Tuesday, July 2, 2019
Waiting for Ogdoad
Friday, April 8, 2016
Ogdoads by Curtis
As was previously noted here, the construction of the Miracle Octad Generator
of R. T. Curtis in 1974 may have involved his "folding" the 1×8 octads constructed
in 1967 by Turyn into 2×4 form.
This results in a way of picturing a well-known correspondence (Conwell, 1910)
between partitions of an 8-set and lines of the projective 3-space PG(3,2).
For some background related to the "ogdoads" of the previous post, see
A Seventh Seal (Sept. 15, 2014).
Ogdoads: A Space Odyssey
"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, November 30, 2013
Waiting for Ogdoad
Continued from October 30 (Devil’s Night), 2013.
“In a sense, we would see that change
arises from the structure of the object.”
— Theoretical physicist quoted in a
Simons Foundation article of Sept. 17, 2013
This suggests a review of mathematics and the
“Classic of Change ,” the I Ching .
The physicist quoted above was discussing a rather
complicated object. His words apply to a much simpler
object, an embodiment of the eight trigrams underlying
the I Ching as the corners of a cube.
See also…
(Click for clearer image.)
The Cullinane image above illustrates the seven points of
the Fano plane as seven of the eight I Ching trigrams and as
seven natural ways of slicing the cube.
For a different approach to the mathematics of cube slices,
related to Gauss’s composition law for binary quadratic forms,
see the Bhargava cube in a post of April 9, 2012.
Thursday, October 31, 2013
Interpenetrative Ogdoad
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.
Wednesday, October 30, 2013
Waiting for Ogdoad
The title is from p. xxxix of Michael Dolzani's
introduction to
The "Third Book" Notebooks of Northrop Frye,
1964-1972: The Critical Comedy
(University of Toronto Press, 2002).
Those whose interests are more mathematical
than literary may consult the similar word "octad"
in this journal.
Wednesday, March 20, 2024
Wednesday, February 2, 2022
Groundhog Day Metamorphosis
" 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.
Conway’s Game vs. Pure Geometry
A question attributed to John Horton Conway
about configurations in his Game of Life —
"Indeed, is there a Godlike still-life,
one that can only have existed
for all time . . . . ?"
A simple answer … but not from Conway's Game —
"Before time began, there was the Cube." — Optimus Prime
Related remarks: Ogdoad.
Saturday, March 13, 2021
Eternal Spark
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 —
Tuesday, July 2, 2019
Molloy/Malloy: An Even Break
Monday, August 6, 2018
The Girl with Kaleidoscope Eyes
“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.
A Connecting Link
Wednesday, November 30, 2016
Eightfold Roman
"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
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 — |
Saturday, November 5, 2016
Interpenetration
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.
Friday, August 19, 2016
From Halloween 2013
The orange and black Princeton colors in the previous post
suggest a review of Halloween 2013 —
Tuesday, April 19, 2016
The Folding
A recent post about the eightfold cube suggests a review of two
April 8, 2015, posts on what Northrop Frye called the ogdoad :
As noted on April 8, each 2×4 "brick" in the 1974 Miracle Octad Generator
of R. T. Curtis may be constructed by folding a 1×8 array from Turyn's
1967 construction of the Golay code.
Folding a 2×4 Curtis array yet again yields the 2x2x2 eightfold cube .
Those who prefer an entertainment approach to concepts of space
may enjoy a video (embedded yesterday in a story on theverge.com) —
"Ghost in the Shell: Identity in Space."
Sunday, April 10, 2016
In Memoriam
Sunday, March 20, 2016
Where
"Where indeed might the literary scholar expect to find,
if not in literature, the measure of modern thought?"
— "Ruins of the Ogdoad," by Michael Keefer
"Seven is Heaven, Eight is a Gate, Nine is a Vine."
— Mnemonic rhyme; author anonymous
Saturday, March 12, 2016
For the Church of Synchronology*
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.
Monday, December 1, 2014
Change Arises
Flashback to St. Andrew's Day, 2013 —
Saturday, November 30, 2013
|
If the object is a cube, change arises from the fact
that the object has six faces…
and is the unit cell for the six -dimensional
hyperspace H over the two-element field —
A different representation of the unit cell of
the hyperspace H (and of the I Ching ) —
Thursday, September 4, 2014
Halloween Manifestos, 2013:
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
Monday, December 9, 2013
Heaven Descending
An I Ching study quoted in Waiting for Ogdoad (St. Andrew's Day, 2013)—
(Click for clearer image.)
The author of the above I Ching study calls his lattice "Arising Heaven."
The following lattice might, therefore, be called "Heaven Descending."
Click for the source, mentioned in Anatomy of a Cube (Sept. 18, 2011).
Sunday, December 1, 2013
McX-Men
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).
Monday, November 25, 2013
Voilà
"Waiting for Ogdoad" continues…
"You want Frye's with that?" — A recent humanities graduate.
Frye's backstory: Ogdoad.
Other material suggested by the previous post and by the time of this post…
No Man's Land, Gods and Monsters, and Forty and Eight.
Monday, November 18, 2013
The Four-Gated Song
"Bobbies on bicycles two by two…" — Roger Miller, 1965
A mathematics weblog in Australia today—
Clearly, the full symmetric group contains elements
with no regular cycles, but what about other groups?
Siemons and Zalesskii showed that for any group G
between PSL(n,q) and PGL(n,q) other than for
(n,q)=(2,2) or (2,3), then in any action of G, every
element of G has a regular cycle, except G=PSL(4,2)
acting on 8 points. The exceptions are due to
isomorphisms with the symmetric or alternating groups.