Rubik core:
Non- Rubik core:
Central structure from a Galois plane
(See image below.)
Sunday, June 4, 2023
The Galois Core
Comments Off on The Galois Core
Friday, August 12, 2022
Mathematical Games: The Common Core
“There comes a time when the learner has identified
the abstract content of a number of different games
and is practically crying out for some sort of picture
by means of which to represent that which has been
gleaned as the common core of the various activities.”
— Article at Zoltan Dienes’s website
This quote is from a Log24 post of Feb. 6, 2014,
The Representation of Minus One.
Comments Off on Mathematical Games: The Common Core
Monday, August 16, 2021
In a Nutshell: The Core of Everything
“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."
— Geometer Shiing-Shen Chern in a Wikipedia article
See the "ren" character in Wiktionary. See as well . . .
"The development of ren ( 仁 ) in early Chinese philosophy,"
By Robin Elliott Curtis, U. of B.C. Master's thesis, 2016 —
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.
Wikipedia article on Ren in Confucianism:
|
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 ?
Comments Off on In a Nutshell: The Core of Everything
Monday, August 17, 2020
The Silence at the Core
The title is a phrase by Robert Hughes from the previous post.
Comments Off on The Silence at the Core
Tuesday, April 2, 2019
The Core Experience
"It never occurred to me that someone could so explicitly reject
the core experience of something like Chartres."
— Christopher Alexander to Peter Eisenman, 1982
For a less dramatic core experience , see Hitchcock.
Comments Off on The Core Experience
Saturday, July 8, 2017
Monday, April 3, 2017
Friday, July 1, 2016
Transparent Core
"At the point of convergence the play of similarities and differences
cancels itself out in order that identity alone may shine forth.
The illusion of motionlessness, the play of mirrors of the one:
identity is completely empty; it is a crystallization and
in its transparent core the movement of analogy begins all over
once again." — The Monkey Grammarian by Octavio Paz,
translated by Helen Lane
A more specific "transparent core" —
See all references to this figure
in this journal.
For a more specific "monkey grammarian,"
see W. Tecumseh Fitch in this journal.
Comments Off on Transparent Core
Sunday, June 26, 2016
Common Core versus Central Structure
Rubik's Cube Core Assembly — Swarthmore Cube Project, 2008 —
"Children of the Common Core" —
There is also a central structure within Solomon's Cube —
For a more elaborate entertainment along these lines, see the recent film
"Midnight Special" —
Comments Off on Common Core versus Central Structure
Saturday, May 11, 2013
Invariant Core
The title is from today's noon post, Core.
It also appears, quoted from Popovič, in Susan Bassnett's
Translation Studies (third edition, Routledge, 2002)—
"It is an established fact in Translation Studies that if a dozen
translators tackle the same poem, they will produce a dozen
different versions. And yet somewhere in those dozen versions there
will be what Popovič calls the ‘invariant core’ of the original poem.
This invariant core, he claims, is represented by stable, basic and
constant semantic elements in the text, whose existence can be
proved by experimental semantic condensation. Transformations, or
variants, are those changes which do not modify the core of meaning
but influence the expressive form. In short, the invariant can be
defined as that which exists in common between all existing
translations of a single work. So the invariant is part of a dynamic
relationship and should not be confused with speculative arguments
about the ‘nature’, the ‘spirit’ or ‘soul’ of the text; the ‘indefinable
quality’ that translators are rarely supposed to be able to capture."
"A writer hopes to leave behind a work no one forgets…."
— Song sung on NBC's Smash tonight
Fulsere vere candidi mihi soles….
— André Weil, The Apprenticeship of a Mathematician
nam unguentum dabo, quod meae puellae
donarunt Veneres Cupidinesque….
— Catullus, quoted in Bassnett's Translation Studies
Comments Off on Invariant Core
Tuesday, March 19, 2024
Belgian Puzzle Art
From the Belgian artist of the March 25 New Yorker cover —
“There comes a time when the learner has identified
the abstract content of a number of different games
and is practically crying out for some sort of picture
by means of which to represent that which has been
gleaned as the common core of the various activities.”
— Article at Zoltan Dienes’s website
Comments Off on Belgian Puzzle Art
Wednesday, February 14, 2024
Live Poet Society
RHYMES for Bergen Feb. 13-14, 2024
one fun
two crew
three see
four core
five live
six tricks
seven heaven
eight gate
nine line
core line crew
see live heaven
gate fun tricks
This post was suggested by the
"Night of Lunacy" post of May 5, 2013.
Comments Off on Live Poet Society
Saturday, August 26, 2023
For the Church of Synchronology
Art Blocks in the previous post —
"… making accessibility and IRL viewership a core component" . . .
From this journal on the above art date — April 6, 2021 —
Tuesday, April 6, 2021
|
Comments Off on For the Church of Synchronology
Saturday, July 8, 2023
Blacklist Quote from S10 E20, “Arthur Hudson”
"I am what I am. You made a devil's bargain.
Did you really expect me to stop being the devil?"
Read more at: https://tvshowtranscripts.ourboard.org/
viewtopic.php?f=194&t=64076
See as well yesterday's post CORE and Faustus in this journal.
Comments Off on Blacklist Quote from S10 E20, “Arthur Hudson”
Friday, June 23, 2023
A Little Drama
The broken pencil in a Dial illustration of June 20 —
"I could a tale unfold . . ." — Hamlet's father's ghost
"Thus the entire little drama, from crystallized carbon
and felled pine to this humble implement, to this
transparent thing, unfolds in a twinkle."
— Vladimir Nabokov, Transparent Things
"… a cardboard tube, more or less the same length as
the inner core of a toilet roll, but thicker. He frowned,
took the roll out, laid it on the desk and poked up it
with the butt end of a pencil. Something slid out.
It looked like a rolled-up black plastic dustbin liner;
but when he unfolded it, he recognised it as the funny
sheet thing he’d found in the strongroom and briefly
described as an Acme Portable Door, before losing
his nerve and changing it to something less facetious."
— Holt, Tom. The Portable Door . Orbit. Kindle Edition.
According to goodreads.com, the Holt book was
"first published March 6, 2003."
See also this journal on March 6, 2003, in a search for
Michelangelo Geometry.
Punchline of the above little drama —
"Try the other end of the pencil, Liz."
Comments Off on A Little Drama
Thursday, June 22, 2023
Unfolded Drama
"I could a tale unfold . . ." — Hamlet's father's ghost
"Thus the entire little drama, from crystallized carbon
and felled pine to this humble implement, to this
transparent thing, unfolds in a twinkle."
— Vladimir Nabokov, Transparent Things
"… a cardboard tube, more or less the same length as
the inner core of a toilet roll, but thicker. He frowned,
took the roll out, laid it on the desk and poked up it
with the butt end of a pencil. Something slid out.
It looked like a rolled-up black plastic dustbin liner;
but when he unfolded it, he recognised it as the funny
sheet thing he’d found in the strongroom and briefly
described as an Acme Portable Door, before losing
his nerve and changing it to something less facetious."
— Holt, Tom. The Portable Door . Orbit. Kindle Edition.
According to goodreads.com, the Holt book was
"first published March 6, 2003."
Comments Off on Unfolded Drama
Monday, June 19, 2023
The Original Portable Door
"… a cardboard tube, more or less the same length as
the inner core of a toilet roll, but thicker. He frowned,
took the roll out, laid it on the desk and poked up it
with the butt end of a pencil. Something slid out.
It looked like a rolled-up black plastic dustbin liner;
but when he unfolded it, he recognised it as the funny
sheet thing he’d found in the strongroom and briefly
described as an Acme Portable Door, before losing
his nerve and changing it to something less facetious."
— Holt, Tom. The Portable Door . Orbit. Kindle Edition.
According to goodreads.com, the Holt book was
"first published March 6, 2003."
Compare and contrast the "portable door" as a literary device
with the "tesseract" in A Wrinkle in Time (1962).
See also this journal on March 6, 2003.
Comments Off on The Original Portable Door
Friday, November 18, 2022
The Crimson Riddle
Wednesday's original New York Times headline reporting a Harvard death —
"Henry Rosovsky, Who Redefined
Harvard to Its Core, Dies at 95"
Yesterday that headline was rewritten —
That revision suggests another . . .
An Old Riddle Made New:
"What's black and white and crimson all over?"
Comments Off on The Crimson Riddle
Wednesday, November 16, 2022
Monday, May 23, 2022
Tuesday, February 8, 2022
Directions Out
On reading about DNA:
"Suddenly it was clear to me
that all the beautiful complexity of life
had simplicity at its core," he says.
"This is the kind of thing mathematicians love."
— Eric Lander in "The 2004 TIME 100 — Our list
of the most influential people in the world today"
The date on the above TIME piece is Monday,
Apr. 26, 2004. Remarks in this journal on that date
are now tagged Directions Out.
Comments Off on Directions Out
Sunday, September 5, 2021
Linguistics
A Letterman introduction for Plato's Academy Awards:
"Cunning, Anna. Anna, Cunning." (Rimshot.)
But seriously . . .
"This work [of Wierzbicka and colleagues] has led to
a set of highly concrete proposals about a hypothesized
irreducible core of all human languages. This universal core
is believed to have a fully ‘language-like’ character in the sense
that it consists of a lexicon of semantic primitives together with
a syntax governing how the primitives can be combined
(Goddard, 1998)." — Wikipedia, Semantic Primes
Goddard C. (1998) — Bad arguments against semantic primitives.
Theoretical Linguistics 24:129-156.
Related fiction . . . Lexicon , by Max Barry (2013). See Barry in this journal.
Comments Off on Linguistics
Thursday, August 19, 2021
A Scalpel for Einstein
(A sequel to this morning's post A Subtle Knife for Sean.)
Exhibit A —
Einstein in The Saturday Review, 1949 —
"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."
Exhibit B —
Strogatz in The New Yorker, 2015 —
"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."
Exhibit C —
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.
Strogatz says that . . .
"What we’re seeing here is a quintessential use of
a symmetry argument… scaling….
Throughout his career, Einstein would continue to
deploy symmetry arguments like a scalpel, getting to
the hidden heart of things."
Connoisseurs of bullshit may prefer a faux-Chinese approach to
"the hidden heart of things." See Log24 on August 16, 2021 —
http://m759.net/wordpress/?p=96023 —
In a Nutshell: The Core of Everything .
Comments Off on A Scalpel for Einstein
Tuesday, July 20, 2021
Zen in Cuernavaca
|
https://terebess.hu/zen/mesterek/dtsuzuki.html —
From Larry A. Fader, “D. T. Suzuki's Contribution to the West,” In contrast to Jung's approach is the humanistic psychology of Erich Fromm. Fromm was also influenced by Suzuki, but in different ways. Whereas Jung dealt with Zen Buddhism as an aspect of his psychological thought, Suzuki's influence touches closer to the core of Fromm's thought. Fromm organized an influential workshop on Zen Buddhism and psychoanalysis in Cuernavaca, Mexico, and incorporated many concepts which resemble Suzuki's interpretation of Zen into his psychoanalytic writings. The Cuernavaca workshop of 1957, held at Fromm's Mexico home, brought together eminent psychologists expressly for the purpose of exploring Zen Buddhism and psychoanalysis. As such, it marks an important point of contact between thinkers in the field of psychology and D. T. Suzuki's interpretation of Zen. Suzuki addressed the gathering, and his speeches were later published as “Lectures in Zen Buddhism” together with Fromm's address entitled “Psychoanalysis and Zen Buddhism” and that of Richard DeMartino entitled “The Human Situation and Zen Buddhism,” in a volume which Fromm edited and called Zen Buddhism and Psychoanalysis. Fromm organized the Mexico meeting and issued the invitations to its participants as a result of his feeling that psychotherapists—and in particular, psychoanalysts—were at that time “not just interested, but deeply concerned” with Zen. This “concern,” Fromm believed, was a new and potentially important development in the attitude of psychologists. His own address to the workshop, reformulated, as he says, because of “the stimulation of the conference,” includes language and ideas that may be traced to Dr. Suzuki's Cuernavaca lectures. |
See as well Fromm and Frère Jacques, Cuernavaca in this journal.
Comments Off on Zen in Cuernavaca
Thursday, October 1, 2020
Annals of Academia
New York magazine's "The Cut" —
BAD SCIENCE
JULY 14, 2016
Why It Took Social Science Years to Correct a Simple Error
About ‘Psychoticism’
By Jesse Singal
"What should we make of all of this? Partly, of course, this is
a story of conflicting personalities, of competitiveness between
researchers, of academics acting — let’s be frank — like dicks."
Or, worse, like New York Times reporter Benedict Carey —
|
A Theory About Conspiracy Theories
In a new study, psychologists tried to get a handle on the personality types that might be prone to outlandish beliefs.
By Benedict Carey, New York Times science reporter, . . . . The personality features that were solidly linked to conspiracy beliefs included some usual suspects: entitlement, self-centered impulsivity, cold-heartedness (the confident injustice collector), elevated levels of depressive moods and anxiousness (the moody figure, confined by age or circumstance). Another one emerged from the questionnaire that aimed to assess personality disorders — a pattern of thinking called “psychoticism.” Psychoticism is a core feature of so-called schizo-typal personality disorder, characterized in part by “odd beliefs and magical thinking” and “paranoid ideation.” In the language of psychiatry, it is a milder form of full-blown psychosis, the recurrent delusional state that characterizes schizophrenia. It’s a pattern of magical thinking that goes well beyond garden variety superstition and usually comes across socially as disjointed, uncanny or “off.”
In time, perhaps some scientist or therapist will try to slap a diagnosis on believers in Big Lie conspiracies that seem wildly out of line with reality. For now, Dr. Pennycook said, it is enough to know that, when distracted, people are far more likely to forward headlines and stories without vetting their sources much, if at all. |
Some elementary fact-checking reveals that historical definitions
of "psychoticism" vary greatly. Carey forwards this bullshit without
vetting his sources much, if at all.
Comments Off on Annals of Academia
Monday, April 27, 2020
The Cracked Nut
“At that instant he saw, in one blaze of light, an image of unutterable
conviction, the reason why the artist works and lives and has his being –
the reward he seeks –the only reward he really cares about, without which
there is nothing. It is to snare the spirits of mankind in nets of magic,
to make his life prevail through his creation, to wreak the vision of his life,
the rude and painful substance of his own experience, into the congruence
of blazing and enchanted images that are themselves the core of life, the
essential pattern whence all other things proceed, the kernel of eternity.”
— Thomas Wolfe, Of Time and the River
“… the stabiliser of an octad preserves the affine space structure on its
complement, and (from the construction) induces AGL(4,2) on it.
(It induces A8 on the octad, the kernel of this action being the translation
group of the affine space.)”
— Peter J. Cameron,
The Geometry of the Mathieu Groups (pdf)
“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside…."
— Joseph Conrad in Heart of Darkness
Comments Off on The Cracked Nut
Saturday, February 22, 2020
Remembering Speechlessly
"Remembering speechlessly we seek
the great forgotten language . . . ."
|
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
See also other posts now tagged Transparent Things.
Comments Off on Remembering Speechlessly
Friday, January 24, 2020
Oettinger Quote
Quote Investigator on May 4, 2010* —
"QI has traced the core of the quotation
to the work of an early researcher in
artificial intelligence, Anthony Oettinger,
who was trying to get a computer to
manipulate the English language."
See as well Oettinger in 1963.
"And that was the state of the art."
— Adapted from Stephen Sondheim
* Cf. this journal on that date.
Comments Off on Oettinger Quote
Sunday, September 22, 2019
Colorful Tale
“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”
— Hermann Weyl, Philosophy of Mathematics and
Natural Science , Princeton, 1949, p. 237
"The bond with reality is cut."
— Hans Freudenthal, 1962
From page 180, Logicomix — It was a dark and stormy night …
Comments Off on Colorful Tale
Friday, March 29, 2019
The Blazon World*
“At that instant he saw, in one blaze of light,
an image of unutterable conviction,
the reason why the artist works and lives
and has his being — the reward he seeks —
the only reward he really cares about,
without which there is nothing. It is to snare
the spirits of mankind in nets of magic,
to make his life prevail through his creation,
to wreak the vision of his life, the rude and painful
substance of his own experience, into the congruence
of blazing and enchanted images that are themselves
the core of life, the essential pattern whence
all other things proceed, the kernel of eternity.”
— Thomas Wolfe, Of Time and the River
* Title suggested by that of a Siri Hustvedt novel.
See also Blazon in this journal.
Comments Off on The Blazon World*
Wednesday, October 17, 2018
Aesthetics
|
From "The Phenomenology of Mathematical Beauty," 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?
Comments Off on Aesthetics
Thursday, March 1, 2018
The Movement of Analogy: Hume vs. Paz
Hume, from posts tagged "four-set" in this journal —
"The mind is a kind of theatre, where several perceptions
successively make their appearance; pass, repass, glide away,
and mingle in an infinite variety of postures and situations.
There is properly no simplicity in it at one time, nor identity
in different, whatever natural propension we may have
to imagine that simplicity and identity."
Paz, from a search for Paz + Identity in this journal —
|
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
Comments Off on The Movement of Analogy: Hume vs. Paz
Wednesday, February 7, 2018
Conceptual Minimalism
|
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
See also AS IS.
Comments Off on Conceptual Minimalism
Friday, November 10, 2017
Annals of Rarefied Scholarship
From Cambridge Core, suggested by a reference to
that website in the previous post and by the following
bibliographic data . . .
https://doi.org/10.1017/fmp.2016.5
Downloaded from https://www.cambridge.org/core
on 10 Nov 2017 at 19:06:19
See Conwell + Princeton in this journal.
Related art —
Comments Off on Annals of Rarefied Scholarship
Thursday, October 26, 2017
A Center
This post was suggested by a New York Times obituary this evening —
"Tom Mathews, Promoter of Liberal Causes and Candidates, Dies at 96."
Mathews reportedly died on October 14, 2017.
"Mr. Mathews and his business partner Roger Craver 'dreamed for years
of finding the perfect citizen-candidate,' the authors wrote, 'a man or
woman of the center-left with a feel for issues, a history of independence,
a winning television manner and, most important of all, a center — a core
of beliefs more important to him or her than getting elected.'
Dream on.
From the date of Mathews's death:
Posts now tagged A Center for Krauss —
Comments Off on A Center
Tuesday, October 17, 2017
Status Symbols
"Status: Defunct" …
As is now its owner, who reportedly
died at 80 on Sunday, October 15, 2017.
In memoriam —
Excerpts from Log24 posts on Sunday night
and yesterday evening —
.
" … listen: there's a hell
of a good universe next door; let's go"
— e. e. cummings
Some literary background —
|
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
Comments Off on Status Symbols
Sunday, September 24, 2017
Figures
"On April 23, 2009 ….
'I’m reminded of the character in "The Silence of the Lambs,"
Hannibal Lecter, a very brilliant man,' the prosecutor said,
recognizing 'his ability to intelligently and articulately discuss
things occurring in society.'
'But at his core, as with Mr. Lecter at his core, he is a sociopath,'
the prosecutor said."
— David Stout in an obituary from this evening's online
New York Times
See also this journal on April 23, 2009, and
a figure from this morning's link Cantina —
.
Comments Off on Figures
Saturday, September 23, 2017
The Turn of the Frame
"With respect to the story's content, the frame thus acts
both as an inclusion of the exterior and as an exclusion
of the interior: it is a perturbation of the outside at the
very core of the story's inside, and as such, it is a blurring
of the very difference between inside and outside."
— Shoshana Felman on a Henry James story, p. 123 in
"Turning the Screw of Interpretation,"
Yale French Studies No. 55/56 (1977), pp. 94-207.
Published by Yale University Press.
See also the previous post and The Galois Tesseract.
Comments Off on The Turn of the Frame
Friday, August 18, 2017
The Savvy Philosophers
Flashback in Genial, a post of March 6, 2017 —
From a New York Times book review today by
James Ryerson, instructor at The School of The New York Times —
"Savvy philosophers distill their core insight into a short phrase."
Comments Off on The Savvy Philosophers
Monday, July 10, 2017
Under Bleu Cup
Publishers Weekly on a Nov. 1, 2011, book, Under Blue Cup —
"Krauss’s core argument (what she deems a 'crusade')
is that the 'white cube,' which conceptual and installation
artists have deemed obsolete, actually thrives."
For other "core arguments," see Satuday's post "Common Core"
and the Art Space posts "Odd Core" and "Even Core."
Comments Off on Under Bleu Cup
Monday, March 27, 2017
Groundhog Day and After
Comments Off on Groundhog Day and After
Monday, February 20, 2017
Mathematics and Narrative
Mathematics —
Hudson's parametrization of the
4×4 square, published in 1905:
A later parametrization, from this date in 1986:
A note from later in 1986 shows the equivalence of these
two parametrizations:
Narrative —
Posts tagged Memory-History-Geometry.
The mathematically challenged may prefer the narrative of the
Creation Matrix from the religion of the Transformers:
"According to religious legend, the core of the Matrix
was created from Solomus, the god of wisdom,
trapped in the form of a crystal by Mortilus, the god
of death. Following the defeat of Mortilus, Solomus
managed to transform his crystal prison into the Matrix—
a conduit for the energies of Primus, who had himself
transformed into the life-giving computer Vector Sigma."
Comments Off on Mathematics and Narrative
Friday, February 17, 2017
Fake News: The Definition
See also, on Feb. 8 in this journal, Damning.
Comments Off on Fake News: The Definition
Sunday, February 12, 2017
Colorful Tales
“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”
— Hermann Weyl, Philosophy of Mathematics and
Natural Science , Princeton, 1949, p. 237
Harvard University Press on the late Angus Fletcher, author of
The Topological Imagination and Colors of the Mind —
From the Harvard webpage for Colors of the Mind —
Angus Fletcher is one of our finest theorists of the arts,
the heir to I. A. Richards, Erich Auerbach, Northrop Frye.
This… book… aims to open another field of study:
how thought— the act, the experience of thinking—
is represented in literature.
. . . .
Fletcher’s resources are large, and his step is sure.
The reader samples his piercing vision of Milton’s
Satan, the original Thinker,
leaving the pain of thinking
as his legacy for mankind.
A 1992 review by Vinay Dharwadker of Colors of the Mind —
See also the above word "dianoia" in The Echo in Plato's Cave.
Some context …
This post was suggested by a memorial piece today in
the Los Angeles Review of Books —
A Florilegium for Angus Fletcher
By Kenneth Gross, Lindsay Waters, V. N. Alexander,
Paul Auster, Harold Bloom, Stanley Fish, K. J. Knoespel,
Mitchell Meltzer, Victoria Nelson, Joan Richardson,
Dorian Sagan, Susan Stewart, Eric Wilson, Michael Wood
Fletcher reportedly died on November 28, 2016.
"I learned from Fletcher how to apprehend
the daemonic element in poetic imagination."
— Harold Bloom in today's Los Angeles florilegium
For more on Bloom and the daemonic, see a Log24 post,
"Interpenetration," from the date of Fletcher's death.
Some backstory: Dharwadker in this journal.
Comments Off on Colorful Tales
Tuesday, February 7, 2017
Sunday, January 8, 2017
A Theory of Everything
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 —
Comments Off on A Theory of Everything
Saturday, September 24, 2016
Core Structure
For the director of "Interstellar" and "Inception" —
At the core of the 4x4x4 cube is …
Cover modified.
Comments Off on Core Structure
Wednesday, August 24, 2016
Core Statements
"That in which space itself is contained" — Wallace Stevens
An image by Steven H. Cullinane from April 1, 2013:
The large Desargues configuration of Euclidean 3-space can be
mapped canonically to the 4×4 square of Galois geometry —
On an Auckland University of Technology thesis by Kate Cullinane —
The thesis reportedly won an Art Directors Club award on April 5, 2013.
Comments Off on Core Statements
Monday, August 8, 2016
A Point of Identity
For a Monkey Grammarian (Viennese Version)
|
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
A logo that may be interpreted as one-eighth of a 2x2x2 array
of cubes —
The figure in white above may be viewed as a subcube representing,
when the eight-cube array is coordinatized, the identity (i.e., (0, 0, 0)).
Shown below are a few variations on the figure by VCQ,
the Vienna Center for Quantum Science and Technology —
(Click image to enlarge.)
Comments Off on A Point of Identity
Thursday, August 4, 2016
Routine
Peter Gelzinis in the Boston Herald today —
"What has become painfully clear this week
is that there is no Republican campaign for
the presidency. There is only The Donald,
his
reflex tweets, the folded pieces of paper
he pulls out of his coat pocket and a crazy
stand-up routine that is part Lenny Bruce
and part professor Irwin Corey."
Comments Off on Routine
Tuesday, July 5, 2016
For the Children in the Apple Tree (continued)
(See previous posts now tagged Apple Tree Children.)
See as well the comic book in "Midnight Special" —
(Image previously posted in "Common Core vs. Central Structure")
Comments Off on For the Children in the Apple Tree (continued)
Friday, May 27, 2016
Peer Review
A review of the phrase "Innermost Kernel" in this journal
suggests the following meditation …
"Who am I?" — Existential cry
in "Zoolander" and "Zoolander 2."
A similar question occurs in "Peer Gynt" —
Ben Brantley in yesterday morning's print New York Times *
expressed a nihilistic view of Peer as an onion-peeler —
"Toward the end of Ibsen’s 'Peer Gynt,' a saga of self
under siege, the title character is discovered peeling
an onion, finding in the layers of that humble vegetable
a symbol for the chapters of an eventful life . . . .
… [the director’s] approach is the same one that Peer
applies to the onion: Keep stripping until you find the core.
Of course in Peer’s case what is finally found is
plenty of nothing, an apt conclusion for a man
for whom a solid self remains elusive."
I prefer a view from what Fitzgerald called
"the dark fields of the republic" — the Dordt College view —
* The Times — "A version of this review appears in print on May 26, 2016,
on page C3 of the New York edition with the headline:
'A Saga of Self-Identity, Stripped to Its Core, Still Provokes.' "
Comments Off on Peer Review
Monday, February 15, 2016
Global and Local
- "Dirty Laundry" (Henley, Danny Kortchmar) – 5:36
- "The Boys of Summer" (Mike Campbell, Henley) – 4:45
- "All She Wants to Do Is Dance" (Kortchmar) – 4:28
- "Not Enough Love in the World" (Henley, Kortchmar, Benmont Tench) – 3:54
- "Sunset Grill" (Henley, Kortchmar, Tench) – 6:22
- "The End of the Innocence" (Henley, Bruce Hornsby) – 5:14
- "The Last Worthless Evening" (John Corey, Henley, Stan Lynch) – 6:05
- "New York Minute" (Henley, Kortchmar, Jai Winding) – 6:34
- "I Will Not Go Quietly" (Henley, Kortchmar) – 5:41
- "The Heart of the Matter" (Campbell, Henley, J.D. Souther) – 5:21
- "The Garden of Allah" (Corey, Paul Gurian, Henley, Lynch) – 7:02
- "You Don't Know Me at All" (Corey, Henley, Lynch) – 5:36
- "Everybody Knows" (Leonard Cohen, Sharon Robinson) – 6:10
Comments Off on Global and Local
Friday, June 12, 2015
Friday, May 8, 2015
Spielraum
Review:
Illustrating the Spiegel-Spiel des Gevierts
|
"At the point of convergence
by Octavio Paz, translated by |
Friday December 5, 2008
|
Comments Off on Spielraum
Tuesday, May 5, 2015
Paz
|
"At the point of convergence
by Octavio Paz, translated by |
Comments Off on Paz
Thursday, April 23, 2015
Colorful Tale
(A sequel to yesterday's ART WARS and this
morning's De Colores )
“Perhaps the philosophically most relevant feature
of modern science is the emergence of abstract
symbolic structures as the hard core of objectivity
behind– as Eddington puts it– the colorful tale
of the subjective storyteller mind.” — Hermann Weyl
(Philosophy of Mathematics and Natural Science ,
Princeton, 1949, p. 237)
See also Deathly Hallows.
Comments Off on Colorful Tale
Thursday, April 9, 2015
Core Values
"Yankee Doodle went to London" — Song lyric
“Geometry was very important to us in this movie.”
— The Missing ART (Log24, November 7th, 2014)
ART —
"Faculty Approve Theater Concentration, Affirmation
of Integrity" — Recent Harvard Crimson headline
Comments Off on Core Values
Thursday, February 5, 2015
Core Problem
(As opposed to "The Hard Problem")
Sharon Gaudin at computerworld.com
on artificial intelligence (AI) today—
"Google's [Geoffrey] Hinton said he's most excited
about gains in neural networks that would enable
computers to understand the content of sentences
and documents.
'That is close to the core of Google because
it involves understanding sentences, and if you can
understand what a document is saying, you can do
a much better search,' Hinton said. 'That's a core
AI problem. Can you read a document and know
what it's saying?'"
Sometimes. How about you?
Comments Off on Core Problem
Tuesday, December 30, 2014
Core
JOSEFINE LYCHE
ABSOLUTE ALT. VOL. 2
17. april – 23. mai [2015] —
"I kjernen av mitt arbeid er en pågående
utforskning av esoteriske konsepter…."
"At the core of my work is an ongoing
exploration of esoteric concepts…."
See also
http://issuu.com/tmrk/docs/spritenkunsthall_2015_cut .
Related material: Hard Core.
Comments Off on Core
Tuesday, December 2, 2014
Colorful Tale
"Perhaps the philosophically most relevant feature
of modern science is the emergence of abstract
symbolic structures as the hard core of objectivity
behind— as Eddington puts it— the colorful tale
of the subjective storyteller mind."
— Hermann Weyl in Philosophy of Mathematics
and Natural Science , Princeton, 1949, p. 237
Tom Wolfe on art theorists in The Painted Word (1975) :
"It is important to repeat that Greenberg and Rosenberg
did not create their theories in a vacuum or simply turn up
with them one day like tablets brought down from atop
Green Mountain or Red Mountain (as B. H. Friedman once
called the two men). As tout le monde understood, they
were not only theories but … hot news,
straight from the studios, from the scene."
The Weyl quote is a continuing theme in this journal.
The Wolfe quote appeared here on Nov. 18, 2014,
the reported date of death of Yale graduate student
Natasha Chichilnisky-Heal.
Directions to her burial (see yesterday evening) include
a mention of "Paul Robson Street" (actually Paul
Robeson Place) near "the historic Princeton Cemetery."
This, together with the remarks by Tom Wolfe posted
here on the reported day of her death, suggests a search
for "red green black" —
The late Chichilnisky-Heal was a student of political economy.
The search colors may be interpreted, if one likes, as referring
to politics (red), economics (green), and Robeson (black).
See also Robeson in this journal.
Comments Off on Colorful Tale
Sunday, September 21, 2014
Uncommon Noncore
This post was suggested by Greg Gutfeld’s Sept. 4 remarks on Common Core math.
Problem: What is 9 + 6 ?
Here are two approaches suggested by illustrations of Desargues’s theorem.
Solution 1:
9 + 6 = 10 + 5,
as in Common Core (or, more simply, as in common sense), and
10 + 5 = 5 + 10 = 15 as in Veblen and Young:
Solution 2:
In the figure below,
9 + 6 = no. of V’s + no. of A’s + no. of C’s =
no. of nonempty squares = 16 – 1 = 15.
(Illustration from Feb. 10, 2014.)
The silly educationists’ “partner, anchor, decompose” jargon
discussed by Gutfeld was their attempt to explain “9 + 6 = 10 + 5.”
As he said of the jargon, “That’s not math, that’s the plot from ‘Silence of the Lambs.'”
Or from Richard, Frank, and Marcus in last night’s “Intruders”
(BBC America, 10 PM).
Comments Off on Uncommon Noncore
Thursday, September 18, 2014
Them Apples
John Baez at Google+ has an interesting post on crackpots,
dated September 13, 2014.
Related recent material from this journal:
Sense (Sept. 13) and Sensibility (Sept. 14 and later).
See also a New York Times piece from 2009:
Related material:
“You don’t need to eat a whole apple to know it’s rotten.”
— Warren Siegel
Comments Off on Them Apples
Thursday, September 11, 2014
Oh, Moon of Alabama
The mention of Gauss in today's previous post, along with
recent news, suggested this post.
"How do you get young people excited about space?"
— Megan Garber in The Atlantic , Aug. 16, 2012
Further details: Child Buyers (July 16, 2013).
Comments Off on Oh, Moon of Alabama
Thursday, September 4, 2014
Halloween Manifestos, 2013:
Here and at Catholics for Classical Education.
See also Tom Wolfe on manifestos —
— and part of an interesting Sept. 2, 2014, manifesto by
Common Core supporter Keith Devlin:
“Graduate students of mathematics are introduced to further
assumptions (about handling the infinite, and various other issues),
equally reasonable and useful, and in accord both with our everyday
intuitions (insofar as they are relevant) and with the rest of
mainstream mathematics. And on the basis of those assumptions,
you can prove that
1 + 2 + 3 + … = –1/12.
That’s right, the sum of all the natural numbers equals –1/12.
This result is so much in-your-face, that people whose mathematics
education stopped at the undergraduate level (if they got that far)
typically say it is wrong. It’s not. Just as with the 0.999… example,
where we had to construct a proper meaning for an infinite decimal
expansion before we could determine what its value is, so to we
have to define what that infinite sum means. ….”
For a correction to Devlin’s remarks, see a physics professor’s weblog post —
“From a strictly mathematical point of view,
the equation 1+2+3+4+ … = -1/12 is incorrect,
and involves confusing the Dirichlet series with
the zeta function.” — Greg Gbur, May 25, 2010
Comments Off on Halloween Manifestos, 2013:
Saturday, July 5, 2014
Core Curriculum
This post was suggested by reviews of the David Hare play “Skylight” at
The New York Times , at WorldSocialism.org, and at ChicagoCritic.com.
Vide Atoms in the Family , by Laura Fermi, a book I read in high school.
Comments Off on Core Curriculum
Friday, July 4, 2014
Knockout
(Continued from yesterday’s noon post, from “Block That Metaphor,”
and from “Mystery Box III: Inside, Outside“)
“In one corner are the advocates of the Common Core,
led by the Bill and Melinda Gates Foundation, which
helped develop the standards and has defended them
against efforts by some states to roll them back. In the
challengers’ corner, a lineup of foundations and
philanthropists…. Other funders in the opponents’ corner
read like a ‘who’s who’ of well-heeled conservative
philanthropists, including Pittsburgh media magnate
Richard Mellon Scaife….”
— “Meet the Funders Fighting the Common Core,”
from Inside Philanthropy , Feb. 10, 2014
Scaife reportedly died this morning.
Comments Off on Knockout
Thursday, July 3, 2014
Gates and Windows:
The Los Alamos Vision
“Gates said his foundation is an advocate for the Common Core State Standards
that are part of the national curriculum and focus on mathematics and language
arts. He said learning ‘needs to be on the edge’ where it is challenging but not
too challenging, and that students receive the basics through Common Core.
‘It’s great to teach other things, but you need that foundation,’ he said.”
— T. S. Last in the Albuquerque Journal , 12:05 AM Tuesday, July 1, 2014
See also the previous post (Core Mathematics: Arrays) and, elsewhere
in this journal,
“Eight is a Gate.” — Mnemonic rhyme:
Comments Off on Gates and Windows:
Core Mathematics: Arrays
Mathematics vulgarizer Keith Devlin on July 1
posted an essay on Common Core math education.
His essay was based on a New York Times story from June 29,
“Math Under Common Core Has Even Parents Stumbling.”
An image from that story:
The Times gave no source, other than the photographer’s name,
for the above image. Devlin said,
“… the image of a Common Core math worksheet
the Times chose to illustrate its story showed
a very sensible, and deep use of dot diagrams,
to understand structure in arithmetic.”
Devlin seems ignorant of the fact that there is
no such thing as a “Common Core math worksheet.”
The Core is a set of standards without worksheets
(one of its failings).
Neither the Times nor whoever filled out the worksheet
nor Devlin seemed to grasp that the image the Times used
shows some multiplication word problems that are more
advanced than the topic that Devlin called the
“deep use of dot diagrams to understand structure in arithmetic.”
This Core topic is as follows:
For some worksheets that are (purportedly) relevant, see,
for instance…
http://search.theeducationcenter.com/search/
_Common_Core_Label-2.OA.C.4–keywords-math_worksheets,
in particular the worksheet
http://www.theeducationcenter.com/editorial_content/multipli-city:
Some other exercises said to be related to standard 2.OA.C.4:
| http://www.ixl.com/standards/ common-core/math/grade-2
|
The Common Core of course fails to provide materials for parents
that are easily findable on the Web and that give relevant background
for the above second-grade topic. It leaves this crucial task up to
individual states and school districts, as well as to private enterprise.
This, and not the parents’ ignorance described in Devlin’s snide remarks,
accounts for the frustration that the Times story describes.
Comments Off on Core Mathematics: Arrays
Wednesday, July 2, 2014
An Apple for Devlin
A columnist for the Mathematical Association of America,
Keith Devlin, yesterday posted an essay on Common Core
math education. A response:
Screenshot from a June 14, 2014, New York Times video.
Comments Off on An Apple for Devlin
Thursday, February 6, 2014
The Representation of Minus One
For the late mathematics educator Zoltan Dienes.
“There comes a time when the learner has identified
the abstract content of a number of different games
and is practically crying out for some sort of picture
by means of which to represent that which has been
gleaned as the common core of the various activities.”
— Article by “Melanie” at Zoltan Dienes’s website
Dienes reportedly died at 97 on Jan. 11, 2014.
From this journal on that date —
A star figure and the Galois quaternion.
The square root of the former is the latter.
Update of 5:01 PM ET Feb. 6, 2014 —
An illustration by Dienes related to the diamond theorem —
See also the above 15 images in …
… and versions of the 4×4 coordinatization in The 4×4 Relativity Problem
(Jan. 17, 2014).
Comments Off on The Representation of Minus One
Sunday, June 30, 2013
Book Award
|
"What on earth is
— Said to be an annotation |
In the spirit of the late Thomas Guinzburg…
See also "Concrete Universal" in this journal.
Related material— From a Bloomsday reply
to a Diamond Theory reader's comment, an excerpt—
The reader's comment suggests the following passages from
the book by Stirling quoted above—
Here Stirling plays a role analogous to that of Professor Irwin Corey
accepting the National Book Award for Gravity's Rainbow in 1974.
Comments Off on Book Award
Saturday, May 11, 2013
Core
Promotional description of a new book:
“Like Gödel, Escher, Bach before it, Surfaces and Essences will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core— the incessant, unconscious quest for strong analogical links to past experiences— this book puts forth a radical and deeply surprising new vision of the act of thinking.”
“Like Gödel, Escher, Bach before it….”
Or like Metamagical Themas .
Rubik core:
Non- Rubik cores:
| Of the odd nxnxn cube:
|
Of the even nxnxn cube:
|
Related material: The Eightfold Cube and…
“A core component in the construction
is a 3-dimensional vector space V over F2 .”
— Page 29 of “A twist in the M24 moonshine story,”
by Anne Taormina and Katrin Wendland.
(Submitted to the arXiv on 13 Mar 2013.)
Comments Off on Core
Sunday, April 28, 2013
C’mon Baby…
 |
Let's do the twist. The image at left See this journal |
A phrase from yesterday's noon post:
Sinking the Magic 8-Ball .
A scene from the above film is related to this phrase.
Another image from the film poster:
A review of the film:
"The final 'twist' seems to negate the entire story,
like a bad shaggy-dog joke."
Such a joke:
“Words and numbers are of equal value,
for, in the cloak of knowledge,
one is warp and the other woof.”
— The princesses Rhyme and Reason
in The Phantom Tollbooth
"A core component in the construction
is a 3-dimensional vector space V over F2 ."
— Page 29 of "A twist in the M24 moonshine story,"
by Anne Taormina and Katrin Wendland.
(Submitted to the arXiv on 13 Mar 2013.)
The number of points in such a space is, of course, 8.
Comments Off on C’mon Baby…
Sunday, December 23, 2012
Digital Recreation
Denzel Washington in Deja Vu (2006), directed by Tony Scott—
See also Tony Scott and four and a half days ago* —
Japanese character
for "field"
Related material from five days ago—
|
"At the point of convergence by Octavio Paz, translated by |
* More precisely, what will be 4.5 days ago at 3:09 AM ET.
Comments Off on Digital Recreation
Tuesday, December 18, 2012
Monkey Grammar
For a modern Adam and Eve—
W. Tecumseh Fitch and Gesche Westphal Fitch,
editors of a new four-volume collection titled
Language Evolution (Feb. 2, 2012, $1,360)—
Related material—
|
"At the point of convergence
by Octavio Paz, translated by |
The "play of mirrors" link above is my own.
Click on W. Tecumseh Fitch for links to some
examples of mirror-play in graphic design—
from, say, my own work in a version of 1977, not from
the Fitches' related work published online last June—
See also Log24 posts from the publication date
of the Fitches' Language Evolution—
Happy birthday to the late Alfred Bester.
Comments Off on Monkey Grammar
Sunday, November 18, 2012
Kernel
Rachel Dodes in The Wall Street Journal
on All Souls' Day, 2012—
"In one of the first lines uttered by Daniel Day-Lewis, playing Abraham Lincoln in the new Steven Spielberg film opening Nov. 9, he says, 'I could be bounded in a nutshell, and count myself a king of infinite space— were it not that I have bad dreams.'
The line was ripped straight from 'Hamlet,' by Lincoln's favorite writer, William Shakespeare. Tony Kushner, the Pulitzer Prize-winning playwright ('Angels in America') who wrote the script for the film, says that Shakespeare, much like Lincoln, 'had extraordinary mastery over the darkest parts of the human spirit.'"
The above quotation omits Shakespeare's words prefacing the nutshell part— "O God."
These same words in a different tongue— "Hey Ram"— have often been quoted as the last words of Gandhi. (See yesterday's noon post.)
"… for the Highest Essence (brahman ),
which is the core of the world, is identical
with the Highest Self (ātman ), the kernel
of man's existence."
— Heinrich Zimmer, Myths and Symbols
in Indian Art and Civilization , Pantheon
Books, 1946, page 142
Related material: A post linked to here on Friday night
that itself links to a different Shakespeare speech.
Comments Off on Kernel
Friday, June 29, 2012
The Uploading (continued)*
It Must Be Abstract
It Must Change
It Must Give Pleasure
— Parts of a poem by Wallace Stevens
“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”
– Thomas Wolfe, Of Time and the River
Of Time and the River and the Frogs —
* This post's title refers to the above uploading date— Jan. 26, 2008.
Comments Off on The Uploading (continued)*
Tuesday, November 1, 2011
For All Hallows Day
The following was suggested by the Sermon
of October 30 (the day preceding Devil's Night)
and by yesterday's Beauty, Truth, Halloween.
"The German language has itself been influenced by Goethe's Faust , particularly by the first part. One example of this is the phrase 'des Pudels
See also the following readings (click to enlarge)—
Note particularly…
"The main enigma of any description of a patternless
unus mundus is to find appropriate partitions which
create relevant patterns." —Hans Primas, above
"In general, the partition of G into right cosets
can differ from its partition into left cosets. Galois
was the first to recognize the importance of when
these partitions agree. This happens when the
subgroup H is normal." — David A. Cox,
Galois Theory , Wiley, 2004, p. 510
Comments Off on For All Hallows Day
Saturday, September 17, 2011
The Uploading
(Continued from March 9.)
A detail from "Feist Sings 1, 2, 3, 4"—
"Uploaded by on Jul 18, 2008"
Those who prefer, as Weyl put it,
"the hard core of objectivity"
to, as Eddington put it,
"the colorful tale of the subjective storyteller mind"
may consult this journal on the same day… July 18, 2008.
Comments Off on The Uploading
Friday, September 16, 2011
Icons
Background: Jung's Aion in this journal discusses this
figure from finite geometry's diamond theorem—
Fig. A
This resembles a figure that served Jung
as a schema of the Self—
Fig. B
Fig. A, with color variations, serves as the core
of many automatically generated Identicons —
a different sort of self-symbol.
Examples from Sept. 6 at MathOverflow—
A user wanting to custom-tailor his self-symbol should consider
the following from the identicon service Gravatar—
1. User Submissions. "… you hereby do and shall grant to Automattic a worldwide, perpetual, irrevocable, royalty-free and fully-paid, transferable (including rights to sublicense) right to perform the Services (e.g., to use, modify, reproduce, distribute, prepare derivative works of, display, perform, and otherwise fully exercise and exploit all intellectual property, publicity, and moral rights with respect to any User Submissions, and to allow others to do so)."
Sounds rather Faustian.
Comments Off on Icons
Monday, July 11, 2011
And/Or Problem
"It was the simultaneous emergence
and mutual determination
of probability and logic
that von Neumann found intriguing
and not at all well understood."
Context:
Update of 7 AM ET July 12, 2011—
Freeman Dyson on John von Neumann's
Sept. 2, 1954, address to the International
Congress of Mathematicians on
"Unsolved Problems in Mathematics"—
…."The hall was packed with
mathematicians, all expecting to hear a brilliant
lecture worthy of such a historic occasion. The
lecture was a huge disappointment. Von Neumann
had probably agreed several years earlier to give
a lecture about unsolved problems and had then
forgotten about it. Being busy with many other
things, he had neglected to prepare the lecture.
Then, at the last moment, when he remembered
that he had to travel to Amsterdam and say something
about mathematics, he pulled an old lecture
from the 1930s out of a drawer and dusted it off.
The lecture was about rings of operators, a subject
that was new and fashionable in the 1930s. Nothing
about unsolved problems. Nothing about the
future."
— Notices of the American Mathematical Society ,
February 2009, page 220
For a different account, see Giovanni Valente's
2009 PhD thesis from the University of Maryland,
Chapter 2, "John von Neumann's Mathematical
'Utopia' in Quantum Theory"—
"During his lecture von Neumann discussed operator theory and its con-
nections with quantum mechanics and noncommutative probability theory,
pinpointing a number of unsolved problems. In his view geometry was so tied
to logic that he ultimately outlined a logical interpretation of quantum prob-
abilities. The core idea of his program is that probability is invariant under
the symmetries of the logical structure of the theory. This is tantamount to
a formal calculus in which logic and probability arise simultaneously. The
problem that exercised von Neumann then was to construct a geometrical
characterization of the whole theory of logic, probability and quantum me-
chanics, which could be derived from a suitable set of axioms…. As he
himself finally admitted, he never managed to set down the sought-after
axiomatic formulation in a way that he felt satisfactory."
Comments Off on And/Or Problem
Sunday, June 19, 2011
Metalibrarianship
This screenshot was suggested by the word "metalibrarianship" in a Bloomsday 2011 post by artist Steve Richards.
Note the words in the search field.
The phrase "Dublin Core metadata" refers to a city in Ohio, not in Ireland.
Related material— The highlighted phrase below is in the epigraph to Borges's "The Library of Babel"—
"I would, for these causes, wish him that is melancholy, to use both humane and divine authors, voluntarily to impose some taske upon himself, to divert his melancholy thoughts; to study the art of memory, Cosmus Rosselius, Pet. Ravennas, Scenkelius Detectus, or practise brachygraphy, &c. that will aske a great deal of attention: or let him demonstrate a proposition in Euclide in his five last books, extract a square root, or studie Algebra: than which, as gClavius holds, in all humane disciplines nothing can be more excellent and pleasant, so abstruse and recondite, so bewitching, so miraculous, so ravishing, so easie withal and full of delight, omnem humanum captum superare videtur . By this means you may define ex ungue leonem , as the diverbe is, by his thumb alone the bigness of Hercules, or the true dimensions of the great hColossus, Solomons temple, and Domitians amphitheater, out of a little part. By this art you may contemplate the variation of the 23 letters…."
g Ad. 2. definit.2. elem. In disciplinis humanis nihil praestantius reperitur: quippe miracula quaedam numerorum eruit tam abstrusa et recondita, tanta nihilo minus facilitate et voluptate, ut, &c.
h Which contained 1080000 weight of brass.
— The Anatomy of Melancholy, Part. 2, Sec. 2, Mem. 4
Comments Off on Metalibrarianship
Friday, November 19, 2010
Absolute Ambition
"It's my absolute ambition that you are touched to the core of your being with the content…."
— Julie Taymor on Spider-Man: Turn Off the Dark (Playbill video, undated)
Another ambitious comic-book promotion —
"What Logicomix does that few works in any medium do is to make intellectual passion palpable. That is its greatest strength. And it’s here that its form becomes its substance."
— Judith Roitman, review (pdf, 3.7 MB) of Logicomix: An Epic Search for Truth , in …
The December 2010 AMS Notices cover has excerpts from Logicomix.
Related material:
"In the classical grammarians’ sense of the power of form over 'content' and style over 'substance,' he originated the phrase, 'the medium is the message.'"
— Joseph P. Duggan on Marshall McLuhan at The University Bookman
See also, in this journal, The Medium is the Message, Wechsler, and Blockheads .
Comments Off on Absolute Ambition
Monday, June 14, 2010
Birkhoff on the Galois “Theory of Ambiguity”
The Principle of Sufficient Reason
from "Three Public Lectures on Scientific Subjects,"
delivered at the Rice Institute, March 6, 7, and 8, 1940
EXCERPT 1—
My primary purpose will be to show how a properly formulated
Principle of Sufficient Reason plays a fundamental
role in scientific thought and, furthermore, is to be regarded
as of the greatest suggestiveness from the philosophic point
of view.2
In the preceding lecture I pointed out that three branches
of philosophy, namely Logic, Aesthetics, and Ethics, fall
more and more under the sway of mathematical methods.
Today I would make a similar claim that the other great
branch of philosophy, Metaphysics, in so far as it possesses
a substantial core, is likely to undergo a similar fate. My
basis for this claim will be that metaphysical reasoning always
relies on the Principle of Sufficient Reason, and that
the true meaning of this Principle is to be found in the
“Theory of Ambiguity” and in the associated mathematical
“Theory of Groups.”
If I were a Leibnizian mystic, believing in his “preestablished
harmony,” and the “best possible world” so
satirized by Voltaire in “Candide,” I would say that the
metaphysical importance of the Principle of Sufficient Reason
and the cognate Theory of Groups arises from the fact that
God thinks multi-dimensionally3 whereas men can only
think in linear syllogistic series, and the Theory of Groups is
2 As far as I am aware, only Scholastic Philosophy has fully recognized and ex-
ploited this principle as one of basic importance for philosophic thought
3 That is, uses multi-dimensional symbols beyond our grasp.
______________________________________________________________________
the appropriate instrument of thought to remedy our deficiency
in this respect.
The founder of the Theory of Groups was the mathematician
Evariste Galois. At the end of a long letter written in
1832 on the eve of a fatal duel, to his friend Auguste
Chevalier, the youthful Galois said in summarizing his
mathematical work,4 “You know, my dear Auguste, that
these subjects are not the only ones which I have explored.
My chief meditations for a considerable time have been
directed towards the application to transcendental Analysis
of the theory of ambiguity. . . . But I have not the time, and
my ideas are not yet well developed in this field, which is
immense.” This passage shows how in Galois’s mind the
Theory of Groups and the Theory of Ambiguity were
interrelated.5
Unfortunately later students of the Theory of Groups
have all too frequently forgotten that, philosophically
speaking, the subject remains neither more nor less than the
Theory of Ambiguity. In the limits of this lecture it is only
possible to elucidate by an elementary example the idea of a
group and of the associated ambiguity.
Consider a uniform square tile which is placed over a
marked equal square on a table. Evidently it is then impossible
to determine without further inspection which one
of four positions the tile occupies. In fact, if we designate
its vertices in order by A, B, C, D, and mark the corresponding
positions on the table, the four possibilities are for the
corners A, B, C, D of the tile to appear respectively in the
positions A, B, C, D; B, C, D, A; C, D, A, B; and D, A, B, C.
These are obtained respectively from the first position by a
4 My translation.
5 It is of interest to recall that Leibniz was interested in ambiguity to the extent
of using a special notation v (Latin, vel ) for “or.” Thus the ambiguously defined
roots 1, 5 of x2-6x+5=0 would be written x = l v 5 by him.
______________________________________________________________________
null rotation ( I ), by a rotation through 90° (R), by a rotation
through 180° (S), and by a rotation through 270° (T).
Furthermore the combination of any two of these rotations
in succession gives another such rotation. Thus a rotation R
through 90° followed by a rotation S through 180° is equivalent
to a single rotation T through 270°, Le., RS = T. Consequently,
the "group" of four operations I, R, S, T has
the "multiplication table" shown here:
This table fully characterizes the group, and shows the exact
nature of the underlying ambiguity of position.
More generally, any collection of operations such that
the resultant of any two performed in succession is one of
them, while there is always some operation which undoes
what any operation does, forms a "group."
__________________________________________________
EXCERPT 2—
Up to the present point my aim has been to consider a
variety of applications of the Principle of Sufficient Reason,
without attempting any precise formulation of the Principle
itself. With these applications in mind I will venture to
formulate the Principle and a related Heuristic Conjecture
in quasi-mathematical form as follows:
PRINCIPLE OF SUFFICIENT REASON. If there appears
in any theory T a set of ambiguously determined ( i e .
symmetrically entering) variables, then these variables can themselves
be determined only to the extent allowed by the corresponding
group G. Consequently any problem concerning these variables
which has a uniquely determined solution, must itself be
formulated so as to be unchanged by the operations of the group
G ( i e . must involve the variables symmetrically).
HEURISTIC CONJECTURE. The final form of any
scientific theory T is: (1) based on a few simple postulates; and
(2) contains an extensive ambiguity, associated symmetry, and
underlying group G, in such wise that, if the language and laws
of the theory of groups be taken for granted, the whole theory T
appears as nearly self-evident in virtue of the above Principle.
The Principle of Sufficient Reason and the Heuristic Conjecture,
as just formulated, have the advantage of not involving
excessively subjective ideas, while at the same time
retaining the essential kernel of the matter.
In my opinion it is essentially this principle and this
conjecture which are destined always to operate as the basic
criteria for the scientist in extending our knowledge and
understanding of the world.
It is also my belief that, in so far as there is anything
definite in the realm of Metaphysics, it will consist in further
applications of the same general type. This general conclu-
sion may be given the following suggestive symbolic form:
While the skillful metaphysical use of the Principle must
always be regarded as of dubious logical status, nevertheless
I believe it will remain the most important weapon of the
philosopher.
___________________________________________________________________________
A more recent lecture on the same subject —
by Jean-Pierre Ramis (Johann Bernoulli Lecture at U. of Groningen, March 2005)
Comments Off on Birkhoff on the Galois “Theory of Ambiguity”
Sunday, April 18, 2010
For Trevanian
Where Entertainment Is God
(continued)
Google News at about 7:37 PM —
| The Eiger Sanction, by Trevanian –
"Because CII men worked in foreign countries without invitation, and often to the detriment of the established governments, they had no recourse to official protection. Organization men to the core, the CII heads decided that another Division must be established to combat the problem. They relied on their computers to find the ideal man to head the new arm, and the card that survived the final sorting bore the name Yurasis Dragon. In order to bring Mr. Dragon to the United States, it was necessary to absolve him of accusations lodged at the War Crimes Tribunal concerning certain genocidal peccadillos, but CII considered him worth the effort." |
Comments Off on For Trevanian
Friday, October 3, 2008
Friday October 3, 2008
The Prize
“The secret to life, and
to love, is getting started,
keeping going, and then
getting started again.”
Nobel Laureate
Seamus Heaney
at Sanders Theatre,
Harvard College,
September 30, 2008
On Elke Sommer:
“…Young Elke… studied
in the prestigious
Gymnasium School
in Erlangen….”
Erlangen Prize Lecture:
Variations on a Theme of
Plato, Goethe, and Klein
(Background:
Christmas Knot, Sept. 26,
and Hard Core, July 17-18.)
Saturday, July 19, 2008
Saturday July 19, 2008
Hard Core
Bertram Kostant, Professor Emeritus of Mathematics at MIT, on an object discussed in this week's New Yorker:
"A word about E(8). In my opinion, and shared by others, E(8) is the most magnificent 'object' in all of mathematics. It is like a diamond with thousands of facets. Each facet offering a different view of its unbelievable intricate internal structure."
Hermann Weyl on the hard core of objectivity:
"Perhaps the philosophically most relevant feature of modern science is the emergence of abstract symbolic structures as the hard core of objectivity behind– as Eddington puts it– the colorful tale of the subjective storyteller mind." (Philosophy of Mathematics and Natural Science, Princeton, 1949, p. 237)
Steven H. Cullinane on the symmetries of a 4×4 array of points:
|
A Structure-Endowed Entity
"A guiding principle in modern mathematics is this lesson: Whenever you have to do with a structure-endowed entity S, try to determine its group of automorphisms, the group of those element-wise transformations which leave all structural relations undisturbed. You can expect to gain a deep insight into the constitution of S in this way." — Hermann Weyl in Symmetry Let us apply Weyl's lesson to the following "structure-endowed entity."
What is the order of the resulting group of automorphisms? |
The above group of
automorphisms plays
a role in what Weyl,
following Eddington,
called a "colorful tale"–
This puzzle shows
that the 4×4 array can
also be viewed in
thousands of ways.
"You can make 322,560
pairs of patterns. Each
pair pictures a different
symmetry of the underlying
16-point space."
— Steven H. Cullinane,
July 17, 2008
For other parts of the tale,
see Ashay Dharwadker,
the Four-Color Theorem,
and Usenet Postings.
Comments Off on Saturday July 19, 2008
Friday, July 18, 2008
Friday July 18, 2008
Hard Core
David Corfield quotes Weyl in a weblog entry, "Hierarchy and Emergence," at the n-Category Cafe this morning:
"Perhaps the philosophically most relevant feature of modern science is the emergence of abstract symbolic structures as the hard core of objectivity behind– as Eddington puts it– the colorful tale of the subjective storyteller mind." (Philosophy of Mathematics and Natural Science [Princeton, 1949], p. 237)
For the same quotation in a combinatorial context, see the foreword by A. W. Tucker, "Combinatorial Problems," to a special issue of the IBM Journal of Research and Development, November 1960 (1-page pdf).
See also yesterday's Log24 entry.
Comments Off on Friday July 18, 2008
Tuesday, April 29, 2008
Tuesday April 29, 2008
Sacerdotal Jargon
at Harvard:
at Harvard:
Thomas Wolfe
(Harvard M.A., 1922)
versus
Rosalind Krauss
(Harvard M.A., 1964,
Ph.D., 1969)
on
"No culture has a pact with eternity."
— George Steiner, interview in
The Guardian of
"At that instant he saw,
in one blaze of light, an image
of unutterable conviction….
the core of life, the essential
pattern whence all other things
proceed, the kernel of eternity."
— Thomas Wolfe, Of Time
and the River, quoted in
Log24 on June 9, 2005
From today's online Harvard Crimson:
"… under the leadership of Faust,
Harvard students should look forward
to an ever-growing opportunity for
international experience
and artistic endeavor."
Pauli as Mephistopheles
in a 1932 parody of
Goethe's Faust at Niels Bohr's
institute in Copenhagen
From a recent book
on Wolfgang Pauli,
The Innermost Kernel:
A belated happy birthday
to the late
Felix Christian Klein
(born on April 25) —
Another Harvard figure quoted here on Dec. 5, 2002:
"The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety, a subtlety in which it was natural for Cézanne to say: 'I see planes bestriding each other and sometimes straight lines seem to me to fall' or 'Planes in color…. The colored area where shimmer the souls of the planes, in the blaze of the kindled prism, the meeting of planes in the sunlight.' The conversion of our Lumpenwelt went far beyond this. It was from the point of view of another subtlety that Klee could write: 'But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space– which he calls the mind or heart of creation– determines every function.' Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less."
— Wallace Stevens, Harvard College Class of 1901, "The Relations between Poetry and Painting" in The Necessary Angel (Knopf, 1951)
From a review of Rosalind Krauss's The Optical Unconscious (MIT Press hardcover, 1993):
Krauss is concerned to present Modernism less in terms of its history than its structure, which she seeks to represent by means of a kind of diagram: "It is more interesting to think of modernism as a graph or table than a history." The "table" is a square with diagonally connected corners, of the kind most likely to be familiar to readers as the Square of Opposition, found in elementary logic texts since the mid-19th century. The square, as Krauss sees it, defines a kind of idealized space "within which to work out unbearable contradictions produced within the real field of history." This she calls, using the inevitable gallicism, "the site of Jameson's Political Unconscious" and then, in art, the optical unconscious, which consists of what Utopian Modernism had to kick downstairs, to repress, to "evacuate… from its field."
— Arthur C. Danto in ArtForum, Summer 1993
Rosalind Kraus in The Optical Unconscious (MIT Press paperback, 1994):
For a presentation of the Klein Group, see Marc Barbut, "On the Meaning of the Word 'Structure' in Mathematics," in Introduction to Structuralism, ed. Michael Lane (New York: Basic Books, 1970). Claude Lévi-Strauss uses the Klein group in his analysis of the relation between Kwakiutl and Salish masks in The Way of the Masks, trans. Sylvia Modelski (Seattle: University of Washington Press, 1982), p. 125; and in relation to the Oedipus myth in "The Structural Analysis of Myth," Structural Anthropology, trans. Claire Jackobson [sic] and Brooke Grundfest Schoepf (New York: Basic Books, 1963). In a transformation of the Klein Group, A. J. Greimas has developed the semiotic square, which he describes as giving "a slightly different formulation to the same structure," in "The Interaction of Semiotic Constraints," On Meaning (Minneapolis: University of Minnesota Press, 1987), p. 50. Jameson uses the semiotic square in The Political Unconscious (see pp. 167, 254, 256, 277) [Fredric Jameson, The Political Unconscious: Narrative as a Socially Symbolic Act (Ithaca: Cornell University Press, 1981)], as does Louis Marin in "Disneyland: A Degenerate Utopia," Glyph, no. 1 (1977), p. 64.
For related non-sacerdotal jargon, see…
Wikipedia on the Klein group (denoted V, for Vierergruppe):
In this representation, V is a normal subgroup of the alternating group A4 (and also the symmetric group S4) on 4 letters. In fact, it is the kernel of a surjective map from S4 to S3. According to Galois theory, the existence of the Klein four-group (and in particular, this representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals.
For radicals of another sort, see A Logocentric Meditation, A Mass for Lucero, and [update of 7 PM] Steven Erlanger in today's New York Times— "France Still Divided Over Lessons of 1968 Unrest."
For material related to Klee's phrase mentioned above by Stevens, "the organic center of all movement in time and space," see the following Google search:
Comments Off on Tuesday April 29, 2008
Thursday, June 21, 2007
Thursday June 21, 2007
Let No Man
Write My Epigraph
"His graceful accounts of the Bach Suites for Unaccompanied Cello illuminated the works’ structural logic as well as their inner spirituality."
—Allan Kozinn on Mstislav Rostropovich in The New York Times, quoted in Log24 on April 29, 2007
"At that instant he saw, in one blaze of light, an image of unutterable conviction…. the core of life, the essential pattern whence all other things proceed, the kernel of eternity."
— Thomas Wolfe, Of Time and the River, quoted in Log24 on June 9, 2005
"… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)"
— Peter J. Cameron, "The Geometry of the Mathieu Groups" (pdf)
"… donc Dieu existe, réponse!"
"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"
(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)
"Pauli as Mephistopheles
in a 1932 parody of
Goethe's Faust at Niels Bohr's
institute in Copenhagen.
The drawing is one of
many by George Gamow
illustrating the script."
— Physics Today
"Borja dropped the mutilated book on the floor with the others. He was looking at the nine engravings and at the circle, checking strange correspondences between them.
"Pauli linked this symbolism
with the concept of automorphism."
'To meet someone' was his enigmatic answer. 'To search for the stone that the Great Architect rejected, the philosopher's stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso.'"
— The Club Dumas, basis for the Roman Polanski film "The Ninth Gate" (See 12/24/05.)
"Pauli linked this symbolism
with the concept of automorphism."
— The Innermost Kernel
(previous entry)
And from
"Symmetry in Mathematics
and Mathematics of Symmetry"
(pdf), by Peter J. Cameron,
a paper presented at the
International Symmetry Conference,
Edinburgh, Jan. 14-17, 2007,
we have
The Epigraph–
(Here "whatever" should
of course be "whenever.")
Also from the
Cameron paper:
|
Local or global?
Among other (mostly more vague) definitions of symmetry, the dictionary will typically list two, something like this:
• exact correspondence of parts; Mathematicians typically consider the second, global, notion, but what about the first, local, notion, and what is the relationship between them? A structure M is homogeneous if every isomorphism between finite substructures of M can be extended to an automorphism of M; in other words, "any local symmetry is global." |
Some Log24 entries
related to the above politically
(women in mathematics)–
Global and Local:
One Small Step
and mathematically–
Structural Logic continued:
Structure and Logic (4/30/07):
This entry cites
Alice Devillers of Brussels–
"The aim of this thesis
is to classify certain structures
which are, from a certain
point of view, as homogeneous
as possible, that is which have
as many symmetries as possible."
"There is such a thing
as a tesseract."
Comments Off on Thursday June 21, 2007
Thursday, November 10, 2005
Thursday November 10, 2005
The Rhetoric of
Scientism
Scientism
“… the Board of Education went as far as to redefine what science is: it’s no longer just a search for natural explanations for natural phenomena. Now it’s a search for… well, that’s a bit hard to say. Any sort of explanation, apparently. Pixies, ghosts, telekinesis, auras, ancient astronauts, excesses of choleric humor, they all seem to be fair game in the interest of ‘academic freedom.'”
The shocking redefinition
(with changes highlighted):
(with changes highlighted):
| Kansas Definition of Science Adopted Feb. 14, 2001 “Science is the human activity of seeking natural explanations for what we observe in the world around us. Science does so through the use of observation, experimentation, and logical argument while maintaining strict empirical standards and healthy skepticism. Scientific explanations are built on observations, hypotheses, and theories. A hypothesis is a testable statement about the natural world that can be used to build more complex inferences and explanations. A theory is a well-substantiated explanation of some aspect of the natural world that can incorporate observations, inferences, and tested hypotheses |
Kansas Definition of Science Approved Nov. 8, 2005 “Science is a systematic method of continuing investigation that uses observations, hypothesis testing, measurement, experimentation, logical argument and theory building to lead to more adequate explanations of natural phenomena. Science does so while maintaining strict empirical standards and healthy skepticism. Scientific explanations are built on observations, hypotheses, and theories. A hypothesis is a testable statement about the natural world that can be used to build more complex inferences and explanations. A theory is a well-substantiated explanation of some aspect of the natural world that can incorporate observations, inferences, and tested hypotheses. |
| Scientific explanations must meet certain criteria. Scientific explanations are consistent with experimental and/or observational data and testable by scientists through additional experimentation and/or observation. Scientific explanation must meet criteria that govern the repeatability of observations and experiments. The effect of these criteria is to insure that scientific explanations about the world are open to criticism and that they will be modified or abandoned in favor of new explanations if empirical evidence so warrants. Because all scientific explanations depend on observational and experimental confirmation, all scientific knowledge is, in principle, subject to change as new evidence becomes available. The core theories of science have been subjected to a wide variety of confirmations and have a high degree of reliability within the limits to which they have been tested. In areas where data or understanding are incomplete, new data may lead to changes in current theories or resolve current conflicts. In situations where information is still fragmentary, it is normal for scientific ideas to be incomplete, but this is also where the opportunity for making advances may be greatest. Science has flourished in different regions during different time periods, and in history, diverse cultures have contributed scientific knowledge and technological inventions. Changes in scientific knowledge usually occur as gradual modifications, but the scientific enterprise also experiences periods of rapid advancement. The daily work of science and technology results in incremental advances in our understanding of the world about us.” | Scientific explanations must meet certain criteria. Scientific explanations are consistent with experimental and/or observational data and testable by scientists through additional experimentation and/or observation. Scientific explanation must meet criteria that govern the repeatability of observations and experiments. The effect of these criteria is to insure that scientific explanations about the world are open to criticism and that they will be modified or abandoned in favor of new explanations if empirical evidence so warrants. Because all scientific explanations depend on observational and experimental confirmation, all scientific knowledge is, in principle, subject to change as new evidence becomes available. The core theories of science have been subjected to a wide variety of confirmations and have a high degree of reliability within the limits to which they have been tested. In areas where data or understanding is incomplete, new data may lead to changes in current theories or resolve current conflicts. In situations where information is still fragmentary, it is normal for scientific ideas to be incomplete, but this is also where the opportunity for making advances may be greatest. Science has flourished in different regions during different time periods, and in history, diverse cultures have contributed scientific knowledge and technological inventions. Changes in scientific knowledge usually occur as gradual modifications, but the scientific enterprise also experiences periods of rapid advancement. The daily work of science and technology results in incremental advances in understanding the world.” |
From both old (2001) and
new (2005) Kansas standards:
Teaching With Tolerance and Respect
new (2005) Kansas standards:
Teaching With Tolerance and Respect
“A teacher is an important role model for demonstrating respect, sensitivity, and civility. Teachers should not ridicule, belittle or embarrass a student for expressing an alternative view or belief.”
It’s a very ancient saying,
But a true and honest thought,
That if you become a teacher,
By your pupils you’ll be taught.
But a true and honest thought,
That if you become a teacher,
By your pupils you’ll be taught.
— Oscar Hammerstein,
“Getting to Know You”
Scientism and Civility:
A Google blog search for
fucking kansas evolution standards -fuck
yields “about 47” entries.
A search for
fuck kansas evolution standards -fucking
yields “about 34” entries.
A search for
fuck fucking kansas evolution standards
yields “about 42” entries.
Comments Off on Thursday November 10, 2005
Thursday, June 9, 2005
Thursday June 9, 2005
Kernel of Eternity
continued
"At that instant he saw,
in one blaze of light,
an image of unutterable conviction….
the core of life, the essential pattern
whence all other things proceed,
the kernel of eternity."
— Thomas Wolfe,
Of Time and the River
From "The Relations between
Poetry and Painting," by Wallace Stevens:
"The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety…. It was from the point of view of… [such a] subtlety that Klee could write: 'But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space—which he calls the mind or heart of creation— determines every function.' Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less."
As yesterday's entry "Kernel of Eternity" indicated, the word "kernel" has a definite meaning in mathematics. The Klein four-group, beloved of structural anthropologists and art theorists, is a particularly apt example of a kernel. (See PlanetMath for details.)
Diagrams of this group may have influenced Giovanni Sambin, professor of mathematical logic at the University of Padua; the following impressive-looking diagram is from Sambin's
Sambin argues that this diagram reflects some of the basic structures of thought itself… making it perhaps one way to describe what Klee called the "mind or heart of creation."
But this verges on what Stevens called the sacerdotal. It seems that a simple picture of the "kernel of eternity" as the four-group, a picture without reference to logic or philosophy, and without distracting letters and labels, is required. The following is my attempt to supply such a picture:
This is a picture of the four-group
as a permutation group on four points.
Pairs of colored arrows indicate the three
transformations other than the identity,
which may be regarded either as
invisible or as rendered by
the four black points themselves.
Update of 7:45 PM Thursday:
Review of the above (see comments)
by a typical Xanga reader:
"Ur a FUCKIN' LOSER!!!!! LMFAO!!!!"
For more merriment, see
The Optical Unconscious
and
The Painted Word.
A recent Xangan movie review:
"Annakin's an idiot, but he's not an idiot because that's the way the character works, he's an idiot because George Lucas was too lazy to make him anything else. He has to descend to the Daaaahk Side, but the dark side never really seems all that dark. He kills children, but offscreen. We never get to see the transformation. One minute he cares about the republic, the next he's killing his friends, and then for some reason he's duelling with Obi Wan on a lava flow. Who cares? Not me….
So a big ol' fuck you to George Lucas. Fuck you, George!"
Both Xangans seem to be fluent in what Tom Wolfe has called the "fuck patois."
A related suggestion from Google:
These remarks from Xangans and Google
suggest the following photo gift,
based on a 2003 journal entry:
Wednesday, June 8, 2005
Wednesday June 8, 2005
Kernel of Eternity
Today is the feast day of Saint Gerard Manley Hopkins, “immortal diamond.”
“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”
— Thomas Wolfe, Of Time and the River
“… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)”
— Peter J. Cameron,
The Geometry of the Mathieu Groups (pdf)
“… donc Dieu existe, réponse!”
— attributed, some say falsely, to Leonhard Euler
Comments Off on Wednesday June 8, 2005
Wednesday, March 2, 2005
Wednesday March 2, 2005
White Stone
"I have stolen more quotes and thoughts and purely elegant little starbursts of writing from the Book of Revelation than anything else in the English language– and it is not because I am a biblical scholar, or because of any religious faith, but because I love the wild power of the language and the purity of the madness that governs it and makes it music."
— Hunter S. Thompson, Author's Note, Generation of Swine
"And I will give him a white stone…."
Related material:
2003 2/17: "immortal diamond"
2004 2/17: "hard core"
2005 2/17: "the diamond"
For an "elegant starburst," see
"Starflight," from 10/10, 2004 —
the date of
Christopher Reeve's death.
See also
Revelation 10:10 —
"And I took the little book
out of the angel's hand,
and ate it up; and it was in my mouth
sweet as honey: and as soon as I had
eaten it, my belly was bitter."
For the relationship of this verse to
the style of Hunter Thompson, see
From the Department of Justice:
"LSD generally is taken by mouth.
The drug is colorless and odorless
but has a slightly bitter taste."
Among the street terms for LSD
is "Superman."
Friday, July 9, 2004
Friday July 9, 2004
Scoop
This afternoon I came across, in a briefcase I seldom use, two books I had not looked at since I bought them last month:
- The Footprints of God, a recently published paperback by Greg Iles, a writer who graduated from Trinity High School, Natchez, Mississippi, in 1979, and from the University of Mississippi in Oxford in 1983.
- Sanctuary, by the better-known Mississippi writer William Faulkner.
At the time I purchased the books, indeed until I looked up Iles on the Web today, I was not aware of the Mississippi connection. Their physical connection, lying together today in my briefcase, is, of course, purely coincidental. My view of coincidence is close to that of Arthur Koestler, who wrote The Challenge of Chance and The Roots of Coincidence, and to that of Loren Eiseley, who wrote of a dice game and of "the Other Player" in his autobiography, All the Strange Hours.
A Log24 entry yesterday referred to a comedic novel on the role of chance in physics, Cosmic Banditos. Today's New York Times quotes an entertainer who referred to President Bush yesterday, at a political fund-raiser, as a bandito. Another coincidence… this one related directly to the philosophy of coincidences expounded jokingly in Cosmic Banditos.
I draw no conclusions from such coincidences, but they do inspire me to look a little deeper into life's details — where, some say, God is. Free association on these details, together with a passage in Sanctuary, inspired the following collage:
Related Texts
Faulkner on a trinity of women
in Sanctuary (Ch. 25):
"Miss Reba emerged from behind the screen with three glasses of gin. 'This'll put some heart into us,' she said. 'We're setting here like three old sick cats.' They bowed formally and drank, patting their lips. Then they began to talk. They were all talking at once,* again in half-completed sentences, but without pauses for agreement or affirmation."
"In Defense of the Brand":
"In Defense of the Brand":
"When I was helping Frito corn chips expand its core user group in the mid-'90s, we didn't ask Frito-Lay to just wave the Fritos banner. The brand was elevated to a place where it could address its core users in a way that was relevant to their lifestyle. We took the profile of the audience and created a campaign starring Reba McEntire. It captured the brand's essence, and set Frito eaters amidst good music, good people, and good fun."
Song lyric, Reba McEntire:
"I might have been born
just plain white trash,
but Fancy was my name."
just plain white trash,
but Fancy was my name."
Loren Eiseley,
Notes of an Alchemist:
I never found
the hole in the wall;
I never found
Pancho Villa country
where you see the enemy first.
— "The Invisible Horseman"
* A significant phrase. See
Sunday, April 25, 2004
Sunday April 25, 2004
Small World
Added a note to 4×4 Geometry:
The 4×4 square model 
lets us visualize the projective space PG(3,2) as well as the affine space AG(4,2). For tetrahedral and circular models of PG(3,2), see the work of Burkard Polster. The following is from an advertisement of a talk by Polster on PG(3,2).
|
The Smallest Perfect Universe “After a short introduction to finite geometries, I’ll take you on a… guided tour of the smallest perfect universe — a complex universe of breathtaking abstract beauty, consisting of only 15 points, 35 lines and 15 planes — a space whose overall design incorporates and improves many of the standard features of the three-dimensional Euclidean space we live in…. Among mathematicians our perfect universe is known as — Burkard Polster, May 2001 |
Comments Off on Sunday April 25, 2004
Wednesday, February 18, 2004
Wednesday February 18, 2004
Hard Core, Part II:
Star of Africa
|
|
|
In memory of St. Katharine Hepburn,
who died on St. Peter’s Day, 2003:
“Although the greater saints
are more acceptable to God
than the lesser,
it is sometimes profitable
to pray to the lesser.”
— St. Thomas Aquinas
From The Times, UK, Feb. 18, 2004:
Straw denies
a big-three takeover
at EU summit
Britain’s Foreign Secretary “said that there were no plans to set up a small body within the EU to take control of its affairs.
However, he told a news conference at the Foreign Office that it made sense for the three biggest economies to work ‘collaboratively’ on matters of common interest….
At tonight’s summit Mr Blair, Gerhard Schröder, the German Chancellor, and President Chirac of France will discuss initiatives to co-ordinate and strengthen the EU’s industrial policy….
German commentators regard the summit as a sea-change in British policy towards Europe — a signal that London’s main aim is no longer to split Paris and Berlin.”
Tuesday, February 17, 2004
Tuesday February 17, 2004
Hard Core
From USATODAY.com,
Posted 2/16/2004 11:16 PM
Diamond at heart of star
outweighs any on Earth
Astronomers announced Friday that a white dwarf star they’ve been studying is a chunk of crystallized carbon that weighs 5 million trillion trillion pounds. That’s the same as a diamond that is approximately 10 billion trillion trillion carats, or a one followed by 34 zeros.
 |
Twinkle-twinkle indeed: An artist’s conception of the diamond core of a dead white-dwarf star. Harvard-Smithsonian |
“It’s the mother of all diamonds,” said astronomer Travis Metcalfe, Harvard-Smithsonian Center for Astrophysics….
The biggest diamond on Earth is the 530-carat Star of Africa, part of the Crown Jewels of England. It was cut from a 3,100-carat gem*, the biggest ever found.
Monday, November 17, 2003
Monday November 17, 2003
Total Recall:
in which Philip K. Dick
meets Joan Didion yet again
From Joan Didion’s new work on California history, Where I Was From:
“There was never just the golden dream of riches and bountiful nature, but always a scene of exploitation and false promises, indifference and ruthlessness, a kind of hollow core.”
 |
 |
Hollow no more.
Monday, August 18, 2003
Monday August 18, 2003
Entries since Xanga’s
August 10 Failure:
Sunday, August 17, 2003 2:00 PM
A Thorny Crown of…
From the first episode of
the television series
“The West Wing“:
|
Original airdate: Sept. 22, 1999 MARY MARSH CALDWELL MARY MARSH JOSH TOBY [A stunned silence. Everyone stares at Toby.] TOBY (CONT.) JOSH |
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 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” Varnedoe’s death coincided with “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 The flag design in that entry
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 word “idea” (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
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, |
Dr. Mengele, |
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, |
|
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
- Today’s anniversary of a
1727 Moravian Pentecost, - An April 7, 2003,
lecture at Moravian College, and - St. Bonaventure’s 1259
remarks on the Trinity,
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
“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: |
‘Stein: |
For answers, click on the pictures
of Franken and ‘Stein.
Comments Off on Monday August 18, 2003
Sunday, June 8, 2003
Sunday June 8, 2003
Of Time and the River
Today is the feast day of Saint Gerard Manley Hopkins, “immortal diamond.”
“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”
“entered the university at Chapel Hill at fifteen ‘an awkward, unhappy misfit.’ By the time he graduated, he was editor of the college newspaper….”
Jeff MacNelly, who died on this date in the Year of Our Lord 2000,
“in 1977 started drawing the comic strip ‘Shoe‘…. The strip was named in honor of the legendary Jim Shumaker, for whom MacNelly worked at the Chapel Hill Weekly.”
From my Monday, June 2, 2003 entry:
Two quotations from “The Diamond Project“:
“We all know that something is eternal,” the Stage Manager says. “And it ain’t houses and it ain’t names, and it ain’t earth, and it ain’t even stars—everybody knows in their bones that something is eternal, and that something has to do with human beings.”
— John Lahr, review of “Our Town““Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave. Its flashes are flashes of fire, a raging flame.”
— Song of Solomon
Here are some other thoughts from the same date, but a different time, fictional time, Faulkner time:
Where the shadow of the bridge fell I could see down for a long way, but not as far as the bottom. When you leave a leaf in water a long time after a while the tissue will be gone and the delicate fibers waving slow as the motion of sleep. They dont touch one another, no matter how knotted up they once were, no matter how close they lay once to the bones. And maybe when He says Rise the eyes will come floating up too, out of the deep quiet and the sleep, to look on glory.
— William Faulkner, The Sound and the Fury
The concluding link from my June 2, 2003, entry furnishes a clue to the timelessness of Quentin Compson‘s thoughts above:
Glory… Song of Songs 8. 7-8
From the King James Bible‘s rendition of the Song of Songs:
8:7 Many waters cannot quench love, neither can the floods drown it: if a man would give all the substance of his house for love, it would utterly be contemned.
8:8 We have a little sister, and she hath no breasts: what shall we do for our sister in the day when she shall be spoken for?
For Quentin Compson’s thoughts on his little sister Caddy, consult the online hypertext edition of
Comments Off on Sunday June 8, 2003
Friday, November 8, 2002
Friday November 8, 2002
Religious Symbolism
at Princeton
In memory of Steve McQueen (“The Great Escape” and “The Thomas Crown Affair”… see preceding entry) and of Rudolf Augstein (publisher of Der Spiegel), both of whom died on November 7 (in 1980 and 2002, respectively), in memory of the following residents of
The Princeton Cemetery
of the Nassau Presbyterian Church
Established 1757
|
SYLVIA BEACH (1887-1962), whose father was pastor of the First Presbyterian Church, founded Shakespeare & Company, a Paris bookshop which became a focus for struggling expatriate writers. In 1922 she published James Joyce’s Ulysses when others considered it obscene, and she defiantly closed her shop in 1941 in protest against the Nazi occupation. KURT GÖDEL (1906-1978), a world-class mathematician famous for a vast array of major contributions to logic, was a longtime professor at the Institute for Advanced Study, founded in 1930. He was a corecipient of the Einstein Award in 1951. JOHN (HENRY) O’HARA (1905-1970) was a voluminous and much-honored writer. His novels, Appointment in Samarra (1934) and Ten North Frederick (1955), and his collection of short stories, Pal Joey (1940), are among his best-known works. |
and of the long and powerful association of Princeton University with the Presbyterian Church, as well as the theological perspective of Carl Jung in Man and His Symbols, I offer the following “windmill,” taken from the Presbyterian Creedal Standards website, as a memorial:
The background music Les Moulins de Mon Coeur, selected yesterday morning in memory of Steve McQueen, continues to be appropriate.
“A is for Anna.”
— James Joyce
Comments Off on Friday November 8, 2002