Log24

Sunday, May 7, 2017

Art Space

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

Detail of an image in the previous post

This suggests a review of a post on a work of art by fashion photographer
Peter Lindbergh, made when he was younger and known as "Sultan."

The balls in the foreground relate Sultan's work to my own.

Linguistic backstory —

The art space where the pieces by Talman and by Lindbergh
were displayed is Museum Tinguely in Basel.

As the previous post notes, the etymology of "glamour" (as in
fashion photography) has been linked to "grammar" (as in 
George Steiner's Grammars of Creation ). A sculpture by 
Tinguely (fancifully representing Heidegger) adorns one edition
of Grammars .

Yale University Press, 2001:

Tinguely, "Martin Heidegger,
Philosopher," sculpture, 1988

Sunday, October 9, 2016

Tinguely Museum

Filed under: General — m759 @ 7:01 AM

Yale University Press, 2001:

Tinguely, "Martin Heidegger,
Philosopher," sculpture, 1988

See also Talman in this journal.

Wednesday, September 7, 2016

Grammar and Patterns

Filed under: General,Geometry — m759 @ 10:00 PM

"May, / The months [sic ] of understanding" — Wallace Stevens

Saturday, May 21, 2016

Grammar

Filed under: Uncategorized — m759 @ 12:00 PM 

Related material 

The Lindbergh Manifesto and The Leibniz Medal.

 

"If pure mathematics does spring from sub-conscious intuitions— already deep-structured as are grammatical patterns in the transformational-generative theory of language?— if the algebraic operation arises from wholly internalized pattern-weaving, how then can it, at so many points, mesh with, correspond to, the material forms of the world?"

— Steiner, George. Grammars of Creation
(Gifford Lectures, 1990). (Kindle Locations 2494-2496).
Open Road Media. Kindle Edition. 

Good question.

See Bedtime Story (Sept. 1, 2016).

Sunday, September 15, 2013

Sermon

Filed under: General — Tags: — m759 @ 11:00 AM

Suggested by a poem in the current  New Yorker.

Today's text —

"We have no more beginnings. 
Incipit : that proud Latin word
which signals the start
survives in our dusty 'inception'."

— George Steiner, beginning of
      Grammars of Creation

Reply in the Latin tradition—

.

Cast

(From the Log24 posts
of August 23-24, 2013)

Friday, March 30, 2012

Steiner on Language

Filed under: General — Tags: — m759 @ 4:00 PM

March 28 review in the Times Literary Supplement  of
George Steiner's new book The Poetry of Thought

"If this new book opens with the concession that
language has neither the performative power of music
nor the elegant precision of mathematics,
it is language, for Steiner, that defines the human.

The survey accordingly begins from the ancient Greek
view of man as the 'language-animal.'" 

A check of this phrase yields, in a 1969 Steiner essay,
"The Language Animal," a Greek form of the phrase—

In short, the least inadequate definition we can arrive at
of the genus homo , the definition that fully distinguishes
him from all neighbouring life-forms, is this:
man is a zoon phonanta , a language-animal.

— p. 10 in Encounter , August 1969 (essay on pp. 7-23)

After introducing "language-animal" as a translation of  "zoon phonanta " in 1969,
Steiner in later writing went on to attribute this phrase to the ancient Greeks.

 "The inception of critical thought, of a philosophic anthropology, 
is contained in the archaic Greek definition of man as a
'language-animal'…."

— George Steiner, Real Presences , U. of Chicago Press, 1991, p. 89

"… the 'language-animal' we have been since ancient Greece
so designated us…. "

— George Steiner, Grammars of Creation , Yale U. Press, 2002, p. 265

Despite this, there seems to be no evidence for use of this phrase
by the ancient Greeks.

A Google search today for zoon phonanta  (ζῷον φωνᾶντα)—

There are also no results from searches for the similar phrases
"ζωον φωναντα," "ζωον φωνᾶντα," and "ζῷον φωναντα."

Monday, December 27, 2010

Church Diamond

Filed under: General,Geometry — m759 @ 3:09 PM

IMAGE- The diamond property

Also known, roughly speaking, as confluence  or the Church-Rosser property.

From "NYU Lambda Seminar, Week 2" —

[See also the parent page Seminar in Semantics / Philosophy of Language or:
 What Philosophers and Linguists Can Learn From Theoretical Computer Science But Didn't Know To Ask)
]

A computational system is said to be confluent, or to have the Church-Rosser or diamond property, if, whenever there are multiple possible evaluation paths, those that terminate always terminate in the same value. In such a system, the choice of which sub-expressions to evaluate first will only matter if some of them but not others might lead down a non-terminating path.

The untyped lambda calculus is confluent. So long as a computation terminates, it always terminates in the same way. It doesn't matter which order the sub-expressions are evaluated in.

A computational system is said to be strongly normalizing if every permitted evaluation path is guaranteed to terminate. The untyped lambda calculus is not strongly normalizing: ω ω doesn't terminate by any evaluation path; and (\x. y) (ω ω) terminates only by some evaluation paths but not by others.

But the untyped lambda calculus enjoys some compensation for this weakness. It's Turing complete! It can represent any computation we know how to describe. (That's the cash value of being Turing complete, not the rigorous definition. There is a rigorous definition. However, we don't know how to rigorously define "any computation we know how to describe.") And in fact, it's been proven that you can't have both. If a computational system is Turing complete, it cannot be strongly normalizing.

There is no connection, apart from the common reference to an elementary geometric shape, between the use of "diamond" in the above Church-Rosser sense and the use of "diamond" in the mathematics of (Cullinane's) Diamond Theory.

Any attempt to establish such a connection would, it seems, lead quickly into logically dubious territory.

Nevertheless, in the synchronistic spirit of Carl Jung and Arthur Koestler, here are some links to such a territory —

 Link One — "Insane Symmetry"  (Click image for further details)—

http://www.log24.com/log/pix10B/101227-InsaneSymmetry.jpg

See also the quilt symmetry in this  journal on Christmas Day.

Link Two — Divine Symmetry

(George Steiner on the Name in this journal on Dec. 31 last year ("All about Eve")) —

"The links are direct between the tautology out of the Burning Bush, that 'I am' which accords to language the privilege of phrasing the identity of God, on the one hand, and the presumptions of concordance, of equivalence, of translatability, which, though imperfect, empower our dictionaries, our syntax, our rhetoric, on the other. That 'I am' has, as it were, at an overwhelming distance, informed all predication. It has spanned the arc between noun and verb, a leap primary to creation and the exercise of creative consciousness in metaphor. Where that fire in the branches has gone out or has been exposed as an optical illusion, the textuality of the world, the agency of the Logos in logic—be it Mosaic, Heraclitean, or Johannine—becomes 'a dead letter.'"

George Steiner, Grammars of Creation

(See also, from Hanukkah this year,  A Geometric Merkabah and The Dreidel is Cast.)

Link Three – Spanning the Arc —

Part A — Architect Louis Sullivan on "span" (see also Kindergarten at Stonehenge)

Part B — "Span" in category theory at nLab —

http://www.log24.com/log/pix10B/101227-nLabSpanImage.jpg

Also from nLab — Completing Spans to Diamonds

"It is often interesting whether a given span in some partial ordered set can be completed into a diamond. The property of a collection of spans to consist of spans which are expandable into diamonds is very useful in the theory of rewriting systems and producing normal forms in algebra. There are classical results e.g. Newman’s diamond lemma, Širšov-Bergman’s diamond lemma (Širšov is also sometimes spelled as Shirshov), and Church-Rosser theorem (and the corresponding Church-Rosser confluence property)."

The concepts in this last paragraph may or may not have influenced the diamond theory of Rudolf Kaehr (apparently dating from 2007).

They certainly have nothing to do with the Diamond Theory of Steven H. Cullinane (dating from 1976).

For more on what the above San Francisco art curator is pleased to call "insane symmetry," see this journal on Christmas Day.

For related philosophical lucubrations (more in the spirit of Kaehr than of Steiner), see the New York Times  "The Stone" essay "Span: A Remembrance," from December 22—

“To understand ourselves well,” [architect Louis] Sullivan writes, “we must arrive first at a simple basis: then build up from it.”

Around 300 BC, Euclid arrived at this: “A point is that which has no part. A line is breadthless length.”

See also the link from Christmas Day to remarks on Euclid and "architectonic" in Mere Geometry.

Thursday, December 31, 2009

All About Eve

Filed under: General — Tags: — m759 @ 9:57 AM

NY Times obituaries on New Year's Eve, 2009-- Carlene Hatcher Polite and David Levine

Genesis 3:24
So he drove out the man; and he placed
at the east of the garden of Eden Cherubims,
and a flaming sword which turned every way,
to keep the way of the tree of life.

"The links are direct between the tautology out of the Burning Bush, that 'I am' which accords to language the privilege of phrasing the identity of God, on the one hand, and the presumptions of concordance, of equivalence, of translatability, which, though imperfect, empower our dictionaries, our syntax, our rhetoric, on the other. That 'I am' has, as it were, at an overwhelming distance, informed all predication. It has spanned the arc between noun and verb, a leap primary to creation and the exercise of creative consciousness in metaphor. Where that fire in the branches has gone out or has been exposed as an optical illusion, the textuality of the world, the agency of the Logos in logic—be it Mosaic, Heraclitean, or Johannine—becomes 'a dead letter.'"

George Steiner, Grammars of Creation

Carlene Hatcher Polite–
"Shall I help you?" asked a bass voice.
"If you can," answered a contralto.
"Trace down this tree. Let me show you
men in its stead. Leaf through this bush,
extinguish the burning fire…"
The Flagellants, page 8

"How much story do you want?"
George Balanchine

Tuesday, April 8, 2008

Tuesday April 8, 2008

Filed under: General,Geometry — m759 @ 8:00 AM
Eight is a Gate

Part I:

December 2002

Part II:

Epiphany 2008

How the eightfold cube works
This figure is related to
the mathematics of
reflection groups
.


Part III:

“The capacity of music to operate simultaneously along horizontal and vertical axes, to proceed simultaneously in opposite directions (as in inverse canons), may well constitute the nearest that men and women can come to absolute freedom.  Music does ‘keep time’ for itself and for us.”

— George Steiner in Grammars of Creation

Inverse Canon —

From Werner Icking Music Archive:

Bach, Fourteen Canons
on the First Eight Notes
of the Goldberg Ground,
No. 11 —

Bach, 14 Canons on the Goldberg Ground, Canon 11
Click to enlarge.

Play midi of Canon 11.

At a different site
an mp3 of the 14 canons.

Part IV:

That Crown of Thorns,
by Timothy A. Smith

Monday, February 13, 2006

Monday February 13, 2006

Filed under: General — m759 @ 8:00 PM
The Lincoln Brigade

The image “http://www.log24.com/log/pix06/060213-Lincoln1.jpg” cannot be displayed, because it contains errors.

Marches On.

As yesterday’s Lincoln’s Birthday entry indicated, my own sympathies are not with the “created equal” crowd.  Still, the Catholic Fascism of Franco admirer Andrew Cusack seems somewhat over-the-top.  A more thoughtful approach to these matters may be found in a recommendation by Ross Douthat at The American Scene:

Read Eve Tushnet on the virtues of The Man in the High Castle.

Related material: Log24 on Nov. 14, Nov. 15, and Nov. 16, 2003.

Another item of interest from Eve:

“Transubstantiation [is equivalent but not equal to] art (deceptive accident hides truthful substance), as vs. Plato’s condemnation of the physical & the fictive? (Geo. Steiner)”

Related material:

The End of Endings
(excerpt)
by Father Richard John Neuhaus,
First Things
115 (Aug.-Sept. 2001), 47-56:

“In Grammars of Creation, more than in his 1989 book Real Presences, Steiner acknowledges that his argument rests on inescapably Christian foundations. In fact, he has in the past sometimes written in a strongly anti–Christian vein, while the present book reflects the influence of, among others, Miri Rubin, whose Corpus Christi: The Eucharist in Late Medieval Culture is credited in a footnote. Steiner asserts that, after the Platonisms and Gnosticisms of late antiquity, it is the doctrines of incarnation and transubstantiation that mark ‘the disciplining of Western syntax and conceptualization’ in philosophy and art. ‘Every heading met with in a study of “creation,” every nuance of analytic and figural discourse,’ he says, derives from incarnation and transubstantiation, ‘concepts utterly alien to either Judaic or Hellenic perspectives– though they did, in a sense, arise from the collisions and commerce between both.’….

The incarnation of God in the Son, the transubstantiation of bread and wine into his body and blood, are ‘a mysterium, an articulated, subtly innervated attempt to reason the irrational at the very highest levels of intellectual pressure.’ ‘Uniquely, perhaps, the hammering out of the teaching of the eucharist compels Western thought to relate the depth of the unconscious and of pre-history with speculative abstractions at the boundaries of logic and of linguistic philosophy.’ Later, the ‘perhaps’ in that claim seems to have disappeared:

At every significant point, Western philosophies of art and Western poetics draw their secular idiom from the substratum of Christological debate. Like no other event in our mental history, the postulate of God’s kenosis through Jesus and of the never-ending availability of the Savior in the wafer and wine of the eucharist, conditions not only the development of Western art and rhetoric itself, but at a much deeper level, that of our understanding and reception of the truth of art– a truth antithetical to the condemnation of the fictive in Plato.

This truth reaches its unrepeated perfection in Dante, says Steiner. In Dante, ‘It rounds in glory the investigation of creativity and creation, of divine authorship and human poesis, of the concentric spheres of the aesthetic, the philosophical, and the theological. Now truth and fiction are made one, now imagination is prayer, and Plato’s exile of the poets refuted.’ In the fashionable critical theories of our day, we witness ‘endeavors of the aesthetic to flee from incarnation.’ ‘It is the old heresies which revive in the models of absence, of negation or erasure, of the deferral of meaning in late–twentieth–century deconstruction. The counter-semantics of the deconstructionist, his refusal to ascribe a stable significance to the sign, are moves familiar to [an earlier] negative theology.’ Heidegger’s poetics of ‘pure immanence’ are but one more attempt ‘to liberate our experience of sense and of form from the grip of the theophanic.’ But, Steiner suggests, attempted flights from the reality of Corpus Christi will not carry the day. ‘Two millennia are only a brief moment.’

Sunday, July 3, 2005

Sunday July 3, 2005

Filed under: General — m759 @ 2:28 PM

Intersections

1. Blue Ridge meets Black Mountain,

2. Vertical meets horizontal in music,

3. The timeless meets time in religion.

Details:

1. Blue Ridge, Black Mountain

Montreat College is located in the beautiful Blue Ridge Mountains of Western North Carolina…. The Black Mountain Campus is… three miles from the main campus in the historic town of Black Mountain.”

Black Mountain College was “established on the Blue Ridge Assembly grounds outside the town of Black Mountain in North Carolina in the fall of 1933.”

USA Today, May 15, 2005, on Billy Graham
:

“MONTREAT, N.C. — … It’s here at his… homestead, where the Blue Ridge meets the Black Mountain range east of Asheville, that Graham gave a rare personal interview.”

See also the following from June 24:


The image “http://www.log24.com/log/pix05A/050624-Cross.jpg” cannot be displayed, because it contains errors.

“No bridge reaches God, except one…
God’s Bridge: The Cross.”

— Billy Graham Evangelistic Association,
according to messiahpage.com

For some remarks more in the spirit of Black Mountain than of the Blue Ridge, see today’s earlier entry on pianist Grete Sultan and composer Tui St. George Tucker.

2. Vertical, Horizontal in Music

Richard Neuhaus on George Steiner’s
Grammars of Creation
:

 “… the facts of the world are not and will never be ‘the end of the matter.’ Music joins grammar in pointing to the possibility, the reality, of more. He thinks Schopenhauer was on to something when he said music will continue after the world ends.

‘The capacity of music to operate simultaneously along horizontal and vertical axes, to proceed simultaneously in opposite directions (as in inverse canons), may well constitute the nearest that men and women can come to absolute freedom.  Music does “keep time” for itself and for us.'”

3. Timeless, Time

A Trinity Sunday sermon quotes T. S. Eliot:

“… to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint.”

See also The Diamond Project.

Update of July 8, 2005, 3 AM:

A Bridge for Private Ryan

The image “http://www.log24.com/log/pix05A/050708-RyansBridge.jpg” cannot be displayed, because it contains errors.

In memory of actor
Harrison Richard Young, 75,
who died on Sunday, July 3, 2005

Friday, July 1, 2005

Friday July 1, 2005

Filed under: General — m759 @ 8:00 PM

Big Dreams

“For more than a century, Los Angeles has been synonymous with big dreams. The Australian writer and critic Clive James said it this way. ‘Call Los Angeles any dirty name you like… The fact remains that you are already living in it before you get there.'”

— Today’s inaugural address by Mayor Villaraigosa

See also the previous entry.

Update of 2:24 PM July 2:

Yesterday afternoon I picked up a copy of George Steiner’s Grammars of Creation I had ordered.  A check of Amazon.com to see what others had to say about this book yielded the following:

“Steiner’s account of Hope as something exclusively transcendental and relative to the future is poor and superficial: the person who hopes is not only walking ‘towards’ Eternal Life, but is already walking ‘in’ Eternal Life, walking the Kingdom.”

— Matías Cordero, Santiago, Chile

See also an entry of April 7, 2005, Nine is a Vine.

Sunday, April 3, 2005

Sunday April 3, 2005

Filed under: General — m759 @ 3:26 PM
Wager

Pennsylvania Lottery Daily Number

for yesterday evening,
Saturday, April 2, 2005:

613

Related material:

From 6/13 2004

An 8-rayed star:

Another 8-rayed star:

The image “http://www.log24.com/log/pix05/050403-StPetersSq.jpg” cannot be displayed, because it contains errors.

St. Peter’s Square in Rome
 
From 6/13 2003

A link to a 2001 First Things essay,

The End of Endings:

“Here is the heart of the matter:

The underwriting of Hebraic–Hellenic literacy, of the normative analogue between divine and mortal acts of creation, was, in the fullest sense, theological. As was the wager (pronounced lost in deconstruction and postmodernism) on ultimate possibilities of accord between sign and sense, between word and meaning, between form and phenomenality. The links are direct between the tautology out of the Burning Bush, that ‘I am’ which accords to language the privilege of phrasing the identity of God, on the one hand, and the presumptions of concordance, of equivalence, of translatability, which, though imperfect, empower our dictionaries, our syntax, our rhetoric, on the other. That ‘I am’ has, as it were, at an overwhelming distance, informed all predication. It has spanned the arc between noun and verb, a leap primary to creation and the exercise of creative consciousness in metaphor. Where that fire in the branches has gone out or has been exposed as an optical illusion, the textuality of the world, the agency of the Logos in logic—be it Mosaic, Heraclitean, or Johannine—becomes ‘a dead letter.’

That passage bears rereading.”

— Richard John Neuhaus quoting
   George Steiner’s Grammars of Creation
   (Yale University Press, April 1, 2001)

Sunday, July 25, 2004

Sunday July 25, 2004

Filed under: General — Tags: — m759 @ 8:30 AM

Keeping Time

Richard Neuhaus on George Steiner's
Grammars of Creation
:

 "… the facts of the world are not and will never be 'the end of the matter.' Music joins grammar in pointing to the possibility, the reality, of more. He thinks Schopenhauer was on to something when he said music will continue after the world ends.

'The capacity of music to operate simultaneously along horizontal and vertical axes, to proceed simultaneously in opposite directions (as in inverse canons), may well constitute the nearest that men and women can come to absolute freedom.  Music does "keep time" for itself and for us.'"

"Goin' to Carolina in my mind…."

Sunday, September 22, 2002

Sunday September 22, 2002

Filed under: General,Geometry — Tags: , , , — m759 @ 8:02 PM

Force Field of Dreams

Metaphysics and chess in today’s New York Times Magazine:

  • From “Must-See Metaphysics,” by Emily Nussbaum:

    Joss Whedon, creator of a new TV series —

    “I’m a very hard-line, angry atheist” and
    “I want to invade people’s dreams.”

  • From “Check This,” by Wm. Ferguson:

    Garry Kasparov on chess —

    “When the computer sees forced lines,
    it plays like God.”

Putting these quotations together, one is tempted to imagine God having a little game of chess with Whedon, along the lines suggested by C. S. Lewis:

As Lewis tells it the time had come for his “Adversary [as he was wont to speak of the God he had so earnestly sought to avoid] to make His final moves.” (C. S. Lewis, Surprised by Joy, Harcourt, Brace, and World, Inc., 1955, p. 216) Lewis called them “moves” because his life seemed like a chess match in which his pieces were spread all over the board in the most disadvantageous positions. The board was set for a checkmate….

For those who would like to imagine such a game (God vs. Whedon), the following may be helpful.

George Steiner has observed that

The common bond between chess, music, and mathematics may, finally, be the absence of language.

This quotation is apparently from

Fields of Force:
Fischer and Spassky at Reykjavik
. by George Steiner, Viking hardcover, June 1974.

George Steiner as quoted in a review of his book Grammars of Creation:

“I put forward the intuition, provisional and qualified, that the ‘language-animal’ we have been since ancient Greece so designated us, is undergoing mutation.”

The phrase “language-animal” is telling.  A Google search reveals that it is by no means a common phrase, and that Steiner may have taken it from Heidegger.  From another review, by Roger Kimball:

In ”Grammars of Creation,” for example, he tells us that ”the classical and Judaic ideal of man as ‘language animal,’ as uniquely defined by the dignity of speech . . . came to an end in the antilanguage of the death camps.”

This use of the Holocaust not only gives the appearance of establishing one’s credentials as a person of great moral gravity; it also stymies criticism. Who wants to risk the charge of insensitivity by objecting that the Holocaust had nothing to do with the ”ideal of man as ‘language animal’ ”?

Steiner has about as clear an idea of the difference between “classical” and “Judaic” ideals of man as did Michael Dukakis. (See my notes of September 9, 2002.)

Clearly what music, mathematics, and chess have in common is that they are activities based on pure form, not on language. Steiner is correct to that extent. The Greeks had, of course, an extremely strong sense of form, and, indeed, the foremost philosopher of the West, Plato, based his teachings on the notion of Forms. Jews, on the other hand, have based their culture mainly on stories… that is, on language rather than on form. The phrase “language-animal” sounds much more Jewish than Greek. Steiner is himself rather adept at the manipulation of language (and of people by means of language), but, while admiring form-based disciplines, is not particularly adept at them.

I would argue that developing a strong sense of form — of the sort required to, as Lewis would have it, play chess with God — does not require any “mutation,” but merely learning two very powerful non-Jewish approaches to thought and life: the Forms of Plato and the “archetypes” of Jung as exemplified by the 64 hexagrams of the 3,000-year-old Chinese classic, the I Ching.

For a picture of how these 64 Forms, or Hexagrams, might function as a chessboard,

click here.

Other relevant links:

“As you read, watch for patterns. Pay special attention to imagery that is geometric…”

and


from Shakhmatnaia goriachka

Powered by WordPress