Log24

Sunday, March 24, 2024

Religious Art:  Scene of the Articulation*

Filed under: General — Tags: — m759 @ 11:27 am

* See Atwood on tricksters.

 

Sunday, December 29, 2019

Articulation Raid

Filed under: General — Tags: — m759 @ 7:45 am

“… And so each venture Is a new beginning,
a raid on the inarticulate….”

— T. S. Eliot, “East Coker V” in Four Quartets

arXiv:1409.5691v1 [math.CO]  17 Sep 2014

The Complement of Binary Klein Quadric as
a Combinatorial Grassmannian

Metod Saniga,
Institute for Discrete Mathematics and Geometry,
Vienna University of Technology,
Wiedner Hauptstraße 8–10, A-1040 Vienna, Austria
(metod.saniga@tuwien.ac.at) and
Astronomical Institute, Slovak Academy of Sciences,
SK-05960 Tatransk ́a Lomnica, Slovak Republic
(msaniga@astro.sk)

Abstract

Given a hyperbolic quadric of PG(5, 2), there are 28 points off this quadric and 56 lines skew to it. It is shown that the (286,563)-configuration formed by these points and lines is isomorphic to the combinatorial Grassmannian of type G2(8). It is also pointed out that a set of seven points of G2(8) whose labels share a mark corresponds to a Conwell heptad of PG(5, 2). Gradual removal of Conwell heptads from the (286,563)-configuration yields a nested sequence of binomial configurations identical with part of that found to be associated with Cayley-Dickson algebras (arXiv:1405.6888).

Keywords:

Combinatorial Grassmannian −
Binary Klein Quadric − Conwell Heptad

See also this  journal on the above date — 17 September 2014.

Thursday, September 29, 2016

Articulation

Filed under: General — Tags: , , — m759 @ 10:30 pm

Cassirer vs. Heidegger at Harvard —

A remembrance for Michaelmas —

A version of Heidegger’s “Sternwürfel ” —

From Log24 on the upload date for the above figure —

Sunday, July 3, 2016

Articulation

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

Notes for a monkey grammarian

"Visual forms— lines, colors, proportions, etc.—
are just as capable of articulation ,
i.e. of complex combination, as words.
But the laws that govern this sort of articulation
are altogether different from the laws of syntax
that govern language. The most radical difference
is that visual forms are not discursive .
They do not present their constituents successively,
but simultaneously, so the relations determining
a visual structure are grasped in one act of vision."

— Susanne K. LangerPhilosophy in a New Key

See also Langer's New Key in this journal.

Related material —

Wednesday, September 17, 2014

Raiders of the Lost Articulation

Tom Hanks as Indiana Langdon in Raiders of the Lost Articulation :

An unarticulated (but colored) cube:

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

A 2x2x2 articulated cube:

IMAGE- Eightfold cube with detail of triskelion structure

A 4x4x4 articulated cube built from subcubes like
the one viewed by Tom Hanks above:

Image-- Solomon's Cube

Solomon’s Cube

Friday, June 30, 2023

Trickster Fuge (German for Joint)

Filed under: General — Tags: , , — m759 @ 12:28 pm
 

Margaret Atwood on Lewis Hyde's 
Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

Pythagorean theorem proof by overlapping similar figures

"Drop me a line" — Request attributed to Emma Stone

Tuesday, August 10, 2021

Ex Fano Apollinis

Filed under: General — Tags: , , , , — m759 @ 9:41 am
 

Margaret Atwood on Lewis Hyde's 
Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.


"As a Chinese jar . . . ."
     — Four Quartets

 

Rosalind Krauss
in "Grids," 1979:

"If we open any tract– Plastic Art and Pure Plastic Art  or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.

Or, to take a more up-to-date example…."

"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
– The Club Dumas , 1993

"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
– Robert Plant, 1971

The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.

An example of the universal— or, according to Krauss,
a "staircase" to the universal— is the ninefold square:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo,
  the field of Reason…."
– John Outram, architect    

The "Katz" of the August 7 post Art Angles
is a product of Princeton's
Department of Art and Archaeology.

 

ART —

 

The Lo Shu as a Finite Space
 

ARCHAEOLOGY —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71

Thursday, June 24, 2021

Persons of Interest

Filed under: General — Tags: — m759 @ 5:21 pm

Margaret Atwood on Lewis Hyde's 
Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

Punch Line . . .

Wrap Party!

Friday, June 18, 2021

Memorial

Filed under: General — m759 @ 11:59 am

From the previous post:

"Words are events, happenings, not things,
as letters make them appear to be."
— Walter J. Ong, S.J., page 2 in 
"Writing and the Evolution of Consciousness,"

". . . originally delivered by Walter J. Ong
as the 7th Annual 'Sidney Warhaft Memorial Lecture',
January 26, 1984, University of Manitoba, Winnipeg."

A different Sidney Warhaft memorial —

Photographs are also events.

See this journal on the above photo date — Sept. 17, 2014.

Sunday, October 11, 2020

Saniga on Einstein

Filed under: General — m759 @ 8:25 am

See Einstein on Acid” by Stephen Battersby
(New Scientist , Vol. 180, issue 2426 — 20 Dec. 2003, 40-43).

That 2003 article is about some speculations of Metod Saniga.

“Saniga is not a professional mystic or
a peddler of drugs, he is an astrophysicist
at the Slovak Academy of Sciences in Bratislava.
It seems unlikely that studying stars led him to
such a way-out view of space and time. Has he
undergone a drug-induced epiphany, or a period
of mental instability? ‘No, no, no,’ Saniga says,
‘I am a perfectly sane person.'”

Some more recent and much less speculative remarks by Saniga
are related to the Klein correspondence —

arXiv.org > math > arXiv:1409.5691:
Mathematics > Combinatorics
[Submitted on 17 Sep 2014]
The Complement of Binary Klein Quadric
as a Combinatorial Grassmannian

By Metod Saniga

“Given a hyperbolic quadric of PG(5,2), there are 28 points
off this quadric and 56 lines skew to it. It is shown that the
(286,563)-configuration formed by these points and lines
is isomorphic to the combinatorial Grassmannian of type
G2(8). It is also pointed out that a set of seven points of
G2(8) whose labels share a mark corresponds to a
Conwell heptad of PG(5,2). Gradual removal of Conwell
heptads from the (286,563)-configuration yields a nested
sequence of binomial configurations identical with part of
that found to be associated with Cayley-Dickson algebras
(arXiv:1405.6888).”

Related entertainment —

See Log24 on the date, 17 Sept. 2014, of Saniga’s Klein-quadric article:

Articulation Day.

Monday, January 6, 2020

Art as Experience (Minus Baldessari)

Filed under: General — Tags: — m759 @ 12:36 pm

In memory of an artist who reportedly died in Venice, CA, on Jan. 2 —

Two quotes from the website Quotes Sayings

"I always felt like I was right out of Dickens, looking in the window
of the Christmas feast, but not at the feast." — John Baldessari

"A TWO-DIMENSIONAL SURFACE WITHOUT ANY ARTICULATION
IS A DEAD EXPERIENCE" — John Baldessari

The "dead experience" quote is actually from Gyorgy Kepes:

Sunday, October 13, 2019

Langer

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

"Visual forms— lines, colors, proportions, etc.—
are just as capable of articulation ,
i.e. of complex combination, as words.
But the laws that govern this sort of articulation
are altogether different from the laws of syntax
that govern language. The most radical difference
is that visual forms are not discursive .
They do not present their constituents successively,
but simultaneously, so the relations determining
a visual structure are grasped in one act of vision."

— Susanne K. LangerPhilosophy in a New Key

Sunday, September 8, 2019

A Harvard*-Resistant Book Search

Filed under: General — m759 @ 7:36 pm

(The above title was suggested by today's "Child-Resistant 4×4.")

* Specifically, resistant to the above revelation attributed to Barbara Johnson
   by  Harvard University Press

   "Deconstruction calls attention to gaps and reveals
    that their claims upon us are fraudulent."

    A related search at Amazon.com:

Barbara Johnson explains Lacan:

" The 'gap' in the real is the leap 
from the empirical to 
the signifying articulation 
of the object of desire
it cannot be perceived empirically. 
It is 'nothing.' "

Persons and Things , paperback (2010),
  Harvard University Press, page 213

Tuesday, June 25, 2019

Rhetorical Question, Rhetorical Answer

Filed under: General — Tags: — m759 @ 11:07 am

Q —

"What kind of person
bokehs an inscape?" 


A —

Robert Gorham Davis:

McLuhan's " 'mosaic' mode of presentation
rules out discriminations, qualifications,
close reasoning, the structuring of
articulated wholes."

Robert Gorham Davis on Marshall McLuhan.

See also Articulation  in this  journal.

Friday, June 21, 2019

Cubehenge

Filed under: General — Tags: — m759 @ 1:15 am

Thursday, June 30, 2016

Rubik vs. Galois: Preconception vs. Pre-conception

Filed under: General,Geometry — Tags: , — m759 @ 1:20 pm

From Psychoanalytic Aesthetics: The British School ,
by Nicola Glover, Chapter 4  —

In his last theoretical book, Attention and Interpretation  (1970), Bion has clearly cast off the mathematical and scientific scaffolding of his earlier writings and moved into the aesthetic and mystical domain. He builds upon the central role of aesthetic intuition and the Keats's notion of the 'Language of Achievement', which

… includes language that is both
a prelude to action and itself a kind of action;
the meeting of psycho-analyst and analysand
is itself an example of this language.29.

Bion distinguishes it from the kind of language which is a substitute  for thought and action, a blocking of achievement which is lies [sic ] in the realm of 'preconception' – mindlessness as opposed to mindfulness. The articulation of this language is possible only through love and gratitude; the forces of envy and greed are inimical to it..

This language is expressed only by one who has cast off the 'bondage of memory and desire'. He advised analysts (and this has caused a certain amount of controversy) to free themselves from the tyranny of the past and the future; for Bion believed that in order to make deep contact with the patient's unconscious the analyst must rid himself of all preconceptions about his patient – this superhuman task means abandoning even the desire to cure . The analyst should suspend memories of past experiences with his patient which could act as restricting the evolution of truth. The task of the analyst is to patiently 'wait for a pattern to emerge'. For as T.S. Eliot recognised in Four Quartets , 'only by the form, the pattern / Can words or music reach/ The stillness'.30. The poet also understood that 'knowledge' (in Bion's sense of it designating a 'preconception' which blocks  thought, as opposed to his designation of a 'pre -conception' which awaits  its sensory realisation), 'imposes a pattern and falsifies'

For the pattern is new in every moment
And every moment is a new and shocking
Valuation of all we have ever been.31.

The analyst, by freeing himself from the 'enchainment to past and future', casts off the arbitrary pattern and waits for new aesthetic form to emerge, which will (it is hoped) transform the content of the analytic encounter.

29. Attention and Interpretation  (Tavistock, 1970), p. 125

30. Collected Poems  (Faber, 1985), p. 194.

31. Ibid., p. 199.

See also the previous posts now tagged Bion.

Preconception  as mindlessness is illustrated by Rubik's cube, and
"pre -conception" as mindfulness is illustrated by n×n×n Froebel  cubes
for n= 1, 2, 3, 4. 

Suitably coordinatized, the Froebel  cubes become Galois  cubes,
and illustrate a new approach to the mathematics of space .

Monday, July 13, 2015

The Omega Cube

Filed under: General — m759 @ 12:00 pm

Why "Omega?"

Omega is a Greek letter, Ω , used in
mathematics to denote 
a set on which
a group acts. 

Friday, October 17, 2014

Raiders of the Inarticulate

Filed under: General — m759 @ 9:00 pm

On Walter Isaacson’s The Innovators :

“Yet as the book’s five hundred–plus pages unwind, Isaacson interrupts himself to present small bromides about what it means to innovate and what we might learn from these innovators, our presumed betters. “Innovation requires articulation,” he tells us, after explaining how the main strength of Grace Hopper, a trailblazing computer scientist for the US Navy, was her ability to speak in the languages of mathematicians, engineers, programmers, and soldiers alike. ‘One useful leadership talent is knowing when to push ahead against doubters and when to heed them,’ he offers later.

The book is peppered with these kinds of passages, which often intrude on the narrative, depriving us of moments of real emotional power.”

— Jacob Silverman in Bookforum , Sept/Oct/Nov 2014

From Isaacson’s book:

IMAGE- Bletchley Park and the Colossus computer

Related material:

In memory of T. S. Eliot…

… and in memory of Stanley Chase, producer of Colossus: The Forbin Project
and of Threepenny Opera :

Ninefold square from Colossus
(“There is another system”) —

Fourfold square introducing Brecht
in  Dreigroschen Trifft Vierfarben —

Wednesday, September 17, 2014

A Raid on the Inarticulate

Filed under: General — Tags: , — m759 @ 6:00 pm

                                “… And so each venture
Is a new beginning, a raid on the inarticulate….”

— T. S. Eliot, “East Coker V” in Four Quartets

Monday, August 11, 2014

Syntactic/Symplectic

(Continued from August 9, 2014.)

Syntactic:

Symplectic:

"Visual forms— lines, colors, proportions, etc.— are just as capable of
articulation , i.e. of complex combination, as words. But the laws that govern
this sort of articulation are altogether different from the laws of syntax that
govern language. The most radical difference is that visual forms are not
discursive 
. They do not present their constituents successively, but
simultaneously, so the relations determining a visual structure are grasped
in one act of vision."

– Susanne K. LangerPhilosophy in a New Key

For examples, see The Diamond-Theorem Correlation
in Rosenhain and Göpel Tetrads in PG(3,2).

This is a symplectic  correlation,* constructed using the following
visual structure:

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven).

* Defined in (for instance) Paul B. Yale, Geometry and Symmetry ,
Holden-Day, 1968, sections 6.9 and 6.10.

Thursday, June 20, 2013

ART WARS: Chesterton Thursday

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

The New York Times  philosophy column "The Stone"
last evening had an essay on art by a sarcastic anarchist,
one Crispin Sartwell

"… whole generations of art lovers have been
trained in modernist dogma, and arts institutions’
access to various forms of state or foundation
support depend on it completely. One goes to
the museum to gasp at stunning works of
incomparable, super-human genius by beings
who are infinitely more exalted and important
than the mere humans staring at their paintings.
That’s why ordinary people staring at a Picasso
(allegedly) experience a kind of transcendence
or re-articulation of their lives and world."

 Cubism Re-Articulated:

  Click image for some backstory.

(IMAGE: Walter Gropius and Froebel's Third Gift,
from a Google image search today)

Background: Cubism in this journal and
Pilate Goes to Kindergarten.

Related material: Chesterton + Thursday in this journal.

Tuesday, October 11, 2011

24 Hour DeLillo

Filed under: General — m759 @ 12:00 pm

Review of DeLillo's novel Point Omega

"One difference between art and entertainment has to do with the speed of perception. Art deliberately slows and complicates reading, hearing, and/or viewing so that you’re challenged to re-think and re-feel form and experience. Entertainment deliberately accelerates and simplifies them so that you don’t have to think about or feel very much of anything at all except, perhaps, the adrenalin rush before dazzling spectacle. Although, of course, there can be myriad gradations between the former and latter, in their starkest articulation we’re talking about the distance between, say, David Foster Wallace’s Infinite Jest  and Dan Brown’s The Lost Symbol…."

— Lance Olsen, March 1, 2010, in The Quarterly Conversation

Robert Hughes on fast and slow art—

"We have had a gutful of fast art and fast food. What we need more of is slow art: art that holds time as a vase holds water: art that grows out of modes of perception and whose skill and doggedness make you think and feel; art that isn't merely sensational, that doesn't get its message across in 10 seconds, that isn't falsely iconic, that hooks onto something deep-running in our natures. In a word, art that is the very opposite of mass media. For no spiritually authentic art can beat mass media at their own game."

– Speech of June 1, 2004

Log24 on art speeds—

A Study in Art Education (June 15, 2007)

Twenty-four (March 13, 2011)

Monday, May 2, 2011

The Vine*

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

See "Nine is a Vine" and "Hereafter" in this journal.

IMAGE- Matt Damon and the perception of doors in 'Hereafter'

As quoted here last October 23

Margaret Atwood on Lewis Hyde's Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

* April 7, 2005

Monday, November 22, 2010

Backstory

Filed under: General,Geometry — Tags: , — m759 @ 8:48 am

Steve Martin’s new novel An Object of Beauty  will be released tomorrow.

“The most charmingly rendered female schemer since Truman Capote’s Holly Golightly.”
Elle  magazine

“Martin compresses the wild and crazy end of the millennium
and finds in this piercing novel a sardonic morality tale….
Exposes the sound and fury of the rarified Manhattan art world.”
Publishers Weekly

“Like Steve Martin’s Shopgirl , this very different novel will captivate your attention from start to finish.”
— Joyce Carol Oates

Martin on his character Ray Porter in the novella Shopgirl  (published Oct. 11, 2000)—

http://www.log24.com/log/pix10B/101122-MartinShopgirl-loq.jpg

“He said, ‘I wrote a piece of code
that they just can’t seem to do without.’
He was a symbolic logician. That was his career….”

As the above review notes, Martin’s new book is about art at the end of the millennium.

See also Art Wars: Geometry as Conceptual Art
and some of my own notes from 2000 (March 9) in “Is Nothing Sacred?

Some related material —

A paperback with a striking cover (artist unknown)—

http://www.log24.com/log/pix10B/101027-LangerSymbolicLogic.jpg

Note that the background may be constructed from
any of four distinct motifs. For another approach to these
motifs in a philosophical context, see June 8, 2010.

“Visual forms— lines, colors, proportions, etc.— are just as capable of articulation , i.e. of complex combination, as words. But the laws that govern this sort of articulation are altogether different from the laws of syntax that govern language. The most radical difference is that visual forms are not discursive . They do not present their constituents successively, but simultaneously, so the relations determining a visual structure are grasped in one act of vision.”

Susanne K. Langer, Philosophy in a New Key

Wednesday, October 27, 2010

Language and Form

Filed under: General — Tags: — m759 @ 4:00 am

In memory of S. Neil Fujita, who died last Saturday—

http://www.log24.com/log/pix10B/101027-PhilosophicalSketches2.jpg

Fujita did the cover art for this edition.

Another book by Langer with a striking cover (artist unknown)—

http://www.log24.com/log/pix10B/101027-LangerSymbolicLogic.jpg

Note that the background may be constructed from
any of four distinct motifs. For another approach to these
motifs in a philosophical context, see June 8, 2010.

"Visual forms— lines, colors, proportions, etc.— are just as capable of articulation , i.e. of complex combination, as words. But the laws that govern this sort of articulation are altogether different from the laws of syntax that govern language. The most radical difference is that visual forms are not discursive . They do not present their constituents successively, but simultaneously, so the relations determining a visual structure are grasped in one act of vision."
Susanne K. Langer, Philosophy in a New Key

Saturday, October 23, 2010

Paranormal Jackass

Filed under: General — Tags: , — m759 @ 8:28 pm

From MTV.com this afternoon

The follow-up to last year's runaway horror hit, "Paranormal Activity 2," kicked off its first weekend in theaters with a major haul. The creepy tale… pulled in $20.1 million on Friday.

Trailing behind "Paranormal" is last week's box-office busting debut "Jackass 3D. " The prank-fest, which landed about $50 million its first weekend in theaters, slipped to the second-place slot….

The Clint Eastwood-helmed ensemble drama "Hereafter" landed in fourth place. Exploring the lives of three people who are dealing with death and the afterlife in several ways, including the story of a psychic played by Matt Damon, the screen legend's latest turn in the director's chair made approximately $4.1 million on Friday.

Related material—

IMAGE-- Matt Damon stands where a door opens in 'Hereafter'

Margaret Atwood on Lewis Hyde's Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

The Paranormal Trickster Blog

George P. Hansen on Martin Gardner and the paranormal.

Saturday, October 16, 2010

The Mandelbrot Numbers

Filed under: General — m759 @ 11:36 am
 

Benoît Mandelbrot died on Oct. 14.
 

NY Lottery Thursday, Oct. 14, 2010-- Midday 109, Evening 060

— New York Lottery on Thursday, Oct. 14, 2010

Related material on 109: See 1/09, 2009.
Related material on 060: See Hexagram 60 of the I Ching  and…

IMAGE-- Matt Damon stands where a door opens in 'Hereafter'

Margaret Atwood on Lewis Hyde's Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

Friday, October 15, 2010

Mathematics and Narrative, continued

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

The Story of N

http://www.log24.com/log/pix09/090109-Stories.jpg

Roberta Smith in the New York Times  of July 7, 2006

Art Review

Endgame Art? It's Borrow, Sample and Multiply in an Exhibition at Bard College

"… The show has an endgame, end-time mood, as if we are looking at the end of the end of the end of Pop, hyperrealism and appropriation art. The techniques of replication and copying have become so meticulous that they are beside the point. This is truly magic realism: the kind you can't see, that has to be explained. It is also a time when artists cultivate hybridism and multiplicity and disdain stylistic coherence, in keeping with the fashionable interest in collectivity, lack of ego, the fluidity of individual identity. But too often these avoidance tactics eliminate the thread of a personal sensibility or focus.

I would call all these strategies fear of form, which can be parsed as fear of materials, of working with the hands in an overt way and of originality. Most of all originality. Can we just say it? This far from Andy Warhol and Duchamp, the dismissal of originality is perhaps the oldest ploy in the postmodern playbook. To call yourself an artist at all is by definition to announce a faith, however unacknowledged, in some form of originality, first for yourself, second, perhaps, for the rest of us.

Fear of form above all means fear of compression— of an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible. With a few exceptions, forms of collage and assemblage dominate this show: the putting together (or simply putting side by side) of existing images and objects prevails. The consistency of this technique in two and three dimensions should have been a red flag for the curators. Collage has driven much art since the late 1970's. Lately, and especially in this exhibition, it often seems to have become so distended and pulled apart that its components have become virtually autonomous and unrelated, which brings us back to square one. This is most obvious in the large installations of graphic works whose individual parts gain impact and meaning from juxtaposition but are in fact considered distinct artworks."

Margaret Atwood on art and the trickster

"The pleasures of fabulation, the charming and playful lie— this line of thought leads Hyde* to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning 'to join,' 'to fit,' and 'to make.'  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart."

* Lewis Hyde, Trickster Makes This World: Mischief, Myth, and Art,  Farrar Straus & Giroux, January 1998

Smith mentions "an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible."

Atwood mentions "a seamless whole."

For some related remarks, see "A Study in Art Education" and the central figure pictured above. (There "N" can stand for "number," "nine," or "narrative.")

Thursday, June 3, 2010

Trickster

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

Margaret Atwood (pdf) on Lewis Hyde’s
Trickster Makes This World: Mischief, Myth, and Art

“Trickster,” says Hyde, “feels no anxiety when he deceives…. He… can tell his lies with creative abandon, charm, playfulness, and by that affirm the pleasures of fabulation.” (71) As Hyde says, “…  almost everything that can be said about psychopaths can also be said about tricksters,” (158), although the reverse is not the case. “Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists.” (159)

What is “the next world”? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning to join, to fit, and to make. (254) If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

See also George P. Hansen on Martin Gardner, Trickster.

Tuesday, August 18, 2009

Tuesday August 18, 2009

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

Prima Materia

(Background: Art Humor: Sein Feld (March 11, 2009) and Ides of March Sermon, 2009)

From Cardinal Manning's review of Kirkman's Philosophy Without Assumptions

"And here I must confess… that between something and nothing I can find no intermediate except potentia, which does not mean force but possibility."

— Contemporary Review, Vol. 28 (June-November, 1876), page 1017

Furthermore….

Cardinal Manning, Contemporary Review, Vol. 28, pages 1026-1027:

The following will be, I believe, a correct statement of the Scholastic teaching:–

1. By strict process of reason we demonstrate a First Existence, a First Cause, a First Mover; and that this Existence, Cause, and Mover is Intelligence and Power.

2. This Power is eternal, and from all eternity has been in its fullest amplitude; nothing in it is latent, dormant, or in germ: but its whole existence is in actu, that is, in actual perfection, and in complete expansion or actuality. In other words God is Actus Purus, in whose being nothing is potential, in potentia, but in Him all things potentially exist.

3. In the power of God, therefore, exists the original matter (prima materia) of all things; but that prima materia is pura potentia, a nihilo distincta, a mere potentiality or possibility; nevertheless, it is not a nothing, but a possible existence. When it is said that the prima materia of all things exists in the power of God, it does not mean that it is of the existence of God, which would involve Pantheism, but that its actual existence is possible.

4. Of things possible by the power of God, some come into actual existence, and their existence is determined by the impression of a form upon this materia prima. The form is the first act which determines the existence and the species of each, and this act is wrought by the will and power of God. By this union of form with the materia prima, the materia secunda or the materia signata is constituted.

5. This form is called forma substantialis because it determines the being of each existence, and is the root of all its properties and the cause of all its operations.

6. And yet the materia prima has no actual existence before the form is impressed. They come into existence simultaneously;

[p. 1027 begins]

as the voice and articulation, to use St. Augustine's illustration, are simultaneous in speech.

7. In all existing things there are, therefore, two principles; the one active, which is the form– the other passive, which is the matter; but when united, they have a unity which determines the existence of the species. The form is that by which each is what it is.

8. It is the form that gives to each its unity of cohesion, its law, and its specific nature.*

When, therefore, we are asked whether matter exists or no, we answer, It is as certain that matter exists as that form exists; but all the phenomena which fall under sense prove the existence of the unity, cohesion, species, that is, of the form of each, and this is a proof that what was once in mere possibility is now in actual existence. It is, and that is both form and matter.

When we are further asked what is matter, we answer readily, It is not God, nor the substance of God; nor the presence of God arrayed in phenomena; nor the uncreated will of God veiled in a world of illusions, deluding us with shadows into the belief of substance: much less is it catter [pejorative term in the book under review], and still less is it nothing. It is a reality, the physical kind or nature of which is as unknown in its quiddity or quality as its existence is certainly known to the reason of man.

* "… its specific nature"
        (Click to enlarge) —

Footnote by Cardinal Manning on Aquinas
The Catholic physics expounded by Cardinal Manning above is the physics of Aristotle.

 

For a more modern treatment of these topics, see Werner Heisenberg's Physics and Philosophy. For instance:

"The probability wave of Bohr, Kramers, Slater, however, meant… a tendency for something. It was a quantitative version of the old concept of 'potentia' in Aristotelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality."

Compare to Cardinal Manning's statement above:

"… between something and nothing I can find no intermediate except potentia…"

To the mathematician, the cardinal's statement suggests the set of real numbers between 1 and 0, inclusive, by which probabilities are measured. Mappings of purely physical events to this set of numbers are perhaps better described by applied mathematicians and physicists than by philosophers, theologians, or storytellers. (Cf. Voltaire's mockery of possible-worlds philosophy and, more recently, The Onion's mockery of the fictional storyteller Fournier's quantum flux. See also Mathematics and Narrative.)

Regarding events that are not purely physical– those that have meaning for mankind, and perhaps for God– events affecting conception, birth, life, and death– the remarks of applied mathematicians and physicists are often ignorant and obnoxious, and very often do more harm than good. For such meaningful events, the philosophers, theologians, and storytellers are better guides. See, for instance, the works of Jung and those of his school. Meaningful events sometimes (perhaps, to God, always) exhibit striking correspondences. For the study of such correspondences, the compact topological space [0, 1] discussed above is perhaps less helpful than the finite Galois field GF(64)– in its guise as the I Ching. Those who insist on dragging God into the picture may consult St. Augustine's Day, 2006, and Hitler's Still Point.

Friday, December 19, 2008

Friday December 19, 2008

Filed under: General,Geometry — Tags: , , , , — m759 @ 1:06 pm
Inside the
White Cube

Part I: The White Cube

The Eightfold Cube

Part II: Inside
 
The Paradise of Childhood'-- Froebel's Third Gift

Part III: Outside

Mark Tansey, 'The Key' (1984)

Click to enlarge.

Mark Tansey, The Key (1984)

For remarks on religion
related to the above, see
Log24 on the Garden of Eden
and also Mark C. Taylor,
"What Derrida Really Meant"
(New York Times, Oct. 14, 2004).

For some background on Taylor,
see Wikipedia. Taylor, Chairman
of the Department of Religion
at
Columbia University, has a
1973 doctorate in religion from
Harvard University. His opinion
of Derrida indicates that his
sympathies lie more with
the serpent than with the angel
in the Tansey picture above.

For some remarks by Taylor on
the art of Tansey relevant to the
structure of the white cube
(Part I above), see Taylor's
The Picture in Question:
Mark Tansey and the
Ends of Representation

(U. of Chicago Press, 1999):

From Chapter 3,
"Sutures* of Structures," p. 58:

"What, then, is a frame, and what is frame work?

This question is deceptive in its simplicity. A frame is, of course, 'a basic skeletal structure designed to give shape or support' (American Heritage Dictionary)…. when the frame is in question, it is difficult to determine what is inside and what is outside. Rather than being on one side or the other, the frame is neither inside nor outside. Where, then, Derrida queries, 'does the frame take place….'"

* P. 61:
"… the frame forms the suture of structure. A suture is 'a seamless [sic**] joint or line of articulation,' which, while joining two surfaces, leaves the trace of their separation."

 ** A dictionary says "a seamlike joint or line of articulation," with no mention of "trace," a term from Derrida's jargon.

Sunday, November 16, 2008

Sunday November 16, 2008

Filed under: General,Geometry — Tags: , — m759 @ 8:00 pm
Art and Lies

Observations suggested by an article on author Lewis Hyde– "What is Art For?"–  in today's New York Times Magazine:

Margaret Atwood (pdf) on Lewis Hyde's
Trickster Makes This World: Mischief, Myth, and Art

"Trickster," says Hyde, "feels no anxiety when he deceives…. He… can tell his lies with creative abandon, charm, playfulness, and by that affirm the pleasures of fabulation." (71) As Hyde says, "…  almost everything that can be said about psychopaths can also be said about tricksters," (158), although the reverse is not the case. "Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning to join, to fit, and to make. (254) If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

For more about
"where things are
joined together," see
 Eight is a Gate and
The Eightfold Cube.
Related material:

The Trickster
and the Paranormal

and
Martin Gardner on
   a disappearing cube —

"What happened to that… cube?"

Apollinax laughed until his eyes teared. "I'll give you a hint, my dear. Perhaps it slid off into a higher dimension."

"Are you pulling my leg?"

"I wish I were," he sighed. "The fourth dimension, as you know, is an extension along a fourth coordinate perpendicular to the three coordinates of three-dimensional space. Now consider a cube. It has four main diagonals, each running from one corner through the cube's center to the opposite corner. Because of the cube's symmetry, each diagonal is clearly at right angles to the other three. So why shouldn't a cube, if it feels like it, slide along a fourth coordinate?"

— "Mr. Apollinax Visits New York," by Martin Gardner, Scientific American, May 1961, reprinted in The Night is Large


For such a cube, see

Cube with its four internal diagonals


ashevillecreative.com

this illustration in


The Religion of Cubism
(and the four entries
preceding it —
 Log24, May 9, 2003).

Beware of Gardner's
"clearly" and other lies.

Tuesday, May 24, 2005

Tuesday May 24, 2005

Filed under: General — m759 @ 2:00 pm
Final Arrangements, continued:

Two Poles

From today’s New York Times:

The image “http://www.log24.com/log/pix05/050524-NYT.jpg” cannot be displayed, because it contains errors.

From erraticimpact.com on Paul Ricoeur:

“Ricoeur reserves his greatest admiration for
the narratologist Algirdas-Julien Greimas.
[See below.]
Ricoeur also explores the relationship
between the philosophical and religious
domains, attempting to reconcile
the two poles in his thought.”

From today’s NYT obituary of Sol Stetin:

“Mr. Stetin, who emigrated from Poland at the age of 10 and dropped out of high school in the ninth grade, was fond of saying he got his education in the labor movement.”

The image “http://www.log24.com/log/pix05/050524-JP2.jpg” cannot be displayed, because it contains errors.


“… it is not in isolation that the rhetorical power of such oppositions resides, but in their articulation in relation to other oppositions. In Aristotle’s Physics the four elements of earth, air, fire and water were said to be opposed in pairs. For more than two thousand years oppositional patterns based on these four elements were widely accepted as the fundamental structure underlying surface reality….


The structuralist semiotician Algirdas Greimas introduced the semiotic square (which he adapted from the ‘logical square’ of scholastic philosophy) as a means of analysing paired concepts more fully….”

Daniel Chandler, Semiotics for Beginners

Related material:

Poetry’s Bones and
Theme and Variations.

Other readings on polarity:

Log24, May 24, 2003, and
from July 26, 2003:

Bright Star and Dark Lady

“Mexico is a solar country — but it is also a black country, a dark country. This duality of Mexico has preoccupied me since I was a child.”

Octavio Paz,
quoted by Homero Aridjis

Bright Star

Amen.

Dark Lady

Monday, May 2, 2005

Monday May 2, 2005

Filed under: General — m759 @ 11:00 am
A Dance Results

 

Roger Kimball on Rosalind Krauss's
The Optical Unconscious:

"Professor Krauss even uses many of the same decorations with which she festooned earlier volumes. Bataille’s photograph of a big toe, for example, which I like to think of as her mascot, reappears. As does her favorite doodle, a little graph known as a 'Klein Group' or 'L Schema' whose sides and diagonals sport arrows pointing to corners labeled with various opposing pairs: e.g., 'ground' and 'not ground,' 'figure' and 'not figure.' Professor Krauss seems to believe that this device, lifted from the pages of structuralist theory, illuminates any number of deep mysteries: the nature of modernism, to begin with, but also the essence of gender relations, self-consciousness, perception, vision, castration anxiety, and other pressing conundrums that, as it happens, she has trouble distinguishing from the nature of modernism. Altogether, the doodle is a handy thing to have around. One is not surprised that Professor Krauss reproduces it many times in her new book."
 

From Drid Williams,
The Semiotics of Human Action,
Ritual, and Dance:

A Klein four-group in the context of dance

This is closely related to
Beckett's "Quad" figure

The image “http://www.log24.com/log/pix05/050501-Quad.jpg” cannot be displayed, because it contains errors.

A Jungian on this six-line figure:

"They are the same six lines
that exist in the I Ching….
Now observe the square more closely:
four of the lines are of equal length,
the other two are longer….
For this reason symmetry
cannot be statically produced
and a dance results."
 
— Marie-Louise von Franz,
Number and Time (1970)

and to the Greimas "semiotic square":

"People have believed in the fundamental character of binary oppositions since at least classical times. For instance, in his Metaphysics Aristotle advanced as primary oppositions: form/matter, natural/unnatural, active/passive, whole/part, unity/variety, before/after and being/not-being.*  But it is not in isolation that the rhetorical power of such oppositions resides, but in their articulation in relation to other oppositions. In Aristotle's Physics the four elements of earth, air, fire and water were said to be opposed in pairs. For more than two thousand years oppositional patterns based on these four elements were widely accepted as the fundamental structure underlying surface reality….

The structuralist semiotician Algirdas Greimas introduced the semiotic square (which he adapted from the 'logical square' of scholastic philosophy) as a means of analysing paired concepts more fully…."

 

Daniel Chandler, Semiotics for Beginners.

* Compare Chandler's list of Aristotle's primary oppositions with Aristotle's list (also in the  Metaphysics) of Pythagorean oppositions (see Midrash Jazz Quartet).
 

Tuesday, January 25, 2005

Tuesday January 25, 2005

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

Diamonds Are Forever

 
The image “http://www.log24.com/theory/images/Modal-diamondinbox.gif” cannot be displayed, because it contains errors.

 

Robert Stone,
A Flag for Sunrise:

" 'That old Jew gave me this here.'  Egan looked at the diamond.  'I ain't giving this to you, understand?  The old man gave it to me for my boy.  It's worth a whole lot of money– you can tell that just by looking– but it means something, I think.  It's got a meaning, like.'

'Let's see,' Egan said, 'what would it mean?'  He took hold of Pablo's hand cupping the stone and held his own hand under it.  '"The jewel is in the lotus," perhaps that's what it means.  The eternal in the temporal.  The Boddhisattva declining nirvana out of compassion.   Contemplating the ignorance of you and me, eh?  That's a metaphor of our Buddhist friends.'

Pablo's eyes glazed over.  'Holy shit,' he said.  'Santa Maria.'  He stared at the diamond in his palm with passion.

'Hey,' he said to the priest, 'diamonds are forever!  You heard of that, right?  That means something, don't it?'

'I have heard it,' Egan said.  'Perhaps it has a religious meaning.' "
 


"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz

From

DIALECTIC AND EXISTENCE
IN KIERKEGAARD AND KANT

Nythamar Fernandes de Oliveira

Pontifical Catholic University
at Porto Alegre, Brazil

"Such is the paradoxical 'encounter' of the eternal with the temporal. Just like the Moment of the Incarnation, when the Eternal entered the temporal, Kierkegaard refers to the category of the Instant (Danish Ojeblikket, 'a glance of the eye, eyeblink,' German Augenblick) as the dialectical kernel of our existential consciousness:

If the instant is posited, so is the eternal –but also the future, which comes again like the past … The concept around which everything turns in Christianity, the concept which makes all things new, is the fullness of time, is the instant as eternity, and yet this eternity is at once the future and the past.

Although I cannot examine here the Kierkegaardian conception of time, the dialectical articulation of time and existence, as can be seen, underlies his entire philosophy of existence, just as the opposition between 'eternity' and 'temporality': the instant, as 'an atom of eternity,' serves to restructure the whole synthesis of selfhood into a spiritual one, in man’s 'ascent' toward its Other and the Unknown. In the last analysis, the Eternal transcends every synthesis between eternity and time, infinity and finiteness, preserving not only the Absolute Paradox in itself but above all the wholly otherness of God. It is only because of the Eternal, therefore, that humans can still hope to attain their ultimate vocation of becoming a Chistian. As Kierkegaard writes in Works of Love (1847),

The possibility of the good is more than possibility, for it is the eternal. This is the basis of the fact that one who hopes can never be deceived, for to hope is to expect the possibility of the good; but the possibility of the good is eternal. …But if there is less love in him, there is also less of the eternal in him; but if there is less of the eternal in him, there is also less possibility, less awareness of possibility (for possibility appears through the temporal movement of the eternal within the eternal in a human being)."

Sunday, April 11, 2004

Sunday April 11, 2004

Filed under: General,Geometry — m759 @ 3:28 pm

Good Friday and
Descartes’s Easter Egg

“The use of z, y, x . . . to represent unknowns is due to René Descartes, in his La géometrie (1637)…. In a paper on Cartesian ovals, prepared before 1629, x alone occurs as unknown…. This is the earliest place in which Descartes used one of the last letters of the alphabet to represent an unknown.”

— Florian Cajori, A History of Mathematical Notations. 2 volumes. Lasalle, Illinois: The Open Court Publishing Co., 1928-1929. (Vol. 1, page 381)

This is from

http://members.aol.com/jeff570/variables.html.

Descartes’s Easter Egg is found at

EggMath: The Shape of an Egg —
Cartesian Ovals
 

An Easter Meditation
on Humpty Dumpty

The following is excerpted from a web page headed “Catholic Way.”  It is one of a series of vicious and stupid Roman Catholic attacks on Descartes.  Such attacks have been encouraged by the present Pope, who today said “may the culture of life and love render vain the logic of death.”

The culture of life and love is that of the geometry (if not the philosophy) of Descartes.  The logic of death is that of Karol Wojtyla, as was made very clear in the past century by the National Socialist Party, which had its roots in Roman Catholicism.

Humpty Dumpty sat on a wall.
Humpty Dumpty had a great fall

“In the century just completed, the human race found itself in a position not unlike the scrambled mess at the base of an imaginary English wall….

… we are heirs to a humanity that is broken, fractured, confused, unsure of what to make of itself….

 … ‘postmodernism’ is merely the articulation of the fractured, dissipated state of the human being…. 

Without relating a history of modern philosophy, our unfortunate human shell has suffered a continual fragmentation for a period of roughly 500 years. (You philosophers out there will recognize immediately that I am referring to the legacy of René Descartes.) And this fragmentation has been a one-way street: one assault after another on the integrity and dignity of the human person until you have, well, the 20th Century.

But now it’s the 21st Century.

The beauty … the marvel … the miracle of our time is the possibility that gravity will reverse itself: Humpty Dumpty may be able, once again, to assume his perch.”

—  Ted Papa,
Raising Humpty Dumpty

Voilà.

The upper part
of the above icon
is from EggMath.
For the lower part,
see Good Friday.

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