Thursday, March 14, 2013

Nutshell continued

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

For the new Jesuit pope (see previous post)

Now among Log24 posts tagged "Khora" is one
from July 15, 2010, dealing with a book called
Deconstruction in a Nutshell: A Conversation with
Jacques Derrida 
, edited and with a commentary by
John D. Caputo (Fordham University Press, 1997).

Related material:

"Khora  is the felix culpa  of a passion for the impossible,
the happy fault of a poetics of the possible, the heartless
heart of an ethical and religious eschatology.
Khora  is the devil that justice demands we give his due."

— John D. Caputo, conclusion of "Abyssus Abyssum Invocat :
A Response to Kearney." Caputo's remarks followed
Richard Kearney's "Khora  or God?," pp. 107-122 in
A Passion for the Impossible: John D. Caputo in Focus ,
edited by Mark Dooley, State University of New York Press,
Albany, 2003. See "Abyssus " on pp. 123-127.

See also other uses here of the phrase "In a Nutshell."

Wednesday, March 13, 2013

Verbum Sat

Filed under: General — Tags: — m759 @ 6:00 PM


Monday, December 24, 2012

Eternal Recreation

Filed under: General,Geometry — Tags: , , , , , — m759 @ 3:17 AM

Memories, Dreams, Reflections
by C. G. Jung

Recorded and edited By Aniela Jaffé, translated from the German
by Richard and Clara Winston, Vintage Books edition of April 1989

From pages 195-196:

“Only gradually did I discover what the mandala really is:
‘Formation, Transformation, Eternal Mind’s eternal recreation.’*
And that is the self, the wholeness of the personality, which if all
goes well is harmonious, but which cannot tolerate self-deceptions.”

* Faust , Part Two, trans. by Philip Wayne (Harmondsworth,
England, Penguin Books Ltd., 1959), p. 79. The original:

                   … Gestaltung, Umgestaltung, 
  Des ewigen Sinnes ewige Unterhaltung….

Jung’s “Formation, Transformation” quote is from the realm of
the Mothers (Faust Part Two, Act 1, Scene 5: A Dark Gallery).
The speaker is Mephistopheles.

See also Prof. Bruce J. MacLennan on this realm
in a Web page from his Spring 2005 seminar on Faust:

“In alchemical terms, F is descending into the dark, formless
primary matter from which all things are born. Psychologically
he is descending into the deepest regions of the
collective unconscious, to the source of life and all creation.
Mater (mother), matrix (womb, generative substance), and matter
all come from the same root. This is Faust’s next encounter with
the feminine, but it’s obviously of a very different kind than his
relationship with Gretchen.”

The phrase “Gestaltung, Umgestaltung ” suggests a more mathematical
approach to the Unterhaltung . Hence

Part I: Mothers

“The ultimate, deep symbol of motherhood raised to
the universal and the cosmic, of the birth, sending forth,
death, and return of all things in an eternal cycle,
is expressed in the Mothers, the matrices of all forms,
at the timeless, placeless originating womb or hearth
where chaos is transmuted into cosmos and whence
the forms of creation issue forth into the world of
place and time.”

— Harold Stein Jantz, The Mothers in Faust:
The Myth of Time and Creativity 
Johns Hopkins Press, 1969, page 37

Part II: Matrices


Part III: Spaces and Hypercubes

Click image for some background.

Part IV: Forms

Forms from the I Ching :

Click image for some background.

Forms from Diamond Theory :

Click image for some background.

Tuesday, February 15, 2011

Annals of Symbolism

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

A phrase from last night's post— "God's empty chair."

For related material from this journal, see The Empty Chair.

A related scene from mathematics education (the theme of the new March 2011 AMS Notices )—

IMAGE- Richard Kiley in 'Blackboard Jungle,' with grids and broken records

"Plato acknowledges how khora  challenges our normal categories
 of rational understanding. He suggests that we might best approach it
 through a kind of dream  consciousness."

  –Richard Kearney, quoted here Sunday afternoon

"You make me feel like I'm living a teenage dream."

Song at Sunday night's Grammy awards

"Put your glad rags on and join me, hon…"

Monday, February 14, 2011

Simplify (continued)

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

"Plato acknowledges how khora  challenges our normal categories
 of rational understanding. He suggests that we might best approach it
 through a kind of dream  consciousness."
  —Richard Kearney, quoted here yesterday afternoon

"You make me feel like I'm living a teenage dream."
 — Song at last night's Grammy awards

Image-- Richard Kiley with record collection in 'Blackboard Jungle,' 1955

Richard Kiley in "Blackboard Jungle" (1955)
Note the directive on the blackboard.

Quoted here last year on this date

Alexandre Borovik's Mathematics Under the Microscope  (American Mathematical Society, 2010)—

"Once I mentioned to Gelfand that I read his Functions and Graphs ; in response, he rather sceptically asked me what I had learned from the book. He was delighted to hear my answer: 'The general principle of always looking at the simplest possible example.'….

So, let us look at the principle in more detail:

Always test a mathematical theory on the simplest possible example…

This is a banality, of course. Everyone knows it; therefore, almost no one follows it."

Related material— Geometry Simplified and A Simple Reflection Group of Order 168.

"Great indeed is the riddle of the universe.
 Beautiful indeed is the source of truth."

– Shing-Tung Yau, Chairman,
Department of Mathematics, Harvard University

"Always keep a diamond in your mind."

King Solomon at the Paradiso

IMAGE-- Imaginary movie poster- 'The Galois Connection'- from stoneship.org

Image from stoneship.org

Sunday, February 13, 2011

Where Entertainment is God (continued)

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

"… the clocks were striking thirteen…"

"Entertainment continued," a Log24 post last year on this date, suggests…

A reading from Richard Kearney's Strangers, Gods and Monsters  (Routledge, 2003)—

IMAGE- Richard Kearney on 'khora' in 'Strangers, Gods and Monsters'

Neither earth nor air nor fire nor water… perhaps a Fifth Element  ?

Thursday, July 15, 2010

Brightness at Noon, continued

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

"What exactly was Point Omega?"

This is Robert Wright in Nonzero: The Logic of Human Destiny.

Wright is discussing not the novel Point Omega  by Don DeLillo,
but rather a (related) concept of  the Jesuit philosopher Pierre Teilhard de Chardin.

My own idiosyncratic version of a personal "point omega"—

Image- Josefine Lyche work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

Click for further details.

The circular sculpture in the foreground
is called by the artist "The Omega Point."
This has been described as
"a portal that leads in or out of time and space."

For some other sorts of points, see the drawings
on the wall and Geometry Simplified

Image-- The trivial two-point affine space and the trivial one-point projective space, visualized

The two points of the trivial affine space are represented by squares,
and the one point of the trivial projective space is represented by
a line segment separating the affine-space squares.

For related darkness  at noon, see Derrida on différance
as a version of Plato's khôra

(Click to enlarge.)

Image-- Fordham University Press on Derrida, differance, and khora

The above excerpts are from a work on and by Derrida
published in 1997 by Fordham University,
a Jesuit institutionDeconstruction in a Nutshell

Image-- A Catholic view of Derrida

For an alternative to the Villanova view of Derrida,
see Angels in the Architecture.

Tuesday, July 13, 2010

Quest for the Lost Origin…

Filed under: General — Tags: — m759 @ 6:12 PM

Project Management at Villanova

Image-- NY Times review of 'Sorcerer's Apprentice' with ad for Project Management Institute program at Villanova University

Yesterday's noon post, "Lying Forth," linked to a passage by Walter A. Brogan, Professor of Philosophy at Villanova University.

A related Brogan remark for Harrison Ford's birthday—

"The last few pages of the text 'Différance' [an essay by Derrida] are a refutation of the nostalgia and hope involved in Heidegger's ontology, a rejection of the quest for the lost origin and final word."

Walter A. Brogan, "The Original Difference," pp. 31-40 in Derrida and Différance, ed. by David C. Wood and Robert Bernasconi (Northwestern University Press, 1988), p. 32

See, too, "Make a Différance."

Tuesday, July 6, 2010

Window, continued

“Simplicity, simplicity, simplicity!
I say, let your affairs be as two or three,
and not a hundred or a thousand;
instead of a million count half a dozen,
and keep your accounts on your thumb-nail.”
— Henry David Thoreau, Walden

This quotation is the epigraph to
Section 1.1 of Alexandre V. Borovik’s
Mathematics Under the Microscope:
Notes on Cognitive Aspects of Mathematical Practice
(American Mathematical Society,
Jan. 15, 2010, 317 pages).

From Peter J. Cameron’s review notes for
his new course in group theory


From Log24 on June 24

Geometry Simplified

Image-- The Four-Point Plane: A Finite Affine Space
(an affine  space with subsquares as points
and sets  of subsquares as hyperplanes)

Image-- The Three-Point Line: A Finite Projective Space
(a projective  space with, as points, sets
of line segments that separate subsquares)


Show that the above geometry is a model
for the algebra discussed by Cameron.

Saturday, July 3, 2010

Beyond the Limits

Filed under: General,Geometry — Tags: — m759 @ 7:29 PM

"Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation…."

– Don DeLillo, Point Omega

Capitalized, the letter omega figures in the theology of two Jesuits, Teilhard de Chardin and Gerard Manley Hopkins. For the former, see a review of DeLillo. For the latter, see James Finn Cotter's Inscape  and "Hopkins and Augustine."

The lower-case omega is found in the standard symbolic representation of the Galois field GF(4)—

GF(4) = {0, 1, ω, ω2}

A representation of GF(4) that goes beyond the standard representation—


Here the four diagonally-divided two-color squares represent the four elements of GF(4).

The graphic properties of these design elements are closely related to the algebraic properties of GF(4).

This is demonstrated by a decomposition theorem used in the proof of the diamond theorem.

To what extent these theorems are part of "a saga of created reality" may be debated.

I prefer the Platonist's "discovered, not created" side of the debate.

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