"The hint half guessed, the gift half understood, is Incarnation."
— T. S. Eliot in Four Quartets
Note also the four 4×4 arrays surrounding the central diamond
in the chi of the chi-rho page of the Book of Kells —
From a Log24 post
of March 17, 2012
"Interlocking, interlacing, interweaving"
— Condensed version of page 141 in Eddington's
1939 Philosophy of Physical Science
See a search for the title in this journal.
Related material:
The incarnation of three permutations,
named A, B, and C,
on the 7-set of digits {1, 2, 3, 4, 5, 6, 7}
as permutations on the eightfold cube.
See Minimal ABC Art, a post of August 22, 2016.
"… a list of group theoretic invariants
and their geometric incarnation…"
— David Lehavi on the Kummer 166 configuration in 2007
Related material —
"The hint half guessed, the gift half understood, is Incarnation."
— T. S. Eliot in Four Quartets
"This is not theology; this is mathematics."
— Steven H. Cullinane on four quartets
To wit:
The Kummer 166 configuration is the configuration of sixteen
6-sets within a 4×4 square array of points in which each 6-set
is determined by one of the 16 points of the array and
consists of the 3 other points in that point's row and the
3 other points in that point's column.
See Configurations and Squares.
The Wikipedia article Kummer surface uses a rather poetic
phrase* to describe the relationship of the 166 to a number
of other mathematical concepts — "geometric incarnation."
Related material from finitegeometry.org —
* Apparently from David Lehavi on March 18, 2007, at Citizendium .
The previous post's title, "Unfolding," and a search in this
journal for "porpentine," yield . . .
Cynthia Zarin in The New Yorker, issue dated April 12, 2004 –
"Time, for L'Engle, is accordion-pleated. She elaborated,
'When you bring a sheet off the line, you can't handle it until
it's folded, and in a sense, I think, the universe can't exist until
it's folded– or it's a story without a book.'"
"Words move, music moves
Only in time . . . ." — Eliot, "Four Quartets"
* Related reading — http://m759.net/wordpress/?s=Static+Dynamic .
vulture.com/article/15-movies-were-excited-to-see-
at-2025s-sxsw-film-festival.html
Some may prefer an earlier incarnation of this concept . . .
And then there is a more abstract incarnation of the concept
(with the third person of the threesome being the beholder ) . . .
(Adapted from unsigned art in a Venice Beach apartment)
Cinematic High Concept . . .
A Roots Rising X-Fantasy:
[ A temporal incarnation of this high
concept: January 3 and January 9. ]
Update at 3:33 PM EST —
For Women's History Month,
Another Coming Attraction —
"Ready when you are, C. B.!"
For a Hollywood version of Archimedes, see . . .
A related image from what Ray Bradbury called "October Country" —
"A dark illimitable Ocean" — John Milton, Paradise Lost , Book II
"All is number" — Attributed to Pythagoras
|
"For a fraction of a second, Phocan senses |
From the MANIFESTO link in the Breakthrough Prize page above —
Our Mission . . . Should We Choose to Accept It
Related reading —
|
" He, in his turn, gazes at the couple, at these stand-ins called upon to underwrite a thousand marriages, a thousand renewed couplings. Diamond’s had the same idea as him: the woman’s forehead has a bindi-nipple on it too. For a fraction of a second, Phocan senses one more act of standing-in or substitution at work here; the presence, veiled, redacted, of a coupling unconsummated, of a bride uncaptured—too young, a child almost—exiting the frame. Sennet’s briefing the students further: 'Once you take your bathrobes off,' he says, 'the cameras will detect the markers, and, through these, your exact positions. As long,' he adds, pointing at the floor’s tape-demarcated central area, 'as you stay within the borders of this square—that is, inside the white lines. Of course, you’ve got the bed, but…' Perera picks the thread up: 'As discussed,' she tells them, 'we want to ascertain the stress occasioned by a wide range of positions.' Her diction, coupled with the Sri Lankan accent in which they’re delivered, makes Phocan wonder whether these words are reproduced verbatim from her research brief or whether she always speaks with such lilting formality. 'To that end,' she carries on, 'we ask you to engage with one another in as many variable configurations as you are able. You can move about the bed, the bed’s edge, floor or table…' "
— McCarthy, Tom. The Making of Incarnation: A Novel |
|
“Isn’t your work—our work—all about accessing and deploying underlying sequences and patterns? Mapping particulars on to great universals? Isn’t that the art to which, in one way or another, we’ve both devoted our best years?”
— McCarthy, Tom. The Making of Incarnation: A Novel
The hardcover first edition was published by Knopf |
|
"It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato's (realist) reaction to the sophists (nominalists). What is often called 'postmodernism' is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth."
— Simon Blackburn, Think, |
The "quantum kernel" of Koen Thas is a version of the incidence
structure — the Cremona-Richmond configuration — discussed
in the previous post, Doily vs. Inscape .
That post's inscape is, as noted there, an incarnation of the
abstract incidence structure. More generally, see incarnation
in this journal . . . In particular, from Michaelmas last year,
Annals of Mathematical Theology.
A somewhat more sophisticated "incarnation" example
related to the "inscape" concept —
"The hint half guessed, the gift half understood, is Incarnation."
— T. S. Eliot in Four Quartets
See also Numberland in this journal.
-Thas-2020.jpg)
My own term "inscape" names a square incarnation of what is also
known as the "Cremona-Richmond configuration," the "generalized
quadrangle of order (2, 2)," and the "doily." —
"As McCarthy peers through the screen, or veil, of technological modernity
to reveal the underlying symbolic structures of human experience,
The Making of Incarnation weaves a set of stories one inside the other,
rings within rings, a perpetual motion machine."
— Amazon.com description of a novel published on All Souls' Day
(Dia de los Muertos), 2021.
See also the underlying symbolic structures of Boolean functions . . .
as discussed, for instance, on Sept. 23 at medium.com —
"As McCarthy peers through the screen, or veil,
of technological modernity to reveal the underlying
symbolic structures of human experience,
The Making of Incarnation weaves a set of stories
one inside the other, rings within rings, a perpetual
motion machine." — Amazon.com description
of a novel published on All Souls' Day (Dia de los
Muertos), 2021.
The McCarthy novel is mentioned in The New York Times today —
For a simpler perpetual motion machine, see T. S. Eliot's "Chinese jar."
The misleading image at right above is from the cover of
an edition of Charles Williams's classic 1931 novel
Many Dimensions published in 1993 by Wm. B. Eerdmans.
But seriously . . .
"Pray for the grace of accuracy." — Robert Lowell
What is wrong with this picture?
Related material from November 22, 2018 —
Twelves (in memory of Robert de Marrais) —
Receipt date for the above article —
Synchronicity check —
Related reading —
http://www.universityreaders.com/pdf/
Incarnations-of-the-Blaring-Bluesblinger_sneak_preview.pdf
Two of the thumbnail previews
from yesterday's 1 AM post …
Further down in the "6 Prescott St." post, the link 5 Divinity Avenue
leads to …
|
A Letter from Timothy Leary, Ph.D., July 17, 1961
Harvard University July 17, 1961
Dr. Thomas S. Szasz Dear Dr. Szasz: Your book arrived several days ago. I've spent eight hours on it and realize the task (and joy) of reading it has just begun. The Myth of Mental Illness is the most important book in the history of psychiatry. I know it is rash and premature to make this earlier judgment. I reserve the right later to revise and perhaps suggest it is the most important book published in the twentieth century. It is great in so many ways–scholarship, clinical insight, political savvy, common sense, historical sweep, human concern– and most of all for its compassionate, shattering honesty. . . . . |
The small Morton Prince House in the above letter might, according to
the above-quoted remarks by Corinna S. Rohse, be called a "jewel box."
Harvard moved it in 1978 from Divinity Avenue to its current location at
6 Prescott Street.
Related "jewel box" material for those who
prefer narrative to mathematics —
"In The Electric Kool-Aid Acid Test , Tom Wolfe writes about encountering
'a young psychologist,' 'Clifton Fadiman’s nephew, it turned out,' in the
waiting room of the San Mateo County jail. Fadiman and his wife were
'happily stuffing three I-Ching coins into some interminable dense volume*
of Oriental mysticism' that they planned to give Ken Kesey, the Prankster-
in-Chief whom the FBI had just nabbed after eight months on the lam.
Wolfe had been granted an interview with Kesey, and they wanted him to
tell their friend about the hidden coins. During this difficult time, they
explained, Kesey needed oracular advice."
— Tim Doody in The Morning News web 'zine on July 26, 2012**
Oracular advice related to yesterday evening's
"jewel box" post …
A 4-dimensional hypercube H (a tesseract ) has 24 square
2-dimensional faces. In its incarnation as a Galois tesseract
(a 4×4 square array of points for which the appropriate transformations
are those of the affine 4-space over the finite (i.e., Galois) two-element
field GF(2)), the 24 faces transform into 140 4-point "facets." The Galois
version of H has a group of 322,560 automorphisms. Therefore, by the
orbit-stabilizer theorem, each of the 140 facets of the Galois version has
a stabilizer group of 2,304 affine transformations.
Similar remarks apply to the I Ching In its incarnation as
a Galois hexaract , for which the symmetry group — the group of
affine transformations of the 6-dimensional affine space over GF(2) —
has not 322,560 elements, but rather 1,290,157,424,640.
* The volume Wolfe mentions was, according to Fadiman, the I Ching.
** See also this journal on that date — July 26, 2012.
"The purpose of mathematics cannot be derived from an activity
inferior to it but from a higher sphere of human activity, namely,
religion."
"The hint half guessed, the gift half understood, is Incarnation."
— T. S. Eliot in Four Quartets
See also Ultron Cube.
Those pleased by what Ross Douthat today called
"The Return of Paganism" are free to devise rituals
involving what might be called "the sacred geometry
of the Kummer 166 configuration."
As noted previously in this journal,
"The hint half guessed, the gift half understood, is Incarnation."
— T. S. Eliot in Four Quartets
See also earlier posts also tagged "Kummerhenge" and
another property of the remarkable Kummer 166 —
For some related literary remarks, see "Transposed" in this journal.
Some background from 2001 —
(Continued from this morning)
"The hint half guessed, the gift half understood, is Incarnation."
— T. S. Eliot in Four Quartets
See also other Log24 posts tagged Kummerhenge.
"The hint half guessed, the gift half understood, is Incarnation."
— T. S. Eliot in Four Quartets
See too "The Ruler of Reality" in this journal.
Related material —
A more esoteric artifact: The Kummer 166 Configuration . . .
An array of Göpel tetrads appears in the background below.
"As you can see, we've had our eye on you
for some time now, Mr. Anderson."
From Chapter 1 of R. D. Laing's The Politics of Experience —
"An activity has to be understood in terms of the experience
from which it emerges. These arabesques that mysteriously
embody mathematical truths only glimpsed by a very few —
how beautiful, how exquisite — no matter that they were
the threshing and thrashing of a drowning man.
We are here beyond all questions except those of being
and nonbeing, incarnation, birth, life and death.
Creation ex nihilo has been pronounced impossible even for
God. But we are concerned with miracles. We must hear the
music of those Braque guitars (Lorca*)."
See also Christmas Day, 2009.
* Update of Sunday afternoon: A search for the Lorca quote yields
no result, but Cocteau wrote that "Mon rêve, en musique, serait
d'entendre la musique des guitares de Picasso. "
(Oeuvres complètes , Vol. 10, p. 107)
See also Stevens + "Blue Guitar" in this journal.
The title was suggested by this morning's post "Follow This."
From a previous incarnation of my home website, m759.com —
The second of the site's three pages mentions authors
Alfred Bester and Zenna Henderson :
"Bester and Henderson are particularly good at
fictional accounts of telepathy. The noted Harvard
philosopher W. V. Quine doubts such a thing exists,
but I prefer the 'There must be a pony' argument."
Related material: The date Nov. 27, 2014, in a web search today …
… in The Washington Post …
… and in this journal …
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