Log24

Sunday, June 2, 2019

Interpenetration

Filed under: General — Tags: — m759 @ 10:32 pm

A remark on coordinatization linked to by John Baez today —

This suggests a more historical perspective:

See as well a search for Interpenetration in this  journal.

Monday, November 28, 2016

Interpenetration

Filed under: General — Tags: , — m759 @ 3:00 pm

Or:  A Candle for Sunrise  

(Continued)

Commentary —

“Looking carefully at Golay’s code is like staring into the sun.”

— Richard Evan Schwartz

Saturday, November 5, 2016

Interpenetration

Filed under: General — Tags: — m759 @ 7:31 pm

Wikipedia— "The first Million Mask March occurred in 2013."

A check of the date of that march in this journal yields

See as well, more generally, "Interpenetration" in this journal.

Thursday, October 31, 2013

Interpenetrative Ogdoad

Filed under: General,Geometry — m759 @ 2:21 pm

The title is from an essay by James C. Nohrnberg

(Click to enlarge.)

"Just another shake of the kaleidoscope" —

Related material:

Kaleidoscope Puzzle,  
Design Cube 2x2x2, and 
Through the Looking Glass: A Sort of Eternity.

Saturday, February 5, 2022

Mathieu Cube Labeling

Filed under: General — Tags: , , , , — m759 @ 2:08 pm

Shown below is an illustration from "The Puzzle Layout Problem" —

Exercise:  Using the above numerals 1 through 24
(with 23 as 0 and 24 as ∞) to represent the points 
, 0, 1, 2, 3 … 22  of the projective line over GF(23),
reposition the labels 1 through 24 in the above illustration
so that they appropriately* illustrate the cube-parts discussed
by Iain Aitchison in his March 2018 Hiroshima slides on 
cube-part permutations by the Mathieu group M24

A note for Northrop Frye —

Interpenetration in the eightfold cube — the three midplanes —

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

A deeper example of interpenetration:

Aitchison has shown that the Mathieu group M24 has a natural
action on the 24 center points of the subsquares on the eightfold
cube's six faces (four such points on each of the six faces). Thus
the 759 octads of the Steiner system S(5, 8, 24) interpenetrate
on the surface of the cube.

* "Appropriately" — I.e. , so that the Aitchison cube octads correspond
exactly, via the projective-point labels, to the Curtis MOG octads.

Wednesday, February 2, 2022

Groundhog Day Metamorphosis

Filed under: General — m759 @ 1:11 pm

" Whether correspondences were achieved by means of
wordplay, atavistic formal resemblances, or serendipitous
coincidences, the attendant metamorphosis of literary
material into Frye's own scripture could become tiresome:
'just another shake of the kaleidoscope.' " [Link added.]

— From p. 61 of "The Master of the Myth of Literature:
An Interpenetrative Ogdoad for Northrop Frye,"
by Nohrnberg, James C., Comparative Literature
Vol. 53 (1), pp. 58-82, Duke University Press, 
January 1, 2001.

Saturday, March 13, 2021

Eternal Spark

Filed under: General — Tags: , — m759 @ 9:43 am

According to Lt. Col. Wayne M. McDonnell in June 1983 —

“… it is accurate to observe that when a person experiences
the out-of- body state he is, in fact, projecting that eternal spark
of consciousness and memory which constitutes the ultimate
source of his identity….”

— Section 27, “Consciousness in Perspective,” of
“Analysis and Assessment of Gateway Process.”

A related quotation —

“In truth, the physical AllSpark  is but a shell….”

https://tfwiki.net/wiki/AllSpark

From the post Ghost in the Shell  (Feb. 26, 2019) —

See also, from posts tagged Ogdoad Space

“Like the Valentinian Ogdoad— a self-creating theogonic system
of eight Aeons in four begetting pairs— the projected eightfold work
had an esoteric, gnostic quality; much of Frye’s formal interest lay in
the ‘schematosis’ and fearful symmetries of his own presentations.”

— From p. 61 of James C. Nohrnberg’s “The Master of the Myth
of Literature: An Interpenetrative Ogdoad for Northrop Frye,”
Comparative Literature , Vol. 53 No. 1, pp. 58-82, Duke University
Press (quarterlyJanuary 2001)

— as well as . . .

Related illustration from posts tagged with
the quilt term Yankee Puzzle

IMAGE- 'Yankee Puzzle' quilt block pattern on cover of Northrop Frye's 'Anatomy of Criticism'

Friday, March 12, 2021

Grid

Filed under: General — Tags: — m759 @ 10:45 am

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

See Trinity Cube in this  journal and . . .

McDonnell’s illustration is from 9 June 1983.
See as well a less official note from later that June.

Sunday, May 17, 2020

“The Ultimate Epistemological Fact”

Filed under: General — Tags: , , , — m759 @ 11:49 pm

"Let me say this about that." — Richard Nixon

Interpenetration in Weyl's epistemology —

Interpenetration in Mazzola's music theory —

Interpenetration in the eightfold cube — the three midplanes —

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

A deeper example of interpenetration:

Aitchison has shown that the Mathieu group M24 has a natural
action on the 24 center points of the subsquares on the eightfold
cube's six faces (four such points on each of the six faces). Thus
the 759 octads of the Steiner system S(5, 8, 24) interpenetrate
on the surface of the cube.

Monday, November 18, 2019

Annals of Science Woo:

Filed under: General — Tags: — m759 @ 10:53 am

Impenetrability  vs.  Interpenetration

The previous post discussed impenetrability .

To give the opposing concept of interpenetration 
a fair hearing, see . . .

More generally, see a search for interpenetration in this journal.

Monday, August 6, 2018

The Girl with Kaleidoscope Eyes

Filed under: General,Geometry — Tags: , , — m759 @ 11:00 pm

http://www.log24.com/log/pix18/180806-Lexicon-image-search.jpg

“All right, Jessshica. It’s time to open the boxsssschhh.”

“Gahh,” she said. She began to walk toward the box, but her heart failed her and she retreated back to the chair. “Fuck. Fuck.” Something mechanical purred. The seam she had found cracked open and the top of the box began to rise. She squeezed shut her eyes and groped her way into a corner, curling up against the concrete and plugging her ears with her fingers. That song she’d heard the busker playing on the train platform with Eliot, “Lucy in the Sky with Diamonds”; she used to sing that. Back in San Francisco, before she learned card tricks. It was how she’d met Benny: He played guitar. Lucy was the best earner, Benny said, so that was mainly what she sang. She must have sung it five times an hour, day after day. At first she liked it but then it was like an infection, and there was nothing she could do and nowhere she could go without it running across her brain or humming on her lips, and God knew she tried; she was smashing herself with sex and drugs but the song began to find its way even there. One day, Benny played the opening chord and she just couldn’t do it. She could not sing that fucking song. Not again. She broke down, because she was only fifteen, and Benny took her behind the mall and told her it would be okay. But she had to sing. It was the biggest earner. She kind of lost it and then so did Benny and that was the first time he hit her. She ran away for a while. But she came back to him, because she had nothing else, and it seemed okay. It seemed like they had a truce: She would not complain about her bruised face and he would not ask her to sing “Lucy.” She had been all right with this. She had thought that was a pretty good deal.

Now there was something coming out of a box, and she reached for the most virulent meme she knew. “Lucy in the sky!” she sang. “With diamonds!”

•   •   •

Barry, Max. Lexicon: A Novel  (pp. 247-248).
Penguin Publishing Group. Kindle Edition.

Related material from Log24 on All Hallows' Eve 2013

"Just another shake of the kaleidoscope" —

Related material:

Kaleidoscope Puzzle,  
Design Cube 2x2x2, and 
Through the Looking Glass: A Sort of Eternity.

A Connecting Link

Filed under: General — m759 @ 2:00 pm

http://www.log24.com/log/pix18/180806-Frye-Interpenetrative_Ogdoad.jpg

From New York City on All Hallows' Eve 2013 —

http://www.log24.com/log/pix18/180806-St_Ann-warehouse-with-bridge.jpg

From this  journal on All Hallows' Eve 2013 —

Sunday, July 22, 2018

Space

Filed under: General,Geometry — Tags: , , , — m759 @ 10:29 am

See also interality in the eightfold cube.

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

Thursday, June 28, 2018

Trinity Meditation

Filed under: General — Tags: — m759 @ 2:45 am

See Interpenetration and Trinity Cube.

Thursday, May 10, 2018

Backstory for Eden*

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

* I.e., Hemingway's novel The Garden of Eden.
  See also Northrop Frye and "interpenetration"
  in this journal and a University of Montana master's
  thesis from 1994 on the Hemingway novel,
  "And a river went out of Eden," by Howard A. Schmid.

  See as well remarks by Stanley Fish quoted here on May 7.

Thursday, August 3, 2017

Poetic Theology at the New York Times

Filed under: General — Tags: , — m759 @ 12:19 pm

Or:  Trinity Test Site

From the New York Times Book Review  of
next Sunday, August 6, 2017 —

"In a more conventional narrative sequence,
even a sequence of poems,
this interpenetration would acquire
sequence and evolution." [Link added.]

The concept under review is that of the Holy Trinity.

See also, in this  journal, Cube Trinity.

For a simpler Trinity model, see the three-point line  

Sunday, February 12, 2017

Colorful Tales

Filed under: General — Tags: — m759 @ 1:23 pm

“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”

— Hermann Weyl, Philosophy of  Mathematics and
    Natural Science 
, Princeton, 1949, p. 237

Harvard University Press on the late Angus Fletcher, author of
The Topological Imagination  and Colors of the Mind

From the Harvard webpage for Colors of the Mind

Angus Fletcher is one of our finest theorists of the arts,
the heir to I. A. Richards, Erich Auerbach, Northrop Frye.
This… book…  aims to open another field of study:
how thought— the act, the experience of thinking—
is represented in literature.

. . . .

Fletcher’s resources are large, and his step is sure.
The reader samples his piercing vision of Milton’s

Satan, the original Thinker,
leaving the pain of thinking
as his legacy for mankind.

A 1992 review by Vinay Dharwadker of Colors of the Mind —

See also the above word "dianoia" in The Echo in Plato's Cave.
Some context 

This post was suggested by a memorial piece today in
the Los Angeles Review of Books

A Florilegium for Angus Fletcher

By Kenneth Gross, Lindsay Waters, V. N. Alexander,
Paul Auster, Harold Bloom, Stanley Fish, K. J. Knoespel,
Mitchell Meltzer, Victoria Nelson, Joan Richardson,
Dorian Sagan, Susan Stewart, Eric Wilson, Michael Wood

Fletcher reportedly died on November 28, 2016.

"I learned from Fletcher how to apprehend
the daemonic element in poetic imagination."

— Harold Bloom in today's Los Angeles florilegium

For more on Bloom and the daemonic, see a Log24 post,
"Interpenetration," from the date of Fletcher's death.

Some backstory:  Dharwadker in this journal.

Sunday, December 4, 2016

Sunday Sermon

Filed under: General — m759 @ 2:45 am

Interpenetration of Opposites

See also "Interpenetration" in this journal.

Wednesday, November 30, 2016

Eightfold Roman

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

"Frye's largely imaginary eightfold roman 
may have provided him a personal substitute—
or alternative— for both ideology and myth."

— P. 63 of James C. Nohrnberg, "The Master of
the Myth of Literature: An Interpenetrative Ogdoad
for Northrop Frye," Comparative Literature  Vol. 53,
No. 1 (Winter, 2001), pp. 58-82

See also today's earlier post In Nuce .

In Nuce

Filed under: General,Geometry — Tags: , , — m759 @ 3:48 am
 

Excerpts from James C. Nohrnberg, "The Master of the Myth of Literature: An Interpenetrative Ogdoad for Northrop Frye," Comparative Literature  Vol. 53, No. 1 (Winter, 2001), pp. 58-82

From page 58 —
"… the posthumously revealed Notebooks. A major project of the latter was his 'Ogdoad': two groups of four books each. '[T]he second group of four […] were considered to be Blakean "emanations" or counterparts of the first four,' like 'the "double mirror" structure of The Great Code  and Words with Power : two inter-reflecting parts of four chapters apiece,' Michael Dolzani reports.* "

* P. 22 of Rereading Frye: The Published and Unpublished Works , ed. David Boyd and Imre Salusinszky, Frye Studies [series] (Toronto: University of Toronto Press, 1998). [Abbreviated as RF .]


From page 62 —
"Visionaries like Blake and dramatists like Wagner seem to be working from some larger, mythic blueprint present in nuce  from very early on."

From page 63 —
"Frye's hypothetical books and will-to-totality were obviously fruitful; if the beckoning star was illusory, it nonetheless settled on a real birthplace. The sought-for constructs substituted their scaffolding for a backbone-like confidence in pre-given beliefs; possession of the latter is why Tories like Dr. Johnson and T.S. Eliot could do quite nicely without the constructs. Frye's largely imaginary eightfold roman  may have provided him a personal substitute— or alternative— for both ideology and myth."

From page 69 —
"For Frye the chief element of imaginative or expressive form is the myth, which functions structurally in literature like geometric shapes in painting."

From page 71 —
"The metaphysical skyhook lifting the artist free from unreflective social commitment is often a latent or manifest archetype that his work renews or reworks."

From page 77 —
"Frye's treatises— so little annotated themselves— are the notes writ large; the notes in the Notebooks are treatises writ small. They interpenetrate. Denham quotes 'the masters of the T'ien-tai school of Mahayana Buddhism' as saying '[t]he whole world is contained in a mustard seed' (RF  158, 160), and Frye quotes Keats: 'Every point of thought is the center of an intellectual world' (Study  159; cf. Great Code  167-68 and AC  61). …. [Frye’s] complex books were all generated out of the monadic obiter dicta . His kingdom 'is like a grain of mustard seed, which a man took, and cast into his garden, and it grew' (Luke 13:18-19)."

Friday, August 19, 2016

From Halloween 2013

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

The orange and black Princeton colors in the previous post
suggest a review of Halloween 2013 —

Friday, April 8, 2016

Ogdoads: A Space Odyssey

Filed under: General — Tags: , , — m759 @ 5:01 am

"Like the Valentinian Ogdoad— a self-creating theogonic system
of eight Aeons in four begetting pairs— the projected eightfold work
had an esoteric, gnostic quality; much of Frye's formal interest lay in
the 'schematosis' and fearful symmetries of his own presentations." 

— From p. 61 of James C. Nohrnberg's "The Master of the Myth
of Literature: An Interpenetrative Ogdoad for Northrop Frye," 
Comparative Literature , Vol. 53 No. 1, pp. 58-82, Duke University
Press (quarterly, January 2001)

See also Two by Four  in this  journal.

Saturday, March 12, 2016

For the Church of Synchronology*

Filed under: General — Tags: , — m759 @ 2:16 pm

From the Wikipedia article Bauhaus (band)

"On 31 October 2013 (Halloween), David J and Jill Tracy released
'Bela Lugosi's Dead (Undead Is Forever),' a cinematic piano-led
rework of 'Bela Lugosi's Dead.'"

Halloween 2013 here  (click to enlarge) —

* See "synchronolog…" in this journal.

Sunday, September 27, 2015

Strings

Filed under: General — m759 @ 12:01 pm

The dateline from a slide at a string-theory conference:

See also this journal on that date.

A related "string theory," for those who like to compare and contrast:

A paper on the late Michael Weinstein by Robert L. Oprisko —

"Strings: A Political Theory of Multi-Dimensional Reality."*

From the abstract:

"An 'unfaithful' interpretation of Michael Weinstein's oeuvre
illuminates a complex, interpenetrative system of realities
that reflects the lived experience of his vitalist ontology."

* Theoria & Praxis: International Journal of Interdisciplinary Thought ,
   Vol 2, No 2 (2014): On the Concept of Globality.

Saturday, January 3, 2015

Trinity for Jews

Filed under: General — Tags: — m759 @ 2:08 pm

See also Interpenet-  in this  journal.

"Interpenetration, that's what I  say!"
— Adapted from Humpty Dumpty

Thursday, September 4, 2014

Halloween Manifestos, 2013:

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

Here and at Catholics for Classical Education.

See also Tom Wolfe on manifestos —

Wolfe on manifestos in 'From Bauhaus to Our House'

— and part of an interesting Sept. 2, 2014, manifesto by
Common Core supporter Keith Devlin:

“Graduate students of mathematics are introduced to further
assumptions (about handling the infinite, and various other issues),
equally reasonable and useful, and in accord both with our everyday
intuitions (insofar as they are relevant) and with the rest of
mainstream mathematics. And on the basis of those assumptions,
you can prove that

1 + 2 + 3 + … = –1/12.

That’s right, the sum of all the natural numbers equals –1/12.

This result is so much in-your-face, that people whose mathematics
education stopped at the undergraduate level (if they got that far)
typically say it is wrong. It’s not. Just as with the 0.999… example,
where we had to construct a proper meaning for an infinite decimal
expansion before we could determine what its value is, so to we
have to define what that infinite sum means. ….”

For a correction to Devlin’s remarks, see a physics professor’s weblog post —

“From a strictly mathematical point of view,
the equation 1+2+3+4+ … = -1/12 is incorrect,
and involves confusing the Dirichlet series with
the zeta function.”  — Greg Gbur, May 25, 2010

Sunday, December 1, 2013

McX-Men

Filed under: General — m759 @ 10:16 am

Click for clearer image.

From Willard Van Orman Quine Guest Book Volume 1

"May 7, 1997 'McX and Wyman' — In his essay 'On What There Is', Willard Quine introduces two fictional philosophers who put forward certain ontological doctrines: McX and Wyman. It would be interesting to know whether Quine was thereby alluding to some real philosophers. My guess for McX would be Hugh MacColl, but I have no idea who Wyman might stand for. Thanks for considering the question! from Dr. Kai F. Wehmeier — Email: Kai.Wehmeier (at) math.uni-muenster.de Web Page: http://wwwmath.uni-muenster.de/math/users/wehmeier/"

"I spoke with Prof Quine last night regarding your question which he found interesting. He says his intention was to create some fictional philosophers ('X' and 'Y') to illustrate some of his concerns. There may also have been a 'Z' man. These fictional philosophers were not designed to represent any particular philosophers although their viewpoints may happen [to] reflect those of actual philosophers. – Doug” [Douglas Boynton Quine]

Related material: 

The X-Men Tree (Nov. 12),
X-Men Tree continued (Nov. 17),
Waiting for Ogdoad (Oct. 30),
Interpenetrative Ogdoad (Oct. 31),
Waiting for Ogdoad continued (Nov. 30),
For Sean Connery on St. Andrew's Day (Nov. 30).

Tuesday, November 5, 2013

For St. Robert de Marrais

Filed under: General — m759 @ 11:01 pm

Bead-Game Structuralism:
Excerpts from Comments by Robert de Marrais
on Interpenetration and The Raw and the Cooked

Click the image below for the webpage:

Culinary Note

Filed under: General — m759 @ 12:03 pm

Suggested by a story in today's Harvard Crimson 

"You want Frye's with that?"

Sunday, June 3, 2012

Child’s Play

Filed under: General,Geometry — Tags: , , , — m759 @ 2:56 pm

(Continued)

“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”

– Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art
, Cornell U. Press, 1975

IMAGE- The Trinity of Max Black (a 3-set, with its eight subsets arranged in a Hasse diagram that is also a cube)

Related material—

The Trinity Cube

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

Tuesday, January 10, 2012

Frye’s

Filed under: General — Tags: — m759 @ 6:29 pm

"'Interpenetration'" — Stanley Fish in yesterday evening's online New York Times

"You want Frye's with that?" — A recent humanities graduate

http://www.log24.com/log/pix12/120110-Frye-Denham.jpg

http://www.log24.com/log/pix12/120110-Denham51.gif

Defining Form

Filed under: General,Geometry — Tags: , , — m759 @ 9:00 am

(Continued from Epiphany and from yesterday.)

Detail from the current American Mathematical Society homepage

http://www.log24.com/log/pix12/120110-AMS_page-Detail.jpg

Further detail, with a comparison to Dürer’s magic square—

http://www.log24.com/log/pix12/120110-Donmoyer-Still-Life-Detail.jpg http://www.log24.com/log/pix12/120110-DurerSquare.jpg

The three interpenetrating planes in the foreground of Donmoyer‘s picture
provide a clue to the structure of the the magic square array behind them.

Group the 16 elements of Donmoyer’s array into four 4-sets corresponding to the
four rows of Dürer’s square, and apply the 4-color decomposition theorem.
Note the symmetry of the set of 3 line diagrams that result.

Now consider the 4-sets 1-4, 5-8, 9-12, and 13-16, and note that these
occupy the same positions in the Donmoyer square that 4-sets of
like elements occupy in the diamond-puzzle figure below—

http://www.log24.com/log/pix12/120110-DiamondPuzzleFigure.jpg

Thus the Donmoyer array also enjoys the structural  symmetry,
invariant under 322,560 transformations, of the diamond-puzzle figure.

Just as the decomposition theorem’s interpenetrating lines  explain the structure
of a 4×4 square , the foreground’s interpenetrating planes  explain the structure
of a 2x2x2 cube .

For an application to theology, recall that interpenetration  is a technical term
in that field, and see the following post from last year—

Saturday, June 25, 2011 

Theology for Antichristmas

— m759 @ 12:00 PM

Hypostasis (philosophy)

“… the formula ‘Three Hypostases  in one Ousia
came to be everywhere accepted as an epitome
of the orthodox doctrine of the Holy Trinity.
This consensus, however, was not achieved
without some confusion….” —Wikipedia

http://www.log24.com/log/pix11A/110625-CubeHypostases.gif

Ousia

Click for further details:

http://www.log24.com/log/pix11A/110625-ProjectiveTrinitySm.jpg

 

Monday, January 9, 2012

M Theory

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

Yesterday's All About Eve post featured Pope John Paul II
with his close friend and confidant Jerzy Kluger.
Their counterparts Xavier and Magneto in the recent film
"X-Men: First Class," together with Catholic doctrine on telepathy,
suggest  the following meditations.

Douglas Hofstadter on interpenetration

IMAGE- 'Interpenetration' in Douglas Hofstadter's 'I Am a Strange Loop'

— as well as Trinity in this journal.

First the punchline—

Script M (interpreted by some scanners as '771.')

Then the joke.

Wednesday, November 2, 2011

For All Souls Day

Filed under: General — Tags: — m759 @ 10:31 am

"It's still the same old story…"

See Glory in this journal.

'But "glory" doesn't mean "a nice knock-down argument",' Alice objected.

'When I  use a word,' Humpty Dumpty said, in rather a scornful tone, 'it means just what I choose it to mean— neither more nor less.'

'The question is,' said Alice, 'whether you can  make words mean so many different things.'

'The question is,' said Humpty Dumpty, 'which is to be master— that's all.'

Alice was too much puzzled to say anything; so after a minute Humpty Dumpty began again. 'They've a temper, some of them — particularly verbs: they're the proudest— adjectives you can do anything with, but not verbs— however, can manage the whole lot of them! Impenetrability! That's what I  say!'

'Would you tell me please,' said Alice, 'what that means?'

'Now you talk like a reasonable child,' said Humpty Dumpty, looking very much pleased. 'I meant by "impenetrability" that we've had enough of that subject, and it would be just as well if you'd mention what you mean to do next, as I suppose you don't mean to stop here all the rest of your life.'

'That's a great deal to make one word mean,' Alice said in a thoughtful tone.

'When I make a word do a lot of work like that,' said Humpty Dumpty, 'I always pay it extra.'

See also Interpenetration in this journal… and in Northrop Frye.

Sunday, October 14, 2007

Sunday October 14, 2007

Filed under: General — Tags: , — m759 @ 11:00 am
The Dipolar God

Steven H. Cullinane, 'The Line'

"Logos and logic, crystal hypothesis,
Incipit and a form to speak the word
And every latent double in the word…."

— Wallace Stevens,
   "Notes Toward a Supreme Fiction"

Yesterday's meditation ("Simon's Shema") on the interpenetration of opposites continues:

Part I: The Jewel in the Lotus

"The fundamental conception of Tantric Buddhist metaphysics, namely, yuganaddha, signifies the coincidence of opposites.  It is symbolized by the conjugal embrace (maithuna or kama-kala) of a god and goddess or a Buddha and his consort (signifying karuna and sunyata or upaya and prajna, respectively), also commonly depicted in Tantric Buddhist iconography as the union of vajra (diamond sceptre) and padme (lotus flower).  Thus, yuganaddha essentially means the interpenetration of opposites or dipolar fusion, and is a fundamental restatement of Hua-yen theoretic structures."

— p. 148 in "Part II: A Whiteheadian Process Critique of Hua-yen Buddhism," in Process Metaphysics and Hua-Yen Buddhism: A Critical Study of Cumulative Penetration vs. Interpenetration (SUNY Series in Systematic Philosophy), by Steve Odin, State University of New York Press, 1982

Part II: The Dipolar God

And on p. 163 of Odin, op. cit., in "Part III: Theology of the Deep Unconscious: A Reconstruction of Process Theology," in the section titled "Whitehead's Dipolar God as the Collective Unconscious"–

"An effort is made to transpose Whitehead's theory of the dipolar God into the terms of the collective unconscious, so that now the dipolar God is to be comprehended not as a transcendent deity, but the deepest dimension and highest potentiality of one's own psyche."

Part III: Piled High and Deep

Odin obtained his Ph.D. degree from the Department of Philosophy at the State University of New York (SUNY) at Stony Brook in 1980. (See curriculum vitae (pdf).)

For an academic review of Odin's book, see David Applebaum, Philosophy East and West, Vol. 34 (1984), pp. 107-108.

It is perhaps worth noting, in light of the final footnote of Mark D. Brimblecombe's Ph.D. thesis "Dipolarity and God" quoted yesterday, that "tantra" is said to mean "loom." For some less-academic background on the Tantric iconography Odin describes, see the webpage "Love and Passion in Tantric Buddhist Art." For a fiction combining love and passion with the word "loom" in a religious context, see Clive Barker's Weaveworld.  This fiction– which is, if not "supreme" in the Wallace Stevens sense, at least entertaining– may correspond to some aspects of the deep Jungian psychological reality discussed by Odin.

Happy Birthday,
Hannah Arendt

(Oct. 14, 1906-
Dec. 4, 1975)

OPPOSITES:

Hannah (Arendt) and Martin (Heidegger) as portrayed in a play of that name

Actors portraying
Arendt and Heidegger

Click on image for details.

Saturday, October 13, 2007

Saturday October 13, 2007

Filed under: General — Tags: — m759 @ 9:22 am

Simon’s Shema

“When times are mysterious
Serious numbers will always be heard
And after all is said and done
And the numbers all come home
The four rolls into three
The three turns into two
And the two becomes a
One”

Paul Simon, 1983


Related material:

Simon’s theology here, though radically reductive, is at least consistent with traditional Jewish thought. It may help counteract the thoughtless drift to the left of academic writing in recent decades. Another weapon against leftist nonsense appears, surprisingly, on the op-ed page of today’s New York Times:

“There is a Communist jargon recognizable after a single sentence. Few people in Europe have not joked in their time about ‘concrete steps,’ ‘contradictions,’ ‘the interpenetration of opposites,’ and the rest.”

— Doris Lessing, winner of this year’s Nobel Prize in Literature

The Times offers Lessing’s essay to counter Harold Bloom’s remark that this year’s award of a Nobel Prize to Lessing is “pure political correctness.” The following may serve as a further antidote to Bloom.

The Communist use of “interpenetration,” a term long used to describe the Holy Trinity, suggests– along with Simon’s hymn to the Unity, and the rhetorical advice of Norman Mailer quoted here yesterday—  a search for the full phrase “interpenetration of opposites” in the context* of theology.  Such a search yields a rhetorical gem from New Zealand:

“Dipolarity and God”
by Mark D. Brimblecombe,
Ph.D. thesis,
University of Auckland, 1999
.

* See the final footnote on the final page (249) of Brimblecombe’s thesis:

3 The Latin word contexo means to interweave, join, or braid together.

A check of the Online Eymology Dictionary supports this assertion:

context 1432, from L. contextus “a joining together,” orig. pp. of contexere “to weave together,” from com “together” + textere “to weave” (see texture).

See also Wittgenstein on “theology as grammar” and “context-sensitive” grammars as (unlike Simon’s reductive process) “noncontracting”– Log24, April 16, 2007: Happy Birthday, Benedict XVI.

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

Sunday, May 8, 2005

Sunday May 8, 2005

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

Geometry and Theology

See

the science fiction writer mentioned in a Friday entry.

Mark Olson’s article is at the website of the New England Science Fiction Association, publisher of Ingathering: The Complete People Stories of Zenna Henderson.  This book, by one of my favorite science-fiction authors, was apparently edited by the same Mark Olson.

The following remarks seem relevant to the recurring telepathy theme in Henderson:

From the first article cited above,
David L. Neuhouser,
Higher Dimensions in the Writings of C. S. Lewis (pdf):

“If we are three-dimensional cross-sections of four-dimensional reality, perhaps we are parts of the same body. In fact, we know we are parts of the same body in some way, this four-dimensional idea just may help us to see it more clearly. Remember the preceding comments are mine, not Lewis’s. He puts it this way, ‘That we can die “in” Adam and live “in” Christ seems to me to imply that man as he really is differs a good deal from man as our categories of thought and our three-dimensional imaginations represent him; that the separateness… which we discern between individuals, is balanced, in absolute reality, by some kind of inter-inanimation of which we have no conception at all. It may be that the acts and sufferings of great archetypal individuals such as Adam and Christ are ours, not by legal fiction, metaphor, or causality, but in some much deeper fashion. There is no question, of course, of individuals melting down into a kind of spiritual continuum such as Pantheistic systems believe in; that is excluded by the whole tenor of our faith.'”

From Webster’s Unabridged, 1913 edition:

inanimate
, v. t.

[Pref. in- in (or intensively) + animate.]
 To animate. [Obs.] — Donne.

inanimation, n.

Infusion of life or vigor;
animation; inspiration.
[Obs.]
The inanimation of Christ
living and breathing within us.
Bp. Hall.

Related words…

Also from the 1913 Webster’s:

circumincession, n.

[Pref. circum- + L. incedere, incessum, to walk.]
(Theol.) The reciprocal existence in each other
of the three persons of the Trinity.

From an online essay:

perichoresis
, n.

“The term means mutual indwelling or, better, mutual interpenetration and refers to the understanding of both the Trinity and Christology. In the divine perichoresis, each person has ‘being in each other without coalescence’ (John of Damascus ca. 650). The roots of this doctrine are long and deep.”

—  Bert Waggoner

coinherence, n.

“In our human experience of personhood, at any rate in a fallen world, there is in each person an inevitable element of exclusiveness, of opaqueness and impenetrability.  But with the three divine persons it is not so.  Each is entirely ‘open’ to the others, totally transparent and receptive.  This transparency and receptivity is summed up in the Greek notion of perichoresis, which Gibbon once called ‘the deepest and darkest corner of the whole theological abyss.’  Rendered in Latin as circumincessio and in English usually as ‘coinherence,’ the Greek term means literally, cyclical movement, and so reciprocity, interchange, mutual indwelling.  The prefix peri bears the sense ‘around,’ while choresis is linked with chora, ‘room,’ space,’ ‘place’ or ‘container,’ and with chorein, to ‘go,’ ‘advance,’ ‘make room for’ or ‘contain.’  Some also see a connection with choros, ‘dance,’ and so they take perichoresis to mean ’round dance.’  Applied to Christ, the term signifies that his two natures, the divine and the human, interpenetrate one another without separation and without confusion.  Applied to the Trinity, it signifies that each person ‘contains’ the other two and ‘moves’ within them.  In the words of St Gregory of Nyssa, ‘All that is the Father’s is seen in the Son, and all that is the Son’s belongs also the Father. For the whole Son abides in the Father, and he has in his turn the whole Father abiding in himself.’ 

By virtue of this perichoresis, Father, Son and Holy Spirit ‘coinhere‘ in one another, each dwelling in the other two through an unceasing movement of mutual love – the ’round dance’ of the Trinity.”

— Timothy Ware, Bishop Kallistos of Diokleia,
    The Human Person as an Icon of the Trinity

Saturday, January 24, 2004

Saturday January 24, 2004

Filed under: General — Tags: — m759 @ 9:09 am

Taking Lucifer Seriously:

Michael Sprinker
versus
The Society of Jesus

As the previous entry indicates, I do not take Christian poetry too seriously.  The Prince of Darkness is another matter.  I encountered him this morning in a book on the Christian poet Hopkins by the late Michael Sprinker.

“You were never on the debating team when you were in high school, were you, ace? When you’re in a debate, you don’t try to convince the other side; they’re never going to agree with you. You try to convince the judges and the audience.”

— Michael Sprinker, quoted in The Minnesota Review, 2003

“For Hopkins, poetry was the act of producing the self, one version of that selving which he associated not only with Christ but with Lucifer.”

— Michael Sprinker, “A Counterpoint of Dissonance” — The Aesthetics and Poetry of Gerard Manley Hopkins, Johns Hopkins University Press, 1980, p. 95

A counterbalance to Sprinker on Hopkins and Lucifer is Hopkins, the Self, and God, by Walter J. Ong, S. J. (University of Toronto Press, 1986).  From p. 119:

“The interior dynamism of the Three Persons in One God was not for Hopkins some sort of formula for theological juggling acts but was rather the centre of his personal devotional life and thus of his own ‘selving.’ ….  He writes to Bridges 24 October 1883…

‘For if the Trinity… is to be explained by grammar and by tropes… where wd. be the mystery? the true mystery, the incomprehensible one.’ “

For the dynamics of the Trinity, see the Jan. 22 entry, Perichoresis, or Coinherence.  Another word for coinherence is “indwelling,” as expressed in what might be called the

Song of Lucifer:

Me into you, 
You into me, 
 Me into you…

Atlanta Rhythm Section

For a Christian version of this “indwelling,” see

Coinherence,
Interpenetration,
Mutual Indwelling

See also last year’s entries of 9/09.

Thursday, January 22, 2004

Thursday January 22, 2004

Filed under: General — Tags: — 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).

Sunday, May 25, 2003

Sunday May 25, 2003

Filed under: General,Geometry — Tags: — m759 @ 9:26 pm

 STAR WARS  
opened on this date in 1977.

From the web page Amande:

Le Christ et la Vierge apparurent souvent entourés d’une auréole en forme d’amande: la mandorle.

Étymologiquement, le mot amande est une altération de amandala, qui dérive lui-même du latin classique amygdala….

L’amande a… une connotation symbolique, celle du sexe féminin. Elle figure souvent la vulve. Elle est alors en analogie avec la yoni du vocabulaire de l’hindouisme, la vulve ou la matrice, représentée par une amande ou une noix coupée en deux.

Screenshot of the online
New York Times, May 25, 2003:

Ariel the Hutt and Princess Amygdala

Introduction to Yantra

by Horia Cristescu and
Dan Bozaru 

The Triangle (TRIKONA)
The triangle (TRIKONA) is the symbol of
SHAKTI , the feminine energy or aspect of Creation. The triangle pointing down represents the YONI , the feminine sexual organ and the symbol of the supreme source of the Universe, and when the triangle is pointing upwards it signifies intense spiritual aspiration, the sublimation of one’s nature into the most subtle planes and the element of fire (AGNI TATTVA). The fire is always oriented upwards, thus the correlation with the upward triangle – SHIVA KONA. On the other hand, the downward pointing triangle signifies the element of water which always tends to flown and occupy the lowest possible position. This triangle is known as SHAKTI KONA.

The intersection of two geometric forms (lines, triangles, circles, etc.) represents forces that are even more intense than those generated by the simple forms. Such an interpenetration indicates a high level in the dynamic interaction of the correspondent energies. The empty spaces generated by such combinations are described as very efficient operational fields of the forces emanating from the central point of the YANTRA. That is why we can very often encounter representations of MANTRAS in such spaces. YANTRA and MANTRA are complementary aspects of SHIVA and their use together is much more efficient than the use of one alone.


The Six Points Star (SHATKONA)
A typical combination often found in the graphical structure of a YANTRA is the superposition of two triangles, one pointing upwards and the other downwards, forming a star with six points (SHATKONA), also known as David’s Star. This form symbolically represents the union of
PURUSHA and PRAKRITI or SHIVA-SHAKTI, without which there could be no Creation.

AMEN.

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