Sunday, July 10, 2011
Philosophical Investigations (1953)—
97. Thought is surrounded by a halo.
—Its essence, logic, presents an order,
in fact the a priori order of the world:
that is, the order of possibilities * ,
which must be common to both world and thought.
But this order, it seems, must be
utterly simple . It is prior to all experience,
must run through all experience;
no empirical cloudiness or uncertainty can be allowed to affect it
——It must rather be of the purest crystal.
But this crystal does not appear as an abstraction;
but as something concrete, indeed, as the most concrete,
as it were the hardest thing there is
(Tractatus Logico-Philosophicus No. 5.5563).
— Translation by G.E.M. Anscombe
5.5563
All propositions of our colloquial language
are actually, just as they are, logically completely in order.
That simple thing which we ought to give here is not
a model of the truth but the complete truth itself.
(Our problems are not abstract but perhaps
the most concrete that there are.)
97. Das Denken ist mit einem Nimbus umgeben.
—Sein Wesen, die Logik, stellt eine Ordnung dar,
und zwar die Ordnung a priori der Welt,
d.i. die Ordnung der Möglichkeiten ,
die Welt und Denken gemeinsam sein muß.
Diese Ordnung aber, scheint es, muß
höchst einfach sein. Sie ist vor aller Erfahrung;
muß sich durch die ganze Erfahrung hindurchziehen;
ihr selbst darf keine erfahrungsmäßige Trübe oder Unsicherheit anhaften.
——Sie muß vielmehr vom reinsten Kristall sein.
Dieser Kristall aber erscheint nicht als eine Abstraktion;
sondern als etwas Konkretes, ja als das Konkreteste,
gleichsam Härteste . (Log. Phil. Abh. No. 5.5563.)
See also—
Related language in Łukasiewicz (1937)—
* Updates of 9:29 PM ET July 10, 2011—
A mnemonic from a course titled “Galois Connections and Modal Logics“—
“Traditionally, there are two modalities, namely, possibility and necessity.
The basic modal operators are usually written (square) for necessarily
and (diamond) for possibly. Then, for example, P can be read as
‘it is possibly the case that P .'”
See also Intensional Semantics , lecture notes by Kai von Fintel and Irene Heim, MIT, Spring 2007 edition—
“The diamond ⋄ symbol for possibility is due to C.I. Lewis, first introduced in Lewis & Langford (1932), but he made no use of a symbol for the dual combination ¬⋄¬. The dual symbol □ was later devised by F.B. Fitch and first appeared in print in 1946 in a paper by his doctoral student Barcan (1946). See footnote 425 of Hughes & Cresswell (1968). Another notation one finds is L for necessity and M for possibility, the latter from the German möglich ‘possible.’”
Barcan, Ruth C.: 1946. “A Functional Calculus of First Order Based on Strict Implication.” Journal of Symbolic Logic, 11(1): 1–16. URL http://www.jstor.org/pss/2269159.
Hughes, G.E. & Cresswell, M.J.: 1968. An Introduction to Modal Logic. London: Methuen.
Lewis, Clarence Irving & Langford, Cooper Harold: 1932. Symbolic Logic. New York: Century.
|
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Saturday, July 9, 2011
The New York Times has a skateboarder obit with a URL date of July 9.
Here is an earlier version from the LA Times—
July 4, 2011
By Keith Thursby, Los Angeles Times
Chris Cahill, one of the original Dogtown Z-Boys
who brought seismic changes to skateboarding
with their style and attitude, has died. He was 54.
Cahill was found June 24 at his Los Angeles home,
said Larry Dietz of the Los Angeles County
coroner's office. A cause of death has not been
determined and tests are ongoing, Dietz said.
More…
Related material from Midsummer Day, June 24, the day Cahill was found dead—
The Gleaming and The Cube.
An illustration from the latter—
The above was adapted from a 1996 cover—
Vintage Books, July 1996. Cover: Evan Gaffney.
For the significance of the flames,
see PyrE in the book. For the significance
of the cube in the altered cover, see
The 2×2×2 Cube and The Diamond Archetype.
Comments Off on Gleaming the Cube (continued)
Part I, Midday —
Yesterday's midday NY Lottery "689" suggests (from April 3, 2005)—
689 |
|
[fú] blessing, good fortune |
Diagram taken from R. Sing,
“Chinese New Year’s Dragon Teacher’s Guide”
— and the 4-digit midday number suggests a NASA Picture of the Day
that was published (not taken) on 7795 (7/7/95)—
Part II, Evening —
Suggested by yesterday's evening NY Lottery "068"
and by Weltschmerz and the Ursprache —
— Walter Benjamin, “On Language as Such and On the Language of Man” (1916),
Edmund Jephcott, tr., Walter Benjamin, Selected Writings, Volume I: 1913-1926 ,
Marcus Bullock and Michael W. Jennings, eds., Cambridge, MA,
Harvard University Press, 1996, pp. 62-74. The above is page 68.
A more entertaining meditation is suggested by yesterday's 4-digit evening NY number—
a video tribute to a song said to have been released as a single on 7383 (7/3/83)—
Related material— "Dark Side of the Moon" in this journal.
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Connecting the dots with Clarke's Last Tale—
"The book is about a young Sri Lankan mathematician
who finds a short proof of Fermat's Last Theorem
while an alien invasion of Earth is in progress."
— Wikipedia on Arthur C. Clarke's 2008 novel The Last Theorem
Related material—
The May 7, 2006 link from Thursday morning's The 256 Code
and the Tribute link in last night's Your Shiny Friend.
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Friday, July 8, 2011
See also Grand Rapids in this journal.
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Google Translate version of a recent Norwegian art review—
Josefine Lyche show is working on the basis of crop circles occur in Pewsey, Wiltshire in England for exactly one year ago on 21 June. Three circulars forms of aluminum quote forms from the field in England. With this as a starting point invites Lyche viewer to explore the sacred shapes and patterns through painting, floor work and sculpture. In the monumental painting "Wisdom Luxury Romance" draws Lyche lines to both Matisse and Baudelaire in his poem "L'invitation au voyage ."
From the artist's website, JosefineLyche.com—
Click to enlarge
WISDOM LUXURY ROMANCE
From elsewhere—
Related material—
From Antichristmas 2002— Aluminum, Your Shiny Friend.
From Sept. 22, 2004— Tribute… in the context of
today's previous entry and of the conclusion of the story
that later became Childhood's End —
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Thursday, July 7, 2011
Earlier Determinations —
"I could tell you a lot, but you got
to be true to your code…." —Sinatra
Update of 4:28 PM ET 7/7—
The above remark by Griess is from a preprint of an article
published in Journal of Combinatorial Theory Series A
Volume 115 Issue 7, October 2008. (A copy dated
April 28, 2006, was placed in the arXiv on May 7, 2006.)
Comments Off on The 256 Code:
Wednesday, July 6, 2011
A 2008 statement on the order of the automorphism group of the Nordstrom-Robinson code—
"The Nordstrom-Robinson code has an unusually large group of automorphisms (of order 8! = 40,320) and is optimal in many respects. It can be found inside the binary Golay code."
— Jürgen Bierbrauer and Jessica Fridrich, preprint of "Constructing Good Covering Codes for Applications in Steganography," Transactions on Data Hiding and Multimedia Security III, Springer Lecture Notes in Computer Science, 2008, Volume 4920/2008, 1-22
A statement by Bierbrauer from 2004 has an error that doubles the above figure—
The automorphism group of the binary Golay code G is the simple Mathieu group M24 of order |M24| = 24 × 23 × 22 × 21 × 20 × 48 in its 5-transitive action on the 24 coordinates. As M24 is transitive on octads, the stabilizer of an octad has order |M24|/759 [=322,560]. The stabilizer of NR has index 8 in this group. It follows that NR admits an automorphism group of order |M24| / (759 × 8 ) = [?] 16 × 7! [=80,640]. This is a huge symmetry group. Its structure can be inferred from the embedding in G as well. The automorphism group of NR is a semidirect product of an elementary abelian group of order 16 and the alternating group A7.
— Jürgen Bierbrauer, "Nordstrom-Robinson Code and A7-Geometry," preprint dated April 14, 2004, published in Finite Fields and Their Applications , Volume 13, Issue 1, January 2007, Pages 158-170
The error is corrected (though not detected) later in the same 2004 paper—
In fact the symmetry group of the octacode is a semidirect product of an elementary abelian group of order 16 and the simple group GL(3, 2) of order 168. This constitutes a large automorphism group (of order 2688), but the automorphism group of NR is larger yet as we saw earlier (order 40,320).
For some background, see a well-known construction of the code from the Miracle Octad Generator of R.T. Curtis—
Click to enlarge:
For some context, see the group of order 322,560 in Geometry of the 4×4 Square.
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Monday, July 4, 2011
"When you have only one way of expressing yourself, you have
limits that you don’t appreciate. When you get a new way to
express yourself, it teaches you that there could be a third or a
fourth way. It opens up your eyes to a much broader universe."
— David Donoho
The above quote appears as the epigraph to Chapter 4,
"Beyond Wavelets," in A Primer on Wavelets by James S. Walker
(Chapman & Hall/CRC, 1999). It originally appeared as the
conclusion (p. 234) of "The Mathematical Microscope: Waves,
Wavelets, and Beyond," by Barbara Burke, pp. 196-235 in
A Positron Named Priscilla , National Academy of Sciences, 1994.
For other ways of expression suitable for today's holiday,
see Shell Beach in this journal.
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Sunday, July 3, 2011
The "232" was suggested by today's evening New York lottery, as
was the work of mathematician David Donoho (born 3/5/57).
Donoho is an expert on wavelets and related functions.
This post's title was suggested by the Mexican Hat wavelet
and by the Wallace Stevens poem "The Pastor Caballero"
quoted in last night's post.
As for today's midday lottery, see a reference to 645
in Imago Creationis and remarks from 3354 (3/3/54)
by Pauli on quantum theory and "small macroscopic spheres"
[for instance, Ping Pong balls].
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Saturday, July 2, 2011
Von Neumann's theory…
"tries to make the imponderable ponderable." — Various authors
As does some poetry.
For further details, click on the hat.
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A portrait reproduced here on October 11, 2007—
The above was suggested by yesterday's New York Lottery and by
items dated February 8, 1958 (date of receipt of an AMS Bulletin article)
and February 1, 1953 (newspaper article on applied game theory).
(This covers three of the four relevant lottery numbers.
For the fourth, see 9/19 and recent discussions of
The End of Mr. Y (Sunday Dinner and A Link for Sunrise)).
See also Saint John Neumann.
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Friday, July 1, 2011
Popular novelist Dan Brown is to speak at Chautauqua Institution on August 1.
This suggests a review of some figures discussed here in a note on Brown from February 20, 2004—
Related material: Notes from Nov. 5, 1981, and from Dec. 24, 1981.
For the lower figure in context, see the diamond theorem.
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Thursday, June 30, 2011
In memory of Robert Morris, former chief scientist
of the National Security Agency's
National Computer Security Center—
Here is a link to a post from last Sunday, the day Morris died.
From a novel mentioned in that post—
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Wednesday, June 29, 2011
For more about Rome, see two pages from Stevens suggested
by the New York Lottery numbers from today, St. Peter's Day.
The pages mention "Rome after dark" and a "disused ambit
of the soul." Those who prefer a "more severe, more
harassing master" may consult the date 8/6/79 suggested by
the New York Lottery this afternoon and, from that date,
Freeman Dyson's memoir in The New Yorker .
This evening's four-digit number, 0006, may, if one likes,
be regarded as an "artist's signature" of sorts.
The New Yorker on Dyson—
"He recalls that at age 8 he read 'The Magic City,'
by Edith Nesbit. It is the story of a crazy universe.
He now sees that this universe bears a strong
resemblance to the one we live in."
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For St. Peter's Day
"For Stevens, the poem 'makes meanings of the rock.'
In the mind, 'its barrenness becomes a thousand things/
And so exists no more.' In fact, in a peculiar irony
that only a poet with Stevens's particular notion
of the imagination's function could develop,
the rock becomes the mind itself, shattered
into such diamond-faceted brilliance
that it encompasses all possibilities for human thought…."
—A discussion of Stevens's late poem "The Rock" (1954)
in Wallace Stevens: A World of Transforming Shapes,
by Alan D. Perlis, Bucknell University Press, 1976, p. 120
Related material on transforming shapes:
The Diamond 16 Puzzle and…
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Tuesday, June 28, 2011
See the signature link in last night's post for a representation of Madison Avenue.
For a representation by Madison Avenue, see today's New York Times—
"As a movement Pop Art came and went in a flash, but it was the kind of flash that left everything changed. The art public was now a different public— larger, to be sure, but less serious, less introspective, less willing or able to distinguish between achievement and its trashy simulacrum. Moreover, everything connected with the life of art— everything, anyway, that might have been expected to offer some resistance to this wholesale vulgarization and demoralization— was now cheapened and corrupted. The museums began their rapid descent into show biz and the retail trade. Their exhibitions were now mounted like Broadway shows, complete with set designers and lighting consultants, and their directors pressed into service as hucksters, promoting their wares in radio and television spots and selling their facilities for cocktail parties and other entertainments, while their so-called education programs likewise degenerated into sundry forms of entertainment and promotion. The critics were co-opted, the art magazines commercialized, and the academy, which had once taken a certain pride in remaining aloof from the blandishments of the cultural marketplace, now proved eager to join the crowd— for there was no longer any standard in the name of which a sellout could be rejected. When the boundary separating art and fashion was breached, so was the dividing line between high art and popular culture, and upon all those institutions and professions which had been painstakingly created to preserve high art from the corruptions of popular culture. The effect was devastating. Some surrendered their standards with greater alacrity than others, but the drift was unmistakable and all in the same direction— and the momentum has only accelerated with the passage of time."
— Hilton Kramer, The Triumph of Modernism: The Art World, 1985-2005 , publ. by Ivan R. Dee on Oct. 26, 2006, pp. 146-147
Related material— Rubik in this journal, Exorcist in this journal, and For the Class of '11.
Comments Off on ART WARS continued
"He gazed out of the window hoping that somehow everything could make sense to him."
— "Passing in Silence," by Oliver Humpage
"You gotta be true to your code." —Sinatra
Exercise: Trace a path from the June 27 NY Lottery numbers
to the above two quotations. Hint: See Cuernavaca and
Pilgrim's Progress in TIME Magazine, May 3, 1948.
For some further background, click on the CBS quote above.
I still prefer, as I did in 1948, less up-to-the-minute developments.
* The title refers to the phrase "the artist's signature."
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Monday, June 27, 2011
The 3×3×3 Galois Cube
See Unity and Multiplicity.
This cube, unlike Rubik's, is a
purely mathematical structure.
Its properties may be compared
with those of the order-2 Galois
cube (of eight subcubes, or
elements ) and the order-4 Galois
cube (of 64 elements). The
order-3 cube (of 27 elements)
lacks, because it is based on
an odd prime, the remarkable
symmetry properties of its smaller
and larger cube neighbors.
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Sunday, June 26, 2011
This evening's NY Lottery numbers were 531 and 8372.
Hermeneutics—
From a Google search for "531 Log24"—
Log24 on Sunday, Sept. 21, 2008
531 , Revelation without belief 116. Evening (Belief), Belief without… The date, 5/24, of the entries linked to in Thursday's noon Log24 entry…
Pynchon on Quaternions – Log24
8. on Page 531 : "… to imps of ingenious discomfort. "Is this a stag affair, or are there likely to be one or two lady Quaternion- ists?…" |
The "531" linked to in the Sept. 21, 2008, post above is a mini-drama ending at midnight on 5/31, 2008— the conclusion of Mental Health Month.
And the above 4-digit evening number suggests a search for births on 8/3/72 that yields—
Erika Marozsán, Hungarian actress, 38.
Marozsán starred in "Gloomy Sunday—A Song of Love and Death" (A German/Hungarian film from 1999).
Wikipedia informs us that this "is inaccurately claimed to be the world's longest running film."
Whether Marozsán is a Quaternionist, I do not know.
For love, death, and quaternions, see the post Metaphor from Feb. 22 linked to in this afternoon's Sunday Dinner.
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From "Sunday Dinner" in this journal—
"'If Jesus were to visit us, it would have been
the Sunday dinner he would have insisted on
being a part of, not the worship service at the church.'"
—Judith Shulevitz at The New York Times
on Sunday, July 18, 2010
Some table topics—
Today's midday New York Lottery numbers were 027 and 7002.
The former suggests a Galois cube, the latter a course syllabus—
CSC 7002
Graduate Computer Security (Spring 2011)
University of Colorado at Denver
Department of Computer Science
An item from that syllabus:
Six |
22 February 2011 |
|
DES |
History of DES; Encryption process; Decryption; Expander function; S-boxes and their output; Key; the function f that takes the modified key and part of the text as input; mulitple Rounds of DES; Present-day lack of Security in DES, which led to the new Encryption Standard, namely AES. Warmup for AES: the mathematics of Fields: Galois Fields, particularly the one of order 256 and its relation to the irreducible polynomial x^8 + x^4 + x^3 + x + 1 with coefficients from the field Z_2. |
Related material: A novel, PopCo , was required reading for the course.
Discuss a different novel by the same author—
The End of Mr. Y .
Discuss the author herself, Scarlett Thomas.
Background for the discussion—
Derrida in this journal versus Charles Williams in this journal.
Related topics from the above syllabus date—
Metaphor and Gestell and Quadrat.
Some context— Midsummer Eve's Dream.
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Continued from March 10, 2011 — A post that says
"If Galois geometry is thought of as a paradigm shift
from Euclidean geometry, both… the Kuhn cover
and the nine-point affine plane may be viewed…
as illustrating the shift."
Yesterday's posts The Fano Entity and Theology for Antichristmas,
together with this morning's New York Times obituaries (below)—
—suggest a Sunday School review from last year's
Devil's Night (October 30-31, 2010)—
Sunday, October 31, 2010
ART WARS –
m759 @ 2:00 AM
… There is a Cave
Within the Mount of God, fast by his Throne,
Where light and darkness in perpetual round
Lodge and dislodge by turns, which makes through Heav'n
Grateful vicissitude, like Day and Night….
– Paradise Lost , by John Milton
|
See also Ash Wednesday Surprise and Geometry for Jews.
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Saturday, June 25, 2011
Hypostasis (philosophy)
“… the formula ‘Three Hypostases in one Ousia ‘
came to be everywhere accepted as an epitome
of the orthodox doctrine of the Holy Trinity.
This consensus, however, was not achieved
without some confusion….” —Wikipedia
Ousia
Click for further details:
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The New York Times at 9 PM ET June 23, 2011—
ROBERT FANO: I’m trying to think briefly how to put it.
GINO FANO: "On the Fundamental Postulates"—
"E la prova di questo si ha precisamente nel fatto che si è potuto costruire (o, dirò meglio immaginare) un ente per cui sono verificati tutti i postulati precedenti…."
"The proof of this is precisely the fact that you could build (or, to say it better, imagine) an entity by which are verified all previous assumptions…."
Also from the Times article quoted above…
"… like working on a cathedral. We laid our bricks and knew that others might later replace them with better bricks. We believed in the cause even if we didn’t completely understand the implications.”
— Tom Van Vleck
Some art that is related, if only by a shared metaphor, to Van Vleck's cathedral—
The art is also related to the mathematics of Gino Fano.
For an explanation of this relationship (implicit in the above note from 1984),
see "The Fano plane revisualized—or: the eIghtfold cube."
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Friday, June 24, 2011
THESEUS
Moonshine and Lion
are left to bury the dead.
DEMETRIUS
Ay, and Wall too.
BOTTOM
[Starting up] No assure you;
the wall is down
that parted their fathers.
Click image for details.
Comments Off on Just One More Thing…
Click the above image for some background.
Related material:
Skateboard legend Andy Kessler,
this morning's The Gleaming,
and But Sometimes I Hit London.
Comments Off on The Cube
The Gleaming
The column at left is from Galois Geometry.
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This evening's New York Lottery number was 776.
From this journal's post number 776—
ART WARS:
Lindsay Lohan was back in court today.
"The judge… ordered Lindsay may have no more than one friend
over at a time for the remainder of her house arrest" —Star Magazine
"Winter, spring, summer or fall
All you have to do is call"
— Eustace Tilley
Comments Off on Midsummer Night Comedy
Thursday, June 23, 2011
In a Jewish Cathedral
From The New York Times Magazine of Sunday, April 6, 1986—
"David Rayfiel's Script Magic" by Alex Ward
WHEN THE CALL came last year to revise ''The Morning After,'' Rayfiel was working on a screenplay about the 1911 Triangle Shirtwaist Company fire for Barbra Streisand and Jane Fonda. He has now resumed work— as the principal writer, not the reviser— on that script. But chances are good that he will have further interruptions. Pollack will probably call and say, as he usually does, ''David, I need access to your brain.'' And Rayfiel will probably say, as he usually does, ''That's O.K., I'm not using it.'' He will revise another script, and be reluctant about taking credit for it.
''I guess it's like the medieval stonecutters who worked on the cathedrals,'' he says. ''There's all that elaborate work. The saints were carved by one guy, the cherubs by someone else. They didn't care about getting credit, they knew what they'd done. I'm like that. I'm the guy who does the cherubs.''
Related material:
Proginoskes in this journal and Abracadabra from the midnight of June 18-19.
See also Rayfiel's obituary in today"s Times .
For some quite different work, also from April 1986, see—
Oslo: Points and Hyperplanes.
Comments Off on Script Magic…
Wednesday, June 22, 2011
This evening's New York Times obituaries—
A work of art suggested by the first and third items above—
I prefer a work of art that is structurally similar—
and is related to a picture, Portrait of O, from October 1, 1983—
For a recent unexpected Web appearance of Portrait of O,
aee Abracadabra from the midnight of June 18-19.
Comments Off on ART WARS continued
Thomas N. Armstrong III, a former director of the Whitney Museum of American Art, died at 78 on Monday in Manhattan.
William Grimes in this morning's New York Times—
"… Mr. Armstrong set about strengthening the museum’s permanent collection, buying Frank Stella’s 1959 black painting “Die Fahne Hoch!” for $75,000 in 1977…."
See also "Fahne Hoch" in this journal and the following from the date of Armstrong's death—
"Sunrise — Hast thou a Flag for me?" — Emily Dickinson
Related material: Piracy Project and, from Flag Day,
"Dawn's Early Light" and "Expressionistic Depth."
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Tuesday, June 21, 2011
The AND Publishing weblog page referred to in
a Sunday post has been changed to reflect the
source— my finite-geometry website— of pages
copied and altered by London artist Steve Richards
that are a large part of his contribution to the
AND Publishing Piracy Project.
The new version is as follows—
Note, however, that the cover page is a figure titled
by Richards "metalibrarianship" that has nothing
whatever to do with the concepts in the pages he copied
from my site, finitegeometry.org/sc.
Other pages within Richards's contribution to the
Piracy Project are similarly completely unrelated to
the content of my own site, which deals with geometry.
The image on the cover page also appears, it turns out,
on a website called intertwining.org.
At that site, it occurs in the following resume item:
The links in the resume item do not work,
but some background is available at a page titled
"Circularity, Practicality and Philosophy of Librarianship, or
The Making of 'The Nitecki Trilogy'" by Joanne Twining.
Other images in Richards's contribution to the Piracy Project also occur
in Twining's webpage "Dimensional Advances for Information Architecture."
I never heard of Twining or Nitecki before I encountered Richards's
Piracy Project contribution, and I do not wish to be associated
again in any way with Twining, with Nitecki, or with Richards.
Comments Off on The Longest Day Continues
This post is for the Stonehenge solstice crowd, who might,
like the London artist Steve Richards, confuse bullshit
with scholarship and inspire the same confusion
in others.
The image, apparently an epigraph put there
by the author, is from the Forgotten Books edition
of Cassirer's Substance and Function:
And Einstein's Theory of Relativity .
This is a scanned copy of the 1923 original.
The egg-figure above, however, is from the publisher's
prefatory notes and not from the original.
A check of other Forgotten Books publications
shows that the motto and the Bacon
attribution are those of Forgotten Books and
not of the authors they reprint — in particular,
not of Ernst Cassirer, who would probably
be dismayed to have this nonsense associated
with his work.
Why nonsense? The attribution to Francis Bacon is
false. The lines are from "The Phoenix and the Turtle"
by William Shakespeare.
Comments Off on Truth, Beauty, Bullshit
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This post was suggested by a book advertised
above A. Whitney Ellsworth's obituary in tonight's
online New York Times .
See also the following illustrations—
From this journal on June 1, 2008:
Click for background
From artist Steve Richards on January 14, 2010:
Click to enlarge
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In memory of A. Whitney Ellsworth, first publisher of
The New York Review of Books , who died at 75
on Saturday—
The Review has sometimes been cited in this journal.
See also posts from the date of Ellsworth's death—
Comments Off on Requiem for a Publisher
Recent piracy of my work as part of a London art project suggests the following.
From http://www.trussel.com/rls/rlsgb1.htm
The 2011 Long John Silver Award for academic piracy
goes to ….
Hermann Weyl, for the remark on objectivity and invariance
in his classic work Symmetry that skillfully pirated
the much earlier work of philosopher Ernst Cassirer.
And the 2011 Parrot Award for adept academic idea-lifting
goes to …
Richard Evan Schwartz of Brown University, for his
use, without citation, of Cullinane’s work illustrating
Weyl’s “relativity problem” in a finite-geometry context.
For further details, click on the above names.
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Monday, June 20, 2011
The title of a recent contribution to a London art-related "Piracy Project" begins with the phrase "The Search for Invariants."
A search for that phrase elsewhere yields a notable 1944* paper by Ernst Cassirer, "The Concept of Group and the Theory of Perception."
Page 20: "It is a process of objectification, the characteristic nature
and tendency of which finds expression in the formation of invariants."
Cassirer's concepts seem related to Weyl's famous remark that
“Objectivity means invariance with respect to the group of automorphisms.”
—Symmetry (Princeton University Press, 1952, page 132)
See also this journal on June 23, 2010— "Group Theory and Philosophy"— as well as some Math Forum remarks on Cassirer and Weyl.
Update of 6 to 7:50 PM June 20, 2011—
Weyl's 1952 remark seems to echo remarks in 1910 and 1921 by Cassirer.
See Cassirer in 1910 and 1921 on Objectivity.
Another source on Cassirer, invariance, and objectivity—
The conclusion of Maja Lovrenov's
"The Role of Invariance in Cassirer’s Interpretation of the Theory of Relativity"—
"… physical theories prove to be theories of invariants
with regard to certain groups of transformations and
it is exactly the invariance that secures the objectivity
of a physical theory."
— SYNTHESIS PHILOSOPHICA 42 (2/2006), pp. 233–241
A search in Weyl's Symmetry for any reference to Ernst Cassirer yields no results.
* Published in French in 1938.
Comments Off on The Search for Invariants
Sunday, June 19, 2011
My work has been pirated by an artist in London.
An organization there, AND Publishing, sponsors what it calls
"The Piracy Project." The artist's piracy was a contribution
to the project.
The above material now reflects the following update:
UPDATE of June 21, 2011, 10:00 PM ET:
The organization's weblog (a post for 19th June)
has now been updated, and this post, which originally
discussed that weblog, has been altered to reflect the
changes that were made at AND Publishing's weblog.
In this weblog, changes have been made to correct my
earlier incorrect statements that the Piracy Project was
sponsored by the art school where it takes place.
It was not. The organization has informed me that
"AND Publishing is not sponsored by the art school.
We are an independent artist's publishing house,
kindly hosted by the art school. While we are offered
office space on campus, our program and website
are funded, directed and managed by ourselves –
we are an independent entity running an
autonomous program."
|
As this post originally stated…
The web pages from the site finitegeometry.org/sc that
the artist, Steve Richards, copied as part of his contribution to
the AND Publishing Piracy Project have had the author's name,
Steven H. Cullinane, and the date of composition systematically removed.
See a sample (jpg, 2.1 MB).
Here is some background on Richards.
Comments Off on The London Piracy Project
This screenshot was suggested by the word "metalibrarianship" in a Bloomsday 2011 post by artist Steve Richards.
Note the words in the search field.
The phrase "Dublin Core metadata" refers to a city in Ohio, not in Ireland.
Related material— The highlighted phrase below is in the epigraph to Borges's "The Library of Babel"—
"I would, for these causes, wish him that is melancholy, to use both humane and divine authors, voluntarily to impose some taske upon himself, to divert his melancholy thoughts; to study the art of memory, Cosmus Rosselius, Pet. Ravennas, Scenkelius Detectus, or practise brachygraphy, &c. that will aske a great deal of attention: or let him demonstrate a proposition in Euclide in his five last books, extract a square root, or studie Algebra: than which, as gClavius holds, in all humane disciplines nothing can be more excellent and pleasant, so abstruse and recondite, so bewitching, so miraculous, so ravishing, so easie withal and full of delight, omnem humanum captum superare videtur . By this means you may define ex ungue leonem , as the diverbe is, by his thumb alone the bigness of Hercules, or the true dimensions of the great hColossus, Solomons temple, and Domitians amphitheater, out of a little part. By this art you may contemplate the variation of the 23 letters…."
g Ad. 2. definit.2. elem. In disciplinis humanis nihil praestantius reperitur: quippe miracula quaedam numerorum eruit tam abstrusa et recondita, tanta nihilo minus facilitate et voluptate, ut, &c.
h Which contained 1080000 weight of brass.
— The Anatomy of Melancholy, Part. 2, Sec. 2, Mem. 4
Comments Off on Metalibrarianship
Yesterday's post Ad Meld featured Harry Potter (succeeding in business),
a 4×6 array from a video of the song "Abracadabra," and a link to a post
with some background on the 4×6 Miracle Octad Generator of R.T. Curtis.
A search tonight for related material on the Web yielded…
(Click to enlarge.)
Weblog post by Steve Richards titled "The Search for Invariants:
The Diamond Theory of Truth, the Miracle Octad Generator
and Metalibrarianship." The artwork is by Steven H. Cullinane.
Richards has omitted Cullinane's name and retitled the artwork.
The author of the post is an artist who seems to be interested in the occult.
His post continues with photos of pages, some from my own work (as above), some not.
My own work does not deal with the occult, but some enthusiasts of "sacred geometry" may imagine otherwise.
The artist's post concludes with the following (note also the beginning of the preceding post)—
"The Struggle of the Magicians" is a 1914 ballet by Gurdjieff. Perhaps it would interest Harry.
Comments Off on Abracadabra (continued)
Saturday, June 18, 2011
Step One
Step Two
Step Three
For further details, click on step two.
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Comments Off on Here Be Dragons
"Oh, I've got something inside me
To drive a princess blind.
There's a wild man, wizard, he's hiding in me
Illuminating my mind."
-- Harry Chapin
And she said, "How are you, Harry?"
Comments Off on Gate of Ivory
(Continued from June 14)
From tonight's midnight post—
“Stranger, dreams verily are baffling and unclear of meaning,
and in no wise do they find fulfillment in all things for men.
For two are the gates of shadowy dreams,
and one is fashioned of horn and one of ivory.
Those dreams that pass through the gate of sawn ivory
deceive men, bringing words that find no fulfillment.
But those that come forth through the gate of polished horn
bring true issues to pass, when any mortal sees them."
Homer, Odyssey , Book 19
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Tracking Shot
Related material—
See also this journal's September 2009 posts.
This post was suggested by today's previous post and by today's NY Lottery.
For some background to the ioncinema.com post numbered 4210 above,
see, in conjunction with the page headed "Azazel" linked to here earlier today,
the ioncinema.com post numbered 5601.
“Stranger, dreams verily are baffling and unclear of meaning,
and in no wise do they find fulfillment in all things for men.
For two are the gates of shadowy dreams,
and one is fashioned of horn and one of ivory.
Those dreams that pass through the gate of sawn ivory
deceive men, bringing words that find no fulfillment.
But those that come forth through the gate of polished horn
bring true issues to pass, when any mortal sees them.
But in my case it was not from thence, methinks,
that my strange dream came.”
Homer, Odyssey , Book 19
Translation by A.T. Murray, in two volumes.
Harvard University Press, 1919
Quoted in a press release for the film "Two Gates of Sleep."
|
From the post numbered 460 in this journal—
At the still point… from the film "Absolute Power" :
Photo credit – Graham Kuhn
I’ve heard of affairs that are strictly plutonic,
But diamonds are a girl’s best friend!
— Marilyn Monroe, modeling a Freudian slip
Comments Off on Midnight in the Garden (continued)–
Friday, June 17, 2011
"Philosophy seeks not absolute first principles,
nor yet purely immediate insights,
but the self-mediation of the system of truth,
and an insight into this self-mediation."
— Josiah Royce in his article "Axiom" in Encyclopaedia of Religion and Ethics ,
edited by James Hastings (New York: Charles Scribner's Sons, 1910),
Vol. II, pp. 279-282, on page 282.
Related material: Time and Chance (Dec. 17, 2010).
Comments Off on Royce on Philosophy
This morning's exercise in lottery hermeneutics is unusually difficult.
Yesterday was Bloomsday (the date described in
James Joyce's Ulysses ) and the New York Lottery numbers were…
Midday numbers: 3-digit 181, 4-digit 9219.
Evening numbers: 3-digit 478, 4-digit 6449.
For 181 and 9219, see the following—
"With respect to every event, we must ask
which element has been subjected directly to change."
— Ferdinand de Saussure, Course in General Linguistics
(New York, The Philosophical Library, Inc., 1959), page 181
That Saussure page number was referenced in the following thesis
on James Joyce's other major novel, Finnegans Wake—
The thesis is from the University of Vienna (Universität Wien ).
The word Wien , in the derived form denoting an inhabitant of that city,
figured prominently in yesterday's news.
As for the evening numbers—
478 perhaps signifies the year 478 BC,
cited in Lawrence Durrell's Sicilian Carousel as the year
the ruler Gelon died.
For the evening 6449, note that the poem by Wallace Stevens quoted
here on June 15 in A for Anastasios deals with "the river of rivers"…
perhaps signifying time.
Interpreting 6449 chronologically yields 6/4/49.
The film artist John Huston, discussed in an essay from that date,
might appreciate the representation of the ancient Sicilian
river god Gelas as a man-headed bull on a coin from
around the year 478 BC.
For some perceptive remarks about Durrell, see the
article by Nigel Dennis in LIFE magazine's Nov. 21, 1960
issue (with cover noting Kennedy's victory in that year's
presidential election).
All of the above may be viewed as an approach to the aesthetic
problem posed by Dennis in yesterday's Bloomsday post—
"The problem that arises with this sort of writing is
one of form, i.e. , how to make one strong parcel
out of so many differently shaped commodities,
how to impose method on what would otherwise
be madness."
"The world has gone mad today…." — Cole Porter
For some related remarks, see page 161 of
Joyce's Catholic Comedy of Language *
by Beryl Schlossman (U. of Wisconsin Press, 1985)
and James Joyce in the final pages of The Left Hand of God
by Adolf Holl.
* Update of July 6, 2011—
This title is a correction from the previous title
given here, Moral Language by Mary Gore Forrester.
Google Books had Schlossman's content previewed
under Forrester's title.
Comments Off on Bloomsday Lottery
Thursday, June 16, 2011
(A note for Bloomsday)
Comments Off on Now Heaven Knows
Wednesday, June 15, 2011
The title was suggested by this evening's 4-digit NY lottery number.
"… the rhetoric might be a bit over the top."
According to Amazon.com, 2198 (i.e., 2/1/98) was the publication
date of Geometry of Vector Sheaves , Volume I, by Anastasios Mallios.
Related material—
The question of S.S. Chern quoted here June 10: —
"What is Geometry?"— and the remark by Stevens that
accompanied the quotation—
"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."
— Wallace Stevens,
“An Ordinary Evening in New Haven” VI
The work of Mallios in pure mathematics cited above seems
quite respectable (unlike his later remarks on physics).
His Vector Sheaves appears to be trying to explore new territory;
hence the relevance of Stevens's "Alpha." See also the phrase
"A-Invariance" in an undated preprint by Mallios*.
For the evening 3-digit number, 533, see a Stevens poem—
This meditation by Stevens is related to the female form of Mallios's Christian name.
As for the afternoon numbers, see "62" in The Beauty Test (May 23, 2007), Geometry and Death, and "9181" as the date 9/1/81.
* Later published in International Journal of Theoretical Physics , Vol. 47, No. 7, cover date 2008-07-01
Comments Off on A for Anastasios
The New York Times today on a new show by tightrope artist Philippe Petit—
“He comes out of that really wonderful European tradition of street performance— it blends a boundary of what’s art and what’s life,” said Jay Wegman, the director of the Abrons Arts Center, who offered Mr. Petit the three-night run. “He’s also kind of mischievous, not in a threatening or evil way, but in a child’s way of teasing and having fun.”
For a much darker approach to street performance that also involves mischief and blended boundaries, see "Tightrope" (1984)—
Background: Men in Feminism , edited by Alice Jardine and
published by Taylor & Francis in 1987, "Walking the Tightrope
of Feminism and Male Desire," by Judith Mayne, page 64
See also yesterday's Another Opening and Football in this journal.
Comments Off on Mischief
Tuesday, June 14, 2011
NY Lottery this evening: 3-digit 444, 4-digit 0519.
444:
"… of our history … and of our destructive paths.
We are beginning to sense the need to restore
the sacred feminine." She paused. "You
mentioned you are writing a manuscript about
the symbols of the sacred feminine, are you not?"
"I …"
519 (or 5/19):
Related material— "Eightfold Geometry" + Spider in this journal.
For this afternoon's NY numbers— 511 and 9891— see
511 in the "Going Up" post of July 12, 2007, as well as
Ben Brantley's recent suggestion of Paris Hilton as a
matinee attraction and her 9891 photo on the Web.
Comments Off on Another Opening
Comments Off on Searchin’
Update of 7 AM —
Carl Gardner's 1956 hit "Down in Mexico" was featured in the following Hollywood classic:
Click image for video.
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Note that the structure of the central flag above is not unlike that of the skull and crossbones flag.
O say can you see…?
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But seriously—
Degreeless Noon—
Click to enlarge.
“My card.”
Related material:
"Start the new year off with a new job at Pheedo."
See January 1, 2, 3 of 2010.
Comments Off on Plato’s Pheedo
Monday, June 13, 2011
Comments Off on Oscar Nightmare
Yesterday was the anniversary of "Raiders of the Lost Ark."
"And thirty years,
in the galaxies of birth,
Are time for counting
and remembering…."
— Wallace Stevens,
"Of Ideal Time and Choice"
Thirty years and a day after "Raiders" opened…
a more tranquil religious meditation.
Comments Off on Thirty Years
Click images for further details.
See also Job: A Comedy of Justice and
the death of Wolf Birger, reportedly on D-Day.
Comments Off on If I Forget Thee…
Ben Brantley in The New York Times on May 26—
While you theatergoing butterflies out there keep nattering on about the Tonys— who will win, who should win, and so on— I have been focused on an issue of far greater momentousness and urgency. That’s the shameful squandering on Broadway of what our country would seem to believe is our most valued (and infinitely exploitable) natural resource: our celebrities….
Lindsay Lohan: This undeniably talented (and for all intents and purposes, former) film actress poses a special challenge. Her only recent work appears to have been as a paparazzi model and professional partygoer, and a big, line-laden dramatic part like Blanche DuBois might be too onerous to start with. So why not put her in the Broadway premiere of “Finishing the Picture,” a late-career Arthur Miller play inspired by the travails of making a movie (“The Misfits”) with his wife Marilyn Monroe? Having seen a production of this play in Chicago, I can testify that the Marilyn part requires only that the actress playing her be willing to appear asleep and stupefied and, briefly, to walk across the stage naked. For Ms. Lohan, who credibly impersonated Marilyn for a New York magazine photo shoot, this ought to be a cinch. Should an eight-performance week prove too taxing, I suggest Paris Hilton for matinees.
This midnight post was suggested by Sunday's midday 4-digit NY Lottery number, 7286, and by the following web pages:
7286 Style by Lindsay Lohan and 7286 Prisoner Transport.
Some background from a third 7286 web page—
Starlet Lindsay Lohan is bringing her signature Hollywood style to the masses with her new 7286 line. The starlet's stylish stamp is on every aspect of the line, from the name (7-2-86 is her birthday) to the brand's tag line : "Give a girl the right handbag, and she can conquer the world!"
Comments Off on Broadway Cinderella
Sunday, June 12, 2011
Magic Time!
For fans of Douglas Adams and St. Augustine
Update of 2:20 AM June 13:
For the midday "042" as a reference to Adams, see Wikipedia. The "828" may be interpreted as a reference to St. Augustine's feast day, 8/28… or, for the more secularly minded, a reference to the time 8:28 PM (to go with the evening "0845" as a reference to 8:45 PM). For further details, see Times of the Times . The midday "7286" is more difficult. See midnight's Broadway Cinderella.
Comments Off on Tony Awards Night
See also June 2, 2007, and June 19, 2010,
as well as Kernel of Eternity in this journal.
Some background— Square of Opposition
in the Stanford Encyclopedia of Philosophy
and Deep Structures in this journal.
Comments Off on For Commencement Day at Stanford
Saturday, June 11, 2011
" Try this one."
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Godfather
"Mr. Messina is no ordinary Twitter user. The self-described
'hash godfather,' he officially invented the Twitter hashtag
in August 2007…."
— Ashley Parker (page ST1 of tomorrow's
NY Times National Edition)
But seriously—
Degreeless Noon—
Click to enlarge.
“My card.”
Comments Off on But Seriously–
Comments Off on Baccalaureate–
Friday, June 10, 2011
Some background for yesterday’s posts:
Midrash for Gnostics and related notes,
as well as yesterday’s New York Lottery.
…. “We seek
The poem of pure reality, untouched
By trope or deviation, straight to the word,
Straight to the transfixing object, to the object
At the exactest point at which it is itself,
Transfixing by being purely what it is….”
— Wallace Stevens (1879-1955),
“An Ordinary Evening in New Haven” IX
“Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals.”
— Wallace Stevens,
“An Ordinary Evening in New Haven” VI
Wikipedia—
“A hierophant is a person who brings religious congregants into the presence of that which is deemed holy . The word comes from Ancient Greece, where it was constructed from the combination of ta hiera , ‘the holy,’ and phainein , ‘to show.’ In Attica it was the title of the chief priest at the Eleusinian Mysteries. A hierophant is an interpreter of sacred mysteries and arcane principles.”
Weyl as Alpha, Chern as Omega—
(Click to enlarge.)
Postscript for Ellen Page, star of “Smart People”
and of “X-Men: The Last Stand“— a different page 679.
Your assignment, should you choose to accept it—
Interpret today’s NY lottery numbers— Midday 815, Evening 888.
My own bias is toward 815 as 8/15 and 888 as a trinity,
but there may be less obvious and more interesting approaches.
Comments Off on Hierophant
Thursday, June 9, 2011
Click to enlarge.
Good question. See also
Chern died on the evening of Friday, Dec. 3, 2004 (Chinese time).
From the morning of that day (also Chinese time)—
i.e. , the evening of the preceding day here— some poetry.
Comments Off on Page 679
Suggested by this afternoon’s NY Lottery number, 541—
Click for higher quality.
Related material: Finite Relativity and The Schwartz Notes.
Comments Off on Upshot
Meet Max
Also* in today's New York Times —
The Times piece is about Max Mathews, computer-music pioneer,
who died at 84 on Maundy Thursday, April 21.
* See Historical Fiction, 1 PM ET
Comments Off on Proof of Concept
… But perhaps not a supreme fiction.
"When we left the theater, my son and I knew we had experienced the most thrilling movie of the summer. 'First Class' is narratively lean, beautifully acted and, at all the right moments, visually stunning. But I had experienced something else. My son is 10 and a romantic, as all 10-year-olds surely have the right to be. How then do I speak to him of this world’s masterminds who render you a supporting actor in your own story?"
Comments Off on Historical Fiction
Wednesday, June 8, 2011
A meditation, while watching the Country Music Television
CMT Awards, on today's evening NY lottery number 469.
For Reese Witherspoon* and Dionysus, not Apollo—
A Funny Thing Happened
on the Way to the Edifice
— Page 469 of Wallace Stevens's Collected Poems
See also page 469 of Gravity's Rainbow (Penguin Classics 1995 paperback)—
* Not the Witherspoon Church of this evening's 6 PM entry.
Reese won Sunday's 2011 MTV Movie Awards' Generation Award .
Both the MTV Movie Awards and the CMT Awards are productions
of MTV Networks, a subsidiary of Viacom Inc. For some background,
see Sumner Redstone (formerly Rothstein).
Comments Off on CMT Awards Night
…To Pay Paul
From Princeton Public Library (65 Witherspoon St., on map above)—
Songs and Fingerplays—
Fingerplay— See this morning's 10:30 AM post.
Song— Paul Robeson sings "Summertime."
See also the Harvard version.
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Comments Off on … And Rosetta Stone
… and Arthur Koestler
The theme of the January 2010 issue of the
Notices of the American Mathematical Society
was “Mathematics and the Arts.”
Related material:
|
See also two posts from the day Peter Jennings died—
Presbyterian Justice and Religious Symbolism at Harvard.
Comments Off on For Saint Peter
The New Yorker 's review of The Great Escape (Simon & Schuster, $27), by Kati Marton—
"Marton, who fled Hungary as a child in 1957, illuminates Budapest's vertiginous Golden Age and the darkness that followed (a darkness that some of her subjects, notably Arthur Koestler, never shook)."
— Issue dated November 6, 2006
See also The Ninth Gate in this journal and the life of Marton's second husband, Peter Jennings.
* Continued from April 12.
Comments Off on Hellgate Joke (continued*)
Apollo (not Orpheus) versus Robert Kaplow,
author of The Cat Who Killed Lilian Jackson Braun—
Comments Off on A Look Back
Tuesday, June 7, 2011
Robert A. Heinlein—
"How about those empty universes?" I demanded.
"Maybe they are places about which stories will be written
or maybe stories have already been told but aren't favorites
of us four, so we don't emerge close to their scenes.
But those are guesses. So far as my theory is concerned,
such Universes are 'null' — they don't count one way or the other.
We find our universes."
"Sharpie, you have just invented pantheistic multiperson solipsism.
I didn't think it was mathematically possible."
"Zeb, anything is mathematically possible."
"Thanks, Jacob. Zebbie, 'solipsism' is a buzz word. I'm saying that
we've stumbled onto 'The Door in the Wall,' the one that leads to
the Land of Heart's Desire. I don't know how and have no use for
fancy rationalizations. I see a pattern; I'm not trying to explain it.
It just is ."
Ernest Hemingway—
"Isn't it pretty to think so?"
Comments Off on … Are Gods
Today's midday NY lottery number was 176.
An occurrence of that number in this journal—
Umberto Eco,
Foucault’s Pendulum, page 176:
Here, too, you entered through a little garden…
Here is a picture of 176.
Comments Off on Here, Too
Comments Off on Cock Tale
Monday, June 6, 2011
The NY Lottery's evening number today was 975.
See today's previous remarks and Post 975.
"… What Paris says to me is love story, awash with painters,
shots of the Seine, Champagne. Thank God I have a
can’t-miss notion to sell you. I call it ‘Midnight in Paris.’ ”
“Romantic title,” I had to admit. “Is there a script?”
“Actually, there’s nothing on paper yet, but I can spitball
the main points,” he said, slipping on his tap shoes.
“Maybe some other time,” I said, mindful of Cubbage’s
unbroken string of theatrical Hiroshimas.
— Woody Allen, May 5, 2011
See also "Some Other Time" in Post 552.
Comments Off on Evening Number
Today's midday NY Lottery number was 753, the number of a significant page in Gravity's Rainbow .
An excerpt from that page ((Penguin Classics paperback, June 1, 1995)—
"… the Abyss had crept intolerably close, only an accident away…."
Midrash— See Ben Stein in this journal.
But seriously… See "Geometry and Death" in this journal.
See also PlanetMath.org on the Hesse configuration—
A picture of the Hesse configuration—
.
Some context— A Study in Art Education.
Comments Off on Tree of Life — Jewish Version
Dreamtime
"…we're presented with the dream within the dream within the dream…."
— Remark on "Inception" in a review of Malick's "The Tree of Life"
The Way of Nature
Singer/songwriter/musician Andrew Gold died on Friday, June 3, reportedly in the early morning.
The Way of Grace
"They've heard lonely songs they thought were the livin' end."
— Reviewer's parody of James Taylor's "Fire and Rain"
printed in the Spokane Chronicle on May 28, 1991—
the Feast of St. Germain—
See also First Class, from the day of Gold's death, as well as the later
Midnight and Paris and Mystery.
Background— The above 1991 story about Taylor mentions his interpretation of
"Getting to Know You," from "The King and I." Gold's mother, Marni Nixon, was
the singing voice of Deborah Kerr in the film of that musical.
“It's a very ancient saying, but a true and honest thought…."
Comments Off on The Way of Grace
Sunday, June 5, 2011
"Total grandeur of a total edifice,
Chosen by an inquisitor of structures
For himself. He stops upon this threshold,
As if the design of all his words takes form
And frame from thinking and is realized."
— Wallace Stevens, "To an Old Philosopher in Rome"
The following edifice may be lacking in grandeur,
and its properties as a configuration were known long
before I stumbled across a description of it… still…
"What we do may be small, but it has
a certain character of permanence…."
— G.H. Hardy, A Mathematician's Apology
The Kummer 166 Configuration
as seen by Kantor in 1969— (pdf, 2.5 MB)
For some background, see Configurations and Squares.
For some quite different geometry of the 4×4 square that is
original with me, see a page with that title. (The geometry's
importance depends in part on its connection with the
Miracle Octad Generator (MOG) of R.T. Curtis. I of course
had nothing to do with the MOG's discovery, but I do claim credit
for discovering some geometric properties of the 4×4 square
that constitutes two-thirds of the MOG as originally defined .)
Related material— The Schwartz Notes of June 1.
Comments Off on Edifice Complex
Saturday, June 4, 2011
"… a little mystery to figure out…." — Bonnie Raitt, 1991
Two writers walk into a bar…
(A phrase from Immoveable Feast on May 28, 2005. See also May 28 this year.)
Yesterday's post First Class featured a picture of Mystique.
A related passage* from a book pictured here May 28—
See also Wallace Stevens on the Center.
* on participation mystique — "The primitive mind
does not differentiate the supernatural from reality,
but rather uses 'mystical participation'
to manipulate the world."
— Wikipedia
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'X-Men: First Class' Does
Good Midnight Business
“Madame, all stories, if continued far enough, end in death,
and he is no true-story teller who would keep that from you.”
– Ernest Hemingway,
Death in the Afternoon, Ch. 11
“There is never any ending to Paris….”
– Ernest Hemingway, A Moveable Feast
See also Back from the Shadows.
Comments Off on Midnight and Paris
Friday, June 3, 2011
“It's a very ancient saying, but a true and honest thought,
that if you become a teacher, by your pupils you'll be taught.”
Related material—
* Spiritual Exercises of Ignatius Loyola—
Composition of Place
It should be noted here that for contemplation or meditation about
visible things… the ‘composition’ will consist in seeing through the
gaze of the imagination the material place where the object I want
to contemplate is situated.
West Side Memories (an off-off-off-off Broadway production)—
Comments Off on First Class
Comments Off on Brightness at Noon (continued)
This morning's previous post suggests the following…
* See May 16.
Comments Off on Waiting for Corky*
Today is Commencement Day at MIT.
“To measure the changes
of time and space
the smartest are nothing.”
— Shing-Tung Yau,
The Emperor of Math
and Harvard philosopher
To measure the changes:
The smartest are nothing:
|
Well, perhaps not quite nothing.
The above pictures were posted here on the day the following book was published—
The lives of the nine Jews in the above book amount to more than Yau's "nothing."
Note, however, that claims by Jews (see Jill Abramson yesterday)
that their secular publications constitute a substitute for religion
and contain only "absolute truth" should be viewed with at least one
raised eyebrow.
Abramson's remark yesterday that her promotion to New York Times executive editor
was like "ascending to Valhalla" had a religious flavor worthy of yesterday's
Feast of the Ascension.
In related news from yesterday's Times—
See also a symbol related to Apollo, to nine, and to "nothing"—
A minimalist 3×3 matrix favicon—
This may, if one likes, be viewed as the "nothing"
present at the Creation. See Jim Holt on physics.
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Thursday, June 2, 2011
See posts on Keller in this journal.
A sample piece by the new editor— “The Lionesses” (2006 book review).
Comments Off on Exit Keller
Wednesday, June 1, 2011
See today's NY lottery numbers* and Gravity's Rainbow , pp. 656-657.
(Penguin Classics paperback, June 1, 1995.)
"Show me all the blueprints."
— Howard Hughes, according to Hollywood
* Readers new to lottery hermeneutics may consult
some remarks by Stuart Moulthrop.
Comments Off on Schwarzgerät
A Google search today for material on the Web that puts the diamond theorem
in context yielded a satisfyingly complete list. (See the first 21 results.)
(Customization based on signed-out search activity was disabled.)
The same search limited to results from only the past month yielded,
in addition, the following—
This turns out to be a document by one Richard Evan Schwartz,
Chancellor’s Professor of Mathematics at Brown University.
Pages 12-14 of the document, which is untitled, undated, and
unsigned, discuss the finite-geometry background of the R.T.
Curtis Miracle Octad Generator (MOG) . As today’s earlier search indicates,
this is closely related to the diamond theorem. The section relating
the geometry to the MOG is titled “The MOG and Projective Space.”
It does not mention my own work.
See Schwartz’s page 12, page 13, and page 14.
Compare to the web pages from today’s earlier search.
There are no references at the end of the Schwartz document,
but there is this at the beginning—
These are some notes on error correcting codes. Two good sources for
this material are
• From Error Correcting Codes through Sphere Packings to Simple Groups ,
by Thomas Thompson.
• Sphere Packings, Lattices, and Simple Groups by J. H. Conway and N.
Sloane
Planet Math (on the internet) also some information.
It seems clear that these inadequate remarks by Schwartz on his sources
can and should be expanded.
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Tuesday, May 31, 2011
"I hope with all my heart that his gallant little soul may find its Door into Summer…."
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Monday, May 30, 2011
A Meditation on the NY Lottery of May 29
Yesterday's NY Lottery— Midday 981, Evening 275.
As noted in yesterday morning's linked-to post,
The Shining of May 29…
"By groping toward the light we are made to realize
how deep the darkness is around us."
— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118
One interpretation of the mystic numbers revealed by the Lottery yesterday—
981 as the final page* of David Foster Wallace's famed novel Infinite Jest …
275 as a page in Wallace's non-fiction book about infinity Everything and More …
Gregory Chaitin points out that this is nonsense …
As noted elsewhere in this journal, I have a different concept of "math's absolute
Prince of Darkness"— and, indeed, of a "quest for Omega." (See posts of May 2010.)
Yesterday's numbers indicate a different struggle between darkness and light—
Light —
Darkness —
* From infinitesummer.org/archives/168 — "A note about editions:
As it turns out, all (physical) editions of Infinite Jest have 981 pages:
the one from 1996, the one from 2004, the paperback, the hardcover, etc.
A big thank you to the men and women in the publishing industry who
were kind and/or lazy enough to keep things consistent."
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Sunday, May 29, 2011
"You think you've seen the sun but you ain't seen it shine."
— "The Best Is Yet to Come," lyrics by Carolyn Leigh, music by Cy Coleman
Related material— The Shining of May 29.
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Background— Midnight's post.
This journal on the above "Take a Number" Dairy Queen date—
m759 @ 11:07 PM
“Teach us to
number our days.”
– Psalm 90, verse 12
“At any time, God can cancel a life. ‘So teach us to number our days,’ as the King James Version has it, ‘that we may apply our hearts unto wisdom.’….
The ancient Hebrew word for the shadowy underworld where the dead go, Sheol, was Christianized as ‘Hell,’ even though there is no such concept in the Hebrew Bible. Alter prefers the words ‘victory’ and ‘rescue’ as translations of yeshu’ah, and eschews the Christian version, which is the heavily loaded ‘salvation.’ And so on. Stripping his English of these artificial cleansers, Alter takes us back to the essence of the meaning. Suddenly, in a world without Heaven, Hell, the soul, and eternal salvation or redemption, the theological stakes seem more local and temporal: ‘So teach us to number our days.’”
Today’s numbers from the
Pennsylvania Lottery:
which, being interpreted,
is 5/10 and 7/24.
Selah.
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Against the Day
New York Lottery, May 28, 2011—
Page 548
General Boulanger
That the General was 'reactionary' and that the C of C bureaucracy had a 'defiant residue' of Boulangism, continues the characterization of the organization for which the Chums 'work'.
See p. 543 above, regarding a 2007 book in which Boulanger is called the 'father of fascism'.
timbres fictifs
French: fictive postage stamps. Cf "Lot 49".
Yes, stamps mean something in Pynchon's works; here, it seems important that these stamps are characterized as frauds.
Page 935
transform
A mathematical operation that "maps" a relation from one domain to another.
Here, "Belgian Congo" maps to "Balkan Penninsula". By 1912, everyone at Yz-le-Bans would be familiar with Conrad's Heart of Darkness , if not with other descriptions of the atrocities of exploitation of indigenous people in Congo. The conversation here and to follow describes the dawning realization of the imperialist exploitation of Eastern Europe by European powers. (Zora Neale Hurston famously commented that Hitler did in Europe what Europeans had been doing in Africa for a century. Cf. The Hereros sections in V .). It begins with railroads and "other straight line" constructions.
The themes of ATD might also "map" to current events in another warzone, where a contemporary Great Game is being played out.
common in dreams
Such as Frank's and Reef's. And/or, dreams require interpretation.
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Saturday, May 28, 2011
Max Black "notes, for instance, that in a study on wolves,
the implications of the metaphor 'Man is a wolf' will be
different than they might be in everyday discourse."
Alec Baldwin and Anthony Hopkins
in "The Edge" (1997)
From an obituary in today's New York Times—
"His daughter Jessamyn West said he was driven 'to understand everything.'
'He knew a million things — it didn’t matter:
worms, plumbing, literature. He could give you
a discourse. It seemed like he could never rest
until he had a sense of control over the things around him.'"
From "Meet Joe Black" (1998)—
“Should I be afraid?”
“Not a man like you.”
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Alan McGlashan
From Savage Logic—
Sunday, March 15, 2009 5:24 PM
The Origin of Change
A note on the figure
from this morning's sermon:
"Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined
On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come."
— Wallace Stevens,
"Notes Toward a Supreme Fiction,"
Canto IV of "It Must Change"
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Friday, May 27, 2011
See a search for maltesecross.jpg in this journal.
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It is not enough to cover the rock with leaves.
We must be cured of it by a cure of the ground
Or a cure of ourselves, that is equal to a cure
Of the ground, a cure beyond forgetfulness.
And yet the leaves, if they broke into bud,
If they broke into bloom, if they bore fruit,
And if we ate the incipient colorings
Of their fresh culls might be a cure of the ground.
— "The Rock," a poem by Wallace Stevens from
a section with the same title in the Collected Poems .
"A little bit of Las Vegas in the 1960s has
splashed down Off Broadway…. Actually,
the show as a whole could benefit from a softer sell."
— Charles Isherwood's review of
"The Best Is Yet to Come"
on page C1, NY edition, today's NY Times
"Out of the tree of life I just picked me a plum…"
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Thursday, May 26, 2011
This afternoon's online New York Times reviews "The Tree of Life," a film that opens tomorrow.
With disarming sincerity and daunting formal sophistication “The Tree of Life” ponders some of the hardest and most persistent questions, the kind that leave adults speechless when children ask them. In this case a boy, in whispered voice-over, speaks directly to God, whose responses are characteristically oblique, conveyed by the rustling of wind in trees or the play of shadows on a bedroom wall. Where are you? the boy wants to know, and lurking within this question is another: What am I doing here?
Persistent answers… Perhaps conveyed by wind, perhaps by shadows, perhaps by the New York Lottery.
For the nihilist alternative— the universe arose by chance out of nothing and all is meaningless— see Stephen Hawking and Jennifer Ouellette.
Update of 10:30 PM EDT May 26—
Today's NY Lottery results: Midday 407, Evening 756. The first is perhaps about the date April 7, the second about the phrase "three bricks shy"— in the context of the number 759 and the Miracle Octad Generator. (See also Robert Langdon and The Poetics of Space.)
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But leave the wise to wrangle, and with me
the quarrel of the universe let be;
and, in some corner of the hubbub couched,
make game of that which makes as much of thee.
—John McKay at sci.math
Related material: Harvard Treasure, Favicon, and Crimson Tide.
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The title refers not to numbers of the form p 3, p prime, but to geometric cubes with p 3 subcubes.
Such cubes are natural models for the finite vector spaces acted upon by general linear groups viewed as permutation groups of degree (not order ) p 3.
For the case p =2, see The Eightfold Cube.
For the case p =3, see the "External links" section of the Nov. 30, 2009, version of Wikipedia article "General Linear Group." (That is the version just prior to the Dec. 14, 2009, revision by anonymous user "Greenfernglade.")
For symmetries of group actions for larger primes, see the related 1985 remark* on two -dimensional linear groups—
"Actions of GL(2,p ) on a p ×p coordinate-array
have the same sorts of symmetries,
where p is any odd prime."
* Group Actions, 1984-2009
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Tuesday, May 24, 2011
The web page has been updated.
An example, the action of the Mathieu group M24
on the Miracle Octad Generator of R.T. Curtis,
was added, with an illustration from a book cover—
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Monday, May 23, 2011
This morning's previous post quoted a reader on the NY Times "Stoner" series. A different Stoner story—
"Most mysteries begin in confusion and end in certainty; Pynchon likes to change this trajectory, so that what begins a mystery ends as pure chaos. (Well aware how frustrating some readers find this, Pynchon sets up a running gag in Inherent Vice about a class action suit brought against MGM by audiences who don't like the way its stories end.)"
— Sarah Churchwell in the Guardian , Sunday, July 26, 2009
For a pure-chaos ending that can't be blamed on MGM, see this morning's online New York Times .
A perhaps happier ending— That of the author of the Irish Wine trilogy, Dick Wimmer, who died on Wednesday. We may imagine Wimmer enjoying the afterlife with Bing and Grace. See Log24 on the date of the above Guardian review.
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A reader comments on yesterday afternoon's New York Times
"The Stone" column by Justin E.H. Smith—
"I did indeed appreciate Mr. Smith’s essay.
And I’m curious as to what future contributions of his,
to the Stoner series, that we can look forward to."
From August 24, 2010—
Happy day 23 of Mental Health Month.
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Sunday, May 22, 2011
The New York Times philosophy column "The Stone" has returned—
"There will certainly always be a place for epistemology,
or the theory of knowledge. But in order for a theory of
knowledge to tell us much, it needs to draw on examples
of knowledge of something or other." — Justin E.H. Smith
Amen.
Examples: Quine on geometry and Quine on universals.
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A year ago today—
2:02 AM EDT—
Art Space
10:31 AM EDT—
* See Vonnegut.
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Saturday, May 21, 2011
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Heisenberg on Heraclitus
From Physics and Philosophy , by Werner Heisenberg, 1958, reprinted by Penguin Classics, 2003—
Page 28—
… In the philosophy of Heraclitus of Ephesus the concept of Becoming occupies the foremost
place. He regarded that which moves, the fire, as the basic element. The difficulty, to reconcile
the idea of one fundamental principle with the infinite variety of phenomena, is solved for him by
recognizing that the strife of the opposites is really a kind of harmony. For Heraclitus the world is
at once one and many, it is just 'the opposite tension' of the opposites that constitutes the unity
of the One. He says: 'We must know that war is common to all and strife is justice, and that all
things come into being and pass away through strife.'
Looking back to the development of Greek philosophy up to this point one realizes that it has
been borne from the beginning to this
Page 29—
stage by the tension between the One and the Many. For our senses the world consists of an
infinite variety of things and events, colors and sounds. But in order to understand it we have to
introduce some kind of order, and order means to recognize what is equal, it means some sort
of unity. From this springs the belief that there is one fundamental principle, and at the same
time the difficulty to derive from it the infinite variety of things. That there should be a material
cause for all things was a natural starting point since the world consists of matter. But when one
carried the idea of fundamental unity to the extreme one came to that infinite and eternal
undifferentiated Being which, whether material or not, cannot in itself explain the infinite variety
of things. This leads to the antithesis of Being and Becoming and finally to the solution of
Heraclitus, that the change itself is the fundamental principle; the 'imperishable change, that
renovates the world,' as the poets have called it. But the change in itself is not a material cause
and therefore is represented in the philosophy of Heraclitus by the fire as the basic element,
which is both matter and a moving force.
We may remark at this point that modern physics is in some way extremely near to the
doctrines of Heraclitus. If we replace the word 'fire' by the word 'energy' we can almost repeat
his statements word for word from our modern point of view. Energy is in fact the substance
from which all elementary particles, all atoms and therefore all things are made, and energy is
that which moves. Energy is a substance, since its total amount does not change, and the
elementary particles can actually be made from this substance as is seen in many experiments on
the creation of elementary particles. Energy can be changed into motion, into heat, into light
and into tension. Energy may be called the fundamental cause for all change in the world. But this
comparison of Greek philosophy with the ideas of modern science will be discussed later.
* See earlier uses of the phrase in this journal. Further background— Hopkins and Heraclitus.
Comments Off on Unity and Multiplicity (continued*)
Friday, May 20, 2011
Recent New York Lottery numbers—
The interpretation of "056" in yesterday's
The Aleph, the Lottery, and the Eightfold Way
was not without interest, but the interpretation there
of "236" was somewhat lacking in poetic resonance.
For aspiring students of lottery hermeneutics,
here are some notes that may help. The "236" may
be reinterpreted as a page number in Stevens's
Collected Poems . It then resonates rather nicely
("answers when I ask," "visible and responsive")
with yesterday evening's "434"—
For today's midday "022," see Hexagram 22: Grace in the context of the following—
As for yesterday afternoon's 609, see a particular Stevens-related page with that number…
For "a body of thought or poetry larger than the subject's," see The Dome of the Rock.
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Thursday, May 19, 2011
Today's previous post suggests the following—
Bester on bedrock and "the bottom line of all existence" suggests
a review of Wallace Stevens's "The Rock." Some background:
See Succor, May 11, and But Seriously, May 12.
See also Waiting for Benjamin, May 15.
Larry McMurtry famously wrote of reading Walter Benjamin
at the Dairy Queen. I never read Benjamin there, but I did
read at least some of the Bester book quoted above.
The bottom lines of this peculiar meditation—
It is not enough to cover the rock with leaves.
We must be cured of it by a cure of the ground
Or a cure of ourselves, that is equal to a cure
Of the ground, a cure beyond forgetfulness.
And yet the leaves, if they broke into bud,
If they broke into bloom, if they bore fruit,
And if we ate the incipient colorings
Of their fresh culls might be a cure of the ground.
— "The Rock," a poem by Wallace Stevens from
a section with the same title in the Collected Poems .
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Three links with a Borges flavor—
Related material
The 236 in yesterday evening's NY lottery may be
viewed as the 236 in March 18's Defining Configurations.
For some background, see Configurations and Squares.
A new illustration for that topic—
This shows a reconcilation of the triples described by Sloane
in Defining Configurations with the square geometric
arrangement described by Coxeter in the Aleph link above.
Note that the 56 from yesterday's midday NY lottery
describes the triples that appear both in the Eightfold Way
link above and also in a possible source for
the eight triples of Sloane's 83 configuration—
The geometric square arrangement discussed in the Aleph link
above appears in a different, but still rather Borgesian, context
in yesterday morning's Minimalist Icon.
Comments Off on The Aleph, the Lottery, and the Eightfold Way
Wednesday, May 18, 2011
The source of the mysterious generic
3×3 favicon with one green cell —
— has been identified.
For minimalists, here is a purer 3×3 matrix favicon—
This may, if one likes, be viewed as the "nothing"
present at the Creation. See Jim Holt on physics.
See also Visualizing GL(2,p), Coxeter and the Aleph, and Ayn Sof.
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Tuesday, May 17, 2011
24 Frames
MOVIES: PAST, PRESENT AND FUTURE (LA Times )
"But what feels like standard movie exposition quickly takes
a sharp turn when we're feted with about 20 minutes of the
elemental and cosmic footage that's been making all the
headlines. At first it looks like it could be a depiction of heaven
or hell, but it soon becomes clear that it's a story of creation—
or of Creation, as some iteration of the Big Bang unfolds
before our eyes."
— "Cannes 2011: What Terrence Malick's 'The Tree of Life'
Is Actually About," by Steven Zeitchik of the LA Times
Hannibal Pictures
THE BIG BANG (Click for Cannes details.)
See Peter Woit's review from Sunday.
The generic 3×3 HannibalPictures.com
favicon has an apt connotation—
Plan 9 from Outer Space.
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