“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.
“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.
Infolded:
“In the garden of Adding,
Live Even and Odd….”
— The Midrash Jazz Quartet in
City of God , by E. L. Doctorow
Perspectives:
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…."
Related philosophical reflections . . .
Waxing poetic . . .
"In the Garden of Adding live Even and Odd" — E. L. Doctorow
To wit:
1/2 + 1/3 = 5/6, since the LCM of 2 and 3 is 6.
See as well . . .
“… 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 |
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.
"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
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
Ainsi….
"In the garden of Adding,
Live Even and Odd"
— E. L. Doctorow
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 |
God was apparently not
available this week;
record producer Joel Dorn,
who died on Monday,
will have to do.
"… when you get the feel of it, and the record actually transports you back to that time, then it's a real explanation of what's going on… of what went on. And here I think you can– it's one thing to get the music, it's another thing to get the place and the people and the interaction. When it's really right, the audience is the fifth member of a quartet." —Joel Dorn
"Philosophers ponder the idea
of identity: what it is to
give something a name
on Monday and have it
respond to that name
on Friday."
—Bernard Holland in
The New York Times,
Monday, May 20, 1996
"Daddy's like
an old knight."
–Allison in "Meet Joe Black"
For Joe Black himself,
see the previous entry.
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.
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”…
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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