Log24

Tuesday, February 13, 2018

A Titan of the Field

Filed under: Uncategorized — Tags: — m759 @ 9:45 AM
 

On the late Cambridge astronomer Donald Lynden-Bell —

"As an academic at a time when students listened and lecturers lectured, he had the disconcerting habit of instead picking on a random undergraduate and testing them on the topic. One former student, now a professor, remembered how he would 'ask on-the-spot questions while announcing that his daughter would solve these problems at the breakfast table'.

He got away with it because he was genuinely interested in the work of his colleagues and students, and came to be viewed with great affection by them. He also got away with it because he was well established as a titan of the field."

The London Times  on Feb. 8, 2018, at 5 PM (British time)

Related material —

Two Log24 posts from yesteday, Art Wars and The Void.

See as well the field GF(9)

http://www.log24.com/log/pix12/120220-CoxeterFig10.jpg

and the 3×3 grid as a symbol of Apollo
    (an Olympian rather than a Titan) —

 .

Friday, December 25, 2015

At Play in the Fields

Filed under: Uncategorized — Tags: — m759 @ 1:00 PM

See Fields of Force  and recent posts.

From PR Newswire  in July 2011 —

Campus Crusade for Christ Adopts New Name: Cru
60-year-old Int'l Ministry Aims to Increase
Relevance and Global Effectiveness

Related material:

Yin + Yang —

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

Friday, April 4, 2014

Dream of the Expanded Field

Filed under: Uncategorized — 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.”

Saturday, November 10, 2012

Battlefield Geometry

Filed under: Uncategorized — Tags: — m759 @ 5:24 AM

(Continued)

Click to enlarge.

Related material from Wikipedia— Baseball metaphors for sex.

"Build it…"

Friday, November 9, 2012

Battlefield Geometry

Filed under: Uncategorized — Tags: — m759 @ 3:28 PM

(Continued from Sept. 11, 2007)

CIA Director David Petraeus resigns, cites extramarital affair

Trouble with the curve?

Tuesday, March 27, 2012

Literary Field

Filed under: Uncategorized — 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 .

Tuesday, March 20, 2012

Field (continued)

Filed under: Uncategorized — Tags: — m759 @ 11:11 PM

In memory of director Ulu Grosbard (continued from yesterday)

From  http://scripturetext.com/matthew/13-44.htm —

Again the kingdom of heaven is like unto treasure hid in a field
the which when a man hath found he hideth and for joy thereof
goeth and selleth all that he hath and buyeth that field

ΚΑΤΑ ΜΑΤΘΑΙΟΝ 13:44 Greek NT: Byzantine/Majority Text (2000)
παλιν ομοια εστιν η βασιλεια των ουρανων θησαυρω κεκρυμμενω εν τω αγρω

LEXICON  


παλιν  adverb


palin  pal'-in:  (adverbially) anew, i.e. (of place) back, (of time) once more, or (conjunctionally) furthermore or on the other hand — again.


ομοια  adjective – nominative singular feminine


homoios  hom'-oy-os:  similar (in appearance or character) — like, + manner.


εστιν  verb – present indicative – third person singular 


esti  es-tee':  he (she or it) is; also (with neuter plural) they are


η  definite article – nominative singular feminine


ho  ho:  the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.


βασιλεια  noun – nominative singular feminine


basileia  bas-il-i'-ah:  royalty, i.e. (abstractly) rule, or (concretely) a realm — kingdom, + reign.


των  definite article – genitive plural masculine


ho  ho:  the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.


ουρανων  noun – genitive plural masculine


ouranos  oo-ran-os':  the sky; by extension, heaven (as the abode of God); by implication, happiness, power, eternity; specially, the Gospel (Christianity) — air, heaven(-ly), sky.


θησαυρω  noun – dative singular masculine


thesauros  thay-sow-ros':  a deposit, i.e. wealth — treasure.


κεκρυμμενω  verb – perfect passive participle – dative singular masculine 


krupto  kroop'-to:  to conceal (properly, by covering) — hide (self), keep secret, secret(-ly).


εν  preposition


en  en:  in, at, (up-)on, by, etc.


τω  definite article – dative singular masculine


ho  ho:  the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.


αγρω  noun – dative singular masculine


agros  ag-ros':  a field (as a drive for cattle); genitive case, the country; specially, a farm, i.e. hamlet — country, farm, piece of ground, land.

Monday, March 19, 2012

Field

Filed under: Uncategorized — Tags: , — m759 @ 9:08 AM

IMAGE- Two versions of 'field'

— Illustration by Neill Cameron for his father, combinatorialist Peter J. Cameron

Illustration by Nao of the Japanese (and Chinese) character for "field"—

IMAGE- Japanese character for 'field'

Related material—

Finitegeometry.org favicon from February 24, 2012

Wednesday, June 30, 2010

Field Dream

Filed under: Uncategorized — 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.”

Wednesday, June 16, 2010

Field of Dreams

Filed under: Uncategorized — Tags: , — m759 @ 8:28 PM

Long Day's Journey into Nighttown

http://www.log24.com/log/pix10A/100616-LitField.gif

Click for larger, clearer image.

New Yorker  cover, fiction issue of June 14 and 21, 2010.
"Finish Line," by Chris Ware.

See also Shakespeare's Birthday, 2009.

Saturday, March 20, 2010

Field Theory

Filed under: Uncategorized — 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.

Tuesday, January 3, 2017

Cultist Space

Filed under: Uncategorized — Tags: — m759 @ 6:29 PM

The image of art historian Rosalind Krauss in the previous post
suggests a review of a page from her 1979 essay "Grids" —

The previous post illustrated a 3×3 grid. That  cultist space does
provide a place for a few "vestiges of the nineteenth century" —
namely, the elements of the Galois field GF(9) — to hide.
See Coxeter's Aleph in this journal.

Monday, February 20, 2012

Coxeter and the Relativity Problem

Filed under: Uncategorized — m759 @ 12:00 PM

In the Beginning…

"As is well known, the Aleph is the first letter of the Hebrew alphabet."
– Borges, "The Aleph" (1945)

From some 1949 remarks of Weyl—

"The relativity problem is one of central significance throughout geometry and algebra and has been recognized as such by the mathematicians at an early time."

Hermann Weyl, "Relativity Theory as a Stimulus in Mathematical Research," Proceedings of the American Philosophical Society , Vol. 93, No. 7, Theory of Relativity in Contemporary Science: Papers Read at the Celebration of the Seventieth Birthday of Professor Albert Einstein in Princeton, March 19, 1949  (Dec. 30, 1949), pp. 535-541

Weyl in 1946—:

"This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them."

— Hermann Weyl, The Classical Groups , Princeton University Press, 1946, p. 16

Coxeter in 1950 described the elements of the Galois field GF(9) as powers of a primitive root and as ordered pairs of the field of residue-classes modulo 3—

"… the successive powers of  the primitive root λ or 10 are

λ = 10,  λ2 = 21,  λ3 = 22,  λ4 = 02,
λ5 = 20,  λ6 = 12,  λ7 = 11,  λ8 = 01.

These are the proper coordinate symbols….

(See Fig. 10, where the points are represented in the Euclidean plane as if the coordinate residue 2 were the ordinary number -1. This representation naturally obscures the collinearity of such points as λ4, λ5, λ7.)"

http://www.log24.com/log/pix12/120220-CoxeterFig10.jpg

Coxeter's Figure 10 yields...

http://www.log24.com/log/pix11/110107-The1950Aleph-Sm.jpg

The Aleph

The details:

(Click to enlarge)

http://www.log24.com/log/pix11/110107-Aleph-Sm.jpg

Coxeter's phrase "in the Euclidean plane" obscures the noncontinuous nature of the transformations that are automorphisms of the above linear 2-space over GF(3).

Thursday, September 8, 2011

Starring the Diamond

Filed under: Uncategorized — m759 @ 2:02 PM

"In any geometry satisfying Pappus's Theorem,
the four pairs of opposite points of 83
are joined by four concurrent lines.
"
— H. S. M. Coxeter (see below)

Continued from Tuesday, Sept. 6

The Diamond Star

http://www.log24.com/log/pix11B/110905-StellaOctangulaView.jpg

The above is a version of a figure from Configurations and Squares.

Yesterday's post related the the Pappus configuration to this figure.

Coxeter, in "Self-Dual Configurations and Regular Graphs," also relates Pappus to the figure.

Some excerpts from Coxeter—

http://www.log24.com/log/pix11B/110908-Coxeter83.jpg

The relabeling uses the 8 superscripts
from the first picture above (plus 0).
The order of the superscripts is from
an 8-cycle in the Galois field GF(9).

The relabeled configuration is used in a discussion of Pappus—

http://www.log24.com/log/pix11B/110908-Coxeter83part2.jpg

(Update of Sept. 10, 2011—
Coxeter here has a note referring to page 335 of
G. A. Miller, H. F. Blichfeldt, and L. E. Dickson,
Theory and Applications of Finite Groups , New York, 1916.)

Coxeter later uses the the 3×3 array (with center omitted) again to illustrate the Desargues  configuration—

http://www.log24.com/log/pix11B/110908-Coxeter103.jpg

The Desargues configuration is discussed by Gian-Carlo Rota on pp. 145-146 of Indiscrete Thoughts

"The value  of Desargues' theorem and the reason  why the statement of this theorem has survived through the centuries, while other equally striking geometrical theorems have been forgotten, is in the realization that Desargues' theorem opened a horizon of possibilities  that relate geometry and algebra in unexpected ways."

Sunday, April 30, 2017

Exegesis*

Filed under: Uncategorized — Tags: — m759 @ 2:00 PM

See also the Potter  and the field  of the previous post.

"Authority is connected with the word ‘auto’, which means ‘self’,
as in ‘automobile’ and ‘autobiography’. But if authority is related
to the ‘self’, which self should we start with?"

— Potter, Ellis. How Do You Know That?  (p. 7), Kindle Edition. 

Click the above book cover for a post on
the four-square Chinese symbol for 'field.'

* A footnote . . . 

for those who, like the Potter of the previous post,
are epistemologically challenged

Related scripture —

"Authority is connected with the word ‘auto’, which means ‘self’,
as in ‘automobile’ and ‘autobiography’. But if authority is related
to the ‘self’, which self should we start with?"

— Potter, Ellis. How Do You Know That?  (p. 7), Kindle Edition. 

"Off the top of my head . . . ." — Phrase attributed to Ellis Potter

For the Church of Synchronology — See also this  journal
on the above interview date — September 20, 2010
as well as "Smallest Perfect" and "Unfolding."

Saturday, April 29, 2017

For the Church of Synchronology*

Filed under: Uncategorized — Tags: — m759 @ 2:00 PM

A book cover from Amazon.com —

See also this journal on the above date, September 27, 2016 —

Chomsky and Levi-Strauss in China,
Or: Philosophy for Jews
.

Some other remarks related to the figure on the book cover —

Field Theology and Galois Window.

* See Synchronology in this journal.

Monday, December 26, 2016

Bright and Dark at Christmas

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

See also this journal on Christmas night.

"Adam Frank, an astrophysicist who writes for NPR's
13.7 blog, described dark matter by comparing it to
a ghost in a horror movie. You can't see it, he writes —
'but you know it's with you because it messes with
the things you can see. ' " — NPR.org this evening

See as well today's post Old News and the Nov. 4, 2008,
book on Charles Dickens, The Man Who Invented Christmas .

Sunday, December 25, 2016

Last Christmas*

Filed under: Uncategorized — Tags: — m759 @ 11:30 PM

From "Bright Symbol," a post of 12 AM
on December 25, 2015 —

From "Dark Symbol," a post of 12 PM
on December 25, 2015 —

* Title suggested by a song released by Epic Records in 1984.

Friday, December 25, 2015

Dark Symbol

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

Related material:

The previous post (Bright Symbol) and
a post from Wednesday
December 23, 2015, that links to posts
on Boolean algebra vs. Galois geometry.

"An analogy between mathematics and religion is apposite."

— Harvard Magazine  review by Avner Ash of
     Mathematics without Apologies
     
(Princeton University Press, January 18, 2015)
 

Bright Symbol

Filed under: Uncategorized — Tags: — m759 @ 12:00 AM

Detail:

Thursday, December 24, 2015

Group Actions…

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

On the Eight

Thursday, July 9, 2015

Man and His Symbols

Filed under: Uncategorized — m759 @ 2:24 PM

(Continued)

A post of July 7, Haiku for DeLillo, had a link to posts tagged "Holy Field GF(3)."

As the smallest Galois field based on an odd prime, this structure 
clearly is of fundamental importance.  

The Galois field GF(3)

It is, however, perhaps too  small  to be visually impressive.

A larger, closely related, field, GF(9), may be pictured as a 3×3 array

hence as the traditional Chinese  Holy Field.

Marketing the Holy Field

IMAGE- The Ninefold Square, in China 'The Holy Field'

The above illustration of China's  Holy Field occurred in the context of
Log24 posts on Child Buyers.   For more on child buyers, see an excellent
condemnation today by Diane Ravitch of the U. S. Secretary of Education.

Tuesday, July 7, 2015

Haiku for DeLillo*

Filed under: Uncategorized — Tags: — m759 @ 4:23 PM

A music video that opens with remarks by Lawrence Ferlinghetti
at the Last Waltz concert (Thanksgiving Day, Nov. 25, 1976):

"Our Father, whose art's in heaven…" —

For other religious remarks from the above upload date,
Sept. 9, 2011, see Holy Field GF(3).

Click the above "ripple" image for a Grateful Dead haiku
quoted here on Sunday, July 5, 2015.

For another meditation from the second upload date above,
March 19, 2012, see some thoughts on the word "field."

IMAGE- Japanese character for 'field'

* For the title, see an excerpt from Point Omega .

Sunday, July 6, 2014

Sticks and Stones

Filed under: Uncategorized — 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: Uncategorized — 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, November 10, 2013

Abstraction

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

(Continued from Dec. 6, 2012)

Context:
Chinese Field  and Modal Diamond .

(See also today’s previous post.)

Tuesday, August 13, 2013

The Story of N

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

(Continued from this morning)

http://www.log24.com/log/pix11/110107-The1950Aleph-Sm.jpg

The above stylized "N," based on
an 8-cycle in the 9-element Galois field
GF(9), may also be read as
an Aleph.

Graphic designers may prefer a simpler,
bolder version:

Thursday, June 13, 2013

Gate

Filed under: Uncategorized — 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:

Monday, October 8, 2012

Air America

Filed under: Uncategorized — Tags: , — m759 @ 4:00 AM

Related entertainment—

The song being performed in the above trailer 
for Air America  is "A Horse with No Name."

See  "Instantia Crucis" and "Winning."

Friday, March 30, 2012

Brain Boost*

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

See "Dark Fields" in this journal
and Peter J. Cameron's weblog today.

* Phrase from "Forbidden Planet" (1956).
  See previous post.

Wednesday, March 21, 2012

Digital Theology

Filed under: Uncategorized — Tags: — m759 @ 7:20 AM

See also remarks on Digital Space and Digital Time in this journal.

Such remarks can, of course, easily verge on crackpot territory.

For some related  pure  mathematics, see Symmetry of Walsh Functions.

Saturday, February 18, 2012

Logo

Filed under: Uncategorized — Tags: — m759 @ 8:48 AM

Pentagram design agency on the new Windows 8 logo

"… the logo re-imagines the familiar four-color symbol
as a modern geometric shape"—

http://www.log24.com/log/pix12/120218-Windows8Logo.jpg

Sam Moreau, Principal Director of User Experience for Windows,
yesterday—

On Redesigning the Windows Logo

"To see what is in front of one's nose
needs a constant struggle."
George Orwell

That is the feeling we had when Paula Scher
(from the renowned Pentagram design agency)
showed us her sketches for the new Windows logo.

Related material:

http://www.log24.com/log/pix12/120218-SmallSpaces-256w.gif

Wednesday, November 30, 2011

Lines

Filed under: Uncategorized — Tags: — m759 @ 11:30 PM

From the release date of the film of Alan Glynn’s
novel The Dark Fields  (now retitled “Limitless“)—

http://www.log24.com/log/pix11/110318-NYTobitsWirthlin.jpg

“The time is now.”

Related material—

“Why does the dog wag its tail?
Because the dog is smarter than the tail.
If the tail were smarter, it would wag the dog.”

IMAGE- The perception of doors in 'Sunshine Cleaning'

Above: Amy Adams in “Sunshine Cleaning

“Now, I’ll open up a line of credit for you.
You’ll be wantin’ a few toys.”

Friday, September 9, 2011

Galois vs. Rubik

Filed under: Uncategorized — Tags: , — m759 @ 2:56 PM

(Continued from Abel Prize, August 26)

IMAGE- Elementary Galois Geometry over GF(3)

The situation is rather different when the
underlying Galois field has two rather than
three elements… See Galois Geometry.

Image-- Sugar cube in coffee, from 'Bleu'

The coffee scene from "Bleu"

Related material from this journal:

The Dream of
the Expanded Field

Image-- 4x4 square and 4x4x4 cube

A Beginning

Filed under: Uncategorized — Tags: — m759 @ 5:29 AM
 

From MIT Commencement Day, 2011—

A symbol related to Apollo, to nine, and to "nothing"

A minimalist favicon—

IMAGE- Generic 3x3 square as favicon

This miniature 3×3 square— http://log24.com/log/pix11A/110518-3x3favicon.ico — may, if one likes,
be viewed as the "nothing" present at the Creation. 
See Feb. 19, 2011, and Jim Holt on physics.

Thursday, June 17, 2010

Nighttown

Filed under: Uncategorized — Tags: — m759 @ 2:02 PM

Continued from yesterday evening's "Long Day's Journey into Nighttown"—

A detail from that post—

Image-- Detail of New Yorker cover 'Finish Line,' double fiction issue of June 14 & 21, 2010

Related material from Nighttown—
The Sebastian Horsley Guide to Whoring

Image-- YouTube video, 'The Sebastian Horsley Guide to Whoring'

Horsley, the author of Dandy in the Underworld, was
found dead this morning of a suspected heroin overdose.

"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

Thursday, October 25, 2007

Thursday October 25, 2007

Filed under: Uncategorized — Tags: — m759 @ 9:19 AM

Something Anonymous

From this date–
Picasso's birthday–
five years ago:
 
"A work of art has an author
and yet,
when it is perfect,
it has something
which is
essentially anonymous about it."

Simone Weil, Gravity and Grace   

 
Michelangelo's birthday, 2003

4x4 square grid

Yesterday:

The color-analogy figures of Descartes

Nineteenth-century quilt design:

Tents of Armageddon quilt design

Related material:

Battlefield Geometry
 

Tuesday, September 11, 2007

Tuesday September 11, 2007

Filed under: Uncategorized — Tags: — m759 @ 12:07 AM

Battlefield Geometry

"The general, who wrote the Army's book on counterinsurgency, said he and his staff were 'trying to do the battlefield geometry right now' as he prepared his troop-level recommendations."
Steven R. Hurst, The Associated Press, Wednesday, Aug. 15, 2007

"'… we are in the process of doing the battlefield geometry to determine the way ahead.'"
Charles M. Sennott, Boston Globe, Friday, Sept. 7, 2007

"Based on these considerations, and having worked the battlefield geometry … I have recommended a drawdown of the surge forces from Iraq."
United States Army, Monday, Sept. 10, 2007

Related material:

Log24 entries of
June 11 and 12, 2005:

Desert Square, from xxi.ac-reims.fr/terres-rouges/essai/histoire.htm

"In the desert you can
remember your name
'Cause there ain't no one
for to give you no pain."

Saturday, July 29, 2006

Saturday July 29, 2006

Filed under: Uncategorized — Tags: — m759 @ 5:01 PM

Dark Fields
of the Republic

Today’s birthday: Ken Burns

Charley Reese on the republic:

“The republic died at Appomattox, and it’s been empire ever since.”

Charley Reese on Lincoln:

“Washington and Jefferson created the republic; Lincoln destroyed it.”

In closing…

A link in memory of Donald G. Higman, dead on Feb. 13, 2006, the day after Lincoln’s birthday:

On the Graphs of Hoffman-Singleton and Higman-Sims (pdf)

His truth is marching on.

Sunday, September 22, 2002

Sunday September 22, 2002

Filed under: Uncategorized — 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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