"William Blake's statement in The Marriage of Heaven and Hell
'Eternity is in love with the productions of time' is an adumbration
of the paradoxology of the game of hide-and-seek that Non-duality
is playing with and in celebration of itself in Ia divina commedia of
this night of its dream."
— Joseph Campbell in "The Inner Reaches of Outer Space" (©1986)
Related material from a Log24 search for "inscapes4"—
See "Two Approaches to Local-Global Symmetry"
(this journal, Jan. 19, 2023), which discusses
local group actions on plane and solid graphic
patterns that induce global group actions.
See also local and global group actions of a different sort in
the July 11, 1986, note "Inner and Outer Group Actions."
This post was suggested by some remarks of Barry Mazur,
quoted in the previous post, on " Wittgenstein's 'language game,' "
Grothendieck, global views, local views and "locales."
Further reading on "locales" — Wikipedia, Pointless topology.
The word "locale" in mathematics was apparently* introduced by Isbell —
ISBELL, JOHN R. “ATOMLESS PARTS OF SPACES.”
Mathematica Scandinavica, vol. 31, no. 1, 1972, pp. 5–32.
JSTOR, http://www.jstor.org/stable/24490585.
* According to page 841 of . . .
Johnstone, P. (2001). "Elements of the History of Locale Theory."
Pp. 835–851 in: Aull, C.E., Lowen, R. (eds) Handbook of the
History of General Topology, Vol 3. Springer, Dordrecht.
WIkipedia on the URL suffix ".io" —
"In computer science, "IO" or "I/O" is commonly used
as an abbreviation for input/output, which makes the
.io domain desirable for services that want to be
associated with technology. .io domains are often used
for open source projects, application programming
interfaces ("APIs"), startup companies, browser games,
and other online services."
An association with the Bead Game from a post of April 7, 2018 —
|
Glasperlenspiel passage quoted here in Summa Mythologica —
“"I suddenly realized that in the language, or at any rate A less poetic meditation on the above 4x4x4 design cube —
"I saw that in the alternation between front and back, See also a related remark by Lévi-Strauss in 1955:
"…three different readings become possible: |
The recent use by a startup company of the URL "interality.io" suggests
a fourth reading for the 1955 list of Lévi-Strauss — in and out —
i.e., inner and outer group automorphisms — from a 2011 post
on the birthday of T. S. Eliot :
A transformation:
Click on the picture for details.
For fans of Space Fleet and of "reclusive but gifted" programmers—
"With respect to the story's content, the frame thus acts
both as an inclusion of the exterior and as an exclusion
of the interior: it is a perturbation of the outside at the
very core of the story's inside, and as such, it is a blurring
of the very difference between inside and outside."
— Shoshana Felman on a Henry James story, p. 123 in
"Turning the Screw of Interpretation,"
Yale French Studies No. 55/56 (1977), pp. 94-207.
Published by Yale University Press.
See also the previous post and The Galois Tesseract.
This is a followup to Tuesday's post on the Nov. 15 American
Mathematical Society (AMS) obituary of Joseph J. Rotman.
Detail of a page in "Notes on Finite Geometry, 1978-1986,"
"An outer automorphism of S6 related to M24" —
Related work of Rotman —
"Outer Automorphisms of S6," by
Gerald Janusz and Joseph Rotman,
The American Mathematical Monthly ,
Vol. 89, No. 6 (Jun. – Jul., 1982), pp. 407-410
Some background —
"In a Nutshell: The Seed," Log24 post of Sept. 4, 2006:
Some webpages at finitegeometry.org discuss
group actions on Sylvester’s duads and synthemes.
Those pages are based on the square model of
PG(3,2) described in the 1980’s by Steven H. Cullinane.
A rival tetrahedral model of PG(3,2) was described
in the 1990’s by Burkard Polster.
Polster’s tetrahedral model appears, notably, in
a Mathematics Magazine article from April 2009—
Click for a pdf of the article.
Related material:
“The Religion of Cubism” (May 9, 2003) and “Art and Lies”
(Nov. 16, 2008).
This post was suggested by following the link in yesterday’s
Sunday School post to High White Noon, and the link from
there to A Study in Art Education, which mentions the date of
Rudolf Arnheim‘s death, June 9, 2007. This journal
on that date—
The Fink-Guy article was announced in a Mathematical
Association of America newsletter dated April 15, 2009.
Those who prefer narrative to mathematics may consult
a Log24 post from a few days earlier, “Where Entertainment is God”
(April 12, 2009), and, for some backstory, The Judas Seat
(February 16, 2007).
For T.S. Eliot's Birthday
Last night's post "Transformation" was suggested in part
by the title of a Sunday New York Times article on
George Harrison, "Within Him, Without Him," and by
the song title "Within You Without You" in the post
Death and the Apple Tree.
Related material— "Hamlet's Transformation"—
Something have you heard
Of Hamlet’s transformation; so call it,
Sith nor the exterior nor the inward man
Resembles that it was….”
A transformation:
Click on picture for details.
See also, from this year's Feast of the Transfiguration,
Correspondences and Happy Web Day.
For those who prefer the paganism of Yeats to
the Christianity of Eliot, there is the sequel to
"Death and the Apple Tree," "Dancers and the Dance."
Thursday, April 7, 2005 7:26 PM
In the Details
Wallace Stevens,
An Ordinary Evening in New Haven:
Professor Eucalyptus said, "The search
For reality is as momentous as
The search for God." It is the philosopher's search
For an interior made exterior
And the poet's search for the same exterior made
Interior….
… Likewise to say of the evening star,
The most ancient light in the most ancient sky,
That it is wholly an inner light, that it shines
From the sleepy bosom of the real, re-creates,
Searches a possible for its possibleness.
Julie Taymor, "Skewed Mirrors" interview:
"… they were performing for God. Now God can mean whatever you want it to mean. But for me, I understood it so totally. The detail….
They did it from the inside to the outside. And from the outside to the in. And that profoundly moved me then. It was…it was the most important thing that I ever experienced."
"Skewed Mirrors"
illustrated:
|
Click on the above to enlarge.
Details:
The above may be of interest to students
of iconology — what Dan Brown in
The Da Vinci Code calls "symbology" —
and of redheads.
The artist of Details,
"Brenda Starr" creator
Dale Messick, died on Tuesday,
April 5, 2005, at 98.
AP Photo
Dale Messick in 1982
For further details on
April 5, see
Art History:
The Pope of Hope
"O God, I could be bounded in a nutshell
and count myself a king of infinite space,
were it not that I have bad dreams."
— Hamlet
Background:
"… Something have you heard
Of Hamlet's transformation; so call it,
Sith nor the exterior nor the inward man
Resembles that it was…."
The transformation:
Click on picture for details.
Related material:
Figures of Speech (June 7, 2006) and
Ursprache Revisited (June 9, 2006).
"The symmetric group S6 of permutations of 6 objects is the only symmetric group with an outer automorphism….
This outer automorphism can be regarded as the seed from which grow about half of the sporadic simple groups…."
This "seed" may be pictured as
within what Burkard Polster has called "the smallest perfect universe"– PG(3,2), the projective 3-space over the 2-element field.
Related material: yesterday's entry for Sylvester's birthday.
In the Details
Wallace Stevens,
An Ordinary Evening in New Haven:
XXII
Professor Eucalyptus said, "The search
For reality is as momentous as
The search for God." It is the philosopher's search
For an interior made exterior
And the poet's search for the same exterior made
Interior….
… Likewise to say of the evening star,
The most ancient light in the most ancient sky,
That it is wholly an inner light, that it shines
From the sleepy bosom of the real, re-creates,
Searches a possible for its possibleness.
Julie Taymor, "Skewed Mirrors" interview:
"… they were performing for God. Now God can mean whatever you want it to mean. But for me, I understood it so totally. The detail….
They did it from the inside to the outside. And from the outside to the in. And that profoundly moved me then. It was…it was the most important thing that I ever experienced."
"Skewed Mirrors"
illustrated:
|
Click on the above to enlarge.
The above may be of interest to students
of iconology — what Dan Brown in
The Da Vinci Code calls "symbology" —
and of redheads.
The artist of Details,
"Brenda Starr" creator
Dale Messick, died on Tuesday,
April 5, 2005, at 98.
AP Photo
Dale Messick in 1982
For further details on
April 5, see
Art History:
The Pope of Hope
Skewed Mirrors
Readings on Aesthetics for the
Feast of the Triumph of the Cross
Part I —
Bill Moyers and Julie Taymor
Director Taymor on her own passion play (see previous entry), "Frida":
"We always write stories of tragedies because that's how we reach our human depth. How we get to the other side of it. We look at the cruelty, the darkness and horrific events that happened in our life whether it be a miscarriage or a husband who is not faithful. Then you find this ability to transcend. And that is called the passion, like the passion of Christ. You could call this the passion of Frida Kahlo, in a way."
— 10/25/02 interview with Bill Moyers
|
From transcript MOYERS: What happened to you in Indonesia. TAYMOR: This is probably it for me. This is the story that moves me the most…. I went to Bali to a remote village by a volcanic mountain on the lake. They were having a ceremony that only happens only every 10 years for the young men. I wanted to be alone. I was listening to this music and all of a sudden out of the darkness I could see glints of mirrors and 30 or 40 old men in full warrior costume– there was nobody in this village square. I was alone. They couldn't see me in the shadows. They came out with these spears and they started to dance. They did, I don't know, it felt like an eternity but probably a half hour dance. With these voices coming out of them. And they danced to nobody. Right after that, they and I went oh, my God. The first man came out and they were performing for God. Now God can mean whatever you want it to mean. But for me, I understood it so totally. The detail on the costumes. They didn't care if someone was paying tickets, writing reviews. They didn't care if an audience was watching. They did it from the inside to the outside. And from the outside to the in. And that profoundly moved me then. MOYERS: How did you see the world differently after you were in Indonesia? |
From transcript ….They did it from the inside to the outside. And from the outside to the in. And that profoundly moved me then. It was…it was the most important thing that I ever experienced. … ………………….. MOYERS: Now that you are so popular, now that your work is… TAYMOR: [INAUDIBLE]. MOYERS: No, I'm serious. Now that you're popular, now that your work is celebrated and people are seeking you, do you feel your creativity is threatened by that popularity or liberated by it? TAYMOR: No, I think it's neither one. I don't do things any differently now than I would before. And you think that sometimes perhaps if I get a bigger budget for a movie, then it will just be the same thing… MOYERS: Ruination. Ruination. TAYMOR: No, because LION KING is a combination of high tech and low tech. There are things up on that stage that cost 30 cents, like a little shadow puppet and a lamp, and it couldn't be any better than that. It just couldn't. Sometimes you are forced to become more creative because you have limitations. …. |
|
TAYMOR: Well I understood really the power of art to transform. I think transformation become the main word in my life. Transformation because you don't want to just put a mirror in front of people and say, here, look at yourself. What do you see? You want to have a skewed mirror. You want a mirror that says you didn't know you could see the back of your head. You didn't know that you could amount cubistic see almost all the same aspects at the same time. It allows human beings to step out of their lives and to revisit it and maybe find something different about it. |
It's not about the technology. It's about the power of art to transform. I think transformation becomes the main word in my life, transformation. Because you don't want to just put a mirror in front of people and say, here, look at yourself. What do you see? You want to have a skewed mirror. You want a mirror that says, you didn't know you could see the back of your head. You didn't know that you could…almost cubistic, see all aspects at the same time. And what that does for human beings is it allows them to step out of their lives and to revisit it and maybe find something different about it. |
Part II —
Inside and Outside: Transformation
(Research note, July 11, 1986)
|
|
Click on the above typewritten note to enlarge.
Summary of
Parts I and II:
See also
Geometry for Jews.
"We're not here to stick a mirror on you. Anybody can do that, We're here to give you a more cubist or skewed mirror, where you get to see yourself with fresh eyes. That's what an artist does. When you paint the Crucifixion, you're not painting an exact reproduction."
— Julie Taymor on "Frida" (AP, 10/22/02)
"She made 'real' an oxymoron,
she made mirrors, she made smoke.
She had a curve ball
that wouldn't quit,
a girlfriend for a joke."
— "Arizona Star," Guy Clark / Rich Alves
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