Log24

Saturday, October 21, 2023

Chapter 11 Continues: A Larger Box

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

"… really we should use larger boxes." — Ursula K. Le Guin

"The Steiner system S (5, 8, 24) is a block design
made up of 24 points and 759 blocks, each of size 8,
with the property that every 5 points lie in exactly one block.
This design is naturally associated with the Golay code, and
its automorphism group is the simple Mathieu group M24;
see [3, Ch. 11].

3.  J.H. Conway and N.J.A. Sloane, Sphere Packings,
     Lattices and Groups
, Springer-Verlag, New York, 1988."

New Zealand Journal of Mathematics,
Volume 25 (1996), 133-139.
"Markings of the Golay Code," by
Marston Conder and John McKay.
(Received July 1995.)

See also the Harlan Kane Special from Broomsday 2023.
That post relates properties of the 4×4 box (Cullinane, 1979)
to those of the 4×6 box (Conway and Sloane, 1988, without
mention of Cullinane 1979).

Monday, October 16, 2023

A Harlan Kane Rite Aid Special:  Chapter 11

Filed under: General — Tags: , , — m759 @ 11:01 pm

From a search in this journal for "Chapter 11" —

 

Inner structure —

IMAGE- Hyperplanes (square and triangular) in PG(3,2), and coordinates for AG(4,2)

The above three images share the same
vector-space structure —

   0     c     d   c + d
   a   a + c   a + d a + c + d
   b   b + c   b + d b + c + d

a + b

a + b + c

a + b + d

  a + b + 
  c + d

   (This vector-space a b c d  diagram is from  
    Chapter 11 of Sphere Packings, Lattices 
    and Groups
 , by John Horton Conway and
    N. J. A. Sloane, first published by Springer
    in 1988.)

Sunday, October 1, 2023

Hassabis

Filed under: General — Tags: — m759 @ 11:05 am

Related religious remarks from this  journal on Augustine's Day 2023:

"We stopped at the Trocadero and there was hardly anyone there.  We had Lanson 1926.  'Drink up, sweet.  You gotta go some.  How I love music.  Frère Jacques, Cuernavaca, ach du lieber August.  All languages.  A walking Berlitz.  Berlitz sounds like you with that champagne, my sweet, or how you're gonna sound.'"

— John O'Hara, Hope of Heaven, Chapter 11, 1938

"And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance."

— Acts, Chapter 2, Verse 4

"Lps. The keys to. Given! A way a lone a last a loved a long the

PARIS,
1922-1939."

— James Joyce, conclusion of Finnegans Wake

Monday, August 28, 2023

“Ach du lieber August” — John O’Hara, Hope of Heaven

Filed under: General — Tags: , , — m759 @ 12:11 am

"We stopped at the Trocadero and there was hardly anyone there.  We had Lanson 1926.  'Drink up, sweet.  You gotta go some.  How I love music.  Frère Jacques, Cuernavaca, ach du lieber August.  All languages.  A walking Berlitz.  Berlitz sounds like you with that champagne, my sweet, or how you're gonna sound.'"

— John O'Hara, Hope of Heaven, Chapter 11, 1938

"And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance."

— Acts, Chapter 2, Verse 4

"Lps. The keys to. Given! A way a lone a last a loved a long the

PARIS,
1922-1939."

— James Joyce, conclusion of Finnegans Wake

Sunday, July 29, 2012

The Galois Tesseract

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

(Continued)

The three parts of the figure in today's earlier post "Defining Form"—

IMAGE- Hyperplanes (square and triangular) in PG(3,2), and coordinates for AG(4,2)

— share the same vector-space structure:

   0     c     d   c + d
   a   a + c   a + d a + c + d
   b   b + c   b + d b + c + d
a + b a + b + c a + b + d   a + b + 
  c + d

   (This vector-space a b c d  diagram is from  Chapter 11 of 
    Sphere Packings, Lattices and Groups , by John Horton
    Conway and N. J. A. Sloane, first published by Springer
    in 1988.)

The fact that any  4×4 array embodies such a structure was implicit in
the diamond theorem (February 1979). Any 4×4 array, regarded as
a model of the finite geometry AG(4, 2), may be called a Galois tesseract.
(So called because of the Galois geometry involved, and because the
16 cells of a 4×4 array with opposite edges identified have the same
adjacency pattern as the 16 vertices of a tesseract (see, for instance,
Coxeter's 1950 "Self-Dual Configurations and Regular Graphs," figures
5 and 6).)

A 1982 discussion of a more abstract form of AG(4, 2):

Source:

The above 1982 remarks by Brouwer may or may not have influenced
the drawing of the above 1988 Conway-Sloane diagram.

Monday, July 16, 2012

Mapping Problem continued

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

Another approach to the square-to-triangle
mapping problem (see also previous post)—

IMAGE- Triangular analogs of the hyperplanes in the square model of PG(3,2)

For the square model referred to in the above picture, see (for instance)

Coordinates for the 16 points in the triangular arrays 
of the corresponding affine space may be deduced
from the patterns in the projective-hyperplanes array above.

This should solve the inverse problem of mapping,
in a natural way, the triangular array of 16 points 
to the square array of 16 points.

Update of 9:35 AM ET July 16, 2012:

Note that the square model's 15 hyperplanes S 
and the triangular model's 15 hyperplanes T —

— share the following vector-space structure —

   0     c     d   c + d
   a   a + c   a + d a + c + d
   b   b + c   b + d b + c + d
a + b a + b + c a + b + d   a + b + 
  c + d

   (This vector-space a b c d  diagram is from
   Chapter 11 of   Sphere Packings, Lattices
   and Groups
, by   John Horton Conway and
   N. J. A. Sloane, first published by Springer
   in 1988.)

Wednesday, November 23, 2011

Music and Motion

Filed under: General — m759 @ 9:29 am

See Chapter 11, "Meter and Rhythm," of…

IMAGE- 'Sound and Symbol' by Victor Zuckerkandl

Wednesday, February 20, 2008

Wednesday February 20, 2008

Filed under: General — Tags: , , — m759 @ 11:48 am
 About Five Years Ago:

M. V. Ramana on a famous quotation–
 
"Oppenheimer had learned Sanskrit at Berkeley so as to read the Gita in the original; he always kept a worn pink copy on the bookshelf closest to his desk. It is therefore likely that he may have actually thought of the original, Sanskrit, verse rather than the English translation. The closest that fits this meaning is in the 32nd verse from the 11th chapter of the Gita.

 kalosmi lokaksaya krt pravrddho

This literally means: I am kAla, the great destroyer of Worlds. What is intriguing about this verse, then, is the interpretation of kAla by Jungk and others to mean death. While death is technically one of the meanings of kAla, a more common one is time."

"KAla" (in the Harvard-Kyoto transliteration scheme) is more familiar to the West in the related form of Kali, a goddess sometimes depicted as a dancing girl; Kali is related to kAla, time, according to one website, as "the force which governs and stops time."  See also the novel The Fermata, by Nicholson Baker.

The fact that Oppenheimer thought of Chapter 11, verse 32, of the Gita may, as a mnemonic device, be associated with the use of the number 1132 in Finnegans Wake.

 See 1132 A. D. & Saint Brighid, and my weblog entries of January 5 (Twelfth Night and the whirligig of time), January 31 (St. Bridget's Eve), and February 1 (St. Bridget's Day), 2003

The custom-made asterisk
above may be regarded
as a version of
the "Spider" symbol
of Fritz Leiber.

Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte
.

Rubén Darío

Related material:

The previous five entries
and the entries of
this date three years ago.

Time of this entry:

11:48:17 AM.

Monday, February 27, 2006

Monday February 27, 2006

Filed under: General — Tags: , , — m759 @ 9:26 am

Sudden View

From John O'Hara's Birthday:

"We stopped at the Trocadero and there was hardly anyone there.  We had Lanson 1926.  'Drink up, sweet.  You gotta go some.  How I love music.  Frère Jacques, Cuernavaca, ach du lieber August.  All languages.  A walking Berlitz.  Berlitz sounds like you with that champagne, my sweet, or how you're gonna sound.'"

— John O'Hara, Hope of Heaven, Chapter 11, 1938

"And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance."

Acts, Chapter 2, Verse 4

"Lps. The keys to. Given! A way a lone a last a loved a long the

PARIS,
1922-1939."

— James Joyce, conclusion of Finnegans Wake

"Using illustrative material from religion, myth, and culture, he starts with the descent of the dove on Jesus and ends with the poetic ramblings of James Joyce."

Review of a biography of the Holy Spirit

Monica Potts in today's New York Times on Sybille Bedford:

"Though her works were not always widely popular, they inspired a deeply fervent following of committed admirers, starting with her first published work, A Sudden View, in 1953. Later retitled A Visit to Don Otavio, it was an account of her journey through Mexico."

… "I addressed him.  'Is Cuernavaca not below Mexico City?'
    'It is low.'
    'Then what is this?'  Another summit had sprung up above a curve.
    'At your orders, the Three Marias.'
    'What are the Three Marias?'
    'These.'
    Later, I learned from Terry that they were the three peaks by the La Cima Pass which is indeed one of the highest passes in the Republic; and still later from experience, that before running down to anywhere in this country one must first run up some six or seven thousand feet.  The descents are more alarming than the climbs.  We hurtled towards Cuernavaca down unparapeted slopes with the speed and angle, if not the precision, of a scenic railway– cacti flashed past like telegraph poles, the sun was brilliant, the air like laughing gas, below an enchanting valley, and the lack of brakes became part of a general allegro accelerando."

— Sybille Bedford, A Sudden View, Counterpoint Press, Counterpoint edition (April 2003), page 77

"How continually, how startlingly, the landscape changed!  Now the fields were full of stones: there was a row of dead trees.  An abandoned plough, silhouetted against the sky, raised its arms to heaven in mute supplication; another planet, he reflected again, a strange planet where, if you looked a little further, beyond the Tres Marias, you would find every sort of landscape at once, the Cotswolds, Windermere, New Hampshire, the meadows of the Eure-et-Loire, even the grey dunes of Cheshire, even the Sahara, a planet upon which, in the twinkling of an eye, you could change climates, and, if you cared to think so, in the crossing of a highway, three civilizations; but beautiful, there was no denying its beauty, fatal or cleansing as it happened to be, the beauty of the Earthly Paradise itself."

— Malcolm Lowry, Under the Volcano, Harper Perennial Modern Classics, 1st Perennial Classics edition (May 1, 2000), page 10

Saturday, July 16, 2005

Saturday July 16, 2005

Filed under: General — Tags: , , — m759 @ 3:00 pm
Tribute

to the Dance of Kali:

  From Feb. 18, 2003

Fat Man and Dancing Girl

Dance of
Shiva and Kali

Paul Newman as
General Groves

From "The Bomb of the Blue God," by M. V. Ramana

Gita 11:32 —

kalosmi lokaksaya krt pravrddho

"This literally means: I am kala, the great destroyer of Worlds. What is intriguing about this verse, then, is the interpretation of kala by Jungk and others to mean death. While death is technically one of the meanings of kala, a more common one is time."

 See 1132 AD & Saint Brighid, and my 2003 weblog entries of January 5 (Twelfth Night and the whirligig of time), January 31 (St. Bridget's Eve), and February 1 (St. Bridget's Day).

The fact that Oppenheimer thought, on this date in 1945, of Chapter 11, verse 32, of the Gita may, as a mnemonic device, be associated with the use of the number 1132 in Finnegans Wake.

Related material for
Michael Flatley on his
July 16 birthday:

The image “http://www.log24.com/log/pix05A/050716-nataraj2.jpg” cannot be displayed, because it contains errors.

Shiva as Lord of the Dance

Michael and other Irish persons
may benefit from the film
"Indiana Jones and the Temple of Doom"
as an introduction to
the Dance of Shiva and Kali.

On a more personal level:
Log24 entries of July 12 and July 13.

Thursday, April 22, 2004

Thursday April 22, 2004

Filed under: General,Geometry — Tags: , — m759 @ 10:07 pm

Minimalism

"It's become our form of modern classicism."

— Nancy Spector in 
   the New York Times of April 23, 2004

Part I: Aesthetics

In honor of the current Guggenheim exhibition, "Singular Forms" — A quotation from the Guggenheim's own website

"Minimalism refers to painting or sculpture

  1. made with an extreme economy of means
  2. and reduced to the essentials of geometric abstraction….
  3. Minimalist art is generally characterized by precise, hard-edged, unitary geometric forms….
  4. mathematically regular compositions, often based on a grid….
  5. the reduction to pure self-referential form, emptied of all external references….
  6. In Minimal art what is important is the phenomenological basis of the viewer’s experience, how he or she perceives the internal relationships among the parts of the work and of the parts to the whole….
  7. The repetition of forms in Minimalist sculpture serves to emphasize the subtle differences in the perception of those forms in space and time as the spectator’s viewpoint shifts in time and space."

Discuss these seven points
in relation to the following:

 
Form,
by S. H. Cullinane

Logos and Logic

Mark Rothko's reference
to geometry as a "swamp"
and his talk of "the idea" in art

Michael Kimmelman's
remarks on ideas in art 

Notes on ideas and art

Geometry
of the 4×4 square

The Grid of Time

ART WARS:
Judgment Day
(2003, 10/07)

Part II: Theology

Today's previous entry, "Skylark," concluded with an invocation of the Lord.   Of course, the Lord one expects may not be the Lord that appears.


 John Barth on minimalism:

"… the idea that, in art at least, less is more.

It is an idea surely as old, as enduringly attractive and as ubiquitous as its opposite. In the beginning was the Word: only later came the Bible, not to mention the three-decker Victorian novel. The oracle at Delphi did not say, 'Exhaustive analysis and comprehension of one's own psyche may be prerequisite to an understanding of one's behavior and of the world at large'; it said, 'Know thyself.' Such inherently minimalist genres as oracles (from the Delphic shrine of Apollo to the modern fortune cookie), proverbs, maxims, aphorisms, epigrams, pensees, mottoes, slogans and quips are popular in every human century and culture–especially in oral cultures and subcultures, where mnemonic staying power has high priority–and many specimens of them are self-reflexive or self-demonstrative: minimalism about minimalism. 'Brevity is the soul of wit.' "


Another form of the oracle at Delphi, in minimalist prose that might make Hemingway proud:

"He would think about Bert.  Bert was an interesting man.  Bert had said something about the way a gambler wants to lose.  That did not make sense.  Anyway, he did not want to think about it.  It was dark now, but the air was still hot.  He realized that he was sweating, forced himself to slow down the walking.  Some children were playing a game with a ball, in the street, hitting it against the side of a building.  He wanted to see Sarah.

When he came in, she was reading a book, a tumbler of dark whiskey beside her on the end table.  She did not seem to see him and he sat down before he spoke, looking at her and, at first, hardly seeing her.  The room was hot; she had opened the windows, but the air was still.  The street noises from outside seemed almost to be in the room with them, as if the shifting of gears were being done in the closet, the children playing in the bathroom.  The only light in the room was from the lamp over the couch where she was reading.

He looked at her face.  She was very drunk.  Her eyes were swollen, pink at the corners.  'What's the book,' he said, trying to make his voice conversational.  But it sounded loud in the room, and hard.

She blinked up at him, smiled sleepily, and said nothing.

'What's the book?'  His voice had an edge now.

'Oh,' she said.  'It's Kierkegaard.  Soren Kierkegaard.' She pushed her legs out straight on the couch, stretching her feet.  Her skirt fell back a few inches from her knees.  He looked away.

'What's that?' he said.

'Well, I don't exactly know, myself."  Her voice was soft and thick.

He turned his face away from her again, not knowing what he was angry with.  'What does that mean, you don't know, yourself?'

She blinked at him.  'It means, Eddie, that I don't exactly know what the book is about.  Somebody told me to read it once, and that's what I'm doing.  Reading it.'

He looked at her, tried to grin at her — the old, meaningless, automatic grin, the grin that made everbody like him — but he could not.  'That's great,' he said, and it came out with more irritation than he had intended.

She closed the book, tucked it beside her on the couch.  She folded her arms around her, hugging herself, smiling at him.  'I guess this isn't your night, Eddie.  Why don't we have a drink?'

'No.'  He did not like that, did not want her being nice to him, forgiving.  Nor did he want a drink.

Her smile, her drunk, amused smile, did not change.  'Then let's talk about something else,' she said.  'What about that case you have?  What's in it?'  Her voice was not prying, only friendly, 'Pencils?'

'That's it,' he said.  'Pencils.'

She raised her eyebrows slightly.  Her voice seemed thick.  'What's in it, Eddie?'

'Figure it out yourself.'  He tossed the case on the couch."

— Walter Tevis, The Hustler, 1959,
    Chapter 11


See, too, the invocation of Apollo in

A Mass for Lucero, as well as 

GENERAL AUDIENCE OF JOHN PAUL II
Wednesday 15 January 2003
:

"The invocation of the Lord is relentless…."

and

JOURNAL ENTRY OF S. H. CULLINANE
Wednesday 15 January 2003
:

Karl Cullinane —
"I will fear no evil, for I am the
meanest son of a bitch in the valley."

Tuesday, February 18, 2003

Tuesday February 18, 2003

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

Fat Man and Dancing Girl

Dance of
Shiva and Kali

Paul Newman as
General Groves

Physicist J. Robert Oppenheimer, portrayed in the film "Fat Man and Little Boy," died on this date in 1967.

He is sometimes called the "father of the A-bomb."  He said that at the time of the first nuclear test he thought of a line from the Sanskrit holy book, the Bhagavad Gita: "I am become death, the destroyer of worlds."  The following gives more details.

The Bomb of the Blue God

M. V. Ramana

Center for Energy and Environmental Studies, Princeton University

Published in SAMAR: South Asian Magazine for Action and Reflection, Issue 13

Oppenheimer had learned Sanskrit at Berkeley so as to read the Gita in the original; he always kept a worn pink copy on the bookshelf closest to his desk. It is therefore likely that he may have actually thought of the original, Sanskrit, verse rather than the English translation. The closest that fits this meaning is in the 32nd verse from the 11th chapter of the Gita.

 kalosmi lokaksaya krt pravrddho

This literally means: I am kAla, the great destroyer of Worlds. What is intriguing about this verse, then, is the interpretation of kAla by Jungk and others to mean death. While death is technically one of the meanings of kAla, a more common one is time.  Indeed, the translations of the Gita by S. Radhakrishnan, A. C. Bhaktivedanta, Nataraja Guru and Eliot Deutsch say precisely that. One exception to this, however, is the 1929 translation by Arthur Ryder. And, indeed, in a 1933 letter to his brother, Robert Oppenheimer does mention that he has "been reading the Bhagavad Gita with Ryder and two other Sanskritists." The misinterpretation, therefore, may not have been the fault of Oppenheimer or Jungk. Nevertheless, the verse does not have anything to do with an apocalyptic or catastrophic destruction, as most people have interpreted it in connection with nuclear weapons. When kAla is understood as time, the meaning is drastically changed to being a reminder of our mortality and finite lifetimes ­ as also the lifetimes of everything else in this world (including plutonium and uranium, despite their long, long, half-lives!). It then becomes more akin to western notions of the "slow march of time" and thus having little to do with the immense destruction caused by a nuclear explosion. While the very first images that arose in the father of the atomic bomb are a somewhat wrong application of Hindu mythology, his recollection of the Bhagavad Gita may have been quite pertinent. As is well known, the Bhagavad Gita was supposedly intended to persuade Arjuna to participate in the Kurukshetra battle that resulted in the killing of thousands. Thus, Oppenheimer may well have been trying to rationalize his involvement in the development of a terrible weapon.

Source: Google cache of
http://www.geocities.com/CollegePark/5409/samar_bluegod.pdf

See also
http://www.samarmagazine.org/archive/article.php?id=36.
 
"KAla" (in the Harvard-Kyoto transliteration scheme) is more familiar to the West in the related form of Kali, a goddess sometimes depicted as a dancing girl; Kali is related to kAla, time, according to one website, as "the force which governs and stops time."  See also the novel The Fermata, by Nicholson Baker.

The fact that Oppenheimer thought of Chapter 11, verse 32, of the Gita may, as a mnemonic device, be associated with the use of the number 1132 in Finnegans Wake.

 See 1132 A. D. & Saint Brighid, and my weblog entries of January 5 (Twelfth Night and the whirligig of time), January 31 (St. Bridget's Eve), and February 1 (St. Bridget's Day), 2003.

Friday, January 31, 2003

Friday January 31, 2003

Filed under: General — Tags: — m759 @ 6:20 am

John O'Hara's Birthday

"We stopped at the Trocadero and there was hardly anyone there.  We had Lanson 1926.  'Drink up, sweet.  You gotta go some.  How I love music.  Frère Jacques, Cuernavaca, ach du lieber August.  All languages.  A walking Berlitz.  Berlitz sounds like you with that champagne, my sweet, or how you're gonna sound.'"

— John O'Hara, Hope of Heaven, Chapter 11, 1938

"And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance."

Acts, Chapter 2, Verse 4

"Lps. The keys to. Given! A way a lone a last a loved a long the

PARIS,
1922-1939."

— James Joyce, conclusion of Finnegans Wake

"Using illustrative material from religion, myth, and culture, he starts with the descent of the dove on Jesus and ends with the poetic ramblings of James Joyce."

Review of a biography of the Holy Spirit

Illustration added at 3:21 AM Feb. 3, 2003:

Firefall

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