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.
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.
Or: A Candle for Sunrise
Commentary —
“Looking carefully at Golay’s code is like staring into the sun.”
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.
The title is from an essay by James C. Nohrnberg—
"Just another shake of the kaleidoscope" —
Related material:
Kaleidoscope Puzzle,
Design Cube 2x2x2, and
Through the Looking Glass: A Sort of Eternity.
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 —
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.
" 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.
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 (quarterly, January 2001)
— as well as . . .
Related illustration from posts tagged with
the quilt term Yankee Puzzle —
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.
"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 —
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.
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.
|
“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). |
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.
* 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.
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 …
“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.
"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 .
|
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 — * 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 —
From page 63 —
From page 69 —
From page 71 —
From page 77 — |
The orange and black Princeton colors in the previous post
suggest a review of Halloween 2013 —
"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.
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.
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.
See also Interpenet- in this journal.
"Interpenetration, that's what I say!"
— Adapted from Humpty Dumpty
Here and at Catholics for Classical Education.
See also Tom Wolfe on manifestos —

— 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
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).
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:
“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

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