Log24

Wednesday, October 24, 2018

Raiders of the Lost Crucible Continues

Filed under: General — Tags: , , — m759 @ 10:22 PM

Tuesday, October 2, 2018

Raiders of the Lost Crucible

Filed under: General — Tags: — m759 @ 11:22 AM

See other posts now tagged Crucible Raiders.

Related entertainment —

From YouTube:

From NBC:

For more from the above date,
Oct. 8, 2016, click "seriously" below.

But seriously

Thursday, March 2, 2017

Raiders of the Lost Crucible Continues

Filed under: General — m759 @ 9:59 PM

Cover, 2005 paperback edition of 'Refiner's Fire,' a 1977 novel by Mark Helprin

Mariner Books paperback, 2005

See, too, this evening's A Common Space
and earlier posts on Raiders of the Lost Crucible.

Also not without relevance —

The diamond theorem correlation at the University of Bradford

Friday, May 27, 2016

Raiders of the Lost Crucible

Filed under: General — m759 @ 8:00 AM

Continues .

Number and Time, by Marie-Louise von Franz

For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.

The above passage suggests a meditation on this morning's
New York Times * —

"When shall we three meet again?" — William Shakespeare

“We three have scattered, leaving only me behind
to clean up the scene,” Ms. Yang wrote.
“I am alone, missing us three.” — Amy Qin

Saturday, April 9, 2016

Raiders of the Lost Crucible

Filed under: General — Tags: — m759 @ 2:28 PM

(Continued)

Vanity Fair illustrated —

Detail of illustration by Frederick Alfred Rhead of Vanity Fair,
page 96 in the John Bunyan classic Pilgrim's Progress 
(New York, The Century Co., 1912)

See also

Saturday, October 31, 2015

Raiders of the Lost Crucible

Filed under: General,Geometry — Tags: , — m759 @ 10:15 AM

Stanford Encyclopedia of Philosophy
on the date Friday, April 5, 2013 —

Paraconsistent Logic

“First published Tue Sep 24, 1996;
substantive revision Fri Apr 5, 2013”

This  journal on the date Friday, April 5, 2013 —

The object most closely resembling a “philosophers’ stone”
that I know of is the eightfold cube .

For some related philosophical remarks that may appeal
to a general Internet audience, see (for instance) a website
by I Ching  enthusiast Andreas Schöter that displays a labeled
eightfold cube in the form of a lattice diagram —

Related material by Schöter —

A 20-page PDF, “Boolean Algebra and the Yi Jing.”
(First published in The Oracle: The Journal of Yijing Studies ,
Vol 2, No 7, Summer 1998, pp. 19–34.)

I differ with Schöter’s emphasis on Boolean algebra.
The appropriate mathematics for I Ching  studies is,
I maintain, not Boolean algebra  but rather Galois geometry.

See last Saturday’s post Two Views of Finite Space.
Unfortunately, that post is, unlike Schöter’s work, not
suitable for a general Internet audience.

Friday, January 25, 2019

Crucible Raiders Continues.

Filed under: General — Tags: — m759 @ 12:00 AM

Fans of the New York Times  philosophy series "The Stone"
(named for the legendary philosophers' stone) may consult 
posts tagged "Crucible Raiders" in this journal.

Some context — the previous post, "Night at the Social Media."

Wednesday, July 4, 2018

Raiders of the Lost Spell

Filed under: General — Tags: — m759 @ 2:01 PM

From The New York Review of Books ,
issue dated July 19, 2018 —

"The only useful thing about The Seventh Function of Language 
is the idea that one would need some magical means to persuade
through language, some secret spell. Useful, because perfectly
ridiculous. The spell, we know, exists . . . ."

— "Imagining the Real," by Wyatt Mason

Some nineteenth-century thoughts along these lines:

See also Declarations.

Tuesday, July 3, 2018

Lost in Quantum Space

Filed under: General,Geometry — Tags: — m759 @ 10:45 AM

Combining concepts from the two previous posts, we have the above title.

A more concise alternative title

Lost in the Matrix

For some related non -fiction, see posts tagged Dirac and Geometry.

For a Generation Lost in Space

Filed under: General — Tags: — m759 @ 7:38 AM

So here's to you, Mrs. Robinson …

Friday, April 5, 2013

The Crucible

Filed under: General — Tags: — m759 @ 6:12 AM

"Though we had many pieces, we did not have the whole.
It was thirty years before we deciphered the formula.
But we did it at last.

There at night in the darkness of Fourier’s laboratory,
the four of us stood and watched the philosophers’ stone
forming in the crucible."

The Eight , by Katherine Neville
     (2008 Ballantine Books mass market edition, p. 640)

A journal post from August 25, 2009:

Image from a different journal earlier that same day, August 25, 2009:

Thirty-year medallion from Alcoholics Anonymous —

 

See also, in this  journal, "The Eight" + Damnation.

Friday, January 25, 2019

Design Theory

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

Last night's post "Night at the Social Media" suggests . . .

A 404 for Katherine Neville (born on 4/04) —

Thursday, January 24, 2019

Night at the Social Media

Filed under: General — Tags: — m759 @ 11:40 PM

See also Katherine Neville,  Karl Pribram, and Cooper Hewitt in this journal.

“The Stone” Contributor Dies

Filed under: General — Tags: — m759 @ 3:00 AM

"He was a regular contributor to the New York Times 
philosophical forum, The Stone." — South Bend Tribune

See also Gutting in this  journal.

Sunday, December 30, 2018

Mechanical Parable

Filed under: General — m759 @ 3:59 PM

Raiders of the Lost Crucible and Bee Season continue 

"Walter Kerr, in his 1953 review in the New York Herald Tribune ,
wrote, 'The Crucible , which opened at the Martin Beck Thursday,
…seems to me to be taking a step backward into mechanical parable,
into the sort of play which lives not in the warmth of humbly observed
souls but in the ideological heat of polemic.' For Kerr, Miller’s play is
an analytical argument, a treatise, rather than a heartfelt play about
human lives."

— http://www.americanpopularculture.com/
archive/bestsellers/authur_miller.htm

A more heartfelt approach —

" … this beautiful love story . . . ."

Sunday, September 30, 2018

Advocate

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

Click the above for an example.

Iconology of the Eightfold Cube

Filed under: General,Geometry — Tags: — m759 @ 11:13 AM

Found today in an Internet image search, from the website of
an anonymous amateur mathematics enthusiast

Forming Gray codes in the eightfold cube with the eight
I Ching  trigrams (bagua ) —

Forming Gray codes in the eightfold cube with the eight I Ching trigrams (bagua)

This  journal on Nov. 7, 2016

A different sort of cube, from the makers of the recent
Netflix miniseries "Maniac" —

See also Rubik in this  journal.

Thursday, July 5, 2018

Paz:

Filed under: General,Geometry — Tags: — m759 @ 1:44 PM

Some context for what Heidegger called
das Spiegel-Spiel des Gevierts

From Helen Lane's translation of El Mono Gramático ,
a book by Nobel winner Octavio Paz first published
in Barcelona by Seix Barral in 1974 —

Simultaneous perspective does not look upon language as a path because it is not the search for meaning that orients it. Poetry does not attempt to discover what there is at the end of the road; it conceives of the text as a series of transparent strata within which the various parts—the different verbal and semantic currents—produce momentary configurations as they intertwine or break apart, as they reflect each other or efface each other. Poetry contemplates itself, fuses with itself, and obliterates itself in the crystallizations of language. Apparitions, metamorphoses, volatilizations, precipitations of presences. These configurations are crystallized time: although they are perpetually in motion, they always point to the same hour—the hour of change. Each one of them contains all the others, each one is inside the others: change is only the oft-repeated and ever-different metaphor of identity.

— Paz, Octavio. The Monkey Grammarian 
(Kindle Locations 1185-1191). 
Arcade Publishing. Kindle Edition. 

A related 1960 meditation from Claude Lévi-Strauss taken from a 
Log24 post of St. Andrew's Day 2017,  "The Matrix for Quantum Mystics":

The Matrix of Lévi-Strauss —

"In Vol. I of Structural Anthropology , p. 209, I have shown that
this analysis alone can account for the double aspect of time
representation in all mythical systems: the narrative is both
'in time' (it consists of a succession of events) and 'beyond'
(its value is permanent)." — Claude Lévi-Strauss

I prefer the earlier, better-known, remarks on time by T. S. Eliot
in Four Quartets , and the following four quartets
(from The Matrix Meets the Grid) —

.

Wednesday, July 4, 2018

New from Oxford University Press —

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

From the Afterword to a 2017 novel titled Quantum Space

Now from Oxford University Press,

non-fiction approach to
 

Quantum Space
 

See also the previous post and other posts tagged Lost.

Tuesday, July 3, 2018

Propriation

Filed under: General,Geometry — Tags: — m759 @ 7:55 PM

The phrase "quantum space" in today's 10:45 AM post
was used earlier in a book title —

Amazon.com gives the Quantum Space  publication date
for its Kindle edition as April 10, 2017.

I prefer my own remarks of April 10, 2017 —

From "Heidegger for Passover

"Propriation1 gathers the rift-design2 of the saying
and unfolds it3 in such a way that it becomes 
the well-joined structure4 of a manifold showing."

— p. 415 of Heidegger's Basic Writings ,
edited by David Farrell Krell,
HarperCollins paperback, 1993

"Das Ereignis versammelt den Aufriß der Sage
und entfaltet ihn zum Gefüge des vielfältigen Zeigens." 

— Heidegger, Weg zur Sprache

1. "Mirror-Play of the Fourfold"

2. "Christ descending into the abyss"

3. Barrancas of Cuernavaca

4. Combinatorics, Philosophy, Geometry

The Ant and the WASP

Filed under: General — Tags: , — m759 @ 4:56 PM

See also posts tagged "Lost" and a search for "Excellent Adventure."

Fiction in a Cartoon Graveyard

Filed under: General — Tags: — m759 @ 10:02 AM

Jonathan Franzen on fiction —

"Fiction is storytelling, and our reality arguably consists of
the stories we tell about ourselves."

Or stories we are told by others

Thursday, March 8, 2018

The Trial

Filed under: General — m759 @ 8:08 PM

"At the heart of the trial was the question of
whether the complainant could have agreed
to have sex with the defendant . . .
on Halloween night in 2015 . . . ."

Vivian Wang in The New York Times  this evening

This  journal on Halloween night in 2015 —

Thursday, January 4, 2018

For a Cartoon Graveyard

Filed under: General — Tags: , , — m759 @ 4:56 AM

“… the horizon is not the limit of meaning,
but that which extends meaning
from what is directly given
to the whole context in which it is given,
including a sense of a world.”

— David Vessey,
Gadamer and the Fusion of Horizons

(Quoted here on Saturday, June 4, 2005.)

Tuesday, January 2, 2018

Hell and Easter

Filed under: General — Tags: — m759 @ 11:22 PM

This post was suggested by the reported Monday, Jan. 1, 2018,
death of the Juilliard String Quartet founding violinist and by the
reported Thursday, Feb. 25, 2016 death of his brother, a
biotech entrepreneur.

Details from Feb. 25-26, 2016

Related material from this evening's New York Times

The archaeologist above reportedly died on Friday, Dec. 29, 2016. 
See too a Log24 post from that date, On Becket's Day.

Sunday, January 1, 2017

Like the Horizon

Filed under: General,Geometry — Tags: , , , — m759 @ 1:00 PM

(Continued from a remark by art critic Peter Schjeldahl quoted here
last  year on New Year’s Day in the post “Art as Religion.”)

“The unhurried curve got me.
It was like the horizon of a world
that made a non-world of
all of the space outside it.”

— Peter Schjeldahl, “Postscript: Ellsworth Kelly,”
The New Yorker , December 30, 2015

This suggests some further material from the paper
that was quoted here yesterday on New Year’s Eve —

“In teaching a course on combinatorics I have found
students doubting the existence of a finite projective
plane geometry with thirteen points on the grounds
that they could not draw it (with ‘straight’ lines)
on paper although they had tried to do so. Such a
lack of appreciation of the spirit of the subject is but
a consequence of the elements of formal geometry
no longer being taught in undergraduate courses.
Yet these students were demanding the best proof of
existence, namely, production of the object described.”

— Derrick Breach (See his obituary from 1996.)

A related illustration of the 13-point projective plane
from the University of Western Australia:

Projective plane of order 3

(The four points on the curve
at the right of the image are
the points on the line at infinity .)

The above image is from a post of August 7, 2012,
The Space of Horizons.”  A related image —

Click on the above image for further remarks.

Thursday, September 15, 2016

Metaphysics at Notre Dame

Filed under: General,Geometry — Tags: , — m759 @ 11:07 PM

Recommended reading —

"When Analogies Fail," by Alexander Stern,
a doctoral candidate in philosophy at Notre Dame, in
The Chronicle of Higher Education  online September 11, 2016.

Related material —

That same Alexander Stern in this  journal on April 17, 2016:

See also the eightfold cube in the previous post,
Metaphysics at Scientific American:

Friday, April 22, 2016

Elixir

Filed under: General — m759 @ 12:26 PM

The prominent display of an ad for Elixir Vitae in
today's 11:02 AM post suggests a review of that concept.

See also Raiders of the Lost Crucible in this journal.

Thursday, March 17, 2016

On the Eightfold Cube

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

The following page quotes "Raiders of the Lost Crucible,"
a Log24 post from Halloween 2015.

Discussion of Cullinane's eightfold cube as exhibited by Josefine Lyche at the Vigeland Museum in Oslo

From KUNSTforum.as, a Norwegian art quarterly, issue no. 1 of 2016.

Related posts — See Lyche Eightfold.

Thursday, November 5, 2015

ABC Art or: Guitart Solo

Filed under: General,Geometry — Tags: , — m759 @ 5:55 PM

“… the A B C of being….” — Wallace Stevens

Scholia —

Compare to my own later note, from March 4, 2010 —

“It seems that Guitart discovered these ‘A, B, C’ generators first,
though he did not display them in their natural setting,
the eightfold cube.” — Borromean Generators (Log24, Oct. 19)

See also Raiders of the Lost Crucible (Halloween 2015)
and “Guitar Solo” from the 2015 CMA Awards on ABC.

Saturday, October 24, 2015

Two Views of Finite Space

Filed under: General,Geometry — Tags: , , — m759 @ 10:00 AM

The following slides are from lectures on “Advanced Boolean Algebra” —

The small Boolean  spaces above correspond exactly to some small
Galois  spaces. These two names indicate approaches to the spaces
via Boolean algebra  and via Galois geometry .

A reading from Atiyah that seems relevant to this sort of algebra
and this sort of geometry —

” ‘All you need to do is give me your soul:  give up geometry
and you will have this marvellous machine.’ (Nowadays you
can think of it as a computer!) “

Related material — The article “Diamond Theory” in the journal
Computer Graphics and Art , Vol. 2 No. 1, February 1977.  That
article, despite the word “computer” in the journal’s title, was
much less about Boolean algebra  than about Galois geometry .

For later remarks on diamond theory, see finitegeometry.org/sc.

Friday, July 10, 2015

Without Border

Filed under: General — Tags: , — m759 @ 3:18 PM

The previous post's Holy Field symbol, 
with border removed, becomes the
Chinese character for "well."

See also The Lost Well.

Saturday, October 4, 2014

The Source

Filed under: General — Tags: , — m759 @ 9:00 PM

“In ancient Greece, 9 was the number of
the Muses, patron goddesses of the arts.
They were the daughters of Mnemosyne (‘memory’),
the source of imagination, which in turn is
the carrier of archetypal, elementary ideas to
artistic realization in the field of space-time.”

— Joseph Campbell in The Inner Reaches of Outer Space

In memoriam:

 See also Raiders of the Lost Well and…

 The Eliot Omen 


Ground plan for a game of Noughts and Crosses

Saturday, February 22, 2014

Grundlagenkrise*

Filed under: General — Tags: , — m759 @ 12:00 PM

The title was suggested by a 1921 article
by Hermann Weyl and by a review* of
a more recent publication —

The above Harvard Gazette  piece on Davos is
from St. Ursula’s Day, 2010. See also this  journal
on that date.

See as well a Log24 search for Davos.

A more interesting piece by Peter E. Gordon
(author of the above Davos book) is his review
of Charles Taylor’s A Secular Age .
The review is titled

The Place of the Sacred
in the Absence of God
.”

(The place of the sacred is not, perhaps, Davos,
but a more abstract location.)

* Grundlagenkrise  was a tag for a Jan. 13, 2011,
review in The New Republic  of Gordon’s
book on Cassirer and Heidegger at Davos.

Wednesday, January 22, 2014

A Riddle for Davos

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

Hexagonale Unwesen

Einstein and Thomas Mann, Princeton, 1938


IMAGE- Redefining the cube's symmetry planes: 13 planes, not 9.


See also the life of Diogenes Allen, a professor at Princeton
Theological Seminary, a life that reportedly ended on the date—
January 13, 2013— of the above Log24 post.

January 13 was also the dies natalis  of St. James Joyce.

Some related reflections —

"Praeterit figura huius mundi  " — I Corinthians 7:31 —

Conclusion of of "The Dead," by James Joyce—

The air of the room chilled his shoulders. He stretched himself cautiously along under the sheets and lay down beside his wife. One by one, they were all becoming shades. Better pass boldly into that other world, in the full glory of some passion, than fade and wither dismally with age. He thought of how she who lay beside him had locked in her heart for so many years that image of her lover's eyes when he had told her that he did not wish to live.

Generous tears filled Gabriel's eyes. He had never felt like that himself towards any woman, but he knew that such a feeling must be love. The tears gathered more thickly in his eyes and in the partial darkness he imagined he saw the form of a young man standing under a dripping tree. Other forms were near. His soul had approached that region where dwell the vast hosts of the dead. He was conscious of, but could not apprehend, their wayward and flickering existence. His own identity was fading out into a grey impalpable world: the solid world itself, which these dead had one time reared and lived in, was dissolving and dwindling.

A few light taps upon the pane made him turn to the window. It had begun to snow again. He watched sleepily the flakes, silver and dark, falling obliquely against the lamplight. The time had come for him to set out on his journey westward. Yes, the newspapers were right: snow was general all over Ireland. It was falling on every part of the dark central plain, on the treeless hills, falling softly upon the Bog of Allen and, farther westward, softly falling into the dark mutinous Shannon waves. It was falling, too, upon every part of the lonely churchyard on the hill where Michael Furey lay buried. It lay thickly drifted on the crooked crosses and headstones, on the spears of the little gate, on the barren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the living and the dead.

Thursday, December 27, 2012

Object Lesson

Yesterday's post on the current Museum of Modern Art exhibition
"Inventing Abstraction: 1910-1925" suggests a renewed look at
abstraction and a fundamental building block: the cube.

From a recent Harvard University Press philosophical treatise on symmetry—

The treatise corrects Nozick's error of not crediting Weyl's 1952 remarks
on objectivity and symmetry, but repeats Weyl's error of not crediting
Cassirer's extensive 1910 (and later) remarks on this subject.

For greater depth see Cassirer's 1910 passage on Vorstellung :

IMAGE- Ernst Cassirer on 'representation' or 'Vorstellung' in 'Substance and Function' as 'the riddle of knowledge'

This of course echoes Schopenhauer, as do discussions of "Will and Idea" in this journal.

For the relationship of all this to MoMA and abstraction, see Cube Space and Inside the White Cube.

"The sacramental nature of the space becomes clear…." — Brian O'Doherty

Saturday, September 24, 2011

Kernels of Being

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

For the Pope in Germany

"We wish to see Jesus. For somehow we know, we suspect, we intuit, that if we see Jesus we will see what Meister Eckhart might call “The Divine Kernel of Being”— that Divine Spark of God’s essence, God’s imago Dei, the image in which we are created. We seem to know that in seeing Jesus we just might find something essential about ourselves."

—The Reverend Kirk Alan Kubicek, St. Peter’s at Ellicott Mills, Maryland, weblog post of Saturday, March 28, 2009, on a sermon for Sunday, March 29, 2009

See also this journal in March 2009.

Related non-theology—

Weyl on coordinate systems, Cassirer on the kernel of being, and A Study in Art Education.

Wednesday, September 21, 2011

Symmetric Generation

Filed under: General,Geometry — Tags: , , , , — m759 @ 2:00 PM

Suggested by yesterday's Relativity Problem Revisited and by Cassirer on Objectivity

From Symmetric Generation of Groups , by R.T. Curtis (Cambridge U. Press, 2007)—

"… we are saying much more than that G M 24 is generated by
some set of seven involutions, which would be a very weak
requirement. We are asserting that M 24 is generated by a set
of seven involutions which possesses all the symmetries of L3(2)
acting on the points of the 7-point projective plane…."
Symmetric Generation , p. 41

"It turns out that this approach is particularly revealing and that
many simple groups, both sporadic and classical, have surprisingly
simple definitions of this type."
Symmetric Generation , p. 42

See also (click to enlarge)—

http://www.log24.com/log/pix11B/110921-CassirerOnObjectivity-400w.jpg

Cassirer's remarks connect the concept of objectivity  with that of object .

The above quotations perhaps indicate how the Mathieu group M 24 may be viewed as an object.

"This is the moment which I call epiphany. First we recognise that the object is one  integral thing, then we recognise that it is an organised composite structure, a thing  in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that  thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany."

— James Joyce, Stephen Hero

For a simpler object "which possesses all the symmetries of L3(2) acting on the points of the 7-point projective plane…." see The Eightfold Cube.

For symmetric generation of L3(2) on that cube, see A Simple Reflection Group of Order 168.

Wednesday, February 18, 2009

Wednesday February 18, 2009

Filed under: General — Tags: , , — m759 @ 11:30 AM

Raiders of
the Lost Well

“The challenge is to
keep high standards of
scholarship while maintaining
showmanship as well.”

— Olga Raggio, a graduate of the Vatican library school and the University of Rome who, at one point in her almost 60 years with the Metropolitan Museum of Art, organized “The Vatican Collections,” a blockbuster show. Dr. Raggio died on January 24.

The next day, “The Last Templar,” starring Mira Sorvino, debuted on NBC.

Mira Sorvino in 'The Last Templar'
“The story, involving the Knights Templar, the Vatican, sunken treasure, the fate of Christianity and a decoding device that looks as if it came out of a really big box of medieval Cracker Jack, is the latest attempt to combine Indiana Jones derring-do with ‘Da Vinci Code’ mysticism.”

The New York Times

Sorvino in “The Last Templar”
at the Church of the Lost Well:

Mira Sorvino at the Church of the Lost Well in 'The Last Templar'

One highlight of Secretary of State Hillary Clinton’s first overseas trip will be a stop in China. Her main mission in Beijing will be to ensure that US-China relations under the new Obama administration get off to a positive start.”

— Stephanie Ho, Voice of America Beijing bureau chief, today

Symbol of The Positive,
from this journal
on Valentine’s Day:

'Enlarge' symbol from USA Today

“Stephanie started at the Voice of America as an intern in 1991. She left briefly to attend film school in London in 2000. Although she didn’t finish, she has always wanted to be a film school dropout, so now she’s living one of her dreams.

Stephanie was born in Ohio and grew up in California. She has a bachelor’s degree in Asian studies with an emphasis on Chinese history and economics, from the University of California at Berkeley.”

“She is fluent in
Mandrin Chinese.”
VOA

As is Mira Sorvino.

Chinese character for 'well' and I Ching Hexagram 48, 'The Well'

Those who, like Clinton, Raggio, and
Sorvino’s fictional archaeologist in
“The Last Templar,” prefer Judeo-
Christian myths to Asian myths,
may convert the above Chinese
“well” symbol to a cross
(or a thick “+” sign)
by filling in five of
the nine spaces outlined
by the well symbol.

In so doing, they of course
run the risk, so dramatically
portrayed by Angelina Jolie
as Lara Croft, of opening
Pandora’s Box.

(See Rosalind Krauss, Professor
of Art and Theory at Columbia,
for scholarly details.)

Rosalind Krauss

Krauss

Greek Cross, adapted from painting by Ad Reinhardt

The Krauss Cross

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