Log24

Tuesday, March 20, 2018

Springtime for Bavaria

Filed under: Uncategorized — Tags: — m759 @ 12:15 PM

Monday, March 19, 2018

Such an Air of Spring About It

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

"Ready for More?" — The Times

Thursday, August 17, 2017

Down in the Jungle Room

Filed under: Uncategorized — Tags: — m759 @ 4:04 PM

See also other posts now tagged Jungle Room.

Friday, June 16, 2017

Chalkroom Jungle

Filed under: Uncategorized — Tags: , , , — m759 @ 3:33 AM

At MASS MoCA, the installation "Chalkroom" quotes a lyric —

Oh beauty in all its forms
funny how hatred can also be a beautiful thing
When it's as sharp as a knife
as hard as a diamond

Perfect

— From "One Beautiful Evening," by Laurie Anderson.

See also the previous post and "Smallest Perfect" in this journal.

Sunday, May 15, 2016

One Ring

Filed under: Uncategorized — Tags: — m759 @ 5:06 PM

(Continued from May 11 and May 15.)

Poem by Eleanor Wilner from 'Reversing the Spell' speaks of diamonds and 'glitter.' (Pbk. publ. Nov. 1, 1997)

Tuesday, April 10, 2012

Turing Gate

Filed under: Uncategorized — Tags: , — m759 @ 2:02 AM

In memory of Christine Brooke-Rose,
an image from the date of her death

IMAGE- Excerpt from book 'Turing's Cathedral'

See also A Little Story and Before Dehors.

Monday, March 19, 2018

Tough Crowd.

Filed under: Uncategorized — Tags: — m759 @ 7:04 PM

Sunday, March 18, 2018

Draper at the Mother Church

Filed under: Uncategorized — Tags: — m759 @ 1:01 PM

From The Atlantic , September 2017 issue, online —
"How America Lost Its Mind," by former Harvard Lampoon  
writer Kurt Andersen —

Related material —

"There is a transformation, a metamorphosis that's going on here."
— Alexander Nix, CEO of Cambridge Analytica

The Lucasian Version —

Saturday, March 17, 2018

A Question for Cambridge Analytica

Filed under: Uncategorized — Tags: — m759 @ 8:42 PM

Detail —

Related material —

See as well a search in this journal for (mixed) Emojis.

Lucasian

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

From "Star Wars: The Last Jedi" —

From elsewhere —

Friday, March 16, 2018

Cast

Filed under: Uncategorized — Tags: — m759 @ 1:00 PM

Wednesday, March 14, 2018

Review

Filed under: Uncategorized — Tags: — m759 @ 1:44 PM

Recent Log24 posts on a mobile phone —

Tuesday, February 27, 2018

Raiders of the Lost Images

Filed under: Uncategorized — m759 @ 11:28 AM

On the recent film "Justice League" —

From DC Extended Universe Wiki, "Mother Box" —

"However, during World War I, the British rediscovered
mankind's lost Mother Box. They conducted numerous studies
but were unable to date it due to its age. The Box was then
shelved in an archive, up until the night Superman died,
where it was then sent to Doctor Silas Stone, who
recognized it as a perpetual energy matrix. . . ." [Link added.]

The cubic shape of the lost Mother Box, also known as the
Change Engine, is shared by the stone in a novel by Charles Williams,
Many Dimensions . See the Solomon's Cube webpage.

See too the matrix of Claude Lévi-Strauss in posts tagged
Verwandlungslehre .

Some literary background:

Who speaks in primordial images speaks to us
as with a thousand trumpets, he grips and overpowers,
and at the same time he elevates that which he treats
out of the individual and transitory into the sphere of
the eternal. 
— C. G. JUNG

"In the conscious use of primordial images—
the archetypes of thought—
one modern novelist stands out as adept and
grand master: Charles Williams.
In The Place of the Lion  he incarnates Plato’s
celestial archetypes with hair-raising plausibility.
In Many Dimensions  he brings a flock of ordinary
mortals face to face with the stone bearing
the Tetragrammaton, the Divine Name, the sign of Four.
Whether we understand every line of a Williams novel
or not, we feel something deep inside us quicken
as Williams tells the tale.

Here, in The Greater Trumps , he has turned to
one of the prime mysteries of earth . . . ."

— William Lindsay Gresham, Preface (1950) to
Charles Williams's The Greater Trumps  (1932)

For fans of what the recent series Westworld  called "bulk apperception" —

Wednesday, December 13, 2017

Portland News

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

An obituary from this afternoon suggests a review of
a Log24 post from last year — 

See also today's earlier post Once in a Lullaby and yesterday's
London Daily Mail — "Kristen Stewart Cuts a Cool Figure" —

.

Over the Rainbow Bridge

Filed under: Uncategorized — Tags: — m759 @ 12:52 PM

Trends

Filed under: Uncategorized — Tags: , — m759 @ 2:04 AM

"The philosopher Jerry Fodor was important for the same reason
you’ve probably never heard of him: he was unimpressed,
to put it politely, by the intellectual trends of the day."

—  Stephen Metcalf in The New Yorker , Dec. 12, 2017

See also "The French Invasion," a Dec. 11 Quarterly Conversation
essay about Derrida in Baltimore in 1966, and the Dec. 10 posts
in this  journal tagged Interlacing Derrida. (The deplorable Derrida
trend is apparently still alive in Buffalo.)

According to Metcalf, Fodor's "occasional review-essays in the L.R.B. 
were masterpieces of a plainspoken and withering sarcasm. To Steven
Pinker’s suggestion that we read fiction because ' it supplies us with a
mental catalogue of the fatal conundrums we might face someday,' for
instance, Fodor replied, ' What if it turns out that, having just used the ring
that I got by kidnapping a dwarf to pay off the giants who built me my
new castle, I should discover that it is the very ring that I need in order to
continue to be immortal and rule the world? ' "

In the Fodor-Pinker dispute, my sympathies are with Pinker.

Related material — Google Sutra (the previous Log24 post) and earlier posts
found in a Log24 search for Ring + Bear + Jung —

Four Colours and Waiting for Logos.

Wednesday, August 16, 2017

Punctum

Filed under: Uncategorized — Tags: — m759 @ 9:00 AM

Or:  Every Picture Tells a Story  (Continued)

Related material —

The New York Times  online today, in a book review

"What if . . . Barthes was murdered? . . . in order to
procure a document that Barthes possessed . . . .
That document explained that, beyond the six
functions of language proposed by the Russian
linguist Roman Jakobson, there was a seventh
secret one:  an occult kind of language-use
guaranteed to persuade, a 'magic' power of
control over a listener."

See also Barthes in this  journal.

"Down in the Jungle Room" — Marc Cohn

Monday, August 14, 2017

Sound Track

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

Two songs by Chuck Berry on Chess Records in 1958

Sweet Little Sixteen  and  Sweet Little Rock and Roller .

Rock and Roller  begins

She's 9 years old and sweet as she can be
All dressed up like a downtown Christmas tree
Dancin' and hummin' a rock-roll melody

For meditations on Sixteen , see Berry + Sixteen in this journal.

A meditation on Rock and Roller —

Related material — From the above post's date,
March 21, 2017, a memoir by one Siva Vaidhyanathan,
"Robertson Professor of Media Studies and Director of
the Center for Media and Citizenship at the University of Virginia."

Sunday, May 15, 2016

Fake Eliot

Filed under: Uncategorized — Tags: — m759 @ 11:30 PM

The New Yorker

Poems | September 3, 2012 issue

House Master

BY FREDERICK SEIDEL

. . . .

"I remember everything.
I remember nothing.
I remember ancient Greek sparkles like a diamond ring."

. . . .

See also posts now tagged "One Ring"
and a search in this journal for "Glitter."

Quarter to Three

Filed under: Uncategorized — Tags: , — m759 @ 2:45 PM
 

Hilary Swank in 'Million Dollar Baby'

O.C.D.          

The "O.C.D." does not refer to obsessive-
compulsive disorder, but to "Our Class, Dear."

Aesthetics

Filed under: Uncategorized — Tags: , — m759 @ 2:09 AM

A college girl's remarks in the previous post suggested
a search in this journal for "vulgar and stupid."
That search yielded date — March 2, 2014.

In the spirit of the Church of Synchronology, a further search —
for that date — yielded, in a March 2, 2014, post, the following —

Square Dance

From The Telegraph —

And no fact of Alain Resnais’s life seemed to strike a stranger note than his assertion that the films which first inspired his ambition to become a film director were those in which Fred Astaire and Ginger Rogers danced. Or was it Dick Powell and Ruby Keeler? He could never be sure. “I wondered if I could find the equivalent of that exhilaration,” he recalled.

If he never did it was perhaps because of his highly cultivated attitude to serious cinema. His character and temperament were more attuned to the theory of film and a kind of intellectual square dance* which was far harder to bring to the screen with “exhilaration” than the art of Astaire and Rogers.

*See today's 11 AM ET Sermon.

"Heaven, I'm in Heaven!"

The college girl, who reportedly died at 70 on May 11, was
Katherine Dunn, author of the book One Ring Circus  quoted
above. She apparently improved with age.

Saturday, May 14, 2016

Yeah, Art, Beauty

Filed under: Uncategorized — Tags: , — m759 @ 11:17 PM

From a New York Times  obituary this evening —

"She entered Reed College in Portland as a philosophy major.

'I enjoyed it until I ran aground in an aesthetics class,' 
Ms. Dunn told Wired  magazine. 'I went in thinking, yeah,
art, beauty — my meat, drink and air. But on the first day,
I didn’t understand a word that was said in class, so I
marched out and changed my major to psychology.' "

Could have marched out and bought a dictionary .

Friday, May 13, 2016

Geometry and Kinematics

Filed under: Uncategorized — Tags: — m759 @ 10:31 PM

"Just as both tragedy and comedy can be written
by using the same letters of the alphabet, the vast
variety of events in this world can be realized by
the same atoms through their different arrangements
and movements. Geometry and kinematics, which
were made possible by the void, proved to be still
more important in some way than pure being."

— Werner Heisenberg in Physics and Philosophy

For more about geometry and kinematics, see (for instance)

"An introduction to line geometry with applications,"
by Helmut Pottmann, Martin Peternell, and Bahram Ravani,
Computer-Aided Design  31 (1999), 3-16.

The concepts of line geometry (null point, null plane, null polarity,
linear complex, Klein quadric, etc.) are also of interest in finite  geometry.
Some small finite spaces have as their natural models arrays of cubes .

Wednesday, May 11, 2016

Null Point

Filed under: Uncategorized — Tags: — m759 @ 7:59 PM

This evening's previous post links to an earlier post
on a book by DeLillo.  This suggests a review
of DeLillo's most recent book, Zero K .

A title I prefer: that of this post, Null Point. *
For related mathematics, see Zero System .

Wikipedia — 

The Kelvin scale is an absolute, 
thermodynamic temperature scale 
using as its null point  absolute zero,
the temperature at which
all thermal motion ceases in the
classical description of thermodynamics.

By Diction Possessed

Filed under: Uncategorized — Tags: — m759 @ 12:00 PM

Continued from Saturday, May 7, 2016 .

From an obituary in yesterday evening's online New York Times —

"I was writing plays, one-acters, about musicians
who were speakers of the idiom I loved most:
black American male speech, full of curse words,"
he wrote in an autobiographical essay. . . .

The obituary is for a poet who reportedly died on Saturday, May 7.

This  journal on that day ("By Diction Possessed") recalled the death
(on Valentine's Day 2015) of an English actor who was the voice of
the Ring in two of the "Lord of the Rings" films —

Backstory from Wikipedia — See Black Speech —

"The only example of 'pure' Black Speech is
the inscription upon the One Ring . . .

One Ring to rule them all,
One Ring to find them,
One Ring to bring them all
And in the darkness bind them. 
"

Sunday, May 8, 2016

Gesamtkunstwerke

Filed under: Uncategorized — Tags: — m759 @ 10:00 PM

„Ich begriff plötzlich, daß in der Sprache oder doch
mindestens im Geist des Glasperlenspiels tatsächlich
alles allbedeutend sei, daß jedes Symbol und jede
Kombination von Symbolen nicht hierhin oder dorthin,
nicht zu einzelnen Beispielen, Experimenten und
Beweisen führe, sondern ins Zentrum, ins Geheimnis
und Innerste der Welt, in das Urwissen. Jeder Übergang
von Dur zu Moll in einer Sonate, jede Wandlung eines
Mythos oder eines Kultes, jede klassische, künstlerische
Formulierung sei, so erkannte ich im Blitz jenes
Augenblicks, bei echter meditativer Betrachtung,
nichts andres als ein unmittelbarer Weg ins Innere
des Weltgeheimnisses, wo im Hin und Wider zwischen
Ein- und Ausatmen, zwischen Himmel und Erde,
zwischen Yin und Yang sich ewig das Heilige vollzieht.“

— Hermann Hesse, Das Glasperlenspiel .
Berlin:  Suhrkamp Taschenbuch Verlag, 2012, p. 172,
as quoted in a weblog.

"Only connect." — Howards End

Saturday, May 7, 2016

By Diction Possessed

Filed under: Uncategorized — Tags: , — m759 @ 3:00 PM

Mr. Howard reportedly died on Valentine's Day, 2015.

Tuesday, April 5, 2016

“Puzzle Cube of a Novel”

Filed under: Uncategorized — Tags: , — m759 @ 2:00 AM

"To know the mind of the creator"

Or that of Orson Welles

Related material — Cube Coloring.

Friday, August 7, 2015

Parts

Filed under: Uncategorized — Tags: — m759 @ 2:19 AM

Spielerei  —

"On the most recent visit, Arthur had given him
a brightly colored cube, with sides you could twist
in all directions, a new toy that had just come onto
the market."

— Daniel Kehlmann, F: A Novel  (2014),
     translated from the German by
     Carol Brown Janeway

Nicht Spielerei  —

A figure from this journal at 2 AM ET
on Monday, August 3, 2015

Also on August 3 —

FRANKFURT — "Johanna Quandt, the matriarch of the family
that controls the automaker BMW and one of the wealthiest
people in Germany, died on Monday in Bad Homburg, Germany.
She was 89."

MANHATTAN — "Carol Brown Janeway, a Scottish-born
publishing executive, editor and award-winning translator who
introduced American readers to dozens of international authors,
died on Monday in Manhattan. She was 71."

Related material —  Heisenberg on beauty, Munich, 1970                       

Monday, February 23, 2015

For Katy Perry

Filed under: Uncategorized — Tags: — m759 @ 10:15 PM

See also this  journal on the date of Mr. Howard's death:

"Mark my words
This love will make you levitate
Like a bird"

— Katy Perry, "Dark Horse"

“It’s the Super Bowl, I guess,”
Michael Keaton said in the first minutes
of ABC’s official Oscar red-carpet special."

— Hallie Cantor in the online New Yorker  today

Wednesday, September 17, 2014

Raiders of the Lost Articulation

Filed under: Uncategorized — Tags: , , — m759 @ 6:14 PM

Tom Hanks as Indiana Langdon in Raiders of the Lost Articulation :

An unarticulated (but colored) cube:

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

A 2x2x2 articulated cube:

IMAGE- Eightfold cube with detail of triskelion structure

A 4x4x4 articulated cube built from subcubes like
the one viewed by Tom Hanks above:

Image-- Solomon's Cube

Solomon’s Cube

Saturday, April 13, 2013

Princeton’s Christopher Robin

The title is that of a talk (see video) given by
George Dyson at a Princeton land preservation trust,
reportedly on March 21, 2013.  The talk's subtitle was
"Oswald Veblen and the Six-hundred-acre Woods."

Meanwhile

Thursday, March 21, 2013

Geometry of Göpel Tetrads (continued)

m759 @ 7:00 PM

An update to Rosenhain and Göpel Tetrads in PG(3,2)
supplies some background from
Notes on Groups and Geometry, 1978-1986,
and from a 2002 AMS Transactions  paper.

IMAGE- Göpel tetrads in an inscape, April 1986

Related material for those who prefer narrative
to mathematics:

Log24 on June 6, 2006:

 

The Omen:


Now we are 
 

6!

Related material for those who prefer mathematics
to narrative:

What the Omen narrative above and the mathematics of Veblen
have in common is the number 6. Veblen, who came to
Princeton in 1905 and later helped establish the Institute,
wrote extensively on projective geometry.  As the British
geometer H. F. Baker pointed out,  6 is a rather important number
in that discipline.  For the connection of 6 to the Göpel tetrads
figure above from March 21, see a note from May 1986.

See also last night's Veblen and Young in Light of Galois.

"There is  such a thing as a tesseract." — Madeleine L'Engle

Friday, December 28, 2012

Cube Koan

Filed under: Uncategorized — Tags: , , , — m759 @ 4:56 AM
 

From Don DeLillo's novel Point Omega —

I knew what he was, or what he was supposed to be, a defense intellectual, without the usual credentials, and when I used the term it made him tense his jaw with a proud longing for the early weeks and months, before he began to understand that he was occupying an empty seat. "There were times when no map existed to match the reality we were trying to create."

"What reality?"

"This is something we do with every eyeblink. Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation. Lying is necessary. The state has to lie. There is no lie in war or in preparation for war that can't be defended. We went beyond this. We tried to create new realities overnight, careful sets of words that resemble advertising slogans in memorability and repeatability. These were words that would yield pictures eventually and then become three-dimensional. The reality stands, it walks, it squats. Except when it doesn't."

He didn't smoke but his voice had a sandlike texture, maybe just raspy with age, sometimes slipping inward, becoming nearly inaudible. We sat for some time. He was slouched in the middle of the sofa, looking off toward some point in a high corner of the room. He had scotch and water in a coffee mug secured to his midsection. Finally he said, "Haiku."

I nodded thoughtfully, idiotically, a slow series of gestures meant to indicate that I understood completely.

"Haiku means nothing beyond what it is. A pond in summer, a leaf in the wind. It's human consciousness located in nature. It's the answer to everything in a set number of lines, a prescribed syllable count. I wanted a haiku war," he said. "I wanted a war in three lines. This was not a matter of force levels or logistics. What I wanted was a set of ideas linked to transient things. This is the soul of haiku. Bare everything to plain sight. See what's there. Things in war are transient. See what's there and then be prepared to watch it disappear."

What's there—

This view of a die's faces 3, 6, and 5, in counter-
clockwise order (see previous post) suggests a way
of labeling the eight corners  of a die (or cube):

123, 135, 142, 154, 246, 263, 365, 456.

Here opposite faces of the die sum to 7, and the
three faces meeting at each corner are listed
in counter-clockwise order. (This corresponds
to a labeling of one of MacMahon's* 30 colored cubes.)
A similar vertex-labeling may be used in describing 
the automorphisms of the order-8 quaternion group.

For a more literary approach to quaternions, see
Pynchon's novel Against the Day .

* From Peter J. Cameron's weblog:

  "The big name associated with this is Major MacMahon,
   an associate of Hardy, Littlewood and Ramanujan,
   of whom Robert Kanigel said,

His expertise lay in combinatorics, a sort of
glorified dice-throwing, and in it he had made
contributions original enough to be named
a Fellow of the Royal Society.

   Glorified dice-throwing, indeed…"

Monday, February 21, 2011

The Abacus Conundrum*

Filed under: Uncategorized — Tags: — m759 @ 2:02 PM

From Das Glasperlenspiel  (Hermann Hesse, 1943) —

“Bastian Perrot… constructed a frame, modeled on a child’s abacus, a frame with several dozen wires on which could be strung glass beads of various sizes, shapes, and colors. The wires corresponded to the lines of the musical staff, the beads to the time values of the notes, and so on. In this way he could represent with beads musical quotations or invented themes, could alter, transpose, and develop them, change them and set them in counterpoint to one another. In technical terms this was a mere plaything, but the pupils liked it.… …what later evolved out of that students’ sport and Perrot’s bead-strung wires bears to this day the name by which it became popularly known, the Glass Bead Game.”

From "Mimsy Were the Borogoves" (Lewis Padgett, 1943)—

…"Paradine looked up. He frowned, staring. What in—
…"Is that an abacus?" he asked. "Let's see it, please."
…Somewhat unwillingly Scott brought the gadget across to his father's chair. Paradine blinked. The "abacus," unfolded, was more than a foot square, composed of thin,  rigid wires that interlocked here and there. On the wires the colored beads were strung. They could be slid back and forth, and from one support to another, even at the points of jointure. But— a pierced bead couldn't cross interlocking  wires—
…So, apparently, they weren't pierced. Paradine looked closer. Each small sphere had a deep groove running around it, so that it could be revolved and slid along the wire at the same time. Paradine tried to pull one free. It clung as though magnetically. Iron? It looked more like plastic.
…The framework itself— Paradine wasn't a mathematician. But the angles formed by the wires were vaguely shocking, in their ridiculous lack of Euclidean logic. They were a maze. Perhaps that's what the gadget was— a puzzle.
…"Where'd you get this?"
…"Uncle Harry gave it to me," Scott said on the spur of the moment. "Last Sunday, when he came over." Uncle Harry was out of town, a circumstance Scott well knew. At the age of seven, a boy soon learns that the vagaries of adults follow a certain definite pattern, and that they are fussy about the donors of gifts. Moreover, Uncle Harry would not return for several weeks; the expiration of that period was unimaginable to Scott, or, at least, the fact that his lie would ultimately be discovered meant less to him than the advantages of being allowed to keep the toy.
…Paradine found himself growing slightly confused as he attempted to manipulate the beads. The angles were vaguely illogical. It was like a puzzle. This red bead, if slid along this  wire to that  junction, should reach there— but it didn’t. A maze, odd, but no doubt instructive. Paradine had a well-founded feeling that he’d have no patience with the thing himself.
…Scott did, however, retiring to a corner and sliding beads around with much fumbling and grunting. The beads did  sting, when Scott chose the wrong ones or tried to slide them in the wrong direction. At last he crowed exultantly.
…”I did it, dad!”
…””Eh? What? Let’s see.” The device looked exactly the same to Paradine, but Scott pointed and beamed.
…”I made it disappear.”
…”It’s still there.”
…”That blue bead. It’s gone now.”
…Paradine didn’t believe that, so he merely snorted. Scott puzzled over the framework again. He experimented. This time there were no shocks, even slight. The abacus had showed him the correct method. Now it was up to him to do it on his own. The bizarre angles of the wires seemed a little less confusing now, somehow.
…It was a most instructive toy—
…It worked, Scott thought, rather like the crystal cube.

* Title thanks to Saturday Night Live  (Dec. 4-5, 2010).

Saturday, August 11, 2007

Saturday August 11, 2007

Filed under: Uncategorized — Tags: — m759 @ 10:00 PM
Four Colours

The previous entry dealt with Plato's myth of the ring of Gyges that conferred invisibility. Another legendary ring, from Hermann Hesse, with some background from Carl Jung:

From C. G. Jung, Collected Works (Princeton U. Press), Volume 12– Psychology and Alchemy (1944)– Part II– "Individual Dream Symbolism in Relation to Alchemy"– Chapter 3, "The Symbolism of the Mandala"– as quoted in Jung, Dreams, published by Routledge, 2001– Page 265–
 

"… the dreamer is wandering about in a dark cave, where a battle is going on between good and evil. But there is also a prince who knows everything. He gives the dreamer a ring set with a diamond….

Visual impression (waking dream):

The dreamer is falling into the abyss. At the bottom there is a bear whose eyes gleam alternately in four colours: red, yellow, green, and blue. Actually it has four eyes that change into four lights. The bear disappears and the dreamer goes through a long dark tunnel. Light is shimmering at the far end. A treasure is there, and on top of it the ring with the diamond. It is said that this ring will lead him on a long journey to the east."

Hermann Hesse, The Journey to the East (1932):

"'… Despair is the result of each earnest attempt to go through life with virtue, justice, and understanding and to fulfil their requirements. Children live on one side of despair, the awakened on the other side. Defendant H. is no longer a child and is not yet fully awakened. He is still in the midst of despair. He will overcome it and thereby go through his second novitiate. We welcome him anew into the League, the meaning of which he no longer claims to understand. We give back to him his lost ring, which the servant Leo has kept for him.'

The Speaker then brought the ring, kissed me on the cheek and placed the ring on my finger. Hardly had I looked at the ring, hardly had I felt its metallic coolness on my fingers, when a thousand things occurred to me, a thousand inconceivable acts of neglect. Above all, it occurred to me that the ring had four stones at equal distances apart, and that it was a rule of the League and part of the vow to turn the ring slowly on the finger at least once a day, and at each of the four stones to bring to mind one of the four basic precepts of the vow. I had not only lost the ring and had not once missed it, but during all those dreadful years I had also no longer repeated the four basic precepts or thought of them. Immediately, I tried to say them again inwardly. I had an idea what they were, they were still within me, they belonged to me as does a name which one will remember in a moment but at that particular moment cannot be recalled. No, it remained silent within me, I could not repeat the rules, I had forgotten the wording. I had forgotten the rules; for many years I had not repeated them, for many years I had not observed them and held them sacred– and yet I had considered myself a loyal League brother.

The Speaker patted my arm kindly when he observed my dismay and deep shame."

Monday, January 29, 2007

Monday January 29, 2007

Filed under: Uncategorized — Tags: — m759 @ 9:00 AM

By Indirections
(Hamlet, II, i)

“Michael Taylor (1971)…. contends that the central conflict in Hamlet is between ‘man as victim of fate and as controller of his own destiny.'”– The Gale Group, Shakespearean Criticism, Vol. 71, at eNotes

Doonesbury today:

The image “http://www.log24.com/log/pix07/070129-Robot4A.gif” cannot be displayed, because it contains errors.

“Personality is a synthesis of possibility and necessity.”– Soren Kierkegaard

On Fate (Necessity),
Freedom (Possibility),
and Machine Personality–


Part I: Google as Skynet

George Dyson–
The Godel-to-Google Net [March 8, 2005]
A Cathedral for Turing [October 24, 2005]

Dyson: “The correspondence between Google and biology is not an analogy, it’s a fact of life.”

Part II: The Galois Connection

David Ellerman–
“A Theory of Adjoint Functors– with some Thoughts about their Philosophical Significance” (pdf) [November 15, 2005]

Ellerman: “Such a mechanism seems key to understanding how an organism can perceive and learn from its environment without being under the direct stimulus control of the environment– thus resolving the ancient conundrum of receiving an external determination while exercising self-determination.”

For a less technical version, see Ellerman’s “Adjoints and Emergence: Applications of a New Theory of Adjoint Functors” (pdf).

Ellerman was apparently a friend of, and a co-author with, Gian-Carlo Rota.  His “theory of adjoint functors” is related to the standard mathematical concepts known as profunctors, distributors, and bimodules. The applications of his theory, however, seem to be less to mathematics itself than to a kind of philosophical poetry that seems rather closely related to the above metaphors of George Dyson. For a less poetic approach to related purely mathematical concepts, see, for instance, the survey Practical Foundations of Mathematics by Paul Taylor (Cambridge University Press, 1999).  For less poetically appealing, but perhaps more perspicuous, extramathematical applications of category theory, see the work of, for instance, Joseph Goguen: Algebraic Semiotics and Information Integration, Databases, and Ontologies.

Sunday, August 17, 2003

Sunday August 17, 2003

Filed under: Uncategorized — Tags: — m759 @ 6:21 PM

Diamond theory is the theory of affine groups over GF(2) acting on small square and cubic arrays. In the simplest case, the symmetric group of degree 4 acts on a two-colored diamond figure like that in Plato's Meno dialogue, yielding 24 distinct patterns, each of which has some ordinary or color-interchange symmetry .

This symmetry invariance can be generalized to (at least) a group of order approximately 1.3 trillion acting on a 4x4x4 array of cubes.

The theory has applications to finite geometry and to the construction of the large Witt design underlying the Mathieu group of degree 24.

Further Reading:

Wednesday, November 27, 2002

Wednesday November 27, 2002

Filed under: Uncategorized — Tags: — m759 @ 11:30 PM

Waiting for Logos

Searching for background on the phrase "logos and logic" in yesterday's "Notes toward a Supreme Fact," I found this passage:

"…a theory of psychology based on the idea of the soul as the dialectical, self-contradictory syzygy of a) soul as anima and b) soul as animus. Jungian and archetypal psychology appear to have taken heed more or less of only one half of the whole syzygy, predominantly serving an anima cut loose from her own Other, the animus as logos and logic (whose first and most extreme phenomenological image is the killer of the anima, Bluebeard). Thus psychology tends to defend the virginal innocence of the anima and her imagination…"

— Wolfgang Giegerich, "Once More the Reality/Irreality Issue: A Reply to Hillman's Reply," website 

The anima and other Jungian concepts are used to analyze Wallace Stevens in an excellent essay by Michael Bryson, "The Quest for the Fiction of an Absolute." Part of Bryson's motivation in this essay is the conflict between the trendy leftist nominalism of postmodern critics and the conservative realism of more traditional critics:

"David Jarraway, in his Stevens and the Question of Belief, writes about a Stevens figured as a proto-deconstructionist, insisting on 'Steven's insistence on dismantling the logocentric models of belief' (311) in 'An Ordinary Evening in New Haven.' In opposition to these readings comes a work like Janet McCann's Wallace Stevens Revisited: 'The Celestial Possible', in which the claim is made (speaking of the post-1940 period of Stevens' life) that 'God preoccupied him for the rest of his career.'"

Here "logocentric" is a buzz word for "Christian." Stevens, unlike the postmodernists, was not anti-Christian. He did, however, see that the old structures of belief could not be maintained indefinitely, and pondered what could be found to replace them. "Notes toward a Supreme Fiction" deals with this problem. In his essay on Stevens' "Notes," Bryson emphasizes the "negative capability" of Keats as a contemplative technique:

"The willingness to exist in a state of negative capability, to accept that sometimes what we are seeking is not that which reason can impose…."

For some related material, see Simone Weil's remarks on Electra waiting for her brother Orestes. Simone Weil's brother was one of the greatest mathematicians of the past century, André Weil.

"Electra did not seek Orestes, she waited for him…"

— Simone Weil

"…at the end, she pulls it all together brilliantly in the story of Electra and Orestes, where the importance of waiting on God rather than seeking is brought home forcefully."

— Tom Hinkle, review of Waiting for God

Compare her remarks on waiting for Orestes with the following passage from Waiting for God:

"We do not obtain the most precious gifts by going in search of them but by waiting for them. Man cannot discover them by his own powers, and if he sets out to seek for them he will find in their place counterfeits of which he will be unable to discern falsity.

The solution of a geometry problem does not in itself constitute a precious gift, but the same law applies to it because it is the image of something precious. Being a little fragment of particular truth, it is a pure image of the unique, eternal, and living Truth, the very Truth that once in a human voice declared: "I am the Truth."

Every school exercise, thought of in this way, is like a sacrament.

In every school exercise there is a special way of waiting upon truth, setting our hearts upon it, yet not allowing ourselves to go out in search of it. There is a way of giving our attention to the data of a problem in geometry without trying to find the solution…."

— Simone Weil, "Reflections on the Right Use of School Studies with a View to the Love of  God"

Weil concludes the preceding essay with the following passage:

"Academic work is one of those fields containing a pearl so precious that it is worth while to sell all of our possessions, keeping nothing for ourselves, in order to be able to acquire it."

This biblical metaphor is also echoed in the work of Pascal, who combined in one person the theological talent of Simone Weil and the mathematical talent of her brother. After discussing how proofs should be written, Pascal says

"The method of not erring is sought by all the world. The logicians profess to guide to it, the geometricians alone attain it, and apart from their science, and the imitations of it, there are no true demonstrations. The whole art is included in the simple precepts that we have given; they alone are sufficient, they alone afford proofs; all other rules are useless or injurious. This I know by long experience of all kinds of books and persons.

And on this point I pass the same judgment as those who say that geometricians give them nothing new by these rules, because they possessed them in reality, but confounded with a multitude of others, either useless or false, from which they could not discriminate them, as those who, seeking a diamond of great price amidst a number of false ones, but from which they know not how to distinguish it, should boast, in holding them all together, of possessing the true one equally with him who without pausing at this mass of rubbish lays his hand upon the costly stone which they are seeking and for which they do not throw away the rest."

— Blaise Pascal, The Art of Persuasion

 

For more diamond metaphors and Jungian analysis, see

The Diamond Archetype.

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