Log24

Thursday, November 29, 2012

Lines of Symbols

Filed under: General,Geometry — m759 @ 3:00 PM

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—

IMAGE- Image from Wikipedia articles 'Finite geometry' and 'Hesse configuration.'

The Hesse here is not Hermann, but Otto.

Tuesday, March 26, 2013

Raiders of the Lost Symbols

Filed under: General — m759 @ 10:09 AM

See Lines of Symbols in this journal.

Wednesday, June 5, 2019

The Tigerman Kaballah

Filed under: General — Tags: , , — m759 @ 4:00 AM

See also Life of Pi   in this  journal.

Tuesday, June 4, 2019

Zen and the Art

Filed under: General — Tags: — m759 @ 6:13 PM

Or:  Burning Bright

A post in memory of Chicago architect Stanley Tigerman,
who reportedly died at 88 on Monday.

“Hello the Camp”

Filed under: General — Tags: — m759 @ 12:20 AM

The title is a quotation from the 2015 film "Mojave."

Saturday, October 13, 2018

Location: Endor

Filed under: General — Tags: — m759 @ 2:26 PM

See also Space Writer in this  journal.

Space 101

Filed under: General — Tags: — m759 @ 1:01 PM

Screenshot of a tweet by space writer Shannon Stirone
posted at 10:57 PM ET October 12 —

See also NASA + Wiig.

Stirone has an opinion piece in today's online New York Times  promoting NASA.

Discussing the Hubble Space Telescope, she claims that . . .

"Hubble peers deep into space, patiently collecting the universe’s traveling light,
then delivering it to us in never before seen images: galaxies, supernovas and
nebulae. It is a time machine. And without it we wouldn’t know we are inside
a galaxy that is just one of possibly trillions."

Thursday, September 20, 2018

Clash of the Titans

Filed under: General — Tags: , — m759 @ 6:18 PM

Thursday, July 12, 2018

The Bell

Filed under: General — Tags: , — m759 @ 6:11 PM

Three hidden keys open three secret gates
Wherein the errant will be tested for worthy traits
And those with the skill to survive these straits
Will reach The End where the prize awaits

— Ready Player One , by Ernest Cline

"Look, my favorite expression is,
'When you go up to the bell, ring it,
or don’t go up to the bell.'
We’ve gone too far. We have to ring the bell."

Mel Brooks on "The Producers"
     in The New York Times  today.

A 2016 Scribner edition of Stephen King's IT —

Related material —

Mystery box  merchandise from the 2011  J. J. Abrams film  Super 8 

Wednesday, July 11, 2018

Titans

Filed under: General — Tags: — m759 @ 5:01 PM

"By The Boston Globe

July 10, 2018

The private jets have begun clogging the jetways
in Sun Valley, Idaho, which can only mean one thing:
'Billionaire summer camp’' has begun.

The annual Allen & Company conference, the investment
firm’s invite-only gathering of some of the world’s most
powerful corporate titans, officially begins on Wednesday."

In other news —

"NASHVILLE, Tenn. 

Get ready to see the Titans in training camp."

See also another  post now tagged "Clash of the Titans."

Monday, April 23, 2018

Facets

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

Counting symmetries with the orbit-stabilizer theorem

See also the Feb. 17, 2017, post on Bertram Kostant
as well as "Mathieu Moonshine and Symmetry Surfing."

Saturday, April 7, 2018

Sides

Filed under: General,Geometry — Tags: — m759 @ 11:47 AM

The FBI holding cube in "The Blacklist" —

" 'The Front' is not the whole story . . . ."

— Vincent Canby, New York Times  film review, 1976,
     as quoted in Wikipedia.

See also Solomon's Cube in this  journal.

IMAGE- 'Solomon's Cube'

Webpage demonstrating symmetries of 'Solomon's Cube'

Some may view the above web page as illustrating the
Glasperlenspiel  passage quoted here in Summa Mythologica 

“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above 4x4x4 design cube —

"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."

See also a related remark by Lévi-Strauss in 1955

"…three different readings become possible:
left to right, top to bottom, front to back."

Friday, February 2, 2018

For Plato’s Cave

Filed under: General,Geometry — Tags: , , — m759 @ 12:06 PM

"Plato's allegory of the cave describes prisoners,
inhabiting the cave since childhood, immobile,
facing an interior wall. A large fire burns behind
the prisoners, and as people pass this fire their
shadows are cast upon the cave's wall, and
these shadows of the activity being played out
behind the prisoner become the only version of
reality that the prisoner knows."

— From the Occupy Space gallery in Ireland

IMAGE- Patrick McGoohan as 'The Prisoner,' with lapel button that says '6.'

Sunday, August 27, 2017

Profiling

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

See also earlier posts tagged Profiling Trump.

Friday, August 11, 2017

Symmetry’s Lifeboat

Filed under: General,Geometry — Tags: , , — m759 @ 9:16 PM

A post suggested by the word tzimtzum  (see Wednesday)
or tsimtsum  (see this morning) —

Lifeboat from the Tsimtsum  in Life of Pi  —

Another sort of tsimtsum, contracting infinite space to a finite space —

IMAGE- Desargues's theorem in light of Galois geometry

Thursday, May 25, 2017

Presidential Address of November 19, 1976

Filed under: General — Tags: — m759 @ 2:14 PM

Deep Problems in the Faculty Lounge

Filed under: General — Tags: — m759 @ 7:14 AM

The Story of Six Continues

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

A post of March 22, 2017, was titled "The Story of Six."

Related material from that date —

"I meant… a larger map." — Number Six in "The Prisoner"

Wednesday, April 26, 2017

A Tale Unfolded

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

A sketch, adapted tonight from Girl Scouts of Palo Alto

From the April 14 noon post High Concept

From the April 14 3 AM post Hudson and Finite Geometry

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

From the April 24 evening post The Trials of Device

Pentagon with pentagram    

Note that Hudson's 1905 "unfolding" of even and odd puts even on top of
the square array, but my own 2013 unfolding above puts even at its left.

Wednesday, March 22, 2017

The Story of Six

Filed under: General,Geometry — Tags: , , — m759 @ 8:01 PM

On a psychotherapist who died at 86 on Monday —

"He studied mathematics and statistics at the Courant Institute,
a part of New York University — he would later write   a
mathematical fable, Numberland  (1987)."

The New York Times  online this evening
 


 

From Publishers Weekly

This wry parable by a psychotherapist contains one basic message: though death is inevitable, each moment in life is to be cherished. In the orderly but sterile kingdom of Numberland, digits live together harmoniously under a rigid president called The Professor. Their stable society is held intact by the firm conviction that they are immortal: When has a number ever died? This placid universe is plunged into chaos when the inquisitive hero SIX crosses over into the human world and converses with a young mathematician. This supposedly impossible transition convinces the ruling hierarchy that if SIX can talk to a mortal, then the rest of the numbers are, after all, mortal. The digits conclude that any effort or achievement is pointless in the face of inevitable death, and the cipher society breaks down completely. The solution? Banish SIX to the farthest corners of kingdom. Weinberg (The Heart of Psychotherapy ) uses his fable to gently satirize the military, academics, politicians and, above all, psychiatrists. But his tale is basically inspirational; a triumphant SIX miraculously returns from exile and quells the turmoil by showing his fellow digits that knowledge of one's mortality should enrich all other experiences and that death ultimately provides a frame for the magnificent picture that is life. 

Copyright 1987 Reed Business Information, Inc.

See also The Prisoner in this journal.

Thursday, December 8, 2016

Finite Groups and Their Geometric Representations

Filed under: General,Geometry — Tags: — m759 @ 8:06 AM

The title is that of a presentation by Arnold Emch
at the 1928 International Congress of Mathematicians:

See also yesterday's "Emch as a Forerunner of S(5, 8, 24)."

Related material: Diamond Theory in 1937.

Further remarks:  Christmas 2013 and the fact that
759 × 322,560 = the order of the large Mathieu group  M24 .

Wednesday, November 30, 2016

Language Game

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

Tuesday, September 27, 2016

Chomsky and Lévi-Strauss in China

Filed under: General,Geometry — Tags: — m759 @ 7:31 AM

Or:  Philosophy for Jews

From a New Yorker  weblog post dated Dec. 6, 2012 —

"Happy Birthday, Noam Chomsky" by Gary Marcus—

"… two titans facing off, with Chomsky, as ever,
defining the contest"

"Chomsky sees himself, correctly, as continuing
a conversation that goes back to Plato, especially
the Meno dialogue, in which a slave boy is
revealed by Socrates to know truths about
geometry that he hadn’t realized he knew."

Socrates and the slave boy discussed a rather elementary "truth
about geometry" — A diamond inscribed in a square has area 2
(and side the square root of 2) if the square itself has area 4
(and side 2).

Consider that not-particularly-deep structure from the Meno dialogue
in the light of the following…

The following analysis of the Meno diagram from yesterday's
post "The Embedding" contradicts the Lévi-Strauss dictum on
the impossibility of going beyond a simple binary opposition.
(The Chinese word taiji  denotes the fundamental concept in
Chinese philosophy that such a going-beyond is both useful
and possible.)

The matrix at left below represents the feminine yin  principle
and the diamond at right represents the masculine yang .

      From a post of Sept. 22,
  "Binary Opposition Illustrated" —

A symbol of the unity of yin and yang —

Related material:

A much more sophisticated approach to the "deep structure" of the
Meno diagram —

The larger cases —

The diamond theorem

Monday, September 12, 2016

The Kummer Lattice

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

The previous post quoted Tom Wolfe on Chomsky's use of
the word "array." 

An example of particular interest is the 4×4  array
(whether of dots or of unit squares) —

      .

Some context for the 4×4 array —

The following definition indicates that the 4×4 array, when
suitably coordinatized, underlies the Kummer lattice .

Further background on the Kummer lattice:

Alice Garbagnati and Alessandra Sarti, 
"Kummer Surfaces and K3 surfaces
with $(Z/2Z)^4$ symplectic action." 
To appear in Rocky Mountain J. Math.

The above article is written from the viewpoint of traditional
algebraic geometry. For a less traditional view of the underlying
affine 4-space from finite  geometry, see the website
Finite Geometry of the Square and Cube.

Some further context

"To our knowledge, the relation of the Golay code
to the Kummer lattice is a new observation."

— Anne Taormina and Katrin Wendland,
"The overarching finite symmetry group of
Kummer surfaces in the Mathieu group M24 
"

As noted earlier, Taormina and Wendland seem not to be aware of
R. W. H. T. Hudson's use of the (uncoordinatized*) 4×4 array in his
1905 book Kummer's Quartic Surface.  The array was coordinatized,
i.e. given a "vector space structure," by Cullinane eight years prior to
the cited remarks of Curtis.

* Update of Sept. 14: "Uncoordinatized," but parametrized  by 0 and
the 15 two-subsets of a six-set. See the post of Sept. 13.

The Kingdom of Arrays

Filed under: General — Tags: — m759 @ 11:07 AM

Chomsky and arrays, from Tom Wolfe's 'The Kingdom of Speech'

See also Array  in this journal.

Thursday, September 1, 2016

Bedtime Story

Filed under: General — Tags: — m759 @ 12:00 AM

For midnight retirees —

See also Leibniz medal in this journal.

Friday, August 26, 2016

Wolfe vs. Chomsky

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

1.  Tom Wolfe has a new book on Chomsky, "The Kingdom of Speech."

2.  This suggests a review of a post of Aug. 11, 2014, Syntactic/Symplectic.

To paraphrase Wittgenstein, sentence 1 above is about "correlating in real life"
(cf. Crooked House and Wolfe's From Bauhaus to Our House ), and may be 
compared to sentence 2 above, which links to a sort of "correlating in
mathematics" that is a particular example of the more general sort of
mathematical correlating mentioned by Wittgenstein in 1939.

Thursday, August 4, 2016

Routine

Filed under: General — Tags: — m759 @ 10:30 PM

Peter Gelzinis in the Boston Herald  today

"What has become painfully clear this week
is that there is no Republican campaign for
the presidency. There is only The Donald,
his 
reflex tweets, the folded pieces of paper
he pulls out of his coat pocket and a crazy
stand-up routine that is part Lenny Bruce
and part professor Irwin Corey."

APPLAUSE

Another Diagnostic Jew

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

"Take that baby,  please! "

See also the previous post.

The Soltan Diagnosis

Filed under: General — Tags: — m759 @ 2:26 PM

Prof. Margaret Soltan's psychiatric diagnosis of Donald Trump

Professor Soltan, a fan of James Joyce, would do well
to apply her diagnostic powers to Finnegans Wake , 
a word salad if ever there was one.

Related recommended reading:

Tuesday, May 3, 2016

Symmetry

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

A note related to the diamond theorem and to the site
Finite Geometry of the Square and Cube —

The last link in the previous post leads to a post of last October whose
final link leads, in turn, to a 2009 post titled Summa Mythologica .

Webpage demonstrating symmetries of 'Solomon's Cube'

Some may view the above web page as illustrating the
Glasperlenspiel  passage quoted here in Summa Mythologica 

“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above web page* —

"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."

Update of Sept. 5, 2016 — See also a related remark
by Lévi-Strauss in 1955: "…three different readings
become possible: left to right, top to bottom, front 
to back."

* For the underlying mathematics, see a June 21, 1983, research note

Sunday, December 27, 2015

Rigorous

Filed under: General,Geometry — Tags: , — m759 @ 5:05 AM

A death on Xmas Day

Artist Josefine Lyche

IMAGE- Josefine Lyche bowling, from her Facebook page

Symbol

Monday, November 7, 2011

The X Box

Filed under: Uncategorized — m759 @ 10:30 AM 

"Design is how it works." — Steve Jobs, quoted in
The New York Times Magazine  on St. Andrew's Day, 2003.

The X-Box Sum .

For some background on this enigmatic equation,
see Geometry of the I Ching.

Saturday, December 26, 2015

Midnight Reflection

Filed under: General — Tags: — m759 @ 12:00 AM

Mirror, Mirror, on the wall,
Robbing Peter, paying Paul

Friday, December 25, 2015

At Play in the Fields

Filed under: General,Geometry — Tags: — m759 @ 1:00 PM

See Fields of Force  and recent posts.

From PR Newswire  in July 2011 —

Campus Crusade for Christ Adopts New Name: Cru
60-year-old Int'l Ministry Aims to Increase
Relevance and Global Effectiveness

Related material:

Yin + Yang —

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

Dark Symbol

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

Related material:

The previous post (Bright Symbol) and
a post from Wednesday
December 23, 2015, that links to posts
on Boolean algebra vs. Galois geometry.

"An analogy between mathematics and religion is apposite."

— Harvard Magazine  review by Avner Ash of
     Mathematics without Apologies
     
(Princeton University Press, January 18, 2015)
 

Bright Symbol

Filed under: General — Tags: — m759 @ 12:00 AM

Detail:

Thursday, December 24, 2015

Group Actions…

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

On the Eight

Sunday, December 6, 2015

Form and Idea

Filed under: General,Geometry — Tags: , , , — m759 @ 3:24 PM

"Those early works are succinct and uncompromising
in how they give shape to the philosophical perplexities
of form and idea…."

J. J. Charlesworth, artnet news, Dec. 16, 2014

"Form" and "idea" are somewhat synonymous, 
as opposed to "form" and "substance." A reading:

IMAGE- 'American Hustle' and Art Cube

Discuss.

Monday, November 16, 2015

Good Question.

Filed under: General — Tags: — m759 @ 4:00 PM

YouTube 

Uploaded on Sep 17, 2009

Who'll love the devil?
Who'll sing his song?
Who will love the devil and his song?

"The pictures are understood to have been taken
just a few minutes before three gunmen burst into
the venue at 9.40pm (8.40pm GMT) as the
Californian rock band were launching into one of
their favourites, Kiss The Devil."

Read more: DailyMail.com.

The End of the Tour

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

From this date four years ago —

Click the following image for other examples of "complex style."

Sunday, August 9, 2015

The Cauldron

Filed under: General — Tags: — m759 @ 7:19 AM

From a review of the 2013 film "The Wolverine" —

"The rituals, culture and hierarchies of Japan
have intrigued and baffled the typical Westerner
for centuries …."

Not to mention those of China 

 Hexagram 50:
         
Ding
The Cauldron

Nine is a Vine

Filed under: General — Tags: — m759 @ 6:50 AM

Backstory:  That phrase in this journal.

““The serpent’s eyes shine
As he wraps around the vine….”
– Don Henley

With Derrida, as usual, playing the role of
the serpent, see a philosophical meditation from
October 9, 2014, by a perceptive and thoughtful Eve
that includes the following passage:

“But, before this and first of all, there is
the resistance posed by the work itself,
the hard kernel formed when the intelligibility
of a universal ‘message’ is joined to the
unintelligible secret of a singularity.”

See as well the word “kernel” here.

Cryptomorphisms

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

Backstory:  Other posts tagged “Cryptomorphisms,”
and the word itself in Wikipedia.

Compare and contrast:

Baez and Baez

Hegel and Genet

Heaven and Hell.

Knell

Filed under: General — Tags: , — m759 @ 5:19 AM

From a French dictionary

Tintement lent, sur une seule note,
d’une cloche d’église pour annoncer
l’agonie, la mort ou les obsèques de
quelqu’un.
 

” I go, and it is done: the bell invites me.
Hear it not, Duncan, for it is a knell
That summons thee to heaven, or to hell. “

Wednesday, July 22, 2015

Harvard Death

Filed under: General — Tags: — m759 @ 3:00 AM

Bloomberg.com —
July 21, 2015 — 3:51 PM EDT
Updated on July 21, 2015 — 6:04 PM EDT —

James Rothenberg of Capital Group
Dies at 69 of Heart Attack

"He was  chairman of Harvard Management Co.,
which invests the university’s $36.4 billion endowment."

See also  
The Harvard Crimson —
UPDATED: July 22, 2015, at 1:28 a.m.

"Rothenberg’s death, reportedly of a heart attack,
was unexpected."

He reportedly "chaired Harvard Management Company’s
board of directors from 2004 until his death."

Tuesday, July 21, 2015

“Ragtime” Author Dies at 84

Filed under: General — Tags: — m759 @ 11:55 PM

“…right through hell
     there is a path…”
 
  — Malcolm Lowry

E!

Filed under: General — Tags: — m759 @ 6:19 PM

Wednesday, May 27, 2015

The Coffee Detective

Filed under: General — Tags: , — m759 @ 7:01 AM

See also this morning's earlier posts.

Voiced

Filed under: General — Tags: , — m759 @ 6:06 AM

"J.A.R.V.I.S. (Stands for Just A Rather Very Intelligent System),
also stylized as JARVIS, or Jarvis, is a highly advanced
computerized A.I. developed by Tony Stark, and was voiced
by actor Paul Bettany, to manage almost everything, especially
matters related to technology, in Tony's life."

Happy birthday, Mr. Bettany.

View from the intersection of U.S. Routes 6 and 62.

Grindhouse

Filed under: General — Tags: , — m759 @ 5:12 AM

For Madonna —

Mainlining

Filed under: General — Tags: , — m759 @ 4:45 AM

"Looking for what was, where it used to be" —Wallace Stevens

A section of Route 6 at the former location of an A&P store —

"Wake up and smell the coffee" —

Tuesday, May 26, 2015

Colorful Tales

Filed under: General — Tags: , — m759 @ 9:50 PM

See also the Log24 post from May 18,
the date of Eric Caidin's reported death,
as well as Hexagram 50 and May 14, 2014—
Death in Mathmagic Land.

Thursday, April 16, 2015

National Library Week

Filed under: General,Geometry — Tags: , — m759 @ 7:00 PM

"Celebrate National Library Week 2015 (April 12-18, 2015)
with the theme "Unlimited possibilities @ your library®."

See also Library of Hell.

A page from Princeton University Press on March 18, 2012:

IMAGE- 'Circles Disturbed: The Interplay of Mathematics and Narrative,' p. xvi

… "mathematics and narrative…." (top of page xvii).

I prefer the interplay of Euclidean  and Galois  mathematics.

Forms of Luminosity

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

"Visibilities are not forms of objects, nor even forms
that would show up under light, but rather forms of
luminosity which are created by the light itself and
allow a thing or object to exist only as a flash, sparkle
or shimmer."

— Deleuze, Foucault

Clap if you believe in Plotnitsky .

From his "Teaching" page

Capitalism and Paranoia, Capitalism and Schizophrenia: Foucault, Deleuze, and Modernist Novel. The course offers a comprehensive examination of the works of Michel Foucault and Gilles Deleuze, and of the relationships between their ideas and the culture of modernity and, then, postmodernity, as the culture of capitalism. The course also considers, through the optics of Foucault's and Deleuze's work, how this culture is reflected in modernist and postmodernist novels of the twentieth century, and in the genre of the novel itself, which has been the dominant and indeed defining literary genre of this culture, from early to late capitalism. While Foucault's and Deleuze's work may be seen as a radical philosophical critique of modernity and capitalism by the philosophical means, the novel enacts an analogous and often equally radical literary critique. The works to be discussed include selections from Marx, Nietzsche, and Freud; Foucault's The Order of ThingsDiscipline and Punish, History of Sexuality, vol.1, and selected essays; and substantive selections from such works by Deleuze (and Deleuze and Guattari) as Anti-OedipusA Thousand Plateaus, and Foucault, as well as several shorter essays. Among the works of fiction to be considered are Joyce's A Portrait of the Artist as a Young Man; Kafka's The Trial; Woolf's Orlando; and Pynchon's The Crying of Lot 49.

Monday, April 13, 2015

Is That a Fish in Your Ear?*

Filed under: General — Tags: — m759 @ 7:24 PM

(Continued from April 9)

*… Or a Spearhead?

Hermeneutics for Academics

Filed under: General — Tags: — m759 @ 6:00 PM

Würfel-Märchen  continued 

"Again, you are free to interpret these symbols
 as you like."

See also

Through the Looking Glass: A Sort of Eternity —

and The Library of Hell.

Unorthodox Easter

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

(A sequel to yesterday's Orthodox Easter posts)

This morning's Google News —

The New York Times  on the late Günter Grass —

"Many of Mr. Grass’s books are phantasmagorical
mixtures of fact and fantasy, some of them inviting
comparison with the Latin American style known as
magical realism. His own name for this style was
'broadened reality.'"

From p. xii of the 2005 second edition of a book discussed
in yesterday's Orthodox Easter posts —

(Click image to enlarge.)

Early editions of The Heart of Mathematics  include 
Gary Larson's legendary Hell's Library "Far Side" cartoon. 
Books in Hell's Library include Big Book of Story Problems ,
More Story Problems , and Even More Story Problems .

— Adapted from a review of the 2000 first edition

See also Mathematics and Narrative in this journal.

Wednesday, April 8, 2015

For Students of the Forked Tongue

Filed under: General — Tags: — m759 @ 8:42 PM

IMAGE- Daily Princetonian- U. acquires personal library of philosopher Jacques Derrida

See also "Derrida + Serpent" in this journal.

Tuesday, March 31, 2015

Würfel-Märchen

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

See also Würfel in this journal.

Saturday, December 20, 2014

Dark Fields continued

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

A  Christmas  Ornament  for  Amy  Adams —

Friday, March 28, 2014

Chinese Rune

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

"The Geometry of the I Ching introduces something called the Cullinane sequence
for the hexagrams, and uses a notation based on the four sides and two diagonals
in a square to indicate the yin and yang lines. The resulting rune-like symbols
are intriguing…."

— Andreas Schöter's  I Ching  home page

Actually, the geometry is a bit deeper than the rune-like symbols.

" 'Harriet Burden has been really great to me,'
Rune says in an interview, 'not only as a collector
of my work but as a true supporter. And I think of her
as a muse for the project … ' "

— In The Blazing World , the artist known as Rune

Tuesday, December 31, 2013

Objects of Beauty

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

(Continued)

"I am a town." — Mary Chapin Carpenter

"A town, huh?" — Sydney Prosser

Related material — "Put on your red dress, baby."

Christmas Ornaments

Filed under: General,Geometry — Tags: , — m759 @ 12:25 AM

Continued from December 25

IMAGE- Count rotational symmetries by rotating facets. Illustrated with 'Plato's Dice.'

A link from Sunday afternoon to Nov. 26, 2012,
suggests a review of one of the above structures.

The Dreaming Jewels  cover at left is taken from a review
by Jo Walton at Tor.com—

"This is a book that it’s clearly been difficult
for publishers to market. The covers have been
generally pretty awful, and also very different.
I own a 1975 Corgi SF Collectors Library
paperback that I bought new for 40p in the later
seventies. It’s purple, and it has a slightly grainy
cover, and it matches my editions of The Menace
From Earth
  and A Canticle for Leibowitz .
(Dear old Corgi SF Collectors Editions with their
very seventies fonts! How I imprinted on them at
an early age!) I mention this, however, because
the (uncredited) illustration actually represents and
illustrates the book much better than any of the other
cover pictures I’ve seen. It shows a hexagon with an
attempt at facets, a man, a woman, hands, a snake,
and stars, all in shades of green. It isn’t attractive,
but it wouldn’t put off people who’d enjoy what’s inside
either."

The "hexagon with an attempt at facets" is actually
an icosahedron, as the above diagram shows.
(The geometric part of the diagram is from a Euclid webpage.)

For Plato's dream about these jewels, see his Timaeus.

Thursday, December 26, 2013

Dicey

Filed under: General — Tags: — m759 @ 7:00 PM

For fans of Hunger Games  and Elysium —

Roberta Smith in this evening's* online New York Times

"Especially with the gap between the wealthiest
and everyone else so wide, it is dicey
for a major museum to celebrate the often frivolous
objects on which the rich spend their ever increasing
surplus income. Such a show must be beyond reproach
in every way: transparent in organization, impeccable
in exhibition design, illuminating in catalog and labeling
and, most of all, self-evidently excellent in the quality of
the objects on display."

Da capo:  "I've heard of affairs that are strictly Platonic."

* 5:08 PM ET

How It Works

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

(Continued)

“Design is how it works.” — Steve Jobs

“By far the most important structure in design theory
is the Steiner system S(5, 8, 24).”

— “Block Designs,” by Andries E. Brouwer (Ch. 14 (pp. 693-746),
Section 16 (p. 716) of Handbook of Combinatorics, Vol. I ,
MIT Press, 1995, edited by Ronald L. Graham, Martin Grötschel,
and László Lovász)

For some background on that Steiner system, see the footnote to
yesterday’s Christmas post.

Wednesday, December 25, 2013

Rotating the Facets

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

Previous post

"… her mind rotated the facts…."

Related material— hypercube rotation,* in the context
of rotational symmetries of the Platonic solids:

IMAGE- Count rotational symmetries by rotating facets. Illustrated with 'Plato's Dice.'

"I've heard of affairs that are strictly Platonic"

Song lyric by Leo Robin

* Footnote added on Dec. 26, 2013 —

 See Arnold Emch, "Triple and Multiple Systems, Their Geometric 
 Configurations and Groups
," Trans. Amer. Math. Soc.  31 (1929),
 No. 1, 25–42. 

 On page 42, Emch describes the above method of rotating a
 hypercube's 8 facets (i.e., three-dimensional cubes) to count
 rotational symmetries —

See also Diamond Theory in 1937.

Also on p. 42, Emch mentions work of Carmichael on a
Steiner system with the Mathieu group M11 as automorphism
group, and poses the problem of finding such systems and
groups that are larger. This may have inspired the 1931
discovery by Carmichael of the Steiner system S(5, 8, 24),
which has as automorphisms the Mathieu group M24 .

Rotating the Facts

Filed under: General,Geometry — Tags: , , — m759 @ 4:00 AM

IMAGE- 'American Hustle' and Art Cube

"She never looked up while her mind rotated the facts,
trying to see them from all sides, trying to piece them
together into theory. All she could think was that she
was flunking an IQ test."

— Steve Martin, An Object of Beauty

"So you should not feel so all alone…"
— Adapted song lyric

Saturday, August 17, 2013

The Story of N…

Filed under: General — Tags: — m759 @ 8:28 PM

Continues.

IMAGE- Marissa Mayer on numbers in Vogue magazine

— Marissa Mayer in the current Vogue  online

Tuesday, August 13, 2013

The Story of N

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

(Continued from this morning)

http://www.log24.com/log/pix11/110107-The1950Aleph-Sm.jpg

The above stylized "N," based on
an 8-cycle in the 9-element Galois field
GF(9), may also be read as
an Aleph.

Graphic designers may prefer a simpler,
bolder version:

Plan 9

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

(Continued from August 28 last year)

Backstory— 

Reflections from today's date, August 13, in 2003, that included
the following remark by Aldous Huxley on an artist's work:

"All the turmoil, all the emotions of the scenes
have been digested by the mind into a
grave intellectual whole. It is as though
Bach had written the 1812 Overture."

Related art—

Josefine Lyche, from her 2013 Crackquarelle  series:

IMAGE- From the 2013 Josefine Lyche 'Crackquarelle' series

Steven H. Cullinane, The Story of N ,
from The Misalignment of Mars and Venus series:

http://www.log24.com/log/pix11B/110720-Misaligned.jpg

See, too, previous posts on The Story of N.

Friday, June 14, 2013

Amy’s Shadow

Filed under: General — Tags: , — m759 @ 2:18 PM

Why knows what evil lurks…? — The Shadow

Backstory: "Amy Adams" + Shadow in this journal.

Related material —

Amy Adams as Lois Lane:

In the new Amy Adams version, Superman's Smallville mom
is played by Diane  Lane.

Lane also played George Reeves's sugar mommy
in the 2006 film Hollywoodland .

Ben Affleck and Diane Lane at the 2006 Venice Film Festival
premiere of  Hollywoodland :

See, too, today's previous post, and Amy Adams as Lacey Yeager
in the yet-to-be-made film version of An Object of Beauty .

Saturday, May 11, 2013

Core

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

Promotional description of a new book:

"Like Gödel, Escher, Bach  before it, Surfaces and Essences  will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core— the incessant, unconscious quest for strong analogical links to past experiences— this book puts forth a radical and deeply surprising new vision of the act of thinking."

"Like Gödel, Escher, Bach  before it…."

Or like Metamagical Themas

Rubik core:

Swarthmore Cube Project, 2008

Non- Rubik cores:

Of the odd  nxnxn cube:

Of the even  nxnxn cube:

The image “http://www.log24.com/theory/images/cube2x2x2.gif” cannot be displayed, because it contains errors.

Related material: The Eightfold Cube and

"A core component in the construction
is a 3-dimensional vector space  over F."

—  Page 29 of "A twist in the M24 moonshine story," 
      by Anne Taormina and Katrin Wendland.
      (Submitted to the arXiv on 13 Mar 2013.)

Saturday, March 2, 2013

Discourse

Filed under: General — Tags: — m759 @ 2:04 PM

(Continued)

"No puzzle has exercised more fascination
upon writers interested in the history of mathematics."

— Sir Thomas Little Heath, quoted by Mark Dominus in
his journal "The Universe of Discourse" on January 22, 2009.

If synchronicity is admitted to the universe of discourse,
a post in this  journal on that same date may be of interest.

Life of Pi

Filed under: General — Tags: — m759 @ 1:06 AM

Earlier

Princeton Harvard Eating —

Harvard Math Department Pi Day event

"But the tigers come at night,
With their voices soft as thunder."

Les Miserables

Sunday, February 10, 2013

Semiotics for Kearney*

Filed under: General — Tags: — m759 @ 4:16 PM

Click image for some background.

Context:

and the following post from last October:

* Who is Kearney? See, for instance, this book.

Tuesday, February 5, 2013

Arsenal

Filed under: General,Geometry — Tags: , — m759 @ 1:06 PM

The previous post discussed some fundamentals of logic.

The name "Boole" in that post naturally suggests the
concept of Boolean algebra . This is not  the algebra
needed for Galois geometry . See below. 

IMAGE- Logic related to 'the arsenal of algebraic analysis tools for fields'

Some, like Dan Brown, prefer to interpret symbols using
religion, not logic. They may consult Diamond Mandorla,
as well as Blade and Chalice, in this journal.

See also yesterday's Universe of Discourse.

Entities

Filed under: General — Tags: — m759 @ 12:24 PM

From January 26, 2013

IMAGE- Yahoo CEO Marissa Mayer at Davos and the ontology of entities

Related material: "universe of discourse"

Monday, February 4, 2013

The Universe of Discourse

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

A Raven's Remark—

Related material:

Fish Story, Object Lesson, The Universe of Discourse,
Archimedes's Approximation of Pi, and

Sunday, February 3, 2013

Trophy

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

From the 1984 New Orleans film Tightrope

http://www.log24.com/log/pix11A/110615-EastwoodFootball400w.jpg

Related material: Walking the Tightrope and Transgressing.

Sunday, November 18, 2012

Kernel

Filed under: General — m759 @ 5:24 AM

(Continued)

Rachel Dodes in The Wall Street Journal
on All Souls' Day, 2012

"In one of the first lines uttered by Daniel Day-Lewis, playing Abraham Lincoln in the new Steven Spielberg film opening Nov. 9, he says, 'I could be bounded in a nutshell, and count myself a king of infinite space— were it not that I have bad dreams.'

The line was ripped straight from 'Hamlet,' by Lincoln's favorite writer, William Shakespeare. Tony Kushner, the Pulitzer Prize-winning playwright ('Angels in America') who wrote the script for the film, says that Shakespeare, much like Lincoln, 'had extraordinary mastery over the darkest parts of the human spirit.'"

The above quotation omits Shakespeare's words prefacing the nutshell part— "O God."

These same words in a different tongue—  "Hey Ram"— have often been quoted as the last words of Gandhi. (See yesterday's noon post.)

"… for the Highest Essence (brahman ),
which is the core of the world, is identical
with the Highest Self (ātman ), the kernel
of man's existence."

— Heinrich Zimmer, Myths and Symbols
in Indian Art and Civilization
, Pantheon
Books, 1946, page 142 

Related material: A post linked to here on Friday night
that itself links to a different Shakespeare speech.

Thursday, March 1, 2012

Block That Metaphor:

Filed under: General,Geometry — m759 @ 11:09 PM

The Cube Model and Peano Arithmetic

The eightfold cube  model of the Fano plane may or may not have influenced a new paper (with the date Feb. 10, 2011, in its URL) on an attempted consistency proof of Peano arithmetic—

The Consistency of Arithmetic, by Storrs McCall

"Is Peano arithmetic (PA) consistent?  This paper contains a proof that it is. …

Axiomatic proofs we may categorize as 'syntactic', meaning that they concern only symbols and the derivation of one string of symbols from another, according to set rules.  'Semantic' proofs, on the other hand, differ from syntactic proofs in being based not only on symbols but on a non-symbolic, non-linguistic component, a domain of objects.    If the sole paradigm of 'proof ' in mathematics is 'axiomatic proof ', in which to prove a formula means to deduce it from axioms using specified rules of inference, then Gödel indeed appears to have had the last word on the question of PA-consistency.  But in addition to axiomatic proofs there is another kind of proof.   In this paper I give a proof of PA's consistency based on a formal semantics for PA.   To my knowledge, no semantic consistency proof of Peano arithmetic has yet been constructed.

The difference between 'semantic' and 'syntactic' theories is described by van Fraassen in his book The Scientific Image :

"The syntactic picture of a theory identifies it with a body of theorems, stated in one particular language chosen for the expression of that theory.  This should be contrasted with the alternative of presenting a theory in the first instance by identifying a class of structures as its models.  In this second, semantic, approach the language used to express the theory is neither basic nor unique; the same class of structures could well be described in radically different ways, each with its own limitations.  The models occupy centre stage." (1980, p. 44)

Van Fraassen gives the example on p. 42 of a consistency proof in formal geometry that is based on a non-linguistic model.  Suppose we wish to prove the consistency of the following geometric axioms:

A1.  For any two lines, there is at most one point that lies on both.
A2.  For any two points, there is exactly one line that lies on both.
A3.  On every line there lie at least two points.

The following diagram shows the axioms to be consistent:

Figure 1
 

The consistency proof is not a 'syntactic' one, in which the consistency of A1-A3 is derived as a theorem of a deductive system, but is based on a non-linguistic structure.  It is a semantic as opposed to a syntactic proof.  The proof constructed in this paper, like van Fraassen's, is based on a non-linguistic component, not a diagram in this case but a physical domain of three-dimensional cube-shaped blocks. ….

… The semantics presented in this paper I call 'block semantics', for reasons that will become clear….  Block semantics is based on domains consisting of cube-shaped objects of the same size, e.g. children's wooden building blocks.  These can be arranged either in a linear array or in a rectangular array, i.e. either in a row with no space between the blocks, or in a rectangle composed of rows and columns.  A linear array can consist of a single block, and the order of individual blocks in a linear or rectangular array is irrelevant. Given three blocks A, B and C, the linear arrays ABC and BCA are indistinguishable.  Two linear arrays can be joined together or concatenated into a single linear array, and a rectangle can be re-arranged or transformed into a linear array by successive concatenation of its rows.  The result is called the 'linear transformation' of the rectangle.  An essential characteristic of block semantics is that every domain of every block model is finite.  In this respect it differs from Tarski’s semantics for first-order logic, which permits infinite domains.  But although every block model is finite, there is no upper limit to the number of such models, nor to the size of their domains.

It should be emphasized that block models are physical models, the elements of which can be physically manipulated.  Their manipulation differs in obvious and fundamental ways from the manipulation of symbols in formal axiomatic systems and in mathematics.  For example the transformations described above, in which two linear arrays are joined together to form one array, or a rectangle of blocks is re-assembled into a linear array, are physical transformations not symbolic transformations. …" 

Storrs McCall, Department of Philosophy, McGill University

See also…

Wednesday, January 11, 2012

Cuber

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

"Examples galore of this feeling must have arisen in the minds of the people who extended the Magic Cube concept to other polyhedra, other dimensions, other ways of slicing.  And once you have made or acquired a new 'cube'… you will want to know how to export a known algorithm , broken up into its fundamental operators , from a familiar cube.  What is the essence of each operator?  One senses a deep invariant lying somehow 'down underneath' it all, something that one can’t quite verbalize but that one recognizes so clearly and unmistakably in each new example, even though that example might violate some feature one had thought necessary up to that very moment.  In fact, sometimes that violation is what makes you sure you’re seeing the same thing , because it reveals slippabilities you hadn’t sensed up till that time….

… example: There is clearly only one sensible 4 × 4 × 4 Magic Cube.  It is the  answer; it simply has the right spirit ."

— Douglas R. Hofstadter, 1985, Metamagical Themas: Questing for the Essence of Mind and Pattern  (Kindle edition, locations 11557-11572)

See also Many Dimensions in this journal and Solomon's Cube.

Monday, January 9, 2012

M Theory

Filed under: General — Tags: — m759 @ 7:59 AM

Yesterday's All About Eve post featured Pope John Paul II
with his close friend and confidant Jerzy Kluger.
Their counterparts Xavier and Magneto in the recent film
"X-Men: First Class," together with Catholic doctrine on telepathy,
suggest  the following meditations.

Douglas Hofstadter on interpenetration

IMAGE- 'Interpenetration' in Douglas Hofstadter's 'I Am a Strange Loop'

— as well as Trinity in this journal.

First the punchline—

Script M (interpreted by some scanners as '771.')

Then the joke.

Thursday, December 22, 2011

The Speed of Thought

Filed under: General — Tags: — m759 @ 4:18 AM

"As if an apparently meaningless frame of reference,
traveling at the speed of thought, suddenly became relevant…."

— Stephen Rachman, "Lost in Translation"

Unclean Frame

IMAGE- The perception of doors in the film 'Sunshine Cleaning'

Detail from the film "Sunshine Cleaning"

Clean Frame

IMAGE- Part of 'Grids, You Say?' installation by Josefine Lyche

See also Psychic Art and "The Speed of Thought."

For another form of psychic art, see Game of Shadows.

Wednesday, December 21, 2011

The Purloined Diamond

Filed under: General — Tags: , — m759 @ 9:48 AM

Stephen Rachman on "The Purloined Letter"

"Poe’s tale established the modern paradigm (which, as it happens, Dashiell Hammett and John Huston followed) of the hermetically sealed fiction of cross and double-cross in which spirited antagonists pursue a prized artifact of dubious or uncertain value."

For one such artifact, the diamond rhombus formed by two equilateral triangles, see Osserman in this journal.

Some background on the artifact is given by John T. Irwin's essay "Mysteries We Reread…" reprinted in Detecting Texts: The Metaphysical Detective Story from Poe to Postmodernism .

Related material—

Mathematics vulgarizer Robert Osserman died on St. Andrew's Day, 2011.

A Rhetorical Question

Osserman in 2004

"The past decade has been an exciting one in the world of mathematics and a fabulous one (in the literal sense) for mathematicians, who saw themselves transformed from the frogs of fairy tales— regarded with a who-would-want-to-kiss-that aversion, when they were noticed at all— into fascinating royalty, portrayed on stage and screen….

Who bestowed the magic kiss on the mathematical frog?"

A Rhetorical Answer

http://www.log24.com/log/pix11C/111130-SunshineCleaning.jpg

Above: Amy Adams in "Sunshine Cleaning"

Monday, December 19, 2011

X Marks a Spot

Filed under: General — Tags: , — m759 @ 11:30 AM

(Where Entertainment is God, continued)

IMAGE- LA Times on Korean transition and Galaxy Nexus

Related material— The Nexus (Jan. 8, 2010).

That post contains the following—

"A Nexus is a place equidistant from the five elements as explained in the TV series Charmed . Using this as a point of reference, it is quite possible that there could be several Nexus points of power scattered throughout the world, though rare."

Nexus (Charmed) in Wikipedia

Happy birthday, Alyssa Milano.

Bumped

Filed under: General — Tags: , — m759 @ 1:22 AM

http://www.log24.com/log/pix11C/111219-Bumped-NYTobits1AM.jpg


Related material— Hitchens on Heaven—

http://www.log24.com/log/pix11C/111219-HitchensOnHeaven.jpg

Sunday, December 18, 2011

Dateline Seoul

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

For those who prefer their news straight

http://www.log24.com/log/pix11C/111218-SeoulNews.jpg

Happy birthday, Steven Spielberg.

Transition

Filed under: General — Tags: — m759 @ 7:25 PM

"Vaclav Havel oversaw a bumpy transition…." —New York Times  today

"Is it over— or is it just beginning?" —"All About Eve"

Vets Club

Filed under: General — Tags: — m759 @ 1:13 PM

Continued from August 16

http://www.log24.com/log11/saved/111218-NYTobits102PM-360w.jpg

Closure

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

Christopher Hitchens on J. K. Rowling—

“We must not let in daylight upon magic,” as Walter Bagehot remarked in another connection, and the wish to have everything clarified is eventually self-defeating in its own terms. In her correct determination to bring down the curtain decisively, Rowling has gone further than she should, and given us not so much a happy ending as an ending which suggests that evil has actually been defeated (you should forgive the expression) for good.

Greater authors— Arthur Conan Doyle most notably— have been in the same dilemma when seeking closure. And, like Conan Doyle, Rowling has won imperishable renown for giving us an identifiable hero and a fine caricature of a villain, and for making a fictional bit of King’s Cross station as luminous as a certain address on nearby Baker Street. It is given to few authors to create a world apart, and to populate it as well as illustrate it in the mind.

"A fictional bit of King's Cross Station"—

Throughout the series, Harry has traveled to King's Cross Station, either to depart for Hogwarts or return to London on the Hogwarts Express. The station has always symbolized the crossroad between the Muggle world and the Wizarding realm and Harry's constant shuffling between, and his conflict with, the two extremes. As Harry now finds himself at a transition point between life and death, it is purely to be expected that he would see it within his own mind as a simulacrum of that station. And though Dumbledore assures Harry that he (Harry) is not actually dead, it seems Harry can choose that option if he so wishes. Harry has literally and figuratively been stripped bare, and must decide either to board a train that will transport him to the "other side", or return to the living world…. — Wikibooks.org

Saturday, December 17, 2011

Lining the Train

Filed under: General — Tags: — m759 @ 7:30 PM

IMAGE- Wilfred Owen, 'faces grimly gay' in 'The Send-Off'

See also Thursday morning's "As Is."

Friday, December 16, 2011

Take Your Pick

Filed under: General — Tags: , — m759 @ 1:31 PM

Two recent quotes in this journal—

December 14

"Hoban once ruefully observed that death would be a good career move:
'People will say, "Yes, Hoban, he seems an interesting writer, let’s look at him again."'"

December 15

"This poem is concerned with language on a very plain level."

— "Paradoxes and Oxymorons" in Shadow Train

Michael Kinsley in The New York Times  on Sunday, May 13, 2007

Kinsley on the career of Christopher Hitchens—

Interesting! …. Interesting!! …. Interesting!!! …. Interesting!!!!

Where was this train heading?

Kinsley on a book in which Hitchens …

… pronounces the movie “It’s a Wonderful Life” “engaging but abysmal” (a typical Hitchens aside: cleverly paradoxical? witlessly oxymoronic? take your pick)….

Midnight in LA

Filed under: General — Tags: — m759 @ 3:00 AM

The Sherlock Holmes film "A Game of Shadows"
is apparently showing around midnight
(12:00 AM PST, 3:00 AM EST) tonight in LA
at the ArcLight Hollywood.

IMAGE- A Jesuit on words and shadows

This passage was quoted here on Sunday, November 27, this year.

For other words related to that date, see tonight's 11:02 post.

The serpent's eyes shine
As he wraps around the vine
In the Garden of Allah

— Don Henley

Friday

Filed under: General — Tags: — m759 @ 2:56 AM

"Just the facts." — Attributed to Joe Friday

A search in this journal in honor of the late
Christopher Hitchens yields links to two of his reviews—
a review of the author of The Girl with the Dragon Tattoo  and
a review of a work by a rather different author—

Harry Potter and the Deathly Hallows .

Thursday, December 15, 2011

As Is

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

What "As" Is —

Image- The Three-Point Line: A Finite Projective Geometry

"This poem is concerned with language on a very plain level."

Shadow Train

"You got to ride it like you find it."
Song lyric

Related entertainment —

IMAGE- Sherlock Holmes: A Game of Shadows

Saturday, November 12, 2011

The Boys from Uruguay

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

(Continued from September 7th, 2002)

Happy Birthday, Wallace Shawn!

http://www.log24.com/log/pix11C/111112-SpeedOfThought-Shawn.jpg

Shawn in "The Speed of Thought,"
a 2011 film by Evan Oppenheimer.

Uruguay is featured in that film.

See also Lichtung!.

Friday, September 23, 2011

Pallbearer

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

For those who prefer Nick Stahl (star of "The Speed of Thought"— see previous post)
to Keanu Reeves as a savior figure, here is a still from another film with Stahl as savior—

IMAGE- Schwarzenegger carries coffin in 'Terminator 3: Rise of the Machines'

Backstory —

IMAGE- NY Times obits for Julius Blank and A. Richard Turner

See also a Log24 post from the day of Blank's death, The Uploading.

Times Square Church

Filed under: General — Tags: , — m759 @ 2:56 AM

Continued from April 29, 2011
 

http://www.log24.com/log/pix11B/110923-ReleaseDate.jpg


Related material— Inception and Feed Them on Your Dreams.

Tuesday, July 26, 2011

Venus at St. Anne’s

Filed under: General — Tags: — m759 @ 7:20 PM

The title is that of a chapter in the C.S. Lewis classic  That Hideous Strength .

A search suggested by this afternoon's NY Lottery four-digit number,
8002, yields a forum post at WebOfNarcissism.com—

"a book that changed my life"—

"Here is the book:

http://www.amazon.com/What-Loved-Novel-Siri-Hustvedt/dp/0312421192

Warning.  It is dark.  But it is also lovely."

Whether it is deep as well, the reader may judge.

The quoted review is from a discussion by an anonymous user
of her relationship with someone called N. See also, in this journal,
The Story of N.

Happy St. Anne's Day.

Wednesday, July 20, 2011

Cover Art

Filed under: General — Tags: , , — m759 @ 8:00 AM

The Misalignment of Mars and Venus

A death in Sarasota on Sunday leads to a weblog post from Tuesday
that suggests a review of Dan Brown's graphic philosophy—

From The Da Vinci Code :

Langdon pulled a pen from his pocket.  “Sophie are you familiar with the modern icons for male and female?”  He drew the common male symbol ♂ and female symbol ♀.

Of course,” she said.

“These,” he said quietly, are not the original symbols for male and female.  Many people incorrectly assume the male symbol is derived from a shield and spear, while the female represents a mirror reflecting beauty.  In fact, the symbols originated as ancient astronomical symbols for the planet-god Mars and the planet-goddess Venus.  The original symbols are far simpler.”  Langdon drew another icon on the paper.

 

 

 

“This symbol is the original icon for male ,” he told her.  “A rudimentary phallus.”

“Quite to the point,” Sophie said.

“As it were,” Teabing added.

Langdon went on.  “This icon is formally known as the blade , and it represents aggression and manhood.  In fact, this exact phallus symbol is still used today on modern military uniforms to denote rank.”

“Indeed.”  Teabing grinned.  “The more penises you have, the higher your rank.  Boys will be boys.”

Langdon winced.  “Moving on, the female symbol, as you might imagine, is the exact opposite.”  He drew another symbol on the page.  “This is called the chalice .”

 

 

Sophie glanced up, looking surprised.

Langdon could see she had made the connection.  “The chalice,” he said, “resembles a cup or vessel, and more important, it resembles the shape of a woman’s womb.  This symbol communicates femininity, womanhood, and fertility.”

Langdon's simplified symbols, in disguised form, illustrate
a musical meditation on the misalignment of Mars and Venus—

http://www.log24.com/log/pix11B/110720-Misaligned.jpg

This was adapted from an album cover by "Meyers/Monogram"—

http://www.log24.com/log/pix11B/110720-BladeAndChalice-RomeoAndJuliet-500w.jpg

  See also Secret History and The Story of N.

Thursday, July 14, 2011

ART WARS continued:

Filed under: General — Tags: — m759 @ 5:01 AM

The Bauhaus Dance

http://www.log24.com/log/pix11B/110714-BauhausRoof.jpg

See also The Ya Ya Mandorla

http://www.log24.com/log/pix11B/110714-VesicaXOR.jpg

 

http://www.log24.com/log/pix11B/110714-Michelangelo.jpg

Tuesday, July 12, 2011

An Object of Beauty and…

Filed under: General — Tags: — m759 @ 1:23 PM

http://www.log24.com/log/pix11B/110712-ObjectOfBeauty.jpg

 

The Usual Suspects

http://www.log24.com/log/pix11B/110712-NYnews.jpg

 

http://www.log24.com/log/pix11B/110711-ANDOR.jpg

http://www.log24.com/log/pix11B/110712-HotRock.jpg

For some background, click on the diamond above.

See also Harrison Ford in "Harvard Defeats Holy Cross."

Wednesday, June 22, 2011

ART WARS continued

Filed under: General,Geometry — Tags: — m759 @ 8:06 PM

This evening's New York Times  obituaries—

http://www.log24.com/log/pix11A/110622-NYTobits720PM.jpg

A work of art suggested by the first and third items above—

http://www.log24.com/log/pix11A/110614-TarantinoCar.jpg

I prefer a work of art that is structurally similar—

IMAGE- The Klein group as art

and is related to a picture, Portrait of O, from October 1, 1983—

IMAGE- A work by Cullinane pirated by artist Steve RIchards in his contribution to London's 'Piracy Project'

For a recent unexpected Web appearance of Portrait of O,
aee Abracadabra from the midnight of June 18-19.

Tuesday, June 14, 2011

Expressionistic Depth

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

http://www.log24.com/log/pix11A/110614-DoubleDown.jpg

Update of 7 AM —

Carl Gardner's 1956 hit "Down in Mexico" was featured in the following Hollywood classic:

http://www.log24.com/log/pix11A/110614-TarantinoCar.jpg

Click image for video.

Thursday, May 5, 2011

Beyond Forgetfulness

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

From this journal on July 23, 2007

It is not enough to cover the rock with leaves.
We must be cured of it by a cure of the ground
Or a cure of ourselves, that is equal to a cure

Of the ground, a cure beyond forgetfulness.
And yet the leaves, if they broke into bud,
If they broke into bloom, if they bore fruit
,

And if we ate the incipient colorings
Of their fresh culls might be a cure of the ground.

– Wallace Stevens, "The Rock"

This quotation from Stevens (Harvard class of 1901) was posted here on when Daniel Radcliffe (i.e., Harry Potter) turned 18 in July 2007.

Other material from that post suggests it is time for a review of magic at Harvard.

On September 9, 2007, President Faust of Harvard

"encouraged the incoming class to explore Harvard’s many opportunities.

'Think of it as a treasure room of hidden objects Harry discovers at Hogwarts,' Faust said."

That class is now about to graduate.

It is not clear what "hidden objects" it will take from four years in the Harvard treasure room.

Perhaps the following from a book published in 1985 will help…

http://www.log24.com/log/pix11A/110505-MetamagicalIntro.gif

The March 8, 2011, Harvard Crimson  illustrates a central topic of Metamagical Themas , the Rubik's Cube—

http://www.log24.com/log/pix11A/110427-CrimsonAtlas300w.jpg

Hofstadter in 1985 offered a similar picture—

http://www.log24.com/log/pix11A/110505-RubikGlobe.gif

Hofstadter asks in his Metamagical  introduction, "How can both Rubik's Cube and nuclear Armageddon be discussed at equal length in one book by one author?"

For a different approach to such a discussion, see Paradigms Lost, a post made here a few hours before the March 11, 2011, Japanese earthquake, tsunami, and nuclear disaster—

http://www.log24.com/log/pix11A/110427-ParadigmsLost.jpg

Whether Paradigms Lost is beyond forgetfulness is open to question.

Perhaps a later post, in the lighthearted spirit of Faust, will help. See April 20th's "Ready When You Are, C.B."

Sunday, April 17, 2011

Sunday School

Filed under: General,Geometry — Tags: — m759 @ 7:00 AM

Apollo and the Tricksters

From The Story of N (Oct. 15, 2010)—

Roberta Smith on what she calls "endgame art"—

"Fear of form above all means fear of compression— of an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible."

Margaret Atwood on tricksters and art—

"If it’s a seamless whole you want, pray to Apollo."

Here is some related material In memory of CIA officer Clare Edward Petty, who died at 90 on March 18—

A review of a sort of storyteller's MacGuffin — the 3×3 grid. This is, in Smith's terms, an "artistic focus" that appears  to be visually comprehensible but is not as simple as it seems.

The Hesse configuration can serve as more than a sort of Dan Brown MacGuffin. As a post of January 14th notes, it can (rather fancifullly) illustrate the soul—

http://www.log24.com/log/pix11/110417-AlderTilleyColoredSm.jpg

" … I feel I understand
Existence, or at least a minute part
Of my existence, only through my art,
In terms of combinational delight…."

— Vladimir Nabokov, Pale Fire

Friday, March 18, 2011

Defining Configurations*

Filed under: General,Geometry — m759 @ 7:00 PM

The On-Line Encyclopedia of Integer Sequences has an article titled "Number of combinatorial configurations of type (n_3)," by N.J.A. Sloane and D. Glynn.

From that article:

  • DEFINITION: A combinatorial configuration of type (n_3) consists of an (abstract) set of n points together with a set of n triples of points, called lines, such that each point belongs to 3 lines and each line contains 3 points.
  • EXAMPLE: The unique (8_3) configuration consists of the triples 125, 148, 167, 236, 278, 347, 358, 456.

The following corrects the word "unique" in the example.

http://www.log24.com/log/pix11/110320-MoebiusKantorConfig500w.jpg

* This post corrects an earlier post, also numbered 14660 and dated 7 PM March 18, 2011, that was in error.
   The correction was made at about 11:50 AM on March 20, 2011.

_____________________________________________________________

Update of March 21

The problem here is of course with the definition. Sloane and Glynn failed to include in their definition a condition that is common in other definitions of configurations, even abstract or purely "combinatorial" configurations. See, for instance, Configurations of Points and Lines , by Branko Grunbaum (American Mathematical Society, 2009), p. 17—

In the most general sense we shall consider combinatorial (or abstract) configurations; we shall use the term set-configurations as well. In this setting "points" are interpreted as any symbols (usually letters or integers), and "lines" are families of such symbols; "incidence" means that a "point" is an element of a "line". It follows that combinatorial configurations are special kinds of general incidence structures. Occasionally, in order to simplify and clarify the language, for "points" we shall use the term marks, and for "lines" we shall use blocks. The main property of geometric configurations that is preserved in the generalization to set-configurations (and that characterizes such configurations) is that two marks are incident with at most one block, and two blocks with at most one mark.

Whether or not omitting this "at most one" condition from the definition is aesthetically the best choice, it dramatically changes the number  of configurations in the resulting theory, as the above (8_3) examples show.

Update of March 22 (itself updated on March 25)

For further background on configurations, see Dolgachev—

http://www.log24.com/log/pix11/110322-DolgachevIntro.gif

Note that the two examples Dolgachev mentions here, with 16 points and 9 points, are not unrelated to the geometry of 4×4 and 3×3 square arrays. For the Kummer and related 16-point configurations, see section 10.3, "The Three Biplanes of Order 4," in Burkard Polster's A Geometrical Picture Book  (Springer, 1998). See also the 4×4 array described by Gordon Royle in an undated web page and in 1980 by Assmus and Sardi. For the Hesse configuration, see (for instance) the passage from Coxeter quoted in Quaternions in an Affine Galois Plane.

Update of March 27

See the above link to the (16,6) 4×4 array and the (16,6) exercises using this array in R.D. Carmichael's classic Introduction to the Theory of Groups of Finite Order  (1937), pp. 42-43. For a connection of this sort of 4×4 geometry to the geometry of the diamond theorem, read "The 2-subsets of a 6-set are the points of a PG(3,2)" (a note from 1986) in light of R.W.H.T. Hudson's 1905 classic Kummer's Quartic Surface , pages 8-9, 16-17, 44-45, 76-77, 78-79, and 80.

Sunday, December 12, 2010

Brightness at Noon continued…

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

A picture one might view as
related to the novel An Object of Beauty
and the film "The Object of Beauty" —

The 3x3 square

Click for some background.

"If it's a seamless whole you want,
 pray to Apollo." — Margaret Atwood

Tuesday, November 23, 2010

Tale

Filed under: General — Tags: , — m759 @ 8:00 PM

A reviewer says Steve Martin finds in his new novel An Object of Beauty  "a sardonic morality tale."

From this journal on the day The Cube  was published (see today's Art Object ) —

Monday February 20, 2006

m759 @ 12:00 AM

The Past Revisited

From Log24 a year ago on this date, a quote from Many Dimensions  (1931), by Charles Williams:

“Lord Arglay had a suspicion that the Stone would be purely logical.  Yes, he thought, but what, in that sense, were the rules of its pure logic?”

For the rest of the story, see the downloadable version at Project Gutenberg of Australia.

See also a post on Mathematics and Narrative from Nov. 14, 2009.

That post compares characters in Many Dimensions  to those in Logicomix

Whitehead and Russell, 'Logicomix' page 181

Art Object

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

There is more than one way
to look at a cube.

http://www.log24.com/log/pix10B/101123-plain_cube_200x227.gif

 From Cambridge U. Press on Feb. 20, 2006 —

IMAGE- 'Cambridge Tracts in Mathematics 168: The Cube'

and from this journal on June 30, 2010 —

In memory of Wu Guanzhong, Chinese artist
who died in Beijing on June 25, 2010

Image-- The Dream of the Expanded Field

See also this journal on Feb. 20, 2006
(the day The Cube  was published).

Monday, November 22, 2010

Backstory

Filed under: General,Geometry — Tags: — m759 @ 8:48 AM

Steve Martin's new novel An Object of Beauty  will be released tomorrow.

"The most charmingly rendered female schemer since Truman Capote's Holly Golightly."
Elle  magazine

"Martin compresses the wild and crazy end of the millennium
 and finds in this piercing novel a sardonic morality tale….
 Exposes the sound and fury of the rarified Manhattan art world."
Publishers Weekly

"Like Steve Martin's Shopgirl , this very different novel will captivate your attention from start to finish."
— Joyce Carol Oates

Martin on his character Ray Porter in the novella Shopgirl  (published Oct. 11, 2000)—

http://www.log24.com/log/pix10B/101122-MartinShopgirl-loq.jpg

"He said, 'I wrote a piece of code
 that they just can’t seem to do without.'
 He was a symbolic logician. That was his career…."

As the above review notes, Martin's new book is about art at the end of the millennium.

See also Art Wars: Geometry as Conceptual Art
and some of my own notes from 2000 (March 9) in "Is Nothing Sacred?"

Some related material —

A paperback with a striking cover (artist unknown)—

http://www.log24.com/log/pix10B/101027-LangerSymbolicLogic.jpg

Note that the background may be constructed from
any of four distinct motifs. For another approach to these
motifs in a philosophical context, see June 8, 2010.

"Visual forms— lines, colors, proportions, etc.— are just as capable of articulation , i.e. of complex combination, as words. But the laws that govern this sort of articulation are altogether different from the laws of syntax that govern language. The most radical difference is that visual forms are not discursive . They do not present their constituents successively, but simultaneously, so the relations determining a visual structure are grasped in one act of vision."

Susanne K. Langer, Philosophy in a New Key

Friday, October 15, 2010

Mathematics and Narrative, continued

Filed under: General — Tags: — m759 @ 6:29 AM
 

The Story of N

http://www.log24.com/log/pix09/090109-Stories.jpg

Roberta Smith in the New York Times  of July 7, 2006

Art Review

Endgame Art? It's Borrow, Sample and Multiply in an Exhibition at Bard College

"… The show has an endgame, end-time mood, as if we are looking at the end of the end of the end of Pop, hyperrealism and appropriation art. The techniques of replication and copying have become so meticulous that they are beside the point. This is truly magic realism: the kind you can't see, that has to be explained. It is also a time when artists cultivate hybridism and multiplicity and disdain stylistic coherence, in keeping with the fashionable interest in collectivity, lack of ego, the fluidity of individual identity. But too often these avoidance tactics eliminate the thread of a personal sensibility or focus.

I would call all these strategies fear of form, which can be parsed as fear of materials, of working with the hands in an overt way and of originality. Most of all originality. Can we just say it? This far from Andy Warhol and Duchamp, the dismissal of originality is perhaps the oldest ploy in the postmodern playbook. To call yourself an artist at all is by definition to announce a faith, however unacknowledged, in some form of originality, first for yourself, second, perhaps, for the rest of us.

Fear of form above all means fear of compression— of an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible. With a few exceptions, forms of collage and assemblage dominate this show: the putting together (or simply putting side by side) of existing images and objects prevails. The consistency of this technique in two and three dimensions should have been a red flag for the curators. Collage has driven much art since the late 1970's. Lately, and especially in this exhibition, it often seems to have become so distended and pulled apart that its components have become virtually autonomous and unrelated, which brings us back to square one. This is most obvious in the large installations of graphic works whose individual parts gain impact and meaning from juxtaposition but are in fact considered distinct artworks."

Margaret Atwood on art and the trickster

"The pleasures of fabulation, the charming and playful lie— this line of thought leads Hyde* to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning 'to join,' 'to fit,' and 'to make.'  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart."

* Lewis Hyde, Trickster Makes This World: Mischief, Myth, and Art,  Farrar Straus & Giroux, January 1998

Smith mentions "an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible."

Atwood mentions "a seamless whole."

For some related remarks, see "A Study in Art Education" and the central figure pictured above. (There "N" can stand for "number," "nine," or "narrative.")

Sunday, August 15, 2010

The Game

Filed under: General — Tags: — m759 @ 11:07 PM
'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse

We shall now give a brief summary of the beginnings of the Glass Bead Game. It appears to have arisen simultaneously in Germany and in England. In both countries, moreover, it was originally a kind of exercise employed by those small groups of musicologists and musicians who worked and studied in the new seminaries of musical theory. If we compare the original state of the Game with its subsequent developments and its present form, it is much like comparing a musical score of the period before 1500, with its primitive notes and absence of bar lines, with an eighteenth-century score, let alone with one from the nineteenth with its confusing excess of symbols for dynamics, tempi, phrasing, and so on, which often made the printing of such scores a complex technical problem.

The Game was at first nothing more than a witty method for developing memory and ingenuity among students and musicians. And as we have said, it was played both in England and Germany before it was ‘invented’ here in the Musical Academy of Cologne, and was given the name it bears to this day, after so many generations, although it has long ceased to have anything to do with glass beads.

The inventor, Bastian Perrot of Calw, a rather eccentric but clever, sociable, and humane musicologist, used glass beads instead of letters, numerals, notes, or other graphic symbols. Perrot, who incidentally has also bequeathed to us a treatise on the Apogee and Decline of Counterpoint, found that the pupils at the Cologne Seminary had a rather elaborate game they used to play. One would call out, in the standardized abbreviations of their science, motifs or initial bars of classical compositions, whereupon the other had to respond with the continuation of the piece, or better still with a higher or lower voice, a contrasting theme, and so forth. It was an exercise in memory and improvisation quite similar to the sort of thing probably in vogue among ardent pupils of counterpoint in the days of Schütz, Pachelbel, and Bach — although it would then not have been done in theoretical formulas, but in practice on the cembalo, lute, or flute, or with the voice.

Bastian Perrot in all probability was a member of the Journeyers to the East. He was partial to handicrafts and had himself built several pianos and clavichords in the ancient style. Legend has it that he was adept at playing the violin in the old way, forgotten since 1800, with a high-arched bow and hand-regulated tension of the bow hairs. Given these interests, it was perhaps only natural that he should have constructed a frame, modeled on a child’s abacus, a frame with several dozen wires on which could be strung glass beads of various sizes, shapes, and colors. The wires corresponded to the lines of the musical staff, the beads to the time-values of the notes, and so on. In this way he could represent with beads musical quotations or invented themes, could alter, transpose, and develop them, change them and set them in counterpoint to one another. In technical terms this was a mere plaything, but the pupils liked it; it was imitated and became fashionable in England too. For a time the game of musical exercises was played in this charmingly primitive manner. And as is so often the case, an enduring and significant institution received its name from a passing and incidental circumstance. For what later evolved out of that students’ sport and Perrot’s bead-strung wires bears to this day the name by which it became popularly known, the Glass Bead Game.

Hermann Hesse

“For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.”

— “Albertus Secundus,” epigraph to The Glass Bead Game

From DownloadThat.com

(Click to enlarge.)

http://www.log24.com/log/pix10B/100815-ThePaletteSm.jpg

Tuesday, November 3, 2009

Summa Mythologica

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

Book review by Jadran Mimica in Oceania, Vol. 74, 2003:

"In his classic essay of 1955 'The Structural Study of Myth' Levi-Strauss came up with a universal formula of mythopeic dynamics

[fx(a) : fy(b) :: fx(b) : fa-1(y)]

that he called canonical 'for it can represent any mythic transformation'. This formulation received its consummation in the four massive Mythologiques volumes, the last of which crystallises the fundamental dialectics of mythopoeic thought: that there is 'one myth only' and the primal ground of this 'one' is 'nothing'. The elucidation of the generative matrix of the myth-work is thus completed as is the self-totalisation of both the thinker and his object."

So there.

At least one mathematician has claimed that the Levi-Strauss formula makes sense. (Jack Morava, arXiv pdf, 2003.)

I prefer the earlier (1943) remarks of Hermann Hesse on transformations of myth:

"…in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created."

Tuesday, September 15, 2009

Tuesday September 15, 2009

Filed under: General — Tags: — m759 @ 12:00 AM
 
RAIDERS
http://www.log24.com/images/spacer12w6h.bmp
OF THE LOST
DINGBAT
 
Table of Unicode dingbats

My personal favorite:

Dingbat 275A, 
"heavy vertical bar"–

Unicode symbol 'heavy vertical bar'

Cf. March 7, 2003.
 

Friday, August 28, 2009

Friday August 28, 2009

Filed under: General — m759 @ 3:09 AM
Rites of Passage

“Things fall apart;
   the centre cannot hold….

Part I:

“Inside the church, the grief was real. Sen. Edward Kennedy’s voice caught as he read his lovely eulogy, and when he was done, Caroline Kennedy Schlossberg stood up and hugged him. She bravely read from Shakespeare’s ‘The Tempest‘ (‘Our revels now are ended. We are such stuff as dreams are made on‘). Many of the 315 mourners, family and friends of the Kennedys and Bessettes, swallowed hard through a gospel choir’s rendition of ‘Amazing Grace,’ and afterward, they sang lustily as Uncle Teddy led the old Irish songs at the wake.”

Newsweek magazine, issue dated August 2, 1999

Part II:

The Ba gua (Chinese….) are eight diagrams used in Taoist cosmology to represent a range of interrelated concepts. Each consists of three lines, each either ‘broken’ or ‘unbroken,’ representing a yin line or a yang line, respectively. Due to their tripartite structure, they are often referred to as ‘trigrams’ in English. —Wikipedia

Part III:

3x3 array of symbols, cover of 'Dorm Room Feng Shui'

Above: detail from the cover of

Bagua in Brief, from 'Dorm Room Feng Shui'
Figures explaining 'Dorm Room Feng Shui'

Friday, January 9, 2009

Friday January 9, 2009

Filed under: General — Tags: , — m759 @ 5:01 PM
Stories
for Mary Karr

"In reality, my prose books
probably sit between
I Was a Teenage Sex Slave
and some other contemporary
memoir written in five minutes…."

Mary Karr in the NY Times
of July 6, 2007

Story of M, Story of N, Story of O

See also
Ballet Blanc
and the true story
0, 1, 2, 3, ….

"In a dream scenario, my memoirs…
would find another shelf.
They’d sit between St. Augustine
  and Nabokov’s Speak, Memory…."

— Mary Karr, loc. cit.

Recall the
mnemonic rhyme
"Nine is a Vine."

Sunday, May 25, 2008

Sunday May 25, 2008

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

 "Confusion is nothing new."
— Song lyric, Cyndi Lauper  

Part I:
Magister Ludi

Hermann Hesse's 1943 The Glass Bead Game (Picador paperback, Dec. 6, 2002, pp. 139-140)–

"For the present, the Master showed him a bulky memorandum, a proposal he had received from an organist– one of the innumerable proposals which the directorate of the Game regularly had to examine. Usually these were suggestions for the admission of new material to the Archives. One man, for example, had made a meticulous study of the history of the madrigal and discovered in the development of the style a curved that he had expressed both musically and mathematically, so that it could be included in the vocabulary of the Game. Another had examined the rhythmic structure of Julius Caesar's Latin and discovered the most striking congruences with the results of well-known studies of the intervals in Byzantine hymns. Or again some fanatic had once more unearthed some new cabala hidden in the musical notation of the fifteenth century. Then there were the tempestuous letters from abstruse experimenters who could arrive at the most astounding conclusions from, say, a comparison of the horoscopes of Goethe and Spinoza; such letters often included pretty and seemingly enlightening geometric drawings in several colors."

Part II:
A Bulky Memorandum

From Siri Hustvedt, author of Mysteries of the Rectangle: Essays on Painting (Princeton Architectural Press, 2005)– What I Loved: A Novel (Picador paperback, March 1, 2004, page 168)–

A description of the work of Bill Wechsler, a fictional artist:

"Bill worked long hours on a series of autonomous pieces about numbers. Like O's Journey, the works took place inside glass cubes, but these were twice as large– about two feet square. He drew his inspiration from sources as varied as the Cabbala, physics, baseball box scores, and stock market reports. He painted, cut, sculpted, distorted, and broke the numerical signs in each work until they became unrecognizable. He included figures, objects, books, windows, and always the written word for the number. It was rambunctious art, thick with allusion– to voids, blanks, holes, to monotheism and the individual, the the dialectic and yin-yang, to the Trinity, the three fates, and three wishes, to the golden rectangle, to seven heavens, the seven lower orders of the sephiroth, the nine Muses, the nine circles of Hell, the nine worlds of Norse mythology, but also to popular references like A Better Marriage in Five Easy Lessons and Thinner Thighs in Seven Days. Twelve-step programs were referred to in both cube one and cube two. A miniature copy of a book called The Six Mistakes Parents Make Most Often lay at the bottom of cube six. Puns appeared, usually well disguised– one, won; two, too, and Tuesday; four, for, forth; ate, eight. Bill was partial to rhymes as well, both in images and words. In cube nine, the geometric figure for a line had been painted on one glass wall. In cube three, a tiny man wearing the black-and-white prison garb of cartoons and dragging a leg iron has

— End of page 168 —

opened the door to his cell. The hidden rhyme is "free." Looking closely through the walls of the cube, one can see the parallel rhyme in another language: the German word drei is scratched into one glass wall. Lying at the bottom of the same box is a tiny black-and-white photograph cut from a book that shows the entrance to Auschwitz: ARBEIT MACHT FREI. With every number, the arbitrary dance of associations worked togethere to create a tiny mental landscape that ranged in tone from wish-fulfillment dream to nightmare. Although dense, the effect of the cubes wasn't visually disorienting. Each object, painting, drawing, bit of text, or sculpted figure found its rightful place under the glass according to the necessary, if mad, logic of numerical, pictorial, and verbal connection– and the colors of each were startling. Every number had been given a thematic hue. Bill had been interested in Goethe's color wheel and in Alfred Jensen's use of it in his thick, hallucinatory paintings of numbers. He had assigned each number a color. Like Goethe, he included black and white, although he didn't bother with the poet's meanings. Zero and one were white. Two was blue. Three was red, four was yellow, and he mixed colors: pale blue for five, purples in six, oranges in seven, greens in eight, and blacks and grays in nine. Although other colors and omnipresent newsprint always intruded on the basic scheme, the myriad shades of a single color dominated each cube.

The number pieces were the work of a man at the top of his form. An organic extension of everything Bill had done before, these knots of symbols had an explosive effect. The longer I looked at them, the more the miniature constructions seemed on the brink of bursting from internal pressure. They were tightly orchestrated semantic bombs through which Bill laid bare the arbitrary roots of meaning itself– that peculiar social contract generated by little squiggles, dashes, lines, and loops on a page."

Part III:
Wechsler Cubes

(named not for
Bill Wechsler, the
fictional artist above,
but for the non-fictional
   David Wechsler) —

From 2002:

Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest.


Part IV:
A Magic Gallery
 
Log24, March 4, 2004
 

ZZ
WW

Figures from the
Kaleidoscope Puzzle
of Steven H. Cullinane:


Poem by Eugen Jost:
Zahlen und Zeichen,
Wörter und Worte

Mit Zeichen und Zahlen
vermessen wir Himmel und Erde
schwarz
auf weiss
schaffen wir neue Welten
oder gar Universen


 Numbers and Names,
Wording and Words


With numbers and names
we measure heaven and earth
black
on white
we create new worlds
and universes


English translation
by Catherine Schelbert



A related poem:

Alphabets
by Hermann Hesse

From time to time
we take our pen in hand
and scribble symbols
on a blank white sheet
Their meaning is
at everyone's command;
it is a game whose rules
are nice and neat.

But if a savage
or a moon-man came
and found a page,
a furrowed runic field,
and curiously studied
lines and frame:
How strange would be
the world that they revealed.
a magic gallery of oddities.
He would see A and B
as man and beast,
as moving tongues or
arms or legs or eyes,
now slow, now rushing,
all constraint released,
like prints of ravens'
feet upon the snow.
He'd hop about with them,
fly to and fro,
and see a thousand worlds
of might-have-been
hidden within the black
and frozen symbols,
beneath the ornate strokes,
the thick and thin.
He'd see the way love burns
and anguish trembles,
He'd wonder, laugh,
shake with fear and weep
because beyond this cipher's
cross-barred keep
he'd see the world
in all its aimless passion,
diminished, dwarfed, and
spellbound in the symbols,
and rigorously marching
prisoner-fashion.
He'd think: each sign
all others so resembles
that love of life and death,
or lust and anguish,
are simply twins whom
no one can distinguish…
until at last the savage
with a sound
of mortal terror
lights and stirs a fire,
chants and beats his brow
against the ground
and consecrates the writing
to his pyre.
Perhaps before his
consciousness is drowned
in slumber there will come
to him some sense
of how this world
of magic fraudulence,
this horror utterly
behind endurance,
has vanished as if
it had never been.
He'll sigh, and smile,
and feel all right again.

— Hermann Hesse (1943),
"Buchstaben," from
Das Glasperlenspiel,
translated by
Richard and Clara Winston

Friday, May 9, 2008

Friday May 9, 2008

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM
Kernel of Eternity
continued from April 29

 
The Klein Group: The four elements in four colors, with black points representing the identity


Wikipedia on the Klein group (denoted V, for Vierergruppe):

In this representation, V is a normal subgroup of the alternating group A4 (and also the symmetric group S4) on 4 letters. In fact, it is the kernel of a surjective map from S4 to S3. According to Galois theory, the existence of the Klein four-group (and in particular, this representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals.

For radicals of another sort, see A Logocentric Meditation, A Mass for Lucero, and Steven Erlanger in The New York Times— "France Still Divided Over Lessons of 1968 Unrest."

The Klein Group as Kernel
of a Map from S4 to S3:

Portrait of O:  The Klein Group as Kernel in  the Symmetric Group of Degree Four

Click to enlarge.

For those who prefer Galois's
politics to his mathematics,
there is
MAY 68: STREET POSTERS
FROM THE PARIS REBELLION

at London's Southbank Centre
 (May 1 – June 1, 2008).

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