Log24

Thursday, July 18, 2019

Split

Filed under: General — Tags: — m759 @ 6:55 PM

"My words say split, but my words they lie" — Bruce Springsteen

See a search for "Split" in this journal.

Thursday, January 26, 2017

Split

Filed under: General — Tags: — m759 @ 11:09 AM

(Continued from Tuesday, Jan. 24, 2017)

"We have reached peak polarization."

— Olga Khazan in the online Atlantic  today,
     as quoted in the Muck Rack image below.

Perhaps not yet.

Consider the headline below,

"Why Trump Supporters Lie About the Inauguration Photo."

Consider also Olga's "Brain Bro" below in the context of 
the film "Limitless" and of the book A Wrinkle in Time .

See also all posts now tagged "Split."

Tuesday, January 24, 2017

Split

Filed under: General — Tags: — m759 @ 1:33 PM

At left, just prior to the inauguration in 2009;
at right, during the inauguration in 2017.

Source of photos —

http://news.wgbh.org/2017/01/23/news/
photos-compare-crowd-trumps-inauguration-obamas
.

For a more detailed image of the 2017 inauguration
from the new president's point of view, click here.

Wednesday, December 23, 2015

Splitting Apart

Filed under: General,Geometry — m759 @ 1:01 PM

Bleecker Street logo —

Click image for some background.

Related remarks on mathematics:

Boole vs. Galois

Saturday, April 21, 2012

Split

Filed under: General — m759 @ 11:07 PM

"So the sundering we sense between nature and culture
lies not like a canyon outside us, but splits our being
at its most intimate depths the way mind breaks off from body.
It is still another version of that bitter bifurcation
long ago decreed— our expulsion from Eden…."

— William H. Gass in Finding a Form ,
     Cornell U. Press paperback, 1997, page 138

See also…

IMAGE- 'The Line,' a post on Blatty's 'The Ninth Configuration'

For another bitter bifurcation, see La Despedida .

Thursday, July 18, 2019

Apperception

Filed under: General — Tags: — m759 @ 8:00 PM

From BUtterfield 8 (1960) —

Elizabeth Taylor in 'BUtterfield 8' (1960)

From the 7/20/2017 post "Divided Attention" —

Another phrase for divided  attention is "bulk apperception."

Avatar for Inspector Tennison

Filed under: General — Tags: — m759 @ 7:35 AM

The image “http://www.log24.com/log/pix06B/061113-Mirren.jpg” cannot be displayed, because it contains errors. 

Image from a post of November 13, 2006.
See as well Schoolgirl Tetrahedron.

Related lyrics from Bruce Springsteen and
the Pointer Sisters

Well, Romeo and Juliet, Samson and Delilah
Baby you can bet a love they couldn't deny
My words say split, but my words they lie
Cause when we kiss, ooh, fire

{Bridge}

Oh fire
Kisses like fire…
Burn me up with fire
I like what you're doin now, fire
Touchin' me, fire
Touchin' me, burnin me, fire
Take me home

E is for Energy.

Friday, May 10, 2019

I Ching g6

Filed under: General — Tags: , , — m759 @ 12:25 PM

For fans of Resonance Science

"When the men on the chessboard
get up and tell you where to go …."

Tuesday, April 2, 2019

Plan

Filed under: General — m759 @ 4:14 AM

"If this weren't a public situation, I'd be tempted to get into this on a
psychiatric level." — Christopher Alexander to Peter Eisenman, 1982

Scene from the sequel to Unbreakable  and Split  

Not to mention elevation .

Sunday, July 22, 2018

Space

Filed under: General,Geometry — Tags: , — m759 @ 10:29 AM


See also interality in the eightfold cube.

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

Thursday, July 20, 2017

Divided Attention

Filed under: General — Tags: — m759 @ 11:54 AM

The previous post alluded to the phrase "undivided attention."

An example of divided  attention —

The "Orphan Black" scene (at right above) is from a post, "Art's Space,"
of Saturday, July 15, 2017.  The themes of the Orphan Black series —
in the context of Silicon Valley, not of Orphan Black — were discussed
in the Los Angeles Review of Books  on Monday, July 17, 2017. Other
Silicon Valley themes appear in the recent film "The Circle" (at left above).

Another phrase for divided  attention is "bulk apperception."

Sunday, April 9, 2017

23 for 23 for …

Filed under: General — m759 @ 11:01 PM

James McAvoy —

Wednesday, February 8, 2017

Rhymes with Prize

Filed under: General,Geometry — m759 @ 3:01 PM

On the triangle in the excerpt above —

"A golden triangle can be split into
a golden triangle and a golden gnomon.
The same is true for a golden gnomon.
A golden gnomon and a golden triangle
with their equal sides matching each other
in length are also referred to as the obtuse
and acute Robinson triangles.

These isosceles triangles can be used to
produce Penrose tilings."

— Adapted from Wikipedia (Wikipedia's word
"bisected" is replaced above by the word "split.")
 

The previous post dealt with women and lies.

Related material — Quilt Prize in this journal.

Tuesday, January 24, 2017

The Frisk Version

Filed under: General — Tags: — m759 @ 11:04 PM

Adam Frisk reports from a Canadian network, Global News

Compare and contrast with the photos in the previous post,
Inauguration Crowd Size According to Getty Images.

Inauguration Crowd Size According to Getty Images

Filed under: General — Tags: — m759 @ 5:31 PM


The "Spectators fill the National Mall" photo above seems
to correspond to the crowd during , not before  the inauguration
(as shown in the second photo above, the "People gather" photo).

Compare to the photo in today's earlier post taken during  the Inauguration:

Monday, January 23, 2017

Believe It or Not

Filed under: General — Tags: — m759 @ 7:11 PM

"It's not a lie if you believe it."

Poster for "Operation Avalanche"

“We keep coming back and coming back
To the real: to the hotel instead of the hymns . . . .

— Wallace Stevens, quoted in posts tagged Portal1937

The In Crowd

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

The New York Times  online on Thursday, Jan. 19, 2017 —

" 'Split' is being released by Universal under the Blumhouse label,
a brand associated with unpretentious, clever, neo-traditionalist
scare-pictures like 'Insidious,' 'Paranormal Activity' and 'The Purge.'
That seems like the right company for Mr. Shyamalan . . . ."

A check of the Blumhouse label leads to a NY Times article
dated July 15, 2012 —

Related material

Whose Crowd? OUR Crowd!

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

"The reception which has been accorded 'Our Crowd'
shows that the subject was certainly ripe for exploitation."

Wikipedia 

Crowdsourcing

Filed under: General — Tags: — m759 @ 11:45 AM

Alternative fact  from the New York Times  crowd —

Screenshot of online NY Times front page at 11:30 AM ET
on Monday, January 23, 2017 —

"Crowd scientists estimated that 160,000 people
attended President Trump's inauguration."

Wednesday, August 26, 2015

“The Quality Without a Name”

Filed under: General,Geometry — Tags: , — m759 @ 8:00 AM

The title phrase, paraphrased without quotes in
the previous post, is from Christopher Alexander's book
The Timeless Way of Building  (Oxford University Press, 1979).

A quote from the publisher:

"Now, at last, there is a coherent theory
which describes in modern terms
an architecture as ancient as
human society itself."

Three paragraphs from the book (pp. xiii-xiv):

19. Within this process, every individual act
of building is a process in which space gets
differentiated. It is not a process of addition,
in which preformed parts are combined to
create a whole, but a process of unfolding,
like the evolution of an embryo, in which
the whole precedes the parts, and actualy
gives birth to then, by splitting.

20. The process of unfolding goes step by step,
one pattern at a time. Each step brings just one
pattern to life; and the intensity of the result
depends on the intensity of each one of these
individual steps.

21. From a sequence of these individual patterns,
whole buildings with the character of nature
will form themselves within your thoughts,
as easily as sentences.

Compare to, and contrast with, these illustrations of "Boolean space":

(See also similar illustrations from Berkeley and Purdue.)

Detail of the above image —

Note the "unfolding," as Christopher Alexander would have it.

These "Boolean" spaces of 1, 2, 4, 8, and 16 points
are also Galois  spaces.  See the diamond theorem —

Saturday, March 8, 2014

Conwell Heptads in Eastern Europe

Filed under: General,Geometry — Tags: — m759 @ 11:07 AM

“Charting the Real Four-Qubit Pauli Group
via Ovoids of a Hyperbolic Quadric of PG(7,2),”
by Metod Saniga, Péter Lévay and Petr Pracna,
arXiv:1202.2973v2 [math-ph] 26 Jun 2012 —

P. 4— “It was found that +(5,2) (the Klein quadric)
has, up to isomorphism, a unique  one — also known,
after its discoverer, as a Conwell heptad  [18].
The set of 28 points lying off +(5,2) comprises
eight such heptads, any two having exactly one
point in common.”

P. 11— “This split reminds us of a similar split of
63 points of PG(5,2) into 35/28 points lying on/off
a Klein quadric +(5,2).”

[18] G. M. Conwell, Ann. Math. 11 (1910) 60–76

A similar split occurs in yesterday’s Kummer Varieties post.
See the 63 = 28 + 35 vectors of R8 discussed there.

For more about Conwell heptads, see The Klein Correspondence,
Penrose Space-Time, and a Finite Model
.

For my own remarks on the date of the above arXiv paper
by Saniga et. al., click on the image below —

Walter Gropius

Monday, December 2, 2013

Finite-Geometry Notes

Filed under: General,Geometry — m759 @ 8:30 PM

See my Google Sites page if you would like to
download a zipped copy (31 MB) of my
Finite-Geometry Notes  site
(not zipped, at finitegeometry.org/sc/map.html).
Or you can of course use a website downloader.

(Suggested by a recent NY Times  piece on
a company, Citia, that splits books into pieces 
for easier electronic access. The large zipped
file referred to above is sort of a reverse of this
process.)

Sunday, June 3, 2012

Child’s Play

Filed under: General,Geometry — Tags: — m759 @ 2:56 PM

(Continued)

“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”

– Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art
, Cornell U. Press, 1975

IMAGE- The Trinity of Max Black (a 3-set, with its eight subsets arranged in a Hasse diagram that is also a cube)

Related material—

The Trinity Cube

IMAGE- The Trinity Cube (three interpenetrating planes that split the eightfold cube into its eight subcubes)

Wednesday, April 6, 2011

Harvard Hicks

Filed under: General — m759 @ 2:40 PM

Austin Considine on a Tennessee tourist trap

"It would be easy for a city slicker to assume this place misses its own punch lines."

It probably doesn't, but a certain academic  tourist trap does .

A trio of Harvard hicks—

1. The chairman of the Harvard philosophy department, Sean D. Kelly—

"Football can literally bring meaning to life."

(See also Garry Wills on Kelly, Rite of Spring, and Heisman Trophy.)

2. A professor of English at Harvard, Marjorie Garber, in a deconstructive meditation—

Garber notes that the word "literature" has two meanings– the English department's meaning, and that of other departments' references to "the literature."

"Whenever there is a split like this, it is worth pausing to wonder why. High/low, privileged/popular, aesthetic/professional, keep/throw away. It seems as if the category of literature in what we might inelegantly call the literary sense of the word is being both protected and preserved in amber by the encroachment, on all sides, of the nonliterary literature that proliferates in professional-managerial culture. But literature has always been situated on the boundary between itself and its other."

The Use and Abuse of Literature , published by Pantheon on March 29, 2011

3. The president of Harvard, Drew Faust—

A comment recently made to Faust—

“[A] tyrant wanted a crimson-tinged report that he was running a democracy, and for a price, a Harvard expert obliged…."

Her response—

"Faust replied that for her to say anything about this would make her 'scold in chief.'"

—  University Diaries  today. See the excellent commentary there.

Saturday, August 7, 2010

Rift Designs

Filed under: General — m759 @ 8:28 PM

From the current index to obituaries at Telegraph.co.uk—

Teufel is also featured in today's New York Times

"Mr. Teufel became a semicelebrity, helped in no small part by his last name, which means 'devil' in German."

From Group Analysis ,  June 1993, vol. 26 no. 2, 203-212—

The Problem of Good and Evil

by Ronald Sandison, Ledbury, Herefordshire HR8 2EY, UK

In my contribution to the Group Analysis Special Section: "Aspects of Religion in Group Analysis" (Sandison, 1993) I hinted that any consideration of a spiritual dimension to the group involves us in a discussion on whether we are dealing with good or evil spirits. But if we say that God is in the group, why is not the Devil there also? Can good and evil coexist in the same group matrix? Is the recognition of evil "nothing but" the ability to distinguish between good and bad? If not, then what is evil? Is it no more than the absence of good?

These and other questions were worked on at a joint Institute of Group Analysis and Group-Analytic Society (London) Workshop entitled "The Problem of Good and Evil." We considered the likelihood that good and evil coexist in all of us, as well as in the whole of the natural world, not only on earth, but in the cosmos and in God himself What we actually do with good and evil is to split them apart, thereby shelving the problem but at the same time creating irreconcilable opposites. This article examines this splitting and how we can work with it psychoanalytically.

This suggests a biblical remark—

"Now there was a day… when the sons of God
came to present themselves before the Lord,
and Satan came also among them."

Job 1:6, quoted by Chesterton in The Man Who Was Thursday

Sandison died on June 18. See the Thursday, August 5, Log24 post "The Matrix."

Teufel died on July 6. See the Log24 posts for that day.

The title of this  post, "rift designs," refers to a recurring theme in the July 6 posts. It is taken from Heidegger.

From a recent New Yorker  review of Absence of Mind  by Marilynne Robinson—

"Robinson is eloquent in her defense of the mind’s prerogatives, but her call for a renewed metaphysics might be better served by rereading Heidegger than by dusting off the Psalms."

Following this advice, we find—

"Propriation gathers the rift-design of the saying and unfolds it  in such a way that it becomes the well-joined structure of a manifold showing."

p. 415 of Heidegger's Basic Writings , edited by David Farrell Krell, HarperCollins paperback, 1993

"Das Ereignis versammelt den Aufriß der Sage und entfaltet ihn zum Gefüge des vielfältigen Zeigens." 

— Heidegger, Weg zur Sprache

Thursday, July 1, 2010

Plato’s Code

Filed under: General,Geometry — m759 @ 12:00 PM

John Allen Paulos yesterday at Twitter

"Plato's code cracked? http://bit.ly/ad6k1S
Fascinating if not a hoax or hype."

The story that Paulos linked to is about a British
academic who claims to have found some
symbolism hidden in Plato's writings by
splitting each into 12 parts and correlating
the 12 parts with semitones of a musical scale.

I prefer a different approach to Plato that is
related to the following hoax and hype—

HOAX:

From Dan Brown's novel Angels & Demons  (2000)

IMAGE- Illuminati Diamond, pp. 359-360 in 'Angels & Demons,' Simon & Schuster Pocket Books 2005, 448 pages, ISBN 0743412397

HYPE:

Image-- From 'Alchemy,' by Holmyard, the diamond of Aristotle's 4 elements and 4 qualities

This  four-elements diamond summarizes the classical
four elements and four qualities neatly, but some scholars
might call the figure "hype" since it deals with an academically
disreputable subject, alchemy, and since its origin is unclear.

For the four elements' role in some literature more respectable
than Dan Brown's, see Poetry's Bones.

Although an author like Brown might spin the remarks
below into a narrative—  The Plato Code — they are
neither  hoax nor hype.

NOT  HOAX:

Image-- From the Diamond in Plato's Meno to Modern Finite Geometry

NOT  HYPE:

http://www.log24.com/log/pix10A/100626-CrossOnSocratesSm.gif

For related non-hoax, non-hype remarks, see
The Rational Enterprise: Logos in Plato's Theaetetus,
by Rosemary Desjardins.

Those who prefer  hoax and hype in their philosophy may consult
the writings of, say, Barbara Johnson, Rosalind Krauss, and—
in yesterday's NY Times's  "The Stone" columnNancy Bauer.

Image-- The Philosophers' Stone according to The New York Times

— The New York Times

Thursday, February 5, 2009

Thursday February 5, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 1:00 PM

Through the
Looking Glass:

A Sort of Eternity

From the new president's inaugural address:

"… in the words of Scripture, the time has come to set aside childish things."

The words of Scripture:

9 For we know in part, and we prophesy in part.
10 But when that which is perfect is come, then that which is in part shall be done away.
11 When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.
12 For now we see through a glass, darkly, but then face to face: now I know in part; but then shall I know even as also I am known.

 

First Corinthians 13

"through a glass"

[di’ esoptrou].
By means of
a mirror [esoptron]
.

Childish things:

Froebel's third gift, the eightfold cube
© 2005 The Institute for Figuring
 
Photo by Norman Brosterman
fom the Inventing Kindergarten
exhibit at The Institute for Figuring
(co-founded by Margaret Wertheim)

 

Not-so-childish:

Three planes through
the center of a cube
that split it into
eight subcubes:
Cube subdivided into 8 subcubes by planes through the center
Through a glass, darkly:

A group of 8 transformations is
generated by affine reflections
in the above three planes.
Shown below is a pattern on
the faces of the 2x2x2 cube
 that is symmetric under one of
these 8 transformations–
a 180-degree rotation:

Design Cube 2x2x2 for demonstrating Galois geometry

(Click on image
for further details.)

But then face to face:

A larger group of 1344,
rather than 8, transformations
of the 2x2x2 cube
is generated by a different
sort of affine reflections– not
in the infinite Euclidean 3-space
over the field of real numbers,
but rather in the finite Galois
3-space over the 2-element field.

Galois age fifteen, drawn by a classmate.

Galois age fifteen,
drawn by a classmate.

These transformations
in the Galois space with
finitely many points
produce a set of 168 patterns
like the one above.
For each such pattern,
at least one nontrivial
transformation in the group of 8
described above is a symmetry
in the Euclidean space with
infinitely many points.

For some generalizations,
see Galois Geometry.

Related material:

The central aim of Western religion–

 

"Each of us has something to offer the Creator...
the bridging of
 masculine and feminine,
 life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist (1998)

The central aim of Western philosophy–

 Dualities of Pythagoras
 as reconstructed by Aristotle:
  Limited Unlimited
  Odd Even
  Male Female
  Light Dark
  Straight Curved
  ... and so on ....

"Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy."

— Jamie James in The Music of the Spheres (1993)

"In the garden of Adding
live Even and Odd…
And the song of love's recision
is the music of the spheres."

— The Midrash Jazz Quartet in City of God, by E. L. Doctorow (2000)

A quotation today at art critic Carol Kino's website, slightly expanded:

"Art inherited from the old religion
the power of consecrating things
and endowing them with
a sort of eternity;
museums are our temples,
and the objects displayed in them
are beyond history."

— Octavio Paz,"Seeing and Using: Art and Craftsmanship," in Convergences: Essays on Art and Literature (New York: Harcourt Brace Jovanovich 1987), 52 

From Brian O'Doherty's 1976 Artforum essays– not on museums, but rather on gallery space:

"Inside the White Cube"

"We have now reached
a point where we see
not the art but the space first….
An image comes to mind
of a white, ideal space
that, more than any single picture,
may be the archetypal image
of 20th-century art."

http://www.log24.com/log/pix09/090205-cube2x2x2.gif

"Space: what you
damn well have to see."

— James Joyce, Ulysses  

Monday, July 30, 2007

Monday July 30, 2007

Filed under: General,Geometry — m759 @ 7:00 PM
The Deathly Hallows Symbol

The image “http://www.log24.com/log/pix07/070730-HallowsSymbol.jpg” cannot be displayed, because it contains errors.

Some fear that the Harry Potter books introduce children to the occult; they are not entirely mistaken.

According to Wikipedia, the “Deathly Hallows” of the final Harry Potter novel are “three fictional magical objects that appear in the book.”

The vertical line, circle, and triangle in the symbol pictured above are said to refer to these three magical objects.

One fan relates the “Deathly Hallows” symbol above, taken from the spine of a British children’s edition of the book, to a symbol for “the divine (or sacred, or secret) fire” of alchemy. She relates this fire in turn to “serpent power” and the number seven:

Kristin Devoe at a Potter fan site:

“We know that seven is a powerful number in the novels. Tom Riddle calls it ‘the most powerfully magic number.‘ The ability to balance the seven chakras within oneself allows the person to harness the secret fire. This secret fire in alchemy is the same as the kundalini or coiled snake in yogic philosophy. It is also known as ‘serpent power’ or the ‘dragon’ depending on the tradition. The kundalini is polar in nature and this energy, this internal fire, is very powerful for those who are able to harness it and it purifies the aspirant allowing them the knowledge of the universe. This secret fire is the Serpent Power which transmutes the base metals into the Perfect Gold of the Sun.

It is interesting that the symbol of the caduceus in alchemy is thought to have been taken from the symbol of the kundalini. Perched on the top of the caduceus, or the staff of Hermes, the messenger of the gods and revealer of alchemy, is the golden snitch itself! Many fans have compared this to the scene in The Order of the Phoenix where Harry tells Dumbledore about the attack on Mr. Weasley and says, ‘I was the snake, I saw it from the snake’s point of view.

The chapter continues with Dumbledore consulting ‘one of the fragile silver instruments whose function Harry had never known,’ tapping it with his wand:

The instrument tinkled into life at once with rhythmic clinking noises. Tiny puffs of pale green smoke issued from the minuscule silver tube at the top. Dumbledore watched the smoke closely, his brow furrowed, and after a few seconds, the tiny puffs became a steady stream of smoke that thickened and coiled into he air… A serpent’s head grew out of the end of it, opening its mouth wide. Harry wondered whether the instrument was confirming his story; He looked eagerly at Dumbledore for a sign that he was right, but Dumbledore did not look up.

“Naturally, Naturally,” muttered Dumbledore apparently to himself, still observing the stream of smoke without the slightest sign of surprise. “But in essence divided?”

Harry could make neither head not tail of this question. The smoke serpent, however split instantly into two snakes, both coiling and undulating in the dark air. With a look of grim satisfaction Dumbledore gave the instrument another gentle tap with his wand; The clinking noise slowed and died, and the smoke serpents grew faint, became a formless haze, and vanished.

Could these coiling serpents of smoke be foreshadowing events to come in Deathly Hallows where Harry learns to ‘awaken the serpent’ within himself? Could the snake’s splitting in two symbolize the dual nature of the kundalini?”

Related material

The previous entry

“And the serpent’s eyes shine    
As he wraps around the vine
In The Garden of Allah” —

and the following
famous illustration of
the double-helix
structure of DNA:

 Odile Crick, drawing of DNA structure in the journal Nature, 1953
This is taken from
a figure accompanying
an obituary, in today’s
New York Times, of the
artist who drew the figure
.

The double helix
is not a structure
from magic; it may,
however, as the Rowling
quote above shows, have
certain occult uses,
better suited to
Don Henley’s
Garden of Allah
than to the
  Garden of Apollo.

Seven is Heaven...

Similarly, the three objects
above (Log24 on April 9)
are from pure mathematics–
the realm of Apollo, not
of those in Henley’s song.

The similarity of the
top object of the three —
the “Fano plane” — to
the “Deathly Hallows”
symbol is probably
entirely coincidental.

Wednesday, November 22, 2006

Wednesday November 22, 2006

Filed under: General — m759 @ 9:00 PM
Rock of Ages

“Who knows where madness lies?”
— Rhetorical question
in “Man of La Mancha”
(See previous entry.)

Using madness to
seek out madness, let us
  consult today’s numbers…

Pennsylvania Lottery
Nov. 22, 2006:

Mid-day 487
Evening 814

The number 487 leads us to
page 487 in the
May 1977 PMLA,
The Form of Carnival
in Under the Volcano
“:

“The printing presses’ flywheel
marks the whirl of time*
    that will split La Despedida….”

The image “http://www.log24.com/log/pix06B/061122-Flywheel.gif” cannot be displayed, because it contains errors.

Flywheel

From Dana Grove,
A Rhetorical Analysis of
Under the Volcano
,
page 92:

“… In this way, mystical as well as psychological dimensions are established.  Later on, the two pass by a printer’s shop window and curiously stop to inspect, amidst wedding portraits and well in front of the revolving flywheel of the printing machines, ‘a photographic enlargement purporting to show the disintegration of a glacial deposit in the Sierra Madre, of a great rock split by forest fires.’  Significantly the picture is called ‘La Despedida,’ the Parting.  Yvonne cannot help but see the symbolic significance of the photograph and wishes with all of her might ‘to heal the cleft rock’ just as she wishes to heal the divorce….”

Some method in this madness
is revealed by the evening
lottery number, 814, which
leads to an entry of 8/14:

Cleavage Term

“… a point of common understanding
between the classic and romantic worlds.
Quality, the cleavage term between
hip and square, seemed to be it.”
Robert M. Pirsig 

The image “http://www.log24.com/log/pix06B/061122-Goldstein.jpg” cannot be displayed, because it contains errors.

Rebecca Goldstein

The 8/14 entry also deals with
Rebecca Goldstein, who
seems to understand
such cleavage
very well.

(See also today’s previous entry.)

* Cf. Shakespeare’s “whirligig of time
linked to in the previous entry.)

Saturday, October 14, 2006

Saturday October 14, 2006

Filed under: General — m759 @ 7:00 PM
The Line
 
Continued
from Aug. 15, 2004:

Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, Part III:

“The wave of crystallization rolled ahead. He was seeing two worlds, simultaneously. On the intellectual side, the square side, he saw now that Quality was a cleavage term. What every intellectual analyst looks for. You take your analytic knife, put the point directly on the term Quality and just tap, not hard, gently, and the whole world splits, cleaves, right in two…

The Line,
by S. H. Cullinane

hip and square, classic and romantic, technological and humanistic…and the split is clean. There’s no mess. No slop. No little items that could be one way or the other. Not just a skilled break but a very lucky break. Sometimes the best analysts, working with the most obvious lines of cleavage, can tap and get nothing but a pile of trash. And yet here was Quality; a tiny, almost unnoticeable fault line; a line of illogic in our concept of the universe; and you tapped it, and the whole universe came apart, so neatly it was almost unbelievable. He wished Kant were alive. Kant would have appreciated it. That master diamond cutter. He would see. Hold Quality undefined. That was the secret.”

The image “http://www.log24.com/log/pix06A/061014-Kant.gif” cannot be displayed, because it contains errors.

See also the discussion of
subjective and objective
by Robert M. Pirsig in
Zen and the Art of
Motorcycle Maintenance
,
Part III,
followed by this dialogue:

Are We There Yet?

Chris shouts, “When are we
going to get to the top?”

“Probably quite a way yet,”
I reply.

“Will we see a lot?”

“I think so. Look for blue sky
between the trees. As long as we
can’t see sky we know it’s a way yet.
The light will come through the trees
when we round the top.”

Related material:

The Boys from Uruguay,
Lichtung!,
The Shining of May 29,
A Guiding Philosophy,
Ticket Home.

The philosophy of Heidegger
discussed and illustrated
in the above entries may
be regarded as honoring
today’s 100th anniversary
of the birth of Heidegger’s
girlfriend, Hannah Arendt.

See also

 Hannah and Martin
and
Snowblind.

Thursday, December 15, 2005

Thursday December 15, 2005

Filed under: General — m759 @ 3:48 PM
In honor of Freeman Dyson’s birthday:

Dance of the Numbers

“Mahlburg likens his approach to an analogous one for deciding whether a dance party has an even or odd number of attendees. Instead of counting all the participants, a quicker method is to see whether everyone has a partner—in effect making groups that are divisible by 2.

In Mahlburg’s work, the partition numbers play the role of the dance participants, and the crank splits them not into couples but into groups of a size divisible by the prime number in question. The total number of partitions is, therefore, also divisible by that prime.

Mahlburg’s work ‘has effectively written the final chapter on Ramanujan congruences,’ Ono says.

‘Each step in the story is a work of art,’ Dyson says, ‘and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination.'”

Erica Klarreich in Science News Online, week of June 18, 2005

This would seem to meet the criteria set by Fritz Leiber for “a story that works.” (See previous entry.)  Whether the muse of dance (played in “Xanadu” by a granddaughter of physicist Max Born– see recent entries) has a role in the Dyson story is debatable.

Born Dec. 11, 1882, Breslau, Germany.

Died Jan. 5, 1970, Göttingen,
West Germany.

The image “http://www.log24.com/log/pix05B/051215-Born.jpg” cannot be displayed, because it contains errors.
Max Born

Those who prefer less abstract stories may enjoy a mythic tale by Robert Graves, Watch the North Wind Rise, or a Christian tale by George MacDonald, At the Back of the North Wind.

Related material:

“The valley spirit never dies. It’s named the mystic woman.”

Tao Te Ching

For an image of a particular
incarnation of the mystic woman
(whether as muse, as goddess,
or as the White Witch of Narnia,
I do not know) see Julie Taymor.

“Down in the valley,
 valley so low,
 hang your head over,
 hear the wind blow.”

Folk song

“Which is the sound of the land
Full of the same wind
That is blowing in
    the same bare place

For the listener,
    who listens in the snow,
And, nothing himself, beholds
Nothing that is not there
    and the nothing that is.”

Wallace Stevens

Thursday, December 8, 2005

Thursday December 8, 2005

Filed under: General,Geometry — Tags: — m759 @ 2:56 PM
Aion Flux

That Nature is a Heraclitean Fire…
— Poem title, Gerard Manley Hopkins  

From Jung’s Map of the Soul, by Murray Stein:

“… Jung thinks of the self as undergoing continual transformation during the course of a lifetime…. At the end of his late work Aion, Jung presents a diagram to illustrate the dynamic movements of the self….”

The image “http://www.log24.com/theory/images/JungDiamonds.gif” cannot be displayed, because it contains errors.

“The formula presents a symbol of the self, for the self is not just a stable quantity or constant form, but is also a dynamic process.  In the same way, the ancients saw the imago Dei in man not as a mere imprint, as a sort of lifeless, stereotyped impression, but as an active force…. The four transformations represent a process of restoration or rejuvenation taking place, as it were, inside the self….”

“The formula reproduces exactly the essential features of the symbolic process of transformation. It shows the rotation of the mandala, the antithetical play of complementary (or compensatory) processes, then the apocatastasis, i.e., the restoration of an original state of wholeness, which the alchemists expressed through the symbol of the uroboros, and finally the formula repeats the ancient alchemical tetrameria, which is implicit in the fourfold structure of unity. 

What the formula can only hint at, however, is the higher plane that is reached through the process of transformation and integration. The ‘sublimation’ or progress or qualitative change consists in an unfolding of totality into four parts four times, which means nothing less than its becoming conscious. When psychic contents are split up into four aspects, it means that they have been subjected to discrimination by the four orienting functions of consciousness. Only the production of these four aspects makes a total description possible. The process depicted by our formula changes the originally unconscious totality into a conscious one.” 

— Jung, Collected Works, Vol. 9, Part 2, Aion: Researches into the Phenomenology of the Self (1951) 

Related material: 

  The diamond theorem

“Although ‘wholeness’ seems at first sight to be nothing but an abstract idea (like anima and animus), it is nevertheless empirical in so far as it is anticipated by the psyche in the form of  spontaneous or autonomous symbols. These are the quaternity or mandala symbols, which occur not only in the dreams of modern people who have never heard of them, but are widely disseminated in the historical recods of many peoples and many epochs. Their significance as symbols of unity and totality is amply confirmed by history as well as by empirical psychology.  What at first looks like an abstract idea stands in reality for something that exists and can be experienced, that demonstrates its a priori presence spontaneously. Wholeness is thus an objective factor that confronts the subject independently of him… Unity and totality stand at the highest point on the scale of objective values because their symbols can no longer be distinguished from the imago Dei. Hence all statements about the God-image apply also to the empirical symbols of totality.”

— Jung, Aion, as quoted in
Carl Jung and Thomas Merton

Thursday, October 6, 2005

Thursday October 6, 2005

Filed under: General — m759 @ 2:00 AM
A Voice

In memory of Harold Leventhal,
  folk-music concert producer,
who died on Tuesday
(Rosh Hashana, 2005)

Leventhal recently appeared in the American Masters Bob Dylan documentary on PBS.  According to today’s NYT obituary, “Mr. Leventhal was… widely, if tacitly, acknowledged to have been the inspiration for Irving Steinbloom, the folk impresario whose memorial concert sets in motion the plot of the 2003 film comedy ‘A Mighty Wind.'”

From a Rosh Hashana sermon by Devra Felder Noily:

“Throughout these Holy Days we will chant Unetaneh Tokef, a liturgical poem more than a thousand years old. In it we find the words:

U-ve shofar gadol yi-ta-ka. V’ kol d’ma-ma da-kah yi-shama. The great shofar is sounded. And a still small voice is heard….

The prayer quotes from the book of Kings. There, the prophet Elijah has reached his breaking point, and God reaches out to him. The text tells us:

Then the Eternal passed by. There was a great and mighty wind, splitting mountains and shattering rocks by the power of God, but God was not in the wind. After the wind, an earthquake– but God was not in the earthquake. After the earthquake, fire– but God was not in the fire. And after the fire, a still small voice.”

Wednesday, May 4, 2005

Wednesday May 4, 2005

Filed under: General,Geometry — Tags: , — m759 @ 1:00 PM
The Fano Plane
Revisualized:

 

 The Eightfold Cube

or, The Eightfold Cube

Here is the usual model of the seven points and seven lines (including the circle) of the smallest finite projective plane (the Fano plane):
 
The image “http://www.log24.com/theory/images/Fano.gif” cannot be displayed, because it contains errors.
 

Every permutation of the plane's points that preserves collinearity is a symmetry of the  plane.  The group of symmetries of the Fano plane is of order 168 and is isomorphic to the group  PSL(2,7) = PSL(3,2) = GL(3,2). (See Cameron on linear groups (pdf).)

The above model indicates with great clarity six symmetries of the plane– those it shares with the equilateral triangle.  It does not, however, indicate where the other 162 symmetries come from.  

Shown below is a new model of this same projective plane, using partitions of cubes to represent points:

 

Fano plane with cubes as points
 
The cubes' partitioning planes are added in binary (1+1=0) fashion.  Three partitioned cubes are collinear if and only if their partitioning planes' binary sum equals zero.

 

The second model is useful because it lets us generate naturally all 168 symmetries of the Fano plane by splitting a cube into a set of four parallel 1x1x2 slices in the three ways possible, then arbitrarily permuting the slices in each of the three sets of four. See examples below.

 

Fano plane group - generating permutations

For a proof that such permutations generate the 168 symmetries, see Binary Coordinate Systems.

 

(Note that this procedure, if regarded as acting on the set of eight individual subcubes of each cube in the diagram, actually generates a group of 168*8 = 1,344 permutations.  But the group's action on the diagram's seven partitions of the subcubes yields only 168 distinct results.  This illustrates the difference between affine and projective spaces over the binary field GF(2).  In a related 2x2x2 cubic model of the affine 3-space over GF(2) whose "points" are individual subcubes, the group of eight translations is generated by interchanges of parallel 2x2x1 cube-slices.  This is clearly a subgroup of the group generated by permuting 1x1x2 cube-slices.  Such translations in the affine 3-space have no effect on the projective plane, since they leave each of the plane model's seven partitions– the "points" of the plane– invariant.)

To view the cubes model in a wider context, see Galois Geometry, Block Designs, and Finite-Geometry Models.

 

For another application of the points-as-partitions technique, see Latin-Square Geometry: Orthogonal Latin Squares as Skew Lines.

For more on the plane's symmetry group in another guise, see John Baez on Klein's Quartic Curve and the online book The Eightfold Way.  For more on the mathematics of cubic models, see Solomon's Cube.

 

For a large downloadable folder with many other related web pages, see Notes on Finite Geometry.

Thursday, December 16, 2004

Thursday December 16, 2004

Filed under: General — Tags: — m759 @ 3:00 AM

Nothing Nothings
(Again)

Background: recent Log24 entries (beginning with Chorus from the Rock on Dec. 5, 2004) and Is Nothing Sacred? (quotations compiled on March 9, 2000).

From an obituary of Paul Edwards, a writer on philosophy, in this morning's New York Times:

"Heidegger's Confusions, a collection of Professor Edwards's scholarly articles, was published last month by Prometheus."

Edwards, born in Vienna in 1923 to Jewish parents, died on December 9.

Some sites I visited earlier this evening, before reading of Edwards's death:

  • " 'Nothingness itself nothings' — with these words, uttered by Martin Heidegger in the early 1930s, the incipient (and now-familiar) split between analytic and continental philosophy began tearing open. For Rudolf Carnap, a leader of the Vienna Circle [Wiener Kreis] of logical empiricists and a strident advocate of a new, scientific approach to philosophy, this Heideggerian proposition exemplified 'a metaphysical pseudo-sentence,' meaningless and unable to withstand any logical analysis. Heidegger countered that Carnap’s misplaced obsession with logic missed the point entirely."
    Review of A Parting of the Ways: Carnap, Cassirer, and Heidegger
  • "Death and Metaphysics," by Peter Kraus, pp. 98-111 in Death and Philosophy, ed. by Jeff Malpas and Robert Solomon.  Heidegger's famous phrase (misquoted by Quine in Gray Particular in Hartford) "Das Nichts selbst nichtet" is discussed on page 102.

Sunday, December 12, 2004

Sunday December 12, 2004

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

Ideas, Stories, Values:
Literati in Deep Confusion

Joan Didion, The White Album:

“We tell ourselves stories in order to live….

We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the ‘ideas‘ with which we have learned to freeze the shifting phantasmagoria which is our actual experience.

Or at least we do for a while. I am talking here about a time when I began to doubt the premises of all the stories I had ever told myself, a common condition but one I found troubling.”

Interview with Joseph Epstein:

“You can do in stories things that are above those in essays,” says Epstein.  “In essays and piecework, you are trying to make a point, whereas in stories you are not quite sure what the point is. T.S. Eliot once said of Henry James, ‘He had a mind so fine no idea could violate it,’ which, I think, is the ultimate compliment for an author. Stories are above ideas.”

Harvard President Lawrence H. Summers, Sept. 12, 2004:

“You are entering a remarkable community, the Harvard community. It is a community built on the idea of searching for truth… on the idea of respect for others….

… we practice the values we venerate. The values of seeking truth, the values of respecting others….”

Paul Redding on Hegel:

“… Hegel discusses ‘culture’ as the ‘world of self-alienated spirit.’ The idea seems to be that humans in society not only interact, but that they collectively create relatively enduring cultural products (stories, dramas, and so forth) within which they can recognise their own patterns of life reflected.”

The “phantasmagoria” of Didion seems related to the “phenomenology” of Hegel…

From Michael N. Forster,  Hegel’s Idea of a Phenomenology of Spirit:

“This whole system is conceived, on one level at least, as a defense or rational reworking of the Christian conception of God.  In particular, its three parts are an attempt to make sense of the Christian idea of a God who is three in one — the Logic depicting God as he is in himself, the Philosophy of Nature God the Son, and the Philosophy of Spirit God the Holy Spirit.”

and, indeed, to the phenomenology of narrative itself….

From Patrick Vert,
The Narrative of Acceleration:

“There are plenty of anecdotes to highlight the personal, phenomenological experience of railway passage…

… a unique study on phantasmagoria and the history of imagination. The word originates [in] light-projection, the so-called ghost-shows of the early 19th century….

… thought becomes a phantasmagorical process, a spectral, representative location for the personal imagination that had been marginalized by scientific rationalism….

Truly, ‘immediate experience is [or becomes] the phantasmagoria of the idler’ [Walter Benjamin, The Arcades Project.  Cambridge: Harvard University Press, 1999.  Page 801.]….

Thought as phantasm is a consequence of the Cartesian split, and… a further consequence to this is the broad take-over of perceptual faculty…. What better example than that of the American railway?  As a case-study it offers explanation to the ‘phantasmagoria of the idler’….

This phantasmagoria became more mediated over time…. Perception became increasingly visually oriented…. As this occurred, a narrative formed to encapsulate the phenomenology of it all….”

For such a narrative, see
the Log24.net entries of

November 5, 2002, 2:56 AM,
November 5, 2002, 6:29 AM,
January 3, 2003, 11:59 PM,
August 17, 2004, 7:29 PM,
August 18, 2004, 2:18 AM,
August 18, 2004, 3:00 AM, and
November 24, 2004, 10:00 AM.

Sunday, September 5, 2004

Sunday September 5, 2004

Filed under: General — m759 @ 4:00 PM

Symmetry and Change
in the Dreamtime

Notes from the Journal
of Steven H. Cullinane

Summary:

Aug 31 2004 
07:31:01 PM
Early Evening,
Shining Star 
Sep 01 2004
09:00:35 AM
Words
and Images
Sep 01 2004
12:07:28 PM
Whale Rider
Sep 02 2004
11:11:42 AM
Heaven
and Earth

Sep 02 2004
07:00:23 PM
Whale Road

Sep 03 2004
12:00:54 AM

Cinderella’s
Slipper
 
Sep 03 2004
10:01:56 AM
Another
September Morn

 

Sep 03 2004
12:00:25 PM

Noon

Sep 03 2004
01:13:49 PM

De Nada

Sep 03 2004
03:17:13 
PM

Ite, Missa Est 


Tuesday, August 31, 2004

Symmetry and Change, Part 1…

Early Evening,
Shining Star

7:31:01 PM ET

Hexagram 01
The Creative:

 

The Image

Heaven

Heaven

The movement of heaven
is full of power.

Click on picture
for details.

The Clare Lawler Prize
for Literature goes to…

Under the Volcano,
Chapter VI:

“What have I got out of my life? Contacts with famous men… The occasion Einstein asked me the time, for instance. That summer evening…. smiles when I say I don’t know. And yet asked me. Yes: the great Jew, who has upset the whole world’s notions of time and space, once leaned down… to ask me… ragged freshman… at the first approach of the evening star, the time. And smiled again when I pointed out the clock neither of us had noticed.”

For the thoughts on time
of another famous man,
from Mexico, see the
Nobel Prize acceptance speech
of Octavio Paz,
In Search of the Present.”


Wednesday, September 1, 2004

Symmetry and Change, Part 2…

Words and Images

9:00:35 AM ET

Hexagram 35
Progress:

The Image

Fire

Earth

The sun rises over the earth.

From Aug. 18, 2004:

“Oh, my Lolita. I have only words
to play with!” (Nabokov, Lolita)

“This is the best toy train set
a boy ever had!”
(Orson Welles, after first touring
RKO Studios, quoted in Halliwell)

“As the quotes above by Nabokov and Welles suggest, we need to be able to account for the specific functions available to narrative in each medium, for the specific elements that empirical creators will ‘play with’ in crafting their narratives.”

Donald F. Larsson

For
James Whale
and
William French Anderson —

Words
In the Spirit of
Dave Barry’s Book of Bad Songs:

Stay for just a while…
Stay, and let me look at you.
It’s been so long, I hardly knew you.
Standing in the door…
Stay with me a while.
I only want to talk to you.
We’ve traveled halfway ’round the world
To find ourselves again.

September morn…
We danced until the night
      became a brand new day,
Two lovers playing scenes
      from some romantic play.
September morning still can
      make me feel this way.

Look at what you’ve done…
Why, you’ve become a grown-up girl…

— Neil Diamond

Images
In the Spirit of
September Morn:

The Last Day of Summer:
Photographs by Jock Sturges

In 1990, the FBI entered Sturges’s studio and seized his work, claiming violation of child pornography laws.”

Related material:

Bill’s Diamond Theory

and

Log24 entries of
Aug. 15, 2004
.

Those interested in the political implications of Diamond’s songs may enjoy Neil Performs at Kerry Fundraiser.

I personally enjoyed this site’s description of Billy Crystal’s remarks, which included “a joke about former President Clinton’s forthcoming children’s book — ‘It’s called The Little Engine That Could Because It Could.'”

“Puff, puff, woo, woo, off we go!” 

 


 

Wednesday, September 1, 2004

Symmetry and Change, Part 3…

Whale Rider

12:07:28 PM

Hexagram 28
Preponderance of
the Great:

The Image

Lake

Wind

The lake rises
above
the trees.

 

Cullinane College News:

“Congratulations to Clare Lawler, who participated very successfully in the recently held Secondary Schools Judo Championships in Wellington.”

For an explanation of this entry’s title, see the previous two entries and

Oxford Word
(Log24, July 10, 2004) 


Thursday, September 2, 2004

Symmetry and Change, Part 4…

Heaven and Earth

11:11:42 AM ET

Hexagram 42
Increase:

The Image

Wind

Thunder

Wind and thunder:
the image of Increase.

“This time resembles that of
the marriage of heaven and earth”


Kylie


Finney

Well if you want to ride
you gotta ride it like you find it.
Get your ticket at the station
of the Rock Island Line.
Lonnie Donegan (d. Nov. 3)
and others
The Rock Island Line’s namesake depot 
in Rock Island, Illinois

“What it all boiled down to really was everybody giving everybody else a hard time for no good reason whatever… You just couldn’t march to your own music. Nowadays, you couldn’t even hear it… It was lost, the music which each person had inside himself, and which put him in step with things as they should be.”

The Grifters, Ch. 10, 1963, by
James Myers Thompson

“The Old Man’s still an artist
with a Thompson.”
— Terry in “Miller’s Crossing

For some of “the music which
each person had inside,”
click on the picture
with the Thompson.

It may be that Kylie is,
in her own way, an artist…
with a 357:

(Hits counter at
The Quality of Diamond
as of 11:05 AM Sept. 2, 2004)

For more on
“the marriage of heaven and earth,”
see
Plato, Pegasus, and the Evening Star


Thursday, September 2, 2004

Symmetry and Change, Part 5…

Whale Road

7:00:23 PM

Hexagram 23
Splitting Apart:

The Image

Mountain

Earth

The mountain rests
on the earth
.

“… the plot is different but the monsters, names, and manner of speaking will ring a bell.”

— Frank Pinto, Jr., review of Seamus Heaney’s translation of Beowulf 

Other recommended reading, found during a search for the implications of today’s previous entry, “Hexagram 42”:

Water Wings.

This excellent meditation
on symmetry and change
comes from a site whose
home page
has the following image:


Friday, September 3, 2004

 Symmetry and Change, Part 6…

Cinderella’s Slipper

12:00:54 AM ET

Hexagram 54
The Marrying Maiden:

 

The Image

Thunder


Lake
See
The hundredletter
thunderwords of
Finnegans Wake


“… a Thoreau-like retreat
by a nearby lake….
Both men have
a ‘touch of the poet’….
The symmetry is perfect.”

Friday, September 3, 2004  

Symmetry and Change, Part 7…

Another September Morn

10:01:56 AM ET

Hexagram 56:
The Wanderer

 

The Image

Fire


Mountain

Fire on the mountain,
Run boys run…
Devil’s in the House of
The Rising Sun!
 


Friday, September 3, 2004

Symmetry and Change, Part 8…

Noon

12:00:25 PM ET

Hexagram 25
Innocence:

The Image

Heaven


Thunder

Under heaven
thunder rolls.
 


Friday, September 3, 2004

Symmetry and Change, Part 9…

De Nada

Helen Lane

1:13:49 PM ET

Hexagram 49
Revolution:

The Image

Lake


Fire
 Fire in the lake:
the image of Revolution
.

“I sit now in a little room off the bar at four-thirty in the morning drinking ochas and then mescal and writing this on some Bella Vista notepaper I filched the other night…. But this is worst of all, to feel your soul dying. I wonder if it is because to-night my soul has really died that I feel at the moment something like peace. Or is it because right through hell there is a path, as Blake well knew, and though I may not take it, sometimes lately in dreams I have been able to see it? …And this is how I sometimes think of myself, as a great explorer who has discovered some extraordinary land from which he can never return to give his knowledge to the world: but the name of this land is hell. It is not Mexico of course but in the heart.”

— Malcolm Lowry, Under the Volcano 


Friday, September 3, 2004

Symmetry and Change, conclusion…

Ite, Missa Est

3:17:13 PM ET

Hexagram 13
Fellowship With Men:

The Image

Heaven


Fire

Heaven together with fire.

“A pretty girl —
is like a melody —- !”

 For details, see
A Mass for Lucero


Thursday, September 2, 2004

Thursday September 2, 2004

Filed under: General — m759 @ 7:00 PM

Symmetry and Change, Part 5…

Whale Road

7:00:23 PM

Hexagram 23
Splitting Apart:

The Image

Mountain

Earth

The mountain rests
on the earth
.

“… the plot is different but the monsters, names, and manner of speaking will ring a bell.”

— Frank Pinto, Jr., review of Seamus Heaney’s translation of Beowulf 

Other recommended reading, found during a search for the implications of today’s previous entry, “Hexagram 42”:

Water Wings.

This excellent meditation
on symmetry and change
comes from a site whose
home page
has the following image:


Sunday, August 15, 2004

Sunday August 15, 2004

Filed under: General — m759 @ 3:17 PM

The Line

Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, Ch. 6 (italics are mine):

“A classical understanding sees the world primarily as underlying form itself. A romantic understanding sees it primarily in terms of immediate appearance.”

The Sophist, by Plato:

STRANGER – We are far from having exhausted the more exact thinkers who treat of being and not-being. But let us be content to leave them, and proceed to view those who speak less precisely; and we shall find as the result of all, that the nature of being is quite as difficult to comprehend as that of not-being.

THEAETETUS – Then now we will go to the others.

STRANGER – There appears to be a sort of war of Giants and Gods going on amongst them; they are fighting with one another about the nature of essence.

THEAETETUS – How is that?

STRANGER – Some of them are dragging down all things from heaven and from the unseen to earth, and they literally grasp in their hands rocks and oaks; of these they lay hold, and obstinately maintain, that the things only which can be touched or handled have being or essence, because they define being and body as one, and if any one else says that what is not a body exists they altogether despise him, and will hear of nothing but body.

THEAETETUS – I have often met with such men, and terrible fellows they are.

STRANGER – And that is the reason why their opponents cautiously defend themselves from above, out of an unseen world, mightily contending that true essence consists of certain intelligible and incorporeal ideas; the bodies of the materialists, which by them are maintained to be the very truth, they break up into little bits by their arguments, and affirm them to be, not essence, but generation and motion. Between the two armies, Theaetetus, there is always an endless conflict raging concerning these matters.

THEAETETUS – True.

— Translated by Benjamin Jowett

Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, Ch. 18:

“The wave of crystallization rolled ahead. He was seeing two worlds, simultaneously. On the intellectual side, the square side, he saw now that Quality was a cleavage term. What every intellectual analyst looks for. You take your analytic knife, put the point directly on the term Quality and just tap, not hard, gently, and the whole world splits, cleaves, right in two…

The Line,
by S. H. Cullinane

hip and square, classic and romantic, technological and humanistic…and the split is clean. There’s no mess. No slop. No little items that could be one way or the other. Not just a skilled break but a very lucky break. Sometimes the best analysts, working with the most obvious lines of cleavage, can tap and get nothing but a pile of trash. And yet here was Quality; a tiny, almost unnoticeable fault line; a line of illogic in our concept of the universe; and you tapped it, and the whole universe came apart, so neatly it was almost unbelievable. He wished Kant were alive. Kant would have appreciated it. That master diamond cutter. He would see. Hold Quality undefined. That was the secret.”

What Pirsig means by “quality” is close to what Yagoda means, in the previous entry, by “style.”

Thursday, July 8, 2004

Thursday July 8, 2004

Filed under: General — m759 @ 12:25 PM

Bandito

12:25 PM July 8:

"Willst Du lieber
einen gelben Stern
haben?
" she asked.
"Oder einen roten?"

— Martin Cruz Smith,
Stallion Gate,
Ballantine paperback,
1987, page 101

The image �http://www.log24.com/log/pix04A/040708-StarWars.jpg� cannot be displayed, because it contains errors.

Personally, I prefer
a blue-green star:

The image �http://www.log24.com/log/pix04A/040708-Spirit.jpg� cannot be displayed, because it contains errors.

Follow-up of
2 PM July 9, 2004 —

From today's New York Times:

"Texas Bandito, how much money
did you put in your pocket today?"
John Mellencamp crooned
in a country ballad.

In a two-and-a-half hour gala
that raised $7.5 million,
a record for a single event,
Chevy Chase poked fun at
the president's pronunciation
of "nuclear"…
 
The image “http://www.log24.com/log/pix04A/040709-Three.jpg” cannot be displayed, because it contains errors.

The concert brought 6,200 people,
paying $250 to $25,000 each…
beating the $6.8 million haul
from a parallel gala last month
in Los Angeles featuring
Barbra Streisand,
Willie Nelson,
and Billy Crystal.
The take will be split….

Here, Chevy, is another

  way to pronounce "nuclear"–

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The Source:

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Click on picture for details.

Wednesday, March 10, 2004

Wednesday March 10, 2004

Filed under: General — m759 @ 6:01 PM

Split

The first idea was not our own. Adam
in Eden was the father of Descartes.

— Wallace Stevens,
Notes Toward a Supreme Fiction

A very interesting web site at
Middle Tennessee State University
relates the Stevens quote
to two others:

“The sundering we sense, between nature and culture, lies not like a canyon outside us but splits our being at its most intimate depths the way mind breaks off from body. It is still another version of that bitter bifurcation long ago decreed: our expulsion from Eden. It differs from the apparently similar Cartesian crease across things in the fact that the two halves of us once were one; that we did not always stand askance like molasses and madness–logically at odds–but grew apart over the years like those husbands and wives who draw themselves into different corners of contemplation.”

— William Gass,
“The Polemical Philosopher”

“The experiment [to make rationality primary] reached the reductio ad absurdum following the attempt by Descartes to solve problems of human knowledge by giving ontological status to the dichotomy of thinking substance and extended substance, that is subject and object. Not only were God and man, sacred and secular, being and becoming, play and seriousness severed, but now also the subject which wished to unite these fragmented dichotomies was itself severed from that which it would attempt to reconcile.”

— David Miller, God and Games

“Which is it then? For Gass, the Cartesian schism is a post- lapsarian divorce-in progress, only apparently similar to the expulsion from paradise. For Stevens the fault is primordial and Descartes only its latter-day avatar. For Miller, Descartes is the historical culprit, the patriarch of the split.”

The Evil Genius Notebook,
by
David Lavery

Tuesday, March 2, 2004

Tuesday March 2, 2004

Filed under: General — m759 @ 3:01 PM

Passion

From the previous entry:

 1.
Oscar:
military phonetic
for the letter
‘O’

From an entry of Dec. 21, 2002, some background in literary theory:

“I know what ‘nothing’ means….”
— Maria Wyeth in Play It As It Lays

“How do you solve a problem like Maria?”
— Oscar Hammerstein II

“…problems can be solved by manipulating just two symbols, 1 and 0….” 
— George Johnson, obituary of Claude Shannon

“The female and the male continue this charming dance, populating the world with all living beings.” 
— Leonard Shlain, The Alphabet Versus the Goddess, Penguin Arkana paperback, 1999, Chapter 17, “Lingam/Yoni” 

“According to Showalter’s essay*, ‘In Elizabethan slang, ‘nothing’ was a term for the female genitalia . . . what lies between maids’ legs, for, in the male visual system of representation and desire…. Ophelia’s story becomes

the Story of O — the zero, the empty circle or mystery of feminine difference, the cipher of female sexuality to be deciphered by feminist interpretation.’ (222)* Ophelia is a highly sexual being…”

— Leigh DiAngelo,
   Ophelia as a Sexual Being

*Showalter, Elaine. “Representing Ophelia: Women, Madness, and the Responsibilities of Feminist Criticism.” Hamlet. Ed. Susanne L. Wofford. Boston: Bedford Books of St.Martin’s Press, 1994. 220-238.

At the Oscars Sunday night, a thought attributed by Billy Crystal to Sean Connery:

“Pussy Galore! I just got it! That’s vulgar.”

For further background, see

Passing the Crown (Aug. 24, 2003) and

The Agony and the Ya-Ya (Oct. 4, 2002).

Wednesday, February 18, 2004

Wednesday February 18, 2004

Filed under: General — m759 @ 11:11 AM

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.”

Wednesday, September 10, 2003

Wednesday September 10, 2003

Filed under: General — m759 @ 4:04 PM

4:04:08

The title refers to my entry of last April 4,

The Eight,

and to the time of this entry.

From D. H. Lawrence and the Dialogical Principle:

“Plato’s Dialogues…are queer little novels….[I]t was the greatest pity in the world, when philosophy and fiction got split.  They used to be one, right from the days of myth.  Then they went and parted, like a nagging married couple, with Aristotle and Thomas Aquinas and that beastly Kant.  So the novel went sloppy, and philosophy went abstract-dry.  The two should come together again, in the novel.”

— pp. 154-5 in D. H. Lawrence, “The Future of the Novel,” in Study of Thomas Hardy and Other Essays. Ed.  Bruce Steele.  Cambridge: Cambridge University Press,1983. 149-55.



Philosophy



Fiction

“The wild, brilliant, alert head of St. Mawr seemed to look at her out of another world… the large, brilliant eyes of that horse looked at her with demonish question…. ‘Meet him half way,’ Lewis [the groom] said.  But halfway across from our human world to that terrific equine twilight was not a small step.”    

— pp. 30, 35 in D. H. Lawrence, “St. Mawr.” 1925.  St. Mawr and Other Stories.  Ed. Brian Finney.  Cambridge: Cambridge University Press, 1983.

See also

Plato, Pegasus, and the Evening Star.

Katherine Neville’s novel The Eight, referred to in my note of April 4, is an excellent example of how not to combine philosophy with fiction.  Lest this be thought too harsh, let me say that the New Testament offers a similarly ludicrous mixture.

On the other hand, there do exist successful combinations of philosophy with fiction… For example, The Glass Bead Game, Zen and The Art of Motorcycle Maintenance, Under the Volcano, the novels of Charles Williams, and the C. S. Lewis classic That Hideous Strength.

This entry was prompted by the appearance of the god Pan in my entry on this date last year, by Hugh Grant’s comedic encounters with Pan in “Sirens,” by Lawrence’s remarks on Pan in “St. Mawr,” and by the classic film “Picnic at Hanging Rock.”

Tuesday, January 21, 2003

Tuesday January 21, 2003

Filed under: General — m759 @ 5:09 PM

Diablo Ballet

Thanks to Meghan for the following:

not going, not coming,
rooted, deep and still
not reaching out, not reaching in
just resting, at the center
a single jewel, the flawless crystal drop
in the blaze of its brilliance
the way beyond.

— Shih Te (c. 730)

It turns out that Shih Te (“Foundling”) was the sidekick of Han Shan (“Cold Mountain”).  Here are some relevant links:

Thoughts of Robert Frost (see past two days’ entries) lead to “Two Tramps in Mud Time,” which in turn leads to Jack Kerouac and Gary Snyder splitting wood in The Dharma Bums.

This in turn leads, via a search on “Kerouac” and “axe,” to the sentence

“There’s the grace of an axe handle 
 as good as an Eglevsky ballet,”

in Big Sur

Kerouac taught me when I was 16 and he is still teaching me now that I am 60.

Searching for “Eglevsky ballet” leads to this site on André Eglevsky, his work, his life, and his children.  A further search leads to his daughter Marina Eglevsky, who stages dance for the Diablo Ballet.

Born to Dance

Marina Eglevsky and
the Diablo Ballet —
a rare and gifted
pas de deux

Those who feel the above is too “arty” for them may nevertheless appreciate the movie by the same name: “Born to Dance” (1936), starring Eleanor Powell and James Stewart.

In the larger metaphorical sense, of course, Powell and Eglevsky are both part of the same dance… at the “still point” described so well by Shih Te. 

“just resting, at the center
a single jewel…”

“At the still point,
there the dance is.”
— T. S. Eliot

From Marshall’s Jewelers, Tucson —

A Diamond-Cutter Sutra:

The ideal cut is a mathematical formula for cutting diamonds to precise angles and proportions to maximize the reflection and refraction of light. In addition to these ideal proportions, the polish and symmetry of the diamond is done to the highest standards also. Only then does it qualify to receive the American Gem Society (AGS) “triple zero” rating. A “zero” rating is the most perfect rating that the AGS gives evaluating the cut, polish, and symmetry of the diamond.

When a diamond receives the “zero” rating for each of these areas, (cut, polish, and symmetry), it gets three “zeros,” hence the “triple zero” rating. Because of this attention to detail, it takes up to four times longer to cut a diamond to these standards than an “average” diamond.

You may choose to compromise on color or clarity but to ensure the most brilliant diamond you should not compromise on cut….

The “triple zero” ideal cut guarantees you a magnificent balance of brilliance, sparkle, and fire.

Postscript of 1/25/03:

See also the obituary of Irene Diamond, ballet patron, for whom the New York City Ballet’s “Diamond Project” is named.  Diamond died on January 21, 2003, the date of the above weblog entry.

Friday, December 6, 2002

Friday December 6, 2002

Filed under: General — m759 @ 1:06 PM

Great Simplicity

Frank Tall

Iaido

 

Daisetsu

 

 

Today

is the day that Daisetsu Suzuki attained satori,
according to the Zen Calendar.  “Daisetsu” is
said to mean “Great Simplicity.”

For those who prefer Harry Potter and
Diagon Alley, here is another calendar:


To Have and Have Not

Those who prefer traditional Western religions may like a site on the Trinity that contains this:

“Zen metaphysics is perhaps most succinctly set forth in the words ‘not-two.”  But even when he uses this expression, Suzuki is quick to assert that it implies no monism.  Not-two, it is claimed, is not the same as one.*  But when Suzuki discusses the relationship of Zen with Western mysticism, it is more difficult to escape the obvious monistic implications of his thinking.  Consider the following:

We are possessed of the habit of looking at Reality by dividing it into two… It is all due to the human habit of splitting one solid Reality into two, and the result is that my ‘have’ is no ‘have’ and my ‘have not’ is no ‘have not.’  While we are actually passing, we insist that the gap is impassable.**”

*See: Daisetz T. Suzuki, ‘Basic Thoughts Underlying  Eastern Ethical and Social Practice’ in Philosophy and Culture  East and West: East-West Philosophy in Practical Perspective, ed. Charles A. Moore (Honolulu: University of Hawaii Press, 1968), p. 429

** Daisetsu Teitaro Suzuki, Mysticism Christian and Buddhist (London: George Allen & Unwin, 1957, Unwin paperback, 1979), p. 57.


Personally, I am reminded by Suzuki’s satori on this date that today is the eve of the anniversary of Pearl Harbor.  I am also reminded by the rather intolerant tract on the Trinity quoted above that the first atomic bomb was exploded in the New Mexico desert at a test site named Trinity.  Of course, sometimes intolerance is justified.

Concluding unscientific postscript:

On the same day in 1896 that D. T. Suzuki attained satori,
lyricist Ira Gershwin was born.

Dies irae, dies illa.

Monday, November 25, 2002

Monday November 25, 2002

Filed under: General — m759 @ 3:43 PM

ART WARS

Driving the Point Home

From

SUSAN WEIL

EAR'S EYE FOR JAMES JOYCE:


From Finnegans Wake,
by James Joyce, p. 293:

The Vesica Piscis,
also known as
The Ya-Ya:

See also the
Geometries of Creation
art exhibit at the University of Waterloo.

Sunday, September 15, 2002

Sunday September 15, 2002

Filed under: General,Geometry — m759 @ 11:07 PM

Evariste Galois and 
The Rock That Changed Things

An article in the current New York Review of Books (dated Sept. 26) on Ursula K. Le Guin prompted me to search the Web this evening for information on a short story of hers I remembered liking.  I found the following in the journal of mathematician Peter Berman:

  • A Fisherman of the Inland Sea, Ursula K. Le Guin, 1994:
    A book of short stories. Good, entertaining. I especially liked “The Rock That Changed Things.” This story is set in a highly stratified society, one split between elite and enslaved populations. In this community, the most important art form is a type of mosaic made from rocks, whose patterns are read and interpreted by scholars from the elite group. The main character is a slave woman who discovers new patterns in the mosaics. The story is slightly over-the-top but elegant all the same.

I agree that the story is elegant (from a mathematician, a high compliment), so searched Berman’s pages further, finding this:

A table of parallels

between The French Mathematician (a novel about Galois) and Harry Potter and the Sorcerer’s Stone

My own version of the Philosopher’s Stone (the phrase used instead of “Sorcerer’s Stone” in the British editions of Harry Potter) appears in my profile picture at top left; see also the picture of Plato’s diamond figure in my main math website.  The mathematics of finite (or “Galois”) fields plays a role in the underlying theory of this figure’s hidden symmetries.  Since the perception of color plays a large role in the Le Guin story and since my version of Plato’s diamond is obtained by coloring Plato’s version, this particular “rock that changes things” might, I hope, inspire Berman to extend his table to include Le Guin’s tale as well.

Even the mosaic theme is appropriate, this being the holiest of the Mosaic holy days.

Dr. Berman, G’mar Chatimah Tova.

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