… and for Louise Bourgeois
"The épateurs were as boring as the bourgeois,
two halves of one dreariness."
— D. H. Lawrence, The Plumed Serpent
… and for Louise Bourgeois
"The épateurs were as boring as the bourgeois,
two halves of one dreariness."
— D. H. Lawrence, The Plumed Serpent
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.)
"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—
For some context,
see May 6, 2010.
See also this journal's post
"The Omen" on the date 6/6/6.
"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
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."
"The exhibition title Theme and Variations
hints at the analytical-intellectual undertone
Josefine Lyche takes this time, but
not without humorous touches."
complete, crystalline, pure."
See also The Cruciatus Curse.
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…."
With a little effort,
— Opening sentence
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).
Star of "An Education"
In "An Education," Mulligan's character
applies for admission to Oxford.
Today's New York Times:
Comes to This:
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.
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—
May 17 was, by the way, the day
that R. L. Gregory, author of
The Intelligent Eye, died.
For Memorial Day Weekend:
✝ 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
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
"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."
“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.)
Lyche probably could easily make her own list of what Joyce might call “sisteen shimmers.”
The inevitable tribute to Martin Gardner
has now appeared at the AMS website—
The following is an image from Saturday morning—
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—
(from Saturday morning)
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.
"Mathematics is forever."
— Gian-Carlo Rota
"Nine is a very powerful
— Katherine Neville
"Nine tailors make a man."
— Dorothy Sayers
Busy Night at the Lyche Gate
"Theme and Variations" (Oslo, 2009)—
Some images in reply—
Click on images for further details.
"In the name of the former
and of the latter
and of their holocaust.
Today's New York Times—
"…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. 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—
From Log24 on Jan. 5, 2010—
Artifice of Eternity—
In memory of Byzantine scholar Ihor Sevcenko,
who died at 87 on St. Stephen's Day, 2009–
Thie above image results from a Byzantine
meditation based on a detail in the previous post—
"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.
|Title||Ancient English ecclesiastical architecture
and its principles, applied to the wants of
the church at the present day
American culture series II ; 029.008
|Publisher||Stanford and Swords, 1850|
|Original from||the New York Public Library|
|Digitized||Apr 24, 2008|
– 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.
“Space: what you damn well have to see.”
– James Joyce, Ulysses
From an art exhibition in Oslo last year–
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—
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.
of Hexagram 20,
A Handful of Dust
by J. G. Ballard
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—
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."
Juliette Binoche in "Bleu"
"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.
"Gestalt Gestell Geviert: The Way of the Lighting,"
by David Michael Levin in The Philosopher's Gaze
"This is in point of form Heraclitus' masterpiece,
the most perfectly symmetrical of all the fragments."
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."
* The title is a reference to Jim Dodge's 1989 novel Stone Junction: An Alchemical Potboiler.
A Google search suggested by Dexter Gordon's "Round Midnight" yields…
4 posts – 1 author – Last post: Aug 19, 2009
May 18 update — The Russian link has been replaced by a link to a cached copy of the relevant content.
A new NY Times column:
John Baez's paper
Duality in Logic and Physics
(for a May 29 meeting at Oxford),
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
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—
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—
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.
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 —
Related material —
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
Clicking on the Shift Lock key leads to the following page—
—The Philosopher's Gaze,
by David Michael Levin,
University of California Press, 1999
Detail from May 4 image:
Holocaust Museum, Washington, DC:
Paul Robeson in
"King Solomon's Mines," 1937—
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.
"What might have been and what has been
Point to one end, which is always present."
— Four Quartets
Friday's post "Religion at Harvard" continues…
This list may be of some use to
Rebecca Newberger Goldstein, who, like Prothero,
spoke recently at Harvard Book Store.
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
Another possibility, from 1953— not Theo Rhee, but rather "Loo Ree."
The Unreliable Narrator Meets the Unreliable Reader
Vladimir Nabokov — "Examples are the stained-glass windows of knowledge."
"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."
"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."
"… to make the author manifestly unreliable"
Not to mention the reader.
Related material —
"If you can bounce high, bounce for her too."
Happy birthday, George.
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.
A metaphor for "More" —
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 —
Related material from a story of the Philippines —
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).
For the 1937 grid, see Diamond Theory, 1937.
The grid is, as Mere Geometry points out, a non-Euclidean hyperspace.
“…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.”
Related material– Diamond Theory, 1937
“Mere anarchy is loosed upon the world”
“…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”
“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?”
The Secret Life of Walter Murphy
Continued from last night…
"On 1 March 07, I was scheduled
to fly on American Airlines…."
A hymn for Murphy — "I'll Fly Away."
See also this journal on
that same date– 1 March 07— along with
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—
Send "In My Room" Ringtone to Cell
There's a world where I can go
In this world I lock out
Do my dreaming and my scheming lie awake and pray
Now it's dark and I'm alone
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
"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
"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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