Log24

Saturday, June 13, 2015

The Holy Field

Filed under: General,Geometry — m759 @ 7:45 PM

( A Chinese designation for the 3×3 square )

Tuesday, October 17, 2017

Plan 9 Continues

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

See also Holy Field in this journal.

Some related mathematics —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Analysis of the Lo Shu structure —

Structure of the 3×3 magic square:

4  9  2
3  5  7    decreased by 1 is
8  1  6

3  8  1
2  4  6
7  0  5

In base 3 —

10  22  01
02  11  20
21  00  12

As orthogonal Latin squares
(a well-known construction) —

1  2  0     0  2  1
0  1  2     2  1  0
2  0  1     1  0  2 .

— Steven H. Cullinane,
     October 17, 2017

Friday, December 9, 2016

Sacred Space (continued)

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

See Plan 9 in this journal.

 The 3x3 square 

Monday, June 20, 2016

Sacred Space

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

For further background to this morning's post Plan 9 Continues,
see posts tagged Sacred Space

The 3x3 square .

Friday, May 27, 2016

Plan 9

Filed under: General — m759 @ 9:00 AM

http://m759.net/wordpress/?tag=holy-field-gf3

Sunday, October 18, 2015

Coordinatization Problem

Filed under: General,Geometry — m759 @ 1:06 AM

There are various ways to coordinatize a 3×3 array
(the Chinese "Holy Field'). Here are some —

See  Cullinane,  Coxeter,  and  Knight tour.

Sunday, July 12, 2015

Characteristica Universalis

Filed under: General — m759 @ 7:00 PM

From Wikipedia —

"Many Leibniz scholars… seem to agree that he intended
his characteristica universalis  … to be a form of … 
ideographic language. This was to be based on a
rationalised version of the 'principles' of Chinese characters…."

See as well O Nine,  Chinese Calligraphy, and Holy Field.

Friday, July 10, 2015

Without Border

Filed under: General — Tags: , — m759 @ 3:18 PM

The previous post's Holy Field symbol, 
with border removed, becomes the
Chinese character for "well."

See also The Lost Well.

Thursday, July 9, 2015

Man and His Symbols

Filed under: General,Geometry — m759 @ 2:24 PM

(Continued)

A post of July 7, Haiku for DeLillo, had a link to posts tagged "Holy Field GF(3)."

As the smallest Galois field based on an odd prime, this structure 
clearly is of fundamental importance.  

The Galois field GF(3)

It is, however, perhaps too  small  to be visually impressive.

A larger, closely related, field, GF(9), may be pictured as a 3×3 array

hence as the traditional Chinese  Holy Field.

Marketing the Holy Field

IMAGE- The Ninefold Square, in China 'The Holy Field'

The above illustration of China's  Holy Field occurred in the context of
Log24 posts on Child Buyers.   For more on child buyers, see an excellent
condemnation today by Diane Ravitch of the U. S. Secretary of Education.

Tuesday, July 7, 2015

Haiku for DeLillo*

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

A music video that opens with remarks by Lawrence Ferlinghetti
at the Last Waltz concert (Thanksgiving Day, Nov. 25, 1976):

"Our Father, whose art's in heaven…" —

For other religious remarks from the above upload date,
Sept. 9, 2011, see Holy Field GF(3).

Click the above "ripple" image for a Grateful Dead haiku
quoted here on Sunday, July 5, 2015.

For another meditation from the second upload date above,
March 19, 2012, see some thoughts on the word "field."

IMAGE- Japanese character for 'field'

* For the title, see an excerpt from Point Omega .

Saturday, June 20, 2015

Conceptual Art for Basel

Filed under: General,Geometry — Tags: — m759 @ 7:59 PM

The previous post's link to The Lindbergh Manifesto
and Thursday's post on Basel-born artist Wolf Barth 
suggest the following —

See as well a June 14 New York Times
piece on Art Basel.

The logo of the University of Basel 

suggests a review of The Holy Field —

 .

Tuesday, May 12, 2015

Writing Well*

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

See Stevens + New Haven.

* The above figure may be viewed as
   the Chinese "Holy Field" or as the
   Chinese character for "Well"
   inscribed in a square.

Thursday, February 19, 2015

The Bluebird of Happiness

Filed under: General — m759 @ 12:48 PM

(Chinese style)

Tuesday, November 18, 2014

The Abacus Conundrum…

Filed under: General — Tags: — m759 @ 1:44 AM

Continues.

http://www.log24.com/log/pix10B/101206-AbacusConundrum.jpg

Prequel from 1961 (click image for context):

Detail that may be interpreted as the Chinese
3×3 "Holy Field" and a Chinese temple bell—

"Ting-a-ling." — Kurt Vonnegut.

Thursday, November 13, 2014

Progressive Matrix

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

Yesterday's post and recent Hollywood news suggest
a meditation on a Progressive Matrix —

Oct. 12-14, 2005:

'A Poem for Pinter,' conclusion: 'Tick Tick Hash.'

'The Interpreter'-- Sean Penn to Nicole Kidman-- 'My Card.'

Click to enlarge.

"My card."

Structurally related images —

A sample Raven's Progressive Matrices  test item
(such items share the 3×3 structure of the hash symbol above):

IMAGE- Raven's Progressive Matrices item with symbols from Cullinane's box-style I Ching

Structural background —

Tuesday, October 21, 2014

Art as a Tool

Filed under: General,Geometry — m759 @ 12:35 PM

Two news items on art as a tool:

Two Log24 posts related to the 3×3 grid, the underlying structure for China’s
ancient Lo Shu “magic” square:

Finally, leftist art theorist Rosalind Krauss in this journal
on Anti-Christmas, 2010:

Which is the tool here, the grid or Krauss?

Saturday, May 17, 2014

It’s Time for You to…

Filed under: General,Geometry — m759 @ 11:30 PM

See the Field

“There have long been rumors of a mythical Ninth Element
that grants ultimate power to the Wizard who masters it.
The Order of Magick says there is no such thing. But….”

— Website of Magicka: The Ninth Element Novel

William Worthy in Beijing —

This journal on the date of Worthy’s death,
May 4, 2014, had a link to…

    The Holy Field

Sunday, May 4, 2014

Geometry for Scarlett

Filed under: General,Geometry — Tags: , — m759 @ 11:16 AM

Scarlett Johansson stars in a new film, “Lucy,” due to be
released on August 8, directed by Luc Besson, auteur  of
The Fifth Element  (1997). In other pop culture…

 “There have long been rumors of a mythical Ninth Element
that grants ultimate power to the Wizard who masters it.
The Order of Magick says there is no such thing. But….”

— Website of Magicka: The Ninth Element Novel

See also, in this journal, Holy Field as well as Power of the Center.

Wednesday, March 26, 2014

Grid

Filed under: General — m759 @ 12:00 PM

For some context, see Holy Field
and Krauss Grid.

Tuesday, July 16, 2013

Child Buyers

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

The title refers to a classic 1960 novel by John Hersey.

“How do you  get young people excited about space?”

— Megan Garber in The Atlantic , Aug. 16, 2012
(Italics added.) (See previous four posts.)

Allyn Jackson on “Simplicity, in Mathematics and in Art,”
in the new August 2013 issue of Notices of the American
Mathematical Society

“As conventions evolve, so do notions of simplicity.
Franks mentioned Gauss’s 1831 paper that
established the respectability of complex numbers.”

This suggests a related image by Gauss, with a
remark on simplicity—

IMAGE- Complex Grid, by Gauss

Here Gauss’s diagram is not, as may appear at first glance,
a 3×3 array of squares, but is rather a 4×4 array of discrete
points (part of an infinite plane array).

Related material that does  feature the somewhat simpler 3×3 array
of squares, not  seen as part of an infinite array—

Marketing the Holy Field

IMAGE- The Ninefold Square, in China 'The Holy Field'

Click image for the original post.

For a purely mathematical view of the holy field, see Visualizing GL(2,p).

Sunday, October 21, 2012

Multispeech

Filed under: General — m759 @ 9:00 PM

IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

     Click image above
     for some background.

IMAGE- Snow White Imprisoned- An image for the Snow Queen

IMAGE- Charlize Theron as Ravenna: 'She drifted.'

Saturday, June 2, 2012

Matrix Problem Revolutions

Filed under: General — m759 @ 1:28 AM

(The sequel to yesterday's Matrix Problem Reloaded)

Wikipedia on the sci-fi weblog  io9.com

Newitz explained the significance of the name "io9":

"Well, io9s are input-output devices that let you see into the future.
They're brain implants that were outlawed because they drove
anyone who used one insane. We totally made that (device) up
to name the blog."

Jenna Wortham at wired.com, Jan. 2, 2008

From io9.com itself—

"Science fiction writer Ken MacLeod has another term for io9ers.
He calls them rapture fuckers.*"

— io9.com/explanations/

For the relevance of the term "revolutions" in this post's title, see
Wikipedia on Ken MacLeod.

I prefer to associate the number 9 with The Holy Field.

 

 

* MacLeod used this phrase in one of his novels, Newton's Wake.

Saturday, March 24, 2012

The David Waltz…

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

In Turing's Cathedral

"At the still point…" — T. S. Eliot

In memory of David L. Waltz, artificial-intelligence pioneer,
who died Thursday, March 22, 2012—

  1. The Log24 post of March 22 on the square-triangle theorem
  2. The March 18 post, Square-Triangle Diamond
  3. Remarks from the BBC on linguistic embedding
    that begin as follows—
         "If we draw a large triangle and embed smaller triangles in it,
          how does it look?"—
    and include discussion of a South American "tribe called Piranha" [sic ]
  4. The result of a Cartoon Bank search suggested by no. 3 above—
    (Click image for some related material.)
  5. A suggestion from the Cartoon Bank—
    IMAGE- 'Try our new grid view.'
  6. The following from the First of May, 2010

    The Nine Divisions of Heaven–

    Image-- Routledge Encyclopedia of Taoism, Vol. I, on the Nine Heavens, 'jiutian,' ed. by Fabrizio Pregadio

    Some context–

    IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

    "This pattern is a square divided into nine equal parts.
    It has been called the 'Holy Field' division and
    was used throughout Chinese history for many
    different purposes, most of which were connected
    with things religious, political, or philosophical."

    – The Magic Square: Cities in Ancient China,
    by Alfred Schinz, Edition Axel Menges, 1996, p. 71

  7. The phrase "embedding the stone" —

Sunday, January 22, 2012

Year of the Dragon

Filed under: General — m759 @ 3:33 PM

In China, the Year of the Dragon
has now begun. See Holy Field
in this journal.

Thursday, November 3, 2011

The China Conundrum

Filed under: General — m759 @ 5:48 PM
 
 

http://www.log24.com/log/pix11C/111103-3x3favicon-BlowupTo256w.bmp

The Holy Field

http://www.log24.com/log/pix11C/111103-ChinaConundrum-240w.jpg

"Buckle up!" — Harlan Kane, in the spirit of strategic stupidity.

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

A Beginning

Filed under: General — Tags: , — m759 @ 5:29 AM
 

From MIT Commencement Day, 2011—

A symbol related to Apollo, to nine, and to "nothing"

A minimalist favicon—

IMAGE- Generic 3x3 square as favicon

This miniature 3×3 square— http://log24.com/log/pix11A/110518-3x3favicon.ico — may, if one likes,
be viewed as the "nothing" present at the Creation. 
See Feb. 19, 2011, and Jim Holt on physics.

Saturday, May 1, 2010

An Education

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

天鈞

 

Made famous by Ursula K. Le Guin
as the book title "Lathe of Heaven,"
this Chinese phrase, tianjun, apparently
means something more like "Scales of Heaven"–
an appropriate image for Law Day 2010.

Image--Scales (the legal symbol)

An anonymous forum user says that

"…if you switch the two characters around,
you get: 鈞天, which is one of
the nine heavens, more specifically,
the middle heaven."

This is supported by a
non-anonymous source:

"I follow A.C. Graham’s translation of
Juntian as 'Level Heaven (the innermost
of the nine divisions of heaven)';
he renders Juntian guangyue as
'the mighty music of the innermost heaven.'"

— "Music in the World of Su Shi (1037-1101):
Terminology
," by Stuart H. Sargent,
Colorado State University,
Journal of Sung-Yuan Studies 32 (2002), 39-81

The Nine Divisions of Heaven–

Image-- Routledge Encyclopedia of Taoism, Vol. I, on the Nine Heavens, 'jiutian,' ed. by Fabrizio Pregadio

Some context–

The 3x3 ('ninefold') square

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71

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