Throughout Schwartz's poetry a question of belief is central. He thought we could not live without an interpretation of the whole of life, and that modern social orders were inevitably deficient in satisfying this need. He wrote studies and poetry explicitly concerned with the decline of Christian belief and the impossibility of any belief whatsoever. He read Rimbaud's ''Season in Hell,'' Valery's ''Cimetiere Marin,'' Arnold's ''Dover Beach,'' Hardy's ''Oxen,'' Stevens' ''Sunday Morning'' as poems forged in just such a dilemma. His own preferred poem, ''Starlight Like Intuition Pierced the Twelve,'' continued this argument.
See also Log24 posts tagged Central Myth, and the following image:
"Something invisible and pernicious seems to be preventing
even good literary men from either reaching for books with
women’s names on the spines, or from summoning women’s
books to mind when asked to list their influences. I wonder
what such a thing could possibly be."
"It seems no coincidence that all of these titles
are written by women, for a primary angle of Gunpowder Milkshake is one that tries its best
to promote 'feminism'… in a Quentin Tarantino
sort of way."
There are geometries in which lengths are not invariant
because they are not relevant — for instance, projective
geometry, finite geometry, and of course finite projective
geometry.
"I am not a scholar. I am not in the least an intellectual, which is not to say that when I hear the word 'intellectual' I reach for my gun, but only to say that I do not think in abstracts. During the years when I was an undergraduate at Berkeley I tried, with a kind of hopeless late-adolescent energy, to buy some temporary visa into the world of ideas, to forge for myself a mind that could deal with the abstract.
All I knew then was what I wasn’t, and it took me some years to discover what I was.
In short I tried to think. I failed. My attention veered inexorably back to the specific, to the tangible, to what was generally considered, by everyone I knew then and for that matter have known since, the peripheral. I would try to contemplate the Hegelian dialectic and would find myself concentrating instead on a flowering pear tree outside my window and the particular way the petals fell on my floor. I would try to read linguistic theory and would find myself wondering instead if the lights were on in the Bevatron up the hill. When I say that I was wondering if the lights were on in the Bevatron you might immediately suspect, if you deal in ideas at all, that I was registering the Bevatron as a political symbol, thinking in shorthand about the military-industrial complex and its role in the university community, but you would be wrong. I was only wondering if the lights were on in the Bevatron, and how they looked. A physical fact.
I had trouble graduating from Berkeley, not because of this inability to deal with ideas—I was majoring in English, and I could locate the house-and-garden imagery in The Portrait of a Lady as well as the next person, 'imagery' being by definition the kind of specific that got my attention—but simply because I had neglected to take a course in Milton. For reasons which now sound baroque I needed a degree by the end of that summer, and the English department finally agreed, if I would come down from Sacramento every Friday and talk about the cosmology of Paradise Lost , to certify me proficient in Milton. I did this. Some Fridays I took the Greyhound bus, other Fridays I caught the Southern Pacific’s City of San Francisco on the last leg of its transcontinental trip. I can no longer tell you whether Milton put the sun or the earth at the center of his universe in Paradise Lost , the central question of at least one century and a topic about which I wrote ten thousand words that summer, but I can still recall the exact rancidity of the butter in the City of San Francisco’s dining car, and the way the tinted windows on the Greyhound bus cast the oil refineries around Carquinez Strait into a grayed and obscurely sinister light. In short my attention was always on the periphery, on what I could see and taste and touch, on the butter, and the Greyhound bus. During those years I was traveling on what I knew to be a very shaky passport, forged papers: I knew that I was no legitimate resident in any world of ideas. I knew I couldn’t think. All I knew then was what I couldn’t do. All I knew then was what I wasn’t, and it took me some years to discover what I was."
"I knew that I was no legitimate resident in any world of ideas."
— Joan Didion, December 5, 1976
"In the 1988 interview with Scripps Howard, Mr. Poynter mused
about the device he wanted to invent for his own tombstone.
'When you walked up to it,' he said, 'you’d activate
an electronic voice. And it would say, "Come on down."’”
The authors of the above article have perhaps more respect for
marble columns than do Scarlett, Madonna, and the current
pandering leadership of the American Mathematical Society.
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"This is the purpose of being alive, to find someone
who sharpens the corners of the world for you and
allows you to peer into the souls of your fellow man!"
"Although the use of their work for good versus evil
was the concern for three of the main protagonists,
for one character – Dr Tim Horton – the bigger question
was one of academic and intellectual morality."
See as well this journal on the above article's date — November 20, 2012.
If we read the above "art" as a scythe blade to which the "signature" —
Snaith ("the crooked handle or shaft of a scythe") — is attached,
an image of the late art critic Robert Hughes comes to mind:
That image of Hughes appeared here in a post of June 17, 2015 —
"Slow Art, Continued" — that also referenced the Kummer Threefold
paper above.
"First, it must be possible in principle to arrange and organize
the chaos of our many individual sensory images by tracing
the connections that hold among them. This Kant called
the synthetic unity of the sensory manifold.
Second, it must be possible in principle for a single subject
to perform this organization by discovering the connections
among perceived images. This is satisfied by what Kant called
the transcendental unity of apperception."
"In any case it was quite sufficient for me
if I could peg proofs upon propositions
the validity of which did not seem to me to be dubious.
For example, I remember that an uncle told me
the Pythagorean theorem before the holy geometry booklet
had come into my hands. After much effort I succeeded
in 'proving' this theorem on the basis of the similarity
of triangles; in doing so it seemed to me 'evident' that
the relations of the sides of the right-angled triangles
would have to be completely determined by one of the
acute angles. Only something which did not in similar fashion
seem to be 'evident' appeared to me to be in need of any proof
at all. Also, the objects with which geometry deals seemed to
be of no different type than the objects of sensory perception,
'which can be seen and touched.' This primitive idea, which
probably also lies at the bottom of the well-known Kantian
problematic concerning the possibility of 'synthetic judgments
a priori' rests obviously upon the fact that the relation of
geometrical concepts to objects of direct experience
(rigid rod, finite interval, etc.) was unconsciously present."
"Einstein, unfortunately, left no … record of his childhood proof.
In his Saturday Review essay, he described it in general terms,
mentioning only that it relied on 'the similarity of triangles.'
The consensus among Einstein’s biographers is that he probably
discovered, on his own, a standard textbook proof in which similar
triangles (meaning triangles that are like photographic reductions
or enlargements of one another) do indeed play a starring role.
Walter Isaacson, Jeremy Bernstein, and Banesh Hoffman all come
to this deflating conclusion, and each of them describes the steps
that Einstein would have followed as he unwittingly reinvented
a well-known proof."
Schroeder presents an elegant and memorable proof. He attributes
the proof to Einstein, citing purely hearsay evidence in a footnote.
The only other evidence for Einstein's connection with the proof
is his 1949 Saturday Review remarks. If Einstein did come up with
the proof at age 11 and discuss it with others later, as Schroeder
claims, it seems he might have felt a certain pride and been more
specific in 1949, instead of merely mentioning the theorem in passing
before he discussed Kantian philosophy relating concepts to objects.
"The subject of K -theory takes its name from a 1957 construction of Alexander Grothendieck which appeared in the Grothendieck–Riemann–Roch theorem, his generalization of
Hirzebruch's theorem.[2] Let X be a smooth algebraic variety.
To each vector bundle on X , Grothendieck associates an invariant, its class .
The set of all classes on X was called K(X) from the German Klasse ."
"You and I are separated by a thin piece of silk
which neither the strongest man could tear,
nor the sharpest tool could pierce.
Nothing can cross this membrane that divides us
except art, music, poetry and love."
“The great Confucius guided China spiritually for over 2,000 years.
The main doctrine is ' 仁 ' pronounced 'ren', meaning two people,
i.e., human relationship. Modern science has been highly competitive.
I think an injection of the human element will make our subject more
healthy and enjoyable."
Thus, we can conclude that several different forms of
the character ren , were in existence during the
Warring States period. This shows that etymological analyses
focusing exclusively on the combination of 人 and 二 are inadequate.
It should also serve as a warning against “character fetishization,” or giving “exaggerated status to Chinese characters in the interpretation
of Chinese language, thought, and culture.” 46
46 Edward McDonald 2009, p. 1194.
McDonald, Edward. 2009. “Getting over the Walls of
Discourse: 'Character Fetishization' in Chinese Studies.” The Journal of Asian Studies 68 (4): 1189 – 1213.
人 + 二 = 仁 (Rén)
man on left two on right,
the relationship between two human beings,
means co-humanity. Originally the character
was just written as丨二 [citation needed]
representing yin yang,
the vertical line is yang
(bright, traditionally masculine, heaven, odd numbers),
the two horizontal lines are yin
(dark, traditionally feminine, earth, even numbers),
仁 is the core of everything.
"The core of everything" . . . Citation needed ?
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Ardila: … in a nutshell, what combinatorics is about is just
the study of possibilities and how do you organize them,
given that there’s too many of them to list them.
Strogatz: So, I love it. Combinatorics is not just
the art of the possible, but the enumeration of the possible,
the counting of the possible and the organizing of the possible.
Strogatz: It’s such a poetic image, actually: the space of possibilities.
This journal on the podcast date, March 29, 2021 —
A more precise approach to the space of possibilities:
"He had with him a small red book of Mao's poems, and as he talked he squared it on the table, aligned it with the table edge first vertically and then horizontally. To understand who Michael Laski is you must have a feeling for that kind of compulsion."
— Joan Didion in the Saturday Evening Post,
Nov. 18, 1967 (reprinted in Slouching Towards Bethlehem)
"Or were you," I said.
He said nothing.
"Raised a Catholic," I said.
He aligned a square crystal paperweight with the edge of his desk blotter.
— Joan Didion in The Last Thing He Wanted, Knopf, 1996
"It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….
Plato clearly loved them both, both mathematics and poetry. But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry. Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto. Let none ignorant of geometry enter. This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge. Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason. Mathematics is the threshold we cross to pass into the ideal, the truly real."
"In a career that took him to Hong Kong and Taiwan,
as well as a succession of Ivy League universities,
Professor Yu often returned to the theme that China’s
long traditions could be a wellspring, not an enemy,
of enlightenment, individual dignity and democracy."
"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)
What is "the next world"? It might be the Underworld….
The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation and art all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254) If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist. Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.
"If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit. From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.
Or, to take a more up-to-date example…."
"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
– The Club Dumas , 1993
"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
– Robert Plant, 1971
The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.
An example of the universal— or, according to Krauss,
a "staircase" to the universal— is the ninefold square:
"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."
" A Harvard Medical School professor emeritus in psychiatry,
Dr. Hobson told the Globe in 2011 that he didn’t 'feel bad about
taking on Sigmund Freud. I think Sigmund Freud has become
politically correct. Psychoanalysis has become the bible, and
I think that’s crazy.'
He also forcefully set aside the theories of Carl Jung, the Swiss
psychiatrist who analyzed dreams and saw them as important
messages sent from the psyche.
'If you’re a pure scientist, Jung is just deadly,' Dr. Hobson said
in [a] 2005 interview. 'The collective unconscious, the anima …
these are literary constructs. You can’t do any science on that
kind of stuff.' ”
"Bowden applied what he viewed as the lessons of the battlefield
to the football field. While bedridden with rheumatic fever at age 13,
he had listened to radio broadcasts telling of World War II battles,
and he later studied the campaigns of Patton, MacArthur and
Germany’s Erwin Rommel.
'They all demonstrate discipline,' Bowden once said, 'and that you
need reserves so that if you’re getting annihilated on one front, you
can attack somewhere else.' ” — Richard Goldstein
Amen.
See as well "Geometry Battlefield" in this morning's previous post.
its relationship to feminism, multiculturalism and
the counterculture, as well as its (now questionable)
cultural appropriation and even its underlying debt
to Minimalism (the use of repetition and the grid)."
This is from a Roberta Smith piece yesterday morning
in The New York Times print version:
"A version of this article appears in print on Aug. 6, 2021,
Section C, Page 6 of the New York edition with the headline:
Celebrating a Riotous Decor That Keeps Eyes Moving."
A play by George Bernard Shaw is the source of the book title at
the end of the previous post — "Music is the brandy of the damned ."
This suggests a corresponding song title . . .
An Ordinary Evening in New Haven (iv)
Stanza: 61; Line Number: 7
They only know a savage assuagement cries
Stanza: 62; Line Number: 8
With a savage voice; and in that cry they hear
Stanza: 64; Line Number: 10
In a savage and subtle and simple harmony,
Credences of Summer (vii)
Stanza: 101; Line Number: 11
The object, grips it in savage scrutiny,
Examination of the Hero in a Time of War (ii)
Stanza: 26; Line Number: 12
And rainbow sortilege, the savage weapon
Exposition of the Contents of a Cab (OP)
Line Number: 12
And savage blooms;
From the Journal of Crispin (II) (OP)
Stanza: 114; Line Number: 20
Into a savage color he goes on.
Gubbinal
Line Number: 9
That savage of fire,
Less and Less Human, O Savage Spirit
Title
Less and Less Human, O Savage Spirit
Page from a Tale
Line Number: 20
They looked back at Hans’ look with savage faces.
Sunday Morning (vii)
Stanza: 95; Line Number: 5
Naked among them, like a savage source.
The Comedian as the Letter C, ii: Concerning the Thunderstorms of Yucatan
Stanza: 14; Line Number: 14
Into a savage color he went on.
The Man with the Blue Guitar (iii)
Stanza: 29; Line Number: 9
To bang it from a savage blue,
The Pediment of Appearance
Line Number: 10
The savage transparence. They go crying
The World as Meditation
Line Number: 6
Whose mere savage presence awakens the world in which she dwells.
_________________________________________________________________________
Online Concordance to Wallace Stevens’s Poetry
Filed under: General — Tags: Fields — m759 @ 2:10 am
Hans Freudenthal in 1962 on the axiomatic approach to geometry
of Fano and Hilbert —
"The bond with reality is cut."
Some philosophical background —
For Weyl's "few isolated relational concepts," see (for instance) Projective Geometries over Finite Fields , by
J. W. P. Hirschfeld (first published by Oxford University Press in 1979).
Weyl in 1932 —
Mathematics is the science of the infinite , its goal the symbolic comprehension of the infinite with human, that is finite, means. It is the great achievement of the Greeks to have made the contrast between the finite and the infinite fruitful for the cognition of reality. The intuitive feeling for, the quiet unquestioning acceptance of the infinite, is peculiar to the Orient; but it remains merely an abstract consciousness, which is indifferent to the concrete manifold of reality and leaves it unformed, unpenetrated. Coming from the Orient, the religious intuition of the infinite, the apeiron , takes hold of the Greek soul in the Dionysiac-Orphic epoch which precedes the Persian wars. Also in this respect the Persian wars mark the separation of the Occident from the Orient. This tension between the finite and the infinite and its conciliation now become the driving motive of Greek investigation; but every synthesis, when it has hardly been accomplished, causes the old contrast to break through anew and in a deepened sense. In this way it determines the history of theoretical cognition to our day.
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