Log24

Monday, December 30, 2019

Number and Time

Filed under: General — Tags: , — m759 @ 9:37 AM

(Hat tip for the title to Marie-Louise von Franz.)

Remarks by Metod Saniga from the previous post

Remarks by Wolfgang Pauli, a friend of von Franz

"This is to show the world that I can paint like Titian.
[Empty frame with jagged sides]. Only technical details
are missing."
— As quoted at Derevianko Group.

Related material (see Oct. 11, 2010) —

http://www.log24.com/log/pix10B/101011-137JungPauli-sm.jpg

Saturday, February 14, 2015

Number and Time

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

"Continue a search for thirty-three and three."
— Katherine Neville in The Eight

"Close enough for government work."
— Stephen King in Doctor Sleep

Saturday, September 4, 2021

Number, Time, and Dan Brown*

Filed under: General — Tags: — m759 @ 2:12 PM

The title is a nod to the book Number and Time  ( not  by Dan Brown ).

An illustration —

This journal 10 years ago today

"Dan Brown certainly packed a lot into
the 500-plus pages of The Lost Symbol ."

— DailyGrail.com

That sentence suggests a review of Efficient Packing

Friday, July 2, 2021

Number, Time, and The New Mutants

Filed under: General — Tags: — m759 @ 10:33 PM

From Number and Time ,
by Marie-Louise von Franz,
Northwestern U. Press paperback,
December 31, 1974 —

Star Wars Chess:

Originally chess seems to have represented
an earthly mirror-image of "the stars' battles
in Heaven,"22 an outline of those battles from
which man's destiny proceeded.

22. See Joseph Needham, Science and Civilization
in China (Cambridge, 1959), III, 540ff., 303ff.;
see also IV, pt. 1, 230, 265, 327 ff.

From the recent film The New Mutants —

Anya Taylor-Joy plays in a pool: 

"Roll credits."

The Motive for Metaphor

Filed under: General — Tags: , — m759 @ 3:29 PM

The above title is  from Wallace Stevens.

Related meditations — This journal on March 9, 2021, and . . .

See as well recent posts in this  journal
now tagged The Chinese Room Experiment

For the source of the above Wallace Stevens phrase, see (for instance) . . .

The above weblog post on Stevens is dated November 17, 2010.

Posts in this  weblog on that same date and its eve  are now tagged . . .

The Horcrux Narrative.


Related Scholarly Remarks:

Number and Time, by Marie-Louise von Franz

Wednesday, January 1, 2020

A Hexagram for Pauli*

Filed under: General — Tags: — m759 @ 9:21 AM

I Ching box symbol

Pictorial version
of Hexagram 20,
Contemplation  (View)

* See Pauli in the Dec. 30
post Number and Time.

Thursday, February 2, 2017

Hollywood Easter Egg

Filed under: General — Tags: — m759 @ 9:33 PM

From yesterday's post Hollywood Arrival

Yesterday's events at 6407 Sunset Blvd. in Hollywood,
together with the logic of number and time from recent
posts based on a Heinlein short story, suggest that the
character played by Adams is a sort of 'fifth element'
needed to save the world. 

In other words, the strange logic of recent posts ties the
California lottery number  6407 to the date  April 12, 2015, 
and a check of that date in this journal yields posts tagged
Orthodox Easter 2015 that relate to the 'fifth element.' "

A related image from Arrival  (at 1:37:18) —

A related passage of scientific prose —

"Paramount discoveries are still being made…."

Or at least distributed.

Wednesday, February 1, 2017

Hollywood Arrival

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

In the new film Arrival , Amy Adams plays a linguist
who must interpret the language used by aliens whose
spaceships hover at 12 points around the globe.

Yesterday's events at 6407 Sunset Blvd. in Hollywood,
together with the logic of number and time from recent
posts based on a Heinlein short story, suggest that the
character played by Adams is a sort of "fifth element"
needed to save the world. 

In other words, the strange logic of recent posts ties the
California lottery number  6407 to the date  April 12, 2015, 
and a check of that date in this journal yields posts tagged
Orthodox Easter 2015 that relate to the "fifth element."

Midrash by Ted Chiang from the story on which Arrival  was based  —

After the breakthrough with Fermat's Principle, discussions of scientific concepts became more fruitful. It wasn't as if all of heptapod physics was suddenly rendered transparent, but progress was suddenly steady. According to Gary, the heptapods' formulation of physics was indeed topsy-turvy relative to ours. Physical attributes that humans defined using integral calculus were seen as fundamental by the heptapods. As an example, Gary described an attribute that, in physics jargon, bore the deceptively simple name “action,” which represented “the difference between kinetic and potential energy, integrated over time,” whatever that meant. Calculus for us; elementary to them.

Conversely, to define attributes that humans thought of as fundamental, like velocity, the heptapods employed mathematics that were, Gary assured me, “highly weird.” The physicists were ultimately able to prove the equivalence of heptapod mathematics and human mathematics; even though their approaches were almost the reverse of one another, both were systems of describing the same physical universe.

Monday, January 16, 2017

Various Schemata

Filed under: General,Geometry — m759 @ 8:35 PM

The New York Times  this evening

"Hans Berliner, a former world champion of correspondence chess
who won one of the greatest games ever played on his way to
the title and later became a pioneering developer of game-playing
computers, died on Friday [Jan. 13th] in Riviera Beach, Fla.
He was 87."

Dylan Loeb McClain

In memoriam

Number and Time, by Marie-Louise von Franz

Friday, May 27, 2016

Raiders of the Lost Crucible…

Filed under: General — m759 @ 8:00 AM

Continues .

Number and Time, by Marie-Louise von Franz

For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.

The above passage suggests a meditation on this morning's
New York Times * —

"When shall we three meet again?" — William Shakespeare

“We three have scattered, leaving only me behind
to clean up the scene,” Ms. Yang wrote.
“I am alone, missing us three.” — Amy Qin

Saturday, February 14, 2015

Valentine Dance

Filed under: General,Geometry — Tags: , — m759 @ 2:00 PM

For Eliot and von Franz —

"A dance results."

— Marie-Louise von Franz
     in Number and Time

IMAGE- Halftime dance in 4x4 square, 2015 Super Bowl, with Katy Perry

Sunday, December 2, 2012

Realism

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

From the Los Angeles Times  yesterday

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

Linda Shaw, Seattle Times :

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

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

more »

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

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

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

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

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

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

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

"Yes, they are."

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

Sunday, November 18, 2012

Sermon

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

Happy birthday to

IMAGE- Margaret Atwood, Kim Wilde, Peta Wilson

Today's sermon, by Marie-Louise von Franz

Number and Time, by Marie-Louise von Franz

For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.

Another modern physicist, Niels Bohr, died
on this date in 1962

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

The circle above is marked with a version
of the classic Chinese symbol
adopted as a personal emblem
by Danish physicist Niels Bohr,
leader of the Copenhagen School.

For the square, see the diamond theorem.

"Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined
On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come."

— Wallace Stevens,
  "Notes Toward a Supreme Fiction,"
  Canto IV of "It Must Change"

Sunday, March 21, 2010

Galois Field of Dreams

Filed under: General,Geometry — Tags: — m759 @ 10:01 AM

It is well known that the seven (22 + 2 +1) points of the projective plane of order 2 correspond to 2-point subspaces (lines) of the linear 3-space over the two-element field Galois field GF(2), and may be therefore be visualized as 2-cube subsets of the 2×2×2 cube.

Similarly, recent posts* have noted that the thirteen (32 + 3 + 1) points of the projective plane of order 3 may be seen as 3-cube subsets in the 3×3×3 cube.

The twenty-one (42 + 4 +1) points of the (unique) projective plane of order 4 may also be visualized as subsets of a cube– in this case, the 4×4×4 cube. This visualization is somewhat more complicated than the 3×3×3 case, since the 4×4×4 cube has no central subcube, and each projective-plane point corresponds to four, not three, subcubes.

These three cubes, with 8, 27, and 64 subcubes, thus serve as geometric models in a straightforward way– first as models of finite linear spaces, hence as models for small Galois geometries derived from the linear spaces. (The cubes with 8 and 64 subcubes also serve in a less straightforward, and new, way as finite-geometry models– see The Eightfold Cube, Block Designs, and Solomon's Cube.)

A group of collineations** of the 21-point plane is one of two nonisomorphic simple groups of order 20,160. The other is the linear group acting on the linear 4-space over the two-element Galois field  GF(2). The 1899 paper establishing the nonisomorphism notes that "the expression Galois Field is perhaps not yet in general use."

Coordinates of the 4×4×4 cube's subcubes can, of course, be regarded as elements of the Galois field GF(64).

The preceding remarks were purely mathematical. The "dreams" of this post's title are not. See…

Number and Time, by Marie-Louise von Franz

See also Geometry of the I Ching and a search in this journal for "Galois + Ching."

* February 27 and March 13

** G20160 in Mitchell 1910,  LF(3,22) in Edge 1965

— Mitchell, Ulysses Grant, "Geometry and Collineation Groups
   of the Finite Projective Plane PG(2,22),"
   Princeton Ph.D. dissertation (1910)

— Edge, W. L., "Some Implications of the Geometry of
   the 21-Point Plane," Math. Zeitschr. 87, 348-362 (1965)

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, February 14, 2006

Tuesday February 14, 2006

Filed under: General — m759 @ 7:20 AM
Elitist Valentine

“… ‘elite’ is a term of opprobrium on both sides of the Atlantic for both left and right for entirely different reasons–  for the right, an ‘elitist’ is an unpatriotic, degenerate left-wing fan of the avant-garde; for the left, he is an undemocratic enemy of the people.”

— Charles Rosen, review of The Oxford History of Western Music in the Feb. 23, 2006, New York Review of Books

The first person that comes to mind as fitting both left and right descriptions is T. S. Eliot.  Hence the following:

The image “http://www.log24.com/log/pix05/050503-Poets.jpg” cannot be displayed, because it contains errors.


The image “http://www.log24.com/log/pix05/050501-Quad.jpg” cannot be displayed, because it contains errors.

A Jungian on this six-line figure:

“They are the same six lines that exist in the I Ching…. Now observe the square more closely: four of the lines are of equal length, the other two are longer…. For this reason symmetry cannot be statically produced and a dance results.”
 
— Marie-Louise von Franz,
   Number and Time (1970)


Monday, December 26, 2005

Monday December 26, 2005

Filed under: General — Tags: — m759 @ 7:00 PM
Language Game on
Boxing Day

In the box-style I Ching
Hexagram 34,
The Power of the Great,
is represented by

  The image “http://www.log24.com/theory/images/Box34.gif” cannot be displayed, because it contains errors. .

Art is represented
by a box
(Hexagram 20,
Contemplation, View)

  The image “http://www.log24.com/theory/images/Box20.gif” cannot be displayed, because it contains errors. .

  And of course 
great art
is represented by
an X in a box.
(Hexagram 2,
The Receptive)

  The image “http://www.log24.com/theory/images/Box02.gif” cannot be displayed, because it contains errors. .

“… as a Chinese jar still   
Moves perpetually
 in its stillness”

“… at the still point,  
there the dance is.”

— T. S. Eliot 

The image “http://www.log24.com/log/pix05/050501-Quad.jpg” cannot be displayed, because it contains errors.

A Jungian on this six-line figure:

“They are the same six lines that exist in the I Ching…. Now observe the square more closely: four of the lines are of equal length, the other two are longer…. For this reason symmetry cannot be statically produced and a dance results.”
 
— Marie-Louise von Franz,
   Number and Time


For those who prefer
technology to poetry,
there is the Xbox 360.

(Today is day 360 of 2005.)

Monday, May 2, 2005

Monday May 2, 2005

Filed under: General — m759 @ 11:00 AM
A Dance Results

 

Roger Kimball on Rosalind Krauss's
The Optical Unconscious:

"Professor Krauss even uses many of the same decorations with which she festooned earlier volumes. Bataille’s photograph of a big toe, for example, which I like to think of as her mascot, reappears. As does her favorite doodle, a little graph known as a 'Klein Group' or 'L Schema' whose sides and diagonals sport arrows pointing to corners labeled with various opposing pairs: e.g., 'ground' and 'not ground,' 'figure' and 'not figure.' Professor Krauss seems to believe that this device, lifted from the pages of structuralist theory, illuminates any number of deep mysteries: the nature of modernism, to begin with, but also the essence of gender relations, self-consciousness, perception, vision, castration anxiety, and other pressing conundrums that, as it happens, she has trouble distinguishing from the nature of modernism. Altogether, the doodle is a handy thing to have around. One is not surprised that Professor Krauss reproduces it many times in her new book."
 

From Drid Williams,
The Semiotics of Human Action,
Ritual, and Dance:

A Klein four-group in the context of dance

This is closely related to
Beckett's "Quad" figure

The image “http://www.log24.com/log/pix05/050501-Quad.jpg” cannot be displayed, because it contains errors.

A Jungian on this six-line figure:

"They are the same six lines
that exist in the I Ching….
Now observe the square more closely:
four of the lines are of equal length,
the other two are longer….
For this reason symmetry
cannot be statically produced
and a dance results."
 
— Marie-Louise von Franz,
Number and Time (1970)

and to the Greimas "semiotic square":

"People have believed in the fundamental character of binary oppositions since at least classical times. For instance, in his Metaphysics Aristotle advanced as primary oppositions: form/matter, natural/unnatural, active/passive, whole/part, unity/variety, before/after and being/not-being.*  But it is not in isolation that the rhetorical power of such oppositions resides, but in their articulation in relation to other oppositions. In Aristotle's Physics the four elements of earth, air, fire and water were said to be opposed in pairs. For more than two thousand years oppositional patterns based on these four elements were widely accepted as the fundamental structure underlying surface reality….

The structuralist semiotician Algirdas Greimas introduced the semiotic square (which he adapted from the 'logical square' of scholastic philosophy) as a means of analysing paired concepts more fully…."

 

Daniel Chandler, Semiotics for Beginners.

* Compare Chandler's list of Aristotle's primary oppositions with Aristotle's list (also in the  Metaphysics) of Pythagorean oppositions (see Midrash Jazz Quartet).
 

Sunday, May 1, 2005

Sunday May 1, 2005

Filed under: General — m759 @ 1:11 PM
Logos

Harvard’s Barry Mazur on
one mathematical style:

“It’s the barest, most Beckett-like vocabulary
that incorporates the theory and nothing else.”

Samuel Beckett, Quad (1981):

The image “http://www.log24.com/log/pix05/050501-Quad.jpg” cannot be displayed, because it contains errors.

A Jungian on this six-line logo:

“They are the same six lines
that exist in the I Ching….
Now observe the square more closely:
four of the lines are of equal length,
the other two are longer….
For this reason symmetry
cannot be statically produced
and a dance results.”
 
— Marie-Louise von Franz,
Number and Time (1970),
Northwestern U. Press
paperback, 1979, p. 108

A related logo from
Columbia University’s
Department of Art History
and Archaeology
:

The image “http://www.log24.com/log/pix05/050501-ArtHist2.gif” cannot be displayed, because it contains errors.
 
Also from that department:

Rosalind Krauss,

The image “http://www.log24.com/log/pix05/050501-Krauss.jpg” cannot be displayed, because it contains errors.

Meyer Schapiro Professor
of Modern Art and Theory:

“There is no painter in the West
who can be unaware of
the symbolic power
of the cruciform shape
and the Pandora’s box
of spiritual reference
that is opened
once one uses it.”

“In the garden of Adding
live Even and Odd…”
— The Midrash Jazz Quartet in
City of God
, by E. L. Doctorow


THE GREEK CROSS

A cross in which all the arms
are the same length.

Here, for reference, is a Greek cross
within a nine-square grid:

The image “http://www.log24.com/log/pix05/050501-GrCross.gif” cannot be displayed, because it contains errors.

 Related religious meditation for
    Doctorow’s “Garden of Adding”…

 4 + 5 = 9.

Types of Greek cross
illustrated in Wikipedia
under “cross“:

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

From designboom.com:

THE BAPTISMAL CROSS

The image “http://www.log24.com/log/pix05/050501-BaptismalCross.gif” cannot be displayed, because it contains errors.

is a cross with eight arms:
a Greek cross, which is superimposed
on a Greek ‘chi,’ the first letter
of the Greek word for ‘Christ.’
Since the number eight is symbolic
of rebirth or regeneration,
this cross is often used
as a baptismal cross.

Related material:

The image “http://www.log24.com/theory/images/Symm-axes.jpg” cannot be displayed, because it contains errors.

Fritz Leiber’s “spider”
or “double cross” logo.
See Why Me? and
A Shot at Redemption.

Happy Orthodox Easter.

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