Log24

Wednesday, April 25, 2018

A Deathly Triangle

Filed under: General,Geometry — Tags: , — m759 @ 11:27 PM

'Imprisoned in a Tesseract,' a study of novelist James Blish

Wednesday, July 22, 2015

Harvard Death

Filed under: General — Tags: — m759 @ 3:00 AM

Bloomberg.com —
July 21, 2015 — 3:51 PM EDT
Updated on July 21, 2015 — 6:04 PM EDT —

James Rothenberg of Capital Group
Dies at 69 of Heart Attack

"He was  chairman of Harvard Management Co.,
which invests the university’s $36.4 billion endowment."

See also  
The Harvard Crimson —
UPDATED: July 22, 2015, at 1:28 a.m.

"Rothenberg’s death, reportedly of a heart attack,
was unexpected."

He reportedly "chaired Harvard Management Company’s
board of directors from 2004 until his death."

Saturday, June 27, 2015

A Death of Kings

Filed under: General — m759 @ 10:25 PM

The title is that of  a classic 1968 New Yorker  essay
by George Steiner. See previous posts on this topic.

Sunday, March 29, 2015

Death in East Hampton

Filed under: General — Tags: — m759 @ 1:28 PM

See also Deathtrap in this journal.

Saturday, November 23, 2013

Chess

Filed under: General — m759 @ 9:29 AM

Norwegian, 22, Takes World Chess Title

Quoted here on Thursday, the date of Kavli's death:

Herbert Mitgang's New York Times  
obituary of Cleanth Brooks

"The New Critics advocated close reading of literary texts
and detailed analysis, concentrating on semantics, meter,
imagery, metaphor and symbol as well as references to
history, biography and cultural background."

See also Steiner, Chess, and Death.

Sunday, May 23, 2010

Death Story

Filed under: General — Tags: — m759 @ 9:40 PM

Image-- Arts & Letters Daily, news item on Bloglines first posted at 12 AM Sunday, May 23, 2010

Tuesday, August 27, 2019

Tiger Leaps

Filed under: General — Tags: , — m759 @ 10:33 AM

Walter Benjamin on 'a tiger's leap into the past'

See also Tiger in this journal, esp.

The image “http://www.log24.com/log/pix05/050123-Tiger.JPG” cannot be displayed, because it contains errors.   and . . .

other "Death and the Spirit" posts.

Thursday, May 9, 2019

The Birdseye Requiem

Filed under: General — Tags: — m759 @ 9:10 AM

From The Boston Globe  yesterday evening —

" Ms. Adams 'had this quiet intelligence that made you feel like
she understood you and she loved you. She was a true friend —
a true generous, generous friend. This is the kind of person
you keep in your life,' Birdseye added.

'And she had such a great sense of humor,' Birdseye said.
“She would always have the last laugh. She wasn’t always
the loudest, but she was always the funniest, and in the
smartest way.' "

"Ms. Adams, who lived in Waltham, was 55 when she died April 9 . . . ."

See as well April 9 in the post Math Death and a post from April 8,
also now tagged "Berlekamp's Game" — Horses of a Dream.

"When logic and proportion have fallen sloppy dead
And the white knight is talking backwards . . . ."

— Grace Slick in a song from yesterday's post "When the Men"

Wednesday, January 2, 2019

Wolf as Lamb

Filed under: General,Geometry — Tags: — m759 @ 10:30 PM

The above graphic design is by Noma Bar.

See as well the lamb-in-triangle of the Dec. 27 post
A Candle for Lily

Related material —

Remarks by Evelyn  Lamb on the Deathly Hallows symbol.

Saturday, January 6, 2018

Yale News

Filed under: General,Geometry — Tags: — m759 @ 5:24 AM

The Yale of the title is not the university, but rather the
mathematician Paul B. Yale. Yale's illustration of the Fano
plane is below.

IMAGE- Triangular models of the 4-point affine plane A and 7-point projective plane PA

A different illustration from a mathematician named Greenberg —

This illustration of the ominous phrase "line at infinity"
may serve as a sort of Deathly Hallows  for Greenberg.
According to the AMS website yesterday, he died on
December 12, 2017:

A search of this  journal for Greenberg yields no mention of
the dead mathematician, but does yield some remarks
on art that are pehaps less bleak than the above illustration.

For instance —

Art adapted from the Google search screen. Discuss.

Saturday, April 22, 2017

Science Marches On

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

Connoisseurs of bullshit who enjoyed the previous post
might also enjoy the following:

The previous two posts introduced Mazzola's noxious combination of 
category theory and Hegel. The current version (Rev. 254) of the above 
nLab "Science of Logic" article, though not by Mazzola, displays this
combination in its full hideous splendor.

Some posts in this  journal that might be viewed as leading up to 
the original Sept. 2, 2012, "Science of Logic" article are now tagged
Death Warmed Over.

Thursday, December 17, 2015

S-Curves by Peter Dickinson

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

British author Peter Dickinson, who reportedly died yesterday,
Dec. 16, 2015, at 88, wrote the following (published in the UK
in 1975 and in the US in 1976) —

'Chance, Luck and Destiny' by Peter Dickinson, page 34

Inverted image of the above page —

'Chance, Luck and Destiny' by Peter Dickinson, page 34

See also, from the date of Dickinson's death, a post on
"A Fight for the Soul…" and a post on the symbol "S."

Of interest too are some remarks related to today's earlier post,
"Hint of Reality" 

Hint of Reality

Filed under: General,Geometry — Tags: , , — m759 @ 12:45 PM

From an article* in Proceedings of Bridges 2014

As artists, we are particularly interested in the symmetries of real world physical objects.

Three natural questions arise:

1. Which groups can be represented as the group of symmetries of some real-world physical object?

2. Which groups have actually  been represented as the group of symmetries of some real-world physical object?

3. Are there any glaring gaps – small, beautiful groups that should have a physical representation in a symmetric object but up until now have not?

The article was cited by Evelyn Lamb in her Scientific American  
weblog on May 19, 2014.

The above three questions from the article are relevant to a more
recent (Oct. 24, 2015) remark by Lamb:

" finite projective planes [in particular, the 7-point Fano plane,
about which Lamb is writing] 
seem like a triumph of purely 
axiomatic thinking over any hint of reality…."

For related hints of reality, see Eightfold Cube  in this journal.

* "The Quaternion Group as a Symmetry Group," by Vi Hart and Henry Segerman

Tuesday, July 21, 2015

“Ragtime” Author Dies at 84

Filed under: General — Tags: — m759 @ 11:55 PM

“…right through hell
     there is a path…”
 
  — Malcolm Lowry

E!

Filed under: General — Tags: — m759 @ 6:19 PM

Wednesday, April 29, 2015

Scenes from…

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

An Epic for Drink Boy —

Context:  The post in which the above scenes occur.

Gone

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

Update of 12:25 AM — See, too, The Oxford Murders.

Monday, February 23, 2015

Symbolic Poetry*

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

“When life itself seems lunatic,
who knows where madness lies?

Man of La Mancha

Windmill of Time and Diamond of Eternity

Perhaps the late Sidney Lumet?

           The setting for the Sidney Lumet film "Deathtrap" (1982)

* Continued from yesterday's Backstory and Sermon.

Sunday, February 8, 2015

Hungarian Phenomenon

Filed under: General — Tags: , , — m759 @ 2:07 PM

For Autism Sunday —

Mathematician John von Neumann
reportedly died on this date.

"He belonged  to that so-called
Hungarian phenomenon…."

A webpage titled 
"Von Neumann, Jewish Catholic"

Illustrations of another Hungarian phenomenon:

IMAGE- Anthony Hopkins exorcises a Rubik cube

Friday, October 10, 2014

Autistic Enchantment

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

(Continued from Sept. 3, 2009)

George Steiner on chess:

"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

A related remark from Dudeney:

See also a different context for 16 squares and 322,560 arrangements.

Both Hands and an Ass Map

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

(Continued from Grids and Space and posts tagged Riddle for Caltech)

IMAGE- Scene from 'Deathtrap,' with subtitle

Tuesday, October 7, 2014

Grids and Space

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

In honor of the late Sidney Lumet

(See Makom Kadosh , April 9, 2011.)

IMAGE- Christopher Reeve in the 1982 film 'Deathtrap,' illustrating concepts of space

Sunday, December 2, 2012

Realism

Filed under: General — Tags: — m759 @ 4:30 PM

From the Los Angeles Times  yesterday

"Chess player Elena Akhmilovskaya Donaldson sits
in deep concentration at the U.S. chess championship
in Seattle in 2002. (Greg Gilbert / Seattle Times / 
January 5, 2002)"

Linda Shaw, Seattle Times :

"Elena Akhmilovskaya Donaldson, who was once the world's
second-ranked women's chess player and eloped in 1988
with the captain of the U.S. chess team when they were both
playing at a tournament in Greece, has died. She was 55.

Donaldson, who earned the title of international women's
grandmaster, died Nov. 18 in her adopted hometown of Seattle…."

more »

From the Log24 post "Sermon" on the date of Donaldson's death,
Sunday, Nov. 18, 2012—

"You must allow us to play every conceivable combination of chess."
— Marie-Louise von Franz in Number and Time

An October 2011 post titled  Realism in Plato's Cave displays
the following image:

Cover illustration: Durer's 'Knight, Death, and the Devil'

Cover illustration: Knight, Death, and the Devil,
by Albrecht Dürer

George Steiner and myself  in Closing the Circle, a Log24 post
of Sept. 4, 2009: 

“Allegoric associations of death with chess are perennial….”

"Yes, they are."

For related remarks on knight moves and the devil, see
today's previous two posts, Knight's Labyrinth and The Rite.

Sunday, September 2, 2012

The Word in the Desert

Filed under: General — Tags: — m759 @ 3:09 AM

(Continued)

For Trotsky's Birthday (Old Style), 2009—

IMAGE- Two Log24 posts, on Rosalind Krauss and on the occult, from Oct. 25, 2009

Related material:

IMAGE- Video- On the road to the U2 Rose Bowl concert of Oct. 25, 2009- 'Quest for the U2 Joshua Tree + Zabriskie'

IMAGE- NY Times Sept. 1, 2012, online obituary for Alexander Saxton, who died by his own hand on Aug. 20, 2012

(Click for further details.)

See also St. Stephen's Day, 2011.

Saturday, September 1, 2012

College of the Desert

Filed under: General — Tags: — m759 @ 6:08 AM

(Continued from 6:08 AM EDT yesterday and the day before)

"Richard Elster was seventy-three, I was less than half his age. He’d invited me to join him here, old house, under-furnished, somewhere south of nowhere in the Sonoran Desert or maybe it was the Mojave Desert or another desert altogether.* Not a long visit, he’d said."

— Don DeLillo, Point Omega

IMAGE- Detail of John Ritter's NY Times illustration for Geoff Dyer's review of 'Point Omega,' plus link to Twitter beneath illustration

Maybe it was the desert near Twentynine Palms.

IMAGE- Twentynine Palms in Geoff Dyer's review of 'Point Omega'

"Sometimes a wind comes before the rain
and sends birds sailing past the window,
spirit birds that ride the night,
stranger than dreams."

— Ending of Point Omega

* Update of Sept. 2, 2012— A different passage yields a more precise location.

Friday, August 31, 2012

Translation

Filed under: General — Tags: — m759 @ 6:08 AM

"Translation in the direction
conceptual -> concrete and symbolic
is much easier than
translation in the reverse direction…."

The late William P. Thurston

(See also "Atlas to the Text," Harvard Crimson , March 8, 2011).

Related cinematic imagery

Conceptual  (thanks to Don DeLillo and The New York Times )—

IMAGE- NY Times headline 'A Wrinkle in Time' with 24 Hour Psycho and Point Omega scene

Concrete and symbolic (thanks to Amy Adams and Emily Blunt, as well as
Frederick Seidel in the September 3, 2012, New Yorker )

"Biddies still cleaned the student rooms."

IMAGE- Shower wall in 'Sunshine Cleaning'

Thursday, August 30, 2012

The Cruelest Month

Filed under: General — Tags: — m759 @ 6:08 AM

Last night's 10 PM post linked to an April 7, 2012,
post that through a series of further links leads
to Columbia Film Theory .

For other film-related remarks, by a
Columbia alumnus,* see last night's post.

See also the 1.3 MB image from Aug. 16, the night 
of Elvis's Wrap Party. An excerpt from that image
stars Amy Adams—

Images, including the late Richard Zanuck

For Amy, from the current New Yorker

The Master

* N.O.C.D.

Wednesday, August 29, 2012

It’s 10 PM…

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

Do you know where your children are?

Continued from Plan 9 , a Log24 post of  9 PM Monday

See another weblog's April 7, 2012, post on
God and Horror Movies.

See also this  weblog's post on that date.

Hexagram 18

Filed under: General — Tags: — m759 @ 9:14 AM

(Continued from June 14, 2007)

The late William P. Thurston on how mathematical knowledge may decay:

"There are several obvious mechanisms of decay. The experts in a subject retire and die, or simply move on to other subjects and forget. Mathematics is commonly explained and recorded in symbolic and concrete forms that are easy to communicate, rather than in conceptual forms that are easy to understand once communicated. Translation in the direction conceptual -> concrete and symbolic is much easier than translation in the reverse direction, and symbolic forms often replaces [sic ] the conceptual forms of understanding. And mathematical conventions and taken-for-granted knowledge change, so older texts may become hard to understand.

In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths [sic ] life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining — they depend very heavily on the community of mathematicians."

At mathoverflow.net, October 30, 2010.
     The discussion has been "closed as no longer relevant."
     For another Thurston quote of interest, see a more recent
     mathoverflow discussion "closed as not a real question."

Tuesday, August 28, 2012

Dark and Stormy

Filed under: General — Tags: , — m759 @ 10:31 PM

It  was a  dark and stormy night.

A Wrinkle in Time  (brought  up to date)

Up to Date

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

"Plato's cave was brought up to date in 1978…."

— Keith Devlin in Mathematics: The Science of Patterns

Related material from yesterday: Touchy-Feely and Plan 9.

"Plan 9 deals with the resurrection of the dead.

IMAGE- Bill Murray explains Ed Wood's 'Plan 9 from Outer Space'

For a rather different approach to Plato, see three posts of August 16, 2012—

Hope and Pope

Filed under: General — Tags: , , — m759 @ 4:59 AM

IMAGE- 'Hope of Heaven,' by John O'Hara, 1947 Avon paperback

Hope of Heaven , by John O'Hara
Avon paperback edition, 1947

   Heaven from all creatures hides the book of Fate,
All but the page prescribed, their present state:
From brutes what men, from men what spirits know:
Or who could suffer being here below?
The lamb thy riot dooms to bleed to-day,
Had he thy reason, would he skip and play?
Pleased to the last, he crops the flowery food,
And licks the hand just raised to shed his blood.
Oh, blindness to the future! kindly given,
That each may fill the circle, marked by Heaven:
Who sees with equal eye, as God of all,
A hero perish, or a sparrow fall,
Atoms or systems into ruin hurled,
And now a bubble burst, and now a world.
   Hope humbly, then; with trembling pinions soar;
Wait the great teacher Death; and God adore.
What future bliss, He gives not thee to know,
But gives that hope to be thy blessing now.
Hope springs eternal in the human breast:
Man never is, but always to be blest:
The soul, uneasy and confined from home,
Rests and expatiates in a life to come.

— Alexander Pope in An Essay on Man

Monday, August 27, 2012

Plan 9

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

(Continued)

IMAGE- 'The Ninth Configuration,' based on a novel by William Peter Blatty

See also "Or Only Die" and Corpus Hypercubus .

Touchy-Feely

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

A remark by the late William P. Thurston

Please note: I'm not advocating that
we turn mathematics into a touchy-feely subject.

Noted. But see this passage—

The Mathematical Experience , by Philip J. Davis and Reuben Hersh (1981), updated study edition, Springer, 2011—

From the section titled "Four-Dimensional Intuition," pages 445-446:

"At Brown University Thomas Banchoff, a mathematician, and Charles Strauss, a computer scientist, have made computer-generated motion pictures of a hypercube….

… at the Brown University Computing Center, Strauss gave me a demonstration of the interactive graphic system which made it possible to produce such a film….

… Strauss showed me how all these controls could be used to get various views of three-dimensional projections of a hypercube. I watched, and tried my best to grasp what I was looking at. Then he stood up, and offered me the chair at the control.

I tried turning the hypercube around, moving it away, bringing it up close, turning it around another way. Suddenly I could feel  it!. The hypercube had leaped into palpable reality, as I learned how to manipulate it, feeling in my fingertips the power to change what I saw and change it back again. The active control at the computer console created a union of kinesthetics and visual thinking which brought the hypercube up to the level of intuitive understanding."

Thanks to the Web, a version of this experience created by Harry J. Smith
has been available to non-academics for some time.

IMAGE- The Harry J. Smith Memorial Tesseract

IMAGE- From 'Touchy-Feely: The Musical!'

Saturday, August 25, 2012

One Small Step

Filed under: General — Tags: — m759 @ 8:19 PM

Click image for some related material.

Wednesday, June 22, 2011

ART WARS continued

Filed under: General,Geometry — Tags: — m759 @ 8:06 PM

This evening's New York Times  obituaries—

http://www.log24.com/log/pix11A/110622-NYTobits720PM.jpg

A work of art suggested by the first and third items above—

http://www.log24.com/log/pix11A/110614-TarantinoCar.jpg

I prefer a work of art that is structurally similar—

IMAGE- The Klein group as art

and is related to a picture, Portrait of O, from October 1, 1983—

IMAGE- A work by Cullinane pirated by artist Steve RIchards in his contribution to London's 'Piracy Project'

For a recent unexpected Web appearance of Portrait of O,
aee Abracadabra from the midnight of June 18-19.

Tuesday, June 14, 2011

Expressionistic Depth

Filed under: General — Tags: — m759 @ 6:20 AM

http://www.log24.com/log/pix11A/110614-DoubleDown.jpg

Update of 7 AM —

Carl Gardner's 1956 hit "Down in Mexico" was featured in the following Hollywood classic:

http://www.log24.com/log/pix11A/110614-TarantinoCar.jpg

Click image for video.

Sunday, May 23, 2010

For Your Consideration —

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

Cannes Festival Readies for Awards Night

Uncertified Copy

Image-- Uncertified copy of 1986 figures by Cullinane in a 2009 art exhibit in Oslo

The pictures in the detail are copies of
figures created by S. H. Cullinane in 1986.
They illustrate his model of hyperplanes
and points in the finite projective space
known as PG(3,2) that underlies
Cullinane's diamond theorem.

The title of the pictures in the detail
is that of a film by Burkard Polster
that portrays a rival model of PG(3,2).

The artist credits neither Cullinane nor Polster.

Sunday School

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

"Mathematics is forever."
— Gian-Carlo Rota   

"Nine is a very powerful
  Nordic number."
— Katherine Neville    

 "Nine tailors make a man."
— Dorothy Sayers 

Annals of Philosophy

Filed under: General — Tags: — m759 @ 3:33 AM

Busy Night at the Lyche Gate

http://www.log24.com/log/pix10A/100523-NYTobits.jpg

"When Death tells a story, you really have to listen."
 

Annals of Conceptual Art

Filed under: General — Tags: — m759 @ 2:02 AM

Josefine Lyche's
  "Theme and Variations" (Oslo, 2009)

http://www.log24.com/log/pix10A/100523-LycheTandV.jpg

Some images in reply—

  Frame Tale

Image by R. T. Curtis from 'Further Elementary Techniques...'

Click on images for further details.

"In the name of the former
and of the latter
and of their holocaust.
  Allmen."

Finnegans Wake

Friday, September 4, 2009

Friday September 4, 2009

Filed under: General — m759 @ 2:02 PM
Closing the Circle

Continued from Monday

“This is a chapel 
 of mischance;
ill luck betide it, ’tis
the cursedest kirk
  that ever I came in!”

Philip Kennicott on
Kirk Varnedoe in
The Washington Post:

“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….”

Kennicott’s remarks were
 on Sunday, May 18, 2003.
They were subtitled
“Closing the Circle
on Abstract Art.”

Also on Sunday, May 18, 2003:

 “Will the circle be unbroken?
  As if some southern congregation
  is praying we will come to understand.”


Princeton University Press
:

Empty canvas on cover of Varnedoe's 'Pictures of Nothing'

See also

Parmiggiani’s 
  Giordano Bruno

Parmiggiani's Bruno: empty canvas with sculpture of Durer's solid

Dürer’s Melencolia I

Durer, Melencolia I

and Log24 entries
of May 19-22, 2009,
ending with
    “Steiner System” —

Diamond-shaped face of Durer's 'Melencolia I' solid, with  four colored pencils from Diane Robertson Design

George Steiner on chess
(see yesterday morning):

“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.”

Steiner continues

“Allegoric associations of death with chess are perennial….”

Yes, they are.

April is Math Awareness Month.
This year’s theme is “mathematics and art.”

Mathematics and Art: Totentanz from Seventh Seal

Cf. both of yesterday’s entries.

Thursday, September 3, 2009

Thursday September 3, 2009

Filed under: General,Geometry — 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, April 23, 2009

Thursday April 23, 2009

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

 

The Geometry
of Language

(continued from April 16)

Background:

Professor Arielle Saiber with chess set

Click on the image for an
interview with the author of
Giordano Bruno and
the Geometry of Language
.

Related material:

Joyce on language —

The sigla of 'Finnegans Wake'

Bruno, Joyce, and coincidentia oppositorum

Cullinane on geometry —

Geometry of the I Ching (for comparison to Joyce's 'sigla')

Click on images for details.
 

Saturday, April 4, 2009

Saturday April 4, 2009

Filed under: General,Geometry — Tags: — m759 @ 7:01 PM
Steiner Systems

 
"Music, mathematics, and chess are in vital respects dynamic acts of location. Symbolic counters are arranged in significant rows. Solutions, be they of a discord, of an algebraic equation, or of a positional impasse, are achieved by a regrouping, by a sequential reordering of individual units and unit-clusters (notes, integers, rooks or pawns). The child-master, like his adult counterpart, is able to visualize in an instantaneous yet preternaturally confident way how the thing should look several moves hence. He sees the logical, the necessary harmonic and melodic argument as it arises out of an initial key relation or the preliminary fragments of a theme. He knows the order, the appropriate dimension, of the sum or geometric figure before he has performed the intervening steps. He announces mate in six because the victorious end position, the maximally efficient configuration of his pieces on the board, lies somehow 'out there' in graphic, inexplicably clear sight of his mind…."

"… in some autistic enchantment,http://www.log24.com/images/asterisk8.gif pure as one of Bach's inverted canons or Euler's formula for polyhedra."

— George Steiner, "A Death of Kings," in The New Yorker, issue dated Sept. 7, 1968

Related material:

A correspondence underlying
the Steiner system S(5,8,24)–

http://www.log24.com/log/pix09/090404-MOGCurtis.gif

The Steiner here is
 Jakob, not George.

http://www.log24.com/images/asterisk8.gif See "Pope to Pray on
   Autism Sunday 2009."
    See also Log24 on that
  Sunday– February 8:

Memorial sermon for John von Neumann, who died on Feb. 8,  1957

 

Tuesday, March 10, 2009

Tuesday March 10, 2009

Filed under: General,Geometry — m759 @ 9:26 AM
Language Game

“Music, mathematics, and chess are in vital respects dynamic acts of location. Symbolic counters are arranged in significant rows. Solutions, be they of a discord, of an algebraic equation, or of a positional impasse, are achieved by a regrouping, by a sequential reordering of individual units and unit-clusters (notes, integers, rooks or pawns). The child-master, like his adult counterpart, is able to visualize in an instantaneous yet preternaturally confident way how the thing should look several moves hence. He sees the logical, the necessary harmonic and melodic argument as it arises out of an initial key relation or the preliminary fragments of a theme. He knows the order, the appropriate dimension, of the sum or geometric figure before he has performed the intervening steps. He announces mate in six because the victorious end position, the maximally efficient configuration of his pieces on the board, lies somehow ‘out there’ in graphic, inexplicably clear sight of his mind….”

“… in some autistic enchantment, pure as one of Bach’s inverted canons or Euler’s formula for polyhedra.”

— George Steiner, “A Death of Kings,” in The New Yorker, issue dated Sept. 7, 1968

Related material:

“Classrooms are filled with discussions not of the Bible and Jesus but of 10 ‘core values’– perseverance and curiosity, for instance– that are woven into the curriculum.”

— “Secular Education, Catholic Values,” by Javier C. Hernandez, The New York Times, Sunday, March 8, 2009

“… There was a problem laid out on the board, a six-mover. I couldn’t solve it, like a lot of my problems. I reached down and moved a knight…. I looked down at the chessboard. The move with the knight was wrong. I put it back where I had moved it from. Knights had no meaning in this game. It wasn’t a game for knights.”


— Raymond Chandler, The Big Sleep

The Chandler quotation appears in “Language Game,” an entry in this journal on April 7, 2008.

Some say the “Language Game” date, April 7, is the true date (fixed, permanent) of the Crucifixion– by analogy, Eliot’s “still point” and Jung’s “centre.” (See yesterday, noon.)

Saturday, January 19, 2008

Saturday January 19, 2008

Filed under: General — m759 @ 7:00 AM
In Memory of
Bobby Fischer

Edward Rothstein has a piece on Bobby Fischer in today’s New York Times.  The Rothstein opening:

“There may be only three human activities in which miraculous accomplishment is possible before adulthood: mathematics, music and chess.”

This echoes the opening of a classic George Steiner essay (The New Yorker, Sept. 7, 1968):

“There are three intellectual pursuits, and, so far as I am aware, only three, in which human beings have performed major feats before the age of puberty. They are music, mathematics, and chess.”

— “A Death of Kings,” reprinted in George Steiner: A Reader, Oxford University Press, 1984, pp. 171-178.

Despite its promising (if unoriginal) opening, the New York Times piece is mainly an attack on Fischer’s anti-Jewish stance.  Rothstein actually has little of interest to say about what he calls the “glass-bead games” of music, mathematics, and chess. For a better-written piece on chess and madness, see Charles Krauthammer’s 2005 essay in TIME. The feuilletons of Rothstein and Krauthammer do not, of course, come close to the genuinely bead-game-like writing of Steiner.

Related material on
chess and religion:
Magical Thinking
(December 7th, 2005)

Friday, January 18, 2008

Friday January 18, 2008

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

Front page top center, online NY Times: Bobby Fischer Dead at 64

Friday January 18, 2008

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

Nativity

… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

Rubén Darío,
born January 18, 1867

Thursday, January 17, 2008

Thursday January 17, 2008

Filed under: General — Tags: — m759 @ 5:24 PM
Well, she was
   just seventeen…
 
(continued)

"Mazur introduced the topic of prime numbers with a story from Don Quixote in which Quixote asked a poet to write a poem with 17 lines. Because 17 is prime, the poet couldn't find a length for the poem's stanzas and was thus stymied."

— Undated American Mathematical Society news item about a Nov. 1, 2007, event

Related material:

Desconvencida,
Jueves, Enero 17, 2008

Horses of a Dream
(Log24, Sept. 12, 2003)

Knight Moves
(Log24 yesterday–
anniversary of the
Jan. 16 publication
of Don Quixote)

Windmill and Diamond
(St. Cecilia's Day 2006)

Wednesday, January 16, 2008

Wednesday January 16, 2008

Filed under: General,Geometry — Tags: — m759 @ 12:25 PM
Knight Moves:
Geometry of the
Eightfold Cube

Actions of PSL(2, 7) on the eightfold cube

Click on the image for a larger version
and an expansion of some remarks
quoted here on Christmas 2005.

Wednesday, June 20, 2007

Wednesday June 20, 2007

Filed under: General,Geometry — Tags: — m759 @ 1:06 AM

Kernel

Mathematical Reviews citation:

MR2163497 (2006g:81002) 81-03 (81P05)
Gieser, Suzanne The innermost kernel. Depth psychology and quantum physics. Wolfgang Pauli's dialogue with C. G. Jung. Springer-Verlag, Berlin, 2005. xiv+378 pp. ISBN: 3-540-20856-9

A quote from MR at Amazon.com:

"This revised translation of a Swedish Ph. D. thesis in philosophy offers far more than a discussion of Wolfgang Pauli's encounters with the psychoanalyst Carl Gustav Jung…. Here the book explains very well how Pauli attempted to extend his understanding beyond superficial esotericism and spiritism…. To understand Pauli one needs books like this one, which… seems to open a path to a fuller understanding of Pauli, who was seeking to solve a quest even deeper than quantum physics." (Arne Schirrmacher, Mathematical Reviews, Issue 2006g)
 

An excerpt:

 

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

I do not yet know what Gieser means by "the innermost kernel." The following is my version of a "kernel" of sorts– a diagram well-known to students of anthropologist Claude Levi-Strauss and art theorist Rosalind Krauss:

The four-group is also known as the Vierergruppe or Klein group.  It appears, notably, as the translation subgroup of A, the group of 24 automorphisms of the affine plane over the 2-element field, and therefore as the kernel of the homomorphism taking A to the group of 6 automorphisms of the projective line over the 2-element field. (See Finite Geometry of the Square and Cube.)

Related material:

The "chessboard" of
   Nov. 7, 2006
(as revised Nov. 7, 2012)–

I Ching chessboard. Previous version replaced on Nov. 7, 2012, by original 1989 chessboard arrangement

I Ching chessboard

None of this material really has much to do with the history of physics, except for its relation to the life and thought of physicist Wolfgang Pauli— the "Mephistopheles" of the new book Faust in Copenhagen. (See previous entry.)

"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"

(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)
 

Friday, June 15, 2007

Friday June 15, 2007

Filed under: General,Geometry — Tags: — m759 @ 10:31 PM
Geometry and Death

(continued from Dec. 11, 2006):

J. G. Ballard on "the architecture of death":

"… a huge system of German fortifications that included the Siegfried line, submarine pens and huge flak towers that threatened the surrounding land like lines of Teutonic knights. Almost all had survived the war and seemed to be waiting for the next one, left behind by a race of warrior scientists obsessed with geometry and death."

The Guardian, March 20, 2006

From the previous entry, which provided a lesson in geometry related, if only by synchronicity, to the death of Jewish art theorist Rudolf Arnheim:

"We are going to keep doing this until we get it right."

Here is a lesson related, again by synchronicity, to the death of a Christian art scholar of "uncommon erudition, wit, and grace"– Robert R. Wark of the Huntington Library.  Wark died on June 8, a date I think of as the feast day of St. Gerard Manley Hopkins, a Jesuit priest-poet of the nineteenth century.

From a Log24 entry on the date of Wark's death

Samuel Pepys on a musical performance (Diary, Feb. 27, 1668):

"When the Angel comes down"

"When the Angel Comes Down, and the Soul Departs," a webpage on dance in Bali:

"Dance is also a devotion to the Supreme Being."

Julie Taymor, interview:

"I went to Bali to a remote village by a volcanic mountain…."

The above three quotations were intended to supply some background for a link to an entry on Taymor, on what Taymor has called "skewed mirrors," and on a related mathematical concept named, using a term Hopkins coined, "inscapes."

They might form part of an introductory class in mathematics and art given, like the class of the previous entry, in Purgatory.

Wark, who is now, one imagines, in Paradise, needs no such class.  He nevertheless might enjoy listening in.

A guest teacher in
the purgatorial class
on mathematics
and art:

Olivier as Dr. Christian Szell

The icosahedron (a source of duads and synthemes)

"Is it safe?"

Monday, June 11, 2007

Monday June 11, 2007

Filed under: General — Tags: — m759 @ 12:00 AM
Continued from June 7

Second Billing, Part III:

Philosophy of
Communication

Obituaries: Richard Rorty, Ousmane Sembene

Pictures are more accessible
than words. See Logos
(May 17) and Torbellino
(June 10), as well as
the entries for June 8,
the date of Rorty's death.

Friday, June 8, 2007

Friday June 8, 2007

Filed under: General — Tags: — m759 @ 4:00 PM
For the Author of
the Word "Inscape"

n His Feast Day


Samuel Pepys on a musical performance (Diary, Feb. 27, 1668):

"When the Angel comes down"

"When the Angel Comes Down, and the Soul Departs," a webpage on dance in Bali:

"Dance is also a devotion to the Supreme Being."

Julie Taymor, interview:

"I went to Bali to a remote village by a volcanic mountain…."

Under the Volcano:

"No se puede vivir sin amar.

Log24 on St. Peter's Day, 2004:

"And so to bed."

Thursday, March 8, 2007

Thursday March 8, 2007

Filed under: General — Tags: — m759 @ 7:13 PM
Introduction to Logic
for International Women's Day

"The logic behind such utterances is the logic
of binary opposition, the principle of non-contra-
diction, often thought of as the very essence of
Logic as such….

Now, my understanding of what is most radical
in deconstruction is precisely that it questions
this basic logic of binary opposition….

Instead of a simple 'either/or' structure,
deconstruction attempts to elaborate a discourse
that says neither "either/or", nor "both/and"
nor even "neither/nor", while at the same time
not totally abandoning these logics either."

Harvard professor Barbara Johnson
in "Nothing Fails Like Success."
(See the previous entry, Day Without Logic.)

The 16 Binary Connectives, with Venn Diagrams

Click to enlarge.

Those who value literary theory
more than they value truth
may prefer, on this
International Women's Day,
the "mandorla" interpretation
of the above diagrams.

For this interpretation, see
Death and the Spirit III,
Burning Bright,
and
The Agony and the Ya-Ya.

Tuesday, November 7, 2006

Tuesday November 7, 2006

Filed under: General,Geometry — Tags: — m759 @ 12:00 AM
A Game of Chess

The image “http://www.log24.com/log/pix06B/061107-McQueen.jpg” cannot be displayed, because it contains errors.

"And these chessmen are men and women as they appear to themselves and to one another in this world. And the silver table is Time. And those who stand and watch are the immortal souls of these same men and women."

— C. S. Lewis,
The Great Divorce

I Ching chessboard

I Ching chessboard

Related material:

"At the still point,
there the dance is
"

and

Number and Time, by Marie-Louise von Franz
 

Sunday, September 10, 2006

Sunday September 10, 2006

Filed under: General,Geometry — Tags: — m759 @ 4:00 AM

And the
"
Meet Max Black"
Award goes to…

The image “http://www.log24.com/log/pix06A/060910-Obits.jpg” cannot be displayed, because it contains errors.

"For the Aeron and other designs,
Mr. Stumpf won this year’s
National Design Award
in Product Design
,
which is to be presented
posthumously on Oct. 18
by the Cooper-Hewitt
National Design Museum
in Manhattan."

— Today's New York Times

Stumpf died on August 30,
the date of the Log24 entry
"The Seventh Symbol."

Related material:

From
Geometry of the I Ching,
chessboard:

I Ching chessboard (original 1989 arrangement)

From the
 National Design Museum:

The image “http://www.log24.com/log/pix06A/060910-DesignAwards.gif” cannot be displayed, because it contains errors.

 From Log24 on the
date of Stumpf's death,

The Seventh Symbol:

The image “http://www.log24.com/log/pix06A/060910-Box121.jpg” cannot be displayed, because it contains errors.

Pictorial version of
Hexagram 20,
Contemplation (View)

See also
Fearful Symmetry
and
Symmetry Framed.

Tuesday, December 27, 2005

Tuesday December 27, 2005

Filed under: General — Tags: — m759 @ 12:11 PM
Dance of the Numbers
(continued)

The Pennsylvania lottery 
on St. Stephen's Day–

Midday: 105
Evening: 064

From a new
branch of theology, 
lottery hermeneutics:

See Log24, 1/05,
Death and the Spirit,

and the 64 hexagrams of
the box-style I Ching.

From the Wikipedia
article on hermeneutics:

"One prominent theme which arises in contemporary philosophical hermeneutics (i.e., the work of Hans-Georg Gadamer) is a serious calling into question of scientism. Scientism is the more or less unquestioned belief in the supremacy of the natural sciences when it comes to serving as models of knowledge. By calling scientism into question, hermeneutics is arguing for the legitimacy of (among other things) aesthetic, literary, spiritual, and philosophical knowledge, alongside (but not instead of) scientific knowledge."

Saturday, December 10, 2005

Saturday December 10, 2005

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

Roger Shattuck, Scholar, Is Dead at 82

In his honor, some excerpts from previous entries:

Wednesday, January 19, 2005

I just subscribed to The New York Review of Books online for another year,
prompted by my desire to read Roger Shattuck on Rimbaud….

"How did this poetic sensibility come to burn so bright?"

The Shattuck piece is from 1967, the year of The Doors' first album.

(See Death and the Spirit, Part II.)

The image “http://www.log24.com/log/pix05B/051210-Blue.jpg” cannot be displayed, because it contains errors.

The photo of Nicole Kidman
is from Globe Song
(Log24, Jan. 18, 2005).

The Times says Shattuck died
on Thursday (Dec. 8, 2005).

Here, from 4:00 AM on the
morning of Shattuck's death,
is a brief companion-piece
to Eight is a Gate:

Four is a Door:

From Carole A. Holdsworth,
Dulcinea and Pynchon's V:

Tanner may have stated it best:

“V. is whatever lights you to
 the end of the street:
 she is also the dark annihilation
 waiting at the end of the street.”

(Tony Tanner, page 36,
 "V. and V-2," in
 Pynchon: A Collection
 of Critical Essays.

 Ed. Edward Mendelson.
 Englewood Cliffs, N. J.:
 Prentice-Hall, 1978. 16-55).

She's a mystery
She's everything
   a woman should be
Woman in black
   got a hold on me

Foreigner 4

She's in midnight blue,
 still the words ring true;
woman in blue
got a hold on you.

Sunday, January 23, 2005

Sunday January 23, 2005

Filed under: General — Tags: — m759 @ 6:06 PM

Death and the Spirit,
Part IV

From Tuesday:

The image “http://www.log24.com/log/pix05/050123-Tiger.JPG” cannot be displayed, because it contains errors.

Seriously.

See also

Death and the Spirit, Part I,

Death and the Spirit, Part II, and

Death and the Spirit, Part III.

 

Wednesday, January 19, 2005

Wednesday January 19, 2005

Filed under: General — Tags: — m759 @ 3:00 PM

But seriously…

A follow-up to the previous "tiger" entry (which was about an old but good dirty joke).

I just subscribed to The New York Review of Books online for another year, prompted by my desire to read Roger Shattuck on Rimbaud, a tiger of another sort:

"How did this poetic sensibility come to burn so bright?"

The Shattuck piece is from 1967, the year of The Doors' first album.  (See Sunday's Death and the Spirit, Part II.)

Tuesday, January 18, 2005

Tuesday January 18, 2005

Filed under: General — Tags: — m759 @ 1:44 PM
Death and
the Spirit, Part III

In memory of comedian
Gene Baylos, who died
on Jan. 10, 2005:

From the dark jungle
as a tiger bright,
Form from the viewless Spirit
leaps to light.

— Rumi, "Reality and Appearance"

The image “http://www.log24.com/log/pix05/050118-Tiger2.gif” cannot be displayed, because it contains errors.

 

Related material:

Sunday, January 16, 2005

Sunday January 16, 2005

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

Death and the
Spirit, Part II

Readings

Are you a lucky little lady
in The City of Light
Or just another lost angel…

City of Night

— Jim Morrison, L.A. Woman

Fourmillante cité,
cité pleine de rêves,
Où le spectre en plein jour
raccroche le passant

— Baudelaire,
Les Fleurs du Mal,
and T. S. Eliot,
Notes to The Waste Land

"When you got the mojo, brother —
when you're on the inside —
the world is fantastic."

— Pablo Tabor in Robert Stone's
A Flag for Sunrise,
Knopf, 1981, p. 428

Now it was Avril's turn to understand and he was frightened out of his wits.

"The Science of Luck," he said cautiously. "You watch, do you?  That takes a lot of self-discipline."

"Of course it does, but it's worth it.  I watch everything, all the time.  I'm one of the lucky ones.  I've got the gift.  I knew it when I was a kid, but I didn't grasp it."  The murmur had intensified.  "This last time, when I was alone so long, I got it right.  I watch for every opportunity and I never do the soft thing.  That's why I succeed."

Avril was silent for a long time.  "It is the fashion," he said at last.  "You've been reading the Frenchmen, I suppose?  Or no, no, perhaps you haven't.  How absurd of me."

"Don't blether."  The voice, stripped of all its disguises, was harsh and naive.  "You always blethered.  You never said anything straight.  What do you know about the Science of Luck?  Go on, tell me.  You're the only one who's understood at all.  Have you ever heard of it before?"

"Not under that name."

"I don't suppose you have.  That's my name for it.  What's its real name?"

"The Pursuit of Death."

— Margery Allingham,
Chapter Seventeen,
"On the Staircase," from
The Tiger in the Smoke

Anagrams

In memory of Danny Sugerman,
late manager of The Doors:

The image “http://www.log24.com/log/pix05/050116-Sugerman.jpg” cannot be displayed, because it contains errors.
Danny Sugerman
Photo by
Frank Alan Bella, 2002

"Mr Mojo Risin" = "Jim Morrison."
"Audible Era" = "Baudelaire."
"Bad Rumi" = "Rimbaud."

From the dark jungle
as a tiger bright,
Form from the viewless Spirit
leaps to light.

— Rumi,  "Reality and Appearance,"
translated by R. A. Nicholson

(See also Death and the Spirit
from Twelfth Night, 2005, the date
of Danny Sugerman's death.)

Wednesday, January 5, 2005

Wednesday January 5, 2005

Filed under: General — Tags: — m759 @ 7:11 AM

Death and the Spirit

A meditation for Twelfth Night
on "the whirligig of time"

Today's New York Times obituaries feature two notable graphic artists: 
  • Frank Kelly Freas, who created, among other works, 400 portraits of saints for the Franciscans and the covers of Mad Magazine from 1958 through 1962. "I found it difficult to shift my artistic gears from the sublime to the ridiculous and back again," he said of his departure from Mad.
  • Will Eisner, "an innovative comic-book artist who created the Spirit, a hero without superpowers, and the first modern graphic novel."

Yesterday's entry provided an approach to The Dark Lady, Kali, that was, in Freas's apt word, "ridiculous."  The illustration below, "Mate," is an attempt to balance yesterday's entry with an approach that is, if not sublime, at least more serious.  It is based on a similar illustration from Jan. 31, 2003, with actress Judy Davis playing The Dark Lady.  Today it seems appropriate to replace Davis with another actress (anonymous here, though some may recognize her).  I once knew her (unlike Davis) personally.  One of my fondest memories of high school is reading Mad Magazine with her in the school lunch room.  Our lives diverged after high school, but I could happily have spent my life in her company.

Mate

– S. H. Cullinane, Twelfth Night, 2005

The image “http://log24.com/log/pix05/050105-Mate.jpg” cannot be displayed, because it contains errors.

A diamond and its dual "whirl" figure—
or a "jewel-box and its mate"

For details, see the five Log24 entries
ending on Feb. 1, 2003, and the
perceptive remarks of Ryan Benedetti
on Sam Spade and Brigid O'Shaughnessy.

As for Eisner and "The Spirit,"
which has been called
"the quintessential noir detective series,"
those preferring non-graphic stories
may picture Spade or his creator,
Dashiell Hammett, in the title role.

Then, of course, there are Eisner's later
  story, "A Contract With God,"
  John 4:24, and 1916 4/24.

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