Log24

Saturday, March 23, 2024

Alpha Bets

Filed under: General — Tags: , — m759 @ 6:31 am

"So you wanna play with magic?" — Katy Perry

Wednesday, September 27, 2023

The Alpha Bet

Filed under: General — Tags: — m759 @ 8:58 pm

"AI Studio will be available in alpha to start,
and Meta says that it’ll scale the toolkit further
beginning next year."

Thursday, April 20, 2023

Alphabet Meets Gestalt . . .

Filed under: General — Tags: , , — m759 @ 2:25 pm

Continued from April 18 .

"Working with words to create art
and working with your hands to create art
seem like two separate activities to me."

Cover artist, The New Yorker , on April 17

See also Alphabet Blocks in this  journal
as well as Escher's Verbum.

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

Tuesday, April 18, 2023

Alphabet Meets Gestalt

Filed under: General — Tags: , , — m759 @ 11:25 pm

From May 19, 2010 —

Meanwhile . . .

Sunday, January 1, 2023

Alpha

Filed under: General — Tags: — m759 @ 6:18 am

Wallace Stevens —

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
Of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

Wednesday, September 14, 2022

For Odd Jean-Luc: Alpha Alpha Double Feature

Filed under: General — Tags: — m759 @ 7:16 am

. . . as well as starring in Alpha Dog and in . . .

Monday, September 7, 2015

Alpha Bet

Filed under: General — m759 @ 7:59 pm

The title pun is from a letter about Google's new parent
company, named "Alphabet" by its founders.

Related material:  Alpha and Omega in this journal.

Wednesday, August 12, 2015

The Alphabet of Things

Filed under: General — m759 @ 8:48 am

Thursday, February 5, 2015

Alphabet Soup

Filed under: General — Tags: — m759 @ 11:03 am

Sunday, September 18, 2011

Alpha and Omega

Filed under: General,Geometry — Tags: , — m759 @ 2:22 am

http://www.log24.com/log/pix11B/110918-AlphaAndOmega.jpg

A transcription—

"Now suppose that α  is an element of order 23 in M 24 ; we number the points of Ω
as the projective line , 0, 1, 2, … , 22 so that α : i i  + 1 (modulo 23) and fixes . In
fact there is a full L 2 (23) acting on this line and preserving the octads…."

— R. T. Curtis, "A New Combinatorial Approach to M 24 ,"
Mathematical Proceedings of the Cambridge Philosophical Society  (1976), 79: 25-42

Friday, February 23, 2024

North by Northwest: The Local Edge

Filed under: General — Tags: — m759 @ 3:18 pm

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

 

— "Is this your business?"

— "No, but this  is."

Sunday, December 24, 2023

Let Us Now Praise Famous Omega*

Filed under: General — Tags: — m759 @ 2:35 am

   * The title is of course a reference to the Knoxville of the previous post.

Sunday, November 5, 2023

Old-Guy Aesthetics

Filed under: General — Tags: — m759 @ 7:50 am

For Guy Fawkes Day, images from first and last posts —
an alpha and an omega of sorts —
from this journal in the month of December 2021 . . .





Some remarks on an artist who reportedly died
on the second day of that month —

Saturday, November 4, 2023

Patterning

Filed under: General — Tags: — m759 @ 1:59 am

Tuesday, October 31, 2023

“Omega is as real  as we need it to be.”
— “The Osterman Weekend”

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

For art more closely related to the title "Alpha and Omega,"
see a different view of the above Hoyersten exhibition.

Saturday, September 30, 2023

The Algorithm and Mrs. Davis

Filed under: General — Tags: , , , — m759 @ 8:39 am

On the recent Peacock series "Mrs. Davis" —

"The algorithm is known as Mrs. Davis and is
the all-seeing, all-knowing, not-quite-all-merciful
manifestation of artificial intelligence to whom
humanity has plighted its troth in this eight-part
manifestation of real intelligence from creators 
Tara Hernandez and Damon Lindelof."
— John Anderson in The Wall Street Journal ,
    Tuesday, April 18, 2023

For The Algorithm , see last evening's Michaelmas post and . . .

For a different Mrs. Davis,  see  . . .

From Tom McCarthy's review yesterday of The Maniac , a novel about 1940s social life at Los Alamos —

"The mathematician Martin Davis’s wife, Lydia, storms out of a Trinity dinner party, condemning the men’s failure to fully take on board the consequences of their atom splitting. Besides sharing her name with our own age’s great translator of Blanchot and Proust, this Lydia Davis is a textile artist — a hanging detail that points back toward the novel’s many looms and weavings.

For the Greeks, the fates spinning the threads of human lives were female (as Conrad knew, recasting them as Belgian secretaries in 'Heart of Darkness'). So was Theseus’ wool-ball navigator, Ariadne. And so, too, was the Ithacan ur-weaver Penelope, whose perpetual making and unraveling of her tapestry beat Gödel to an incompleteness theory by thousands of years.

'Text,' by the way, means something woven, from which we get 'textile.' It might just be that Penelope was not only testing her own version of the ontological limit, but also embedding it — in absent form, a hole — within the weft and warp of what we would eventually call the novel."

Martin Davis reportedly died this year on New Year's Day.

This  journal on that date —

Saturday, April 29, 2023

Seeking Limits

Filed under: General — Tags: — m759 @ 8:11 pm

"Even though he’s not currently part of a Star Wars  movie,
Lindelof seems open to working on the franchise down the line.
'Will I get back in line outside the club and try to get back in again?
Of course,' he added. '[Star Wars ] was the alpha and the omega.
It’s the first movie I saw in a movie theater. I love all of the storytelling
in that world. If at first you don’t succeed, try, try again. Or again, again,
try, as Yoda would say.' ” — Jay Peters, The Verge , April 28, 2023

Wednesday, April 19, 2023

Remystifying A.D.

Filed under: General — m759 @ 11:42 am

Demystifying Alpha Delta, the original 'Animal House'

"Dartmouth officially recognized its chapter of
the Alpha Delta Phi fraternity in 1846."

Harvard, on the other hand . . .

All the Way to the Bank

Thursday, March 9, 2023

Meditation on a URL:
Putting the “de” in
https://www.hu-berlin.de/

Filed under: General — Tags: — m759 @ 9:28 am

From other posts tagged Tetrahedron vs. Square —

A Scholium for Chomsky

The ABC of words —

A nutshell —

Wednesday, January 25, 2023

Victor’s Spoils:  Space, Space, Space

Filed under: General — m759 @ 2:51 am

A check of the phrase "memory-alpha" in the above URL
reveals that it comes from a 1969 Star Trek episode 
written by Shari Lewis and her husband Jeremy Tarcher.

Tarcher reportedly died on Sunday, Sept. 20, 2015.
From this journal on that date

On the editor of the anthology Space, Space, Space :

"Sloane’s writing is drum-tight, but his approach
is looser; he pulls the reader in and then begins
turning up the heat. He understood that before
a pot can boil, it must simmer." — Stephen King

Of related literary interest to fans of the late Russell Banks,
whose novel title Cloudsplitter  refers to Mt. Marcy, the 
highest mountain in New York State —

Marcy was a New York State politician who is said to have
coined the above phrase 

"to the victor go the spoils."

Monday, January 23, 2023

“You’re so vain…” — Song lyric

Filed under: General — m759 @ 3:22 pm

A remark by Esther Dyson on Jan. 19:

See as well the above group-theory author here  on Jan. 19.

Related material:  "Same Staircase, DIfferent Day."

Wednesday, November 16, 2022

“A wondrous woven magic” — Song lyric

Filed under: General — Tags: — m759 @ 12:17 pm

Monday, June 20, 2022

Deep Space

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

From https://memory-alpha.fandom.com/wiki/Leslie_Engelberg

Leslie Engelberg (born 16 June 1975 …)
(also known as Leslie Kendall and Leslie Kendall Dye)
is the actress who played Yareth in the 
Star Trek: Deep Space Nine  first season episode "Vortex".

She has an essay in The Atlantic  dated  

"The complexity of the human heart
can be expressed in the arrangement
of one’s books."

Wednesday, April 20, 2022

Physics for Poets

Filed under: General — Tags: , , — m759 @ 9:23 am

Excerpt from a long poem by Eliza Griswold


The square array above does not  contain Arfken's variant
labels
for ρ1, ρ2, and ρ3, although those variant labels were
included in Arfken's 1985 square array and in Arfken's 1985
list of six anticommuting sets, copied at MathWorld as above.
The omission of variant labels prevents a revised list of the
six anticommuting sets from containing more  distinct symbols
than there are matrices.

Revised list of anticommuting sets:

α1   α2   α3  ρ2  ρ3

γ1   γ2   γ3   ρ1   ρ

δ δ2   δ ρ1   ρ2 

α1    γ1   δσ2  σ3 

α  γ2   δσ1   σ3

α  γ3   δ3  σ1   σ2  .

Context for the poem: Quark Rock.
Context for the physics: Dirac Matrices.

Thursday, February 17, 2022

Space Memorial

Filed under: General — m759 @ 1:27 pm

"FILE – Retired Sandinista Gen. Hugo Torres poses for portrait
at his home, in Managua, Nicaragua, May 2, 2018."

— Photo caption from a Feb. 12 Washington Post  obituary 

Also on May 2, 2018 —

Related theology —

Tuesday, February 23, 2016

Revolutionary

Filed under: General — m759 @ 7:14 PM 

From New York Times  obituary today —

"The Rev. Fernando Cardenal, a son of privilege
who embraced Latin America’s poor as a revolutionary
priest and brazenly defied Pope John Paul II’s order to
quit Nicaragua’s leftist cabinet in the 1980s, died on
Saturday in Managua. He was 82."

Photo caption from the same obituary —

"Fernando Cardenal in 1990. As education minister of
Nicaragua under the Sandinistas in the 1980s, he
oversaw a sweeping campaign credited with reducing
illiteracy to 13 percent from 51 percent."

This alleged literacy improvement makes him sound like
Protestant  revolutionary.

For a Catholic  view of literacy, see The Gutenberg Galaxy .

See also the post Being Interpreted (Aug. 14, 2015) — 

Sunday, November 14, 2021

Greek-Letter Structures

Filed under: General — m759 @ 6:29 pm
 

Α, ϴ, Ω 

Alpha,    Theta,    Omega

Related line

"Falls  the  Shadow."
 

Also from a Culture Desk  of sorts:

Related art — Background colors for the letters in the NPR logo

Thursday, September 9, 2021

Set Design for an 18-Hour Play

Filed under: General — Tags: , — m759 @ 9:25 pm

Source data for an Instagram story this evening —

An image from the story itself —

Related reading — "Flame Alphabet" in this journal.

From that link . . .

See also . . .

Thursday, July 2, 2020

Two Bits

Filed under: General — m759 @ 7:18 pm

“…problems can be solved by manipulating just two symbols, 1 and 0….”
— George Johnson, obituary of Claude Shannon

“The female and the male continue this charming dance, populating
the world with all living beings.”
— Leonard Shlain, The Alphabet Versus the Goddess,
Penguin Arkana paperback, 1999, Chapter 17,
“Lingam/Yoni” 

Sunday, March 8, 2020

Joyce and Einstein on the Beach

Filed under: General — m759 @ 12:49 am

"Hello! Kinch here. Put me on to Edenville.
Aleph, alpha: nought, nought, one." 

"A very short space of time through very short times of space….
Am I walking into eternity along Sandymount strand?"

— James Joyce, Ulysses , Proteus chapter

See also the previous post and Masks of the Illuminati .

Sunday, December 29, 2019

Springer Link

Filed under: General — Tags: , , , — m759 @ 5:08 pm

Related reading

"I closed my eyes and saw the number 137—
so very close to the reciprocal of alpha—
on the chest of the runner in Van Cortlandt Park.
Should I start the story there? "

— Alpert, Mark.  Saint Joan of New York
(Science and Fiction) (p. 103).
Springer International Publishing. Kindle edition. 

Cover detail:

See as well St. Joan in this  journal.

Wednesday, October 9, 2019

Philosophical Infanticide

Filed under: General — Tags: — m759 @ 5:51 am

From Wallace Stevens —

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
Of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

From The Point  magazine yesterday, October 8, 2019
Parricide:  On Irad Kimhi's Thinking and Being .
Book review by Steven Methven.

The conclusion:

"Parricide is nothing that the philosopher need fear . . . .
What sustains can be no threat. Perhaps what the
unique genesis of this extraordinary work suggests is that
the true threat to philosophy is infanticide."

This remark suggests revisiting a post from Monday

Monday, October 7, 2019

Berlekamp Garden vs. Kinder Garten

Filed under: General — m759 @ 11:00 PM

Stevens's Omega and Alpha (see previous post)
suggest a review.

Omega — The Berlekamp Garden. 
                  See Misère Play (April 8, 2019).
Alpha  —  The Kinder Garten. 
                  See Eighfold Cube.

. . . .

Monday, October 7, 2019

Berlekamp Garden vs. Kinder Garten

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

Stevens's Omega and Alpha (see previous post) suggest a review.

Omega — The Berlekamp Garden.  See Misère Play (April 8, 2019).
Alpha  —  The Kinder Garten.  See Eighfold Cube.

Illustrations —

The sculpture above illustrates Klein's order-168 simple group.
So does the sculpture below.

Froebel's Third Gift: A cube made up of eight subcubes  

Cube Bricks 1984 —

An Approach to Symmetric Generation of the Simple Group of Order 168

Lenz

Filed under: General — m759 @ 2:56 pm

Or:  Je repars .

From Wallace Stevens —

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
Of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

Mathematician Hanfried Lenz reportedly died in Berlin on June 1, 2013.

This journal that weekend

Wednesday, October 2, 2019

Social Climbing

Filed under: General — Tags: — m759 @ 2:13 pm

"When the queen came, they said she was wanton.
Or a witch, or a saint."

Ursula Whitcher,  "Alphabet of Signs"

Related images —

Friday, September 27, 2019

The Black List

Filed under: General — Tags: , , — m759 @ 11:46 am

"… Max Black, the Cornell philosopher, and others have pointed out
how 'perhaps every science must start with metaphor and end with
algebra, and perhaps without the metaphor there would never have
been any algebra' …."

— Max Black, Models and Metaphors, Cornell U. Press, 1962,
page 242, as quoted in Dramas, Fields, and Metaphors, by 
Victor Witter Turner, Cornell U. Press, paperback, 1975, page 25
 

Metaphor —

Algebra —

The 16 Dirac matrices form six anticommuting sets of five matrices each (Arfken 1985, p. 214):

1. alpha_1alpha_2alpha_3alpha_4alpha_5,

2. y_1y_2y_3y_4y_5,

3. delta_1delta_2delta_3rho_1rho_2,

4. alpha_1y_1delta_1sigma_2sigma_3,

5. alpha_2y_2delta_2sigma_1sigma_3,

6. alpha_3y_3delta_3sigma_1sigma_2.

SEE ALSO:  Pauli Matrices

REFERENCES:

Arfken, G. Mathematical Methods for Physicists, 3rd ed.  Orlando, FL: Academic Press, pp. 211-217, 1985.

Berestetskii, V. B.; Lifshitz, E. M.; and Pitaevskii, L. P. "Algebra of Dirac Matrices." §22 in Quantum Electrodynamics, 2nd ed.  Oxford, England: Pergamon Press, pp. 80-84, 1982.

Bethe, H. A. and Salpeter, E. Quantum Mechanics of One- and Two-Electron Atoms.  New York: Plenum, pp. 47-48, 1977.

Bjorken, J. D. and Drell, S. D. Relativistic Quantum Mechanics.  New York: McGraw-Hill, 1964.

Dirac, P. A. M. Principles of Quantum Mechanics, 4th ed.  Oxford, England: Oxford University Press, 1982.

Goldstein, H. Classical Mechanics, 2nd ed.  Reading, MA: Addison-Wesley, p. 580, 1980.

Good, R. H. Jr. "Properties of Dirac Matrices." Rev. Mod. Phys. 27, 187-211, 1955.

Referenced on Wolfram|Alpha:  Dirac Matrices

CITE THIS AS:

Weisstein, Eric W.  "Dirac Matrices."

From MathWorld— A Wolfram Web Resource. 
http://mathworld.wolfram.com/DiracMatrices.html

Desiring the exhilarations of changes:
The motive for metaphor, shrinking from
The weight of primary noon,
The A B C of being,

The ruddy temper, the hammer
Of red and blue, the hard sound—
Steel against intimation—the sharp flash,
The vital, arrogant, fatal, dominant X.

— Wallace Stevens, "The Motive for Metaphor"

Monday, August 19, 2019

A Couple of Tots

Filed under: General — Tags: , — m759 @ 10:15 pm

The title is from the post "Child's Play" of May 21, 2012 . . .

"It seems that only one course is open to the philosopher
who values knowledge and truth above all else. He must
refuse to accept from the champions of the forms the
doctrine that all reality is changeless [and exclusively
immaterial], and he must turn a deaf ear to the other party
who represent reality as everywhere changing [and as only
material]. Like a child begging for 'both', he must declare
that reality or the sum of things is both at once  [το όν τε και
το παν συναμφότερα] (Sophist  246a-249d)."

Related material —

"Schoolgirl Space: 1984 Revisited" (July 9, 2019) and
posts tagged Tetrahedron vs. Square.

Sunday, December 30, 2018

Meanwhile, in a different New Yorker department…

Filed under: General — m759 @ 4:00 am

From Annals of Technology

Thursday, December 27, 2018

A Candle for Lily

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

Detail —

See also . . . http://m759.net/wordpress/?s=Alpha+Omega .

Tuesday, October 9, 2018

Nicht Spielerei

Filed under: General — m759 @ 10:48 pm

Continues.

A YouTube description —

"Walter Klien performing Mozart's 12 Variations in C Major
on the French Song: "Ah vous dirai-je, Maman" K.265 on
the piano. Used in Twinkle Twinkle Little Star, Baa Baa
Black Sheep, and the Alphabet Song."

https://www.youtube.com/watch?v=fS7yiD6cz8A 

"Published on May 23, 2010"

See also this  journal on May 23, 2010 —

Posts now tagged Death Story.

Related material —

Thursday, October 4, 2018

Mage Studies: Art vs. Bullshit

Filed under: General — Tags: — m759 @ 10:32 pm

Art:

From an October 3 post

Bullshit:

From an academic's website —

Wednesday, October 3, 2018

Adamantine Meditation

Filed under: General,Geometry — Tags: — m759 @ 12:24 pm

http://www.log24.com/log/pix10B/101127-LukasiewiczAdamantine.jpg

A Catholic philosopher —

Related art —

Image result for mog miracle octad bricks

Monday, September 24, 2018

Mathematics as Art

Filed under: General — m759 @ 8:45 am

[Revised throughout the day on Sept. 24, 2018.]

"Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to explain
how art fits into our subject and what we mean by beauty."

— Sir Michael Atiyah, quoted here on April 4, 2016

Atiyah's remarks today on the Riemann hypothesis, based on his earlier
remarks on "arithmetic physics" and α, the fine-structure constant,
seem to exemplify the "magic and mystery" approach.

From some previous Log24 posts

AMS on 'mathematics, magic, and mystery,' April 2014

MAA on 'mathematics, magic, and mystery,' April 2014

Update of 6:06 PM ET the same day —

https://twitter.com/mpoessel/status/1044131977950109696

For related magic and mystery, see Log24 posts tagged on090405.

Sunday, January 21, 2018

At Which Point

Filed under: General — m759 @ 6:06 pm

"In 'Sophistry,' a new play by Jonathan Marc Sherman
at the Playwrights Horizons Studio, a popular tenured
professor stands accused of sexual harassment
by a male student."

— Frank Rich in The New York Times , theater review
on October 12, 1993

"At which point another play, inchoate but arresting,
edges into view." — Rich, ibid.

"Johansson began acting during childhood,
after her mother started taking her to auditions.
She made her professional acting debut
at the age of eight in the off-Broadway production
of 'Sophistry' with Ethan Hawke, at New York's
Playwrights Horizons."

— IMDb Mini Biography by: Pedro Borges 

" 'Suddenly, I was 19 again and I started to remember
all the men I'd known who had taken advantage of
the fact that I was a young woman who didn't yet have
the tools to say no, or to understand the value of
my own self-worth,' the Avengers star described. 
'I had many relationships both personal and professional
where the power dynamic was so off that I had to create
a narrative in which I was the cool girl who could hang in
and hang out, and that sometimes meant compromising
what felt right for me . . . . ' "

— Scarlett Johansson yesterday at the 2018 Women's March
in Los Angeles, as reported in E! News .

Bill Murray and Scarlett Johansson in 'Lost in Translation'

Image in a Log24 post
of March 12, 2009.

Tuesday, August 22, 2017

Link Degree Zero

Filed under: General — m759 @ 12:17 pm

From a 2009-2016 exhibition by David Link

Related material —

The object now sails slowly ahead, before starting to climb up and up, until it docks some way up in the discourse. And it sits there glowing. Yes, in an elevated position, just as Roland Barthes describes it in Writing Degree Zero . We let the magnifying glass glide over Barthes’s text, and see the word “discontinuous.” We carefully study a sentence we love: “The interrupted flow of the new poetic language initiates a discontinuous nature, which is only revealed piecemeal. At the very moment when the withdrawal of functions obscures the relations existing in the world, the object in discourse assumes an exalted place.” It is absolutely no surprise that at this point we have the picture of a luminous green prism sailing in through the dark and taking an exalted place on our retina, a bit like when you’ve been staring too hard at a lamp on the ceiling and then close your eyes! How strange, we think, that a sentence that was written to explain an aspect of modern poetry can have roughly the same effect on our imagination as science fiction. In particular, the phrase A DISCONTINUOUS NATURE, WHICH IS ONLY REVEALED PIECEMEAL makes us imagine a vast darkness and then rectangular blocks of bright green sections of nature, and they are not lined up as such, but appear in flashes. The blocks of bright green and sudden nature appear in flashes.

Gunnhild Øyehaug, from 
"The Object Assumes an Exalted Place in the Discourse,"
in Knots: Stories  (pp. 139-140).
Farrar, Straus and Giroux. Kindle Edition.
Knots  was first published in 2004, in Norwegian.

Sunday, March 12, 2017

Raise High the Ridgepole, Architects*

Filed under: General — m759 @ 2:40 pm

A post suggested by remarks of J. D. Salinger in 
The New Yorker  of November 19, 1955 —

Wikipedia:  Taiji (philosophy)

Etymology

The word 太極 comes from I Ching : "易有太極,是生兩儀,兩儀生四象,四象生八卦,八卦定吉凶,吉凶生大業。"

Taiji  (太極) is a compound of tai   "great; grand; supreme; extreme; very; too" (a superlative variant of da   "big; large; great; very") and ji   "pole; roof ridge; highest/utmost point; extreme; earth's pole; reach the end; attain; exhaust". In analogy with the figurative meanings of English pole, Chinese ji  極 "ridgepole" can mean "geographical pole; direction" (e.g., siji  四極 "four corners of the earth; world's end"), "magnetic pole" (Beiji  北極 "North Pole" or yinji  陰極 "negative pole; cathode"), or "celestial pole" (baji  八極 "farthest points of the universe; remotest place"). Combining the two words, 太極 means "the source, the beginning of the world".

Common English translations of the cosmological Taiji  are the "Supreme Ultimate" (Le Blanc 1985, Zhang and Ryden 2002) or "Great Ultimate" (Chen 1989, Robinet 2008); but other versions are the "Supreme Pole" (Needham and Ronan 1978), "Great Absolute", or "Supreme Polarity" (Adler 1999).

See also Polarity in this journal.

* A phrase adapted, via Salinger,
from a poem by Sappho

Ἴψοι δὴ τὸ μέλαθρον,
     Υ᾽μήναον
ἀέρρετε τέκτονεσ ἄνδρεσ,
     Υ᾽μήναον
γάμβροσ ἔρχεται ἶσοσ Ά᾽ρευϊ,
     [Υ᾽μήναον]
ανδροσ μεγάλο πόλυ μείζων
     [Υ᾽μήναον]

Wednesday, March 8, 2017

Inscapes

Filed under: General,Geometry — Tags: — m759 @ 6:42 pm

"The particulars of attention,
whether subjective or objective,
are unshackled through form,
and offered as a relational matrix …."

— Kent Johnson in a 1993 essay

Illustration

Commentary

The 16 Dirac matrices form six anticommuting sets of five matrices each (Arfken 1985, p. 214):

1. alpha_1alpha_2alpha_3alpha_4alpha_5,

2. y_1y_2y_3y_4y_5,

3. delta_1delta_2delta_3rho_1rho_2,

4. alpha_1y_1delta_1sigma_2sigma_3,

5. alpha_2y_2delta_2sigma_1sigma_3,

6. alpha_3y_3delta_3sigma_1sigma_2.

SEE ALSO:  Pauli Matrices

REFERENCES:

Arfken, G. Mathematical Methods for Physicists, 3rd ed.  Orlando, FL: Academic Press, pp. 211-217, 1985.

Berestetskii, V. B.; Lifshitz, E. M.; and Pitaevskii, L. P. "Algebra of Dirac Matrices." §22 in Quantum Electrodynamics, 2nd ed.  Oxford, England: Pergamon Press, pp. 80-84, 1982.

Bethe, H. A. and Salpeter, E. Quantum Mechanics of One- and Two-Electron Atoms.  New York: Plenum, pp. 47-48, 1977.

Bjorken, J. D. and Drell, S. D. Relativistic Quantum Mechanics.  New York: McGraw-Hill, 1964.

Dirac, P. A. M. Principles of Quantum Mechanics, 4th ed.  Oxford, England: Oxford University Press, 1982.

Goldstein, H. Classical Mechanics, 2nd ed.  Reading, MA: Addison-Wesley, p. 580, 1980.

Good, R. H. Jr. "Properties of Dirac Matrices." Rev. Mod. Phys. 27, 187-211, 1955.

Referenced on Wolfram|Alpha:  Dirac Matrices

CITE THIS AS:

Weisstein, Eric W.  "Dirac Matrices."

From MathWorld— A Wolfram Web Resource. 
http://mathworld.wolfram.com/DiracMatrices.html

Saturday, February 11, 2017

Artistic Signifier

Filed under: General — m759 @ 1:58 am

RSS feed screenshot of 1:53 AM ET today —

'Step aside, beauty and truth... Art's new  alpha and omega is identity.'

Friday, December 2, 2016

A Small Witt Design*

Filed under: General — Tags: , , — m759 @ 2:00 pm

The New York Times 's  online T Magazine  yesterday —

"A version of this article appears in print on December 4, 2016, on page
M263 of T Magazine with the headline: The Year of Magical Thinking."

* Thanks to Emily Witt for inadvertently publicizing the
   Miracle Octad Generator  of R. T. Curtis, which
   summarizes the 759 octads found in the large Witt design.

Wednesday, June 22, 2016

Fragments Against My Ruins, by Odd Thomas

Filed under: General — m759 @ 5:42 am
  1. "Inside of a dog, it's too dark to read"
  2. "Alpha Dog"
  3. "B. J. Leggett is professor emeritus at UT Knoxville"
  4. "Seven is Heaven, Eight is a Gate, Nine is a Vine"

Update of about 6:40 AM ET on June 22, 2016 —

"Que cantaba el rey David."  Happy birthday to Kris Kristofferson.

Thursday, June 16, 2016

Polytropos

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

Πολυμερῶς καὶ πολυτρόπως πάλαι ὁ Θεὸς λαλήσας . . . .

Long Day's Journey into Nighttown  continues. )

Friday, May 13, 2016

Geometry and Kinematics

Filed under: General,Geometry — Tags: — m759 @ 10:31 pm

"Just as both tragedy and comedy can be written
by using the same letters of the alphabet, the vast
variety of events in this world can be realized by
the same atoms through their different arrangements
and movements. Geometry and kinematics, which
were made possible by the void, proved to be still
more important in some way than pure being."

— Werner Heisenberg in Physics and Philosophy

For more about geometry and kinematics, see (for instance)

"An introduction to line geometry with applications,"
by Helmut Pottmann, Martin Peternell, and Bahram Ravani,
Computer-Aided Design  31 (1999), 3-16.

The concepts of line geometry (null point, null plane, null polarity,
linear complex, Klein quadric, etc.) are also of interest in finite  geometry.
Some small finite spaces have as their natural models arrays of cubes .

Wednesday, March 23, 2016

Lottery Hermeneutics

Filed under: General — m759 @ 11:29 am

(Continued)

The New York Lottery numbers yesterday evening:
897 and 3454. See the corresponding Log24 posts.

Related material: Moloney (op. cit.), pp. 91 and 92.

Tuesday, March 22, 2016

The Green Night

Filed under: General — m759 @ 9:29 pm

A search from the previous post (The Zero Obit) yields
two lines from Wallace Stevens that are echoed as follows

"That elemental parent, the green night,
Teaching a fusky alphabet."

See also this journal on St. Patrick's Day 2016.

Tuesday, February 23, 2016

Revolutionary

Filed under: General — m759 @ 7:14 pm

From New York Times  obituary today —

"The Rev. Fernando Cardenal, a son of privilege
who embraced Latin America’s poor as a revolutionary
priest and brazenly defied Pope John Paul II’s order to
quit Nicaragua’s leftist cabinet in the 1980s, died on
Saturday in Managua. He was 82."

Photo caption from the same obituary —

"Fernando Cardenal in 1990. As education minister of
Nicaragua under the Sandinistas in the 1980s, he
oversaw a sweeping campaign credited with reducing
illiteracy to 13 percent from 51 percent."

This alleged literacy improvement makes him sound like
a Protestant  revolutionary.

For a Catholic  view of literacy, see The Gutenberg Galaxy .

See also the post Being Interpreted (Aug. 14, 2015) — 

Sunday, February 7, 2016

For Fast EDI

Filed under: General — m759 @ 6:29 pm

Stealth (the movie) and Stealth (the Super Bowl ad)

Monday, January 18, 2016

First and Last

Filed under: General,Geometry — m759 @ 11:15 am

"First and last, he was a skeptic …."

— Home page of Martin-Gardner.org

See also, in this  journal, Alpha and Omega.

Related material from the last full day of Gardner's life —

See as well Symplectic in this journal.

Wednesday, December 23, 2015

Class of 64

Filed under: General — m759 @ 9:00 pm

The previous post dealt with one of the 64 symbols
(in a redesigned format) of the ancient Chinese classic 
The I Ching .

For those who prefer to be guided by programmed
responses to alphabetical  symbols

A lyric by Ira Gershwin —

A cinematic "T"

See also "T for Texas" in this journal and
George Clooney's recent attempt to commercialize
both the space program and the letter Omega: 

From a post of May 13, 2015 —

Wednesday, October 14, 2015

The Tombstone Code

Filed under: General — Tags: — m759 @ 2:00 am

For Dan Brown enthusiasts, a sequel to the previous post, "The Tombstone Source."

As that post notes, the following symbol is now used as a story-end "tombstone" at
T : The New York Times Style Magazine.  The Times  uses style-sheet code, not
the rarely used unicode character below, to produce the tombstone.

Related material — The novel The Flame Alphabet  by Ben Marcus
that was reviewed in January 2012 by Commentary  magazine :

Fiction, Fiction, Burning Bright

D. G. MYERS / JAN. 19, 2012

Ben Marcus, The Flame Alphabet 
(New York: Alfred A. Knopf, 2012).
304 pp. $25.95.

According to the Jews, the world begins
with speech. God says, “There is light,”
and so there is light. But what if something
happened — it doesn’t really matter what —
and speech turned lethal?

That’s the premise of The Flame Alphabet ,
the third novel by Ben Marcus,
a creative writing professor at Columbia
University….

A much better novel along these lines is Lexicon  (2013) by Max Barry.

Friday, October 2, 2015

Letters

Filed under: General,Geometry — m759 @ 9:28 pm

"The close of trading today will spell a new era for Google
as the search giant becomes a part of new holding company 
Alphabet Inc." — ABC News, 1:53 PM ET today

From an Aug. 10, 2015, letter by Larry Page announcing the change:

Other business philosophy:

Strategy Rules: Five Timeless Lessons from
Bill Gates, Andy Grove, and Steve Jobs

by David B. Yoffie, Michael A. Cusumano

On Sale: 04/14/2015

A not-so-timeless lesson: a synchronicity check
(of this journal, not of the oeuvre  of Joseph Jaworski) —

04/14/2015 — Sacramental Geometry.

Sunday, September 6, 2015

Elementally, My Dear Watson

Filed under: General,Geometry — Tags: — m759 @ 9:45 am

Sarah Larson in the online New Yorker  on Sept. 3, 2015,
discussed Google’s new parent company, “Alphabet”—

“… Alphabet takes our most elementally wonderful
general-use word—the name of the components of
language itself*—and reassigns it, like the words
tweet, twitter, vine, facebook, friend, and so on,
into a branded realm.”

Emma Watson in “The Bling Ring”

This journal, also on September 3 —

Thursday, September 3, 2015

Rings of August

Filed under: Uncategorized — m759 @ 7:20 AM

For the title, see posts from August 2007
tagged Gyges.

Related theological remarks:

Boolean  spaces (old)  vs. Galois  spaces (new)  in 
The Quality Without a Name. . . .

* Actually, Sarah, that would be “phonemes.”

Saturday, September 5, 2015

Operation Blockhead

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

New Yorker  writer on the new parent corporation of
Google, named Alphabet:

"In Larry Page’s letter explaining it to us, Alphabet
is illustrated with a bunch of kids’ building blocks. 
Operation Childlike Innocence, Phase One."

— Sarah Larson

Building blocks, Sarah, are not the same thing
as alphabet blocks.  For the distinction, see a
Log24 post of August 14, 2015, "Being Interpreted."

The New Yorker  apparently also has another fact wrong.
The official version of Page's letter is not  "illustrated."
Perhaps, Sarah, you mistook the new Alphabet website
abc.xyz, which did show alphabet blocks and quoted
Page's letter, for the letter itself.

Blockheads

Filed under: General — Tags: , — m759 @ 11:35 am

(Continued)

Cartoon from the current (Sept. 7, 2015) New Yorker , p. 25 —

See as well searches in this journal for Montessori and Machiavelli.

Midrash from Sept. 3 at the online New Yorker

"We don’t instinctively care about the brand unity
Google wants to achieve with its new mega-company,
Alphabet, of which it is now a part. Especially because
Alphabet takes our most elementally wonderful
general-use word—the name of the components of
language itself—and reassigns it, like the words tweet,
twitter, vine, facebook, friend, and so on, into a branded
realm. In Larry Page’s letter explaining it to us,
Alphabet is illustrated with a bunch of kids’ building blocks.
Operation Childlike Innocence, Phase One."

— Sarah Larson

Friday, August 14, 2015

Being Interpreted

Filed under: General,Geometry — Tags: , — m759 @ 12:31 am

The ABC of things —

Froebel's Third Gift: A cube made up of eight subcubes

The ABC of words —

A nutshell —

Book lessons —

IMAGE- History of Mathematics in a Nutshell

Tuesday, August 11, 2015

The XYZ of Being

Filed under: General — m759 @ 11:00 am

"The Stone" column in yesterday's New York Times :

"But where, exactly, is the border between
the private exchange of money or gifts
and the impersonal profit-making of the market?"

Good question.

Some background on the market —

Sunday, August 2, 2015

Symplectic

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

See "Symplectic" in this journal.  Some illustrations —

 

Midrash —

"Adorned with cryptic stones and sliding shines,
An immaculate personage in nothingness,
With the whole spirit sparkling in its cloth,

Generations of the imagination piled
In the manner of its stitchings, of its thread,
In the weaving round the wonder of its need,

And the first flowers upon it, an alphabet
By which to spell out holy doom and end,
A bee for the remembering of happiness."

— Wallace Stevens, "The Owl in the Sarcophagus"

Tuesday, March 31, 2015

Flame Diary

Filed under: General — m759 @ 1:00 pm

Last Saturday's post Against Dryness quoted "Gone Girl,"
a recent film about an untypical couple. 

Other works of interest:

The Flame Alphabet  (Ben Marcus, 2012) and
The Folded Clock  (Heidi Julavits, 2015).

Marcus and Julavits are husband and wife. As in
"Gone Girl," both are very bright, and the wife
writes a diary. (No other resemblance between
the couples is apparent.)

Update of 6:40 PM ET March 31:

A 1983 review by the parents of Ben Marcus —

Update of 7:09 PM March 31:

Tuesday, February 24, 2015

Amy’s After-Party

Filed under: General — m759 @ 2:21 pm

Continued from Putting the A in VANITY,
Putting the AI in FAIR, and Core Problem:

Friday, January 16, 2015

A versus PA

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

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

From the series of posts tagged "Defining Form" —

The 4-point affine plane A  and
the 7-point projective plane PA  —

IMAGE- Triangular models of the 4-point affine plane A and 7-point projective plane PA

The circle-in-triangle of Yale's Figure 30b (PA ) may,
if one likes, be seen as having an occult meaning.

For the mathematical  meaning of the circle in PA
see a search for "line at infinity."

A different, cubic, model of PA  is perhaps more perspicuous.

Saturday, May 24, 2014

Lyric Stupidity

Filed under: General — m759 @ 7:25 pm

From a song discussed in yesterday’s online NY Times :

“Blue, blue, my love is blue.”*

Trigger warning from SNL’s Weekend Update on April 12, 2014:

“It was announced this week that in an upcoming issue of
Life With Archie , the main character Archie Andrews
will die, following a lifelong struggle with blue balls.”

* Misheard version of Bryan Blackburn‘s “blue, blue, my world is blue”
translation of the Pierre Cour lyric “bleu, bleu, l’amour est bleu 

Sunday, February 9, 2014

Green Night

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

See “Babbled” in this journal and

Update of 3:15 AM ET —

Suggestions for Terry Gilliam, director of The Zero Theorem  and Brazil —

See posts of April 26, 2013, and of February 2, 2014, as well as
a note from the São Paulo Symphony Orchestra.

Sunday, November 10, 2013

The Field of the Possible

Filed under: General — m759 @ 7:20 am

This post was suggested by the recent Log24
posts Film Politics,  The Wind Rises,  and
Figure and Ground, as well as the related
Wikipedia article The Wind Has Risen.

Cover design by Helen Yentus.​
 

Μή, φίλα ψυχά, βίον ἀθάνατον σπεῦδε,
τὰν δ' ἔμπρακτον ἄντλει μαχανάν.

— Pindar, Pythian III ,  epigraph to
Le Cimetière Marin  by Paul Valéry (1920)
 

O mon âme, n’aspire à la vie immortelle,
mais épuise le champ du possible.

— Pindar, 3e Pythique ,  epigraph to
   The Myth of Sisyphus  by Albert Camus (1942)
 

O my soul, do not aspire to immortal life,
but exhaust the limits of the possible.

— Pindar, Pythian iii , as translated 
    from the French (or Greek) by Justin O'Brien
​    in the Knopf Myth of Sisyphus , 1955

Monday, October 14, 2013

Up and Down

Filed under: General — Tags: , , — m759 @ 9:29 am

Heraclitus, Fragment 60 (Diels number):

The way up and the way down is one and the same.

ὁδὸς ἄνω κάτω μία καὶ ὡυτή

hodòs áno káto mía kaì houté

— http://www.heraclitusfragments.com/B60/index.html

IMAGE- Fetzer on ambiguity in Mann's 'Doctor Faustus'

See also Blade and Chalice and, for a less Faustian
approach, Universe of Discourse.

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

Further context:  Not Theology.

Sunday, October 21, 2012

Logos

Filed under: General — m759 @ 11:01 pm

In memory of Leonard Shlain, author
of The Alphabet Versus the Goddess

Alphabet logo from the website
of a religious publishing company—

A logo for Charlize Theron, who played
a goddess figure in "Hancock"—

Click images for further details.

Wednesday, June 27, 2012

Architectural Memorial

Filed under: General — m759 @ 1:00 am

In memory of two figures from tonight's NY Times  obituaries index
(not  Nora Ephron and Anthony J. Wiener)—

IMAGE- Obits for art historian Paula Hays Harper and architect Gerhard Kallmann

Tower Envy

Erin Burnett and Jenga blocks yesterday

Related material—

The Bible Puzzle Book

IMAGE- Tower of alphabet blocks

and the monumental treatise
by Leonard Shlain

The Alphabet Versus
the Goddess: The Conflict
Between Word and Image
.

Monday, May 21, 2012

Child’s Play (continued*)

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

You and I …

we are just like a couple of tots…

Sinatra

JOSEFINE LYCHE

Born 1973 in Bergen. Lives and works in Oslo.

Education

2000 – 2004 National Academy of Fine Arts, Oslo
1998 – 2000 Strykejernet Art School, Oslo, NO
1995 – 1998 Philosophy, University of Bergen

University of Bergen—

 It might therefore seem that the idea of digital and analogical systems as rival fundaments to human experience is a new suggestion and, like digital technology, very modern. In fact, however, the idea is as old as philosophy itself (and may be much older). In his Sophist, Plato sets out the following ‘battle’ over the question of ‘true reality’:

What we shall see is something like a battle of gods and giants going on between them over their quarrel about reality [γιγαντομαχία περì της ουσίας] ….One party is trying to drag everything down to earth out of heaven and the unseen, literally grasping rocks and trees in their hands, for they lay hold upon every stock and stone and strenuously affirm that real existence belongs only to that which can be handled and offers resistance to the touch. They define reality as the same thing as body, and as soon as one of the opposite party asserts that anything without a body is real, they are utterly contemptuous and will not listen to another word. (…) Their adversaries are very wary in defending their position somewhere in the heights of the unseen, maintaining with all their force that true reality [την αληθινήν ουσίαν] consists in certain intelligible and bodiless forms. In the clash of argument they shatter and pulverize those bodies which their opponents wield, and what those others allege to be true reality they call, not real being, but a sort of moving process of becoming. On this issue an interminable battle is always going on between the two camps [εν μέσω δε περι ταυτα απλετος αμφοτέρων μάχη τις (…) αει συνέστηκεν]. (…) It seems that only one course is open to the philosopher who values knowledge and truth above all else. He must refuse to accept from the champions of the forms the doctrine that all reality is changeless [and exclusively immaterial], and he must turn a deaf ear to the other party who represent reality as everywhere changing [and as only material]. Like a child begging for 'both', he must declare that reality or the sum of things is both at once [το όν τε και το παν συναμφότερα] (Sophist 246a-249d).

The gods and the giants in Plato’s battle present two varieties of the analog position. Each believes that ‘true reality’ is singular, that "real existence belongs only to" one side or other of competing possibilities. For them, difference and complexity are secondary and, as secondary, deficient in respect to truth, reality and being (την αληθινήν ουσίαν, το όν τε και το παν). Difference and complexity are therefore matters of "interminable battle" whose intended end for each is, and must be (given their shared analogical logic), only to eradicate the other. The philosophical child, by contrast, holds to ‘both’ and therefore represents the digital position where the differentiated two yet belong originally together. Here difference, complexity and systematicity are primary and exemplary.

It is an unfailing mark of the greatest thinkers of the tradition, like Plato, that they recognize the digital possibility and therefore recognize the principal difference of it from analog possibilities.

— Cameron McEwen, "The Digital Wittgenstein,"
    The Wittgenstein Archives at the University of Bergen

* See that phrase in this journal.

Friday, May 4, 2012

That Krell Lab (continued)

Filed under: General — m759 @ 12:00 pm

“… Which makes it a gilt-edged priority that one  of us
 gets into that Krell lab and takes that brain boost.”

— American adaptation of Shakespeare's Tempest , 1956

From "The Onto-theological Origin of Play:
Heraclitus and Plato," by Yücel Dursun, in
Lingua ac Communitas  Vol 17 (October 2007)—

"Heraclitus’s Aion and His Transformations

 The saying is as follows:

αἰὼν παῖς ἐστι παίζων, πεττεύων·
παιδὸς ἡ βασιληίη

(Aion is a child playing draughts;
the kingship is the child’s)

(Krell 1972: 64).*

 * KRELL, David Farrell.
   “Towards an Ontology of Play:
   Eugen Fink’s Notion of Spiel,”
   Research in Phenomemology ,
   2, 1972: 63-93.

This is the translation of the fragment in Greek by Krell.
There are many versions of the translation of the fragment….."

See also Child's Play and Froebel's Magic Box.

Update of May 5— For some background
from the date May 4 seven years ago, see
The Fano Plane Revisualized.

For some background on the word "aion,"
see that word in this journal.

Friday, March 30, 2012

Steiner on Language

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

March 28 review in the Times Literary Supplement  of
George Steiner's new book The Poetry of Thought

"If this new book opens with the concession that
language has neither the performative power of music
nor the elegant precision of mathematics,
it is language, for Steiner, that defines the human.

The survey accordingly begins from the ancient Greek
view of man as the 'language-animal.'" 

A check of this phrase yields, in a 1969 Steiner essay,
"The Language Animal," a Greek form of the phrase—

In short, the least inadequate definition we can arrive at
of the genus homo , the definition that fully distinguishes
him from all neighbouring life-forms, is this:
man is a zoon phonanta , a language-animal.

— p. 10 in Encounter , August 1969 (essay on pp. 7-23)

After introducing "language-animal" as a translation of  "zoon phonanta " in 1969,
Steiner in later writing went on to attribute this phrase to the ancient Greeks.

 "The inception of critical thought, of a philosophic anthropology, 
is contained in the archaic Greek definition of man as a
'language-animal'…."

— George Steiner, Real Presences , U. of Chicago Press, 1991, p. 89

"… the 'language-animal' we have been since ancient Greece
so designated us…. "

— George Steiner, Grammars of Creation , Yale U. Press, 2002, p. 265

Despite this, there seems to be no evidence for use of this phrase
by the ancient Greeks.

A Google search today for zoon phonanta  (ζῷον φωνᾶντα)—

There are also no results from searches for the similar phrases
"ζωον φωναντα," "ζωον φωνᾶντα," and "ζῷον φωναντα."

Tuesday, March 20, 2012

Field (continued)

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

In memory of director Ulu Grosbard (continued from yesterday)

From  http://scripturetext.com/matthew/13-44.htm —

Again the kingdom of heaven is like unto treasure hid in a field
the which when a man hath found he hideth and for joy thereof
goeth and selleth all that he hath and buyeth that field

ΚΑΤΑ ΜΑΤΘΑΙΟΝ 13:44 Greek NT: Byzantine/Majority Text (2000)
παλιν ομοια εστιν η βασιλεια των ουρανων θησαυρω κεκρυμμενω εν τω αγρω

LEXICON  


παλιν  adverb


palin  pal'-in:  (adverbially) anew, i.e. (of place) back, (of time) once more, or (conjunctionally) furthermore or on the other hand — again.


ομοια  adjective – nominative singular feminine


homoios  hom'-oy-os:  similar (in appearance or character) — like, + manner.


εστιν  verb – present indicative – third person singular 


esti  es-tee':  he (she or it) is; also (with neuter plural) they are


η  definite article – nominative singular feminine


ho  ho:  the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.


βασιλεια  noun – nominative singular feminine


basileia  bas-il-i'-ah:  royalty, i.e. (abstractly) rule, or (concretely) a realm — kingdom, + reign.


των  definite article – genitive plural masculine


ho  ho:  the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.


ουρανων  noun – genitive plural masculine


ouranos  oo-ran-os':  the sky; by extension, heaven (as the abode of God); by implication, happiness, power, eternity; specially, the Gospel (Christianity) — air, heaven(-ly), sky.


θησαυρω  noun – dative singular masculine


thesauros  thay-sow-ros':  a deposit, i.e. wealth — treasure.


κεκρυμμενω  verb – perfect passive participle – dative singular masculine 


krupto  kroop'-to:  to conceal (properly, by covering) — hide (self), keep secret, secret(-ly).


εν  preposition


en  en:  in, at, (up-)on, by, etc.


τω  definite article – dative singular masculine


ho  ho:  the definite article; the (sometimes to be supplied, at others omitted, in English idiom) — the, this, that, one, he, she, it, etc.


αγρω  noun – dative singular masculine


agros  ag-ros':  a field (as a drive for cattle); genitive case, the country; specially, a farm, i.e. hamlet — country, farm, piece of ground, land.

Sunday, February 26, 2012

Sermon for Nabokov

Filed under: General — m759 @ 11:00 am

"In linear algebra, the basis of a vector space
is an alphabet in which all vectors
can be expressed uniquely. The thing to remember
is that there are many such alphabets."

—  "A Vector Alphabet of Interstellar Travel,"
       by Yoon Ha Lee

See also Starflight in this journal.

Monday, February 20, 2012

Coxeter and the Relativity Problem

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

In the Beginning…

"As is well known, the Aleph is the first letter of the Hebrew alphabet."
– Borges, "The Aleph" (1945)

From some 1949 remarks of Weyl—

"The relativity problem is one of central significance throughout geometry and algebra and has been recognized as such by the mathematicians at an early time."

Hermann Weyl, "Relativity Theory as a Stimulus in Mathematical Research," Proceedings of the American Philosophical Society , Vol. 93, No. 7, Theory of Relativity in Contemporary Science: Papers Read at the Celebration of the Seventieth Birthday of Professor Albert Einstein in Princeton, March 19, 1949  (Dec. 30, 1949), pp. 535-541

Weyl in 1946—:

"This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them."

— Hermann Weyl, The Classical Groups , Princeton University Press, 1946, p. 16

Coxeter in 1950 described the elements of the Galois field GF(9) as powers of a primitive root and as ordered pairs of the field of residue-classes modulo 3—

"… the successive powers of  the primitive root λ or 10 are

λ = 10,  λ2 = 21,  λ3 = 22,  λ4 = 02,
λ5 = 20,  λ6 = 12,  λ7 = 11,  λ8 = 01.

These are the proper coordinate symbols….

(See Fig. 10, where the points are represented in the Euclidean plane as if the coordinate residue 2 were the ordinary number -1. This representation naturally obscures the collinearity of such points as λ4, λ5, λ7.)"

http://www.log24.com/log/pix12/120220-CoxeterFig10.jpg

Coxeter's Figure 10 yields...

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

The Aleph

The details:

(Click to enlarge)

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

Coxeter's phrase "in the Euclidean plane" obscures the noncontinuous nature of the transformations that are automorphisms of the above linear 2-space over GF(3).

Saturday, October 22, 2011

Lunch at the Y

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

Or: Starting Out in the Evening, continued from noon yesterday

Yesterday evening's New York Lottery numbers were 510 and 5256.

For the former, see post  510, Music for Patricias.

For the latter, see Richard Feynman at the Caltech YMCA Lunch Forum on 5/2/56—

"The Relation of Science and Religion."

Some background….

The Aleph

"As is well known, the Aleph is the first letter of the Hebrew alphabet.
Its use for the strange sphere in my story may not be accidental.
For the Kabbala, the letter stands for the En Soph ,
the pure and boundless godhead; it is also said that it takes
the shape of a man pointing to both heaven and earth…."

— Borges, "The Aleph," quoted in Ayn Sof (January 7th, 2011)

The Y

See "Pythagorean Letter" in this journal.

Edenville

"Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one." 

"A very short space of time through very short times of space…. Am I walking into eternity along Sandymount strand?"

James Joyce, Ulysses , Proteus chapter

Monday, October 10, 2011

The Aleph

Filed under: General — m759 @ 12:00 am

COLLEGE OF THE DESERT
Minutes — Organization Meeting
11:00 a.m., Saturday, July 1, 1961—

15. Preparation of College Seal:

By unanimous consent preparation of a College
Seal to contain the following features was
authorized: A likeness of the Library building
set in a matrix of date palms, backed by
a mountain skyline and rising sun; before
the Library an open book, the Greek symbol
Alpha on one page and Omega on the other;
the Latin Lux et Veritas, College of the
Desert, and 1958 to be imprinted within or
around the periphery of the seal.

From the website http://geofhagopian.net/ of
Geoff Hagopian, Professor of Mathematics,
College of the Desert—

http://www.log24.com/log/pix11C/111010-CollegeOfTheDesert-Seal.gif

Note that this version of the seal contains
an Aleph  and Omega instead of Alpha and Omega.

From another Hagopian website, another seal.

Saturday, October 8, 2011

An Ordinary Evening in Hartford

Filed under: General — Tags: , — m759 @ 7:59 am

From Rebecca Goldstein's Talks and Appearances page—

• "36 (Bad) Arguments for the Existence of God,"
   Annual Meeting of the Freedom from Religion Foundation,
   Marriot, Hartford, CT, Oct 7 [2011], 7 PM

From Wallace Stevens—

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

For those who prefer greater depth on Yom Kippur, yesterday's cinematic link suggests…

"Yo sé de un laberinto griego que es una línea única, recta."
 —Borges, "La Muerte y la Brújula " ("Death and the Compass")

See also Alpha and Omega (Sept. 18, 2011) and some context from 1931.

Thursday, August 4, 2011

Midnight in Oslo

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

For Norway's Niels Henrik Abel (1802-1829)
on his birthday, August Fifth

(6 PM Aug. 4, Eastern Time, is 12 AM Aug. 5 in Oslo.)

http://www.log24.com/log/pix11B/110804-Pesic-PlatosDiamond.jpg

Plato's Diamond

The above version by Peter Pesic is from Chapter I of his book Abel's Proof , titled "The Scandal of the Irrational." Plato's diamond also occurs in a much later mathematical story that might be called "The Scandal of the Noncontinuous." The story—

Paradigms

"These passages suggest that the Form is a character or set of characters common to a number of things, i.e. the feature in reality which corresponds to a general word. But Plato also uses language which suggests not only that the forms exist separately (χωριστά ) from all the particulars, but also that each form is a peculiarly accurate or good particular of its own kind, i.e. the standard particular of the kind in question or the model (παράδειγμα ) [i.e. paradigm ] to which other particulars approximate….

… Both in the Republic  and in the Sophist  there is a strong suggestion that correct thinking is following out the connexions between Forms. The model is mathematical thinking, e.g. the proof given in the Meno  that the square on the diagonal is double the original square in area."

– William and Martha Kneale, The Development of Logic , Oxford University Press paperback, 1985

Plato's paradigm in the Meno

http://www.log24.com/log/pix11/110217-MenoFigure16bmp.bmp

Changed paradigm in the diamond theorem (2×2 case) —

http://www.log24.com/log/pix11/110217-MenoFigureColored16bmp.bmp

Aspects of the paradigm change—

Monochrome figures to
   colored figures

Areas to
   transformations

Continuous transformations to
   non-continuous transformations

Euclidean geometry to
   finite geometry

Euclidean quantities to
   finite fields

The 24 patterns resulting from the paradigm change—

http://www.log24.com/log/pix11B/110805-The24.jpg

Each pattern has some ordinary or color-interchange symmetry.

This is the 2×2 case of a more general result. The patterns become more interesting in the 4×4 case. For their relationship to finite geometry and finite fields, see the diamond theorem.

Related material: Plato's Diamond by Oslo artist Josefine Lyche.

Plato’s Ghost  evokes Yeats’s lament that any claim to worldly perfection inevitably is proven wrong by the philosopher’s ghost….”

— Princeton University Press on Plato’s Ghost: The Modernist Transformation of Mathematics  (by Jeremy Gray, September 2008)

"Remember me to her."

— Closing words of the Algis Budrys novel Rogue Moon .

Background— Some posts in this journal related to Abel or to random thoughts from his birthday.

Wednesday, June 15, 2011

A for Anastasios

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

The title was suggested by this evening's 4-digit NY lottery number.

"… the rhetoric might be a bit over the top."

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

According to Amazon.com, 2198 (i.e., 2/1/98) was the publication
date of Geometry of Vector Sheaves , Volume I, by Anastasios Mallios.

Related material—

The question of S.S. Chern quoted here June 10: —
"What is Geometry?"— and the remark by Stevens that
accompanied the quotation—

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."
— Wallace Stevens,
“An Ordinary Evening in New Haven” VI

The work of Mallios in pure mathematics cited above seems
quite respectable (unlike his later remarks on physics).
His Vector Sheaves  appears to be trying to explore new territory;
hence the relevance of Stevens's "Alpha." See also the phrase
"A-Invariance" in an undated preprint by Mallios*.

For the evening 3-digit number, 533, see a Stevens poem—

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

This meditation by Stevens is related to the female form of Mallios's Christian name.

As for the afternoon numbers, see "62" in The Beauty Test (May 23, 2007), Geometry and Death, and "9181" as the date 9/1/81.

* Later published in International Journal of Theoretical Physics , Vol. 47, No. 7, cover date 2008-07-01

Friday, June 10, 2011

Hierophant

Filed under: General — Tags: , , — m759 @ 7:59 pm

Some background for yesterday’s posts:

Midrash for Gnostics and related notes,
as well as yesterday’s New York Lottery.

….    “We seek
The poem of pure reality, untouched
By trope or deviation, straight to the word,
Straight to the transfixing object, to the object
At the exactest point at which it is itself,
Transfixing by being purely what it is….”
— Wallace Stevens (1879-1955),
“An Ordinary Evening in New Haven” IX

“Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals.”
— Wallace Stevens,
“An Ordinary Evening in New Haven” VI

Wikipedia

“A hierophant is a person who brings religious congregants into the presence of that which is deemed holy . The word comes from Ancient Greece, where it was constructed from the combination of ta hiera , ‘the holy,’ and phainein , ‘to show.’ In Attica it was the title of the chief priest at the Eleusinian Mysteries. A hierophant is an interpreter of sacred mysteries and arcane principles.”

Weyl as Alpha, Chern as Omega—

(Click to enlarge.)

http://www.log24.com/log/pix11A/110610-WeylChernSm.jpg

Postscript for Ellen Page, star of “Smart People
and of “X-Men: The Last Stand“— a different  page 679.

Your assignment, should you choose to accept it—

Interpret today’s  NY lottery numbers— Midday 815, Evening 888.

My own bias is toward 815 as 8/15 and 888 as a trinity,
but there may be less obvious and more interesting approaches.

Thursday, February 17, 2011

Paradigms

Filed under: General,Geometry — Tags: , — m759 @ 4:16 pm

"These passages suggest that the Form is a character or set of characters
common to a number of things, i.e. the feature in reality which corresponds
to a general word. But Plato also uses language which suggests not only
that the forms exist separately (χωριστά ) from all the particulars, but also
that each form is a peculiarly accurate or good particular of its own kind,
i.e. the standard particular of the kind in question or the model (παράδειγμα )
[i.e. paradigm ] to which other particulars approximate….

… Both in the Republic  and in the Sophist  there is a strong suggestion
that correct thinking is following out the connexions between Forms.
The model is mathematical thinking, e.g. the proof given in the Meno
that the square on the diagonal is double the original square in area."

— William and Martha Kneale, The Development of Logic,
Oxford University Press paperback, 1985

Plato's paradigm in the Meno

http://www.log24.com/log/pix11/110217-MenoFigure16bmp.bmp

Changed paradigm in the diamond theorem (2×2 case) —

http://www.log24.com/log/pix11/110217-MenoFigureColored16bmp.bmp

Aspects of the paradigm change* —

Monochrome figures to
colored figures

Areas to
transformations

Continuous transformations to
non-continuous transformations

Euclidean geometry to
finite geometry

Euclidean quantities to
finite fields

Some pedagogues may find handling all of these
conceptual changes simultaneously somewhat difficult.

* "Paradigm shift " is a phrase that, as John Baez has rightly pointed out,
should be used with caution. The related phrase here was suggested by Plato's
term παράδειγμα  above, along with the commentators' specific reference to
the Meno  figure that serves as a model. (For "model" in a different sense,
see Burkard Polster.) But note that Baez's own beloved category theory
has been called a paradigm shift.

Friday, January 7, 2011

Ayn Sof

Filed under: General — Tags: , — m759 @ 7:26 pm

(A continuation of this morning's Coxeter and the Aleph)

"You've got to pick up every stitch… Must be the season of the witch."
Donovan song at the end of Nicole Kidman's "To Die For"

Mathematics and Narrative, Illustrated
http://www.log24.com/log/pix11/110107-The1950Aleph-Sm.jpg

Mathematics

http://www.log24.com/log/pix11/110107-ScriptAlephSm.jpg
Narrative

"As is well known, the Aleph is the first letter of the Hebrew alphabet.
Its use for the strange sphere in my story may not be accidental.
For the Kabbala, the letter stands for the En Soph ,
the pure and boundless godhead; it is also said that it takes
the shape of a man pointing to both heaven and earth, in order to show
that the lower world is the map and mirror of the higher; for Cantor's
Mengenlehre , it is the symbol of transfinite numbers,
of which any part is as great as the whole."

— Borges, "The Aleph"

From WorldLingo.com

Ein Sof

Ein Soph or Ayn Sof (Hebrew  אין סוף, literally "without end", denoting "boundlessness" and/or "nothingness"), is a Kabbalistic term that usually refers to an abstract state of existence preceding God's Creation of the limited universe. This Ein Sof , typically referred to figuratively as the "light of Ein Sof " ("Or Ein Sof "), is the most fundamental emanation manifested by God. The Ein Sof  is the material basis of Creation that, when focused, restricted, and filtered through the sefirot , results in the created, dynamic universe.
….

Cultural impact

Mathematician Georg Cantor labeled different sizes of infinity using the Aleph. The smallest size of infinity is aleph-null (0), the second size is aleph-one (1), etc. One theory about why Cantor chose to use the aleph is because it is the first letter of Ein-Sof. (See Aleph number)

"Infinite Jest… now stands as the principal contender
for what serious literature can aspire to
in the late twentieth and early twenty-first centuries."

All Things Shining, a work of pop philosophy published January 4th

http://www.log24.com/log/pix10B/101231-AllThingsShining-Cover.jpg

"You're gonna need a bigger boat." — Roy Scheider in "Jaws"

"We're gonna need more holy water." — "Season of the Witch," a film opening tonight

See also, with respect to David Foster Wallace, infinity, nihilism,
and the above reading of "Ayn Sof" as "nothingness,"
the quotations compiled as "Is Nothing Sacred?"

Tuesday, September 8, 2009

Tuesday September 8, 2009

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

Froebel's   
Magic Box  
 

Box containing Froebel's Third Gift-- The Eightfold Cube
 
 Continued from Dec. 7, 2008,
and from yesterday.

 

Non-Euclidean
Blocks

 

Passages from a classic story:

… he took from his pocket a gadget he had found in the box, and began to unfold it. The result resembled a tesseract, strung with beads….

Tesseract
 Tesseract

 

"Your mind has been conditioned to Euclid," Holloway said. "So this– thing– bores us, and seems pointless. But a child knows nothing of Euclid. A different sort of geometry from ours wouldn't impress him as being illogical. He believes what he sees."

"Are you trying to tell me that this gadget's got a fourth dimensional extension?" Paradine demanded.
 
"Not visually, anyway," Holloway denied. "All I say is that our minds, conditioned to Euclid, can see nothing in this but an illogical tangle of wires. But a child– especially a baby– might see more. Not at first. It'd be a puzzle, of course. Only a child wouldn't be handicapped by too many preconceived ideas."

"Hardening of the thought-arteries," Jane interjected.

Paradine was not convinced. "Then a baby could work calculus better than Einstein? No, I don't mean that. I can see your point, more or less clearly. Only–"

"Well, look. Let's suppose there are two kinds of geometry– we'll limit it, for the sake of the example. Our kind, Euclidean, and another, which we'll call x. X hasn't much relationship to Euclid. It's based on different theorems. Two and two needn't equal four in it; they could equal y, or they might not even equal. A baby's mind is not yet conditioned, except by certain questionable factors of heredity and environment. Start the infant on Euclid–"

"Poor kid," Jane said.

Holloway shot her a quick glance. "The basis of Euclid. Alphabet blocks. Math, geometry, algebra– they come much later. We're familiar with that development. On the other hand, start the baby with the basic principles of our x logic–"

"Blocks? What kind?"

Holloway looked at the abacus. "It wouldn't make much sense to us. But we've been conditioned to Euclid."

— "Mimsy Were the Borogoves," Lewis Padgett, 1943


Padgett (pseudonym of a husband-and-wife writing team) says that alphabet blocks are the intuitive "basis of Euclid." Au contraire; they are the basis of Gutenberg.

For the intuitive basis of one type of non-Euclidean* geometry– finite geometry over the two-element Galois field– see the work of…


Friedrich Froebel
 (1782-1852), who
 invented kindergarten.

His "third gift" —

Froebel's Third Gift-- The Eightfold Cube
© 2005 The Institute for Figuring
 
Photo by Norman Brosterman
fom the Inventing Kindergarten
exhibit at The Institute for Figuring

Go figure.

* i.e., other than Euclidean

Thursday, July 23, 2009

Thursday July 23, 2009

Filed under: General,Geometry — Tags: , — m759 @ 5:01 am

A Tangled Tale

Proposed task for a quantum computer:

"Using Twistor Theory to determine the plotline of Bob Dylan's 'Tangled up in Blue'"

One approach to a solution:

"In this scheme the structure of spacetime is intrinsically quantum mechanical…. We shall demonstrate that the breaking of symmetry in a QST [quantum space-time] is intimately linked to the notion of quantum entanglement."

— "Theory of Quantum Space-Time," by Dorje C. Brody and Lane P. Hughston, Royal Society of London Proceedings Series A, Vol. 461, Issue 2061, August 2005, pp. 2679-2699

(See also The Klein Correspondence, Penrose Space-Time, and a Finite Model.)

For some less technical examples of broken symmetries, see yesterday's entry, "Alphabet vs. Goddess."

That entry displays a painting in 16 parts by Kimberly Brooks (daughter of Leonard Shlain– author of The Alphabet Versus the Goddess— and wife of comedian Albert Brooks (real name: Albert Einstein)). Kimberly Brooks is shown below with another of her paintings, titled "Blue."

http://www.log24.com/log/pix09A/090722-ArtisticVision-Sm.jpg

Click image to enlarge.

"She was workin' in a topless place
 And I stopped in for a beer,
 I just kept lookin' at the side of her face
 In the spotlight so clear.
 And later on as the crowd thinned out
 I's just about to do the same,
 She was standing there in back of my chair
 Said to me, 'Don't I know your name?'
 I muttered somethin' underneath my breath,
 She studied the lines on my face.
 I must admit I felt a little uneasy
 When she bent down to tie the laces of my shoe,
 Tangled up in blue."

-- Bob Dylan

Further entanglement with blue:

The website of the Los Angeles Police Department, designed by Kimberly Brooks's firm, Lightray Productions.

Further entanglement with shoelaces:

"Entanglement can be transmitted through chains of cause and effect– and if you speak, and another hears, that too is cause and effect.  When you say 'My shoelaces are untied' over a cellphone, you're sharing your entanglement with your shoelaces with a friend."

— "What is Evidence?," by Eliezer Yudkowsky

Wednesday, July 22, 2009

Wednesday July 22, 2009

Filed under: General,Geometry — Tags: , — m759 @ 9:48 am
Alphabet vs. Goddess

Continued…

Roy Lichtenstein girl and Hand of God pointing to the letter B

… from June 11, 2008.

"Just as both tragedy and comedy can be written by using the same letters of the alphabet, the vast variety of events in this world can be realized by the same atoms through their different arrangements and movements. Geometry and kinematics, which were made possible by the void, proved to be still more important in some way than pure being."

— Werner Heisenberg in
  Physics and Philosophy

Werner, Kimberly;
Kimberly, Werner.

Wechsler cubes, with 'Certainty,' by Kimberly Brooks

Happy Feast of
St. Mary Magdalene.

Thursday, July 9, 2009

Thursday July 9, 2009

Filed under: General — m759 @ 8:00 am
Mathematics
and Poetry

http://www.log24.com/log/pix09A/090709-Heaven.gif
Click on the image for
some background related
to yesterday’s The Aleph
 and its  link  to  a 2003
 entry, At Mt. Sinai.

A related entry on Mt. Sinai
mentions the monumental
treatise by Leonard Shlain

The Alphabet Versus
the Goddess: The Conflict
Between Word and Image
.

Friday, April 17, 2009

Friday April 17, 2009

Filed under: General,Geometry — Tags: — m759 @ 10:31 am

Begettings of
the Broken Bold

Thanks for the following
quotation (“Non deve…
nella testa“) go to the
weblog writer who signs
himself “Conrad H. Roth.”

Autobiography
of Goethe

(Vol. II, London, Bell & Daldy,
1868, at Google Books):

… Yesterday I took leave of my Captain, with a promise of visiting him at Bologna on my return. He is a true

A PAPAL SOLDIER’S IDEAS OF PROTESTANTS 339

representative of the majority of his countrymen. Here, however, I would record a peculiarity which personally distinguished him. As I often sat quiet and lost in thought he once exclaimed “Che pensa? non deve mai pensar l’uomo, pensando s’invecchia;” which being interpreted is as much as to say, “What are you thinking about: a man ought never to think; thinking makes one old.” And now for another apophthegm of his; “Non deve fermarsi l’uomo in una sola cosa, perche allora divien matto; bisogna aver mille cose, una confusione nella testa;” in plain English, “A man ought not to rivet his thoughts exclusively on any one thing, otherwise he is sure to go mad; he ought to have in his head a thousand things, a regular medley.”

Certainly the good man could not know that the very thing that made me so thoughtful was my having my head mazed by a regular confusion of things, old and new. The following anecdote will serve to elucidate still more clearly the mental character of an Italian of this class. Having soon discovered that I was a Protestant, he observed after some circumlocution, that he hoped I would allow him to ask me a few questions, for he had heard such strange things about us Protestants that he wished to know for a certainty what to think of us.

Notes for Roth:

Roth and Corleone in Havana

The title of this entry,
“Begettings of the Broken Bold,”
is from Wallace Stevens’s
“The Owl in the Sarcophagus”–

This was peace after death, the brother of sleep,
The inhuman brother so much like, so near,
Yet vested in a foreign absolute,

Adorned with cryptic stones and sliding shines,
An immaculate personage in nothingness,
With the whole spirit sparkling in its cloth,

Generations of the imagination piled
In the manner of its stitchings, of its thread,
In the weaving round the wonder of its need,

And the first flowers upon it, an alphabet
By which to spell out holy doom and end,
A bee for the remembering of happiness.

Peace stood with our last blood adorned, last mind,
Damasked in the originals of green,
A thousand begettings of the broken bold.

This is that figure stationed at our end,
Always, in brilliance, fatal, final, formed
Out of our lives to keep us in our death....

Related material:

  • Yesterday’s entry on Giordano Bruno and the Geometry of Language
  • James Joyce and Heraldry
  • “One might say that he [Joyce] invented a non-Euclidean geometry of language; and that he worked over it with doggedness and devotion….” —Unsigned notice in The New Republic, 20 January 1941
  • Joyce’s “collideorscape” (scroll down for a citation)
  • “A Hanukkah Tale” (Log24, Dec. 22, 2008)
  • Stevens’s phrase from “An Ordinary Evening in New Haven” (Canto XXV)

Some further context:

Roth’s entry of Nov. 3, 2006–
Why blog, sinners?“–
and Log24 on that date:
First to Illuminate.”

Sunday, March 29, 2009

Sunday March 29, 2009

Filed under: General,Geometry — Tags: , — m759 @ 7:48 pm

Getting All
the Meaning In

Webpage heading for the
2009 meeting of the
American Comparative
Literature Association:

ACLA 2009 web page heading with map and alphabetic symbols

The mysterious symbols on
the above map suggest the
following reflections:


From A Cure of the Mind: The Poetics of Wallace Stevens, by Theodore Sampson, published by Black Rose Books Ltd., 2000–

Page x:

"… if what he calls 'the spirit's alchemicana' (CP [Collected Poems] 471) addresses itself to the irrational element in poetry, to what extent is such an element dominant in his theory and practice of poetry, and therefore in what way is Stevens' intricate verbal music dependent on his irrational use of language– a 'pure rhetoric of a language without words?' (CP 374)?"

Related material:

 

From "'When Novelists Become Cubists:' The Prose Ideograms of Guy Davenport," by Andre Furlani:

Laurence Zachar argues that Davenport's writing is situated "aux frontieres intergeneriques" where manifold modes are brought into concord: "L'etonnant chez Davenport est la facon don't ce materiau qui parait l'incarnation meme du chaos– hermetique, enigmatique, obscur, avec son tropplein de references– se revele en fait etre construit, ordonne, structure. Plus l'on s'y plonge, et plus l'on distingue de cohesion dans le texte." 'What astonishes in Davenport is the way in which material that seems the very incarnation of chaos– hermetic, enigmatic, obscure, with its proliferation of allusions– in fact reveals itself to be constructed, organized, structured. The more one immerses oneself in them the more one discerns the texts' cohesion.' (62).

Davenport also works along the intergeneric border between text and graphic, for he illustrates many of his texts. (1) "The prime use of words is for imagery: my writing is drawing," he states in an interview (Hoeppfner 123). Visual imagery is not subordinated to writing in Davenport, who draws on the assemblage practice of superimposing image and writing. "I trust the image; my business is to get it onto the page," he writes in the essay "Ernst Machs Max Ernst." "A page, which I think of as a picture, is essentially a texture of images. […] The text of a story is therefore a continuous graph, kin to the imagist poem, to a collage (Ernst, Willi Baumeister, El Lissitzky), a page of Pound, a Brakhage film" (Geography 374-75).

Note:

(1.) Davenport is an illustrator of books (such as Hugh Kenner's The Stoic Comedians and The Counterfeiters) and journals (such as The Kenyon Review, Parnassus, and Paideuma). His art is the subject of Erik Anderson Reece's monograph, A Balance of Quinces, which reveals the inseparable relationship between Davenport's literary and pictorial work.

References:

Davenport, Guy. The Geography of the Imagination. San Francisco: North Point Press, 1981. Rpt. New York: Pantheon, 1992.

Hoepffner, Bernard. "Pleasant Hill: An Interview with Guy Davenport." Conjunctions 24 (1995): 118-24.

Reece, Erik Anderson. A Balance of Quinces: The Paintings and Drawings of Guy Davenport. New York: New Directions, 1996.

Zachar, Laurence. "Guy Davenport: Une Mosaique du genres." Recherches Anglaises et Nord-Americaines 21 (1994): 51-63.

"… when novelists become Cubists; that is, when they see the possibilities of making a hieroglyph, a coherent symbol, an ideogram of the total work. A symbol comes into being when an artist sees that it is the only way to get all the meaning in."

— Guy Davenport, The Geography of the Imagination

See also last night's
commentary on the
 following symbols:

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

Wednesday, June 11, 2008

Wednesday June 11, 2008

Filed under: General — m759 @ 6:01 pm
The Goddess
vs. the Alphabet

in today’s New York Times:

Roy Lichtenstein girl and Hand of God pointing to the letter B

(continued from
Einstein’s birthday, 2003
)

Links from the above image:
The Painter and Letters

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

Wednesday, October 3, 2007

Wednesday October 3, 2007

Filed under: General,Geometry — Tags: — m759 @ 3:09 pm
Janitor Monitor

 

The image “http://www.log24.com/log/pix07A/070803-Trees.jpg” cannot be displayed, because it contains errors.

Will Hunting may be
interested in the following
vacant editorships at
The Open Directory:

Graph Theory
and
Combinatorics.

Related material:

The Long Hello and
On the Holy Trinity

"Hey, Carrie-Anne, what's
your game now….?
"

The image “http://www.log24.com/log/pix07A/071003-Magdalene.GIF” cannot be displayed, because it contains errors.

Picture sources:
azstarnet.com,
vibrationdata.com.

Personally, I prefer
Carol Ann:

From Criticism,  Fall, 2001,
by Carol Ann Johnston

"Drawing upon Platonic thought, Augustine argues that ideas are actually God's objective pattern and as such exist in God's mind. These ideas appear in the mirror of the soul. (35)."

(35.) In Augustine, De Trinitate, trans., Stephen McKenna (Washington, D.C.: Catholic University Press, 1970). See A. B. Acton, "Idealism," in The Encyclopedia of Philosophy, ed., Paul Edwards. Vol. 4 (New York: Macmillan, 1967): 110-118; Robert McRae, "`Idea' as a Philosophical Term in the Seventeenth Century," JHI 26 (1965): 175-190, and Erwin Panofsky, Idea: A Concept in Art History, trans., Joseph J. S. Peake (Columbia, S.C.: University of South Carolina Press, 1968) for explications of this term.

 

See also
Art Wars: Geometry as Conceptual Art
and Ideas and Art: Notes on Iconology.

 

For more on Augustine and geometry,
see Today's Sinner (Aug. 28, 2006).

 

 

Saturday, March 3, 2007

Saturday March 3, 2007

Filed under: General — m759 @ 3:00 am
The Shadow
of the Owl

                             ” … an alphabet
By which to spell out holy doom and end,
A bee for the remembering of happiness.”

— Wallace Stevens,
“The Owl in the Sarcophagus”

(See Log24, Tuesday, Feb. 27.
For an alphabet and a bee,
see yesterday’s entries.)

In memory of
Myer Feldman,
presidential adviser
and theatrical producer,
who died two days ago,
on Thursday, March 1:

The image “http://www.log24.com/log/pix07/070303-Feldman.jpg” cannot be displayed, because it contains errors.

See also Seymour Hersh,
The Samson Option:
Israel’s Nuclear Arsenal and
American Foreign Policy
.
  Random House, 1991,
page 100.

Friday, March 2, 2007

Friday March 2, 2007

Filed under: General — Tags: — m759 @ 6:00 pm
"I was reading Durant's section on Plato, struggling to understand his theory of the ideal Forms that lay in inviolable perfection out beyond the phantasmagoria. (That was the first, and I think the last, time that I encountered that word.)"

Part I: Phantasmagoria
 

Enlarge this image
Father and daughter in Bee Season
Photo by Phil Bray

Transcendence through spelling:
Richard Gere and Flora Cross
as father and daughter
in the film of Bee Season.

"Every aspect of the alef's
construction has been
Divinely designed
to teach us something."

Alef– The Difference Between
Exile And Redemption,
by Rabbi Aaron L. Raskin

Related material–

Art Theory for Yom Kippur
and
Log24 entries, Nov. 2005.


Part II: Hunt for the Real

The Alphabet Versus the Goddess:
The Conflict Between Word and Image
.

See also the references
to Zelazny's Eye of Cat
in the Nov. 2005 entries
as well as
today's previous entry
with the Norton Simon motto
"Hunt for the best"– and…

The image “http://www.log24.com/log/pix07/070302-EyeOfCat.jpg” cannot be displayed, because it contains errors.
Click for details.

"Photography has always involved waiting…. the photographer is understood to be waiting for the right convergence of subject, lighting and frame before clicking the shutter– waiting for what a master of the genre, Henri Cartier-Bresson, famously called 'the decisive moment.' Lee Friedlander, another great street photographer, compared this anticipatory state to the hunting alertness of a 'one-eyed cat.' The metaphor of the hunt has seeped into the essential language of photography."

Arthur Lubow in The New York Times, Feb. 25, 2007

Tuesday, February 27, 2007

Tuesday February 27, 2007

Filed under: General,Geometry — m759 @ 9:25 pm
Suggested by today’s 
New York Times story
on a Harvard student’s
research on pattern in
Islamic art —

and in memory of
George Sadek

From Log24 in July 2005:

Intersections

A Trinity Sunday sermon
quotes T. S. Eliot:

“… to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint.”

See also The Diamond Project.

Related material:

                                  ” … an alphabet
By which to spell out holy doom and end,
A bee for the remembering of happiness.”

— Wallace Stevens,
“The Owl in the Sarcophagus”

The image “http://www.log24.com/theory/images/HeathI47A-Illustrations.jpg” cannot be displayed, because it contains errors.

Some context for these figures:
The Diamond Theory of Truth

Tuesday, February 13, 2007

Tuesday February 13, 2007

Filed under: General — Tags: — m759 @ 5:24 am
Modern Times
vs. City Lights

Bob Dylan Wins a Folk Grammy

"Modern Times, his first album since Love and Theft, debuted at No. 1
on the US pop charts last September. At 65, Dylan became the oldest
living person to achieve this feat."  –New Zealand Herald, Feb. 12

From an entry of 
October 29, 2004:

"Each epoch has its singer."
Jack London,
    Oakland, California, 1901

"Anything but the void. And so we keep hoping to luck into a winning combination, to tap into a subtle harmony, trying like lock pickers to negotiate a compromise with the 'mystery tramp,' as Bob Dylan put it…."
— Dennis Overbye,
   Quantum Baseball,
   New York Times,
   Oct.  26, 2004

"You said you'd never compromise
With the mystery tramp,
    but now you realize
He's not selling any alibis
As you stare into
    the vacuum of his eyes
And ask him do you want to
    make a deal?"
— Bob Dylan,
    Like a Rolling Stone

"Climbing up on 
Solsbury Hill"

In today's meditation for
the Church of Peter Gabriel,
Dennis Overbye plays
the role of Jack Horner.

Jack Horner with Christmas pie

(See Overbye on Sagan in today's
New York Times, Sagan on Pi,
and Pi Day at Harvard.)

For more on Jack Horner, see
The Rise and Fall
of Popular Music
,
by Donald Clarke,
Chapter One.

For two contrasting approaches
to popular music, see two artists
whose birthdays are today:

Peter Hook and Peter Gabriel

In other Grammy news–
At the end of Sunday's awards,

"Scarlett Johansson and Don Henley
 put themselves in the pole position
to star in a remake of 'Adam's Rib'
with the following exchange:

Henley: So you're recording
your first album?

Johansson: Yeah. Do you
have any advice for me?

Henley: No."

David Marchese, Salon.com

"Her wall is filled with pictures,
she gets 'em one by one….
"

Friday, October 13, 2006

Friday October 13, 2006

Filed under: General — m759 @ 12:00 am

To a
Dark Lady*

“Something inside
is telling me that
I’ve got your secret.
Are you still listening?
Fear is the lock, and laughter
the key to your heart….

… you are what you are.
And you make it hard,
and you make it hard….”

Stephen Stills Songbook

* Suggested by…

  (1) A Harvard Crimson opinion piece
       of Oct. 12, “A Psychosexual Sham
  (2) Remarks on the sin of masturbation
        (Ask Father Hardon)
  (3) Shem was a sham…. (FW I.7, 170).

  See also the Crimson on Jack Nicholson
  and Log24 on a food joke.

  “Ours is a very gutsy religion, Cullinane.”
    — The Source, by James A. Michener
  
   Tell it to James Joyce.

Saturday, March 25, 2006

Saturday March 25, 2006

Filed under: General — m759 @ 4:23 pm
Built

In memory of Rolf Myller,
who died on Thursday,
March 23, 2006, at
Mount Sinai Hospital
in Manhattan:

Myller was,
according to the
New York Times,
an architect
whose eclectic pursuits
included writing
children’s books,
The Bible Puzzle Book, and
Fantasex: A Book of Erotic Games.

He also wrote, the Times says,
Symbols and Their Meaning
(1978), a graphic overview of
children’s nonverbal communication.”
This is of interest in view of the
Log24 reference to “symbol-mongers”
on the date of Myller’s death.

In honor of Women’s History Month
and of Myller’s interests in the erotic
and in architecture, we present
the following work from a British gallery.

The image “http://www.log24.com/log/pix06/060325-WhiteCube.jpg” cannot be displayed, because it contains errors.

This work might aptly be
  retitled “Brick Shithouse.”

Related material:

(1) the artist’s self-portrait

The image “http://www.log24.com/log/pix06/060325-LizaLouSelfPortrait.jpg” cannot be displayed, because it contains errors.

and, in view of the cover
illustration for Myller’s
The Bible Puzzle Book,

The image “http://www.log24.com/log/pix06/060325-Tower.jpg” cannot be displayed, because it contains errors.

(2) the monumental treatise
by Leonard Shlain

The Alphabet Versus
the Goddess: The Conflict
Between Word and Image
.

For devotees of women’s history
and of the Goddess,
here are further details from
the White Cube gallery:

Liza Lou

03.03.06 – 08.04.06

White Cube is pleased to present the first UK solo exhibition by Los Angeles-based artist Liza Lou.

Combining visionary, conceptual and craft approaches, Lou makes mixed-media sculptures and room-size installations that are suggestive of a transcendental reality. Lou’s work often employs familiar, domestic forms, crafted from a variety of materials such as steel, wood, papier-mâché and fibreglass, which is then covered with tiny glass beads that are painstakingly applied, one at a time, with tweezers. Dazzling and opulent and constantly glistening with refracted light, her sculptures bristle with what Peter Schjeldahl has aptly described as ‘surreal excrescence’.

This exhibition, a meditation on the vulnerability of the human body and the architecture of confinement, will include several new figurative sculptures as well as two major sculptural installations. Security Fence (2005) is a large scale cage made up of four steel, chain link walls, topped by rings of barbed wire and Cell (2004-2006), as its name suggests, is a room based on the approximate dimensions of a death row prison cell, a kind of externalized map of the prisoner’s mind. Both Security Fence and Cell, like Lou’s immense earlier installations Kitchen (1991-1995) and Back Yard (1995-1999) are characterized by the absence of their real human subject. But whereas the absent subject in Kitchen and Back Yard could be imagined through the details and accessories carefully laid out to view, in Lou’s two new installations the human body is implied simply through the empty volume created by the surrounding architecture. Both Cell and Security Fence are monochromatic and employ iconic forms that make direct reference to Minimalist art in its use of repetition, formal perfection and materiality. In contrast to this, the organic form of a gnarled tree trunk, Scaffold (2005-2006), its surface covered with shimmering golden beads, juts directly out from the wall.

Lou’s work has an immediate ‘shock’ content that works on different levels: first, an acknowledgement of the work’s sheer aesthetic impact and secondly the slower comprehension of the labour that underlies its construction. But whereas in Lou’s earlier works the startling clarity of the image is often a counterpoint to the lengthy process of its realization, for the execution of Cell, Lou further slowed down the process by using beads of the smallest variety with their holes all facing up in an exacting hour-by-hour approach in order to ‘use time as an art material’.

Concluding this body of work are three male figures in states of anguish. In The Seer (2005-2006), a man becomes the means of turning his body back in on himself. Bent over double, his body becomes an instrument of impending self-mutilation, the surface of his body covered with silver-lined beads, placed with the exactitude and precision of a surgeon. In Homeostasis (2005-2006) a naked man stands prostrate with his hands up against the wall in an act of surrender. In this work, the dissolution between inside and outside is explored as the ornate surface of Lou’s cell-like material ‘covers’ the form while exposing the systems of the body, both corporeal and esoteric. In The Vessel (2005-2006), Christ, the universal symbol of torture and agony holds up a broken log over his shoulders. This figure is beheaded, and bejewelled, with its neck carved out, becoming a vessel into which the world deposits its pain and suffering.

Lou has had numerous solo exhibitions internationally, including Museum Kunst Palast, Düsseldorf, Henie Onstad Kunstsenter, Oslo and Fondació Joan Miró, Barcelona. She was a 2002 recipient of the MacArthur Foundation Fellowship.

Liza Lou’s film Born Again (2004), in which the artist tells the compelling and traumatic story* of her Pentecostal upbringing in Minnesota, will be screened at 52 Hoxton Square from 3 – 25 March courtesy of Penny Govett and Mick Kerr.

Liza Lou will be discussing her work following a screening of her film at the ICA, The Mall, London on Friday 3 March at 7pm. Tickets are available from the ICA box office (+ 44 (0) 20 7930 3647).

A fully illustrated catalogue, with a text by Jeanette Winterson and an interview with Tim Marlow, will accompany the exhibition.

White Cube is open Tuesday to Saturday, 10.00 am to 6.00 pm.

For further information please contact Honey Luard or Susannah Hyman on + 44 (0) 20 7930 5373

* Warning note from Adrian Searle
    in The Guardian of March 21:
   “How much of her story is
    gospel truth we’ll never know.”

For deeper background on
art, patriarchal religion,
and feminism, see
The Agony and the Ya-Ya.

Monday, August 29, 2005

Monday August 29, 2005

Filed under: General — Tags: — m759 @ 4:00 pm
VALE

The image “http://www.log24.com/log/pix05B/050829-GeorgeAndEsther2.jpg” cannot be displayed, because it contains errors.

George and Esther Szekeres

From the weblog of
David Michael Brown, Jr.:
 

Date:     Sun, 28 Aug 2005
             12:30:40 -0400
From:    Alf van der Poorten AM
           
Subject: Vale George Szekeres and
             Esther Klein Szekeres

Members of the Number Theory List will be sad to learn that George and Esther Szekeres both died this morning.  George, 94, had been quite ill for the last 2-3 days, barely conscious, and died first at 06:30.  Esther, 95, died a half hour later.

Both George Szekeres and Esther Klein will be recalled by number theorists as members of the group of young Hungarian mathematicians of the 1930s including Turan and Erdos.  George and Esther's coming to Australia in the late 40s played an important role in the invigoration of Australian Mathematics.  George was also an expert in group theory and relativity; he was my PhD supervisor.

Emeritus Professor
Alf van der Poorten AM
Centre for Number Theory Research
1 Bimbil Place, Killara NSW

 

Related material:

AVE

3:09 PM EDT Thursday, Aug. 25, 2005:
 

  "Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one." 

 

  "A very short space of time through very short times of space….
   Am I walking into eternity along Sandymount strand?"

   — James Joyce, Ulysses, Proteus chapter

A very short space of time through very short times of space….

   "It is demonstrated that space-time should possess a discrete structure on Planck scales."

   — Peter Szekeres, abstract of Discrete Space-Time

Peter Szekeres is the son of George and Esther Szekeres.
 

ATQUE

"At present, such relationships can at best be heuristically described in terms that invoke some notion of an 'intelligent user standing outside the system.'"

Gian-Carlo Rota in Indiscrete Thoughts, p. 152
 

Related material:
High Concept and
Nothing Nothings (Again).

Thursday, August 25, 2005

Thursday August 25, 2005

Filed under: General,Geometry — m759 @ 3:09 pm
Analogical
Train of Thought

Part I: The 24-Cell

From S. H. Cullinane,
 Visualizing GL(2,p),
 March 26, 1985–

Visualizing the
binary tetrahedral group
(the 24-cell):

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

Another representation of
the 24-cell
:

The image “http://www.log24.com/theory/images/24-cell.jpg” cannot be displayed, because it contains errors.

 From John Baez,
This Week’s Finds in
Mathematical Physics (Week 198)
,”
September 6, 2003: 

Noam Elkies writes to John Baez:

Hello again,

You write:

[…]

“I’d like to wrap up with a few small comments about last Week.  There I said a bit about a 24-element group called the ‘binary tetrahedral group’, a 24-element group called SL(2,Z/3), and the vertices of a regular polytope in 4 dimensions called the ’24-cell’.  The most important fact is that these are all the same thing! And I’ve learned a bit more about this thing from here:”

[…]

Here’s yet another way to see this: the 24-cell is the subgroup of the unit quaternions (a.k.a. SU(2)) consisting of the elements of norm 1 in the Hurwitz quaternions – the ring of quaternions obtained from the Z-span of {1,i,j,k} by plugging up the holes at (1+i+j+k)/2 and its <1,i,j,k> translates. Call this ring A. Then this group maps injectively to A/3A, because for any g,g’ in the group |g-g’| is at most 2 so g-g’ is not in 3A unless g=g’. But for any odd prime p the (Z/pZ)-algebra A/pA is isomorphic with the algebra of 2*2 matrices with entries in Z/pZ, with the quaternion norm identified with the determinant. So our 24-element group injects into SL2(Z/3Z) – which is barely large enough to accommodate it. So the injection must be an isomorphism.

Continuing a bit longer in this vein: this 24-element group then injects into SL2(Z/pZ) for any odd prime p, but this injection is not an isomorphism once p>3. For instance, when p=5 the image has index 5 – which, however, does give us a map from SL2(Z/5Z) to the symmetric group of order 5, using the action of SL2(Z/5Z) by conjugation on the 5 conjugates of the 24-element group. This turns out to be one way to see the isomorphism of PSL2(Z/5Z) with the alternating group A5.

Likewise the octahedral and icosahedral groups S4 and A5 can be found in PSL2(Z/7Z) and PSL2(Z/11Z), which gives the permutation representations of those two groups on 7 and 11 letters respectively; and A5 is also an index-6 subgroup of PSL2(F9), which yields the identification of that group with A6.

NDE


The enrapturing discoveries of our field systematically conceal, like footprints erased in the sand, the analogical train of thought that is the authentic life of mathematics – Gian-Carlo Rota

Like footprints erased in the sand….

Part II: Discrete Space

The James Joyce School
 of Theoretical Physics
:


Log24, May 27, 2004

  “Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one.” 

  “A very short space of time through very short times of space….
   Am I walking into eternity along Sandymount strand?”

   — James Joyce, Ulysses, Proteus chapter

A very short space of time through very short times of space….

   “It is demonstrated that space-time should possess a discrete structure on Planck scales.”

   — Peter Szekeres, abstract of Discrete Space-Time

   “A theory…. predicts that space and time are indeed made of discrete pieces.”

   — Lee Smolin in Atoms of Space and Time (pdf), Scientific American, Jan. 2004

   “… a fundamental discreteness of spacetime seems to be a prediction of the theory….”

   — Thomas Thiemann, abstract of Introduction to Modern Canonical Quantum General Relativity

   “Theories of discrete space-time structure are being studied from a variety of perspectives.”

   — Quantum Gravity and the Foundations of Quantum Mechanics at Imperial College, London

Disclaimer:

The above speculations by physicists
are offered as curiosities.
I have no idea whether
 any of them are correct.

Related material:

Stephen Wolfram offers a brief
History of Discrete Space.

For a discussion of space as discrete
by a non-physicist, see John Bigelow‘s
Space and Timaeus.

Part III: Quaternions
in a Discrete Space

Apart from any considerations of
physics, there are of course many
purely mathematical discrete spaces.
See Visible Mathematics, continued
 (Aug. 4, 2005):

The image “http://www.log24.com/theory/images/Quaternions2.jpg” cannot be displayed, because it contains errors.

Tuesday, June 7, 2005

Tuesday June 7, 2005

Filed under: General — m759 @ 9:39 pm
939, or
Too Clever by Half

On the new
Prime Minister of France:

In Praise of Those Who Stole the Fire, M. de Villepin’s grandest literary effort to date…. will enhance his reputation within a small Paris set, but not in Washington, where he is already regarded as too clever by half.”

— Philip Delves Broughton,
    “De Villepin bares soul
     as France’s politician poet
,”
    The Telegraph, May 23, 2003

From a Study Guide to
Frankenstein, or The Modern Prometheus:

The Titan Prometheus was “‘… chained to Mount Caucasus where an eagle preyed on his liver’ (Bullfinch [sic] 939).”  The study guide does not say whether 939 is a page number or paragraph number, nor does it name which edition of Bulfinch’s Mythology is meant.

The rest of the story:

From the Web-Guide to Thomas Pynchon’s V:

“Prometheus —  One of the Titans of Greek myth, famous as a benefactor of man. Zeus had him make men out of mud and water; however, pitying mankind, he stole fire from heaven and gave it to them. As punishment, Zeus chained him to Mount Caucasus where an eagle preyed on his liver all day, the liver being renewed at night. Hercules eventually released him and killed the eagle. Zeus sent Pandora to Earth with her box of evils to balance the gift of fire.”

Related material:

Pandora’s Box

The image “http://www.log24.com/log/pix05/050310-hex.jpg” cannot be displayed, because it contains errors.

 and

The Barest Vocabulary

The image “http://www.log24.com/log/pix05A/050602-BallotBox.jpg” cannot be displayed, because it contains errors.


Postscript for John Nash:

  Why 939 signifies
“too clever by half” —
see 6:26 and 313.

See also


Joke #939
Date: Thu, 13 Nov 1997
From: Rainybow
Q: Do you know why God created woman second?
A: Because he didn’t want all the advice.

Sunday, February 13, 2005

Sunday February 13, 2005

Filed under: General — m759 @ 8:00 pm

Eight is a Gate,
continued

“The eighth letter of the Hebrew alphabet is called ‘Chet’ (rhymes with ‘let’) and has the (light scraping) sound of ‘ch’ as in ‘Bach.'”

The Letter Chet    

The image “http://www.log24.com/log/pix05/050213-Chet.gif” cannot be displayed, because it contains errors.

Akhlah.com    

Thursday, May 27, 2004

Thursday May 27, 2004

Filed under: General — Tags: , — m759 @ 10:10 am

Ineluctable

On the poetry of Geoffrey Hill:

"… why read him? Because of the things he writes about—war and peace and sacrifice, and the search for meaning and the truths of the heart, and for that haunting sense that, in spite of war and terror and the indifferences that make up our daily hells, there really is some grander reality, some ineluctable presence we keep touching. There remains in Hill the daunting possibility that it may actually all cohere in the end, or at least enough of it to keep us searching for more.

There is a hard edge to Hill, a strong Calvinist streak in him, and an intelligence that reminds one of Milton….."

— Paul Mariani, review in America of Geoffrey Hill's The Orchards of Syon

"Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one." 

"A very short space of time through very short times of space…. Am I walking into eternity along Sandymount strand?"

James Joyce, Ulysses, Proteus chapter

"Time has been unfolded into space."

James O. Coplien, Bell Labs

"Pattern and symmetry are closely related."

James O. Coplien on Symmetry Breaking

"… as the critic S. L. Goldberg puts it, 'the chapter explores the Protean transformations of matter in time . . . apprehensible only in the condition of flux . . . as object . . . and Stephen himself, as subject. In the one aspect Stephen is seeking the principles of change and the underlying substance of sensory experience; in the other, he is seeking his self among its temporal manifestations'….

— Goldberg, S.L. 'Homer and the Nightmare of History.' Modern Critical Views: James Joyce. Ed. Harold Bloom. New York: Chelsea House, 1986. 21-38."

from the Choate site of David M. Loeb

In summary:

 

James Joyce
Joyce

Aleph,
alpha:
nought,
nought,
one
:

See also Time Fold.

(By the way, Jorn Barger seems
to have emerged from seclusion.)

 

Sunday, April 11, 2004

Sunday April 11, 2004

Filed under: General,Geometry — m759 @ 3:28 pm

Good Friday and
Descartes’s Easter Egg

“The use of z, y, x . . . to represent unknowns is due to René Descartes, in his La géometrie (1637)…. In a paper on Cartesian ovals, prepared before 1629, x alone occurs as unknown…. This is the earliest place in which Descartes used one of the last letters of the alphabet to represent an unknown.”

— Florian Cajori, A History of Mathematical Notations. 2 volumes. Lasalle, Illinois: The Open Court Publishing Co., 1928-1929. (Vol. 1, page 381)

This is from

http://members.aol.com/jeff570/variables.html.

Descartes’s Easter Egg is found at

EggMath: The Shape of an Egg —
Cartesian Ovals
 

An Easter Meditation
on Humpty Dumpty

The following is excerpted from a web page headed “Catholic Way.”  It is one of a series of vicious and stupid Roman Catholic attacks on Descartes.  Such attacks have been encouraged by the present Pope, who today said “may the culture of life and love render vain the logic of death.”

The culture of life and love is that of the geometry (if not the philosophy) of Descartes.  The logic of death is that of Karol Wojtyla, as was made very clear in the past century by the National Socialist Party, which had its roots in Roman Catholicism.

Humpty Dumpty sat on a wall.
Humpty Dumpty had a great fall

“In the century just completed, the human race found itself in a position not unlike the scrambled mess at the base of an imaginary English wall….

… we are heirs to a humanity that is broken, fractured, confused, unsure of what to make of itself….

 … ‘postmodernism’ is merely the articulation of the fractured, dissipated state of the human being…. 

Without relating a history of modern philosophy, our unfortunate human shell has suffered a continual fragmentation for a period of roughly 500 years. (You philosophers out there will recognize immediately that I am referring to the legacy of René Descartes.) And this fragmentation has been a one-way street: one assault after another on the integrity and dignity of the human person until you have, well, the 20th Century.

But now it’s the 21st Century.

The beauty … the marvel … the miracle of our time is the possibility that gravity will reverse itself: Humpty Dumpty may be able, once again, to assume his perch.”

—  Ted Papa,
Raising Humpty Dumpty

Voilà.

The upper part
of the above icon
is from EggMath.
For the lower part,
see Good Friday.

Thursday, March 4, 2004

Thursday March 4, 2004

Filed under: General — Tags: , — m759 @ 1:44 pm

ZZ

Mit Zeichen und Zahlen
vermessen wir Himmel und Erde
schwarz
auf weiss
schaffen wir neue Welten
oder gar Universen
 
With numbers and names
we measure heaven and earth
black
on white
we create new worlds
and universes
 
— from “Zahlen und Zeichen,
  Wörter und Worte”
 
 

“Numbers and Names,
Wording and Words”

by Eugen Jost

English translation by Catherine Schelbert

Alphabets

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

See also the previous entry,
on the dream
of El Pato-lógico.

Tuesday, March 2, 2004

Tuesday March 2, 2004

Filed under: General — m759 @ 3:01 pm

Passion

From the previous entry:

 1.
Oscar:
military phonetic
for the letter
‘O’

From an entry of Dec. 21, 2002, some background in literary theory:

“I know what ‘nothing’ means….”
— Maria Wyeth in Play It As It Lays

“How do you solve a problem like Maria?”
— Oscar Hammerstein II

“…problems can be solved by manipulating just two symbols, 1 and 0….” 
— George Johnson, obituary of Claude Shannon

“The female and the male continue this charming dance, populating the world with all living beings.” 
— Leonard Shlain, The Alphabet Versus the Goddess, Penguin Arkana paperback, 1999, Chapter 17, “Lingam/Yoni” 

“According to Showalter’s essay*, ‘In Elizabethan slang, ‘nothing’ was a term for the female genitalia . . . what lies between maids’ legs, for, in the male visual system of representation and desire…. Ophelia’s story becomes

the Story of O — the zero, the empty circle or mystery of feminine difference, the cipher of female sexuality to be deciphered by feminist interpretation.’ (222)* Ophelia is a highly sexual being…”

— Leigh DiAngelo,
   Ophelia as a Sexual Being

*Showalter, Elaine. “Representing Ophelia: Women, Madness, and the Responsibilities of Feminist Criticism.” Hamlet. Ed. Susanne L. Wofford. Boston: Bedford Books of St.Martin’s Press, 1994. 220-238.

At the Oscars Sunday night, a thought attributed by Billy Crystal to Sean Connery:

“Pussy Galore! I just got it! That’s vulgar.”

For further background, see

Passing the Crown (Aug. 24, 2003) and

The Agony and the Ya-Ya (Oct. 4, 2002).

Saturday, December 20, 2003

Saturday December 20, 2003

Filed under: General,Geometry — Tags: — m759 @ 5:00 pm

White, Geometric, and Eternal

This afternoon's surfing:

Prompted by Edward Rothstein's own Fides et Ratio encyclical in today's NY Times, I googled him.

At the New York Review of Books, I came across the following by Rothstein:

"… statements about TNT can be represented within TNT: the formal system can, in a precise way, 'talk' about itself."

This naturally prompted me to check what is on TNT on this, the feast day of St. Emil Artin.  At 5 PM this afternoon, we have Al Pacino in "The Devil's Advocate" — a perfect choice for the festival of an alleged saint.

Preparing for Al, I meditated on the mystical significance of the number 373, as explained in Zen and Language Games: the page number 373 in Robert Stone's theological classic A Flag for Sunrise conveys the metaphysical significance of the phrase "diamonds are forever" — "the eternal in the temporal," according to Stone's Catholic priest.  This suggests a check of another theological classic, Pynchon's Gravity's RainbowPage 373 there begins with the following description of prewar Berlin:

"white and geometric."

This suggests the following illustration of a white and geometric object related to yesterday's entry on Helmut Wielandt:

From antiquark.com

Figure 1

(This object, which illustrates the phrase "makin' the changes," also occurs in this morning's entry on the death of a jazz musician.)

A further search for books containing "white" and "geometric" at Amazon.com yields the following:

Figure 2

From Mosaics, by
Fassett, Bahouth, and Patterson:

"A risco fountain in Mexico city, begun circa 1740 and made up of Mexican pottery and Chinese porcelain, including Ming.

The delicate oriental patterns on so many different-sized plates and saucers [are] underlined by the bold blue and white geometric tiles at the base."

Note that the tiles are those of Diamond Theory; the geometric object in figure 1 above illustrates a group that plays a central role in that theory.

Finally, the word "risco" (from Casa del Risco) associated with figure 2 above leads us to a rather significant theological site associated with the holy city of Santiago de Compostela:

Figure 3

Vicente Risco's
Dedalus in Compostela.

Figure 3 shows James Joyce (alias Dedalus), whose daughter Lucia inspired the recent entry Jazz on St. Lucia's Day — which in turn is related, by last night's 2:45 entry and by Figure 1, to the mathematics of group theory so well expounded by the putative saint Emil Artin.

"His lectures are best described as
polished diamonds."
Fine Hall in its Golden Age,
by Gian-Carlo Rota

If Pynchon plays the role of devil's advocate suggested by his creation, in Gravity's Rainbow, of the character Emil Bummer, we may hope that Rota, no longer in time but now in eternity, can be persuaded to play the important role of saint's advocate for his Emil.
 

Update of 6:30 PM 12/20/03:

Riddled:

The Absolutist Faith
of The New York Times

White and Geometric, but not Eternal.

Friday, March 14, 2003

Friday March 14, 2003

Filed under: General — Tags: — m759 @ 2:20 am

The Producers, Part Deux:

The Consumers

Sidney Lippman, Hit Songwriter,
Dies at 89

From THE NEW YORK TIMES

Sidney Lippman, the composer and songwriter who wrote the music for "A — You're Adorable," died on Tuesday, March 11, 2003, in New Jersey.  He was 89.

He teamed up with lyricists Buddy Kaye and Fred Wise to write

"A — You're Adorable (The Alphabet Song)"

which became a No. 1 hit in 1949 as an RCA Victor recording with Perry Como and the Fontane Sisters.

See also my Tuesday, March 11, entry,

The Producers,

and my entry from 2001,

Random Thoughts for St. Patrick's Eve.

The illustration above, a tribute to Meg Ryan on Einstein's birthday, may serve as a counterpoint to the "Producers" entry of March 11, the date of Lippman's death.

The St. Patrick's Eve note contains a rather different meditation on the letter "A."  See too

The Alphabet Versus the Goddess,

an intriguing speculation by Leonard Shlain, who claims to show that "patriarchy and misogyny have moved contrapuntually to goddess veneration."

Well, maybe not quite yet; but blessed are the peacemakers.

Sunday, January 12, 2003

Sunday January 12, 2003

Filed under: General — m759 @ 4:17 pm

Ask Not…

For you it's goodbye,
For me it's to cry,
"For whom the bell tolls"…

The Bee Gees


The Bells of Notre Dame

(Recall Julia Ormond in
 the 1995 "
Sabrina.")

 


JAN. 12, 2003,  N. Y. TIMES OBITUARIES  



C. Douglas Dillon, Financier Who Served in Kennedy Cabinet, Dies at 93 C. Douglas Dillon, Financier Who Served in Kennedy Cabinet,
Dies at 93

By ERIC PACE

C.Douglas Dillon was named secretary of the Treasury by President Kennedy and ambassador to France under President Eisenhower.

Monique Wittig, 67, Feminist Writer, Is Dead Monique Wittig, 67, Feminist Writer, Is Dead

By DOUGLAS MARTIN
Monique Wittig was a French writer and literary theorist whose imaginative, fiercely innovative books tried to create a new mythology for the feminist movement. 



Getty Images

Maurice Gibb, Bassist for the Bee Gees,
Dies at 53

By THE ASSOCIATED PRESS
Maurice Gibb played bass and keyboard for the Bee Gees, whose 1977 album, "Saturday Night Fever," sold more than 40 million copies.


Added Jan. 13, 2003 (feast day of St. James Joyce):

For more on feminism and mythology, see

For the rest of the Dillon story,
click on the big red C above.

In this case, the victory of the alphabet over the goddess may have been rather short-lived. Here is Miss Audrey Hepburn (the original film Sabrina) as a very credible — and victorious — goddess:

See also the journal entries below.

Saturday, December 21, 2002

Saturday December 21, 2002

Filed under: General — m759 @ 7:00 pm

To Ophelia
at the Winter Solstice

Introduction

“There is one story and one story only
That will prove worth your telling…

… is it of the Virgin’s silver beauty,
All fish below the thighs?
She in her left hand bears a leafy quince;
When, with her right hand she crooks a finger, smiling,
How many the King hold back?
Royally then he barters life for love.

Or of the undying snake from chaos hatched,
Whose coils contain the ocean,
Into whose chops with naked sword he springs,
Then in black water, tangled by the reeds,
Battles three days and nights,
To be spewed up beside her scalloped shore?”

— Robert Graves, “To Juan at the Winter Solstice”

Illustrations

The Virgin’s Beauty 

 On the Beach

A Maiden’s Prayer

Answered Prayer

Dialogue

Act III Scene ii:

Hamlet   Lady, shall I lie in your lap?
Ophelia  No, my lord.
Hamlet   I mean, my head upon your lap?
Ophelia  Ay, my lord.
Hamlet   Do you think I meant country matters?
Ophelia  I think nothing, my lord.
Hamlet   That’s a fair thought to lie between maid’s legs.
Ophelia   What is, my lord?
Hamlet    Nothing.
Ophelia   You are merry, my lord.  
Hamlet    Who, I?
Ophelia   Ay, my lord.

Quotations

“Do you know nothing? Do you see nothing? Do you remember nothing?” 
— T. S. Eliot, “The Waste Land”

“At the still point, there the dance is.” 
— T. S. Eliot, Four Quartets

“I know what ‘nothing’ means….”
— Maria Wyeth in Play It As It Lays

“How do you solve a problem like Maria?”
— Oscar Hammerstein II

“…problems can be solved by manipulating just two symbols, 1 and 0….” 
— George Johnson, obituary of Claude Shannon

“The female and the male continue this charming dance, populating the world with all living beings.” 
— Leonard Shlain, The Alphabet Versus the Goddess,
    Penguin Arkana paperback, 1999, Chapter 17,
    “Lingam/Yoni” 

“According to Showalter’s essay*, ‘In Elizabethan slang, ‘nothing’ was a term for the female genitalia . . . what lies between maids’ legs, for, in the male visual system of representation and desire…. Ophelia’s story becomes the Story of O — the zero, the empty circle or mystery of feminine difference, the cipher of female sexuality to be deciphered by feminist interpretation.’ (222)* Ophelia is a highly sexual being…”

— Leigh DiAngelo,
   Ophelia as a Sexual Being

S. H. Cullinane: “No shit, Sherlock.”

*Showalter, Elaine. “Representing Ophelia: Women, Madness, and the Responsibilities of Feminist Criticism.” Hamlet. Ed. Susanne L. Wofford. Boston: Bedford Books of St.Martin’s Press, 1994. 220-238.

Dénouement

Is that nothing between your legs
or are you just happy to see me?


See also The Ya-Ya Monologues.

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