Infolded:
“In the garden of Adding,
Live Even and Odd….”
— The Midrash Jazz Quartet in
City of God , by E. L. Doctorow
Perspectives:
Infolded:
“In the garden of Adding,
Live Even and Odd….”
— The Midrash Jazz Quartet in
City of God , by E. L. Doctorow
Perspectives:
From "The Midrash Jazz Quartet Plays the Standards" —
“… and the song of love’s recision is the music of the spheres.”
— E. L. Doctorow, City of God
(Quoted here on Dec. 20, 2020.)
Related imagery from Log24 on January 4, 2023 —
The previous post linked to a review by David Ehrlich of the film
"Dog Years," starring Burt Reynolds. The review was dated April 26, 2017.
Also on that date . . .
This post from 2017 deals with the mathematics of "diamond theory,"
an approach to models of finite geometry.
Related philosophy —
The "diamond theory" of truth, as opposed to the "story theory."
(See Richard Trudeau, The Non-Euclidean Revolution.)
For those who prefer the story theory, there is, for instance,
the novel City of God by E. L. Doctorow —
"In the Garden of Adding
Live Even and Odd…."
“… and the song of love’s recision is the music of the spheres.”
— E. L. Doctorow, City of God
Doctorow’s remark was quoted here earlier, on February 5, 2009 —
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 — 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 — 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: “We have now reached “Space: what you — James Joyce, Ulysses |
“In the garden of Adding,
Live Even and Odd….”
— The Midrash Jazz Quartet in
City of God , by E. L. Doctorow
Related material — Schoolgirls and Six-Set Geometry.
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:
"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.
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:
“through a glass”—
[di’ esoptrou].
By means of
a mirror [esoptron].
Childish things:
Not-so-childish:
Three planes through
the center of a cube
that split it into
eight subcubes:
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:
(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.
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 — 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 — 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: “We have now reached “Space: what you — James Joyce, Ulysses |
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.
The Krauss Cross
"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."
"In the garden of Adding,
Live Even and Odd"
— City of God
Adapted from
Ad Reinhardt
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):
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:
Also from that department:
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
Here, for reference, is a Greek cross
within a nine-square grid:
Related religious meditation for
Doctorow's "Garden of Adding"…
Types of Greek cross
illustrated in Wikipedia
under "cross":
THE BAPTISMAL CROSS
Related material:
Fritz Leiber's "spider"
or "double cross" logo.
See Why Me? and
A Shot at Redemption.
Happy Orthodox Easter.
Kevin Baker in 2001 on
E. L. Doctorow's City of God:
David Van Biema in Time Magazine
(May 2, 2005, p. 43)
on Augustine's City of God:
This year's April –
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:
Damned nonsense. See Math16.com.
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:
• |
Today's birthday: Jerry Seinfeld.
Related material:
Is Nothing Sacred? and Symmetries.
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:
|
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”…
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 CityBy 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.
City of God
Today's site music is
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.
Doctorow’s Epiphany
E. L. Doctorow is 72 today.
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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