Log24

Monday, July 9, 2018

High Concept for Amy

Filed under: General — m759 @ 8:12 PM

Tuesday, August 29, 2017

High Concept WW

Filed under: General — Tags: — m759 @ 11:02 PM

Friday, April 14, 2017

High Concept

Filed under: General — m759 @ 12:00 PM

The twin-column illustration above is 
adapted from Shakespeare's Birthday 2013.

Friday, June 10, 2016

High Concept

Filed under: General — m759 @ 9:00 AM

(Continued)

Orwell Meets Waugh

'Space Cross' from the Cullinane diamond theorem

Sunday, February 28, 2016

High Concept:

Filed under: General — m759 @ 3:00 PM

Daily Globe  Meets  Daily PlaNet

Office scene from "Spotlight," a 2015 film about The Boston Globe

Detail of the above office scene 

A photo from the Web of Mount Baker and Bellingham WA 
that may or may not match the "Spotlight" picture's location.

Update of 1 AM on March 3, 2016 —

A much better match for the "Spotlight" office picture is this image of
Mount Illimani and La Paz, Bolivia, from dreamstime.com

Friday, February 12, 2016

High Concept:

Filed under: General — m759 @ 11:32 AM

Johnny Cash*  Meets  Fritz Leiber**

*  "You can run on for a long time…"

** See Spider + Snake in this journal.

Thursday, December 31, 2015

High Concept

Filed under: General — m759 @ 7:00 AM

(Continued from this date last year,
  "Spiel ist nicht Spielerei")

Monday, March 2, 2015

High Concepts of Space

Filed under: General — m759 @ 3:05 PM

Related material:

Agents of a Great Despair and A Kirk for Spock —

Wednesday, January 21, 2015

High Concept:

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

The Dark Fields  Meet  The Big Seal .

Recall the punchline of Tuesday afternoon's post
on the 2012 film "Travelling Salesman" —

"What am I, the farmer's daughter?"

For background from the dark fields of the republic,
see a speech last night by Iowa Senator Joni Ernst.

Related material:

At the end of the 2012 film "Travelling Salesman,"
the main character holds up to the light a letter that has
at the top the presidential seal of the United States:

The camera pans down, and the character then
sees a watermark that echoes another famous seal,
from the U.S. one-dollar bill:

For related paranoia, see the novels of Dan Brown

as well as

See also Shema and Clocks Striking 13.

Monday, June 30, 2014

High Concept

Filed under: General — Tags: , — m759 @ 5:24 PM

For the title, see a post of Nov. 4, 2007.

Related material:

Hexagram 29, Water, and a pattern resembling
the symbol for Aquarius:

http://www.log24.com/images/IChing/hexagram29.gif          .

For some backstory about the former,
see the June 21 post Hallmark.

For some backstory about the latter,
see today’s post Toward Evening.

Tom Wolfe has supplied some scaffolding*
to support the concept.

* A reference to Grossman and Descartes.

Thursday, January 7, 2010

High Concept

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

Balthasar Meets Blake

Happy birthday, Nicolas Cage.

Saturday, February 21, 2015

High and Low Concepts

Filed under: General,Geometry — Tags: — m759 @ 4:30 PM

Steven Pressfield on April 25, 2012:

What exactly is High Concept?

Let’s start with its opposite, low concept.
Low concept stories are personal,
idiosyncratic, ambiguous, often European. 
“Well, it’s a sensitive fable about a Swedish
sardine fisherman whose wife and daughter
find themselves conflicted over … ”

ZZZZZZZZ.

Fans of Oslo artist Josefine Lyche know she has
valiantly struggled to find a high-concept approach
to the diamond theorem. Any such approach must,
unfortunately, reckon with the following low
(i.e., not easily summarized) concept —

The Diamond Theorem Correlation:

From left to right

http://www.log24.com/log/pix14B/140824-Diamond-Theorem-Correlation-1202w.jpg

http://www.log24.com/log/pix14B/140731-Diamond-Theorem-Correlation-747w.jpg

http://www.log24.com/log/pix14B/140824-Picturing_the_Smallest-1986.gif

http://www.log24.com/log/pix14B/140806-ProjPoints.gif

For some backstory, see ProjPoints.gif and "Symplectic Polarity" in this journal.

Sunday, June 10, 2018

Number Concept

Filed under: General,Geometry — m759 @ 2:45 PM

The previous post was suggested by some April 17, 2016, remarks
by James Propp on the eightfold cube.

Propp's remarks included the following:

"Here’s a caveat about my glib earlier remark that
'There are only finitely many numbers ' in a finite field.
It’s a bit of a stretch to call the elements of finite fields
'numbers'. Elements of GF() can be thought of as
the integers mod q  when q  is prime, and they can be
represented by 0, 1, 2, …, q–1; but when  is a prime
raised to the 2nd power or higher, describing the
elements of GF() is more complicated, and the word
'number' isn’t apt."

Related material —

See also this  journal on the date of Propp's remarks — April 17, 2016.

Saturday, January 7, 2017

Conceptualist Minimalism

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

"Clearly, there is a spirit of openhandedness in post-conceptual art
uses of the term 'Conceptualism.' We can now endow it with a
capital letter because it has grown in scale from its initial designation
of an avant-garde grouping, or various groups in various places, and
has evolved in two further phases. It became something like a movement,
on par with and evolving at the same time as Minimalism. Thus the sense
it has in a book such as Tony Godfrey’s Conceptual Art.  Beyond that,
it has in recent years spread to become a tendency, a resonance within
art practice that is nearly ubiquitous." — Terry Smith, 2011

See also the eightfold cube

The Eightfold Cube

 

Friday, February 20, 2015

Conceptual Art

Filed under: General — m759 @ 12:00 PM

See High White in this journal.

Related material:

The Astoria Column
on Coxcomb Hill,
Astoria, Oregon

See also a tale from today's Daily Astorian  
(click the AP link in Parks and Recreation) and

Early Coxcomb Hill

"McArthur and McArthur in Oregon Geographic Names  (2003, Oregon Historical Society) states:

'… Coxcomb Hill, Clatsop. This is the summit of the ridge south of Astoria, between the Columbia River and Youngs Bay. The compiler has been unable to learn who first applied the name. The spelling used is the customary form applied to court fools and jesters who wore an imitation coxcomb, and were frequently called coxcombs. …'"

Friday, October 26, 2012

High White Noon

Filed under: General — m759 @ 12:00 PM

(Continued)

Today's 11:01 AM post discussed time concepts
in Eliot's Four Quartets.

For the temporally challenged, here is
a somewhat simpler conceptual framework—

Three Trios

From a post of Columbus Day
(i.e., Oct. 12), 2011, titled
    "High White Noon" (after DeLillo) —

The 3x3 square

A Study in Art Education

Thursday, June 21, 2018

Models of Being

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

A Buddhist view —

"Just fancy a scale model of Being 
made out of string and cardboard."

— Nanavira Thera, 1 October 1957,
on a model of Kummer's Quartic Surface
mentioned by Eddington

A Christian view —

A formal view —

From a Log24 search for High Concept:

See also Galois Tesseract.

Wednesday, April 26, 2017

A Tale Unfolded

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

A sketch, adapted tonight from Girl Scouts of Palo Alto

From the April 14 noon post High Concept

From the April 14 3 AM post Hudson and Finite Geometry

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

From the April 24 evening post The Trials of Device

Pentagon with pentagram    

Note that Hudson's 1905 "unfolding" of even and odd puts even on top of
the square array, but my own 2013 unfolding above puts even at its left.

Wednesday, June 10, 2015

Traveling Salesmen

Filed under: General,Geometry — m759 @ 11:00 AM

    Click the above image for the IMDb page from which it is taken.

Peter J. Cameron today:

"Course material associated with Jack Edmonds’ lectures
can be found here."

See also High Concept (Jan. 21, 2015) —

Image from the end of the 2012 film "Travelling Salesman" 

— and another eye in a triangle 

From the Log24 post Prize (June 7, 2015)

Tuesday, August 5, 2014

Verhexung

Filed under: General — Tags: — m759 @ 8:15 PM

"Philosophy is a battle against the bewitchment [Verhexung ]
of our intelligence by means of our language."

— Wittgenstein, Philosophical Investigations , Section 109

"The philosophy of logic speaks of sentences and words
in exactly the sense in which we speak of them in ordinary life
when we say e.g. 'Here is a Chinese sentence,' or 'No, that only
looks like writing; it is actually just an ornament' and so on."

— Wittgenstein, Philosophical Investigations , Section 108

Monday, June 30, 2014

High Concept

Tags:  — m759 @ 5:24 PM

For the title, see a post of Nov. 4, 2007.

Related material:

Hexagram 29, Water, and a pattern resembling
the symbol for Aquarius:

http://www.log24.com/images/IChing/hexagram29.gif          .

For some backstory about the former,
see the June 21 post Hallmark.

For some backstory about the latter,
see today’s post Toward Evening.

Tom Wolfe has supplied some scaffolding*
to support the concept.

* A reference to Grossman and Descartes.

Tuesday, July 1, 2014

Latin Word:

Filed under: General — Tags: , — m759 @ 4:36 AM

Aqua

Version 1:

(See the June 30 posts Toward Evening,
Joke, and High Concept.)

Version 2:

Version 3:

Tuesday, March 12, 2013

Smoke and Mirrors

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

Sistine Chapel Smoke

Tromso Kunsthall Mirrors

Background for the smoke  image:
A remark by Michelangelo in a 2007 post,  High Concept.

Background for the mirrors  image:
Note the publication date— Mar. 10, 2013.

See that date in this journal and related material.

Wednesday, January 6, 2010

Epiphany Revisited

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

January 06, 2007
ART WARS: Epiphany

Picture of Nothing
On Kirk Varnedoe’s
2003 Mellon Lectures,
Pictures of Nothing“–

“Varnedoe’s lectures were ultimately about faith, about his faith in the power of abstraction, and abstraction as a kind of anti-religious faith in itself….”

Related material:

The more industrious scholars will derive considerable pleasure from describing how the art-history professors and journalists of the period 1945-75, along with so many students, intellectuals, and art tourists of every sort, actually struggled to see the paintings directly, in the old pre-World War II way, like Plato’s cave dwellers watching the shadows, without knowing what had projected them, which was the Word.”

— Tom Wolfe, The Painted Word

Log24, Aug. 23, 2005:

Concept (scholastics’ verbum mentis)–  theological analogy of Son’s procession  as Verbum Patris, 111-12″ — Index to Joyce and Aquinas, by William T. Noon, S.J., Yale University Press 1957,  second printing 1963, page 162

“So did God cause the big bang? Overcome by metaphysical lassitude, I finally reach over to my bookshelf for The Devil’s Bible. Turning to Genesis I read: ‘In the beginning there was nothing. And God said, ‘Let there be light!’ And there was still nothing, but now you could see it.'”
— Jim Holt, Big-Bang Theology, from Slate‘s “High Concept” department

'In the beginning' according to Jim Holt

“Bang.”

“…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….”

For properties of the “nothing” represented by the 3×3 grid, see The Field of Reason. For religious material related to the above and to Epiphany, a holy day observed by some, see Plato, Pegasus, and the Evening Star and Shining Forth.


Some Context:

Quaternions in Finite Geometry

Click to enlarge.

See also Nativity.

Sunday, July 19, 2009

Sunday July 19, 2009

Filed under: General — m759 @ 7:11 AM
Finite Jest
(continued from
 Monday, July 13)

Blaise Pascal:

"L’unité jointe à l’infini ne l’augmente de rien, non plus qu’un pied à une mesure infinie. Le fini s’anéantit en présence de l’infini, et devient un pur néant….

Nous connaissons qu’il y a un infini, et ignorons sa nature. Comme nous savons qu’il est faux que les nombres soient finis, donc il est vrai qu’il y a un infini en nombre. Mais nous ne savons ce qu’il est: il est faux qu’il soit pair, il est faux qu’il soit impair; car, en ajoutant 1 unité, il ne change point de nature; cependant c’est un nombre, et tout nombre est pair ou impair (il est vrai que cela s’entend de tout nombre fini). Ainsi…."

"Unity joined to infinity adds nothing to it, no more than one foot to an infinite measure. The finite is annihilated in the presence of the infinite, and becomes a pure nothing….

We know that there is an infinite, and are ignorant of its nature. As we know it to be false that numbers are finite, it is therefore true that there is an infinity in number. But we do not know what it is. It is false that it is even, it is false that it is odd; for the addition of a unit can make no change in its nature. Yet it is a number, and every number is odd or even (this is certainly true of every finite number). So…."

Pensées (trans. W. F. Trotter), Courier Dover Publications, 2003

"Le fini s’anéantit
 en présence de l’infini,
      et devient un pur néant
…."

Un Pur Néant:

"So did God cause the big bang?
Overcome by metaphysical lassitude,
I finally reach over to my bookshelf
for The Devil's Bible.
Turning to Genesis I read:
'In the beginning
there was nothing.
And God said,
'Let there be light!'
And there was still nothing,
but now you could see it.'"

— Jim Holt, Big-Bang Theology,
   Slate's "High Concept" department

Illustration:

Fiat Lux, and After

Ainsi….

"In the garden of Adding,
 Live Even and Odd"      
— E. L. Doctorow    

Illustration:

The Cross of Five Ninths

  4 + 5 = 9.

Thursday, July 16, 2009

Thursday July 16, 2009

Filed under: General — m759 @ 4:00 PM

The White Itself

David Ellerman has written that

"The notion of a concrete universal occurred in Plato's Theory of Forms [Malcolm 1991]."

A check shows that Malcolm indeed discussed this notion ("the Form as an Ideal Individual"), but not under the name "concrete universal."

See Plato on the Self-Predication of Forms, by John Malcolm, Oxford U. Press, 1991.

From the publisher's summary:

"Malcolm…. shows that the middle dialogues do indeed take Forms to be both universals and paradigms…. He shows that Plato's concern to explain how the truths of mathematics can indeed be true played an important role in his postulation of the Form as an Ideal Individual."

Ellerman also cites another discussion of Plato published by Oxford:

Kneale and Kneale on Plato's theory of forms and 'the white itself'

For a literary context, see W. K. Wimsatt, Jr., "The Structure of the Concrete Universal," Ch. 6 in Literary Theory: An Anthology, edited by Julie Rivkin and Michael Ryan, Wiley-Blackwell, 2004.

Other uses of the phrase "concrete universal"– Hegelian and/or theological– seem rather distant from the concerns of Plato and Wimsatt, and are best left to debates between Marxists and Catholics. (My own sympathies are with the Catholics.)

Two views of "the white itself" —

 "So did God cause the big bang?
 Overcome by metaphysical lassitude,
 I finally reach over to my bookshelf
 for The Devil's Bible.
 Turning to Genesis I read:
 'In the beginning
 there was nothing.
 And God said,
 'Let there be light!'
 And there was still nothing,
 but now you could see it.'"
 
 -- Jim Holt, Big-Bang Theology,
    Slate's "High Concept" department 
 
   Fiat Lux, and After

"The world was warm and white when I was born:
Beyond the windowpane the world was white,
A glaring whiteness in a leaded frame,
Yet warm as in the hearth and heart of light."

-- Delmore Schwartz

Sunday, November 4, 2007

Sunday November 4, 2007

Filed under: General,Geometry — m759 @ 3:00 AM

High Concept

On this date in 1948, T. S. Eliot
won the Nobel Prize in Literature.

The 4x4 square

 Non ha l'ottimo artista in se alcun concetto,
Ch'un marmo solo in se non circoscriva
Col suo soverchio; e solo a quello arriva
La man che ubbidisce all'intelletto.
 
(The best artist has in himself no concept
in a single block of marble not contained;
only the hand obeying mind will find it.)
 
— Michelangelo, as quoted
by Erwin Panofsky in

Idea: A Concept in Art Theory

Saturday, January 6, 2007

Saturday January 6, 2007

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


Picture of Nothing

On Kirk Varnedoe’s
2003 Mellon Lectures,
Pictures of Nothing“–

“Varnedoe’s lectures were ultimately
about faith, about his faith in
the power of abstraction,
and abstraction as a kind of
anti-religious faith in itself….”

The Washington Post

Related material:

The more industrious scholars
will derive considerable pleasure
from describing how the art-history
professors and journalists of the period
1945-75, along with so many students,
intellectuals, and art tourists of every
sort, actually struggled to see the
paintings directly, in the old
pre-World War II way,
like Plato’s cave dwellers
watching the shadows, without
knowing what had projected them,
which was the Word.”

— Tom Wolfe, The Painted Word

Log24, Aug. 23, 2005:

Concept (scholastics’ verbum mentis)–
theological analogy of Son’s procession
as Verbum Patris, 111-12″

— Index to Joyce and Aquinas,
by William T. Noon, S.J.,
Yale University Press 1957,
second printing 1963, page 162

“So did God cause the big bang?
Overcome by metaphysical lassitude,
I finally reach over to my bookshelf
for The Devil’s Bible.
Turning to Genesis I read:
‘In the beginning
there was nothing.
And God said,
‘Let there be light!’
And there was still nothing,
but now you could see it.'”

— Jim Holt, Big-Bang Theology,
Slate‘s “High Concept” department

The image “http://www.log24.com/log/pix07/070106-Bang.jpg” cannot be displayed, because it contains errors.


“Bang.”

“…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….”

Rosalind Krauss, “Grids”

For properties of the
“nothing” represented
by the 3×3 grid, see
The Field of Reason.

For religious material related
to the above and to Epiphany,
a holy day observed by some,
see Plato, Pegasus, and the
Evening Star
and Shining Forth.

Friday, October 20, 2006

Friday October 20, 2006

Filed under: General — m759 @ 12:00 PM
High Concept

(Continued from 8/23/05)
“At present, such relationships can
at best be heuristically described
in terms that invoke some notion
of an ‘intelligent user standing
outside the system.'”

Gian-Carlo Rota in
Indiscrete Thoughts, p. 152

Related Material

The Devil’s Bible and
Nothing Nothings (Again).

The Context

One context for the Rota quote
is Paul Halmos’s remark, quoted
  in today’s New York Times,
that mathematics is
“almost like being
in touch with God.”

Another context is
Log24 on Aug. 29, 2005.

Here is the original context:

The image “http://www.log24.com/theory/images/Rota152.gif” cannot be displayed, because it contains errors.

Monday, October 9, 2006

Monday October 9, 2006

Filed under: General,Geometry — m759 @ 9:00 AM
 
ART WARS:
To Apollo
 
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

To Apollo (10/09/02)
Art Wars: Apollo and Dionysus
(10/09/02)
Balanchine's Birthday
(01/09/03)

Art Theory for Yom Kippur
(10/05/03)

A Form
(05/22/04)
Ineluctable
(05/27/04)

A Form, continued
(06/05/04)
Parallelisms
(06/06/04)
Ado
(06/25/04)

Deep Game
(06/26/04)
Gameplayers of Zen
(06/27/04)
And So To Bed
(06/29/04)
Translation Plane for Rosh Hashanah
(09/15/04)
Derrida Dead
(10/09/04)
The Nine
(11/09/04)
From Tate to Plato
(11/19/04)
Art History
(05/11/05)
A Miniature Rosetta Stone
(08/06/05)
High Concept
(8/23/05) 
High Concept, Continued
(8/24/05)
Analogical Train of Thought
(8/25/05)
Today's Sermon: Magical Thinking
(10/09/05)
Balance
(10/31/05)
Matrix
(11/01/05)
Seven is Heaven, Eight is a Gate
(11/12/05)
Nine is a Vine
(11/12/05)
Apollo and Christ
(12/02/05)
Hamilton's Whirligig
(01/05/06)
Cross
(01/06/06)
On Beauty
(01/26/06)
Sunday Morning
(01/29/06)
Centre
(01/29/06)
New Haven
(01/29/06) 
Washington Ballet
(02/05/06)
Catholic Schools Sermon
(02/05/06)
The Logic of Apollo
(02/05/06)
Game Boy
(08/06/06)
Art Wars Continued: The Krauss Cross
(09/13/06)
Art Wars Continued: Pandora's Box
(09/16/06)
The Pope in Plato's Cave
(09/16/06)
Today's Birthdays
(09/26/06)
Symbology 101
(09/26/06)

Saturday, December 24, 2005

Saturday December 24, 2005

Filed under: General — m759 @ 12:00 PM
High Concept

Concept (scholastics’ verbum mentis)–
theological analogy of Son’s procession
as Verbum Patris, 111-12″
— index to Joyce and Aquinas,    
by William T. Noon,
Society of Jesus,
Yale University Press 1957,
second printing 1963, page 162

Then there is
the Daughter’s procession:

The image “http://www.log24.com/log/pix05B/051224-String.gif” cannot be displayed, because it contains errors.

For the String Theory
Appreciation Club, see
  Raoul Bott, 1923-2005.

For another
imaginary club, see
The Club Dumas (below).

For a non-imaginary club,
see the organization
that included Noon (above).

Monday, August 29, 2005

Monday August 29, 2005

Filed under: General — Tags: — m759 @ 4:00 PM
VALE

The image “http://www.log24.com/log/pix05B/050829-GeorgeAndEsther2.jpg” cannot be displayed, because it contains errors.

George and Esther Szekeres

From the weblog of
David Michael Brown, Jr.:
 

Date:     Sun, 28 Aug 2005
             12:30:40 -0400
From:    Alf van der Poorten AM
           
Subject: Vale George Szekeres and
             Esther Klein Szekeres

Members of the Number Theory List will be sad to learn that George and Esther Szekeres both died this morning.  George, 94, had been quite ill for the last 2-3 days, barely conscious, and died first at 06:30.  Esther, 95, died a half hour later.

Both George Szekeres and Esther Klein will be recalled by number theorists as members of the group of young Hungarian mathematicians of the 1930s including Turan and Erdos.  George and Esther's coming to Australia in the late 40s played an important role in the invigoration of Australian Mathematics.  George was also an expert in group theory and relativity; he was my PhD supervisor.

Emeritus Professor
Alf van der Poorten AM
Centre for Number Theory Research
1 Bimbil Place, Killara NSW

 

Related material:

AVE

3:09 PM EDT Thursday, Aug. 25, 2005:
 

  "Hello! Kinch here. Put me on to Edenville. Aleph, alpha: nought, nought, one." 

 

  "A very short space of time through very short times of space….
   Am I walking into eternity along Sandymount strand?"

   — James Joyce, Ulysses, Proteus chapter

A very short space of time through very short times of space….

   "It is demonstrated that space-time should possess a discrete structure on Planck scales."

   — Peter Szekeres, abstract of Discrete Space-Time

Peter Szekeres is the son of George and Esther Szekeres.
 

ATQUE

"At present, such relationships can at best be heuristically described in terms that invoke some notion of an 'intelligent user standing outside the system.'"

Gian-Carlo Rota in Indiscrete Thoughts, p. 152
 

Related material:
High Concept and
Nothing Nothings (Again).

Wednesday, August 24, 2005

Wednesday August 24, 2005

Filed under: General — m759 @ 12:00 AM

High Concept, continued:

“In the beginning there was nothing.
 And God said, ‘Let there be light!’
 And there was still nothing,
 but now you could see it.

— Jim Holt, Big-Bang Theology,
    Slate‘s “High Concept” department

Related material:

  1. On the phrase “verbum mentis”
  2. From Satan’s Rhetoric, by Armando Maggi
    (University of Chicago Press, 2001):
Page 110:

“In chapter I I explained that devils first and foremost exist as semioticians of the world’s signs.  Devils solely live in their interpretations, in their destructive syllogisms.  As Visconti puts it, devils speak the idiom of the mind.37  …. The exorcist’s healing voice states that Satan has always been absent from the world, that his disturbing and unclear manifestations in the possessed person’s physicality are really nonexistent occurrences, nothing but disturbances of the mind, since evil itself is a lack of being.”   

Footnote 37, page 110:

“It is necessary to distinguish the devils’ ‘language of the mind’ and Augustine’s verbum mentis (word of the mind), as he theorizes it first of all in On the Trinity (book 15).  The devils’ language of the mind disturbs the subject’s internal and preverbal discourse.”

Tuesday, August 23, 2005

Tuesday August 23, 2005

Filed under: General — m759 @ 12:00 PM

High Concept*

Concept (scholastics’ verbum mentis)–
 theological analogy of Son’s procession
 as Verbum Patris, 111-12″
 — index to Joyce and Aquinas,
 by William T. Noon, S.J.,
Yale University Press 1957,
 second printing 1963, page 162

“So did God cause the big bang? Overcome by metaphysical lassitude, I finally reach over to my bookshelf for The Devil’s Bible. Turning to Genesis I read: ‘In the beginning there was nothing. And God said, ‘Let there be light!’ And there was still nothing, but now you could see it.'”

— Jim Holt, Big-Bang Theology, Slate‘s “High Concept” department

Related material:

Nothing Ventured,
The God-Shaped Hole, and
Is Nothing Sacred?

 * See also John O’Callaghan, Thomistic Realism and the Linguistic Turn: Toward a More Perfect Form of Existence, (University of Notre Dame Press, 2003) and Joshua P. Hochschild, “Does Mental Language Imply Mental Representationalism? The Case of Aquinas’s Verbum Mentis,” Proceedings of the Society for Medieval Logic and Metaphysics, Volume 4, 2004 (pdf), pp. 12-17.

Sunday, March 24, 2019

Espacement: Geometry of the Interstice in Literary Theory

Filed under: General — Tags: , , , , — m759 @ 3:28 AM

"You said something about the significance of spaces between
elements being repeated. Not only the element itself being repeated,
but the space between. I'm very interested in the space between.
That is where we come together." — Peter Eisenman, 1982

https://www.parrhesiajournal.org/
parrhesia03/parrhesia03_blackburne.pdf

Parrhesia  No. 3 • 2007 • 22–32

(Up) Against the (In) Between: Interstitial Spatiality
in Genet and Derrida

by Clare Blackburne

Blackburne — www.parrhesiajournal.org 24 —

"The excessive notion of espacement  as the resurgent spatiality of that which is supposedly ‘without space’ (most notably, writing), alerts us to the highly dynamic nature of the interstice – a movement whose discontinuous and ‘aberrant’ nature requires further analysis."

Blackburne — www.parrhesiajournal.org 25 —

"Espacement  also evokes the ambiguous figure of the interstice, and is related to the equally complex derridean notions of chora , différance , the trace and the supplement. Derrida’s reading of the Platonic chora  in Chora L Works  (a series of discussions with the architect Peter Eisenman) as something which defies the logics of non-contradiction and binarity, implies the internal heterogeneity and instability of all structures, neither ‘sensible’ nor ‘intelligible’ but a third genus which escapes conceptual capture.25 Crucially, chora , spacing, dissemination and différance  are highly dynamic concepts, involving hybridity, an ongoing ‘corruption’ of categories, and a ‘bastard reasoning.’26 Derrida identification of différance  in Margins of  Philosophy , as an ‘unappropriable excess’ that operates through spacing as ‘the becoming-space of time or the becoming-time of space,’27 chimes with his description of chora  as an ‘unidentifiable excess’ that is ‘the spacing which is the condition for everything to take place,’ opening up the interval as the plurivocity of writing in defiance of ‘origin’ and ‘essence.’28  In this unfolding of différance , spacing  ‘insinuates  into  presence an  interval,’29 again alerting us to the crucial role of the interstice in deconstruction, and, as Derrida observes  in Positions ,  its  impact  as  ‘a movement,  a  displacement  that  indicates  an  irreducible alterity’: ‘Spacing is the impossibility for an identity to be closed on itself, on the inside of its proper interiority, or on its coincidence with itself. The irreducibility of spacing is the irreducibility of the other.’30"

25. Quoted in Jeffrey Kipnis and Thomas Leeser, eds., 
Chora L Works. Jacques Derrida and Peter Eisenman  
(New York: The Monacelli Press, 1997), 15.

26. Ibid, 25.

27. Derrida, Margins of Philosophy.
(Brighton: The Harvester Press, 1982), 6 and 13.

28. Derrida, Chora L Works , 19 and 10.

29. Ibid, 203.

30. Derrida, Positions , 94.

Sunday, December 2, 2018

Symmetry at Hiroshima

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 6:43 AM

A search this morning for articles mentioning the Miracle Octad Generator
of R. T. Curtis within the last year yielded an abstract for two talks given
at Hiroshima on March 8 and 9, 2018

http://www.math.sci.hiroshima-u.ac.jp/
branched/files/2018/abstract/Aitchison.txt

Iain AITCHISON

Title:

Construction of highly symmetric Riemann surfaces, related manifolds, and some exceptional objects, I, II

Abstract:

Since antiquity, some mathematical objects have played a special role, underpinning new mathematics as understanding deepened. Perhaps archetypal are the Platonic polyhedra, subsequently related to Platonic idealism, and the contentious notion of existence of mathematical reality independent of human consciousness.

Exceptional or unique objects are often associated with symmetry – manifest or hidden. In topology and geometry, we have natural base points for the moduli spaces of closed genus 2 and 3 surfaces (arising from the 2-fold branched cover of the sphere over the 6 vertices of the octahedron, and Klein's quartic curve, respectively), and Bring's genus 4 curve arises in Klein's description of the solution of polynomial equations of degree greater than 4, as well as in the construction of the Horrocks-Mumford bundle. Poincare's homology 3-sphere, and Kummer's surface in real dimension 4 also play special roles.

In other areas: we have the exceptional Lie algebras such as E8; the sporadic finite simple groups; the division algebras: Golay's binary and ternary codes; the Steiner triple systems S(5,6,12) and S(5,8,24); the Leech lattice; the outer automorphisms of the symmetric group S6; the triality map in dimension 8; and so on. We also note such as: the 27 lines on a cubic, the 28 bitangents of a quartic curve, the 120 tritangents of a sextic curve, and so on, related to Galois' exceptional finite groups PSL2(p) (for p= 5,7,11), and various other so-called `Arnol'd Trinities'.

Motivated originally by the `Eightfold Way' sculpture at MSRI in Berkeley, we discuss inter-relationships between a selection of these objects, illustrating connections arising via highly symmetric Riemann surface patterns. These are constructed starting with a labeled polygon and an involution on its label set.

Necessarily, in two lectures, we will neither delve deeply into, nor describe in full, contexts within which exceptional objects arise. We will, however, give sufficient definition and detail to illustrate essential inter-connectedness of those exceptional objects considered.

Our starting point will be simplistic, arising from ancient Greek ideas underlying atomism, and Plato's concepts of space. There will be some overlap with a previous talk on this material, but we will illustrate with some different examples, and from a different philosophical perspective.

Some new results arising from this work will also be given, such as an alternative graphic-illustrated MOG (Miracle Octad Generator) for the Steiner system S(5,8,24), and an alternative to Singerman – Jones' genus 70 Riemann surface previously proposed as a completion of an Arnol'd Trinity. Our alternative candidate also completes a Trinity whose two other elements are Thurston's highly symmetric 6- and 8-component links, the latter related by Thurston to Klein's quartic curve.

See also yesterday morning's post, "Character."

Update: For a followup, see the next  Log24 post.

Thursday, November 1, 2018

Literary Doodles

Filed under: General — m759 @ 11:59 AM

The Great Doodle of Northrop Frye —

Shown below is a "Story Circle" based on the work of Joseph Campbell.
The author of this particular version is unknown.  

Note that there are 12 steps in the above Story Circle. This suggests
some dialogue from a recent film . . .

Donnie —"We can't ask for help if we don't think there's anyone out there to give it. You have to grasp this concept. And that doesn't have to be fucking Jesus Christ or Buddha or Vanna White."
John — "So, can I choose the genitalia of Raquel Welch?"
Donnie — "I would advise against that, Callahan."
John — "Why?"
Donnie — "'Cause it's not a fucking joke. If you can't look outside yourself and you can't find a higher power, you're fucked."

Read more: https://www.springfieldspringfield.co.uk/movie_script.php?movie=dont-worry-he-wont-get-far-on-foot

Wednesday, October 17, 2018

Aesthetics

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

From "The Phenomenology of Mathematical Beauty,"
by Gian-Carlo Rota —

The Lightbulb Mistake

. . . . Despite the fact that most proofs are long, and despite our need for extensive background, we think back to instances of appreciating mathematical beauty as if they had been perceived in a moment of bliss, in a sudden flash like a lightbulb suddenly being lit. The effort put into understanding the proof, the background material, the difficulties encountered in unraveling an intricate sequence of inferences fade and magically disappear the moment we become aware of the beauty of a theorem. The painful process of learning fades from memory, and only the flash of insight remains.

We would like  mathematical beauty to consist of this flash; mathematical beauty should  be appreciated with the instantaneousness of a lightbulb being lit. However, it would be an error to pretend that the appreciation of mathematical beauty is what we vaingloriously feel it should be, namely, an instantaneous flash. Yet this very denial of the truth occurs much too frequently.

The lightbulb mistake is often taken as a paradigm in teaching mathematics. Forgetful of our learning pains, we demand that our students display a flash of understanding with every argument we present. Worse yet, we mislead our students by trying to convince them that such flashes of understanding are the core of mathematical appreciation.

Attempts have been made to string together beautiful mathematical results and to present them in books bearing such attractive titles as The One Hundred Most Beautiful Theorems of Mathematics . Such anthologies are seldom found on a mathematician’s bookshelf. The beauty of a theorem is best observed when the theorem is presented as the crown jewel within the context of a theory. But when mathematical theorems from disparate areas are strung together and presented as “pearls,” they are likely to be appreciated only by those who are already familiar with them.

The Concept of Mathematical Beauty

The lightbulb mistake is our clue to understanding the hidden sense of mathematical beauty. The stark contrast between the effort required for the appreciation of mathematical beauty and the imaginary view mathematicians cherish of a flashlike perception of beauty is the Leitfaden  that leads us to discover what mathematical beauty is.

Mathematicians are concerned with the truth. In mathematics, however, there is an ambiguity in the use of the word “truth.” This ambiguity can be observed whenever mathematicians claim that beauty is the raison d’être of mathematics, or that mathematical beauty is what gives mathematics a unique standing among the sciences. These claims are as old as mathematics and lead us to suspect that mathematical truth and mathematical beauty may be related.

Mathematical beauty and mathematical truth share one important property. Neither of them admits degrees. Mathematicians are annoyed by the graded truth they observe in other sciences.

Mathematicians ask “What is this good for?” when they are puzzled by some mathematical assertion, not because they are unable to follow the proof or the applications. Quite the contrary. Mathematicians have been able to verify its truth in the logical sense of the term, but something is still missing. The mathematician who is baffled and asks “What is this good for?” is missing the sense  of the statement that has been verified to be true. Verification alone does not give us a clue as to the role of a statement within the theory; it does not explain the relevance  of the statement. In short, the logical truth of a statement does not enlighten us as to the sense of the statement. Enlightenment , not truth, is what the mathematician seeks when asking, “What is this good for?” Enlightenment is a feature of mathematics about which very little has been written.

The property of being enlightening is objectively attributed to certain mathematical statements and denied to others. Whether a mathematical statement is enlightening or not may be the subject of discussion among mathematicians. Every teacher of mathematics knows that students will not learn by merely grasping the formal truth of a statement. Students must be given some enlightenment as to the sense  of the statement or they will quit. Enlightenment is a quality of mathematical statements that one sometimes gets and sometimes misses, like truth. A mathematical theorem may be enlightening or not, just as it may be true or false.

If the statements of mathematics were formally true but in no way enlightening, mathematics would be a curious game played by weird people. Enlightenment is what keeps the mathematical enterprise alive and what gives mathematics a high standing among scientific disciplines.

Mathematics seldom explicitly acknowledges the phenomenon of enlightenment for at least two reasons. First, unlike truth, enlightenment is not easily formalized. Second, enlightenment admits degrees: some statements are more enlightening than others. Mathematicians dislike concepts admitting degrees and will go to any length to deny the logical role of any such concept. Mathematical beauty is the expression mathematicians have invented in order to admit obliquely the phenomenon of enlightenment while avoiding acknowledgment of the fuzziness of this phenomenon. They say that a theorem is beautiful when they mean to say that the theorem is enlightening. We acknowledge a theorem’s beauty when we see how the theorem “fits” in its place, how it sheds light around itself, like Lichtung — a clearing in the woods. We say that a proof is beautiful when it gives away the secret of the theorem, when it leads us to perceive the inevitability of the statement being proved. The term “mathematical beauty,” together with the lightbulb mistake, is a trick mathematicians have devised to avoid facing up to the messy phenomenon of enlightenment. The comfortable one-shot idea of mathematical beauty saves us from having to deal with a concept that comes in degrees. Talk of mathematical beauty is a cop-out to avoid confronting enlightenment, a cop-out intended to keep our description of mathematics as close as possible to the description of a mechanism. This cop-out is one step in a cherished activity of mathematicians, that of building a perfect world immune to the messiness of the ordinary world, a world where what we think should be true turns out to be true, a world that is free from the disappointments, ambiguities, and failures of that other world in which we live.

How many mathematicians does  it take to screw in a lightbulb?

Monday, August 13, 2018

Trojan Horsitude

Filed under: General,Geometry — Tags: — m759 @ 3:33 AM
 

"It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato's (realist) reaction to the sophists (nominalists). What is often called 'postmodernism' is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth."

— Simon Blackburn, Think,
    Oxford University Press, 1999, page 268


". . . a perfect triptych of horsitude"

James Parker on the 2007 film "Michael Clayton"

Related material —

Horsitude in the 4×2 grid, and

http://www.log24.com/log/pix18/180813-Structure_and_Sense-post-160606.gif

http://www.log24.com/log/pix18/180813-Knight_Moves-080116-page-top.gif

Monday, June 11, 2018

Finite Fields in 1956

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

The "more complicated" material mentioned by James Propp
in the previous post was notably described by A. A. Albert in 1956:

Wednesday, April 4, 2018

The Key

Filed under: General,Geometry — Tags: — m759 @ 12:32 PM

"The complete projective group of collineations and dualities of the
[projective] 3-space is shown to be of order [in modern notation] 8! ….
To every transformation of the 3-space there corresponds
a transformation of the [projective] 5-space. In the 5-space, there are
determined 8 sets of 7 points each, 'heptads' …."

— George M. Conwell, "The 3-space PG (3, 2) and Its Group," 
The Annals of Mathematics , Second Series, Vol. 11, No. 2 (Jan., 1910),
pp. 60-76.

"It must be remarked that these 8 heptads are the key to an elegant proof…."

— Philippe Cara, "RWPRI Geometries for the Alternating Group A8," in 
Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference 
(July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis,
James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97.

For those who, like the author of The Eight  (a novel in which today's
date figures prominently), prefer fiction —

See as well . . .

Literary theorists may, if they wish, connect
cabalistically the Insidious  address "414" 
with the date  4/14 of the above post, and
the word Appletree with the biblical Garden.

Friday, February 16, 2018

Nicht Spielerei

Filed under: General — m759 @ 2:19 PM

"What of the night
That lights and dims the stars?
Do you know, Hans Christian,
Now that you see the night?"

— The concluding lines of
"Sonatina to Hans Christian,"
by Wallace Stevens
(in Harmonium  (second edition, 1931))

". . . in the end the space itself is the star. . . ."

Related material — The death Tuesday night
of Prince Consort Henrik of Denmark, and the
New Year's Eve speech on Dec. 31, 2015, of
Queen Margrethe II of Denmark.

Distantly  related material — Yesterday morning's
post The Search for Child's Play.

Thursday, January 25, 2018

Beware of Analogical Extension

Filed under: General,Geometry — Tags: — m759 @ 11:29 AM

"By an archetype  I mean a systematic repertoire
of ideas by means of which a given thinker describes,
by analogical extension , some domain to which
those ideas do not immediately and literally apply."

— Max Black in Models and Metaphors 
    (Cornell, 1962, p. 241)

"Others … spoke of 'ultimate frames of reference' …."
Ibid.

A "frame of reference" for the concept  four quartets

A less reputable analogical extension  of the same
frame of reference

Madeleine L'Engle in A Swiftly Tilting Planet :

"… deep in concentration, bent over the model
they were building of a tesseract:
the square squared, and squared again…."

See also the phrase Galois tesseract .

Monday, November 13, 2017

Plan 9 at Yale

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

Yale Professors Race Google and IBM to the First Quantum Computer

"So, after summer, in the autumn air, 
Comes the cold volume*  of forgotten ghosts,

But soothingly, with pleasant instruments, 
So that this cold, a children's tale of ice, 
Seems like a sheen of heat romanticized."

— Wallace Stevens,
"An Ordinary Evening in New Haven"

* Update of 10:20 the same evening:

An alternative to The Snow Queen  
as "the cold volume" of Wallace Stevens

On The King in the Window , by Adam Gopnik —

"The book is dedicated to Adam Gopnik's son,
Luke Auden, and his late, great godfathers,
Kirk Varnedoe and Richard Avedon.

'A fantasy that is as ambitious in theme,
sophisticated in setting, and cosmic in scope
as the works of Madeline L'Engle.

The unlikely eponymous hero is Oliver Parker,
an 11-year-old American boy living in Paris
with his mother and journalist father.
After he finds a prize in his slice of cake on
The Night of Epiphany and dons the customary
gilt-paper crown, the boy is plunged into
a battle over nothing less than control of the universe.

His enemy is the dreaded Master of Mirrors,
who rose to power during the reign of Louis XIV,
when Parisians developed technology for making
sheet glass. This faceless, evil being,
capable of capturing souls
through mirrors and enslaving them
in an alternate world that lies beyond all mirrors,
now seeks to dominate the entire universe by
mounting a quantum computer on the Eiffel Tower.

Oliver's mission is to defeat the Master of Mirrors
and save his father's stolen soul.' "

— Description at https://biblio.co.nz/. . . .

Tuesday, November 7, 2017

Polarities and Correlation

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

"Read something that means something."
                — New Yorker  ad

'Knight' octad labeling by the 8 points of the projective line over GF(7) .

Friday, May 5, 2017

Pre-Linguistic Thought

Filed under: General,Geometry — m759 @ 11:05 AM

" I know for sure that my best insights (those which 
are not just routine calculations) are pre-linguistic, and
I struggle to put them into words . . . ."

Peter J. Cameron today

See also "George Steiner" + Language in this  journal.

A related figure —

Wednesday, February 1, 2017

Hollywood Arrival

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

In the new film Arrival , Amy Adams plays a linguist
who must interpret the language used by aliens whose
spaceships hover at 12 points around the globe.

Yesterday's events at 6407 Sunset Blvd. in Hollywood,
together with the logic of number and time from recent
posts based on a Heinlein short story, suggest that the
character played by Adams is a sort of "fifth element"
needed to save the world. 

In other words, the strange logic of recent posts ties the
California lottery number  6407 to the date  April 12, 2015, 
and a check of that date in this journal yields posts tagged
Orthodox Easter 2015 that relate to the "fifth element."

Midrash by Ted Chiang from the story on which Arrival  was based  —

After the breakthrough with Fermat's Principle, discussions of scientific concepts became more fruitful. It wasn't as if all of heptapod physics was suddenly rendered transparent, but progress was suddenly steady. According to Gary, the heptapods' formulation of physics was indeed topsy-turvy relative to ours. Physical attributes that humans defined using integral calculus were seen as fundamental by the heptapods. As an example, Gary described an attribute that, in physics jargon, bore the deceptively simple name “action,” which represented “the difference between kinetic and potential energy, integrated over time,” whatever that meant. Calculus for us; elementary to them.

Conversely, to define attributes that humans thought of as fundamental, like velocity, the heptapods employed mathematics that were, Gary assured me, “highly weird.” The physicists were ultimately able to prove the equivalence of heptapod mathematics and human mathematics; even though their approaches were almost the reverse of one another, both were systems of describing the same physical universe.

Sunday, January 8, 2017

A Theory of Everything

Filed under: General,Geometry — Tags: — m759 @ 7:11 PM

The title refers to the Chinese book the I Ching ,
the Classic of Changes .

The 64 hexagrams of the I Ching  may be arranged
naturally in a 4x4x4 cube. The natural form of transformations
("changes") of this cube is given by the diamond theorem.

A related post —

The Eightfold Cube, core structure of the I Ching

Saturday, January 7, 2017

The Lotus Lunch

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

Friday, January 6, 2017

Eightfold Cube at Cornell

Filed under: General,Geometry — Tags: — m759 @ 7:35 PM

The assignments page for a graduate algebra course at Cornell
last fall had a link to the eightfold cube:

Terms Not Dissimilar

Filed under: General — Tags: — m759 @ 11:14 AM

The title is a phrase by New York Times  obituary writer
William Grimes in yesterday's post on an Oxford philosopher.

Related material —

Thursday, January 5, 2017

All Souls’ Confusion

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

Recent reports of the death of a writer on philosophy associated
with All Souls College, Oxford, reflect some confusion.

The New York Times  says the death was on Monday, January 2, 2017.
Other sources, including the college itself, say it was the day before —
Sunday, January 1 (New Year's Day), 2017.

At any rate, perhaps the following post from 9 PM ET Sunday night is relevant:

Sunday, January 1, 2017

9 PM New Year’s Day

Filed under: Uncategorized — m759 @ 9:00 PM

See "Four Gods" in this journal.

Phaedrus  265b:  "And we made four divisions
of the divine madness, ascribing them to four gods . . . ."

See as well a search for All Souls in this journal.

Wednesday, January 4, 2017

Exit

Filed under: General — Tags: — m759 @ 2:48 PM

A post from the end of last year —

Also on New Year's Eve —

A Drama of Many Forms

Filed under: General,Geometry — Tags: — m759 @ 1:24 PM

According to art historian Rosalind Krauss in 1979,
the grid's earliest employers

"can be seen to be participating in a drama
that extended well beyond the domain of art.
That drama, which took many forms, was staged
in many places. One of them was a courtroom,
where early in this century, science did battle with God,
and, reversing all earlier precedents, won."

The previous post discussed the 3×3 grid in the context of
Krauss's drama. In memory of T. S. Eliot, who died on this date
in 1965, an image of the next-largest square grid, the 4×4 array:

 

See instances of the above image.

Tuesday, January 3, 2017

Cultist Space

Filed under: General,Geometry — Tags: — m759 @ 6:29 PM

The image of art historian Rosalind Krauss in the previous post
suggests a review of a page from her 1979 essay "Grids" —

The previous post illustrated a 3×3 grid. That  cultist space does
provide a place for a few "vestiges of the nineteenth century" —
namely, the elements of the Galois field GF(9) — to hide.
See Coxeter's Aleph in this journal.

Ein Eck…

Filed under: General — Tags: — m759 @ 10:19 AM

Continued

By a disciple of the late John Berger

For further ideological remarks from this source, see the now-defunct
web journal Everyday Analysis: An International Collective.

For further remarks from the date of the above post, October 9, 2013,
see this  journal on that date.

Monday, January 2, 2017

John Berger Has Died

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

Screenshot of 11:07 PM ET tonight —

A sample of his work —

An antidote to Berger's remarks —

Constructivist Theology

Filed under: General — Tags: — m759 @ 10:21 PM

This journal on December 24, 2016 (Christmas Eve)
quoted some remarks on "constructivism" in art and 
added a link to the same word as applied in mathematics:

"The word 'constructivism' also refers to
a philosophy of mathematics. See a Log24 post,
'Constructivist Witness. . . ."

From that post

From a post later the same day, Dec. 22— "The Laugh-Hospital"—

Constructivism in mathematics and the laughing academy

This  (Jan. 2, 2017) post was suggested by the reported Christmas Eve death
of a Jesuit priest, Joseph Fitzmyer.

Those entertained by the thought of constructivist laugh-hospitals may
contemplate the New Year's  Eve death of a sitcom actor who played 
a priest. See today's previous post, Sitcom Theology.

Related material — "Laugh Track" in this journal.

Sitcom Theology

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

The Hollywood Reporter

"William Christopher, best known for playing Father Mulcahy
on the hit sitcom M*A*S*H , died Saturday [Dec. 31, 2016] of
lung cancer, his agent confirmed to The Hollywood Reporter.
He was 84.

Christopher died at his home in Pasadena, with his wife by
his bedside, at 5:10 a.m. on New Year's Eve, according to a
statement from his agent."

— 5:59 PM PST 12/31/2016 by Meena Jang

Image reshown in this journal on the midnight (Eastern time)
preceding Christopher's death —

IMAGE- Triangular models of the 4-point affine plane A and 7-point projective plane PA

Related material —

From a Log24 search for "Deathly Hallows" —

Mathematics

http://www.log24.com/log/pix11A/110505-WikipediaFanoPlane.jpg

The Fano plane block design

Magic

http://www.log24.com/log/pix11A/110505-DeathlyHallows.jpg

The Deathly Hallows symbol—
Two blocks short of  a design.

Those who prefer Latin with their theology
may search this journal for "In Nomine Patris."

Sunday, January 1, 2017

9 PM New Year’s Day

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

See "Four Gods" in this journal.

Phaedrus  265b "And we made four divisions
of the divine madness, ascribing them to four gods . . . ."

The Unhurried Curve

Filed under: General — Tags: , — m759 @ 3:33 PM

From today's previous post

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

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

Related figures —

Art critic Robert Hughes in "The Space of Horizons,"
a Log24 post of August 7, 2012:

Religion writer Huston Smith, who reportedly died
on December 30, 2016:

Like the Horizon

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

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

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

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

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

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

— Derrick Breach (See his obituary from 1996.)

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

Projective plane of order 3

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

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

Click on the above image for further remarks.

Friday, November 25, 2016

The Correlative Skeleton

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

Related material from this journal —

Wednesday, September 16, 2015

The World as Myth

Filed under: General — m759 @ 10:48 PM

Three approaches to The World as Myth

From Heinlein's 1985 The Cat Who Walks Through Walls

The World as Myth is a subtle concept. It has sometimes been called multiperson solipsism, despite the internal illogic of that phrase. Yet illogic may be necessary, as the concept denies logic. For many centuries religion held sway as the explanation of the universe- or multiverse. The details of revealed religions differed wildly but were essentially the same: Somewhere up in the sky-or down in the earth-or in a volcano-any inaccessible place- there was an old man in a nightshirt who knew everything and was all powerful and created everything and rewarded and punished and could be bribed.

      "Sometimes this Almighty was female but not often because human males are usually bigger, stronger, and more belligerent; God was created in Pop's image.

      "The Almighty-God idea came under attack because it explained nothing; it simply pushed all explanations one stage farther away. In the nineteenth century atheistic positivism started displacing the Almighty-God notion in that minority of the population that bathed regularly.

      "Atheism had a limited run, as it, too, explains nothing, being merely Godism turned upside down. Logical positivism was based on the physical science of the nineteenth century which, physicists of that century honestly believed, fully explained the universe as a piece of clockwork.

      "The physicists of the twentieth century made short work of that idea. Quantum mechanics and Schrodringer's cat tossed out the clockwork world of 1890 and replaced it with a fog of probability in which anything could happen. Of course the intellectual class did not notice this for many decades, as an intellectual is a highly educated man who can't do arithmetic with his shoes on, and is proud of his lack. Nevertheless, with the death of positivism, Godism and Creationism came back stronger than ever.

      "In the late twentieth century -correct me when I' m wrong, Hilda-Hilda and her family were driven off Earth by a devil, one they dubbed 'the Beast.' They fled in a vehicle you have met, Gay Deceiver, and in their search for safety they visited many dimensions, many universesand Hilda made the greatest philosophical discovery of all time."

      "I'll bet you say that to all the girls!"

      "Quiet, dear. They visited, among more mundane places, the Land of Oz-"

      I sat up with a jerk. Not too much sleep last night and Dr. Harshaw's lecture was sleep-inducing. "Did you say 'Oz'?"

      "I tell you three times. Oz, Oz, Oz. They did indeed visit the fairyland dreamed up by L. Frank Baum. And the Wonderland invented by the Reverend Mr. Dodgson to please Alice. And other places known only to fiction. Hilda discovered what none of us had noticed before because we were inside it: The World is Myth. We create it ourselves-and we change it ourselves. A truly strong myth maker, such as Homer, such as Baum, such as the creator of Tarzan, creates substantial and lasting worlds whereas the fiddlin', unimaginative liars and fabulists shape nothing new and their tedious dreams are forgotten. ….

Friday, November 6, 2009

Where Entertainment is God (continued)

Filed under: Uncategorized — m759 @ 1:06 AM 

Click to enlarge.

Ad, with army base shooter in video, for 'The Men Who Stare at Goats'

Colorado Springs Gazette
movie reviewer Brandon Fibbs yesterday:

“Much of this is genuinely amusing.
So why then am I not laughing?”

NY Times on the Fort Hood shootings that took place in the afternoon of Nov. 5, 2009

Friday, December 5, 2014

Wittgenstein’s Picture

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

From Zettel  (repunctuated for clarity):

249. « Nichts leichter, als sich einen 4-dimensionalen Würfel
vorstellen! Er schaut so aus… »

"Nothing easier than to imagine a 4-dimensional cube!
It looks like this… 

[Here the editor supplied a picture of a 4-dimensional cube
that was omitted by Wittgenstein in the original.]

« Aber das meine ich nicht, ich meine etwas wie…

"But I don't mean that, I mean something like…

…nur mit 4 Ausdehnungen! » 

but with four dimensions!

« Aber das ist nicht, was ich dir gezeigt habe,
eben etwas wie…

"But isn't  what I showed you like

…nur mit 4 Ausdehnungen? » 

…only with four dimensions?"

« Nein; das meine  ich nicht! » 

"No, I don't mean  that!"

« Was aber meine ich? Was ist mein Bild?
Nun der 4-dimensionale Würfel, wie du ihn gezeichnet hast,
ist es nicht ! Ich habe jetzt als Bild nur die Worte  und
die Ablehnung alles dessen, was du mir zeigen kanst. »

"But what do I mean? What is my picture?
Well, it is not  the four-dimensional cube
as you drew it. I have now for a picture only
the words  and my rejection of anything
you can show me."

"Here's your damn Bild , Ludwig —"

Context: The Galois Tesseract.

Wednesday, November 19, 2014

The Eye/Mind Conflict

Filed under: General,Geometry — Tags: — m759 @ 10:25 AM

Harold Rosenberg, "Art and Words," 
The New Yorker , March 29, 1969. From page 110:

"An advanced painting of this century inevitably gives rise
in the spectator to a conflict between his eye and his mind; 
as Thomas Hess has pointed out, the fable of the emperor's 
new clothes is echoed at the birth of every modemist art 
movement. If work in a new mode is to be accepted, the 
eye/mind conflict must be resolved in favor of the mind; 
that is, of the language absorbed into the work. Of itself, 
the eye is incapable of breaking into the intellectual system 
that today distinguishes between objects that are art and 
those that are not. Given its primitive function of 
discriminating among things in shopping centers and on 
highways, the eye will recognize a Noland as a fabric
design, a Judd as a stack of metal bins— until the eye's 
outrageous philistinism has been subdued by the drone of 
formulas concerning breakthroughs in color, space, and 
even optical perception (this, too, unseen by the eye, of 
course). It is scarcely an exaggeration to say that paintings 
are today apprehended with the ears. Miss Barbara Rose, 
once a promoter of striped canvases and aluminum boxes, 
confesses that words are essential to the art she favored 
when she writes, 'Although the logic of minimal art gained 
critical respect, if not admiration, its reductiveness allowed
for a relatively limited art experience.' Recent art criticism 
has reversed earlier procedures: instead of deriving principles 
from what it sees, it teaches the eye to 'see' principles; the 
writings of one of America's influential critics often pivot on 
the drama of how he failed to respond to a painting or 
sculpture the first few times he saw it but, returning to the 
work, penetrated the concept that made it significant and
was then able to appreciate it. To qualify as a member of the 
art public, an individual must be tuned to the appropriate 
verbal reverberations of objects in art galleries, and his 
receptive mechanism must be constantly adjusted to oscillate 
to new vocabularies."

New vocabulary illustrated:

Graphic Design and a Symplectic Polarity —

Background: The diamond theorem
and a zero system .

Monday, October 13, 2014

Raiders of the Lost Theorem

Filed under: General,Geometry — Tags: — m759 @ 12:05 PM

(Continued from Nov. 16, 2013.)

The 48 actions of GL(2,3) on a 3×3 array include the 8-element
quaternion group as a subgroup. This was illustrated in a Log24 post,
Hamilton’s Whirligig, of Jan. 5, 2006, and in a webpage whose
earliest version in the Internet Archive is from June 14, 2006.

One of these quaternion actions is pictured, without any reference
to quaternions, in a 2013 book by a Netherlands author whose
background in pure mathematics is apparently minimal:

In context (click to enlarge):

Update of later the same day —

Lee Sallows, Sept. 2011 foreword to Geometric Magic Squares —

“I first hit on the idea of a geometric magic square* in October 2001,**
and I sensed at once that I had penetrated some previously hidden portal
and was now standing on the threshold of a great adventure. It was going
to be like exploring Aladdin’s Cave. That there were treasures in the cave,
I was convinced, but how they were to be found was far from clear. The
concept of a geometric magic square is so simple that a child will grasp it
in a single glance. Ask a mathematician to create an actual specimen and
you may have a long wait before getting a response; such are the formidable
difficulties confronting the would-be constructor.”

* Defined by Sallows later in the book:

“Geometric  or, less formally, geomagic  is the term I use for
a magic square in which higher dimensional geometrical shapes
(or tiles  or pieces ) may appear in the cells instead of numbers.”

** See some geometric  matrices by Cullinane in a March 2001 webpage.

Earlier actual specimens — see Diamond Theory  excerpts published in
February 1977 and a brief description of the original 1976 monograph:

“51 pp. on the symmetries & algebra of
matrices with geometric-figure entries.”

— Steven H. Cullinane, 1977 ad in
Notices of the American Mathematical Society

The recreational topic of “magic” squares is of little relevance
to my own interests— group actions on such matrices and the
matrices’ role as models of finite geometries.

Tuesday, September 9, 2014

In Memoriam

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

For Loren D. Olson, Harvard '64:

"Even 50 years later, I remember his enthusiasm for a very young
and very gifted Harvard professor named Shlomo Sternberg, one
of whose special areas of interest was Lie groups. I still have no real
understanding of what a Lie group is, but not for want of trying on
Loren’s part. Loren was also quite interested in the thinking of the
theologians Paul Tillich and Reinhold Niebuhr, who were then at
Harvard. He attended some of their lectures, read several of their
books, and enjoyed discussing their ideas."

Harvard classmate David Jackson

See also today's previous post.

Thursday, September 6, 2012

Decomp Revisited

Filed under: General — m759 @ 1:11 PM

Frogs:

"Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time."

— Freeman Dyson (See July 22, 2011)

A Rhetorical Question:

Robert Osserman in 2004

"The past decade has been an exciting one in the world of mathematics and a fabulous one (in the literal sense) for mathematicians, who saw themselves transformed from the frogs of fairy tales— regarded with a who-would-want-to-kiss-that aversion, when they were noticed at all— into fascinating royalty, portrayed on stage and screen….

Who bestowed the magic kiss on the mathematical frog?"

A Rhetorical Answer:

http://www.log24.com/log/pix11C/111130-SunshineCleaning.jpg

Above: Amy Adams in "Sunshine Cleaning"

Related material:

Friday, July 13, 2012

Suddenly

Filed under: General — Tags: — m759 @ 10:25 AM

1940 —

2003 —

"… Conceptualism — suddenly art
could be nothing more than an idea,
a thought on a piece of paper
that played in your head."

— Michael Kimmelman,
    "The Dia Generation,"
    The New York Times Magazine ,
    Sunday, April 6, 2003


Suddenly?

Friday, April 27, 2012

Paradigms Lost continues…

Filed under: General — m759 @ 9:00 PM

This post was suggested by Paradigms Lost
(a post cited here a year ago today),
by David Weinberger's recent essay "Shift Happens,"
and by today's opening of "The Raven."

David Weinberger in The Chronicle of Higher Education April 22

"… Kuhn was trying to understand how Aristotle could be such a brilliant natural scientist except when it came to understanding motion. Aristotle's idea that stones fall and fire rises because they're trying to get to their natural places seems like a simpleton's animism.

Then it became clear to Kuhn all at once. Ever since Newton, we in the West have thought movement changes an object's position in neutral space but does not change the object itself. For Aristotle, a change in position was a change in a quality of the object, and qualitative change tended toward an asymmetric actualization of potential: an acorn becomes an oak, but an oak never becomes an acorn. Motion likewise expressed a tendency for things to actualize their essence by moving to their proper place. With that, 'another initially strange part of Aristotelian doctrine begins to fall into place,' Kuhn wrote in The Road Since Structure ."

Dr. John Raven (of Raven's Progressive Matrices)

"… these tools cannot be immediately applied within our current workplaces, educational systems, and public management systems because the operation of these systems is determined, not by personal developmental or societal needs, but by a range of latent, rarely discussed, and hard to influence sociological forces.

But this is not a cry of despair: It points to another topic which has been widely neglected by psychologists: It tells us that human behaviour is not  mainly determined by internal  properties— such as talents, attitudes, and values— but by external  social forces. Such a transformation in psychological thinking and theorising is as great as the transformation Newton introduced into physics by noting that the movement of inanimate objects is not determined by internal, 'animistic,' properties of the objects but by invisible external forces which act upon them— invisible forces that can nevertheless be mapped, measured, and harnessed to do useful work for humankind.

So this brings us to our fourth conceptualisation and measurement topic: How are these social forces to be conceptualised, mapped, measured, and harnessed in a manner analogous to the way in which Newton made it possible to harness the destructive forces of the wind and the waves to enable sailing boats to get to their destinations?"

Before Newton, boats never arrived?

Sunday, April 1, 2012

The Palpatine Dimension

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

A physics quote relayed at Peter Woit's weblog today—

"The relation between 4D N=4 SYM and the 6D (2, 0) theory
is just like that between Darth Vader and the Emperor.
You see Darth Vader and you think 'Isn’t he just great?
How can anyone be greater than that? No way.'
Then you meet the Emperor."

— Arkani-Hamed

Some related material from this  weblog—

(See Big Apple and Columbia Film Theory)

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

The Meno Embedding:

http://www.log24.com/log/pix10B/101128-TheEmbedding.gif

Some related material from the Web—

IMAGE- The Penrose diamond and the Klein quadric

See also uses of the word triality  in mathematics. For instance…

A discussion of triality by Edward Witten

Triality is in some sense the last of the exceptional isomorphisms,
and the role of triality for n = 6  thus makes it plausible that n = 6
is the maximum dimension for superconformal symmetry,
though I will not give a proof here.

— "Conformal Field Theory in Four and Six Dimensions"

and a discussion by Peter J. Cameron

There are exactly two non-isomorphic ways
to partition the 4-subsets of a 9-set
into nine copies of AG( 3,2).
Both admit 2-transitive groups.

— "The Klein Quadric and Triality"

Exercise: Is Witten's triality related to Cameron's?
(For some historical background, see the triality  link from above
and Cameron's Klein Correspondence and Triality.)

Cameron applies his  triality to the pure geometry of a 9-set.
For a 9-set viewed in the context of physics, see A Beginning

From MIT Commencement Day, 2011—

A symbol related to Apollo, to nine, and to "nothing"

A minimalist favicon—

IMAGE- Generic 3x3 square as favicon

This miniature 3×3 square— http://log24.com/log/pix11A/110518-3x3favicon.ico — may, if one likes,
be viewed as the "nothing" present at the Creation. 
See Feb. 19, 2011, and Jim Holt on physics.

Happy April 1.

Wednesday, October 5, 2011

Hermenautics

Filed under: General — m759 @ 10:30 PM

University Diaries  today

"Educated people— with some exceptions, like Nader— like to explore the senses, and indeed many of your humanities courses (like the one UD ‘s teaching right now about beauty, in which we just read Susan Sontag’s “Against Interpretation,” with its famous concluding lines: In place of a hermeneutics, we need an erotics of art ) feature artworks and ideas that celebrate sensuality."

This suggests a review lecture on the unorthodox concept of lottery hermeneutics .

Today's New York Lottery—

http://www.log24.com/log/pix11C/111005-NYlottery-500w.jpg

A quote suggested by the UD  post

"Sainte-Beuve's Volupté  (1834) introduced the idea of idler as hero (and seeking pleasurable new sensations as the highest good), so Baudelaire indulged himself in sex and drugs."

Article on Baudelaire by Joshua Glenn in the journal Hermenaut

Some reflections suggested by Hermenaut  and by the NY evening numbers, 674 and 1834—

(Click images to enlarge.)

http://www.log24.com/log/pix11C/111005-Sainte-Beuve-P674-300w.jpg

http://www.log24.com/log/pix11C/111005-Sainte-Beuve-1834-300w.jpg

http://www.log24.com/log/pix11C/111005-Sainte-Beuve-CoolMystery-300w.jpg

Cool Mystery:

http://www.log24.com/log/pix11C/111005-PlancksCafe-CruzEnters.jpg

Detective Cruz enters Planck's Constant Café in "The Big Bang."

As for the midday numbers—

For 412, see 4/12, and for 1030, see 10/30, Devil's Night (2005).

For further background, consult Monday's Realism in Plato's Cave.

Friday, September 9, 2011

A Beginning

Filed under: General — Tags: , — m759 @ 5:29 AM
 

From MIT Commencement Day, 2011—

A symbol related to Apollo, to nine, and to "nothing"

A minimalist favicon—

IMAGE- Generic 3x3 square as favicon

This miniature 3×3 square— http://log24.com/log/pix11A/110518-3x3favicon.ico — may, if one likes,
be viewed as the "nothing" present at the Creation. 
See Feb. 19, 2011, and Jim Holt on physics.

Tuesday, August 30, 2011

Boundary

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

A comment yesterday on the New York Times  philosophy column “The Stone” quoted Karl Barth—

Man is the creature of the boundary between heaven and earth.”

See also Plato’s theory of ideas (or “forms”) and the I Ching

The eight trigrams are images not so much of objects as of states of change. This view is associated with the concept expressed in the teachings of Lao-tse, as also in those of Confucius, that every event in the visible world is the effect of an “image,” that is, of an idea in the unseen world. Accordingly, everything that happens on earth is only a reproduction, as it were, of an event in a world beyond our sense perception; as regards its occurrence in time, it is later than the suprasensible event. The holy men and sages, who are in contact with those higher spheres, have access to these ideas through direct intuition and are therefore able to intervene decisively in events in the world. Thus man is linked with heaven, the suprasensible world of ideas, and with earth, the material world of visible things, to form with these a trinity of the primal powers.

— Richard Wilhelm, Introduction to the I Ching

Wednesday, August 10, 2011

Objectivity

Filed under: General,Geometry — m759 @ 12:25 PM

From math16.com

Quotations on Realism
and the Problem of Universals:

"It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato's (realist) reaction to the sophists (nominalists). What is often called 'postmodernism' is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth."
— Simon Blackburn, Think, Oxford University Press, 1999, page 268

"You will all know that in the Middle Ages there were supposed to be various classes of angels…. these hierarchized celsitudes are but the last traces in a less philosophical age of the ideas which Plato taught his disciples existed in the spiritual world."
— Charles Williams, page 31, Chapter Two, "The Eidola and the Angeli," in The Place of the Lion (1933), reprinted in 1991 by Eerdmans Publishing

For Williams's discussion of Divine Universals (i.e., angels), see Chapter Eight of The Place of the Lion.

"People have always longed for truths about the world — not logical truths, for all their utility; or even probable truths, without which daily life would be impossible; but informative, certain truths, the only 'truths' strictly worthy of the name. Such truths I will call 'diamonds'; they are highly desirable but hard to find….The happy metaphor is Morris Kline's in Mathematics in Western Culture (Oxford, 1953), p. 430."
— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987, pages 114 and 117

"A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the 'Story Theory' of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called 'true.' The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes…. My own viewpoint is the Story Theory…. I concluded long ago that each enterprise contains only stories (which the scientists call 'models of reality'). I had started by hunting diamonds; I did find dazzlingly beautiful jewels, but always of human manufacture."
— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987, pages 256 and 259

Trudeau's confusion seems to stem from the nominalism of W. V. Quine, which in turn stems from Quine's appalling ignorance of the nature of geometry. Quine thinks that the geometry of Euclid dealt with "an emphatically empirical subject matter" — "surfaces, curves, and points in real space." Quine says that Euclidean geometry lost "its old status of mathematics with a subject matter" when Einstein established that space itself, as defined by the paths of light, is non-Euclidean. Having totally misunderstood the nature of the subject, Quine concludes that after Einstein, geometry has become "uninterpreted mathematics," which is "devoid not only of empirical content but of all question of truth and falsity." (From Stimulus to Science, Harvard University Press, 1995, page 55)
— S. H. Cullinane, December 12, 2000

The correct statement of the relation between geometry and the physical universe is as follows:

"The contrast between pure and applied mathematics stands out most clearly, perhaps, in geometry. There is the science of pure geometry, in which there are many geometries: projective geometry, Euclidean geometry, non-Euclidean geometry, and so forth. Each of these geometries is a model, a pattern of ideas, and is to be judged by the interest and beauty of its particular pattern. It is a map or picture, the joint product of many hands, a partial and imperfect copy (yet exact so far as it extends) of a section of mathematical reality. But the point which is important to us now is this, that there is one thing at any rate of which pure geometries are not pictures, and that is the spatio-temporal reality of the physical world. It is obvious, surely, that they cannot be, since earthquakes and eclipses are not mathematical concepts."
— G. H. Hardy, section 23, A Mathematician's Apology, Cambridge University Press, 1940

The story of the diamond mine continues
(see Coordinated Steps and Organizing the Mine Workers)— 

From The Search for Invariants (June 20, 2011):

The conclusion of Maja Lovrenov's 
"The Role of Invariance in Cassirer’s Interpretation of the Theory of Relativity"—

"… physical theories prove to be theories of invariants
with regard to certain groups of transformations and
it is exactly the invariance that secures the objectivity
of a physical theory."

— SYNTHESIS PHILOSOPHICA 42 (2/2006), pp. 233–241

http://www.log24.com/log/pix11B/110810-MajaLovrenovBio.jpg

Related material from Sunday's New York Times  travel section—

"Exhibit A is certainly Ljubljana…."

Friday, July 22, 2011

The Aristophanic View

Filed under: General — m759 @ 9:00 AM

"Some mathematicians are birds, others are frogs.
Birds fly high in the air and survey broad vistas of
mathematics out to the far horizon. They delight in
concepts that unify our thinking and bring together
diverse problems from different parts of the
landscape. Frogs live in the mud below and see
only the flowers that grow nearby. They delight in
the details of particular objects, and they solve
problems one at a time. I happen to be a frog, but
many of my best friends are birds. The main theme
of my talk tonight is this. Mathematics needs both
birds and frogs. Mathematics is rich and beautiful
because birds give it broad visions and frogs give it
intricate details. Mathematics is both great art and
important science, because it combines generality
of concepts with depth of structures. It is stupid to
claim that birds are better than frogs because they
see farther, or that frogs are better than birds
because they see deeper. The world of mathematics
is both broad and deep, and we need birds and
frogs working together to explore it.

This talk is called the Einstein lecture…."

— Freeman Dyson, Notices of the American
Mathematical Society
, February 2009

IMAGE- Joan Didion on a naked woman, a fireman in priest's clothing, and a window

The Didion reading was suggested by the "6212" in yesterday evening's New York Lottery.

Wednesday, July 13, 2011

The Sinatra Code

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

From The Da Vinci Code,
by Dan Brown

Chapter 56

Sophie stared at Teabing a long moment and then turned to Langdon.  “The Holy Grail is a person?”

Langdon nodded.  “A woman, in fact.”  From the blank look on Sophie’s face, Langdon could tell they had already lost her.  He recalled having a similar reaction the first time he heard the statement. It was not until he understood the symbology  behind the Grail that the feminine connection became clear.

Teabing apparently had a similar thought.  “Robert, perhaps this is the moment for the symbologist to clarify?”  He went to a nearby end table, found a piece of paper, and laid it in front of Langdon.

Langdon pulled a pen from his pocket.  “Sophie are you familiar with the modern icons for male and female?”  He drew the common male symbol ♂ and female symbol ♀.

“Of course,” she said.

“These,” he said quietly, are not the original symbols for male and female.  Many people incorrectly assume the male symbol is derived from a shield and spear, while the female represents a mirror reflecting beauty.  In fact, the symbols originated as ancient astronomical symbols for the planet-god Mars and the planet-goddess Venus.  The original symbols are far simpler.”  Langdon drew another icon on the paper.

 

 

 

“This symbol is the original icon for male ,” he told her.  “A rudimentary phallus.”

“Quite to the point,” Sophie said.

“As it were,” Teabing added.

Langdon went on.  “This icon is formally known as the blade , and it represents aggression and manhood.  In fact, this exact phallus symbol is still used today on modern military uniforms to denote rank.”

“Indeed.”  Teabing grinned.  “The more penises you have, the higher your rank.  Boys will be boys.”

Langdon winced.  “Moving on, the female symbol, as you might imagine, is the exact opposite.”  He drew another symbol on the page.  “This is called the chalice .”

 

 

Sophie glanced up, looking surprised.

Langdon could see she had made the connection.  “The chalice,” he said, “resembles a cup or vessel, and more important, it resembles the shape of a woman’s womb.  This symbol communicates femininity, womanhood, and fertility.”  Langdon looked directly at her now.  “Sophie, legend tells us the Holy Grail is a chalice—a cup.  But the Grail’s description as a chalice  is actually an allegory to protect the true nature of the Holy Grail.  That is to say, the legend uses the chalice as a metaphor  for something far more important.”

“A woman,” Sophie said.

“Exactly.”  Langdon smiled.  “The Grail is literally the ancient symbol for womankind, and the Holy  Grail represents the sacred feminine and the goddess, which of course has now been lost, virtually eliminated by the Church.  The power of the female and her ability to produce life was once very sacred, but it posed a threat to the rise of the predominantly male Church, and so the sacred feminine was demonized and called unclean.  It was man , not God, who created the concept of ‘original sin,’ whereby Eve tasted of the apple and caused the downfall of the human race.  Woman, once the sacred giver of life, was now the enemy.”

“I should add,” Teabing chimed, “that this concept of woman as life-bringer was the foundation of ancient religion.  Childbirth was mystical and powerful.  Sadly, Christian philosophy decided to embezzle the female’s creative power by ignoring biological truth and making man  the Creator.  Genesis tells us that Eve was created from Adam’s rib.  Woman became an offshoot of man.  And a sinful one at that.  Genesis was the beginning of the end for the goddess.”

“The Grail,” Langdon said, “is symbolic of the lost goddess.  When Christianity came along, the old pagan religions did not die easily.  Legends of chivalric quests for the lost Grail were in fact stories of forbidden quests to find the lost sacred feminine. Knights who claimed to be “searching for the chalice” were speaking in codes as a way to protect themselves from a Church that had subjugated women, banished the Goddess, burned nonbelievers, and forbidden pagan reverence for the sacred feminine.”

http://www.log24.com/log/pix11B/110713-Symbology101.jpg

Happy birthday to Harrison Ford.

One for my baby…

 

 

One more for the road.

 

Wednesday, May 4, 2011

Unity and Multiplicity

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

Continued from Crimson Walpurgisnacht.

EpigraphsTwo quotations from  
Shakespeare's Birthday last year

Rebecca Goldstein
   on first encountering Plato
 

"I was reading Durant's section on Plato, struggling to understand his theory of the ideal Forms that lay in inviolable perfection out beyond the phantasmagoria. (That was the first, and I think the last, time that I encountered that word.)"

Screenwriter Joan Didion

"We tell ourselves stories in order to live….

We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the 'ideas' with which we have learned to freeze the shifting phantasmagoria which is our actual experience."

From Thomas Mann, "Schopenhauer," 1938, in Essays of Three Decades , translated by H. T. Lowe-Porter, Alfred A. Knopf, 1947, pp. 372-410—

Page 372: THE PLEASURE we take in a metaphysical system, the gratification purveyed by the intellectual organization of the world into a closely reasoned, complete, and balanced structure of thought, is always of a pre-eminently aesthetic kind. It flows from the same source as the joy, the high and ever happy satisfaction we get from art, with its power to shape and order its material, to sort out life's manifold confusions so as to give us a clear and general view.

Truth and beauty must always be referred the one to the other. Each by itself, without the support given by the other, remains a very fluctuating value. Beauty that has not truth on its side and cannot have reference to it, does not live in it and through it, would be an empty chimera— and "What is truth?"

….

Page 376: … the life of Plato was a very great event in the history of the human spirit; and first of all it was a scientific and a moral event. Everyone feels that something profoundly moral attaches to this elevation of the ideal as the only actual, above the ephemeralness and multiplicity of the phenomenal, this devaluation  of the senses to the advantage of the spirit, of the temporal to the advantage of the eternal— quite in the spirit of the Christianity that came after it. For in a way the transitory phenomenon, and the sensual attaching to it, are put thereby into a state of sin: he alone finds truth and salvation who turns his face to the eternal. From this point of view Plato's philosophy exhibits the connection between science and ascetic morality.

But it exhibits another relationship: that with the world of art. According to such a philosophy time itself is merely the partial and piecemeal view which an individual holds of ideas— the latter, being outside time, are thus eternal. "Time"— so runs a beautiful phrase of Plato— "is the moving image of eternity." And so this pre-Christian, already Christian doctrine, with all its ascetic wisdom, possesses on the other hand extraordinary charm of a sensuous and creative kind; for a conception of the world as a colourful and moving phantasmagoria of pictures, which are transparencies for the ideal and the spiritual, eminently savours of the world of art, and through it the artist, as it were, first comes into his own.

From last night's online NY Times  obituaries index—

http://www.log24.com/log/pix11A/110503-NYTobits.jpg

"How much story do you want?" — George Balanchine

Tuesday, January 11, 2011

Soul and Spirit

Filed under: General,Geometry — Tags: , — m759 @ 9:29 PM

This morning's post, "Shining," gave James Hillman's 1976 remarks
on the distinction between soul  and spirit .

The following images may help illustrate these concepts.

http://www.log24.com/log/pix11/110111-BlockDesignsAndGeometry.jpg

The distinction as illustrated by Jeff Bridges —

Soul

http://www.log24.com/log/pix11/110110-CrazyHeart225.jpg

Spirit

http://www.log24.com/log/pix11/110111-BridgesObadiahSm.jpg

The mirror has two faces (at least).

Postscript from a story, "The Zahir," in the Borges manner,
  by Mark Jason Dominus (programmer of the quilt designs above)—

"I  left that madhouse gratefully."

Dominus is also the author of…

http://www.log24.com/log/pix11/110111-HigherOrderPerl.gif

Click for details.

Monday, October 4, 2010

Stone Junction

Filed under: General — m759 @ 6:29 AM

Continued from May 18, 2010.

Previous logo for the New York Times  feature "The Stone"—

http://www.log24.com/log/pix10B/101004-IntroducingTheStone100518.jpg

Today's new logo, appearing retroactively

http://www.log24.com/log/pix10B/101004-NYT-newstonelogo.png

Comparison—

http://www.log24.com/log/pix10A/100518-TheStoneNYT.jpg   http://www.log24.com/log/pix10B/101004-NYT-thestone75.gif

From the October 3 "The Stone," Hegel on Wall Street

The “Phenomenology” is a philosophical portrait gallery that presents depictions, one after another, of different, fundamental ways in which individuals and societies have understood themselves.  Each self-understanding has two parts: an account of how a particular kind of self understands itself and, then, an account of the world that the self considers its natural counterpart.  Hegel narrates how each formation of self and world collapses because of a mismatch between self-conception and how that self conceives of the larger world.  Hegel thinks we can see how history has been driven by misshapen forms of life in which the self-understanding of agents and the worldly practices they participate in fail to correspond.  With great drama, he claims that his narrative is a “highway of despair.”

J.M. Bernstein of the New School for Social Research

A two-part self-understanding that is not  from Hegel—

1. An account of how a particular kind of self understands itself:

            … world’s wildfire, leave but ash:
                In a flash, at a trumpet crash,
I am all at once what Christ is, ' since he was what I am, and
This Jack, joke, poor potsherd, ' patch, matchwood, immortal diamond,
                Is immortal diamond.

2. An account of the world that the self considers its natural counterpart:

CLOUD-PUFFBALL, torn tufts, tossed pillows ' flaunt forth, then chevy on an air-
built thoroughfare: heaven-roysterers, in gay-gangs ' they throng; they glitter in marches.
Down roughcast, down dazzling whitewash, ' wherever an elm arches,
Shivelights and shadowtackle in long ' lashes lace, lance, and pair.
Delightfully the bright wind boisterous ' ropes, wrestles, beats earth bare
Of yestertempest’s creases; in pool and rut peel parches
Squandering ooze to squeezed ' dough, crust, dust; stanches, starches
Squadroned masks and manmarks ' treadmire toil there
Footfretted in it. Million-fuelèd, ' nature’s bonfire burns on.

Thursday, July 15, 2010

Angels in the Architecture

Filed under: General — Tags: — m759 @ 3:12 AM

"Things fall apart;
the centre cannot hold
"

http://www.log24.com/log/pix10A/100715-AugustineCenter.jpg

The above building is home to the Derridean leftists
of the Villanova philosophy department.

center loosens,
forms again elsewhere

"The most obvious problem with Derrida's argument in The Gift of Death is his misconception of Christianity. In his description of Christian mystery, the crucified figure of Jesus is strikingly absent, having been replaced by a mysterious 'infinite other.' In this respect, Derrida's understanding of Christianity is essentially gnostic; the humanity of Jesus is displaced by gnostic mystery. Although Derrida claims to describe historical Christianity, in fact, his argument is based on a serious distortion of Christian practice and theology. Although the title might seem an obvious reference to Christ's atoning death, Derrida's book can only be characterized as an overt and unacknowledged displacement of the Crucifixion and its central place in Christian worship."

 

— Peter Goldman, now at Westminster College in Salt Lake City

See also Highway 1 Revisited (August 1, 2006).

Sunday, June 20, 2010

Sunday School

Filed under: General,Geometry — m759 @ 7:59 AM
 

Limited— Good   
Évariste Galois  

 http://www.log24.com/log/pix10A/100620-Galois.jpg    

Unlimited— Bad
H.S.M. Coxeter

http://www.log24.com/log/pix10A/100620-CoxeterSm.jpg

Jamie James in The Music of the Spheres

"The Pythagorean philosophy, like Zoroastrianism, Taoism, and every early system of higher thought, is based upon the concept of dualism. Pythagoras constructed a table of opposites from which he was able to derive every concept needed for a philosophy of the phenomenal world. As reconstructed by Aristotle in his Metaphysics, the table contains ten dualities (ten being a particularly important number in the Pythagorean system, as we shall see):

Limited
Odd
One
Right
Male
Rest
Straight
Light
Good
Square
Unlimited
Even
Many
Left
Female
Motion
Curved
Dark
Bad
Oblong

Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited (man, finite time, and so forth) and the unlimited (the cosmos, eternity, etc.) is not only the aim of Pythagoras's system but the central aim of all Western philosophy."

Monday, April 26, 2010

Types of Ambiguity

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

From Ursula K. Le Guin’s novel
The Dispossessed: An Ambiguous Utopia
(1974)—

Chapter One

“There was a wall. It did not look important. It was built of uncut rocks roughly mortared. An adult could look right over it, and even a child could climb it. Where it crossed the roadway, instead of having a gate it degenerated into mere geometry, a line, an idea of boundary. But the idea was real. It was important. For seven generations there had been nothing in the world more important than that wall.

Like all walls it was ambiguous, two-faced. What was inside it and what was outside it depended upon which side of it you were on.”

Note—

“We note that the phrase ‘instead of having a gate it degenerated into mere geometry’ is mere fatuousness. If there is an idea here, degenerate, mere, and geometry  in concert do not fix it. They bat at it like a kitten at a piece of loose thread.”

— Samuel R. Delany, The Jewel-Hinged Jaw: Notes on the Language of Science Fiction  (Dragon Press, 1977), page 110 of revised edition, Wesleyan University Press, 2009

(For the phrase mere geometry  elsewhere, see a note of April 22. The apparently flat figures in that note’s illustration “Galois Affine Geometry” may be regarded as degenerate  views of cubes.)

Later in the Le Guin novel—

“… The Terrans had been intellectual imperialists, jealous wall builders. Even Ainsetain, the originator of the theory, had felt compelled to give warning that his physics embraced no mode but the physical and should not be taken as implying the metaphysical, the philosophical, or the ethical. Which, of course, was superficially true; and yet he had used number, the bridge between the rational and the perceived, between psyche and matter, ‘Number the Indisputable,’ as the ancient founders of the Noble Science had called it. To employ mathematics in this sense was to employ the mode that preceded and led to all other modes. Ainsetain had known that; with endearing caution he had admitted that he believed his physics did, indeed, describe reality.

Strangeness and familiarity: in every movement of the Terran’s thought Shevek caught this combination, was constantly intrigued. And sympathetic: for Ainsetain, too, had been after a unifying field theory. Having explained the force of gravity as a function of the geometry of spacetime, he had sought to extend the synthesis to include electromagnetic forces. He had not succeeded. Even during his lifetime, and for many decades after his death, the physicists of his own world had turned away from his effort and its failure, pursuing the magnificent incoherences of quantum theory with its high technological yields, at last concentrating on the technological mode so exclusively as to arrive at a dead end, a catastrophic failure of imagination. Yet their original intuition had been sound: at the point where they had been, progress had lain in the indeterminacy which old Ainsetain had refused to accept. And his refusal had been equally correct– in the long run. Only he had lacked the tools to prove it– the Saeba variables and the theories of infinite velocity and complex cause. His unified field existed, in Cetian physics, but it existed on terms which he might not have been willing to accept; for the velocity of light as a limiting factor had been essential to his great theories. Both his Theories of Relativity were as beautiful, as valid, and as useful as ever after these centuries, and yet both depended upon a hypothesis that could not be proved true and that could be and had been proved, in certain circumstances, false.

But was not a theory of which all the elements were provably true a simple tautology? In the region of the unprovable, or even the disprovable, lay the only chance for breaking out of the circle and going ahead.

In which case, did the unprovability of the hypothesis of real coexistence– the problem which Shevek had been pounding his head against desperately for these last three days. and indeed these last ten years– really matter?

He had been groping and grabbing after certainty, as if it were something he could possess. He had been demanding a security, a guarantee, which is not granted, and which, if granted, would become a prison. By simply assuming the validity of real coexistence he was left free to use the lovely geometries of relativity; and then it would be possible to go ahead. The next step was perfectly clear. The coexistence of succession could be handled by a Saeban transformation series; thus approached, successivity and presence offered no antithesis at all. The fundamental unity of the Sequency and Simultaneity points of view became plain; the concept of interval served to connect the static and the dynamic aspect of the universe. How could he have stared at reality for ten years and not seen it? There would be no trouble at all in going on. Indeed he had already gone on. He was there. He saw all that was to come in this first, seemingly casual glimpse of the method, given him by his understanding of a failure in the distant past. The wall was down. The vision was both clear and whole. What he saw was simple, simpler than anything else. It was simplicity: and contained in it all complexity, all promise. It was revelation. It was the way clear, the way home, the light.”

Related material—

Time Fold, Halloween 2005, and May and Zan.

See also The Devil and Wallace Stevens

“In a letter to Harriet Monroe, written December 23, 1926, Stevens refers to the Sapphic fragment that invokes the genius of evening: ‘Evening star that bringest back all that lightsome Dawn hath scattered afar, thou bringest the sheep, thou bringest the goat, thou bringest the child home to the mother.’ Christmas, writes Stevens, ‘is like Sappho’s evening: it brings us all home to the fold’ (Letters of Wallace Stevens, 248).”

— “The Archangel of Evening,” Chapter 5 of Wallace Stevens: The Intensest Rendezvous, by Barbara M. Fisher, The University Press of Virginia, 1990

Sunday, April 18, 2010

A Generation Lost in Space

Filed under: General — m759 @ 2:29 AM

or, Deja Vu All Over Again

Top two obituaries in this morning's NY Times list–

David Simons, Who Flew High
on Eve of Space Age, Dies at 87

Dr. Simons, a physician turned Air Force officer, had sent animals aloft for several years before his record-breaking flight.

James Aubrey, who Portrayed the Hero
in ‘Lord of the Flies’, Is Dead at 62

Mr. Aubrey portrayed Ralph in the film version of the William Golding novel and had a busy career on stage and television in England.

Simons reportedly died on April 5,
Aubrey on April 6.

This journal on those dates–

April 5 —

Monday, April 5, 2010

Space Cowboys

Filed under: Uncategorized — m759 @ 12:00 PM Edit This

http://www.log24.com/log/pix10/100405-Eastwood.jpg

Google News, 11:32 AM ET today–

http://www.log24.com/log/pix10/100405-SpaceCowboysSm.jpg

Related material:

Yesterday's Easter message,
film notes from March 13,
and Dagger Definitions.

April 6 —

Tuesday, April 6, 2010

Clue

Filed under: Uncategorized — m759 @ 12:00 PM Edit This

Excerpt from 'Cosmic Trigger'
 by Robert Anton Wilson

See also Leary on Cuernavaca,
John O'Hara's fleeting reference
to Cuernavaca in Hope of Heaven,
and Cuernavaca in this journal.

Team Daedalus

Filed under: Uncategorized — m759 @ 9:00 AM Edit This

"Concept (scholastics' verbum mentis)– theological analogy of Son's procession as Verbum Patris, 111-12" –Index to Joyce and Aquinas, by William T. Noon, Society of Jesus, Yale University Press 1957, second printing 1963, page 162

"Back in 1958… [four] Air Force pilots were Team Daedalus, the best of the best." –Summary of the film "Space Cowboys"

"Man is nothing if not labyrinthine." –The Vicar in Trevanian's The Loo Sanction\

 

Commentary by T.S. Eliot

"At the moment which is not of action or inaction
You can receive this: 'on whatever sphere of being
The mind of a man may be intent
At the time of death'—that is the one action
(And the time of death is every moment)
Which shall fructify in the lives of others:
And do not think of the fruit of action.
Fare forward."

 

Monday, January 4, 2010

Google’s Apple Tree

Filed under: General — m759 @ 11:30 AM

http://www.log24.com/log/pix10/100104-Apple.jpg

Google has illuminated its search page today with a falling apple in honor of what it is pleased to call the birthday of Newton. (When Newton was born, the calendar showed it was Christmas Day, 1642; Google prefers to associate Sir Isaac with a later version of the calendar.)

Some related observations–

Adapted from a Log24 entry
of Monday, March 24, 2008–
 

 

"Hanging from the highest limb
of the apple tree are
     the three God's Eyes…"

    — Ken Kesey

"But what's beautiful can't be bad. You're not bad, North Wind?"

"No; I'm not bad. But sometimes beautiful things grow bad by doing bad, and it takes some time for their badness to spoil their beauty. So little boys may be mistaken if they go after things because they are beautiful."

"Well, I will go with you because you are beautiful and good, too."

"Ah, but there's another thing, Diamond:– What if I should look ugly without being bad– look ugly myself because I am making ugly things beautiful?– What then?"

"I don't quite understand you, North Wind. You tell me what then."

"Well, I will tell you. If you see me with my face all black, don't be frightened. If you see me flapping wings like a bat's, as big as the whole sky, don't be frightened. If you hear me raging ten times worse than Mrs. Bill, the blacksmith's wife– even if you see me looking in at people's windows like Mrs. Eve Dropper, the gardener's wife– you must believe that I am doing my work. Nay, Diamond, if I change into a serpent or a tiger, you must not let go your hold of me, for my hand will never change in yours if you keep a good hold. If you keep a hold, you will know who I am all the time, even when you look at me and can't see me the least like the North Wind. I may look something very awful. Do you understand?"

"Quite well," said little Diamond.

"Come along, then," said North Wind, and disappeared behind the mountain of hay.

Diamond crept out of bed and followed her.

    — George MacDonald,
      At the Back of the North Wind

   

From Log24 on Sunday, March 23, 2008–

 
A sequel to
The Crimson Passion

Easter Egg

Jill St. John with diamond

Click on image
 for further details.


Duality:


A pair of book covers in honor
  of the dies natalis of T. S. Eliot–

http://www.log24.com/log10/saved/100103-TheAristocrat_files/100104-Duality.jpg

From Virginia Woolf,  "Modern Fiction" (Ch. 13 in The Common Reader, First Series)

Woolf on what she calls "materialist" fiction–

Life escapes; and perhaps without life nothing else is worth while. It is a confession of vagueness to have to make use of such a figure as this, but we scarcely better the matter by speaking, as critics are prone to do, of reality. Admitting the vagueness which afflicts all criticism of novels, let us hazard the opinion that for us at this moment the form of fiction most in vogue more often misses than secures the thing we seek. Whether we call it life or spirit, truth or reality, this, the essential thing, has moved off, or on, and refuses to be contained any longer in such ill-fitting vestments as we provide. Nevertheless, we go on perseveringly, conscientiously, constructing our two and thirty chapters after a design which more and more ceases to resemble the vision in our minds. So much of the enormous labour of proving the solidity, the likeness to life, of the story is not merely labour thrown away but labour misplaced to the extent of obscuring and blotting out the light of the conception. The writer seems constrained, not by his own free will but by some powerful and unscrupulous tyrant who has him in thrall, to provide a plot, to provide comedy, tragedy, love interest, and an air of probability embalming the whole so impeccable that if all his figures were to come to life they would find themselves dressed down to the last button of their coats in the fashion of the hour. The tyrant is obeyed; the novel is done to a turn. But sometimes, more and more often as time goes by, we suspect a momentary doubt, a spasm of rebellion, as the pages fill themselves in the customary way. Is life like this? Must novels be like this?

Look within and life, it seems, is very far from being “like this”. Examine for a moment an ordinary mind on an ordinary day. The mind receives a myriad impressions—trivial, fantastic, evanescent, or engraved with the sharpness of steel. From all sides they come, an incessant shower of innumerable atoms; and as they fall, as they shape themselves into the life of Monday or Tuesday, the accent falls differently from of old; the moment of importance came not here but there; so that, if a writer were a free man and not a slave, if he could write what he chose, not what he must, if he could base his work upon his own feeling and not upon convention, there would be no plot, no comedy, no tragedy, no love interest or catastrophe in the accepted style, and perhaps not a single button sewn on as the Bond Street tailors would have it. Life is not a series of gig lamps symmetrically arranged; life is a luminous halo, a semi-transparent envelope surrounding us from the beginning of consciousness to the end. Is it not the task of the novelist to convey this varying, this unknown and uncircumscribed spirit, whatever aberration or complexity it may display, with as little mixture of the alien and external as possible? We are not pleading merely for courage and sincerity; we are suggesting that the proper stuff of fiction is a little other than custom would have us believe it.

It is, at any rate, in some such fashion as this that we seek to define the quality which distinguishes the work of several young writers, among whom Mr. James Joyce is the most notable….

Wednesday, August 5, 2009

Wednesday August 5, 2009

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

 

Word and Image

NYT obituary summaries for Charles Gwathmey and Edward Hall, morning of Aug. 5, 2009

From Hall's obituary
:

"Edward T. Hall, a cultural anthropologist
who pioneered the study of nonverbal
 communication and interactions between
members of different ethnic groups,
 died July 20 at his home in
 Santa Fe, N.M. He was 95."

NY Times piece quoted here on
 the date of Hall's death:
 

"July 20, 1969, was the moment NASA needed, more than anything else in this world, the Word. But that was something NASA's engineers had no specifications for. At this moment, that remains the only solution to recovering NASA's true destiny, which is, of course, to build that bridge to the stars."

— Tom Wolfe, author of The Right Stuff, an account of the Mercury Seven astronauts.

Commentary
The Word according to St. John:

Jill St. John, star of 'Diamonds are Forever'

 

From Hall's obituary:

"Mr. Hall first became interested in
space and time as forms of cultural
 expression while working on
Navajo and Hopi reservations
 in the 1930s."

Log24, July 29
:

Changing Woman:

"Kaleidoscope turning…

Juliette Binoche in 'Blue'  The 24 2x2 Cullinane Kaleidoscope animated images

Shifting pattern within   
unalterable structure…"
— Roger Zelazny,  
Eye of Cat  

"We are the key."
Eye of Cat  

Update of about 4:45 PM 8/5:

Paul Newall, "Kieślowski's Three Colours Trilogy"

"Julie recognises the music of the busker outside playing a recorder as that of her husband's. When she asks him where he heard it, he replies that he makes up all sorts of things. This is an instance of a theory of Kieślowski's that 'different people, in different places, are thinking the same thing but for different reasons.' With regard to music in particular, he held what might be characterised as a Platonic view according to which notes pre-exist and are picked out and assembled by people. That these can accord with one another is a sign of what connects people, or so he believed."

The above photo of Juliette Binoche in Blue accompanying the quotations from Zelazny illustrates Kieślowski's concept, with graphic designs instead of musical notes. Some of the same designs are discussed in Abstraction and the Holocaust (Mark Godfrey, Yale University Press, 2007). (See the Log24 entries of June 11, 2009.)

Related material:

"Jeffrey Overstreet, in his book Through a Screen Darkly, comments extensively on Blue. He says these stones 'are like strands of suspended crystalline tears, pieces of sharp-edged grief that Julie has not been able to express.'….

Throughout the film the color blue crops up, highlighting the mood of Julie's grief. A blue light occurs frequently, when Julie is caught by some fleeting memory. Accompanied by strains of an orchestral composition, possibly her husband's, these blue screen shots hold for several seconds while Julie is clearly processing something. The meaning of this blue light is unexplained. For Overstreet, it is the spirit of reunification of broken things."

Martin Baggs at Mosaic Movie Connect Group on Sunday, March 15, 2009. (Cf. Log24 on that date.)

For such a spirit, compare Binoche's blue mobile in Blue with Binoche's gathered shards in Bee Season.

Tuesday, February 24, 2009

Tuesday February 24, 2009

Filed under: General,Geometry — Tags: — m759 @ 1:00 PM
 
Hollywood Nihilism
Meets
Pantheistic Solipsism

Tina Fey to Steve Martin
at the Oscars:
"Oh, Steve, no one wants
 to hear about our religion
… that we made up."

Tina Fey and Steve Martin at the 2009 Oscars

From Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 117:

… in 'The Pediment of Appearance,' a slight narrative poem in Transport to Summer

 A group of young men enter some woods 'Hunting for the great ornament, The pediment of appearance.' Though moving through the natural world, the young men seek the artificial, or pure form, believing that in discovering this pediment, this distillation of the real, they will also discover the 'savage transparence,' the rude source of human life. In Stevens's world, such a search is futile, since it is only through observing nature that one reaches beyond it to pure form. As if to demonstrate the degree to which the young men's search is misaligned, Stevens says of them that 'they go crying/The world is myself, life is myself,' believing that what surrounds them is immaterial. Such a proclamation is a cardinal violation of Stevens's principles of the imagination.


Superficially the young men's philosophy seems to resemble what Wikipedia calls "pantheistic solipsism"– noting, however, that "This article has multiple issues."

As, indeed, does pantheistic solipsism– a philosophy (properly called "eschatological pantheistic multiple-ego solipsism") devised, with tongue in cheek, by science-fiction writer Robert A. Heinlein.

Despite their preoccupation with solipsism, Heinlein and Stevens point, each in his own poetic way, to a highly non-solipsistic topic from pure mathematics that is, unlike the religion of Martin and Fey, not made up– namely, the properties of space.

Heinlein:

"Sharpie, we have condensed six dimensions into four, then we either work by analogy into six, or we have to use math that apparently nobody but Jake and my cousin Ed understands. Unless you can think of some way to project six dimensions into three– you seem to be smart at such projections."
    I closed my eyes and thought hard. "Zebbie, I don't think it can be done. Maybe Escher could have done it."

Stevens:

A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:

For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought:

The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...

The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,

Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.

The rock is the habitation of the whole,
Its strength and measure, that which is near,
     point A
In a perspective that begins again

At B: the origin of the mango's rind.

                    (Collected Poems, 528)

Stevens's rock is associated with empty space, a concept that suggests "nothingness" to one literary critic:

B. J. Leggett, "Stevens's Late Poetry" in The Cambridge Companion to Wallace Stevens— On the poem "The Rock":

"… the barren rock of the title is Stevens's symbol for the nothingness that underlies all existence, 'That in which space itself is contained'….  Its subject is its speaker's sense of nothingness and his need to be cured of it."

This interpretation might appeal to Joan Didion, who, as author of the classic novel Play It As It Lays, is perhaps the world's leading expert on Hollywood nihilism.

More positively…

Space is, of course, also a topic
in pure mathematics…
For instance, the 6-dimensional
affine space
(or the corresponding
5-dimensional projective space)

The 4x4x4 cube

over the two-element Galois field
can be viewed as an illustration of
Stevens's metaphor in "The Rock."

Heinlein should perhaps have had in mind the Klein correspondence when he discussed "some way to project six dimensions into three." While such a projection is of course trivial for anyone who has taken an undergraduate course in linear algebra, the following remarks by Philippe Cara present a much more meaningful mapping, using the Klein correspondence, of structures in six (affine) dimensions to structures in three.

Cara:

Philippe Cara on the Klein correspondence
Here the 6-dimensional affine
space contains the 63 points
of PG(5, 2), plus the origin, and
the 3-dimensional affine
space contains as its 8 points
Conwell's eight "heptads," as in
Generating the Octad Generator.

Wednesday, January 14, 2009

Wednesday January 14, 2009

Filed under: General,Geometry — m759 @ 2:45 AM
Eight is a Gate

'The Eight,' by Katherine Neville

Customer reviews of Neville's 'The Eight'

From the most highly
rated negative review:

“I never did figure out
what ‘The Eight’ was.”

Various approaches
to this concept
(click images for details):

The Fritz Leiber 'Spider' symbol in a square

A Singer 7-cycle in the Galois field with eight elements

The Eightfold (2x2x2) Cube

The Jewel in Venn's Lotus (photo by Gerry Gantt)

Tom O'Horgan in his loft. O'Horgan died Sunday, Jan. 11, 2009.

Bach, Canon 14, BWV 1087

Sunday, August 3, 2008

Sunday August 3, 2008

Filed under: General,Geometry — Tags: , — m759 @ 3:00 PM
Kindergarten
Geometry

Preview of a Tom Stoppard play presented at Town Hall in Manhattan on March 14, 2008 (Pi Day and Einstein's birthday):

The play's title, "Every Good Boy Deserves Favour," is a mnemonic for the notes of the treble clef EGBDF.

The place, Town Hall, West 43rd Street. The time, 8 p.m., Friday, March 14. One single performance only, to the tinkle– or the clang?– of a triangle. Echoing perhaps the clang-clack of Warsaw Pact tanks muscling into Prague in August 1968.

The “u” in favour is the British way, the Stoppard way, "EGBDF" being "a Play for Actors and Orchestra" by Tom Stoppard (words) and André Previn (music).

And what a play!– as luminescent as always where Stoppard is concerned. The music component of the one-nighter at Town Hall– a showcase for the Boston University College of Fine Arts– is by a 47-piece live orchestra, the significant instrument being, well, a triangle.

When, in 1974, André Previn, then principal conductor of the London Symphony, invited Stoppard "to write something which had the need of a live full-time orchestra onstage," the 36-year-old playwright jumped at the chance.

One hitch: Stoppard at the time knew "very little about 'serious' music… My qualifications for writing about an orchestra," he says in his introduction to the 1978 Grove Press edition of "EGBDF," "amounted to a spell as a triangle player in a kindergarten percussion band."

Jerry Tallmer in The Villager, March 12-18, 2008

Review of the same play as presented at Chautauqua Institution on July 24, 2008:

"Stoppard's modus operandi– to teasingly introduce numerous clever tidbits designed to challenge the audience."

Jane Vranish, Pittsburgh Post-Gazette, Saturday, August 2, 2008

"The leader of the band is tired
And his eyes are growing old
But his blood runs through
My instrument
And his song is in my soul."

— Dan Fogelberg

"He's watching us all the time."

Lucia Joyce

 

Finnegans Wake,
Book II, Episode 2, pp. 296-297:

I'll make you to see figuratleavely the whome of your eternal geomater. And if you flung her headdress on her from under her highlows you'd wheeze whyse Salmonson set his seel on a hexengown.1 Hissss!, Arrah, go on! Fin for fun!

1 The chape of Doña Speranza of the Nacion.

 

Log 24, Sept. 3, 2003:
 
Reciprocity

From my entry of Sept. 1, 2003:

"…the principle of taking and giving, of learning and teaching, of listening and storytelling, in a word: of reciprocity….

… E. M. Forster famously advised his readers, 'Only connect.' 'Reciprocity' would be Michael Kruger's succinct philosophy, with all that the word implies."

— William Boyd, review of Himmelfarb, a novel by Michael Kruger, in The New York Times Book Review, October 30, 1994

Last year's entry on this date: 

 

Today's birthday:
James Joseph Sylvester

"Mathematics is the music of reason."
— J. J. Sylvester

Sylvester, a nineteenth-century mathematician, coined the phrase "synthematic totals" to describe some structures based on 6-element sets that R. T. Curtis has called "rather unwieldy objects." See Curtis's abstract, Symmetric Generation of Finite Groups, John Baez's essay, Some Thoughts on the Number 6, and my website, Diamond Theory.

 

The picture above is of the complete graph K6  Six points with an edge connecting every pair of points… Fifteen edges in all.

Diamond theory describes how the 15 two-element subsets of a six-element set (represented by edges in the picture above) may be arranged as 15 of the 16 parts of a 4×4 array, and how such an array relates to group-theoretic concepts, including Sylvester's synthematic totals as they relate to constructions of the Mathieu group M24.

If diamond theory illustrates any general philosophical principle, it is probably the interplay of opposites….  "Reciprocity" in the sense of Lao Tzu.  See

Reciprocity and Reversal in Lao Tzu.

For a sense of "reciprocity" more closely related to Michael Kruger's alleged philosophy, see the Confucian concept of Shu (Analects 15:23 or 24) described in

Shu: Reciprocity.

Kruger's novel is in part about a Jew: the quintessential Jewish symbol, the star of David, embedded in the K6 graph above, expresses the reciprocity of male and female, as my May 2003 archives illustrate.  The star of David also appears as part of a graphic design for cubes that illustrate the concepts of diamond theory:

Click on the design for details.

Those who prefer a Jewish approach to physics can find the star of David, in the form of K6, applied to the sixteen 4×4 Dirac matrices, in

A Graphical Representation
of the Dirac Algebra
.

The star of David also appears, if only as a heuristic arrangement, in a note that shows generating partitions of the affine group on 64 points arranged in two opposing triplets.

Having thus, as the New York Times advises, paid tribute to a Jewish symbol, we may note, in closing, a much more sophisticated and subtle concept of reciprocity due to Euler, Legendre, and Gauss.  See

The Jewel of Arithmetic and


FinnegansWiki:

Salmonson set his seel:

"Finn MacCool ate the Salmon of Knowledge."

Wikipedia:

"George Salmon spent his boyhood in Cork City, Ireland. His father was a linen merchant. He graduated from Trinity College Dublin at the age of 19 with exceptionally high honours in mathematics. In 1841 at age 21 he was appointed to a position in the mathematics department at Trinity College Dublin. In 1845 he was appointed concurrently to a position in the theology department at Trinity College Dublin, having been confirmed in that year as an Anglican priest."

Related material:

Kindergarten Theology,

Kindergarten Relativity,

Arrangements for
56 Triangles
.

For more on the
arrangement of
triangles discussed
in Finnegans Wake,
see Log24 on Pi Day,
March 14, 2008.

Happy birthday,
Martin Sheen.
 

Sunday, April 13, 2008

Sunday April 13, 2008

Filed under: General,Geometry — m759 @ 7:59 AM
The Echo
in Plato’s Cave

“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy.”

— Simon Blackburn, Think (Oxford, 1999)

Michael Harris, mathematician at the University of Paris:

“… three ‘parts’ of tragedy identified by Aristotle that transpose to fiction of all types– plot (mythos), character (ethos), and ‘thought’ (dianoia)….”

— paper (pdf) to appear in Mathematics and Narrative, A. Doxiadis and B. Mazur, eds.

Mythos —

A visitor from France this morning viewed the entry of Jan. 23, 2006: “In Defense of Hilbert (On His Birthday).” That entry concerns a remark of Michael Harris.

A check of Harris’s website reveals a new article:

“Do Androids Prove Theorems in Their Sleep?” (slighly longer version of article to appear in Mathematics and Narrative, A. Doxiadis and B. Mazur, eds.) (pdf).

From that article:

“The word ‘key’ functions here to structure the reading of the article, to draw the reader’s attention initially to the element of the proof the author considers most important. Compare E.M. Forster in Aspects of the Novel:

[plot is] something which is measured not be minutes or hours, but by intensity, so that when we look at our past it does not stretch back evenly but piles up into a few notable pinnacles.”

Ethos —

“Forster took pains to widen and deepen the enigmatic character of his novel, to make it a puzzle insoluble within its own terms, or without. Early drafts of A Passage to India reveal a number of false starts. Forster repeatedly revised drafts of chapters thirteen through sixteen, which comprise the crux of the novel, the visit to the Marabar Caves. When he began writing the novel, his intention was to make the cave scene central and significant, but he did not yet know how:

When I began a A Passage to India, I knew something important happened in the Malabar (sic) Caves, and that it would have a central place in the novel– but I didn’t know what it would be… The Malabar Caves represented an area in which concentration can take place. They were to engender an event like an egg.”

E. M. Forster: A Passage to India, by Betty Jay

Dianoia —

Flagrant Triviality
or Resplendent Trinity?

“Despite the flagrant triviality of the proof… this result is the key point in the paper.”

— Michael Harris, op. cit., quoting a mathematical paper

Online Etymology Dictionary
:

flagrant
c.1500, “resplendent,” from L. flagrantem (nom. flagrans) “burning,” prp. of flagrare “to burn,” from L. root *flag-, corresponding to PIE *bhleg (cf. Gk. phlegein “to burn, scorch,” O.E. blæc “black”). Sense of “glaringly offensive” first recorded 1706, probably from common legalese phrase in flagrante delicto “red-handed,” lit. “with the crime still blazing.”

A related use of “resplendent”– applied to a Trinity, not a triviality– appears in the Liturgy of Malabar:

http://www.log24.com/log/pix08/080413-LiturgyOfMalabar.jpg

The Liturgies of SS. Mark, James, Clement, Chrysostom, and Basil, and the Church of Malabar, by the Rev. J.M. Neale and the Rev. R.F. Littledale, reprinted by Gorgias Press, 2002

On Universals and
A Passage to India:

“”The universe, then, is less intimation than cipher: a mask rather than a revelation in the romantic sense. Does love meet with love? Do we receive but what we give? The answer is surely a paradox, the paradox that there are Platonic universals beyond, but that the glass is too dark to see them. Is there a light beyond the glass, or is it a mirror only to the self? The Platonic cave is even darker than Plato made it, for it introduces the echo, and so leaves us back in the world of men, which does not carry total meaning, is just a story of events.”

— Betty Jay,  op. cit.

http://www.log24.com/log/pix08/080413-Marabar.jpg

Judy Davis in the Marabar Caves

In mathematics
(as opposed to narrative),
somewhere between
 a flagrant triviality and
a resplendent Trinity we
have what might be called
“a resplendent triviality.”

For further details, see
A Four-Color Theorem.”

Sunday, October 14, 2007

Sunday October 14, 2007

Filed under: General — m759 @ 11:00 AM
The Dipolar God

Steven H. Cullinane, 'The Line'

“Logos and logic, crystal hypothesis,
Incipit and a form to speak the word
And every latent double in the word….”

— Wallace Stevens,
   “Notes Toward a Supreme Fiction

Yesterday’s meditation (“Simon’s Shema“) on the interpenetration of opposites continues:

Part I: The Jewel in the Lotus

“The fundamental conception of Tantric Buddhist metaphysics, namely, yuganaddha, signifies the coincidence of opposites.  It is symbolized by the conjugal embrace (maithuna or kama-kala) of a god and goddess or a Buddha and his consort (signifying karuna and sunyata or upaya and prajna, respectively), also commonly depicted in Tantric Buddhist iconography as the union of vajra (diamond sceptre) and padme (lotus flower).  Thus, yuganaddha essentially means the interpenetration of opposites or dipolar fusion, and is a fundamental restatement of Hua-yen theoretic structures.”

— p. 148 in “Part II: A Whiteheadian Process Critique of Hua-yen Buddhism,” in Process Metaphysics and Hua-Yen Buddhism: A Critical Study of Cumulative Penetration vs. Interpenetration (SUNY Series in Systematic Philosophy), by Steve Odin, State University of New York Press, 1982

Part II: The Dipolar God

And on p. 163 of Odin, op. cit., in “Part III: Theology of the Deep Unconscious: A Reconstruction of Process Theology,” in the section titled “Whitehead’s Dipolar God as the Collective Unconscious”–

“An effort is made to transpose Whitehead’s theory of the dipolar God into the terms of the collective unconscious, so that now the dipolar God is to be comprehended not as a transcendent deity, but the deepest dimension and highest potentiality of one’s own psyche.”

Part III: Piled High and Deep

Odin obtained his Ph.D. degree from the Department of Philosophy at the State University of New York (SUNY) at Stony Brook in 1980. (See curriculum vitae (pdf).)

For an academic review of Odin’s book, see David Applebaum, Philosophy East and West, Vol. 34 (1984), pp. 107-108.

It is perhaps worth noting, in light of the final footnote of Mark D. Brimblecombe’s Ph.D. thesis “Dipolarity and Godquoted yesterday, that “tantra” is said to mean “loom.” For some less-academic background on the Tantric iconography Odin describes, see the webpage “Love and Passion in Tantric Buddhist Art.” For a fiction combining love and passion with the word “loom” in a religious context, see Clive Barker’s Weaveworld.  This fiction– which is, if not “supreme” in the Wallace Stevens sense, at least entertaining– may correspond to some aspects of the deep Jungian psychological reality discussed by Odin.

Happy Birthday,
Hannah Arendt

(Oct. 14, 1906-
Dec. 4, 1975)

OPPOSITES:

Hannah (Arendt) and Martin (Heidegger) as portrayed in a play of that name

Actors portraying
Arendt and Heidegger

Click on image for details.

Tuesday, July 3, 2007

Tuesday July 3, 2007

Filed under: General — m759 @ 9:29 PM
The Ignorance
of Stanley Fish

(continued from
June 18, 2002)

The “ignorance” referred to
is Fish’s ignorance of the
philosophical background
of the words
“particular” and “universal.”

Postmodern Warfare:
The Ignorance of Our
Warrior Intellectuals,”
by Stanley Fish,
Harper’s Magazine,
July 2002, contains
the following passages:

“The deepest strain in a religion is the particular and particularistic doctrine it asserts at its heart, in the company of such pronouncements as ‘Thou shalt have no other Gods before me.’ Take the deepest strain of religion away… and what remains are the surface pieties– abstractions without substantive bite– to which everyone will assent because they are empty, insipid, and safe. It is this same preference for the vacuously general over the disturbingly particular that informs the attacks on college and university professors who spoke out in ways that led them to be branded as outcasts by those who were patrolling and monitoring the narrow boundaries of acceptable speech. Here one must be careful, for there are fools and knaves on all sides.”

“Although it may not at first be obvious, the substitution for real religions of a religion drained of particulars is of a piece with the desire to exorcise postmodernism.”

“What must be protected, then, is the general, the possibility of making pronouncements from a perspective at once detached from and superior to the sectarian perspectives of particular national interests, ethnic concerns, and religious obligations; and the threat to the general is posed by postmodernism and strong religiosity alike, postmodernism because its critique of master narratives deprives us of a mechanism for determining which of two or more fiercely held beliefs is true (which is not to deny the category of true belief, just the possibility of identifying it uncontroversially), strong religiosity because it insists on its own norms and refuses correction from the outside. The antidote to both is the separation of the private from the public, the establishing of a public sphere to which all could have recourse and to the judgments of which all, who are not criminal or insane, would assent. The point of the public sphere is obvious: it is supposed to be the location of those standards and measures that belong to no one but apply to everyone. It is to be the location of the universal. The problem is not that there is no universal–the universal, the absolutely true, exists, and I know what it is. The problem is that you know, too, and that we know different things, which puts us right back where we were a few sentences ago, armed with universal judgments that are irreconcilable, all dressed up and nowhere to go for an authoritative adjudication.

What to do? Well, you do the only thing you can do, the only honest thing: you assert that your universal is the true one, even though your adversaries clearly do not accept it, and you do not attribute their recalcitrance to insanity or mere criminality–the desired public categories of condemnation–but to the fact, regrettable as it may be, that they are in the grip of a set of beliefs that is false. And there you have to leave it, because the next step, the step of proving the falseness of their beliefs to everyone, including those in their grip, is not a step available to us as finite situated human beings. We have to live with the knowledge of two things: that we are absolutely right and that there is no generally accepted measure by which our rightness can be independently validated. That’s just the way it is, and we should just get on with it, acting in accordance with our true beliefs (what else could we do?) without expecting that some God will descend, like the duck in the old Groucho Marx TV show, and tell us that we have uttered the true and secret word.”

From the public spheres
of the Pennsylvania Lottery:

PA Lottery logo

PA Lottery July 3, 2007: Mid-day 105, Evening 268

105 —

Log24 on 1/05:

“‘From your lips
to God’s ears,’
 goes the old
Yiddish wish.

 The writer, by contrast,
tries to read God’s lips
and pass along
the words….”

— Richard Powers   

268 —

This is a page number
that appears, notably,
in my June 2002
journal entry on Fish
,
and again in an entry,
The Transcendent Signified,”
dated July 26, 2003,
that argues against
Fish’s school, postmodernism,
 and in favor of what the pomos
call “logocentrism.”

Page 268
 
of Simon Blackburn’s Think
(Oxford Univ. Press, 1999):

“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato’s (realist) reaction to the sophists (nominalists). What is often called ‘postmodernism’ is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth.”

Fish may, if he wishes,
regard the particular
page number 268 as
delivered– five years late,
but such is philosophy–
by Groucho’s
winged messenger
in response to
Fish’s utterance of the
  “true and secret word”–
namely, “universal.”

When not arguing politics,
Fish, though from
a Jewish background, is
 said to be a Milton scholar.
Let us therefore hope he
is by now, or comes to be,
aware of the Christian
approach to universals–
an approach true to the
philosophical background
sketched in 1999 by
Blackburn and made
particular in a 1931 novel
 by Charles Williams,
The Place of the Lion.

Wednesday, October 25, 2006

Wednesday October 25, 2006

Filed under: General,Geometry — m759 @ 9:00 AM

Conceit
at Harvard

conceit (See definition.)
“c.1374, from conceiven (see conceive). An Eng. formation based on deceit and receipt. Sense evolved from ‘something formed in the mind,’ to ‘fanciful or witty notion’ (1513), to ‘vanity’ (1605)….”

Online Eytmology Dictionary

“… there is some virtue in tracking cultural trends in terms of their relation to the classic Trinitarian framework of Christian thought.”

Description of lectures to be given Monday, Tuesday, and Wednesday of this week (on Father, Son, and Holy Spirit, respectively, and their relationship to “cultural trends”) at Harvard’s Memorial Church

I prefer more-classic trinitarian frameworks– for example,

the classic Pythagorean
trinity of 4, 3, and 5


The image “http://www.log24.com/log/pix06A/061025-Pyth2.gif” cannot be displayed, because it contains errors.

and the structural trinity
underlying
classic quilt patterns:

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

Click on pictures for further details.

These mathematical trinities are
conceits in the sense of concepts
or notions; examples of the third
kind of conceit are easily
found, especially at Harvard.

For a possible corrective to
examples of the third kind,
see
To Measure the Changes.

Saturday, September 23, 2006

Saturday September 23, 2006

Filed under: General — m759 @ 9:00 AM

“A corpse will be
transported by express!”

Under the Volcano,
by Malcolm Lowry (1947)


Dietrich


Minogue

“It has a ghastly familiarity,
like a half-forgotten dream.”

 — Poppy (Gene Tierney) in
The Shanghai Gesture.”

Temptation


Locomotive

The Star
of Venus


Locomotion

Joan Didion, The White Album:

“We tell ourselves stories in order to live….

We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the ‘ideas‘ with which we have learned to freeze the shifting phantasmagoria which is our actual experience.

Or at least we do for a while. I am talking here about a time when I began to doubt the premises of all the stories I had ever told myself, a common condition but one I found troubling.”

From Patrick Vert,
The Narrative of Acceleration:

“There are plenty of anecdotes to highlight the personal, phenomenological experience of railway passage…

… a unique study on phantasmagoria and the history of imagination. The word originates [in] light-projection, the so-called ghost-shows of the early 19th century….

… thought becomes a phantasmagorical process, a spectral, representative location for the personal imagination that had been marginalized by scientific rationalism….

This phantasmagoria became more mediated over time…. Perception became increasingly visually oriented…. As this occurred, a narrative formed to encapsulate the phenomenology of it all….”

For such a narrative, see
the Log24.net entries of

From a Christian fairy tale:

Aslan’s last words come at the end of The Last Battle: ‘There was a real railway accident […] Your father and mother and all of you are–as you used to call it in the Shadow-Lands–dead. The term is over: the holidays have begun. The dream is ended: this is the morning.’….

Aslan is given the last word in these quiet but emphatic lines. He is the ultimate arbiter of reality: “‘There was a real railway accident.'” Plato, in addition to the Christian tradition, lies behind the closing chapters of The Last Battle. The references here to the Shadowlands and to the dream refer back to an earlier explanation by Digory, now the Lord Digory:

“[…] that was not the real Narnia. That had a beginning and an end. It was only a shadow or a copy of the real Narnia, which has always been here and always will be here: just as our world, England and all, is only a shadow or copy of something in Aslan’s real world. [….] Of course it is different; as different as a real thing is from a shadow or as waking life is from a dream. […] It’s all in Plato, all in Plato: bless me, what do they teach them at these schools!”

Joy Alexander, Aslan’s Speech

“I was reading Durant’s section on Plato, struggling to understand his theory of the ideal Forms that lay in inviolable perfection out beyond the phantasmagoria. (That was the first, and I think the last, time that I encountered that word.)”

Whether any of the above will be of use in comforting the families of those killed in yesterday morning’s train wreck in Germany is not clear.  Pope Benedict XVI, like C. S. Lewis, seems to think Greek philosophy may be of some use to those dealing with train wrecks:

“Modifying the first verse of the Book of Genesis, the first verse of the whole Bible, John began the prologue of his Gospel with the words: ‘In the beginning was the logos.‘ This is the very word used by the emperor: God acts, syn logo, with logos. Logos means both reason and word– a reason which is creative and capable of self-communication, precisely as reason. John thus spoke the final word on the biblical concept of God, and in this word all the often toilsome and tortuous threads of biblical faith find their culmination and synthesis. In the beginning was the logos, and the logos is God, says the Evangelist.”

Remarks of the Pope at the University of Regensburg on Sept. 12, 2006

Thursday, February 16, 2006

Thursday February 16, 2006

Filed under: General — m759 @ 1:00 PM
Monolith
In memory of
Rabbi Yehuda Chitrik, storyteller

From James A. Michener‘s The Source:

“Trouble started in a quarter that neither Uriel nor Zadok could have foreseen.  For many generations the wiser men of Zadok’s clan had worshipped El-Shaddai with the understanding that whereas Canaanites and Egyptians could see their gods directly, El-Shaddai was invisible and inhabited no specific place.  Unequivocally the Hebrew patriarchs had preached this concept and the sager men of the clans accepted it, but to the average Hebrew who was not a philosopher the theory of a god who lived nowhere, who did not even exist in corporeal form, was not easy to comprehend.  Such people were willing to agree with Zadok that their god did not live on this mountain– the one directly ahead– but they suspected that he did live on some mountain nearby, and when they said this they pictured an elderly man with a white beard who lived in a proper tent and whom they might one day see and touch.  If questioned, they would have said that they expected El-Shaddai to look much like their father Zadok, but with a longer beard, a stronger voice, and more penetrating eyes.

Now, as these simpler-minded Hebrews settled down outside the walls of Makor, they began to see Canaanite processions leave the main gate and climb the mountain to the north, seeking the high place where Baal lived, and they witnessed the joy which men experienced when visiting their god, and the Hebrews began in subtle ways and easy steps to evolve the idea that Baal, who obviously lived in a mountain, and El-Shaddai, who was reported to do so, must have much in common.  Furtively at first, and then openly, they began to climb the footpath to the place of Baal, where they found a monolith rising from the highest point of rock.  Here was a tangible thing they could comprehend, and after much searching along the face of the mountain, a group of Hebrew men found a straight rock of size equal to the one accorded Baal, and with much effort they dragged it one starless night to the mountain top, where they installed it not far from the home of Baal….”

Rabbi Chitrik died on
Valentine’s Day, 2006,
having had a heart attack
on Feb. 8, 2006–

The image “http://www.log24.com/log06/saved/060216-Madonna.jpg” cannot be displayed, because it contains errors.

Grammy Night.

The image “http://www.log24.com/log/pix06/060207-Monolith.jpg” cannot be displayed, because it contains errors.

The above monolith is perhaps more
closely related to El-Shaddai than to
Madonna, Grammy Night, and Baal.
It reflects my own interests
(Mathematics and Narrative)
and those of Martin Buber
(Jews on Fiction):
 

“Among Buber’s early philosophical influences were Kant’s Prolegomena, which he read at the age of fourteen, and Nietzsche’s Zarathustra.  Whereas Kant had a calming influence on the young mind troubled by the aporia of infinite versus finite time, Nietzsche’s doctrine of ‘the eternal recurrence of the same’ constituted a powerful negative seduction.  By the time Buber graduated from Gymnasium he felt he had overcome this seduction, but Nietzsche’s prophetic tone and aphoristic style are evident in Buber’s subsequent writings.”

 

The image “http://www.log24.com/log/pix06/060216-RabbiChitrik1.jpg” cannot be displayed, because it contains errors.

Rabbi Chitrik

Monday, February 13, 2006

Monday February 13, 2006

Filed under: General — m759 @ 8:00 PM
The Lincoln Brigade

The image “http://www.log24.com/log/pix06/060213-Lincoln1.jpg” cannot be displayed, because it contains errors.

Marches On.

As yesterday’s Lincoln’s Birthday entry indicated, my own sympathies are not with the “created equal” crowd.  Still, the Catholic Fascism of Franco admirer Andrew Cusack seems somewhat over-the-top.  A more thoughtful approach to these matters may be found in a recommendation by Ross Douthat at The American Scene:

Read Eve Tushnet on the virtues of The Man in the High Castle.

Related material: Log24 on Nov. 14, Nov. 15, and Nov. 16, 2003.

Another item of interest from Eve:

“Transubstantiation [is equivalent but not equal to] art (deceptive accident hides truthful substance), as vs. Plato’s condemnation of the physical & the fictive? (Geo. Steiner)”

Related material:

The End of Endings
(excerpt)
by Father Richard John Neuhaus,
First Things
115 (Aug.-Sept. 2001), 47-56:

“In Grammars of Creation, more than in his 1989 book Real Presences, Steiner acknowledges that his argument rests on inescapably Christian foundations. In fact, he has in the past sometimes written in a strongly anti–Christian vein, while the present book reflects the influence of, among others, Miri Rubin, whose Corpus Christi: The Eucharist in Late Medieval Culture is credited in a footnote. Steiner asserts that, after the Platonisms and Gnosticisms of late antiquity, it is the doctrines of incarnation and transubstantiation that mark ‘the disciplining of Western syntax and conceptualization’ in philosophy and art. ‘Every heading met with in a study of “creation,” every nuance of analytic and figural discourse,’ he says, derives from incarnation and transubstantiation, ‘concepts utterly alien to either Judaic or Hellenic perspectives– though they did, in a sense, arise from the collisions and commerce between both.’….

The incarnation of God in the Son, the transubstantiation of bread and wine into his body and blood, are ‘a mysterium, an articulated, subtly innervated attempt to reason the irrational at the very highest levels of intellectual pressure.’ ‘Uniquely, perhaps, the hammering out of the teaching of the eucharist compels Western thought to relate the depth of the unconscious and of pre-history with speculative abstractions at the boundaries of logic and of linguistic philosophy.’ Later, the ‘perhaps’ in that claim seems to have disappeared:

At every significant point, Western philosophies of art and Western poetics draw their secular idiom from the substratum of Christological debate. Like no other event in our mental history, the postulate of God’s kenosis through Jesus and of the never-ending availability of the Savior in the wafer and wine of the eucharist, conditions not only the development of Western art and rhetoric itself, but at a much deeper level, that of our understanding and reception of the truth of art– a truth antithetical to the condemnation of the fictive in Plato.

This truth reaches its unrepeated perfection in Dante, says Steiner. In Dante, ‘It rounds in glory the investigation of creativity and creation, of divine authorship and human poesis, of the concentric spheres of the aesthetic, the philosophical, and the theological. Now truth and fiction are made one, now imagination is prayer, and Plato’s exile of the poets refuted.’ In the fashionable critical theories of our day, we witness ‘endeavors of the aesthetic to flee from incarnation.’ ‘It is the old heresies which revive in the models of absence, of negation or erasure, of the deferral of meaning in late–twentieth–century deconstruction. The counter-semantics of the deconstructionist, his refusal to ascribe a stable significance to the sign, are moves familiar to [an earlier] negative theology.’ Heidegger’s poetics of ‘pure immanence’ are but one more attempt ‘to liberate our experience of sense and of form from the grip of the theophanic.’ But, Steiner suggests, attempted flights from the reality of Corpus Christi will not carry the day. ‘Two millennia are only a brief moment.’

Monday, January 23, 2006

Monday January 23, 2006

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

In Defense of Hilbert
(On His Birthday)


Michael Harris (Log24, July 25 and 26, 2003) in a recent essay, Why Mathematics? You Might Ask (pdf), to appear in the forthcoming Princeton Companion to Mathematics:

“Mathematicians can… claim to be the first postmodernists: compare an art critic’s definition of postmodernism– ‘meaning is suspended in favor of a game involving free-floating signs’– with Hilbert’s definition of mathematics as ‘a game played according to certain simple rules with meaningless marks on paper.'”

Harris adds in a footnote:

“… the Hilbert quotation is easy to find but is probably apocryphal, which doesn’t make it any less significant.”

If the quotation is probably apocryphal, Harris should not have called it “Hilbert’s definition.”

For a much more scholarly approach to the concepts behind the alleged quotation, see Richard Zach, Hilbert’s Program Then and Now (pdf):

[Weyl, 1925] described Hilbert’s project as replacing meaningful mathematics by a meaningless game of formulas. He noted that Hilbert wanted to ‘secure not truth, but the consistency of analysis’ and suggested a criticism that echoes an earlier one by Frege: Why should we take consistency of a formal system of mathematics as a reason to believe in the truth of the pre-formal mathematics it codifies? Is Hilbert’s meaningless inventory of formulas not just ‘the bloodless ghost of analysis’?”

Some of Zach’s references:

[Ramsey, 1926] Frank P. Ramsey. Mathematical logic. The Mathematical Gazette, 13:185-94, 1926. Reprinted in [Ramsey, 1990, 225-244].

[Ramsey, 1990] Frank P. Ramsey. Philosophical Papers, D. H. Mellor, editor. Cambridge University Press, Cambridge, 1990

From Frank Plumpton Ramsey’s Philosophical Papers, as cited above, page 231:

“… I must say something of the system of Hilbert and his followers…. regarding higher mathematics as the manipulation of meaningless symbols according to fixed rules….
Mathematics proper is thus regarded as a sort of game, played with meaningless marks on paper rather like noughts and crosses; but besides this there will be another subject called metamathematics, which is not meaningless, but consists of real assertions about mathematics, telling us that this or that formula can or cannot be obtained from the axioms according to the rules of deduction….
Now, whatever else a mathematician is doing, he is certainly making marks on paper, and so this point of view consists of nothing but the truth; but it is hard to suppose it the whole truth.”

[Weyl, 1925] Hermann Weyl. Die heutige Erkenntnislage in der Mathematik. Symposion, 1:1-23, 1925. Reprinted in: [Weyl, 1968, 511-42]. English translation in: [Mancosu, 1998a, 123-42]….

[Weyl, 1968] Hermann Weyl. Gesammelte Abhandlungen, volume 1, K. Chandrasekharan, editor. Springer Verlag, Berlin, 1968.

[Mancosu, 1998a] Paolo Mancosu, editor. From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s. Oxford University Press, Oxford, 1998.

From Hermann Weyl, “Section V: Hilbert’s Symbolic Mathematics,” in Weyl’s “The Current Epistemogical Situation in Mathematics,” pp. 123-142 in Mancosu, op. cit.:

“What Hilbert wants to secure is not the truth, but the consistency of the old analysis.  This would, at least, explain that historic phenomenon of the unanimity amongst all the workers in the vineyard of analysis.
To furnish the consistency proof, he has first of all to formalize mathematics.  In the same way in which the contentual meaning of concepts such as “point, plane, between,” etc. in real space was unimportant in geometrical axiomatics in which all interest was focused on the logical connection of the geometrical concepts and statements, one must eliminate here even more thoroughly any meaning, even the purely logical one.  The statements become meaningless figures built up from signs.  Mathematics is no longer knowledge but a game of formulae, ruled by certain conventions, which is very well comparable to the game of chess.  Corresponding to the chess pieces we have a limited stock of signs in mathematics, and an arbitrary configuration of the pieces on the board corresponds to the composition of a formula out of the signs.  One or a few formulae are taken to be axioms; their counterpart is the prescribed configuration of the pieces at the beginning of a game of chess.  And in the same way in which here a configuration occurring in a game is transformed into the next one by making a move that must satisfy the rules of the game, there, formal rules of inference hold according to which new formulae can be gained, or ‘deduced,’ from formulae.  By a game-conforming [spielgerecht] configuration in chess I understand a configuration that is the result of a match played from the initial position according to the rules of the game.  The analogue in mathematics is the provable (or, better, the proven) formula, which follows from the axioms on grounds of the inference rules.  Certain formulae of intuitively specified character are branded as contradictions; in chess we understand by contradictions, say, every configuration which there are 10 queens of the same color.  Formulae of a different structure tempt players of mathematics, in the way checkmate configurations tempt chess players, to try to obtain them through clever combination of moves as the end formula of a correctly played proof game.  Up to this point everything is a game; nothing is knowledge; yet, to use Hilbert’s terminology, in ‘metamathematics,’ this game now becomes the object of knowledge.  What is meant to be recognized is that a contradiction can never occur as an end formula of a proof.  Analogously it is no longer a game, but knowledge, if one shows that in chess, 10 queens of one color cannot occur in a game-conforming configuration.  One can see this in the following way: The rules are teaching us that a move can never increase the sum of the number of queens and pawns of one color.  In the beginning this sum = 9, and thus– here we carry out an intuitively finite [anschaulich-finit] inference through complete induction– it cannot be more than this value in any configuration of a game.  It is only to gain this one piece of knowledge that Hilbert requires contentual and meaningful thought; his proof of consistency proceeds quite analogously to the one just carried out for chess, although it is, obviously, much more complicated.
It follows from our account that mathematics and logic must be formalized together.  Mathematical logic, much scorned by philosophers, plays an indispensable role in this context.”

Constance Reid says it was not Hilbert himself, but his critics, who described Hilbert’s formalism as reducing mathematics to “a meaningless game,” and quotes the Platonist Hardy as saying that Hilbert was ultimately concerned not with meaningless marks on paper, but with ideas:

“Hilbert’s program… received its share of criticism.  Some mathematicians objected that in his formalism he had reduced their science to ‘a meaningless game played with meaningless marks on paper.’  But to those familiar with Hilbert’s work this criticism did not seem valid.
‘… is it really credible that this is a fair account of Hilbert’s view,’ Hardy demanded, ‘the view of the man who has probably added to the structure of significant mathematics a richer and more beautiful aggregate of theorems than any other mathematician of his time?  I can believe that Hilbert’s philosophy is as inadequate as you please, but not that an ambitious mathematical theory which he has elaborated is trivial or ridiculous.  It is impossible to suppose that Hilbert denies the significance and reality of mathematical concepts, and we have the best of reasons for refusing to believe it: “The axioms and demonstrable theorems,” he says himself, “which arise in our formalistic game, are the images of the ideas which form the subject-matter of ordinary mathematics.”‘”

— Constance Reid in Hilbert-Courant, Springer-Verlag, 1986 (The Hardy passage is from “Mathematical Proof,” Mind 38, 1-25, 1929, reprinted in Ewald, From Kant to Hilbert.)

Harris concludes his essay with a footnote giving an unsourced Weyl quotation he found on a web page of David Corfield:

“.. we find ourselves in [mathematics] at exactly that crossing point of constraint and freedom which is the very essence of man’s nature.”

One source for the Weyl quotation is the above-cited book edited by Mancosu, page 136.  The quotation in the English translation given there:

“Mathematics is not the rigid and petrifying schema, as the layman so much likes to view it; with it, we rather stand precisely at the point of intersection of restraint and freedom that makes up the essence of man itself.”

Corfield says of this quotation that he’d love to be told the original German.  He should consult the above references cited by Richard Zach.

For more on the intersection of restraint and freedom and the essence of man’s nature, see the Kierkegaard chapter cited in the previous entry.

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

Sunday, May 8, 2005

Sunday May 8, 2005

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

Geometry and Theology

See

the science fiction writer mentioned in a Friday entry.

Mark Olson’s article is at the website of the New England Science Fiction Association, publisher of Ingathering: The Complete People Stories of Zenna Henderson.  This book, by one of my favorite science-fiction authors, was apparently edited by the same Mark Olson.

The following remarks seem relevant to the recurring telepathy theme in Henderson:

From the first article cited above,
David L. Neuhouser,
Higher Dimensions in the Writings of C. S. Lewis (pdf):

“If we are three-dimensional cross-sections of four-dimensional reality, perhaps we are parts of the same body. In fact, we know we are parts of the same body in some way, this four-dimensional idea just may help us to see it more clearly. Remember the preceding comments are mine, not Lewis’s. He puts it this way, ‘That we can die “in” Adam and live “in” Christ seems to me to imply that man as he really is differs a good deal from man as our categories of thought and our three-dimensional imaginations represent him; that the separateness… which we discern between individuals, is balanced, in absolute reality, by some kind of inter-inanimation of which we have no conception at all. It may be that the acts and sufferings of great archetypal individuals such as Adam and Christ are ours, not by legal fiction, metaphor, or causality, but in some much deeper fashion. There is no question, of course, of individuals melting down into a kind of spiritual continuum such as Pantheistic systems believe in; that is excluded by the whole tenor of our faith.'”

From Webster’s Unabridged, 1913 edition:

inanimate
, v. t.

[Pref. in- in (or intensively) + animate.]
 To animate. [Obs.] — Donne.

inanimation, n.

Infusion of life or vigor;
animation; inspiration.
[Obs.]
The inanimation of Christ
living and breathing within us.
Bp. Hall.

Related words…

Also from the 1913 Webster’s:

circumincession, n.

[Pref. circum- + L. incedere, incessum, to walk.]
(Theol.) The reciprocal existence in each other
of the three persons of the Trinity.

From an online essay:

perichoresis
, n.

“The term means mutual indwelling or, better, mutual interpenetration and refers to the understanding of both the Trinity and Christology. In the divine perichoresis, each person has ‘being in each other without coalescence’ (John of Damascus ca. 650). The roots of this doctrine are long and deep.”

—  Bert Waggoner

coinherence, n.

“In our human experience of personhood, at any rate in a fallen world, there is in each person an inevitable element of exclusiveness, of opaqueness and impenetrability.  But with the three divine persons it is not so.  Each is entirely ‘open’ to the others, totally transparent and receptive.  This transparency and receptivity is summed up in the Greek notion of perichoresis, which Gibbon once called ‘the deepest and darkest corner of the whole theological abyss.’  Rendered in Latin as circumincessio and in English usually as ‘coinherence,’ the Greek term means literally, cyclical movement, and so reciprocity, interchange, mutual indwelling.  The prefix peri bears the sense ‘around,’ while choresis is linked with chora, ‘room,’ space,’ ‘place’ or ‘container,’ and with chorein, to ‘go,’ ‘advance,’ ‘make room for’ or ‘contain.’  Some also see a connection with choros, ‘dance,’ and so they take perichoresis to mean ’round dance.’  Applied to Christ, the term signifies that his two natures, the divine and the human, interpenetrate one another without separation and without confusion.  Applied to the Trinity, it signifies that each person ‘contains’ the other two and ‘moves’ within them.  In the words of St Gregory of Nyssa, ‘All that is the Father’s is seen in the Son, and all that is the Son’s belongs also the Father. For the whole Son abides in the Father, and he has in his turn the whole Father abiding in himself.’ 

By virtue of this perichoresis, Father, Son and Holy Spirit ‘coinhere‘ in one another, each dwelling in the other two through an unceasing movement of mutual love – the ’round dance’ of the Trinity.”

— Timothy Ware, Bishop Kallistos of Diokleia,
    The Human Person as an Icon of the Trinity

Sunday, December 12, 2004

Sunday December 12, 2004

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

Ideas, Stories, Values:
Literati in Deep Confusion

Joan Didion, The White Album:

“We tell ourselves stories in order to live….

We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the ‘ideas‘ with which we have learned to freeze the shifting phantasmagoria which is our actual experience.

Or at least we do for a while. I am talking here about a time when I began to doubt the premises of all the stories I had ever told myself, a common condition but one I found troubling.”

Interview with Joseph Epstein:

“You can do in stories things that are above those in essays,” says Epstein.  “In essays and piecework, you are trying to make a point, whereas in stories you are not quite sure what the point is. T.S. Eliot once said of Henry James, ‘He had a mind so fine no idea could violate it,’ which, I think, is the ultimate compliment for an author. Stories are above ideas.”

Harvard President Lawrence H. Summers, Sept. 12, 2004:

“You are entering a remarkable community, the Harvard community. It is a community built on the idea of searching for truth… on the idea of respect for others….

… we practice the values we venerate. The values of seeking truth, the values of respecting others….”

Paul Redding on Hegel:

“… Hegel discusses ‘culture’ as the ‘world of self-alienated spirit.’ The idea seems to be that humans in society not only interact, but that they collectively create relatively enduring cultural products (stories, dramas, and so forth) within which they can recognise their own patterns of life reflected.”

The “phantasmagoria” of Didion seems related to the “phenomenology” of Hegel…

From Michael N. Forster,  Hegel’s Idea of a Phenomenology of Spirit:

“This whole system is conceived, on one level at least, as a defense or rational reworking of the Christian conception of God.  In particular, its three parts are an attempt to make sense of the Christian idea of a God who is three in one — the Logic depicting God as he is in himself, the Philosophy of Nature God the Son, and the Philosophy of Spirit God the Holy Spirit.”

and, indeed, to the phenomenology of narrative itself….

From Patrick Vert,
The Narrative of Acceleration:

“There are plenty of anecdotes to highlight the personal, phenomenological experience of railway passage…

… a unique study on phantasmagoria and the history of imagination. The word originates [in] light-projection, the so-called ghost-shows of the early 19th century….

… thought becomes a phantasmagorical process, a spectral, representative location for the personal imagination that had been marginalized by scientific rationalism….

Truly, ‘immediate experience is [or becomes] the phantasmagoria of the idler’ [Walter Benjamin, The Arcades Project.  Cambridge: Harvard University Press, 1999.  Page 801.]….

Thought as phantasm is a consequence of the Cartesian split, and… a further consequence to this is the broad take-over of perceptual faculty…. What better example than that of the American railway?  As a case-study it offers explanation to the ‘phantasmagoria of the idler’….

This phantasmagoria became more mediated over time…. Perception became increasingly visually oriented…. As this occurred, a narrative formed to encapsulate the phenomenology of it all….”

For such a narrative, see
the Log24.net entries of

November 5, 2002, 2:56 AM,
November 5, 2002, 6:29 AM,
January 3, 2003, 11:59 PM,
August 17, 2004, 7:29 PM,
August 18, 2004, 2:18 AM,
August 18, 2004, 3:00 AM, and
November 24, 2004, 10:00 AM.

Monday, April 5, 2004

Monday April 5, 2004

Filed under: General,Geometry — Tags: — m759 @ 4:03 AM

Ideas and Art

 
Motto of
Plato's Academy

 

From Minimalist Fantasies,
by Roger Kimball, May 2003:

All I want anyone to get out of my paintings, and all I ever get out of them, is the fact that you can see the whole idea without any confusion. … What you see is what you see.
—Frank Stella, 1966

Minimal Art remains too much a feat of ideation, and not enough anything else. Its idea remains an idea, something deduced instead of felt and discovered.
— Clement Greenberg, 1967

The artists even questioned whether art needed to be a tangible object. Minimalism … Conceptualism — suddenly art could be nothing more than an idea, a thought on a piece of paper….
— Michael Kimmelman, 2003

There was a period, a decade or two ago, when you could hardly open an art journal without encountering the quotation from Frank Stella I used as an epigraph. The bit about “what you see is what you see” was reproduced ad nauseam. It was thought by some to be very deep. In fact, Stella’s remarks—from a joint interview with him and Donald Judd—serve chiefly to underscore the artistic emptiness of the whole project of minimalism. No one can argue with the proposition that “what you see is what you see,” but there’s a lot to argue with in what he calls “the fact that you can see the whole idea without any confusion.” We do not, of course, see ideas. Stella’s assertion to the contrary might be an instance of verbal carelessness, but it is not merely verbal carelessness. At the center of minimalism, as Clement Greenberg noted, is the triumph of ideation over feeling and perception, over aesthetics.
— Roger Kimball, 2003

 

 

From How Not Much Is a Whole World,
by Michael Kimmelman, April 2, 2004

Decades on, it's curious how much Minimalism, the last great high modern movement, still troubles people who just can't see why … a plain white canvas with a line painted across it


"William Clark,"
by Patricia Johanson, 1967

should be considered art. That line might as well be in the sand: on this side is art, it implies. Go ahead. Cross it.

….

The tug of an art that unapologetically sees itself as on a par with science and religion is not to be underestimated, either. Philosophical ambition and formal modesty still constitute Minimalism's bottom line.

If what results can sometimes be more fodder for the brain than exciting to look at, it can also have a serene and exalted eloquence….

That line in the sand doesn't separate good art from bad, or art from nonart, but a wide world from an even wider one.

 

I maintain that of course
we can see ideas.

Example: the idea of
invariant structure.

"What modern painters
are trying to do,
if they only knew it,
is paint invariants."

— James J. Gibson, Leonardo,
    Vol. 11, pp. 227-235.
    Pergamon Press Ltd., 1978

For a discussion
of how this works, see
Block Designs,
4×4 Geometry, and
Diamond Theory.

Incidentally, structures like the one shown above are invariant under an important subgroup of the affine group AGL(4,2)…  That is to say, they are not lost in translation.  (See previous entry.)
 

Tuesday, February 10, 2004

Tuesday February 10, 2004

Filed under: General — m759 @ 12:07 PM

George W. Bush,
Liberal!

Part I:

 

2:09 PM PST, February 9, 2004

President’s Economic Report
Endorses Export of Jobs

By Warren Vieth and Edwin Chen,
Los Angeles Times Staff Writers

WASHINGTON — The movement of American factory jobs and white-collar work to other countries is part of a positive transformation that will enrich the U.S. economy over time, even if it causes short-term pain and dislocation, the Bush administration said today.

The embrace of foreign “outsourcing,” an accelerating trend that has contributed to U.S. job losses in recent years and has become an issue in the 2004 elections, is contained in the president’s annual report to Congress on the health of the U.S. economy….

Although trade expansion inevitably hurts some workers, it says, the benefits will eventually outweigh the costs as Americans are able to buy goods and services at lower costs and as jobs are created in growing sectors of the economy.

The report endorses the relatively new phenomenon of outsourcing high-end white-collar work to India and other countries, a trend that has created concern within affected professions such as computer programming and medical diagnostics.

Part II:

A search on liberal “free trade” leads to the following quote:

“One of the central concepts of classical liberal economic thought is the superiority of free trade over protectionism.”

Therefore George W. Bush, by courageously advocating free trade despite its political unpopularity, is a classic liberal.

Part III:

Context for the above quote:

The Liberal Agenda for the 21st Century

George W. Bush’s free-trade policy
fits right in.

Part IV:

The Conservative Alternative…

Patrick J. Buchanan,

author of “The Death of Manufacturing

and A Republic, Not an Empire.

“Let it be said: George Bush is beatable. He has no explanation and no cure for the hemorrhaging of manufacturing jobs at Depression rates, no plan to stop the outsourcing of white-collar jobs to Asia, no desire or will to stop the invasion from Mexico.

Yet, he remains a favorite against Kerry, because Kerry has no answers, either. Both are globalists. Both are free-traders. Both favor open borders. Again, it needs to be said:  There is no conservative party in America.”

Patrick J. Buchanan, Feb. 2, 2004

Not yet, there isn’t.

Monday, August 25, 2003

Monday August 25, 2003

Filed under: General — Tags: — m759 @ 4:24 AM

Words Are Events

August 12 was the date of death of Joseph Patrick Kennedy, Jr., and the date I entered some theological remarks in a new Harvard weblog.  It turns out that August 12 was also the feast day of a new saint… Walter Jackson Ong, of St. Louis University, St. Louis, Missouri, a Jesuit institution.

Today, August 25, is the feast day of St. Louis himself, for whom the aforementioned city and university are named.

The New York Times states that Ong was "considered an outstanding postmodern theorist, whose ideas spawned college courses…."

There is, of course, no such thing as a postmodern Jesuit, although James Joyce came close.

From The Walter J. Ong Project:

"Ong's work is often presented alongside the postmodern and deconstruction theories of Claude Levi-Strauss, Jacques Derrida, Michel Foucault, Hélène Cixous, and others. His own work in orality and literacy shows deconstruction to be unnecessary: if you consider language to be fundamentally spoken, as language originally is, it does not consist of signs, but of events. Sound, including the spoken word, is an event. It takes time. The concept of 'sign,' by contrast, derives primarily not from the world of events, but from the world of vision. A sign can be physically carried around, an event cannot: it simply happens. Words are events."

 

From a commonplace book
on the number 911:

"We keep coming back and coming back
To the real: to the hotel
    instead of the hymns
That fall upon it out of the wind.
    We seek

The poem of pure reality, untouched
By trope or deviation,
    straight to the word,
Straight to the transfixing object,
    to the object

At the exactest point at which
    it is itself,
Transfixing by being purely
    what it is,
A view of New Haven, say,
    through the certain eye,

The eye made clear of uncertainty,
    with the sight
Of simple seeing, without reflection.
    We seek
Nothing beyond reality. Within it,

Everything, the spirit's alchemicana
Included, the spirit that goes
    roundabout
And through included,
    not merely the visible,

The solid, but the movable,
    the moment,
The coming on of feasts
     and the habits of saints,
The pattern of the heavens
     and high, night air."

Wallace Stevens (1879-1955)
An Ordinary Evening in New Haven
IX.1-18, from The Auroras of Autumn,
Knopf, NY (1950)
(Collected Poems, pp. 465-489)
NY Times Obituary (8-3-1955)

 

The web page where I found the Stevens quote also has the following:

 

Case 9 of Hekiganroku:
Joshu's Four Gates

A monk asked Joshu,
"What is Joshu?" (Chinese: Chao Chou)

Joshu said,
"East Gate, West Gate,
 North Gate, South Gate."

Setcho's Verse:

Its intention concealed,
    the question came;
The Diamond King's eye was
    as clear as a jewel.
There stood the gates,
    north, south, east, and west,
But the heaviest hammer blow
    could not open them.

Setcho (980-1052),
Hekiganroku, 9 (Blue Cliff Records)
(translated by Katsuki Sekida,
Two Zen Classics, 1977, p. 172)

 

See also my previous entry for today,
"Gates to the City."

Monday, August 18, 2003

Monday August 18, 2003

Filed under: General,Geometry — Tags: — m759 @ 3:09 PM

Entries since Xanga’s
August 10 Failure:


Sunday, August 17, 2003  2:00 PM

A Thorny Crown of…

West Wing's Toby Ziegler

From the first episode of
the television series
The West Wing“:

 

Original airdate: Sept. 22, 1999
Written by Aaron Sorkin

MARY MARSH
That New York sense of humor. It always–

CALDWELL
Mary, there’s absolutely no need…

MARY MARSH
Please, Reverend, they think they’re so much smarter. They think it’s smart talk. But nobody else does.

JOSH
I’m actually from Connecticut, but that’s neither here nor there. The point is that I hope…

TOBY
She meant Jewish.

[A stunned silence. Everyone stares at Toby.]

TOBY (CONT.)
When she said “New York sense of humor,” she was talking about you and me.

JOSH
You know what, Toby, let’s just not even go there.

 

Going There, Part I

 

Crown of Ideas

Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003.

From his New York Times obituary:

” ‘He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,’ said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe’s first big show at the Modern, ‘High & Low.’ ‘Art was always material first — it was never, ever bound by a thorny crown of ideas.’ ”

For a mini-exhibit of ideas in honor of Varnedoe, see

Fahne Hoch.

Verlyn Klinkenborg on Varnedoe:

“I was always struck by the tangibility of the words he used….  It was as if he were laying words down on the table one by one as he used them, like brushes in an artist’s studio. That was why students crowded into his classes and why the National Gallery of Art had overflow audiences for his Mellon Lectures earlier this year. Something synaptic happened when you listened to Kirk Varnedoe, and, remarkably, something synaptic happened when he listened to you. You never knew what you might discover together.”

Perhaps even a “thorny crown of ideas“?

“Crown of Thorns”
Cathedral, Brasilia

Varnedoe’s death coincided with
the Great Blackout of 2003.

“To what extent does this idea of a civic life produced by sense of adversity correspond to actual life in Brasília? I wonder if it is something which the city actually cultivates. Consider, for example the cathedral, on the monumental axis, a circular, concrete framed building whose sixteen ribs are both structural and symbolic, making a structure that reads unambiguously as a crown of thorns; other symbolic elements include the subterranean entrance, the visitor passing through a subterranean passage before emerging in the light of the body of the cathedral. And it is light, shockingly so….”

Modernist Civic Space: The Case of Brasilia, by Richard J. Williams, Department of History of Art, University of Edinburgh, Scotland

 

Going There, Part II

Simple, Bold, Clear

Art historian Kirk Varnedoe was, of course, not the only one to die on the day of the Great Blackout.

Claude Martel, 34, a senior art director of The New York Times Magazine, also died on Thursday, August 14, 2003.

Janet Froelich, the magazine’s art director, describes below a sample of work that she and Martel did together:

“A new world of ideas”

Froelich notes that “the elements are simple, bold, and clear.”

For another example of elements with these qualities, see my journal entry

Fahne Hoch.

The flag design in that entry
might appeal to Aaron Sorkin’s
Christian antisemite:

 

Fahne,
S. H. Cullinane,
Aug. 15, 2003

Dr. Mengele,
according to
Hollywood

 

Note that the elements of the flag design have the qualities described so aptly by Froelich– simplicity, boldness, clarity:

They share these qualities with the Elements of Euclid, a treatise on geometrical ideas.

For the manner in which such concepts might serve as, in Gopnik’s memorable phrase, a “thorny crown of ideas,” see

“Geometry for Jews” in

ART WARS: Geometry as Conceptual Art.

See also the discussion of ideas in my journal entry on theology and art titled

Understanding: On Death and Truth

and the discussion of the wordidea” (as well as the word, and the concept, “Aryan”) in the following classic (introduced by poet W. H. Auden):

 

 

Saturday, August 16, 2003  6:00 AM

Varnedoe’s Crown

Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003.

From his New York Times obituary:

” ‘He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,’ said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe’s first big show at the Modern, ‘High & Low.’ ‘Art was always material first — it was never, ever bound by a thorny crown of ideas.’ “

For a mini-exhibit of ideas in honor of Varnedoe, see

Fahne Hoch. 

Verlyn Klinkenborg on Varnedoe:

“I was always struck by the tangibility of the words he used….  It was as if he were laying words down on the table one by one as he used them, like brushes in an artist’s studio. That was why students crowded into his classes and why the National Gallery of Art had overflow audiences for his Mellon Lectures earlier this year. Something synaptic happened when you listened to Kirk Varnedoe, and, remarkably, something synaptic happened when he listened to you. You never knew what you might discover together.”

Perhaps even a “thorny crown of ideas”?

“Crown of Thorns”
Cathedral, Brasilia

Varnedoe’s death coincided with
the Great Blackout of 2003.

“To what extent does this idea of a civic life produced by sense of adversity correspond to actual life in Brasília? I wonder if it is something which the city actually cultivates. Consider, for example the cathedral, on the monumental axis, a circular, concrete framed building whose sixteen ribs are both structural and symbolic, making a structure that reads unambiguously as a crown of thorns; other symbolic elements include the subterranean entrance, the visitor passing through a subterranean passage before emerging in the light of the body of the cathedral. And it is light, shockingly so….”

Modernist Civic Space: The Case of Brasilia, by Richard J. Williams, Department of History of Art, University of Edinburgh, Scotland


Friday, August 15, 2003  3:30 PM

ART WARS:

The Boys from Brazil

It turns out that the elementary half-square designs used in Diamond Theory

 

also appear in the work of artist Nicole Sigaud.

Sigaud’s website The ANACOM Project  has a page that leads to the artist Athos Bulcão, famous for his work in Brasilia.

From the document

Conceptual Art in an
Authoritarian Political Context:
Brasilia, Brazil
,

by Angélica Madeira:

“Athos created unique visual plans, tiles of high poetic significance, icons inseparable from the city.”

As Sigaud notes, two-color diagonally-divided squares play a large part in the art of Bulcão.

The title of Madeira’s article, and the remarks of Anna Chave on the relationship of conceptual/minimalist art to fascist rhetoric (see my May 9, 2003, entries), suggest possible illustrations for a more politicized version of Diamond Theory:

 

Fahne,
S. H. Cullinane,
Aug. 15, 2003

Dr. Mengele,
according to
Hollywood

 

Is it safe?

These illustrations were suggested in part by the fact that today is the anniversary of the death of Macbeth, King of Scotland, and in part by the following illustrations from my journal entries of July 13, 2003 comparing a MOMA curator to Lady Macbeth:

 

Die Fahne Hoch,
Frank Stella,
1959


Dorothy Miller,
MOMA curator,
died at 99 on
July 11, 2003
.

 


Thursday, August 14, 2003  3:45 AM

Famous Last Words

The ending of an Aug. 14 Salon.com article on Mel Gibson’s new film, “The Passion”:

” ‘The Passion’ will most likely offer up the familiar puerile, stereotypical view of the evil Jew calling for Jesus’ blood and the clueless Pilate begging him to reconsider. It is a view guaranteed to stir anew the passions of the rabid Christian, and one that will send the Jews scurrying back to the dark corners of history.”

— Christopher Orlet

“Scurrying”?!  The ghost of Joseph Goebbels, who famously portrayed Jews as sewer rats doing just that, must be laughing — perhaps along with the ghost of Lady Diana Mosley (née Mitford), who died Monday.

This goes well with a story that Orlet tells at his website:

“… to me, the most genuine last words are those that arise naturally from the moment, such as

 

Joseph Goebbels

 

Voltaire’s response to a request that he foreswear Satan: ‘This is no time to make new enemies.’ ”

For a view of Satan as an old, familiar, acquaintance, see the link to Prince Ombra in my entry last October 29 for Goebbels’s birthday.


Wednesday, August 13, 2003  3:00 PM

Best Picture

For some reflections inspired in part by

click here.


Tuesday, August 12, 2003  4:44 PM

Atonement:

A sequel to my entry “Catholic Tastes” of July 27, 2003.

Some remarks of Wallace Stevens that seem appropriate on this date:

“It may be that one life is a punishment
For another, as the son’s life for the father’s.”

—  Esthétique du Mal, Wallace Stevens

Joseph Patrick Kennedy, Jr.

“Unless we believe in the hero, what is there
To believe? ….
Devise, devise, and make him of winter’s
Iciest core, a north star, central
In our oblivion, of summer’s
Imagination, the golden rescue:
The bread and wine of the mind….”

Examination of the Hero in a Time of War, Wallace Stevens

Etymology of “Atonement”:

Middle English atonen, to be reconciled, from at one, in agreement

At One

“… We found,
If we found the central evil, the central good….
… we and the diamond globe at last were one.”

Asides on the Oboe, Wallace Stevens


Tuesday, August 12, 2003  1:52 PM

Franken & ‘Stein,
Attorneys at Law

Tue August 12, 2003 04:10 AM ET
NEW YORK (Reuters) – Fox News Network is suing humor writer Al Franken for trademark infringement over the phrase ‘fair and balanced’ on the cover of his upcoming book, saying it has been ‘a signature slogan’ of the network since 1996.”

Franken:
Fair?

‘Stein:
Balanced?

For answers, click on the pictures
of Franken and ‘Stein.


Wednesday, August 6, 2003

Wednesday August 6, 2003

Filed under: General — m759 @ 10:23 AM

Postmodern
Postmortem

“I had a lot of fun with this audacious and exasperating book. … [which] looks more than a little like Greil Marcus’s Lipstick Traces, a ‘secret history’ tracing punk rock through May 1968….”

— Michael Harris, Institut de Mathématiques de Jussieu, Université Paris 7, review of Mathematics and the Roots of Postmodern Thought, by Vladimir Tasic, Notices of the American Mathematical Society, August 2003

For some observations on the transgressive  predecessors of punk rock, see my entry Funeral March of July 26, 2003 (the last conscious day in the life of actress Marie Trintignant — see below), which contains the following:

“Sky is high and so am I,
If you’re a viper — a vi-paah.”
The Day of the Locust,
    by Nathanael West (1939)

As I noted in another another July 26 entry, the disease of postmodernism has, it seems, now infected mathematics.  For some recent outbreaks of infection in physics, see the works referred to below.

Postmodern Fields of Physics: In his book The Dreams of Reason, H. R. Pagels focuses on the science of complexity as the most outstanding new discipline emerging in recent years….”

— “The Semiotics of ‘Postmodern’ Physics,” by Hans J. Pirner, in Symbol and Physical Knowledge: The Conceptual Structure of Physics, ed. by M. Ferrari and I.-O. Stamatescu, Springer Verlag, August 2001 

For a critical look at Pagels’s work, see Midsummer Eve’s Dream.  For a less critical look, see The Marriage of Science and Mysticism.  Pagels’s book on the so-called “science of complexity” was published in June 1988.  For more recent bullshit on complexity, see

The Critical Idiom of Postmodernity and Its Contributions to an Understanding of Complexity, by Matthew Abraham, 2000,

which describes a book on complexity theory that, besides pronouncements about physics, also provides what “could very well be called a ‘postmodern ethic.’ “

The book reviewed is Paul Cilliers’s Complexity and Postmodernism: Understanding Complex Systems.

A search for related material on Cilliers yields the following:

Janis Joplin, Postmodernist

” …’all’ is ‘one,’ … the time is ‘now’ and … ‘tomorrow never happens,’ …. as Janis Joplin says, ‘it’s all the same fucking day.’

It appears that ‘time,’ … the linear, independent notion of ‘time’ that our culture embraces, is an artifact of our abstract thinking …

The problem is that ‘tomorrow never happens’ …. Aboriginal traditionalists are well aware of this topological paradox and so was Janis Joplin. Her use of the expletive in this context is therefore easy to understand … love is never having to say ‘tomorrow.’ “

Web page citing Paul Cilliers

“That’s the dumbest thing I ever heard.”

— Ryan O’Neal in “What’s Up, Doc?”

A more realistic look at postmodernism in action is provided by the following news story:

Brutal Death of an Actress Is France’s Summertime Drama

By JOHN TAGLIABUE

The actress, Marie Trintignant, died Friday [Aug. 1, 2003] in a Paris hospital, with severe head and face injuries. Her rock star companion, Bertrand Cantat, is confined to a prison hospital….

According to news reports, Ms. Trintignant and Mr. Cantat argued violently in their hotel room in Vilnius in the early hours of [Sunday] July 27 at the end of a night spent eating and drinking….

In coming months, two films starring Ms. Trintignant are scheduled to debut, including “Janis and John” by the director Samuel Benchetrit, her estranged husband and the father of two of her four children. In it, Ms. Trintignant plays Janis Joplin.

New York Times of Aug. 5, 2003

” ‘…as a matter of fact, as we discover all the time, tomorrow never happens, man. It’s all the same f…n’ day, man!’ –Janis Joplin, at live performance in Calgary on 4th July 1970 – exactly four months before her death. (apologies for censoring her exact words which can be heard on the ‘Janis Joplin in Concert’ CD)”

Janis Joplin at FamousTexans.com

All of the above fits in rather nicely with the view of science and scientists in the C. S. Lewis classic That Hideous Strength, which I strongly recommend.

For those few who both abhor postmodernism and regard the American Mathematical Society Notices

as a sort of “holy place” of Platonism, I recommend a biblical reading–

Matthew 24:15, CEV:

“Someday you will see that Horrible Thing in the holy place….”

See also Logos and Logic for more sophisticated religious remarks, by Simone Weil, whose brother, mathematician André Weil, died five years ago today.

Saturday, July 26, 2003

Saturday July 26, 2003

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

The Transcendent
Signified

“God is both the transcendent signifier
and transcendent signified.”

— Caryn Broitman,
Deconstruction and the Bible

“Central to deconstructive theory is the notion that there is no ‘transcendent signified,’ or ‘logos,’ that ultimately grounds ‘meaning’ in language….”

— Henry P. Mills,
The Significance of Language,
Footnote 2

“It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato’s (realist) reaction to the sophists (nominalists). What is often called ‘postmodernism’ is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth.”

Simon Blackburn, Think,
Oxford University Press, 1999, page 268

The question of universals is still being debated in Paris.  See my July 25 entry,

A Logocentric Meditation.

That entry discusses an essay on
mathematics and postmodern thought
by Michael Harris,
professor of mathematics
at l’Université Paris 7 – Denis Diderot.

A different essay by Harris has a discussion that gets to the heart of this matter: whether pi exists as a platonic idea apart from any human definitions.  Harris notes that “one might recall that the theorem that pi is transcendental can be stated as follows: the homomorphism Q[X] –> R taking X to pi is injective.  In other words, pi can be identified algebraically with X, the variable par excellence.”

Harris illustrates this with
an X in a rectangle:

For the complete passage, click here.

If we rotate the Harris X by 90 degrees, we get a representation of the Christian Logos that seems closely related to the God-symbol of Arthur C. Clarke and Stanley Kubrick in 2001: A Space Odyssey.  On the left below, we have a (1x)4×9 black monolith, representing God, and on the right below, we have the Harris slab, with X representing (as in “Xmas,” or the Chi-rho page of the Book of Kells) Christ… who is, in theological terms, also “the variable par excellence.”

Kubrick’s
monolith

Harris’s
slab

For a more serious discussion of deconstruction and Christian theology, see

Walker Percy’s Semiotic.

Saturday, May 24, 2003

Saturday May 24, 2003

Filed under: General — m759 @ 1:06 AM

Mental Health Month, Day 24:

The Sacred Day of
Kali, the Dark Lady

On this day, Gypsies from all over Europe gather in Provence for the sacred day of St. Sarah, also known as Kali.

Various representations of Kali exist; there is a novel about the ways men have pictured her:

From the prologue to
The Dark Lady,

 by Mike Resnick.

She was old when the earth was young.

She stood atop Cemetery Ridge when Pickett made his charge, and she was there when the six hundred rode into the Valley of Death.  She was at Pompeii when Mount Vesuvius blew, and she was in the forests of Siberia when the comet hit.  She hunted elephant with Selous and buffalo with Cody, and she was there the night the high wire broke beneath the Flying Wallendas.  She was at the fall of Troy and the Little Bighorn, and she watched Manolete and Dominguez face the brave bulls in the bloodstained arenas of Madrid….

She has no name, no past, no present, no future.  She wears only black, and though she has been seen by many men, she is known to only a handful of them.  You’ll see her — if you see her at all — just after you’ve taken your last breath.  Then, before you exhale for the final time, she’ll appear, silent and sad-eyed, and beckon to you.

She is the Dark Lady, and this is her story.

The above is one of the best descriptions of Kali I know of in literature; another is in a short story by Fritz Leiber, “Damnation Morning.”   It is not coincidental that one collection of Leiber’s writings is called “Dark Ladies.”

My journal note “Biblical Proportions” was in part inspired by Leiber.

Frank Sinatra may have pictured her as Ava Gardner.  I think I saw her the night Sinatra died… hence my entries of March 31 and April 2, 2003. 

It is perhaps not irrelevant that Kali is, among other things, a mother goddess, and that my entry “Raiders of the Lost Matrix” of May 20 deals with this concept and with the number 24.

The above religious symbol (see “Damnation Morning“) pictures both the axes of symmetry of the square¹ and a pattern with intriguing combinatorial properties².  It also is the basis of a puzzle³ I purchased on August 29, 1997 — Judgment Day in Terminator 2.  Linda Hamilton as Sarah Connor in that film is an excellent representation of the Dark Lady, both as mother figure and as Death Goddess.

 
Sarah Connor

Background music: “Bit by bit…” — Stephen Sondheim… See Sondheim and the Judgment Day puzzle in my entry of May 20. The Lottery Covenant.

¹ A. W. Joshi, Elements of Group Theory for Physicists, Third Edition, Wiley, 1982, p. 5

² V. K. Balakrishnan, Combinatorics, McGraw-Hill, 1995, p. 180

³ The Izzi Puzzle

Monday, December 16, 2002

Monday December 16, 2002

Filed under: General,Geometry — m759 @ 10:00 PM

Rebecca Goldstein
at Heaven’s Gate

This entry is in gratitude for Rebecca Goldstein’s
excellent essay
in The New York Times of December 16, 2002.

She talks about the perennial conflict between two theories of truth that Richard Trudeau called the “story theory” and the “diamond theory.” My entry of December 13, 2002, “Rhyme Scheme,” links the word “real” to an article in the Stanford Encyclopedia of Philosophy that contains the following:

“According to a platonist about arithmetic, the truth of the sentence ‘7 is prime’ entails the existence of an abstract object, the number 7. This object is abstract because it has no spatial or temporal location, and is causally inert. A platonic realist about arithmetic will say that the number 7 exists and instantiates the property of being prime independently of anyone’s beliefs, linguistic practices, conceptual schemes, and so on. A certain kind of nominalist rejects the existence claim which the platonic realist makes: there are no abstract objects, so sentences such as ‘7 is prime’ are false…”

This discussion of “sevenness,” along with the discussion of “eightness” in my December 14, 2002, note on Bach, suggest that I supply a transcription of a note in my paper journal from 2001 that deals with these matters.

From a paper journal note of October 5, 2001:

The 2001 Silver Cup Award
for Realism in Mathematics
goes to…
Glynis Johns, star of
The Sword and the Rose,
Shake Hands with the Devil, and
No Highway in the Sky.

Glynis Johns is 78 today.

“Seven is heaven,
Eight is a gate.”
— from
Dealing with Memory Changes
as You Grow Older
,
by Kathleen Gose and Gloria Levi

“There is no highway in the sky.”
— Quotation attributed to Albert Einstein.
(See
Gotthard Günther’s website
“Achilles and the Tortoise, Part 2”.)

“Don’t give up until you
Drink from the silver cup
And ride that highway in the sky.”
America, 1974

See also page 78 of
Realism in Mathematics
(on Gödel’s Platonism)
by Penelope Maddy,
Clarendon Press, Oxford, 1990
(reprinted, 2000).

Added 12/17/02: See also
the portrait of Rebecca Goldstein in
Hadassah Magazine
 Volume
78
Number 10
(June/July 1997).

For more on the Jewish propensity to
assign mystical significance to numbers, see
Rabbi Zwerin’s Kol Nidre Sermon.

For the significance of “seven” in Judaism, see
Zayin: The Woman of Valor.
For the significance of “eight” in Judaism, see
Chet: The Life Dynamic.

For the cabalistic significance of
“Seven is heaven, Eight is a gate,”
note that Zayin, Seven, signifies
“seven chambers of Paradise”
and that Chet, Eight, signifies
the “gateway to infinity.”

For the significance of the date 12.17, see
Tet: The Concealed Good.

Tuesday, December 3, 2002

Tuesday December 3, 2002

Filed under: General,Geometry — Tags: — m759 @ 1:45 PM

Symmetry, Invariance, and Objectivity

The book Invariances: The Structure of the Objective World, by Harvard philosopher Robert Nozick, was reviewed in the New York Review of Books issue dated June 27, 2002.

On page 76 of this book, published by Harvard University Press in 2001, Nozick writes:

"An objective fact is invariant under various transformations. It is this invariance that constitutes something as an objective truth…."

Compare this with Hermann Weyl's definition in his classic Symmetry (Princeton University Press, 1952, page 132):

"Objectivity means invariance with respect to the group of automorphisms."

It has finally been pointed out in the Review, by a professor at Göttingen, that Nozick's book should have included Weyl's definition.

I pointed this out on June 10, 2002.

For a survey of material on this topic, see this Google search on "nozick invariances weyl" (without the quotes).

Nozick's omitting Weyl's definition amounts to blatant plagiarism of an idea.

Of course, including Weyl's definition would have required Nozick to discuss seriously the concept of groups of automorphisms. Such a discussion would not have been compatible with the current level of philosophical discussion at Harvard, which apparently seldom rises above the level of cocktail-party chatter.

A similarly low level of discourse is found in the essay "Geometrical Creatures," by Jim Holt, also in the issue of the New York Review of Books dated December 19, 2002. Holt at least writes well, and includes (if only in parentheses) a remark that is highly relevant to the Nozick-vs.-Weyl discussion of invariance elsewhere in the Review:

"All the geometries ever imagined turn out to be variations on a single theme: how certain properties of a space remain unchanged when its points get rearranged."  (p. 69)

This is perhaps suitable for intelligent but ignorant adolescents; even they, however, should be given some historical background. Holt is talking here about the Erlangen program of Felix Christian Klein, and should say so. For a more sophisticated and nuanced discussion, see this web page on Klein's Erlangen Program, apparently by Jean-Pierre Marquis, Département de Philosophie, Université de Montréal. For more by Marquis, see my later entry for today, "From the Erlangen Program to Category Theory."

Friday, November 29, 2002

Friday November 29, 2002

Filed under: General,Geometry — Tags: — m759 @ 1:06 PM

A Logocentric Archetype

Today we examine the relativist, nominalist, leftist, nihilist, despairing, depressing, absurd, and abominable work of Samuel Beckett, darling of the postmodernists.

One lens through which to view Beckett is an essay by Jennifer Martin, "Beckettian Drama as Protest: A Postmodern Examination of the 'Delogocentering' of Language." Martin begins her essay with two quotations: one from the contemptible French twerp Jacques Derrida, and one from Beckett's masterpiece of stupidity, Molloy. For a logocentric deconstruction of Derrida, see my note, "The Shining of May 29," which demonstrates how Derrida attempts to convert a rather important mathematical result to his brand of nauseating and pretentious nonsense, and of course gets it wrong. For a logocentric deconstruction of Molloy, consider the following passage:

"I took advantage of being at the seaside to lay in a store of sucking-stones. They were pebbles but I call them stones…. I distributed them equally among my four pockets, and sucked them turn and turn about. This raised a problem which I first solved in the following way. I had say sixteen stones, four in each of my four pockets these being the two pockets of my trousers and the two pockets of my greatcoat. Taking a stone from the right pocket of my greatcoat, and putting it in my mouth, I replaced it in the right pocket of my greatcoat by a stone from the right pocket of my trousers, which I replaced by a stone from the left pocket of my trousers, which I replaced by a stone from the left pocket of my greatcoat, which I replaced by the stone which was in my mouth, as soon as I had finished sucking it. Thus there were still four stones in each of my four pockets, but not quite the same stones….But this solution did not satisfy me fully. For it did not escape me that, by an extraordinary hazard, the four stones circulating thus might always be the same four."

Beckett is describing, in great detail, how a damned moron might approach the extraordinarily beautiful mathematical discipline known as group theory, founded by the French anticleric and leftist Evariste Galois. Disciples of Derrida may play at mimicking the politics of Galois, but will never come close to imitating his genius. For a worthwhile discussion of permutation groups acting on a set of 16 elements, see R. D. Carmichael's masterly work, Introduction to the Theory of Groups of Finite Order, Ginn, Boston, 1937, reprinted by Dover, New York, 1956.

There are at least two ways of approaching permutations on 16 elements in what Pascal calls "l'esprit géométrique." My website Diamond Theory discusses the action of the affine group in a four-dimensional finite geometry of 16 points. For a four-dimensional euclidean hypercube, or tesseract, with 16 vertices, see the highly logocentric movable illustration by Harry J. Smith. The concept of a tesseract was made famous, though seen through a glass darkly, by the Christian writer Madeleine L'Engle in her novel for children and young adults, A Wrinkle in Tme.

This tesseract may serve as an archetype for what Pascal, Simone Weil (see my earlier notes), Harry J. Smith, and Madeleine L'Engle might, borrowing their enemies' language, call their "logocentric" philosophy.

For a more literary antidote to postmodernist nihilism, see Archetypal Theory and Criticism, by Glen R. Gill.

For a discussion of the full range of meaning of the word "logos," which has rational as well as religious connotations, click here.

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