Log24

Tuesday, September 10, 2019

The Wertham Memorandum

Filed under: General — m759 @ 3:38 AM

For Harlan Kane

From this  journal on Feb. 5, 2009:

"In the garden of Adding
live Even and Odd
And the song of love's recision
is the music of the spheres."

— The Midrash Jazz Quartet in 
City of God , by E. L. Doctorow (2000).

From this  journal on the date of
the above post by Gavaler:

Sunday, July 26, 2015

Midrash Jazz for Kristen

Filed under: General — Tags: — m759 @ 12:51 AM

(Title suggested by the Midrash Jazz Quartet
in E. L. Doctorow's novel City of God )

Friday, January 23, 2015

The Consolations of Form

Filed under: General — m759 @ 12:00 PM

"In the garden of Adding
 Live Even and Odd…."

– The Midrash Jazz Quartet
    in the novel City of God
    by E. L. Doctorow (2000)

From a search in this journal
for "Against Dryness":

See also the previous three posts.

Thursday, February 5, 2009

Thursday February 5, 2009

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

Through the
Looking Glass:

A Sort of Eternity

From the new president's inaugural address:

"… in the words of Scripture, the time has come to set aside childish things."

The words of Scripture:

9 For we know in part, and we prophesy in part.
10 But when that which is perfect is come, then that which is in part shall be done away.
11 When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.
12 For now we see through a glass, darkly, but then face to face: now I know in part; but then shall I know even as also I am known.

 

First Corinthians 13

"through a glass"

[di’ esoptrou].
By means of
a mirror [esoptron]
.

Childish things:

Froebel's third gift, the eightfold cube
© 2005 The Institute for Figuring
 
Photo by Norman Brosterman
fom the Inventing Kindergarten
exhibit at The Institute for Figuring
(co-founded by Margaret Wertheim)

 

Not-so-childish:

Three planes through
the center of a cube
that split it into
eight subcubes:
Cube subdivided into 8 subcubes by planes through the center
Through a glass, darkly:

A group of 8 transformations is
generated by affine reflections
in the above three planes.
Shown below is a pattern on
the faces of the 2x2x2 cube
 that is symmetric under one of
these 8 transformations–
a 180-degree rotation:

Design Cube 2x2x2 for demonstrating Galois geometry

(Click on image
for further details.)

But then face to face:

A larger group of 1344,
rather than 8, transformations
of the 2x2x2 cube
is generated by a different
sort of affine reflections– not
in the infinite Euclidean 3-space
over the field of real numbers,
but rather in the finite Galois
3-space over the 2-element field.

Galois age fifteen, drawn by a classmate.

Galois age fifteen,
drawn by a classmate.

These transformations
in the Galois space with
finitely many points
produce a set of 168 patterns
like the one above.
For each such pattern,
at least one nontrivial
transformation in the group of 8
described above is a symmetry
in the Euclidean space with
infinitely many points.

For some generalizations,
see Galois Geometry.

Related material:

The central aim of Western religion–

 

"Each of us has something to offer the Creator...
the bridging of
 masculine and feminine,
 life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist (1998)

The central aim of Western philosophy–

 Dualities of Pythagoras
 as reconstructed by Aristotle:
  Limited Unlimited
  Odd Even
  Male Female
  Light Dark
  Straight Curved
  ... and so on ....

"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, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy."

— Jamie James in The Music of the Spheres (1993)

"In the garden of Adding
live Even and Odd…
And the song of love's recision
is the music of the spheres."

— The Midrash Jazz Quartet in City of God, by E. L. Doctorow (2000)

A quotation today at art critic Carol Kino's website, slightly expanded:

"Art inherited from the old religion
the power of consecrating things
and endowing them with
a sort of eternity;
museums are our temples,
and the objects displayed in them
are beyond history."

— Octavio Paz,"Seeing and Using: Art and Craftsmanship," in Convergences: Essays on Art and Literature (New York: Harcourt Brace Jovanovich 1987), 52 

From Brian O'Doherty's 1976 Artforum essays– not on museums, but rather on gallery space:

"Inside the White Cube"

"We have now reached
a point where we see
not the art but the space first….
An image comes to mind
of a white, ideal space
that, more than any single picture,
may be the archetypal image
of 20th-century art."

http://www.log24.com/log/pix09/090205-cube2x2x2.gif

"Space: what you
damn well have to see."

— James Joyce, Ulysses  

Saturday, January 6, 2007

Saturday January 6, 2007

Filed under: General,Geometry — m759 @ 10:31 AM
An Epiphany
for the Birthday
of E. L. Doctorow,
Author of
City of God

(Doctorow wrote about
 New York. A city more
  closely associated with
 God is Jerusalem.)

On the morning of January 2 this year, inspired by Sambin’s “basic picture,” I considered an entry dealing with Galois lattices (pdf).  This train of thought was halted by news of the death earlier that morning of Teddy Kollek, 95, a founder of the Israeli intelligence service and six-term mayor of Jerusalem. (This led later to the entry “Damnation Morning“– a reference to the Fritz Leiber short story.)

This morning’s entry reboards the Galois train of thought.

Here are some relevant links:

Galois Connections (a French weblog entry providing an brief overview of Galois theory and an introduction to the use of Galois lattices in “formal concept analysis“)

Ontology (an introduction to formal concept analysis linked to on 3/31/06)

One motive for resuming consideration of Galois lattices today is to honor the late A. Richard Newton, a pioneer in engineering design who died at 55– also on Tuesday, Jan. 2, the date of Kollek’s death.  Today’s New York Times obituary for Newton says that “most recently, Professor Newton championed the study of synthetic biology.”

A check of syntheticbiology.org leads to a web page on– again– ontology.

For the relationship between ontology (in the semantic-web sense) and Galois lattices, see (for instance)

Knowledge Organisation and Information Retrieval Using Galois Lattices” (ps) and its references.

An epiphany within all this that Doctorow might appreciate is the following from Wikipedia, found by following a link to “upper ontology” in the syntheticbiology.org ontology page:

  • There is no self-evident way of dividing the world up into concepts.
  • There is no neutral ground that can serve as a means of translating between specialized (lower) ontologies.
  • Human language itself is already an arbitrary approximation of just one among many possible conceptual maps. To draw any necessary correlation between English words and any number of intellectual concepts we might like to represent in our ontologies is just asking for trouble.

Related material:

The intellectual concepts
mentioned by Richard Powers
at the end of tomorrow’s
New York Times Book Review.
(See the links on these concepts
in yesterday’s “Goldberg Variation.”)

See also Old School Tie.

Wednesday, September 13, 2006

Wednesday September 13, 2006

Filed under: General — m759 @ 9:28 PM

ART WARS continued:

The Krauss Cross

The image “http://www.log24.com/log/pix06A/060913-Art.jpg” cannot be displayed, because it contains errors.

Rosalind Krauss in "Grids":

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

Or, to take a more up-to-date example, we could think about Ad Reinhardt who, despite his repeated insistence that 'Art is art,' ended up by painting a series of black nine-square grids in which the motif that inescapably emerges is a Greek cross.  There is no painter in the West who can be unaware of the symbolic power of the cruciform shape and the Pandora's box of spiritual reference that is opened once one uses it."

Rebecca Goldstein on
Mathematics and Narrative
:

"I don't write exclusively on Jewish themes or about Jewish characters. My collection of short stories, Strange Attractors, contained nine pieces, five of which were, to some degree, Jewish, and this ratio has provided me with a precise mathematical answer (for me, still the best kind of answer) to the question of whether I am a Jewish writer. I am five-ninths a Jewish writer."

Jacques Maritain,
October 1941
:

"The passion of Israel
today is taking on
more and more distinctly
the form of the Cross."

E. L. Doctorow,
City of God:

"In the garden of Adding,
Live Even and Odd."

Friday, January 6, 2006

Friday January 6, 2006

Filed under: General — Tags: — m759 @ 8:23 AM
Cross 
 
Today's birthday:
E. L. Doctorow, author of
City of God

"In the garden of Adding,
Live Even and Odd"
City of God

The image “http://www.log24.com/log/pix05B/051202-Cross.gif” cannot be displayed, because it contains errors.
Adapted from
Ad Reinhardt

"… I don't write exclusively on Jewish themes or about Jewish characters. My collection of short stories, Strange Attractors, contained nine pieces, five of which were, to some degree, Jewish, and this ratio has provided me with a precise mathematical answer (for me, still the best kind of answer) to the question of whether I am a Jewish writer. I am five-ninths a Jewish writer."
 
Rebecca Goldstein,
"Against Logic"
 
For related remarks,
click on the cross.

Sunday, May 1, 2005

Sunday May 1, 2005

Filed under: General — m759 @ 1:11 PM
Logos

Harvard’s Barry Mazur on
one mathematical style:

“It’s the barest, most Beckett-like vocabulary
that incorporates the theory and nothing else.”

Samuel Beckett, Quad (1981):

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

A Jungian on this six-line logo:

“They are the same six lines
that exist in the I Ching….
Now observe the square more closely:
four of the lines are of equal length,
the other two are longer….
For this reason symmetry
cannot be statically produced
and a dance results.”
 
— Marie-Louise von Franz,
Number and Time (1970),
Northwestern U. Press
paperback, 1979, p. 108

A related logo from
Columbia University’s
Department of Art History
and Archaeology
:

The image “http://www.log24.com/log/pix05/050501-ArtHist2.gif” cannot be displayed, because it contains errors.
 
Also from that department:

Rosalind Krauss,

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

Meyer Schapiro Professor
of Modern Art and Theory:

“There is no painter in the West
who can be unaware of
the symbolic power
of the cruciform shape
and the Pandora’s box
of spiritual reference
that is opened
once one uses it.”

“In the garden of Adding
live Even and Odd…”
— The Midrash Jazz Quartet in
City of God
, by E. L. Doctorow


THE GREEK CROSS

A cross in which all the arms
are the same length.

Here, for reference, is a Greek cross
within a nine-square grid:

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

 Related religious meditation for
    Doctorow’s “Garden of Adding”…

 4 + 5 = 9.

Types of Greek cross
illustrated in Wikipedia
under “cross“:

The image “http://www.log24.com/log/pix05/GrCross.gif” cannot be displayed, because it contains errors.

From designboom.com:

THE BAPTISMAL CROSS

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

is a cross with eight arms:
a Greek cross, which is superimposed
on a Greek ‘chi,’ the first letter
of the Greek word for ‘Christ.’
Since the number eight is symbolic
of rebirth or regeneration,
this cross is often used
as a baptismal cross.

Related material:

The image “http://www.log24.com/theory/images/Symm-axes.jpg” cannot be displayed, because it contains errors.

Fritz Leiber’s “spider”
or “double cross” logo.
See Why Me? and
A Shot at Redemption.

Happy Orthodox Easter.

Saturday, April 30, 2005

Saturday April 30, 2005

Filed under: General — m759 @ 9:00 PM
City of God

Kevin Baker in 2001 on
E. L. Doctorow’s City of God:

“…the nature of the cosmos
(Augustine’s City of God?)”

David Van Biema in Time Magazine
(May 2, 2005, p. 43)

The image “http://www.log24.com/log/pix05/050430-TIME.jpg” cannot be displayed, because it contains errors.

on Augustine’s City of God:

“A key concept in Augustine’s great
The City of God is that the Christian church
is superior and essentially alien

to its earthly surroundings.”


The image “http://www.log24.com/log/pix05/050430-Easter.jpg” cannot be displayed, because it contains errors.

 
  Click on the above for a rendition of
  Appalachian Spring.

This year’s April – Mathematics Awareness Month –
theme is “Mathematics and the Cosmos.”

For my own views on this theme as it applies
to education, see Wag the Dogma.

For some other views, see this year’s
Mathematics Awareness Month site.

One of the authors at that site,
which is mostly propaganda
for the religion of Scientism,
elsewhere quotes
an ignorant pedagogue:

“‘The discovery of non-Euclidean geometries
contradicted the “absolute truth” view
of the Platonists.'”

Sarah J. Greenwald,
   Associate Professor,
   Department of Mathematics
   Appalachian State University, Boone, NC

Damned nonsense.  See Math16.com.

Friday, April 29, 2005

Friday April 29, 2005

Filed under: General — m759 @ 10:10 AM
Midrash Jazz Quartet

The image “http://www.log24.com/log/pix05/050429-Music.jpg” cannot be displayed, because it contains errors.

Harvard's Barry Mazur likes to quote Aristotle's Metaphysics.  See 1, 2, 3.

Here, with an introductory remark by Martha Cooley, is more from the Metaphysics:

The central aim of Western religion —

"Each of us has something to offer the Creator...
the bridging of
                 masculine and feminine,
                      life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist (1998)

The central aim of Western philosophy —

                 Dualities of Pythagoras
              as reconstructed by Aristotle:
                 Limited     Unlimited
                     Odd     Even
                    Male     Female
                   Light     Dark
                Straight     Curved
                  ... and so on ....

"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, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy."
— Jamie James in The Music of the Spheres (1993)

"In the garden of Adding,
Live Even and Odd….
And the song of love's recision
is the music of the spheres."
— The Midrash Jazz Quartet in City of God, by E. L. Doctorow (2000)

Harvard University, Department of English:

The Morris Gray Lecture, a reading by E.L. Doctorow.
Wednesday, April 27, 6:00 PM

Thompson Room, The Barker Center

CANCELED

Today's birthday: Jerry Seinfeld.
Related material:
Is Nothing Sacred? and Symmetries.

Sunday, October 5, 2003

Sunday October 5, 2003

Filed under: General — Tags: — m759 @ 5:09 AM

At Mount Sinai:
Art Theory for Yom Kippur

From the New York Times of Sunday, October 5, 2003 (the day that Yom Kippur begins at sunset):

"Rabbi Ephraim Oshry, whose interpretations of religious law helped sustain Lithuanian Jews during Nazi occupation…. died on Sept. 28 at Mount Sinai Hospital in Manhattan. He was 89."

For a fictional portrait of Lithuanian Jews during Nazi occupation, see the E. L. Doctorow novel City of God.

For meditations on the spiritual in art, see the Rosalind Krauss essay "Grids."   As a memorial to Rabbi Oshry, here is a grid-based version of the Hebrew letter aleph:


Rabbi Oshry


Aleph

Click on the aleph for details.

"In the garden of Adding,
 Live Even and Odd…."   
— The Midrash Jazz Quartet in
       City of God, by E. L. Doctorow

Here are two meditations
on Even and Odd for Yom Kippur:

Meditation I

From Rosalind Krauss, "Grids":

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

Or, to take a more up-to-date example, we could think about Ad Reinhardt who, despite his repeated insistence that 'Art is art,' ended up by painting a series of black nine-square grids in which the motif that inescapably emerges is a Greek cross.  There is no painter in the West who can be unaware of the symbolic power of the cruciform shape and the Pandora's box of spiritual reference that is opened once one uses it."

Meditation II

Here, for reference, is a Greek cross
within a nine-square grid:

 Related religious meditation for
    Doctorow's "Garden of Adding"…

 4 + 5 = 9.

Monday, August 25, 2003

Monday August 25, 2003

Filed under: General — m759 @ 3:31 AM

Gates to the City

Today’s birthday:

On August 25, 1918, composer Leonard Bernstein was born.

From Winter’s Tale, Harcourt Brace (1983):

Four Gates to the City

By MARK HELPRIN

Every city has its gates, which need not be of stone. Nor need soldiers be upon them or watchers before them. At first, when cities were jewels in a dark and mysterious world, they tended to be round and they had protective walls. To enter, one had to pass through gates, the reward for which was shelter from the overwhelming forests and seas, the merciless and taxing expanse of greens, whites, and blues–wild and free–that stopped at the city walls.

In time the ramparts became higher and the gates more massive, until they simply disappeared and were replaced by barriers, subtler than stone, that girded every city like a crown and held in its spirit. Some claim that the barriers do not exist, and disparage them. Although they themselves can penetrate the new walls with no effort, their spirits (which, also, they claim do not exist) cannot, and are left like orphans around the periphery.

To enter a city intact it is necessary to pass through one of the new gates. They are far more difficult to find than their solid predecessors, for they are tests, mechanisms, devices, and implementations of justice. There once was a map, now long gone, one of the ancient charts upon which colorful animals sleep or rage. Those who saw it said that in its illuminations were figures and symbols of the gates. The east gate was that of acceptance of responsibility, the south gate that of the desire to explore, the west gate that of devotion to beauty, and the north gate that of selfless love. But they were not believed. It was said that a city with entryways like these could not exist, because it would be too wonderful. Those who decide such things decided that whoever had seen the map had only imagined it, and the entire matter was forgotten, treated as if it were a dream, and ignored. This, of course, freed it to live forever.

See also

Lenny’s Gate:

Fred Stein,
Central Park,
1945 

Thanks to Sonja Klein Fine Art
 for pointing out the Stein photo.

Monday, July 28, 2003

Monday July 28, 2003

Filed under: General — m759 @ 9:00 AM

City of God

Today's site music is

Nous Voici Dans La Ville.

The central aim of Western religion —

"Each of us has something to offer the Creator... 
the bridging of                  
masculine and feminine,                       
life and death. It's redemption.... 
nothing else matters." 
-- Martha Cooley in The Archivist (1998) 

The central aim of Western philosophy —

                 Dualities of Pythagoras 
                 as reconstructed by Aristotle: 

                 Limited     Unlimited                      
                 Odd         Even           
                 Male        Female                    
                 Light       Dark                 
                 Straight    Curved                   
                 ... and so on .... 

"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, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy."
— Jamie James in
   The Music of the Spheres (1993)

"In the garden of Adding,
Live Even and Odd….
And the song of love's recision
is the music of the spheres."
— The Midrash Jazz Quartet in
   City of God, by E. L. Doctorow (2000)

Today is the feast of St. Johann Sebastian Bach.

Monday, January 6, 2003

Monday January 6, 2003

Filed under: General — m759 @ 12:00 AM

Doctorow’s Epiphany

E. L. Doctorow is 72 today.

In the Garden of Adding…

The above is a phrase from The Midrash Jazz Quartet in Doctorow’s novel City of God.

Tonight’s site music is “Black Diamond.”

William T. Noon, S.J., Chapter 4 of Joyce and Aquinas, Yale University Press, 1957:

  A related epiphanic question, second only in interest to the question of the nature of epiphany, is how Joyce came by the term. The religious implications would have been obvious to Joyce: no Irish Catholic child could fail to hear of and to understand the name of the liturgical feast celebrated on January 6. But why does Joyce appropriate the term for his literary theory? Oliver St. John Gogarty (the prototype of the Buck Mulligan of Ulysses)… has this to say: “Probably Father Darlington had taught him, as an aside in his Latin class — for Joyce knew no Greek — that ‘Epiphany’ meant ‘a shining forth.'”

From Stanley Kubrick’s The Shining:

Danny Torrance: Is there something bad here?
Dick Hallorann: Well, you know, Doc, when something happens, you can leave a trace of itself behind. Say like, if someone burns toast. Well, maybe things that happen leave other kinds of traces behind. Not things that anyone can notice, but things that people who “shine” can see. Just like they can see things that haven’t happened yet. Well, sometimes they can see things that happened a long time ago. I think a lot of things happened right here in this particular hotel over the years. And not all of ’em was good.

From a website on author Willard Motley:

“Willard Motley’s last published novel is entitled, Let Noon Be Fair, and was actually published post-humously in 1966. The story line takes place in Motley’s adopted country of Mexico, in the fictional fishing village of Las Casas, which was based on Puerta [sic] Vallarta.”

See also “Shining Forth” and yesterday’s entry “Culinary Theology.”

 

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