Log24

Tuesday, August 20, 2019

Ice Giants and Fire Gods: Mind the Gap

Filed under: General — Tags: — m759 @ 5:52 PM

From my reading Monday morning —

From the online New York Times  this afternoon —

Related literature —

For the Church of Synchronology

The Gigantomachia page above is dated September 20, 2003.
See as well my own webpage from that date: "The Form, the Pattern."

Monday, August 19, 2019

Gods and Giants

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

For "the Pergamum altar," see Pergamon in this journal.

See also . . .

Tuesday, January 31, 2017

Where Entertainment Is God

Filed under: General — Tags: — m759 @ 11:18 PM

Continues.

Today's previous post suggests:

Not amused …

The above Los Angeles Film School poster publicizes an event
on December 13, 2014 (St. Lucia's Day). Also on that date —
"Grim Pen" and other posts in this journal.

Monday, November 3, 2014

Gods and Giants

Filed under: General — Tags: — m759 @ 2:01 PM

A weblog reports Chris Rock's remarks
on Saturday Night Live this past weekend:

"It’s America, we commercialize everything.
Look at what we did to Christmas.
Christmas.  Christmas is Jesus’ birthday.
It’s Jesus’ birthday.  Now, I don’t know Jesus
but from what I’ve read, Jesus is the least
materialistic person to ever roam the earth.
No bling on Jesus.
Jesus kept a low profile and we turned his
birthday into the most materialistic day of the
year.  Matter of fact, we have the Jesus birthday
season.  It’s a whole season of materialism.
Then, at the end of the Jesus birthday season
we have the nerve to have an economist come
on TV and tell you how horrible the Jesus birthday
season was this year.  Oh, we had a horrible Jesus’
birthday this year.  Hopefully, business will pick up
by his Crucifixion.”

Related music and image:

"Show us the way to the next little girl …"

Natalie Wood in "Miracle on 34th Street" (1947)

Related non-materialistic meditations:
The Rhetoric of Abstract Concepts and Gods and Giants.

Monday, August 19, 2019

A Couple of Tots

Filed under: General — Tags: — m759 @ 10:15 PM

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

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

Related material —

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

Sunday, August 18, 2019

Structure at Pergamon

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

Some background for The Epstein Chronicles

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

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

See also Robert Maxwell,
Frank Oppenheimer,
and the history of Leonardo .

Click the above Pergamon Press image
for Pergamon-related material.

Tuesday, May 28, 2019

Quaternion at Candlebrow

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

From a Groundhog Day post in 2009 —

The Candlebrow Conference
in Pynchon's Against the Day:

The conferees had gathered here from all around the world…. Their spirits all one way or another invested in, invested by, the siegecraft of Time and its mysteries.

"Fact is, our system of so-called linear time is based on a circular or, if you like, periodic phenomenon– the earth's own spin. Everything spins, up to and including, probably, the whole universe. So we can look to the prairie, the darkening sky, the birthing of a funnel-cloud to see in its vortex the fundamental structure of everything–"

Quaternion in finite geometry
Quaternion  by  S. H. Cullinane

"Um, Professor–"….

… Those in attendance, some at quite high speed, had begun to disperse, the briefest of glances at the sky sufficing to explain why. As if the professor had lectured it into being, there now swung from the swollen and light-pulsing clouds to the west a classic prairie "twister"….

… In the storm cellar, over semiliquid coffee and farmhouse crullers left from the last twister, they got back to the topic of periodic functions….

"Eternal Return, just to begin with. If we may construct such functions in the abstract, then so must it be possible to construct more secular, more physical expressions."

"Build a time machine."

"Not the way I would have put it, but if you like, fine."

Vectorists and Quaternionists in attendance reminded everybody of the function they had recently worked up….

"We thus enter the whirlwind. It becomes the very essence of a refashioned life, providing the axes to which everything will be referred. Time no long 'passes,' with a linear velocity, but 'returns,' with an angular one…. We are returned to ourselves eternally, or, if you like, timelessly."

"Born again!" exclaimed a Christer in the gathering, as if suddenly enlightened.

Above, the devastation had begun.

"As if the professor had lectured it into being . . . ."

See other posts now tagged McLuhan Time.

Monday, May 27, 2019

But Seriously . . .

Filed under: General — Tags: — m759 @ 9:32 PM

McLuhan on Analogy.

I prefer the simple "four dots" figure
of the double colon:

For those who prefer stranger analogies . . .

Actors from "The Eiger Sanction" —

Doctor Strange on Mount Everest —

Dr. Strange at beyondtheopposites.com on 2016/12/02

See as well this  journal on the above Strange date, 2016/12/02,
in posts tagged Lumber Room.

Sunday, September 3, 2017

Dead Poet

Filed under: General — Tags: , — m759 @ 6:48 PM

The time is from
a screenshot 
of my RSS feed.

"All in good time."

(See this morning's
  Mosaic Logic.)

Obit

Filed under: General — Tags: — m759 @ 11:35 AM

See also Steely Dan in this  journal.

Thursday, January 5, 2017

All Souls’ Confusion

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

Recent reports of the death of a writer on philosophy associated
with All Souls College, Oxford, reflect some confusion.

The New York Times  says the death was on Monday, January 2, 2017.
Other sources, including the college itself, say it was the day before —
Sunday, January 1 (New Year's Day), 2017.

At any rate, perhaps the following post from 9 PM ET Sunday night is relevant:

Sunday, January 1, 2017

9 PM New Year’s Day

Filed under: Uncategorized — m759 @ 9:00 PM

See "Four Gods" in this journal.

Phaedrus  265b:  "And we made four divisions
of the divine madness, ascribing them to four gods . . . ."

See as well a search for All Souls in this journal.

Sunday, January 1, 2017

9 PM New Year’s Day

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

See "Four Gods" in this journal.

Phaedrus  265b "And we made four divisions
of the divine madness, ascribing them to four gods . . . ."

Friday, August 19, 2016

Princeton University Press in 1947

Filed under: General — Tags: , , — m759 @ 11:17 AM

From a review, in the context of Hollywood, of a Princeton
University Press book on William Blake from 1947 —

Tuesday, January 6, 2015

Lucy Almighty

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

"God, Lucy  Lucy, God."

Monday, January 5, 2015

In the Sky, with Diamonds

Filed under: General — Tags: — m759 @ 11:32 PM

Saturday, December 13, 2014

Grim Pen

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

The title refers to remarks linked to this afternoon :

"An ingenious story line serves to convey
the mysteriousness of destiny, the 'grim pen'
of fate that encloses Hazel Shade."

— John Burt Foster Jr. on page 224 of
Nabokov's Art of Memory and European Modernism
(Princeton University Press, 1993)

IMAGE- Instances of 'grimpen' in 'Nabokov's Art of Memory'

Vide  a relevant page on Wallace Stevens.

Combinational Delight

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

For St. Lucia's Day —

A book that links the title of today's previous post,
Narrative Metaphysics, with Nabokov's "combinational delight."

Narrative Metaphysics

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

From "Guardians of the Galaxy" —

"Then the Universe exploded into existence…"

For those who prefer a more traditional approach :

See also Symplectic Structure and Stevens's Rock.

Monday, November 3, 2014

Wisconsin Death Trip*

Filed under: General — Tags: — m759 @ 8:59 PM

Courtesy of Mira Sorvino.

Enter Madison :

From "Intruders," BBC America, Season 1, Episode 2, at 1:07 of 43:31.

"You sure know how to show a girl a good time."

* The title is a reference to a Wisconsin-related Halloween post.

Friday, October 31, 2014

For the Late Hans Schneider

Filed under: General — Tags: — m759 @ 3:30 AM

See a University of Wisconsin obituary for Schneider,
a leading expert on linear algebra who reportedly died
at 87 on Tuesday, October 28, 2014.

Some background on linear algebra and "magic" squares:
tonight's 3 AM (ET) post and a search in this
journal for Knight, Death, and the Devil.

Click image to enlarge.

Tuesday, July 29, 2014

Strict Form

Filed under: General — m759 @ 3:00 AM

Two items from this morning’s news:

IMAGE- 'Monk brought strict form of Zen Buddhism to U.S.'

Sasaki Roshi trained for years in a distinctively strict style of Zen
that he transplanted to the U.S. His students rose at 3 a.m.
for chanting, exhausting hours of meditation and one-on-one
meetings with their teacher, who would pose impenetrable
koans, riddles like: ‘When you see the flower, where is God?'”

For a mathematician’s example of an alleged Zen ideal, see the feast day
this year of St. Gerard Manley Hopkins.

Sunday, May 18, 2014

Eyes on the Prize

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

From 1972:

IMAGE- Eyes of girl in 'Rainbow Bridge: Part 5 of 6' video

From 2014:

IMAGE- Commentary by 'Wolven' on Scarlett Johansson's 'Lucy' trailer, April 3, 2014

“Since when did you start writing Chinese?” — Lucy  trailer
See also the Saturday night 11:30 post.

Wolven’s Lucy  midrash is from April 3.  See also this  journal on that date.

Sunday, May 4, 2014

Geometry for Scarlett

Filed under: General,Geometry — Tags: , — m759 @ 11:16 AM

Scarlett Johansson stars in a new film, “Lucy,” due to be
released on August 8, directed by Luc Besson, auteur  of
The Fifth Element  (1997). In other pop culture…

 “There have long been rumors of a mythical Ninth Element
that grants ultimate power to the Wizard who masters it.
The Order of Magick says there is no such thing. But….”

— Website of Magicka: The Ninth Element Novel

See also, in this journal, Holy Field as well as Power of the Center.

Friday, November 30, 2012

Point

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

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

— Dante, Paradiso , 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.

Wednesday, August 1, 2012

Elementary Finite Geometry

Filed under: General,Geometry — Tags: , — m759 @ 7:16 PM

I. General finite geometry (without coordinates):

A finite affine plane of order has n^2 points.

A finite projective plane of order n  has n^2 + n + 1 

points because it is formed from an order-n finite affine 

plane by adding a line at infinity  that contains n + 1 points.

Examples—

Affine plane of order 3

Projective plane of order 3

II. Galois finite geometry (with coordinates over a Galois field):

A finite projective Galois plane of order n has n^2 + n + 1

points because it is formed from a finite affine Galois 3-space

of order n with n^3 points by discarding the point (0,0,0) and 

identifying the points whose coordinates are multiples of the

(n-1) nonzero scalars.

Note: The resulting Galois plane of order n has 

(n^3-1)/(n-1)= (n^2 + n + 1) points because 

(n^2 + n + 1)(n – 1) =

(n^3 + n^2 + n – n^2 – n – 1) = (n^3 – 1) .
 

III. Related art:

Another version of a 1994 picture that accompanied a New Yorker
article, "Atheists with Attitude," in the issue dated May 21, 2007:

IMAGE- 'Four Gods,' by Jonathan Borofsky

The Four Gods  of Borofsky correspond to the four axes of 
symmetry
  of a square and to the four points on a line at infinity 
in an order-3 projective plane as described in Part I above.

Those who prefer literature to mathematics may, if they like,
view the Borofsky work as depicting

"Blake's Four Zoas, which represent four aspects
of the Almighty God" —Wikipedia

Monday, May 21, 2012

Child’s Play (continued*)

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

You and I …

we are just like a couple of tots…

Sinatra

JOSEFINE LYCHE

Born 1973 in Bergen. Lives and works in Oslo.

Education

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

University of Bergen—

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

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

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

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

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

* See that phrase in this journal.

Friday, August 19, 2011

Geezer Puzzle

Filed under: General,Geometry — Tags: — m759 @ 2:02 PM

An RSS item today—

Peter Cameron Diamond squares Fri Aug 19, 2011 05:36 [EDT] from Peter Cameron by Peter Cameron

If you like Latin squares and such things, take a look at Diamond Geezer’s post for today: a pair of orthogonal Latin squares with two disjoint common transversals, and some entries given (if you do the harder puzzle).

 

The post referred to—

http://www.log24.com/log/pix11B/110819-DiamondGeezerPuzzle.jpg

"This Jack, joke, poor potsherd, ' patch, matchwood, immortal diamond,
                Is immortal diamond." —Gerard Manley Hopkins, Society of Jesus

Those now celebrating the Catholic Church's "World Youth" week in Madrid
may prefer a related puzzle for younger and nimbler minds:

The Diamond 16 Puzzle.

Monday, July 11, 2011

The Witch of And/Or

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

AND: Logical conjunction, symbolized as… 

OR:    Logical disjunction, symbolized as…  

AND/OR: Logical confusion, symbolized as…  IMAGE- AND and OR symbols combined as Lacanian AND/OR lozenge
according to a woman Lacanian analyst in this journal.

See also another female disciple of Lacan
writing as co-author with a philosophy professor
in Saturday's online New York Times 's "The Stone"—

"Let Be: An Answer to Hamlet’s Question."

Perhaps they thought the question was…

 

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

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

Wikipedia portrait of New School
philosopher Simon Critchley

"To be and/or not to be?"

For a more philosophically respectable approach to
the same shape, see Sunday morning's Wittgenstein's Diamond.

"We're gonna need more holy water." —Hollywood saying

Dark Lady

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

http://www.log24.com/log/pix11B/110711-5AM-NYT-Inside.jpg

From an obituary of choreographer Roland Petit, who died on Sunday, July 10, 2011—

"Ballerina roles had for more than a century been largely made on pale romantically suffering virgins or royal princesses; Petit’s women were liberated and exciting, modern and tangibly real— and yet archaic femmes fatales . Probably his most popular ballet worldwide is Le jeune homme et la mort , in which a young bloke lazing around in his room is visited by an enigmatic, seductive female— at the end of which brief encounter he hangs himself.

The young man’s role was seized upon by the great ballet stars of the next decades, Rudolf Nureyev and Mikhail Baryshnikov notable among them. As with Carmen, the role of La Mort, the death goddess, has been sought out by a pantheon of great ballerinas, in Paris, Russia and the US as well as in Europe." —Ismene Brown at theartsdesk.com

From the philosophy column "The Stone" in Saturday's online New York Times

July 9, 2011, 4:45 PM: "Let Be: An Answer to Hamlet’s Question"—

"Jamieson Webster is a psychoanalyst in private practice
in New York. She is the author of
'The Life and Death of Psychoanalysis'
forthcoming from Karnac Books.
"

Related ART WARS material:

  1. An illustrated essay by Webster posted on March 7, 2009 at The Symptom 10 weblog
  2. An illustrated essay by Cullinane posted on March 7,  2009 at the Log24 weblog
  3. Time and Eternity
  4. Lovely, Dark and Deep

Monday, March 7, 2011

Punto

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.

Saturday, January 29, 2011

Cold Open

Filed under: General — m759 @ 11:16 PM

Kernel and Moonshine

"The yarns of seamen have a direct simplicity, the whole meaning of which lies within the shell of a cracked nut. But Marlow was not typical (if his propensity to spin yarns be excepted), and to him the meaning of an episode was not inside like a kernel but outside, enveloping the tale which brought it out only as a glow brings out a haze, in the likeness of one of these misty halos that sometimes are made visible by the spectral illumination of moonshine."

— Joseph Conrad in Heart of Darkness

Some background—

Spider and Snake on cover of Fritz Leiber's novel Big Time

An image from yesterday's search
God, TIme, Hopkins

"We got tom-toms over here bigger than a monster
Bla Bla Bla Bla Bla Bla Bla Bla"

— "Massive Attack"

"I'm just checking your math on that. Yes, I got the same thing."

— "The Social Network"

"Live… Uh, check thatFrom New York, it's Saturday Night! "

Friday, January 28, 2011

Meanwhile…

Filed under: General — m759 @ 8:22 AM

From this morning's New York Times

 "On November 12th and 13th, 2010,
  a meeting of Roman Catholic bishops
  convened to respond to the growing demand
  for exorcism rites."
  — Trailer for the film "The Rite," which opens today

http://www.log24.com/log/pix11/110128-RiteTrailer500w.jpg

Meanwhile, in this  journal on November 12th and 13th, 2010… Award Show Story.

Related material — God, Time, Hopkins and a Faustian link from November 12th.

Update of 9:57 AM 1/28— The Faustian link suggests readings from
James G. Hart's The Person and the Common Life  (Kluwer Academic, 1992).

See pages 1,  2,  3,  4,  and  5, and note especially the spider metaphor on page 5 —

http://www.log24.com/log/pix11/110128-SpiderMother.jpg

Monday, December 20, 2010

Contenders

Filed under: General — Tags: , — m759 @ 7:27 PM

http://www.log24.com/log/pix10B/101220-CroweHook2.jpg
Happy birthday to noir queen Audrey Totter. She starred in "The Set-Up," a 1949 fight film.

http://www.log24.com/log/pix10B/101220-Set-Up72minSm.jpg

   "You sure know how to show a girl a good time."
    — Renée Zellweger in "New in Town" (2009)

Monday, September 13, 2010

Outpost

Filed under: General — m759 @ 4:00 AM

In memory of Kevin McCarthy, who died on Saturday, September 11

From a 9/11 post

Anthony Hopkins at Dolly's Little Diner in Slipstream

Sir Anthony Hopkins in "Slipstream." See "Home from Home."

From Script-O-Rama, dialogue from "Slipstream" —

My God, this place
must be a million years old.

Will that be it, sweetie?

I think this gentleman's next.

No, sir. You're next.

Thank you.

That'll be $1.35.

What?

$1.35.

That's all?

Did you want to pay more?

No, it's just so cheap.

That's the way it is out here,
sweetie, free and easy.

Yes, sirree, home on the range
where the buffalo roam,
The deer and the antelope play.

Dolly's Little Diner.
Home from home.

Home from home.

See also "Kevin McCarthy" in this journal.

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

Hermeneutics

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?"

http://www.log24.com/log/pix10A/100710--HustonBoard.GIF

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

Friday, March 12, 2010

Group Characters

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

Steve Pond on "Crazy Heart"

"… this gentle little movie… is, after all, a character study– and in an alcoholic country singer named Bad Blake, we’ve got one hell of a character."

And then there's Baaad Blake–

Group Characters, from 'Symmetry,' Pergamon Press, 1963

Related material:

This journal on the president of
London's Blake Society
and
Wikipedia on the founder of
Pergamon Press

Wednesday, July 9, 2008

Wednesday July 9, 2008

Filed under: General,Geometry — m759 @ 8:28 AM
God, Time, Epiphany

8:28:32 AM

Anthony Hopkins, from
All Hallows’ Eve
last year
:

“For me time is God,
God is time. It’s an equation,
like an Einstein equation.”

James Joyce, from
June 26 (the day after
Anti-Christmas) this year
:

“… he glanced up at the clock
of the Ballast Office and smiled:
— It has not epiphanised yet,
he said.”

Ezra Pound (from a page
linked to yesterday morning):

“It seems quite natural to me
that an artist should have
just as much pleasure in an
arrangement of planes
or in a pattern of figures,
  as in painting portraits….”

From Epiphany 2008:

An arrangement of planes:

http://www.log24.com/log/pix08/080709-Epiphany.gif

From May 10, 2008:

A pattern of figures:

Seven partitions of the 2x2x2 cube in a book from 1906

See also Richard Wilhelm on
Hexagram 32 of the I Ching:

“Duration is a state whose movement is not worn down by hindrances. It is not a state of rest, for mere standstill is regression. Duration is rather the self-contained and therefore self-renewing movement of an organized, firmly integrated whole, taking place in accordance with immutable laws and beginning anew at every ending. The end is reached by an inward movement, by inhalation, systole, contraction, and this movement turns into a new beginning, in which the movement is directed outward, in exhalation, diastole, expansion.”

'The Middle-English Harrowing of Hell,' by Hulme, 1907, page 64, line 672: 'with this he gaf the gaste'

The Middle-English
    Harrowing of Hell…

    by Hulme, 1907, page 64

Wednesday, October 31, 2007

Wednesday October 31, 2007

Filed under: General — m759 @ 8:28 PM
On Time


Anthony Hopkins on time:

"For me time is God, God is time…. I'm fascinated by the fact that we can't grasp anything about time. The magical, supernatural force that is with us every second is time." —Cinema Blend

"For me time is God, God is time. It's an equation, like an Einstein equation." —Washington Square News

A Marxist on time:

"God demands scrutiny beyond his menacingly comic aspects. Primarily, the [Saramago] Gospel 's God is time, and not truth, the other attribute he asserts. Saramago, a Marxist (an eccentric one), and not a Christian, subverts St. Augustine on the theodicy of time. If time is God, then God can be forgiven nothing, and who would desire to forgive him anyway?"

Harold Bloom on José Saramago's The Gospel According to Jesus Christ  (1991). Saramago was awarded the Nobel Prize in Literature in 1998.

Related material:

Augustine's Theodicy
and Joyce's Aesthetics,

Today's Sinner
(St. Augustine's Day, 2006),

Happy Halloween.

Monday, October 29, 2007

Monday October 29, 2007

Filed under: General — m759 @ 7:20 AM
Home from Home

On Anthony Hopkins’s new film:

“At one point during ‘Slipstream,’ Hopkins’s character stumbles upon a Dolly Parton impersonator while Parton’s wonderful song, ‘Coat of Many Colors,’ plays on the soundtrack.  I told Hopkins that I thought he used the tune– which is about a multi-hued coat that little Dolly’s grandmother made for her out of random pieces of cloth when the future superstar’s family was dirt poor– as a sort of commentary on the patchwork structure of ‘Slipstream’ itself.  Hopkins smiled broadly and his eyes lit up.  Yes, he said, that’s exactly what he was doing.  He said he even tried to get Parton to appear in the movie, but she was booked and couldn’t do it.”

—  Paul Tatara, Oct. 22, 2007

Anthony Hopkins:

“Our existence is beyond understanding.  Nobody has an answer.  I sense that life is such a mystery.  To me, God is time.”

Related material:

“Have you ever worried about your memory, because it doesn’t seem to recall exactly the same past from one day to the next? Have you ever thought that the whole universe might be a crazy, mixed-up dream? If you have, then you’ve had hints of the Change War…

Spider and Snake on cover of Fritz Leiber's novel Big Time

It’s been going on for a billion years and it will last another billion or so. Up and down the timeline, the two sides– ‘Spiders’ and ‘Snakes’– battle endlessly to change the future and the past. Our lives, our memories, are their battleground. And in the midst of the war is the Place, outside space and time, where Greta Forzane and the other Entertainers provide solace and r-&-r for tired time warriors.”

— Publisher’s description of Fritz Leiber’s Big Time.

Dialogue from “Slipstream”

“My God, this place must be
a million years old!”

Anthony Hopkins at Dolly's Little Diner in Slipstream

“Dolly’s Little Diner–
Home from Home”

Meanwhile…

Country Star
Porter Wagoner, 80, Dies

Wallace Stevens,
“Country Words”–

“What is it that my feeling seeks?
I know from all the things it touched
And left beside and left behind.
It wants the diamond pivot bright.”

Monday, May 21, 2007

Monday May 21, 2007

Filed under: General — Tags: , — m759 @ 4:48 AM
Down the
Up Staircase

Commentary on a
Jonathan Borofsky
painting in the
May 21 New Yorker:

IMAGE- Borofsky's 'Four Gods' and related structures
 
Commentary

"… Mondrian and Malevich
are not discussing canvas
or pigment or graphite
or any other form of matter.
They are talking about about
Being or Mind or Spirit.
From their point of view,
the grid is a staircase
to the Universal…."

Rosalind Krauss
 

Thursday, December 8, 2005

Thursday December 8, 2005

Filed under: General,Geometry — Tags: — m759 @ 2:56 PM
Aion Flux

That Nature is a Heraclitean Fire…
— Poem title, Gerard Manley Hopkins  

From Jung’s Map of the Soul, by Murray Stein:

“… Jung thinks of the self as undergoing continual transformation during the course of a lifetime…. At the end of his late work Aion, Jung presents a diagram to illustrate the dynamic movements of the self….”

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

“The formula presents a symbol of the self, for the self is not just a stable quantity or constant form, but is also a dynamic process.  In the same way, the ancients saw the imago Dei in man not as a mere imprint, as a sort of lifeless, stereotyped impression, but as an active force…. The four transformations represent a process of restoration or rejuvenation taking place, as it were, inside the self….”

“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. 

What the formula can only hint at, however, is the higher plane that is reached through the process of transformation and integration. The ‘sublimation’ or progress or qualitative change consists in an unfolding of totality into four parts four times, which means nothing less than its becoming conscious. When psychic contents are split up into four aspects, it means that they have been subjected to discrimination by the four orienting functions of consciousness. Only the production of these four aspects makes a total description possible. The process depicted by our formula changes the originally unconscious totality into a conscious one.” 

— Jung, Collected Works, Vol. 9, Part 2, Aion: Researches into the Phenomenology of the Self (1951) 

Related material: 

  The diamond theorem

“Although ‘wholeness’ seems at first sight to be nothing but an abstract idea (like anima and animus), it is nevertheless empirical in so far as it is anticipated by the psyche in the form of  spontaneous or autonomous symbols. These are the quaternity or mandala symbols, which occur not only in the dreams of modern people who have never heard of them, but are widely disseminated in the historical recods of many peoples and many epochs. Their significance as symbols of unity and totality is amply confirmed by history as well as by empirical psychology.  What at first looks like an abstract idea stands in reality for something that exists and can be experienced, that demonstrates its a priori presence spontaneously. Wholeness is thus an objective factor that confronts the subject independently of him… Unity and totality stand at the highest point on the scale of objective values because their symbols can no longer be distinguished from the imago Dei. Hence all statements about the God-image apply also to the empirical symbols of totality.”

— Jung, Aion, as quoted in
Carl Jung and Thomas Merton

Monday, October 31, 2005

Monday October 31, 2005

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

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"

Sunday, June 26, 2005

Sunday June 26, 2005

Filed under: General,Geometry — Tags: — m759 @ 7:26 PM

Thanks for the Memory

As I write, Susannah McCorkle is singing “Thanks for the Memory.”

Below are some photos from the website of Paul Winchell, ventriloquist, inventor, theologian.  Winchell died in his sleep at 82 early on Friday, June 24, 2005.

The image “http://www.log24.com/log/pix05A/050626-LucyAndHope.jpg” cannot be displayed, because it contains errors.

Paul Winchell seems to have
posted a topic for discussion:

God is a mathematical equation
   beyond our understanding.”

Related material:

From Friday’s entry
Cross by Sol LeWitt
(Fifteen Etchings, 1973):

The image “http://www.log24.com/log/pix05A/050626-Cross.jpg” cannot be displayed, because it contains errors.

“No bridge reaches God, except one…
God’s Bridge: The Cross.”
— Billy Graham Evangelistic Association,
quoted in Friday’s entry.

This cross may, of course, also
be interpreted as panes of a window
  — see Lucy photo above —
or as a plus sign — see “a mathematical
equation beyond our understanding”
in, for instance, Algebraic Geometry,
by Robin Hartshorne. For a theological
citation of Hartshorne’s work, see
Midsummer Eve’s Dream
(June 23, 1995).

Friday, May 20, 2005

Friday May 20, 2005

Filed under: General — Tags: , — m759 @ 1:20 PM

The Shining of Apollo

"Plato's most significant passage may be found in Phaedrus 265b: 'And we made four divisions of the divine madness, ascribing them to four gods, saying that prophecy was inspired by Apollo, the mystic madness by Dionysos, the poetic by the Muses, and the madness of love […] by Aphrodite and Eros' (trans. by H.N. Fowler, in the Loeb Classical Library)."

Saverio Marchignoli, note on section 20, paragraphs 115-119, of the Discourse on the Dignity of Man (Oratio de hominis dignitate) (1486) by Pico della Mirandola, considered the "Manifesto of the Renaissance."

Related material:
A Mass for Lucero,
The Shining of May 29,
Shining Forth,
Sermon for St. Patrick's Day, and the phrase
Diamond Struck by the Sun.

Saturday, March 12, 2005

Saturday March 12, 2005

Filed under: General,Geometry — m759 @ 5:09 AM
Three Eleanors

Continued from March 10:

For some children…

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

It takes three Eleanors.

The image “http://www.log24.com/log/pix05/050310-Eleanors.jpg” cannot be displayed, because it contains errors.
1             2              3

For Alice, a beautiful child

who died in London
on Tuesday
at 72:

The image “http://www.log24.com/log/pix05/050312-Form.jpg” cannot be displayed, because it contains errors.

Today’s New York Times says that
Alice, the author of Fairy Tale,
was a
“passionately traditional Catholic.”

For related material, see
Immortal Diamond:
O’Hara, Hopkins, and Joyce
.

See also the conflict between Trudeau’s
  “diamond theory” and
“story theory”
of truth
,

and Suzanne Keen‘s article from the
Catholic publication Commonweal:

Getting to Truth by Lying.

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.

Thursday, August 12, 2004

Thursday August 12, 2004

Filed under: General,Geometry — Tags: — m759 @ 7:26 AM

Battle of Gods and Giants,
Part III:

The Invisible Made Visible

From today's New York Times:

"Leon Golub, an American painter of expressionistic, heroic-scale figures that reflect dire modern political conditions, died on Sunday in Manhattan. He was 82….

In the 1960's he produced a series, called 'Gigantomachies,' of battling, wrestling figures. They were based on classical models, including the Hellenistic Altar of Pergamon. But there was nothing idealized about them."

The Hellenistic Altar of Pergamon,
from  Battle of Gods and Giants:

 

Golub's New York Times obituary concludes with a quote from a 1991 interview:

"Asked about his continuing and future goal he said, 'To head into real!'"

From Tuesday's Battle of Gods and Giants:

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."

Perhaps, if Golub is fortunate enough to escape from the afterlife version of Plato's Cave, he will also be fortunate enough to enter Purgatory, where there awaits a course in reality, in the form of…

Geometry for Jews.

 

Wednesday, August 11, 2004

Wednesday August 11, 2004

Filed under: General,Geometry — Tags: , — m759 @ 5:35 AM

Battle of Gods and Giants,
Part II:

Wonders of the Invisible World

Yesterday at about 5 PM I added a section titled "Invariants" to the 3:01 PM entry Battle of Gods and Giants.  Within this added section was the sentence

"This sort of mathematics illustrates the invisible 'form' or 'idea' behind the visible two-color pattern."

Now, at about 5 AM, I see in today's New York Times a review of a book titled The Invisible Century, by Richard Panek.  The reviewer, David Gelernter, says the "invisible" of the title refers to

"science that is done not by studying what you can see…. but by repairing instead to the privacy of your own mind, with the shades drawn and the lights off: the inner sanctum of intellectual history."

The book concerns the research of Einstein and Freud.  Gelernter says

"As Mr. Panek usefully notes, Einstein himself first called his work an 'invariant theory,' not a 'relativity theory.' Einstein does not say 'everything is relative,' or anything remotely like it."

The reader who clicks on the word "invariants" in Battle of Gods and Giants will receive the same information.

Gelernter's conclusion:

"The Invisible Century is a complex book about a complex topic. Mr. Panek's own topic is not so much invisibility, it seems to me, as a different kind of visibility, centering on mind-pictures revealed by introspection, which are just as sharp and clear as (for example) the mind-music Beethoven heard when he was deaf.

Inner visibility is a fascinating topic…."

As is synchronicity, a topic in the work of a greater man than Freud– Carl Jung.  The above remarks may be viewed as "synchronicity made visible."

All of this was, of course, foreshadowed in my web page "A Mathematician's Aesthetics" of August 2000:

C. G. Jung on Archetypes
and Visible Reality:

"All the most powerful ideas in history go back to archetypes. This is particularly true of religious ideas, but the central concepts of science, philosophy, and ethics are no exception to this rule. In their present form they are variants of archetypal ideas, created by consciously applying and adapting these ideas to reality. For it is the function of consciousness not only to recognize and assimilate the external world through the gateway of the senses, but to translate into visible reality the world within us."

— Carl Gustav Jung, "The Structure of the Psyche" (1927), in Collected Works Vol. 8, Structure and Dynamics of the Psyche, P. 342

Paul Klee on Visible Reality:

"Art does not reproduce the visible; rather, it makes visible…. My aim is always to get hold of the magic of reality and to transfer this reality into painting– to make the invisible visible through reality. It may sound paradoxical, but it is, in fact, reality which forms the mystery of our existence."

— Paul Klee, "Creative Credo" from The Inward Vision: Watercolors, Drawings, Writings. Abrams, not dated; published c. 1958.

Wallace Stevens on
the Visibility of Archetypes:

"These forms are visible
     to the eye that needs,
Needs out of the whole
     necessity of sight."

— Wallace Stevens, "The Owl in the Sarcophagus," (first publ. 1950) in
Collected Poetry and Prose, Library of America, 1997

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:

Invariants 

"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.

Monday, April 5, 2004

Monday April 5, 2004

Filed under: General,Geometry — Tags: , — m759 @ 4:03 AM

Ideas and Art

 
Motto of
Plato's Academy

 

From Minimalist Fantasies,
by Roger Kimball, May 2003:

All I want anyone to get out of my paintings, and all I ever get out of them, is the fact that you can see the whole idea without any confusion. … What you see is what you see.
—Frank Stella, 1966

Minimal Art remains too much a feat of ideation, and not enough anything else. Its idea remains an idea, something deduced instead of felt and discovered.
— Clement Greenberg, 1967

The artists even questioned whether art needed to be a tangible object. Minimalism … Conceptualism — suddenly art could be nothing more than an idea, a thought on a piece of paper….
— Michael Kimmelman, 2003

There was a period, a decade or two ago, when you could hardly open an art journal without encountering the quotation from Frank Stella I used as an epigraph. The bit about “what you see is what you see” was reproduced ad nauseam. It was thought by some to be very deep. In fact, Stella’s remarks—from a joint interview with him and Donald Judd—serve chiefly to underscore the artistic emptiness of the whole project of minimalism. No one can argue with the proposition that “what you see is what you see,” but there’s a lot to argue with in what he calls “the fact that you can see the whole idea without any confusion.” We do not, of course, see ideas. Stella’s assertion to the contrary might be an instance of verbal carelessness, but it is not merely verbal carelessness. At the center of minimalism, as Clement Greenberg noted, is the triumph of ideation over feeling and perception, over aesthetics.
— Roger Kimball, 2003

 

 

From How Not Much Is a Whole World,
by Michael Kimmelman, April 2, 2004

Decades on, it's curious how much Minimalism, the last great high modern movement, still troubles people who just can't see why … a plain white canvas with a line painted across it


"William Clark,"
by Patricia Johanson, 1967

should be considered art. That line might as well be in the sand: on this side is art, it implies. Go ahead. Cross it.

….

The tug of an art that unapologetically sees itself as on a par with science and religion is not to be underestimated, either. Philosophical ambition and formal modesty still constitute Minimalism's bottom line.

If what results can sometimes be more fodder for the brain than exciting to look at, it can also have a serene and exalted eloquence….

That line in the sand doesn't separate good art from bad, or art from nonart, but a wide world from an even wider one.

 

I maintain that of course
we can see ideas.

Example: the idea of
invariant structure.

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

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

For a discussion
of how this works, see
Block Designs,
4×4 Geometry, and
Diamond Theory.

Incidentally, structures like the one shown above are invariant under an important subgroup of the affine group AGL(4,2)…  That is to say, they are not lost in translation.  (See previous entry.)

Sunday, February 22, 2004

Sunday February 22, 2004

Filed under: General,Geometry — Tags: — m759 @ 8:53 AM

Invariants

"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)

Those who have clicked
on the title above
may find the following of interest.

Sean Socha

Imagination/Reality:
Wallace Stevens'
Harmonium

and the Visual Arts

I see modern art's usefulness for Stevens in its reconfiguration of the relationship between imagination and reality…. Stevens will incorporate a device from painting to illustrate his poetic idea. For instance, "Metaphors of a Magnifico" (Harmonium) illustrates an idea about the fragmentation and/or subjectivity of reality and the importance of perspective by incorporating the Cubist technique of multiple perspectives.

Also perhaps relevant:

Einstein wanted to know what was invariant (the same) for all observers. The original title for his theory was (translated from German) "Theory of Invariants." — Wikipedia

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."
 

Thursday, September 11, 2003

Thursday September 11, 2003

Filed under: General — Tags: , — m759 @ 6:25 PM

Particularity

Walter J. Ong

Particularity

Upon learning of the recent death of Walter J. Ong, S. J., philosopher of language, I ordered a copy of his book

Hopkins, the Self, and God
University of Toronto Press, 1986.

As the reader of my previous entry will discover, I have a very low opinion of the literary skills of the first Christians.   This sect’s writing has, however, improved in the past two millennia.

Despite my low opinion of the early Christians, I am still not convinced their religion is totally unfounded.  Hence my ordering of the Ong book.  Since then, I have also ordered two other books, reflecting my interests in philosophical fiction (see previous entry) and in philosophy itself:

Philosophical fiction —

The Hex Witch of Seldom,
by Nancy Springer,
Penguin Putnam Inc., 2002
(See 1 Corinthians 1:26-29)

Philosophy —

Definition,
by Richard Robinson,
Fellow of Oriel College, Oxford,
Oxford U. Press, 1954, reprinted 1962.

Following the scientific advice of Niels Bohr and Freeman Dyson, I articulated on April 25, 2003, a mad theory of the mystical significance of the number 162.

Here is that theory applied to the three works named above, all three of which I received, synchronistically, today.

Page 162 of Hopkins, the Self, and God is part of the long list of references at the back of the book.  Undiscouraged by the seeming insignificance (vide my note Dogma) of this page, I looked more closely.  Behold, there was Christ…  Carol T. Christ, that is, author of The Finer Optic: The Aesthetic of Particularity in Victorian Poetry, Yale University Press, 1975. “Particularity” seemed an apt description of my “162” approach to literature, so I consulted Christ’s remarks as described in the main body of Ong’s book.

Particularity according to Christ —

“Victorian particularist aesthetics has prospered to the present time, and not only in novels.  The isolated, particularized, unique ‘good moment’ [Christ, 105], the flash of awareness at one particular instant in just the right setting, which Hopkins celebrates….”

— Ong, Hopkins, the Self, and God, p. 14

I highly recommend the rest of Ong’s remarks on particularity.

Turning to the other two of the literary trinity of books I received today….

Page 162 of The Hex Witch of Seldom has the following:

“There was a loaf of Stroehmann’s Sunbeam Bread in the grocery sack also; she and Witchie each had several slices.  Bobbi folded and compressed hers into little squares and popped each slice into her mouth all at once.”

The religious significance of this passage seems, in Ong’s Jesuit context, quite clear.

Page 162 of Definition has the following:

“Real Definition as the Search for a Key.  Mr. Santayana, in his book on The Sense of Beauty, made the following extremely large demands on real definition:

‘A definition <of beauty> that should really define must be nothing less than the exposition of the origin, place, and elements of beauty as an object of human experience.  We must learn from it, as far as possible, why, when, and how beauty appears, what conditions an object must fulfil to be beautiful, what elements of our nature make us sensible of beauty, and what the relation is between the constitution of the object and the excitement of our sensibility.  Nothing less will really define beauty or make us understand what aesthetic appreciation is.  The definition of beauty in this sense will be the task of this whole book, a task that can be only very imperfectly accomplished within its limits.’ ”

Here is a rhetorical exercise for Jesuits that James Joyce might appreciate:

Discuss Bobbi’s “little squares” of bread as the Body of Christ.  Formulate, using Santayana’s criteria, a definition of beauty that includes this sacrament.

Refer, if necessary, to
the log24.net entries
Mr. Holland’s Week and Elegance.

Refrain from using the phrase
“scandal of particularity”
unless you can use it as well as
Annie Dillard.

Friday, July 25, 2003

Friday July 25, 2003

Filed under: General — m759 @ 5:24 PM

For Jung’s 7/26 Birthday:
A Logocentric Meditation

Leftist academics are trying to pull a fast one again.  An essay in the most prominent American mathematical publication tries to disguise a leftist attack on Christian theology as harmless philosophical woolgathering.

In a review of Vladimir Tasic’s Mathematics and the Roots of Postmodern Thought, the reviewer, Michael Harris, is being less than candid when he discusses Derrida’s use of “logocentrism”:

“Derrida uses the term ‘logocentrism’… as ‘the metaphysics of phonetic writing’….”

Notices of the American Mathematical Society, August 2003, page 792

We find a rather different version of logocentrism in Tasic’s own Sept. 24, 2001, lecture “Poststructuralism and Deconstruction: A Mathematical History,” which is “an abridged version of some arguments” in Tasic’s book on mathematics and postmodernism:

“Derrida apparently also employs certain ideas of formalist mathematics in his critique of idealist metaphysics: for example, he is on record saying that ‘the effective progress of mathematical notation goes along with the deconstruction of metaphysics.’

Derrida’s position is rather subtle. I think it can be interpreted as a valiant sublation of two completely opposed schools in mathematical philosophy. For this reason it is not possible to reduce it to a readily available philosophy of mathematics. One could perhaps say that Derrida continues and critically reworks Heidegger’s attempt to ‘deconstruct’ traditional metaphysics, and that his method is more ‘mathematical’ than Heidegger’s because he has at his disposal the entire pseudo-mathematical tradition of structuralist thought. He has himself implied in an interview given to Julia Kristeva that mathematics could be used to challenge ‘logocentric theology,’ and hence it does not seem unreasonable to try looking for the mathematical roots of his philosophy.”

The unsuspecting reader would not know from Harris’s review that Derrida’s main concern is not mathematics, but theology.  His ‘deconstruction of metaphysics’ is actually an attack on Christian theology.

From “Derrida and Deconstruction,” by David Arneson, a University of Manitoba professor and writer on literary theory:

Logocentrism: ‘In the beginning was the word.’ Logocentrism is the belief that knowledge is rooted in a primeval language (now lost) given by God to humans. God (or some other transcendental signifier: the Idea, the Great Spirit, the Self, etc.) acts a foundation for all our thought, language and action. He is the truth whose manifestation is the world.”

Some further background, putting my July 23 entry on Lévi-Strauss and structuralism in the proper context:

Part I.  The Roots of Structuralism

“Literary science had to have a firm theoretical basis…”

Part II.  Structuralism/Poststructuralism

“Most [structuralists] insist, as Levi-Strauss does, that structures are universal, therefore timeless.”

Part III.  Structuralism and
             Jung’s Archetypes

Jung’s “theories, like those of Cassirer and Lévi-Strauss, command for myth a central cultural position, unassailable by reductive intellectual methods or procedures.”

And so we are back to logocentrism, with the Logos God in the form of story, myth, or archetype — in the “central cultural position.”

What does all this have to do with mathematics?  See

Plato’s Diamond,

Rosalind Krauss on Art –

“the Klein group (much beloved of Structuralists)”

Another Michael Harris Essay, Note 47 –

“From Krauss’s article I learned that the Klein group is also called the Piaget group.”

and Jung on Quaternity:
      Beyond the Fringe –

“…there is no denying the fact that [analytical] psychology, like an illegitimate child of the spirit, leads an esoteric, special existence beyond the fringe of what is generally acknowledged to be the academic world.”

What attitude should mathematicians have towards all this? 

Towards postmodern French
  atheist literary/art theorists –

Mathematicians should adopt the attitude toward “the demimonde of chic academic theorizing” expressed in Roger Kimball’s essay, Feeling Sorry for Rosalind Krauss.

Towards logocentric German
  Christian literary/art theorists –

Mathematicians should, of course, adopt a posture of humble respect, tugging their forelocks and admitting their ignorance of Christian theology.  They should then, if sincere in their desire to honestly learn something about logocentric philosophy, begin by consulting the website

The Quest for the Fiction of an Absolute.

For a better known, if similarly disrespected, “illegitimate child of the spirit,” see my July 22 entry.

Monday, March 10, 2003

Monday March 10, 2003

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

ART WARS:

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."
 

Monday, January 20, 2003

Monday January 20, 2003

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

Shine On, Robinson Jeffers

"…be in nothing so moderate as in love of man, 
      a clever servant, insufferable master.
There is the trap that catches noblest spirits,
     that caught — they say — God, when he walked on earth."
Shine, Perishing Republic, by Robinson Jeffers

Robinson Jeffers died at Big Sur, California, on January 20, 1962 — a year to the day after Robert Frost spoke at the Kennedy inauguration.

"The poetry of Robinson Jeffers shines with a diamond's brilliance when he depicts Nature's beauty and magnificence.   His verse also flashes with a diamond's hardness when he portrays human pain and folly."
Gary Suttle  

"Praise Him, He hath conferred aesthetic distance
Upon our appetites, and on the bloody
Mess of our birthright, our unseemly need,
Imposed significant form. Through Him the brutes
Enter the pure Euclidean kingdom of number…."
— Howard Nemerov, 
   Grace To Be Said at the Supermarket 

"Across my foundering deck shone 
A beacon, an eternal beam. | Flesh fade, and mortal trash 
Fáll to the resíduary worm; | world's wildfire, leave but ash: 
In a flash, at a trumpet crash, 
I am all at once what Christ is |, since he was what I am, and 
Thís Jack, jóke, poor pótsherd, | patch, matchwood,
    immortal diamond, 
Is immortal diamond."
— Gerard Manley Hopkins,
    That Nature is a Heraclitean Fire and of the Comfort of the Resurrection

"In the last two weeks, I've been returning to Hopkins.  Even in the 'world's wildfire,' he asserts that 'this Jack, joke, poor potsherd, patch, matchwood, immortal diamond,/Is immortal diamond.' A comfort."
— Michael Gerson, head White House speechwriter,
    in Vanity Fair, May 2002, page 162

"There's none but truth can stead you.  Christ is truth."
— Gerard Manley Hopkins

"The rock cannot be broken.  It is the truth."
— Wallace Stevens 

"My ghost you needn't look for; it is probably
Here, but a dark one, deep in the granite…."
— Robinson Jeffers, Tor House

On this date in 1993, the inauguration day of William Jefferson Clinton, Audrey Hepburn died.

"…today, the Rock cries out to us, clearly, forcefully…."
Maya Angelou, January 20, 1993

"So, purposing each moment to retire,
She linger'd still. Meantime, across the moors,
Had come young Porphyro, with heart on fire"
— John Keats, The Eve of St. Agnes (January 20), IX

Top view of
ordinary
diamond

Top view of
Hearts On Fire
diamond

Advertising Copy:

What you see with a Hearts On Fire diamond is an unequalled marriage of math and physics, resulting in the world's most perfectly cut diamond.

 

"Eightpointed symmetrical signs are ancient symbols for the Venus goddess or the planet Venus as either the Morning star or the Evening star."
Symbols.com

"Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave.  Its flashes are flashes of fire, a raging flame."
Song of Solomon

"The last words from the people in the towers and on the planes, over and over again, were 'I love you.'  Over and over again, the message was the same, 'I love you.' …. Perhaps this is the loudest chorus from The Rock:  we are learning just how powerful love really is, even in the face of death."
The Rev. Kenneth E. Kovacs

"Then I'll get on my knees and pray
We don't get fooled again."
The Who 

See also my note, "Bright Star," of October 23, 2002.

 

Saturday, August 3, 2002

Saturday August 3, 2002

Filed under: General — m759 @ 10:42 PM

Miss Sauvé

Homily on Flannery O’Connor

for the Sunday following Corpus Christi Day, 2002:

The part of her fiction that most fascinates me, then and now, is what many critics referred to as “the grotesque,” but what she herself called “the reasonable use of the unreasonable.” [Flannery O’Connor, Mystery and Manners: Occasional Prose, Robert and Sally Fitzgerald, eds. (New York: Farrar, Straus, 1969)] 

 A modest example comes to mind. In a short story  ….  the setting sun appears like a great red ball, but she sees it as “an elevated Host drenched in blood” leaving a “line like a red clay road in the sky.” [Flannery O’Connor, “A Temple of the Holy Ghost” from A Good Man is Hard to Find (New York: Harcourt, Brace & World, 1971)] 

In a letter to a friend of hers, O’Connor would later write, “…like the child, I believe the Host is actually the body and blood of Christ, not just a symbol. If the story grows for you it is because of the mystery of the Eucharist in it.” In that same correspondence, O’Connor relates this awkward experience:

I was once, five or six years ago, taken by [Robert Lowell and Elizabeth Hardwick] to have dinner with Mary McCarthy…. She departed the Church at the age of 15 and is a Big Intellectual. We went and eight and at one, I hadn’t opened my mouth once, there being nothing for me in such company to say…. Having me there was like having a dog present who had been trained to say a few words but overcome with inadequacy had forgotten them. Well, toward morning the conversation turned on the Eucharist, which I, being the Catholic, was obviously supposed to defend. [McCarthy] said that when she was a child and received the Host, she thought of it as the Holy Ghost, He being the “most portable” person of the Trinity; now she thought of it as a symbol and implied that it was a pretty good one. I then said, in a very shaky voice, “Well, if it’s a symbol, to hell with it.” That was all the defense I was capable of but I realize now that this is all I will ever be able to say about it, outside of a story, except that it is the center of existence for me; all the rest of life is expendable. [Sally Fitzgerald, ed., The Habit of Being: The Letters of Flannery O’Connor (Vintage: New York, 1979) 124-125] 

….There is, of course, something entirely preposterous and, well, unreasonable, almost grotesque, about the Catholic doctrine of the Real Presence. We claim, with a perfectly straight face, to eat the body and drink the blood of the Eternal Word of God, the second person of the Most Holy Trinity who, according to some, shouldn’t even have a body to begin with. But therein lies precisely the most outlandish feature of the Eucharist: namely, that it embodies the essential scandal of the Incarnation itself.  

             — Friar Francisco Nahoe, OFM Conv.

From James Joyce

A Portrait Of The Artist As A Young Man

Chapter 3 :

Why was the sacrament of the eucharist instituted under the two species of bread and wine if Jesus Christ be present body and blood, soul and divinity, in the bread alone and in the wine alone? Does a tiny particle of the consecrated bread contain all the body and blood of Jesus Christ or a part only of the body and blood? If the wine change into vinegar and the host crumble into corruption after they have been consecrated, is Jesus Christ still present under their species as God and as man?

— Here he is! Here he is!

From The Gazette, Montreal,

of Sunday, August 20, 1995, page C4:

“Summer of ’69,” a memoir by Judy Lapalme on the death by accidental drowning of her 15-year-old younger brother:

“I had never tasted pizza until Jeff died.  Our family, of staunch Irish Catholic stock with more offspring than money, couldn’t cope with the luxury or the spice.

The Hallidays, neighbors from across the street, sent it over to us the day after the funeral, from Miss Sauvé’s Pizzeria, on Sauvé St., just east of Lajeunesse St. in Ahuntsic.  An all-dressed pizza with the hard hat in the centre….

I was 17 that summer and had just completed Grade 12 at Holy Names High School in Rosemont….

…. Jeff was almost 16, a handsome football star, a rebellious, headstrong, sturdy young man who was forever locking horns with my father…. On Friday, Aug. 1, Jeff went out on the boat… and never came back….    

The day after the funeral, a white Volkswagen from Miss Sauvé’s Pizzeria delivered a jumbo, all-dressed pizza to us. The Hallidays’ daughter,  Diane, had been smitten with Jeff and wanted to do something special.

My father assured us that we wouldn’t like it, too spicy and probably too garlicky. There could not be a worse indictment of a person to my father than to declare them reeking of garlic. 

The rest of us tore into the cardboard and began tasting this exotic offering — melted strands of creamy, rubbery, burn-your-palate mozzarrella that wasn’t Velveeta, crisp, dry, and earthy mushrooms, spicy and salty pepperoni sliding off the crust with each bite, green peppers…. Bread crust both crisp and soggy with tomato sauce laden with garlic and oregano. 

It was an all-dressed pizza, tasted for the first time, the day after we buried Jeff….

The fall of 1969, I went to McGill…. I never had another pizza from Miss Sauvé’s.  It’s gone now — like so many things.”

     Ten thousand places

AS kingfishers catch fire, dragonflies dráw fláme;
As tumbled over rim in roundy wells
Stones ring; like each tucked string tells, each hung bell’s
Bow swung finds tongue to fling out broad its name;
Each mortal thing does one thing and the same:         
Deals out that being indoors each one dwells;
Selves—goes itself; myself it speaks and spells,
Crying Whát I do is me: for that I came.
 
Í say móre: the just man justices;
Kéeps gráce: thát keeps all his goings graces;         
Acts in God’s eye what in God’s eye he is—
Chríst—for Christ plays in ten thousand places,
Lovely in limbs, and lovely in eyes not his
To the Father through the features of men’s faces.

   — Gerard Manley Hopkins, 1844-1889

American Literature Web Resources:

Flannery O’Connor

She died on August 3, 1964 at the age of 39.

In almost all of her works the characters were led to a place where they had to deal with God’s presence in the world.

She once said “in the long run, a people is known, not by its statements or statistics, but by the stories it tells. Fiction is the most impure and the most modest and the most human of the arts.”

Encounter – 02/17/2002:

Flannery OConnor – Southern Prophet:

When a woman wrote to Flannery O’Connor saying that one of her stories “left a bad taste in my mouth,” Flannery wrote back: “You weren’t supposed to eat it.”

Etes-vous sauvé? 

Powered by WordPress