Monday, September 21, 2020

A Dante for Our Times…

Filed under: General — Tags: — m759 @ 9:57 PM

Continues from March 14, 2009.

Wednesday, February 15, 2017

Companion to Dante*

Filed under: General — m759 @ 10:00 PM

Commentary on Inferno ,  Canto XVI,  line 84 —

* " when it pleases you to say 'I was' " —

See also a 1992 poem by Thomas Lux.

Thursday, April 11, 2013

Dante Prize (continued)

Filed under: General — m759 @ 3:00 PM

For the title, see posts of March 25, 2013.

For little Colva  a tune from November 2005

and a New York Times  review.

Monday, March 25, 2013

The Dante Prize

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

(Damnation Morning, continued)

For the late, great Bebo Valdés, who
reportedly died on Friday in Stockholm:

Trailers from Hell: Joe Dante on 'The Prize'

"Mr. Valdés never returned to Cuba. He played piano
in Stockholm hotel lounges for more than three decades."

— Ben Ratliff in this morning's New York Times

"Heaven for climate, Hell for company."

Monday, March 14, 2011

A Dante for Our Times

Filed under: General — m759 @ 7:59 PM

(Continued from this date two years ago)

"Hell is other people." —Sartre
"With a laugh track." —Cullinane

A sequel to Good Will Hunting and Hereafter

The Emory Board

Wednesday, January 29, 2020

The Newman Prize

Filed under: General — m759 @ 2:24 PM

From "Point," a Log24 post on St. Andrew's Day 2012 —

"….mirando il punto  
a cui tutti li tempi son presenti"

— DanteParadiso , XVII, 17-18

 For instance…

IMAGE- Three films from Christmas 1963 (IMDb): Captain Newman, MD; The Prize; Love with the Proper Stranger

Related material —

Tuesday, January 14, 2020

Physics for the Vatican

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

From Devil's Night 2019

Friday, January 10, 2020

Jan. 9 Review

Filed under: General — Tags: , — m759 @ 10:51 AM

“Work as if you were in the
early days of a better nation.”

— God, according to the author of
    1982 Janine

From Carole A. Holdsworth,
"Dulcinea and Pynchon’s V":

Tanner may have stated it best:

“V. is whatever lights you to
 the end of the street:
 she is also the dark annihilation
 waiting at  the end of the street.”

(Tony Tanner, page 36,
 “V. and V-2,” in
 Pynchon: A Collection
 of Critical Essays.

 Ed. Edward Mendelson.
 Englewood Cliffs, N. J.:
 Prentice-Hall, 1978. 16-55).

She’s a mystery
She’s everything
   a woman should be
Woman in black
   got a hold on me

— Foreigner 4

The Lotos Rose

Filed under: General — Tags: , , — m759 @ 12:01 AM

See the title in this journal.

Thursday, January 9, 2020

Universal History (Adapted)

Filed under: General — Tags: , , — m759 @ 11:05 PM

"One of the more fortuitous encounters of late-20th-century popular culture —
almost up there with Lennon meets McCartney and Taylor meets Burton —
took place on Labor Day 1965, at Jane Fonda’s Malibu beach house. The
actress was hosting a daylong bash at which her father, Henry’s,
generation mingled uneasily with her Hollywood hippie friends. The Byrds
played in the backyard. A young comedian-turned-film director named Mike
Nichols was approached by an improv comic-turned-itinerant writer named
Buck Henry, who asked how he was doing. Nichols dourly looked around
at all the proto-Summer of Love vibes and said, 'Here, under the shadow
of the great tree, I have found peace.'

Henry immediately recognized a sardonic East Coast kindred spirit trapped
in Lotusland . . . ."

—  Ty Burr,  Boston Globe  staff, January 9, 2020, 10:34 AM

Adapt or Die

Filed under: General — Tags: , , — m759 @ 11:53 AM

For Hollywood


For Emily Yahr (see second item above) —

Buck Henry reportedly died yesterday, January 8, 2020.
This journal on that date a year earlier —

Monday, December 30, 2019

Death on Becket’s Day

Filed under: General — Tags: , — m759 @ 10:22 AM

Author Alasdair Gray reportedly died yesterday,
on the feast of St. Thomas à Becket.

"His Collected Verse  (2010) was followed by 
Every Short Story 1951-2012 . Hell and Purgatory ,
the first two parts of his version of Dante’s
Divine Comedy , “decorated and Englished in
prosaic verse”, appeared in 2018 and 2019. 
In November Gray received the inaugural 
Saltire Society Scottish Lifetime Achievement award."

— https://www.theguardian.com/books/2019/dec/29/

See some related remarks from May 15, 1998.

Number and Time

Filed under: General — Tags: , — m759 @ 9:37 AM

(Hat tip for the title to Marie-Louise von Franz.)

Remarks by Metod Saniga from the previous post

Remarks by Wolfgang Pauli, a friend of von Franz

"This is to show the world that I can paint like Titian.
[Empty frame with jagged sides]. Only technical details
are missing."
— As quoted at Derevianko Group.

Related material (see Oct. 11, 2010) —


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.

Morning of the Iguana

Filed under: General — Tags: , — m759 @ 9:03 AM

Adam Gopnik in The New Yorker  this morning

" mysteriously durable manner of mythical depiction,
which runs forward to Egyptian wall paintings and,
for that matter, to modern animation. Therianthropes,
it seems, reflect the symbolic practice of giving to
humans the powers of animals, a shamanistic rite
that seems tied to the origins of religion, and here it is,
for the first time, a startup.

 one of the human figures, we’re told, has
'a tapering profile that possibly merges into the base
of a thick tail and with short, curved limbs splayed out
to the side. In our opinion, this part of the body resembles
the lower half of a lizard or crocodile. …' "

Related art

Logo by Saul Bass.

Friday, December 27, 2019

Showbiz Requiems

Filed under: General — Tags: , — m759 @ 11:41 PM


Thursday, December 26, 2019

In Memoriam: Nick Tosches

Filed under: General — Tags: — m759 @ 10:44 AM

Saturday, April 16, 2016

Matinee (continued)

Filed under: General — m759 @ 2:15 PM

Today is Kelli O'Hara's last Saturday matinee in "The King and I."

A show that some may prefer —

Related to the plot of Dante's film

"…it would be quite a long walk
for him if he had to walk straight across."

The image “http://www.log24.com/log/pix07A/070831-Ant1.gif” cannot be displayed, because it contains errors.

Swiftly Mrs. Who brought her hands… together.

"Now, you see," Mrs. Whatsit said,
"he would be  there, without that long trip.
That is how we travel."

The image “http://www.log24.com/log/pix07A/070831-Ant2.gif” cannot be displayed, because it contains errors.

– A Wrinkle in Time , Chapter 5, "The Tesseract"

Thursday, February 4, 2016

Dating a Tigress

Filed under: General — m759 @ 4:40 AM

Continued from January 18, 2005 —

See Lili Anolik, "Tiger of the Week," in Princeton Alumni Weekly  
on April 29, 2015, and this journal on that date.

(This post was suggested by the following sentence
by Anolik in Vanity Fair 's current Hollywood issue

"I think that for the city of Los Angeles,
Didion is the Ángel de la Muerte.")

Sunday, October 4, 2015


Filed under: General — m759 @ 1:29 PM

On a professor of literature who reportedly
died on Michaelmas 2015, a remark by his daughter —

“He was really an artist,” she said.

That’s evident in the 60 years Raffel spent contemplating 
how to translate the terza rima  style of Dante Alighieri’s 
The Divine Comedy — speaking of the three-line rhyme 
scheme first used by the author — before he published
a translation of which he was “most proud” in 2010,
his wife said.

It was his final work.

— Lanie Lee Cook, Baton Rouge Advocate

Wednesday, September 30, 2015


Filed under: General — m759 @ 9:01 PM

See the circle of keys.

Related material: The links in a Log24 search for Doctor Sax.

* For the title, see posts tagged Dante Time.

Monday, June 29, 2015

Barbara Reynolds, 1914-2015

Filed under: General — m759 @ 8:01 PM

In memory of Reynolds, a Dante scholar who reportedly died
on April 29, 2015 —

Sunday, June 14, 2015

Autistic Enchantments

Filed under: General — Tags: — m759 @ 12:45 PM

Continued )

Log24  on January 31, 2015 —

Spellbound (continued)

Filed under: Uncategorized — m759 @ 3:33 AM

The New York Times  this morning, in an
obituary for a maker of crossword puzzles :

“… the first known crossword puzzle appeared in
an American newspaper. (Called a ‘word-cross’
and shaped like a diamond, it was published in
The New York World  on Sunday, Dec. 21, 1913.)”

See St. Nicholas  magazine, November 1874, p. 59 :

For the answer, see this  journal on Aug. 29, 2002
(with a scene from Spellbound ) and on July 15, 2004.

On that same date 

The Seattle Times , Feb. 8, 2015, updated Feb. 12—

How to solve the puzzle:

“… you begin by filling in the missing words
for the limericks.

Dice, yAhtzee, woN, yahTzee, twicE;
Wall, dRawl, geOrgia’s, staTe, minnEsota;
Truck, rEd, fiReman’s, blaZe, hydrAnt;
Bob, sLob, prAy, saiNt, thanK.

The capital letters help to show what comes next,
as clued by the 1,2,3,4,5 in the title.

You take the first letter of the first inserted word,
the second of the second and so on. The resulting
message is ‘Dante wrote terza blank.’ The blank
is RIMA, as terza rima was the rhyme scheme
Dante used in the Divine Comedy.”

See also two other dates, June 3, 2015, and June 10, 2015,
in this  journal and in the life of the puzzle author.

The date of the puzzle’s answer, Feb. 8, 2015, is also
not without interest.

IMAGE- Art Jeffries (Bruce Willis) and Simon Lynch (Miko Hughes), 'Mercury Rising' (1998)

“Click on fanciful .”

Monday, May 4, 2015

Light to Light

Filed under: General — Tags: — m759 @ 5:00 PM

From yesterday —

Another remark on "still light" —

                                      " . . . After the kingfisher's wing
Has answered light to light, and is silent, the light is still
At the still point of the turning world." — Four Quartets

Note the page number, 168, in the above quote from Capobianco.

From another page 168,*  a reproduction of a title page —

"In quella parte del libro…."

IMAGE- Detail of p. 168 in Brooker's 'Eliot: The Contemporary Reviews,' showing title page of Eliot's 'Dante' with epigraph from Dante's 'Vita Nova'

* In Jewel Spears Brooker's book
  T.S. Eliot: The Contemporary Reviews ,
  Cambridge University Press, 2004

Wednesday, April 29, 2015

Scenes from…

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

An Epic for Drink Boy —

Context:  The post in which the above scenes occur.


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

Update of 12:25 AM — See, too, The Oxford Murders.

Tuesday, March 10, 2015


Filed under: General — Tags: — m759 @ 9:14 PM

Backstory for the "Surf's Up!" in the previous post:

"A Dante for Our Times," Part I and Part II.

Thursday, February 26, 2015

Brit Award

Filed under: General,Geometry — m759 @ 1:06 AM

"The Brit Awards are the British equivalent
of the American Grammy Awards." — Wikipedia 

Detail of an image from yesterday's 5:30 PM ET post:

Related material:

From a review: "Imagine 'Raiders of the Lost Ark'
set in 20th-century London, and then imagine it
written by a man steeped not in Hollywood movies
but in Dante and the things of the spirit, and you
might begin to get a picture of Charles Williams's
novel Many Dimensions ."

See also Solomon's Seal (July 26, 2012).

Saturday, August 16, 2014

The Grossman Chronicles

Filed under: General — Tags: , — m759 @ 10:16 PM

"Shakespeare, Dante, Milton, Homer: those writers trafficked in
witches and fairies and ghosts and monsters. Why shouldn’t I?"

Novelist Lev Grossman in The New York Times  this afternoon

Grossman's father was the poet Allen Grossman.

See that Grossman in this journal, as well as a search for Holy Water.

Thursday, May 9, 2013

An Education

Filed under: General — m759 @ 8:00 AM


Click a course description below for some related material.

IMAGE- Harvard students teach classes on Dante and China (Spring 2010).

See also Strike That Pose and Gone to China.

Friday, January 11, 2013

Grapevine Hill

Filed under: General — Tags: — m759 @ 5:55 AM

IMAGE- 'The Ninth Wave,' first page of Ch. 3, 'Across the Grapevine'

See also the song at the end of yesterday morning's
"For Your Consideration."

The setting for that song, "Hot Rod Lincoln," is—
according to Wikipedia— the road described in Ch. 3
of Eugene Burdick's classic 1956 novel
The Ninth Wave . (See above.)

IMAGE- Map showing Grapevine Hill road, southeast of Taft, California

See also A Dante for Our Times.

Friday, November 30, 2012


Filed under: General — Tags: — m759 @ 12:31 PM

"….mirando il punto  
a cui tutti li tempi son presenti"

— DanteParadiso , XVII, 17-18

 For instance

IMAGE- Three films from Christmas 1963 (IMDb): Captain Newman, MD; The Prize; Love with the Proper Stranger

Click image for higher quality.

Thursday, November 8, 2012


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

Dante, Purgatorio XVI

Esce di mano a Lui, che la vagheggia
     Prima che sia, a guisa di fanciulla,
     Che piangendo e ridendo pargoleggia,

L’anima semplicetta, che sa nulla,
     Salvo che, mossa da lieto fattore,
     Volontier torna a ciò che la trastulla.

Dante on the soul in Purgatorio 16
Related material:

and, in this journal,

Tuesday, October 9, 2012

Too Much Meaning

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

Last night’s post discussed ways of draining the world of meaning.

For some tastes, poets like Dante do the opposite, supplying too much  meaning.

See a New Republic  review, dated Oct. 5, in which Harvard atheist Helen Vendler discusses Dante’s

“… assertion that Beatrice herself  ‘was this number [nine],’ since nine is the square of three, the number belonging to the Trinity. Dante’s fantastic reasoning requires pages of annotation, which Frisardi, drawing on a number of commentators, furnishes to the bewildered reader. The theological elaboration of the number nine— merely one instance of how far from our own* are Dante’s habits of thought— will convince any doubting reader that the Vita Nuova  requires annotation far beyond what its pages might seem to demand.”

Related material— Ninefold in this journal, and remarks by Joseph Campbell in a post, Plan 9, from Sept. 5.

* Speak for yourself, Helen.

Friday, May 11, 2012

Fair Play for the Devil

Filed under: General — m759 @ 5:09 PM

IMAGE- Garrett McNamara surfs a 78-foot wave on All Hallows Day, 2011

Quoted here on that date (All Hallows Day)—

See as well A Dante for Our Times.

Tuesday, February 28, 2012

Stolen Glory

Filed under: General — m759 @ 4:04 AM

From University Diaries  yesterday

"A writer for The Atlantic  applauds Santorum's attack on universities
as secular, amoral indoctrination machines.

What can UD  say to this?…."

Below is a screenshot of the new home page for
Columbia University Department of Mathematics.

The impressive building in the photo is not  the math department.

(Click to enlarge.)


The building is actually Columbia's Butler Library.

"Along the front and sides of the library are inscribed the names of
Homer, Herodotus, Sophocles, Plato, Aristotle, Desmosthenes,
Cicero, Virgil, Horace, Tacitus, Saint Augustine, Aquinas, Dante,
Cervantes, Shakespeare, Milton, Voltaire, and Goethe." Wikipedia

The inscribed names outline a defense of liberal education
perhaps more robust than the Feb. 26 effort of Andrew Delbanco,
which University Diaries  calls "tepid." (See the previous Log24 post.)

Monday, March 7, 2011


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

"Time it goes so fast
When you're having fun"

— "Another Manic Monday"

"….mirando il punto 
a cui tutti li tempi son presenti"

Dante, Paradiso , XVII, 17-18

See mirando  in this journal.
       See also Time Fold.

Sunday, July 11, 2010

Philosophers’ Keystone

Filed under: General — Tags: , — m759 @ 2:02 AM

(Background— Yesterday's Quarter to Three,
A Manifold Showing, Class of 64, and Child's Play.)

Image-- Notes on Lowry's arrival in Mexico on the ship 'Pennsylvania'

Image-- PA Lottery Saturday, July 10, 2010-- Midday 017, Evening 673


Fans of Gregory Chaitin and Harry Potter
may consult Writings for Yom Kippur
for the meaning of yesterday's evening 673.

(See also Lowry and Cabbala.)

Fans of Elizabeth Taylor, Ava Gardner,
and the Dark Lady may consult Prime Suspect
for the meaning of yesterday's midday 17.

For some more serious background, see Dante

"….mirando il punto 
a cui tutti li tempi son presenti

Dante, Paradiso, XVII, 17-18

The symbol    is used throughout the entire book
in place of such phrases as ‘Q.E.D.’  or
‘This completes the proof of the theorem’
to signal the end of a proof.”

Measure Theory, by Paul R. Halmos, Van Nostrand, 1950      

Halmos died on the date of Yom Kippur —  
October 2, 2006.            

Saturday, July 10, 2010

Class of 64

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

Samuel Beckett on Dante and Joyce:

"Another point of comparison is the preoccupation
  with the significance of numbers."

"If I'd been out 'til quarter to three
Would you lock the door,
Will you still need me, will you still feed me,
When I'm sixty-four?"


Happy birthday to Sue Lyon (Night of the Iguana, 1964)

Monday, June 14, 2010

Theory of Ambiguity

Filed under: General,Geometry — m759 @ 5:01 PM

Théorie de l'Ambiguité

According to a 2008 paper by Yves André of the École Normale Supérieure  of Paris—

"Ambiguity theory was the name which Galois used
 when he referred to his own theory and its future developments."

The phrase "the theory of ambiguity" occurs in the testamentary letter Galois wrote to a friend, Auguste Chevalier, on the night before Galois was shot in a duel.

Hermann Weyl in Symmetry, Princeton University Press, 1952—

"This letter, if judged by the novelty and profundity of ideas it contains, is perhaps
  the most substantial piece of writing in the whole literature of mankind."

Conclusion of the Galois testamentary letter, according to
the 1897 Paris edition of Galois's collected works—

Image-- Galois on his theory of ambiguity, from Collected Works, Paris, 1897

The original—

Image-- Concluding paragraphs, Galois's 'last testament' letter to Chevalier, May 29, 1832

A transcription—

Évariste GALOIS, Lettre-testament, adressée à Auguste Chevalier—

Tu sais mon cher Auguste, que ces sujets ne sont pas les seuls que j'aie
explorés. Mes principales méditations, depuis quelques temps,
étaient dirigées sur l'application à l'analyse transcendante de la théorie de
l'ambiguité. Il s'agissait de voir a priori, dans une relation entre des quantités
ou fonctions transcendantes, quels échanges on pouvait faire, quelles
quantités on pouvait substituer aux quantités données, sans que la relation
put cesser d'avoir lieu. Cela fait reconnaitre de suite l'impossibilité de beaucoup
d'expressions que l'on pourrait chercher. Mais je n'ai pas le temps, et mes idées
ne sont pas encore bien développées sur ce terrain, qui est

Tu feras imprimer cette lettre dans la Revue encyclopédique.

Je me suis souvent hasardé dans ma vie à avancer des propositions dont je n'étais
pas sûr. Mais tout ce que j'ai écrit là est depuis bientôt un an dans ma
tête, et il est trop de mon intérêt de ne pas me tromper pour qu'on
me soupconne d'avoir énoncé des théorèmes dont je n'aurais pas la démonstration

Tu prieras publiquement Jacobi et Gauss de donner leur avis,
non sur la vérité, mais sur l'importance des théorèmes.

Après cela, il y aura, j'espère, des gens qui trouveront leur profit
à déchiffrer tout ce gachis.

Je t'embrasse avec effusion.

                                               E. Galois   Le 29 Mai 1832

A translation by Dr. Louis Weisner, Hunter College of the City of New York, from A Source Book in Mathematics, by David Eugene Smith, Dover Publications, 1959–

You know, my dear Auguste, that these subjects are not the only ones I have explored. My reflections, for some time, have been directed principally to the application of the theory of ambiguity to transcendental analysis. It is desired see a priori  in a relation among quantities or transcendental functions, what transformations one may make, what quantities one may substitute for the given quantities, without the relation ceasing to be valid. This enables us to recognize at once the impossibility of many expressions which we might seek. But I have no time, and my ideas are not developed in this field, which is immense.

Print this letter in the Revue Encyclopédique.

I have often in my life ventured to advance propositions of which I was uncertain; but all that I have written here has been in my head nearly a year, and it is too much to my interest not to deceive myself that I have been suspected of announcing theorems of which I had not the complete demonstration.

Ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the importance of the theorems.

Subsequently there will be, I hope, some people who will find it to their profit to decipher all this mess.

J t'embrasse avec effusion.
                                                     E. Galois.   May 29, 1832.

Translation, in part, in The Unravelers: Mathematical Snapshots, by Jean Francois Dars, Annick Lesne, and Anne Papillaut (A.K. Peters, 2008)–

"You know, dear Auguste, that these subjects are not the only ones I have explored. For some time my main meditations have been directed on the application to transcendental analysis of the theory of ambiguity. The aim was to see in a relation between quantities or transcendental functions, what exchanges we could make, what quantities could be substituted to the given quantities without the relation ceasing to take place. In that way we see immediately that many expressions that we might look for are impossible. But I don't have the time and my ideas are not yet developed enough in this vast field."

Another translation, by James Dolan at the n-Category Café

"My principal meditations for some time have been directed towards the application of the theory of ambiguity to transcendental analysis. It was a question of seeing a priori in a relation between quantities or transcendent functions, what exchanges one could make, which quantities one could substitute for the given quantities without the original relation ceasing to hold. That immediately made clear the impossibility of finding many expressions that one could look for. But I do not have time and my ideas are not yet well developed on this ground which is immense."

Related material

"Renormalisation et Ambiguité Galoisienne," by Alain Connes, 2004

"La Théorie de l’Ambiguïté : De Galois aux Systèmes Dynamiques," by Jean-Pierre Ramis, 2006

"Ambiguity Theory, Old and New," preprint by Yves André, May 16, 2008,

"Ambiguity Theory," post by David Corfield at the n-Category Café, May 19, 2008

"Measuring Ambiguity," inaugural lecture at Utrecht University by Gunther Cornelissen, Jan. 16, 2009

Sunday, April 4, 2010

Virgil Vigil

Filed under: General — m759 @ 1:00 AM

Two definitions–

"In Dante's Inferno  the Harrowing of Hell is mentioned in Canto IV by the pilgrim's guide Virgil." —Wikipedia

"The Easter Vigil…. is held in the hours of darkness between sunset on Holy Saturday and sunrise on Easter Day." —Wikipedia

Two more, of acronyms coined by Philip Rieff

"Rieff is critical of the present 'pop' culture that glories in the 'primacies of possibility' and prefers 'both/and' to 'either/or.' … the 'via'— the 'vertical in authority'—… teaches us our place as we assent to and ascend on via’s ladder." —Philip Manning

Related material:


The infinity symbol, as sketched in a touching
attempt at scholarship by the late
"both/and" novelist David Foster Wallace


The Cartesian cross


The lemniscate


Lemniscate with Cartesian cross

A more traditional symbol
that has been described as
  the cross of St. Boniface
See also The Eight, a novel
by Katherine Neville related
to today's date, 4/4–

Friday, February 12, 2010

Capital E

Filed under: General,Geometry — m759 @ 10:30 AM

Where Entertainment is God, continued

The following paragraphs are from a review by Piotr Siemion of Infinite Jest, a novel by David Foster Wallace. Illustrations have been added.

"Wallace was somehow able to twist together three yarns…. …there's a J.D Salinger for those who like J.D. Salinger. There's William Burroughs for those hardy souls who like some kick in their prose. And there's a dash of Kurt Vonnegut too. All three voices, though, are amplified in Infinite Jest beyond mere distortion and then projected onto Wallace's peculiar own three-ring circus….

Venn diagram of three sets

… there's entertainment. Make it a capital E.

Hilary Swank in 'Million Dollar Baby'

Illustration by Clint Eastwood
from Log24 post "E is for Everlast"

Infinite Jest revolves, among its many gyrations, around the story of the Entertainment, a film-like creation going by the title of 'Infinite Jest' and created shortly before his suicidal death by the young tennis star's father. The Entertainment's copies are now being disseminated clandestinely all over Wallace's funny America. Problem is, of course, that the film is too good. Anybody who gets to watch it becomes hooked instantly and craves only to watch it again, and again, and again, until the audience drops dead of exhaustion and hunger. Why eat when you're entertained by such a good movie? Wallace's premise brings you back to that apocryphal lab experiment in which rats were treated to a similar choice. When the rat pushed one button, marked FOOD, it would get a food pellet. The other button, marked FUN, would fire up an electrode rigged right into the orgasm center somewhere in the rat's cortex. Needless to add, one rat after another would drop dead from hunger, still twitching luridly and trying to finesse one last push of the button. Same thing in Wallace's story, especially that even those characters who have not seen the Entertainment yet, keep on entertaining themselves by different means."

The title of the Entertainment, "Infinite Jest," might also be applied to a BBC program featuring mathematician Peter J. Cameron. The program's actual title was "To Infinity and Beyond." It was broadcast the night of Feb. 10 (the date of this journal's previous post).

Few, however, are likely to find the Infinity program addictive. For closer approaches to Wallace's ideal Entertainment, see instead Dante (in the context of this journal's Feb. 4 posts on Cameron and the afterlife) and the BBC News.

Thursday, March 19, 2009

Thursday March 19, 2009

Filed under: General — Tags: — m759 @ 4:00 AM
An image from
A Glass Bead Game

by Charles Cameron

Christ and the four elements, 1495

Christ and the Four Elements

This 1495 image is found in
The Janus Faces of Genius:
The Role of Alchemy
in Newton's Thought

by B. J. T. Dobbs,
Cambridge U. Press,
2002, p. 85

Kernel of Eternity:

Pauli's Dream Square from 'The Innermost Kernel'

Sacerdotal Jargon
at Harvard

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

From "The Fifth Element"
(1997, Milla Jovovich
    and Bruce Willis) —

The crossing of the beams:

The Fifth Element, crossing of the beams

Happy birthday, Bruce Willis.

Saturday, March 14, 2009

Saturday March 14, 2009

Filed under: General — m759 @ 11:07 AM
A Dante
for Our Times

“This could be Heaven
or this could be Hell.”
— “Hotel California”

Heaven —

Eugene Burdick, 'The Blue of Capricorn'

or —

Eugene Burdick, 'The 480'

Hell —

Eugene Burdick, 'The Ninth Wave'

Apparently from the back cover of The Ninth Wave:

“Fear + hate = power was Mike Freesmith’s formula for success.  He first tested it in high school when he seduced his English teacher and drove a harmless drunk to suicide.  He used it on the woman who paid his way through college.  He used it to put his candidate in the governor’s chair, and to make himself the most ruthless, powerful kingmaker in American politics.”

Don’t forget greed. See yesterday’s Friday the 13th entries.

Monday, March 2, 2009

Monday March 2, 2009

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

Joyce’s Nightmare

Today in History – March 2

Today is Monday, March 2, the 61st day of 2009. There are 304 days left in the year.

Today’s Highlight in History:

On March 2, 1939, Roman Catholic Cardinal Eugenio Pacelli was elected Pope on his 63rd birthday; he took the name Pius XII.

Angels and Demons, Illuminati Diamond, pages 359-360

Log24 on June 9, 2008

From Gravity’s Rainbow (Penguin Classics, 1995), page 563:

“He brings out the mandala he found.
‘What’s it mean?’

Slothrop gives him the mandala. He hopes it will work like the mantra that Enzian told him once, mba-kayere (I am passed over), mba-kayere… a spell […]. A mezuzah. Safe passage through a bad night….”

In lieu of Slothrop’s mandala, here is another…

Christ and the four elements, 1495

Christ and the Four Elements

This 1495 image is found in
The Janus Faces of Genius:
The Role of Alchemy
in Newton’s Thought,
by B. J. T. Dobbs,
Cambridge University Press,
2002, p. 85


Related mandalas:Diamond arrangement of the four elements

Logo by Steven H. Cullinane for website on finite geometry


For further details,
click on any of the
three mandalas above.

Angels and Demons cross within a diamond (page 306), and Finite Geometry logo

Happy birthday to
Tom Wolfe, author of
The Painted Word.

Monday, December 8, 2008

Monday December 8, 2008

Filed under: General — Tags: — m759 @ 10:12 AM

An Indiana Jones Xmas


Chalice, Grail,


Last night on TNT:
The Librarian Part 3:
Curse of the Judas Chalice,
in which The Librarian
encounters the mysterious
Professor Lazlo

Related material:

An Arthur Waite quotation
from the Feast of St. Nicholas:

“It is like the lapis exilis of
the German Graal legend”

as well as
yesterday’s entry
relating Margaret Wertheim’s
Pearly Gates of Cyberspace:
A History of Space from
Dante to the Internet

 to a different sort of space–
that of the I Ching— and to
Professor Laszlo Lovasz’s
cube space

David Carradine displays a yellow book-- the Princeton I Ching.

“Click on the Yellow Book.”

Happy birthday, David Carradine.

Sunday, December 7, 2008

Sunday December 7, 2008

Filed under: General,Geometry — m759 @ 11:00 AM
Space and
 the Soul

On a book by Margaret Wertheim:

“She traces the history of space beginning with the cosmology of Dante. Her journey continues through the historical foundations of celestial space, relativistic space, hyperspace, and, finally, cyberspace.” –Joe J. Accardi, Northeastern Illinois Univ. Lib., Chicago, in Library Journal, 1999 (quoted at Amazon.com)

There are also other sorts of space.

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
(co-founded by Margaret Wertheim)

This photo may serve as an
introduction to a different
sort of space.

See The Eightfold Cube.

For the religious meaning
of this small space, see

Richard Wilhelm on
the eight I Ching trigrams

For a related larger space,
see the entry and links of
 St. Augustine’s Day, 2006.

Monday, October 20, 2008

Monday October 20, 2008

Filed under: General — Tags: — m759 @ 1:06 AM
Me and My Shadow

Thoughts suggested by Saturday's entry–

"… with primitives the beginnings of art, science, and religion coalesce in the undifferentiated chaos of the magical mentality…."

— Carl G. Jung, "On the Relation of Analytical Psychology to Poetry," Collected Works, Vol. 15, The Spirit in Man, Art, and Literature, Princeton University Press, 1966, excerpted in Twentieth Century Theories of Art, edited by James M. Thompson.

For a video of such undifferentiated chaos, see the Four Tops' "Loco in Acapulco."

"Yes, you'll be goin' loco
  down in Acapulco,

  the magic down there
  is so strong."

This song is from the 1988 film "Buster."

(For a related religious use of that name– "Look, Buster, do you want to live?"– see Fritz Leiber's "Damnation Morning," quoted here on Sept. 28.)

Art, science, and religion are not apparent within the undifferentiated chaos of the Four Tops' Acapulco video, which appears to incorporate time travel in its cross-cutting of scenes that seem to be from the Mexican revolution with contemporary pool-party scenes. Art, science, and religion do, however, appear within my own memories of Acapulco. While staying at a small thatched-roof hostel on a beach at Acapulco in the early 1960's, I read a paperback edition of Three Philosophical Poets, a book by George Santayana on Lucretius, Dante, and Goethe. Here we may regard art as represented by Goethe, science by Lucretius, and religion by Dante. For a more recent and personal combination of these topics, see Juneteenth through Midsummer Night, 2007, which also has references to the "primitives" and "magical mentality" discussed by Jung.

"The major structures of the psyche for Jung include the ego, which is comprised of the persona and the shadow. The persona is the 'mask' which the person presents [to] the world, while the shadow holds the parts of the self which the person feels ashamed and guilty about."

— Brent Dean Robbins, Jung page at Mythos & Logos

As for shame and guilt, see Malcolm Lowry's classic Under the Volcano, a novel dealing not with Acapulco but with a part of Mexico where in my youth I spent much more time– Cuernavaca.

Lest Lowry's reflections prove too depressing, I recommend as background music the jazz piano of the late Dave McKenna… in particular, "Me and My Shadow."

McKenna died on Saturday, the date of the entry that included "Loco in Acapulco." Saturday was also the Feast of Saint Luke.

Monday, August 25, 2008

Monday August 25, 2008

Filed under: General — Tags: — m759 @ 3:23 AM
For the Feast of
St. Louis

The concluding paragraph of Erich Heller's 1953 essay, "The Hazard of Modern Poetry"–

"'The poetry does not matter.' These words from Mr. T.S. Eliot's Four Quartets acquire an all but revolutionary significance if we understand them not only in their particular context but also in the context of a period of poetry in which nothing mattered except poetry. Against this background the Four Quartets themselves appear, in all their complexity, as the poetry of simple civic virtue– the poetry of a poet trying to read the writing of the law that has become all but illegible. This, you may say, has nothing to do with poetry. On the contrary, it is one of the few truly hopeful signs that this civic virtue could once more be realized poetically. For in speaking to the hazard of modern poetry I did not wish to suggest that the end had come for singers and skylarks. There will always be skylarks; perhaps even a few nightingales. But poetry is not only the human equivalent of the song of singing birds. It is also Virgil, Dante, and Hölderlin. It is also, in its own terms, the definition of the state of man."

Wednesday, June 25, 2008

Wednesday June 25, 2008

Filed under: General,Geometry — Tags: , — m759 @ 7:20 PM
The Cycle of
the Elements

John Baez, Week 266
(June 20, 2008):

“The Renaissance thinkers liked to
organize the four elements using
a chain of analogies running
from light to heavy:

fire : air :: air : water :: water : earth

They also organized them
in a diamond, like this:”

Diamond of the four ancient elements, figure by John Baez

This figure of Baez
is related to a saying
attributed to Heraclitus:

Diamond  showing transformation of the four ancient elements

For related thoughts by Jung,
see Aion, which contains the
following diagram:

Jung's four-diamond figure showing transformations of the self as Imago Dei

“The formula reproduces exactly the essential features of the symbolic process of transformation. It shows the rotation of the mandala, the antithetical play of complementary (or compensatory) processes, then the apocatastasis, i.e., the restoration of an original state of wholeness, which the alchemists expressed through the symbol of the uroboros, and finally the formula repeats the ancient alchemical tetrameria, which is implicit in the fourfold structure of unity.”

— Carl Gustav Jung

That the words Maximus of Tyre (second century A.D.) attributed to Heraclitus imply a cycle of the elements (analogous to the rotation in Jung’s diagram) is not a new concept. For further details, see “The Rotation of the Elements,” a 1995 webpage by one  “John Opsopaus.”

Related material:

Log24 entries of June 9, 2008, and

Quintessence: A Glass Bead Game,”
by Charles Cameron.

Monday, June 9, 2008

Monday June 9, 2008

Filed under: General,Geometry — m759 @ 10:20 PM
Lying Rhymes

Readers of the previous entry
who wish to practice their pardes
may contemplate the following:

NY Lottery June 9, 2008: mid-day 007, evening 563

The evening 563 may, as in other recent entries, be interpreted as a page number in Gravity’s Rainbow (Penguin Classics, 1995). From that page:

“He brings out the mandala he found.
‘What’s it mean?’
Slothrop gives him the mandala. He hopes it will work like the mantra that Enzian told him once, mba-kayere (I am passed over), mba-kayere… a spell […]. A mezuzah. Safe passage through a bad night….”

In lieu of Slothrop’s mandala, here
is another, from the Dante link
in today’s previous entry:

Christ and the four elements, 1495

Christ and the Four Elements

This 1495 image is found in
The Janus Faces of Genius:
The Role of Alchemy

in Newton’s Thought,
by B. J. T. Dobbs,
Cambridge University Press,
2002, p. 85

Related mandalas:

Diamond arrangement of the four elements


Logo by Steven H. Cullinane for website on finite geometry

For further details,
click on any of the
three mandalas above.

“For every kind of vampire,
there is a kind of cross.”

— Thomas Pynchon, quoted
here on 9/13, 2007

(As for today’s New York Lottery midday number 007, see (for instance) Edward Rothstein in today’s New York Times on paradise, and also Tom Stoppard on heaven as “just a lying rhyme” for seven.)

Time of entry: 10:20:55 PM

Monday June 9, 2008

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

"With respect, you only interpret."
"Countries have gone to war
after misinterpreting one another."

The Interpreter

"Once upon a time (say, for Dante),
it must have been a revolutionary
and creative move to design works
of art so that they might be
experienced on several levels."

— Susan Sontag,
"Against Interpretation"

Edward Rothstein in today's New York Times review of San Francisco's new Contemporary Jewish Museum:

"An introductory wall panel tells us that in the Jewish mystical tradition the four letters [in Hebrew] of pardes each stand for a level of biblical interpretation: very roughly, the literal, the allusive, the allegorical and the hidden. Pardes, we are told, became the museum’s symbol because it reflected the museum’s intention to cultivate different levels of interpretation: 'to create an environment for exploring multiple perspectives, encouraging open-mindedness' and 'acknowledging diverse backgrounds.' Pardes is treated as a form of mystical multiculturalism.

But even the most elaborate interpretations of a text or tradition require more rigor and must begin with the literal. What is being said? What does it mean? Where does it come from and where else is it used? Yet those are the types of questions– fundamental ones– that are not being asked or examined […].

How can multiple perspectives and open-mindedness and diverse backgrounds be celebrated without a grounding in knowledge, without history, detail, object and belief?"

"It's the system that matters.
How the data arrange
themselves inside it."

Gravity's Rainbow  

"Examples are the stained-
glass windows of knowledge."

Vladimir Nabokov  

Map Systems (decomposition of functions over a finite field)

Click on image to enlarge.   

Wednesday, April 16, 2008

Wednesday April 16, 2008

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

Poetry for Physicists:
The Gates of Hell

From the obituary of physicist John Archibald Wheeler at Princeton:

In the fall of 1967, he was invited to give a talk…. As he spoke, he… [mentioned] something strange… what he called a gravitationally completely collapsed object. But such a phrase was a mouthful, he said, wishing aloud for a better name. "How about black hole?" someone shouted from the audience.

That was it. "I had been searching for just the right term for months, mulling it over in bed, in the bathtub, in my car, wherever I had quiet moments," he later said. "Suddenly this name seemed exactly right." He kept using the term, in lectures and on papers, and it stuck.

From Log24 last year on this date ("Happy Birthday, Benedict XVI"):

"Know the one about the Demiurge and the Abridgment of Hope?"

— Robert Stone, A Flag for Sunrise, Knopf, 1981, the final page, 439

From Dante, The Inferno, inscription on the gates of Hell:

"Abandon all hope, ye who enter."

From Psychoshop, an unfinished novel by Alfred Bester completed by Roger Zelazny:

His manner was all charm and grace; pure cafe society….

He purred a chuckle. "My place. If you want to come, I'll show you."

"Love to. The Luogo Nero? The Black Place?"

"That's what the locals call it. It's really Buoco Nero, the Black Hole."

"Like the Black Hole of Calcutta?"

"No. Black Hole as in astronomy. Corpse of a dead star, but also channel between this universe and its next-door neighbor."

"Here? In Rome?"

"Sure. They drift around in space until they run out of gas and come to a stop. This number happened to park here."

"How long ago?"

"No one knows," he said. "It was there six centuries before Christ, when the Etruscans took over a small town called Roma and began turning it into the capital of the world."


Related material:

Log24 on

Life of the Party
(March 24, 2006),
(March 26, 2006)

Sunday, April 8, 2007

Sunday April 8, 2007

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

Today's sermon

Samuel Beckett on Dante and Joyce:

"Another point of comparison is the preoccupation with the significance of numbers. The death of Beatrice inspired nothing less than a highly complicated poem dealing with the importance of the number 3 in her life. Dante never ceased to be obsessed by this number. Thus the poem is divided into three Cantiche, each composed of 33 Canti…. Why, Mr. Joyce seems to say, should…. the Armistice be celebrated at the eleventh hour of the eleventh day of the eleventh month? He cannot tell you because he is not God Almighty, but in a thousand years he will tell you… He is conscious that things with a common numerical characteristic tend towards a very significant interrelationship. This preoccupation is freely translated in his present work…."

— "Dante… Bruno. Vico.. Joyce," in James Joyce/Finnegans Wake: A Symposium (1929), New Directions paperback, 1972

See also Plato, Pegasus, and the Evening Star.

Sunday April 8, 2007

Filed under: General — Tags: — m759 @ 12:00 AM
Midnight in the Garden
continued from Sept. 30, 2004

Tonight this journal had two Xanga footprints from Italy….

At 11:34 PM ET a visitor from Italy viewed a page containing an entry from Jan. 8, 2005, Splendor of the Light, which offers the following quotation–

From an essay on Guy Davenport

"A disciple of Ezra Pound, he adapts to the short story the ideogrammatic method of The Cantos, where a grammar of images, emblems, and symbols replaces that of logical sequence. This grammar allows for the grafting of particulars into a congeries of implied relation without subordination. In contrast to postmodernists, Davenport does not omit causal connection and linear narrative continuity for the sake of an aleatory play of signification but in order to intimate by combinational logic kinships and correspondences among eras, ideas and forces."

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

The visitor from Italy may, of course, have instead intended to view one of the four earlier entries on the page.  In particular, the visitor may have seen

The Star
of Venus

"He looked at the fading light
in the western sky and saw Mercury,
or perhaps it was Venus,
gleaming at him as the evening star.
Darkness and light,
the old man thought.
It is what every hero legend is about.
The darkness which is more than death,
the light which is love, like our friend
Venus here, or perhaps this star is
Mercury, the messenger of Olympus,
the bringer of hope."

Roderick MacLeish, Prince Ombra.

At 11:38 PM ET, a visitor from Italy (very likely the 11:34 visitor returning) viewed the five Log24 entries ending at 12:06 AM ET on Sept. 30, 2004. 

These entries included Midnight in the Garden and…

A Tune for Michaelmas

Mozart, K 265, midi

The entries on this second visited page also included some remarks on Dante, on time, and on Malcolm Lowry's Under the Volcano that are relevant to Log24 entries earlier this week on Maundy Thursday and on Holy Saturday.

Here's wishing a happy Easter to Italy, to Francis Ford Coppola and Russell Crowe (see yesterday's entry), and to Steven Spielberg (see the Easter page of April 20, 2003).

The image “http://www.log24.com/log/pix07/070408-Prayer.jpg” cannot be displayed, because it contains errors.

Image courtesy of
Hollywood Jesus:

When you wish
upon a star…

Thursday, April 5, 2007

Thursday April 5, 2007

Filed under: General — m759 @ 2:02 PM


The Annual
Maundy Thursday
Dante’s Inferno Reading

“The reading occurs during the Maundy Thursday vigil, the very hours Dante intended the events in the epic poem to take place.”
Featured poets:

Rachel Hadas, Wyatt Prunty, Rachel Wetzsteon, Rika Lesser, David Yezzi, Annie Finch, Honor Moore, Lynn Emanuel, Paul Watsky, Kate Light, Phillis Levin, Michael Palma, Charles Martin

Thursday, April 5, 2007, 9 p.m. to midnight, The Cathedral Church of St. John the Divine, 1047 Amsterdam Avenue at 112th St., NYC, NY

Related material –

The Eight Revisited:

Dante Alighieri Academy
continues Dante’s Christian
philosophy of education….

Thursday, November 16, 2006

Thursday November 16, 2006

Filed under: General,Geometry — m759 @ 12:00 PM
“Let all thy words be counted.”
Dante, Inf., canto X.

G. Robert Crowningshield,
a developer of the

International Diamond
Grading System

According to a
press release,
died on
November 8.

See Grave Matters,
an entry of that date,
and its links to
Geometry’s Tombstones,
Birth, Death, and Symmetry
Religious Symbolism
at Princeton

Dante, Inferno, Canto X, 37-39:

E l’animose man del duca e pronte
mi spinser tra le sepulture a lui,
dicendo: “Le parole tue sien conte.”

And the bold and ready hands
    of my Leader
pushed me between the tombs to him,
saying: “Let thy words be fitting”.

“Make your words count,”
 Virgil instructs Dante:
“Speak aptly, make what you say
 appropriate to the situation.”

Perhaps Crowningshield’s
Leader will be…

The image “http://www.log24.com/log/pix06B/061116-Niemoller.jpg” cannot be displayed, because it contains errors.

Niemoller is noted for his role in
the movement that led to the
Barmen Declaration, discussed in
Presbyterian Creedal Standards
linked to in the above-cited
Religious Symbolism
at Princeton

(…that lay in the house
that Jack built).

The image “http://www.log24.com/log/pix06B/Jack.gif” cannot be displayed, because it contains errors.

Sunday, October 29, 2006

Sunday October 29, 2006

Filed under: General — m759 @ 1:00 AM
(Readings for the
Halloween season)

In 1692 on July 31, at the time of the Salem witchcraft trials, Increase Mather reportedly “delivered a sermon… in Boston in which he posed the question… ‘O what makes the difference between the devils in hell and the angels of heaven?'”

, the father of Cotton Mather, was president of Harvard from June 27, 1692, to Sept. 6, 1701.  His name is memorialized by Harvard’s Mather House.

From Log24 on Jan. 15, 2003:

Locating Hell

“Noi siam venuti al loco ov’ i’ t’ho detto
            che tu vedrai le genti dolorose
    c’hanno perduto il ben de l’intelletto

Dante, Inferno, Canto 3, 16-18

“We have come to where
              I warned you we would find
Those wretched souls
              who no longer have 
The intellectual benefits of the mind.”

Dante, Hell, Canto 3, 16-18

From a Harvard student’s weblog:

Heard in Mather  I hope you get gingivitis You want me to get oral cancer?! Goodnight fartface Turd. Turd. Turd. Turd. Turd. Make your own waffles!! Blah blah blah starcraft blah blah starcraft blah starcraft. It’s da email da email. And some blue hair! Oohoohoo Izod! 10 gigs! Yeah it smells really bad. Only in the stairs though. Starcraft blah blah Starcraft fartface. Yeah it’s hard. You have to get a bunch of battle cruisers. 40 kills! So good! Oh ho ho grunt grunt squeal.  I’m getting sick again. You have a final tomorrow? In What?! Um I don’t even know. Next year we’re draggin him there and sticking the needle in ourselves. 

” … one more line/ unravelling from the dark design/ spun by God and Cotton Mather”

— Robert Lowell


To honor Harvard’s Oct. 28 founding,
here are yesterday’s numbers from
the state of Grace (Kelly, of Philadelphia):

The image “http://www.log24.com/log/pix06A/061028-PAlottery.jpg” cannot be displayed, because it contains errors.

Related material:

Log24 on 1/16,
and Hexagram 41,

The image “http://www.log24.com/images/IChing/hexagram41.gif” cannot be displayed, because it contains errors.


The Image

At the foot of the mountain, the lake:
The image of Decrease.
Thus the superior man controls his anger
And restrains his instincts.

This suggests thoughts of
the novel Cold Mountain
 (see yesterday morning)
and the following from
Log24 on St. Luke’s Day
this year:

The image �http://www.log24.com/log/pix05/050511-Montreat-logo.jpg� cannot be displayed, because it contains errors.

Lucero as portrayed by Megan Follows
Established in 1916,
Montreat College
is a private, Christian
college located in a
beautiful valley in the
Blue Ridge Mountains
of North Carolina.

From Nell:

The image �http://www.log24.com/log/pix05/050511-Nell-valleyview.jpg� cannot be displayed, because it contains errors.

“The valley spirit never dies…”

See also St. Luke’s Day, 2004,
as well as a journal entry
prompted by both
the ignorant religion
of Harvard’s past
and the ignorant scientism
of Harvard’s present–
 Hitler’s Still Point:
A Hate Speech for Harvard

This last may, of course, not
quite fit the description of
the superior man
controlling his anger
so wisely provided by
yesterday’s lottery and
Hexagram 41.
Nobody’s perfect.

Monday, June 19, 2006

Monday June 19, 2006

Filed under: General — m759 @ 4:00 PM

A Reply to John Updike

See Updike on digitized snippets.

The following four snippets were pirated from the end of MathPages Quotations, compiled by Kevin Brown.

They are of synchronistic interest in view of the previous two Log24 entries, which referred (implicitly) to a Poe story and (explicitly) to Pascal.

"That is another of your odd notions,"
said the Prefect, who had the fashion
of calling everything 'odd' that was
beyond his comprehension, and thus
lived amid an absolute legion of 'oddities.'
Edgar Allan Poe

I knew when seven justices could not
take up a quarrel, but when the parties
were met themselves, one of them
thought but of an If, as, 'If you said so,
then I said so'; and they shook hands
and swore brothers. Your If is the only
peacemaker; much virtue in If.

I have made this letter longer than usual
because I lack the time to make it shorter.
Blaise Pascal

S'io credessi che mia risposta fosse
a persona che mai tornasse al mondo,
questa fiamma staria senza piu scosse.
Ma per cio che giammai di questo fondo
non torno vivo alcun, s'i'odo il vero,
senza tema d'infamia ti rispondo.
Dante, 1302

For translations of the Dante (including one by Dorothy Sayers), see everything2.com.

An anonymous author there notes that Dante describes a flame in which is encased a damned soul. The flame vibrates as the soul speaks:

If I thought that I were making
Answer to one that might return to view
The world, this flame should evermore
cease shaking.

But since from this abyss, if I hear true,
None ever came alive, I have no fear
Of infamy, but give thee answer due.

-- Dante, Inferno, Canto 27, lines 61-66,
translated by Dorothy Sayers

Updike says,

“Yes, there is a ton of information on the web but much of it is grievously inaccurate, unedited, unattributed and juvenile. The electronic marvels that abound around us serve, I have the impression, to inflame what is most informally and non-critically human about us. Our computer screens stare back at us with a kind of giant, instant aw-shucks, disarming in its modesty.”

Note Updike’s use of “inflame.”

For an aw-shucks version of “what is most informally and non-critically human about us,” as well as a theological flame, see both the previous entry and the above report from Hell.

Note that the web serves also to correct material that is inaccurate, unedited, unattributed, and juvenile. For examples, see Mathematics and Narrative. The combination of today’s entry for Pascal’s birthday with that web page serves both to light one candle and to curse the darkness.

Thursday, May 4, 2006

Thursday May 4, 2006

Filed under: General — m759 @ 1:09 PM
First of all…

The image “http://www.log24.com/log/pix06A/060504-Hannibal.jpg” cannot be displayed, because it contains errors.

On this date in 1927, the
Academy of Motion Picture
Arts and Sciences was chartered.

Related material:

Dante and Plato,

Plato, Pegasus, and
  the Evening Star

Mathematics and Narrative,

The Tiffany Code

Sunday, March 19, 2006

Sunday March 19, 2006

Filed under: General — m759 @ 6:09 PM
Readings for
St. Joseph’s Day

Cut Numbers and
In the Hand of Dante,
both by Nick Tosches,

The image “http://www.log24.com/log/pix06/060319-Dante3.jpg” cannot be displayed, because it contains errors.

and Symmetry,
by Hermann Weyl:

The image “http://www.log24.com/log/pix06/060319-Weyl.jpg” cannot be displayed, because it contains errors.

Related material:
Kernel of Eternity
(a Log24 entry of June 9, 2005)
and the comment on that entry
by ItAlIaNoBoI.

Monday, February 13, 2006

Monday February 13, 2006

Filed under: General — m759 @ 8:00 PM
The Lincoln Brigade

The image “http://www.log24.com/log/pix06/060213-Lincoln1.jpg” cannot be displayed, because it contains errors.

Marches On.

As yesterday’s Lincoln’s Birthday entry indicated, my own sympathies are not with the “created equal” crowd.  Still, the Catholic Fascism of Franco admirer Andrew Cusack seems somewhat over-the-top.  A more thoughtful approach to these matters may be found in a recommendation by Ross Douthat at The American Scene:

Read Eve Tushnet on the virtues of The Man in the High Castle.

Related material: Log24 on Nov. 14, Nov. 15, and Nov. 16, 2003.

Another item of interest from Eve:

“Transubstantiation [is equivalent but not equal to] art (deceptive accident hides truthful substance), as vs. Plato’s condemnation of the physical & the fictive? (Geo. Steiner)”

Related material:

The End of Endings
by Father Richard John Neuhaus,
First Things
115 (Aug.-Sept. 2001), 47-56:

“In Grammars of Creation, more than in his 1989 book Real Presences, Steiner acknowledges that his argument rests on inescapably Christian foundations. In fact, he has in the past sometimes written in a strongly anti–Christian vein, while the present book reflects the influence of, among others, Miri Rubin, whose Corpus Christi: The Eucharist in Late Medieval Culture is credited in a footnote. Steiner asserts that, after the Platonisms and Gnosticisms of late antiquity, it is the doctrines of incarnation and transubstantiation that mark ‘the disciplining of Western syntax and conceptualization’ in philosophy and art. ‘Every heading met with in a study of “creation,” every nuance of analytic and figural discourse,’ he says, derives from incarnation and transubstantiation, ‘concepts utterly alien to either Judaic or Hellenic perspectives– though they did, in a sense, arise from the collisions and commerce between both.’….

The incarnation of God in the Son, the transubstantiation of bread and wine into his body and blood, are ‘a mysterium, an articulated, subtly innervated attempt to reason the irrational at the very highest levels of intellectual pressure.’ ‘Uniquely, perhaps, the hammering out of the teaching of the eucharist compels Western thought to relate the depth of the unconscious and of pre-history with speculative abstractions at the boundaries of logic and of linguistic philosophy.’ Later, the ‘perhaps’ in that claim seems to have disappeared:

At every significant point, Western philosophies of art and Western poetics draw their secular idiom from the substratum of Christological debate. Like no other event in our mental history, the postulate of God’s kenosis through Jesus and of the never-ending availability of the Savior in the wafer and wine of the eucharist, conditions not only the development of Western art and rhetoric itself, but at a much deeper level, that of our understanding and reception of the truth of art– a truth antithetical to the condemnation of the fictive in Plato.

This truth reaches its unrepeated perfection in Dante, says Steiner. In Dante, ‘It rounds in glory the investigation of creativity and creation, of divine authorship and human poesis, of the concentric spheres of the aesthetic, the philosophical, and the theological. Now truth and fiction are made one, now imagination is prayer, and Plato’s exile of the poets refuted.’ In the fashionable critical theories of our day, we witness ‘endeavors of the aesthetic to flee from incarnation.’ ‘It is the old heresies which revive in the models of absence, of negation or erasure, of the deferral of meaning in late–twentieth–century deconstruction. The counter-semantics of the deconstructionist, his refusal to ascribe a stable significance to the sign, are moves familiar to [an earlier] negative theology.’ Heidegger’s poetics of ‘pure immanence’ are but one more attempt ‘to liberate our experience of sense and of form from the grip of the theophanic.’ But, Steiner suggests, attempted flights from the reality of Corpus Christi will not carry the day. ‘Two millennia are only a brief moment.’

Wednesday, November 16, 2005

Wednesday November 16, 2005

Filed under: General — m759 @ 4:04 PM

Adam Gopnik on C. S. Lewis in this week’s New Yorker:

“Lewis began with a number of haunted images….”

“The best of the books are the ones… where the allegory is at a minimum and the images just flow.”

“‘Everything began with images,’ Lewis wrote….”

“We go to the writing of the marvellous, and to children’s books, for stories, certainly, and for the epic possibilities of good and evil in confrontation, not yet so mixed as they are in life. But we go, above all, for imagery: it is the force of imagery that carries us forward. We have a longing for inexplicable sublime imagery….”

“The religious believer finds consolation, and relief, too, in the world of magic exactly because it is at odds with the necessarily straitened and punitive morality of organized worship, even if the believer is, like Lewis, reluctant to admit it. The irrational images– the street lamp in the snow and the silver chair and the speaking horse– are as much an escape for the Christian imagination as for the rationalist, and we sense a deeper joy in Lewis’s prose as it escapes from the demands of Christian belief into the darker realm of magic. As for faith, well, a handful of images is as good as an armful of arguments, as the old apostles always knew.”

Related material:

The image “http://www.log24.com/log/pix05B/051116-Time.jpg” cannot be displayed, because it contains errors.

Click on pictures for details.

See also Windmills and
Verbum sat sapienti?
as well as

an essay

 at Calvin College
on Simone Weil,
Charles Williams,
Dante, and
the way of images.”

Monday, October 31, 2005

Monday October 31, 2005

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


The image “http://log24.com/log/pix03/030109-gridsmall.gif” cannot be displayed, because it contains errors.

“An asymmetrical balance is sought since it possesses more movement. This is achieved by the imaginary plotting of the character upon a nine-fold square, invented by some ingenious writer of the Tang dynasty. If the square were divided in half or in four, the result would be symmetrical, but the nine-fold square permits balanced asymmetry.”– Chiang Yee, Chinese Calligraphy,
quoted in Aspen no. 10, item 8“‘Burnt Norton’ opens as a meditation on time. Many comparable and contrasting views are introduced. The lines are drenched with reminiscences of Heraclitus’ fragments on flux and movement….  the chief contrast around which Eliot constructs this poem is that between the view of time as a mere continuum, and the difficult paradoxical Christian view of how man lives both ‘in and out of time,’ how he is immersed in the flux and yet can penetrate to the eternal by apprehending timeless existence within time and above it. But even for the Christian the moments of release from the pressures of the flux are rare, though they alone redeem the sad wastage of otherwise unillumined existence. Eliot recalls one such moment of peculiar poignance, a childhood moment in the rose-garden– a symbol he has previously used, in many variants, for the birth of desire. Its implications are intricate and even ambiguous, since they raise the whole problem of how to discriminate between supernatural vision and mere illusion. Other variations here on the theme of how time is conquered are more directly apprehensible. In dwelling on the extension of time into movement, Eliot takes up an image he had used in ‘Triumphal March’: ‘at the still point of the turning world.’ This notion of ‘a mathematically pure point’ (as Philip Wheelwright has called it) seems to be Eliot’s poetic equivalent in our cosmology for Dante’s ‘unmoved Mover,’ another way of symbolising a timeless release from the ‘outer compulsions’ of the world. Still another variation is the passage on the Chinese jar in the final section. Here Eliot, in a conception comparable to Wallace Stevens’ ‘Anecdote of the Jar,’ has suggested how art conquers time:

       Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.”

— F. O. Matthiessen,
The Achievement of T.S. Eliot,
Oxford University Press, 1958,
as quoted in On “Burnt Norton”

Thursday, September 15, 2005

Thursday September 15, 2005

Filed under: General — Tags: — m759 @ 2:45 AM


“… the quality of life as of death
and of light as of darkness is one…”

— Robinson Jeffers

The image “http://www.log24.com/log/pix05B/050915-NYTobits.jpg” cannot be displayed, because it contains errors.

(See previous two entries
and Dante, Paradiso, 25.054.)

Thursday, November 11, 2004

Thursday November 11, 2004

Filed under: General — m759 @ 11:11 AM

11/11 11:11:11

Samuel Beckett on Dante and Joyce:

“Another point of comparison is the preoccupation with the significance of numbers. The death of Beatrice inspired nothing less than a highly complicated poem dealing with the importance of the number 3 in her life. Dante never ceased to be obsessed by this number. Thus the poem is divided into three Cantiche, each composed of 33 Canti…. Why, Mr. Joyce seems to say, should…. the Armistice be celebrated at the eleventh hour of the eleventh day of the eleventh month? He cannot tell you because he is not God Almighty, but in a thousand years he will tell you… He is conscious that things with a common numerical characteristic tend towards a very significant interrelationship. This preoccupation is freely translated in his present work….”

— “Dante… Bruno. Vico.. Joyce,” in James Joyce/Finnegans Wake: A Symposium (1929), New Directions paperback, 1972

See also my entry from five years ago on this date:

Plato, Pegasus, and the Evening Star.

Tuesday, September 28, 2004

Tuesday September 28, 2004

Filed under: General — Tags: , — m759 @ 3:33 PM

3:33:33 PM

Romantic Interaction, continued…

The Rhyme of Time

From American Dante Bibliography for 1983:

Freccero, John. "Paradiso X: The Dance of the Stars" (1968). Reprinted in Dante in America … (q.v.), pp. 345-371. [1983]

Freccero, John. "The Significance of terza rima." In Dante, Petrarch, Boccaccio: Studies in the Italian Trecento … (q.v.), pp. 3-17. [1983]

Interprets the meaning of terza rima in terms of a temporal pattern of past, present, and future, with which the formal structure and the thematics of the whole poem coordinate homologically: "both the verse pattern and the theme proceed by a forward motion which is at the same time recapitulary." Following the same pattern in the three conceptual orders of the formal, thematical, and logical, the autobiographical narrative too is seen "as forward motion that moves towards its own beginning, or as a form of advance and recovery, leading toward a final recapitulation." And the same pattern is found especially to obtain theologically and biblically (i.e., historically). By way of recapitulation, the author concludes with a passage from Augustine's Confessions on the nature of time, which "conforms exactly to the movement of terza rima." Comes with six diagrams illustrating the various patterns elaborated in the text.

From Rachel Jacoff's review of Pinsky's translation of Dante's Inferno:

"John Freccero's Introduction to the translation distills a compelling reading of the Inferno into a few powerful and immediately intelligible pages that make it clear why Freccero is not only a great Dante scholar, but a legendary teacher of the poem as well."

From The Undivine Comedy, Ch. 2, by Teodolinda Barolini (Princeton University Press, 1992):

"… we exist in time which, according to Aristotle, "is a kind of middle-point, uniting in itself both a beginning and an end, a beginning of future time and an end of past time."* It is further to say that we exist in history, a middleness that, according to Kermode, men try to mitigate by making "fictive concords with origins and ends, such as give meaning to lives and to poems." Time and history are the media Dante invokes to begin a text whose narrative journey will strive to imitate– not escape– the journey it undertakes to represent, "il cammin di nostra vita."

* Aristotle is actually referring to the moment, which he considers indistinguishable from time: "Now since time cannot exist and is unthinkable apart from the moment, and the moment is a kind of middle-point, uniting as it does in itself both a beginning and an end, a beginning of future time and an end of past time, it follows that there must always be time: for the extremity of the last period of time that we take must be found in some moment, since time contains no point of contact for us except in the moment. Therefore, since the moment is both a beginning and an end there must always be time on both sides of it" (Physics 8.1.251b18-26; in the translation of R. P. Hardie and R. K. Gaye, in The Basic Works of Aristotle, ed. Richard McKeon [New York: Random House, 1941]).  

From Four Quartets:

And the pool was filled with water out of sunlight,
And the lotos rose, quietly, quietly,
The surface glittered out of heart of light,
And they were behind us, reflected in the pool.
Then a cloud passed, and the pool was empty.
Go, said the bird, for the leaves were full of children,
Hidden excitedly, containing laughter.
Go, go, go, said the bird: human kind
Cannot bear very much reality.
Time past and time future
What might have been and what has been
Point to one end, which is always present.

Tuesday, September 21, 2004

Tuesday September 21, 2004

Filed under: General — m759 @ 10:25 AM

First Idea and Last Night

In memory of Saint Norman Cantor, an author of “stunning heartlessness” — my kind of historian — who died on Saturday, September 18, 2004…

a link to Log24.net entries of that date.

Give ’em Hell, Norman.


Above: recommended videos
from the date of Cantor’s death

Dante’s hell was intended to be a shocking literary device. The Divine Comedy is not a work of theology or a spiritual treatise any more than James Joyce’s Ulysses is a sociological study of Dublin.”

— Norman F. Cantor
   Hollywood, Florida

Tuesday, August 10, 2004

Tuesday August 10, 2004

Filed under: General,Geometry — Tags: , — m759 @ 3:01 PM

Battle of Gods and Giants

In checking the quotations from Dante in the previous entry, I came across the intriguing site Gigantomachia:

"A gigantomachia or primordial battle between the gods has been retold in myth, cult, art and theory for thousands of years, from the Egyptians to Heidegger. This site will present the history of the theme. But it will do so in an attempt to raise the question of the contemporary relevance of it. Does the gigantomachia take place today? Where? When? In what relation to you and me?"

Perhaps atop the Empire State Building?

(See An Affair to Remember and  Empire State Building to Honor Fay Wray.)

Perhaps in relation to what the late poet Donald Justice called "the wood within"?

Perhaps in relation to T. S. Eliot's "The Waste Land" and the Feast of the Metamorphosis?

Or perhaps not.

Perhaps at Pergamon:

Perhaps at Pergamon Press:


"What modern painters are trying to do,
if they only knew it, is paint invariants."

— James J. Gibson in Leonardo
(Vol. 11, pp. 227-235.
Pergamon Press Ltd., 1978)

An example of invariant structure:

The three line diagrams above result from the three partitions, into pairs of 2-element sets, of the 4-element set from which the entries of the bottom colored figure are drawn.  Taken as a set, these three line diagrams describe the structure of the bottom colored figure.  After coordinatizing the figure in a suitable manner, we find that this set of three line diagrams is invariant under the group of 16 binary translations acting on the colored figure.

A more remarkable invariance — that of symmetry itself — is observed if we arbitrarily and repeatedly permute rows and/or columns and/or 2×2 quadrants of the colored figure above. Each resulting figure has some ordinary or color-interchange symmetry.

This sort of mathematics illustrates the invisible "form" or "idea" behind the visible two-color pattern.  Hence it exemplifies, in a way, the conflict described by Plato between those who say that "real existence belongs only to that which can be handled" and those who say that "true reality consists in certain intelligible and bodiless forms."

For further details, see a section on Plato in the Gigantomachia site.

Tuesday August 10, 2004

Filed under: General — m759 @ 5:24 AM

The Day Justice Died

But all things then were oracle and secret.
Remember the night when,
    lost, returning, we turned back
Confused, and our headlights
    singled out the fox?
Our thoughts went with it then,
    turning and turning back
   With the same terror,
                into the deep thicket
   Beside the highway,
                at home in the dark thicket.

I say the wood within is the dark wood….

Donald Justice, “Sadness”

In memory of Justice,
Dante excerpts:

Canto I

Nel mezzo del cammin di nostra vita
 mi ritrovai per una selva oscura,
 che la diritta via era smarrita.
Ahi quanto a dir qual era é cosa dura
 esta selva e selvaggia e aspra e forte
 che nel pensier rinova la paura!

Midway in the journey of our life
 I found myself in a dark wood,
 for the straight way was lost.
Ah, how hard it is to tell what that
 wood was, wild, rugged, harsh;
 the very thought of it renews the fear!

Canto III

Per me si va ne la città dolente,
 per me si va ne l’etterno dolore,
 per me si va tra la perduta gente.
Giustizia mosse il mio alto fattore;
 fecemi la divina podestate,
 la somma sapïenza e ‘l primo amore.
Dinanzi a me non fuor cose create
 se non etterne, e io etterno duro.
 Lasciate ogne speranza, voi ch’intrate.

Through me you enter the woeful city,
 through me you enter eternal grief,
 through me you enter among the lost.
Justice moved my high maker;
 the divine power made me,
 the supreme wisdom, and the primal love.
Before me nothing was created
 if not eternal, and eternal I endure.
 Abandon every hope, you who enter.

— Translation by Charles S. Singleton,
selection by Paul J. Viscuso

Justice moved my high maker…

From the day Justice died,
Friday, August 6, 2004,
The Feast of the Metamorphosis:

Saturday, August 7, 2004

Saturday August 7, 2004

Filed under: General — Tags: — m759 @ 4:07 AM


Ian Lee on the communion of saints and the association of ideas (in The Third Word War, 1978) 

"The association is the idea"

Herman Melville on the association of ideas:

"In me, many worthies recline, and converse."

Stephen Hunter yesterday on the protagonist of the new film Collateral:

"He dresses Italian, shoots German (suits by Versace, pistol by Heckler & Koch), talks like Norman Mailer's White Negro and improvises brilliantly."  

Anagram by Dante (Filipponi, that is) on the name of Gianni Versace:

Can Give a Siren

Sirens, true sirens verily be,
Sirens, waylayers in the sea.

— Herman Melville, quoted
early yesterday by stephenhoy

Siren and White Negro:

See Gates's essay on
Anatole Broyard and
the log24 Bastille Day
on Mr. Motley's

"… there are many associations of ideas which do not correspond to any actual connection of cause and effect in the world of phenomena…."

— John Fiske, "The Primeval Ghost-World," quoted in the Heckler & Coch weblog

And, finally, brilliance:

Fark News yesterday:

"Disrespectful look causes shootout in Houston. Gang telepathy classes enrolling soon."

Log24 entry of Sept. 28, 2003: 

Spirit of East St. Louis

Saturday, June 26, 2004

Saturday June 26, 2004

Filed under: General — m759 @ 3:03 AM
Deep Game

The entry Ado of June 25, 2004 contains a link to an earlier entry, A Form, continued, of June 5, 2004.  This in turn contains a link to a site by Wolfgang Wildgen which contains the following:

“Historically, we may say that the consequence of Bruno’s parallel work on cosmology and artificial memory is a new model of semantic fields which was so radical in its time that the first modern followers (although ignorant of this tradition) are the Von-Neumann automata and the neural net systems of the 1980s (cf. Wildgen 1998: 39, 237f).”

Wildgen, W. 1998. Das kosmische Gedächtnis. Kosmologie, Semiotik und Gedächtniskunst im Werke von Giordano Bruno. Frankfurt/Bern: Lang.

For an applet illustrating
the above remarks, see


The image “http://www.log24.com/log/pix04A/040626-Neighbors.gif” cannot be displayed, because it contains errors. 
Figure A

Neighborhood in a
Cellular Automaton
by Adam Campbell

For more of the Gedächtnis
in this Kunst, see the following
Google search on shc759:

The image “http://www.log24.com/log/pix04A/040626-Search.jpg” cannot be displayed, because it contains errors.

Figure B

Note that the reference to “forerunners” in fig. B occurs in a journal entry of June 12, 2002. See also the reference to a journal entry of the following day, June 13, 2002, in last Tuesday’s Dirty Trick.

Those who have viewed Campbell’s applet (see  fig. A) may appreciate the following observation of poet and Dante translator Robert Pinsky:

“… a grid, and a flow–
that is the essence of terza rima….”

Poetry, Computers, and Dante’s Inferno

For some related remarks
on the muses and epic poetry,
see a paper on Walter Benjamin:

“Here the memory (Gedächtnis) means
‘the epic faculty par excellence.’ “
(Benjamin, Der Erzähler, 1936: in
Gesammelte Schriften, 1991, II.2, 453)

Benjamin on Experience,
Narrative, and History

One possible connection to the muses is, as noted in a link in yesterday’s Ado, via George Balanchine.

An apt link to epic poetry (aside from the reference to Dante above) is, via the June 12, 2002, entry, to the epic The Gameplayers of Zan (the third reference in fig. B above).

The applet linked below fig. A very nicely illustrates the “structured chaos” of a space described by automata theory.  For a literary approach to such a space, see the Gameplayers entry.

For the benefit of art critic Robert Hughes, who recently made a distinction between “fast art” and “slow art,” the Campbell applet has a convenient speed control.

Tuesday, November 11, 2003

Tuesday November 11, 2003

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

Divine Comedy

Michael Joseph Gross:

“The Great Divorce is C.S. Lewis’s Divine Comedy: the narrator bears strong resemblance to Lewis (by way of Dante); his Virgil is the fantasy writer George MacDonald; and upon boarding a bus in a nondescript neighborhood, the narrator is taken to Heaven….”

Sunday, November 2, 2003

Sunday November 2, 2003

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

All Souls' Day
at the Still Point

From remarks on Denis Donoghue's Speaking of Beauty in the New York Review of Books, issue dated Nov. 20, 2003, page 48:

"The Russian theorist Bakhtin lends his august authority to what Donoghue's lively conversation has been saying, or implying, all along.  'Beauty does not know itself; it cannot found and validate itself — it simply is.' "

From The Bakhtin Circle:

"Goethe's imagination was fundamentally chronotopic, he visualised time in space:

Time and space merge … into an inseparable unity … a definite and absolutely concrete locality serves at the starting point for the creative imagination… this is a piece of human history, historical time condensed into space….

Dostoevskii… sought to present the voices of his era in a 'pure simultaneity' unrivalled since Dante. In contradistinction to that of Goethe this chronotope was one of visualising relations in terms of space not time and this leads to a philosophical bent that is distinctly messianic:

Only such things as can conceivably be linked at a single point in time are essential and are incorporated into Dostoevskii's world; such things can be carried over into eternity, for in eternity, according to Dostoevskii, all is simultaneous, everything coexists…. "

Bakhtin's notion of a "chronotope" was rather poorly defined.  For a geometric structure that might well be called by this name, see Poetry's Bones and Time Fold.  For a similar, but somewhat simpler, structure, see Balanchine's Birthday.

From Four Quartets:

"At the still point, there the dance is."

From an essay by William H. Gass on Malcolm Lowry's classic novel Under the Volcano:

"There is no o'clock in a cantina."

Monday, September 8, 2003

Monday September 8, 2003

Filed under: General — m759 @ 1:25 PM

Pre- and Post-Cognition

Majority Report:


A Matter of Life and Death,

an entry from Sept. 13, 2002, linked to in last night’s ART WARS notes:

“In the sun, Dante and Beatrice find themselves surrounded by a circle of souls famous for their wisdom on earth. They appear as splendid lights and precious jewels who dance and sing as they lovingly welcome two more into their company.”

Minority Report:

Doonesbury, Monday morning, Sept. 8, 2003:

©2003 G.B. Trudeau

For more chanting,
click here.

Thursday, March 13, 2003

Thursday March 13, 2003

Filed under: General — Tags: — m759 @ 4:44 PM


From The New Yorker, issue of March 17, 2003, Clive James on Aldous Huxley:

The Perennial Philosophy, his 1945 book compounding all the positive thoughts of West and East into a tutti-frutti of moral uplift, was the equivalent, in its day, of It Takes a Village: there was nothing in it to object to, and that, of course, was the objection.”

For a cultural artifact that is less questionably perennial, see Huxley’s story “Young Archimedes.”

Plato, Pythagoras, and
the diamond figure

Plato’s Diamond in the Meno
Plato as a precursor of Gerard Manley Hopkins’s “immortal diamond.” An illustration shows the ur-diamond figure.

Plato’s Diamond Revisited
Ivars Peterson’s Nov. 27, 2000 column “Square of the Hypotenuse” which discusses the diamond figure as used by Pythagoras (perhaps) and Plato. Other references to the use of Plato’s diamond in the proof of the Pythagorean theorem:


“… and he proceeded to prove the theorem of Pythagoras — not in Euclid’s way, but by the simpler and more satisfying method which was, in all probability, employed by Pythagoras himself….
‘You see,’ he said, ‘it seemed to me so beautiful….’
I nodded. ‘Yes, it’s very beautiful,’ I said — ‘it’s very beautiful indeed.'”
— Aldous Huxley, “Young Archimedes,” in Collected Short Stories, Harper, 1957, pp. 246 – 247


Sir Thomas L. Heath, in his commentary on Euclid I.47, asks how Pythagoreans discovered the Pythagorean theorem and the irrationality of the diagonal of a unit square. His answer? Plato’s diamond.
(See Heath, Sir Thomas Little (1861-1940),
The thirteen books of Euclid’s Elements translated from the text of Heiberg with introduction and commentary. Three volumes. University Press, Cambridge, 1908. Second edition: University Press, Cambridge, 1925. Reprint: Dover Publications, New York, 1956.

Other sites on the alleged
“diamond” proof of Pythagoras

Colorful diagrams at Cut-the-Knot

Illustrated legend of the diamond proof

Babylonian version of the diamond proof

For further details of Huxley’s story, see

The Practice of Mathematics,

Part I, by Robert P. Langlands, from a lecture series at the Institute for Advanced Study, Princeton.

From the New Yorker Contributors page for St. Patrick’s Day, 2003:

Clive James (Books, p. 143) has a new collection, As of This Writing: The Essential Essays, 1968-2002, which will be published in June.”

See also my entry “The Boys from Uruguay” and the later entry “Lichtung!” on the Deutsche Schule Montevideo in Uruguay.

Monday, March 10, 2003

Monday March 10, 2003

Filed under: General,Geometry — Tags: , — m759 @ 5:45 AM


Art at the Vanishing Point

Two readings from The New York Times Book Review of Sunday,

March 9,

2003 are relevant to our recurring "art wars" theme.  The essay on Dante by Judith Shulevitz on page 31 recalls his "point at which all times are present."  (See my March 7 entry.)  On page 12 there is a review of a novel about the alleged "high culture" of the New York art world.  The novel is centered on Leo Hertzberg, a fictional Columbia University art historian.  From Janet Burroway's review of What I Loved, by Siri Hustvedt:

"…the 'zeros' who inhabit the book… dramatize its speculations about the self…. the spectator who is 'the true vanishing point, the pinprick in the canvas.'''

Here is a canvas by Richard McGuire for April Fools' Day 1995, illustrating such a spectator.

For more on the "vanishing point," or "point at infinity," see

"Midsummer Eve's Dream."

Connoisseurs of ArtSpeak may appreciate Burroway's summary of Hustvedt's prose: "…her real canvas is philosophical, and here she explores the nature of identity in a structure of crystalline complexity."

For another "structure of crystalline
complexity," see my March 6 entry,

"Geometry for Jews."

For a more honest account of the
New York art scene, see Tom Wolfe's
The Painted Word.

Friday, March 7, 2003

Friday March 7, 2003

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

Lovely, Dark and Deep

On this date in 1923, "Stopping by Woods on a Snowy Evening," by Robert Frost, was published.  On this date in 1999, director Stanley Kubrick died.  On this date in 1872, Piet Mondrian was born.

"….mirando il punto
a cui tutti li tempi son presenti"

Dante, Paradiso, XVII, 17-18 

Chez Mondrian
Kertész, Paris, 1926 

6:23 PM Friday, March 7:

From Measure Theory, by Paul R. Halmos, Van Nostrand, 1950:

"The symbol is used throughout the entire book in place of such phrases as 'Q.E.D.' or 'This completes the proof of the theorem' to signal the end of a proof."

Wednesday, February 26, 2003

Wednesday February 26, 2003

Filed under: General — m759 @ 12:00 AM

The Eight Revisited

“…search for thirty-three and three…”

The Black Queen in The Eight, by Katherine Neville, Ballantine Books, January 1989, page 140 

Samuel Beckett on Dante and Joyce:

“Another point of comparison is the preoccupation with the significance of numbers….  Thus the poem is divided into three Cantiche, each composed of 33 Canti….”

— “Dante… Bruno. Vico.. Joyce,” in James Joyce/Finnegans Wake: A Symposium (1929), New Directions paperback, 1972

Into the Dark Woods:  

“– Nel mezzo del bloody cammin di nostra vita mi ritrovai in…”
Under the Volcano, by Malcolm Lowry, 1947, beginning of Chapter VI

Dante Alighieri Academy:

“‘The Divine Comedy’ celebrates Dante’s journey of knowledge to God through life: hell, purgatory and paradise. Dante Alighieri Academy continues Dante’s Christian philosophy of education….”

Chorus of the Damned:

I don’t know where it is we’re goin’
and God knows if I ever will,
but what a way this is to get there.
I got those archetypal, rubber-room,
astral-plane Moebius strip blues.
I got those in-and-out, round-about,
which way’s out Moebius strip blues.

© 1997 by C.K. Latham

Added March 3, 2003, 6:00 AM:

For a less confused song, click this Glasgow site.

Wednesday, February 5, 2003

Wednesday February 5, 2003

Filed under: General — m759 @ 12:00 AM

Feast of Saint Marianne

On this date in 1972, poet and Presbyterian saint Marianne Moore died in New York City.

For why she was a saint, see the excellent article by Samuel Terrien,

 Marianne Moore: Poet of Secular Holiness,”

from Theology Today, Vol. 47, No. 4, January 1991, published by Princeton Theological Seminary, Princeton, N. J.

Terrien quotes the following Moore poem:


is an enchanted thing….
Like Gieseking playing Scarlatti….


Tonight’s site music, though not played by Gieseking himself, is, in honor of Moore, the following work by Scarlatti from the Classical Music Archives:

Scarlatti’s Sonata in E major, andante comodo  (Longo 23 = Kirkpatrick 380 = Pestelli 483) 

To purchase a recording of Gieseking playing this work,

click here.

Wednesday, January 15, 2003

Wednesday January 15, 2003

Filed under: General — m759 @ 5:55 PM

Conversations in Hell

Part I: Locating Hell

“Noi siam venuti al loco ov’ i’ t’ho detto
           che tu vedrai le genti dolorose
        c’hanno perduto il ben de l’intelletto

Dante, Inferno, Canto 3, 16-18

“We have come to where I warned you
       we would find
Those wretched souls who no longer have 
The intellectual benefits of the mind.”

Dante, Hell, Canto 3, 16-18

From a Harvard student’s weblog:

Heard in Mather  I hope you get gingivitis You want me to get oral cancer?! Goodnight fartface Turd. Turd. Turd. Turd. Turd. Make your own waffles!! Blah blah blah starcraft blah blah starcraft blah starcraft. It’s da email da email. And some blue hair! Oohoohoo Izod! 10 gigs! Yeah it smells really bad. Only in the stairs though. Starcraft blah blah Starcraft fartface. Yeah it’s hard. You have to get a bunch of battle cruisers. 40 kills! So good! Oh ho ho grunt grunt squeal.  I’m getting sick again. You have a final tomorrow? In What?! Um I don’t even know. Next year we’re draggin him there and sticking the needle in ourselves. 

” … one more line / unravelling from the dark design / spun by God and Cotton Mather”

— Robert Lowell

Part II: The Call of Stories

From a website on college fund-raising

• “The people who come to us bring their stories. They hope they tell them well enough so that we understand the truth of their lives.”—Robert Coles, Harvard professor, The Call of Stories: Teaching and the Moral Imagination

• “If there’s anything worth calling theology, it is listening to people’s stories, listening to them and cherishing them.”—Mary Pellauer, quoted in Kathleen Norris’ Dakota: A Spiritual Geography

From a website on “The West Wing”:

9pm 2003-01-15    


In a special episode guest written by playwright Jon Robin Baitz, C.J. (Allison Janney) reluctantly returns to Dayton, Ohio, to speak at her 20th high school class reunion…”

From a website illustrating language in Catholic religious stories:

“Headquartered in Dayton, Ohio, the Sisters of the Precious Blood is a Catholic religious congregation…”

From a Catholic religious story by J. R. R. Tolkien:

“It shone now as if verily it was
 wrought of living fire.
‘Precious, precious, precious!’ Gollum cried.
‘My Precious! O my Precious!'”

From a website on Philip Pullman, author of His Dark Materials

“‘Stories are the most important thing in the world.  Without stories, we wouldn’t be human beings at all.”

From the same website, a short story:

Philip Pullman was born in Norwich on

19th October 1946.”

Part III: My Story

For a different story, see my weblog of

19th October 2002:

Saturday, October 19, 2002

What is Truth?

Wednesday, January 8, 2003

Wednesday January 8, 2003

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

Into the Woods

From the Words on Film site:

"The proximal literary antecedents for Under the Volcano are Dante Alighieri’s Divine Comedy, especially The Inferno, on the one hand, and on the other, the Faust legend as embodied in the dramatic poem Faust by Johann Wolfgang von Goethe and the play Doctor Faustus by Christopher Marlowe."

"In the opening page of the novel, we find the words "The Hotel Casino de la Selva stands on a slightly higher hill …" (Lowry, Volcano p. 3). "Selva" is one of the Spanish words for "woods." One of the cantinas in the novel is named El Bosque, and bosque is another Spanish word for "woods." The theme of being in a darkling woods is reiterated throughout the novel."

Literary Florence

Tonight's site music is "Children Will Listen,"
by Stephen Sondheim, from "Into the Woods."

Stephen Hawking is 61 today. 
An appropriate gift might be a cassette version of
The Screwtape Letters, by C. S. Lewis,
narrated by John Cleese. 

See also this review of Lewis's That Hideous Strength
and my entries of Dec. 31, 2002, and Jan. 4, 2003.   

Wednesday, December 11, 2002

Wednesday December 11, 2002

Filed under: General — m759 @ 12:00 AM

Culture Clash at Midnight
in the Garden of Good and Evil

From the Catholic Church:
John V. Apczynski
Dept. of Theology
St. Bonaventure U. 

From Paris, Texas:
Sam Shepard, playwright,
actor, and author of
Great Dream of Heaven.

In a future life, if not in this one, Dante might assign these two theologians to Purgatory, where they could teach one another.  Both might benefit if Shepard took Apczynski’s course “The Intellectual Journey” and if Apczynski read Shepard’s new book of short stories, Great Dream of Heaven

Background music might consist of Sinatra singing “Three Coins in the Fountain” (for Shepard — See my journal notes of December 10, 2002) alternating with the Dixie Chicks singing “Cowboy, Take Me Away” (for Apczynski, who is perhaps unfamiliar with life on the range).  Today’s site music is this fervent prayer by the Dixie Chicks to a cowboy-theologian like Shepard.

Tuesday, November 26, 2002

Tuesday November 26, 2002

Filed under: General — m759 @ 11:00 PM

Andante Cantabile

As we prepare to see publicity for Russell Crowe in a new role, that of Captain Jack Aubrey in “The Far Side of the World,” based on Master and Commander by Patrick O’Brian, we bid farewell to Patti LaBelle and her Ya-Ya, and say hello to a piece more attuned to Aubrey’s tastes.  This site’s background music is now Mozart’s Duo for Violin and Viola in Bb, K.424, 2, andante cantabile. 

Friday, September 27, 2002

Friday September 27, 2002

Filed under: General — Tags: — m759 @ 5:10 PM

Modern Times

ART WARS September 27, 2002:

From the Bulletin of the American Mathematical Society, October 2002, p. 563:

"To produce decorations for their weaving, pottery, and other objects, early artists experimented with symmetries and repeating patterns.  Later the study of symmetries of patterns led to tilings, group theory, crystallography, finite geometries, and in modern times to security codes and digital picture compactifications.  Early artists also explored various methods of representing existing objects and living things.  These explorations led to…. [among other things] computer-generated movies (for example, Toy Story)."

— David W. Henderson, Cornell University

From an earlier log24.net note: 


ART WARS   September 12, 2002


John Frankenheimer's film "The Train" —

Und was für ein Bild des Christentums 
ist dabei herausgekommen?

From Today in Science History:

Locomotion No. 1

[On September 27] 1825, the first locomotive to haul a passenger train was operated by George Stephenson's Stockton & Darlington's line in England. The engine "Locomotion No. 1" pulled 34 wagons and 1 solitary coach…. This epic journey was the launchpad for the development of the railways….

From Inventors World Magazine:

Some inventions enjoyed no single moment of birth. For the steam engine or the motion-picture, the birth-process was, on close examination, a gradual series of steps. To quote Robert Stevenson: 'The Locomotive is not the invention of one man, but a nation of mechanical engineers.' George Stevenson (no relation) probably built the first decent, workable steam engines…  Likewise the motion camera developed into cinema through a line of inventors including Prince, Edison and the Lumière brothers, with others fighting for patents. No consensus exists that one of these was its inventor. The first public display was achieved by the Lumière brothers in Paris.

From my log24.net note of Friday, Sept. 13th:

"Dante compares their dance and song to God’s bride on earth, the Church, when she answers the morning bells to rise from bed and 'woo with matins song her Bridegroom's love.' Some critics consider this passage the most 'spiritually erotic' of all the one hundred cantos of the Comedy."

From my log24.net note of September 12:


Everybody's doin'
a brand new dance now…

Friday, September 13, 2002

Friday September 13, 2002

Filed under: General — m759 @ 2:24 PM

Meditation for Friday the 13th

The 1946 British film below (released as “Stairway to Heaven” in the U.S.) is one of my favorites.  I saw it as a child. Since costar Kim Hunter died this week (on 9/11), and since today is Friday the 13th, the following material seems relevant.

Kim Hunter in 1946

R.A.F pilot
and psychiatrist 

Alan McGlashan

Alan McGlashan has practiced as a psychiatrist in London for more than forty years.  He also served as a pilot for the R.A.F. (with MC and Croix de Guerre decorations). 

The doctor in “A Matter of Life and Death” addresses a heavenly court on behalf of his patient, R.A.F pilot David Niven:

In the film, David Niven is saved by mistake from a fated death and his doctor must argue to a heavenly court that he be allowed to live. 

In a similar situation, I would want Dr. Alan McGlashan, a real-life psychiatrist, on my side.  For an excerpt from one of my favorite books, McGlashan’s The Savage and Beautiful Country,

click here.

As Walker Percy has observed (see my Sept. 7 note, “The Boys from Uruguay”), a characteristic activity of human beings is what Percy called “symbol-mongering.”  In honor of today’s anniversary of the births of two R.A.F. fighter pilots,

Sir Peter Guy Wykeham-Barnes (b. 1915) and author

Roald Dahl (b. 1916),

here is one of the better symbols of the past century:

The circle is of course a universal symbol, and can be made to mean just about whatever one wants it to mean.  In keeping with Clint Eastwood’s advice, in the soundtrack album for “Midnight in the Garden of Good and Evil,” to “accentuate the positive,” here are some positive observations on a circle from the poet (and perhaps saint) Dante, who died on the night of September 13-14:

In the sun, Dante and Beatrice find themselves surrounded by a circle of souls famous for their wisdom on earth. They appear as splendid lights and precious jewels who dance and sing as they lovingly welcome two more into their company. Their love for God is kindled even more and grows as they find more individuals to love. Among the blessed souls are St. Thomas Aquinas and one of his intellectual “enemies”, Siger of Brabant, a brilliant philosopher at the University of Paris, some of whose teachings were condemned as heretical. Conflicts and divisions on earth are now forgotten and absorbed into a communal love song and dance “whose sweetness and harmony are unknown on earth and whose joy becomes one with eternity.”

Dante compares their dance and song to God’s bride on earth, the Church, when she answers the morning bells to rise from bed and “woo with matins song her Bridegroom’s love.” Some critics consider this passage the most “spiritually erotic” of all the one hundred cantos of the Comedy. It is the ending of Canto 10, verses 139-148.

— Fr. James J. Collins, “The Spiritual Journey with Dante V,” Priestly People October 1997

The above material on Dante is from the Servants of the Paraclete website.

For more on the Paraclete, see

The Left Hand of God.

See also the illustration in the note below.

Saturday, August 31, 2002

Saturday August 31, 2002

Filed under: General,Geometry — m759 @ 3:36 AM
Today’s birthday: Dr. Maria Montessori



“Let all thy words be counted.”
Dante, Inf., canto X.


Dante gives excellent advice to teachers when he says, “Let thy words be counted.” The more carefully we cut away useless words, the more perfect will become the lesson….

Another characteristic quality of the lesson… is its simplicity. It must be stripped of all that is not absolute truth…. The carefully chosen words must be the most simple it is possible to find, and must refer to the truth.

The third quality of the lesson is its objectivity. The lesson must be presented in such a way that the personality of the teacher shall disappear. There shall remain in evidence only the object to which she wishes to call the attention of the child….

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

Mathematicians mean something different by the phrase “block design.”

A University of London site on mathematical design theory includes a link to my diamond theory site, which discusses the mathematics of the sorts of visual designs that Professor Pope is demonstrating. For an introduction to the subject that is, I hope, concise, simple, and objective, see my diamond 16 puzzle.

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