(Adapted from Encyclopaedia Britannica,
Eleventh Edition (1911), Crystallography .)
Friday, December 13, 2019
Apollo’s 13 Revisited
Friday, May 13, 2011
Apollo’s 13
Continued … See related previous posts.
Those who prefer narrative to mathematics
may consult Wikipedia on The Cosmic Cube.
Sunday, August 19, 2018
Apollo and the Furies
Narration by the fictional schoolgirl Pagan Moore in a novel
apparently first published on March 4, 2004 —
"Now, can anyone else tell me or shall I ask Miss Moore again to help us out?” “Apollo is a symbol for the male, the rational, the young, and the civilized. The Furies represent the female, the violent, the old, and the primal. Aeschylus captures a mythical moment in history, one in which the world was torn between a savage and archaic past and the bold new order of Greek civilization, the young Olympian gods, and rationality. The difficulty of the struggle between these two worlds is dramatized by the cycle of violence in the House of Atreus and the clash between Apollo and the Furies.” No one giggled after Dank finished.
—Existence (first novel of a trilogy), pp. 80-81. |
Update at 1:37 PM ET the same day —
A check for the source of the above speech yields …
"Apollo is a symbol for the male, the rational, the young, and the civilized.
The Furies represent the female, the violent, the old, and the primal."
This passage is from
https://www.gradesaver.com/the-eumenides/study-guide/themes.
From the citation data there —
"By Borey, Eddie. 'The Eumenides Themes.'
GradeSaver, 24 October 2000 Web."
Tuesday, July 26, 2016
Installation: Area 51 Meets Apollo
Ben Lerner on Judd's art at Marfa —
"as if the installation were waiting to be visited
by an alien or god" — 10:04: A Novel
Oslo artist Josefine Lyche's public Instagram today —
See also Space (May 13, 2015).
Wednesday, October 9, 2013
To Apollo*
Saturday, July 9, 2011
Blessings from the Apollo
Part I, Midday —
Yesterday's midday NY Lottery "689" suggests (from April 3, 2005)—
689 | [fú] blessing, good fortune |
Diagram taken from R. Sing,
“Chinese New Year’s Dragon Teacher’s Guide”
— and the 4-digit midday number suggests a NASA Picture of the Day
that was published (not taken) on 7795 (7/7/95)—
Part II, Evening —
Suggested by yesterday's evening NY Lottery "068"
and by Weltschmerz and the Ursprache —
— Walter Benjamin, “On Language as Such and On the Language of Man” (1916),
Edmund Jephcott, tr., Walter Benjamin, Selected Writings, Volume I: 1913-1926 ,
Marcus Bullock and Michael W. Jennings, eds., Cambridge, MA,
Harvard University Press, 1996, pp. 62-74. The above is page 68.
A more entertaining meditation is suggested by yesterday's 4-digit evening NY number—
a video tribute to a song said to have been released as a single on 7383 (7/3/83)—
Related material— "Dark Side of the Moon" in this journal.
Sunday, June 27, 2010
Sunday at the Apollo
27
The 13 symmetry axes of the (Euclidean) cube–
exactly one axis for each pair of opposite
subcubes in the 27-part (Galois) 3×3×3 cube–
Sunday, May 13, 2007
Sunday May 13, 2007
Prime Blue
"To the two gods of art, Apollo and Dionysus, we owe our recognition that… there is a tremendous opposition, as regards both origins and aims, between the Apolline art of the sculptor and the non-visual, Dionysiac art of music."
— The Birth of Tragedy,
by Friedrich Nietzsche,
Penguin, 1993, page 14.
Quoted in "A Mass for Lucero."
Half the Answer:
Commentary by spookytruth
from Log24, 2/22/2005:
"I mean, come on, Hunter, a stupid bullet through the head??? how creative, you brain-addled simpleton… if you take the assignment, if you are going to hook up your afterlife keyboard and transmit back and tell us about what it is REALLY like out there, if you decided to let your electric-shock fingers hot wire us the truth of the afterlife… if you really planned to tell us the answer to our ultimate, emotional question…… 'does God prefer beer, wine, or a shot of whiskey.' well, if that is what you decided to do well then, for God's sake, don't forget (oh, wait, yeah, you already DID FORGET, you half-baked, half brained, half witted, half-a-loaf, half pint pin head, you forgot, THE JOURNEY IS HALF THE ANSWER!!!!!!!!!!!!!!!!"
On Dionysus:
"For wine, he loves to view
his altars stain,
But prime blue ruin*–
goes against the grain."
— page 69, Jack Randall's Diary
* name "given by
the modern Greeks to gin"
— page 4, Jack Randall's Diary
Monday, June 13, 2005
Monday June 13, 2005
STAR WARS
continued
Picture from Feb. 8
(Martin Buber’s birthday)
For John Nash on his birthday:
I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.
Sunday, April 13, 2003
Sunday April 13, 2003
Palm Sunday, Part II:
Cold Mountain
From the notes to the CD of Songs From the Mountain (John Herrmann, Dirk Powell, Tim O’Brien):
“John [Herrmann, banjo player] would like to dedicate his work on this recording to Philip Kapleau Roshi, Kalu Rimpoche, and Harada Tangen Roshi, who all know the way to Cold Mountain….”
See Buddha’s Birthday (April 8) and The Diamond Project.
“What are you thinking of? What thinking? What?
I never know what you are thinking. Think.”
— Tom Eliot, The Waste Land
“I am thinking…
… of the midnight picnic
Once upon a time….”
— Suzanne Vega, “Tom’s Diner“
Once upon a time… |
|
“De donde crece la palma” — Song lyric
From On Beauty, by Elaine Scarry, Princeton University Press, 1999, a quotation from Homer —
“in Delos, beside Apollo’s altar —
the young slip of a palm-tree
springing into the light.”
See also A Mass for Lucero and The Shining of Lucero.
— George Balanchine
Sunday, October 2, 2016
Sermon
"I don't care about what anything was designed to do,
I care about what it can do."
Tuesday, August 10, 2010
A Problem
From Telegraph.co.uk (published: 5:56 PM BST 10 Aug 2010), a note on British-born Canadian journalist Bruce Garvey, who died at 70 on August 1—
In 1970, while reporting on the Apollo 13 mission at Nasa Mission Control for the Toronto Star, he was one of only two journalists— alongside Richard Killian of the Daily Express— to hear the famous message: "Houston we've had a problem."
See also Log24 posts of 10 AM and noon today.
The latter post poses the problem "You're dead. Now what?"
Again, as in this morning's post, applying Jungian synchronicity—
A check of this journal on the date of Garvey's death yields a link to 4/28's "Eightfold Geometry."
That post deals with a piece of rather esoteric mathematical folklore. Those who prefer easier problems may follow the ongoing struggles of Julie Taymor with "Spider-Man: Turn Off the Dark."
The problems of death, geometry, and Taymor meet in "Spider Woman" (April 29) and "Memorial for Galois" (May 31).
Friday, September 1, 2006
Friday September 1, 2006
“Some friends of mine
are in this band.”
— David Auburn, Proof
“And if the band you’re in
starts playing different tunes
I’ll see you on
the dark side of the moon.”
— Quoted in Log24 on the
July 20, 2005, anniversary
of the 1969 Apollo 11
“one small step” moon landing
Last night’s entry on Glenn Ford, freemasonry, and the business of narrative leads to the following meditation.
This morning’s New York Times obituary of the Apollo 11 launch director brings back memories of Dean Martin’s classic refrain “when the moon hits your eye like a big pizza pie….” This in turn is a reminder of one of the great subtitles– Dino: Living High in the Dirty Business of Dreams (by Nick Tosches, published by Secker & Warburg on November 9, 1992). I respect the launch director, Rocco A. Petrone, who later headed the successful recovery of Apollo 13 (and also headed the entire Apollo program), but I also greatly respect Nick Tosches as a guide to the dark side of humanity. Secular humanism and the religion of scientism are all very well as cheerleaders for physics, but Tosches and the Roman Catholic Church have a much better understanding of human nature and original sin.
Monday, September 30, 2024
September Song, Day XXX:
“One, two, three . . . But where is the fourth?”
The "Where is the fourth?" question above is also by Plato.
One possible answer . . .
Other possible "fourth" locations . . .
Pizza photo credit: Marcela Nowak on Instagram
“One, two, three . . . But where is the fourth?”
Wednesday, June 5, 2024
For a future Michael Crichton*— The Tachikawa Hint
Hat tip to Peter Woit for quoting the above yesterday.
* See Crichton in this weblog and the solar Apollo symbols
of CBS Sunday Morning, which this week featured Crichton.
As an Apollo symbol, I prefer the Chinese "holy field" —
a ninefold square.
Sunday, June 2, 2024
Close Enough
“… the walkway between here and there would be colder than a witch’s belt buckle. Or a well-digger’s tit. Or whatever the saying was. Vera had been hanging by a thread for a week now, comatose, in and out of Cheyne-Stokes respiration, and this was exactly the sort of night the frail ones picked to go out on. Usually at 4 a.m. He checked his watch. Only 3:20, but that was close enough for government work.”
— King, Stephen (2013-09-24). |
Related material: Apollo Shining.
Sunday, March 24, 2024
Saturday, June 3, 2023
Space Drama
"It seems fitting that a handsome, professional and future-minded
space drama in fine color, like 'Marooned,' should open a new
jewel box of a theater, the Ziegfeld."
— Howard Thompson in The New York Times , Dec. 19, 1969
A related film tells of a real-life April 1970 sequel
to the 1969 film "Marooned."
Then there is my own "jewel box" picture with three horses . . .
Friday, April 23, 2021
“And . . . Cut!”
The title is a line spoken by an independent film maker
in “The Big Bang” . . . which opened in limited theaters
on May 13, 2011.
Also on May 13, 2011 —
Monday, February 17, 2020
RIP Charles Portis
See also "True Grid " in this journal.
Rosalind Krauss "If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit. From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete. Or, to take a more up-to-date example…."
"He was looking at the nine engravings and at the circle,
"And it's whispered that soon if we all call the tune
The nine engravings of The Club Dumas
An example of the universal— or, according to Krauss,
"This is the garden of Apollo, the field of Reason…." |
See as well . . .
Monday, March 25, 2019
Tuesday, February 13, 2018
A Titan of the Field
On the late Cambridge astronomer Donald Lynden-Bell — "As an academic at a time when students listened and lecturers lectured, he had the disconcerting habit of instead picking on a random undergraduate and testing them on the topic. One former student, now a professor, remembered how he would 'ask on-the-spot questions while announcing that his daughter would solve these problems at the breakfast table'. He got away with it because he was genuinely interested in the work of his colleagues and students, and came to be viewed with great affection by them. He also got away with it because he was well established as a titan of the field." — The London Times on Feb. 8, 2018, at 5 PM (British time) |
Related material —
Two Log24 posts from yesteday, Art Wars and The Void.
See as well the field GF(9) …
… and the 3×3 grid as a symbol of Apollo
(an Olympian rather than a Titan) —
Monday, October 9, 2017
Friday, March 3, 2017
PSI
(Notes for Josefine, continued from December 22, 2013)
From a prequel to The Shining , by Stephen King—
You had to keep an eye on the boiler
because if you didn’t, she would creep on you.
What did that mean, anyway? Or was it just
one of those nonsensical things that sometimes
came to you in dreams, so much gibberish?
Of course there was undoubtedly a boiler
in the basement or somewhere to heat the place,
even summer resorts had to have heat sometimes,
didn’t they (if only to supply hot water)? But creep ?
Would a boiler creep ?
You had to keep an eye on the boiler.
It was like one of those crazy riddles,
why is a mouse when it runs,
when is a raven like a writing desk,
what is a creeping boiler?
A related figure —
Wednesday, December 23, 2015
Class of 64
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, June 24, 2015
It’s 10 PM
Do you know where your watch is?
From a post of May 13, 2015 —
From the recent film "Interstellar" —
Wednesday, May 13, 2015
Motto
See the previous post, "Space," as well as…
SymOmega in this journal and a suggested motto
for The University of Western Australia.
Space
Notes on space for day 13 of May, 2015 —
The 13 symmetry axes of the cube may be viewed as
the 13 points of the Galois projective space PG(2,3).
This space (a plane) may also be viewed as the nine points
of the Galois affine space AG(2,3) plus the four points on
an added "line at infinity."
Related poetic material:
The ninefold square and Apollo, as well as …
Wednesday, June 18, 2014
A Dark and Stormy Night
This journal on the morning of January 27, 2010,
the day of J. D. Salinger’s death, had a post on
Nietzsche and Heraclitus titled “To Apollo.”
Related material:
“… the wind was noisy the way it is in spooky movies
on the night the old slob with the will gets murdered.”
— From the opening sentence of the first Holden Caulfield
story, published in the Collier’s of December 22, 1945
See also Peter Matthiessen on Zen, Salinger and Vedanta,
and Heraclitus in this journal. Some background—
A quotation from Nietzsche…
(Sämtliche Werke, Kritische Studienausgabe in 15 Bänden (KSA).
Herausgegeben von Giorgio Colli und Mazzino Montinari.
Berlin: De Gruyter, 1980):
“Nietzsche wrote:
‘Seeing the world as a divine game and beyond good and evil:
in this both the Vedanta and Heraclitus are my predecessors.'”
— KSA vol. 11, page 26, as quoted by André van der Braak
in a chapter from his 2011 book Nietzsche and Zen
(Darin, dass die Welt ein göttliches Spiel sei
und jenseits von Gut und Böse —
habe ich die Vedanta-Philosophie
und Heraklit zum Vorgänger.)
Tuesday, October 15, 2013
The Field of Reason*
Or perhaps the Richman.
Roger Richman, agent who represented image rights for the
estates of celebrities, reportedly died on October 9, 2013.
This journal on that date —
* For the title, see Apollo + Outram in this journal.
Monday, August 26, 2013
Dark Side Tales
"Got to keep the loonies on the path."
— Lyrics to Dark Side of the Moon
For those who, like Tom Stoppard, prefer the dark side—
NEW ANGLE:
INT. OFFICE BUILDING – NIGHT
NIGHT WATCHMAN
Bateman wheels around and shoots him.
NEW ANGLE:
INT. PIERCE & PIERCE LOBBY – NIGHT
— AMERICAN PSYCHO |
Not quite so dark—
"And then one day you find ten years have got behind you."
— Lyrics to Dark Side of the Moon
This journal ten years ago, on August 25, 2003—
… We seek
The poem of pure reality, untouched
At the exactest point at which it is itself,
The eye made clear of uncertainty, with the sight
Everything, the spirit's alchemicana
The solid, but the movable, the moment,
— Wallace Stevens, "An Ordinary Evening |
"A view of New Haven, say…." —
"This is the garden of Apollo,
the field of Reason…."
John Outram, architect
A similar version of this Apollonian image —
Detail:
Related material for the loonies:
Sunday, April 1, 2012
The Palpatine Dimension
A physics quote relayed at Peter Woit's weblog today—
"The relation between 4D N=4 SYM and the 6D (2, 0) theory
is just like that between Darth Vader and the Emperor.
You see Darth Vader and you think 'Isn’t he just great?
How can anyone be greater than that? No way.'
Then you meet the Emperor."
Some related material from this weblog—
(See Big Apple and Columbia Film Theory)
The Meno Embedding:
Some related material from the Web—
See also uses of the word triality in mathematics. For instance…
A discussion of triality by Edward Witten—
Triality is in some sense the last of the exceptional isomorphisms,
and the role of triality for n = 6 thus makes it plausible that n = 6
is the maximum dimension for superconformal symmetry,
though I will not give a proof here.
— "Conformal Field Theory in Four and Six Dimensions"
and a discussion by Peter J. Cameron—
There are exactly two non-isomorphic ways
to partition the 4-subsets of a 9-set
into nine copies of AG(3,2).
Both admit 2-transitive groups.
— "The Klein Quadric and Triality"
Exercise: Is Witten's triality related to Cameron's?
(For some historical background, see the triality link from above
and Cameron's Klein Correspondence and Triality.)
Cameron applies his triality to the pure geometry of a 9-set.
For a 9-set viewed in the context of physics, see A Beginning—
From MIT Commencement Day, 2011— A symbol related to Apollo, to nine, and to "nothing"— A minimalist favicon—
This miniature 3×3 square— — may, if one likes, |
Happy April 1.
Monday, March 5, 2012
For the Nine Muses
From "The Talented," a post of April 26, 2011—
And for Josefine Lyche—
Unity in Multiplicity —
Pink in Wikipedia
Wednesday, October 12, 2011
High White Noon
Grid from a post linked to in yesterday's 24 Hour DeLillo—
For an example of this grid as slow art , consider the following—
"One can show that the binary tetrahedral group
is isomorphic to the special linear group SL(2,3)—
the group of all 2×2 matrices over the finite field F3
with unit determinant." —Wikipedia
As John Baez has noted, these two groups have the same structure as the geometric 24-cell.
For the connection of the grid to the groups and the 24-cell, see Visualizing GL(2,p).
Related material—
The 3×3 grid has been called a symbol of Apollo (Greek god of reason and of the sun).
"This is where we sat through his hushed hour,
a torchlit sky, the closeness of hills barely visible
at high white noon." — Don DeLillo, Point Omega
Friday, September 9, 2011
A Beginning
From MIT Commencement Day, 2011— A symbol related to Apollo, to nine, and to "nothing"— A minimalist favicon—
This miniature 3×3 square— — may, if one likes, |
Saturday, June 18, 2011
Midnight in the Garden (continued)–
Tracking Shot
Related material—
See also this journal's September 2009 posts.
This post was suggested by today's previous post and by today's NY Lottery.
For some background to the ioncinema.com post numbered 4210 above,
see, in conjunction with the page headed "Azazel" linked to here earlier today,
the ioncinema.com post numbered 5601.
“Stranger, dreams verily are baffling and unclear of meaning, For two are the gates of shadowy dreams, But in my case it was not from thence, methinks, Translation by A.T. Murray, in two volumes. Quoted in a press release for the film "Two Gates of Sleep." |
From the post numbered 460 in this journal—
At the still point… from the film "Absolute Power" :
Photo credit – Graham Kuhn
I’ve heard of affairs that are strictly plutonic,
But diamonds are a girl’s best friend!
Friday, June 3, 2011
MIT Day
Today is Commencement Day at MIT.
“To measure the changes — Shing-Tung Yau, To measure the changes: The smartest are nothing: |
Well, perhaps not quite nothing.
The above pictures were posted here on the day the following book was published—
The lives of the nine Jews in the above book amount to more than Yau's "nothing."
Note, however, that claims by Jews (see Jill Abramson yesterday)
that their secular publications constitute a substitute for religion
and contain only "absolute truth" should be viewed with at least one
raised eyebrow.
Abramson's remark yesterday that her promotion to New York Times executive editor
was like "ascending to Valhalla" had a religious flavor worthy of yesterday's
Feast of the Ascension.
In related news from yesterday's Times—
See also a symbol related to Apollo, to nine, and to "nothing"—
A minimalist 3×3 matrix favicon—
This may, if one likes, be viewed as the "nothing"
present at the Creation. See Jim Holt on physics.
Tuesday, April 26, 2011
The Talented
"It's going to be accomplished in steps, this establishment of the Talented in the scheme of things."
— Anne McCaffrey, Radcliffe ’47, To Ride Pegasus
"Character, as we have stated, is revealed through action.
We are not yet telepathic; we must embody even the most intellectual traits
and express them physically."
— The Craftsmen of Dionysus: An Approach to Acting by Jerome Rockwood
Dionysus Meets Apollo
in "Thirty Two Short Films About Glenn Gould"—
Step I — Tiny Dancer in My Hand (0.48.46)
Step II — The Bridge (0.52.46)
Step III — Liftoff (1.27.37)
Sunday, April 17, 2011
Sunday School
Apollo and the Tricksters
From The Story of N (Oct. 15, 2010)—
Roberta Smith on what she calls "endgame art"—
"Fear of form above all means fear of compression— of an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible."
Margaret Atwood on tricksters and art—
"If it’s a seamless whole you want, pray to Apollo."
Here is some related material In memory of CIA officer Clare Edward Petty, who died at 90 on March 18—
A review of a sort of storyteller's MacGuffin — the 3×3 grid. This is, in Smith's terms, an "artistic focus" that appears to be visually comprehensible but is not as simple as it seems.
- The Pope in Plato's Cave (Sept. 16, 2006)
- A search for "einsatz" in this journal
- True Grid (Jan. 8, 2011)
- The Hesse configuration revisited (a post initially from the date of Petty's death, but later much reworked)
The Hesse configuration can serve as more than a sort of Dan Brown MacGuffin. As a post of January 14th notes, it can (rather fancifullly) illustrate the soul—
" … I feel I understand
Existence, or at least a minute part
Of my existence, only through my art,
In terms of combinational delight…."
— Vladimir Nabokov, Pale Fire
Saturday, January 8, 2011
True Grid (continued)
"Rosetta Stone" as a Metaphor
in Mathematical Narratives
For some backgound, see Mathematics and Narrative from 2005.
Yesterday's posts on mathematics and narrative discussed some properties
of the 3×3 grid (also known as the ninefold square ).
For some other properties, see (at the college-undergraduate, or MAA, level)–
Ezra Brown, 2001, "Magic Squares, Finite Planes, and Points of Inflection on Elliptic Curves."
His conclusion:
When you are done, you will be able to arrange the points into [a] 3×3 magic square,
which resembles the one in the book [5] I was reading on elliptic curves….
This result ties together threads from finite geometry, recreational mathematics,
combinatorics, calculus, algebra, and number theory. Quite a feat!
5. Viktor Prasolov and Yuri Solvyev, Elliptic Functions and Elliptic Integrals ,
American Mathematical Society, 1997.
Brown fails to give an important clue to the historical background of this topic —
the word Hessian . (See, however, this word in the book on elliptic functions that he cites.)
Investigation of this word yields a related essay at the graduate-student, or AMS, level–
Igor Dolgachev and Michela Artebani, 2009, "The Hesse Pencil of Plane Cubic Curves ."
From the Dolgachev-Artebani introduction–
In this paper we discuss some old and new results about the widely known Hesse
configuration of 9 points and 12 lines in the projective plane P2(k ): each point lies
on 4 lines and each line contains 3 points, giving an abstract configuration (123, 94).
PlanetMath.org on the Hesse configuration—
A picture of the Hesse configuration–
(See Visualizing GL(2,p), a note from 1985).
Related notes from this journal —
From last November —
From the December 2010 American Mathematical Society Notices—
Related material from this journal— Consolation Prize (August 19, 2010) |
From 2006 —
Sunday December 10, 2006
“Function defined form, expressed in a pure geometry
– J. G. Ballard on Modernism
“The greatest obstacle to discovery is not ignorance –
— Daniel J. Boorstin, |
Also from 2006 —
Sunday November 26, 2006
Rosalind Krauss "If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit. From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete. Or, to take a more up-to-date example…."
"He was looking at the nine engravings and at the circle,
"And it's whispered that soon if we all call the tune
The nine engravings of The Club Dumas
An example of the universal*– or, according to Krauss,
"This is the garden of Apollo, the field of Reason…."
For more on the field of reason, see
A reasonable set of "strange correspondences" Unreason is, of course, more popular. * The ninefold square is perhaps a "concrete universal" in the sense of Hegel: "Two determinations found in all philosophy are the concretion of the Idea and the presence of the spirit in the same; my content must at the same time be something concrete, present. This concrete was termed Reason, and for it the more noble of those men contended with the greatest enthusiasm and warmth. Thought was raised like a standard among the nations, liberty of conviction and of conscience in me. They said to mankind, 'In this sign thou shalt conquer,' for they had before their eyes what had been done in the name of the cross alone, what had been made a matter of faith and law and religion– they saw how the sign of the cross had been degraded."
– Hegel, Lectures on the History of Philosophy ,
"For every kind of vampire, |
And from last October —
Friday, October 8, 2010
Starting Out in the Evening This post was suggested by last evening's post on mathematics and narrative and by Michiko Kakutani on Vargas Llosa in this morning's New York Times .
"One must proceed cautiously, for this road— of truth and falsehood in the realm of fiction— is riddled with traps and any enticing oasis is usually a mirage."
– "Is Fiction the Art of Lying?"* by Mario Vargas Llosa,
* The Web version's title has a misprint— |
Monday, December 13, 2010
Plan 9 Revisited
Leading today's New York Times obituaries —
— is that of Nassos Daphnis, a painter of geometric abstractions
who in 1995 had an exhibition at a Leo Castelli gallery
titled "Energies in Outer Space." (See pictures here.)
Daphnis died, according to the Times, on November 23.
See Art Object, a post in this journal on that date—
There is more than one way
to look at a cube.
Some context— this morning's previous post (Apollo's 13,
on the geometry of the 3×3×3 cube), yesterday's noon post
featuring the 3×3 square grid (said to be a symbol of Apollo),
and, for connoisseurs of the Ed Wood school of cinematic art,
a search in this journal for the phrase "Plan 9."
You can't make this stuff up.
Mathematics and Narrative continued…
Apollo's 13: A Group Theory Narrative —
I. At Wikipedia —
II. Here —
See Cube Spaces and Cubist Geometries.
The 13 symmetry axes of the (Euclidean) cube–
exactly one axis for each pair of opposite
subcubes in the 27-part (Galois) 3×3×3 cube–
A note from 1985 describing group actions on a 3×3 plane array—
Undated software by Ed Pegg Jr. displays
group actions on a 3×3×3 cube that extend the
3×3 group actions from 1985 described above—
Pegg gives no reference to the 1985 work on group actions.
Thursday, August 19, 2010
Consolation Prize
For Kathrin Bringmann, who has been mentioned as a possible candidate for a Fields Medal.
The four Fields medal winners were announced today at the International Congress of Mathematicians in Hyderabad, India. Bringmann was not among them.
Bringmann was, however, the winner of the 2009 SASTRA Ramanujan Prize—
See The Hindu of September 30, 2009 and this journal on that date—
For more about Bringmann's work, see an article on what has been called Ramanujan's "final problem."
For another problem with a claim to this title, see "Mathematician Untangles Legendary Problem" and search in this journal for Dyson + crank.
Sunday, July 18, 2010
Today’s Sermon
New York Lottery on Saturday, July 17, 2010—
Midday 049, Evening 613.
Related material:
Hexagram 49 and 6/13.
A quotation from this journal on 6/13—
"Christianity offers the critic a privileged ontological window…."
— Aaron Urbanczyk's 2005 review of Christ and Apollo
by William Lynch, S.J., a book first published in 1960
Picture from today's New York Times (page ST1 in New York edition)—
Sunday, June 13, 2010
Sunday School
“What on earth is a 'concrete universal'?"
— Said to be an annotation (undated)
by Robert M. Pirsig of A History of Philosophy,
by Frederick Copleston, Society of Jesus.
From Aaron Urbanczyk's 2005 review of Christ and Apollo by William Lynch, S.J., a book first published in 1960—
"Lynch's use of analogy vis-a-vis literature provides, in a sense, a philosophical basis to the theoretical paradox popularized by W. K. Wimsatt (1907-1975), which contends that literature is a sort of 'concrete universal.'"
The following figure has often been
offered in this journal as a symbol of Apollo—
Arguments that it is, rather, a symbol of Christ
may be left to the Society of Jesus.
One possible approach—
Urbanczyk's review says that
"Christianity offers the critic
a privileged ontological window…."
"The world was warm and white when I was born:
Beyond the windowpane the world was white,
A glaring whiteness in a leaded frame,
Yet warm as in the hearth and heart of light."
Saturday, March 13, 2010
Space Cowboy
From yesterday's Seattle Times—
According to police, employees of a Second Avenue mission said the suspect, clad in black and covered in duct tape, had come into the mission "and threatened to blow the place up." He then told staffers "that he was a vampire and wanted to eat people."
The man… also called himself "a space cowboy"….
This suggests two film titles…
and Apollo's 13—
The 13 symmetry axes of the (Euclidean) cube–
exactly one axis for each pair of opposite
subcubes in the (Galois) 3×3×3 cube–
Wednesday, September 30, 2009
Wednesday September 30, 2009
Midnight in the Garden, Autumn 2009
Review:
|
From this journal on the following day, Sept. 21:
Happy birthday, Stephen King.
Today's previous entry is based on a song, "Unthought Known,"
from the above album; the cover of the album uses the 3×3 grid
shown in Sept. 20's midnight review. For related material
on the unconscious, see June 13-15, 2005.
I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.
Thursday, February 19, 2009
Thursday February 19, 2009
A Sunrise
for Sunrise
“If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World, for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit. From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.”
Yesterday’s entry featured a rather simple-minded example from Krauss of how the ninefold square (said to be a symbol of Apollo)
may be used to create a graphic design– a Greek cross, which appears also in crossword puzzles:
Illustration by
Paul Rand
(born Peretz Rosenbaum)
A more sophisticated example
of the ninefold square
in graphic design:
“That old Jew
gave me this here.”
— A Flag for Sunrise
Wednesday, January 21, 2009
Wednesday January 21, 2009
“… while some are elected,
others not elect are
passed by….”
— A commentary on the
Calvinist doctrine of preterition
Gravity’s Rainbow, Penguin Classics, 1995, page 742:
“… knowing his Tarot, we would expect to look among the Humility, among the gray and preterite souls, to look for him adrift in the hostile light of the sky, the darkness of the sea…. Now there’s only a long cat’s-eye of bleak sunset left over the plain tonight, bright gray against a purple ceiling of clouds, with an iris of 742″ |
“God is the original
conspiracy theory.”
“We remain a young nation, but in the words of Scripture, the time has come to set aside childish things.”
— President Obama yesterday
It is not entirely clear what these “childish things” are. Perhaps the young nation’s “childish things” that the new President refers to are part of what Robert Stone memorably called “our secret culture.” Stone was referring to Puritanism, which some advocates of the new religion of Scientism might call “childish.” I do not. Lunatic, perhaps, but not childish.
Related meditations:
A year ago yesterday, on Sunday, Jan. 20, 2008, the mid-day lottery for New York State was 605.
A midrash in the Judeo-Christian tradition of paranoia a year ago today suggested that 605 might be a veiled reference to “God, the Devil, and a Bridge,” a weblog entry on mathematician André Weil.
Continuing in this vein a year later, we are confronted with the mid-day New York lottery for yesterday:
Taking a hint from another
entry on Weil, this may be
regarded as a reference to
The Oxford Book of
English Verse (1919 edition):
Selection 742 in that book
comports well with this
jounal’s recent meditations
on death and Brooklyn:
“Let me glide noiselessly forth; | |
With the key of softness unlock the locks….” — Walt Whitman |
Applying this method of
exegesis to last year’s
lottery, we have
“And all that did then attend and follow, |
|
Were silent with love, as you now, Apollo, |
|
With envy of my sweet pipings.” |
— Pan: God of Shepherds, Flocks, and Fornication
Hymn 605 thus supplies a reference to the devil mentioned by Weil in the entry of 6/05.
“… thus far, I have not heard any priests of Apollo, nor of any other God, issuing any auguries.”
Neither have I, but hearing is only one of the senses.
“Heard melodies are sweet,
but those unheard
Are sweeter.”— John Keats
Wednesday, December 10, 2008
Wednesday December 10, 2008
ho anax, hou to manteion esti
to en Delphois, oute legei oute
kruptei, alla sêmainei
— Heraclitus, DK 22 B 93,
Kahn XXXIII:
“The lord whose oracle is
at Delphi neither reveals nor
conceals, but gives a sign.“
A sign, perhaps of the sort
given by Apollo’s oracle:
Click on the sign for further details.
Related material:
… as well as
today’s previous entry —
“Symbol,” discussing Apollo
and a web page
by Nick Wedd —
and Wedd’s home page,
which states that
“I have now found a
source of Polish sandals.”
Saturday, November 8, 2008
Saturday November 8, 2008
AEDIFICABO ECCLESIAM
MEAM ET PORTAE INFERI
NON PRAEVALEBUNT
ADVERSUS EAM
Benedict XVI, before he became Pope:
“… a purely harmonious concept of beauty is not enough…. Apollo, who for Plato’s Socrates was ‘the God’ and the guarantor of unruffled beauty as ‘the truly divine’ is absolutely no longer sufficient.”
“The lapis manalis (Latin: ‘stone of the Manes‘) was a name given to two sacred stones used in the Roman religion. One covered a gate to Hades, abode of the dead….
One such stone covered the mundus Cereris, a pit thought to contain an entrance to the underworld….
The… mundus was located in the Comitium, on the Palatine Hill. This stone was ceremonially opened three times a year, during which spirits of the blessed dead (the Manes) were able to commune with the living. The three days upon which the mundus was opened were August 24, October 5, and November 8. Fruits of the harvest were offered to the dead at this time.”
Log24 on
August 24,
October 5, and
November 8.
Sunday, October 5, 2008
Sunday October 5, 2008
Last night's entry presented a
short story summarized by
four lottery numbers.
Today's mid-day lotteries
and associated material:
Pennsylvania, 201– i.e., 2/01:
Kindergarten Theology —
"In a game of chess, the knight's move is unique because it alone goes around corners. In this way, it combines the continuity of a set sequence with the discontinuity of an unpredictable turn in the middle. This meaningful combination of continuity and discontinuity in an otherwise linear set of possibilities has led some to refer to the creative act of discovery in any field of research as a 'knight's move' in intelligence."
I Have a Dreamtime —
"One must join forces with friends of like mind"
Related material:
"Schizophrenia is not a psychological disorder peculiar to human beings. Schizophrenia is not a disease at all but rather a localized traveling discontinuity of the space time matrix itself. It is like a travelling whirl-wind of radical understanding that haunts time. It haunts time in the same way that Alfred North Whitehead said that the color dove grey 'haunts time like a ghost.'"
"'Knight's move thinking' is a psychiatric term describing a thought disorder where in speech the usual logical sequence of ideas is lost, the sufferer jumping from one idea to another with no apparent connection. It is most commonly found in schizophrenia."
I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.
For more on the sleep of Apollo,
see the front page of today's
New York Times Book Review.
Garrison Keillor's piece there,
"Dying of the Light," is
about the fear of death felt
by an agnostic British twit.
For relevant remarks by
a British non-twit, see
William Dunbar–
Saturday, March 10, 2007
Saturday March 10, 2007
The Logic of Dreams
From A Beautiful Mind–
“How could you,” began Mackey, “how could you, a mathematician, a man devoted to reason and logical proof…how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you…?”
Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. “Because,” Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, “the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”
Ideas:
A link in the 7/11 entry leads to a remark of Noel Gray on Plato’s Meno and “graphic austerity as the tool to bring to the surface, literally and figuratively, the inherent presence of geometry in the mind of the slave.”
Also Friday: an example of graphic austerity– indeed, Gray graphic austerity– in Log24:
(Related material: the Harvard Gazette of April 6, 2006, “Mathematician George W. Mackey, 90: Obituary“– “A memorial service will be held at Harvard’s Memorial Church on April 29 at 2 p.m.“)
Friday’s Pennsylvania evening number 038 tells two other parts of the story involving Mackey…
As Mackey himself might hope, the number may be regarded as a reference to the 38 impressive pages of Varadarajan’s “Mackey Memorial Lecture” (pdf).
More in the spirit of Nash, 38 may also be taken as a reference to Harvard’s old postal address, Cambridge 38, and to the year, 1938, that Mackey entered graduate study at Harvard, having completed his undergraduate studies at what is now Rice University.
Returning to the concept of graphic austerity, we may further simplify the already abstract chessboard figure above to obtain an illustration that has been called both “the field of reason” and “the Garden of Apollo” by an architect, John Outram, discussing his work at Mackey’s undergraduate alma mater:
Let us hope that Mackey,
a devotee of reason,
is now enjoying the company
of Apollo rather than that of
Tom O’Bedlam:
For John Nash on his birthday:
I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.
Sunday, December 10, 2006
Sunday December 10, 2006
"Like all men of the Library,
I have traveled in my youth."
— Jorge Luis Borges,
The Library of Babel
"Papá me mandó un artículo
de J. G. Ballard en el que
se refiere a cómo el lugar
de la muerte es central en
nuestra cultura contemporánea."
— Sonya Walger,
interview dated September 14
(Feast of the Triumph of the Cross),
Anno Domini 2006
Sonya Walger,
said to have been
born on D-Day,
the sixth of June,
in 1974
Walger's father is, like Borges,
from Argentina.
She "studied English Literature
at Christ Church College, Oxford,
where she received
a First Class degree…. "
"… un artículo de J. G. Ballard…."–
A Handful of Dust, by J. G. Ballard
(The Guardian, March 20, 2006):
"… The Atlantic wall was only part of a huge system of German fortifications that included the Siegfried line, submarine pens and huge flak towers that threatened the surrounding land like lines of Teutonic knights. Almost all had survived the war and seemed to be waiting for the next one, left behind by a race of warrior scientists obsessed with geometry and death.
Death was what the Atlantic wall and Siegfried line were all about….
… modernism of the heroic period, from 1920 to 1939, is dead, and it died first in the blockhouses of Utah beach and the Siegfried line…
Modernism's attempt to build a better world with the aid of science and technology now seems almost heroic. Bertolt Brecht, no fan of modernism, remarked that the mud, blood and carnage of the first world war trenches left its survivors longing for a future that resembled a white-tiled bathroom. Architects were in the vanguard of the new movement, led by Le Corbusier and the Bauhaus design school. The old models were thrown out. Function defined form, expressed in a pure geometry that the eye could easily grasp in its entirety."
"This is the garden of Apollo,
the field of Reason…."
— John Outram, architect
(Click on picture for details.)
Related material:
Monday, December 4, 2006
Monday December 4, 2006
Related material:
All Hallows’ Eve,
2005:
as well as
C. S. Lewis,
That Hideous Strength,
Chapter 15,
“The Descent of the Gods,”
and
Charles Williams,
“The Carol of Amen House“:
Beauty arose of old
And dreamed of a perfect thing,
Where none shall be angry or cold
Or armed with an evil sting;
Where the world shall be made anew,
For the gods shall breathe its air,
And Phoebus Apollo there-through
Shall move on a golden stair.
(For the musical score, see
The Masques of Amen House.)
See also
A Mass for Lucero.
Monday, October 9, 2006
Monday October 9, 2006
To Apollo
“This is the garden of Apollo,
the field of Reason….”
John Outram, architect
To Apollo (10/09/02)
Art Wars: Apollo and Dionysus (10/09/02)
Balanchine’s Birthday (01/09/03)
Art Theory for Yom Kippur (10/05/03)
A Form (05/22/04)
Ineluctable (05/27/04)
A Form, continued (06/05/04)
Parallelisms (06/06/04)
Ado (06/25/04)
Deep Game (06/26/04)
Gameplayers of Zen (06/27/04)
And So To Bed (06/29/04)
Translation Plane for Rosh Hashanah (09/15/04)
Derrida Dead (10/09/04)
The Nine (11/09/04)
From Tate to Plato (11/19/04)
Art History (05/11/05)
A Miniature Rosetta Stone (08/06/05)
High Concept (8/23/05)
High Concept, Continued (8/24/05)
Analogical Train of Thought (8/25/05)
Today’s Sermon: Magical Thinking (10/09/05)
Balance (10/31/05)
Matrix (11/01/05)
Seven is Heaven, Eight is a Gate (11/12/05)
Nine is a Vine (11/12/05)
Apollo and Christ (12/02/05)
Hamilton’s Whirligig (01/05/06)
Cross (01/06/06)
On Beauty (01/26/06)
Sunday Morning (01/29/06)
Centre (01/29/06)
New Haven (01/29/06)
Washington Ballet (02/05/06)
Catholic Schools Sermon (02/05/06)
The Logic of Apollo (02/05/06)
Game Boy (08/06/06)
Art Wars Continued: The Krauss Cross (09/13/06)
Art Wars Continued: Pandora’s Box (09/16/06)
The Pope in Plato’s Cave (09/16/06)
Today’s Birthdays (09/26/06)
Symbology 101 (09/26/06)
Saturday, September 16, 2006
Saturday September 16, 2006
Pandora's Box
Part I:
The Pandora Cross
— Rosalind Krauss in "Grids"
Part II:
The Opening
Remarks by the Pope on Sept. 12,
as reported by the Vatican:
Faith, Reason, and the University:
Memories and Reflections
For the result of
the Pope's remarks, see
a transcript of
yesterday's Google News
and the following
from BBC today:
Click to enlarge the screenshot.
Part III:
Hope
"In September [2005], she had a private audience with Pope Benedict XVI at Castel Gandolfo, his summer residence outside Rome. She had criticized John Paul II for making overtures to Muslims, and for not condemning terrorism heartily enough, but she has hopes for Joseph Ratzinger."
For further details, see yesterday's Log24.
Part IV:
The Sibyl's Song
— From The Magic Circle,
a spiritual narrative
by Katherine Neville
For more on "the long-mute voice
of the past," on "darkness beneath
the volcano," and on uncorking,
see Glory Season and Harrowing.
Related material from
Log24 on Dec. 2, 2005:
Benedict XVI, before he became Pope:
and a related
Christian symbol,
the Greek Cross
(adapted from
Ad Reinhardt).
Moral of the Pandora Cross:
"Nine is a very powerful Nordic number."
— Katherine Neville in The Magic Circle…
quoted in The Nine, a Log24 entry
for Hermann Weyl's birthday,
November 9, 2004.
Friday, August 4, 2006
Friday August 4, 2006
ART WARS
continued from
previous entry
In memory of
Elisabeth Schwarzkopf:
This question might
well be posed by…
Rosalind Krauss,
Meyer Schapiro Professor
of Modern Art and Theory
at Columbia University
(Ph.D., Harvard U., 1969).
"The grid is a staircase to the Universal….
We could think about Ad Reinhardt, who,
despite his repeated insistence that
'Art is art,'
ended up by painting a series of…
nine-square grids in which the motif
that inescapably emerges is
a Greek cross.
Adapted from
Ad Reinhardt
There is no painter in the West
who can be unaware of
the symbolic power
of the cruciform shape and the
Pandora's box of spiritual reference
that is opened once one uses it."
— Rosalind Krauss in "Grids"
"Nine is a very powerful Nordic number."
— Katherine Neville, author of The Eight
Related material:
Wednesday, February 8, 2006
Wednesday February 8, 2006
From A Mass for Lucero:
“To the two gods of art, Apollo and Dionysus, we owe our recognition that… there is a tremendous opposition, as regards both origins and aims, between the Apolline art of the sculptor and the non-visual, Dionysiac art of music.”
— The Birth of Tragedy, by Friedrich Nietzsche, Penguin, 1993, page 14
“Melody, then, is both primary and universal.” (Author’s italics)
— Nietzsche, op. cit., page 33
“…in so far as he interprets music in images, he himself lies amidst the peaceful waves of Apolline contemplation….”
— Nietzsche, op. cit., page 35
From The Miracle of the Bells, by Russell Janney, Prentice-Hall, 1946, page 333–
“He was singing softly:
‘A pretty girl–
is like a melody—- !‘
But that was always
Bill Dunnigan’s
Song of Victory….
Thus thought the…
press agent for
‘The Garden of the Soul.'”
Monday, December 5, 2005
Monday December 5, 2005
The Associated Press on the Kennedy Center honors yesterday:
"Dancer Suzanne Farrell was feted by her former colleague at the New York City Ballet, Jacques d'Amboise. The company, led by George Balanchine, 'was the center of American ballet and she was the diamond in its crown,' d'Amboise said."
As Sir Arthur Quiller-Couch, paraphrasing Horace, remarks in his Whitsun, 1939, preface to the new edition of the Oxford Book of English Verse, "tamen usque recurret Apollo."
The mid-day number was 926;
the evening number was 373.
For the significance of 926,
see 9/26 2002 and
Balanchine's Birthday.
For the significance of 373, see
Art Wars,
May 2, 2003,
White, Geometric, and Eternal,
Dec. 20, 2003,
Directions Out,
April 26, 2004,
Outside the World,
April 26, 2004,
The Last Minute,
Sept. 15, 2004,
and
Diamonds Are Forever,
Jan. 25, 2005.
See also the link
at the end of
yesterday's entry.
For related material that is
more personally linked to
Joan Didion, see
Log24, June 1-16, 2004.
Friday, December 2, 2005
Friday December 2, 2005
“… a purely harmonious concept of beauty is not enough…. Apollo, who for Plato’s Socrates was ‘the God’ and the guarantor of unruffled beauty as ‘the truly divine’ is absolutely no longer sufficient.”
symbol of Apollo
as the source of
a Christian symbol–
the Greek Cross.
Related material:
The play
“now then again“
(Time-Bending Love Story
Comes Home to Fermilab)
with cover art by Roz Francis
illustrating the time 8:05:19,
Hexagram 19 in the
Cullinane series
(“A dance results”
— Marie-Louise von Franz),
and
Paul Preuss on Apollo,
quantum physics, and
the isle of Delos.
Saturday, July 30, 2005
Saturday July 30, 2005
Born today: Laurence Fishburne
on work at Rice University
Yale Daily News, Jan. 11, 2001:
“When New Haven was founded, the city was laid out into a grid of nine squares surrounded by a great wilderness.
Last year History of Art Professor Emeritus Vincent Scully said the original town plan reflected a feeling that the new city should be sacred.
Scully said the colony’s founders thought of their new Puritan settlement as a ‘nine-square paradise on Earth, heaven on earth, New Haven, New Jerusalem.'”
“Real and unreal are two in one:
New Haven
Before and after one arrives….”
— Wallace Stevens,
“An Ordinary Evening in New Haven,’ XXVIII
Friday, May 20, 2005
Friday May 20, 2005
The Shining of Apollo
"Plato's most significant passage may be found in Phaedrus 265b: 'And we made four divisions of the divine madness, ascribing them to four gods, saying that prophecy was inspired by Apollo, the mystic madness by Dionysos, the poetic by the Muses, and the madness of love […] by Aphrodite and Eros' (trans. by H.N. Fowler, in the Loeb Classical Library)."
— Saverio Marchignoli, note on section 20, paragraphs 115-119, of the Discourse on the Dignity of Man (Oratio de hominis dignitate) (1486) by Pico della Mirandola, considered the "Manifesto of the Renaissance."
Related material:
A Mass for Lucero,
The Shining of May 29,
Shining Forth,
Sermon for St. Patrick's Day, and the phrase
Diamond Struck by the Sun.
Thursday, April 22, 2004
Thursday April 22, 2004
Minimalism
"It's become our form of modern classicism."
— Nancy Spector in
the New York Times of April 23, 2004
Part I: Aesthetics
In honor of the current Guggenheim exhibition, "Singular Forms" — A quotation from the Guggenheim's own website:
"Minimalism refers to painting or sculpture
- made with an extreme economy of means
- and reduced to the essentials of geometric abstraction….
- Minimalist art is generally characterized by precise, hard-edged, unitary geometric forms….
- mathematically regular compositions, often based on a grid….
- the reduction to pure self-referential form, emptied of all external references….
- In Minimal art what is important is the phenomenological basis of the viewer’s experience, how he or she perceives the internal relationships among the parts of the work and of the parts to the whole….
- The repetition of forms in Minimalist sculpture serves to emphasize the subtle differences in the perception of those forms in space and time as the spectator’s viewpoint shifts in time and space."
Discuss these seven points
in relation to the following:
Form,
by S. H. Cullinane
Mark Rothko's reference
to geometry as a "swamp"
and his talk of "the idea" in art
Michael Kimmelman's
remarks on ideas in art
ART WARS:
Judgment Day
(2003, 10/07)
Part II: Theology
Today's previous entry, "Skylark," concluded with an invocation of the Lord. Of course, the Lord one expects may not be the Lord that appears.
"… the idea that, in art at least, less is more.
It is an idea surely as old, as enduringly attractive and as ubiquitous as its opposite. In the beginning was the Word: only later came the Bible, not to mention the three-decker Victorian novel. The oracle at Delphi did not say, 'Exhaustive analysis and comprehension of one's own psyche may be prerequisite to an understanding of one's behavior and of the world at large'; it said, 'Know thyself.' Such inherently minimalist genres as oracles (from the Delphic shrine of Apollo to the modern fortune cookie), proverbs, maxims, aphorisms, epigrams, pensees, mottoes, slogans and quips are popular in every human century and culture–especially in oral cultures and subcultures, where mnemonic staying power has high priority–and many specimens of them are self-reflexive or self-demonstrative: minimalism about minimalism. 'Brevity is the soul of wit.' "
Another form of the oracle at Delphi, in minimalist prose that might make Hemingway proud:
"He would think about Bert. Bert was an interesting man. Bert had said something about the way a gambler wants to lose. That did not make sense. Anyway, he did not want to think about it. It was dark now, but the air was still hot. He realized that he was sweating, forced himself to slow down the walking. Some children were playing a game with a ball, in the street, hitting it against the side of a building. He wanted to see Sarah.
When he came in, she was reading a book, a tumbler of dark whiskey beside her on the end table. She did not seem to see him and he sat down before he spoke, looking at her and, at first, hardly seeing her. The room was hot; she had opened the windows, but the air was still. The street noises from outside seemed almost to be in the room with them, as if the shifting of gears were being done in the closet, the children playing in the bathroom. The only light in the room was from the lamp over the couch where she was reading.
He looked at her face. She was very drunk. Her eyes were swollen, pink at the corners. 'What's the book,' he said, trying to make his voice conversational. But it sounded loud in the room, and hard.
She blinked up at him, smiled sleepily, and said nothing.
'What's the book?' His voice had an edge now.
'Oh,' she said. 'It's Kierkegaard. Soren Kierkegaard.' She pushed her legs out straight on the couch, stretching her feet. Her skirt fell back a few inches from her knees. He looked away.
'What's that?' he said.
'Well, I don't exactly know, myself." Her voice was soft and thick.
He turned his face away from her again, not knowing what he was angry with. 'What does that mean, you don't know, yourself?'
She blinked at him. 'It means, Eddie, that I don't exactly know what the book is about. Somebody told me to read it once, and that's what I'm doing. Reading it.'
He looked at her, tried to grin at her — the old, meaningless, automatic grin, the grin that made everbody like him — but he could not. 'That's great,' he said, and it came out with more irritation than he had intended.
She closed the book, tucked it beside her on the couch. She folded her arms around her, hugging herself, smiling at him. 'I guess this isn't your night, Eddie. Why don't we have a drink?'
'No.' He did not like that, did not want her being nice to him, forgiving. Nor did he want a drink.
Her smile, her drunk, amused smile, did not change. 'Then let's talk about something else,' she said. 'What about that case you have? What's in it?' Her voice was not prying, only friendly, 'Pencils?'
'That's it,' he said. 'Pencils.'
She raised her eyebrows slightly. Her voice seemed thick. 'What's in it, Eddie?'
'Figure it out yourself.' He tossed the case on the couch."
— Walter Tevis, The Hustler, 1959,
Chapter 11
See, too, the invocation of Apollo in
A Mass for Lucero, as well as
GENERAL AUDIENCE OF JOHN PAUL II
Wednesday 15 January 2003:
"The invocation of the Lord is relentless…."
and
JOURNAL ENTRY OF S. H. CULLINANE
Wednesday 15 January 2003:
Karl Cullinane —
"I will fear no evil, for I am the
meanest son of a bitch in the valley."
Saturday, December 20, 2003
Saturday December 20, 2003
For St. Emil’s Day
On this date in 1962, Emil Artin died.
He was, in his way, a priest of Apollo, god of music, light, and reason.
The previous entry dealt with permutation groups, in the context of a Jan. 2004 AMS Notices review of a book on the mathematics of juggling.
It turns out that juggling is, in fact, related to Artin’s theory of “braid groups.” For details, see Juggling Braids.
For more on Apollo, see my entry of
1/09.
Sunday, April 27, 2003
Sunday April 27, 2003
ART WARS:
Graphical Password
From a summary of “The Design and Analysis of Graphical Passwords“:
“Results from cognitive science show that people can remember pictures much better than words….
The 5×5 grid creates a good balance between security and memorability.”
— Ian Jermyn, New York University; Alain Mayer, Fabian Monrose, Michael K. Reiter, Bell Labs, Lucent Technologies; Aviel Rubin, AT&T Labs — Research
Illustration — Warren Beatty as
a graphical password:
“Town & Country,”
released April 27, 2001
Those who prefer the simplicity of a 3×3 grid are referred to my entry of Jan. 9, 2003, Balanchine’s Birthday. For material related to the “Town & Country” theme and to Balanchine, see Leadbelly Under the Volcano (Jan. 27, 2003). (“Sometimes I live in the country, sometimes I live in town…” – Huddie Ledbetter). Those with more sophisticated tastes may prefer the work of Stephen Ledbetter on Gershwin’s piano preludes or, in view of Warren Beatty’s architectural work in “Town & Country,” the work of Stephen R. Ledbetter on window architecture.
As noted in Balanchine’s Birthday, Apollo (of the Balanchine ballet) has been associated by an architect with the 3×3, or “ninefold” grid. The reader who wishes a deeper meditation on the number nine, related to the “Town & Country” theme and more suited to the fact that April is Poetry Month, is referred to my note of April 27 two years ago, Nine Gates to the Temple of Poetry.
Intermediate between the simplicity of the 3×3 square and the (apparent) complexity of the 5×5 square, the 4×4 square offers an introduction to geometrical concepts that appears deceptively simple, but is in reality fiendishly complex. See Geometry for Jews. The moral of this megilla?
32 + 42 = 52.
Friday, April 25, 2003
Friday April 25, 2003
Mark
Today is the feast of Saint Mark. It seems an appropriate day to thank Dr. Gerald McDaniel for his online cultural calendar, which is invaluable for suggesting blog topics.
Yesterday's entry "Cross-Referenced" referred to a bizarre meditation of mine titled "The Matthias Defense," which combines some thoughts of Nabokov on lunacy with some of my own thoughts on the Judeo-Christian tradition (i.e., also on lunacy). In this connection, the following is of interest:
From a site titled Meaning of the Twentieth Century —
"Freeman Dyson has expressed some thoughts on craziness. In a Scientific American article called 'Innovation in Physics,' he began by quoting Niels Bohr. Bohr had been in attendance at a lecture in which Wolfgang Pauli proposed a new theory of elementary particles. Pauli came under heavy criticism, which Bohr summed up for him: 'We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that is not crazy enough.' To that Freeman added: 'When a great innovation appears, it will almost certainly be in a muddled, incomplete and confusing form. To the discoverer, himself, it will be only half understood; to everyone else, it will be a mystery. For any speculation which does not at first glance look crazy, there is no hope!' "
— Kenneth Brower, The Starship and the Canoe, 1979, pp. 146, 147
It is my hope that the speculation, implied in The Matthias Defense, that the number 162 has astonishing mystical properties (as a page number, article number, etc.) is sufficiently crazy to satisfy Pauli and his friend Jung as well as the more conventional thinkers Bohr and Dyson. It is no less crazy than Christianity, and has a certain mad simplicity that perhaps improves on some of that religion's lunatic doctrines.
Some fruits of the "162 theory" —
Searching on Google for muses 162, we find the following Orphic Hymn to Apollo and a footnote of interest:
27 Tis thine all Nature's music to inspire,
28 With various-sounding, harmonising lyre;
29 Now the last string thou tun'ft to sweet accord,
30 Divinely warbling now the highest chord….
"Page 162 Verse 29…. Now the last string…. Gesner well observes, in his notes to this Hymn, that the comparison and conjunction of the musical and astronomical elements are most ancient; being derived from Orpheus and Pythagoras, to Plato. Now, according to the Orphic and Pythagoric doctrine, the lyre of Apollo is an image of the celestial harmony…."
For the "highest chord" in a metaphorical sense, see selection 162 of the 1919 edition of The Oxford Book of English Verse (whose editor apparently had a strong religious belief in the Muses (led by Apollo)). This selection contains the phrase "an ever-fixèd mark" — appropriately enough for this saint's day. The word "mark," in turn, suggests a Google search for the phrase "runes to grave" Hardy, after a poem quoted in G. H. Hardy's A Mathematician's Apology.
Such a search yields a website that quotes Housman as the source of the "runes" phrase, and a further search yields what is apparently the entire poem:
Smooth Between Sea and Land
by A. E. Housman
Smooth between sea and land
Is laid the yellow sand,
And here through summer days
The seed of Adam plays.Here the child comes to found
His unremaining mound,
And the grown lad to score
Two names upon the shore.Here, on the level sand,
Between the sea and land,
What shall I build or write
Against the fall of night?Tell me of runes to grave
That hold the bursting wave,
Or bastions to design
For longer date than mine.Shall it be Troy or Rome
I fence against the foam
Or my own name, to stay
When I depart for aye?Nothing: too near at hand
Planing the figured sand,
Effacing clean and fast
Cities not built to last
And charms devised in vain,
Pours the confounding main.(Said to be from More Poems (Knopf, 1936), p. 64)
Housman asks the reader to tell him of runes to grave or bastions to design. Here, as examples, are one rune and one bastion.
Represents |
Dagaz: (Pronounced thaw-gauze, but with the "th" voiced as in "the," not unvoiced as in "thick") (Day or dawn.)
From Rune Meanings:
Dagaz means "breakthrough, awakening, awareness. Daylight clarity as opposed to nighttime uncertainty. A time to plan or embark upon an enterprise. The power of change directed by your own will, transformation. Hope/happiness, the ideal. Security and certainty. Growth and release. Balance point, the place where opposites meet."
Also known as "the rune of transformation."
For the Dagaz rune in another context, see Geometry of the I Ching. The geometry discussed there does, in a sense, "hold the bursting wave," through its connection with Walsh functions, hence with harmonic analysis.
Temple of Athena Nike on the Nike Bastion, the Acropolis, Athens. Here is a relevant passage from Paul Valéry's Eupalinos ou L'Architecte about another temple of four columns:
Et puis… Écoute, Phèdre (me disait-il encore), ce petit temple que j'ai bâti pour Hermès, à quelques pas d'ici, si tu savais ce qu'il est pour moi ! — Où le passant ne voit qu'une élégante chapelle, — c'est peu de chose: quatre colonnes, un style très simple, — j'ai mis le souvenir d'un clair jour de ma vie. Ô douce métamorphose ! Ce temple délicat, nul ne le sait, est l'image mathématique d'une fille de Corinthe que j'ai heureusement aimée. Il en reproduit fidèlement les proportions particulières. Il vit pour moi !
Four columns, in a sense more suited to Hardy's interests, are also a recurrent theme in The Diamond 16 Puzzle and Diamond Theory.
Apart from the word "mark" in The Oxford Book of English Verse, as noted above, neither the rune nor the bastion discussed has any apparent connection with the number 162… but seek and ye shall find.
Wednesday, October 9, 2002
Wednesday October 9, 2002
ART WARS:
Apollo and Dionysus
From the New York Times of October 9, 2002:
Daniel Deverell Perry, a Long Island architect who created the marble temple of art housing the Sterling and Francine Clark Art Institute in Williamstown, Mass., died Oct. 2 in Woodstock, N.Y…. He was 97.
From The Birth of Tragedy, by Friedrich Nietzsche (tr. by Shaun Whiteside):
Chapter 1….
To the two gods of art, Apollo and Dionysus, we owe our recognition that in the Greek world there is a tremendous opposition, as regards both origins and aims, between the Apolline art of the sculptor and the non-visual, Dionysiac art of music.
Chapter 25….
From the foundation of all existence, the Dionysiac substratum of the world, no more can enter the consciousness of the human individual than can be overcome once more by that Apolline power of transfiguration, so that both of these artistic impulses are forced to unfold in strict proportion to one another, according to the law of eternal justice. Where the Dionysiac powers have risen as impetuously as we now experience them, Apollo, enveloped in a cloud, must also have descended to us; some future generation will behold his most luxuriant effects of beauty.
Notes:
- On the Clark Art Institute, from Perry’s obituary in the Times:
“When it opened in 1955, overlooking 140 acres of fields and ponds, Arts News celebrated its elegant galleries as the ‘best organized and most highly functional museum erected anywhere.'”
- The “Nymphs and Satyr” illustration above is on the cover of “CAI: Journal of the Clark Art Institute,” Volume 3, 2002. It is a detail from the larger work of the same title by William Bouguereau.
- Today, October 9, is the anniversary of the dedication in 28 B.C. of the Temple to Apollo on the Palatine Hill in Rome. See the journal entry below, which emphasizes the point that Apollo and Dionysus are not as greatly opposed as one might think.
Tuesday, September 24, 2002
Tuesday September 24, 2002
The Shining of Lucero
From my journal note, “Shining Forth“:
The Spanish for “Bright Star” is “Lucero.”
The Eye of the Beholder:
When you stand in the dark and look at a star a hundred light years away, not only have the retarded light waves from the star been travelling for a hundred years toward your eyes, but also advanced waves from your eyes have reached a hundred years into the past to encourage the star to shine in your direction.
— John Cramer, “The Quantum Handshake“
From Broken Symmetries, by Paul Preuss, 1983:
He’d toyed with “psi” himself…. The reason he and so many other theoretical physicists were suckers for the stuff was easy to understand — for two-thirds of a century an enigma had rested at the heart of theoretical physics, a contradiction, a hard kernel of paradox….
Peter [Slater] had never thirsted after “hidden variables” to explain what could not be pictured. Mathematical relationships were enough to satisfy him, mere formal relationships which existed at all times, everywhere, at once. It was a thin nectar, but he was convinced it was the nectar of the gods.
……………… Those so-called crazy psychics were too sane, that was their problem — they were too stubborn to admit that the universe was already more bizarre than anything they could imagine in their wildest dreams of wizardry. (Ch. 16)
From Secret Passages, by Paul Preuss, 1997:
Minakis caught up and walked beside him in silence, moving with easy strides over the bare ground, listening as Peter [Slater] spoke. “Delos One was ten years ago — quantum theory seemed as natural as water to me then; I could play in it without a care. If I’d had any sense of history, I would have recognized that I’d swallowed the Copenhagen interpretation whole.”
“Back then, you insisted that the quantum world is not a world at all,” Minakis prompted him. “No microworld, only mathematical descriptions.”
“Yes, I was adamant. Those who protested were naive — one has to be willing to tolerate ambiguity, even to be crazy.”
“Bohr’s words?”
“The party line. Of course Bohr did say, ‘It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.’ Meaning that when we start to talk what sounds like philosophy, our colleagues should rip us to pieces.” Peter smiled. “They smell my blood already.”
……………… Peter glanced at Minakis. “Let’s say there are indications — I have personal indications — not convincing, perhaps, but suggestive, that the quantum world penetrates the classical world deeply.” He was silent for a moment, then waved his hand at the ruins. “The world of classical physics, I mean. I suppose I’ve come to realize that the world is more than a laboratory.” “We are standing where Apollo was born,” Minakis said. “Leto squatted just there, holding fast to a palm tree, and after nine days of labor gave birth to the god of light and music….”
To Lucero, in memory of
1962 in CuernavacaFrom On Beauty, by Elaine Scarry,
Princeton University Press, 1999 —“Homer sings of the beauty of particular things. Odysseus, washed up on shore, covered with brine, having nearly drowned, comes upon a human community and one person in particular, Nausicaa, whose beauty simply astonishes him. He has never anywhere seen a face so lovely; he has never anywhere seen any thing so lovely….
I have never laid eyes on anyone like you,
neither man nor woman…
I look at you and a sense of wonder takes me.Wait, once I saw the like —
in Delos, beside Apollo’s altar —
the young slip of a palm-tree
springing into the light.”
From Secret Passages, by Paul Preuss, 1997:
“When we try to look inside atoms,” Peter said, “not only can we not see what’s going on, we cannot even construct a coherent picture of what’s going on.”
“If you will forgive me, Peter,” Minakis said, turning to the others. “He means that we can construct several pictures — that light and matter are waves, for example, or that light and matter are particles — but that all these pictures are inadequate. What’s left to us is the bare mathematics of quantum theory.”
…. “Whatever the really real world is like, my friend, it is not what you might imagine.”
……………… Talking physics, Peter tended to bluntness. “Tell me more about this real world you imagine but can’t describe.”Minakis turned away from the view of the sunset. “Are you familiar with John Cramer’s transactional interpretation of quantum mechanics?”
“No I’m not.”
……………… “Read Cramer. I’ll give you his papers. Then we can talk.”
From John Cramer, “The Quantum Handshake“:
Advanced waves could perhaps, under the right circumstances, lead to “ansible-type” FTL communication favored by Le Guin and Card….
For more on Le Guin and Card, see my journal notes below.
For more on the meaning of “lucero,” see the Wallace Stevens poem “Martial Cadenza.”
Monday, September 9, 2002
Monday September 9, 2002
On this, his birthday, actor Hugh Grant
is hereby named an
Honorary Waco Wacko.
By the authority vested in me by the possession of
- Knowledge of Vivienne Browning’s My Browning Family Album, a work dedicated to Dr. Joseph Armstrong, “founder of the Armstrong Browning Library, Baylor University, Waco, Texas,”
- Knowledge that today is the date of the Battle of Marathon, and of the claim that
“The spread of Pan’s worship beyond his home pastures of Arcadia was said to have arisen around the 5th Century BCE. Pan asked why the Athenians neglected him, and promised them victory over the Persians if they would worship him. At Marathon, the Persians were routed and fled in Panic; so, the Athenians built a temple for him on the Acropolis, and his worship soon extended to all Greece.”
2a. (including subsidiary knowledge of the ridiculous falseness of all political statements, including the following contemptible lie by Michael Dukakis in his 1988 Democratic National Convention acceptance speech:
“And as I accept your nomination tonight, I can’t help recalling that the first marathon was run in ancient Greece, and that on important occasions like this one, the citizens of Athens would complete their ceremonies by taking a pledge. That pledge, that covenant, is as eloquent and timely today as it was 2000 years ago.
‘We will never bring disgrace to this, our country, by any act of dishonesty or cowardice. We will fight for the ideals of this, our country. We will revere and obey the laws. We will strive to quicken our sense of civic duty. Thus, in all these ways, we will transmit this country greater, better, stronger, prouder and more beautiful than it was transmitted to us.’ “)
(None of the Harvard intellects associated with Dukakis saw fit to point out that there never was any such pledge. As a consequence, both Harvard University and the Democratic Party remain cursed to this day.),
- Knowledge (both intellectual and carnal) of the female form of the god Pan, as seen in the classic and great movie “Sirens” (starring, among others, Hugh Grant) and on the cover of the 1977 Olivia Newton-John album “Making a Good Thing Better,”
- Knowledge that even the best critics can be wrong, as exemplified by Roger Ebert’s remarks in his review of “Sirens”…
“Although they are often charged with being emotionally distant, the British have produced more than their share of sexual outlaws, from Oscar Wilde to Aleister Crowley to D.H. Lawrence to Francis Bacon, to balance the ledger. The central figure in ‘Sirens’ is perhaps vaguely inspired by another legendary British bohemian, Augustus John, an artist whose models and mistresses were interchangeable, and who delighted in scandal.
- Named Norman Lindsay, the film’s hero is played by Sam Neill as a notorious painter who lives on an estate in Australia where his art coexists side-by-side with an experiment in living.”
(Actually, the central figure is not “vaguely inspired” by anyone. He is precisely inspired by an artist named exactly Norman Lindsay, as Roger will learn if he searches the Web. Roger also gets Pan wrong in this film; he says, “the bearded Lindsay is a Pan of sorts.” No. The “Pan of sorts” is in fact the girl who romps joyfully with the local boys and who later, with great amusement, uses her divine x-ray vision to view Tara Fitzgerald naked in church.),
and, finally,
- Knowledge that, as the Greeks well knew, there is a dark side to all this Pan business (Vivienne Browning’s book reveals that her father was a friend, not only of the bohemian artist Norman Lindsay, but also of the black mage Aleister Crowley. Let us pray that Hugh Grant’s performance as a clergyman in “Sirens” and as a defender of the faith in “The Lair of the White Worm” have prepared him to cope with the dark (or, sometimes, “Brown”) side of the divine.),
I hereby declare Hugh Grant an honorary Waco (home of the Dr. Pepper Museum, the Texas Ranger Hall of Fame, and the Armstrong Browning Library) Wacko.
Monday, September 2, 2002
Monday September 2, 2002
Elevation of the Host
Some religious fanatics may be offended by my account, in the note below, of a theatrical bartender-priest at Lincoln Center who last night held a CD aloft in what may seem a parody or satire of the elevation of the host in the Mass. They should consider the following account of how a medieval nun viewed the host:
…she saw a great brightness between the priest’s hands, so vivid and so bright and of such wonderful beauty that in her opinion it could not be compared to anything the human spirit could imagine. And it seemed to her that this brightness had a circular shape….
For another appearance of a priest associated, if only by synchronicity, with Lincoln Center, see the photographs below, both from the New York Times obituaries section of Friday, August 30, 2002.
Richard Lippold, a sculptor known for radiant, expansive abstractions in metal, died on Aug. 22…. Richard Lippold’s ‘‘Orpheus and Apollo’’ at Avery Fisher Hall in 1996. Jack Manning/The New York Times |
|
Bill Wassmuth, a former Roman Catholic priest who opposed the Aryan Nations group in northern Idaho, died on Tuesday, Aug. 27. |
In this little drama of August 30, played out in the obituary section of the New York Times, it is not clear from the Lippold sculpture who is to play the role of Orpheus and who the role of Apollo. One might interpret the note below, written two days later, as implying that Orpheus is to be played by Lionel Hampton and Apollo by Christ himself. Such a drama is neither parody nor satire. It is, on the contrary, deadly serious.
“A great brightness,” as seen by the medieval nun described above, is traditionally associated with the Aryan sun god Apollo. For more on this theme in Roman Catholic art, see
The Monstrance and the Wafer God, and
For a less dogmatic approach to these matters, see my journal note of June 13, 2002,