Log24

Saturday, June 25, 2016

Convergence

Filed under: General — m759 @ 2:45 pm

Continued from Halloween Manifestos 2013 and from Poster —

Dauntless

Filed under: General — m759 @ 2:00 pm

" 'Hear what he says,' the speaker concludes,
'The dauntless master, as he starts the human tale.' "

— B. J. Leggett on page 66 of 
The Cambridge Companion to Wallace Stevens

(See "An Ordinary Evening on Page 66,"
this journal on Monday, June 20, 2016.)

See also "Dauntless" in the Divergent  saga
and a character from that saga in the previous post.

ART WARS: The Story of Four

Filed under: General — m759 @ 4:00 am

The title is a reference to the Chicago character named "Four"
in Veronica Roth's Divergent  series.

"In July 2014, Roth revealed that she initially wrote 
Divergent  from Four's point of view . . . ." — Wikipedia

Other Chicago-related stories — "Raiders of the Lost Code
(on the recent murder-suicide of two Chicago Jungians)
and the following —

See also Jungian narrative art in

https://redice.tv/news/
on-the-nature-of-four-jung-s-quarternity-mandalas-the-stone-and-the-self
.

Friday, June 24, 2016

Contrast

Filed under: General — m759 @ 11:24 pm

From a work cited in the previous post —

"… representation of hell and the horrors
of the burial ground are missing."

— Page 384 of Joseph Campbell's The Mythic Image ,
    Princeton University Press, 1981
    (First published in 1974)

For those who regret the above omission

A review of a book published in 1977 —

"Its materials are fear and death, hallucination
and the burning of souls." 

The book's author reportedly died Thursday, June 23, 2016.

See also, from 11 AM ET that day, "Raiders of the Lost Code."

Compare

Filed under: General — m759 @ 8:00 pm

The above Mythic Image  quote is from page  384.

See also "Order  384" in this journal.

Symbol of the Self

Filed under: General — m759 @ 1:00 am

The previous post suggests a review of the phrase
symbol of the self " in this journal.

Thursday, June 23, 2016

Raiders of the Lost Code

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

From a web page

Breaking the Code of the Archetypal Self:
An Introductory Overview of the Research Discoveries
Leading to Neo-Jungian Structural Psychoanalysis

Dr. Moore will introduce his research and discoveries
with regard to the deep structures of the Self.
Tracing the foundations in the tradition of Jung’s
affirmation of the collective unconscious, Moore
will present his “decoding of the Diamond Body,”
a mapping of the deep structures of the Great Code
of the psyche. . . .

From the same web site

Googling "Jung" + "Diamond Body" shows that
Moore's terminology differs from Jung's.
The octahedron that Moore apparently associates
with his "diamond body" was discussed by Jung
in a different context. See selections from Ch. 14
of Jung's Aion
 "The Structure and Dynamics of the Self."

Dr. Moore appears as well in the murder-suicide story 
of last night's 11:18 PM ET post.

For the relevance of Aion  to "deep structures,"
see Jung + Diamond + Structure in this  journal
and, more specifically, "Deep  Structure."

Figures of Speech

Filed under: General — m759 @ 12:00 am

See posts now tagged Starbursts,
and a search for Nabokov + Starflight.

Wednesday, June 22, 2016

Tutelary Figures

Filed under: General — m759 @ 11:18 pm

(Continued from December 19, 2007)

http://chicago.suntimes.com/news/
colleagues-shocked-as-noted-psychologists-die-in-murder-suicide/

Another tutelary figure —

"You got to know when to hold 'em "

Versatile Figure

Filed under: General — m759 @ 1:37 pm

"I need a photo opportunity " — Paul Simon

NYT 'distinctive cultural tang' obit

Click image to enlarge.

Bloomsday Trinity

Filed under: General — m759 @ 12:48 pm

NYT 'distinctive cultural tang' obituary

"He attended the Trinity School in Manhattan
before enrolling in the Lawrenceville School
in New Jersey, where he began writing poetry.
He graduated in 1957. Under his yearbook
photograph appeared the motto:

'Plato or comic books, I’m versatile.' "

He reportedly died on Bloomsday, June 16.
See also this journal on that date —

Model Citizen

Filed under: General — m759 @ 7:45 am

of a paper town

Fragments Against My Ruins, by Odd Thomas

Filed under: General — m759 @ 5:42 am
  1. "Inside of a dog, it's too dark to read"
  2. "Alpha Dog"
  3. "B. J. Leggett is professor emeritus at UT Knoxville"
  4. "Seven is Heaven, Eight is a Gate, Nine is a Vine"

Update of about 6:40 AM ET on June 22, 2016 —

"Que cantaba el rey David."  Happy birthday to Kris Kristofferson.

Tuesday, June 21, 2016

The Central Structure

Filed under: General,Geometry — Tags: , , — m759 @ 8:00 am

“The central poem is the poem of the whole,
The poem of the composition of the whole”

— Wallace Stevens, “A Primitive like an Orb”

The symmetries of the central four squares in any pattern
from the 4×4 version of the diamond theorem  extend to
symmetries of the entire pattern.  This is true also of the
central eight cubes in the 4×4×4  Solomon’s cube .

Monday, June 20, 2016

An Ordinary Evening on Page 66

Filed under: General — m759 @ 9:00 pm

Shema, Salinger

Filed under: General — Tags: — m759 @ 1:00 pm

"I've got a brand-new pair of roller skates "

Melanie, 1971

Related material —  Salinger in the Park and
                                 Philosophy in a New Key.

Sacred Space

Filed under: General,Geometry — m759 @ 12:00 pm

For further background to this morning's post Plan 9 Continues,
see posts tagged Sacred Space

The 3x3 square .

Plan 9 Continues

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

See …

At the Still Point … (February 12, 2008)

For Balanchine's Birthday (January 9, 2007)

Go Set a Structure (Various dates)

and …

Sunday, June 19, 2016

In Memoriam

Filed under: General — m759 @ 10:30 pm

For those who prefer the red pill to the blue pill

See as well this afternoon's related Vanity Fair  piece.

Making Gatsby Great Again

Filed under: General,Geometry — m759 @ 2:24 pm

Image-- From the Diamond in Plato's Meno to Modern Finite Geometry

See also the previous post.

Saturday, June 18, 2016

Meno

Filed under: General — m759 @ 10:00 pm

From a poet discussed in Plato's Meno  —

Click the above image for an animated version of Feb. 12, 2008.

See also this journal on Feb. 12, 2008.

A Small Scholarship

Filed under: General — m759 @ 4:00 pm

"He grew up near Stratford-upon-Avon
and went to school on a small scholarship."

NY Times  obit this afternoon for
    a theatre designer who reportedly died 
    on June 10.  See also this  journal 
    on that date.

Poster

Filed under: General — m759 @ 3:33 pm

See also the previous post.

Tie a Yellow Ribbon

Filed under: General — m759 @ 12:31 pm

Click to enlarge.

Joke

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

See also some recent related posts.

Alms for Oblivion

Filed under: General — Tags: — m759 @ 11:20 am

Clock Folding*

Filed under: General — Tags: — m759 @ 1:00 am

* The title refers to the recent posts Hypertime 
and Midnight in Herald Square. See also Julavits 
in a post of March 31, 2015.

Midnight in Herald Square

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

In memory of New Yorker  artist Anatol Kovarsky,
who reportedly died at 97 on June 1.

Note the Santa, a figure associated with Macy's at Herald Square.

See also posts tagged Herald Square, as well as the following
figure from this journal on the day preceding Kovarsky's death.

A note related both to Galois space and to
the "Herald Square"-tagged posts —

"There is  such a thing as a length-16 sequence."
— Saying adapted from a young-adult novel.

Friday, June 17, 2016

Hypertime

Filed under: General — m759 @ 2:45 pm

The Hypertime  post from 11 PM yesterday suggests
a review of one sort of narrative sequence —

Here the aleph may be regarded as a sort of 
glass slipper (see last midnight's post) found by
Alan Moore. (Moore​, mentioned in last night's
Hypertime post, is the author of Lost Girls .)

Making Stuff Up

Filed under: General — m759 @ 12:00 am

See Three Approaches to The World as Myth
(Log24, September 16, 2015).

Thursday, June 16, 2016

Klock’s Hypertime

Filed under: General — Tags: , — m759 @ 11:00 pm

Polytropos

Filed under: General — Tags: — m759 @ 10:00 pm

Πολυμερῶς καὶ πολυτρόπως πάλαι ὁ Θεὸς λαλήσας . . . .

Long Day's Journey into Nighttown  continues. )

Practically

Filed under: General — Tags: — m759 @ 8:00 am

— From a book reviewed in the April 1923 
Bulletin of the American Mathematical Society

Wednesday, June 15, 2016

The Garden of Allah

Filed under: General — Tags: — m759 @ 10:00 pm

Continues .

From "The Back Page," Notices of the American Mathematical Society ,
June-July 2016 —

Related material:  Page 1 of Screenland , April 1923 —

Rubik’s Deathtrap

Filed under: General — Tags: — m759 @ 7:20 pm

The previous post suggests a search in this journal
for "Deathtrap."

"Rubik’s Cube® used by permission
Rubik’s Brand Ltd. www.rubiks.com."

— Bernd Sturmfels, June-July 2016 Notices
of the American Mathematical Society
,
Volume 63, Number 6, page 605

"Tenser, said the Tensor …." — The Demolished Man
 

Max von Sydow in Branded  (2012)

Expanding the Spielraum …

Filed under: General — Tags: — m759 @ 2:40 pm

Continues

Rubik cube in the heading of the homepage of the Notices of the American Mathematical Society

"My AMS invited address at the SIAM Annual Meeting July 11–15
in Boston discusses the extension of eigenvectors and singular
vectors from matrices to higher order tensors."

Bernd Sturmfels in the June-July 2016 AMS Notices

See also Sturmfels in this  journal — for instance, in
"Expanding the Spielraum," a post of Feb. 3, 2015 —

Stephen King’s “Pulse”

Filed under: General — Tags: — m759 @ 1:00 pm

You can  make this stuff up.

Venn’s Lotus …

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

Continues .

A search for "Purple" in this journal suggests a review of Transition,
a Log24 post of November 21, 2011.  A related image —

Tuesday, June 14, 2016

Color Code

Filed under: General — m759 @ 10:00 pm

For Megyn Kelly

The following animation is
by Robert Foote:

Red-Blue-Purple theorem, illustrated by Robert Foote

Hamiltonian Philosophy

Filed under: General — m759 @ 2:40 pm

For some philosophical background, see (for instance) Jeremy Butterfield,
"Some Aspects of Modality in Analytical Mechanics," and

 .

For those who prefer entertainment —

Model Kit

Filed under: General,Geometry — Tags: — m759 @ 12:14 pm

The title refers to the previous post, which quotes a 
remark by a poetry critic in the current New Yorker .

Scholia —

From the post Structure and Sense of June 6, 2016 —

Structure

Sense

A set of 7 partitions of the 2x2x2 cube that is invariant under PSL(2, 7) acting on the 'knight' coordinatization

From the post Design Cube of July 23, 2015 —

Broken Symmetries  in  Diamond Space 

Monday, June 13, 2016

Primordial Stone

Filed under: General — m759 @ 10:00 pm

"The poem on its own is negligible,
instructing a human 'intelligence /
So late dredged up' to master
the primordial stone,
which 'may have contempt /
For too-familiar hands.' 
The stone is language,
the diamond is a poem:
as in a model kit,
all the pieces come labelled
and the instructions are easy to follow."

Dan Chiasson in The New Yorker ,
issue dated June 20, 2016, on a
1955 Adrienne Rich poem,
"The Diamond Cutters"

Sunday, June 12, 2016

Table Talk

Filed under: General,Geometry — m759 @ 1:00 pm

See also the previous post and posts on "The Lost Theorem."

Saturday, June 11, 2016

Café Society

Filed under: General — m759 @ 9:00 pm

A post linked to here at 9 AM on May 27, 2016 —

Novaculae

Filed under: General — m759 @ 2:01 pm

In memory of philosopher Morton White,
who reportedly died at 99 on May 27.

See Lowry + Razor and Joyce + Razor.

Where Credit Is Due

Filed under: General — Tags: — m759 @ 4:16 am

"White is credited with broadening the scope of
topics traditionally studied by philosophers…."

Friday, June 10, 2016

High Concept

Filed under: General — m759 @ 9:00 am

(Continued)

Orwell Meets Waugh

'Space Cross' from the Cullinane diamond theorem

Thursday, June 9, 2016

Actor’s Nightmare

Filed under: General — m759 @ 4:00 pm

See a commencement address from Friday, May 22, 2015,
and a post from this journal on that date.

Triple Cross…

Filed under: General — m759 @ 7:00 am

Continues.

Wednesday, June 8, 2016

In Memoriam

Filed under: General — m759 @ 12:06 pm

Riverrun.

But is it good for the narrative?

Filed under: General — m759 @ 4:16 am

Jews on Style  continues

From a Washington Post  obituary  this morning —

"For the past 30 years, while teaching at New York University’s
law school, Dr. Bruner explored the idea of storytelling as a
fundamental way of understanding the nature of the world
around us. He believed that the choices we make in telling
stories 'become so habitual that they finally become recipes
for structuring experience itself, for laying down routes into
memory,' he said in 1987.

'This is a mode of cognition,' Gardner said, 'at least as
important as STEM' — the science, technology, engineering
and mathematics model of instruction that has gained
currency in recent years.

'He made narrative a form of thinking,' Gardner added.

Jerome Seymour Bruner was born Oct. 1, 1915,
in New York City to Jewish immigrants from Eastern Europe."

Related material —

Tuesday, June 7, 2016

Art and Space…

Filed under: General,Geometry — Tags: , — m759 @ 6:00 am

Continues, in memory of chess grandmaster Viktor Korchnoi,
who reportedly died at 85 yesterday in Switzerland —

IMAGE- Spielfeld (1982-83), by Wolf Barth

The coloring of the 4×4 "base" in the above image
suggests St. Bridget's cross.

From this journal on St. Bridget's Day this year —

"Possible title: 

A new graphic approach 
to an old geometric approach
to a new combinatorial approach
to an old algebraic approach
to M24
"

The narrative leap from image to date may be regarded as
an example of "knight's move" thinking.

Monday, June 6, 2016

Structure and Sense

Filed under: General,Geometry — Tags: , — m759 @ 2:01 pm

"… the war of 70-some years ago
has already become something like the Trojan War
had been for the Homeric bards:
a major event in the mythic past
that gives structure and sense to our present reality."

— Justin E. H. Smith, a professor of philosophy at
     the University of Paris 7–Denis Diderot,
     in the New York Times  column "The Stone"
     (print edition published Sunday, June 5, 2016)

In memory of a British playwright who reportedly
died at 90 this morning —

Structure

Sense

A set of 7 partitions of the 2x2x2 cube that is invariant under PSL(2, 7) acting on the 'knight' coordinatization

Intellect Limited

Filed under: General — Tags: — m759 @ 6:29 am

Explorations in Media Ecology
Volume 12 Numbers 3 & 4
© 2013 Intellect Ltd Article.

For some background, see Bullshit Studies.

Sunday, June 5, 2016

The Shining of May 29…

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

Continues .

A death on May 29,  from The Fresno Bee —

See as well "La Diadema de la Muerte."

http://www.log24.com/log/pix12/120108-CardinalPreoccupied.jpg

"The Cardinal seemed a little preoccupied today."

Sunday School: Seven Seals

Filed under: General,Geometry — Tags: , — m759 @ 7:00 am

A set of 7 partitions of the 2x2x2 cube that is invariant under PSL(2, 7) acting on the 'knight' coordinatization

Click image for some background.

See also Standard Disclaimer.

Saturday, June 4, 2016

Mythos

Filed under: General — Tags: , — m759 @ 1:23 pm

Previous references in this journal to the "Church of Synchronology"
suggest a review of that phrase's source —

"The fine line between hokum and rational thinking
is precisely the point of The Lost Time Accidents ;
a brick of a book not just because of its length but
because of the density of both the prose and the
ideas it contains.

It is, in a nutshell, a sweeping historical novel that's
also a love story but is rooted in time-travel
science fiction and takes on as its subject
the meaning of time itself. This is no small endeavor."

Janelle Brown in The Los Angeles Times
     on February 4, 2016

See also … 

Logos

Filed under: General — Tags: — m759 @ 1:06 pm

Icons

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

From this morning's news, a  cultural icon —

From November 18, 2015, four  icons —

— the three favicons above, and the following:

Jack in the Box, by Natasha Wescoat

A Personal View

Filed under: General — Tags: , — m759 @ 3:20 am

"The editors are also grateful to
T. Kibble and Imperial College Press
for permission to reprint B. Zumino's paper
'Supersymmetry: A Personal View' . . . ."

— Preface to Symmetry in Mathematics and Physics
(AMS, 2009), a book based on talks at
a UCLA conference of Jan. 18-20, 2008

(For the book's title page, see yesterday morning's post Symmetry.)

This suggests a search in this journal for the term "supersymmetry."
That search yields some links that may be of further interest to
devotees of the Church of Synchronology.

Friday, June 3, 2016

Physics Saint?

Filed under: General — Tags: — m759 @ 7:00 pm

For a physicist who reportedly died at 83 yesterday
(Thursday, June 2, 2016) —

Also on March 13, 2013 —

A note for the Church of Synchronology

See as well the word "contemporary" in the previous post.

Symmetry

Filed under: General — m759 @ 9:00 am

(Continued)

Bruins and van Dam

Filed under: General,Geometry — Tags: , — m759 @ 8:00 am

A review of some recent posts on Dirac and geometry,
each of which mentions the late physicist Hendrik van Dam:

The first of these posts mentions the work of E. M. Bruins.
Some earlier posts that cite Bruins:

Thursday, June 2, 2016

Bullshit Studies

Filed under: General,Geometry — Tags: , — m759 @ 11:30 am

(Continued)

"The allusion to 'the most precious square of sense' shows
Shakespeare doing an almost scholastic demonstration of
the need for a ratio and interplay among the senses as
the very constitution of rationality."

— Marshall McLuhan, The Gutenberg Galaxy ,
University of Toronto Press, 1962, page 13

"What Shakespeare refers to in Lear  as the 'precious
square of sense' probably has reference to the traditional
'square of opposition' in logic and to that four-part analogy
of proportionality which is the interplay of sense and reason."     

— McLuhan, ibid. , page 241

This is of course nonsense, and, in view of McLuhan's pose
as a defender of the Catholic faith, damned  nonsense.

Epigraph by McLuhan —

"The Gutenberg Galaxy  develops a mosaic or field
approach to its problems."

I prefer a different "mosaic or field" related to the movable
blocks  of Fröbel, not the movable type  of Gutenberg.

Wednesday, June 1, 2016

Mathematics and Narrative

Filed under: General — Tags: , — m759 @ 12:06 pm

Principles before Personalities — AA  Saying .

Principles —

See Schoolgirl Problem in Wikipedia.

Personalities — 

See Alexandra Alter in the May 26 online New York Times :

"With the proliferation of 'girl' titles,
there are signs that the trend may have peaked;
it already seems ripe for parody." 

Update of 12:40 PM ET on Wednesday, June 1, 2016 —

A note for the Church of Synchronology 
See a post from this  journal on the date of the Alter piece, May 26:

(Click image for the rest of the post .)

Tuesday, May 31, 2016

Galois Space —

Filed under: General,Geometry — Tags: — m759 @ 7:00 pm

A very brief introduction:

Seven is Heaven...

Und Dann …

Filed under: General — m759 @ 5:48 pm

In memory of CBS TV programmer Michael Dann,
who reportedly died at 94 on Friday, May 27 —

Don't Forget Hoss

Judy Carne and Hoss in NBC's "Bonanza,"  a nemesis
of CBS Sunday programming.

In other entertainment news

Cartoonist Frank Modell reportedly died at 98, 
also on Friday, May 27.

In his  memory, part of a Weird Tale from 1948 that is
illustrated (sort of) by a more recent Modell drawing —

Wild Devising

"No one ever found out who the dead man was.
He had no luggage and no identification;
he had been hitchhiking, and he had
over ninety dollars in his pocket.
He might have been anybody—
someone from show business, or a writer perhaps,
on a haywire vacation of his own wild devising.
I suppose that doesn't matter either.
What does matter is that he died while
Grace was in a very close communion
with what he was doing, and her mind was
wide open for his fantasy. …. "

— Theodore Stugeon, "The Perfect Host,"
Weird Tales , November 1948, page 15

Some context:  This morning's post
"Entertainment in Plato's Cave," and
a few titles from my Kindle library —

Entertainment in Plato’s Cave

Filed under: General — m759 @ 9:00 am

"Plato's allegory of the cave describes prisoners,
inhabiting the cave since childhood, immobile,
facing an interior wall. A large fire burns behind
the prisoners, and as people pass this fire their
shadows are cast upon the cave's wall, and
these shadows of the activity being played out
behind the prisoner become the only version of
reality that the prisoner knows."

From the Occupy Space gallery in Ireland

IMAGE- Patrick McGoohan as 'The Prisoner,' with lapel button that says '6.'

See also the number 6 in yesterday's posts,
Perfect Number and Perfect Universe.

Monday, May 30, 2016

Perfect Universe

Filed under: General,Geometry — Tags: — m759 @ 7:00 pm

(A sequel to the previous post, Perfect Number)

Since antiquity,  six has been known as
"the smallest perfect number." The word "perfect"
here means that a number is the sum of its 
proper divisors — in the case of six: 1, 2, and 3.

The properties of a six-element set (a "6-set") 
divided into three 2-sets and divided into two 3-sets
are those of what Burkard Polster, using the same 
adjective in a different sense, has called 
"the smallest perfect universe" — PG(3,2), the projective
3-dimensional space over the 2-element Galois field.

A Google search for the phrase "smallest perfect universe"
suggests a turnaround in meaning , if not in finance, 
that might please Yahoo CEO Marissa Mayer on her birthday —

The semantic  turnaround here in the meaning  of "perfect"
is accompanied by a model  turnaround in the picture  of PG(3,2) as
Polster's tetrahedral  model is replaced by Cullinane's square  model.

Further background from the previous post —

See also Kirkman's Schoolgirl Problem.

Perfect Number

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

"Ageometretos me eisito."—
"Let no one ignorant of geometry enter."—
Said to be a saying of Plato, part of the
seal of the American Mathematical Society—

For the birthday of Marissa Mayer, who turns 41 today —

VOGUE Magazine,
AUGUST 16, 2013 12:01 AM
by JACOB WEISBERG —

"As she works to reverse the fortunes of a failing Silicon Valley
giant, Yahoo’s Marissa Mayer has fueled a national debate
about the office life, motherhood, and what it takes to be the
CEO of the moment.

'I really like even numbers, and
I like heavily divisible numbers.
Twelve is my lucky number—
I just love how divisible it is.
I don’t like odd numbers, and
I really don’t like primes.
When I turned 37,
I put on a strong face, but
I was not looking forward to 37.
But 37 turned out to be a pretty amazing year.
Especially considering that
36 is divisible by twelve!'

A few things may strike you while listening to Marissa Mayer
deliver this riff . . . . "

Yes, they may.

A smaller number for Marissa's meditations:

Six has been known since antiquity as the first "perfect" number.
Why it was so called is of little interest to anyone but historians
of number theory  (a discipline that is not, as Wikipedia notes, 
to be confused with numerology .)

What part geometry , on the other hand, played in Marissa's education,
I do not know.

Here, for what it's worth, is a figure from a review of posts in this journal
on the key role played by the number six in geometry —

Sunday, May 29, 2016

The Ideogram Principle …

According to McLuhan

Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—

"The American mind is not even close to being amenable
to the ideogram principle as yet.  The reason is simply this.
America is 100% 18th Century. The 18th century had
chucked out the principle of metaphor and analogy—
the basic fact that as A is to B so is C to D.  AB:CD.   
It can see AB relations.  But relations in four terms are still
verboten.  This amounts to deep occultation of nearly all
human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  
Until stated and publicly recognized for what it is, poetry and
the arts can’t exist in America."

For context, see Cameron McEwen,
"Marshall McLuhan, John Pick, and Gerard Manley Hopkins."
(Renascence , Fall 2011, Vol. 64 Issue 1, 55-76)

A relation in four terms

A : B  ::  C : D   as   Model : Crutch  ::  Metaphor : Ornament —

See also Dueling Formulas and Symmetry.

Sunday School

Filed under: General — Tags: — m759 @ 8:00 am

Analogy

Saturday, May 28, 2016

Plan 4

Filed under: General — Tags: , — m759 @ 2:45 am

See a search in this journal for "As Is."

Friday, May 27, 2016

Plan 9

Filed under: General — m759 @ 9:00 am

http://m759.net/wordpress/?tag=holy-field-gf3

Raiders of the Lost Crucible…

Filed under: General — Tags: — 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

Peer Review

Filed under: General — Tags: , — m759 @ 7:00 am

A review of the phrase "Innermost Kernel" in this journal
suggests the following meditation

"Who am I?" — Existential cry
in "Zoolander" and "Zoolander 2."

A similar question occurs in "Peer Gynt" —

Ben Brantley in yesterday morning's print New York Times *
expressed a nihilistic view of Peer as an onion-peeler —

"Toward the end of Ibsen’s 'Peer Gynt,' a saga of self
under siege, the title character is discovered peeling
an onion, finding in the layers of that humble vegetable
a symbol for the chapters of an eventful life . . . .

[the director’s] approach is the same one that Peer
applies to the onion: Keep stripping until you find the core.
Of course in Peer’s case what is finally found is
plenty of nothing, an apt conclusion for a man
for whom a solid self remains elusive."

I prefer a view from what Fitzgerald called
"the dark fields of the republic" — the Dordt College view —

* The Times — "A version of this review appears in print on May 26, 2016, 
on page C3 of the New York edition with the headline:
'A Saga of Self-Identity, Stripped to Its Core, Still Provokes.' "

Thursday, May 26, 2016

Dorje

Filed under: General,Geometry — Tags: — m759 @ 6:40 pm

Images suggested by the previous post

Note the name "Dorje" in the first image above.

Remarks related to the name "Dorje," as well as to
 "Projective Geometry and PT-Symmetric Dirac Hamiltonian,"
a 2009 paper by Y. Jack Ng  and the late Hendrik van Dam —

Dorje C. Brody, 'Consistency of PT-Symmetric Quantum Mechanics'

Remarks for the Church of Synchronology from December 16, 2015,
the date of the above Dorje  arXiv upload —

Expanding the Spielraum

Filed under: General — m759 @ 1:45 am

(Continued)

The physicist Hendrik van Dam was mentioned in recent posts.

He reportedly died at 78 on February 11, 2013.

A post from that date, and a followup —

Wednesday, May 25, 2016

Framework

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

"Studies of spin-½ theories in the framework of projective geometry
have been undertaken before." — Y. Jack Ng  and H. van Dam
February 20, 2009

For one such framework,* see posts from that same date 
four years earlier — February 20, 2005.

* A 4×4 array. See the 19771978, and 1986 versions by 
Steven H. Cullinane,   the 1987 version by R. T. Curtis, and
the 1988 Conway-Sloane version illustrated below —

Cullinane, 1977

IMAGE- Hypercube and 4x4 matrix from the 1976 'Diamond Theory' preprint, as excerpted in 'Computer Graphics and Art'

Cullinane, 1978

Cullinane, 1986

Curtis, 1987

Update of 10:42 PM ET on Sunday, June 19, 2016 —

The above images are precursors to

Conway and Sloane, 1988

Update of 10 AM ET Sept. 16, 2016 — The excerpt from the
1977 "Diamond Theory" article was added above.

Crucifers

Filed under: General — Tags: — m759 @ 11:30 am

For the Church of Synchronology

Marissa Mayer, as illustrated on the cover
of the current issue of Variety , and
Mira Sorvino, as discussed in posts of
Feb. 20, 2009 (a date suggested by the
arXiv upload date in the previous post).

Kummer and Dirac

From "Projective Geometry and PT-Symmetric Dirac Hamiltonian,"
Y. Jack Ng  and H. van Dam, 
Physics Letters B , Volume 673, Issue 3,
23 March 2009, Pages 237–239

(http://arxiv.org/abs/0901.2579v2, last revised Feb. 20, 2009)

" Studies of spin-½ theories in the framework of projective geometry
have been undertaken before. See, e.g., Ref. [4]. 1 "

1 These papers are rather mathematical and technical.
The authors of the first two papers discuss the Dirac equation
in terms of the Plucker-Klein correspondence between lines of
a three-dimensional projective space and points of a quadric
in a five-dimensional projective space. The last paper shows
that the Dirac equation bears a certain relation to Kummer’s
surface, viz., the structure of the Dirac ring of matrices is 
related to that of Kummer’s 166 configuration . . . ."

[4]

O. Veblen
Proc. Natl. Acad. Sci. USA , 19 (1933), p. 503
Full Text via CrossRef

E.M. Bruins
Proc. Nederl. Akad. Wetensch. , 52 (1949), p. 1135

F.C. Taylor Jr., Master thesis, University of North Carolina
at Chapel Hill (1968), unpublished


A remark of my own on the structure of Kummer’s 166 configuration . . . .

See that structure in this  journal, for instance —

See as well yesterday morning's post.

Nothing Illustrated

Filed under: General — m759 @ 3:33 am


Illustration by Javier Jaén

See also "Box of Nothing" in this journal.

Tuesday, May 24, 2016

Rosenhain and Göpel Revisited

The authors Taormina and Wendland in the previous post
discussed some mathematics they apparently did not know was
related to a classic 1905 book by R. W. H. T. Hudson, Kummer's
Quartic Surface
.

"This famous book is a prototype for the possibility
of explaining and exploring a many-faceted topic of
research, without focussing on general definitions,
formal techniques, or even fancy machinery. In this
regard, the book still stands as a highly recommendable,
unparalleled introduction to Kummer surfaces, as a
permanent source of inspiration and, last but not least, 
as an everlasting symbol of mathematical culture."

— Werner Kleinert, Mathematical Reviews ,
     as quoted at Amazon.com

Some 4×4 diagrams from that book are highly relevant to the
discussion by Taormina and Wendland of the 4×4 squares within
the 1974 Miracle Octad Generator of R. T. Curtis that were later,
in 1987, described by Curtis as pictures of the vector 4-space over
the two-element Galois field GF(2).

Hudson did not think of his 4×4 diagrams as illustrating a vector space,
but he did use them to picture certain subsets of the 16 cells in each
diagram that he called Rosenhain and Göpel tetrads .

Some related work of my own (click images for related posts)—

Rosenhain tetrads as 20 of the 35 projective lines in PG(3,2)

IMAGE- Desargues's theorem in light of Galois geometry

Göpel tetrads as 15 of the 35 projective lines in PG(3,2)

Anticommuting Dirac matrices as spreads of projective lines

Related terminology describing the Göpel tetrads above

Ron Shaw on symplectic geometry and a linear complex in PG(3,2)

Monday, May 23, 2016

Springer

Filed under: General — Tags: , — m759 @ 10:00 am

In memory of the late mathematician John Nash
and of the late actor Alan Young ...

A Talking Horse — 

What the horse says: "First online: 28 August 2013."

See also OverarchingPsychonauts, and Spider Tale in this journal.

23

Filed under: General,Geometry — m759 @ 8:25 am

IMAGE- R. D. Carmichael's 1931 construction of the Steiner system S(5, 8, 24)

Keywords: Golay, Mathieu, Steiner system, Carmichael, Harvard

Sunday, May 22, 2016

Definitive

Filed under: General — m759 @ 7:30 pm

"(CBS News) Two decades after Morley Safer took
a critical look at contemporary art in his 60 Minutes
story  'Yes…But is it Art?'  he has found the definitive
answer to his snide question . . . ."

— March 30, 2012, introduction to a "60 Minutes" piece 
dated April 1, 2012

Sunday School

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

From 'The Politics of Experience,' by R.D. Laing

A less metaphysical approach to a "pre-form" —

From Wallace Stevens, "The Man with the Blue Guitar":

IX

And the color, the overcast blue
Of the air, in which the blue guitar
Is a form, described but difficult,
And I am merely a shadow hunched
Above the arrowy, still strings,
The maker of a thing yet to be made . . . .

"Arrowy, still strings" from the diamond theorem

See also "preforming" and the blue guitar
in a post of May 19, 2010.

Update of 7:11 PM ET:
More generally, see posts tagged May 19 Gestalt.

Saturday, May 21, 2016

Meet the Fitzgeralds

Filed under: General — m759 @ 10:54 pm

Grammar

Filed under: General — m759 @ 12:00 pm

Related material:  The Lindbergh Manifesto and The Leibniz Medal.

Fitzgerald and Paris

Filed under: General — Tags: — m759 @ 10:08 am

The previous post suggests two images

The date of the above Promoted Tweet is October 19, 2015.

For the Church of Synchronology, an image from Log24 on that date:

"So we beat on, boats against the current " — F. Scott Fitzgerald

New Base

Filed under: General — m759 @ 12:48 am

Three reflections suggested by the previous post

1. A Whit Stillman film mentions favorably Scrooge McDuck —

2. A "promoted tweet" at the Twitter of the previous post's author leads to

3. The above phrase "New Base" suggests a related literary note —

Friday, May 20, 2016

Well Received

Filed under: General — Tags: — m759 @ 11:25 pm

Steve Almasy, CNN

Updated 10:46 PM ET, Fri., May 20, 2016

" (CNN)  Alan Young, who played the hapless yet protective
owner of a talking horse on the popular television comedy
'Mister Ed,' has died at age 96, according to officials at the
Motion Picture & Television Home in Woodland Hills, California.

He died Thursday of natural causes with his children at his side,
the organization said.

Young also was a well-received voice actor, with appearances
as Scrooge McDuck in many Disney productions . . . ."

[McDuck link added.]

Plan 9 Revival

Filed under: General — m759 @ 12:00 pm

Amy Adams as Amelia Earhart in 'Night at the Museum: Battle of the Smithsonian'

It from Bit*

Filed under: General — m759 @ 11:00 am

For Galatea 2.2 on Eliza Doolittle Day

My Google searches are set to ignore my own private
search history. Still, I am not sure whether others would
see the same results as those below, which do  seem to
reflect rather closely my own interests.  Google-as-Galatea
perhaps based the search results partly on associations
from this weblog. An exception: the "Family Circus " novel
in the list below. I have not heard of this book before, but
it seems to be a tale analogous to Stephen King's It ,
from which the searched-for quotation below is drawn.

I prefer a different Family Circus.

* A phrase coined by the late John Archibald Wheeler.

20

Filed under: General — Tags: — m759 @ 2:14 am

"… Thursday morning at 7:30 a.m. at a hospice
      in Danvers, Massachusetts."

Read more:  http://www.rollingstone.com/music/news/
original-beastie-boys-member-john-berry-dead-at-52-20160519

From a search for Danvers in this journal, two quotations
for Stephen King fans

"Danvers is a town in Essex County, Massachusetts, 
United States, located on the Danvers River near the
northeastern coast of Massachusetts. Originally known
as Salem Village, the town is most widely known for its
association with the 1692 Salem witch trials. It is also
known for the Danvers State Hospital, one of the state's
19th-century psychiatric hospitals, which was located here." 

"The summer's gone and all the roses fallin' "

[CHORUS]
In a world gone mad it's hard to think right

Read more:  Beastie Boys – In A World Gone Mad Lyrics

Illustrations: Thursday's 3:28 AM ET post and

THE HOURGLASS CODE
    (Sketch for a favicon)

Thursday, May 19, 2016

I have seen it, I have seen it!

Filed under: General — Tags: — m759 @ 3:28 am

The title is a quote from Sir Galahad in
"Monty Python and the Holy Grail."

Immediately following these words

Note also posts on The Hourglass Code .

This  post was suggested by an album cover 
mentioned in tonight's New York Times  story 
on the May 11 death at 73 in London of one
David King , a graphic designer and design historian — 

"For the third Hendrix album, 'Electric Ladyland,'
Mr. King commissioned a photograph of 19
nude women, in various sizes and shapes, which
he intended as a rebuttal to the Playboy image of
women. In the United States, it was regarded as
risqué and was replaced with a head shot of Hendrix."

— William Grimes

Kulturkampf

Filed under: General,Geometry — Tags: — m759 @ 2:27 am

From a check tonight of The New York Review of Books

These NYRB  stories from May 15 and May 13 suggest a
review of images on Ratner's Star  and on the Eye of God.

IMAGE- 'Ratner's Star,' by Don DeLillo (1976)

Above image reposted from Jan. 10, 2014

I. The structures in the Diamond Puzzle

Adam and God (Sistine Chapel), with Jungian Self-Symbol and Ojo de Dios (The Diamond Puzzle)

Click on image for Jungian background.

II: The structure on a recent cover of Semiotica

'Semiotica' cover and article by Solomon Marcus on Levi-Strauss's 'canonic formula' of myth

Above images reposted from May 5, 2016

Related material:  The previous post, Dueling Formulas.

Wednesday, May 18, 2016

Dueling Formulas

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

Jung's four-diamond formula vs. Levi-Strauss's 'canonical formula'

Note the echo of Jung's formula in the diamond theorem.

An attempt by Lévi-Strauss to defend his  formula —

"… reducing the life of the mind to an abstract game . . . ." —

For a fictional version of such a game, see Das Glasperlenspiel .

Tuesday, May 17, 2016

Death on May Day

Filed under: General — Tags: — m759 @ 2:45 am

So set 'em up, Joe  . . . .

Bullshit Studies

The originator of the phrase 'Fab Four' reportedly
died at 80 on Saturday, May 14, 2016.

This suggests a review of another noted four-set.

The above image is from a study of Lévi-Strauss's "Canonical Formula"

Midrash —

Log24 post titled 'As Is'

[Above photo of Lévi-Strauss and formula added June 6, 2016.]

Monday, May 16, 2016

Sermons

Filed under: General — m759 @ 1:06 pm

Click the tweets below for a related news story.

See also this  journal on the same weekend —

Friday, March 11, through Monday, March 14, 2016.

A sample —

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.'"

Fake Religion

Filed under: General — Tags: — m759 @ 1:00 am

(A companion-piece to Fake Eliot.)

The President at Rutgers on Sunday

Point number one

When you hear someone longing for the ‘good old days,’
take it with a grain of salt.  (Laughter and applause.)
Take it with a grain of salt.”

Boris Karloff as a modernist architect in a 1934 horror film —

Cum grano salis.

Jew at the Glitter Ball

Filed under: General — m759 @ 12:00 am

The title refers to Frederick Seidel and
to a post of April 29, "At the Still Point."

Sunday, May 15, 2016

Fake Eliot

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

The New Yorker

Poems | September 3, 2012 issue

House Master

BY FREDERICK SEIDEL

. . . .

“I remember everything.
I remember nothing.
I remember ancient Greek sparkles like a diamond ring.”

. . . .

See also posts now tagged “One Ring
and a search in this journal for “Glitter.”

One Ring

Filed under: General,Geometry — Tags: , — m759 @ 5:06 pm

(Continued from May 11 and May 15.)

Poem by Eleanor Wilner from 'Reversing the Spell' speaks of diamonds and 'glitter.' (Pbk. publ. Nov. 1, 1997)

Quarter to Three

Filed under: General — Tags: , — m759 @ 2:45 pm
 

Hilary Swank in 'Million Dollar Baby'

O.C.D.          

The "O.C.D." does not refer to obsessive-
compulsive disorder, but to "Our Class, Dear."

Aesthetics

Filed under: General — Tags: , , — m759 @ 2:09 am

A college girl's remarks in the previous post suggested
a search in this journal for "vulgar and stupid."
That search yielded date — March 2, 2014.

In the spirit of the Church of Synchronology, a further search —
for that date — yielded, in a March 2, 2014, post, the following —

Square Dance

From The Telegraph —

And no fact of Alain Resnais’s life seemed to strike a stranger note than his assertion that the films which first inspired his ambition to become a film director were those in which Fred Astaire and Ginger Rogers danced. Or was it Dick Powell and Ruby Keeler? He could never be sure. “I wondered if I could find the equivalent of that exhilaration,” he recalled.

If he never did it was perhaps because of his highly cultivated attitude to serious cinema. His character and temperament were more attuned to the theory of film and a kind of intellectual square dance* which was far harder to bring to the screen with “exhilaration” than the art of Astaire and Rogers.

*See today's 11 AM ET Sermon.

"Heaven, I'm in Heaven!"

The college girl, who reportedly died at 70 on May 11, was
Katherine Dunn, author of the book One Ring Circus  quoted
above. She apparently improved with age.

Saturday, May 14, 2016

Yeah, Art, Beauty

Filed under: General — Tags: , — m759 @ 11:17 pm

From a New York Times  obituary this evening —

"She entered Reed College in Portland as a philosophy major.

'I enjoyed it until I ran aground in an aesthetics class,' 
Ms. Dunn told Wired  magazine. 'I went in thinking, yeah,
art, beauty — my meat, drink and air. But on the first day,
I didn’t understand a word that was said in class, so I
marched out and changed my major to psychology.' "

Could have marched out and bought a dictionary .

The Hourglass Code

Filed under: General,Geometry — Tags: — m759 @ 1:28 pm

version of the I Ching’s Hexagram 19:

I Ching Hexagram 19, 'Approach,' the box-style version

From Katherine Neville's The Eight , a book on the significance
of the date April 4 — the author's birthday —

Axe image from Katherine Neville's 'The Eight'

The Eight  by Katherine Neville —

    “What does this have to do with why we’re here?”
    “I saw it in a chess book Mordecai showed me.  The most ancient chess service ever discovered was found at the palace of King Minos on Crete– the place where the famous Labyrinth was built, named after this sacred axe.  The chess service dates to 2000 B.C.  It was made of gold and silver and jewels…. And in the center was carved a labrys.”
… “But I thought chess wasn’t even invented until six or seven hundred A.D.,” I added.  “They always say it came from Persia or India.  How could this Minoan chess service be so old?”
    “Mordecai’s written a lot himself on the history of chess,” said Lily…. “He thinks that chess set in Crete was designed by the same guy who built the Labyrinth– the sculptor Daedalus….”
    Now things were beginning to click into place….
    “Why was this axe carved on the chessboard?” I asked Lily, knowing the answer in my heart before she spoke.  “What did Mordecai say was the connection?”….
    “That’s what it’s all about,” she said quietly.  “To kill the King.”
 
     The sacred axe was used to kill the King.  The ritual had been the same since the beginning of time. The game of chess was merely a reenactment.  Why hadn’t I recognized it before?

Related material:  Posts now tagged Hourglass Code.

See also the hourglass in a search for Pilgrim's Progress Illustration.

Friday, May 13, 2016

Geometry and Kinematics

Filed under: General,Geometry — Tags: — m759 @ 10:31 pm

"Just as both tragedy and comedy can be written
by using the same letters of the alphabet, the vast
variety of events in this world can be realized by
the same atoms through their different arrangements
and movements. Geometry and kinematics, which
were made possible by the void, proved to be still
more important in some way than pure being."

— Werner Heisenberg in Physics and Philosophy

For more about geometry and kinematics, see (for instance)

"An introduction to line geometry with applications,"
by Helmut Pottmann, Martin Peternell, and Bahram Ravani,
Computer-Aided Design  31 (1999), 3-16.

The concepts of line geometry (null point, null plane, null polarity,
linear complex, Klein quadric, etc.) are also of interest in finite  geometry.
Some small finite spaces have as their natural models arrays of cubes .

The Zorro of Mark

Filed under: General — m759 @ 3:57 pm

(Continued from Code Name Zero .)

Also on May 2, 2014 — Cross Quote .

Code Name Zero

Filed under: General — Tags: — m759 @ 3:09 pm

NY Times  obit for Mark Lane with erroneous book title:

NY Times obit for Mark Lane with erroneous book title

Sounds like a case for Zimbalist.

For the Late Mark Lane

Filed under: General — Tags: — m759 @ 5:01 am

Sixties conspiracy theorist Mark Lane reportedly
died at 89 on Tuesday night.

From the previous post, But Seriously . . .  —

"Today, we are excited to share the fruits of our research
with the broader community . . . ."

Thursday, May 12, 2016

But Seriously …

Filed under: General — Tags: — m759 @ 7:31 pm

Google today released on GitHub an English parser,
Parsey McParseface .  From Google Research Blog

"Today, we are excited to share the fruits of our research
with the broader community by releasing SyntaxNet,
an open-source neural network framework implemented in 
TensorFlow that provides a foundation for 
Natural Language Understanding (NLU) systems.
Our release includes all the code needed to train new
SyntaxNet models on your own data, as well as 
Parsey McParseface , an English parser that we have
trained for you and that you can use to analyze English text."

"While the accuracy is not perfect, it’s certainly high enough
to be useful in many applications. The major source of errors
at this point are examples such as the prepositional phrase
attachment ambiguity described above, which require real
world knowledge (e.g. that a street is not likely to be located
in a car) and deep contextual reasoning. Machine learning
(and in particular, neural networks) have made significant
progress in resolving these ambiguities. But our work is still
cut out for us: we would like to develop methods that can
learn world knowledge and enable equal understanding of
natural language across all  languages and contexts."

But seriously

For some historical background, see (for instance) a book by
Ekaterina Ovchinnikova —

Integration of World Knowledge for
Natural Language Understanding
 
,
Atlantis Press, Springer, 2012.

A PDF of Chapter 2, "Natural Language Understanding
and World Knowledge," is available for download.

The philosophical background is the distinction between
syntax  and semantics . See (for instance)

Gian-Carlo Rota on Syntax and Semantics

Wednesday, May 11, 2016

Null Point

Filed under: General — Tags: — m759 @ 7:59 pm

This evening's previous post links to an earlier post
on a book by DeLillo.  This suggests a review
of DeLillo's most recent book, Zero K .

A title I prefer: that of this post, Null Point. *
For related mathematics, see Zero System .

Wikipedia — 

The Kelvin scale is an absolute, 
thermodynamic temperature scale 
using as its null point  absolute zero,
the temperature at which
all thermal motion ceases in the
classical description of thermodynamics.

Hear Ye*

Filed under: General — m759 @ 7:31 pm

* Here the "Ye" may be interpreted in light of the "Yi"
   of today's noon post. See also Ratner in this journal.

Jewel of Odin

Filed under: General — m759 @ 1:00 pm

The tesseract in last night's post Game Theory
suggests a search in Log24 for "Jewel of Odin."

See also Trinkets.

By Diction Possessed

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

Continued from Saturday, May 7, 2016 .

From an obituary in yesterday evening's online New York Times —

"I was writing plays, one-acters, about musicians
who were speakers of the idiom I loved most:
black American male speech, full of curse words,"
he wrote in an autobiographical essay. . . .

The obituary is for a poet who reportedly died on Saturday, May 7.

This  journal on that day ("By Diction Possessed") recalled the death
(on Valentine's Day 2015) of an English actor who was the voice of
the Ring in two of the "Lord of the Rings" films —

Backstory from Wikipedia — See Black Speech —

"The only example of 'pure' Black Speech is
the inscription upon the One Ring . . .

One Ring to rule them all,
One Ring to find them,
One Ring to bring them all
And in the darkness bind them. 
"

Tuesday, May 10, 2016

Game Theory

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

The following passage appeared in this journal
on the night of May 23-24, 2015.

IMAGE- A fictional vision of resurrection within a tesseract

The afternoon  of May 23, 2015, was significant
for devotees of mathematics and narrative.

Monday, May 9, 2016

Requiem for an Authority Figure

Filed under: General — Tags: — m759 @ 2:45 pm

Today's online New York Times  describes an authority
figure who reportedly died on Sunday (May 8, 2016) —

"With his preternaturally mature, intelligent but
(by Hollywood standards) unremarkable looks,
he was cast almost from the beginning as an
authority figure — a father or a teacher, a doctor
or a scientist, a mayor or a judge."

This  journal on Sunday

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