Log24

Thursday, January 17, 2019

The Dreaming Jewels’ Nightmares

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

Some Log24 posts related to Theodore Sturgeon's 1950 tale
of The Dreaming Jewels  have been tagged with that title.

For a purely mathematical approach to Sturgeon's concept see . . .

July 6, 2014, Amsterdam master's thesis on geometric models of the Golay code and Mathieu group

For some related nightmares, see July 2014 in this journal.

Wednesday, January 16, 2019

Permutahedron Dream

Filed under: General — Tags: , , , — m759 @ 3:21 PM

The geometric object of the title appears in a post mentioning Bourgain 
in this journal.  Bourgain appears also in today's online New York Times —

https://www.nytimes.com/2019/01/16/
obituaries/jean-bourgain-dead.html
 .

Bourgain reportedly died on December 22.

An image from this journal on that date

Related poetic meditations —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

The Dreaming Polyhedron

Filed under: General — Tags: , — m759 @ 5:32 AM

"Here is a recipe for preparing a copy of the Mathieu group M24.
The main ingredient is a genus-3 regular polyhedron X
with 56 triangular faces, 84 edges, and 24 vertices.
The most delicate part of this recipe is to hold the polyhedron
by the 24 vertices and immerse the rest of it in 3-dimensional space."

— "How to Make the Mathieu Group M24 ," undated webpage
by David A. Richter, Western Michigan University

Illustration from that page —

Illustration from a webpage by David A. Richter, Western Michigan University

"Another model of the (universal cover of the) polyhedron X"

Related fiction —

Cover of a 1971 British paperback edition of The Dreaming Jewels,  
a story by Theodore Sturgeon (first version published in 1950):

Discuss Richter's model and the Sturgeon tale 
in the context of posts tagged Aitchison.

Friday, April 4, 2014

Dream of the Expanded Field

Filed under: General — Tags: — m759 @ 10:00 PM

(Continued)

From today’s news:

“His daughter, the poet Jorie Graham, confirmed the death.”

From an artist on Oct. 3, 2013:

“‘This is St. Francis country,’ she says of Umbria.”

Friday, March 29, 2013

The Dreaming Jewels (continued)

Filed under: General — Tags: , — m759 @ 8:00 AM

In Memoriam

"In the late ’60s, Williams became a friend and confidant
of science fiction writer Philip K. Dick and wrote about
the iconoclastic author in Rolling Stone  in 1974.
Williams eventually completed a biography on Dick
and became his literary executor after the writer’s death
in 1982. He also edited The Complete Stories of
Theodore Sturgeon, Vol. I-XII 
."

— Yesterday in the Hollywood Reporter —
Pioneering Rock Journalist Paul S. Williams Dies at 64
4:06 PM PDT 3/28/2013 by Mitch Myers

See also Crawdaddy Story and The Dreaming Jewels
in this journal.

Related reading: Yesterday's noon post and Puzzles.

Update of 8:20 AM Good Friday, 2013:

IMAGE- Daily Princetonian, Good Friday, 2013: James Diamond, rabbi and retired director of Princeton's University's Center for Jewish Life. Diamond was killed in a Princeton auto accident Thursday morning at about 9:42 AM ET.

Wednesday, June 30, 2010

Field Dream

Filed under: General,Geometry — Tags: , — m759 @ 10:23 AM

In memory of Wu Guanzhong, Chinese artist who died in Beijing on Friday

Image-- The Dream of the Expanded Field

“Once Knecht confessed to his teacher that he wished to learn enough to be able to incorporate the system of the I Ching into the Glass Bead Game.  Elder Brother laughed.  ‘Go ahead and try,’ he exclaimed.  ‘You’ll see how it turns out.  Anyone can create a pretty little bamboo garden in the world.  But I doubt that the gardener would succeed in incorporating the world in his bamboo grove.'”

— Hermann Hesse, The Glass Bead Game, translated by Richard and Clara Winston

“The Chinese painter Wu Tao-tzu was famous because he could paint nature in a unique realistic way that was able to deceive all who viewed the picture. At the end of his life he painted his last work and invited all his friends and admirers to its presentation. They saw a wonderful landscape with a romantic path, starting in the foreground between flowers and moving through meadows to high mountains in the background, where it disappeared in an evening fog. He explained that this picture summed up all his life’s work and at the end of his short talk he jumped into the painting and onto the path, walked to the background and disappeared forever.”

Jürgen Teichmann. Teichmann notes that “the German poet Hermann Hesse tells a variation of this anecdote, according to his own personal view, as found in his ‘Kurzgefasster Lebenslauf,’ 1925.”

Friday, November 8, 2019

Perspective at the End

Filed under: General — Tags: — m759 @ 8:50 AM

This  journal on the last full day of Matthiessen's life —

Thursday, January 10, 2019

Archimedes at Hiroshima

Filed under: General,Geometry — Tags: , , , — m759 @ 7:35 PM

Two examples from the Wikipedia article  "Archimedean solid" —

Iain Aitchison said in a talk last year at Hiroshima that
the Mathieu group M24  can be represented as permuting
naturally the 24 edges  of the cuboctahedron.

The 24 vertices  of the truncated  octahedron are labeled 
naturally by the 24 elements of S4  in a permutahedron

Can M24  be represented as permuting naturally
the 24 vertices  of the truncated octahedron?

 
 

Sunday, January 6, 2019

For Broom Bridge*

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

GL(2,3) is not unrelated to GL(3,2).

See Quaternion Automorphisms 
and Spinning in Infinity.

* See Wikipedia.

Wednesday, July 18, 2018

Mira and the Intruders* Present …

Filed under: General — m759 @ 9:11 PM

Epiphany 2012: An Exercise
in Bulk Apperception

This post was suggested by a Marrific photo posted today,
by a New Orleans song as played by Bix Beiderbecke,
by a trailer for a new Zemeckis film that appeared at YouTube
on the way to the New Orleans song, and by
the longing for Bix by Mira Sorvino in "Intruders."

The YouTube Bix date, Jan. 6, 2012, suggested a trip back
to that date via a Zemeckis Cube (see "Ready Player One.")

From Log24 on Epiphany 2012

IMAGE- Cathy Hull, detail from cover of Hillman's 'The Dream and the Underworld'

A version of the Zemeckis Cube

From the Zemeckis trailer —

* See a Log24 search for Mira + Intruders.

Monday, December 7, 2015

Neon Joe, Werewolf Hunter

Filed under: General — Tags: , , — m759 @ 10:48 PM

For the title, see The New York Times  and the oeuvre  of Joseph Kosuth.

From The Dreaming Jewels , by Theodore Sturgeon:

"Oh. And the crystals make things — even complete things — like Tin Pan Alley makes songs."

"Something like it." Zena smiled. It was the first smile in a long while. "Sit down, honey; I'll bring the toast. Now — this is my guess — when two crystals mate, something different happens. They make a whole thing. But they don't make it from just anything the way the single crystals do. First they seem to die together. For weeks they lie like that. After that they begin a together-dream. They find something near them that's alive, and they make it over. They replace it, cell by cell. You can't see the change going on in the thing they're replacing. It might be a dog; the dog will keep on eating and running around; it will howl at the moon and chase cats. But one day — I don't know how long it takes — it will be completely replaced, every bit of it."

"Then what?"

"Then it can change itself — if it ever thinks of changing itself. It can be almost anything if it wants to be."

Bunny stopped chewing, thought, swallowed, and asked, "Change how?"

"Oh, it could get bigger or smaller. Grow more limbs. Go into a funny shape — thin and flat, or round like a ball. If it's hurt it can grow new limbs. And it could do things with thought that we can't even imagine. Bunny, did you ever read about werewolves?"

"Those nasty things that change from wolves to men and back again?"

Zena sipped coffee. "Mmm. Well, those are mostly legends, but they could have started when someone saw a change like that."

See as well The Dreaming Jewels 
and "Steven Universe" in this journal.

You can't make this stuff up.

Wittgenstein Illustrated

Filed under: General,Geometry — Tags: , , — m759 @ 1:17 PM

From "AMNESIA: VARIOUS, LUMINOUS, FIXED,"
An exhibition by Joseph Kosuth at
Sprüth Magers Gallery London,
NOVEMBER 26 2014 – FEBRUARY 14 2015 —

This journal, NOVEMBER 26 2014 –

Wednesday, November 26, 2014

Mathematics and Narrative

Filed under: Uncategorized — m759 @ 10:00 PM 

Mathematics:  Galois-Plane Models.

Narrative: "The Dreaming Jewels."

This journal, FEBRUARY 14 2015 —

Tuesday, April 14, 2015

Sacramental Geometry:

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

The Dreaming Jewels  continued

" the icosahedron and dodecahedron have the same properties
of symmetry. For the centres of the twenty faces of an icosahedron
may be joined to form a regular dodecahedron, and conversely, the
twelve vertices of an icosahedron can be placed at the centres
of the faces of a suitable dodecahedron. Thus the icosahedral and
dodecahedral groups are identical
 , and either solid may be used to
examine the nature of the group elements."

— Walter Ledermann, Introduction to the Theory
of Finite Groups
  (Oliver and Boyd, 1949, p. 93)

Salvador Dali, The Sacrament of the Last Supper

Omar Sharif and Gregory Peck in Behold a Pale Horse

Above: soccer-ball geometry.
              See also

             See as well
"In Sunlight and in Shadow."

Monday, December 29, 2014

Dodecahedron Model of PG(2,5)

Filed under: General,Geometry — Tags: , , — m759 @ 2:28 PM

Recent posts tagged Sagan Dodecahedron 
mention an association between that Platonic
solid and the 5×5 grid. That grid, when extended
by the six points on a "line at infinity," yields
the 31 points of the finite projective plane of
order five.  

For details of how the dodecahedron serves as
a model of this projective plane (PG(2,5)), see
Polster's A Geometrical Picture Book , p. 120:

For associations of the grid with magic rather than
with Plato, see a search for 5×5 in this journal.

Wednesday, November 26, 2014

Mathematics and Narrative

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

Mathematics:  Galois-Plane Models.

Narrative: "The Dreaming Jewels."

Sunday, July 6, 2014

Sticks and Stones

Filed under: General,Geometry — Tags: — m759 @ 6:29 AM

The title is from this morning’s previous post.

From a theater review in that post—

… “all flying edges and angles, a perpetually moving and hungry soul”

… “a formidably centered presence, the still counterpoint”

A more abstract perspective:

IMAGE- Concepts of Space

See also Desargues via Galois (August 6, 2013).

Friday, April 4, 2014

Eight Gate

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

From a Huffington Post  discussion of aesthetics:

“The image below on the left… is… overly simplistic, and lacks reality:

IMAGE - Two eightfold cubes-  axonometric view on left, perspective view on right

It’s all a matter of perspective: the problem here is that opposite sides
of the cube, which are parallel in real life, actually look parallel in the
left image! The image on the right is better….”

A related discussion:  Eight is a Gate.

Sunday, February 2, 2014

A Shadow for Groundhog Day

Filed under: General — Tags: — m759 @ 8:00 AM

Alec Baldwin as Lamont Cranston

IMAGE- Conclusion of Hillman's 'The Dream and the Underworld'

Compare and contrast with the psychoanalyst in Remembrance
(January 27, 2014).

Tuesday, December 31, 2013

Christmas Ornaments

Filed under: General,Geometry — Tags: , — m759 @ 12:25 AM

Continued from December 25

IMAGE- Count rotational symmetries by rotating facets. Illustrated with 'Plato's Dice.'

A link from Sunday afternoon to Nov. 26, 2012,
suggests a review of one of the above structures.

The Dreaming Jewels  cover at left is taken from a review
by Jo Walton at Tor.com—

"This is a book that it’s clearly been difficult
for publishers to market. The covers have been
generally pretty awful, and also very different.
I own a 1975 Corgi SF Collectors Library
paperback that I bought new for 40p in the later
seventies. It’s purple, and it has a slightly grainy
cover, and it matches my editions of The Menace
From Earth
  and A Canticle for Leibowitz .
(Dear old Corgi SF Collectors Editions with their
very seventies fonts! How I imprinted on them at
an early age!) I mention this, however, because
the (uncredited) illustration actually represents and
illustrates the book much better than any of the other
cover pictures I’ve seen. It shows a hexagon with an
attempt at facets, a man, a woman, hands, a snake,
and stars, all in shades of green. It isn’t attractive,
but it wouldn’t put off people who’d enjoy what’s inside
either."

The "hexagon with an attempt at facets" is actually
an icosahedron, as the above diagram shows.
(The geometric part of the diagram is from a Euclid webpage.)

For Plato's dream about these jewels, see his Timaeus.

Sunday, November 10, 2013

Abstraction

Filed under: General — Tags: — m759 @ 5:24 PM

(Continued from Dec. 6, 2012)

Context:
Chinese Field  and Modal Diamond .

(See also today’s previous post.)

Thursday, June 13, 2013

Gate

Filed under: General,Geometry — Tags: , — m759 @ 2:13 PM

"Eight is a Gate." — Mnemonic rhyme

Today's previous post, Window, showed a version
of the Chinese character for "field"—

This suggests a related image

The related image in turn suggests

Unlike linear perspective, axonometry has no vanishing point,
and hence it does not assume a fixed position by the viewer.
This makes axonometry 'scrollable'. Art historians often speak of
the 'moving' or 'shifting' perspective in Chinese paintings.

Axonometry was introduced to Europe in the 17th century by
Jesuits returning from China.

Jan Krikke

As was the I Ching.  A related structure:

Saturday, March 30, 2013

Blackboard Jungle

Filed under: General — Tags: — m759 @ 10:30 AM

(Continued)

Harrowing of Hell (Catholic Encyclopedia )

"This is the Old English and Middle English term
for the triumphant descent of Christ into hell (or Hades)
between the time of His Crucifixion and His Resurrection,
when, according to Christian belief, He brought salvation
to the souls held captive there since the beginning of the world."

Through the Blackboard (Feb. 25, 2010)—

Physicist accelerated against his blackboard in 'A Serious Man'

See also The Dreaming Jewels and Colorful Tale.

Thursday, March 28, 2013

Woman at the Well

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

For some images related to this rather biblical topic,

see Hillman + Dream in this journal.

“She was dazzled by light and shade, by the confusing
duplication of reflections and of frames. All coming from
too many directions for the mind to take account of.
The various images bounced against each other
until she felt a desperate vertigo….”

Cold Mountain

Summary image:

IMAGE- Quilt blocks- Devil's Claws and Yankee Puzzle

“… Margaret Murry, wrapped in an old patchwork quilt, sat on the foot of her bed….”

A Wrinkle in Time

Monday, November 26, 2012

“The Eight”…

Filed under: General — Tags: — m759 @ 2:18 PM

Meets "The Master"—

IMAGE- Joaquin Phoenix, corridor scene in 'The Master'

Today's midday NY Lottery: 333 and 5885.

"Continue a search for thirty-three and three." — The Eight  (1988)

"Make me young." — Kilgore Trout in
Breakfast of Champions . Trout was modeled after
author Theodore Sturgeon who died on 5/8/85.

(An example of Sturgeon's work: The Dreaming Jewels  (1950).)

Related illustrations from the eighth day of 2012—

See also "I'm sorry to be catechizing you like this."

Tuesday, March 27, 2012

Literary Field

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

An image suggested by Google's observance today
of Mies van der Rohe's 126th birthday—

Related material:

See also yesterday's Chapter and Verse  by Stanley Fish,
and today's Arts & Letters Daily .

Sunday, January 8, 2012

All About Eve (continued)

Filed under: General — m759 @ 4:23 AM

Literary symbolism, offered without comment—

http://www.log24.com/log/pix12/120108-NYTfront305AM.jpg http://www.log24.com/log/pix12/120108-NYTobits.jpg

http://www.log24.com/log/pix12/120108-Tilley.gif

Log24 post of January 14, 2011

http://www.log24.com/log/pix12/120108-EveAndApple.jpg

Saturday, January 7, 2012

Fearful Cold Intelligence

Filed under: General,Geometry — Tags: — m759 @ 7:00 AM

"Dreams are sleep's watchful brother, of death's fraternity,
heralds, watchmen of that coming night, and our attitude
toward them may be modeled upon Hades, receiving, hospitable,
yet relentlessly deepening, attuned to the nocturne, dusky, and
with a fearful cold intelligence that gives permanent shelter
in his house to the incurable conditions of human being."

— James Hillman, conclusion of
The Dream and the Underworld  (Harper & Row, 1979)

In memory of Raymond Edward Alan Christopher Paley

IMAGE- 'Note on the Mathieu Group M12' by Marshall Hall, Jr.

Related material— Mathieu Symmetry.

Little Morning

Filed under: General — Tags: — m759 @ 5:01 AM

IMAGE- Conclusion of Hillman's 'The Dream and the Underworld'

… que cantaba el rey David.

Friday, January 6, 2012

Form

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

An example for the Feast of the Epiphany*
IMAGE- Cathy Hull, detail from cover of Hillman's 'The Dream and the Underworld'

For one approach to defining this form, see Diamond Star.

* And for Pomona College

Saturday, March 20, 2010

Field Theory

Filed under: General — Tags: , — m759 @ 12:29 PM

Parker’s Wake

A continuation of Wednesday’s “Field of Dreams” link

Internet Movie Database comment

“The Kid From Left Field” is a wonderful baseball film made in the early fifties and breathes the nostalgia of that time period. Child actor Billy Chapin becomes a batboy for the woeful Bisons (a copy of the old St. Louis Browns) and proceeds to inform the players of how they can correct their individual problems. Unbeknownst to the team, Chapin’s wisdom is from his father, a washed-up player who has become a peanut vendor and lacks confidence and courage– in spite of his obvious baseball knowledge. Pretty soon, Chapin becomes the nine year old manager of the team with dramatic results that bind father to son; you can’t help but root for the Bisons! A baseball fantasy– but filled with much innocence and charm.

“…dramatic results that bind father to son….”

Not to mention the Holy Ghost. See Fess Parker, who died Thursday, in the “Left Field” film and in an essay by Roger Cooke in the April Notices of the American Mathematical Society

Life on the Mathematical Frontier: Legendary Figures and Their Adventures

http://www.log24.com/log/pix10/100320-Field.jpg

Fess Parker in
“The Kid from Left Field,” 1953

Possible associative links between recent Log24 posts and the baseball theme of the April AMS Notices

  1. The film “Field of Dreams” mentioned above is a resurrection story.
  2. Wednesday’s link to simultaneous multiple-level associations leads to the Gameplayers of Zan cover that also appears in Thursday’s post. That cover deals with a resurrection myth in Gameplayers.
  3. The Finnegans Wake resurrection myth is mentioned in Wednesday’s post “Spring Training.”

Associative links, though entertaining, have of course their limitations in logical argument.

A notable recent example– Jon Stewart’s parody of Glenn Beck.

Saturday, August 29, 2009

Saturday August 29, 2009

Filed under: General — m759 @ 8:00 PM
Continued from
Father’s Day
  last year–

Shoe cartoon, detail, Sunday, June 15, 2008

I Ching hexagram 48, The Well

“For further details,
 click on the well.”

From the above link:

James Hillman

“The kind of movement Olson urges is
 an inward deepening of the image,
an in-sighting of the superimposed
 levels of significance within it.
This is the very mode that Jung
suggested for grasping dreams
 not as a sequence in time,
but as revolving around
 a nodal complex.”

And from Feb. 29, 2008:

http://www.log24.com/log/pix08/080229-Doonesbury3.jpg

and the following day:

Heraclitus: '...so deep is its logos'

— Heraclitus

Sunday, December 16, 2007

Sunday December 16, 2007

Filed under: General — Tags: — m759 @ 1:09 PM
 
Mad Phaedrus
Meets Mad Ezra

 

"Plato's Good was a fixed and eternal and unmoving Idea, whereas for the rhetoricians it was not an Idea at all. The Good was not a form of reality. It was reality itself, ever changing, ultimately unknowable in any kind of fixed, rigid way." –Phaedrus in Zen and the Art of Motorcycle Maintenance

This apparent conflict between eternity and time, fixity and motion, permanence and change, is resolved by the philosophy of the I Ching and by the Imagism of Ezra Pound.  Consider, for example, the image of The Well

as discussed here on All Saints' Day 2003 and in the previous entry.

As background, consider the following remarks of James Hillman in "Egalitarian Typologies Versus the Perception of the Unique," Part  III: Persons as Images
 

"To conceive images as static is to forget that they are numens that move.  Charles Olson, a later poet in this tradition, said:  'One perception must immediately and directly lead to a further perception… always, always one perception must must must move instanter, on another.' 80  Remember Lavater and his insistence on instantaneity for reading the facial image.  This is a kind of movement that is not narrational, and the Imagists had no place for narrative.  'Indeed the great poems to come after the Imagist period– Eliot’s The Waste Land and Four Quartets; Pound’s Cantos; Williams’s Paterson– contain no defining narrative.' 81  The kind of movement Olson urges is an inward deepening of the image, an in-sighting of the superimposed levels of significance within it. 82  This is the very mode that Jung suggested for grasping dreams– not as a sequence in time, but as revolving around a nodal complex.  If dreams, then why not the dreamers.  We too are not only a sequence in time, a process of individuation. We are also each an image of individuality."

80  The New American Poetry (D. M. Allen, ed.) N.Y.: Evergreen, Grove, 1960, pp. 387-88. from Jones, p. 42.

81  Jones,* p. 40.

82  H. D. later turned narration itself into image by writing a novel in which the stories were "compounded like faces seen one on top of another," or as she says "superimposed on one another like a stack of photographic negatives" (Jones, p. 42).  Cf. Berry,** p. 63: "An image is simultaneous. No part precedes or causes another part, although all parts are involved with each other… We might imagine the dream as a series of superimpositions, each event adding texture and thickening to the rest."

    * Imagist Poetry (Peter Jones, ed.) London: Penguin, 1972

    ** The contrast between image simultaneity and narrative succession, and the different psychological effects of the two modes, is developed by Patricia Berry, "An Approach to the Dream," Spring 1974 (N. Y./Zürich: Spring Publ.), pp. 63, 68-71

Hillman also says that

"Jung’s 'complex' and Pound's definition of Image and Lavater's 'whole heap of images, thoughts, sensations, all at once' are all remarkably similar.  Pound calls an Image, 'that which presents an intellectual and emotional complex in an instant of time'… 'the Image is more than an Idea.  It is a vortex or cluster of fused ideas and is endowed with energy'… 'a Vortex, from which and through which, and into which, ideas are constantly rushing.' 79 Thus the movement, the dynamics, are within the complex and not only between complexes, as tensions of opposites told about in narrational sequences, stories that require arbitrary syntactical connectives which are unnecessary for reading an image where all is given at once."

79  These definitions of Image by Pound come from his various writings and can all be found in Jones, pp. 32-41.  Further on complex and image, see J. B. Harmer, Victory in Limbo: Imagism 1908-17, London: Secker & Warburg, 1975, pp. 164-68.

These remarks may help the reader to identify with Ada during her well-viewing in Cold Mountain (previous entry):

"She was dazzled by light and shade, by the confusing duplication of reflections and of frames. All coming from too many directions for the mind to take account of. The various images bounced against each other until she felt a desperate vertigo…."

If such complexity can be suggested by Hexagram 48, The Well, alone, consider the effect of the "cluster of fused ideas… endowed with energy" that is the entire 64-hexagram I Ching.

Related material:St. Augustine's Day 2006

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

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