Log24

Thursday, September 3, 2009

Thursday September 3, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 11:07 am
Autistic Enchantment

“Music and mathematics are among the pre-eminent wonders of the race. Levi-Strauss sees in the invention of melody ‘a key to the supreme mystery’ of man– a clue, could we but follow it, to the singular structure and genius of the species. The power of mathematics to devise actions for reasons as subtle, witty, manifold as any offered by sensory experience and to move forward in an endless unfolding of self-creating life is one of the strange, deep marks man leaves on the world. Chess, on the other hand, is a game in which thirty-two bits of ivory, horn, wood, metal, or (in stalags) sawdust stuck together with shoe polish, are pushed around on sixty-four alternately coloured squares. To the addict, such a description is blasphemy. The origins of chess are shrouded in mists of controversy, but unquestionably this very ancient, trivial pastime has seemed to many exceptionally intelligent human beings of many races and centuries to constitute a reality, a focus for the emotions, as substantial as, often more substantial than, reality itself. Cards can come to mean the same absolute. But their magnetism is impure. A mania for whist or poker hooks into the obvious, universal magic of money. The financial element in chess, where it exists at all, has always been small or accidental.

To a true chess player, the pushing about of thirty-two counters on 8×8 squares is an end in itself, a whole world next to which that of a mere biological or political or social life seems messy, stale, and contingent. Even the patzer, the wretched amateur who charges out with his knight pawn when the opponent’s bishop decamps to R4, feels this daemonic spell. There are siren moments when quite normal creatures otherwise engaged, men such as Lenin and myself, feel like giving up everything– marriage, mortgages, careers, the Russian Revolution– in order to spend their days and nights moving little carved objects up and down a quadrate board. At the sight of a set, even the tawdriest of plastic pocket sets, one’s fingers arch and a coldness as in a light sleep steals over one’s spine. Not for gain, not for knowledge or reknown, but in some autistic enchantment, pure as one of Bach’s inverted canons or Euler’s formula for polyhedra.”

— George Steiner in “A Death of Kings,” The New Yorker, issue dated September 7, 1968, page 133

“Examples are the stained-glass windows of knowledge.” —Nabokov

Quaternion rotations in a finite geometry
Click above images for some context.

See also:

Log24 entries of May 30, 2006, as well as “For John Cramer’s daughter Kathryn”– August 27, 2009— and related material at Wikipedia (where Kathryn is known as “Pleasantville”).

Thursday, August 20, 2009

Thursday August 20, 2009

Filed under: General,Geometry — m759 @ 4:00 pm

Sophists

From David Lavery’s weblog today

Kierkegaard on Sophists:

“If the natural sciences had been developed in Socrates’ day as they are now, all the sophists would have been scientists. One would have hung a microscope outside his shop in order to attract customers, and then would have had a sign painted saying: Learn and see through a giant microscope how a man thinks (and on reading the advertisement Socrates would have said: that is how men who do not think behave).”

— Søren Kierkegaard, Journals, edited and translated by Alexander Dru

To anyone familiar with Pirsig’s classic Zen and the Art of Motorcycle Maintenance, the above remarks of Kierkegaard ring false. Actually, the sophists as described by Pirsig are not at all like scientists, but rather like relativist purveyors of postmodern literary “theory.” According to Pirsig, the scientists are like Plato (and hence Socrates)– defenders of objective truth.

Pirsig on Sophists:

“The pre-Socratic philosophers mentioned so far all sought to establish a universal Immortal Principle in the external world they found around them. Their common effort united them into a group that may be called Cosmologists. They all agreed that such a principle existed but their disagreements as to what it was seemed irresolvable. The followers of Heraclitus insisted the Immortal Principle was change and motion. But Parmenides’ disciple, Zeno, proved through a series of paradoxes that any perception of motion and change is illusory. Reality had to be motionless.

The resolution of the arguments of the Cosmologists came from a new direction entirely, from a group Phædrus seemed to feel were early humanists. They were teachers, but what they sought to teach was not principles, but beliefs of men. Their object was not any single absolute truth, but the improvement of men. All principles, all truths, are relative, they said. ‘Man is the measure of all things.’ These were the famous teachers of ‘wisdom,’ the Sophists of ancient Greece.

To Phaedrus, this backlight from the conflict between the Sophists and the Cosmologists adds an entirely new dimension to the Dialogues of Plato. Socrates is not just expounding noble ideas in a vacuum. He is in the middle of a war between those who think truth is absolute and those who think truth is relative. He is fighting that war with everything he has. The Sophists are the enemy.

Now Plato’s hatred of the Sophists makes sense. He and Socrates are defending the Immortal Principle of the Cosmologists against what they consider to be the decadence of the Sophists. Truth. Knowledge. That which is independent of what anyone thinks about it. The ideal that Socrates died for. The ideal that Greece alone possesses for the first time in the history of the world. It is still a very fragile thing. It can disappear completely. Plato abhors and damns the Sophists without restraint, not because they are low and immoral people… there are obviously much lower and more immoral people in Greece he completely ignores. He damns them because they threaten mankind’s first beginning grasp of the idea of truth. That’s what it is all about.

The results of Socrates’ martyrdom and Plato’s unexcelled prose that followed are nothing less than the whole world of Western man as we know it. If the idea of truth had been allowed to perish unrediscovered by the Renaissance it’s unlikely that we would be much beyond the level of prehistoric man today. The ideas of science and technology and other systematically organized efforts of man are dead-centered on it. It is the nucleus of it all.

And yet, Phaedrus understands, what he is saying about Quality is somehow opposed to all this. It seems to agree much more closely with the Sophists.”

I agree with Plato’s (and Rebecca Goldstein’s) contempt for relativists. Yet Pirsig makes a very important point. It is not the scientists but rather the storytellers (not, mind you, the literary theorists) who sometimes seem to embody Quality.

As for hanging a sign outside the shop, I suggest (particularly to New Zealand’s Cullinane College) that either or both of the following pictures would be more suggestive of Quality than a microscope:

Alfred Bester covers showing 'primordial protomatter' (altered here) from 'Stars' and Rogue Winter from 'Deceivers'

For the “primordial protomatter”
in the picture at left, see
The Diamond Archetype.

Tuesday, July 21, 2009

Tuesday July 21, 2009

Filed under: General — Tags: , — m759 @ 9:00 am

Today's Readings:

Monday, July 20, 2009

Monday July 20, 2009

Filed under: General — Tags: , — m759 @ 7:00 pm
The First Post
in this weblog:

The Diamond Theorem

Related material:

From Sunday’s New York Times, Tom Wolfe on the moon landing forty years ago:

What NASA needs now is the power of the Word. On Darwin’s tongue, the Word created a revolutionary and now well-nigh universal conception of the nature of human beings, or, rather, human beasts. On Freud’s tongue, the Word means that at this very moment there are probably several million orgasms occurring that would not have occurred had Freud never lived. Even the fact that he is proved to be a quack has not diminished the power of his Word.

July 20, 1969, was the moment NASA needed, more than anything else in this world, the Word. But that was something NASA’s engineers had no specifications for. At this moment, that remains the only solution to recovering NASA’s true destiny, which is, of course, to build that bridge to the stars.

Tom Wolfe is the author of “The Right Stuff,” an account of the Mercury Seven astronauts.

Commentary

The Word according to St. John:

Jill St. John, star of 'Diamonds are Forever'

Thursday, July 16, 2009

Thursday July 16, 2009

Filed under: General — m759 @ 4:00 pm

The White Itself

David Ellerman has written that

"The notion of a concrete universal occurred in Plato's Theory of Forms [Malcolm 1991]."

A check shows that Malcolm indeed discussed this notion ("the Form as an Ideal Individual"), but not under the name "concrete universal."

See Plato on the Self-Predication of Forms, by John Malcolm, Oxford U. Press, 1991.

From the publisher's summary:

"Malcolm…. shows that the middle dialogues do indeed take Forms to be both universals and paradigms…. He shows that Plato's concern to explain how the truths of mathematics can indeed be true played an important role in his postulation of the Form as an Ideal Individual."

Ellerman also cites another discussion of Plato published by Oxford:

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

For a literary context, see W. K. Wimsatt, Jr., "The Structure of the Concrete Universal," Ch. 6 in Literary Theory: An Anthology, edited by Julie Rivkin and Michael Ryan, Wiley-Blackwell, 2004.

Other uses of the phrase "concrete universal"– Hegelian and/or theological– seem rather distant from the concerns of Plato and Wimsatt, and are best left to debates between Marxists and Catholics. (My own sympathies are with the Catholics.)

Two views of "the white itself" —

 "So did God cause the big bang?
 Overcome by metaphysical lassitude,
 I finally reach over to my bookshelf
 for The Devil's Bible.
 Turning to Genesis I read:
 'In the beginning
 there was nothing.
 And God said,
 'Let there be light!'
 And there was still nothing,
 but now you could see it.'"
 
 -- Jim Holt, Big-Bang Theology,
    Slate's "High Concept" department 
 
   Fiat Lux, and After

"The world was warm and white when I was born:
Beyond the windowpane the world was white,
A glaring whiteness in a leaded frame,
Yet warm as in the hearth and heart of light."

-- Delmore Schwartz

Friday, June 26, 2009

Friday June 26, 2009

Filed under: General — Tags: , — m759 @ 3:48 pm

Apocatastasis Now

I give you the end of a golden string,
Only wind it into a ball:
It will lead you in at Heavens gate,
Built in Jerusalems wall.
— WILLIAM BLAKE

"In 'Apocatastasis Now: A Very Condensed Reading of William Blake's Jerusalem' (JBSSJ [Journal of the Blake Society at St James's] 6 [2001] 18–25), Susanne Sklar argues that Blake is not apocalyptic but apocatastatic, that is (following a doctrine of Origen and Gregory of Nyssa) he believes that all free creatures will be redeemed by God's universal love."

The Year's Work in English Studies, 2003: Vol. 82, No. 1, pp. 493-547

Related material:

 

Thriller

 

From the website of Philip Pullman,
president of The Blake Society:

 

"I must create a System…"

The Blake Society, 25 October 2005: St James’s Church, Piccadilly

I see that the title of this lecture is given as BLAKE'S DARK MATERIALS. Now in the lecturer's handbook, the second rule says "You need take no obsessive notice of the title that has been announced in advance." Whether Blake's materials are dark or not I couldn't really say, but I am going to talk about Blake, partly, and partly about religion. Appropriate, perhaps, in a place like this, but you might think not appropriate from someone whose reputation is that of a scoffer or mocker or critic of religion; but I haven't come here to scoff or mock. Nor have I come here to recant, as a matter of fact. I'm profoundly interested in religion, and I think it's extremely important to understand it. I've been trying to understand it all my life, and every so often it's useful to put one's thoughts in order; but I shall never like God.

Download the full lecture
(pdf format, 155.62 KB)

 

For more dark materials
from the Halloween season
of 2005 — in fact, from the
  very date of Pullman's lecture–
see Darkness Doubled.

Sunday, June 21, 2009

Sunday June 21, 2009

Filed under: General — m759 @ 12:00 pm
Abstraction

From Mitchell Stephens, author of a website mentioned here yesterday:

“This paper is designed to be a conversation….

The ideas are organized loosely around a single theme: the Roman leader Pompey’s forced entry into the most sacred place of the Jewish temple. At issue are the origins and prevalence of doubt, even at the heart of religion….

The paper will be initially presented, with comments and additions, to the working group on ‘Secularism, Religious Authority, and the Mediation of Knowledge’ of the Center for Religion and Media at New York University on December 8, 2006.”

From the paper itself:

“All Pompey’s intrusion into the Holy of Holies will leave behind is one sentence in Tacitus; still, it is not hard to imagine it as a media show. As he enters this hidden room in the Temple of those weird, unGreek, Asian, tribal Jews, this cosmopolitan, sophisticated Roman is not just the insensitive anthropologist. He wants, to continue our imagining, to display the lack of contents of the Holy of Holies in a museum, to take them, like the treasures of Tutankhamen’s tomb, on tour. This all-powerful Roman wields klieg lights; he brings the press. He exposes. His expedition is something of an exposé. The whole scene feels as if it might have been filmed: like Dorothy’s peek behind the curtain at the diminutive Wizard of Oz. It feels as if it might have been televised: like Geraldo Rivera’s opening of Al Capone’s ‘secret vault.’ Pompey has in common with all journalists a desire to shove a microphone in God’s face. He wants to rant about what he has learned on his blog.

In his desecration of the Holy of Holies, Pompey has with him, in other words, what Jacques Derrida, in his essay ‘Faith and Knowledge,’ calls the ‘powers of abstraction’: ‘deracination, delocalization, disincarnation, formalization, universalizing schematization, objectification, telecommunication etc.'”

Related material:

Log24 entries of
 June 9-11, 2009.

Et cetera, et cetera.

Film posters-- 'Solomon and Sheba,' 'Strange Bedfellows'

Thursday, February 19, 2009

Thursday February 19, 2009

Filed under: General — Tags: — m759 @ 7:07 am

A Sunrise
for Sunrise

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

Rosalind Krauss, “Grids”

Yesterday’s entry featured a rather simple-minded example from Krauss of how the ninefold square (said to be a symbol of Apollo)

The 3x3 grid

may be used to create a graphic design– a Greek cross, which appears also in crossword puzzles:

Crossword-puzzle design that includes Greek-cross elements

Illustration by
Paul Rand
(born Peretz Rosenbaum)

A more sophisticated example
of the ninefold square
in graphic design:

“That old Jew
gave me this here.”

— A Flag for Sunrise  

The 3x3 grid as an organizing frame for Chinese calligraphy. Example-- the character for 'sunrise'
From Paul-Rand.com

Monday, December 15, 2008

Monday December 15, 2008

Filed under: General,Geometry — Tags: — m759 @ 3:09 pm
Happy Birthday,
Julie Taymor

The image “http://www.log24.com/log/pix05B/Gameplayers12.jpg” cannot be displayed, because it contains errors.

"Julie Taymor… will be directing Helen Mirren in a big-screen adaptation of The Tempest. Dame Helen, in a gender-switch from the original, will be playing Prospera, the usurped Duchess possessed of a vast library and magical powers."

— John Murphy at Bardolatry.com on November 21, 2008

A vast library…

On searching for Garden of Eden patterns (GEP's):

"The grid is a staircase to the Universal…."

— Rosalind Krauss, quoted here on Weyl's birthday, 2004

"I find the whole topic of GEPs a deeply interesting one, from many viewpoints: mathematical, philosophical, physical….

… the obvious problem is, that the required computational time is growing rapidly with the size of the grid, and even for a small grid, like 4×4 (=16 cells) there are 216=65536 possible patterns…."

cateye at RichardDawkins.net

… and magical powers

The date of cateye's post was Sunday, October 21, 2007.

For related material see Log24 on Sunday, October 21, 2007.
 

Sunday, November 30, 2008

Sunday November 30, 2008

Filed under: General,Geometry — m759 @ 10:31 am
Abstraction and Faith
 

From Sol LeWitt: A Retrospective, edited by Gary Garrels, Yale University Press, 2000, p. 376:

THE SQUARE AND THE CUBE
by Sol LeWitt

The best that can be said for either the square or the cube is that they are relatively uninteresting in themselves. Being basic representations of two- and three-dimensional form, they lack the expressive force of other more interesting forms and shapes. They are standard and universally recognized, no initiation being required of the viewer; it is immediately evident that a square is a square and a cube a cube. Released from the necessity of being significant in themselves, they can be better used as grammatical devices from which the work may proceed.

Reprinted from Lucy R. Lippard et al., "Homage to the Square," Art in America 55, No. 4 (July-August 1967): 54. (LeWitt's contribution was originally untitled.)

A vulgarized version
of LeWitt's remarks
appears on a webpage of
the National Gallery of Art.

Today's Sermon

"Closing the Circle on Abstract Art"

On Kirk Varnedoe's National Gallery lectures in 2003 (Philip Kennicott, Washington Post, Sunday, May 18, 2003):

"Varnedoe's lectures were ultimately about faith, about his faith in the power of abstraction, and abstraction as a kind of anti-religious faith in itself."

For related remarks on abstraction perhaps less easily vulgarized than those of LeWitt, see Finite Geometry of the Square and Cube.

For the relation of this sort of geometry to faith, see All Hallows' Eve, 2006.

Thursday, October 30, 2008

Thursday October 30, 2008

Filed under: General — m759 @ 5:01 am
From the Mountaintop

Katherine Neville, author of perhaps the greatest bad novel of the twentieth century, The Eight, has now graced a new century with her sequel, titled The Fire. An excerpt:

“Our family lodge had been built at about this same period in the prior century, by neighboring tribes, for my great-great-grandmother, a pioneering mountain lass. Constructed of hand-hewn rock and massive tree trunks chinked together, it was a huge log cabin that was shaped like an octagon– patterned after a hogan or sweat lodge– with many-paned windows facing in each cardinal direction, like a vast, architectural compass rose.
……..
From here on the mountaintop, fourteen thousand feet atop the Colorado Plateau, I could see the vast, billowing sea of three-mile-high mountain peaks, licked by the rosy morning light. On a clear day like this, I could see all the way to Mount Hesperus– which the Diné call Dibé Nitsaa: Black Mountain. One of the four sacred mountains created by First Man and First Woman.

Together with Sisnaajinii, white mountain (Mt. Blanca) in the east; Tsoodzil, blue mountain (Mt. Taylor) in the south, and Dook’o’osliid, yellow mountain (San Francisco Peaks) in the west, these four marked out the four corners of Dinétah– ‘Home of the Diné,’ as the Navajo call themselves.

And they pointed as well to the high plateau I was standing on: Four Corners, the only place in the U.S. where four states– Colorado, Utah, New Mexico, and Arizona– come together at right angles to form a cross.”


Related material
(Oct. 14, 2004):

The Eight

Lest the reader of the previous entry mistakenly take Katherine Neville’s book The Eight more seriously than Fritz Leiber’s greatly superior writings on eightness, here are two classic interpretations of Leiber’s “spider” or “double cross” symbol:

Greek: The Four Elements

Aristotle:
The 4 elements and
the 4 qualities
(On Generation and
Corruption, II, 3
)

Chinese: The Eight Trigrams

Richard Wilhelm:
The 8 trigrams
(Understanding
the I Ching
,
154-175)

The eight-rayed star may be taken
as representing what is known
in philosophy as a “universal.”

See also

The Divine Universals,

Plato, Pegasus, and the Evening Star,

A Little Extra Reading, and

Quine in Purgatory.

Wednesday, October 15, 2008

Wednesday October 15, 2008

Filed under: General,Geometry — Tags: — m759 @ 5:01 am

Links for the birthday of the late mathematician Bernhard H. Neumann:

MacTutor biography of Neumann

Variety (Universal Algebra) at Wikipedia

Preface to Varieties of Groups (1967), by Hanna Neumann

Biography (1974 obituary) of Hanna Neumann

Peter M. Neumann home page

Some related notes on algebra suggested by finite geometry:

Dynamic and algebraic compatibility of groups (1985 Dec. 11)

Groups related by a nontrivial identity (1985 Nov. 17)

Transformations over a bridge (1983 Aug. 16)

Group identity algebras (1983 Aug. 4)

I have no idea if any work has been done in this area since my own efforts in 1983-1985.

Wednesday, June 25, 2008

Wednesday June 25, 2008

Filed under: General — m759 @ 2:02 am
Born 100 years ago today:

Willard Van Orman Quine, picture from cover of his autobiography

From A Logical Point of View,  Harvard U. Press, 1980, p. 72
From A Logical Point of View,  Harvard U. Press, 1980, p. 73
Other approaches to the
eight-ray star figure

Figure by Quine for an argument against univesals in 'From a Logical Point of View'

have been sketched in
various Log24 entries.

See, for instance, the
June 21 entries on
the Kyoto Prize for
arts and philosophy.
Quine won this prize
 in 1996.

Quine’s figure, cited in an
argument against universals,
is also a classic symbol for
the morning or evening star.

This year’s winner http://www.log24.com/images/asterisk8.gif
of the Kyoto Prize has
a more poetic approach
to philosophy:

“… the object sets up
 a kind of frame or space or field
   within which there can be epiphany.”

For one such frame or space,
a Mexican cantina, see
Shining Forth.

See also Damnation Morning and
The Devil and Wallace Stevens.

http://www.log24.com/images/asterisk8.gif Charles Taylor.  See
“Epiphanies of Modernism,”
Chapter 24 of Sources of the Self
  (Cambridge U. Press, 1989, p. 477)

Sunday, April 13, 2008

Sunday April 13, 2008

Filed under: General,Geometry — Tags: , , — m759 @ 7:59 am
The Echo
in Plato’s Cave

“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy.”

— Simon Blackburn, Think (Oxford, 1999)

Michael Harris, mathematician at the University of Paris:

“… three ‘parts’ of tragedy identified by Aristotle that transpose to fiction of all types– plot (mythos), character (ethos), and ‘thought’ (dianoia)….”

— paper (pdf) to appear in Mathematics and Narrative, A. Doxiadis and B. Mazur, eds.

Mythos —

A visitor from France this morning viewed the entry of Jan. 23, 2006: “In Defense of Hilbert (On His Birthday).” That entry concerns a remark of Michael Harris.

A check of Harris’s website reveals a new article:

“Do Androids Prove Theorems in Their Sleep?” (slighly longer version of article to appear in Mathematics and Narrative, A. Doxiadis and B. Mazur, eds.) (pdf).

From that article:

“The word ‘key’ functions here to structure the reading of the article, to draw the reader’s attention initially to the element of the proof the author considers most important. Compare E.M. Forster in Aspects of the Novel:

[plot is] something which is measured not be minutes or hours, but by intensity, so that when we look at our past it does not stretch back evenly but piles up into a few notable pinnacles.”

Ethos —

“Forster took pains to widen and deepen the enigmatic character of his novel, to make it a puzzle insoluble within its own terms, or without. Early drafts of A Passage to India reveal a number of false starts. Forster repeatedly revised drafts of chapters thirteen through sixteen, which comprise the crux of the novel, the visit to the Marabar Caves. When he began writing the novel, his intention was to make the cave scene central and significant, but he did not yet know how:

When I began a A Passage to India, I knew something important happened in the Malabar (sic) Caves, and that it would have a central place in the novel– but I didn’t know what it would be… The Malabar Caves represented an area in which concentration can take place. They were to engender an event like an egg.”

E. M. Forster: A Passage to India, by Betty Jay

Dianoia —

Flagrant Triviality
or Resplendent Trinity?

“Despite the flagrant triviality of the proof… this result is the key point in the paper.”

— Michael Harris, op. cit., quoting a mathematical paper

Online Etymology Dictionary
:

flagrant
c.1500, “resplendent,” from L. flagrantem (nom. flagrans) “burning,” prp. of flagrare “to burn,” from L. root *flag-, corresponding to PIE *bhleg (cf. Gk. phlegein “to burn, scorch,” O.E. blæc “black”). Sense of “glaringly offensive” first recorded 1706, probably from common legalese phrase in flagrante delicto “red-handed,” lit. “with the crime still blazing.”

A related use of “resplendent”– applied to a Trinity, not a triviality– appears in the Liturgy of Malabar:

http://www.log24.com/log/pix08/080413-LiturgyOfMalabar.jpg

The Liturgies of SS. Mark, James, Clement, Chrysostom, and Basil, and the Church of Malabar, by the Rev. J.M. Neale and the Rev. R.F. Littledale, reprinted by Gorgias Press, 2002

On Universals and
A Passage to India:

 

“”The universe, then, is less intimation than cipher: a mask rather than a revelation in the romantic sense. Does love meet with love? Do we receive but what we give? The answer is surely a paradox, the paradox that there are Platonic universals beyond, but that the glass is too dark to see them. Is there a light beyond the glass, or is it a mirror only to the self? The Platonic cave is even darker than Plato made it, for it introduces the echo, and so leaves us back in the world of men, which does not carry total meaning, is just a story of events.”

 

— Betty Jay,  op. cit.

 

http://www.log24.com/log/pix08/080413-Marabar.jpg

Judy Davis in the Marabar Caves

In mathematics
(as opposed to narrative),
somewhere between
a flagrant triviality and
a resplendent Trinity we
have what might be called
“a resplendent triviality.”

For further details, see
A Four-Color Theorem.”

Wednesday, December 19, 2007

Wednesday December 19, 2007

Filed under: General — Tags: — m759 @ 9:00 am
Tutelary Figures

An entry in memory of
Dr. Joseph L. Henderson,
Jungian analyst, who died
on Nov. 17 at 104

(An obituary appears in
today’s New York Times.)


Some remarks by Dr. Henderson
:

The myth of the hero is the most common and the best known myth in the world… classical mythology… Greece and Rome… Middle Ages… Far East… contemporary primitive tribes. It also appears in dreams… obvious dramatic… profound… importance. P. 101

… structurally very similar… universal pattern… over and over again… a tale of… miraculous… humble birth… early proof of superhuman strength… rapid rise to prominence… triumphant struggle with the forces of evil… fallibility to the sin of pride (hybris)… and his fall through betrayal or a “heroic” sacrifice that ends in his death. P. 101

… another important characteristic… provides a clue… the early weakness… is balanced by… strong “tutelary” figures… who enable him to perform the superhuman tasks that he cannot accomplish unaided. Theseus had Poseidon… Perseus had Athena… Achilles had Cheiron… the wise centaur, as his tutor. P. 101 

And Stan Carlisle had
Dr. Lilith Ritter
:

http://www.log24.com/log/pix07A/071219-StanLilith.jpg

See also the noir entry on
“Nightmare Alley” for
Winter Solstice 2002,
as well as a solstice-related
commentary on I Ching
Hexagram 41, Decrease.

Related material:

http://www.log24.com/log/pix07A/071219-Authors2.jpg

Dr. Dyane N. Sherwood and
Dr. Joseph L. Henderson, authors
of Transformation of the Psyche
(Routledge, Nov. 7, 2003)

Dr. Henderson is said to
have been, in his youth,
a student of Thornton Wilder
as well as of Dr. Jung.

Wednesday, August 22, 2007

Wednesday August 22, 2007

Filed under: General — m759 @ 10:31 am
The Enchanted Twilight

The Associated Press
Tuesday, August 21, 2007

GENEVA: British-born author Magdalen Nabb, whose crime novels about a quirky Italian investigator were acclaimed by her idol Georges Simenon, has died, her Swiss publishing house said Tuesday. She was 60.

Nabb, who also wrote stories for children and young adults, died of a stroke on Saturday [August 18, 2007] in Florence, Italy, where she had lived and worked since 1975, said Diogenes Verlag AG of Zurich….

Nabb published 13 books for children and young adults, including “The Enchanted Horse,” “Twilight Ghost” and the “Josie Smith” series about a “girl who always has plenty of ideas.”

See also, from the
date of Nabb’s death,

Happy Birthday,
Robert Redford:
 A Concrete Universal
.

No matter how it’s done,
you won’t like it.

— Robert Redford to     
  Robert M. Pirsig in Lila 

Material related to
Twilight Ghost:

Logos and Epiphany
and
Fire Chaplain.

“A twilight ghost doesn’t come to
frighten people, though it might
want to tell them something.
A twilight ghost is just
     a kind of long lost memory….”

Magdalen Nabb

Saturday, August 18, 2007

Saturday August 18, 2007

Filed under: General — m759 @ 7:20 pm
A Concrete Universal

What on earth is
a ‘concrete universal’?

Said to be an annotation
(undated) by Robert M. Pirsig
of A History of Philosophy,
by Frederick Copleston,
Society of Jesus.

No matter how it’s done,
you won’t like it.

— Robert Redford to     
  Robert M. Pirsig in Lila    


“In chapters 19 and 20 of LILA there is a discussion about the possibility of making Zen and the Art into a movie. It opens with a scene where Robert Redford, who ‘really would like to have the film rights,’ comes to meet and negotiate with Phaedrus in his New York City hotel room. Phaedrus tells the famous actor that he can have the rights to the book, but maybe that’s just because he’s star-struck and doesn’t like to haggle. Under his excitement, Phaedrus has a bad feeling about it. He tells us that he’s been warned by several different people not to allow such a film to be made. Even Redford warned him not to do it. So what’s the problem? As it’s put at the end of that discussion, ‘Films are social media; his book was largely intellectual. That was the center of the problem.'”

David Buchanan at robertpirsig.org

“The insight is constituted precisely by ‘seeing’ the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete.”

— Fr. Brian Cronin‘s Foundations of Philosophy, Ch. 2, “Identifying Direct Insights,” quoted in Ideas and Art

See also Smiles of a Summer Evening, the current issue of TIME, the time of this entry (7:20:11 PM ET), and Plato, Pegasus, and the Evening Star.

Tuesday, August 7, 2007

Tuesday August 7, 2007

Filed under: General — Tags: — m759 @ 8:00 am
The Horse Whisperer

Scarlett Johansson and friend in The Horse Whisperer

Scarlett Johansson and friend
in “The Horse Whisperer” (1998)

Thanks to University Diaries (Aug. 6) for the following:

“‘The University of Sydney has ordered an independent review into allegations that the dean of the Conservatorium of Music hired a horse whisperer to conduct management workshops.’ [Are you, like UD, a bit vague on exactly what a horse whisperer is? And are you having trouble figuring out what a horse whisperer would have to offer a management workshop? But then, what exactly is a management workshop? Read on.]”

For some background on horse whispering and management workshops, see IABC Steal Sheet, March 2004.

Related material:

The recent Log24 entries

University Diaries:
“God, isn’t there already
enough crap in this story?”

See also Log24,
Dec. 10, 2003:

Putting Descartes Before Dehors

      

“Descartes déclare que
c’est en moi, non hors de moi,
en moi, non dans le monde,
que je pourrais voir
si quelque chose existe
hors de moi.”

ATRIUM, Philosophie     

For further details,
see ART WARS.

Monday, August 6, 2007

Monday August 6, 2007

Filed under: General — Tags: — m759 @ 8:00 am
The Divine Universals

"The tigers of wrath          
 are wiser than                
 the horses of instruction."

— William Blake,
Proverbs of Hell

From Shining Forth:

  The Place of the Lion, by Charles Williams, 1931, Chapter Eight:

"Besides, if this fellow were right, what harm would the Divine Universals do us? I mean, aren't the angels supposed to be rather gentle and helpful and all that?"

"You're doing what Marcellus warned you against… judging them by English pictures. All nightgowns and body and a kind of flacculent sweetness. As in cemeteries, with broken bits of marble. These are Angels– not a bit the same thing. These are the principles of the tiger and the volcano and the flaming suns of space."

 Under the Volcano, Chapter Two:

"But if you look at that sunlight there, then perhaps you'll get the answer, see, look at the way it falls through the window: what beauty can compare to that of a cantina in the early morning? Your volcanoes outside? Your stars– Ras Algethi? Antares raging south southeast? Forgive me, no." 

 A Spanish-English dictionary:

lucero m.
morning or evening star:
any bright star….
hole in a window panel
     for the admission of light….

Look at the way it
falls through the window….

— Malcolm Lowry

How art thou fallen from heaven,
O Lucifer, son of the morning!
— Isaiah 14:12

For more on Spanish
and the evening star,
see Plato, Pegasus, and
the Evening Star.

 Symmetry axes
of the square:

Symmetry axes of the square

(See Damnation Morning.)

From the cover of the
 Martin Cruz Smith novel
Stallion Gate:

Atom on cover of Stallion

"That old Jew
gave me this here."

Dialogue from the
Robert Stone novel
A Flag for Sunrise.

Related material:

A Mass for Lucero,

Log24, Sept. 13, 2006

Mathematics, Religion, Art

— and this morning's online
New York Times obituaries:

Cardinal Lustiger of Paris and jazz pianist Sal Mosca, New York Times obituaries on August 6, 2007

The above image contains summary obituaries for Cardinal Lustiger, Archbishop of Paris, 1981-2005, and for Sal Mosca, jazz pianist and teacher. In memory of the former, see all of the remarks preceding the image above. In memory of the latter, the remarks of a character in Martin Cruz Smith's Stallion Gate on jazz piano may have some relevance:

"I hate arguments. I'm a coward. Arguments are full of words, and each person is sure he's the only one who knows what the words mean. Each word is a basket of eels, as far as I'm concerned. Everybody gets to grab just one eel and that's his interpretation and he'll fight to the death for it…. Which is why I love music. You hit a C and it's a C and that's all it is. Like speaking clearly for the first time. Like being intelligent. Like understanding. A Mozart or an Art Tatum sits at the piano and picks out the undeniable truth."

Wednesday, July 18, 2007

Wednesday July 18, 2007

Filed under: General — m759 @ 6:28 pm
Reminder

Reuters News Agency,
Wed., July 18, 2007,
3:48 PM EDT

By Mauricio Savarese

SAO PAULO (Reuters) – The flames from Brazil’s worst plane crash were contained around dawn on Wednesday, but the smell of smoke and death wafted over travelers at Sao Paulo’s airport as a reminder of disaster….

The airport resumed flights on an alternate runway.

Despite the deterioration of Brazil’s air safety record over the past year, Guilherme Braghetto, 72, showed little concern for his son, whom he brought to the airport for a flight to Goiania.

‘I feel for those who lost loved ones, but I don’t think lightning so strong will hit twice,’ he said.

On September 29, 2006, a Boeing 737 operated by Brazilian carrier Gol Linhas Aereas Inteligentes crashed after clipping wings with a Legacy business jet over the Amazon rainforest, killing 154 people.

Elsewhere:

Log24, Sept. 28, 2006
:

The image “http://www.log24.com/music/images/Keys-Piano.gif” cannot be displayed, because it contains errors.

Click on picture for a midi.

“…consonant intervals
as an example of alleged
perceptual universals.’

Related material on universals
suitable for today, the Feast of
St. Michael and All Angels:
Shining Forth….”

The New Yorker, issue dated
July 23, 2007, page 42:

“While out-of-body experiences
have the character of
a perceptual illusion
(albeit a complex and
singular one), near-death
experiences have all the
hallmarks of mystical
experience, as William
James defines it….”

— Oliver Sacks,
A Bolt from the Blue

The New Yorker, issue dated
July 23, 2007, page 70:

IMAGE- Barsotti cartoon, 'You're a good listener'

Wednesday July 18, 2007

Filed under: General — m759 @ 7:03 am
Burning Bright

“What is real?”
Pope Benedict XVI
in Brazil on May 13

Yesterday in
the Keystone State:

PA Lottery July 17, 2007: Mid-day 853, Evening 856

This suggests– via a search on “853-856” + “universals”– that we consult pages 853-856 in The Library of America’s William James: Writings 1902-1910.

Beginning on page 853 in this book, and ending on page 856, is an excerpt from a James address that the editor has titled…

The Tigers in India

“There are two ways of knowing things, knowing them immediately or intuitively, and knowing them conceptually or representatively.  Altho such things as the white paper before our eyes can be known intuitively, most of the things we know, the tigers now in India, for example, or the scholastic system of philosophy, are known only representatively or symbolically.

Suppose, to fix our ideas, that we take first a case of conceptual knowledge, and let it be our knowledge of the tigers in India, as we sit here.  Exactly what do we mean by saying that we here know the tigers? ….

Most men would answer that what we mean by knowing the tigers is having them, however absent in body, become in some way present to our thought…. At the very least, people would say that what we mean by knowing the tigers is mentally pointing towards them as we sit here….

… The pointing of our thought to the tigers is known simply and solely as a procession of mental associates and motor consequences that follow on the thought, and that would lead harmoniously, if followed out, into some ideal or real context, or even into the immediate presence, of the tigers….

… In all this there is no self-transcendency in our mental images taken by themselves. They are one phenomenal fact; the tigers are another; and their pointing to the tigers is a perfectly commonplace intra-experiential relation, if you once grant a connecting world to be there.  In short, the ideas and the tigers are in themselves as loose and separate, to use Hume’s language, as any two things can be, and pointing means here an operation as external and adventitious as any that nature yields.

I hope you may agree with me now that in representative knowledge there is no special inner mystery, but only an outer chain of physical or mental intermediaries connecting thought and thing. To know an object is here to lead to it through a context which the world supplies….

Let us next pass on to the case of immediate or intuitive acquaintance with an object, and let the object be the white paper before our eyes…. What now do we mean by ‘knowing’ such a sort of object as this?  For this is also the way in which we should know the tiger if our conceptual idea of him were to terminate by having led us to his lair?

… the paper seen and the seeing of it are only two names for one indivisible fact which, properly named, is the datum, the phenomenon, or the experience. The paper is in the mind and the mind is around the paper, because paper and mind are only two names that are given later to the one experience, when, taken in a larger world of which it forms a part, its connections are traced in different directions.1

James, Writings 1902-1910, page 856

The same volume also contains
James’s The Varieties of
Religious Experience.

“The Tigers in India” is
only a part of a 20-page
James address originally titled
The Knowing of Things Together
(my emphasis).

Friday, July 13, 2007

Friday July 13, 2007

Filed under: General,Geometry — m759 @ 7:00 am
Today’s birthday:
Harrison Ford is 65.

The image “http://www.log24.com/log/pix07/070713-Ford2.jpg” cannot be displayed, because it contains errors.

“Three times the concentred
     self takes hold, three times
The thrice concentred self,
     having possessed
The object, grips it
     in savage scrutiny,
Once to make captive,
     once to subjugate
Or yield to subjugation,
     once to proclaim
The meaning of the capture,
     this hard prize,
Fully made, fully apparent,
     fully found.”

— “Credences of Summer,” VII,
    by Wallace Stevens, from
    Transport to Summer (1947)

“It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….


Plato clearly loved them both, both mathematics and poetry.  But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry.  Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto.  Let none ignorant of geometry enter.  This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge.  Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason.  Mathematics is the threshold we cross to pass into the ideal, the truly real.”

   — Rebecca Goldstein, Mathematics and the Character of Tragedy

Related material:

Previous entry,
entries of July 1, 2007,
and A Little Story
(9/30/06)

Friday, July 6, 2007

Friday July 6, 2007

Filed under: General — m759 @ 8:00 pm
Mearingstone, or:
 
“Last to the Lost,”
continued from
July 1, 2007


Finnegans Wake 293:

Vieus Von DVbLIn, ’twas one of dozedeams
a darkies ding in dewood) the Turnpike under
the Great Ulm (with Mearingstone in Fore
ground). 1 Given now ann linch you take enn
all. Allow me! And, heaving alljawbreakical
expressions out of old Sare Isaac’s 2 universal
of specious aristmystic unsaid, A is for Anna
like L is for liv. Aha hahah, Ante Ann you’re
apt to ape aunty annalive! Dawn gives rise.
Lo, lo, lives love! Eve takes fall. La, la, laugh
leaves alass! Aiaiaiai, Antiann, we’re last to
the lost, Loulou! Tis perfect. Now (lens

“with Mearingstone in Fore ground….
we’re last to the lost, Loulou!”

Desconvencida at Blogspot -- Monolito -- Midnight July 1-2, 2007

Midnight, July 1-2, 2007
Click on image for details.

Thursday, July 5, 2007

Thursday July 5, 2007

Filed under: General,Geometry — Tags: — m759 @ 7:11 pm

In Defense of
Plato’s Realism

(vs. sophists’ nominalism–
see recent entries.)

Plato cited geometry,
notably in the Meno,
in defense of his realism.
Consideration of the
Meno’s diamond figure
leads to the following:

The Eightfold Cube and its Inner Structure

Click on image for details.

As noted in an entry,
Plato, Pegasus, and
the Evening Star,

linked to
at the end of today’s
previous entry,
the “universals”
of Platonic realism
are exemplified by
the hexagrams of
the I Ching,
which in turn are
based on the seven
trigrams above and
on the eighth trigram,
of all yin lines,
not shown above:

Trigram of K'un, the Receptive

K’un
The Receptive

_____________________________________________

Update of Nov. 30, 2013:

From  a little-known website in Kuala Lumpur:
(Click to enlarge.)

The remarks on Platonic realism are from Wikipedia.
The eightfold cube is apparently from this post.

Thursday July 5, 2007

Filed under: General — Tags: — m759 @ 12:48 pm
Their Name is Legion

“Although it may not at first be obvious,
the substitution for real religions
 of a religion drained of particulars
is of a piece with the desire to
exorcise postmodernism.”

Stanley Fish, July 2002

The previous entry linked to an entry of June 2002 that attacked the nominalism of Stanley Fish.  Here is another such attack:

From “Stanley Fish: The Critic as Sophist,” by R.V. Young, in Modern Age, June 22, 2003:

In one of the definitive works of conservatism in the twentieth century, Richard Weaver designates the rise of nominalism as a critical turn in the emergence of the intellectual and cultural disintegration associated with liberalism, which it is the business of a reviving conservatism to contest: “The defeat of logical realism in the great medieval debate was the crucial event in the history of Western culture; from this flowed those acts which issue now in modern decadence.” It is nominalism that provides the intellectual foundation– if a paradox may be hazarded– for the attack by Fish and numerous others (their name is Legion) on the very idea of intellectual foundations:  

It was William of Occam who propounded the fateful doctrine of nominalism, which denies that universals have real existence. His triumph tended to leave universal terms mere names serving our  convenience. The issue ultimately involved is whether there is a  source of truth higher than, and independent of, man; and the answer to the question is decisive for one’s view of the nature and destiny of humankind. The practical result of nominalist philosophy is to banish the reality which is perceived by the intellect and to posit as reality that which is perceived by the senses. (4)

(4). Ideas Have Consequences (Chicago and London, 1948), 3.

R.V. YOUNG is Professor of English at North Carolina State University and author of At War With the Word and Doctrine and Devotion in Seventeenth-Century Poetry (2000).


Related material:

Simon Blackburn on
Plato and sophists,
realism and nominalism
(previous entry)

and

Plato, Pegasus, and

the Evening Star

Tuesday, July 3, 2007

Tuesday July 3, 2007

Filed under: General — m759 @ 9:29 pm
The Ignorance
of Stanley Fish

(continued from
June 18, 2002)

The “ignorance” referred to
is Fish’s ignorance of the
philosophical background
of the words
“particular” and “universal.”

Postmodern Warfare:
The Ignorance of Our
Warrior Intellectuals,”
by Stanley Fish,
Harper’s Magazine,
July 2002, contains
the following passages:

“The deepest strain in a religion is the particular and particularistic doctrine it asserts at its heart, in the company of such pronouncements as ‘Thou shalt have no other Gods before me.’ Take the deepest strain of religion away… and what remains are the surface pieties– abstractions without substantive bite– to which everyone will assent because they are empty, insipid, and safe. It is this same preference for the vacuously general over the disturbingly particular that informs the attacks on college and university professors who spoke out in ways that led them to be branded as outcasts by those who were patrolling and monitoring the narrow boundaries of acceptable speech. Here one must be careful, for there are fools and knaves on all sides.”

“Although it may not at first be obvious, the substitution for real religions of a religion drained of particulars is of a piece with the desire to exorcise postmodernism.”

“What must be protected, then, is the general, the possibility of making pronouncements from a perspective at once detached from and superior to the sectarian perspectives of particular national interests, ethnic concerns, and religious obligations; and the threat to the general is posed by postmodernism and strong religiosity alike, postmodernism because its critique of master narratives deprives us of a mechanism for determining which of two or more fiercely held beliefs is true (which is not to deny the category of true belief, just the possibility of identifying it uncontroversially), strong religiosity because it insists on its own norms and refuses correction from the outside. The antidote to both is the separation of the private from the public, the establishing of a public sphere to which all could have recourse and to the judgments of which all, who are not criminal or insane, would assent. The point of the public sphere is obvious: it is supposed to be the location of those standards and measures that belong to no one but apply to everyone. It is to be the location of the universal. The problem is not that there is no universal–the universal, the absolutely true, exists, and I know what it is. The problem is that you know, too, and that we know different things, which puts us right back where we were a few sentences ago, armed with universal judgments that are irreconcilable, all dressed up and nowhere to go for an authoritative adjudication.

What to do? Well, you do the only thing you can do, the only honest thing: you assert that your universal is the true one, even though your adversaries clearly do not accept it, and you do not attribute their recalcitrance to insanity or mere criminality–the desired public categories of condemnation–but to the fact, regrettable as it may be, that they are in the grip of a set of beliefs that is false. And there you have to leave it, because the next step, the step of proving the falseness of their beliefs to everyone, including those in their grip, is not a step available to us as finite situated human beings. We have to live with the knowledge of two things: that we are absolutely right and that there is no generally accepted measure by which our rightness can be independently validated. That’s just the way it is, and we should just get on with it, acting in accordance with our true beliefs (what else could we do?) without expecting that some God will descend, like the duck in the old Groucho Marx TV show, and tell us that we have uttered the true and secret word.”

From the public spheres
of the Pennsylvania Lottery:

PA Lottery logo

PA Lottery July 3, 2007: Mid-day 105, Evening 268

105 —

Log24 on 1/05:

“‘From your lips
to God’s ears,’
 goes the old
Yiddish wish.

 The writer, by contrast,
tries to read God’s lips
and pass along
the words….”

— Richard Powers   

268 —

This is a page number
that appears, notably,
in my June 2002
journal entry on Fish
,
and again in an entry,
The Transcendent Signified,”
dated July 26, 2003,
that argues against
Fish’s school, postmodernism,
 and in favor of what the pomos
call “logocentrism.”

Page 268
 
of Simon Blackburn’s Think
(Oxford Univ. Press, 1999):

“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato’s (realist) reaction to the sophists (nominalists). What is often called ‘postmodernism’ is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth.”

Fish may, if he wishes,
regard the particular
page number 268 as
delivered– five years late,
but such is philosophy–
by Groucho’s
winged messenger
in response to
Fish’s utterance of the
  “true and secret word”–
namely, “universal.”

When not arguing politics,
Fish, though from
a Jewish background, is
 said to be a Milton scholar.
Let us therefore hope he
is by now, or comes to be,
aware of the Christian
approach to universals–
an approach true to the
philosophical background
sketched in 1999 by
Blackburn and made
particular in a 1931 novel
 by Charles Williams,
The Place of the Lion.

Sunday, July 1, 2007

Sunday July 1, 2007

Filed under: General,Geometry — m759 @ 1:27 pm
Mozart
by the Numbers

PA Lottery June 30, 2007: Mid-day 221, Evening 127

2/21


A Superficial Beauty:

Structural Certainty:

murphy plant, murphy grow, a maryamyria- 10
meliamurphies, in the lazily eye of his lapis, 11

12
Geometry lesson 13

14
Uteralterance or Vieus Von DVbLIn, ’twas one of dozedeams 15
the Interplay of a darkies ding in dewood) the Turnpike under 16
Bones in the the Great Ulm (with Mearingstone in Fore 17
Womb. ground). 1 Given now ann linch you take enn 18
all. Allow me! And, heaving alljawbreakical 19
expressions out of old Sare Isaac’s 2 universal 20
The Vortex. of specious aristmystic unsaid, A is for Anna 21
Spring of Sprung like L is for liv. Aha hahah, Ante Ann you’re 22
Verse. The Ver- apt to ape aunty annalive! Dawn gives rise. 23
tex. Lo, lo, lives love! Eve takes fall. La, la, laugh 24
leaves alass! Aiaiaiai, Antiann, we’re last to 25
the lost, Loulou! Tis perfect. Now (lens 26

Finnegans Wake, Book II,
    Episode 2, page 293


1/27

“Mozart is a menace to musical progress, a relic of rituals that were losing relevance in his own time and are meaningless to ours. Beyond a superficial beauty and structural certainty, Mozart has nothing to give to mind or spirit in the 21st century. Let him rest.” —Norman Lebrecht

Monday, May 21, 2007

Monday May 21, 2007

Filed under: General — Tags: , — m759 @ 4:48 am
Down the
Up Staircase

Commentary on a
Jonathan Borofsky
painting in the
May 21 New Yorker:

IMAGE- Borofsky's 'Four Gods' and related structures
 
Commentary

"… Mondrian and Malevich
are not discussing canvas
or pigment or graphite
or any other form of matter.
They are talking about about
Being or Mind or Spirit.
From their point of view,
the grid is a staircase
to the Universal…."

Rosalind Krauss
 

Friday, May 11, 2007

Friday May 11, 2007

Filed under: General — m759 @ 11:30 pm
Today’s Lottery Commentary:

Lonesome No More!

In keeping with the spirit of previous Log24 entries, here is today’s Pennsylvania Lottery commentary.  This afternoon’s entry suggests an interpretation of today’s numbers as comments on the new film “Georgia Rule.”

Pennsylvania Lottery today:
Mid-day 384
Evening 952

Today’s mid-day number, 384, is the number of symmetries of the tesseract, a geometric figure illustrated on the cover of the novel The Gameplayers of Zan (see, for instance, May 10, 2007).  That novel suggests an interpretation of today’s evening number, 952, as addressing (literally) the subject of Life.

See the address mathforum.org/library/view/952.html.

From that address:

“The Game of Life is played on a field of cells, each of which has eight neighbors (adjacent cells). A cell is either occupied (by an organism) or not. The rules for deriving a generation from the previous one are these: Death – If an occupied cell has 0, 1, 4, 5, 6, 7, or 8 occupied neighbors, the organism dies (0, 1: of loneliness; 4 thru 8: of overcrowding). Survival – If an occupied cell has two or three neighbors, the organism survives to the next generation. Birth – If an unoccupied cell has three occupied neighbors, it becomes occupied.”

Relevance to the film “Georgia Rule”: lonesomeness, generations, and the Lord’s name–

Georgia is a “lonesome and decent widow in wholesome Hull, Idaho…. her framed motto is ‘Count Your Blessings’ and she’s ready to ram [a] soap bar into your mouth if you insult the Lord’s name.” –David Elliott, San Diego Union-Tribune, May 11, 2007

There is not universal agreement on just what is the Lord’s name. Perhaps it includes the number 952.

From The Gameplayers of Zan:

“The Game in the Ship cannot be approached as a job, a vocation, a career, or a recreation. To the contrary, it is Life and Death itself at work there. In the Inner Game, we call the Game Dhum Welur, the Mind of God. And that Mind is a terrible mind, that one may not face directly and remain whole. Some of the forerunners guessed it long ago– first the Hebrews far back in time, others along the way, and they wisely left it alone, left the Arcana alone.”

From Bartlett’s Familiar Quotations:

“Nothing can be produced out of nothing.”
— 10th edition, 1919, page 952

See also “Zen and Language Games
and “Is Nothing Sacred?

Saturday, February 17, 2007

Saturday February 17, 2007

Filed under: General — m759 @ 9:00 am

Zen Mind, Empty Mind

Introduction:

A mathematician hopes for more exciting vulgarizations of his subject–

“I would hope that clever writers might point out how mathematics is altering our lifestyles and do it in a manner that would not lead Garfield the Cat to say ‘ho hum.'”

— Philip J. Davis, “The Media and Mathematics Look at Each Other” (pdf), Notices of the American Mathematical Society, March 2006

Part I:

“Our mathematical skills are assumed to derive from a special ‘mental vacuum state,’ whose origin is explained on the basis of anthropic and biological arguments, taking into account the need for the informational processes associated with such a state to be of a life-supporting character.  ESP is then explained in terms of shared ‘thought bubbles’ generated by the participants out of the mental vacuum state.”

— Nobel laureate Brian D. Josephson, Department of Physics, University of Cambridge, “String Theory, Universal Mind, and the Paranormal” (Dec. 2003)

Part II:

The image “http://www.log24.com/log/pix07/070217-Garfield2.jpg” cannot be displayed, because it contains errors.

Thanks to “Q” at Peter Woit’s weblog
for the link to Josephson.

Wednesday, January 31, 2007

Wednesday January 31, 2007

Filed under: General — Tags: — m759 @ 3:09 pm
Ontotheology

“At times, bullshit can only be
countered with superior bullshit.”
Norman Mailer

“It may be that universal history is the
history of the different intonations
given a handful of metaphors.”
— Jorge Luis Borges (1951),
“The Fearful Sphere of Pascal,”
in Labyrinths, New Directions, 1962

“Before introducing algebraic semiotics and structural blending, it is good to be clear about their philosophical orientation. The reason for taking special care with this is that, in Western culture, mathematical formalisms are often given a status beyond what they deserve. For example, Euclid wrote, ‘The laws of nature are but the mathematical thoughts of God.'”

— Joseph A. Goguen, “Ontology, Society, and Ontotheology” (pdf)

Goguen does not give a source for this alleged “thoughts of God” statement.

A Web search for the source leads only to A Mathematical Journey, by Stanley Gudder, who apparently also attributes the saying to Euclid.

Neither Goguen nor Gudder seems to have had any interest in the accuracy of the Euclid attribution.

Talk of “nature” and “God” seems unlikely from Euclid, a pre-Christian Greek whose pure mathematics has (as G. H. Hardy might be happy to point out) little to do with either.

Loose talk about God’s thoughts has also been attributed to Kepler and Einstein… and we all know about Stephen Hawking.

Gudder may have been misquoting some other author’s blather about Kepler.  Another possible source of the “thoughts of God” phrase is Hans Christian Oersted. The following is from Oersted’s The Soul in Nature

“Sophia. Nothing of importance; though indeed I had one question on my lips when the conversion took the last turn. When you alluded to the idea, that the Reason manifested in Nature is infallible, while ours is fallible, should you not rather have said, that our Reason accords with that of Nature, as that in the voice of Nature with ours?

Alfred. Each of these interpretations may be justified by the idea to which it applies, whether we start from ourselves or external nature. There are yet other ways of expressing it; for instance, the laws of Nature are the thoughts of  Nature.

Sophia. Then these thoughts of Nature are also thoughts of God.

Alfred. Undoubtedly so, but however valuable the expression may be, I would rather that we should not make use of it till we are convinced that our investigation leads to a view of Nature, which is also the contemplation of God. We shall then feel justified by a different and more perfect knowledge to call the thoughts of Nature those of God; I therefore beg you will not proceed to [sic] fast.”

Oersted also allegedly said that “The Universe is a manifestation of an Infinite Reason and the laws of Nature are the thoughts of God.” This remark was found (via Google book search) in an obscure journal that does not give a precise source for the words it attributes to Oersted.

The image “http://www.log24.com/log/pix07/070131-OerstedGudder.jpg” cannot be displayed, because it contains errors.

Tuesday, January 9, 2007

Tuesday January 9, 2007

Filed under: General — Tags: — m759 @ 12:00 pm
For Balanchine's Birthday

(continued from
January 9, 2003)

George Balanchine

Encyclopædia Britannica Article

born January 22
[January 9, Old Style], 1904,
St. Petersburg, Russia
died April 30, 1983, New York,
New York, U.S.

Photograph:George Balanchine.
George Balanchine.
©1983 Martha Swope

original name 
Georgy Melitonovich Balanchivadze

most influential choreographer of classical ballet in the United States in the 20th century.  His works, characterized by a cool neoclassicism, include The Nutcracker (1954) and Don Quixote (1965), both pieces choreographed for the New York City Ballet, of which he was a founder (1948), the artistic director, and the…


Balanchine,  George… (75 of 1212 words)

"What on earth is
a concrete universal?"
— Robert M. Pirsig

Review:

From Wikipedia's
"Upper Ontology"
and
Epiphany 2007:

"There is no neutral ground
that can serve as
a means of translating between
specialized (lower) ontologies."

There is, however,
"the field of reason"–

the 3×3 grid:

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

Click on grid
for details.

As Rosalind Krauss
has noted, some artists
regard the grid as

"a staircase to
  the Universal."

Other artists regard
Epiphany itself as an
approach to
the Universal:

"Epiphany signals the traversal
of the finite by the infinite,
of the particular by the universal,
of the mundane by the mystical,
of time by eternity.
"

Richard Kearney, 2005,
in The New Arcadia Review

The image “http://www.log24.com/log/pix07/070109-Kearney2.jpg” cannot be displayed, because it contains errors.

Kearney (right) with
Martin Scorsese (left)
and Gregory Peck
in 1997.

"… one of the things that worried me about traditional metaphysics, at least as I imbibed it in a very Scholastic manner at University College Dublin in the seventies, is that philosophy was realism and realism was truth. What disturbed me about that was that everything was already acquired; truth was always a systematic given and it was there to be learned from Creation onwards; it was spoken by Jesus Christ and then published by St. Thomas Aquinas: the system as perfect synthesis. Hence, my philosophy grew out of a hunger for the 'possible' and it was definitely a reaction to my own philosophical formation. Yet that wasn't my only reaction. I was also reacting to what I considered to be the deep pessimism, and even at times 'nihilism' of the postmodern turn."

— Richard Kearney, interview (pdf) in The Leuven Philosophy Newsletter, Vol. 14, 2005-2006

For more on "the possible," see Kearney's The God Who May Be, Diamonds Are Forever, and the conclusion of Mathematics and Narrative:

 

"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

 

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity,
Christ Church College, Oxford
(the home of Lewis Carroll)

Saturday, January 6, 2007

Saturday January 6, 2007

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


Picture of Nothing

On Kirk Varnedoe’s
2003 Mellon Lectures,
Pictures of Nothing“–

“Varnedoe’s lectures were ultimately
about faith, about his faith in
the power of abstraction,
and abstraction as a kind of
anti-religious faith in itself….”

The Washington Post

Related material:

The more industrious scholars
will derive considerable pleasure
from describing how the art-history
professors and journalists of the period
1945-75, along with so many students,
intellectuals, and art tourists of every
sort, actually struggled to see the
paintings directly, in the old
pre-World War II way,
like Plato’s cave dwellers
watching the shadows, without
knowing what had projected them,
which was the Word.”

— Tom Wolfe, The Painted Word

Log24, Aug. 23, 2005:

“Concept (scholastics’ verbum mentis)–
theological analogy of Son’s procession
as Verbum Patris, 111-12″

— Index to Joyce and Aquinas,
by William T. Noon, S.J.,
Yale University Press 1957,
second printing 1963, page 162

“So did God cause the big bang?
Overcome by metaphysical lassitude,
I finally reach over to my bookshelf
for The Devil’s Bible.
Turning to Genesis I read:
‘In the beginning
there was nothing.
And God said,
‘Let there be light!’
And there was still nothing,
but now you could see it.'”

— Jim Holt, Big-Bang Theology,
Slate‘s “High Concept” department

The image “http://www.log24.com/log/pix07/070106-Bang.jpg” cannot be displayed, because it contains errors.


“Bang.”

“…Mondrian and Malevich
are not discussing canvas
or pigment or graphite or
any other form of matter.
They are talking about
Being or Mind or Spirit.
From their point of view,
the grid is a staircase
to the Universal….”

Rosalind Krauss, “Grids”

For properties of the
“nothing” represented
by the 3×3 grid, see
The Field of Reason.

For religious material related
to the above and to Epiphany,
a holy day observed by some,
see Plato, Pegasus, and the
Evening Star
and Shining Forth.

Wednesday, January 3, 2007

Wednesday January 3, 2007

Filed under: General — m759 @ 11:32 am
The Wanderer:
 
11:32:56

“What on earth is
a concrete universal?”
Robert M. Pirsig  

Hexagram 56

“James Joyce meant Finnegans Wake to become a universal book. His universe was primarily Dublin, but Joyce believed that the universal can be found in the particular. ‘I always write about Dublin,’ he said to Arthur Power, ‘because if I can get to the heart of Dublin I can get to the heart of all the cities of the world’ (Ellmann 505). He achieved that goal in Ulysses by making Bloom a universal wanderer, the everyman trying to find his way in the labyrinth of the world.” —The Joyce of Science

Related material:

From A Shot at Redemption

The Past as Prologue:
Grand Rapids Revisited

Constantine (cartoon) and Donald Knuth

John Constantine,
cartoon character, and
Donald E. Knuth,
Lutheran mathematician

“…. recent books testify
further to Calvin College’s
unparalleled leadership
in the field of
Christian historiography….”

“I need a photo opportunity,
I want a shot at redemption.
Don’t want to end up a cartoon
In a cartoon graveyard.”

A photo opportunity —

Photo op for Gerald Ford

and a recent cartoon:

Cartoon of Gerald Ford with halo

History, said Stephen….

From Calvin College,
today’s meditation:

Wednesday, December 13, 2006

Wednesday December 13, 2006

Filed under: General — m759 @ 9:29 am

 Best Wishes for a
C. S. Lewis
Christmas

 

 C.S. Lewis

Image of Lewis from
Into the Wardrobe

What on earth
  is a concrete
  universal?”

— Robert M. Pirsig, author of Zen and the Art of Motorcyle Maintenance

For one approach to an answer, click on the picture at left.

Update of 4:23 PM:

The Lewis link above deals with the separation of Heaven from Hell.  The emphasis is on Heaven.  A mysterious visitor to this website, “United States,” seems to be seeking equal time for Hell.  And so…

Storyboard

Based on Xanga footprints of Dec. 13, 2006
from m759’s site-visitor “United States”
(possibly a robot; if so, a robot with strange tastes).

TIME OF     DATE OF             PAGE VISITED   
VISIT         PAGE VISITED 

1217 040520  Parable
1218 060606  The Omen
1220 051205  Don’t Know Much About History
1225 030822  Mr. Holland’s Week (And in Three Days…)
1233 030114  Remarks on Day 14 (What is Truth?)
1238 040818  Train of Thought (Oh, My Lolita)
1244 020929  Angel Night (Ellis Larkins)
1249 040715  Identity Crisis (Bourne and Treadstone)
1252 050322  Make a Differance (Lacan, Derrida, Reba)
1255 050221  Quarter to Three on Night of HST’s death
1256 040408  Triple Crown on Holy Thursday
1258 040714  Welcome to Mr. Motley’s Neighborhood
1258 030221  All About Lilith
0103 040808  Quartet (for Alexander Hammid)
0104 030106  Dead Poet in the City of Angels
0109 030914  Skewed Mirrors (Readings on Aesthetics)
0110 050126  A Theorem in Musical Form
0125 021007  Music for R. D. Laing
0138 020806  Butterflies & Popes (Transfiguration)
0140 060606  The Omen (again)
0156 030313  ART WARS: Perennial Tutti-Frutti
0202 030112  Ask Not (A Bee Gees Requiem)
0202 050527  Drama of the Diagonal, Part Deux
0202 060514  STAR WARS continued (Eclipse and Venus)
0207 030112  Ask Not (again… Victory of the Goddess)
0207 030221  All About Lilith (again… Roll credits.)

“How much story do you want?”
— George Balanchine
 

Monday, November 27, 2006

Monday November 27, 2006

Filed under: General — m759 @ 2:45 am
The Poetry
of Philosophy

“What on earth is
   a ‘concrete universal’?”

Said to be an annotation
(undated)
by Robert M. Pirsig of
A History of Philosophy,
by Frederick Copleston,
Society of Jesus
.

For an answer, see
The Structure of the
‘Concrete Universal’
in Literature
,”
by W. K. Wimsatt, Jr.,
PMLA, Vol. 62, No. 1
(March, 1947), pp. 262-280.

This is reprinted in Wimsatt’s
The Verbal Icon:
Studies in the
Meaning of Poetry
.

The final chapter of
The Verbal Icon
is titled
“Poetry and Christian Thinking.”
For more on Wimsatt
and this topic, see
Reclaiming the Bible
as Literature,”
by Louis A. Markos.

Sunday, November 26, 2006

Sunday November 26, 2006

Filed under: General — m759 @ 7:26 am

Rosalind Krauss
in "Grids," 1979:

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

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

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

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

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

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

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

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

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

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

Unreason is, of course,
more popular.

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

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

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

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

Friday, September 29, 2006

Friday September 29, 2006

Filed under: General — m759 @ 8:00 am
Values
for the High Holy Days


(Rosh Hashanah began at sundown September 22; Yom Kippur begins at sundown October 1.  —holidays.net)

Mark Finkelstein today:
 

"Today comes more evidence of the left's painful struggle to deal with its diminished standing and repeated rejection at the polls. In the subscription-required Why Voters Like Values, [New York] Times columnist Judith Warner claims that "the Christian right's ability to stir voter passions is based not on values, but on psychology." Warner describes having bravely gone inside the belly of the conservative beast, recently attending a Values Voters Summit in DC, and declaring it "imbued with so much intolerance and hate." This is presumably in contrast with liberal love-ins, where Bush & Co. are regularly depicted as liars, murderers, Hitlers, etc.

She later describes a schadenfreude-provoking scene of the day after Kerry's 2004 defeat, picking through the rubble with Harvard psychology professor emeritus, Jerome Kagan, who tried to console Warner and presumably himself. As she describes it:

"Our conversation drifted to the Republicans' 'values' [note scare quotes] agenda, and Kagan's belief that values sell because they're an antidote to the endemic mental health problem of our time: depression.

"'Humans demand that there be a clear right and wrong,' he said. 'You've got to believe that the track you've taken is the right track. You get depressed if you're not certain as to what it is you're supposed to be doing or what's right and wrong in the world."

"People need to divide the world into good and evil, us and them, Kagan continued. To do otherwise– to entertain the possibility that life is not black and white, but variously shaded in gray– is perhaps more honest, rational and decent. But it's also, psychically, a recipe for disaster."

Got it? Liberalism is "more honest, rational and decent" than conservativism, but that's just not what the benighted public wants. They're looking for political Prozac, a Manichean worldview they can cling to, and that's what conservatism cunningly offers.

Less controversial values are provided by yesterday evening's Pennsylvania lottery— namely, the values 4, 5, and 6.

For a discussion of these values under the guise of musical intervals, see Professor Kagan again, in a paper (pdf) he wrote with Marcel R. Zentner, "Infants' Perception of Consonance and Dissonance in Music" (Infant Behavior & Development, Vol. 21, No. 3, 1998):

Adults judge as most consonant either the octave (difference of 12 semitones) [or the unison, difference of 0 semitones], the fifth (7 semitones), or the major third (4 semitones).

Illustration (see also yesterday evening):

The image “http://www.log24.com/music/images/Keys-Values.gif” cannot be displayed, because it contains errors.

Notes and frequency ratios

The paper discusses consonant intervals
as an example of alleged
"perceptual universals."

Related material on universals
suitable for today, the Feast of
St. Michael and All Angels:

Shining Forth and
Midsummer Eve's Dream.

The material in Shining Forth
is also related, tangentially, to the
following presentation of the
Warner "values" essay
in today's online New York Times:

The image “http://www.log24.com/log/pix06A/060929-NYT.jpg” cannot be displayed, because it contains errors.

The above three Times items,
taken together, suggest that
those in search of "values"
should consult Betty Suarez:

The image “http://www.log24.com/log/pix06A/060929-BettyPoncho.gif” cannot be displayed, because it contains errors.

Click on picture for further details.

Wednesday, September 13, 2006

Wednesday September 13, 2006

Filed under: General — Tags: — m759 @ 9:28 pm

ART WARS continued:

The Krauss Cross

The image “http://www.log24.com/log/pix06A/060913-Art.jpg” cannot be displayed, because it contains errors.

Rosalind Krauss in "Grids":

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

Or, to take a more up-to-date example, we could think about Ad Reinhardt who, despite his repeated insistence that 'Art is art,' ended up by painting a series of black nine-square grids in which the motif that inescapably emerges is a Greek cross.  There is no painter in the West who can be unaware of the symbolic power of the cruciform shape and the Pandora's box of spiritual reference that is opened once one uses it."

Rebecca Goldstein on
Mathematics and Narrative
:

"I don't write exclusively on Jewish themes or about Jewish characters. My collection of short stories, Strange Attractors, contained nine pieces, five of which were, to some degree, Jewish, and this ratio has provided me with a precise mathematical answer (for me, still the best kind of answer) to the question of whether I am a Jewish writer. I am five-ninths a Jewish writer."

Jacques Maritain,
October 1941
:

"The passion of Israel
today is taking on
more and more distinctly
the form of the Cross."

E. L. Doctorow,
City of God:

"In the garden of Adding,
Live Even and Odd."

Friday, August 4, 2006

Friday August 4, 2006

Filed under: General — Tags: — m759 @ 2:56 am

ART WARS
continued from
previous entry

In memory of
Elisabeth Schwarzkopf:

"Who is the fairest of them all?"

This question might
well be posed by…

The image “http://www.log24.com/log/pix05/050501-Krauss.jpg” cannot be displayed, because it contains errors.

Rosalind Krauss,
Meyer Schapiro Professor
of Modern Art and Theory
at Columbia University
(Ph.D., Harvard U., 1969).

"The grid is a staircase to the Universal….
We could think about Ad Reinhardt, who,
despite his repeated insistence that
'Art is art,'
ended up by painting a series of…
nine-square grids in which the motif
that inescapably emerges is
a Greek cross.

The image “http://www.log24.com/log/pix05B/051202-Cross.gif” cannot be displayed, because it contains errors.
Adapted from
Ad Reinhardt

There is no painter in the West
who can be unaware of
the symbolic power
of the cruciform shape and the
Pandora's box of spiritual reference
that is opened once one uses it."

— Rosalind Krauss in "Grids"

"Nine is a very powerful Nordic number."
— Katherine Neville, author of The Eight

Related material:

Balanchine's Birthday,

Apollo and Christ.
 

Monday, June 26, 2006

Monday June 26, 2006

Filed under: General — Tags: — m759 @ 9:29 am

A Little Extra Reading

In memory of
Mary Martin McLaughlin,
a scholar of Heloise and Abelard.
McLaughlin died on June 8, 2006.

"Following the parade, a speech is given by Charles Williams, based on his book The Place of the Lion. Williams explains the true meaning of the word 'realism' in both philosophy and theology. His guard of honor, bayonets gleaming, is led by William of Ockham."

Midsummer Eve's Dream

A review by John D. Burlinson of Charles Williams's novel The Place of the Lion:

"… a little extra reading regarding Abelard's take on 'universals' might add a little extra spice– since Abelard is the subject of the heroine's … doctoral dissertation. I'd suggest the article 'The Medieval Problem of Universals' in the online Stanford Encyclopedia of Philosophy."

Michael L. Czapkay, a student of philosophical theology at Oxford:

"The development of logic in the schools and universities of western Europe between the eleventh and fifteenth centuries constituted a significant contribution to the history of philosophy. But no less significant was the influence of this development of logic on medieval theology. It provided the necessary conceptual apparatus for the systematization of theology. Abelard, Ockham, and Thomas Aquinas are paradigm cases of the extent to which logic played an active role in the systematic formulation of Christian theology. In fact, at certain points, for instance in modal logic, logical concepts were intimately related to theological problems, such as God's knowledge of future contingent truths."

The Medieval Problem of Universals, by Fordham's Gyula Klima, 2004:

"… for Abelard, a status is an object of the divine mind, whereby God preconceives the state of his creation from eternity."

Status Symbol

(based on Weyl's Symmetry):

The image “http://www.log24.com/log/pix06A/060604-Roots.jpg” cannot be displayed, because it contains errors.

"… for then we would know

the mind of God"
Stephen Hawking, 1988

For further details,
click on the picture.

Wednesday, May 3, 2006

Wednesday May 3, 2006

Filed under: General — m759 @ 1:00 pm
Ontology Alignment
continued

“Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason.  Mathematics is the threshold we cross to pass into the ideal, the truly real.”

     — Rebecca Goldstein,
       Mathematics and
       the Character of Tragedy

Pennsylvania Lottery:

The winning numbers
for Tuesday, May 2–
the feast of
St. Athanasius:

Mid-day 703
Evening 462

“You gotta be true to your code”
— Sinatra (see previous entry)

 Dewey Decimal Code:

703 The Arts:
       Dictionaries &
       Encyclopedias
462 Spanish Etymology

Related material:

For the arts, see
the previous entry.
For Spanish etymology,
see the remarks on
a Spanish word in
Plato, Pegasus, and
the Evening Star,
a note linked to in the
April 30 memorial entry
for John Kenneth Galbraith.

The numbers 703 and 462 are, in Goldstein’s phrase, “truly real.”  However, their link to St. Athanasius and to the Spanish language is, as purveyors of fiction* say, “purely coincidental”– as is much of what makes life interesting.

“All persons living and dead are purely coincidental….”– Kurt Vonnegut, epigraph to Bagombo Snuff Box

* For instance,
   David Auburn in Proof,

   The image “http://www.log24.com/log/pix06A/060503-DrLecter2.jpg” cannot be displayed, because it contains errors.

   which also involves
   Dewey decimal numbers

Friday, March 31, 2006

Friday March 31, 2006

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

Women's History Month continues…
 
Ontology Alignment

"He had with him a small red book of Mao's poems, and as he talked he squared it on the table, aligned it with the table edge first vertically and then horizontally.  To understand who Michael Laski is you must have a feeling for that kind of compulsion."

— Joan Didion in the
Saturday Evening Post,
Nov. 18, 1967 (reprinted in
Slouching Towards Bethlehem)

"Or were you," I said.
He said nothing.
"Raised a Catholic," I said.
He aligned a square crystal paperweight with the edge of his desk blotter.

— Joan Didion in
The Last Thing He Wanted,
Knopf, 1996

"It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….

Plato clearly loved them both, both mathematics and poetry.  But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry.  Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto.  Let none ignorant of geometry enter.  This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge.  Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason.  Mathematics is the threshold we cross to pass into the ideal, the truly real."

— Rebecca Goldstein,
Mathematics and
the Character of Tragedy

Tuesday, March 28, 2006

Tuesday March 28, 2006

Filed under: General — Tags: — m759 @ 4:00 pm
A Prince of Darkness


“What did he fear? It was not a fear or dread, It was a nothing that he knew too well. It was all a nothing and a man was a nothing too. It was only that and light was all it needed and a certain cleanness and order. Some lived in it and never felt it but he knew it all was nada y pues nada y nada y pues nada. Our nada who art in nada, nada be thy name thy kingdom nada thy will be nada in nada as it is in nada. Give us this nada our daily nada and nada us our nada as we nada our nadas and nada us not into nada but deliver us from nada; pues nada. Hail nothing full of nothing, nothing is with thee.”

— From Ernest Hemingway,
A Clean, Well-Lighted Place

“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

From a review of
Teilhard de Chardin’s
The Phenomenon of Man:

“It would have been
 a great disappointment
 to me if Vibration did not
 somewhere make itself felt,
 for all scientific mystics
 either vibrate in person
 or find themselves
 resonant with cosmic
 vibrations….”

Sir Peter Brian Medawar

“He’s good.”
“Good? He’s the fucking
Prince of Darkness!”

— Paul Newman
and Jack Warden
in “The Verdict

Sanskrit (transliterated) —

    nada:
 
 
  the universal sound, vibration.

“So Nada Brahma means not only:
 God the Creator is sound; but also
 (and above all), Creation,
 the cosmos, the world, is sound.
 And: Sound is the world.”

Joachim-Ernst Berendt,  
   author of Nada Brahma

 
“This book is the outcome of
a course given at Harvard
first by G. W. Mackey….”

— Lynn H. Loomis, 1953, preface to
An Introduction to
Abstract Harmonic Analysis

For more on Mackey and Harvard, see
the Log24 entries of March 14-17.

Saturday, March 25, 2006

Saturday March 25, 2006

Filed under: General — m759 @ 4:23 pm
Built

In memory of Rolf Myller,
who died on Thursday,
March 23, 2006, at
Mount Sinai Hospital
in Manhattan:

Myller was,
according to the
New York Times,
an architect
whose eclectic pursuits
included writing
children’s books,
The Bible Puzzle Book, and
Fantasex: A Book of Erotic Games.

He also wrote, the Times says,
Symbols and Their Meaning
(1978), a graphic overview of
children’s nonverbal communication.”
This is of interest in view of the
Log24 reference to “symbol-mongers”
on the date of Myller’s death.

In honor of Women’s History Month
and of Myller’s interests in the erotic
and in architecture, we present
the following work from a British gallery.

The image “http://www.log24.com/log/pix06/060325-WhiteCube.jpg” cannot be displayed, because it contains errors.

This work might aptly be
  retitled “Brick Shithouse.”

Related material:

(1) the artist’s self-portrait

The image “http://www.log24.com/log/pix06/060325-LizaLouSelfPortrait.jpg” cannot be displayed, because it contains errors.

and, in view of the cover
illustration for Myller’s
The Bible Puzzle Book,

The image “http://www.log24.com/log/pix06/060325-Tower.jpg” cannot be displayed, because it contains errors.

(2) the monumental treatise
by Leonard Shlain

The Alphabet Versus
the Goddess: The Conflict
Between Word and Image
.

For devotees of women’s history
and of the Goddess,
here are further details from
the White Cube gallery:

Liza Lou

03.03.06 – 08.04.06

White Cube is pleased to present the first UK solo exhibition by Los Angeles-based artist Liza Lou.

Combining visionary, conceptual and craft approaches, Lou makes mixed-media sculptures and room-size installations that are suggestive of a transcendental reality. Lou’s work often employs familiar, domestic forms, crafted from a variety of materials such as steel, wood, papier-mâché and fibreglass, which is then covered with tiny glass beads that are painstakingly applied, one at a time, with tweezers. Dazzling and opulent and constantly glistening with refracted light, her sculptures bristle with what Peter Schjeldahl has aptly described as ‘surreal excrescence’.

This exhibition, a meditation on the vulnerability of the human body and the architecture of confinement, will include several new figurative sculptures as well as two major sculptural installations. Security Fence (2005) is a large scale cage made up of four steel, chain link walls, topped by rings of barbed wire and Cell (2004-2006), as its name suggests, is a room based on the approximate dimensions of a death row prison cell, a kind of externalized map of the prisoner’s mind. Both Security Fence and Cell, like Lou’s immense earlier installations Kitchen (1991-1995) and Back Yard (1995-1999) are characterized by the absence of their real human subject. But whereas the absent subject in Kitchen and Back Yard could be imagined through the details and accessories carefully laid out to view, in Lou’s two new installations the human body is implied simply through the empty volume created by the surrounding architecture. Both Cell and Security Fence are monochromatic and employ iconic forms that make direct reference to Minimalist art in its use of repetition, formal perfection and materiality. In contrast to this, the organic form of a gnarled tree trunk, Scaffold (2005-2006), its surface covered with shimmering golden beads, juts directly out from the wall.

Lou’s work has an immediate ‘shock’ content that works on different levels: first, an acknowledgement of the work’s sheer aesthetic impact and secondly the slower comprehension of the labour that underlies its construction. But whereas in Lou’s earlier works the startling clarity of the image is often a counterpoint to the lengthy process of its realization, for the execution of Cell, Lou further slowed down the process by using beads of the smallest variety with their holes all facing up in an exacting hour-by-hour approach in order to ‘use time as an art material’.

Concluding this body of work are three male figures in states of anguish. In The Seer (2005-2006), a man becomes the means of turning his body back in on himself. Bent over double, his body becomes an instrument of impending self-mutilation, the surface of his body covered with silver-lined beads, placed with the exactitude and precision of a surgeon. In Homeostasis (2005-2006) a naked man stands prostrate with his hands up against the wall in an act of surrender. In this work, the dissolution between inside and outside is explored as the ornate surface of Lou’s cell-like material ‘covers’ the form while exposing the systems of the body, both corporeal and esoteric. In The Vessel (2005-2006), Christ, the universal symbol of torture and agony holds up a broken log over his shoulders. This figure is beheaded, and bejewelled, with its neck carved out, becoming a vessel into which the world deposits its pain and suffering.

Lou has had numerous solo exhibitions internationally, including Museum Kunst Palast, Düsseldorf, Henie Onstad Kunstsenter, Oslo and Fondació Joan Miró, Barcelona. She was a 2002 recipient of the MacArthur Foundation Fellowship.

Liza Lou’s film Born Again (2004), in which the artist tells the compelling and traumatic story* of her Pentecostal upbringing in Minnesota, will be screened at 52 Hoxton Square from 3 – 25 March courtesy of Penny Govett and Mick Kerr.

Liza Lou will be discussing her work following a screening of her film at the ICA, The Mall, London on Friday 3 March at 7pm. Tickets are available from the ICA box office (+ 44 (0) 20 7930 3647).

A fully illustrated catalogue, with a text by Jeanette Winterson and an interview with Tim Marlow, will accompany the exhibition.

White Cube is open Tuesday to Saturday, 10.00 am to 6.00 pm.

For further information please contact Honey Luard or Susannah Hyman on + 44 (0) 20 7930 5373

* Warning note from Adrian Searle
    in The Guardian of March 21:
   “How much of her story is
    gospel truth we’ll never know.”

For deeper background on
art, patriarchal religion,
and feminism, see
The Agony and the Ya-Ya.

Saturday, March 18, 2006

Saturday March 18, 2006

Filed under: General — Tags: — m759 @ 4:07 pm

ART WARS:
The Crimson Passion continues…

How to Grow
a Crimson Clover

Published in the Harvard Crimson
on Thursday, March 16, 2006, 6:24 PM
by Patrick R. Chesnut,
Crimson staff writer


Stephen Dedalus, James Joyce’s literary alter ego, once described the trappings of Irish culture as nets that hold a soul back from flight. By his standards, Harvard has soared.

Irish culture has been an indelible part of Boston, but the names on our red-brick buildings tell a different story: Adams, Lowell, Winthrop. It would be easy to assume that for Harvard students, Irish culture consists of little more than guzzling alcohol in Tommy Doyle’s Irish Pub or at St. Patrick’s Day Stein Club.

Recently, however, a small but lively Irish subculture, centered on Celtic music and language, has been developing at Harvard. But despite its vivacity, it remains largely unnoticed by the broader student body.

Efforts by groups like the Harvard College Celtic Club and by the producers of the upcoming Loeb mainstage of J.M. Synge’s “The Playboy of the Western World” may be just the sort of first step needed to finally make Harvard a place where Irish artistic culture lives….

REACHING OUT

“The Playboy”– which will run from April 28 through May 6– revolves around the disruption of life in a provincial Irish village when an outsider arrives with an extravagant story. All points converge at this play’s production: members of the Celtic Club coordinated and will perform the play’s music, the producers hope to draw Boston’s Irish community, and the production will present Harvard’s students with a script deeply entrenched in Irish history, but that boasts a universal appeal.

As Kelly points out, the Irish roots of “The Playboy” are clearer than in the plays of the nominally Irish, but Francophone, absurdist writer Samuel Beckett. And unlike the plays of Sean O’Casey, which are extremely rooted in Irish culture, “The Playboy” boasts a visceral appeal that will be accessible to Harvard students.

From a site linked to in yesterday’s St. Patrick’s Day sermon as the keys to the kingdom:

“In the western world, we tend to take for granted our musical scale, formed of whole tone and half tone steps. These steps are arranged in two ways: the major scale and the minor.”

From the obituary in today’s online New York Times of fashion designer Oleg Cassini, who died at 92 on St. Patrick’s Day, Friday, March 17, 2006:

“… he was always seen in the company of heiresses, debutantes, showgirls, ingenues. Between, before or after [his first] two marriages, he dated young starlets like Betty Grable and Lana Turner and actresses like Ursula Andress and Grace Kelly, to whom he was briefly engaged.

‘He was a true playboy, in the Hollywood sense,’ said Diane von Furstenberg, the fashion designer and a friend of Mr. Cassini’s. ‘Well into his 90’s, he was a flirt.'”

“How strange the change from major to minor…
      Ev’ry time we say goodbye.”
   — Cole Porter

Sunday, March 12, 2006

Sunday March 12, 2006

Filed under: General,Geometry — Tags: , — m759 @ 1:00 pm

A Circle of Quiet

From the Harvard Math Table page:

“No Math table this week. We will reconvene next week on March 14 for a special Pi Day talk by Paul Bamberg.”

The image “http://www.log24.com/log/pix06/060312-PaulBamberg21.jpg” cannot be displayed, because it contains errors.

Paul Bamberg

Transcript of the movie “Proof”–

Some friends of mine are in this band.
They’re playing in a bar on Diversey,
way down the bill, around…

I said I’d be there.

Great.
They’re all in the math department.
They’re good.
They have this song called “i.”
You’d like it. Lowercase i.
They just stand there.
They don’t play anything for three minutes.

Imaginary number?

It’s a math joke.
You see why they’re way down the bill.

From the April 2006 Notices of the American Mathematical Society, a footnote in a review by Juliette Kennedy (pdf) of Rebecca Goldstein’s Incompleteness:

4 There is a growing literature in the area of postmodern commentaries of [sic] Gödel’s theorems. For example, Régis Debray has used Gödel’s theorems to demonstrate the logical inconsistency of self-government. For a critical view of this and related developments, see Bricmont and Sokal’s Fashionable Nonsense [13]. For a more positive view see Michael Harris’s review of the latter, “I know what you mean!” [9]….

[9] MICHAEL HARRIS, “I know what you mean!,” http://www.math.jussieu.fr/~harris/Iknow.pdf.
[13] ALAN SOKAL and JEAN BRICMONT, Fashionable Nonsense, Picador, 1999.

Following the trail marked by Ms. Kennedy, we find the following in Harris’s paper:

“Their [Sokal’s and Bricmont’s] philosophy of mathematics, for instance, is summarized in the sentence ‘A mathematical constant like The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. doesn’t change, even if the idea one has about it may change.’ ( p. 263). This claim, referring to a ‘crescendo of absurdity’ in Sokal’s original hoax in Social Text, is criticized by anthropologist Joan Fujimura, in an article translated for IS*. Most of Fujimura’s article consists of an astonishingly bland account of the history of non-euclidean geometry, in which she points out that the ratio of the circumference to the diameter depends on the metric. Sokal and Bricmont know this, and Fujimura’s remarks are about as helpful as FN’s** referral of Quine’s readers to Hume (p. 70). Anyway, Sokal explicitly referred to “Euclid’s pi”, presumably to avoid trivial objections like Fujimura’s — wasted effort on both sides.32 If one insists on making trivial objections, one might recall that the theorem
that p is transcendental can be stated as follows: the homomorphism Q[X] –> R taking X to The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. is injective.  In other words, The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. can be identified algebraically with X, the variable par excellence.33

The image “http://www.log24.com/log/pix06/060312-X.jpg” cannot be displayed, because it contains errors.

More interestingly, one can ask what kind of object The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. was before the formal definition of real numbers. To assume the real numbers were there all along, waiting to be defined, is to adhere to a form of Platonism.34  Dedekind wouldn’t have agreed.35  In a debate marked by the accusation that postmodern writers deny the reality of the external world, it is a peculiar move, to say the least, to make mathematical Platonism a litmus test for rationality.36 Not that it makes any more sense simply to declare Platonism out of bounds, like Lévy-Leblond, who calls Stephen Weinberg’s gloss on Sokal’s comment ‘une absurdité, tant il est clair que la signification d’un concept quelconque est évidemment affectée par sa mise en oeuvre dans un contexte nouveau!’37 Now I find it hard to defend Platonism with a straight face, and I prefer to regard the formula

The image “http://www.log24.com/log/pix06/060312-pi.jpg” cannot be displayed, because it contains errors.

as a creation rather than a discovery. But Platonism does correspond to the familiar experience that there is something about mathematics, and not just about other mathematicians, that precisely doesn’t let us get away with saying ‘évidemment’!38

32 There are many circles in Euclid, but no pi, so I can’t think of any other reason for Sokal to have written ‘Euclid’s pi,’ unless this anachronism was an intentional part of the hoax.  Sokal’s full quotation was ‘the The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. of Euclid and the G of Newton, formerly thought to be constant and universal, are now perceived in their ineluctable historicity.’  But there is no need to invoke non-Euclidean geometry to perceive the historicity of the circle, or of pi: see Catherine Goldstein’s ‘L’un est l’autre: pour une histoire du cercle,’ in M. Serres, Elements d’histoire des sciences, Bordas, 1989, pp. 129-149.
33 This is not mere sophistry: the construction of models over number fields actually uses arguments of this kind. A careless construction of the equations defining modular curves may make it appear that pi is included in their field of scalars.
34 Unless you claim, like the present French Minister of Education [at the time of writing, i.e. 1999], that real numbers exist in nature, while imaginary numbers were invented by mathematicians. Thus The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. would be a physical constant, like the mass of the electron, that can be determined experimentally with increasing accuracy, say by measuring physical circles with ever more sensitive rulers. This sort of position has not been welcomed by most French mathematicians.
35 Cf. M. Kline, Mathematics The Loss of Certainty, p. 324.
36 Compare Morris Hirsch’s remarks in BAMS April 94.
37 IS*, p. 38, footnote 26. Weinberg’s remarks are contained in his article “Sokal’s Hoax,” in the New York Review of Books, August 8, 1996.
38 Metaphors from virtual reality may help here.”

* Earlier defined by Harris as “Impostures Scientifiques (IS), a collection of articles compiled or commissioned by Baudouin Jurdant and published simultaneously as an issue of the journal Alliage and as a book by La Découverte press.”
** Earlier defined by Harris as “Fashionable Nonsense (FN), the North American translation of Impostures Intellectuelles.”

What is the moral of all this French noise?

Perhaps that, in spite of the contemptible nonsense at last summer’s Mykonos conference on mathematics and narrative, stories do have an important role to play in mathematics — specifically, in the history of mathematics.

Despite his disdain for Platonism, exemplified in his remarks on the noteworthy connection of pi with the zeta function in the formula given above, Harris has performed a valuable service to mathematics by pointing out the excellent historical work of Catherine Goldstein.   Ms. Goldstein has demonstrated that even a French nominalist can be a first-rate scholar.  Her essay on circles that Harris cites in a French version is also available in English, and will repay the study of those who, like Barry Mazur and other Harvard savants, are much too careless with the facts of history.  They should consult her “Stories of the Circle,” pp. 160-190 in A History of Scientific Thought, edited by Michel Serres, Blackwell Publishers (December 1995).

For the historically-challenged mathematicians of Harvard, this essay would provide a valuable supplement to the upcoming “Pi Day” talk by Bamberg.

For those who insist on limiting their attention to mathematics proper, and ignoring its history, a suitable Pi Day observance might include becoming familiar with various proofs of the formula, pictured above, that connects pi with the zeta function of 2.  For a survey, see Robin Chapman, Evaluating Zeta(2) (pdf).  Zeta functions in a much wider context will be discussed at next May’s politically correct “Women in Mathematics” program at Princeton, “Zeta Functions All the Way” (pdf).

Saturday, March 11, 2006

Saturday March 11, 2006

Filed under: General — m759 @ 12:00 pm
Holy the Firm
by Annie Dillard

    Esoteric Christianity, I read, posits a substance.  It is a created substance, lower than metals and minerals on a “spiritual scale” and lower than salts and earths, occurring beneath salts and earths in the waxy deepness of planets, but never on the surface of planets where men could discern it; and it is in touch with the Absolute, at base.  In touch with the Absolute!  At base.  The name of this substance is Holy the Firm.
    Holy the Firm: and is Holy the Firm in touch with metals and minerals?  With salts and earths?  Of course, and straight on up, till “up” ends by curving back.  Does something that touched something that touched Holy the Firm in touch with the Absolute at base seep into ground water, into grain; are islands rooted in it, and trees?  Of course.
    Scholarship has long distinguished between two strains of thought which proceed in the West from human knowledge of God.  In one, the ascetic’s metaphysic, the world is far from God.  Emanating from God, and linked to him by Christ, the world is yet infinitely other than God, furled away from him like the end of a long banner falling.  This notion makes, to my mind, a vertical line of the world, a great chain of burning.  The more accessible and universal view, held by Eckhart and by many peoples in various forms, is scarcely different from pantheism: that the world is immanation, that God is in the thing, and eternally present here, if nowhere else.  By these lights the world is flattened on a horizontal plane, singular, all here, crammed with heaven, and alone.  But I know that it is not alone, nor singular, nor all.  The notion of immanence needs a handle, and the two ideas themselves need a link, so that life can mean aught to the one, and Christ to the other.
    For to immanence, to the heart, Christ is redundant and all things are one.  To emanance, to the mind, Christ touches only the top, skims off only the top, as it were, the souls of men, the wheat grains whole, and lets the chaff fall where?  To the world flat and patently unredeemed; to the entire rest of the universe, which is irrelevant and nonparticipant; to time and matter unreal, and so unknowable, an illusory, absurd, accidental, and overelaborate stage.
    But if Holy the Firm is “underneath salts,” if Holy the Firm is matter at its dullest, Aristotle’s materia prima, absolute zero, and since Holy the Firm is in touch with the Absolute at base, then the circle is unbroken.  And it is.  Thought advances, and the world creates itself, by the gradual positing of, and belief in, a series of bright ideas.  Time and space are in touch with the Absolute at base.  Eternity sockets twice into time and space curves, bound and bound by idea.  Matter and spirit are of a piece but distinguishable; God has a stake guaranteed in all the world.  And the universe is real and not a dream, not a manufacture of the senses; subject may know object, knowedge may proceed, and Holy the Firm is in short the philosopher’s stone.

    These are only ideas, by the single handful.  Lines, lines, and their infinite points!  Hold hands and crack the whip, and yank the Absolute out of there and into the light, God pale and astounded, spraying a spiral of salts and earths, God footloose and flung.  And cry down the line to his passing white ear, “Old Sir!  Do you hold space from buckling by a finger in its hole?  O Old!  Where is your other hand?”  His right hand is clenching, calm, round the exploding left hand of Holy the Firm.

— Annie Dillard, Holy the Firm, Harper & Row 1977, reissued by Harper Perennial Library in 1988 as a paperback, pp. 68-71.

Tuesday, February 21, 2006

Tuesday February 21, 2006

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

Now Lens

  murphy plant, murphy grow, a maryamyria-   10
  meliamurphies, in the lazily eye of his lapis,   11
      12
  Geometry lesson   13
      14
Uteralterance or Vieus Von DVbLIn, 'twas one of dozedeams   15
the Interplay of a darkies ding in dewood) the Turnpike under   16
Bones in the the Great Ulm (with Mearingstone in Fore   17
Womb. ground). 1 Given now ann linch you take enn   18
  all. Allow me! And, heaving alljawbreakical   19
  expressions out of old Sare Isaac's 2 universal   20
The Vortex. of specious aristmystic unsaid, A is for Anna   21
Spring of Sprung like L is for liv. Aha hahah, Ante Ann you're   22
Verse. The Ver- apt to ape aunty annalive! Dawn gives rise.   23
tex. Lo, lo, lives love! Eve takes fall. La, la, laugh   24
  leaves alass! Aiaiaiai, Antiann, we're last to   25
  the lost, Loulou! Tis perfect. Now (lens   26

Finnegans Wake, Book II,
Episode 2, page 293

Related material:
Fours and 1132

Wednesday, February 8, 2006

Wednesday February 8, 2006

Filed under: General — m759 @ 5:11 pm
For Grammy Night

From A Mass for Lucero:

“To the two gods of art, Apollo and Dionysus, we owe our recognition that… there is a tremendous opposition, as regards both origins and aims, between the Apolline art of the sculptor and the non-visual, Dionysiac art of music.”
The Birth of Tragedy, by Friedrich Nietzsche, Penguin, 1993, page 14

Melody, then, is both primary and universal.” (Author’s italics)
— Nietzsche, op. cit., page 33

“…in so far as he interprets music in images, he himself lies amidst the peaceful waves of Apolline contemplation….”
— Nietzsche, op. cit., page 35

The image “http://www.log24.com/log/pix06/060208-Scarlett.jpg” cannot be displayed, because it contains errors.

Apolline Contemplation

From The Miracle of the Bells, by Russell Janney, Prentice-Hall, 1946, page 333–

“He was singing softly:
A pretty girl–
 is like a melody—- !
 But that was always
 Bill Dunnigan’s
 Song of Victory….
 Thus thought the…
 press agent for
‘The Garden of the Soul.'”

Sunday, February 5, 2006

Sunday February 5, 2006

Filed under: General — m759 @ 11:00 am

Catholic Schools Sermon

For those who might be tempted today, following yesterday’s conclusion of Catholic Schools Week, to sing (for whatever reason) “Ding Dong, the Witch is Dead”–

Here, from his classic Witchcraft (first published by Faber and Faber, London, 1941, reprinted by Apocryphile Press, Berkeley, CA, Oct. 1, 2005) is Charles Williams on the strong resemblance between witchcraft and the rituals of the Church:

Charles Williams on
Witchcraft and the Church

From Witchcraft, 2005 Apocryphile edition, pages 77-80–

[77] … The predisposition towards the idea of magic might be said to begin with a moment which seems to be of fairly common experience– the moment when it seems that anything might turn into anything else.  We have grown used– and properly used– to regarding this sensation invalid because, on the whole, things do not turn into other things except by processes which we realize, or else at least so frequently that we appreciate the probability.  But the occasional sensation remains.  A room, a street, a field becomes unsure.  The edge of a possibility of utter alteration intrudes.  A door, untouched, might close; a picture might walk; a tree might speak; an animal might not be an animal; a man might not be a man.  One may be with a friend, and a terror will take one even while his admirable voice is speaking; one will be with a lover and the hand will become a different and terrifying thing, moving in one’s own like a malicious intruder, too real for anything but fear.  All this may be due to racial memories or to any other cause; the point is that it exists.  It exists and can be communicated; it can even be shared.  There is, in our human centre, a heart-gripping fear of irrational change, of perilous and malevolent change.
    Secondly, there is the human body, and the movements of the human body.  Even now, when, as a general rule, the human body is not supposed to mean [78] anything, there are moments when it seems, in spite of ourselves, packed with significance.  This sensation is almost exactly the opposite of the last.  There, one was aware that any phenomenon might alter into another and truer self.  Here, one is aware that a phenomenon, being wholly itself, is laden with universal meaning.  A hand lighting a cigarette is the explanation of everything; a foot stepping from a train is the rock of all existence.  If the first group of sensations are due to racial fear, I do not know to what the second group are due– unless indeed to the Mercy of God, who has not left us without a cloud of witnesses.  But intellectually they are both as valid or invalid as each other; any distinction must be a matter of choice.  And they justify each other, at least to this extent, that (although the first suggests irrationality and the second rationality) they both at first overthrow a simple trust that phenomena are what phenomena seem.
    But if the human body is capable of seeming so, so are the controlled movements of the human body– ritual movements, or rather movements that seem like ritual.  A finger pointing is quite capable of seeming not only a significant finger, but a ritual finger; an evocative finger; not only a finger of meaning, but a finger of magic.  Two light dancing steps by a girl may (if one is in that state) appear to be what all the Schoolmen were trying to express; they are (only one cannot quite catch it) an intellectual statement of beatitude.  But two quiet steps by an old man may seem like the very speech of hell.  Or the other way round.  Youth and age have nothing to do with it, nor did the ages that defined and [79] denounced witchcraft think so.  The youngest witch, it is said, that was ever burned was a girl of eleven years old.
    Ordered movement, ritual, is natural to men.  But some ages are better at it, are more used to it, and more sensitive to it, than others.  The Middle Ages liked great spectacle, and therefore (if for no other reasons– but there were many) they liked ritual.  They were nourished by ritual– the Eucharist exhibited it.  They made love by ritual– the convention of courtly love preserved it.  Certainly also they did all these things without ritual– but ritual (outside the inner experience) was the norm.  And ritual maintains and increases that natural sense of the significance of movement.  And, of course, of formulae, of words.
    The value of formulae was asserted to be very high.  The whole religious life ‘as generally necessary to salvation’ depended on formulae.  The High God had submitted himself to formulae.  He sent his graces.  He came Himself, according to ritual movements and ritual formulae.  Words controlled the God.  All generations who have believed in God have believed that He will come on interior prayer; not all that He will come, if not visibly yet in visible sacraments, on exterior incantation.  But so it was.  Water and a Triune formula concentrated grace; so did oil and other formulae; so– supremely– did bread and wine and yet other formulae.   Invocations of saints were assumed, if less explicitly guaranteed, to be effective.  The corollaries of the Incarnation had spread, in word and gesture, very far.
    The sense of alteration, the sense of meaning, the [80] evocation of power, the expectation of the God, lay all about the world.  The whole movement of the Church had, in its rituals, a remarkable similarity to the other rites it denounced.  But the other rites had been there first, both in the Empire and outside the Empire.  In many cases the Church turned them to its own purposes.  But also in many cases it entirely failed to turn them to its own purposes.  In many cases it adopted statues and shrines.  But in others it was adopted by, at least, the less serious spells and incantations.  Wells and trees were dedicated to saints.  But the offerings at many wells and trees were to something other than the saint; had it not been so they would not have been, as we find they often were, forbidden.  Within this double and intertwined life existed those other capacities, of which we know more now, but of which we still know little– clairvoyance, clairaudience, foresight, telepathy.

Tuesday, November 1, 2005

Tuesday November 1, 2005

Filed under: General — Tags: , , — m759 @ 12:00 pm

Antidote to Atiyah

In a recent talk, "The Nature of Space," Sir Michael Atiyah gave a misleading description of Plato's doctrine of "ideas," or "idealism."  Atiyah said that according to Plato, ideas reside in  "an imaginary world–  the world of the mind," and that what we see in the external world is "some pale reflection" of ideas in the mind.

An antidote to Atiyah's nonsense may be found in the Catholic Encyclopedia:

"So it came to pass that the word idea in various languages took on more and more the meaning of 'representation,' 'mental image,' and the like. Hence too, there was gradually introduced the terminology which we find in the writings of Berkeley, and according to which idealism is the doctrine that ascribes reality to our ideas, i.e. our representations, but denies the reality of the physical world. This sort of idealism is just the reverse of that which was held by the philosophers of antiquity and their Christian successors; it does away with the reality of ideal principles by confining them exclusively to the thinking subject; it is a spurious idealism…."

Atiyah contrasts his mistaken view of Plato with what he calls the "realism" of Hume.  He does not mention that Plato's doctrine of ideas is also known as "realism."  For details, see, again, the Catholic Encyclopedia:

"The conciliation of the one and the many, the changing and the permanent, was a favourite problem with the Greeks; it leads to the problem of universals. The typical affirmation of Exaggerated Realism, the most outspoken ever made, appears in Plato's philosophy; the real must possess the attributes of necessity, universality, unity, and immutability which are found in our intellectual representations. And as the sensible world contains only the contingent, the particular, the unstable, it follows that the real exists outside and above the sensible world. Plato calls it eîdos, idea. The idea is absolutely stable and exists by itself (ontos on; auta kath' auta), isolated from the phenomenal world, distinct from the Divine and human intellect…. The exaggerated Realism of Plato… is the principal doctrine of his metaphysics."
 
Atiyah's misleading remarks may appeal to believers in the contemptible religion of Scientism, but they have little to do with either historical reality or authentic philosophy.

Thursday, August 11, 2005

Thursday August 11, 2005

Filed under: General,Geometry — Tags: , , — m759 @ 8:16 am

Kaleidoscope, continued

From Clifford Geertz, The Cerebral Savage:

"Savage logic works like a kaleidoscope whose chips can fall into a variety of patterns while remaining unchanged in quantity, form, or color. The number of patterns producible in this way may be large if the chips are numerous and varied enough, but it is not infinite. The patterns consist in the disposition of the chips vis-a-vis one another (that is, they are a function of the relationships among the chips rather than their individual properties considered separately).  And their range of possible transformations is strictly determined by the construction of the kaleidoscope, the inner law which governs its operation. And so it is too with savage thought.  Both anecdotal and geometric, it builds coherent structures out of 'the odds and ends left over from psychological or historical process.'

These odds and ends, the chips of the kaleidoscope, are images drawn from myth, ritual, magic, and empirical lore….  as in a kaleidoscope, one always sees the chips distributed in some pattern, however ill-formed or irregular.   But, as in a kaleidoscope, they are detachable from these structures and arrangeable into different ones of a similar sort….  Levi-Strauss generalizes this permutational view of thinking to savage thought in general.  It is all a matter of shuffling discrete (and concrete) images–totem animals, sacred colors, wind directions, sun deities, or whatever–so as to produce symbolic structures capable of formulating and communicating objective (which is not to say accurate) analyses of the social and physical worlds.

…. And the point is general.  The relationship between a symbolic structure and its referent, the basis of its meaning,  is fundamentally 'logical,' a coincidence of form– not affective, not historical, not functional.  Savage thought is frozen reason and anthropology is, like music and mathematics, 'one of the few true vocations.'

Or like linguistics."

Edward Sapir on Linguistics, Mathematics, and Music:

"… linguistics has also that profoundly serene and satisfying quality which inheres in mathematics and in music and which may be described as the creation out of simple elements of a self-contained universe of forms.  Linguistics has neither the sweep nor the instrumental power of mathematics, nor has it the universal aesthetic appeal of music.  But under its crabbed, technical, appearance there lies hidden the same classical spirit, the same freedom in restraint, which animates mathematics and music at their purest."

— Edward Sapir, "The Grammarian and his Language,"
  American Mercury 1:149-155,1924

From Robert de Marrais, Canonical Collage-oscopes:

"…underwriting the form languages of ever more domains of mathematics is a set of deep patterns which not only offer access to a kind of ideality that Plato claimed to see the universe as created with in the Timaeus; more than this, the realm of Platonic forms is itself subsumed in this new set of design elements– and their most general instances are not the regular solids, but crystallographic reflection groups.  You know, those things the non-professionals call . . . kaleidoscopes! *  (In the next exciting episode, we'll see how Derrida claims mathematics is the key to freeing us from 'logocentrism' **— then ask him why, then, he jettisoned the deepest structures of mathematical patterning just to make his name…)

* H. S. M. Coxeter, Regular Polytopes (New York: Dover, 1973) is the great classic text by a great creative force in this beautiful area of geometry  (A polytope is an n-dimensional analog of a polygon or polyhedron.  Chapter V of this book is entitled 'The Kaleidoscope'….)

** … contemporary with the Johns Hopkins hatchet job that won him American marketshare, Derrida was also being subjected to a series of probing interviews in Paris by the hometown crowd.  He first gained academic notoriety in France for his book-length reading of Husserl's two-dozen-page essay on 'The Origin of Geometry.'  The interviews were collected under the rubric of Positions (Chicago: U. of Chicago Press, 1981…).  On pp. 34-5 he says the following: 'the resistance to logico-mathematical notation has always been the signature of logocentrism and phonologism in the event to which they have dominated metaphysics and the classical semiological and linguistic projects…. A grammatology that would break with this system of presuppositions, then, must in effect liberate the mathematization of language…. The effective progress of mathematical notation thus goes along with the deconstruction of metaphysics, with the profound renewal of mathematics itself, and the concept of science for which mathematics has always been the model.'  Nice campaign speech, Jacques; but as we'll see, you reneged on your promise not just with the kaleidoscope (and we'll investigate, in depth, the many layers of contradiction and cluelessness you put on display in that disingenuous 'playing to the house'); no, we'll see how, at numerous other critical junctures, you instinctively took the wrong fork in the road whenever mathematical issues arose… henceforth, monsieur, as Joe Louis once said, 'You can run, but you just can't hide.'…."

Saturday, July 30, 2005

Saturday July 30, 2005

Filed under: General — Tags: — m759 @ 11:07 am

Born today: Arnold Schwarzenegger

Staircase

 

Frame not included in
 Terminator 2: Judgment Day

From Log24, Oct. 7, 2003:

"…Mondrian and Malevich are not
discussing canvas or pigment or graphite
or any other form of matter.
They are talking about
Being or Mind or Spirit.
From their point of view, the grid
is a staircase to the Universal…."

 

— Rosalind Krauss, "Grids"
 

Saturday July 30, 2005

Filed under: General — Tags: — m759 @ 10:18 am

Born today: Hilary Swank

  E is for Everlast

  The image “http://www.log24.com/log/pix05A/050730-Everlast2.jpg” cannot be displayed, because it contains errors.

"The grid is a staircase to the Universal."
— Rosalind Krauss

"To live is to defend a form."
— attributed to Hölderlin
 

Sunday, June 19, 2005

Sunday June 19, 2005

Filed under: General,Geometry — Tags: , , — m759 @ 4:00 am
ART WARS:
Darkness Visible
"No light, but rather darkness visible
 Serv'd only to discover sights of woe"
John Milton, Paradise Lost,
Book I,  lines 63-64
 
From the cover article (pdf) in the
June/July 2005 Notices of the
American Mathematical Society–

Martin Gardner

A famed vulgarizer, Martin Gardner,
summarizes the art of Ad Reinhardt
(Adolph Dietrich Friedrich Reinhardt,
  Dec. 24, 1913 – Aug. 30, 1967):
 
"Ed Rinehart [sic] made a fortune painting canvases that were just one solid color.  He had his black period in which the canvas was totally black.  And then he had a blue period in which he was painting the canvas blue.  He was exhibited in top shows in New York, and his pictures wound up in museums.  I did a column in Scientific American on minimal art, and I reproduced one of Ed Rinehart's black paintings.  Of course, it was just a solid square of pure black.  The publisher insisted on getting permission from the gallery to reproduce it."
 
Related material
from Log24.net,
Nov. 9-12, 2004:
 

Fade to Black

"…that ineffable constellation of talents that makes the player of rank: a gift for conceiving abstract schematic possibilities; a sense of mathematical poetry in the light of which the infinite chaos of probability and permutation is crystallized under the pressure of intense concentration into geometric blossoms; the ruthless focus of force on the subtlest weakness of an opponent."

— Trevanian, Shibumi

"'Haven't there been splendidly elegant colors in Japan since ancient times?'

'Even black has various subtle shades,' Sosuke nodded."

— Yasunari Kawabata, The Old Capital

An Ad Reinhardt painting
described in the entry of
noon, November 9, 2004
is illustrated below.

Ad Reinhardt,  Greek Cross

Ad Reinhardt,
Abstract Painting, 1960-66.
Oil on canvas, 60 x 60 inches.
Solomon R. Guggenheim Museum

The viewer may need to tilt
the screen to see that this
painting is not uniformly black,
but is instead a picture of a
Greek cross, as described below.

"The grid is a staircase to the Universal…. We could think about Ad Reinhardt, who, despite his repeated insistence that 'Art is art,' ended up by painting a series of… nine-square grids in which the motif that inescapably emerges is a Greek cross.

 

Greek Cross

There is no painter in the West who can be unaware of the symbolic power of the cruciform shape and the Pandora's box of spiritual reference that is opened once one uses it."

— Rosalind Krauss,
Meyer Schapiro Professor
of Modern Art and Theory
at Columbia University

(Ph.D., Harvard U., 1969),
in "Grids"

The image “http://www.log24.com/log/pix04B/041109-Krauss.jpg” cannot be displayed, because it contains errors.

Krauss

 In memory of
St. William Golding
(Sept. 19, 1911 – June 19, 1993)

Friday, April 15, 2005

Friday April 15, 2005

Filed under: General — Tags: — m759 @ 7:11 am
Leonardo Day

The image “http://www.log24.com/log/pix05/050415-Google.gif” cannot be displayed, because it contains errors.

In memory of Leonardo and of Chen Yifei (previous entry), a link to the Sino-Judaic Institute’s review of Chen’s film “Escape to Shanghai” —

The image “http://www.log24.com/log/pix05/050415-PointsEast.gif” cannot be displayed, because it contains errors.
Click on the above for details.

Related material
from Log24.net:


Saturday, December 27, 2003  10:21 PM

Toy

“If little else, the brain is an educational toy.  While it may be a frustrating plaything — one whose finer points recede just when you think you are mastering them — it is nonetheless perpetually fascinating, frequently surprising, occasionally rewarding, and it comes already assembled; you don’t have to put it together on Christmas morning.

The problem with possessing such an engaging toy is that other people want to play with it, too.  Sometimes they’d rather play with yours than theirs.  Or they object if you play with yours in a different manner from the way they play with theirs.  The result is, a few games out of a toy department of possibilities are universally and endlessly repeated.  If you don’t play some people’s game, they say that you have ‘lost your marbles,’ not recognizing that,

while Chinese checkers is indeed a fine pastime, a person may also play dominoes, chess, strip poker, tiddlywinks, drop-the-soap or Russian roulette with his brain.

One brain game that is widely, if poorly, played is a gimmick called ‘rational thought.’ “

— Tom Robbins, Even Cowgirls Get the Blues

Sol LeWitt
June 12, 1969
:

“I took the number twenty-four and there’s twenty-four ways of expressing the numbers one, two, three, four.  And I assigned one kind of line to one, one to two, one to three, and one to four.  One was a vertical line, two was a horizontal line, three was diagonal left to right, and four was diagonal right to left.  These are the basic kind of directions that lines can take…. the absolute ways that lines can be drawn.   And I drew these things as parallel lines very close to one another in boxes.  And then there was a system of changing them so that within twenty-four pages there were different arrangements of actually sixteen squares, four sets of four.  Everything was based on four.  So this was kind of a… more of a… less of a rational… I mean, it gets into the whole idea of methodology.”

Yes, it does.
See Art Wars, Poetry’s Bones, and Time Fold.


Friday, December 26, 2003  7:59 PM

ART WARS, St. Stephen’s Day:

The Magdalene Code

Got The Da Vinci Code for Xmas.

From page 262:

When Langdon had first seen The Little Mermaid, he had actually gasped aloud when he noticed that the painting in Ariel’s underwater home was none other than seventeenth-century artist Georges de la Tour’s The Penitent Magdalene — a famous homage to the banished Mary Magdalene — fitting decor considering the movie turned out to be a ninety-minute collage of blatant symbolic references to the lost sanctity of Isis, Eve, Pisces the fish goddess, and, repeatedly, Mary Magdalene.

Related Log24 material —

December 21, 2002:

A Maiden’s Prayer

The Da Vinci Code, pages 445-446:

“The blade and chalice?” Marie asked.  “What exactly do they look like?”

Langdon sensed she was toying with him, but he played along, quickly describing the symbols.

A look of vague recollection crossed her face.  “Ah, yes, of course.  The blade represents all that is masculine.  I believe it is drawn like this, no?”  Using her index finger, she traced a shape on her palm.

“Yes,” Langdon said.  Marie had drawn the less common “closed” form of the blade, although Langdon had seen the symbol portrayed both ways.

“And the inverse,” she said, drawing again upon her palm, “is the chalice, which represents the feminine.”

“Correct,” Langdon said….

… Marie turned on the lights and pointed….

“There you are, Mr. Langdon.  The blade and chalice.”….

“But that’s the Star of Dav–“

Langdon stopped short, mute with amazement as it dawned on him.

The blade and chalice.

Fused as one.

The Star of David… the perfect union of male and female… Solomon’s Seal… marking the Holy of Holies, where the male and female deities — Yahweh and Shekinah — were thought to dwell.

Related Log24 material —

May 25, 2003:
Star Wars.
 


Concluding remark of April 15, 2005:
For a more serious approach to portraits of
redheads, see Chen Yifei’s work.

The image “http://www.log24.com/log/pix05/050415-TheDuet-ChenYifei.jpg” cannot be displayed, because it contains errors.

Friday, November 26, 2004

Friday November 26, 2004

Filed under: General — m759 @ 1:11 pm

Dinner Theater?

“Philosophers ponder the idea of identity: what it is to give something a name on Monday and have it respond to that name on Friday….”
— Bernard Holland in the New York Times of Monday, May 20, 1996

From an entry of last Monday,
“Lynchburg Law” — 

The image “http://www.log24.com/log/pix04B/041122-Witchcraft.jpg” cannot be displayed, because it contains errors.

Critic Frank Rich in Wednesday’s Times on a recent televised promotion:

“… it was a manufactured scandal, as over-the-top as a dinner theater production of ‘The Crucible.’ “

From a Friday, Nov. 19, entry:

“the Platonist… is more interested in deriving an abstraction of the object into a universal….”

— Radu Surdulescu, Form, Structure, and Structurality

From El Universal online today:

“Meanwhile, [Mexico] continued to deal with the savagery of Tuesday night’s televised lynchings, with some saying the media had exploited the occurrence.

‘This is a new and worrisome phenomenon,’ security analyst José Reveles said in an interview… ‘It’s like the evil offspring of all the violent exploitation in the media.’  ‘It was Fuenteovejuna,’ he said, referring to the work by the Spanish golden age playwright Lope de Vega in which an entire town covers up the slaying of a corrupt official.”

Frank Rich has the last word:

“A ‘moral values’ crusade that stands between a TV show this popular and its audience will quickly learn the limits of its power in a country where entertainment is god.”

Friday, November 19, 2004

Friday November 19, 2004

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

From Tate to Plato
In honor of Allen Tate's birthday (today)
and of the MoMA re-opening (tomorrow)

"For Allen Tate the concept of tension was the most useful formal tool at the critic’s disposal, as irony and paradox were for Brooks. The principle of tension sustains the whole structure of meaning, and, as Tate declares in Tension in Poetry (1938), he derives it from lopping the prefixes off the logical terms extension and intension (which define the abstract and denotative aspect of the poetic language and, respectively, the concrete and connotative one). The meaning of the poem is 'the full organized body of all the extension and intension that we can find in it.'  There is an infinite line between extreme extension and extreme intension and the readers select the meaning at the point they wish along that line, according to their personal drives, interests or approaches. Thus the Platonist will tend to stay near the extension end, for he is more interested in deriving an abstraction of the object into a universal…."

— from Form, Structure, and Structurality,
   by Radu Surdulescu

"Eliot, in a conception comparable to Wallace Stevens' 'Anecdote of the Jar,' has suggested how art conquers time:

        Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness."

F. O. Matthiessen
   in The Achievement of T.S. Eliot,
   Oxford University Press, 1958

From Writing Chinese Characters:

"It is practical to think of a character centered within an imaginary square grid…. The grid can… be… subdivided, usually to 9 or 16 squares…."

The image “http://www.log24.com/log/pix04B/041119-ZhongGuo.jpg” cannot be displayed, because it contains errors.

These "Chinese jars"
(as opposed to their contents)
are as follows:

The image “http://www.log24.com/log/pix04B/041119-Grids.gif” cannot be displayed, because it contains errors.

Various previous Log24.net entries have
dealt with the 3×3 "form" or "pattern"
(to use the terms of T. S. Eliot).

For the 4×4 form, see Poetry's Bones
and Geometry of the 4×4 Square.

Tuesday, November 9, 2004

Tuesday November 9, 2004

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

The Nine
(Readings for
Weyl’s birthday)

“The grid is a staircase to the Universal….
We could think about Ad Reinhardt, who,
despite his repeated insistence that
‘Art is art,’
ended up by painting a series of…
nine-square grids in which the motif
that inescapably emerges is
a Greek cross.


Greek Cross

There is no painter in the West
who can be unaware of
the symbolic power
of the cruciform shape and the
Pandora’s box of spiritual reference
that is opened once one uses it.”

— Rosalind Krauss,
Meyer Schapiro Professor
of Modern Art and Theory
at Columbia University

(Ph.D., Harvard U., 1969),
in “Grids”

The image “http://www.log24.com/log/pix04B/041109-Krauss.jpg” cannot be displayed, because it contains errors.

Krauss

“Nine is a very powerful Nordic number.”
— Katherine Neville, author of The Eight,

The image “http://www.log24.com/log/pix04B/041109-Magic.jpg” cannot be displayed, because it contains errors.

in The Magic Circle,
Ballantine paperback,
1999, p. 339

The image “http://www.log24.com/log/pix04B/041109-Neville.jpg” cannot be displayed, because it contains errors.

Neville

“To live is to defend a form.”

(“Leben, das heisst eine Form verteidigen“)
attributed to Hölderlin

For details on the above picture,
which deals with properties of the
nine-square grid, see

Translation Plane.

For more on the defense
of this form,


see the Log24.net entry of
June 5, 2004, A Form,
and the Art Wars entries
for St. Peter’s Day, 2004.

Thursday, August 5, 2004

Thursday August 5, 2004

Filed under: General — Tags: — m759 @ 4:06 pm

In the beginning
was…
the recursion?

"Words are events."
— The Walter J. Ong Project,
    quoted in Log24 on Aug. 25, 2003 

"Words are events."
— The Walter J. Ong Project,
    quoted in the Heckler & Coch weblog
    on July 17, 2004 as part of a section
    titled "Recursive, Wide, and Loopy"

Walter J. Ong was a Jesuit.  The Feast of St. Ignatius Loyola, founder of the Jesuit order, is celebrated on July 31 each year.

"Recursive, Wide, and Loopy 2", a Heckler & Coch entry dated July 31, 2004, leads to the following:

MSNBC, Jan. 15, 2004:

How humans got
the gift of gab
:

Why do other primates
lag behind in language?
 

"New research may help scientists dissect just what it is about the human brain that endows us with language.

Researchers have found that tamarin monkeys have some distinctly languagelike abilities but that they can’t quite master the more complex rules of human grammar. The findings appear in Friday’s issue of the journal Science, published by AAAS, the non-profit science society.

 The grammatical toolkit

'A relatively open question concerning language evolution is, "What aspects of the language faculty are shared with other animals, and what aspects are unique to humans?" ' said study author Marc Hauser of Harvard University.

To investigate, Hauser and W. Tecumseh Fitch of the University of St. Andrews, in Scotland, devised tests for cotton-top tamarin monkeys and human volunteers. Tamarins have been evolving separately from humans for approximately 40 million years –suggesting that any shared machinery in human and tamarin brains is old enough to be relatively common among primates.

Instead of trying to teach the monkeys real words, Hauser and Fitch generated strings of one-syllable words that followed various grammatical rules.

According to linguistics expert Noam Chomsky, the simplest type of grammar is a 'finite state grammar' or 'FSG,' which dictates which types of words go near each other in a sentence. In English, for example, an adjective like 'fast' must go directly in front of 'car,' the noun it's describing.

Building on previous experiments, Hauser and Fitch recorded word-strings that obeyed a specific FSG, in which any syllable spoken by a female voice was automatically followed by one from a male voice.

Audio: Listen to an FSG word-string.
(Requires Windows Media Player.)

After listening to a series of word-strings, the monkeys were able to distinguish between those that followed this rule and others that didn't. Human test subjects could tell the difference as well, implying that tamarins and humans may share at least some components of what Hauser called 'the universal toolkit underlying all languages.'

Mastering this type of grammar represents the ability to compute some simple statistics, something human infants accomplish early on as they learn to speak. This ability may not be specific to language, however.

'Either the same mechanism or some approximation of it is used in mathematics, vision, music and other activities,' Hauser said.

Upping the Complexity

The grammatical rules of real languages govern more than just the placement of neighboring words, as anyone who had to diagram sentences in English class may remember all too well.

One of the more complex types of grammar is known as a 'phrase structure grammar,' or PSG. These grammars involve relationships between words that aren't next to each other in a sentence and thus allow for a more complex range of expression. The 'if … then' construction is an example of a PSG.

The researchers generated a second set of word-strings that followed a PSG in which a pairing of syllables spoken by a female and a male could be embedded within another pairing. This grammar produces structures like [female [female, male] male].

Audio: Listen to a PSG word-string.
(Requires Windows Media Player)

After playing these recordings repeatedly to the monkeys, the researchers found that the animals didn't seem to notice the difference between word strings that obeyed the PSG and other strings that did not. In contrast, the human volunteers did notice the difference."

— Kathleen Wren

"The grammar or syntax of human language is certainly unique. Like an onion or Russian doll, it is recursive: One instance of an item is embedded in another instance of the same item. Recursion makes it possible for the words in a sentence to be widely separated and yet dependent on one another. 'If-then' is a classic example…. Are animals capable of such recursion? Fitch and Hauser have reported that tamarin monkeys are not capable of recursion. Although the monkeys learned a nonrecursive grammar, they failed to learn a grammar that is recursive. Humans readily learn both."

— David Premack (Science 2004 303:318, quoted in ScienceWeek)

These citations by Heckler & Coch show that inability to understand complex language is not limited to monkeys.

The examples given by Wren in the audio samples are of alternating female (Hi) and male (Lo) voices, thus —

FSG:  Hi Lo Hi Lo Hi Lo

PSG:  Hi Hi Hi Lo Lo Lo

As these examples show, neither monkeys nor humans heard the sound of parentheses (or square brackets) as Wren describes them:

"structures like [female [female, male] male]."

There of course is, in ordinary language (which does not include the monologues of Victor Borge), no such thing as the sound of parentheses.

Thus the research of Hauser and Fitch is not only invalid, but ridiculous.

This point is driven strongly home by the following two articles:

Greg Kochanski, Research Fellow,
 Oxford University Phonetics Lab
:

Is a Phrase Structure Grammar
the Important Difference
between Humans and Monkeys?
,

and

Mark Liberman, Professor,
University of Pennsylvania

Departments of Linguistics
and of Computer Science,
and co-director of the
Institute for Research
in Cognitive Science,
in his

Language Log,
January 17, 2004:

Hi Lo Hi Lo,
it's off to
formal language theory
we go
.

Wednesday, May 19, 2004

Wednesday May 19, 2004

Filed under: General,Geometry — Tags: , — m759 @ 2:00 pm

Style

In memory of Lynn H. Loomis:

The above diagram is from a
(paper) journal note of October 21, 1999.

It pictures the relationship of my own discovery, diamond theory (at center), to the field, harmonic analysis, of Professor Loomis, a writer whose style I have long admired.

A quotation from the 1999 note:

"…it is not impossible to draw a fairly sharp dividing line between our mental disposition in the case of esthetic response and that of the responses of ordinary life.  A far more difficult question arises if we try to distinguish it from the responses made by us to certain abstract mental constructions such as those of pure mathematics…. Perhaps the distinction lies in this, that in the case of works of art the whole end and purpose is found in the exact quality of the emotional state, whereas in the case of mathematics the purpose is the constatation of the universal validity of the relations without regard to the quality of the emotion accompanying apprehension.  Still, it would be impossible to deny the close similarity of the orientation of faculties and attention in the two cases."
— Roger Fry, Transformations (1926), Doubleday Anchor paperback, 1956, p. 8

In other words, appreciating mathematics is much like appreciating art.

(Digitized diagram courtesy of Violet.)

Tuesday, April 6, 2004

Tuesday April 6, 2004

Filed under: General — Tags: , , , — m759 @ 10:00 pm

Ideas and Art, Part III

The first idea was not our own.  Adam
In Eden was the father of Descartes…

— Wallace Stevens, from
Notes Toward a Supreme Fiction

"Quaedam ex his tanquam rerum imagines sunt, quibus solis proprie convenit ideae nomen: ut cùm hominem, vel Chimaeram, vel Coelum, vel Angelum, vel Deum cogito."

Descartes, Meditationes III, 5

"Of my thoughts some are, as it were, images of things, and to these alone properly belongs the name idea; as when I think [represent to my mind] a man, a chimera, the sky, an angel or God."

Descartes, Meditations III, 5

Begin, ephebe, by perceiving the idea
Of this invention, this invented world,
The inconceivable idea of the sun.

You must become an ignorant man again
And see the sun again with an ignorant eye
And see it clearly in the idea of it.

— Wallace Stevens, from
Notes Toward a Supreme Fiction

"… Quinimo in multis saepe magnum discrimen videor deprehendisse: ut, exempli causâ, duas diversas solis ideas apud me invenio, unam tanquam a sensibus haustam, & quae maxime inter illas quas adventitias existimo est recensenda, per quam mihi valde parvus apparet, aliam verò ex rationibus Astronomiae desumptam, hoc est ex notionibus quibusdam mihi innatis elicitam, vel quocumque alio modo a me factam, per quam aliquoties major quàm terra exhibetur; utraque profecto similis eidem soli extra me existenti esse non potest, & ratio persuadet illam ei maxime esse dissimilem, quae quàm proxime ab ipso videtur emanasse."

Descartes, Meditationes III, 11

"… I have observed, in a number of instances, that there was a great difference between the object and its idea. Thus, for example, I find in my mind two wholly diverse ideas of the sun; the one, by which it appears to me extremely small draws its origin from the senses, and should be placed in the class of adventitious ideas; the other, by which it seems to be many times larger than the whole earth, is taken up on astronomical grounds, that is, elicited from certain notions born with me, or is framed by myself in some other manner. These two ideas cannot certainly both resemble the same sun; and reason teaches me that the one which seems to have immediately emanated from it is the most unlike."

Descartes, Meditations III, 11

"Et quamvis forte una idea ex aliâ nasci possit, non tamen hîc datur progressus in infinitum, sed tandem ad aliquam primam debet deveniri, cujus causa sit in star archetypi, in quo omnis realitas formaliter contineatur, quae est in ideâ tantùm objective."

Descartes, Meditationes III, 15

"And although an idea may give rise to another idea, this regress cannot, nevertheless, be infinite; we must in the end reach a first idea, the cause of which is, as it were, the archetype in which all the reality [or perfection] that is found objectively [or by representation] in these ideas is contained formally [and in act]."

Descartes, Meditations III, 15

Michael Bryson in an essay on Stevens's "Notes Toward a Supreme Fiction,"

The Quest for the Fiction of the Absolute:

"Canto nine considers the movement of the poem between the particular and the general, the immanent and the transcendent: "The poem goes from the poet's gibberish to / The gibberish of the vulgate and back again. / Does it move to and fro or is it of both / At once?" The poet, the creator-figure, the shadowy god-figure, is elided, evading us, "as in a senseless element."  The poet seeks to find the transcendent in the immanent, the general in the particular, trying "by a peculiar speech to speak / The peculiar potency of the general." In playing on the senses of "peculiar" as particular and strange or uncanny, these lines play on the mystical relation of one and many, of concrete and abstract."

Brian Cronin in Foundations of Philosophy:

"The insight is constituted precisely by 'seeing' the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight."

— From Ch. 2, Identifying Direct Insights

Michael Bryson in an essay on Stevens's "Notes Toward a Supreme Fiction":

"The fourth canto returns to the theme of opposites. 'Two things of opposite natures seem to depend / On one another . . . . / This is the origin of change.'  Change resulting from a meeting of opposities is at the root of Taoism: 'Tao produced the One. / The One produced the two. / The two produced the three. / And the three produced the ten thousand things' (Tao Te Ching 42) …."

From an entry of March 7, 2004

 

From the web page

Introduction to the I Ching–
By Richard Wilhelm
:

"He who has perceived the meaning of change fixes his attention no longer on transitory individual things but on the immutable, eternal law at work in all change. This law is the tao of Lao-tse, the course of things, the principle of the one in the many. That it may become manifest, a decision, a postulate, is necessary. This fundamental postulate is the 'great primal beginning' of all that exists, t'ai chi — in its original meaning, the 'ridgepole.' Later Chinese philosophers devoted much thought to this idea of a primal beginning. A still earlier beginning, wu chi, was represented by the symbol of a circle. Under this conception, t'ai chi was represented by the circle divided into the light and the dark, yang and yin,

.

This symbol has also played a significant part in India and Europe. However, speculations of a gnostic-dualistic character are foreign to the original thought of the I Ching; what it posits is simply the ridgepole, the line. With this line, which in itself represents oneness, duality comes into the world, for the line at the same time posits an above and a below, a right and left, front and back-in a word, the world of the opposites."

The t'ai chi symbol is also illustrated on the web page Cognitive Iconology, which says that

"W.J.T. Mitchell calls 'iconology'
a study of the 'logos'
(the words, ideas, discourse, or 'science')
of 'icons' (images, pictures, or likenesses).
It is thus a 'rhetoric of images'
(Iconology: Image, Text, Ideology, p. 1)."

A variation on the t'ai chi symbol appears in a log24.net entry for March 5:

The Line,
by S. H. Cullinane

See too my web page Logos and Logic, which has the following:

"The beautiful in mathematics resides in contradiction. Incommensurability, logoi alogoi, was the first splendor in mathematics."

— Simone Weil, Oeuvres Choisies, ed. Quarto, Gallimard, 1999, p. 100

 Logos Alogos,
by S. H. Cullinane 

In the conclusion of Section 3, Canto X, of "Notes," Stevens says

"They will get it straight one day
at the Sorbonne.
We shall return at twilight
from the lecture
Pleased that
the irrational is rational…."

This is the logoi alogoi of Simone Weil.

In "Notes toward a Supreme Fiction,"
Wallace Stevens lists three criteria
for a work of the imagination:

It Must Be Abstract

The Line,
by S.H. Cullinane 

It Must Change

 The 24,
by S. H. Cullinane

It Must Give Pleasure

Puzzle,
by S. H. Cullinane

Related material:

Logos and Logic.

 

Tuesday April 6, 2004

Filed under: General — m759 @ 2:45 am

Ideas and Art, Part II

"We do not, of course, see  ideas."

— Roger Kimball, Minimalist Fantasies, 2003

"Idea (Lat. idea , forma , species ; Gk. idea , eidos , from idein , to see; Fr. idée ; Ger. Bild ; Begriff )

Probably to no other philosophical term have there been attached so many different shades of meaning as to the word idea. Yet what this word signifies is of much importance. Its sense in the minds of some philosophers is the key to their entire system. But from Descartes onwards usage has become confused and inconstant. Locke, in particular, ruined the term altogether in English philosophical literature…."

The Catholic Encylopedia, 1910  

James Hillman, A Blue Fire , p. 53:

"For us ideas are ways of regarding things (modi res considerandi ), perspectives.  Ideas give us eyes, let us see …. Ideas are ways of seeing and knowing….

Our word idea  comes from the Greek eidos , which meant originally in early Greek thought, and as Plato used it, both that which one sees — an appearance or shape in a concrete sense — and that by means of which one sees.  We see them, and by means of them.  Ideas are both the shape of events, their constellation in this or that archetypal pattern, and the modes that make possible our ability to see through events into their pattern.  By means of an idea we can see the idea cloaked in the passing parade.  The implicit connection between having ideas to see with  and seeing ideas themselves suggests that the more ideas we have, the more we see, and the deeper the ideas we have, the deeper we see.  It also suggests that ideas engender other ideas, breeding new perspectives for viewing ourselves and world.

Moreover, without them we cannot 'see' even what we sense with the eyes in our heads, for our perceptions are shaped according to particular ideas …. And our ideas change as changes take place in the soul, for as Plato said, soul and idea refer to each other, in that an idea is the 'eye of the soul,' opening us through its insight and vision."

Hillman does not say where in Plato this extraordinary saying, that an idea is the eye of the soul, occurs.  He is probably wrong.

Both Kimball and Hillman seem confused.

A more sensible approach to these matters is available in Brian Cronin's Foundations of Philosophy:

"3.4 An Insight Pivots between the Abstract and the Concrete

On the one hand, an insight is dealing with data and images which are concrete and particular: Archimedes had one chalice, one King, and one particular problem to solve. On the other hand, what the insight grasps is an idea, a relation, a universal, a law; and that is abstract. The laws that Archimedes eventually formulated were universal, referring not only to this chalice but also to any other material body immersed in any other liquid at any time or any place. The insight is constituted precisely by 'seeing' the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete. We pivot back and forth between images and ideas as we search for the correct insight. First let us now clarify the difference between images, ideas and concepts…."

— From Ch. 2, Identifying Direct Insights

Tuesday, February 3, 2004

Tuesday February 3, 2004

Filed under: General — m759 @ 11:11 am

The Quality with No Name

And what is good, Phædrus,
and what is not good…
Need we ask anyone to tell us these things?

— Epigraph to
   Zen and the Art of Motorcyle Maintenance

Brad Appleton discusses a phrase of Christopher Alexander:

“The ‘Quality Without A Name‘ (abbreviated as the acronym QWAN) is the quality that imparts incommunicable beauty and immeasurable value to a structure….

Alexander proposes the existence of an objective quality of aesthetic beauty that is universally recognizable. He claims there are certain timeless attributes and properties which are considered beautiful and aesthetically pleasing to all people in all cultures (not just ‘in the eye of the beholder’). It is these fundamental properties which combine to generate the QWAN….”

See, too, The Alexander-Pirsig Connection.

Saturday, December 27, 2003

Saturday December 27, 2003

Filed under: General — m759 @ 10:21 pm

Toy

“If little else, the brain is an educational toy.  While it may be a frustrating plaything — one whose finer points recede just when you think you are mastering them — it is nonetheless perpetually fascinating, frequently surprising, occasionally rewarding, and it comes already assembled; you don’t have to put it together on Christmas morning.

The problem with possessing such an engaging toy is that other people want to play with it, too.  Sometimes they’d rather play with yours than theirs.  Or they object if you play with yours in a different manner from the way they play with theirs.  The result is, a few games out of a toy department of possibilities are universally and endlessly repeated.  If you don’t play some people’s game, they say that you have ‘lost your marbles,’ not recognizing that,

while Chinese checkers is indeed a fine pastime, a person may also play dominoes, chess, strip poker, tiddlywinks, drop-the-soap or Russian roulette with his brain.

One brain game that is widely, if poorly, played is a gimmick called ‘rational thought.’ “

— Tom Robbins, Even Cowgirls Get the Blues

Sol LeWitt
June 12, 1969
:

“I took the number twenty-four and there’s twenty-four ways of expressing the numbers one, two, three, four.  And I assigned one kind of line to one, one to two, one to three, and one to four.  One was a vertical line, two was a horizontal line, three was diagonal left to right, and four was diagonal right to left.  These are the basic kind of directions that lines can take…. the absolute ways that lines can be drawn.   And I drew these things as parallel lines very close to one another in boxes.  And then there was a system of changing them so that within twenty-four pages there were different arrangements of actually sixteen squares, four sets of four.  Everything was based on four.  So this was kind of a… more of a… less of a rational… I mean, it gets into the whole idea of methodology.”

Yes, it does.
See Art Wars, Poetry’s Bones, and Time Fold.

Tuesday, October 7, 2003

Tuesday October 7, 2003

Filed under: General — m759 @ 5:09 pm

ART WARS:
Judgment Day

“…Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal….”

— Rosalind Krauss, “Grids”

Krauss is the Meyer Schapiro Professor of Modern Art and Theory at Columbia University.

For more on Meyer Schapiro, see the link on the phrase “art historian” in my March 10, 2003, entry.

To view that entry in a larger context, see the web page Art at the Vanishing Point, which includes a picture of Mondrian’s own Paris staircase.  The picture below might be thought of as illustrating Krauss’s “grid is a staircase”… a staircase to, in fact, a vanishing point.

 

Frame not included in
 Terminator 2: Judgment Day

For a different view of what the New York Times Book Review has characterized as “high culture,” see the link on that phrase also in my March 10, 2003, entry.  This leads to a work by T. S. Eliot titled Christianity and Culture.   See too the remarks of the Meyer Schapiro Professor in my Oct. 5, 2003, entry, “Art Theory for Yom Kippur,”  in which she likens the Cross to Pandora’s box.

Eliot’s attitude toward this Jewish approach to high culture might be summarized by the following remarks of Sarah Connor in Terminator 2: Judgment Day

Dr. Silberman: You broke my arm!

Sarah Connor: There are two-hundred-fifteen bones in the human body, [expletive deleted]. That’s one.

Sunday, October 5, 2003

Sunday October 5, 2003

Filed under: General — Tags: , , — m759 @ 5:09 am

At Mount Sinai:
Art Theory for Yom Kippur

From the New York Times of Sunday, October 5, 2003 (the day that Yom Kippur begins at sunset):

Rabbi Ephraim Oshry, whose interpretations of religious law helped sustain Lithuanian Jews during Nazi occupation…. died on Sept. 28 at Mount Sinai Hospital in Manhattan. He was 89.”

For a fictional portrait of Lithuanian Jews during Nazi occupation, see the E. L. Doctorow novel City of God.

For meditations on the spiritual in art, see the Rosalind Krauss essay “Grids.”   As a memorial to Rabbi Oshry, here is a grid-based version of the Hebrew letter aleph:


Rabbi Oshry


Aleph

Click on the aleph for details.

“In the garden of Adding,
Live Even and Odd….”
— The Midrash Jazz Quartet in
       City of God, by E. L. Doctorow

Here are two meditations
on Even and Odd for Yom Kippur:

Meditation I

From Rosalind Krauss, “Grids”:

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

Or, to take a more up-to-date example, we could think about Ad Reinhardt who, despite his repeated insistence that ‘Art is art,’ ended up by painting a series of black nine-square grids in which the motif that inescapably emerges is a Greek cross.  There is no painter in the West who can be unaware of the symbolic power of the cruciform shape and the Pandora’s box of spiritual reference that is opened once one uses it.”

Meditation II

Here, for reference, is a Greek cross
within a nine-square grid:

 Related religious meditation for
Doctorow’s “Garden of Adding”…

 4 + 5 = 9.

Saturday, July 26, 2003

Saturday July 26, 2003

Filed under: General,Geometry — Tags: — m759 @ 11:11 pm

The Transcendent
Signified

“God is both the transcendent signifier
and transcendent signified.”

— Caryn Broitman,
Deconstruction and the Bible

“Central to deconstructive theory is the notion that there is no ‘transcendent signified,’ or ‘logos,’ that ultimately grounds ‘meaning’ in language….”

— Henry P. Mills,
The Significance of Language,
Footnote 2

“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato’s (realist) reaction to the sophists (nominalists). What is often called ‘postmodernism’ is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth.”

Simon Blackburn, Think,
Oxford University Press, 1999, page 268

The question of universals is still being debated in Paris.  See my July 25 entry,

A Logocentric Meditation.

That entry discusses an essay on
mathematics and postmodern thought
by Michael Harris,
professor of mathematics
at l’Université Paris 7 – Denis Diderot.

A different essay by Harris has a discussion that gets to the heart of this matter: whether pi exists as a platonic idea apart from any human definitions.  Harris notes that “one might recall that the theorem that pi is transcendental can be stated as follows: the homomorphism Q[X] –> R taking X to pi is injective.  In other words, pi can be identified algebraically with X, the variable par excellence.”

Harris illustrates this with
an X in a rectangle:

For the complete passage, click here.

If we rotate the Harris X by 90 degrees, we get a representation of the Christian Logos that seems closely related to the God-symbol of Arthur C. Clarke and Stanley Kubrick in 2001: A Space Odyssey.  On the left below, we have a (1x)4×9 black monolith, representing God, and on the right below, we have the Harris slab, with X representing (as in “Xmas,” or the Chi-rho page of the Book of Kells) Christ… who is, in theological terms, also “the variable par excellence.”

Kubrick’s
monolith

Harris’s
slab

For a more serious discussion of deconstruction and Christian theology, see

Walker Percy’s Semiotic.

Friday, July 25, 2003

Friday July 25, 2003

Filed under: General — Tags: , , — m759 @ 5:24 pm

For Jung’s 7/26 Birthday:
A Logocentric Meditation

Leftist academics are trying to pull a fast one again.  An essay in the most prominent American mathematical publication tries to disguise a leftist attack on Christian theology as harmless philosophical woolgathering.

In a review of Vladimir Tasic’s Mathematics and the Roots of Postmodern Thought, the reviewer, Michael Harris, is being less than candid when he discusses Derrida’s use of “logocentrism”:

“Derrida uses the term ‘logocentrism’… as ‘the metaphysics of phonetic writing’….”

Notices of the American Mathematical Society, August 2003, page 792

We find a rather different version of logocentrism in Tasic’s own Sept. 24, 2001, lecture “Poststructuralism and Deconstruction: A Mathematical History,” which is “an abridged version of some arguments” in Tasic’s book on mathematics and postmodernism:

“Derrida apparently also employs certain ideas of formalist mathematics in his critique of idealist metaphysics: for example, he is on record saying that ‘the effective progress of mathematical notation goes along with the deconstruction of metaphysics.’

Derrida’s position is rather subtle. I think it can be interpreted as a valiant sublation of two completely opposed schools in mathematical philosophy. For this reason it is not possible to reduce it to a readily available philosophy of mathematics. One could perhaps say that Derrida continues and critically reworks Heidegger’s attempt to ‘deconstruct’ traditional metaphysics, and that his method is more ‘mathematical’ than Heidegger’s because he has at his disposal the entire pseudo-mathematical tradition of structuralist thought. He has himself implied in an interview given to Julia Kristeva that mathematics could be used to challenge ‘logocentric theology,’ and hence it does not seem unreasonable to try looking for the mathematical roots of his philosophy.”

The unsuspecting reader would not know from Harris’s review that Derrida’s main concern is not mathematics, but theology.  His ‘deconstruction of metaphysics’ is actually an attack on Christian theology.

From “Derrida and Deconstruction,” by David Arneson, a University of Manitoba professor and writer on literary theory:

Logocentrism: ‘In the beginning was the word.’ Logocentrism is the belief that knowledge is rooted in a primeval language (now lost) given by God to humans. God (or some other transcendental signifier: the Idea, the Great Spirit, the Self, etc.) acts a foundation for all our thought, language and action. He is the truth whose manifestation is the world.”

Some further background, putting my July 23 entry on Lévi-Strauss and structuralism in the proper context:

Part I.  The Roots of Structuralism

“Literary science had to have a firm theoretical basis…”

Part II.  Structuralism/Poststructuralism

“Most [structuralists] insist, as Levi-Strauss does, that structures are universal, therefore timeless.”

Part III.  Structuralism and
Jung’s Archetypes

Jung’s “theories, like those of Cassirer and Lévi-Strauss, command for myth a central cultural position, unassailable by reductive intellectual methods or procedures.”

And so we are back to logocentrism, with the Logos — God in the form of story, myth, or archetype — in the “central cultural position.”

What does all this have to do with mathematics?  See

Plato’s Diamond,

Rosalind Krauss on Art –

“the Klein group (much beloved of Structuralists)”

Another Michael Harris Essay, Note 47 –

“From Krauss’s article I learned that the Klein group is also called the Piaget group.”

and Jung on Quaternity:
Beyond the Fringe –

“…there is no denying the fact that [analytical] psychology, like an illegitimate child of the spirit, leads an esoteric, special existence beyond the fringe of what is generally acknowledged to be the academic world.”

What attitude should mathematicians have towards all this?

Towards postmodern French
atheist literary/art theorists –

Mathematicians should adopt the attitude toward “the demimonde of chic academic theorizing” expressed in Roger Kimball’s essay, Feeling Sorry for Rosalind Krauss.

Towards logocentric German
Christian literary/art theorists –

Mathematicians should, of course, adopt a posture of humble respect, tugging their forelocks and admitting their ignorance of Christian theology.  They should then, if sincere in their desire to honestly learn something about logocentric philosophy, begin by consulting the website

The Quest for the Fiction of an Absolute.

For a better known, if similarly disrespected, “illegitimate child of the spirit,” see my July 22 entry.

Friday, July 11, 2003

Friday July 11, 2003

Filed under: General — m759 @ 10:23 pm

Father, Son,
and Holy Coast

Here are some religious meditations for the holy day 7-11:

As the website Hollywood Jesus perceptively points out, defending the story theory of truth, “Images that carry universal truths move us from the mundane to the sacred.  Jesus knew this when he spoke in parables.”

Here is a parable about my own name.

The Hollywood Jesus site tries to connect the cross of Christ, “holy wood,” with Hollywood by claiming that the words “holly” and “holy” are cognate.

See Hollywood and the Cross.

From the Online Etymology Dictionary

holly – O.E. holegn, from P.Gmc. *khuli-.

holy – O.E. halig “holy,” from P.Gmc. *khailagas. Adopted at conversion for L. sanctus. Primary meaning may have been “that must be preserved whole or intact, that cannot be transgressed or violated,” which would connect it with O.E. hal (see whole).

This shows that the holly-holy connection is, pace Neil Diamond, like nearly every other Christian claim, a damned lie.

Connoisseurs of junk culture may enjoy
a midi of Neil Diamond as background
for this Hollywood Jesus.

Here is a different Hollywood etymology that may be somewhat truer.

From the RootsWeb.com archives:

Re: CULLINANE-HOLLYWOOD-holly tree

“Cullen in Irish is Ó Cuillin (holly tree). …  This astonishingly simple name has worked its way through an astonishing number of variations including Cullion, Culhoun, MacCullen and Cullinane. …

In a message dated 6/5/01 8:24:18 PM Pacific Daylight Time, lawlerc@aol.comnojunk writes:

‘I do not have the surname in my family, but while looking at the Old Age Pension applications for the Barony of Strabane Upper, in the County of Tyrone, there was a notation that

the English equivalent of the surname CULLINANE is HOLLYWOOD.‘ “

Friday, July 4, 2003

Friday July 4, 2003

Filed under: General — m759 @ 12:00 am

Self-Evident

Today many Americans celebrate a declaration of certain “self-evident” truths.  Others feel that these alleged “truths” are misleading.  Seeking a worthy opponent for the authors of the Declaration on this secular holy day, I settled on the following recently published book, a sort of Declaration of Dependence of government on God (an imaginary entity who speaks only through politicians, clergymen, and other liars):

Christian Faith
and Modern Democracy:

God and Politics in the Fallen World
By Robert P. Kraynak
Univ. of Notre Dame Press. 304p
$49.95 (cloth) $24.95 (paper)

From a review in the Dec. 24, 2001, issue of America, a Jesuit publication:

“The author, who identifies himself as a practicing Catholic, asserts that Christianity is weakened by its close alliance with the contemporary version of democracy and human rights…. 

The author states that ‘modern liberal democracy…subverts in practice the dignity of man.’  He defends his thesis relentlessly and persuasively…. 

Some readers of this well-organized volume will be disappointed that the author makes no mention of the four billion non-Christians among the world’s 6.1 billion inhabitants. The four billion Hindus, Muslims and Buddhists must be included in any attempt to make the modern state responsive to traditional and generally accepted norms of morality.”

— Robert F. Drinan, S.J.

Jefferson would probably appreciate Drinan’s remark on catholic (i.e., universal, or “generally accepted”) norms.

The “traditional and generally accepted norms of morality” Drinan mentions are discussed ably by Christian apologist C. S. Lewis in his book The Abolition of Man, which argues for the existence of a universal moral code that I am pleased to note he calls, rightly, the Tao.  As an Amazon.com reviewer notes, Lewis uses this term in the manner of Confucius rather than that of Lao Tsu.  I prefer the latter. 

For details, see the Tao Te Ching, (The Way and Its Power).  This is a far more holy scripture than the collections of lies called sacred by most other religions.  Both the leftist Jefferson and the rightist Kraynak wrongly assume that talk of a “Creator” means something.  It does not.  Classical Chinese thought is free from this absurd Western error.  Lewis at least had the grace to acknowledge the importance of non-Western thought, though he himself was unable to escape the lies of Christianity.

Friday, March 21, 2003

Friday March 21, 2003

Filed under: General — Tags: , , — m759 @ 9:29 am

ART WARS:

Readings for Bach's Birthday

Larry J. Solomon:

Symmetry as a Compositional Determinant,
Chapter VIII: New Transformations

In Solomon's work, a sequence of notes is represented as a set of positions within a Latin square:

Transformations of the Latin square correspond to transformations of the musical notes.  For related material, see The Glass Bead Game, by Hermann Hesse, and Charles Cameron's sites on the Game.

Steven H. Cullinane:

Orthogonal Latin Squares as Skew Lines, and

Map Systems

Dorothy Sayers:

"The function of imaginative speech is not to prove, but to create–to discover new similarities, and to arrange them to form new entities, to build new self-consistent worlds out of the universe of undifferentiated mind-stuff." (Christian Letters to a Post-Christian World, Grand Rapids: Eerdmans, 1969, p. xiii)

— Quoted by Timothy A. Smith, "Intentionality and Meaningfulness in Bach's Cyclical Works"

Edward Sapir:

"…linguistics has also that profoundly serene and satisfying quality which inheres in mathematics and in music and which may be described as the creation out of simple elements of a self-contained universe of forms.  Linguistics has neither the sweep nor the instrumental power of mathematics, nor has it the universal aesthetic appeal of music.  But under its crabbed, technical, appearance there lies hidden the same classical spirit, the same freedom in restraint, which animates mathematics and music at their purest."

 "The Grammarian and his Language,"
American Mercury 1:149-155, 1924

Tuesday, March 4, 2003

Tuesday March 4, 2003

Filed under: General — Tags: — m759 @ 9:25 pm

Fearful Symmetry

I just Googled this phrase and found the following site, which turns out to be related to my previous entry on the Bead Game and the death of John P. Thompson.

Fearful Symmetry:
The Music Master’s Lecture
,

by Daniel d’Quincy.

This in turn links to an excerpt from The Glass Bead Game that includes this passage: 

“I suddenly realized that in the language, or at any rate in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created.”

It is very easy to get dangerously confused about holiness, but here are some relevant quotes:

“You will have to allow me to digress a bit in order to bring ourselves to a sufficiently elevated perspective… I warn you, it will require an attitude of playfulness on your part. Our approach will aim more at sincerity than seriousness. The attitude I’m aiming at is best expressed, I suppose, in the playing of a unique game, known by its German name as Das Glasperlenspiel, and which we may translate as the Glass Bead Game.”

— Daniel d’Quincy, Fearful Symmetry 

“7:11”

— God himself said this, at least according to the previous entry and to my Jan. 28 entry, State of the Communion.

“Seven is heaven.”

— See my web page Eight is a Gate.

“An excellent example of a ‘universal’ in the sense of Charles Williams, Jung, or Plato is Hexagram 11 in China’s 3,000-year-old classic, the I Ching:

Hexagram 11

‘Heaven and earth unite:
 the image of PEACE.’ 
 (Wilhelm/Baynes translation,
 Princeton University Press, 1967)” 

— S. H. Cullinane, Plato, Pegasus, and the Evening Star

Thus we may associate the numbers 7 and 11 with the notions of heaven and peace; for a somewhat darker association of the time 7:11 with Kali as Time the Destroyer, see my last entry and also my previous entries

Fat Man and Dancing Girl (Feb. 18, 2003), and 

Time and Eternity (Feb. 1, 2003).

Monday, December 30, 2002

Monday December 30, 2002

Filed under: General — m759 @ 8:30 pm

Homer

“No matter how it’s done, you won’t like it.”
— Robert Redford to Robert M. Pirsig in Lila

The evening before Harriet injures Roy,
she asks him, in a restaurant car,
whether he has read Homer.”
Oxford website on the film of The Natural

“Brush Up Your Shakespeare”
— Cole Porter lyric for a show that opened
on December 30, 1948

Judy Davis as Harriet Bird

                                        

Thine eyes I love…
Shakespeare, Sonnet 132

“Roy’s Guenevere-like lover is named Memo Paris,
presumably the face that launched a thousand strikes.”
Oxford website on the film of The Natural 

Nicole Kidman
as Memo Paris

“Iris is someone to watch over Roy.”
Oxford website on the film of The Natural 

Kate Winslet as young Iris Murdoch

From the second-draft screenplay
for The Sting,
with Robert Redford as Hooker:

HOOKER
(shuffling a little)
I, ah…thought you might wanna come out for a while.  Maybe have a drink or somethin’.

LORETTA
You move right along, don’t ya.

HOOKER
(with more innocence than confidence)
I don’t mean nothin’ by it.  I just don’t know many regular girls, that’s all.

LORETTA
And you expect me to come over, just like that.

HOOKER
If I expected somethin’, I wouldn’t be still standin’ out here in the hall.

Loretta looks at him carefully.  She knows it’s not a line.

LORETTA
(with less resistance now)
I don’t even know you.

HOOKER
(slowly)
You know me.  I’m just like you…
It’s two in the morning and I don’t know nobody.

The two just stand there in silence a second.  There’s nothing more to say.  She stands back and lets him in.

Iris Murdoch on Plato’s Form of the Good,
by Joseph Malikail:

For Murdoch as for Plato, the Good belongs to Plato’s Realm of Being not the Realm of Becoming…. However, Murdoch does not read Plato as declaring his faith in a divine being when he says that the Good is

the universal author of all things beautiful and right, parent of light and the lord of light in the visible world, and the immediate source of reason and truth in the intellectual; and that this is the power upon which [one who] would act rationally either in public or private life must have his eyes fixed (Republic…).

Though she acknowledges the influence of Simone Weil in her reading of Plato, her understanding of Plato on Good and God is not Weil’s (1952, ch.7)*. For Murdoch,

Plato never identified his Form of the Good with God (the use of theos in the Republic… is a façon de parler), and this separation is for him an essential one. Religion is above the level of the ‘gods.’ There are no gods and no God either. Neo-Platonic thinkers made the identification (of God with good) possible; and the Judaeo-Christian tradition has made it easy and natural for us to gather together the aesthetic and consoling impression of Good as a person (1992, 38)**.

As she understands Plato:

The Form of the Good as creative power is not a Book of Genesis creator ex nihilo … Plato does not set up the Form of the Good as God, this would be absolutely un-Platonic, nor does he anywhere give the sign of missing or needing a real God to assist his explanations. On the contrary, Good is above the level of the gods or God (ibid., 475)**.

Mary Warnock, her friend and fellow-philosopher, sums up Murdoch’s metaphysical view of the Vision of the Good:

She [Murdoch] holds that goodness has a real though abstract existence in the world. The actual existence of goodness is, in her view, the way it is now possible to understand the idea of God.

Or as Murdoch herself puts it, ‘Good represents the reality of which God is the dream.’ (1992, 496)**”

*Weil, Simone. 1952. Intimations of Christianity Among The Ancient Greeks. Ark Paperbacks, 1987/1952.

**Murdoch, Iris. 1992. Metaphysics As A Guide To Morals. London: Chatto and Windus. 

From the conclusion of Lila,
by Robert M. Pirsig:

“Good is a noun. That was it. That was what Phaedrus had been looking for. That was the homer over the fence that ended the ballgame.”

Friday, September 13, 2002

Friday September 13, 2002

Filed under: General — m759 @ 2:24 pm

Meditation for Friday the 13th

The 1946 British film below (released as “Stairway to Heaven” in the U.S.) is one of my favorites.  I saw it as a child. Since costar Kim Hunter died this week (on 9/11), and since today is Friday the 13th, the following material seems relevant.

Kim Hunter in 1946

R.A.F pilot
and psychiatrist 

Alan McGlashan

Alan McGlashan has practiced as a psychiatrist in London for more than forty years.  He also served as a pilot for the R.A.F. (with MC and Croix de Guerre decorations). 

The doctor in “A Matter of Life and Death” addresses a heavenly court on behalf of his patient, R.A.F pilot David Niven:

In the film, David Niven is saved by mistake from a fated death and his doctor must argue to a heavenly court that he be allowed to live. 

In a similar situation, I would want Dr. Alan McGlashan, a real-life psychiatrist, on my side.  For an excerpt from one of my favorite books, McGlashan’s The Savage and Beautiful Country,

click here.

As Walker Percy has observed (see my Sept. 7 note, “The Boys from Uruguay”), a characteristic activity of human beings is what Percy called “symbol-mongering.”  In honor of today’s anniversary of the births of two R.A.F. fighter pilots,

Sir Peter Guy Wykeham-Barnes (b. 1915) and author

Roald Dahl (b. 1916),

here is one of the better symbols of the past century:

The circle is of course a universal symbol, and can be made to mean just about whatever one wants it to mean.  In keeping with Clint Eastwood’s advice, in the soundtrack album for “Midnight in the Garden of Good and Evil,” to “accentuate the positive,” here are some positive observations on a circle from the poet (and perhaps saint) Dante, who died on the night of September 13-14:

In the sun, Dante and Beatrice find themselves surrounded by a circle of souls famous for their wisdom on earth. They appear as splendid lights and precious jewels who dance and sing as they lovingly welcome two more into their company. Their love for God is kindled even more and grows as they find more individuals to love. Among the blessed souls are St. Thomas Aquinas and one of his intellectual “enemies”, Siger of Brabant, a brilliant philosopher at the University of Paris, some of whose teachings were condemned as heretical. Conflicts and divisions on earth are now forgotten and absorbed into a communal love song and dance “whose sweetness and harmony are unknown on earth and whose joy becomes one with eternity.”

Dante compares their dance and song to God’s bride on earth, the Church, when she answers the morning bells to rise from bed and “woo with matins song her Bridegroom’s love.” Some critics consider this passage the most “spiritually erotic” of all the one hundred cantos of the Comedy. It is the ending of Canto 10, verses 139-148.

— Fr. James J. Collins, “The Spiritual Journey with Dante V,” Priestly People October 1997

The above material on Dante is from the Servants of the Paraclete website.

For more on the Paraclete, see

The Left Hand of God.

See also the illustration in the note below.

Tuesday, August 6, 2002

Tuesday August 6, 2002

Filed under: General — m759 @ 12:24 pm

Veritatis Splendor

Black Holes 

Conclusion of the Nobel Prize lecture of Subrahmanyan Chandrasekhar on December 8, 1983:

The mathematical theory of black holes is a subject of immense complexity; but its study has convinced me of the basic truth of the ancient mottoes,

The simple is the seal of the true

and

Beauty is the splendour of truth.

White Holes

Statement by Karol Wojtyla on August 6, 1993: 

The splendour of truth shines forth in all the works of the Creator and, in a special way, in man, created in the image and likeness of God (cf. Gen 1:26).

Wojtyla, who apparently prefers folk-tales to truth, may appreciate the website White Hole Theory at the World University Library

Is the Pope Catholic?

The World University Library furnishes an answer to the question that has long troubled many:  Is the Pope Catholic?

According to Catholic.com,

The Greek roots of the term “Catholic” mean “according to (kata-) the whole (holos),” or more colloquially, “universal.”

Upon comparing the contents of the World University Library with the contents of Wojtyla’s 1993 statement, it becomes apparent that the World University Library is catholic (i.e., universal), but the Pope is not.  

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