Log24

From posts tagged Modernism —

See the 27-part structure of
the 3x3x3 Galois cube

as well as Autism Sunday 2015.

Michiko Kakutani in The New York Times —

"The detective story genre concerns the finding of clues
and the search for hidden designs, and its very form
underscores Mr. Pynchon’s obsession with conspiracies
and the existence of systems too complicated to understand."

— Review of Pynchon's Bleeding Edge , Sept. 10, 2013

Background:  "Moss on the Wall," this  journal on that date.

A less complicated system —

"Plan 9 deals with the resurrection of the dead."

— Bill Murray in "Ed Wood"
 

For The Church of Plan 9

(The plan , as well as the elevation ,
of the above structure is a 3×3 grid.)

See also Plan 9.

Click image for a search.

* Parent company of Westworld.
  See also Delos  in this journal.

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

 .

See posts tagged Clooney Omega in this journal.

(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.  

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

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.

( A Chinese designation for the 3×3 square )

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

The title is both a legal phrase and a phrase
used by Tom Wolfe in his writings on art.

See, too, the pattern of nine triangular half-squares
arranged in a 3×3 square used in the logo of  the
Jean Stephen art galleries in Minneapolis…

… and in a print at the Tate in London  (click to enlarge)—

See as well an obit of the print’s artist, Justin Knowles, who reportedly died
on Feb. 24, 2004.

Some instances of that date in this journal are related to Knowles’s aesthetics.

“… the object sets up a kind of 
 frame or space or field 
 within which there can be epiphany.”

— Charles Taylor

A frame or space or field —

Related material —

Star Wars (January 11, 2014),

The Lyche Gate Asterisk , from 10:31 AM ET on May 22, 2010,
the date of Martin Gardner's death —

— and the March 2014 issue of the
Notices of the American Mathematical Society  —

See as well Epiphany 2014 (Jan. 6) in this journal and the
March Notices  on the Shaw prize —

"Established under the auspices of Run Run Shaw
in November 2002, the prize is managed and
administered by the Shaw Prize Foundation
based in Hong Kong." 

C. P. Snow on G. H. Hardy, in Snow's foreword to A Mathematician's Apology—

"One morning early in 1913, he found, among the letters on his breakfast table, a large untidy envelope decorated with Indian stamps. When he opened it, he found sheets of paper by no means fresh, on which, in a non-English holograph, were line after line of symbols. Hardy glanced at them without enthusiasm. He was by this time, at the age of thirty-six, a world famous mathematician: and world famous mathematicians, he had already discovered, are unusually exposed to cranks. He was accustomed to receiving manuscripts from strangers, proving the prophetic wisdom of the Great Pyramid, the revelations of the Elders of Zion, or the cryptograms that Bacon has inserted in the plays of the so-called Shakespeare."

Some related material (click to enlarge)—

The author links to, but does not name, the source of the above
"line after line of symbols." It is "Visualizing GL(2,p)." See that webpage
for some less esoteric background.

See also the two Wikipedia articles Finite geometry and Hesse configuration
and an image they share—

The Hesse here is not Hermann, but Otto.

The 3×3×3 Galois Cube

Backstory— The Talented, from April 26 last year,
and Atlas Shrugged, from April 27 last year.

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—
   

6. The following from the First of May, 2010—

   The Nine Divisions of Heaven–
   

   

   Some context–

   

   "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" —
   • in an article on buying jewelry,
   • in this journal yesterday, and
   • in the Bible.

The twin topics of autism and of narrowing definitions
suggested the following remarks.

The mystical number "318" in the pilot episode
of Kiefer Sutherland's new series about autism, "Touch,"
is so small that it can easily apply (as the pilot
illustrated) to many different things: a date, a
time, a bus number, an address, etc.

The last 3/18 Log24 post— Defining Configurations—
led, after a false start and some further research,
to the writing of the webpage Configurations and Squares.

An image from that page—

Interpreting this, in an autistic manner, as the number
287501346 lets us search for more specific items
than those labeled simply 318.

The search yields, among other things, an offer of
Night Magic Cologne  (unsold)—

For further mystery and magic, see, from the date
the Night Magic offer closed— May 8, 2010— "A Better Story."
See also the next day's followup, "The Ninth Gate."

Grid from a post linked to in yesterday's 24 Hour DeLillo—

A Study in Art Education

For an example of this grid as slow art , consider the following—

"One can show that the binary tetrahedral group
is isomorphic to the special linear group SL(2,3)—
the group of all 2×2 matrices over the finite field F₃
with unit determinant." —Wikipedia

As John Baez has noted, these two groups have the same structure as the geometric 24-cell.

For the connection of the grid to the groups and the 24-cell, see Visualizing GL(2,p).

Related material—

The 3×3 grid has been called a symbol of Apollo (Greek god of reason and of the sun).

"This is where we sat through his hushed hour,
a torchlit sky, the closeness of hills barely visible
at high white noon." — Don DeLillo, Point Omega

"In any geometry satisfying Pappus's Theorem,
the four pairs of opposite points of 8₃
are joined by four concurrent lines."
— H. S. M. Coxeter (see below)

Continued from Tuesday, Sept. 6—

A reader comments on yesterday afternoon's New York Times
"The Stone" column by Justin E.H. Smith—

"I did indeed appreciate Mr. Smith’s essay.
And I’m curious as to what future contributions of his,
to the Stoner series, that we can look forward to."

From August 24, 2010—

Happy day 23 of Mental Health Month.

Today's earlier post mentions one approach to the concepts of unity and multiplicity. Here is another.

Unity:
The 3×3×3 Galois Cube

Multiplicity:

One of a group, GL(3,3), of 11,232
natural transformations of the 3×3×3 Cube

See also the earlier 1985 3×3 version by Cullinane.