Log24

Thursday, August 17, 2017

Down in the Jungle Room

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

See also other posts now tagged Jungle Room.

Friday, June 16, 2017

Chalkroom Jungle

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

At MASS MoCA, the installation "Chalkroom" quotes a lyric —

Oh beauty in all its forms
funny how hatred can also be a beautiful thing
When it's as sharp as a knife
as hard as a diamond

Perfect

— From "One Beautiful Evening," by Laurie Anderson.

See also the previous post and "Smallest Perfect" in this journal.

Monday, October 22, 2018

For Connoisseurs of Conceptual Art

Filed under: General — Tags: — m759 @ 1:32 PM

In related news . . .

Sunday, October 21, 2018

For Connoisseurs of Bad Art

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

Yesterday afternoon's post "Study in Blue and Pink" featured 
an image related to the "Blade and Chalice" of Dan Brown 

Requiem for a comics character known as "The Blue Blade" —

 

"We all float down here."

About the corresponding "Pink Chalice," the less said the better.

Saturday, October 20, 2018

Study in Blue and Pink

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

Related Log24 posts — See Blade + Chalice.

Wednesday, August 16, 2017

Punctum

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

Or:  Every Picture Tells a Story  (Continued)

Related material —

The New York Times  online today, in a book review

"What if . . . Barthes was murdered? . . . in order to
procure a document that Barthes possessed . . . .
That document explained that, beyond the six
functions of language proposed by the Russian
linguist Roman Jakobson, there was a seventh
secret one:  an occult kind of language-use
guaranteed to persuade, a 'magic' power of
control over a listener."

See also Barthes in this  journal.

"Down in the Jungle Room" — Marc Cohn

Monday, August 14, 2017

Sound Track

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

Two songs by Chuck Berry on Chess Records in 1958

Sweet Little Sixteen  and  Sweet Little Rock and Roller .

Rock and Roller  begins

She's 9 years old and sweet as she can be
All dressed up like a downtown Christmas tree
Dancin' and hummin' a rock-roll melody

For meditations on Sixteen , see Berry + Sixteen in this journal.

A meditation on Rock and Roller —

Related material — From the above post's date,
March 21, 2017, a memoir by one Siva Vaidhyanathan,
"Robertson Professor of Media Studies and Director of
the Center for Media and Citizenship at the University of Virginia."

Thursday, June 23, 2016

Raiders of the Lost Code

Filed under: General — m759 @ 11:00 AM

From a web page

Breaking the Code of the Archetypal Self:
An Introductory Overview of the Research Discoveries
Leading to Neo-Jungian Structural Psychoanalysis

Dr. Moore will introduce his research and discoveries
with regard to the deep structures of the Self.
Tracing the foundations in the tradition of Jung’s
affirmation of the collective unconscious, Moore
will present his “decoding of the Diamond Body,”
a mapping of the deep structures of the Great Code
of the psyche. . . .

From the same web site

Googling "Jung" + "Diamond Body" shows that
Moore's terminology differs from Jung's.
The octahedron that Moore apparently associates
with his "diamond body" was discussed by Jung
in a different context. See selections from Ch. 14
of Jung's Aion
 "The Structure and Dynamics of the Self."

Dr. Moore appears as well in the murder-suicide story 
of last night's 11:18 PM ET post.

For the relevance of Aion  to "deep structures,"
see Jung + Diamond + Structure in this  journal
and, more specifically, "Deep  Structure."

Thursday, April 21, 2016

The Alchemist’s Chessboard

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

Material related to the previous post and to Alfred Bester's
1981 followup to The Stars My Destination  titled The Deceivers

The Lapis Philosophorum :

"The lapis  was thought of as a unity and therefore often stands for the prima materia  in general."
— Aion , by C. G. Jung

"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

And from Bester's The Deceivers :

Meta  Physics

"'… Think of a match.  You've got a chemical head of potash, antimony, and stuff, full of energy waiting to be released.  Friction does it.  But when Meta  excites and releases energy, it's like a stick of dynamite compared to a match.  It's the chess legend for real.'

'I don't know it.'

'Oh, the story goes that a philosopher invented chess for the amusement of an Indian rajah.  The king was so delighted that he told the inventor to name his reward and he'd get it, no matter what.  The philosopher asked that one grain of rice be placed on the first square of the chessboard, two on the second, four on the third, and so on to the sixty-fourth.'

'That doesn't sound like much.'"

Related material :

Geometry of the I Ching

Friday, September 16, 2011

Icons

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

Background: Jung's Aion in this journal discusses this
figure from finite geometry's diamond theorem

http://www.log24.com/log/pix11B/110915-FourDiamondsIcon.gif

Fig. A

This resembles a figure that served Jung
as a schema of the Self

http://www.log24.com/log/pix11B/110915-Jung-FourDiamonds.gif

Fig. B

Fig. A, with color variations, serves as the core
of many automatically generated Identicons
a different sort of self-symbol.

Examples from Sept. 6 at MathOverflow

http://www.log24.com/log/pix11B/110915-ChuangGravatar.png     http://www.log24.com/log/pix11B/110915-JacobLurieGravatar.png

A user wanting to custom-tailor his self-symbol should consider
the following from the identicon service Gravatar

1. User Submissions.  " you hereby do and shall grant to Automattic a worldwide, perpetual, irrevocable, royalty-free and fully-paid, transferable (including rights to sublicense) right to perform the Services (e.g., to use, modify, reproduce, distribute, prepare derivative works of, display, perform, and otherwise fully exercise and exploit all intellectual property, publicity, and moral rights with respect to any User Submissions, and to allow others to do so)."

Sounds rather Faustian.

Saturday, June 19, 2010

Imago Creationis

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

Image-- The Four-Diamond Tesseract

In the above view, four of the tesseract's 16
vertices are overlaid by other vertices.
For views that are more complete and
moveable, see Smith's tesseract page.

Four-Part Tesseract Divisions

http://www.log24.com/log/pix10A/100619-TesseractAnd4x4.gif

The above figure shows how four-part partitions
of the 16 vertices  of a tesseract in an infinite
Euclidean  space are related to four-part partitions
of the 16 points  in a finite Galois  space

Euclidean spaces versus Galois spaces
in a larger context—

 

 


Infinite versus Finite

The central aim of Western religion —

"Each of us has something to offer the Creator...
the bridging of
                 masculine and feminine,
                      life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist  (1998)

The central aim of Western philosophy —

              Dualities of Pythagoras
              as reconstructed by Aristotle:
                 Limited     Unlimited
                     Odd     Even
                    Male     Female
                   Light      Dark
                Straight    Curved
                  ... and so on ....

"Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy."
— Jamie James in The Music of the Spheres  (1993)

Another picture related to philosophy and religion—

Jung's Four-Diamond Figure from Aion

http://www.log24.com/log/pix10A/100615-JungImago.gif

This figure was devised by Jung
to represent the Self. Compare the
remarks of Paul Valéry on the Self—

Flight from Eden: The Origins of Modern Literary Criticism and Theory, by Steven Cassedy, U. of California Press, 1990, pages 156-157—

 

 

Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. "Every act of understanding is based on a group," he says (C, 1:331). "My specialty— reducing everything to the study of a system closed on itself and finite" (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one "group" undergoes a "transformation" and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: "The S[elf] is invariant, origin, locus or field, it's a functional property of consciousness" (C, 15:170 [2:315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind's momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. "Mathematical science…  reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind" (O, 1:36). "Psychology is a theory of transformations, we just need to isolate the invariants and the groups" (C, 1:915). "Man is a system that transforms itself" (C, 2:896).

Notes:

  Paul Valéry, Oeuvres  (Paris: Pléiade, 1957-60)

C   Valéry, Cahiers, 29 vols. (Paris: Centre National de le Recherche Scientifique, 1957-61)

Note also the remarks of George David Birkhoff at Rice University
in 1940 (pdf) on Galois's theory of groups and the related
"theory of ambiguity" in Galois's testamentary letter—

… metaphysical reasoning always relies on the Principle of Sufficient Reason, and… the true meaning of this Principle is to be found in the “Theory of Ambiguity” and in the associated mathematical “Theory of Groups.”

If I were a Leibnizian mystic, believing in his “preestablished harmony,” and the “best possible world” so satirized by Voltaire in “Candide,” I would say that the metaphysical importance of the Principle of Sufficient Reason and the cognate Theory of Groups arises from the fact that God thinks multi-dimensionally* whereas men can only think in linear syllogistic series, and the Theory of Groups is the appropriate instrument of thought to remedy our deficiency in this respect.

* That is, uses multi-dimensional symbols beyond our grasp.

Related material:

Imago Creationis

A medal designed by Leibniz to show how
binary arithmetic mirrors the creation by God
of something (1) from nothing (0).

http://www.log24.com/log/pix10A/100618-LeibnizMedaille.jpg

Another array of 16 strings of 0's and 1's, this time
regarded as coordinates rather than binary numbers—

Frame of Reference

http://www.log24.com/log/pix10A/100619-ReferenceFrame.gif

The Diamond Theorem

http://www.log24.com/log/pix10A/100619-Dtheorem.gif

Some context by a British mathematician —

http://www.log24.com/log/pix10A/100619-Cameron.gif

Imago

by Wallace Stevens

Who can pick up the weight of Britain, 
Who can move the German load 
Or say to the French here is France again? 
Imago. Imago. Imago. 

It is nothing, no great thing, nor man 
Of ten brilliancies of battered gold 
And fortunate stone. It moves its parade 
Of motions in the mind and heart, 

A gorgeous fortitude. Medium man 
In February hears the imagination's hymns 
And sees its images, its motions 
And multitudes of motions 

And feels the imagination's mercies, 
In a season more than sun and south wind, 
Something returning from a deeper quarter, 
A glacier running through delirium, 

Making this heavy rock a place, 
Which is not of our lives composed . . . 
Lightly and lightly, O my land, 
Move lightly through the air again.

Tuesday, June 15, 2010

Imago, Imago, Imago

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

Recommended— an online book—

Flight from Eden: The Origins of Modern Literary Criticism and Theory,
by Steven Cassedy, U. of California Press, 1990.

See in particular

Valéry and the Discourse On His Method.

Pages 156-157—

Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. “Every act of understanding is based on a group,” he says (C, 1:331). “My specialty—reducing everything to the study of a system closed on itself and finite” (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one “group” undergoes a “transformation” and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: “The S[elf] is invariant, origin, locus or field, it’s a functional property of consciousness” (C, 15:170 [2: 315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind’s momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. “Mathematical science . . . reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind” (O, 1:36). “Psychology is a theory of transformations, we just need to isolate the invariants and the groups” (C, 1:915). “Man is a system that transforms itself” (C, 2:896).

Notes:

  Paul Valéry, Oeuvres (Paris: Pléiade, 1957-60)

C   Valéry, Cahiers, 29 vols. (Paris: Centre National de le Recherche Scientifique, 1957-61)

Compare Jung’s image in Aion  of the Self as a four-diamond figure:

http://www.log24.com/log/pix10A/100615-JungImago.gif

and Cullinane’s purely geometric four-diamond figure:

http://www.log24.com/log/pix10A/100615-FourD.gif

For a natural group of 322,560 transformations acting on the latter figure, see the diamond theorem.

What remains fixed (globally, not pointwise) under these transformations is the system  of points and hyperplanes from the diamond theorem. This system was depicted by artist Josefine Lyche in her installation “Theme and Variations” in Oslo in 2009.  Lyche titled this part of her installation “The Smallest Perfect Universe,” a phrase used earlier by Burkard Polster to describe the projective 3-space PG(3,2) that contains these points (at right below) and hyperplanes (at left below).

Image-- Josefine Lyche's combination of Polster's phrase with<br /> Cullinane's images in her gallery show, Oslo, 2009-- 'The Smallest<br /> Perfect Universe -- Points and Hyperplanes'

Although the system of points (at right above) and hyperplanes (at left above) exemplifies Valéry’s notion of invariant, it seems unlikely to be the sort of thing he had in mind as an image of the Self.

Saturday, December 5, 2009

Holiday Book

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

Time and Chance, continued…

NY Lottery numbers today–
Midday 401, Evening 717  

_________________________________________________

From this journal on 4/01, 2009:

The Cruelest Month

Fictional Harvard professor of symbology Robert Langdon, as portrayed by Tom Hanks

"Langdon sensed she was
      toying with him…."

Dan Brown

___________________________________________

From this journal on 7/17, 2008:

Jung’s four-diamond figure from
Aiona symbol of the self

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

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

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

For related dynamic movements,
see the Diamond 16 Puzzle
and the diamond theorem.

______________________________________________
 
A piece related to both of the above posts–
 
"The Symbologist," a review, respectful despite the editor's sarcastic title, of Jung's Red Book in the December 6th New York Times Book Review.

Thursday, June 25, 2009

Thursday June 25, 2009

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

“… T. S. Eliot tried to recompose,
   in Four Quartets, the fragments
   he had grieved over
    in The Waste Land.”

— “Beauty and Desecration,”
   Roger Scruton
 (link at aldaily.com today)

The formula reproduces exactly the essential features of the symbolic process of transformation. It shows the rotation of the mandala, the antithetical play of complementary (or compensatory) processes, then the apocatastasis, i.e., the restoration of an original state of wholeness….”

— Carl G. Jung in Aion

Related material:
this journal
one year ago today.

Saturday, March 28, 2009

Saturday March 28, 2009

Filed under: General,Geometry — m759 @ 11:07 PM

The Rest
of the Story

Today's previous entry discussed the hermeneutics of the midday NY and PA lottery numbers.

The rest of the story:
 

The Revelation Game
(continued from 7/26, 2008)

 
Lotteries
on Reba's
birthday,
2009
Pennsylvania
(No revelation)
New York
(Revelation)
Mid-day
(No belief)
No belief,
no revelation

726
Revelation
without belief

378
Evening
(Belief)
Belief without
revelation

006
Belief and
revelation

091

Interpretations of the evening numbers–

The PA evening number, 006, may be viewed as a followup to the PA midday 726 (or 7/26, the birthday of Kate Beckinsale and Carl Jung). Here 006 is the prestigious "00" number assigned to Beckinsale.
 

Will: Do you like apples?     
Clark: Yeah.                       
Will: Well, I got her number.
 How do you like them apples?

— "Good Will Hunting

Kate Beckinsale in 'Underworld: Evolution'

The NY evening number, 091, may be viewed as a followup to the NY midday 378 (the number of pages in The Innermost Kernel by Suzanne Gieser, published by Springer, 2005)–

Page 91: The entire page is devoted to the title of the book's Part 3– "The Copenhagen School and Psychology"–
 

Page 91 of 'The Innermost Kernel' by Suzanne Gieser, Springer 2005

The next page begins: "With the crisis of physics, interest in epistemological and psychological questions grew among many theoretical physicists. This interest was particularly marked in the circle around Niels Bohr."
 

A particularly
marked circle
 from March 15:

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

The circle above is
marked with a version of
the classic Chinese symbol
adopted as a personal emblem
by Danish physicist Niels Bohr,
leader of the Copenhagen School.

"Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined

On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come."

-- Wallace Stevens,
  "Notes Toward a Supreme Fiction,"
   Canto IV of "It Must Change"

The square above is marked
with a graphic design
related to the four-diamond
figure of Jung's Aion.

Monday, March 9, 2009

Monday March 9, 2009

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

Humorism

'The Manchurian Candidate' campaign button

"Always with a
little humor."
Dr. Yen Lo  

Diamond diagram of the four humors, the four qualities, the four elements, the four seasons, and four colors

From Temperament: A Brief Survey

For other interpretations
of the above shape, see
The Illuminati Diamond.

from Jung's Aion:

"From the circle and quaternity motif is derived the symbol of the geometrically formed crystal and the wonder-working stone. From here analogy formation leads on to the city, castle, church, house, room, and vessel. Another variant is the wheel. The former motif emphasizes the ego’s containment in the greater dimension of the self; the latter emphasizes the rotation which also appears as a ritual circumambulation. Psychologically, it denotes concentration on and preoccupation with a centre…." –Jung, Collected Works, Vol. 9, Part II, paragraph 352

As for rotation, see the ambigrams in Dan Brown's Angels & Demons (to appear as a film May 15) and the following figures:

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison
 
Click on image
for a related puzzle.
For a solution, see
 The Diamond Theorem.

A related note on
"Angels & Demons"
director Ron Howard:

Director Ron Howard with illustration of the fictional discipline 'symbology'
 
Click image for details.

Monday, February 9, 2009

Monday February 9, 2009

Filed under: General,Geometry — m759 @ 12:12 PM
The Vision Thing

The British Academy Awards last night showed two Paul Newman clips:

“Sometimes nothin’ can be a real cool hand.”

“Boy, I got vision and the rest of the world wears bifocals.”

Related material: This journal, September 2008.

As for bifocals…

Ben Franklin
 
Pennsylvania Lottery
 
PA Lottery Feb. 8, 2009-- Midday 017, Evening 717
Versus
7/17:

Aion
A symbol
   of the self

Four-diamond symbol of the self from Jung's 'Aion'

Thursday, January 8, 2009

Thursday January 8, 2009

Filed under: General,Geometry — m759 @ 11:07 PM
Report of Arrival

A PBS broadcast of Cyrano de Bergerac was shown yesterday nationally and this evening, a day late, by WNED TV, Buffalo.

From the translation by Anthony Burgess:

Cyrano speaks of falling leaves–

  They fall well. With a sort of panache.
  They plume down in their last
  Loveliness, disguising their fear
  Of being dried and pounded to ash
  To mix with the common dust.
  They go in grace, making their fall appear
  Like flying.
ROXANE  You’re melancholy today.
CYRANO  Never. I’m not the melancholy sort.
ROXANE  Very well, then. We’ll let
  The leaves of the fall fall while you
  Turn the leaves of my gazette.
  What’s new at court?
CYRANO … There have been some scandals
  To do with witches. A bishop went to heaven,
  Or so it’s believed: there’s been as yet no report
  Of his arrival….”

Later….

CYRANO … See it there, a white plume
  Over the battle– A diamond in the ash
  Of the ultimate combustion–
  My panache.”


Related material:

Today’s previous entry
and the Epiphany
link to the
four-diamond symbol
in Jung’s Aion
with an epigraph by
Gerard Manley Hopkins:

That Nature is a Heraclitean Fire…

Tuesday, January 6, 2009

Tuesday January 6, 2009

Filed under: General,Geometry — m759 @ 12:00 AM
Archetypes, Synchronicity,
and Dyson on Jung

The current (Feb. 2009) Notices of the American Mathematical Society has a written version of Freeman Dyson’s 2008 Einstein Lecture, which was to have been given in October but had to be canceled. Dyson paraphrases a mathematician on Carl Jung’s theory of archetypes:

“… we do not need to accept Jung’s theory as true in order to find it illuminating.”

The same is true of Jung’s remarks on synchronicity.

For example —

Yesterday’s entry, “A Wealth of Algebraic Structure,” lists two articles– each, as it happens, related to Jung’s four-diamond figure from Aion as well as to my own Notes on Finite Geometry. The articles were placed online recently by Cambridge University Press on the following dates:

R. T. Curtis’s 1974 article defining his Miracle Octad Generator (MOG) was published online on Oct. 24, 2008.

Curtis’s 1987 article on geometry and algebraic structure in the MOG was published online on Dec. 19, 2008.

On these dates, the entries in this journal discussed…

Oct. 24:
Cube Space, 1984-2003

Material related to that entry:

Dec. 19:
Art and Religion: Inside the White Cube

That entry discusses a book by Mark C. Taylor:

The Picture in Question: Mark Tansey and the Ends of Representation (U. of Chicago Press, 1999).

In Chapter 3, “Sutures of Structures,” Taylor asks —

“What, then, is a frame, and what is frame work?”

One possible answer —

Hermann Weyl on the relativity problem in the context of the 4×4 “frame of reference” found in the above Cambridge University Press articles.

“Examples are the stained-glass
windows of knowledge.”
— Vladimir Nabokov 

Thursday, July 17, 2008

Thursday July 17, 2008

Filed under: General,Geometry — m759 @ 4:28 PM
CHANGE
 FEW CAN BELIEVE IN

Continued from June 18.

Jungian Symbols
of the Self —

User icons (identicons) from Secret Blogging Seminar
Compare and contrast:

Jung’s four-diamond figure from
Aiona symbol of the self

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

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

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

For related dynamic movements,
see the Diamond 16 Puzzle
and the diamond theorem.

Wednesday, June 25, 2008

Wednesday June 25, 2008

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

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

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

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

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

Diamond of the four ancient elements, figure by John Baez

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

Diamond  showing transformation of the four ancient elements

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

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

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

— Carl Gustav Jung

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

Related material:

Log24 entries of June 9, 2008, and

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

Thursday, June 21, 2007

Thursday June 21, 2007

Filed under: General,Geometry — m759 @ 4:30 PM

Schopenhauer on the Kernel of Eternity

Philos Website

“Ich aber, hier auf dem objektiven Wege, bin jetzt bemüht, das Positive der Sache nachzuweisen, daß nämlich das Ding an sich von der Zeit und Dem, was nur durch sie möglich ist, dem Entstehen und Vergehen, unberührt bleibt, und daß die Erscheinungen in der Zeit sogar jenes rastlos flüchtige, dem Nichts zunächst stehende Dasein nicht haben könnten, wenn nicht in ihnen ein Kern aus der Ewigkeit* wäre. Die Ewigkeit ist freilich ein Begriff, dem keine Anschauung zum Grunde liegt: er ist auch deshalb bloß negativen Inhalts, besagt nämlich ein zeitloses Dasein. Die Zeit ist demnach ein bloßes Bild der Ewigkeit, ho chronos eikôn tou aiônos,** wie es Plotinus*** hat: und ebenso ist unser zeitliches Dasein das bloße Bild unsers Wesens an sich. Dieses muß in der Ewigkeit liegen, eben weil die Zeit nur die Form unsers Erkennens ist: vermöge dieser allein aber erkennen wir unser und aller Dinge Wesen als vergänglich, endlich und der Vernichtung anheimgefallen.”

*    “a kernel of eternity
**  “Time is the image of eternity.”
*** “wie es Plotinus hat”–
       Actually, not Plotinus, but Plato,
       according to Diogenes Laertius.

Related material:

Time Fold,

J. N. Darby,
On the Greek Words for
Eternity and Eternal

(aion and aionios),”

Carl Gustav Jung, Aion,
which contains the following
four-diamond figure,

Jung's four-diamond figure

and Jung and the Imago Dei.

Wednesday, June 6, 2007

Wednesday June 6, 2007

Filed under: General,Geometry — m759 @ 11:07 AM
It is now 3:07 AM
June 7 in New Zealand.
Today at Cullinane College:

Examination Day

IMAGE- Rogue Winter with spear, Jupiter in background, on cover of 'The Deceivers,' a novel by Alfred Bester.

(For the college curriculum,
see the New Zealand
Qualifications Authority.)

If Cullinane College were Hogwarts–

Last-minute exam info:

The Lapis Philosophorum

"The lapis was thought of as a unity and therefore often stands for the prima materia in general."
Aion, by C. G. Jung

"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

And from Bester's The Deceivers:

Meta Physics

"'… Think of a match.  You've got a chemical head of potash, antimony, and stuff, full of energy waiting to be released.  Friction does it.  But when Meta excites and releases energy, it's like a stick of dynamite compared to a match.  It's the chess legend for real.'

'I don't know it.'

'Oh, the story goes that a philosopher invented chess for the amusement of an Indian rajah.  The king was so delighted that he told the inventor to name his reward and he'd get it, no matter what.  The philosopher asked that one grain of rice be placed on the first square of the chessboard, two on the second, four on the third, and so on to the sixty-fourth.'

'That doesn't sound like much.'

'So the rajah said. …'"

Related material:

Geometry of the I Ching
 

Saturday, August 26, 2006

Saturday August 26, 2006

Filed under: General,Geometry — Tags: — m759 @ 8:00 PM
Philosopher's Rock
 
(continued from  

previous entry)

"Alcatraz, Spanish for pelican, was named Isla de los Alcatraces after the birds that were the island's only inhabitants." —Bay City Guide

Related material

Thomas Kuhn's "Pelican Brief":

"… the Philosopher’s Stone was a psychic rather than a physical product.  It symbolized one’s Self…."

Philosopher's Pelican:

"The formula presents a symbol of the self…."

Jung and the Imago Dei:

"… Jung presents a diagram to illustrate the dynamic movements of the self…."

…the movement of
a self in the rock…

Stevens, The Rock, and Piranesi's Prisons

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

Thursday, December 8, 2005

Thursday December 8, 2005

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

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

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

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

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

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

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

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

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

Related material: 

  The diamond theorem

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

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

Saturday, October 29, 2005

Saturday October 29, 2005

Filed under: General — m759 @ 3:17 PM

Aion

From AP’s “Today in History” for October 29:

On this date:
In 1967, the counter-culture musical “Hair” opened off-Broadway.

Related material:

Jung on Pisces and Aquarius in Aion

The Da Vinci Code and Symbology at Harvard

“This is the turning point
Funny
But by the end
Bitter and serious and deadly”

— Jill O’Hara singing “The Climax
    in “Hair”
    (original cast recording)

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)

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.

Friday, February 20, 2004

Friday February 20, 2004

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

The Da Vinci Code
and
Symbology at Harvard

The protagonist of the recent bestseller The Da Vinci Code is Robert Langdon, "a professor of Religious Symbology at Harvard University."  A prominent part in the novel is played by the well-known Catholic organization Opus Dei.  Less well known (indeed, like Langdon, nonexistent) is the academic discipline of "symbology."  (For related disciplines that do exist, click here.) What might a course in this subject at Harvard be like?

Harvard Crimson, April 10, 2003:

While Opus Dei members said that they do not refer to their practices of recruitment as "fishing," the Work’s founder does describe the process of what he calls "winning new apostles" with an aquatic metaphor.

Point #978 of The Way invokes a passage in the New Testament in which Jesus tells Peter that he will make him a "fisher of men." The point reads:

" ‘Follow me, and I will make you into fishers of men.’ Not without reason does our Lord use these words: men—like fish—have to be caught by the head. What evangelical depth there is in the ‘intellectual apostolate!’ ”

IMAGE- Escher, 'Fishes and Scales'

IMAGE- Cullinane, 'Invariance'

Exercise for Symbology 101:

Describe the symmetry
in each of the pictures above.
Show that the second picture
retains its underlying structural
symmetry under a group of
322,560 transformations.

Having reviewed yesterday's notes
on Gombrich, Gadamer, and Panofsky,
discuss the astrological meaning of
the above symbols in light of
today's date, February 20.

Extra credit:

Relate the above astrological
symbolism to the four-diamond
symbol in Jung's Aion.

Happy metaphors!

Robert Langdon

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