever."
— Gian-Carlo Rota   

"Nine is a very powerful
  Nordic number."
— Katherine Neville    

 "Nine tailors make a man."
— Dorothy Sayers 

Annals of Philosophy

Filed under: Uncategorized — m759 @ 3:33 AM

Busy Night at the Lyche Gate

http://www.log24.com/log/pix10A/100523-NYTobits.jpg

"When Death tells a story, you really have to listen."
 

Annals of Conceptual Art

Filed under: Uncategorized — m759 @ 2:02 AM

Josefine Lyche's
  "Theme and Variations" (Oslo, 2009)

http://www.log24.com/log/pix10A/100523-LycheTandV.jpg

Some images in reply—

  Frame Tale

Image by R. T. Curtis from 'Further Elementary Techniques...'

Click on images for further details.

"In the name of the former
and of the latter
and of their holocaust.
  Allmen."

Finnegans Wake

Saturday, May 22, 2010

In the Details

Filed under: Uncategorized — Tags: — m759 @ 10:31 AM

Today's New York Times

Byzantine

"…there were fresh questions about whether the intelligence overhaul that created the post of national intelligence director was fatally flawed, and whether Mr. Obama would move gradually to further weaken the authorities granted to the director and give additional power to individual spy agencies like the Central Intelligence Agency. Mr. Blair and each of his predecessors have lamented openly that the intelligence director does not have enough power to deliver the intended shock therapy to America’s byzantine spying apparatus."

Catch-22 in Doonesbury today—

Image-- Chaplain and doctor in Doonesbury

From Log24 on Jan. 5, 2010—
   Artifice of Eternity

A Medal

In memory of Byzantine scholar Ihor Sevcenko,
who died at 87 on St. Stephen's Day, 2009–

Image-- Cross-in-circle design based on figure in Weyl's 'Symmetry'

Thie above image results from a Byzantine
meditation based on a detail in the previous post

Image-- 'Lyche Gate' with asterisk, from Google Books, digitized April 24, 2008

 

Image-- The Case of the Lyche Gate Asterisk

"This might be a good time to
call it a day." –Today's Doonesbury

"TOMORROW ALWAYS BELONGS TO US"
Title of an exhibition by young Nordic artists
in Sweden during the summer of 2008.

The exhibition included, notably, Josefine Lyche.

But seriously…

Filed under: Uncategorized — m759 @ 9:29 AM

Lyche gate, Ecclesfield Church, photo by pd prop

Lyche Gate

http://www.log24.com/log/pix10A/100522-EnglishChurch.png

Google Books data

Art Space

Filed under: Uncategorized — m759 @ 2:02 AM

From an interview with artist Josefine Lyche (see previous post) dated March 11, 2009—

Can you name a writer or book, fiction or theory that has inspired your works?
– Right now I am reading David Foster Wallace, which is great and inspiring. Others would be Aleister Crowley, Terence McKenna, James Joyce, J.L Borges, J.D Ballard, Stanislaw Lem, C. S. Lewis and Plato to mention some. Books, both fiction and theory are a great part of my life and work.

This journal on the date of the interview had a post about a NY Times  story, Paris | A Show About Nothing."

Related images—

 

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

http://www.log24.com/log/pix10A/100522-Clouseau.gif

Space: what you damn well have to see.
– James Joyce, Ulysses

Friday, May 21, 2010

The Oslo Version

Filed under: Uncategorized — m759 @ 9:29 AM

From an art exhibition in Oslo last year–

Image-- Josefine Lyche's combination of Polster's phrase with Cullinane's images in her gallery show, Oslo, 2009-- 'The Smallest Perfect Universe -- Points and Hyperplanes'

The artist's description above is not in correct left-to-right order.
Actually the hyperplanes above are at left, the points at right.

Compare to "Picturing the Smallest Projective 3-Space,"
a note of mine from April 26, 1986—

Image-- Points and hyperplanes in the finite 3-space PG(3,2), April 1986, by Cullinane

Click for the original full version.

Compare also to Burkard Polster's original use of
the phrase "the smallest perfect universe."

Polster's tetrahedral model of points and hyperplanes
is quite different from my own square version above.

See also Cullinane on Polster.

Here are links to the gallery press release
and the artist's own photos.

Thursday, May 20, 2010

The Prize

Filed under: Uncategorized — m759 @ 12:00 PM

Update of NY Times Art & Design
(See today's earlier posts
Annals of Conceptual Art and View.)

http://www.log24.com/log/pix10A/100520-Architects.gif

The architecture award ceremony was
at Ellis Island on Monday evening.

Arakawa died Tuesday.

Related material:

And He Built a Crooked House

View

Filed under: Uncategorized — m759 @ 11:07 AM
 

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

Related material:

A Handful of Dust
by J. G. Ballard

Annals of Conceptual Art

Filed under: Uncategorized — m759 @ 2:02 AM

New York Times  Art & Design section, morning of Thursday, May 20, 2010—

Arakawa, Whose Art Tried to Halt Aging, Dies at 73

By FRED A. BERNSTEIN
Published: May 19, 2010

Arakawa, a Japanese-born conceptual artist and designer, who with his wife, Madeline Gins, explored ideas about mortality by creating buildings meant to stop aging and preclude death, died Tuesday in Manhattan. He was 73.

He had been hospitalized for a week, said Ms. Gins, who declined to give the cause of death.

Perhaps it was white space—

http://www.log24.com/log/pix10A/100520-NYTdesignSm.jpg

Click to enlarge.

Wednesday, May 19, 2010

Preforming

Filed under: Uncategorized — Tags: , — m759 @ 11:00 AM

Photo caption in NY Times  today— a pianist "preforming" in 1967. (See today's previous post.)

The pianist's life story seems in part to echo that of Juliette Binoche in the film "Bleu." Binoche appeared in this journal yesterday, before I had seen the pianist in today's Times  obituaries. The Binoche appearance was related to the blue diamond in the film "Duelle " (Tuesday morning's post) and the saying of Heraclitus "immortals mortal, mortals immortal" (Tuesday afternoon's post).

This somewhat uncanny echo brings to mind Nabokov

Life Everlasting—based on a misprint!
I mused as I drove homeward: take the hint,
And stop investigating my abyss?
But all at once it dawned on me that this
Was the real point, the contrapuntal theme;
Just this: not text, but texture; not the dream
But topsy-turvical coincidence,
Not flimsy nonsense, but a web of sense.

Whether sense or nonsense, the following quotation seems relevant—

"Archetypes function as living dispositions, ideas in the Platonic sense, that preform and continually influence our thoughts and feelings and actions." –C.G. Jung in Four Archetypes: Mother, Rebirth, Spirit, Trickster, the section titled "On the Concept of the Archetype."

That section is notable for its likening of Jungian archetypes to Platonic ideas and to axial systems of crystals. See also "Cubist Tune," March 18 —

 

Blue tesseract cover<br /><br />
art, blue crystals in 'Bleu,' lines from 'Blue Guitar'

Blue Note à Quatre

Filed under: Uncategorized — Tags: , — m759 @ 3:00 AM

The Concert à Quatre  "was Messiaen's last work, left unfinished on his desk at his death. His widow undoubtedly followed his wishes and style in completing the orchestration." —Leslie Gerber

Related material:

http://www.log24.com/log/pix10A/100519-Loriod.jpg

See also yesterday's Stone Junction, this morning's note on Heidegger 's Geviert, and Moulin Bleu from Beethoven's birthday, 2003—

Juliette Binoche in "Bleu"

Mathematics and Gestalt

Filed under: Uncategorized — Tags: — m759 @ 2:01 AM

"We acknowledge a theorem's beauty
 when we see how the theorem 'fits'
 in its place, how it sheds light around itself,
 like a Lichtung, a clearing in the woods."

 — Gian-Carlo Rota, Indiscrete Thoughts

Here Rota is referring to a concept of Heidegger.

Some context—

"Gestalt Gestell Geviert: The Way of the Lighting,"
 by David Michael Levin in The Philosopher's Gaze

Tuesday, May 18, 2010

Philosophy: An Example

Filed under: Uncategorized — m759 @ 3:33 PM

http://www.log24.com/log/pix10A/100518-KahnXCII.jpg

  "This is in point of form Heraclitus' masterpiece,
   the most perfectly symmetrical of all the fragments."

    — Charles H. Kahn

Stone Junction*

Filed under: Uncategorized — m759 @ 8:00 AM

The Philosophers' Stone
according to
  The New York Times

http://www.log24.com/log/pix10A/100518-TheStoneNYT.jpg

Related material
from French cinema—

"a 'non-existent myth' of a battle between
goddesses of the sun and the moon
for a mysterious blue diamond
that has the power to make
mortals immortal and vice versa."

See also

   Word and Image

Juliette Binoche in 'Blue'  The
 24 2x2 Cullinane Kaleidoscope animated images

* The title is a reference to Jim Dodge's 1989 novel Stone Junction: An Alchemical Potboiler.

Monday, May 17, 2010

Round Midnight

Filed under: Uncategorized — m759 @ 11:55 PM

A Google search suggested by Dexter Gordon's "Round Midnight" yields…

May 18 update — The Russian link has been replaced by a link to a cached copy of the relevant content.

Rolling the Stone

Filed under: Uncategorized — m759 @ 10:12 PM

A new NY Times column:

http://www.log24.com/log/pix10A/100517-NYT-Stone.jpg

Today's New York Times
re-edited for philosophers:

http://www.log24.com/log/pix10A/100517-JonesClue.jpg

See also

Eightfold Symmetry,

John Baez's paper
Duality in Logic and Physics
(for a May 29 meeting at Oxford),

The Shining of May 29, and

Lubtchansky's Key, with its links
to Duelle (French, f. adj., dual)
and Art Wars for Trotsky's Birthday.

Sunday, May 16, 2010

Simplify.

Filed under: Uncategorized — m759 @ 7:20 PM

Image-- Richard Kiley with record collection in 'Blackboard Jungle,' 1955

Richard Kiley in "Blackboard Jungle" (1955)

Saturday, May 15, 2010

Mathematics and Narrative continued…

Filed under: Uncategorized — m759 @ 4:16 PM

Step Two

Image-- 'Then a miracle occurs' cartoon
Cartoon by S.Harris

Image-- Google search on 'miracle octad'-- top 3 results

For St. Cecilia

Filed under: Uncategorized — m759 @ 5:24 AM

In memory of David Randolph, longtime director of Manhattan's St. Cecilia Chorus. Randolph died at 95 on May 12. (See May 12's "Soul Song.")

A book by Randolph and other remarks
related to St. Cecilia, whose
  feast day is November 22

http://www.log24.com/log/pix10A/100515-ForStCecilia.jpg

Friday, May 14, 2010

Competing MOG Definitions

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

A recently created Wikipedia article says that  "The Miracle Octad Generator [MOG] is an array of coordinates, arranged in four rows and six columns, capable of describing any point in 24-dimensional space…." (Clearly any  array with 24 parts is so capable.) The article ignores the fact that the MOG, as defined by R.T. Curtis in 1976, is not  an array of coordinates, but rather a picture of a correspondence between two sets, each containing 35 structures. (As a later commentator has remarked, this correspondence is a well-known one that preserves a certain incidence property. See Eightfold Geometry.)

From the 1976 paper defining the MOG—

"There is a correspondence between the two systems of 35 groups, which is illustrated in Fig. 4 (the MOG or Miracle Octad Generator)." —R.T. Curtis, "A New Combinatorial Approach to M24," Mathematical Proceedings of the Cambridge Philosophical Society  (1976), 79: 25-42

http://www.log24.com/log/pix10A/100514-Curtis1976MOG.jpg

Curtis's 1976 Fig. 4. (The MOG.)

The Wikipedia article, like a similar article at PlanetMath, is based on a different definition, from a book first published in 1988—

http://www.log24.com/log/pix10A/100514-SpherePack.jpg

I have not seen the 1973 Curtis paper, so I do not know whether it uses the 35-sets correspondence definition or the 6×4 array definition. The remarks of Conway and Sloane on page 312 of the 1998 edition of their book about "Curtis's original way of finding octads in the MOG [Cur2]" indicate that the correspondence definition was the one Curtis used in 1973—

http://www.log24.com/log/pix10A/100514-ConwaySloaneMOG.jpg

Here the picture of  "the 35 standard sextets of the MOG"
is very like (modulo a reflection) Curtis's 1976 picture
of the MOG as a correspondence between two 35-sets.

A later paper by Curtis does  use the array definition. See "Further Elementary Techniques Using the Miracle Octad Generator," Proceedings of the Edinburgh Mathematical Society  (1989) 32, 345-353.

The array definition is better suited to Conway's use of his hexacode  to describe octads, but it obscures the close connection of the MOG with finite geometry. That connection, apparent in the phrases "vector space structure in the standard square" and "parallel 2-spaces" (Conway and Sloane, third ed., p. 312, illustrated above), was not discussed in the 1976 Curtis paper.  See my own page on the MOG at finitegeometry.org.

Wednesday, May 12, 2010

Soul Song

Filed under: Uncategorized — m759 @ 9:00 AM

Today's top New York Times obituary
mentions Irving Berlin's 1919 tune
"A Pretty Girl Is Like a Melody."

("That's show business." — Berlin)

I prefer a different song —

Image-- 'Estas son las mananitas....'

Related material —

Garden of the Soul and
A Mass for Lucero.

Tuesday, May 11, 2010

Lubtchansky’s Key

Filed under: Uncategorized — m759 @ 12:00 PM

William Lubtchansky, a cinematographer, was born on October 26, 1937, and died on May 4, 2010.

Yesterday's post included an illustration from this journal on the date of his death.

Here is a Log24 entry from last year on the date of his birth—

Monday, October 26, 2009
The Keys Enigma

Image-- Back Space key from manual typewriter, linking to Babich on Music, Nietzsche, and Heidegger
Image-- Shift Lock key from manual typewriter, linking to Levin's 'The Philosopher's Gaze'

Related material:

Posts of Sept. 21-25

Clicking on the Shift Lock key leads to the following page—

Image-- Page 432 of 'The Philosopher's Gaze'-- Heidegger on Gestell and shining forth

The Philosopher's Gaze,
by David Michael Levin,
University of California Press, 1999

Related images—

Detail from May 4 image:

Image-- The 4-dimensional space over the 2-element field

Holocaust Museum, Washington, DC:

Image-- Holocaust Museum tour group entrance
(http://www.scrapbookpages.com/USHMM/Exterior.html)

See also Lubtchansky's Duelle and
Art Wars for Trotsky's Birthday, 2003.

Monday, May 10, 2010

Requiem for Georgia Brown

Filed under: Uncategorized — m759 @ 2:45 AM

Image-- Lena Horne in 'Cabin in the Sky'

Paul Robeson in
"King Solomon's Mines," 1937—

Image -- The cast of 1937's 'King Solomon's Mines' goes back to the future

The image above is an illustration from
  "Romancing the Hyperspace," May 4, 2010.

This illustration, along with Georgia Brown's
song from "Cabin in the Sky"—
"There's honey in the honeycomb"—
suggests the following picture.

Image-- Tesseract and Hyperspace (the 4-space over GF(2)). Source: Coxeter's 'Twisted Honeycombs'

"What might have been and what has been
   Point to one end, which is always present."
Four Quartets

Sunday, May 9, 2010

Today’s Sermon

Filed under: Uncategorized — m759 @ 11:00 AM

School Book Depository
(Revisited)

Image-- Heath, 'A History of Greek Mathematics'
Pro-Truth
Image-- Trudeau, 'The Non-Euclidean Revolution'
Pro-Lies

For Miss Prothero (and Dylan Thomas)

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

 

The Ninth Gate

Friday's post "Religion at Harvard" continues…

Image-- List of nine religions in the chapters of Prothero's 'God is Not One'

This list may be of some use to
Rebecca Newberger Goldstein, who, like Prothero,
spoke recently at Harvard Book Store.

See also Rosalind Krauss on Grids,
An Education, and Plan 9 from Outer Space.

Readers more advanced than Harvard audiences
may wish to compare yesterday's linked-to story
"Loo Ree" with the works of Alison Lurie
in particular, Imaginary Friends and Familiar Spirits.

Saturday, May 8, 2010

A Better Story —

Filed under: Uncategorized — m759 @ 1:00 PM

Or, "Get me rewrite!"

Today's New York Times online–

Rebecca Newberger Goldstein imagines a story about academics discussing literary theory—

"Rumors had reached us of a doctrine called Theory emanating from distant corners of the university. We in the Department of Philosophy understood it immediately as a grand hoax. I will not dwell on my particular amusement, in which I was so tragically at odds with my collaborator, Theo Rhee….

… It was at this moment that Hans Furth appeared and ambled over…."

And thanks to Google Books, here he is—

"…I can imagine the decisive evolutionary beginnings of humans and societies… not in an adult version, but in the playful mentality of children…. An unlikely story? Perhaps. I am looking out for a better story."

Hans G. Furth, Desire for Society: Children's Knowledge as Social Imagination, published by Springer, 1996, p. 181

As am I. (See previous post.) One possibility, from 1943— "Mimsy Were the Borogoves."

Another possibility, from 1953—  not Theo Rhee, but rather "Loo Ree."

Friday, May 7, 2010

Religion at Harvard —

Filed under: Uncategorized — Tags: — m759 @ 4:01 PM

The Unreliable Narrator Meets the Unreliable Reader

The Unreliable Narrator meets The Unreliable Reader
Aaron Diaz at Dresden Codak

Comment by John Farrier on a list of 42 contrived plot devices
"My favorite is the Unreliable Reader — a counterpart to the Unreliable Narrator."

Vladimir Nabokov — "Examples are the stained-glass windows of knowledge."

  • Harvard Registrar's Office
    2010 Spring Reading Period Ends–  May 6 (Th).
     
  • Press release about a Harvard Square event at 7 PM Thursday —

    "Harvard Book Store is pleased to welcome religion scholar and bestselling author STEPHEN PROTHERO for a conversation about his new book, God Is Not One: The Eight Rival Religions That Run the World—And Why Their Differences Matter." ….

    Prothero's book avoids "the naive equating of them all as merely different paths to the same summit."
     

  • Harvard Crimson photo caption today —

    "Religion scholar and bestselling author Stephen Prothero speaks at the Harvard Book Store last night about his new book 'God Is Not One' in which he seeks to demonstrate how differences in paths leading to the same destination can enrich, not prevent, dialogue and cooperation."

Thursday, May 6, 2010

Infinite Jest

Filed under: Uncategorized — m759 @ 10:31 PM

Leg-Pulling

Jim Holt, review of David Foster Wallace's book on infinity 'Everything and More'

Michael Harris in AMS Notices suggests David Foster Wallace may be pulling our legs in 'Everything and More'

"… to make the author manifestly unreliable"

Not to mention the reader.

Famous author hangs himself in the 2005 film 'Neverwas'

Related material —

But seriously…

The Great Clooney

Filed under: Uncategorized — m759 @ 3:31 PM

Image-- George Clooney in 'Ocean's 13'

NY Times -- Markets Plunge, Rebound

Click to enlarge.

"If you can bounce high, bounce for her too."

F. Scott Fitzgerald

Happy birthday, George.

Metamorphosis

Filed under: Uncategorized — Tags: — m759 @ 1:06 PM

From Google yesterday —

A spring metamorphosis —
Google’s new look

5/05/2010 09:00:00 AM

Using Google today, you may have noticed that something feels slightly different — the look and feel of our search results have changed! Today’s metamorphosis responds to the increasing richness of the web and the increasing power of search — revealing search tools on the left and updating the visual look and feel throughout.

For example…

Everything and More

Image-- Google search for 'Oh, Euclid, I suppose'

A metaphor for "Everything"

Image--Chess game in Escher's 'Metamorphosis II'

A metaphor for "More" —

Image-- PA lottery, May 5, 2010-- Midday 720, Evening 666

Mathematics and Narrative, continued…

Filed under: Uncategorized — m759 @ 5:01 AM

The Unfolding

A post for Florencio Campomanes,
former president of the World Chess Federation.

Campomanes died at 83 in the Philippines
at 1:30 PM local time (1:30 AM Manhattan time)
on Monday, May 3, 2010.

From this journal on the date of his death —

"There is such a thing as a tesseract."
Madeleine L'Engle

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

http://www.log24.com/log/pix10A/100506-Hcube_fold.gif

Image--Chess game from 'The Seventh Seal'

Related material from a story of the Philippines —

Image-- Alex Garland on how a hypercube unfolds to what he calls a tesseract

Wednesday, May 5, 2010

Symmetry and Parallelisms

Filed under: Uncategorized — m759 @ 10:00 AM

From a post of Peter J. Cameron today —

"… I want to consider the question: What is the role of the symmetric group in mathematics? "

Cameron's examples include, notably, parallelisms of lines in affine spaces over GF(2).

Tuesday, May 4, 2010

Mathematics and Narrative, continued

Filed under: Uncategorized — Tags: — m759 @ 8:28 PM

Romancing the
Non-Euclidean Hyperspace

Backstory
Mere Geometry, Types of Ambiguity,
Dream Time, and Diamond Theory, 1937

The cast of 1937's 'King Solomon's Mines' goes back to the future

For the 1937 grid, see Diamond Theory, 1937.

The grid is, as Mere Geometry points out, a non-Euclidean hyperspace.

For the diamonds of 2010, see Galois Geometry and Solomon’s Cube.

Monday, May 3, 2010

An Ordinary Evening

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

“…geometrically organized, with the parts labeled”

— Ursula K. Le Guin on what she calls “the Euclidean utopia

“There is such a thing as a tesseract.”

Madeleine L’Engle

Related material– Diamond Theory, 1937

Dream Time

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

“Mere anarchy is loosed upon the world”

William Butler Yeats

From a document linked to here on April 30, Walpurgisnacht–

“…the Golden Age, or Dream Time, is remote only from the rational mind. It is not accessible to euclidean reason….”

“The utopia of the Grand Inquisitor ‘is the product of “the euclidean mind” (a phrase Dostoyevsky often used)….'”

“The purer, the more euclidean the reason that builds a utopia, the greater is its self-destructive capacity. I submit that our lack of faith in the benevolence of reason as the controlling power is well founded. We must test and trust our reason, but to have faith  in it is to elevate it to godhead.”

“Utopia has been euclidean, it has been European, and it has been masculine. I am trying to suggest, in an evasive, distrustful, untrustworthy fashion, and as obscurely as I can, that our final loss of faith in that radiant sandcastle may enable our eyes to adjust to a dimmer light and in it perceive another kind of utopia.”

“You will recall that the quality of static perfection is an essential element of the non-inhabitability of the euclidean utopia….”

“The euclidean utopia is mapped; it is geometrically organized, with the parts labeled….”

— Ursula K. Le Guin, “A Non-Euclidean View of California as a Cold Place to Be”

San Francisco Chronicle  today

“A May Day rally in Santa Cruz erupted into chaos Saturday night….”

“Had Goodman Brown fallen asleep in the forest,
and only dreamed a wild dream of a witch-meeting?”

Nathaniel Hawthorne

Sunday, May 2, 2010

Today’s Sermon

Filed under: Uncategorized — m759 @ 9:29 AM

The Secret Life of Walter Murphy

Continued from last night

"On 1 March 07, I was scheduled
 to fly on American Airlines…."

A tale by the late Walter F. Murphy,
professor emeritus of constitutional law at Princeton

Related material:

A hymn for Murphy — "I'll Fly Away."

See also this journal on
that same date– 1 March 07— along with

Parallelisms of Complete Designs and

Parallelism in Hebrew Poetry.

Legal Fiction–

Filed under: Uncategorized — m759 @ 1:00 AM

Murphy's Last Stand

In memory of Walter F. Murphy, a leading constitutional scholar and McCormick Professor of Jurisprudence at Princeton from 1968 to 1995. Murphy was also the author of a bestselling 1979 novel, The Vicar of Christ. He died at 80 on Tuesday, April 20, 2010, quod vide.

His novel, according to this morning's New York Times, "tells the story of an American who fights valiantly in the Korean War (as Professor Murphy did), becomes chief justice of the United States, resigns to become a monk and is eventually elected the first American pope." An eventful tale.

For a good review of Murphy's novel, see "The Doomed Hero." This review, and yesterday's Log24 Law Day post, which mentions the concept of "the mighty music of the innermost heaven," suggest revisiting a Log24 post of August 28, 2009 and a hymn by Brian Wilson—

Lyrics007.com

  Send "In My Room" Ringtone to Cell

There's a world where I can go
and tell my secrets to
In my room
In my room

In this world I lock out
all my worries and my fears
In my room
In my room

Do my dreaming and my scheming lie awake and pray
Do my crying and my sighing laugh at yesterday

Now it's dark and I'm alone
but I won't be afraid
In my room
In my room

Saturday, May 1, 2010

An Education

Filed under: Uncategorized — m759 @ 9:00 AM
 

天鈞

 

Made famous by Ursula K. Le Guin
as the book title "Lathe of Heaven,"
this Chinese phrase, tianjun, apparently
means something more like "Scales of Heaven"–
an appropriate image for Law Day 2010.

Image--Scales (the legal symbol)

An anonymous forum user says that

"…if you switch the two characters around,
you get: 鈞天, which is one of
the nine heavens, more specifically,
the middle heaven."

This is supported by a
non-anonymous source:

"I follow A.C. Graham’s translation of
Juntian as 'Level Heaven (the innermost
of the nine divisions of heaven)';
he renders Juntian guangyue as
'the mighty music of the innermost heaven.'"

— "Music in the World of Su Shi (1037-1101):
Terminology
," by Stuart H. Sargent,
Colorado State University,
Journal of Sung-Yuan Studies 32 (2002), 39-81

The Nine Divisions of Heaven–

Image-- Routledge Encyclopedia of Taoism, Vol. I, on the Nine Heavens, 'jiutian,' ed. by Fabrizio Pregadio

Some context–

The 3x3 ('ninefold') square

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71

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