Wednesday, August 27, 2014

Schau der Gestalt

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

(Continued from Aug. 19, 2014)

“Christian contemplation is the opposite
of distanced consideration of an image:
as Paul says, it is the metamorphosis of
the beholder into the image he beholds
(2 Cor 3.18), the ‘realisation’ of what the
image expresses (Newman). This is
possible only by giving up one’s own
standards and being assimilated to the
dimensions of the image.”

— Hans Urs von Balthasar,
The Glory of the Lord:
A Theological Aesthetics,

Vol. I: Seeing the Form
[ Schau der Gestalt ],
Ignatius Press, 1982, p. 485

A Bauhaus approach to Schau der Gestalt :

I prefer the I Ching ‘s approach to the laws of cubical space.

Sunday, August 18, 2013

Seeing a Form

Filed under: General — m759 @ 4:28 PM

A book noted here on Sept. 16, 2010—

On that date, Harvard historian of science
John E. Murdoch died.

"It's still the same old story…"

Related material: Faust + Potter in this journal.

Happy birthday, Roman Polanski.

Friday, September 17, 2010

The Galois Window

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

Yesterday’s excerpt from von Balthasar supplies some Catholic aesthetic background for Galois geometry.

That approach will appeal to few mathematicians, so here is another.

Euclid’s Window: The Story of Geometry from Parallel Lines to Hyperspace  is a book by Leonard Mlodinow published in 2002.

More recently, Mlodinow is the co-author, with Stephen Hawking, of The Grand Design  (published on September 7, 2010).

A review of Mlodinow’s book on geometry—

“This is a shallow book on deep matters, about which the author knows next to nothing.”
— Robert P. Langlands, Notices of the American Mathematical Society,  May 2002

The Langlands remark is an apt introduction to Mlodinow’s more recent work.

It also applies to Martin Gardner’s comments on Galois in 2007 and, posthumously, in 2010.

For the latter, see a Google search done this morning—


Here, for future reference, is a copy of the current Google cache of this journal’s “paged=4” page.

Note the link at the bottom of the page in the May 5, 2010, post to Peter J. Cameron’s web journal. Following the link, we find…

For n=4, there is only one factorisation, which we can write concisely as 12|34, 13|24, 14|23. Its automorphism group is the symmetric group S4, and acts as S3 on the set of three partitions, as we saw last time; the group of strong automorphisms is the Klein group.

This example generalises, by taking the factorisation to consist of the parallel classes of lines in an affine space over GF(2). The automorphism group is the affine group, and the group of strong automorphisms is its translation subgroup.

See also, in this  journal, Window and Window, continued (July 5 and 6, 2010).

Gardner scoffs at the importance of Galois’s last letter —

“Galois had written several articles on group theory, and was
merely annotating and correcting those earlier published papers.”
Last Recreations, page 156

For refutations, see the Bulletin of the American Mathematical Society  in March 1899 and February 1909.

Thursday, September 16, 2010

For the Pope in Scotland

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

From Seeing the Form, by Hans Urs von Balthasar


Related material:

  1. "This Jack, joke, poor potsherd, patch, matchwood…."
  2. Geometry Simplified
  3. The Diamond Archetype

Thursday, January 7, 2010

High Concept

Filed under: General — Tags: — m759 @ 7:00 PM

Balthasar Meets Blake

Happy birthday, Nicolas Cage.

Thursday, July 16, 2009

Thursday July 16, 2009

Filed under: General — m759 @ 4:00 PM

The White Itself

David Ellerman has written that

"The notion of a concrete universal occurred in Plato's Theory of Forms [Malcolm 1991]."

A check shows that Malcolm indeed discussed this notion ("the Form as an Ideal Individual"), but not under the name "concrete universal."

See Plato on the Self-Predication of Forms, by John Malcolm, Oxford U. Press, 1991.

From the publisher's summary:

"Malcolm…. shows that the middle dialogues do indeed take Forms to be both universals and paradigms…. He shows that Plato's concern to explain how the truths of mathematics can indeed be true played an important role in his postulation of the Form as an Ideal Individual."

Ellerman also cites another discussion of Plato published by Oxford:

Kneale and Kneale on Plato's theory of forms and 'the white itself'

For a literary context, see W. K. Wimsatt, Jr., "The Structure of the Concrete Universal," Ch. 6 in Literary Theory: An Anthology, edited by Julie Rivkin and Michael Ryan, Wiley-Blackwell, 2004.

Other uses of the phrase "concrete universal"– Hegelian and/or theological– seem rather distant from the concerns of Plato and Wimsatt, and are best left to debates between Marxists and Catholics. (My own sympathies are with the Catholics.)

Two views of "the white itself" —

 "So did God cause the big bang?
 Overcome by metaphysical lassitude,
 I finally reach over to my bookshelf
 for The Devil's Bible.
 Turning to Genesis I read:
 'In the beginning
 there was nothing.
 And God said,
 'Let there be light!'
 And there was still nothing,
 but now you could see it.'"
 -- Jim Holt, Big-Bang Theology,
    Slate's "High Concept" department 
   Fiat Lux, and After

"The world was warm and white when I was born:
Beyond the windowpane the world was white,
A glaring whiteness in a leaded frame,
Yet warm as in the hearth and heart of light."

-- Delmore Schwartz

Thursday, May 29, 2008

Thursday May 29, 2008

Filed under: General — m759 @ 1:14 AM
The Diadem
of Death

Washington Post Death Notices:

Dead on
St. Sarah’s Day,
May 24 —

Sophie B. Altman

Star of David in Washington Post death notice of Sophie B. Altman

Sophie B. Altman at Christmas 2006 dinner at DeCarlo's

Mother-in-law of
Wonder Woman
Lynda Carter
and founder and
producer of TV’s
It’s Academic

In Memoriam:

Rubén Darío

—Yo soy Gaspar. Aquí traigo el incienso.
Vengo a decir: La vida es pura y bella.
Existe Dios. El amor es inmenso.
¡Todo lo sé por la divina Estrella!

—Yo soy Melchor. Mi mirra aroma todo.
Existe Dios. El es la luz del día.
¡La blanca flor tiene sus pies en lodo
y en el placer hay la melancolía!

—Soy Baltasar. Traigo el oro. Aseguro
que existe Dios. El es el grande y fuerte.
Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

—Gaspar, Melchor y Baltasar, callaos.
Triunfa el amor, ya su fiesta os convida.
¡Cristo resurge, hace la luz del caos
y tiene la corona de la Vida!


I am Caspar. I bring with me the myrrh,
And have this to say: Life is pure and beautiful.
There is a God. His love is immense.
I can see all by the divine Star!

I am Melchior. My frankincense perfumes the air.
There is a God. He is the light of day.
The whitest flower has its stem in the mire
And in joy is also found sorrow!

I am Balthasar. I bring the gold. And I
Assure you: There is a God, great and mighty.
And I know this from the pure light
That radiates from the Diadem of Death.

Caspar, Melchior, Balthasar — say no more.
Love is triumphant, and beckons you to His feast:
Christ is born! The Chaos He has turned to light,
And he wears the crown of Life!


Wonder Woman and the Secret of the Magic Tiara

Wonder Woman and the Secret of the Magic Tiara-- The End

Powered by WordPress