Log24

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.

Saturday, April 28, 2012

Play and Interplay

Filed under: General — m759 @ 7:59 PM

The last paragraph of the previous post
(as updated at about 7:20 PM today)
suggests a search for the phrase
"play and interplay" that yields…

"He had accepted the world as the world,
but now he was comprehending the
organization of it, the play and interplay
of force and matter."

Martin Eden  by Jack London

This in turn suggests a review of the film "Queen to Play" —

(Background: Nabokov + Patterns.)

The review announces showings of the film at Clark University
in Worcester, Mass., on Sunday, October 30, 2011.

See also this journal on that date— "The Idea Idea"— and
references to a knight figure from today's  date in 1985.

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, February 17, 2011

Figure in the Carpet

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

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

– Steppenwolf lyrics

"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

http://www.log24.com/log/pix11/110217-IndexTo202.jpg

See also Nabokov at Harvard in today's Crimson
and the Russian boxes of Henry James.

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, December 3, 2009

Out of What Chaos

Filed under: General — m759 @ 2:28 PM

Mathematics and Narrative, continued…

Out of What Chaos, a novel by Lee Oser

"This book is more or less what one would expect if Walker Percy wrote about a cynical rock musician who converts to Catholicism, and then Nabokov added some of his verbal pyrotechnics, and then Buster Keaton and the Marquis de Sade and Lionel Trilling inserted a few extra passages. It is a loving and yet appalled description of the underground music scene in the Pacific Northwest. And it is a convincing representation of someone very, very smart."

Matt Greenfield in The Valve

"If Evelyn Waugh had lived amid the American Northwest rock music scene, he might have written a book like this."

–Anonymous Amazon.com reviewer

A possible source for Oser's title–

"…Lytton Strachey described Pope's theme as 'civilization illumined by animosity; such was the passionate and complicated material from which he wove his patterns of balanced precision and polished clarity.' But out of what chaos did that clarity and precision come!"

Authors at Work, by  Herman W. Liebert and Robert H. Taylor, New York, Grolier Club, 1957, p. 16

Related material:

Unthought Known

Pearl Jam 'Backspacer' album released Sept. 20, 2009

and the

Catholic Analyst's Couch, White Cube Gallery, 2002

White Cube Gallery, 2002

Saturday, April 4, 2009

Saturday April 4, 2009

Filed under: General — m759 @ 9:48 PM
Angels & Demons

Los Angeles Times, April 1:
obituary for the green demon of
  Joss Whedon‘s TV series “Angel“–

LA Times obituary from April 1, 2009, for Andy Hallett, who played a green demon in the Joss Whedon TV series 'Angel'

“As you read,
watch for patterns.”

— “Pattern in The Defense,”
apparently by Jeff Edmunds

Related material:

Today’s previous entries
and
Force Field of Dreams
(which contains the
above quotation)
in this journal on
Sept. 22, 2002

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

Powered by WordPress