Log24

Friday, April 4, 2014

Dream of the Expanded Field

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

(Continued)

From today’s news:

“His daughter, the poet Jorie Graham, confirmed the death.”

From an artist on Oct. 3, 2013:

“‘This is St. Francis country,’ she says of Umbria.”

Monday, October 14, 2013

Dream of the Expanded Field

Filed under: General,Geometry — m759 @ 8:28 PM

(Continued)

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman

Further context: Galois I Ching

Sunday, November 7, 2010

Dream of the Expanded Field

Filed under: General — m759 @ 12:00 PM

Continued from July 26, 2010

http://www.log24.com/log/pix10B/101107-JonHanSm.jpg

Sunday, July 1, 2018

The Perpetual Motion of T. S. Eliot

Filed under: General — m759 @ 10:28 AM

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman

Friday, June 29, 2018

For St. Stanley

Filed under: General,Geometry — m759 @ 1:26 PM

The phrase "Blue Dream" in the previous post
suggests a Web search for Traumnovelle .
That search yields an interesting weblog post
from 2014 commemorating the 1999 dies natalis 
(birth into heaven) of St. Stanley Kubrick.

Related material from March 7, 2014,
in this  journal

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

That  2014 post was titled "Kummer Varieties." It is now tagged
"Kummerhenge." For some backstory, see other posts so tagged.

Wednesday, March 29, 2017

Art Space, Continued

Filed under: General — Tags: , — m759 @ 4:35 AM

"And as the characters in the meme twitch into the abyss
that is the sky, this meme will disappear into whatever
internet abyss swallowed MySpace."

—Staff writer Kamila Czachorowski, Harvard Crimson  today

From Log24 posts tagged Art Space

From a recent paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
The Universal Kummer Threefold,” by
Qingchun Ren, Steven V Sam, Gus Schrader, and
Bernd Sturmfels —

IMAGE- 'Consider the 6-dimensional vector space over the 2-element field,' from 'The Universal Kummer Threefold'

Two such considerations —

IMAGE- 'American Hustle' and Art Cube

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

Monday, October 26, 2015

Expanding the Spielraum

Filed under: General — m759 @ 4:00 PM

(Continued)

Halloween meditation  on  the Tummelplatz  at Innsbruck

"Die Ritter und Knappen des nahegelegenen Ambras
pflegten hier ihre Rosse zu tummeln, woher sich auch
der Name Tummelplatz  schreibt."

"The knights and squires of nearby Ambras used to let their
steeds romp here, whence came the name Tummelplatz ." 

— Quelle: Ludwig von Hörmann, "Der Tummelplatz  bei Amras,"
in: Der Alpenfreund , 1. Band, Gera 1870, S. 72 – 73.

See as well Sigmund Freud, Erinnern, Wiederholen und Durcharbeiten
(1914) —

"Wir eröffnen ihm die Übertragung als den Tummel­platz ,
auf dem ihm gestattet wird, sich in fast völliger Freiheit
zu entfalten, und auferlegt ist, uns alles vorzuführen,
was sich an pathogenen Trieben im Seelenleben des
Analysierten verborgen hat."

"We admit it into the transference as a playground
in which it is allowed to expand in almost complete freedom
and in which it is expected to display to us everything in the
way of pathogenic instincts that is hidden in the patient's mind."

This passage has been discussed by later psychotherapists,
notably Russell Meares.  Dr. Meares, working from a translation
that has "playground" for Freud's Tummelplatz , uses Spielraum  
in place of Freud's own word.

For related material in this  journal, see Expanding the Spielraum.
An illustration from that search —

IMAGE- Concepts of Space

Wednesday, September 2, 2015

Expanding the Field

Filed under: General — m759 @ 7:59 PM

(Continued)

See The Nordic Journal of Aesthetics ,
Vol. 23, No. 42 (2012), pp. 14-31, 
"Art in an Expanded Field: Wittgenstein and Aesthetics,"
by Noël Carroll.

Abstract:

"This article reviews the various ways in which the later writings
of Ludwig Wittgenstein have been employed to address the question
'What is Art?' These include the family resemblance model, the
cluster concept model and the form of life model. The article defends
a version of the form of life approach. Also, addressed the charge that
it would have been more profitable had aestheticians explored what
Wittgenstein actually said about art instead of trying to extrapolate from
his writings an approach to what Nigel Warburton calls the art question."

Tuesday, February 3, 2015

Expanding the Spielraum

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

A short poem by several authors:

"The role of
the 16 singular points
on the Kummer surface
is now played by
the 64 singular points
on the Kummer threefold."

— From Remark 2.4 on page 9 of
"The Universal Kummer Threefold,"
by Qingchun Ren, Steven V Sam,
Gus Schrader, and Bernd Sturmfels,
http://arxiv.org/abs/1208.1229v3,
August 6, 2012 — June 12, 2013.

See also "Expanded Field" in this journal.

IMAGE- Concepts of Space

Illustration from "Sunday School," July 20, 2014.

Other Log24 background:  Kummer, Spielraum, Art Space.

Sunday, July 20, 2014

Sunday School

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

Paradigms of Geometry:
Continuous and Discrete

The discovery of the incommensurability of a square's
side with its diagonal contrasted a well-known discrete 
length (the side) with a new continuous  length (the diagonal).
The figures below illustrate a shift in the other direction.
The essential structure of the continuous  configuration at
left is embodied in the discrete  unit cells of the square at right.

IMAGE- Concepts of Space: The Large Desargues Configuration, the Related 4x4 Square, and the 4x4x4 Cube

See Desargues via Galois (August 6, 2013).

Sunday, July 6, 2014

Sticks and Stones

Filed under: General,Geometry — Tags: — m759 @ 6:29 AM

The title is from this morning’s previous post.

From a theater review in that post—

… “all flying edges and angles, a perpetually moving and hungry soul”

… “a formidably centered presence, the still counterpoint”

A more abstract perspective:

IMAGE- Concepts of Space

See also Desargues via Galois (August 6, 2013).

Friday, March 7, 2014

Kummer Varieties

Filed under: General,Geometry — Tags: , , — m759 @ 11:20 AM

The Dream of the Expanded Field continues

Image-- The Dream of the Expanded Field

From Klein's 1893 Lectures on Mathematics —

"The varieties introduced by Wirtinger may be called Kummer varieties…."
E. Spanier, 1956

From this journal on March 10, 2013 —

From a recent paper on Kummer varieties,
arXiv:1208.1229v3 [math.AG] 12 Jun 2013,
"The Universal Kummer Threefold," by
Qingchun Ren, Steven V Sam, Gus Schrader, and Bernd Sturmfels —

IMAGE- 'Consider the 6-dimensional vector space over the 2-element field,' from 'The Universal Kummer Threefold'

Two such considerations —

IMAGE- 'American Hustle' and Art Cube

IMAGE- Cube for study of I Ching group actions, with Jackie Chan and Nicole Kidman 

Update of 10 PM ET March 7, 2014 —

The following slides by one of the "Kummer Threefold" authors give
some background related to the above 64-point vector space and
to the Weyl group of type E7(E7):

The Cayley reference is to "Algorithm for the characteristics of the
triple ϑ-functions," Journal für die Reine und Angewandte
Mathematik  87 (1879): 165-169. <http://eudml.org/doc/148412>.
To read this in the context of Cayley's other work, see pp. 441-445
of Volume 10 of his Collected Mathematical Papers .

Friday, November 9, 2012

Ideas

Filed under: General,Geometry — m759 @ 6:21 AM

(Continued from Deconstructing Alice)

The Dream of the Expanded Field

Image-- 4x4 square and 4x4x4 cube

"Somehow it seems to fill my head
with ideas— only I don't exactly know
what they are!"

See also Deep Play.

Friday, September 9, 2011

Galois vs. Rubik

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

(Continued from Abel Prize, August 26)

IMAGE- Elementary Galois Geometry over GF(3)

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

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

The coffee scene from "Bleu"

Related material from this journal:

The Dream of
the Expanded Field

Image-- 4x4 square and 4x4x4 cube

Tuesday, November 23, 2010

Art Object

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

There is more than one way
to look at a cube.

http://www.log24.com/log/pix10B/101123-plain_cube_200x227.gif

 From Cambridge U. Press on Feb. 20, 2006 —

IMAGE- 'Cambridge Tracts in Mathematics 168: The Cube'

and from this journal on June 30, 2010 —

In memory of Wu Guanzhong, Chinese artist
who died in Beijing on June 25, 2010

Image-- The Dream of the Expanded Field

See also this journal on Feb. 20, 2006
(the day The Cube  was published).

Sunday, July 18, 2010

Du Sucre

Filed under: General,Geometry — m759 @ 4:19 AM

http://passionforcinema.com/sapphire/ on "Bleu" —  Jan. 9, 2010 —

"An extremely long lens on an insert of a sugar cube, dipped just enough, in a small cup of coffee, so that it gradually seeps in the dark beverage. Four and a half seconds of unadulterated cinematic bliss."

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

Related material from this journal:

The Dream of
the Expanded Field

Image-- 4x4 square and 4x4x4 cube

Wednesday, June 30, 2010

Field Dream

Filed under: General,Geometry — Tags: — m759 @ 10:23 AM

In memory of Wu Guanzhong, Chinese artist who died in Beijing on Friday

Image-- The Dream of the Expanded Field

“Once Knecht confessed to his teacher that he wished to learn enough to be able to incorporate the system of the I Ching into the Glass Bead Game.  Elder Brother laughed.  ‘Go ahead and try,’ he exclaimed.  ‘You’ll see how it turns out.  Anyone can create a pretty little bamboo garden in the world.  But I doubt that the gardener would succeed in incorporating the world in his bamboo grove.'”

— Hermann Hesse, The Glass Bead Game, translated by Richard and Clara Winston

“The Chinese painter Wu Tao-tzu was famous because he could paint nature in a unique realistic way that was able to deceive all who viewed the picture. At the end of his life he painted his last work and invited all his friends and admirers to its presentation. They saw a wonderful landscape with a romantic path, starting in the foreground between flowers and moving through meadows to high mountains in the background, where it disappeared in an evening fog. He explained that this picture summed up all his life’s work and at the end of his short talk he jumped into the painting and onto the path, walked to the background and disappeared forever.”

Jürgen Teichmann. Teichmann notes that “the German poet Hermann Hesse tells a variation of this anecdote, according to his own personal view, as found in his ‘Kurzgefasster Lebenslauf,’ 1925.”

Friday, June 25, 2010

ART WARS continued

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

The Dream of
the Expanded Field

Image-- 4x4 square and 4x4x4 cube

See The Klein Correspondence.

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