Log24

Sunday, November 12, 2017

Devil’s Music

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

From the groom in the previous post — Swedenborg Chapel

And from November 7 last year —

Monday, November 7, 2016

Subway Art for Times Square Church

Filed under: Uncategorized — m759 @ 9:11 PM 

Click images for related material.

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

"The Cardinal seemed a little preoccupied today."

Friday, December 6, 2019

November Seventh Death

Filed under: General — Tags: — m759 @ 5:47 PM

See as well some notes from the date of the above death:

Related material: Endgame (November 7, 1986).

Friday, November 8, 2019

Glitch

Filed under: General — Tags: — m759 @ 7:12 AM

The terms glitch  and cross-carrier  in the previous post
suggest a review

 

Gerard Manley Hopkins in 1888

Cross-Carrier

For some backstory, see GlitchGerard Manley HopkinsInscape
particularly the post A Balliol Star.

Thursday, November 7, 2019

Forgotten Ghosts

Filed under: General — Tags: — m759 @ 9:46 PM

See that tag.

Cross-carrier glitch sent people ancient texts

For Connoisseurs of Insane Fantasy

Filed under: General — Tags: — m759 @ 11:23 AM

From a 1962 young-adult novel —

"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."

Song adapted from a 1960 musical

"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"

Google News 'For you' comic book news item

Jagged Crest

Filed under: General — Tags: — m759 @ 9:01 AM

"The man touched the white bishop, queen and king,
and ran his finger over the jagged crest of the rook.
Then, sitting down before the chess set owner could nod
his head, he made his first move with the white pawn."

The late Stephen Dixon, "The Chess House," in
The Paris Review Winter-Spring 1963 (early in 1963).

I Ching chessboard (original 1989 arrangement)

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, May 1, 2019

The Medium and the Message

Filed under: General — Tags: — m759 @ 6:45 PM

In memory of Quentin Fiore — from a Log24 search for McLuhan,
an item related to today's previous post . . .

Related material from Log24 on the above-reported date of death —

See also, from a search for Analogy in this journal . . .

 .

Monday, June 26, 2017

Four Dots

Analogies — "A : B  ::  C : D"  may be read  "A is to B  as  C is to D."

Gian-Carlo Rota on Heidegger…

"… The universal as  is given various names in Heidegger's writings….

The discovery of the universal as  is Heidegger's contribution to philosophy….

The universal 'as' is the surgence of sense in Man, the shepherd of Being.

The disclosure of the primordial as  is the end of a search that began with Plato….
This search comes to its conclusion with Heidegger."

— "Three Senses of 'A is B' in Heideggger," Ch. 17 in Indiscrete Thoughts
 

See also Four Dots in this journal. 

Some context:  McLuhan + Analogy.

Friday, August 19, 2016

Princeton University Press in 1947

Filed under: General — Tags: , , — m759 @ 11:17 AM

From a review, in the context of Hollywood, of a Princeton
University Press book on William Blake from 1947 —

Wednesday, August 10, 2016

Analogies Test

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

Obituary for Wilford Stanton Miller, author in 1926
of the Miller Analogies Test  —  
         

Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—

"The American mind is not even close to being amenable
to the ideogram principle as yet.  The reason is simply this.
America is 100% 18th Century. The 18th century had
chucked out the principle of metaphor and analogy—
the basic fact that as A is to B so is C to D.  AB:CD.   
It can see AB relations.  But relations in four terms are still
verboten.  This amounts to deep occultation of nearly all
human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  
Until stated and publicly recognized for what it is, poetry and
the arts can’t exist in America."

A line for W. S. Miller, taken from "Annie Hall" —

"You know nothing of my work."

Thursday, June 2, 2016

Bullshit Studies

Filed under: General,Geometry — Tags: , — m759 @ 11:30 AM

(Continued)

"The allusion to 'the most precious square of sense' shows
Shakespeare doing an almost scholastic demonstration of
the need for a ratio and interplay among the senses as
the very constitution of rationality."

— Marshall McLuhan, The Gutenberg Galaxy ,
University of Toronto Press, 1962, page 13

"What Shakespeare refers to in Lear  as the 'precious
square of sense' probably has reference to the traditional
'square of opposition' in logic and to that four-part analogy
of proportionality which is the interplay of sense and reason."     

— McLuhan, ibid. , page 241

This is of course nonsense, and, in view of McLuhan's pose
as a defender of the Catholic faith, damned  nonsense.

Epigraph by McLuhan —

"The Gutenberg Galaxy  develops a mosaic or field
approach to its problems."

I prefer a different "mosaic or field" related to the movable
blocks  of Fröbel, not the movable type  of Gutenberg.

Sunday, May 29, 2016

The Ideogram Principle …

Filed under: General,Geometry — Tags: , — m759 @ 4:23 PM

According to McLuhan

Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—

"The American mind is not even close to being amenable
to the ideogram principle as yet.  The reason is simply this.
America is 100% 18th Century. The 18th century had
chucked out the principle of metaphor and analogy—
the basic fact that as A is to B so is C to D.  AB:CD.   
It can see AB relations.  But relations in four terms are still
verboten.  This amounts to deep occultation of nearly all
human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  
Until stated and publicly recognized for what it is, poetry and
the arts can’t exist in America."

For context, see Cameron McEwen,
"Marshall McLuhan, John Pick, and Gerard Manley Hopkins."
(Renascence , Fall 2011, Vol. 64 Issue 1, 55-76)

A relation in four terms

A : B  ::  C : D   as   Model : Crutch  ::  Metaphor : Ornament —

See also Dueling Formulas and Symmetry.

Wednesday, January 27, 2016

Game Theory for Steiner

Filed under: General,Geometry — m759 @ 7:00 PM

"The definition of easy to learn, hard to master"

Alex Hern in The Guardian  today on the game of Go

Not unlike music, mathematics, and chess.

A Singer 7-Cycle

Wednesday, July 22, 2015

Ein Kampf

Filed under: General — m759 @ 9:29 PM

"Die Philosophie ist ein Kampf gegen die Verhexung
unsres Verstandes durch die Mittel unserer Sprache."

— Philosophical Investigations  (1953),  Section 109

Actor portraying Bobby Fischer

Related material —

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

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

Thursday, June 26, 2014

The McLuhan Dimension

Filed under: General,Geometry — Tags: , — m759 @ 2:56 AM

"History is a deep and complicated puzzle—
especially when it involves more dimensions than time."

Introduction to a novella in Analog Science Fiction

IMAGE- Marshall McLuhan

IMAGE- Annenberg Hall at Harvard

IMAGE- Search for 'quilt geometry' yields a result from Annenberg Media.

"Annenberg Hall" at Harvard was originally part of a memorial for
Civil War dead. Formerly "Alumni Hall," it was renamed in 1996.

Wednesday, May 21, 2014

Through the Vanishing Point*

Filed under: General,Geometry — Tags: , , — m759 @ 9:48 AM

Marshall McLuhan in "Annie Hall" —

"You know nothing of my work."

Related material — 

"I need a photo opportunity
I want a shot at redemption
Don't want to end up a cartoon
In a cartoon graveyard"

— Paul Simon

It was a dark and stormy night…

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

— Page 180, Logicomix

A photo opportunity for Whitehead
(from Romancing the Cube, April 20, 2011)—

IMAGE- Whitehead on Fano's construction of the 15-point projective Galois space over GF(2)

See also Absolute Ambition (Nov. 19, 2010).

* For the title, see Vanishing Point in this journal.

Tuesday, November 12, 2013

Soundtrack

Filed under: General,Geometry — Tags: , — m759 @ 6:45 AM

IMAGE- 'Devil Music' from 'Kaleidoscopes- Selected Writings of H.S.M. Coxeter'

"DEVIL – MUSIC

20 pages of incidental music written at school
for G. K. Chesterton's play MAGIC

by D. Coxeter."

See also

Related material —  Chesterton + Magic in this journal.

Monday, May 21, 2012

Brightness at Noon

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

Occultation according to McLuhan

Marshall McLuhan writing to Ezra Pound  on Dec. 21, 1948—

"The American mind is not even close to being amenable to the ideogram principle as yet.  The reason is simply this. America is 100% 18th Century. The 18th century had chucked out the principle of metaphor and analogy— the basic fact that as A is to B so is C to D.  AB:CD.   It can see AB relations.  But relations in four terms are still verboten.  This amounts to deep occultation of nearly all human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  Until stated and publicly recognized for what it is, poetry and the arts can’t exist in America."

For context, see Cameron McEwen, "Marshall McLuhan, John Pick, and Gerard Manley Hopkins." (Renascence , Fall 2011, Vol. 64 Issue 1, 55-76)

Friday, September 16, 2011

Art, Jung, Toronto

Filed under: General,Geometry — Tags: — m759 @ 9:29 AM

http://www.log24.com/log/pix11B/110916-ArtJungToronto-NYT.jpg

Related art—

Midnight's Icons,

http://www.log24.com/log/pix11B/110915-Jung-FourDiamonds.gif

Faust in Toronto,

http://www.log24.com/log/pix11B/110916-NYT-Faust.jpg

and…

McLuhan 'tetrad' figure with four diamonds surrounding a fifth, the medium

McLuhan and the Four Diamonds

(Wikipedia figure)

"Visually, a tetrad can be depicted as
 four diamonds forming an X…."

" X never, ever, marks the spot."

Sunday, August 14, 2011

Sunday Review

Filed under: General,Geometry — Tags: — m759 @ 3:33 PM

The Sunday New York Times  today—

http://www.log24.com/log/pix11B/110814-GablerNYT500w.jpg

This suggests…

The Elusive Small Idea—

Part I:

McLuhan and the Seven Snow Whites

http://www.log24.com/log/pix11B/110814-GablerNYT500w7white.jpg

Part II (from "Marshall, Meet Bagger," July 29):

"Time for you to see the field."

http://www.log24.com/log/pix11B/110814-TheFieldGF8.jpg

For further details, see the 1985 note
"Generating the Octad Generator."

McLuhan was a Toronto Catholic philosopher.
For related views of a Montreal Catholic philosopher,
see the Saturday evening post.

Friday, July 29, 2011

Marshall, Meet Bagger

Filed under: General — Tags: — m759 @ 8:28 AM

Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—

"The American mind is not even close to being amenable to the ideogram principle as yet.  The reason is simply this.  America is 100% 18th Century.  The 18th century had chucked out the principle of metaphor and analogy— the basic fact that as A is to B so is C to D.  AB:CD.  It can see AB relations.  But relations in four terms are still verboten.  This amounts to deep occultation of nearly all human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  Until stated and publicly recognized for what it is, poetry and the arts can’t exist in America."

"Time for you to see the field." —Bagger Vance

The field — See June 2010.

Friday, November 19, 2010

Absolute Ambition

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

"It's my absolute ambition that you are touched to the core of your being with the content…."

— Julie Taymor on Spider-Man: Turn Off the Dark  (Playbill video, undated)

Another ambitious comic-book promotion —

"What Logicomix  does that few works in any medium do is to make intellectual passion palpable. That is its greatest strength. And it’s here that its form becomes its substance."

— Judith Roitman, review (pdf, 3.7 MB) of Logicomix: An Epic Search for Truth , in …

http://www.log24.com/log/pix10B/101119-AMSnoticesSm.jpg

 The December 2010 AMS Notices  cover has excerpts from Logicomix.

Related material:

"In the classical grammarians’ sense of the power of form over 'content' and style over 'substance,' he originated the phrase, 'the medium is the message.'"

— Joseph P. Duggan on Marshall McLuhan at The University Bookman

See also, in this  journal, The Medium is the Message, Wechsler, and Blockheads .

Saturday, April 24, 2010

Go Ask Alice

Filed under: General — Tags: — m759 @ 1:13 PM

McLuhan in Space  by Richard Cavell—

As the word "through" in the title of Through the Vanishing Point hints… key reference points for McLuhan and Parker in writing Through the Vanishing Point  were the "Alice" books.

[The footnote symbol here is mine.]

Alice Rae, McLuhan's Unconscious, doctoral dissertation, School of History and Politics, University of Adelaide, May 2008

What McLuhan calls the "unconscious"' is more often named by him as Logos, "acoustic space" or the "media environment," and I trace the debts that these concepts owe not only to Freud and Jung, but to Aristotle, St. Thomas Aquinas, gestalt theory, art theory, Henri Bergson, Pierre Teilhard de Chardin, Wyndham Lewis, Siegfried Giedion, Harold Innis, the French symbolist poets of the late nineteenth century and the British modernists of the early twentieth.

The declaration section of the thesis is dated November 19, 2008.

Related material— Halloween 2005 and The Gospel According to Father Hardon.

A work suggested by Ander Monson's new Vanishing Point . (See April 17 and April 23, together with the April 22 picture of a non-Euclidean  point in the context of "The Seventh Symbol.")

Tuesday, March 16, 2010

Gameplayers of the Academy

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

New Game

In memory of a Jesuit who died on February 22 (see yesterday's "For the Ides of March")–

“The Game in the Ship cannot be approached as a job, a vocation, a career, or a recreation. To the contrary, it is Life and Death itself at work there. In the Inner Game, we call the Game Dhum Welur, the Mind of God."

— M. A. Foster, The Gameplayers of Zan

"… for Othello, no less than his creator Shakespeare, death without speechmaking is almost unthinkable."

"Walter Ong," by Jeet Heer (Book & Culture, July/August 2004)

"This Jack, joke, poor potsherd, patch, matchwood…."

— Jesuit quote at David Lavery's weblog today

See also this journal on February 22, the date of the Jesuit death. A post on that date mentions Ong and his teacher McLuhan, and displays a McLuhan figure related to the "joke" quote above–

McLuhan 'tetrad' figure with four diamonds surrounding a fifth, the medium

Click figure for background.

Ong discussed "agonistic" culture.
See "Sunday's Theater" and a film
based on the novel discussed there–

Menin... First line, in Greek, of the Iliad

Classics 101

IMAGE- Anthony Hopkins in 'The Human Stain'

Prof. Coleman Silk introduces
freshmen to academic values

For academic gameplayers who prefer
less emotionally challenging subjects,
there is Othello Online —

http://www.log24.com/log/pix10/100316-NewGame.jpg

"New Game. You May Pass for White to Start."

Monday, February 22, 2010

Annals of Philosophy

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

The Medium is the Message

http://www.log24.com/log/pix10/100222-McLuhan.jpg
Marshall McLuhan

From the Wikipedia article
on Marshall McLuhan–

McLuhan 'tetrad' figure with four diamonds surrounding a fifth, the medium

From yesterday

(Click images for some background.)

Ian McKellen at 'Neverwas' diamond windows

Related material:

Feast of St. Louis, 2003,

a web page on McLuhan's
student Walter J. Ong, S. J.,

and Jung and the Imago Dei

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 — Tags: — m759 @ 11:07 AM
Autistic Enchantment

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

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

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

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

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

See also:

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

Thursday, 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.
 

Wednesday, April 8, 2009

Wednesday April 8, 2009

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

Good’s Singularity

Irving John “I.J.” Good died Sunday, April 5, 2009.

The date of his death was also Palm Sunday and the day of the Academy of Country Music Awards.

Information from Wikipedia:

Good, 92, was a cryptanalyst at Bletchley Park during World War II.

“He was born as Isidore Jacob Gudak to a Jewish family in London. In his publications he was called I. J. Good. He studied mathematics at Jesus College, Cambridge, graduating in 1938. He did research work under G.H. Hardy and Besicovitch before moving to Bletchley Park in 1941 on completing his doctorate.

At Bletchley Park, he was initially in Hut 8 under the supervision of Alan Turing…”

[Related material: the death of Turing (a major fan of the Evil Queen in Snow White) and yesterday’s entry]

Wikipedia states that “I. J. Good’s vanity car license plate, hinting at his spylike wartime work, was ‘007 IJG’…. He played chess to county standard, and helped to popularise Go, an Asian boardgame, through a 1965 article in New Scientist (he had learned the rules from Turing). In 1965, he described a concept similar to today’s meaning of technological singularity, in that it included in it the advent of superhuman intelligence:

Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an ‘intelligence explosion,’ and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make….
— Good, I. J. (1965). ‘Speculations Concerning the First Ultraintelligent Machine‘, Advances in Computers, Vol. 6.”
“Some say the symbol
of Apple Computers,
the apple with a bite out of it,
is a nod to Alan Turing.”– from “Alan Turing and
the Apple
at Flickr, uploaded
on Epiphany 2006 by guano

Alan Turing and the Apple

http://www.log24.com/log/pix09/090408-TuringApples.jpg

Above: Composite by “guano” at Flickr

Will: Do you like apples?
Clark: Yeah.
Will: Well, I got her number.
How do you like them apples?

— “Good Will Hunting

Happy Spy Wednesday.

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

 

Saturday, March 21, 2009

Saturday March 21, 2009

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

Counters in Rows

"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)."

— George Steiner
   (See March 10, "Language Game.")
 



For example:

Model of the 21-point projective plane consisting of the 1- and 2- subsets of a 6-set

Click to enlarge.

Context:

Notes on Finite Geometry
(Section on 6-set structures)
 

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.)

Wednesday, February 4, 2009

Wednesday February 4, 2009

Filed under: General — Tags: — m759 @ 1:23 PM
Overkill
 
In memory of
James Joyce and of
Patrick McGoohan.
who both died on
a January 13th —
Scene from 'The Seventh Seal' on McLuhan book cover
Baby Blues cartoon on global positioning systems

 

Related material:

The phrase
"Habitat Global Village"
in the previous entry.

Marshall McLuhan was
apparently the originator
of the phrase
"global village."

The phrase, coined by McLuhan,
 a Catholic, should be associated
more with Rome than
with Americus, Georgia.

"The association is the idea."
— Ian Lee, The Third Word War

Number Six meets Global Village
 

Wednesday, January 28, 2009

Wednesday January 28, 2009

Filed under: General — Tags: , — m759 @ 7:59 AM
ACTUAL BEING
continued from
October 25, 2008

John Updike at Boston Public Library, 2006, photo by Robert Spencer for The New York Times
 

"The only wealth he bestowed on his subjects lay in the richness of his descriptive language, the detailed fineness of which won him comparisons with painters like Vermeer and Andrew Wyeth."

Christopher Lehmann-Haupt in today's International Herald Tribune  

 

"These people have discovered how to turn dreams into reality. They know how to enter their dream realities. They can stay there, live there, perhaps forever."

— Alfred Bester on the inmates of Ward T in his 1953 short story, "Disappearing Act"

Related material:
"Is Nothing Sacred?"
 

 

When?

Going to dark bed there was a square round Sinbad the Sailor roc's auk's egg in the night of the bed of all the auks of the rocs of Darkinbad the Brightdayler.

Where?

Black disc from end of Ch. 17 in Ulysses

Ulysses, conclusion of Episode 17

 

Cover of 'Through the Vanishing Point,' by Marshall McLuhan and Harley Parker

Happy Feast of
St. Thomas Aquinas.

Saturday, January 19, 2008

Saturday January 19, 2008

Filed under: General — Tags: — 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.

Monday, December 24, 2007

Monday December 24, 2007

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

From Saturday's entry
(Log24, Dec. 22, 2007)
a link goes to–
The five entries of June 14, 2007.

From there, the link
"One Two Three Four,
Who Are We For?"
goes to–
Princeton: A Whirligig Tour
(Log24, June 5, 2007).

From there, the link
"Taking Christ to Studio 60"
goes to–
The five Log 24 entries
prior to midnight Sept. 18, 2006.

From there, the link
"Log24, January 18, 2004"
goes to–
A Living Church.

From there, the link
"click here"
goes to–
In the Bleak Midwinter
(Internet Movie Database)…

Tagline:

The drama. The passion. The intrigue… And the rehearsals haven't even started.

Plot Summary:

Out of work actor Joe volunteers to help try and save his sister's local church
for the community by putting on a Christmas production of Hamlet…

"… were it not that
  I have bad dreams."
— Hamlet

Related material:

The New York Times online
obituaries of December 22,

 Ike Turner's
 "Bad Dreams" album
(see Log24, July 12, 2004),

"Devil Music," a composition
by H. S. M. Coxeter,

and

King of Infinite Space.

Those desiring more literary depth
may consult the G. K. Chesterton
play "Magic" for which Coxeter
wrote his "Devil Music" and
the Ingmar Bergman film
"The Magician" said to have
been inspired by Chesterton.

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)
 

Sunday, December 31, 2006

Sunday December 31, 2006

Filed under: General — Tags: — m759 @ 8:00 PM
Tools of
Christ Church
(Continued from
St. Thomas Becket’s day)

The author of the thesis
“Conversations with the Dead”

described in this morning’s entry,

Aesthetics of Evil
vs. Christ Church
,

is Darren Joseph Danylyshen.

 
This may be the same
Darren Danylyshen who has
taught at St. Stephen’s SS
(a Catholic secondary school
in Bowmanville, Ontario).
 
Following a link in the
section of that school’s site
beneath the title
“St. Stephen’s Goes Hollywood,”
we find the following:
 
The image “http://www.log24.com/log/pix06B/061231-McLuhan.jpg” cannot be displayed, because it contains errors.
 
This ties in rather neatly with the
“Tools of Christ Church” entry
for last Friday–
St. Thomas Becket’s day–
and with the fact that
today would be the feast day
of Marshall McLuhan,
if McLuhan were a saint.
(McLuhan, a Catholic, died on
Dec. 31, 1980.)
 
Related material:
 
The Communion of Saints as
the Association of Ideas
 

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
 

Tuesday, October 10, 2006

Tuesday October 10, 2006

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

 

The image “http://www.log24.com/log/pix04A/041010-Welles.gif” cannot be displayed, because it contains errors.

Orson Welles

Welles died on
this date in 1985,
the same day as
Yul Brynner.

The image “http://www.log24.com/log/pix05B/051010-Yul2.jpg” cannot be displayed, because it contains errors.

“The crème de la crème
of the chess world in a
show with everything
 but Yul Brynner”

One Night in Bangkok

New York Lottery,
mid-day on Yom Kippur,
October 2, 2006:

256.

Pennsylvania Lottery,
mid-day on the same day:

723.

For more on 256,
see Symmetries
and 7/23.

It is a very difficult
philosophical question,
 the question of

  what ‘random’ is.”

Herbert Robbins, co-author
   of What is Mathematics?

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.

Sunday, November 20, 2005

Sunday November 20, 2005

Filed under: General,Geometry — Tags: — m759 @ 4:04 PM

An Exercise
of Power

Johnny Cash:
“And behold,
a white horse.”

The image “http://www.log24.com/log/pix05B/051120-SpringerLogo9.gif” cannot be displayed, because it contains errors.
Adapted from
illustration below:

The image “http://www.log24.com/log/pix05B/051120-NonEuclideanRev.jpg” cannot be displayed, because it contains errors.

“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?'”

H. S. M. Coxeter, 1987, introduction to Richard J. Trudeau’s remarks on the “Story Theory” of truth as opposed to  the “Diamond Theory” of truth in The Non-Euclidean Revolution

“A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the ‘Story Theory’ of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called ‘true.’ The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes*….”

Richard J. Trudeau in
The Non-Euclidean Revolution

“‘Deniers’ of truth… insist that each of us is trapped in his own point of view; we make up stories about the world and, in an exercise of power, try to impose them on others.”

— Jim Holt in The New Yorker.

(Click on the box below.)

The image “http://www.log24.com/log/pix05B/050819-Critic4.jpg” cannot be displayed, because it contains errors.

Exercise of Power:

Show that a white horse–

A Singer 7-Cycle

a figure not unlike the
symbol of the mathematics
publisher Springer–
is traced, within a naturally
arranged rectangular array of
polynomials, by the powers of x
modulo a polynomial
irreducible over a Galois field.

This horse, or chess knight–
“Springer,” in German–
plays a role in “Diamond Theory”
(a phrase used in finite geometry
in 1976, some years before its use
by Trudeau in the above book).

Related material

On this date:

 In 1490, The White Knight
 (Tirant lo Blanc The image “http://www.log24.com/images/asterisk8.gif” cannot be displayed, because it contains errors. )–
a major influence on Cervantes–
was published, and in 1910

The image “http://www.log24.com/log/pix05B/051120-Caballo1.jpg” cannot be displayed, because it contains errors.

the Mexican Revolution began.

Illustration:
Zapata by Diego Rivera,
Museum of Modern Art,
New York

The image “http://www.log24.com/images/asterisk8.gif” cannot be displayed, because it contains errors. Description from Amazon.com

“First published in the Catalan language in Valencia in 1490…. Reviewing the first modern Spanish translation in 1969 (Franco had ruthlessly suppressed the Catalan language and literature), Mario Vargas Llosa hailed the epic’s author as ‘the first of that lineage of God-supplanters– Fielding, Balzac, Dickens, Flaubert, Tolstoy, Joyce, Faulkner– who try to create in their novels an all-encompassing reality.'”

Thursday, June 26, 2003

Thursday June 26, 2003

Filed under: General — Tags: , — m759 @ 5:00 AM

ART WARS:
Art at the Vanishing Point

From the web page Art Wars:

"For more on the 'vanishing point,'
or 'point at infinity,' see
Midsummer Eve's Dream."

On Midsummer Eve, June 23, 2003, minimalist artist Fred Sandback killed himself.

Sandback is discussed in The Dia Generation, an April 6, 2003, New York Times Magazine article that is itself discussed at the Art Wars page.

Sandback, who majored in philosophy at Yale, once said that

"Fact and illusion are equivalents."

Two other references that may be relevant:

The Medium is
the Rear View Mirror
,

which deals with McLuhan's book Through the Vanishing Point, and a work I cited on Midsummer Eve  …

Chapter 5 of Through the Looking Glass:

" 'What is it you want to buy?' the Sheep said at last, looking up for a moment from her knitting.

'I don't quite know yet,' Alice said very gently.  'I should like to look all round me first, if I might.'

'You may look in front of you, and on both sides, if you like,' said the Sheep; 'but you ca'n't look all round you — unless you've got eyes at the back of your head.'

But these, as it happened, Alice had not got: so she contented herself with turning round, looking at the shelves as she came to them.

The shop seemed to be full of all manner of curious things — but the oddest part of it all was that, whenever she looked hard at any shelf, to make out exactly what it had on it, that particular shelf was always quite, empty, though the others round it were crowded as full as they could hold.

'Things flow about so here!' she said at last in a plaintive tone…."

 "When Alice went
     through the vanishing point
"
 

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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