Log24

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"

Saturday, December 8, 2012

Defining the Contest…

Filed under: General,Geometry — Tags: , , , , — m759 @ 5:48 AM

Chomsky vs. Santa

From a New Yorker  weblog yesterday—

"Happy Birthday, Noam Chomsky." by Gary Marcus—

"… two titans facing off, with Chomsky, as ever,
defining the contest"

"Chomsky sees himself, correctly, as continuing
a conversation that goes back to Plato, especially
the Meno dialogue, in which a slave boy is
revealed by Socrates to know truths about
geometry that he hadn’t realized he knew."

See Meno Diamond in this journal. For instance, from 
the Feast of Saint Nicholas (Dec. 6th) this year—

The Meno Embedding

http://www.log24.com/log/pix10B/101128-TheEmbedding.gif

For related truths about geometry, see the diamond theorem.

For a related contest of language theory vs. geometry,
see pattern theory (Sept. 11, 16, and 17, 2012).

See esp. the Sept. 11 post,  on a Royal Society paper from July 2012
claiming that

"With the results presented here, we have taken the first steps
in decoding the uniquely human  fascination with visual patterns,
what Gombrich* termed our ‘sense of order.’ "

The sorts of patterns discussed in the 2012 paper —

IMAGE- Diamond Theory patterns found in a 2012 Royal Society paper

"First steps"?  The mathematics underlying such patterns
was presented 35 years earlier, in Diamond Theory.

* See Gombrich-Douat in this journal.

Tuesday, September 11, 2012

Symmetry and Hierarchy

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

A followup to Intelligence Test (April 2, 2012).

Philosophical Transactions of the Royal Society
B  (2012) 367, 2007–2022
(theme issue of July 19, 2012

 
Gesche Westphal-Fitch [1], Ludwig Huber [2],
Juan Carlos Gómez [3], and W. Tecumseh Fitch [1]
 
[1]  Department of Cognitive Biology, University of Vienna,
      Althanstrasse 14, 1090 Vienna, Austria
 
[2]  Messerli Research Institute, University of Veterinary Medicine Vienna,
      Medical University of Vienna and University of Vienna,
      Veterinärplatz 1, 1210 Vienna, Austria
 
[3]  School of Psychology, St Mary’s College, University of St Andrews,
      South Street, St Andrews, KY16 9JP, UK
 
Excerpt (added in an update on Dec. 8, 2012) —
 
 
Conclusion —
 
"…  We believe that applying the theoretical
framework of formal language theory to two-dimensional
patterns offers a rich new perspective on the
human capacity for producing regular, hierarchically
organized structures. Such visual patterns may actually
prove more flexible than music or language for probing
the full extent of human pattern processing abilities.
      With the results presented here, we have taken the
first steps in decoding the uniquely human fascination
with visual patterns, what Gombrich termed our
‘sense of order’.
      Although the patterns we studied are most similar
to tilings or mosaics, they are examples of a much
broader type of abstract plane pattern, a type found
in virtually all of the world’s cultures [4]. Given that
such abstract visual patterns seem to represent
human universals, they have received astonishingly
little attention from psychologists. This neglect is particularly
unfortunate given their democratic nature,
their popular appeal and the ease with which they
can be generated and analysed in the laboratory.
With the current research, we hope to spark renewed
scientific interest in these ‘unregarded arts’, which
we believe have much to teach us about the nature of
the human mind."
 
[4]  Washburn, D. K. & Crowe, D. W.,1988
      Symmetries of Culture
      Theory and Practice of Plane Pattern Analysis
.
      Seattle, WA: University of Washington Press.
 
Commentary —
 
For hierarchy , see my assessment of Gombrich.
For culture , see T. S. Eliot and Russell Kirk on Eliot.

Monday, April 2, 2012

Intelligence Test

Filed under: General,Geometry — Tags: , — m759 @ 6:00 PM

This journal on June 18, 2008

http://www.log24.com/log/pix11B/110724-Hustvedt-WechslerCubes.jpg

The Wechsler Cubes story continues with a paper from December 2009…

"Learning effects were assessed for the block design (BD) task,
on the basis of variation in 2 stimulus parameters:
perceptual cohesiveness (PC) and set size uncertainty (U)." —

(Click image for some background.)

The real intelligence test is, of course, the one Wechsler flunked—
investigating the properties of designs made with sixteen
of his cubes instead of nine.

Thursday, January 6, 2011

Epiphany for Hal

Filed under: General — m759 @ 12:00 PM

IMAGE- 'A Beautiful Mind' on games (from index)

IMAGE- 'War Games' computer- 'How about a nice game of chess?'

See also Nabokov + chess + patterns.

Monday, October 11, 2010

Venue

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

… Don't you know that when you play
at this level there's no ordinary venue?

— Lyrics from Chess

Why don't you come with me little girl
On a magic carpet ride?

— Steppenwolf lyrics in Star Trek: First Contact

I like to fold my magic carpet, after use,
in such a way as to superimpose
one part of the pattern upon another.

Vladimir Nabokov in Speak, Memory

See also recent Log24 posts.

Saturday, September 11, 2010

At Play in the Field

Filed under: General — m759 @ 3:24 AM

For Bent Larsen, Danish chess Grandmaster, who died on Thursday, September 9, 2010—

http://www.log24.com/log/pix10B/100910-AtPlayInTheField-Lg.png

See also "Patrick Blackburn, meet Gideon Summerfield" in Building a Mystery.

"As you read, watch for patterns." — Nabokov

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.
 

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)
 

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, October 8, 2002

Tuesday October 8, 2002

Filed under: General,Geometry — m759 @ 4:08 AM
Starflight Theme

On Graham Greene’s novel
The Human Factor:

“Greene, always the master of economy, never wrote a tighter or more beautifully focused novel.”
 —
Steve Robertson

“The main character is Maurice Castle, the head of the Africa station for a branch of British intelligence….  [the] writing is sparse and neat rather than languid or flowery….”
Kevin Holtsberry 

From Chapter I: 

“Castle could see that telling the truth this time had been an error of judgement, yet, except on really important occasions, he always preferred the truth.  The truth can be double-checked.”

On fiction and truth: 

Here is a short story that is
tight, focused, sparse, and neat.

The story is also true.

Mate in 2 
V. Nabokov, 1919

This problem embodies the “starflight” theme;
for details, see Tim Krabbé’s
 Open Chess Diary, entry 9.

As the example of Nabokov shows, a taste for truth (as in chess or geometry) may accompany a taste for fiction.  This applies also to Krabbé, as shown by the following reviews of his novel The Cave:

New York Times
“Krabbe’s carefully constructed narrative has a geometry so precise that the patterns buried under the surface emerge only in the final pages.”

Library Journal
“A diamond of a book- perfectly proportioned, multifaceted, and containing not one wasted word”

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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