Log24

Sunday, November 17, 2019

E-Elements Revisited

Filed under: General — m759 @ 9:22 AM

The German mathematician Wolf Barth in the above post is not the
same person as the Swiss artist Wolf Barth in today's previous post.

An untitled, undated, picture by the latter

Compare and contrast with an "elements" picture of my own

Logo for 'Elements of Finite Geometry'

and with . . .

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

Many Dimensions  (1931), by Charles Williams

Monday, November 11, 2019

Time and Chance

Filed under: General — m759 @ 2:49 PM

http://www.log24.com/log/pix10B/101202-DreidelAndStone.jpg

The misleading image at right above is from the cover of
an edition of Charles Williams's classic 1931 novel 
Many Dimensions  published in 1993 by Wm. B. Eerdmans.

Compare and constrast —

Goedel Escher Bach cover

Cover of a book by Douglas Hofstadter

IMAGE- 'Solomon's Cube'

An Invariance of Symmetry

Sunday, July 29, 2018

The Materialization

Filed under: General,Geometry — m759 @ 11:01 PM

McCarthy's "materialization of plot and character" does not,
for me, constitute a proof that "there is  being, after all,
beyond the arbitrary flux of existence."

Neither does the above materialization of 281 as the page 
number of her philosophical remark.

See also the materialization of 281 as a page number in
the book Witchcraft  by Charles Williams

The materialization of 168 as a page number in a 
Stephen King novel is somewhat more convincing,
but less convincing than the materialization of Klein's
simple group of of 168 elements in the eightfold cube.

Sunday, July 15, 2018

Jewish Oases

Filed under: General,Geometry — m759 @ 10:06 PM

"… Lincoln Plaza Cinemas, the Juilliard String Quartet,
and the Strand Book Store remained  oases
for cultural and intellectual stimulation."

John S. Friedman in The Forward , Jan. 21, 2018

Read more: 

https://forward.com/culture/392483/
how-fred-bass-dan-talbot-robert-mann
-shaped-new-york-culture/

From  the Oasis  in Steven Spielberg's "Ready Player One" (2018) —

I prefer, from a Log24 search for Flux Capacitor

Symbologist Robert Langdon views a corner of Solomon's Cube

From "Raiders of the Lost Images" —

"The cube shape of the lost Mother Box,
also known as the Change Engine,
is shared by the Stone in a novel by
Charles WilliamsMany Dimensions .
See the Solomon's Cube webpage."

Saturday, May 19, 2018

Flux Capacitor

Filed under: General,Geometry — Tags: , — m759 @ 4:13 PM

For Tom Hanks and Dan Brown —

Symbologist Robert Langdon views a corner of Solomon's Cube

From "Raiders of the Lost Images" —

"The cube shape of the lost Mother Box,
also known as the Change Engine,
is shared by the Stone in a novel by
Charles WilliamsMany Dimensions .
See the Solomon's Cube webpage."

See as well a Google search for flux philosophy
https://www.google.com/search?q=flux+philosophy.

Tuesday, February 27, 2018

Raiders of the Lost Images

Filed under: General,Geometry — m759 @ 11:28 AM

On the recent film "Justice League" —

From DC Extended Universe Wiki, "Mother Box" —

"However, during World War I, the British rediscovered
mankind's lost Mother Box. They conducted numerous studies
but were unable to date it due to its age. The Box was then
shelved in an archive, up until the night Superman died,
where it was then sent to Doctor Silas Stone, who
recognized it as a perpetual energy matrix. . . ." [Link added.]

The cube shape of the lost Mother Box, also known as the
Change Engine, is shared by the Stone in a novel by Charles Williams,
Many Dimensions . See the Solomon's Cube webpage.

See too the matrix of Claude Lévi-Strauss in posts tagged
Verwandlungslehre .

Some literary background:

Who speaks in primordial images speaks to us
as with a thousand trumpets, he grips and overpowers,
and at the same time he elevates that which he treats
out of the individual and transitory into the sphere of
the eternal. 
— C. G. JUNG

"In the conscious use of primordial images—
the archetypes of thought—
one modern novelist stands out as adept and
grand master: Charles Williams.
In The Place of the Lion  he incarnates Plato’s
celestial archetypes with hair-raising plausibility.
In Many Dimensions  he brings a flock of ordinary
mortals face to face with the stone bearing
the Tetragrammaton, the Divine Name, the sign of Four.
Whether we understand every line of a Williams novel
or not, we feel something deep inside us quicken
as Williams tells the tale.

Here, in The Greater Trumps , he has turned to
one of the prime mysteries of earth . . . ."

— William Lindsay Gresham, Preface (1950) to
Charles Williams's The Greater Trumps  (1932)

For fans of what the recent series Westworld  called "bulk apperception" —

Sunday, September 3, 2017

Mosaic Logic

Filed under: General — m759 @ 10:45 AM

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

Many Dimensions  (1931), by Charles Williams

While you're waiting

Click the above illustration for
some remarks on mosaics.

Sunday, August 13, 2017

Logos

Filed under: General,Geometry — m759 @ 1:00 AM

   

In memoriam —

Zadeh is known for the unfortunate phrase "fuzzy logic."

Not-so-fuzzy related material —

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

Many Dimensions  (1931), by Charles Williams

Monday, June 12, 2017

Bubble

Filed under: General,Geometry — m759 @ 1:19 PM

The "bubble" passage in the previous post suggests a review of
a post from December 21, 2006, with the following images —

  

Update of 11:01 PM ET the same day, June 12, 2017 —

Related material for the Church of Synchronology

From a tech-article series that began on Halloween 2006 and
ended on the date of the above Geometry's Tombstones post —

Compare and contrast (from a post of Feb. 27, 2017) —

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

Many Dimensions  (1931), by Charles Williams

See also "The Geometry of Logic:
Finite Geometry and the 16 Boolean Connectives
"
by Steven H. Cullinane in 2007.

Monday, February 27, 2017

Logic for Jews

Filed under: General — Tags: — m759 @ 9:07 PM

(Continued)

Adam Gopnik in The New Yorker  today reacts to the startling
outcomes of three recent contests: the presidential election,
the Super Bowl, and the Oscar for Best Picture —

"The implicit dread logic is plain."

Related material —

Transformers in this journal and

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

Many Dimensions  (1931), by Charles Williams

See also

The above figure is from Ian Stewart's 1996 revision of a 1941 classic, 
What Is Mathematics? , by Richard Courant and Herbert Robbins.

One wonders how the confused slave boy of Plato's Meno  would react
to Stewart's remark that

"The number of copies required to double an
 object's size depends on its dimension."

Saturday, January 28, 2017

Cranking It Up

Filed under: General — m759 @ 12:17 PM

From "Core," a post of St. Lucia's Day, Dec. 13, 2016 —

'We are rooted in yoga and love the magic that happens when that practice is cranked up to eleven.'

In related news yesterday —

California yoga mogul’s mysterious death:
Trevor Tice’s drunken last hours detailed

"Police found Tice dead on the floor in his home office,
blood puddled around his head. They also found blood
on walls, furniture, on a sofa and on sheets in a nearby
bedroom, where there was a large bottle of Grey Goose
vodka under several blood-stained pillows on the floor."

See as well an image from "The Stone," a post of March 18, 2016 —

Some backstory —

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

Many Dimensions  (1931), by Charles Williams

Sunday, April 3, 2016

Logic

Filed under: General — m759 @ 9:29 PM

See also Stone Logical Dimensions 

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

Many Dimensions  (1931), by Charles Williams

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).

Tuesday, July 29, 2014

The Craft

Filed under: General — m759 @ 3:28 PM

See Charles Williams” + Witchcraft  in this journal.

Williams was one of the Inklings, a group of Christian
writers that included C. S. Lewis and J. R. R. Tolkien.

Thursday, January 17, 2013

Brazil Revisited

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

Yesterday's post Treasure Hunt, on a Brazilian weblog,
suggests a review of Brazil  in this journal.  The post
most relevant to yesterday's remarks is from
August 15, 2003, with a link, now broken, to the work
of Brazilian artist Nicole Sigaud* that also uses the
four half-square tiles used in 1704 by Sebastien Truchet 
and somewhat later by myself in Diamond Theory 
(see a 1977 version).

A more recent link that works:

http://vismath9.tripod.com/sigaud/e-index.html

ANACOM PROJECT

 

APPLICATIONS
HISTORY
THE FONT
ALGORITHMS
FAMILY I
FAMILY 2
EXAMPLES
EXAMPLES II
DOWNLOADS
INTERACTIVE PROGRAM (JAVASCRIPT)
 
VisMathHOME

 

© 1997 – 2002 Nicole Sigaud

* Sigaud shares the interests of her fellow Brazilian
   whose weblog was the subject of yesterday's
   Treasure Hunt.—

   "For many years I have dedicated myself to the study
    of medieval magic, demonology, Kabbalah, Astrology,
    Alchemy, Tarot and divination in general."

     — Nicole Sigaud (translated by Google) in a self-profile: 
     http://www.recantodasletras.com.br/autor.php?id=78359.

    I do not share the interest of these authors in such matters,
    except as they are reflected in the works of authors like
    Charles Williams and Umberto Eco.

Tuesday, December 4, 2012

December Days

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

For the Dec. 3rd-4th graduate conference 
at the University of Cambridge on
"Occultism, Magic, and the History of Art"—

Four novels by Charles Williams

IMAGE- Charles Williams novels: Shadows of Ecstasy, The Greater Trumps, Many Dimensions, and The Place of the Lion

See also the life, and Dec. 1st death, of a former Chief Justice of South Africa.

Friday, November 30, 2012

Title

Filed under: General — m759 @ 12:26 AM

The title of yesterday's 11:22 PM post was "The Place of the Lion."

This is also the title of a novel by Charles Williams.

See, too, Midsummer Eve's Dream and Midsummer Night 2007.

Thursday, July 19, 2012

But Seriously…

Filed under: General — m759 @ 9:00 PM

For those who prefer fiction:

"Many Dimensions  (1931) — An evil antiquarian illegally purchases
the fabled Stone of Suleiman (Williams uses this Muslim form
rather than the more familiar King Solomon) from its Islamic guardian
in Baghdad and returns to England to discover not only that the Stone
can multiply itself infinitely without diminishing the original, but that it
also allows its possessor to transcend the barriers of space and time."

Wikipedia article on the author Charles Williams

Thursday, March 1, 2012

Salvation for Gopnik

Filed under: General — m759 @ 1:06 AM

Yesterday afternoon's post Universals Revisited linked
(indirectly) to an article in the current New Yorker  on
the Book of Revelation —

"The Big Reveal: Why Does the Bible End That Way?"

The connection in that post between universals and Revelation
may have eluded readers unfamiliar with a novel by
Charles Williams, The Place of the Lion  (London, Gollancz, 1931).

The article's author, Adam Gopnik, appears in the following
Google Book Search, which may or may not help such readers.

Should Gopnik desire further information on Williams and salvation,
he may consult Steps Toward Salvation: An Examination of Coinherence
and Substitution in the Seven Novels of Charles Williams
 ,
by Dennis L. Weeks (American University Studies: Series 4, English
Language and Literature. Vol. 125), XV + 117 pp., Peter Lang Publishing, 1991.

The ninth item in the above search refers to a boxed set
of the seven novels themselves—

.

Thursday, December 1, 2011

Paranoia Strikes Deep

Filed under: General — m759 @ 2:02 PM

Tens of Millions of Smartphones Come With Spyware
Preinstalled, Security Analyst Says

Published December 01, 2011 – FoxNews.com

For details, see comments at YouTube.

Related entertainment—

1. Tara Fitzgerald in "New World Disorder" (1999)—

http://www.log24.com/log/pix11C/111201-NewWorldDisorder-TaraFitzgerald.jpg

We skipped the light fandango
turned cartwheels 'cross the floor
I was feeling kinda seasick
but the crowd called out for more

2. Tara Fitzgerald in "Broken Glass" (2011)—

http://www.log24.com/log/pix11C/111201-TaraFitgerald-BrokenGlass.jpg

And so it was that later
as the miller told his tale
that her face, at first just ghostly,
turned a whiter shade of pale

Procul Harum song at beginning and end of "The Net" (1995)

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

Many Dimensions  (1931), by Charles Williams,
   quoted here on Kristallnacht 2011

See also, from "The Net"—

Decompiling Wolfenstein

http://www.log24.com/log/pix11C/111201-DecompilingWolfenstein.jpg

"In Wolfenstein 3D , the player assumes the role of an American soldier
of Polish descent… attempting to escape from the Nazi stronghold of
Castle Wolfenstein." — Wikipedia

Wednesday, November 9, 2011

Polish Logic–

Filed under: General — Tags: — m759 @ 11:23 AM

The Big Lukasiewicz

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

Many Dimensions  (1931), by Charles Williams

See also Łukasiewicz in Wikipedia and Lukasiewicz in this journal.

The latter's Christian references seem preferable to yesterday's
link to a scene from the Coen brothers' film "The Big Lebowski."

For those who prefer  a Christ-for-Jews there is
also Harvard's version. See The Crimson Passion.

Monday, August 29, 2011

Many = Six.

Filed under: General,Geometry — m759 @ 7:20 PM

A comment today on yesterday's New York Times  philosophy column "The Stone"
notes that "Augustine… incorporated Greek ideas of perfection into Christianity."

Yesterday's post here  for the Feast of St. Augustine discussed the 2×2×2 cube.

Today's Augustine comment in the Times  reflects (through a glass darkly)
a Log24 post  from Augustine's Day, 2006, that discusses the larger 4×4×4 cube.

For related material, those who prefer narrative to philosophy may consult
Charles Williams's 1931 novel Many Dimensions . Those who prefer mathematics
to either may consult an interpretation in which Many = Six.

Galois space of six dimensions represented in Euclidean spaces of three and of two dimensions

Click image for some background.

Wednesday, August 10, 2011

Objectivity

Filed under: General,Geometry — m759 @ 12:25 PM

From math16.com

Quotations on Realism
and the Problem of Universals:

"It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato's (realist) reaction to the sophists (nominalists). What is often called 'postmodernism' is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth."
— Simon Blackburn, Think, Oxford University Press, 1999, page 268

"You will all know that in the Middle Ages there were supposed to be various classes of angels…. these hierarchized celsitudes are but the last traces in a less philosophical age of the ideas which Plato taught his disciples existed in the spiritual world."
Charles Williams, page 31, Chapter Two, "The Eidola and the Angeli," in The Place of the Lion (1933), reprinted in 1991 by Eerdmans Publishing

For Williams's discussion of Divine Universals (i.e., angels), see Chapter Eight of The Place of the Lion.

"People have always longed for truths about the world — not logical truths, for all their utility; or even probable truths, without which daily life would be impossible; but informative, certain truths, the only 'truths' strictly worthy of the name. Such truths I will call 'diamonds'; they are highly desirable but hard to find….The happy metaphor is Morris Kline's in Mathematics in Western Culture (Oxford, 1953), p. 430."
— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987, pages 114 and 117

"A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the 'Story Theory' of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called 'true.' The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes…. My own viewpoint is the Story Theory…. I concluded long ago that each enterprise contains only stories (which the scientists call 'models of reality'). I had started by hunting diamonds; I did find dazzlingly beautiful jewels, but always of human manufacture."
— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987, pages 256 and 259

Trudeau's confusion seems to stem from the nominalism of W. V. Quine, which in turn stems from Quine's appalling ignorance of the nature of geometry. Quine thinks that the geometry of Euclid dealt with "an emphatically empirical subject matter" — "surfaces, curves, and points in real space." Quine says that Euclidean geometry lost "its old status of mathematics with a subject matter" when Einstein established that space itself, as defined by the paths of light, is non-Euclidean. Having totally misunderstood the nature of the subject, Quine concludes that after Einstein, geometry has become "uninterpreted mathematics," which is "devoid not only of empirical content but of all question of truth and falsity." (From Stimulus to Science, Harvard University Press, 1995, page 55)
— S. H. Cullinane, December 12, 2000

The correct statement of the relation between geometry and the physical universe is as follows:

"The contrast between pure and applied mathematics stands out most clearly, perhaps, in geometry. There is the science of pure geometry, in which there are many geometries: projective geometry, Euclidean geometry, non-Euclidean geometry, and so forth. Each of these geometries is a model, a pattern of ideas, and is to be judged by the interest and beauty of its particular pattern. It is a map or picture, the joint product of many hands, a partial and imperfect copy (yet exact so far as it extends) of a section of mathematical reality. But the point which is important to us now is this, that there is one thing at any rate of which pure geometries are not pictures, and that is the spatio-temporal reality of the physical world. It is obvious, surely, that they cannot be, since earthquakes and eclipses are not mathematical concepts."
— G. H. Hardy, section 23, A Mathematician's Apology, Cambridge University Press, 1940

The story of the diamond mine continues
(see Coordinated Steps and Organizing the Mine Workers)— 

From The Search for Invariants (June 20, 2011):

The conclusion of Maja Lovrenov's 
"The Role of Invariance in Cassirer’s Interpretation of the Theory of Relativity"—

"… physical theories prove to be theories of invariants
with regard to certain groups of transformations and
it is exactly the invariance that secures the objectivity
of a physical theory."

— SYNTHESIS PHILOSOPHICA 42 (2/2006), pp. 233–241

http://www.log24.com/log/pix11B/110810-MajaLovrenovBio.jpg

Related material from Sunday's New York Times  travel section—

"Exhibit A is certainly Ljubljana…."

Sunday, June 26, 2011

Sunday Dinner

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

From "Sunday Dinner" in this journal—

"'If Jesus were to visit us, it would have been
the Sunday dinner he would have insisted on
being a part of, not the worship service at the church.'"

Judith Shulevitz at The New York Times
    on Sunday, July 18, 2010

The image “http://www.log24.com/log/pix06/060410-HotelAdlon2.jpg” cannot be displayed, because it contains errors.

Some table topics—

Today's midday New York Lottery numbers were 027 and 7002.

The former suggests a Galois cube, the latter a course syllabus—

CSC 7002
Graduate Computer Security (Spring 2011)
University of Colorado at Denver
Department of Computer Science

An item from that syllabus:

Six 22 February 2011   DES History of DES; Encryption process; Decryption; Expander function; S-boxes and their output; Key; the function f  that takes the modified key and part of the text as input; mulitple Rounds of DES; Present-day lack of Security in DES, which led to the new Encryption Standard, namely AES. Warmup for AES: the mathematics of Fields: Galois Fields, particularly the one of order 256 and its relation to the irreducible polynomial x^8 + x^4 + x^3 + x + 1 with coefficients from the field Z_2.

Related material: A novel, PopCo , was required reading for the course.

Discuss a different novel by the same author—

The End of Mr. Y .

Discuss the author herself, Scarlett Thomas.

Background for the discussion—

Derrida in this journal versus Charles Williams in this journal.

Related topics from the above syllabus date—

Metaphor and Gestell and Quadrat.

Some context— Midsummer Eve's Dream.

Tuesday, May 10, 2011

Groups Acting

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

The LA Times  on last weekend's film "Thor"—

"… the film… attempts to bridge director Kenneth Branagh's high-minded Shakespearean intentions with Marvel Entertainment's bottom-line-oriented need to crank out entertainment product."

Those averse to Nordic religion may contemplate a different approach to entertainment (such as Taymor's recent approach to Spider-Man).

A high-minded— if not Shakespearean— non-Nordic approach to groups acting—

"What was wrong? I had taken almost four semesters of algebra in college. I had read every page of Herstein, tried every exercise. Somehow, a message had been lost on me. Groups act . The elements of a group do not have to just sit there, abstract and implacable; they can do  things, they can 'produce changes.' In particular, groups arise naturally as the symmetries of a set with structure. And if a group is given abstractly, such as the fundamental group of a simplical complex or a presentation in terms of generators and relators, then it might be a good idea to find something for the group to act on, such as the universal covering space or a graph."

— Thomas W. Tucker, review of Lyndon's Groups and Geometry  in The American Mathematical Monthly , Vol. 94, No. 4 (April 1987), pp. 392-394

"Groups act "… For some examples, see

Related entertainment—

High-minded— Many Dimensions

Not so high-minded— The Cosmic Cube

http://www.log24.com/log/pix11A/110509-SpideySuperStories39Sm.jpg

One way of blending high and low—

The high-minded Charles Williams tells a story
in his novel Many Dimensions about a cosmically
significant cube inscribed with the Tetragrammaton—
the name, in Hebrew, of God.

The following figure can be interpreted as
the Hebrew letter Aleph inscribed in a 3×3 square—

http://www.log24.com/log/pix11A/110510-GaloisAleph.GIF

The above illustration is from undated software by Ed Pegg Jr.

For mathematical background, see a 1985 note, "Visualizing GL(2,p)."

For entertainment purposes, that note can be generalized from square to cube
(as Pegg does with his "GL(3,3)" software button).

For the Nordic-averse, some background on the Hebrew connection—

Tuesday, May 3, 2011

Peace and War

Filed under: General — m759 @ 2:02 PM

This post was suggested by—

  1. A quotation from Under the Volcano :
    "A corpse will be transported by express!"
  2. The wish in a novel by Ernesto Sábato, who died Saturday, April 30,
    for a tombstone that says "PEACE"
  3. A statement by another author in this morning's post:
    "I think of myself as writing about war," said Robson….
    "I try to get away from war, but I can't.
    War forces ordinary people to behave extraordinarily."

The above Sábato novel was translated as The Angel of Darkness .
Its Spanish title was "Abaddón el Exterminador " (Abaddon the Exterminator ).

From a customer review of the novel at Amazon.com—

"Early in the book a drunken outcast will see the vision of the Great Beast of Revelation. Near the end he will tell others of what he has seen. Meanwhile Sábato, who was originally trained as a scientist, seeks out the supernatural and the mystical in order to find an antidote to Stalinism, simple-minded 'Progress' and a superficial positivism."

For a more sophisticated vision of the Beast, see The Ninth Gate.

For Abaddon in a less sophisticated antidote to positivism, see The Chronicle of Abaddon the Destroyer: The War in Heaven .

I prefer Charles Williams's approach to War in Heaven .

If there is an afterlife, perhaps Sábato's experience there will be more lively than his novel's tombstone would imply.

He may, despite his wish for heavenly peace, turn out to be (in a phrase from this morning's post) a badly needed "ghost warrior."

Monday, May 2, 2011

Pasaje

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

http://www.log24.com/log/pix11A/110502-PostcardsFromCuernavaca-500w.jpg

From Under the Volcano , Chapter II—

Hotel Bella Vista
Gran Baile Noviembre 1938
a Beneficio de la Cruz Roja.
Los Mejores Artistas del radio en accion.
No falte Vd.

From Shining Forth

"What he sees is something real."
Charles Williams, The Figure of Beatrice

Friday, January 14, 2011

Ironic Butterfly

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

David Brooks's column today quotes Niebuhr. From the same source—
Reinhold Niebuhr, The Irony of American History

Chapter 8: The Significance of Irony

Any interpretation of historical patterns and configurations raises the question whether the patterns, which the observer discerns, are "objectively" true or are imposed upon the vast stuff of history by his imagination. History might be likened to the confusion of spots on the cards used by psychiatrists in a Rorschach test. The patient is asked to report what he sees in these spots; and he may claim to find the outlines of an elephant, butterfly or frog. The psychiatrist draws conclusions from these judgments about the state of the patient’s imagination rather than about the actual configuration of spots on the card. Are historical patterns equally subjective?
….
The Biblical view of human nature and destiny moves within the framework of irony with remarkable consistency. Adam and Eve are expelled from the Garden of Eden because the first pair allowed "the serpent" to insinuate that, if only they would defy the limits which God had set even for his most unique creature, man, they would be like God. All subsequent human actions are infected with a pretentious denial of human limits. But the actions of those who are particularly wise or mighty or righteous fall under special condemnation. The builders of the Tower of Babel are scattered by a confusion of tongues because they sought to build a tower which would reach into the heavens.

Niebuhr's ironic butterfly may be seen in the context of last
Tuesday's post Shining and of last Saturday's noon post True Grid

http://www.log24.com/log/pix11/110114-AlderTilleyColored.gif

The "butterfly" in the above picture is a diagram showing the 12 lines* of the Hesse configuration from True Grid.

It is also a reference to James Hillman's classical image (see Shining) of the psyche, or soul, as a butterfly.

Fanciful, yes, but this is in exact accordance with Hillman's remarks on the soul (as opposed to the spirit— see Tuesday evening's post).

The 12-line butterfly figure may be viewed as related to the discussions of archetypes and universals in Hillman's Re-Visioning Psychology  and in Charles Williams's The Place of the Lion . It is a figure intended here to suggest philosophy, not entertainment.

Niebuhr and Williams, if not the more secular Hillman, might agree that those who value entertainment above all else may look forward to a future in Hell (or, if they are lucky, Purgatory). Perhaps such a future might include a medley of Bob Lind's "Elusive Butterfly" and Iron Butterfly's "In-a-Gadda-da-Vida."

* Three horizontal, three vertical, two diagonal, and four arc-shaped.

Thursday, December 2, 2010

Caesarian

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

The Dreidel Is Cast

The Nietzschean phrase "ruling and Caesarian spirits" occurred in yesterday morning's post "Novel Ending."

That post was followed yesterday morning by a post marking, instead, a beginning— that of Hanukkah 2010. That Jewish holiday, whose name means "dedication," commemorates the (re)dedication of the Temple in Jerusalem in 165 BC.

The holiday is celebrated with, among other things, the Jewish version of a die—  the dreidel . Note the similarity of the dreidel  to an illustration of The Stone*  on the cover of the 2001 Eerdmans edition of  Charles Williams's 1931 novel Many Dimensions

http://www.log24.com/log/pix10B/101202-DreidelAndStone.jpg

For mathematics related to the dreidel , see Ivars Peterson's column on this date fourteen years ago.
For mathematics related (if only poetically) to The Stone , see "Solomon's Cube" in this journal.

Here is the opening of Many Dimensions

http://www.log24.com/log/pix10B/101202-WilliamsChOne.jpg

For a fanciful linkage of the dreidel 's concept of chance to The Stone 's concept of invariant law, note that the New York Lottery yesterday evening (the beginning of Hanukkah) was 840. See also the number 840 in the final post (July 20, 2002) of the "Solomon's Cube" search.

Some further holiday meditations on a beginning—

Today, on the first full day of Hanukkah, we may or may not choose to mark another beginning— that of George Frederick James Temple, who was born in London on this date in 1901. Temple, a mathematician, was President of the London Mathematical Society in 1951-1953. From his MacTutor biography

"In 1981 (at the age of 80) he published a book on the history of mathematics. This book 100 years of mathematics (1981) took him ten years to write and deals with, in his own words:-

those branches of mathematics in which I had been personally involved.

He declared that it was his last mathematics book, and entered the Benedictine Order as a monk. He was ordained in 1983 and entered Quarr Abbey on the Isle of Wight. However he could not stop doing mathematics and when he died he left a manuscript on the foundations of mathematics. He claims:-

The purpose of this investigation is to carry out the primary part of Hilbert's programme, i.e. to establish the consistency of set theory, abstract arithmetic and propositional logic and the method used is to construct a new and fundamental theory from which these theories can be deduced."

For a brief review of Temple's last work, see the note by Martin Hyland in "Fundamental Mathematical Theories," by George Temple, Philosophical Transactions of the Royal Society, A, Vol. 354, No. 1714 (Aug. 15, 1996), pp. 1941-1967.

The following remarks by Hyland are of more general interest—

"… one might crudely distinguish between philosophical and mathematical motivation. In the first case one tries to convince with a telling conceptual story; in the second one relies more on the elegance of some emergent mathematical structure. If there is a tradition in logic it favours the former, but I have a sneaking affection for the latter. Of course the distinction is not so clear cut. Elegant mathematics will of itself tell a tale, and one with the merit of simplicity. This may carry philosophical weight. But that cannot be guaranteed: in the end one cannot escape the need to form a judgement of significance."

— J. M. E. Hyland. "Proof Theory in the Abstract." (pdf)
Annals of Pure and Applied Logic 114, 2002, 43-78.

Here Hyland appears to be discussing semantic ("philosophical," or conceptual) and syntactic ("mathematical," or structural) approaches to proof theory. Some other remarks along these lines, from the late Gian-Carlo Rota

http://www.log24.com/log/pix10B/101202-RotaChXII-sm.jpg

    (Click to enlarge.)

See also "Galois Connections" at alpheccar.org and "The Galois Connection Between Syntax and Semantics" at logicmatters.net.

* Williams's novel says the letters of The Stone  are those of the Tetragrammaton— i.e., Yod, He, Vau, He  (cf. p. 26 of the 2001 Eerdmans edition). But the letters on the 2001 edition's cover Stone  include the three-pronged letter Shin , also found on the dreidel .  What esoteric religious meaning is implied by this, I do not know.

Tuesday, November 23, 2010

Tale

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

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

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

Monday February 20, 2006

m759 @ 12:00 AM

The Past Revisited

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

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

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

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

That post compares characters in Many Dimensions  to those in Logicomix

Whitehead and Russell, 'Logicomix' page 181

Sunday, November 21, 2010

Sermon

Filed under: General — m759 @ 10:31 AM

For fans of Ian Watson's The Embedding , a miglior fabbro C. S. Lewis on Charles Williams.

This is apparently a brief excerpt from an audio book, "C. S. Lewis Speaks His Mind."

A printed version of Lewis's remarks on Williams, "The Novels of Charles Williams," appears on pages 21-27 of On Stories: And Other Essays on Literature  by C. S. Lewis (Houghton Mifflin Harcourt paperback, 2002 reprint of a book first published in 1982, edited and with a preface by Walter Hooper).

From the preface

"'The Novels of Charles Williams' was written at the request of the British Broadcasting Corporation, and Lewis read it over the Third Programme of the BBC on the 11th February 1949. It has never been published before and, indeed, had lain undetected in the BBC Written Archives until I came across it quite by accident in 1980."

Friday, June 4, 2010

A Better Story

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

Continued from May 8
(Feast of Saint Robert Heinlein)

“Wells and trees were dedicated to saints.  But the offerings at many wells and trees were to something other than the saint; had it not been so they would not have been, as we find they often were, forbidden.  Within this double and intertwined life existed those other capacities, of which we know more now, but of which we still know little– clairvoyance, clairaudience, foresight, telepathy.”

Charles Williams, Witchcraft, Faber and Faber, London, 1941

Why "Saint" Robert? See his accurate depiction of evil– the Eater of Souls in Glory Road.

For more on Williams's "other capacities," see Heinlein's story "Lost Legacy."

A related story– Fritz Leiber's "The Mind Spider." An excerpt:

The conference—it was much more a hyper-intimate
gabfest—proceeded.

"My static box bugged out for a few ticks this morning,"
Evelyn remarked in the course of talking over the
trivia of the past twenty-four hours.

The static boxes were an invention of Grandfather
Horn. They generated a tiny cloud of meaningless brain
waves. Without such individual thought-screens, there was
too much danger of complete loss of individual personality

—once Grandfather Horn had "become" his infant daughter
as well as himself for several hours and the unfledged
mind had come close to being permanently lost in its own
subconscious. The static boxes provided a mental wall be-
– hind which a mind could safely grow and function, similar
to the wall by which ordinary minds are apparently
always enclosed.

In spite of the boxes, the Horns shared thoughts and
emotions to an amazing degree. Their mental togetherness
was as real and as mysterious—and as incredible—as
thought itself . . . and thought is the original angel-cloud
dancing on the head of a pin. Their present conference
was as warm and intimate and tart as any actual family
gathering in one actual room around one actual table.
Five minds, joined together in the vast mental darkness
that shrouds all minds. Five minds hugged together for
comfort and safety in the infinite mental loneliness that
pervades the cosmos.

Evelyn continued, "Your boxes were all working, of
course, so I couldn't get your thoughts—just the blurs of
your boxes like little old dark grey stars. But this time
if gave me a funny uncomfortable feeling, like a spider
Crawling down my—Grayl! Don't feel so wildly! What
Is it?”

Then… just as Grayl started to think her answer…
something crept from the vast mental darkness and infinite
cosmic loneliness surrounding the five minds of the
Horns
.

Grayl was the first to notice. Her panicky thought had
ttie curling too-keen edge of hysteria. "There are six of
us now! There should only be five, but there are six.
Count! Count, I tell you! Six!"

To Mort it seemed that a gigantic spider was racing
across the web of their thoughts….

See also this journal on May 30– "720 in the Book"– and on May 31– "Memorial for Galois."

("Obnoxious nerds"— a phrase Martin Gardner recently applied to Galois— will note that 720 (= 6!) is one possible result of obeying Leiber's command "Count! Count, I tell you! Six!")

Tuesday, May 25, 2010

Sisteen

Filed under: General — Tags: , — m759 @ 9:57 AM

“Nuvoletta in her lightdress, spunn of sisteen shimmers,
was looking down on them, leaning over the bannistars….

Fuvver, that Skand, he was up in Norwood’s sokaparlour….”

Finnegans Wake

To counteract the darkness of today’s 2:01 AM entry—

Part I— Artist Josefine Lyche describes her methods

A “Internet and hard work”
B “Books, both fiction and theory”

Part II I, too, now rely mostly on the Internet for material. However, like Lyche, I have Plan B— books.

Where I happen to be now, there are piles of them. Here is the pile nearest to hand, from top to bottom.

(The books are in no particular order, and put in the same pile for no particular reason.)

  1. Philip Rieff— Sacred Order/Social Order, Vol. I: My Life Among the Deathworks
  2. Dennis L. Weeks— Steps Toward Salvation: An Examination of Coinherence and Substitution in the Seven Novels of Charles Williams
  3. Erwin Panofsky— Idea: A Concept in Art Theory
  4. Max Picard— The World of Silence
  5. Walter J. Ong, S. J.— Hopkins, the Self, and God
  6. Richard Robinson— Definition
  7. X. J. Kennedy and Dana Gioia, eds.— An Introduction to Poetry
  8. Richard J. Trudeau— The Non-Euclidean Revolution
  9. William T. Noon, S. J.— Joyce and Aquinas
  10. Munro Leaf— Four-and-Twenty Watchbirds
  11. Jane Scovell— Oona: Living in the Shadows
  12. Charles Williams— The Figure of Beatrice
  13. Francis L. Fennell, ed.— The Fine Delight: Centenary Essays on the Poetry of Gerard Manley Hopkins
  14. Hilary Putnam— Renewing Philosophy
  15. Paul Tillich— On the Boundary
  16. C. S. Lewis— George MacDonald

Lyche probably could easily make her own list of what Joyce might call “sisteen shimmers.”

Monday, November 16, 2009

A Wrinkle in Dimensions

Filed under: General — m759 @ 9:00 PM

Clifford Pickover now seems to be trying to catch up with Christian fantasists Madeleine L’Engle and Charles Williams. Click on the images below for further details.

Cover of 'Jews in Hyperspace,' by Clifford Pickover

http://www.log24.com/log09/saved/091116-SidKibbitzMusic.JPG

Saturday, November 14, 2009

Mathematics and Narrative, continued:

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

A graphic novel reviewed in the current Washington Post  features Alfred North Whitehead and Bertrand Russell–

Whitehead and Russell, 'Logicomix' page 181

Related material:

Whitehead on Fano’s finite projective three-space:

“This is proved by the consideration of a three dimensional geometry in which there are only fifteen points.”

The Axioms of Projective Geometry , Cambridge University Press, 1906

A related affine six-space:

Grey cube, 4x4x4

Further reading:

See Solomon’s Cube and the link at the end of today’s previous entry, then compare and contrast the above portraits of Whitehead and Russell with Charles Williams’s portraits of Sir Giles Tumulty and Lord Arglay in the novel Many Dimensions .

It was a dark and stormy night….

Sunday, May 17, 2009

Sunday May 17, 2009

Filed under: General,Geometry — Tags: — m759 @ 7:59 AM
Design Theory

Laura A. Smit, Calvin College, "Towards an Aesthetic Teleology: Romantic Love, Imagination and the Beautiful in the Thought of Simone Weil and Charles Williams"–

"My work is motivated by a hope that there may be a way to recapture the ancient and medieval vision of both Beauty and purpose in a way which is relevant to our own century. I even dare to hope that the two ideas may be related, that Beauty is actually part of the meaning and purpose of life."

 

Hans Ludwig de Vries, "On Orthogonal Resolutions of the Classical Steiner Quadruple System SQS(16)," Designs, Codes and Cryptography Vol. 48, No. 3 (Sept. 2008) 287-292 (DOI 10.1007/s10623-008-9207-5)–

"The Reverend T. P. Kirkman knew in 1862 that there exists a group of degree 16 and order 322560 with a normal, elementary abelian, subgroup of order 16 [1, p. 108]. Frobenius identified this group in 1904 as a subgroup of the Mathieu group M24 [4, p. 570]…."

1. Biggs N.L., "T. P. Kirkman, Mathematician," Bulletin of the London Mathematical Society 13, 97–120 (1981).

4. Frobenius G., "Über die Charaktere der mehrfach transitiven Gruppen," Sitzungsber. Königl. Preuss. Akad. Wiss. zu Berlin, 558–571 (1904). Reprinted in Frobenius, Gesammelte Abhandlungen III (J.-P. Serre, editor), pp. 335–348. Springer, Berlin (1968).

Olli Pottonen, "Classification of Steiner Quadruple Systems" (Master's thesis, Helsinki, 2005)–

"The concept of group actions is very useful in the study of isomorphisms of combinatorial structures."

Olli Pottonen,  'Classification of Steiner Quadruple Systems'

"Simplify, simplify."
Thoreau

"Beauty is bound up
with symmetry."
Weyl

Sixteen points in a 4x4 array

Pottonen's thesis is
 dated Nov. 16, 2005.

For some remarks on
images and theology,
see Log24 on that date.

Click on the above image
 for some further details.

Wednesday, March 4, 2009

Wednesday March 4, 2009

Filed under: General — m759 @ 10:07 PM
Cover Art

Cover of 'Angels & Demons,' paperback ISBN-10 0671027360

As religious fictions go,
I prefer…

De Angelis

“Richardson leaned forward and picked up from the table a very old bound book and a very fat exercise book. He again settled himself in his chair, and said, looking firmly at Anthony– ‘This is the De Angelis of Marcellus Victorinus of Bologna, published in the year 1514 at Paris, and dedicated to Leo X.’

‘Is it?’ Anthony said uncertainly.”

Charles Williams, The Place of the Lion, 1931

Cover by Jim Lamb for 'The Place of the Lion,' Eerdmans 1979 paperback, ISBN-10 0802812228

For more about the artist,
see an entry at the weblog
“Through the Wardrobe”
on Aug. 18, 2008.

Related material:
 previous entry.

Sunday, December 14, 2008

Sunday December 14, 2008

Filed under: General — m759 @ 11:00 AM
Ideas and Steps

“Somehow it seems to
fill my head with ideas
 only I don’t exactly know
what they are!…. Let’s have
 a look at the garden first!”

— A passage from
Through the Looking-Glass

“… it’s going to be
 accomplished in steps,
this establishment of
the Talented
 in the scheme of things.”

Anne McCaffrey

On the seven steps of Charles Williams:

“If we assume Williams was responding to a psychological need to express himself, then we may also assume that Williams wrote these seven steps in compliance with Jung’s theory that an author, who believes strongly enough in some set of ideas, has to write about them.”

— Dennis L. Weeks (a former student of Walter J. Ong, S. J.) in Steps Toward Salvation: An Examination of Coinherence and Substitution in the Seven Novels of Charles Williams (New York, Peter Lang Publishing, 1991), page 9

On the twelve steps of Christmas:

So set ’em up, Joe…

Friday, December 12, 2008

Friday December 12, 2008

Filed under: General — m759 @ 12:24 PM
Back to the Garden
of Forking Paths

“Somehow it seems to fill my head with ideas– only I don’t exactly know what they are!…. Let’s have a look at the garden first!”

— A passage from Lewis Carroll’s Through the Looking-Glass. The “garden” part– but not the “ideas” part– was quoted by Jacques Derrida in Dissemination in the epigraph to Chapter 7, “The Time before First.”

“‘For you… he… we aren’t meaning…’ She was almost stammering, as if she were trying to say several things at once…. Suddenly she gave a little tortured scream. ‘O!’ she cried, ‘O! I can’t keep up! it keeps dividing! There’s too many things to think of!'”

— A passage from Charles Williams’s The Place of the Lion, Chapter 12.

“He was thinking faster than he had ever done, and questions rose out of nothing and followed each other– what was to will? Will was determination to choose– what was choice? How could there be choice, unless there was preference, and if there was preference there was no choice, for it was not possible to choose against that preferring nature which was his being; yet being consisted in choice, for only by taking and doing this and not that could being know itself, could it indeed be; to be then consisted in making an inevitable choice, and all that was left was to know the choice, yet even then was the chosen thing the same as the nature that chose, and if not… So swiftly the questions followed each other that he seemed to be standing in flashing coils of subtlety, an infinite ring of vivid intellect and more than intellect, for these questions were not of the mind alone but absorbed into themselves physical passion and twined through all his nature on an unceasing and serpentine journey.”

— A passage from The Place of the Lion, Chapter 10.

Do you like apples?

Good Will Hunting

Thursday, May 22, 2008

Thursday May 22, 2008

Filed under: General,Geometry — m759 @ 9:00 AM
The Undertaking:
An Exercise in
Conceptual Art

I Ching hexagram 54: The Marrying Maiden

Hexagram 54:
THE JUDGMENT

Undertakings bring misfortune.
Nothing that would further.

The image “http://www.log24.com/log/pix08/080522-Irelandslide1.jpg” cannot be displayed, because it contains errors.

Brian O’Doherty, an Irish-born artist,
before the [Tuesday, May 20] wake
of his alter ego* ‘Patrick Ireland’
on the grounds of the
Irish Museum of Modern Art.”
New York Times, May 22, 2008    

THE IMAGE

Thus the superior man
understands the transitory
in the light of
the eternity of the end.

Another version of
the image:

Images of time and eternity in memory of Michelangelo
See 2/22/08
and  4/19/08.


Related material:

Michael Kimmelman in today’s New York Times

“An essay from the ’70s by Mr. O’Doherty, ‘Inside the White Cube,’ became famous in art circles for describing how modern art interacted with the gallery spaces in which it was shown.”

Brian O’Doherty, “Inside the White Cube,” 1976 Artforum essays on the gallery space and 20th-century art:

“The history of modernism is intimately framed by that space. Or rather the history of modern art can be correlated with changes in that space and in the way we see it. We have now reached a point where we see not the art but the space first…. An image comes to mind of a white, ideal space that, more than any single picture, may be the archetypal image of 20th-century art.”

An archetypal image

THE SPACE:

The Eightfold Cube: The Beauty of Klein's Simple Group

A non-archetypal image

THE ART:

Jack in the Box, by Natasha Wescoat

Natasha Wescoat, 2004
See also Epiphany 2008:

How the eightfold cube works

“Nothing that would further.”
— Hexagram 54

Lear’s fool:

 …. Now thou art an 0
without a figure. I am better
than thou art, now. I am a fool;
thou art nothing….

“…. in the last mystery of all the single figure of what is called the World goes joyously dancing in a state beyond moon and sun, and the number of the Trumps is done.  Save only for that which has no number and is called the Fool, because mankind finds it folly till it is known.  It is sovereign or it is nothing, and if it is nothing then man was born dead.”

The Greater Trumps,
by Charles Williams, Ch. 14

* For a different, Jungian, alter ego, see Irish Fourplay (Jan. 31, 2003) and “Outside the Box,” a New York Times review of O’Doherty’s art (featuring a St. Bridget’s Cross) by Bridget L. Goodbody dated April 25, 2007. See also Log24 on that date.

Wednesday, April 23, 2008

Wednesday April 23, 2008

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

Upscale Realism

or, "Have some more
wine and cheese, Barack."

(See April 15, 5:01 AM)

  Allyn Jackson on Rebecca Goldstein
in the April 2006 AMS Notices (pdf)

"Rebecca Goldstein’s 1983 novel The Mind-Body Problem has been widely admired among mathematicians for its authentic depiction of academic life, as well as for its exploration of how philosophical issues impinge on everyday life. Her new book, Incompleteness: The Proof and Paradox of Kurt Gödel, is a volume in the 'Great Discoveries' series published by W. W. Norton….

In March 2005 the Mathematical Sciences Research Institute (MSRI) in Berkeley held a public event in which its special projects director, Robert Osserman, talked with Goldstein about her work. The conversation, which took place before an audience of about fifty people at the Commonwealth Club in San Francisco, was taped….

A member of the audience posed a question that has been on the minds of many of Goldstein’s readers: Is The Mind-Body Problem based on her own life? She did indeed study philosophy at Princeton, finishing her Ph.D. in 1976 with a thesis titled 'Reduction, Realism, and the Mind.' She said that while there are correlations between her life and the novel, the book is not autobiographical….

She… talked about the relationship between Gödel and his colleague at the Institute for Advanced Study, Albert Einstein. The two were very different: As Goldstein put it, 'Einstein was a real mensch, and Gödel was very neurotic.' Nevertheless, a friendship sprang up between the two. It was based in part, Goldstein speculated, on their both being exiles– exiles from Europe and intellectual exiles. Gödel's work was sometimes taken to mean that even mathematical truth is uncertain, she noted, while Einstein's theories of relativity were seen as implying the sweeping view that 'everything is relative.' These misinterpretations irked both men, said Goldstein. 'Einstein and Gödel were realists and did not like it when their work was put to the opposite purpose.'"


Related material:

From Log24 on
March 22 (Tuesday of
Passion Week), 2005:

 
"'What is this Stone?' Chloe asked…. 'It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"

Many Dimensions,
by Charles Williams, 1931

For more on this theme
appropriate to Passion Week
Jews playing God — see

The image “http://www.log24.com/log/pix05/050322-Trio.jpg” cannot be displayed, because it contains errors.

Rebecca Goldstein
in conversation with
Bob Osserman
of the
Mathematical Sciences
Research Institute
at the
Commonwealth Club,
San Francisco,
Tuesday, March 22.

Wine and cheese
reception at 5:15 PM
(San Francisco time).

From
UPSCALE,
a website of the
physics department at
the University of Toronto:

Mirror Symmetry

Robert Fludd: Universe as mirror image of God

"The image [above]
is a depiction of
the universe as a
mirror image of God,
drawn by Robert Fludd
in the early 17th century.

The caption of the
upper triangle reads:

'That most divine and beautiful
counterpart visible below in the
flowing image of the universe.'

The caption of the
lower triangle is:

'A shadow, likeness, or
reflection of the insubstantial*
triangle visible in the image
of the universe.'"

* Sic. The original is incomprehensibilis, a technical theological term. See Dorothy Sayers on the Athanasian Creed and John 1:5.

For further iconology of the
above equilateral triangles,
see Star Wars (May 25, 2003),
Mani Padme (March 10, 2008),
Rite of Sping (March 14, 2008),
and
Art History: The Pope of Hope
(In honor of John Paul II
three days after his death
in April 2005).

Happy Shakespeare's Birthday.

Monday, April 7, 2008

Monday April 7, 2008

Filed under: General,Geometry — m759 @ 2:20 AM

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

Charles Williams, Many Dimensions

Monday, August 6, 2007

Monday August 6, 2007

Filed under: General — Tags: — m759 @ 8:00 AM
The Divine Universals

"The tigers of wrath          
 are wiser than                
 the horses of instruction."

— William Blake,
Proverbs of Hell

From Shining Forth:

  The Place of the Lion, by Charles Williams, 1931, Chapter Eight:

"Besides, if this fellow were right, what harm would the Divine Universals do us? I mean, aren't the angels supposed to be rather gentle and helpful and all that?"

"You're doing what Marcellus warned you against… judging them by English pictures. All nightgowns and body and a kind of flacculent sweetness. As in cemeteries, with broken bits of marble. These are Angels– not a bit the same thing. These are the principles of the tiger and the volcano and the flaming suns of space."

 Under the Volcano, Chapter Two:

"But if you look at that sunlight there, then perhaps you'll get the answer, see, look at the way it falls through the window: what beauty can compare to that of a cantina in the early morning? Your volcanoes outside? Your stars– Ras Algethi? Antares raging south southeast? Forgive me, no." 

 A Spanish-English dictionary:

lucero m.
morning or evening star:
any bright star….
hole in a window panel
     for the admission of light….

Look at the way it
falls through the window….

— Malcolm Lowry

How art thou fallen from heaven,
O Lucifer, son of the morning!
— Isaiah 14:12

For more on Spanish
and the evening star,
see Plato, Pegasus, and
the Evening Star.

 Symmetry axes
of the square:

Symmetry axes of the square

(See Damnation Morning.)

From the cover of the
 Martin Cruz Smith novel
Stallion Gate:

Atom on cover of Stallion

"That old Jew
gave me this here."

Dialogue from the
Robert Stone novel
A Flag for Sunrise.

Related material:

A Mass for Lucero,

Log24, Sept. 13, 2006

Mathematics, Religion, Art

— and this morning's online
New York Times obituaries:

Cardinal Lustiger of Paris and jazz pianist Sal Mosca, New York Times obituaries on August 6, 2007

The above image contains summary obituaries for Cardinal Lustiger, Archbishop of Paris, 1981-2005, and for Sal Mosca, jazz pianist and teacher. In memory of the former, see all of the remarks preceding the image above. In memory of the latter, the remarks of a character in Martin Cruz Smith's Stallion Gate on jazz piano may have some relevance:

"I hate arguments. I'm a coward. Arguments are full of words, and each person is sure he's the only one who knows what the words mean. Each word is a basket of eels, as far as I'm concerned. Everybody gets to grab just one eel and that's his interpretation and he'll fight to the death for it…. Which is why I love music. You hit a C and it's a C and that's all it is. Like speaking clearly for the first time. Like being intelligent. Like understanding. A Mozart or an Art Tatum sits at the piano and picks out the undeniable truth."

Wednesday, August 1, 2007

Wednesday August 1, 2007

Filed under: General,Geometry — m759 @ 8:00 AM
August First,
8:00:14 AM:

Cheap Epiphany

SPORTS OF THE TIMES

Restoring the Faith
After Hitting the Bottom

By SELENA ROBERTS
The New York Times
Published: August 1, 2007

What good is a nadir if it's denied or ignored? What's the value of reaching the lowest of the low if it can't buy a cheap epiphany?

 

Pennsylvania Lottery
on the Feast of
St. Ignatius Loyola:
 
PA Lottery July 31, 2007 - Mid-day 215, Evening 298

Restoring the Booze:
A Look at the 50's-

Grace and Bing in the Fifties

Another Epiphany:

Geometry of the I Ching (Box Style)

Box-style I Ching, January 6, 1989

(Click on image for background.)

Detail:

Detail of Box Style I Ching: Hexagram 14.

Related material:
Logos and Logic 
 and Diagon Alley.

"What a swell
  party this is."

— adapted from
     Cole Porter 

Tuesday, July 24, 2007

Tuesday July 24, 2007

Filed under: General — m759 @ 7:11 AM
The Church of St. Frank

See yesterday’s entries for
some relevant quotations
from Wallace Stevens.

Further quotations for what
Marjorie Garber, replying to
a book review by
Frank Kermode, has called
the Church of St. Frank“–

Frank Kermode on

Harold Bloom:

“He has… a great, almost
selfish passion for poetry,
and he interprets difficult
texts as if there were no
more important activity
in the world, which may
be right.”

Page 348 of Wallace Stevens:
The Poems of Our Climate
,
by Harold Bloom
(1977, Cornell U. Press):

“The fiction of the leaves is now Stevens’ fiction…. Spring, summer, and autumn adorn the rock of reality even as a woman is adorned, the principle being the Platonic one of copying the sun as source of all images….

… They are more than leaves
              that cover the barren rock….

They bear their fruit    
             so that the year is known….

If they are more than leaves, then they are no longer language, and the leaves have ceased to be tropes or poems and have become magic or mysticism, a Will-to-Power over nature rather than over the anteriority of poetic imagery.”

For more on magic, mysticism, and the Platonic “source of all images,” see Scott McLaren on “Hermeticism and the Metaphysics of Goodness in the Novels of Charles Williams.” McLaren quotes Evelyn Underhill on magic vs. mysticism:

The fundamental difference between the two is this: magic wants to get, mysticism wants to give […] In mysticism the will is united with the emotions in an impassioned desire to transcend the sense-world in order that the self may be joined by love to the one eternal and ultimate Object of love […] In magic, the will unites with the intellect in an impassioned desire for supersensible knowledge. This is the intellectual, aggressive, and scientific temperament trying to extend its field of consciousness […] (Underhill 84; see also 178ff.)

— Underhill, Evelyn. Mysticism: A Study in the Nature and Development of Man’s Spiritual Consciousness. New York: Dutton, 1911.

For more on what Bloom calls the “Will-to-Power over nature,” see Faust in Copenhagen and the recent (20th- and 21st-century) history of Harvard University. These matters are also discussed in “Log24 – Juneteenth through Midsummer Night.”

For more on what Underhill calls “the intellectual, aggressive, and scientific temperament trying to extend its field of consciousness,” see the review, in the August 2007 Notices of the American Mathematical Society, of a book by Douglas Hofstadter– a writer on the nature of consciousness— by magician Martin Gardner.

Monday, July 23, 2007

Monday July 23, 2007

Filed under: General,Geometry — Tags: , , , — m759 @ 8:00 AM
 
Daniel Radcliffe
is 18 today.
 
Daniel Radcliffe as Harry Potter
 

Greetings.

“The greatest sorcerer (writes Novalis memorably)
would be the one who bewitched himself to the point of
taking his own phantasmagorias for autonomous apparitions.
Would not this be true of us?”

Jorge Luis Borges, “Avatars of the Tortoise”

El mayor hechicero (escribe memorablemente Novalis)
sería el que se hechizara hasta el punto de
tomar sus propias fantasmagorías por apariciones autónomas.
¿No sería este nuestro caso?”

Jorge Luis Borges, “Los Avatares de la Tortuga

Autonomous Apparition
 
 

At Midsummer Noon:

 
“In Many Dimensions (1931)
Williams sets before his reader the
mysterious Stone of King Solomon,
an image he probably drew from
a brief description in Waite’s
The Holy Kabbalah (1929) of
a supernatural cubic stone
on which was inscribed
‘the Divine Name.’”
 
The image “http://www.log24.com/log/pix07/070624-Waite.gif” cannot be displayed, because it contains errors.
 
Related material:
 
It is not enough to cover the rock with leaves.
We must be cured of it by a cure of the ground
Or a cure of ourselves, that is equal to a cure

 

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

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

– Wallace Stevens, “The Rock”

 
See also
 
as well as
Hofstadter on
his magnum opus:
 
“… I realized that to me,
Gödel and Escher and Bach
were only shadows
cast in different directions by
some central solid essence.
I tried to reconstruct
the central object, and
came up with this book.”
 
Goedel Escher Bach cover

Hofstadter’s cover.

 
Here are three patterns,
“shadows” of a sort,
derived from a different
“central object”:
 
Faces of Solomon's Cube, related to Escher's 'Verbum'

Click on image for details.

Thursday, July 12, 2007

Thursday July 12, 2007

Filed under: General — Tags: — m759 @ 7:00 PM
On Interpenetration,
or Coinherence, of Souls

The August 2007 issue of Notices of the American Mathematical Society contains a review of a new book by Douglas Hofstadter, I Am a Strange Loop. (2007, Basic Books, New York. $26.95, 412 pages.)

A better review, in the Los Angeles Times of March 18, 2007, notes an important phrase in the book, "interpenetration of souls," that the AMS Notices review ignores.

Here is an Amazon.com search on "interpenetration" in the Hofstadter book:

1. on Page 217:
"… described does not create a profound blurring of two people's identities. Tennis and driving do not give rise to deep interpenetrations of souls. …"
2. on Page 237:
"… What seems crucial here is the depth of interpenetration of souls the sense of shared goals, which leads to shared identity. Thus, for instance, Carol always had a deep, …"
3. on Page 270:
"… including the most private feelings and the most confidential confessions, then the interpenetration of our worlds becomes so great that our worldviews start to fuse. Just as I could jump to California when …"
4. on Page 274:
"… we choose to downplay or totally ignore the implications of the everyday manifestations of the interpenetration of souls. Consider how profoundly wrapped up you can become in a close friend's successes and failures, in their very …"
5. on Page 276:
"… Interpenetration of National Souls Earlier in this chapter, I briefly offered the image of a self as analogous to a country …"
6. from Index:
"… birthday party for, 350 "bachelor", elusiveness of concept, 178 bad-breath analogy, 150 bandwidth of communication as determinant of degree of interpenetration, 212 213, 220, …"
7. from Index:
"… phrases denying interpenetration of souls, 270 271; physical phenomena that lack consciousness, 281 282; physical structures lacking hereness, 283; potential personal attributes, 183; …"

The American Mathematical Society editors and reviewer seem to share Hofstadter's ignorance of Christian doctrine; they might otherwise have remembered a rather famous remark: "This is not mathematics, it is theology."
 
For more on the theology of interpenetration, see Log24 on "Perichoresis, or Coinherence" (Jan. 22, 2004).

For a more mathematical approach to this topic, see Spirituality Today, Spring 1991:

"… the most helpful image is perhaps the ellipse often used to surround divine figures in ancient art, a geometrical figure resulting from the overlapping, greater or lesser, of two independent circles, an interpenetration or coinherence which will, in some sense, reunify divided humanity, thus restoring to some imperfect degree the original image of God."

See also the trinitarian doctrine implicit in related Log24 entries of July 1, 2007, which include the following illustration of the geometrical figure described, in a somewhat confused manner, above:

The image “http://www.log24.com/log/pix07/070701-Ratio.jpg” cannot be displayed, because it contains errors.

"Values are rooted
in narrative."

Harvey Cox,    
Hollis Professor
of Divinity
at Harvard,
Atlantic Monthly,
  November 1995  

Related material:

Steps Toward Salvation:
An Examination of
Co-Inherence and
Substitution in
the Seven Novels
of Charles Williams
,
by Dennis L. Weeks

Tuesday, July 3, 2007

Tuesday July 3, 2007

Filed under: General — m759 @ 9:29 PM
The Ignorance
of Stanley Fish

(continued from
June 18, 2002)

The “ignorance” referred to
is Fish’s ignorance of the
philosophical background
of the words
“particular” and “universal.”

Postmodern Warfare:
The Ignorance of Our
Warrior Intellectuals,”
by Stanley Fish,
Harper’s Magazine,
July 2002, contains
the following passages:

“The deepest strain in a religion is the particular and particularistic doctrine it asserts at its heart, in the company of such pronouncements as ‘Thou shalt have no other Gods before me.’ Take the deepest strain of religion away… and what remains are the surface pieties– abstractions without substantive bite– to which everyone will assent because they are empty, insipid, and safe. It is this same preference for the vacuously general over the disturbingly particular that informs the attacks on college and university professors who spoke out in ways that led them to be branded as outcasts by those who were patrolling and monitoring the narrow boundaries of acceptable speech. Here one must be careful, for there are fools and knaves on all sides.”

“Although it may not at first be obvious, the substitution for real religions of a religion drained of particulars is of a piece with the desire to exorcise postmodernism.”

“What must be protected, then, is the general, the possibility of making pronouncements from a perspective at once detached from and superior to the sectarian perspectives of particular national interests, ethnic concerns, and religious obligations; and the threat to the general is posed by postmodernism and strong religiosity alike, postmodernism because its critique of master narratives deprives us of a mechanism for determining which of two or more fiercely held beliefs is true (which is not to deny the category of true belief, just the possibility of identifying it uncontroversially), strong religiosity because it insists on its own norms and refuses correction from the outside. The antidote to both is the separation of the private from the public, the establishing of a public sphere to which all could have recourse and to the judgments of which all, who are not criminal or insane, would assent. The point of the public sphere is obvious: it is supposed to be the location of those standards and measures that belong to no one but apply to everyone. It is to be the location of the universal. The problem is not that there is no universal–the universal, the absolutely true, exists, and I know what it is. The problem is that you know, too, and that we know different things, which puts us right back where we were a few sentences ago, armed with universal judgments that are irreconcilable, all dressed up and nowhere to go for an authoritative adjudication.

What to do? Well, you do the only thing you can do, the only honest thing: you assert that your universal is the true one, even though your adversaries clearly do not accept it, and you do not attribute their recalcitrance to insanity or mere criminality–the desired public categories of condemnation–but to the fact, regrettable as it may be, that they are in the grip of a set of beliefs that is false. And there you have to leave it, because the next step, the step of proving the falseness of their beliefs to everyone, including those in their grip, is not a step available to us as finite situated human beings. We have to live with the knowledge of two things: that we are absolutely right and that there is no generally accepted measure by which our rightness can be independently validated. That’s just the way it is, and we should just get on with it, acting in accordance with our true beliefs (what else could we do?) without expecting that some God will descend, like the duck in the old Groucho Marx TV show, and tell us that we have uttered the true and secret word.”

From the public spheres
of the Pennsylvania Lottery:

PA Lottery logo

PA Lottery July 3, 2007: Mid-day 105, Evening 268

105 —

Log24 on 1/05:

“‘From your lips
to God’s ears,’
 goes the old
Yiddish wish.

 The writer, by contrast,
tries to read God’s lips
and pass along
the words….”

— Richard Powers   

268 —

This is a page number
that appears, notably,
in my June 2002
journal entry on Fish
,
and again in an entry,
The Transcendent Signified,”
dated July 26, 2003,
that argues against
Fish’s school, postmodernism,
 and in favor of what the pomos
call “logocentrism.”

Page 268
 
of Simon Blackburn’s Think
(Oxford Univ. Press, 1999):

“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato’s (realist) reaction to the sophists (nominalists). What is often called ‘postmodernism’ is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth.”

Fish may, if he wishes,
regard the particular
page number 268 as
delivered– five years late,
but such is philosophy–
by Groucho’s
winged messenger
in response to
Fish’s utterance of the
  “true and secret word”–
namely, “universal.”

When not arguing politics,
Fish, though from
a Jewish background, is
 said to be a Milton scholar.
Let us therefore hope he
is by now, or comes to be,
aware of the Christian
approach to universals–
an approach true to the
philosophical background
sketched in 1999 by
Blackburn and made
particular in a 1931 novel
 by Charles Williams,
The Place of the Lion.

Sunday, July 1, 2007

Sunday July 1, 2007

Filed under: General — m759 @ 2:06 AM
At the still point,
there the dance is.
— T. S. Eliot

Humphrey Carpenter in The Inklings, his book on the Christian writers J. R. R. Tolkien, C. S. Lewis, and Charles Williams, says that

“Eliot by his own admission took the ‘still point of the turning world’ in Burnt Norton from the Fool in Williams’s The Greater Trumps.”

The Inklings, Ballantine Books, 1981, p. 106

Today’s Birthdays: …. Actress-dancer Leslie Caron is 76…. Movie director Sydney Pollack is 73….  Dancer-choreographer Twyla Tharp is 66. –AP, “Today in History,” July 1, 2007

The Diamond within the Mandorla

The Diamond
in the Mandorla

Sunday, June 24, 2007

Sunday June 24, 2007

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM
Raiders of
the Lost Stone

(Continued from June 23)

Scott McLaren on
Charles Williams:
 
"In Many Dimensions (1931)
Williams sets before his reader the
mysterious Stone of King Solomon,
an image he probably drew
from a brief description in Waite's
The Holy Kabbalah (1929)
of a supernatural cubic stone
on which was inscribed
'the Divine Name.'"

The image “http://www.log24.com/log/pix07/070624-Waite.gif” cannot be displayed, because it contains errors.

Related material:

The image “http://www.log24.com/log/pix07/070624-Cube.gif” cannot be displayed, because it contains errors.

Solomon's Cube,

Geometry of the 4x4x4 Cube,

The Klein Correspondence,
Penrose Space-Time,
and a Finite Model

Tuesday, May 15, 2007

Tuesday May 15, 2007

Filed under: General — Tags: , — m759 @ 2:11 PM

Tony Nominations Announced

The Rev. Jerry Falwell Dies

The Rev. Jerry Falwell in Montgomery, 2003

The Rev. Jerry Falwell speaks at a rally
on the steps of the Alabama Capitol
in Montgomery in this Saturday,
Aug. 16, 2003, file photo.
(AP Photo/Dave Martin)

The New York Times, Nov. 22, 2004:

"The Rev. Jerry Falwell's Liberty University [at Lynchburg, Virginia] is part of a movement around the nation that brings a religious perspective to the law."

Religious perspective:

See the five Log24 entries ending with "Dinner Theater?" (Nov. 26, 2004).  Note Charles Williams's discussion of the Salem witchcraft trials.

See also yesterday's "Seven Bridges."  In light of that entry's picture of Nicole Kidman in "To Die For," and of Charles Williams's remarks, a discussion of Kidman's "Practical Magic" may also interest some.

"Hey, good lookin',     
whatcha got cookin'?"
Hank Williams      

Friday, February 2, 2007

Friday February 2, 2007

Filed under: General — m759 @ 7:11 AM

The Night Watch

For Catholic Schools Week
(continued from last year)–

Last night’s Log24 Xanga
footprints from Poland:

Poland 2/2/07 1:29 AM
/446066083/item.html
2/20/06: The Past Revisited
(with link to online text of
Many Dimensions, by Charles Williams)

Poland 2/2/07 2:38 AM
/426273644/item.html
1/15/06 Inscape
(the mathematical concept, with
square and “star” diagrams)

Poland 2/2/07 3:30 AM
nextdate=2%252f8%252f20…
2/8/05 The Equation
(Russell Crowe as John Nash
with “star” diagram from a
Princeton lecture by Langlands)

Poland 2/2/07 4:31 AM
/524081776/item.html
8/29/06 Hollywood Birthday
(with link to online text of
Plato on the Human Paradox,
by a Fordham Jesuit)

Poland 2/2/07 4:43 AM
/524459252/item.html
8/30/06 Seven
(Harvard, the etymology of the
word “experience,” and the
Catholic funeral of a professor’s
23-year-old daughter)

Poland 2/2/07 4:56 AM
/409355167/item.html
12/19/05 Quarter to Three (cont.)

(remarks on permutation groups
for the birthday of Helmut Wielandt)

Poland 2/2/07 5:03 AM
/490604390/item.html
5/29/06 For JFK’s Birthday
(The Call Girls revisited)

Poland 2/2/07 5:32 AM
/522299668/item.html
8/24/06 Beginnings
(Nasar in The New Yorker and
T. S. Eliot in Log24, both on the 2006
Beijing String Theory conference)

Poland 2/2/07 5:46 AM
/447354678/item.html
2/22/06 In the Details
(Harvard’s president resigns,
with accompanying “rosebud”)

Thursday, January 4, 2007

Thursday January 4, 2007

Filed under: General — m759 @ 12:00 PM

Readings for wise men
on the date of
T. S. Eliot's death:

"A cold coming we had of it…."

"… a Church is to be judged by its intellectual fruits, by its influence on the sensibility of the most sensitive and on the intellect of the most intelligent, and it must be made real to the eye by monuments of artistic merit."

— T. S. Eliot, For Lancelot Andrewes: Essays on Style and Order, published by Faber & Gwyer, London,  in 1928.

The visual "monuments of artistic merit" I prefer are not those of a Church– except, perhaps, the Church of Modernism.  Literary monuments are another matter.  I recommend:

The Death of Adam
,

The Novels of Charles Williams, and

Let Sleeping Beauties Lie.
 

Related material
on style and order:

Eliot's essay on Andrewes begins,
"The Right Reverend Father in God,
Lancelot Bishop of Winchester,
died on September 25, 1626."

For evidence of Andrewes's
saintliness (hence, that
of Eliot) we may examine
various events of the
25th of September.

("On September 25th most of
the Anglican Communion
commemorates the day on which
Lancelot Andrewes died."
)

In Log24,
these events are…

Sept. 25, 2002

"Las Mañanitas"

Sept. 25, 2003

The image “http://www.log24.com/log/pix07/030925-Bubbles2.jpg” cannot be displayed, because it contains errors.

Aloha.

Sept. 25, 2004

Sept. 25, 2005

The image “http://www.log24.com/log/pix05B/050925-db3.gif” cannot be displayed, because it contains errors.

Sept. 25, 2006

The image “http://www.log24.com/log/pix07/060925-Medal2.jpg” cannot be displayed, because it contains errors.
(Yau and Perelman)

It seems that I am
somewhat out of step with
  the Anglican Communion…
though perhaps, in a sense,
in step with Eliot.

Note his words in
"Journey of the Magi":

Birth or Death?
There was a Birth, certainly,
We had evidence and no doubt.
I had seen birth and death,
But had thought they were different;
this Birth was
Hard and bitter agony for us,
like Death, our death.

See also entries for
Dec. 27, 2006 (the day of
Itche Goldberg's death) —

Photo op for Gerald Ford

— "Least Popular
Christmas Present
Revisited
" —

and for the same date
three years earlier

"If you don't play
some people's game, they say
that you have 'lost your marbles,'
not recognizing that,

while Chinese checkers
is indeed a fine pastime,
a person may also play dominoes,
chess, strip poker, tiddlywinks,
drop-the-soap or Russian roulette
with his brain.

One brain game that is widely,
if poorly, played is a gimmick
called 'rational thought.'"

Tom Robbins
 

Monday, December 4, 2006

Monday December 4, 2006

Filed under: General — m759 @ 11:01 AM
Descent of the God

The image “http://www.log24.com/log/pix06B/061204-Theo2.gif” cannot be displayed, because it contains errors.

Related material:

All Hallows’ Eve,
2005:

Multispeech

The image “http://www.log24.com/log/pix05B/Gameplayers12.jpg” cannot be displayed, because it contains errors.

as well as

C. S. Lewis,
That Hideous Strength,
Chapter 15,
“The Descent of the Gods,”

and
Charles Williams,
The Carol of Amen House“:

Beauty arose of old
And dreamed of a perfect thing,
Where none shall be angry or cold
Or armed with an evil sting;

Where the world shall be made anew,
For the gods shall breathe its air,
And Phoebus Apollo there-through
Shall move on a golden stair.

(For the musical score, see
The Masques of Amen House.)

See also
A Mass for Lucero.

Monday, June 26, 2006

Monday June 26, 2006

Filed under: General — Tags: — m759 @ 9:29 AM

A Little Extra Reading

In memory of
Mary Martin McLaughlin,
a scholar of Heloise and Abelard.
McLaughlin died on June 8, 2006.

"Following the parade, a speech is given by Charles Williams, based on his book The Place of the Lion. Williams explains the true meaning of the word 'realism' in both philosophy and theology. His guard of honor, bayonets gleaming, is led by William of Ockham."

Midsummer Eve's Dream

A review by John D. Burlinson of Charles Williams's novel The Place of the Lion:

"… a little extra reading regarding Abelard's take on 'universals' might add a little extra spice– since Abelard is the subject of the heroine's … doctoral dissertation. I'd suggest the article 'The Medieval Problem of Universals' in the online Stanford Encyclopedia of Philosophy."

Michael L. Czapkay, a student of philosophical theology at Oxford:

"The development of logic in the schools and universities of western Europe between the eleventh and fifteenth centuries constituted a significant contribution to the history of philosophy. But no less significant was the influence of this development of logic on medieval theology. It provided the necessary conceptual apparatus for the systematization of theology. Abelard, Ockham, and Thomas Aquinas are paradigm cases of the extent to which logic played an active role in the systematic formulation of Christian theology. In fact, at certain points, for instance in modal logic, logical concepts were intimately related to theological problems, such as God's knowledge of future contingent truths."

The Medieval Problem of Universals, by Fordham's Gyula Klima, 2004:

"… for Abelard, a status is an object of the divine mind, whereby God preconceives the state of his creation from eternity."

Status Symbol

(based on Weyl's Symmetry):

The image “http://www.log24.com/log/pix06A/060604-Roots.jpg” cannot be displayed, because it contains errors.

"… for then we would know

the mind of God"
Stephen Hawking, 1988

For further details,
click on the picture.

Friday, June 2, 2006

Friday June 2, 2006

Filed under: General — Tags: , — m759 @ 4:23 PM
'Ursprache' beats 'weltschmerz'
to win American spelling bee

 
Weltschmerz

and the
Ursprache

The image “http://www.log24.com/log/pix06A/060602-Weltschmerz.jpg” cannot be displayed, because it contains errors.

From eudaemonist.com,
a quotation from
Paul Zanker's
The Mask of Socrates:

"Zanker describes the photograph [above] as 'Walter Benjamin looking out at the viewer, his head propped on his hand, his face filled with loneliness and weltschmerz.'"

Benjamin was a Jewish Marxist.  For a Jewish perspective on spelling, see Log24, Nov. 11, 2005.  For a leftist perspective on Benjamin and last night's crucial spelling word "Ursprache," see "Ground Zero, an American Origin," by Mary Caputi (Poroi, 2, 1, August 2003):

The Baroque sensibility of ruin emphasizes a meaninglessness that too many possibilities deliver.  Aimlessness and malaise make life into exhausting toil in the absence of  coherence.  In overdetermined realities, meaning appears arbitrary and erratic, as the world's connection to God seems lost or withheld.  At the extreme, everyday life is as full of noise and commotion as it is devoid of intrinsic meaning.  Connections among people wither with the onset of overabundance and despair.  Recognition of this condition induces acedia, a weariness of life.  Here the malaise of modernity and ruins ties to Benjamin's interest in Trauerspiel, German tragic drama, and the tragedies of Shakespeare.  All respond to a plague of lost spiritual connections and a meaningless earthly existence where incessant toil and trouble — "tomorrow and tomorrow and tomorrow" — contribute to a chronic, wearing sense of pain.

Benjamin's interest in this form of melancholia, from suffering a sort of spiritual exile, is evident in his 1916 essay "On Language as Such and On the Language of Man."  In this text, he explains that the Ursprache, our "original" language, is "blissful" precisely because it lacks the arbitrariness that results from overdetermination.  Ur-speech is Adamic language, the linguistic power that God gives to Adam to confer identity on the material world.  It contains no arbitrary component, but reveals the unity between God's divine plan and the world as it exists.  Before ruins and fragments, there is no overdetermination to induce the melancholy of acedia.  Instead the originary language implies a unity of transcendent and immanent realms.  "With the creative omnipotence of language it begins, and at the end of language, as it were, assimilates the created, names it.  Language is therefore both the creative and the finished creation; it is word and nature."6

This blissful state between the world and its creator as expressed in Adamic language has its end, of course, in the Fall.  The "ignorance" introduced into the world that ultimately drives our melancholic state of acedia has its inception with the Fall away from the edenic union that joins God's plan to the immediacy of the material world.  What ensues, says Benjamin, is an overabundance of conventional languages, a prattle of meanings now localized hence arbitrary.  A former connection to a defining origin has been lost; and an overdetermined, plethoric state of melancholia forms.  Over-determination stems from over-naming.  "Things have no proper names except in God.  . . . In the language of men, however, they are overnamed."  Overnaming becomes "the linguistic being of melancholy."7

      6 Walter Benjamin, "On Language as Such and On the Languages of Man," Edmund Jephcott, tr., Walter Benjamin, Selected Writings, Volume I:  1913-1926, Marcus Bullock and Michael W. Jennings, eds., Cambridge, MA, Harvard University Press, 1997, p. 68.  
      7 Ibid., p. 73.

For a Christian perspective on Adamic language, see Charles Williams's The Place of the Lion.

 

See also the previous entry:

Float like a butterfly,
sting like a

The image “http://www.log24.com/log/pix06A/060602-BeeLogo.gif” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix06A/060602-Winner.jpg” cannot be displayed, because it contains errors.

Friday, May 12, 2006

Friday May 12, 2006

Filed under: General,Geometry — Tags: — m759 @ 3:00 AM
Tesseract

"Does the word 'tesseract'
mean anything to you?"
— Robert A. Heinlein in
The Number of the Beast
(1980)

My reply–

Part I:

The image “http://www.log24.com/log/pix06A/WrinkleInTime1A.jpg” cannot be displayed, because it contains errors.

A Wrinkle in Time, by
Madeleine L'Engle
(first published in 1962)

Part II:

Diamond Theory in 1937
and
Geometry of the 4×4 Square

Part III:

Catholic Schools Sermon

Conclusion:
 

"Wells and trees were dedicated to saints.  But the offerings at many wells and trees were to something other than the saint; had it not been so they would not have been, as we find they often were, forbidden.  Within this double and intertwined life existed those other capacities, of which we know more now, but of which we still know little– clairvoyance, clairaudience, foresight, telepathy."

Charles Williams, Witchcraft, Faber and Faber, London, 1941

Related material:

A New Yorker profile of Madeleine L'Engle from April 2004, which I found tonight online for the first time.  For a related reflection on truth, stories, and values, see Saint's Day.  For a wider context, see the Log24 entries of February 1-15, 2003 and February 1-15, 2006.
 

Monday, February 20, 2006

Monday February 20, 2006

Filed under: General — m759 @ 12:00 AM

The Past Revisited

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

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

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

Sunday, February 5, 2006

Sunday February 5, 2006

Filed under: General — m759 @ 11:00 AM

Catholic Schools Sermon

For those who might be tempted today, following yesterday’s conclusion of Catholic Schools Week, to sing (for whatever reason) “Ding Dong, the Witch is Dead”–

Here, from his classic Witchcraft (first published by Faber and Faber, London, 1941, reprinted by Apocryphile Press, Berkeley, CA, Oct. 1, 2005) is Charles Williams on the strong resemblance between witchcraft and the rituals of the Church:

Charles Williams on
Witchcraft and the Church

From Witchcraft, 2005 Apocryphile edition, pages 77-80–

[77] … The predisposition towards the idea of magic might be said to begin with a moment which seems to be of fairly common experience– the moment when it seems that anything might turn into anything else.  We have grown used– and properly used– to regarding this sensation invalid because, on the whole, things do not turn into other things except by processes which we realize, or else at least so frequently that we appreciate the probability.  But the occasional sensation remains.  A room, a street, a field becomes unsure.  The edge of a possibility of utter alteration intrudes.  A door, untouched, might close; a picture might walk; a tree might speak; an animal might not be an animal; a man might not be a man.  One may be with a friend, and a terror will take one even while his admirable voice is speaking; one will be with a lover and the hand will become a different and terrifying thing, moving in one’s own like a malicious intruder, too real for anything but fear.  All this may be due to racial memories or to any other cause; the point is that it exists.  It exists and can be communicated; it can even be shared.  There is, in our human centre, a heart-gripping fear of irrational change, of perilous and malevolent change.
    Secondly, there is the human body, and the movements of the human body.  Even now, when, as a general rule, the human body is not supposed to mean [78] anything, there are moments when it seems, in spite of ourselves, packed with significance.  This sensation is almost exactly the opposite of the last.  There, one was aware that any phenomenon might alter into another and truer self.  Here, one is aware that a phenomenon, being wholly itself, is laden with universal meaning.  A hand lighting a cigarette is the explanation of everything; a foot stepping from a train is the rock of all existence.  If the first group of sensations are due to racial fear, I do not know to what the second group are due– unless indeed to the Mercy of God, who has not left us without a cloud of witnesses.  But intellectually they are both as valid or invalid as each other; any distinction must be a matter of choice.  And they justify each other, at least to this extent, that (although the first suggests irrationality and the second rationality) they both at first overthrow a simple trust that phenomena are what phenomena seem.
    But if the human body is capable of seeming so, so are the controlled movements of the human body– ritual movements, or rather movements that seem like ritual.  A finger pointing is quite capable of seeming not only a significant finger, but a ritual finger; an evocative finger; not only a finger of meaning, but a finger of magic.  Two light dancing steps by a girl may (if one is in that state) appear to be what all the Schoolmen were trying to express; they are (only one cannot quite catch it) an intellectual statement of beatitude.  But two quiet steps by an old man may seem like the very speech of hell.  Or the other way round.  Youth and age have nothing to do with it, nor did the ages that defined and [79] denounced witchcraft think so.  The youngest witch, it is said, that was ever burned was a girl of eleven years old.
    Ordered movement, ritual, is natural to men.  But some ages are better at it, are more used to it, and more sensitive to it, than others.  The Middle Ages liked great spectacle, and therefore (if for no other reasons– but there were many) they liked ritual.  They were nourished by ritual– the Eucharist exhibited it.  They made love by ritual– the convention of courtly love preserved it.  Certainly also they did all these things without ritual– but ritual (outside the inner experience) was the norm.  And ritual maintains and increases that natural sense of the significance of movement.  And, of course, of formulae, of words.
    The value of formulae was asserted to be very high.  The whole religious life ‘as generally necessary to salvation’ depended on formulae.  The High God had submitted himself to formulae.  He sent his graces.  He came Himself, according to ritual movements and ritual formulae.  Words controlled the God.  All generations who have believed in God have believed that He will come on interior prayer; not all that He will come, if not visibly yet in visible sacraments, on exterior incantation.  But so it was.  Water and a Triune formula concentrated grace; so did oil and other formulae; so– supremely– did bread and wine and yet other formulae.   Invocations of saints were assumed, if less explicitly guaranteed, to be effective.  The corollaries of the Incarnation had spread, in word and gesture, very far.
    The sense of alteration, the sense of meaning, the [80] evocation of power, the expectation of the God, lay all about the world.  The whole movement of the Church had, in its rituals, a remarkable similarity to the other rites it denounced.  But the other rites had been there first, both in the Empire and outside the Empire.  In many cases the Church turned them to its own purposes.  But also in many cases it entirely failed to turn them to its own purposes.  In many cases it adopted statues and shrines.  But in others it was adopted by, at least, the less serious spells and incantations.  Wells and trees were dedicated to saints.  But the offerings at many wells and trees were to something other than the saint; had it not been so they would not have been, as we find they often were, forbidden.  Within this double and intertwined life existed those other capacities, of which we know more now, but of which we still know little– clairvoyance, clairaudience, foresight, telepathy.

Wednesday, November 16, 2005

Wednesday November 16, 2005

Filed under: General — m759 @ 4:04 PM
Images

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, August 22, 2005

Monday August 22, 2005

Filed under: General — Tags: — m759 @ 4:07 PM
The Hole

Part I: Mathematics and Narrative

The image “http://www.log24.com/log/pix05B/050822-Narr.jpg” cannot be displayed, because it contains errors.

Apostolos Doxiadis on last month's conference on "mathematics and narrative"–

Doxiadis is describing how talks by two noted mathematicians were related to

    "… a sense of a 'general theory bubbling up' at the meeting… a general theory of the deeper relationship of mathematics to narrative…. "

Doxiadis says both talks had "a big hole in the middle."  

    "Both began by saying something like: 'I believe there is an important connection between story and mathematical thinking. So, my talk has two parts.  [In one part] I’ll tell you a few things about proofs.  [And in the other part] I’ll tell you about stories.' …. And in both talks it was in fact implied by a variation of the post hoc propter hoc, the principle of consecutiveness implying causality, that the two parts of the lectures were intimately related, the one somehow led directly to the other."
  "And the hole?"
  "This was exactly at the point of the link… [connecting math and narrative]… There is this very well-known Sidney Harris cartoon… where two huge arrays of formulas on a blackboard are connected by the sentence ‘THEN A MIRACLE OCCURS.’ And one of the two mathematicians standing before it points at this and tells the other: ‘I think you should be more explicit here at step two.’ Both… talks were one half fascinating expositions of lay narratology– in fact, I was exhilarated to hear the two most purely narratological talks at the meeting coming from number theorists!– and one half a discussion of a purely mathematical kind, the two parts separated by a conjunction roughly synonymous to ‘this is very similar to this.’  But the similarity was not clearly explained: the hole, you see, the ‘miracle.’  Of course, both [speakers]… are brilliant men, and honest too, and so they were very clear about the location of the hole, they did not try to fool us by saying that there was no hole where there was one."
 

Part II: Possible Worlds

"At times, bullshit can only be countered with superior bullshit."
Norman Mailer

Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:

    "The concept of possible worlds dates back to a least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds.  Voltaire satirized this view in his picaresque novel Candide….
    Borges' seminal short story El jardín de senderos que se bifurcan ("The Garden of Forking Paths") is an early example of many worlds in fiction."

 

Background:

Modal Logic in Wikipedia

Possible Worlds in Wikipedia

Possible-Worlds Theory, by Marie-Laure Ryan
(entry for The Routledge Encyclopedia of Narrative Theory)

The God-Shaped Hole
 

Part III: Modal Theology

  "'What is this Stone?' Chloe asked….
  '…It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"

  — Many Dimensions, by Charles Williams, 1931 (Eerdmans paperback, April 1979, pp. 43-44)


"The lapis was thought of as a unity and therefore often stands for the prima materia in general."

  — Aion, by C. G. Jung, 1951 (Princeton paperback, 1979, p. 236)

"Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe."

 
  — The Stars My Destination, by Alfred Bester, 1956 (Vintage hardcover, July 1996, p. 216)
 
"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

Tuesday, March 22, 2005

Tuesday March 22, 2005

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

The God Factor

Reba McEntire on
Make a Difference Day:

"Kids who may never get out of their town will be able to see the world through books. But I'm talking about my passion. What's yours?"

"There is the God factor…."

— NickyJett, Xanga comment

"'What is this Stone?' Chloe asked….
'…It is told that, when the Merciful One
made the worlds, first of all He created
that Stone and gave it to the Divine One
whom the Jews call Shekinah,
and as she gazed upon it
the universes arose and had being.'"

Many Dimensions,
by Charles Williams, 1931

For more on this theme
appropriate to Passion Week
Jews playing God — see

The image “http://www.log24.com/log/pix05/050322-Trio.jpg” cannot be displayed, because it contains errors.

Rebecca Goldstein
in conversation with
Bob Osserman
of the
Mathematical Sciences Research Institute
at the Commonwealth Club, San Francisco,
Tuesday, March 22.  Wine and cheese
reception at 5:15 PM (San Francisco time).
 
For the meaning of the diamond,
see the previous entry.

Sunday, February 20, 2005

Sunday February 20, 2005

Filed under: General,Geometry — Tags: , — m759 @ 2:20 PM

Relativity Blues

Today, February 20, is the 19th anniversary of my note The Relativity Problem in Finite Geometry.  Here is some related material.

In 1931, the Christian writer Charles Williams grappled with the theology of time, space, free will, and the many-worlds interpretation of quantum mechanics (anticipating by many years the discussion of this topic by physicists beginning in the 1950's).

(Some pure mathematics — untainted by physics or theology — that is nevertheless related, if only by poetic analogy, to Williams's 1931 novel, Many Dimensions, is discussed in the above-mentioned note and in a generalization, Solomon's Cube.)

On the back cover of Williams's 1931 novel, the current publisher, William B. Eerdmans Publishing Company of Grand Rapids, Michigan, makes the following statement:

"Replete with rich religious imagery, Many Dimensions explores the relation between predestination and free will as it depicts different human responses to redemptive transcendence."

One possible response to such statements was recently provided in some detail by a Princeton philosophy professor.  See On Bullshit, by Harry G. Frankfurt, Princeton University Press, 2005.

A more thoughtful response would take into account the following:

1. The arguments presented in favor of philosopher John Calvin, who discussed predestination, in The Death of Adam: Essays on Modern Thought, by Marilynne Robinson

2. The physics underlying Einstein's remarks on free will, God, and dice
 
3. The physics underlying Rebecca Goldstein's novel Properties of Light and Paul Preuss's novels  Secret Passages and Broken Symmetries

4. The physics underlying the recent so-called "free will theorem" of John Conway and Simon Kochen of Princeton University

5. The recent novel Gilead, by Marilynne Robinson, which deals not with philosophy, but with lives influenced by philosophy — indirectly, by the philosophy of the aforementioned John Calvin.

From a review of Gilead by Jane Vandenburgh:  

"In The Death of Adam, Robinson shows Jean Cauvin to be the foremost prophet of humanism whose Protestant teachings against the hierarchies of the Roman church set in motion the intellectual movements that promoted widespread literacy among the middle and lower classes, led to both the American and French revolutions, and not only freed African slaves in the United States but brought about suffrage for women. It's odd then that through our culture's reverse historicism, the term 'Calvinism' has come to mean 'moralistic repression.'"

For more on what the Calvinist publishing firm Eerdmans calls "redemptive transcendence," see various July 2003 Log24.net entries.  If these entries include a fair amount of what Princeton philosophers call bullshit, let the Princeton philosophers meditate on the summary of Harvard philosophy quoted here on November 5 of last year, as well as the remarks of November 5, 2003,  and those of November 5, 2002.

From Many Dimensions (Eerdmans paperback, 1963, page 53):

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

A recent answer:

Modal Theology

"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz,
(Log24.net, 1/25/05)

And what do we           
   symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

Thursday, February 17, 2005

Thursday February 17, 2005

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

"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz,
(Log24.net, 1/25/05)

And what do we           
   symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

On the Lapis Philosophorum,
the Philosophers' Stone –

"'What is this Stone?' Chloe asked….
'…It is told that, when the Merciful One
made the worlds, first of all He created
that Stone and gave it to the Divine One
whom the Jews call Shekinah,
and as she gazed upon it
the universes arose and had being.'"
Many Dimensions,
by Charles Williams, 1931
(Eerdmans paperback,
April 1979, pp. 43-44)

"The lapis was thought of as a unity
and therefore often stands for
the prima materia in general."
Aion, by C. G. Jung, 1951
(Princeton paperback,
1979, p. 236)

"Its discoverer was of the opinion that
he had produced the equivalent of
the primordial protomatter
which exploded into the Universe."
The Stars My Destination,
by Alfred Bester, 1956
(Vintage hardcover,
July 1996, p. 216)

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

See also
The Diamond Archetype.

For more on modal theology, see

Kurt Gödel's Ontological Argument
and

 The Ontological Argument
 from Anselm to Gödel.

Monday, November 22, 2004

Monday November 22, 2004

Filed under: General — m759 @ 8:00 PM

Lynchburg Law

From today’s New York Times:

The Rev. Jerry Falwell’s Liberty University [at Lynchburg, Virginia] is part of a movement around the nation that brings a religious perspective to the law.

The image “http://www.log24.com/log/pix04B/041122-Books.jpg” cannot be displayed, because it contains errors.

Sam Dean for The New York Times

The connection between the Bible and the law is part of the curriculum at Liberty, one of a number of new religiously oriented law schools.

Go to Article

The Times’s photo (above) of books on the Bible and the law, apparently at Lynchburg, suggests a related book that may be of considerable value to the legal scholars there:

Charles Williams on the
Salem witchcraft trials:

“The afflicted children continued to testify; there entered into the cases what was called ‘spectral evidence,’ a declaration by the witness that he or she could see that else invisible shape before them, perhaps hurting them.  It was a very ancient tendency of witnesses, and it had occurred at a number of trials in Europe.”

Witchcraft, Meridian Books, Inc., New York,
1959 (first published 1941), page 281

The image “http://www.log24.com/log/pix04B/041122-Witchcraft.jpg” cannot be displayed, because it contains errors.

Monday November 22, 2004

Filed under: General — Tags: — m759 @ 12:12 PM
 
Flores, Flores Para Los Muertos

See entry of
All Hallows' Eve:

"A memorial Mass will be held on Monday,
November 22, 2004, at the Church of
St. Ignatius Loyola, 980 Park Avenue…."

Photo by Gerry Gantt

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…

Related reading:

From a review at Amazon.com
of All Hallows' Eve, by Charles Williams:

"How many other books do you know in which one of the two main characters is dead, in which the dead and living can communicate almost as easily as we do every day, in which magic is serious and scary? Mainstream books, that is, not Goosebumps, with an introduction by T.S. Eliot, with the whole thing to be understood as at least feasible if not truth. This is unusual. And yet, and yet, the whole thing works."

Friday, March 5, 2004

Friday March 5, 2004

Filed under: General — m759 @ 1:20 AM

Songs for Shakespeare

from Willie and Waylon

From today’s New York Times

by Ben Brantley

….”Dost thou know me, fellow?” thunders Christopher Plummer, who is giving the performance of a lifetime in the title role of “King Lear”….

Throughout Jonathan Miller’s engrossing production of Shakespeare’s bleakest tragedy, which opened last night, Mr. Plummer bestrides the boundary between being and nothingness….

The Line,
by S.H. Cullinane

LEAR:

Now you better do some thinkin’
    then you’ll find
You got the only daddy
    that’ll walk the line
.

FOOL:

I’ve always been different
    with one foot over the line….
I’ve always been crazy
    but it’s kept me from going insane.

FOOL:

174. …. Now thou art an 0 without
175. a figure. I am better than thou art, now. I am a fool;
176. thou art nothing….

“…. in the last mystery of all the single figure of what is called the World goes joyously dancing in a state beyond moon and sun, and the number of the Trumps is done.  Save only for that which has no number and is called the Fool, because mankind finds it folly till it is known.  It is sovereign or it is nothing, and if it is nothing then man was born dead.”

The Greater Trumps,
by Charles Williams, Ch. 14

Follow-up of Friday, March 5

From Arts & Letters Daily,
Weekend Edition, March 6-7, 2004 —

Some readers crave awe more than understanding, and lurid pop science is always there to feed their addiction to junk ideas… more»

Does Shakespeare’s Lear have a spiritual dimension? “No,” insists Jonathan Miller. “That’s modern, New Age drivel….” more»

The “more” link of the item at left above leads to an American Scientist article titled

The Importance of
Being Nothingness
.

The appearance of these two items side-by-side at Arts & Letters Daily, together with Brantley’s remark above, is an example of Jungian synchronicity — a concept that the American Scientist author and Jonathan Miller probably both sneer at.  Sneer away.

Thursday, January 22, 2004

Thursday January 22, 2004

Filed under: General — m759 @ 8:19 AM

Perichoresis, or Coinherence

Edward Gibbon, Decline and Fall of the Roman Empire, Chapter XXI

Gibbon, discussing the theology of the Trinity, defines perichoresis as

“… the internal connection and spiritual penetration which indissolubly unites the divine persons59 ….

59 … The perichoresis or ‘circumincessio,’ is perhaps the deepest and darkest corner of the whole theological abyss.”

“Whoever fights monsters should see to it that in the process he does not become a monster.  And when you look long into an abyss, the abyss also looks into you.”

— Friedrich Nietzsche, Beyond Good and Evil, section 146, translated by Walter Kaufmann

Perichoresis does NOT mean “dancing around” ….

From a mailing list message:

If [a correspondent] will but open a lexicon, she will see that perichoresis (with a long o, omega) has nothing to do with “the Greek word for dance,” which is spelt with a short o (omicron).  As a technical term in trinitarian theology, perichoresis means “interpenetration.”

Perichoresis in Theology

Interpenetration in Arthur Machen

Interpenetration in T. S. Eliot:

“Between two worlds
     become much like each other….”

On the Novels of Charles Williams

Coinherence in Charles Williams

Readings on Perichoresis

Saint Athanasius

Per Speculum in Aenigmate

The Per Speculum link is to a discussion of coinherence and the four last films of Kieslowski

La Double Vie de Veronique (1991),

Trois Couleurs: Bleu (1993),

Trois Couleurs: Blanc (1993), and

Trois Couleurs: Rouge (1994).

See, too, previous log24 entries related to Kieslowski’s work and to coinherence:

Moulin Bleu (12/16/03),

Quarter to Three (12/20/03), and

White, Geometric, and Eternal (12/20/03).

Wednesday, September 10, 2003

Wednesday September 10, 2003

Filed under: General — m759 @ 4:04 PM

4:04:08

The title refers to my entry of last April 4,

The Eight,

and to the time of this entry.

From D. H. Lawrence and the Dialogical Principle:

“Plato’s Dialogues…are queer little novels….[I]t was the greatest pity in the world, when philosophy and fiction got split.  They used to be one, right from the days of myth.  Then they went and parted, like a nagging married couple, with Aristotle and Thomas Aquinas and that beastly Kant.  So the novel went sloppy, and philosophy went abstract-dry.  The two should come together again, in the novel.”

— pp. 154-5 in D. H. Lawrence, “The Future of the Novel,” in Study of Thomas Hardy and Other Essays. Ed.  Bruce Steele.  Cambridge: Cambridge University Press,1983. 149-55.



Philosophy



Fiction

“The wild, brilliant, alert head of St. Mawr seemed to look at her out of another world… the large, brilliant eyes of that horse looked at her with demonish question…. ‘Meet him half way,’ Lewis [the groom] said.  But halfway across from our human world to that terrific equine twilight was not a small step.”    

— pp. 30, 35 in D. H. Lawrence, “St. Mawr.” 1925.  St. Mawr and Other Stories.  Ed. Brian Finney.  Cambridge: Cambridge University Press, 1983.

See also

Plato, Pegasus, and the Evening Star.

Katherine Neville’s novel The Eight, referred to in my note of April 4, is an excellent example of how not to combine philosophy with fiction.  Lest this be thought too harsh, let me say that the New Testament offers a similarly ludicrous mixture.

On the other hand, there do exist successful combinations of philosophy with fiction… For example, The Glass Bead Game, Zen and The Art of Motorcycle Maintenance, Under the Volcano, the novels of Charles Williams, and the C. S. Lewis classic That Hideous Strength.

This entry was prompted by the appearance of the god Pan in my entry on this date last year, by Hugh Grant’s comedic encounters with Pan in “Sirens,” by Lawrence’s remarks on Pan in “St. Mawr,” and by the classic film “Picnic at Hanging Rock.”

Sunday, June 22, 2003

Sunday June 22, 2003

Filed under: General,Geometry — m759 @ 2:28 AM

The Real Hogwarts

is at no single geographical location; it is distributed throughout the planet, and it is perhaps best known (apart from its disguises in the fiction of J. K. Rowling, C. S. Lewis, Charles Williams, and other Inklings) as Christ Church.  Some relevant links:

Christ Church College, Oxford

Christchurch, New Zealand

  • University of Canterbury
    Physical Sciences Library:

    Keeping Current with the Web:
    Maths & Statistics, June 2002

    Diamond Theory:
    Symmetry in Binary Spaces

    http://m759.freeservers.com/
    The author of this site is Steven Cullinane, who has also written booklets on the subject.  The web site provides detailed discussions of Diamond Theory, and is intended for college math students or mathematicians.  According to Cullinane, Diamond Theory is best classified in the subject of “finite automorphism groups of algebraic, geometric, or combinatorial structures.” The site also includes links to other resources.    From the NSDL Scout Report for Math, Engineering and Technology, Volume 1, No. 9, 7 June 2002, Copyright Internet Scout Project 1994-2002.  http://scout.cs.wisc.edu

Christ Church, Christchurch Road,
Virginia Water, England

Finally, on this Sunday in June, with The New York Review of Books of July 3, 2003, headlining the religion of Scientism (Freeman Dyson reviewing Gleick’s new book on Newton), it seems fitting to provide a link to an oasis of civilisation in the home town of mathematician John Nash — Bluefield, West Virginia.

Christ Church,
Bluefield, West Virginia

Tuesday, March 4, 2003

Tuesday March 4, 2003

Filed under: General — m759 @ 9:25 PM

Fearful Symmetry

I just Googled this phrase and found the following site, which turns out to be related to my previous entry on the Bead Game and the death of John P. Thompson.

Fearful Symmetry:
The Music Master’s Lecture
,

by Daniel d’Quincy.

This in turn links to an excerpt from The Glass Bead Game that includes this passage: 

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

It is very easy to get dangerously confused about holiness, but here are some relevant quotes:

“You will have to allow me to digress a bit in order to bring ourselves to a sufficiently elevated perspective… I warn you, it will require an attitude of playfulness on your part. Our approach will aim more at sincerity than seriousness. The attitude I’m aiming at is best expressed, I suppose, in the playing of a unique game, known by its German name as Das Glasperlenspiel, and which we may translate as the Glass Bead Game.”

— Daniel d’Quincy, Fearful Symmetry 

“7:11”

— God himself said this, at least according to the previous entry and to my Jan. 28 entry, State of the Communion.

“Seven is heaven.”

— See my web page Eight is a Gate.

“An excellent example of a ‘universal’ in the sense of Charles Williams, Jung, or Plato is Hexagram 11 in China’s 3,000-year-old classic, the I Ching:

Hexagram 11

‘Heaven and earth unite:
 the image of PEACE.’ 
 (Wilhelm/Baynes translation,
 Princeton University Press, 1967)” 

— S. H. Cullinane, Plato, Pegasus, and the Evening Star

Thus we may associate the numbers 7 and 11 with the notions of heaven and peace; for a somewhat darker association of the time 7:11 with Kali as Time the Destroyer, see my last entry and also my previous entries

Fat Man and Dancing Girl (Feb. 18, 2003), and 

Time and Eternity (Feb. 1, 2003).

Thursday, January 16, 2003

Thursday January 16, 2003

Filed under: General — m759 @ 5:05 PM

ART WARS
At the Still Point

“At the still point, there the dance is.”

— T. S. Eliot in Four Quartets

Humphrey Carpenter in The Inklings, his book on the Christian writers J. R. R. Tolkien, C. S. Lewis, and Charles Williams, says that

“Eliot by his own admission took the ‘still point of the turning world’ in Burnt Norton from the Fool in Williams’s The Greater Trumps.”

The Inklings, Ballantine Books, 1981, p. 106

Carpenter says Williams maintained that

It is the Christian’s duty to perceive “the declared pattern of the universe” — the “eternal dance” of Williams’s story The Greater Trumps — and to act according to it.

— Paraphrase of Carpenter, pp. 111-112

“The sun is not yet risen, and if the Fool moves there he comes invisibly, or perhaps in widespread union with the light of the moon which is the reflection of the sun.  But if the Tarots hold, as has been dreamed, the message which all things in all places and times have also been dreamed to hold, then perhaps there was meaning in the order as in the paintings; the tale of the cards being completed when the mystery of the sun has opened in the place of the moon, and after that the trumpets cry in the design which is called the Judgement, and the tombs are broken, and then in the last mystery of all the single figure of what is called the World goes joyously dancing in a state beyond moon and sun, and the number of the Trumps is done.  Save only for that which has no number and is called the Fool, because mankind finds it folly till it is known.  It is sovereign or it is nothing, and if it is nothing then man was born dead.”

The Greater Trumps, by Charles Williams, Ch. 14

If we must have Christians telling stories, let them write like Charles Williams.

Note that although Williams says the Fool Tarot card has no number, it is in fact often numbered 0. See

The Fool as Zero.”

See also Sequel — about the work, life, and afterlife of Stan Rice, husband of Anne Rice (author of The Vampire Chronicles) — and the following story from today’s N.Y. Times:

The New York Times, Jan. 16, 2003:

‘Dance of the Vampires,’
a Broadway Failure, Is Closing

By JESSE McKINLEY

In one of the costliest failures in Broadway history, the producers of “Dance of the Vampires,” a $12 million camp musical at the Minskoff Theater, will close the show on Jan. 25, having lost their entire investment.

Its gross for the week ending on Sunday [Jan. 12], $459,784, was its lowest, and that, finally, was the kiss of death for the show.

The death and arrival at heaven’s gate
of The Producers‘ producer, Sidney Glazier,
on Dec. 14, 2002, is described in the web page
Eight is a Gate.
 

Friday, January 3, 2003

Friday January 3, 2003

Filed under: General — m759 @ 3:33 PM
Tolkien is Eleventy-One Today!

In observance of this milestone, some links:

Tuesday, November 26, 2002

Tuesday November 26, 2002

Filed under: General — Tags: — m759 @ 10:23 AM

Dancing about Architecture

The title’s origin is obscure, but its immediate source is a weblog entry and ensuing comments: “Writing about music is like dancing about architecture.”

A related quote:

“At the still point, there the dance is.”

— T. S. Eliot, “Burnt Norton” in Four Quartets

“Eliot by his own admission took ‘the still point of the turning world’ in ‘Burnt Norton’ from the Fool in Williams’s The Greater Trumps.”

— Humphrey Carpenter, The Inklings (1978), Ballantine Books, 1981, page 106. Carpenter cites an “unpublished journal of Mary Trevelyan (in possession of the author).”

The following was written this morning as a comment on a weblog entry, but may stand on its own as a partial description of Eliot’s and Williams’s “dance.”

Three sermons on the Fool card, each related to Charles Williams’s novel The Greater Trumps:

To Play the Fool,
Games “Not Unlike Chesse,” and
Charles Williams and Inklings Links.

“Here is the Church,
Here is the steeple,
Open the door and see all the People.”

For some architecture that may or may not be worth dancing about, see the illustrations to Simone Weil’s remarks in my note of November 25, 2002, “The Artist’s Signature.”

Monday, September 16, 2002

Monday September 16, 2002

Filed under: General — m759 @ 3:26 PM

A Time to Gather Stones Together
(Ecclesiastes 3:5)

Readings for Yom Kippur:

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