Historic plane crashes at West Virginia air show
"The T-28 aircraft crashed at about 2:40 p.m.
during an acrobatic demonstration at the 2011
Thunder Over the Blue Ridge Open House & Air Show…."
See also Themes—
Saturday, September 17, 2011
As It Were
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Objectivity
The previous two posts, Baggage and The Uploading, suggest
a review of Wroclaw's native son Ernst Cassirer.
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The Uploading
(Continued from March 9.)
A detail from "Feist Sings 1, 2, 3, 4"—
"Uploaded by on Jul 18, 2008"
Those who prefer, as Weyl put it,
"the hard core of objectivity"
to, as Eddington put it,
"the colorful tale of the subjective storyteller mind"
may consult this journal on the same day… July 18, 2008.
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A-Z
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Themes
"'Ain’t No Grave' is Johnny’s final studio recording. The album and its title track
deal heavily with themes of mortality, resurrection, and everlasting life.
The Johnny Cash Project pays tribute to these themes."
And sells products!
Click image to enlarge.
I prefer "And I heard, as it were, the noise of thunder."
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Friday, September 16, 2011
Art, Jung, Toronto
Related art—
Midnight's Icons,
and…
(Wikipedia figure)
"Visually, a tetrad can be depicted as
four diamonds forming an X…."
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Icons
Background: Jung's Aion in this journal discusses this
figure from finite geometry's diamond theorem—
Fig. A
This resembles a figure that served Jung
as a schema of the Self—
Fig. B
Fig. A, with color variations, serves as the core
of many automatically generated Identicons —
a different sort of self-symbol.
Examples from Sept. 6 at MathOverflow—
A user wanting to custom-tailor his self-symbol should consider
the following from the identicon service Gravatar—
1. User Submissions. "… you hereby do and shall grant to Automattic a worldwide, perpetual, irrevocable, royalty-free and fully-paid, transferable (including rights to sublicense) right to perform the Services (e.g., to use, modify, reproduce, distribute, prepare derivative works of, display, perform, and otherwise fully exercise and exploit all intellectual property, publicity, and moral rights with respect to any User Submissions, and to allow others to do so)."
Sounds rather Faustian.
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Thursday, September 15, 2011
Life Story
(Continued from Tuesday's "A Story")
Tuesday's story, a collection of four random posts, was
suggested by Tuesday's NY lottery numbers.
That story leads, by association, to Frame Tale in
a post of 2:02 AM on Sunday, May 23, 2010. For related
material, see Death Story, a post of 9:40 PM that same Sunday.
Wednesday's numbers—
—suggest a counter-story…
Escape to Pine Mountain
A website on films about Latter-Day Saints (i.e., Mormons) asks
Was "Escape to Witch Mountain"
based on Zenna Henderson's "People" stories?
The lottery numbers above suggest the names of three women—
none, as far as I know, with any Mormon background—
who might rightly be called, without capital letters,
"latter-day saints"…
- Madeleine L'Engle (see 529 as the date 5/29),
- June Christy (a singer first recorded on 5/4/45), and
- Mary Rockwell Hook, architect of Pine Mountain
Settlement School, who died on 9/8/78.
These three lives, taken together, may serve as
an antidote to the Death Story mentioned above.
"We tell ourselves stories…" — Joan Didion
"Therefore choose life." —God
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Tuesday, September 13, 2011
A Story
For film producer and studio head John Calley, who died today at 81—
"When Death tells a story, you really have to listen." —The Book Thief (cover)
New York Lottery on Tuesday, September 13th, 2011
This suggests the following random thoughts—
|
797 April 24, 2003 |
451 August 26, 2002 |
|
1734 April 24, 2005 |
3276 March 24, 2008 |
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Day 256
Today is day 256 of 2011, Programmers' Day.
Yesterday, Monday, R. W. Barraclough's website pictured the Octad of the Week—
" X never, ever, marks the spot."
See also The Galois Tesseract.
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Monday, September 12, 2011
Key Paper Now Online
The 3-Space PG(3,2) and Its Group
by George M. Conwell, Annals of Mathematics ,
Second Series, Vol. 11, No. 2 (Jan., 1910), pp. 60-76
Article Stable URL: http://www.jstor.org/stable/1967582
At least for now, this paper may be downloaded without
signing in or making a payment. Click the "View PDF" link.
Update of Sept. 13— From Library Journal on Sept. 7—
The JSTOR journal archive announced today that it is making nearly 500,000 public domain journal articles from more than 220 journals—or about six percent of JSTOR's total content—freely available for use by "anyone, without registration and regardless of institutional affiliation."
The material, entitled Early Journal Content, will be rolled out in batches starting today over the course of one week. It includes content published in the United States before 1923 and international content published before 1870, which ensures that all the content is firmly in the public domain. JSTOR, in an announcement, said that the move was "a first step in a larger effort to provide more access options" to JSTOR content for independent scholars and others unaffiliated with universities.
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Spider Flagship
Microsoft plans Windows 8 compatibility with mobile devices
"This won't be just another upgrade. Windows 8 is nothing less than the linchpin to Microsoft's strategy for keeping Windows relevant— if not resurgent— as the shift to the post-PC computing era unfolds.
'The stakes are huge,' says Charles King, principal analyst at research firm Pund-IT. 'The company must play outside its comfort zone, but if Microsoft succeeds, the potential opportunities could be significant.'"
— Byron Acohido in USA TODAY this evening
Yesterday's 7:20 AM Google News—
From Cliff Robertson's 1958 TV classic "Days of Wine and Roses"—
From Fritz Leiber's 1959 sci-fi classic "Damnation Morning" —
She drew from her handbag a pale grey gleaming implement
that looked by quick turns to me like a knife, a gun,
a slim sceptre, and a delicate branding iron— especially when
its tip sprouted an eight-limbed star of silver wire.
“The test?” I faltered, staring at the thing.
“Yes, to determine whether you can live in the fourth dimension or only die in it.”
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Sunday, September 11, 2011
First Lady
Betty Skelton, "the First Lady of Firsts," died on the last day of August.
From this journal on August thirty-first—
"The Tesseract was the jewel of Odin's treasure room."
Hugo Weaving also played Agent Smith
in The Matrix Trilogy .
For Cynthia Zarin, biographer of Madeleine L'Engle—
"There is such a thing as a tesseract."
— A Wrinkle in Time
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Saturday, September 10, 2011
Cliff Robertson
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Friday, September 9, 2011
Galois vs. Rubik
(Continued from Abel Prize, August 26)
The situation is rather different when the
underlying Galois field has two rather than
three elements… See Galois Geometry.
The coffee scene from "Bleu"
Related material from this journal:
The Dream of
the Expanded Field
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A Beginning
|
From MIT Commencement Day, 2011— A symbol related to Apollo, to nine, and to "nothing"— A minimalist favicon—
This miniature 3×3 square— |
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Thursday, September 8, 2011
Endings
For Fischer's fellow database enthusiast Codd, see Cross-Referenced (April 24, 2003).
For Birtel's fellow pseudoscience enthusiast Frank Tipler, see the artist's comment linked to in Romancing the Omega (April 19, 2011)—
"Omega Point" is a term used by mathematical physicist Frank Tipler for what he maintains is the ultimate fate of the universe required by the laws of physics."
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Starring the Diamond
"In any geometry satisfying Pappus's Theorem,
the four pairs of opposite points of 83
are joined by four concurrent lines."
— H. S. M. Coxeter (see below)
Continued from Tuesday, Sept. 6—
The Diamond Star
The above is a version of a figure from Configurations and Squares.
Yesterday's post related the the Pappus configuration to this figure.
Coxeter, in "Self-Dual Configurations and Regular Graphs," also relates Pappus to the figure.
Some excerpts from Coxeter—
The relabeling uses the 8 superscripts
from the first picture above (plus 0).
The order of the superscripts is from
an 8-cycle in the Galois field GF(9).
The relabeled configuration is used in a discussion of Pappus—
(Update of Sept. 10, 2011—
Coxeter here has a note referring to page 335 of
G. A. Miller, H. F. Blichfeldt, and L. E. Dickson,
Theory and Applications of Finite Groups , New York, 1916.)
Coxeter later uses the the 3×3 array (with center omitted) again to illustrate the Desargues configuration—
The Desargues configuration is discussed by Gian-Carlo Rota on pp. 145-146 of Indiscrete Thoughts—
"The value of Desargues' theorem and the reason why the statement of this theorem has survived through the centuries, while other equally striking geometrical theorems have been forgotten, is in the realization that Desargues' theorem opened a horizon of possibilities that relate geometry and algebra in unexpected ways."
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Wednesday, September 7, 2011
The Most Important Configuration
A search for some background on Gian-Carlo Rota's remarks
in Indiscrete Thoughts * on a geometric configuration
leads to the following passages in Hilbert and Cohn-Vossen's
classic Geometry and the Imagination—
These authors describe the Brianchon-Pascal configuration
of 9 points and 9 lines, with 3 points on each line
and 3 lines through each point, as being
"the most important configuration of all geometry."
Thus it seems worthwhile to relate it to the web page
on square configurations referenced here Tuesday.
The Encyclopaedia of Mathematics , ed. by Michiel Hazewinkel,
supplies a summary of the configuration apparently
derived from Hilbert and Cohn-Vossen—
My own annotation at right above shows one way to picture the
Brianchon-Pascal points and lines— regarded as those of a finite,
purely combinatorial , configuration— as subsets of the nine-point
square array discussed in Configurations and Squares. The
rearrangement of points in the square yields lines that are in
accord with those in the usual square picture of the 9-point
affine plane.
A more explicit picture—
The Brianchon-Pascal configuration is better known as Pappus's configuration,
and a search under that name will give an idea of its importance in geometry.
* Birkhäuser Boston, 1998 2nd printing, p. 145
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Counterexample
An 1978 counterexample to Richard J. Trudeau's
1987 "Story Theory of truth" is now online.
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Tuesday, September 6, 2011
Midnight in the Garden (continued)
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Monday, September 5, 2011
Illuminata*
At Heaven’s Gate
Sunday, Sept. 4, 2011, RSS at 23:59 EDT:
Peter Woit's weblog Not Even Wrong—
"Lisa Randall’s new book is about to come out, it’s entitled
Knocking on Heaven’s Door: How Physics and Scientific Thinking
Illuminate the Universe and the Modern World."
Angels & Demons (the film)—
As she enters the lab she reacts in horror
as she sees an eyeball lying on the floor…
Click images for some backstory —
|
|
 |
"She has taken on the role of a public face of physics,
and has written a book which is in part a very general defense
of science and the materialist, rationalist world-view
that modern science is based on."
See also yesterday's "The Stone" column in The New York Times—
I prefer philosophy enacted by Reba.
* A reference to Dan Brown, not Marianne Williamson
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Sunday, September 4, 2011
The Found Numbers
(A sequel to The Lost Word)
NY Lottery, Sunday, Sept. 4, 2011
The number "38" might refer, notably, to
- The old postal code of Harvard University,
- the caliber of one type of handgun…
… and, less notably, to a page number
that appears in most books.
T.S. Eliot's essay "Tradition and the Individual Talent"
was first published in 1919.*
For some background on that year, see the Harvard Class of 1919.
For a notable instance of the page number 38, see
Poetry and Belief in the Work of T.S. Eliot ,
by Kristian Smidt (first published in 1949 by
the Norwegian Academy of Science and Letters).
* "Tradition and the Individual Talent" in The Egoist
at the Modernist Journals Project:
Part I in Vol. 6, No. 4 (Sept. 1919),
Parts II-III in Vol. 6, No. 5 (Dec. 1919)
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The Lost Word
In memory of Bible translator Eugene Nida, who died on August 25
An excerpt from Log24 on that date—
Related biblical material from DailyGrail.com—
"Dan Brown certainly packed a lot into the 500-plus pages of The Lost Symbol . But perhaps the key element to the story is the search for the ‘Lost Word,’ and— in the final pages— Robert Langdon’s discovery as to what that actually means. In the early chapters, Langdon explains to Sato that the Lost Word was 'one of Freemasonry’s most enduring symbols'…
…a single word, written in an arcane language that man could no longer decipher. The Word, like the Mysteries themselves, promised to unveil its hidden power only to those enlightened enough to decrypt it. “It is said,” Langdon concluded, “that if you can possess and understand the Lost Word . . . then the Ancient Mysteries will become clear to you.”
— and from Amazon.com.
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Saturday, September 3, 2011
The Galois Tesseract (continued)
A post of September 1, The Galois Tesseract, noted that the interplay
of algebraic and geometric properties within the 4×4 array that forms
two-thirds of the Curtis Miracle Octad Generator (MOG) may first have
been described by Cullinane (AMS abstract 79T-A37, Notices , Feb. 1979).
Here is some supporting material—
The passage from Carmichael above emphasizes the importance of
the 4×4 square within the MOG.
The passage from Conway and Sloane, in a book whose first edition
was published in 1988, makes explicit the structure of the MOG's
4×4 square as the affine 4-space over the 2-element Galois field.
The passage from Curtis (1974, published in 1976) describes 35 sets
of four "special tetrads" within the 4×4 square of the MOG. These
correspond to the 35 sets of four parallel 4-point affine planes within
the square. Curtis, however, in 1976 makes no mention of the affine
structure, characterizing his 140 "special tetrads" rather by the parity
of their intersections with the square's rows and columns.
The affine structure appears in the 1979 abstract mentioned above—
The "35 structures" of the abstract were listed, with an application to
Latin-square orthogonality, in a note from December 1978—
See also a 1987 article by R. T. Curtis—
Further elementary techniques using the miracle octad generator, by R. T. Curtis. Abstract:
“In this paper we describe various techniques, some of which are already used by devotees of the art, which relate certain maximal subgroups of the Mathieu group M24, as seen in the MOG, to matrix groups over finite fields. We hope to bring out the wealth of algebraic structure* underlying the device and to enable the reader to move freely between these matrices and permutations. Perhaps the MOG was mis-named as simply an ‘octad generator’; in this paper we intend to show that it is in reality a natural diagram of the binary Golay code.”
(Received July 20 1987)
– Proceedings of the Edinburgh Mathematical Society (Series 2) (1989), 32: 345-353
* For instance:
Update of Sept. 4— This post is now a page at finitegeometry.org.
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Friday, September 2, 2011
Cliffhanger
This afternoon's post—
"… If the cliffhanger is done well, it will not
simply introduce a wholly unprepared turn
into the narrative (a random death, a new character,
an entirely unanticipated obstacle) but rather
tighten the configuration of known elements…."
— Michel Chaouli in "How Interactive Can Fiction Be?"
This evening's Los Angeles Times obituary for Gary Hammer—
"He had been called the Indiana Jones of horticulture,
breaking his leg while hanging from a cliff in Mexico…."
For commentary on the first obituary above,
see Odin's Day (Wednesday, August 31).
"An unlikely story? Perhaps."
— Hans Furth, quoted here on
the date of Hammer's death (Sunday, August 7)
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Rigged?
Sarah Tomlin in a Nature article on the July 12-15 2005 Mykonos meeting on Mathematics and Narrative—
"Today, Mazur says he has woken up to the power of narrative, and in Mykonos gave an example of a 20-year unsolved puzzle in number theory which he described as
Michel Chaouli in "How Interactive Can Fiction Be?" (Critical Inquiry 31, Spring 2005), pages 613-614—
"…a simple thought experiment….*
… If the cliffhanger is done well, it will not simply introduce a wholly unprepared turn into the narrative (a random death, a new character, an entirely unanticipated obstacle) but rather tighten the configuration of known elements to such a degree that the next step appears both inevitable and impossible. We feel the pressure rising to a breaking point, but we simply cannot foresee where the complex narrative structure will give way. This interplay of necessity and contingency produces our anxious— and highly pleasurable— speculation about the future path of the story. But if we could determine that path even slightly, we would narrow the range of possible outcomes and thus the uncertainty in the play of necessity and contingency. The world of the fiction would feel, not open, but rigged."
* The idea of the thought experiment emerged in a conversation with Barry Mazur.
Barry Mazur in the preface to his 2003 book Imagining Numbers—
"But the telltale adjective real suggests two things: that these numbers are somehow real to us and that, in contrast, there are unreal numbers in the offing. These are the imaginary numbers .
The imaginary numbers are well named, for there is some imaginative work to do to make them as much a part of us as the real numbers we use all the time to measure for bookshelves.
This book began as a letter to my friend Michel Chaouli. The two of us had been musing about whether or not one could 'feel' the workings of the imagination in its various labors. Michel had also mentioned that he wanted to 'imagine imaginary numbers.' That very (rainy) evening, I tried to work up an explanation of the idea of these numbers, still in the mood of our conversation."
See also The Galois Quaternion and 2/19.
New York Lottery last evening
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Mathematics and Narrative (continued)
See also this journal on October 10, 2010.
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Thursday, September 1, 2011
How It Works
“Design is how it works.” — Steven Jobs (See Symmetry and Design.)
“By far the most important structure in design theory is the Steiner system S(5, 8, 24).”
— “Block Designs,” by Andries E. Brouwer
The name Carmichael is not to be found in Booher’s thesis. A book he does cite for the history of S(5,8,24) gives the date of Carmichael’s construction of this design as 1937. It should be dated 1931, as the following quotation shows—
From Log24 on Feb. 20, 2010—
“The linear fractional group modulo 23 of order 24•23•11 is often represented as a doubly transitive group of degree 24 on the symbols ∞, 0, 1, 2,…, 22. This transitive group contains a subgroup of order 8 each element of which transforms into itself the set ∞, 0, 1, 3, 12, 15, 21, 22 of eight elements, while the whole group transforms this set into 3•23•11 sets of eight each. This configuration of octuples has the remarkable property that any given set of five of the 24 symbols occurs in one and just one of these octuples. The largest permutation group Γ on the 24 symbols, each element of which leaves this configuration invariant, is a five-fold transitive group of degree 24 and order 24•23•22•21•20•48. This is the Mathieu group of degree 24.”
– R. D. Carmichael, “Tactical Configurations of Rank Two,” in American Journal of Mathematics, Vol. 53, No. 1 (Jan., 1931), pp. 217-240
Epigraph from Ch. 4 of Design Theory , Vol. I:
“Es is eine alte Geschichte,
doch bleibt sie immer neu ”
—Heine (Lyrisches Intermezzo XXXIX)
See also “Do you like apples?“
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Boundary (continued*)
It is now midnight. Yesterday was Odin's Day. Today is Thor's Day.
From a weblog post on Captain America and Thor—
"While all this [Captain America] is happening an SS officer, Johann Schmidt (Hugo Weaving), has found a religious artefact called the Tesseract which Schmidt describes as 'the jewel of Odin’s treasure room,' linking it in with the Thor storyline."
— That's Entertainment weblog, August 14, 2011
From Wallace Stevens, "An Ordinary Evening in New Haven," Canto III—
The point of vision and desire are the same.
It is to the hero of midnight that we pray
On a hill of stones to make beau mont thereof.
Captain America opened in the United States on Friday, July 22, 2011.
Thor opened in the United States on Friday, May 6, 2011.
"There is such a thing as a tesseract." —A Wrinkle in Time
* Continued from August 30.
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Wednesday, August 31, 2011
Odin’s Day
Today is Wednesday.
O.E. Wodnesdæg "Woden's day," a Gmc. loan-translation of L. dies Mercurii "day of Mercury" (cf. O.N. Oðinsdagr , Swed. Onsdag , O.Fris. Wonsdei , M.Du. Wudensdach ). For Woden , see Odin . — Online Etymology Dictionary
Above: Anthony Hopkins as Odin in the 2011 film "Thor"
Hugo Weaving as Johann Schmidt in the related 2011 film "Captain America"—
"The Tesseract* was the jewel of Odin's treasure room."
Weaving also played Agent Smith in The Matrix Trilogy.
The figure at the top in the circle of 13** "Thor" characters above is Agent Coulson.
"I think I'm lucky that they found out they need somebody who's connected to the real world to help bring these characters all together."
— Clark Gregg, who plays Agent Coulson in "Thor," at UGO.com
For another circle of 13, see the Crystal Skull film implicitly referenced in the Bright Star link from Abel Prize (Friday, Aug. 26, 2011)—
Today's New York Times has a quote about a former mathematician who died on that day (Friday, Aug. 26, 2011)—
"He treated it like a puzzle."
Sometimes that's the best you can do.
* See also tesseract in this journal.
** For a different arrangement of 13 things, see the cube's 13 axes in this journal.
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Tuesday, August 30, 2011
Boundary
A comment yesterday on the New York Times philosophy column “The Stone” quoted Karl Barth—
“Man is the creature of the boundary between heaven and earth.”
See also Plato’s theory of ideas (or “forms”) and the I Ching—
The eight trigrams are images not so much of objects as of states of change. This view is associated with the concept expressed in the teachings of Lao-tse, as also in those of Confucius, that every event in the visible world is the effect of an “image,” that is, of an idea in the unseen world. Accordingly, everything that happens on earth is only a reproduction, as it were, of an event in a world beyond our sense perception; as regards its occurrence in time, it is later than the suprasensible event. The holy men and sages, who are in contact with those higher spheres, have access to these ideas through direct intuition and are therefore able to intervene decisively in events in the world. Thus man is linked with heaven, the suprasensible world of ideas, and with earth, the material world of visible things, to form with these a trinity of the primal powers.
— Richard Wilhelm, Introduction to the I Ching
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Monday, August 29, 2011
Many = Six.
A comment today on yesterday's New York Times philosophy column "The Stone"
notes that "Augustine… incorporated Greek ideas of perfection into Christianity."
Yesterday's post here for the Feast of St. Augustine discussed the 2×2×2 cube.
Today's Augustine comment in the Times reflects (through a glass darkly)
a Log24 post from Augustine's Day, 2006, that discusses the larger 4×4×4 cube.
For related material, those who prefer narrative to philosophy may consult
Charles Williams's 1931 novel Many Dimensions . Those who prefer mathematics
to either may consult an interpretation in which Many = Six.
Click image for some background.
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Sunday, August 28, 2011
The Cosmic Part
Yesterday's midday post, borrowing a phrase from the theology of Marvel Comics,
offered Rubik's mechanical contrivance as a rather absurd "Cosmic Cube."
A simpler candidate for the "Cube" part of that phrase:
The Eightfold Cube
As noted elsewhere, a simple reflection group* of order 168 acts naturally on this structure.
"Because of their truly fundamental role in mathematics,
even the simplest diagrams concerning finite reflection groups
(or finite mirror systems, or root systems—
the languages are equivalent) have interpretations
of cosmological proportions."
— Alexandre V. Borovik in "Coxeter Theory: The Cognitive Aspects"
Borovik has a such a diagram—
The planes in Borovik's figure are those separating the parts of the eightfold cube above.
In Coxeter theory, these are Euclidean hyperplanes. In the eightfold cube, they represent three of seven projective points that are permuted by the above group of order 168.
In light of Borovik's remarks, the eightfold cube might serve to illustrate the "Cosmic" part of the Marvel Comics phrase.
For some related theological remarks, see Cube Trinity in this journal.
Happy St. Augustine's Day.
* I.e., one generated by reflections : group actions that fix a hyperplane pointwise. In the eightfold cube, viewed as a vector space of 3 dimensions over the 2-element Galois field, these hyperplanes are certain sets of four subcubes.
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Saturday, August 27, 2011
Cosmic Cube*
Prequel — (Click to enlarge)
Background —
See also Rubik in this journal.
* For the title, see Groups Acting.
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This Way to the Egress*
From http://msa-x.msa-x.org/?p=1064 —
"Exit Art New York, The Labyrinth Wall:
From Mythology to Reality" —
From tonight's online New York Times obituaries —
Ms. Ingberman died Wednesday. Related material—
Symmetry (Wednesday), Design (Thursday), Solomon's Labyrinth (Friday).
See also an essay by John Haber —
"Exit Art may yet offer an alternative: shut them up in the labyrinth, with the Minotaur and, as in Iraq, no Ariadne's thread to guide them out. Jeannette Ingberman and Papo Colo line the space with 'The Labyrinth Wall: From Mythology to Reality,' inviting fifty-one artists to cover its sixty-two panels."
— "Marlene Dumas, The Labyrinth Wall, and Emily Jacir"
Haber (ibid .) also describes artist Marlene Dumas, a recent winner of a Royal Swedish Academy Schock Prize. For a fellow Schock winner— mathematician Michael Aschbacher— see Thursday's Design.)
* For another version of the title, see this morning's front page.
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Friday, August 26, 2011
Abel Prize
The previous posts, Design and Solomon's Labyrinth,
refer, respectively, to concepts of Tits ("buildings") and
of Thompson (imagining a future Origin of Groups ).
This suggests a review of Norway's 2008 Abel Prize,
presented to Thompson and Tits on May 20, 2008.
Poster display before the 2008 Abel Prize ceremony—
A poster of sorts in this journal on the same day, May 20, 2008—
|
Bright Star – … Todo lo sé por el lucero puro – Rubén Darío 
Image adapted from |
Related material— Epiphany Revisited, Four Winds,
and Where Entertainment is God (continued).
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Solomon’s Labyrinth
Some context for last night's post on group theorist Michael Aschbacher—
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Thursday, August 25, 2011
Design
"Design is how it works." — Steven Jobs (See yesterday's Symmetry.)
Today's American Mathematical Society home page—
Some related material—
The above Rowley paragraph in context (click to enlarge)—
"We employ Curtis's MOG …
both as our main descriptive device and
also as an essential tool in our calculations."
— Peter Rowley in the 2009 paper above, p. 122
And the MOG incorporates the
Geometry of the 4×4 Square.
For this geometry's relation to "design"
in the graphic-arts sense, see
Block Designs in Art and Mathematics.
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Wednesday, August 24, 2011
Symmetry
An article from cnet.com tonight —
For Jobs, design is about more than aesthetics
By: Jay Greene
… The look of the iPhone, defined by its seamless pane of glass, its chrome border, its perfect symmetry, sparked an avalanche of copycat devices that tried to mimic its aesthetic.
Virtually all of them failed. And the reason is that Jobs understood that design wasn't merely about what a product looks like. In a 2003 interview with the New York Times' Rob Walker detailing the genesis of the iPod, Jobs laid out his vision for product design.
''Most people make the mistake of thinking design is what it looks like,'' Jobs told Walker. "People think it's this veneer— that the designers are handed this box and told, 'Make it look good!' That's not what we think design is. It's not just what it looks like and feels like. Design is how it works.''
Related material: Open, Sesame Street (Aug. 19) continues… Brought to you by the number 24—
"By far the most important structure in design theory is the Steiner system
— "Block Designs," by Andries E. Brouwer (Ch. 14 (pp. 693-746) of Handbook of Combinatorics , Vol. I, MIT Press, 1995, edited by Ronald L. Graham, Martin Grötschel, and László Lovász, Section 16 (p. 716))
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Conjure
In the catacomb of my mind
Where the dead endure—a kingdom
I conjure by love to rise
— Samuel Menashe, as quoted by
Stephen Spender in a review of four
different poets, "The Last Ditch,"
The New York Review of Books , July 22, 1971
"…the ghost reveals that the beggar
is in fact a sorcerer, a necromancer
who is preparing the mandala in order
to achieve an evil end. The ascetic
intends to bind the ghost to the corpse,
place it in the center of the circle,
and worship it as a deity."
— The King and the Corpse (from synopsis in
"How Many Facets Can a Non-Existent Jewel Have?")
Menashe died on Monday, August 22, 2011.
Related material by and for two other poets
who also died on Monday:
- By Jerry Leiber— "Love Potion #9"
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For Nick Ashford— Nicole Kidman in
Sermon (from Jan. 9) and
Conjure Wife, a 1943 tale by Fritz Leiber
See also an excerpt from Kerouac I cached on Monday, and
Men ask the way to Cold Mountain
Cold Mountain: there's no through trail .
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Tuesday, August 23, 2011
Four Winds
Related remarks —
- Sunday's Log24 post Cuatro Vientos on Jack Kerouac
- The phrase dies natalis in Log24
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Another weblog in 2004 on the dies natalis of Jack Kerouac.
That weblog gives the dies as Oct. 20, but other sources
say Kerouac died at 5:15 AM on Oct. 21. - A Log24 post on Oct. 20 last year related to the Oct. 21 date.
For the eight-limbed star at the top of the quaternion array above,
see "Damnation Morning" in this journal—
She drew from her handbag a pale grey gleaming implement that looked by quick turns to me like a knife, a gun, a slim sceptre, and a delicate branding iron—especially when its tip sprouted an eight-limbed star of silver wire. “The test?” I faltered, staring at the thing. “Yes, to determine whether you can live in the fourth dimension or only die in it.” — Fritz Leiber, short story, 1959
See also Feb. 19, 2011.
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Sunday, August 21, 2011
Cuatro Vientos
Video: Pope to youths in Cuatro Vientos: "Thank you for your joy and resistance" 
Tony Long at Wired.com, Aug. 30, 2007— "Scattered to the four winds"—
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"This Jack, joke, poor potsherd, ' patch, matchwood, immortal diamond,
Is immortal diamond." —Gerard Manley Hopkins, Society of Jesus
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Relativistic Truth
Today's online New York Times on the conclusion of the Roman Catholic Church's "World Youth" week—
"At the end of Sunday’s Mass, the pope announced that the next such event would be in Rio de Janeiro in 2013. Until then, he told those at the service, in Portuguese, that they 'will be swimming against the tide in a society with a relativistic culture, which wishes neither to seek nor hold on to the truth.'*"
* Fact check— This agrees with the Vatican Radio version.
Related material: Relativity Blues and Portal to 1937…
The "Portal" link above is in honor of the May 2 dies natalis of Salomon Bochner (pdf).
For some background, see yesterday's Castles in the Air and Bochner in this journal.
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Saturday, August 20, 2011
Castle Rock
Happy birthday to Amy Adams
(actress from Castle Rock, Colorado)
"The metaphor for metamorphosis…" —Endgame
Related material:
"The idea that reality consists of multiple 'levels,' each mirroring all others in some fashion, is a diagnostic feature of premodern cosmologies in general…."
— Scholarly paper on "Correlative Cosmologies"
"How many layers are there to human thought? Sometimes in art, just as in people’s conversations, we’re aware of only one at a time. On other occasions, though, we realize just how many layers can be in simultaneous action, and we’re given a sense of both revelation and mystery. When a choreographer responds to music— when one artist reacts in detail to another— the sensation of multilayering can affect us as an insight not just into dance but into the regions of the mind.
The triple bill by the Mark Morris Dance Group at the Rose Theater, presented on Thursday night as part of the Mostly Mozart Festival, moves from simple to complex, and from plain entertainment to an astonishingly beautiful and intricate demonstration of genius….
'Socrates' (2010), which closed the program, is a calm and objective work that has no special dance excitement and whips up no vehement audience reaction. Its beauty, however, is extraordinary. It’s possible to trace in it terms of arithmetic, geometry, dualism, epistemology and ontology, and it acts as a demonstration of art and as a reflection of life, philosophy and death."
— Alastair Macaulay in today's New York Times
SOCRATES: Let us turn off the road a little….
— Libretto for Mark Morris's 'Socrates'
See also Amy Adams's new film "On the Road"
in a story from Aug. 5, 2010 as well as a different story,
Eightgate, from that same date:
The above reference to "metamorphosis" may be seen,
if one likes, as a reference to the group of all projectivities
and correlations in the finite projective space PG(3,2)—
a group isomorphic to the 40,320 transformations of S8
acting on the above eight-part figure.
See also The Moore Correspondence from last year
on today's date, August 20.
For some background, see a book by Peter J. Cameron,
who has figured in several recent Log24 posts—
"At the still point, there the dance is."
— Four Quartets
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Castles in the Air
"… the Jews have discovered a way to access a fourth spatial dimension."
— Clifford Pickover, description of his novel Jews in Hyperspace
"If you have built castles in the air, your work need not be lost;
that is where they should be. Now put the foundations under them.”
— Henry David Thoreau
"King Solomon's Mines," 1937—
The image above is an illustration from "Romancing the Hyperspace," May 4, 2010.
Happy birthday to the late Salomon Bochner.
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Problem
Wednesday's Marginal Remarks pictured Robert De Niro
and Sean Penn in "We're No Angels." De Niro appeared
again in a Saturday Night Live sketch linked to
in last night's 9:29 post.
Here are some remarks featuring Penn related to
Peter J. Cameron's description yesterday of Sudoku
as an example of mathematics.
(Recall that the symbol #, known as 'hash,"
can stand for checkmate.)
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"Chess problems are the hymn-tunes of mathematics."
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For a sample chess problem, see a post from Oct. 10, 2005,
the day that the Sudoku remark Cameron describes was
in the news.
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Friday, August 19, 2011
Convoluted Narrative
Related material: Duende meets Saturday Night Live—
The "duende" link above leads to a post containing the following—
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For the Sudoku part, see this afternoon's Geezer Puzzle and a comment
at Diamond Geezer's weblog this morning by combinatorialist Peter J. Cameron—
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This reminds me of an incident a few years ago when Sir Michael Atiyah was interviewed by a journalist, who asked him what he thought of the Sudoku craze. Sir Michael replied that he was delighted to see so many people doing mathematics every day, and was taken to task by the journalist because "there is no mathematics in it: you don't add the numbers or anything".
Anyway, I consider this a mathematical puzzle; I even have some fancy words for it (a Graeco-Latin square with two disjoint diagonals and some entries prescribed). But don't let that scare anyone off trying the puzzle!
Thanks, DG: I put a link to it right away. |
See also the Pope's schedule today.
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Geezer Puzzle
An RSS item today—
 Diamond squares Fri Aug 19, 2011 05:36 [EDT] from Peter Cameron
If you like Latin squares and such things, take a look at Diamond Geezer’s post for today: a pair of orthogonal Latin squares with two disjoint common transversals, and some entries given (if you do the harder puzzle).
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The post referred to—
"This Jack, joke, poor potsherd, ' patch, matchwood, immortal diamond,
Is immortal diamond." —Gerard Manley Hopkins, Society of Jesus
Those now celebrating the Catholic Church's "World Youth" week in Madrid
may prefer a related puzzle for younger and nimbler minds:
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Open, Sesame Street
Y:
“When you come to a fork in the road, take it.” —Yogi Berra
Related material: Alice in the Garden and The Pythagorean Letter.
Z:
Zorro in this journal.
For some other symbology, see selected posts from today’s date, Aug. 19.
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Crux
"Francis Bacon used the phrase instantia crucis, 'crucial instance,' to refer to something in an experiment that proves one of two hypotheses and disproves the other. Bacon's phrase was based on a sense of the Latin word crux, 'cross,' which had come to mean 'a guidepost that gives directions at a place where one road becomes two,' and hence was suitable for Bacon's metaphor."
– The American Heritage® Dictionary of the English Language, Fourth Edition
Such a cross: St. Andrew's. Some context—
X Marks the Spot scene, "The Last Crusade"
Related symbology for Dan Brown—
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Thursday, August 18, 2011
Banderas*
For Ms. Julie and the Pope
For Ms. Julie:
Nuevas Banderas in this journal…
Click on image
for details.
See also Balakrishnan's Last Problem—
For the Pope:
Now playing; click poster for details.
See also "Damnation Morning" in this journal—
She drew from her handbag a pale grey gleaming implement that looked by quick turns to me like a knife, a gun, a slim sceptre, and a delicate branding iron—especially when its tip sprouted an eight-limbed star of silver wire. “The test?” I faltered, staring at the thing. “Yes, to determine whether you can live in the fourth dimension or only die in it.” — Fritz Leiber, short story, 1959
* For a time-leap from Leiber's 1959 to Hollywood's 2011, see yesterday's
Marginal Remarks, "The God particle ?" and a different Banderas.
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Wednesday, August 17, 2011
Marginal Remarks
Today's Google Doodle is in honor of Fermat's birthday—
"I have discovered a truly marvelous proof of this theorem,
which this doodle is too small to contain." — Google's caption
Another marginal remark, from a link target in last night's "Ein Kampf"—
"We are talking about the spatial and temporal phenomenon of language,
not about some non-spatial, non-temporal chimera [Note in margin:
Only it is possible to be interested in a phenomenon in a variety of ways]."
— Ludwig Wittgenstein, Philosophical Investigations (1953), Section 108
Related material on spatial and temporal phenomena—
A Dec. 29, 2010, comment to a Dec. 26 weblog post on
"Unexpected Connections in Mathematics"—
Connoisseurs of synchronicities in the phenomena of language may note that
these December dates mark the feasts of St. Stephen and St. Thomas Becket.
From the feast of the latter, two Log24 posts: Toy Stories and True Grid.
Those less enchanted by pop math than Google may prefer to observe
two other birthdays today— those of Robert De Niro and of Sean Penn:
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Ein Kampf
"Philosophy is a battle against the bewitchment of our intelligence by means of our language."
"Die Philosophie ist ein Kampf gegen die Verhexung unsres Verstandes durch die Mittel unserer Sprache."
— Ludwig Wittgenstein, Philosophical Investigations (1953), Section 109
"When the battle's lost and won" — The Scottish play
Related material— Monday's Language Game.
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Tuesday, August 16, 2011
Harrowing (continued)
There is an unwarranted leap here
from "suggests" to "knowledge."
See Under the Volcano and "harrowing" in this journal.
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Monday, August 15, 2011
Language Game
Related material—
Yesterday, 3:33 PM, in this journal— "Time for you to see the field"— and…
Faulkner's The Sound and the Fury , opening paragraph of part two, "June Second, 1910"—
"When the shadow of the sash appeared on the curtains it was between seven and eight oclock and then I was in time again, hearing the watch. It was Grandfather's and when Father gave it to me he said I give you the mausoleum of all hope and desire; it's rather excruciating-ly apt that you will use it to gain the reducto absurdum of all human experience which can fit your individual needs no better than it fitted his or his father's. I give it to you not that you may remember time, but that you might forget it now and then for a moment and not spend all your breath trying to conquer it. Because no battle is ever won he said. They are not even fought. The field only reveals to man his own folly, and despair, and victory is an illusion of philosophers and fools."
See also Willard Van Orman Quine in this journal on August 15, 2009—
"A tale told by an idiot"— and such a tale—
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Sunday, August 14, 2011
Sunday Review
The Sunday New York Times today—
This suggests…
The Elusive Small Idea—
Part I:
McLuhan and the Seven Snow Whites
Part II (from "Marshall, Meet Bagger," July 29):
"Time for you to see the field."
For further details, see the 1985 note
"Generating the Octad Generator."
McLuhan was a Toronto Catholic philosopher.
For related views of a Montreal Catholic philosopher,
see the Saturday evening post.
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Saturday, August 13, 2011
Taylor Made
The Montreal Catholic philosopher Charles Taylor has been reviewed
online recently in The New Yorker and The Nation .
Here is some background from this journal and from a 1989 book.
Update of 5:01 AM August 14— See also Valéry and the Self in this journal.
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Friday, August 12, 2011
Into the Woods
"What’s best about us, I hope, is that we teach them
the ‘forest of symbols,’ to borrow deliberately from
a poem called ‘Correspondences,’ by Baudelaire."
— The late Stanley Bosworth, founding headmaster
of St. Ann's School in Brooklyn
Bosworth died Sunday.
Related material—
- Saturday's Correspondences,
- Sunday's Coordinated Steps, and
- Monday's Organizing the Mine Workers.
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Wednesday, August 10, 2011
Objectivity
From math16.com—
Quotations on Realism
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The story of the diamond mine continues
(see Coordinated Steps and Organizing the Mine Workers)—
From The Search for Invariants (June 20, 2011):
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
Related material from Sunday's New York Times travel section—
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Monday, August 8, 2011
Diamond Theory vs. Story Theory (continued)
Richard J. Trudeau, a mathematics professor and Unitarian minister, published in 1987 a book, The Non-Euclidean Revolution , that opposes what he calls the Story Theory of truth [i.e., Quine, nominalism, postmodernism] to what he calls the traditional Diamond Theory of truth [i.e., Plato, realism, the Roman Catholic Church]. This opposition goes back to the medieval "problem of universals" debated by scholastic philosophers.
(Trudeau may never have heard of, and at any rate did not mention, an earlier 1976 monograph on geometry, "Diamond Theory," whose subject and title are relevant.)
From yesterday's Sunday morning New York Times—
"Stories were the primary way our ancestors transmitted knowledge and values. Today we seek movies, novels and 'news stories' that put the events of the day in a form that our brains evolved to find compelling and memorable. Children crave bedtime stories…."
— Drew Westen, professor at Emory University
From May 22, 2009—
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The above ad is by
Diamond from last night’s
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For further details, see Saturday's correspondences |
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Organizing the Mine Workers
From this journal on Saturday, August 6, 2011—
Comme de longs échos qui de loin se confondent
Dans une ténébreuse et profonde unité….
— Baudelaire, "Correspondances " (in The Flowers of Evil )
From the New York Times philosophy column "The Stone" earlier that day—
"… a magnificent and colorful parade of disorganized and rhapsodic thoughts"
— Baudelaire
From Uncle Walt— (See yesterday's "Coordinated Steps")—
For a better organized, less rhapsodic parade, see Saturday's Correspondences.
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Sunday, August 7, 2011
Coordinated Steps
From this morning's Sunday New York Times—
"Stories were the primary way our ancestors transmitted knowledge and values. Today we seek movies, novels and 'news stories' that put the events of the day in a form that our brains evolved to find compelling and memorable. Children crave bedtime stories…."
— Drew Westen, professor at Emory University
From this evening's news—
"TOKYO (Dow Jones)–The Group of Seven leading industrial nations said they are committed to taking coordinated steps…."
Who's their choreographer?
My choice would be Uncle Walt—
See also yesterday's "Norway Summer" and the link in
this afternoon's "Reflection Group" to "A Better Story."
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Reflection Group
The European Reflection Group report of Saturday, May 8, 2010—
"Project Europe 2030: Challenges and Opportunities" (pdf, 46 pp.)—
"All our members agree on one fundamental issue:
Europe is currently at a turning point in its history."
This journal on the same date— "A Better Story"—
"…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
"The clocks were striking thirteen." — George Orwell
See also this journal during the rest of May 2010 and "Sermon" from Sunday, February 20, 2011.
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Saturday, August 6, 2011
Happy Web Day
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Norway Summer
(Continued from June 21)
Footnote to a new web page from the European Culture Congress—
Photo credit: Josefine Lyche, “The 2×2 Case (Diamond Theorem)
after Steven H. Cullinane”, 450 x 650 cm,
Tromsø Kunstforening, 2010, image courtesy: the artist.
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Correspondences
Comme de longs échos qui de loin se confondent
Dans une ténébreuse et profonde unité….
— Baudelaire, “Correspondances ”
From “A Four-Color Theorem”—
Figure 1
Note that this illustrates a natural correspondence
between
(A) the seven highly symmetrical four-colorings
of the 4×2 array at the left of Fig. 1, and
(B) the seven points of the smallest
projective plane at the right of Fig. 1.
To see the correspondence, add, in binary
fashion, the pairs of projective points from the
“points” section that correspond to like-colored
squares in a four-coloring from the left of Fig. 1.
(The correspondence can, of course, be described
in terms of cosets rather than of colorings.)
A different correspondence between these 7 four-coloring
structures and these 7 projective-line structures appears in
a structural analysis of the Miracle Octad Generator
(MOG) of R.T. Curtis—
Figure 2
| Here the correspondence between the 7 four-coloring structures (left section) and the 7 projective-line structures (center section) is less obvious, but more fruitful. It yields, as shown, all of the 35 partitions of an 8-element set (an 8-set ) into two 4-sets. The 7 four-colorings in Fig. 2 also appear in the 35 4×4 parts of the MOG that correspond, in a way indicated by Fig. 2, to the 35 8-set paritions. This larger correspondence— of 35 4×2 arrays with 35 4×4 arrays— is the MOG, at least as it was originally defined. See The MOG, Generating the Octad Generator, and Eightfold Geometry.
For some applications of the Curtis MOG, see |
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Thursday, August 4, 2011
Midnight in Oslo
For Norway's Niels Henrik Abel (1802-1829)
on his birthday, August Fifth
(6 PM Aug. 4, Eastern Time, is 12 AM Aug. 5 in Oslo.)
Plato's Diamond
The above version by Peter Pesic is from Chapter I of his book Abel's Proof , titled "The Scandal of the Irrational." Plato's diamond also occurs in a much later mathematical story that might be called "The Scandal of the Noncontinuous." The story—
Paradigms"These passages suggest that the Form is a character or set of characters common to a number of things, i.e. the feature in reality which corresponds to a general word. But Plato also uses language which suggests not only that the forms exist separately (χωριστά ) from all the particulars, but also that each form is a peculiarly accurate or good particular of its own kind, i.e. the standard particular of the kind in question or the model (παράδειγμα ) [i.e. paradigm ] to which other particulars approximate…. … Both in the Republic and in the Sophist there is a strong suggestion that correct thinking is following out the connexions between Forms. The model is mathematical thinking, e.g. the proof given in the Meno that the square on the diagonal is double the original square in area." – William and Martha Kneale, The Development of Logic , Oxford University Press paperback, 1985 Plato's paradigm in the Meno—
Changed paradigm in the diamond theorem (2×2 case) —
Aspects of the paradigm change— Monochrome figures to Areas to Continuous transformations to Euclidean geometry to Euclidean quantities to The 24 patterns resulting from the paradigm change—
Each pattern has some ordinary or color-interchange symmetry. This is the 2×2 case of a more general result. The patterns become more interesting in the 4×4 case. For their relationship to finite geometry and finite fields, see the diamond theorem. |
Related material: Plato's Diamond by Oslo artist Josefine Lyche.
“Plato’s Ghost evokes Yeats’s lament that any claim to worldly perfection inevitably is proven wrong by the philosopher’s ghost….”
— Princeton University Press on Plato’s Ghost: The Modernist Transformation of Mathematics (by Jeremy Gray, September 2008)
"Remember me to her."
— Closing words of the Algis Budrys novel Rogue Moon .
Background— Some posts in this journal related to Abel or to random thoughts from his birthday.
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Sunday, July 31, 2011
Validation
From a writer's requiem—
"Algis points out that at the end of each story, there should be a moment of validation, a place where a person in authority makes some sort of statement that lets the reader know that the story has reached its conclusion." —David Farland, June 9, 2008
Paraphrase of a version by an anonymous reader at Amazon.com (see previous post)—
"… someone who has no other vested interest in the story… steps forward and says 'He's dead, Jim' or 'Who was that masked man?'"
Moments of validation from today's midday NY Lottery— 4639 and 575.
For "He's dead, Jim," see April 6, 1939* (4/6/39) at St. Joseph's Church in Springfield, Mass.
For "Who was that masked man?," see the Mark of Zorro in Post 575.
* This was a Maundy Thursday, not the Good Friday indicated in the linked narrative.
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Short Stories
An Amazon.com reader review of Algis Budrys's Writing to the Point: A Complete Guide to Selling Fiction—
"Mr. Budrys claims to have the secret to writing fiction that will sell. His secret is very useful but short enough to include here:
Beginning: Must consist of introducing a character, in a particular context, with a problem. And if there are important yet unique/unusual aspects of the character that will be revealed later in the story they must be foreshadowed in the beginning.
Middle: Must involve the character attempting to solve the problem and encountering unexpected failure. During this attempt he begins to learn more about the problem and himself. The character must undergo stress which causes hitherto concealed facets of him to be revealed-that must fit in. The character must try to overcome the problem a total of 3 times on a rising scale of effort, commitment, and depth of knowledge of the problem and one's self. At the last possible moment, with maximum effort and staking everything, he achieves victory. This must be done by wagering everything in a do-or-die situation. Conversely the villain, coming closer to his goal experiences defeat snatched from the jaws of victory-because of some flaw in character.
End: Validation and foreclosure by someone who has no other vested interest in the story. They step forward and say 'He's dead, Jim' or 'Who was that masked man?' This serves to close the story in the reader's mind."
Here are two parallel stories suggested by yesterday's New York Lottery numbers:
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Evening: 003 and 8997— From an author born on 8/9/97: For the 003, see
7/11. |
Midday: 004 and 1931— From an author born on 1/9/31:
For the 004, see the ideogram
See also the day of the author's |
Happy Feast of St. Ignatius of Loyola.
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Saturday, July 30, 2011
Groups and Symmetry
"… the best way to understand a group is to
see it as the group of symmetries of something."
— John Baez, p. 239, Bulletin (New Series) of the
American Mathematical Society , Vol. 42, No. 2,
April 2005, book review on pp. 229–243
electronically published on January 26, 2005
"Imagine yourself as a gem cutter,
turning around this diamond…."
— Ibid ., p. 240
See also related material from Log24.
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Friday, July 29, 2011
Marshall, Meet Bagger
Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—
"The American mind is not even close to being amenable to the ideogram principle as yet. The reason is simply this. America is 100% 18th Century. The 18th century had chucked out the principle of metaphor and analogy— the basic fact that as A is to B so is C to D. AB:CD. It can see AB relations. But relations in four terms are still verboten. This amounts to deep occultation of nearly all human thought for the U.S.A.
I am trying to devise a way of stating this difficulty as it exists. Until stated and publicly recognized for what it is, poetry and the arts can’t exist in America."
"Time for you to see the field." —Bagger Vance
The field — See June 2010.
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Thursday, July 28, 2011
Noon
"Anomalies must be expected along the conceptual frontier
between the temporal and the eternal."
– The Death of Adam , by Marilynne Robinson (1998, 2005),
essay on Marguerite de Navarre
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Winning
From a short story:
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One day his mother and his Uncle Oscar came in when he was on one of his furious rides. He did not speak to them. "Hallo, you young jockey! Riding a winner?" said his uncle. "Aren't you growing too big for a rocking-horse? You're not a very little boy any longer, you know," said his mother. But Paul only gave a blue glare from his big, rather close-set eyes. He would speak to nobody when he was in full tilt. His mother watched him with an anxious expression on her face. At last he suddenly stopped forcing his horse into the mechanical gallop and slid down. "Well, I got there!" he announced fiercely, his blue eyes still flaring, and his sturdy long legs straddling apart. "Where did you get to?" asked his mother. "Where I wanted to go," he flared back at her. "That's right, son!" said Uncle Oscar. "Don't you stop till you get there. What's the horse's name?" "He doesn't have a name," said the boy. — "The Rocking-Horse Winner," by D. H. Lawrence |
"In the desert you can remember your name,
'Cause there ain't no one for to give you no pain."
— America
See also June 12, 2005, September 11, 2007, and Something Anonymous.
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Magical Realism Revisited
The magical part— Synchronicity—
See Roger Cohen in this journal on January 15, 2009 and, on the
same date, Jesse Jarnow on Bob Dylan in The Jewish Daily Forward .
The realism part— Cohen's "smart power" and IQ tests involving pattern blocks.
The above quilt pattern software (both versions) is by Jarnow's father Al.
For a realistic approach to such patterns, see Blockheads in this journal.
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Tuesday, July 26, 2011
Venus at St. Anne’s
The title is that of a chapter in the C.S. Lewis classic That Hideous Strength .
A search suggested by this afternoon's NY Lottery four-digit number,
8002, yields a forum post at WebOfNarcissism.com—
"a book that changed my life"—
"Here is the book:
http://www.amazon.com/What-Loved-Novel-Siri-Hustvedt/dp/0312421192
Warning. It is dark. But it is also lovely."
Whether it is deep as well, the reader may judge.
The quoted review is from a discussion by an anonymous user
of her relationship with someone called N. See also, in this journal,
The Story of N.
Happy St. Anne's Day.
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The Case of the Missing Smile
In today's online New York Times , Roger Cohen quotes a manifesto—
A more complete excerpt—
Note that Cohen omits the concluding punctuation—
three exclamation points and a smile emoticon—
!!!:-)
(Compare and contrast with the smile of Hannibal Lecter.)
Related material from this journal on the following day, Flag Day, June 14—
Note that the structure of the central flag above |
See also the remark of author Siri Hustvedt (of Norwegian-American
background) that was quoted here Sunday.
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Monday, July 25, 2011
Halloween Game
Continued from this morning's "The Game"—
"Relativism is not always a coherent way of responding to the rejection of a certain class of facts. When we decided that there were no such things as witches, we didn’t become relativists about witches. Rather, we just gave up witch talk altogether, except by way of characterizing the attitudes of people (such as those in Salem) who mistakenly believed that the world contained witches, or by way of characterizing what it is that children find it fun to pretend to be on Halloween."
— New York Times philosophy column "The Stone" today
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The Game
Virginia Heffernan in Sunday's online New York Times—
"… In the past, information on paper was something to read. Bricks and mortar were a place to be. But, since the first appearance of the Web in 1990, we have come to accept that information in pixels is something to read— and also a place to be . That familiar and yet still jaw-dropping metaphor takes energy to maintain. The odd shared sense that there’s three-dimensionality and immersion and real-world consequences on the Web as in no book or board game— that’s the Web’s sine qua non. Hence, cyberspace . And 'being on' the Internet….
… The dominant social networks are fantasy games built around rigged avatars, outright fictions and a silent— and often unconscious— agreement among players that the game and its somewhat creaky conceits influence the real world…."
— "The Confidence Game at Google+"
"It's just another manic Monday
I wish it was Sunday
'Cause that's my funday"
— The Bangles
"Accentuate the Positive"
— Clint Eastwood, soundtrack album
for "Midnight in the Garden of Good and Evil"
This journal on All Saints' Day, Sunday, November 1, 2009—
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Suggested by the New York State lottery numbers on All Hallows’ Eve [2009]— 430 (mid-day) and 168 (evening)… From 430 as a date, 4/30— Beyond Grief and Nothing: A Reading of Don DeLillo , by Joseph Dewey, University of South Carolina Press, 2006, page 123: “It is as if DeLillo himself had moved to an endgame….” For such an endgame, see yesterday’s link to a Mira Sorvino drama. The number 168 suggested by the Halloween lottery deals with the properties of space itself and requires a more detailed exegesis… For the full picture, consider the Log24 entries of Feb. 16-28 this year, esp. the entries of Feb. 27 and the phrase they suggest— Flores, flores para los muertos. |
See also Pearly Gates of Cyberspace in this journal.
For flores para los muertos , see today's Times .
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Sunday, July 24, 2011
Lottery Royale
Continuing this afternoon's meditation on Hollywood
endings, recall the ending of the 1966 David Niven
version of Casino Royale—
"Eventually, Jimmy's atomic pill explodes, destroying Casino Royale
along with everyone inside…. Sir James and all of his agents then
appear in heaven, with angel wings and harps and Jimmy Bond is
shown descending into the fires of hell." — Wikipedia
This evening's NY Lottery numbers are 169 and 1243.
An occurence of 169 in this journal on June 18, 2008—
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Hollywood Endings
"Nixon has no Rosebud."
— Master's thesis on an Oliver Stone film
(Dan B. Butler, May 2006)
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Sunday School
Venus and Mars Realigned (continued from July 20) …
A review —
“The story, involving the Knights Templar, the Vatican, sunken treasure,
the fate of Christianity and a decoding device that looks as if it came out of
a really big box of medieval Cracker Jack, is the latest attempt to combine
Indiana Jones derring-do with ‘Da Vinci Code’ mysticism.”
A related Google image search yields more Cracker Jack prizes.
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Saturday, July 23, 2011
Death Argument
Suggested by Peter J. Cameron's weblog post today on Halmos,
by a July 18 post in this journal on the Norwegian mathematician Abel,
by a link in the July 18 post to "Death Proof," and by today's
midday New York Lottery (459 and 7404)—
From July 4, 2004 (7404 interpreted as a date)—
"There are two unfortunate connotations of 'proof' that come from mathe-
matics and make the word inappropriate in discussions of the security of cryp-
tographic systems. The first is the notion of 100% certainty. Most people not
working in a given specialty regard a 'theorem' that is 'proved' as something
that they should accept without question. The second connotation is of an intri-
cate, highly technical sequence of steps. From a psychological and sociological
point of view, a 'proof of a theorem' is an intimidating notion: it is something
that no one outside an elite of narrow specialists is likely to understand in detail
or raise doubts about. That is, a 'proof' is something that a non-specialist does
not expect to really have to read and think about.
The word 'argument,' which we prefer here, has very different connotations."
— "Another Look at 'Provable Security',"
by Neal Koblitz and Alfred J. Menezes, July 4, 2004
(updated on July 16, 2004; October 25, 2004; March 31, 2005; and May 4, 2005)
As for 459, see Post 459 in this journal.
Related material: The Race, Crossing the Bridge, Aristophanic View, and Story Theory.
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Story Theory (continued)
"We tell ourselves stories…." * — Joan Didion
in "The Fifth Element"
Priest Vito Cornelius: I… have… a different theory to offer you, sir.
President Lindberg: You have twenty seconds.
* See also Friday morning's post.
** Today's New York Times—
"A version of this op-ed appeared in print
on July 23, 2011, on page A19 of the New York
edition with the headline: The Great Evil." —
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Friday, July 22, 2011
The Aristophanic View
"Some mathematicians are birds, others are frogs.
Birds fly high in the air and survey broad vistas of
mathematics out to the far horizon. They delight in
concepts that unify our thinking and bring together
diverse problems from different parts of the
landscape. Frogs live in the mud below and see
only the flowers that grow nearby. They delight in
the details of particular objects, and they solve
problems one at a time. I happen to be a frog, but
many of my best friends are birds. The main theme
of my talk tonight is this. Mathematics needs both
birds and frogs. Mathematics is rich and beautiful
because birds give it broad visions and frogs give it
intricate details. Mathematics is both great art and
important science, because it combines generality
of concepts with depth of structures. It is stupid to
claim that birds are better than frogs because they
see farther, or that frogs are better than birds
because they see deeper. The world of mathematics
is both broad and deep, and we need birds and
frogs working together to explore it.
This talk is called the Einstein lecture…."
— Freeman Dyson, Notices of the American
Mathematical Society , February 2009
The Didion reading was suggested by the "6212" in yesterday evening's New York Lottery.
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Thursday, July 21, 2011
Crossing the Bridge
Continued from July 15th…
Monstrance
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In memory of painter Lucian Freud, |
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"Just a flesh wound." — The Black Knight
For related material, see Crossing the Bridge
and this morning's post The Race.
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The Race
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An image related to See "As It Lays" in this journal.
(Not as it lies .) |
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New York Times obituaries today—
Click to enlarge.
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"That's GUY-ler, not GAY-ler."
See also Time and the River, Number of the Beast, and Story Theory.
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Wednesday, July 20, 2011
Apocalypse for St. Frank
(For the title, see the previous post.)
Compare and contrast—
Background on the film "The Ninth Gate"—
Pop-sci background, courtesy of Fox Searchlight Pictures, for the film
Update of 2:48 PM July 20th—
See Peter Woit's July 19th post "Questions About the Multiverse."
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Church of St. Frank*
"A New York Jew imitates D. H. Lawrence at his peril."
See also The Ninth Gate and Spider Women.
* For the title, do a search in this journal.
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What Was I Thinking?
An 8:07 AM check of a link in this morning's 8 AM post,
The Misalignment of Mars and Venus, showed an ad—
— that led to the website for the upcoming film "Another Earth."
At that website is an image that might well be titled…
"Mars and Venus Realigned"—
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Cover Art
The Misalignment of Mars and Venus
A death in Sarasota on Sunday leads to a weblog post from Tuesday
that suggests a review of Dan Brown's graphic philosophy—
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From The Da Vinci Code : Langdon pulled a pen from his pocket. “Sophie are you familiar with the modern icons for male and female?” He drew the common male symbol ♂ and female symbol ♀. “Of course,” she said. “These,” he said quietly, are not the original symbols for male and female. Many people incorrectly assume the male symbol is derived from a shield and spear, while the female represents a mirror reflecting beauty. In fact, the symbols originated as ancient astronomical symbols for the planet-god Mars and the planet-goddess Venus. The original symbols are far simpler.” Langdon drew another icon on the paper. ∧
“This symbol is the original icon for male ,” he told her. “A rudimentary phallus.” “Quite to the point,” Sophie said. “As it were,” Teabing added. Langdon went on. “This icon is formally known as the blade , and it represents aggression and manhood. In fact, this exact phallus symbol is still used today on modern military uniforms to denote rank.” “Indeed.” Teabing grinned. “The more penises you have, the higher your rank. Boys will be boys.”
Langdon winced. “Moving on, the female symbol, as you might imagine, is the exact opposite.” He drew another symbol on the page. “This is called the ∨ Sophie glanced up, looking surprised. Langdon could see she had made the connection. “The chalice,” he said, “resembles a cup or vessel, and more important, it resembles the shape of a woman’s womb. This symbol communicates femininity, womanhood, and fertility.” |
Langdon's simplified symbols, in disguised form, illustrate
a musical meditation on the misalignment of Mars and Venus—
This was adapted from an album cover by "Meyers/Monogram"—
See also Secret History and The Story of N.
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Monday, July 18, 2011
The Charlie Sheen Hamlet
“The meeting is closed
with the Lord’s Prayer
and refreshments are served.”
* Courtesy of the NY Lottery.
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The Devil at Midday
Posts suggested by the New York Lottery today at midday— 632 and 2750.
Note the song linked to a quotation in the latter post—
Click on the link or the quote for the song.
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Daimon Theory (continued)
Press Release — Los Angeles, July 18, 2011—
Former Two and a Half Men star Charlie Sheen is planning his return to series television in Anger Management , a new sitcom loosely based on Revolution Studios’ 2003 hit comedy feature of the same name….
… in the series inspired by the film… a mild-mannered, non-confrontational man is ordered to attend group anger management sessions led by a therapist who could probably use some anger management himself.
“I chose Anger Management because, while it might be a big stretch for me to play a guy with serious anger management issues, I think it is a great concept,” Sheen said.
See also Daimon in this journal.
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Short Story
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Voldemort
Continuing yesterday's lottery meditation…
The NY evening numbers yesterday were 244 and 2962.
The latter suggests Post 2962—
There is no Post 244 here, but a search within this journal for 244 yields…
See also Halmos Tombstone and Death Proof.
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Sunday, July 17, 2011
Posts
A Sunday meditation continued from Burning Patrick—
For posts of a different sort, see O'Hara's Fingerpost and Cross-Purposes.
(The numbers of these posts were indicated by today's midday NY Lottery.)
See also "Ready when you are, C.B."
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Insane Symmetry
Continued from December 28, 2010.
The above RSS version of a quilt enthusiast's obituary contains an ad asking
"DO YOU HAVE WHAT IT TAKES?
Flex your brain muscles with the
Ultimate Problem Solver Challenge."
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Saturday, July 16, 2011
Friday, July 15, 2011
Crossing the Bridge
King Arthur and the Deathly Hallows
BLACK KNIGHT: None shall pass.
ARTHUR: What?
BLACK KNIGHT: None shall pass.
ARTHUR: I have no quarrel with you, good Sir Knight,
but I must cross this bridge.
BLACK KNIGHT: Then you shall die.
ARTHUR: I command you as King of the Britons
to stand aside!
BLACK KNIGHT: I move for no man.
ARTHUR: So be it!
— Monty Python
Above: Anthony Bushell as King Arthur in 1954.
Bushell died on April 2, 1997 (4/2/97).
"Well, she was just seventeen…."
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The Magic of Numbers*
NY Lottery this afternoon:
See Post 757— "Release Date"— and The-Numbers.com
on a film with the release date 7/3/85.
* Title of a course at Harvard. See (for instance)
the Harvard page on The Numerology of the Beast—
"Now in math the magic is not in special numbers
like 7 or 28, but in the fabric of number systems…."
Sure it is.
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Spider Women
"Of course, the aesthetic program
of cultural modernism
has long been summed up
by the maxim épater la bourgeoisie."
— The New York Times
Sunday Book Review, July 17
Examples:
"This Extreme and Difficult Sense of Spectacular Representation:
Antonin Artaud's Ontology of 'Live'," by Deborah Levitt
of the New School (See the noon post of July 13), as well as…
and, from mathematician Ellen Gethner's home page—
See also Sunday Dinner, A Link for Sunrise, and Inside CBS News.
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Crucible
The Hogwarts saga may be ending, but there's still…
The Crucible
Related material:
Ay que bonito es volar…
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Inside CBS News
Related material from the June 30 Washington Post—
"Wizardly in his abilities and appearance—
he had a scraggly, gray beard—
Mr. Morris was the digital gatekeeper
of the American government’s computer secrets."
See also audience participation features at The New York Times—
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Thursday, July 14, 2011
Tombstones
Part I: Literal
"Shinin' like a diamond,
she had tombstones in her eyes."
Part II: Figurative
See Halmos Tombstone in this journal.
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Happy Birthday
To an investor in disambiguation —
Looking for Action—
"To me, the meaning was clear: when people search, they aren't just looking for nouns or information; they are looking for action. They want to book a flight, reserve a table, buy a product, cure a hangover, take a class, fix a leak, resolve an argument, or occasionally find a person, for which Facebook is very handy. They mostly want to find something in order to do something."
— Esther Dyson on "The Future of Internet Search,"
dated August 19, 2010.
See also that date in this journal.
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ART WARS continued:
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Wednesday, July 13, 2011
Holden Scott Revisited
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The Dick Code
"Eighteenth century theories of language were often presented as genealogies; instead of looking to the functions or operations of language to describe its 'nature,' they appealed to the story of its origins (with more or less literalist intentions.) The interest in an original 'revealed' language began much earlier, however. Leibniz, for example, searched for a primitive root-language which he felt could be discovered through research into etymology, and asserted that this ur-text, whether its signifiers were natural or conventional, would be composed of rational relations worthy of its original author, or Author, that is, God. He also toyed with the notion that hieroglyphics might be a philosophical language, a kind of meaningful mathematics, whose revelations would be exact and necessary. The debate over the origins of language— and the status of hieroglyphics— as it played out in the eighteenth century was linked to a dispute over metaphor, conceived as a 'primitive' mode of expression which preceded and was less nuanced and precise than the 'arbitrary' modern European languages. What is essential here is not the specifics of the debate on the origins of language (although this would certainly add much to the present inquiry) but rather the link that was thus constituted between hieroglyphics, the primitive ('the savage and the poet speak only in hieroglyphics') and the idea of an archaic language as an original archive of meanings which pre-exists Man and his derivative or arbitrary tongues."
— "This Extreme and Difficult Sense of Spectacular Representation: Antonin Artaud's Ontology of 'Live'," by Deborah Levitt
^
"In several programming languages, such as C, C++, C#, Java, Perl, and Python, a caret (^) is used to denote the bitwise XOR operator. This is not used outside of programming contexts because it is too easily confused with other uses of the caret." —Wikipedia article on Exclusive Or
See also the above date, July 7, 2010, in this journal.
Philip K. Dick, author of the novel
on which the Harrison Ford film
"Blade Runner" (1982) was based.
"You'd never know it, but buddy
I'm a kind of poet."
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The Sinatra Code
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From The Da Vinci Code, Chapter 56 Sophie stared at Teabing a long moment and then turned to Langdon. “The Holy Grail is a person?” Langdon nodded. “A woman, in fact.” From the blank look on Sophie’s face, Langdon could tell they had already lost her. He recalled having a similar reaction the first time he heard the statement. It was not until he understood the symbology behind the Grail that the feminine connection became clear. Teabing apparently had a similar thought. “Robert, perhaps this is the moment for the symbologist to clarify?” He went to a nearby end table, found a piece of paper, and laid it in front of Langdon. Langdon pulled a pen from his pocket. “Sophie are you familiar with the modern icons for male and female?” He drew the common male symbol ♂ and female symbol ♀. “Of course,” she said. “These,” he said quietly, are not the original symbols for male and female. Many people incorrectly assume the male symbol is derived from a shield and spear, while the female represents a mirror reflecting beauty. In fact, the symbols originated as ancient astronomical symbols for the planet-god Mars and the planet-goddess Venus. The original symbols are far simpler.” Langdon drew another icon on the paper. ∧
“This symbol is the original icon for male ,” he told her. “A rudimentary phallus.” “Quite to the point,” Sophie said. “As it were,” Teabing added. Langdon went on. “This icon is formally known as the blade , and it represents aggression and manhood. In fact, this exact phallus symbol is still used today on modern military uniforms to denote rank.” “Indeed.” Teabing grinned. “The more penises you have, the higher your rank. Boys will be boys.” Langdon winced. “Moving on, the female symbol, as you might imagine, is the exact opposite.” He drew another symbol on the page. “This is called the ∨ Sophie glanced up, looking surprised. Langdon could see she had made the connection. “The chalice,” he said, “resembles a cup or vessel, and more important, it resembles the shape of a woman’s womb. This symbol communicates femininity, womanhood, and fertility.” Langdon looked directly at her now. “Sophie, legend tells us the Holy Grail is a chalice—a cup. But the Grail’s description as a chalice is actually an allegory to protect the true nature of the Holy Grail. That is to say, the legend uses the chalice as a metaphor for something far more important.” “A woman,” Sophie said. “Exactly.” Langdon smiled. “The Grail is literally the ancient symbol for womankind, and the Holy Grail represents the sacred feminine and the goddess, which of course has now been lost, virtually eliminated by the Church. The power of the female and her ability to produce life was once very sacred, but it posed a threat to the rise of the predominantly male Church, and so the sacred feminine was demonized and called unclean. It was man , not God, who created the concept of ‘original sin,’ whereby Eve tasted of the apple and caused the downfall of the human race. Woman, once the sacred giver of life, was now the enemy.” “I should add,” Teabing chimed, “that this concept of woman as life-bringer was the foundation of ancient religion. Childbirth was mystical and powerful. Sadly, Christian philosophy decided to embezzle the female’s creative power by ignoring biological truth and making man the Creator. Genesis tells us that Eve was created from Adam’s rib. Woman became an offshoot of man. And a sinful one at that. Genesis was the beginning of the end for the goddess.” “The Grail,” Langdon said, “is symbolic of the lost goddess. When Christianity came along, the old pagan religions did not die easily. Legends of chivalric quests for the lost Grail were in fact stories of forbidden quests to find the lost sacred feminine. Knights who claimed to be “searching for the chalice” were speaking in codes as a way to protect themselves from a Church that had subjugated women, banished the Goddess, burned nonbelievers, and forbidden pagan reverence for the sacred feminine.” |
Happy birthday to Harrison Ford.
One for my baby…
∧
One more for the road.
∨
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Tuesday, July 12, 2011
An Object of Beauty and…
The Usual Suspects
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For some background, click on the diamond above. See also Harrison Ford in "Harvard Defeats Holy Cross." |
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Monday, July 11, 2011
And/Or Problem
"It was the simultaneous emergence
and mutual determination
of probability and logic
that von Neumann found intriguing
and not at all well understood."
Context:
Update of 7 AM ET July 12, 2011—
Freeman Dyson on John von Neumann's
Sept. 2, 1954, address to the International
Congress of Mathematicians on
"Unsolved Problems in Mathematics"—
…."The hall was packed with
mathematicians, all expecting to hear a brilliant
lecture worthy of such a historic occasion. The
lecture was a huge disappointment. Von Neumann
had probably agreed several years earlier to give
a lecture about unsolved problems and had then
forgotten about it. Being busy with many other
things, he had neglected to prepare the lecture.
Then, at the last moment, when he remembered
that he had to travel to Amsterdam and say something
about mathematics, he pulled an old lecture
from the 1930s out of a drawer and dusted it off.
The lecture was about rings of operators, a subject
that was new and fashionable in the 1930s. Nothing
about unsolved problems. Nothing about the
future."
— Notices of the American Mathematical Society ,
February 2009, page 220
For a different account, see Giovanni Valente's
2009 PhD thesis from the University of Maryland,
Chapter 2, "John von Neumann's Mathematical
'Utopia' in Quantum Theory"—
"During his lecture von Neumann discussed operator theory and its con-
nections with quantum mechanics and noncommutative probability theory,
pinpointing a number of unsolved problems. In his view geometry was so tied
to logic that he ultimately outlined a logical interpretation of quantum prob-
abilities. The core idea of his program is that probability is invariant under
the symmetries of the logical structure of the theory. This is tantamount to
a formal calculus in which logic and probability arise simultaneously. The
problem that exercised von Neumann then was to construct a geometrical
characterization of the whole theory of logic, probability and quantum me-
chanics, which could be derived from a suitable set of axioms…. As he
himself finally admitted, he never managed to set down the sought-after
axiomatic formulation in a way that he felt satisfactory."
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Accentuate the Positive
An image that may be viewed as
a cube with a “+“ on each face—
The eightfold cube
Underlying structure
For the Pope and others on St. Benedict’s Day
who prefer narrative to mathematics—
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The Witch of And/Or
AND: Logical conjunction, symbolized as… ∧
OR: Logical disjunction, symbolized as… ∨
AND/OR: Logical confusion, symbolized as… 
according to a woman Lacanian analyst in this journal.
See also another female disciple of Lacan
writing as co-author with a philosophy professor
in Saturday's online New York Times 's "The Stone"—
Let Be: An Answer to Hamlet’s Question."
Perhaps they thought the question was…
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Wikipedia portrait of New School "To be and/or not to be?" |
For a more philosophically respectable approach to
the same shape, see Sunday morning's Wittgenstein's Diamond.
"We're gonna need more holy water." —Hollywood saying
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Dark Lady
From an obituary of choreographer Roland Petit, who died on Sunday, July 10, 2011—
"Ballerina roles had for more than a century been largely made on pale romantically suffering virgins or royal princesses; Petit’s women were liberated and exciting, modern and tangibly real— and yet archaic femmes fatales . Probably his most popular ballet worldwide is Le jeune homme et la mort , in which a young bloke lazing around in his room is visited by an enigmatic, seductive female— at the end of which brief encounter he hangs himself.
The young man’s role was seized upon by the great ballet stars of the next decades, Rudolf Nureyev and Mikhail Baryshnikov notable among them. As with Carmen, the role of La Mort, the death goddess, has been sought out by a pantheon of great ballerinas, in Paris, Russia and the US as well as in Europe." —Ismene Brown at theartsdesk.com
From the philosophy column "The Stone" in Saturday's online New York Times—
Let Be: An Answer to Hamlet’s Question"—
"Jamieson Webster is a psychoanalyst in private practice
in New York. She is the author of
'The Life and Death of Psychoanalysis'
forthcoming from Karnac Books."
Related ART WARS material:
- An illustrated essay by Webster posted on March 7, 2009 at The Symptom 10 weblog
- An illustrated essay by Cullinane posted on March 7, 2009 at the Log24 weblog
- Time and Eternity
- Lovely, Dark and Deep
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