Wednesday October 14, 2009
Singer 7-Cycles

Seven-cycles by R.T. Curtis, 1987


Singer 7-cycles by Cullinane, 1985


Click on images for details.

The 1985 Cullinane version
gives some algebraic background
for the 1987 Curtis version.

The Singer referred to above is James Singer. See his "A Theorem in Finite Projective Geometry and Some Applications to Number Theory," Transactions of the American Mathematical Society 43 (1938), 377-385.

For other singers, see Art Wars and today's obituaries.

Some background: the Log24 entry of this date seven years ago, and the entries preceding it on Las Vegas and painted ponies.

Posted 10/14/2009 at 9:29 AM

Tuesday October 13, 2009
x
Posted 10/13/2009 at 4:04 PM

Tuesday October 13, 2009
Wakes

This morning's New York Times
reports the deaths of Nuremberg interrogator Richard W. Sonnenfeldt and of avant-garde novelist and Beckett scholar Raymond Federman.

Symbols from this journal on the dates of their deaths:

For Sonnenfeldt, who died
 on Friday, Oct. 9,
a symbol from that date:

The 3x3 grid as religious symbol

For connotations of the symbol appropriate to the name Sonnenfeldt, see the link to A Sunrise for Sunrise in the entry of Saturday, Oct. 10.


For Federman, who died
 on Tuesday, Oct. 6,
a symbol from that date:

Black monolith

A quotation that appeared here on Wednesday, Oct. 7, seems relevant to Federman:

But I am a worker, a tombstone mason, anxious to pleace averyburies and jully glad when Christmas comes his once ayear. You are a poorjoist, unctuous to polise nopebobbies....

-- James Joyce, Finnegans Wake

Posted 10/13/2009 at 7:00 AM

Monday October 12, 2009
Happy Columbus Day

Part I and Part II

Posted 10/12/2009 at 7:00 AM

Sunday October 11, 2009
Concepts of Space

Today I revised the illustrations
in Finite Geometry of the
Square and Cube

for consistency in labeling
the eightfold cube.

Related material:

Inside the White Cube:
The Ideology of
the Gallery Space


Dagger Definitions

Posted 10/11/2009 at 7:00 PM

Saturday October 10, 2009
A Sunrise
for Sunrise


Related material:

This morning's obituaries

(click to enlarge)


http://www.log24.com/log/pix09A/091010-NYTobitsSm.jpg


and Zen and Language Games

Posted 10/10/2009 at 7:00 AM

Friday October 9, 2009
Identity:

The 3x3 grid as religious symbol

"...strict grids of nine pictures
    establish an egalitarian
        framework
...."

-- Christopher Knight

Some are more
egalitarian
than others.

Posted 10/9/2009 at 9:00 AM

Thursday October 8, 2009
Knight Moves

Deborah Solomon, New York Times Magazine, Sunday, June 27, 1999:

"While modern art began as an assault on the academy, post-modern art might be described as a return to the academy. Instead of the old academy of rules, now we have the Academy of Cool, schools that treat avant-garde rebellion as a learned occupation."

Christopher Knight, LA Times art critic, on Solomon:

"Back in the day, Solomon interviewed Knight for a Times Magazine story on Los Angeles art schools. 'Having been a journalist (at that time) for almost two decades, I also did my homework,' Knight writes [in a letter to the New York Press]. 'I prepared a couple of quotable quotes on the subject, which might encapsulate larger ideas.' One of Knight's pearls of wisdom, 'Modern art began as an assault on the academy, but post-modern art might be described as a return to the academy,' excited Solomon so much that, according to Knight, she printed it as her own observation in her final piece, which bore no mention of the Knight interview. In the final story, a seriously bitter Knight writes, 'It was not a quote; my words had become her words.'" --Gawker, Oct. 11, 2007

A reference to Solomon's piece appeared in this journal in 2003.

See also yesterday's entry, today's 9 AM entry, and (for the Academy) an example of knight's move thinking.

Posted 10/8/2009 at 10:30 AM

Thursday October 8, 2009
In memory
of Irving Penn:

Graphic
Austerity


Chessboard (Detail)

Christopher Knight
on a current exhibit
of Penn's work:

"In American Vogue,
strict grids of nine pictures
establish an egalitarian
framework; the design
anticipates Minimalist art
by a decade."

Posted 10/8/2009 at 9:00 AM

Wednesday October 7, 2009
Finucane's Wake

Terence McKenna,
"Surfing on Finnegans Wake"--

"Shall I try and find a passage?....

But I am a worker, a tombstone mason, anxious to pleace averyburies and jully glad when Christmas comes his once a year. You are a poorjoist, unctuous to polise nopebobbies...."

The Finucane of the title
was a Holy Ghost Father.

Related material:
"Haunting Time,"
June 3, 2007.

Posted 10/7/2009 at 7:59 AM

Tuesday October 6, 2009
A Halmos
for Gelfand:

Black monolith

See also
The Unity
 of Mathematics
.

Posted 10/6/2009 at 11:07 AM

Monday October 5, 2009
Continued from Saturday-- 

Pieces missing from Wechsler block design test and from IZZI puzzle

Context
for the 16:

Block Designs
and Art

Context
for the 70:

Symmetry
and Counting
  "Kunst ist nicht einfach."
-- Sondheim in translation
 
Posted 10/5/2009 at 4:00 AM

Saturday October 3, 2009
Missing Pieces:  Conceptual art by Cullinane and Bochner

Related material:


Frame Tales, as well as
The Sacred Day of Kali,
this morning's
 New York Times obituaries,
and
Mental Health Month, 2003:

Wechsler blocks

WAIS blocks

IZZI puzzle
IZZI puzzle

Michael Douglas in 'The Game'

Sondheim: 'Putting It Together'


Posted 10/3/2009 at 3:31 AM

Friday October 2, 2009
Edge on Heptads

Part I: Dye on Edge

"Summary:
....we obtain various orbits of partitions of quadrics over GF(2a) by their maximal totally singular subspaces; the corresponding stabilizers in the relevant orthogonal groups are investigated. It is explained how some of these partitions naturally generalize Conwell's heptagons for the Klein quadric in PG(5,2)."

"Introduction:
In 1910 Conwell... produced his heptagons in PG(5,2) associated with the Klein quadric K whose points represent the lines of PG(3,2).... Edge... constructed the 8 heptads of complexes in PG(3,2) directly. Both he and Conwell used their 8 objects to establish geometrically the isomorphisms SL(4,2)=A8 and O6(2)=S8 where O6(2) is the group of K...."

-- "Partitions and Their Stabilizers for Line Complexes and Quadrics," by R.H. Dye, Annali di Matematica Pura ed Applicata, Volume 114, Number 1, December 1977, pp. 173-194

Part II: Edge on Heptads

"The Geometry of the Linear Fractional Group LF(4,2)," by W.L. Edge, Proc. London Math Soc., Volume s3-4, No. 1, 1954, pp. 317-342. See the historical remarks on the first page.

Note added by Edge in proof:
"Since this paper was finished I have found one by G. M. Conwell: Annals of Mathematics (2) 11 (1910), 60-76...."

Some context:

The Klein Correspondence,
Penrose Space-Time,
and a Finite Model


Posted 10/2/2009 at 6:00 AM