Log24

Tuesday, August 20, 2013

The 20

Filed under: General,Geometry — Tags: , — m759 @ 12:00 pm

In memory of author Elmore Leonard

A graphic symbol and a search for "Nowhere"*
in this journal yield

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

"Cotton Mather died
when I was a boy.
The books/ He read,
all day, all night
and all the nights,/
Had got him nowhere."

— Wallace Stevens,
"The Blue Buildings
in the Summer Air"

* See previous post.

Monday, August 19, 2013

Noon

Filed under: General,Geometry — Tags: — m759 @ 12:00 pm

Last midnight's post quoted poet John Hollander
on Cervantes—

"… the Don’s view of the world is correct at midnight,
and Sancho’s at noon."

The post concluded with a figure that might, if
rotated slightly, be regarded as a sort of Star of
David or Solomon's Seal. The figure's six vertices
may be viewed as an illustration of Pascal's
"mystic hexagram."

Pacal's hexagram is usually described
as a hexagon inscribed in a conic
(such as a circle). Clearly the hexagon
above may be so inscribed.

The figure suggests that last midnight's Don be
played by the nineteenth-century mathematician
James Joseph Sylvester. His 1854 remarks on
the nature of geometry describe a different approach
to the Pascal hexagram—

"… the celebrated theorem of Pascal known under the name of the Mystic Hexagram, which is, that if you take two straight lines in a plane, and draw at random other straight lines traversing in a zigzag fashion between them, from A in the first to B in the second, from B in the second to C in the first, from C in the first to D in the second, from D in the second to E in the first, from E in the first to F in the second and finally from F in the second back again to A the starting point in the first, so as to obtain ABCDEF a twisted hexagon, or sort of cat's-cradle figure and if you arrange the six lines so drawn symmetrically in three couples: viz. the 1st and 4th in one couple, the 2nd and 5th in a second couple, the 3rd and 6th in a third couple; then (no matter how the points ACE have been selected upon one of the given lines, and BDF upon the other) the three points through which these three couples of lines respectively pass, or to which they converge (as the case may be) will lie all in one and the same straight line."

For a Sancho view of Sylvester's "cat's cradle," see some twentieth-century
remarks on "the most important configuration of all geometry"—

"Now look, your grace," said Sancho,
"what you see over there aren't giants,
but windmills, and what seems to be arms
are just their sails, that go around in the wind
and turn the millstone."
"Obviously," replied Don Quijote,
"you don't know much about adventures.”

― Miguel de Cervantes Saavedra

Friday, August 16, 2013

Six-Set Geometry

Filed under: General,Geometry — Tags: , — m759 @ 5:24 am

From April 23, 2013, in
​"Classical Geometry in Light of Galois Geometry"—

Click above image for some background from 1986.

Related material on six-set geometry from the classical literature—

Baker, H. F., "Note II: On the Hexagrammum Mysticum  of Pascal,"
in Principles of Geometry , Vol. II, Camb. U. Press, 1930, pp. 219-236  

Richmond, H. W., "The Figure Formed from Six Points in Space of Four Dimensions,"
Mathematische Annalen  (1900), Volume 53, Issue 1-2, pp 161-176

Richmond, H. W., "On the Figure of Six Points in Space of Four Dimensions," 
Quarterly Journal of Pure and Applied Mathematics , Vol. 31 (1900), pp. 125-160

Sunday, July 7, 2013

Mere 61

Filed under: General — m759 @ 9:00 am

Today is the 61st anniversary of the publication
of the book Mere Christianity , by C. S. Lewis.

In its honor, here is a link to "Hexagram 61
in this journal.

See also "Moonshine and Lion."

Sunday, June 16, 2013

Mathematical Review

Filed under: General,Geometry — m759 @ 10:00 pm

From a weblog post on June 11, 2013, by one Pete Trbovich:

Diamond Theory

Here again, I don't think Steven Cullinane is really unhinged per se. At the very least, his geometric study is fun to play with, particularly when you find this toy. And I'm not really sure that anything he says is wrong per se. But you might find yourself asking "So what?" or more to the point, "Why is this supposed to be the central theory to explaining life, the universe, and everything?"

It isn't  supposed to be such a theory.
I do not know why Trbovich thinks it is 

— Steven H. Cullinane

Update of 11 PM June 16:

For one such central theory of everything, see
the I Ching .  Diamond theory is, unlike that
Chinese classic, pure mathematics, but the larger
of the binary-coordinate structures  it is based on
are clearly isomorphic, simply as structures , to
the I Ching 's 
64 hexagrams.

Make of this what you will.

Sunday, May 5, 2013

Night of Lunacy*

Filed under: General — Tags: — m759 @ 9:00 pm

Structure vs. Character continued

   IMAGE- The 3x3 square

Structure

IMAGE- Chinese character for 'well' and I Ching Hexagram 48, 'The Well'


Character

Related vocabulary:

Nick Tosches on the German word “Quell 

and Heidegger on Hölderlin.

* The title is from Heidegger.

Sunday, April 28, 2013

The Octad Generator

Filed under: General,Geometry — Tags: , , , , — m759 @ 11:00 pm

… And the history of geometry  
Desargues, Pascal, Brianchon and Galois
in the light of complete n-points in space.

(Rewritten for clarity at about 10 AM ET April 29, with quote from Dowling added.
Updated with a reference to a Veblen and Young exercise (on p. 53) on April 30.)

Veblen and Young, Projective Geometry, Vol. I ,
Ginn and Company, 1910, page 39:

"The Desargues configuration. A very important configuration
is obtained by taking the plane section of a complete space five-point."

Each of figures 14 and 15 above has 15 points and 20 lines.
The Desargues configuration within each figure is denoted by
10 white points and 10 solid lines, with 3 points on each line and
3 lines on each point. Black  points and dashed  lines indicate the
complete space five-point and lines connecting it to the plane section
containing the Desargues configuration.

In a 1915 University of Chicago doctoral thesis, Archibald Henderson
used a complete space six -point to construct a configuration of
15 points and 20 lines in the context not of Desargues '  theorem, but
rather of Brianchon 's theorem and of the Pascal  hexagram.
Henderson's 1915 configuration is, it turns out, isomorphic to that of
the 15 points and 20 lines in the configuration constructed via a
complete space five -point five years earlier by Veblen and Young.
(See, in Veblen and Young's 1910 Vol. I, exercise 11, page 53:
"A plane section of a 6-point in space can  be considered as
3 triangles perspective in pairs from 3 collinear points with
corresponding sides meeting in 3 collinear points." This is the
large  Desargues configuration. See Classical Geometry in Light of 
Galois Geometry
.)

For this large  Desargues configuration see April 19.
For Henderson's complete six –point, see The Six-Set (April 23).
That post ends with figures relating the large  Desargues configuration
to the Galois  geometry PG(3,2) that underlies the Curtis
Miracle Octad Generator  and the large Mathieu group M24 —

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

See also Note on the MOG Correspondence from April 25, 2013.

That correspondence was also discussed in a note 28 years ago, on this date in 1985.

Saturday, April 27, 2013

Mark and Remark

Filed under: General,Geometry — Tags: — m759 @ 11:00 am

“Fact and fiction weave in and out of novels like a shell game.” —R.B. Kitaj

Not just novels.

Fact: 

IMAGE- Anne Taormina on 'Mathieu Moonshine' and the 'super overarching symmetry group'

The mark preceding A in the above denotes the semidirect product.

Symbol from the box-style
I Ching  (Cullinane, 1/6/89).
This is Hexagram 55,
“Abundance [Fullness].”

The mathematical quote, from last evening’s Symmetry, is from Anne Taormina.

The I Ching  remark is not.

Another version of Abbondanza 

IMAGE- Taormina sunset from inabbondanza.com on June 22, 2009

Fiction:

Found in Translation and the giorno  June 22, 2009here.

Monday, April 8, 2013

Magic for Jews

Filed under: General,Geometry — Tags: , — m759 @ 12:00 pm

A commenter on Saturday's "Seize the Dia" has
suggested a look at the work of one Mark Collins.

Here is such a look (click to enlarge):

I find attempts to associate pure mathematics with the words
"magic" or "mystic" rather nauseating. (H. F. Baker's work
on Pascal's mystic hexagram  is no exception; Baker was
stuck with Pascal's obnoxious adjective, but had no truck
with any mystic aspects of the hexagram.)

The remarks above by Clifford Pickover on Collins, Dürer, and
binary representations may interest some non-mathematicians,
who should not  be encouraged to waste their time on this topic.

For the mathematics underlying the binary representation of
Dürer's square, see, for instance, my 1984 article "Binary
Coordinate Systems
."

Those without the background to understand that article
may enjoy, instead of Pickover's abortive attempts above at
mathematical vulgarization, his impressively awful 2009 novel
Jews in Hyperspace .

Pickover's 2002 book on magic squares was, unfortunately,
published by the formerly reputable Princeton University Press.

Related material from today's Daily Princetonian :

See also Nash + Princeton in this journal.

Sunday, April 7, 2013

Pascal Inscape

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

Click to enlarge.

IMAGE- A Galois-geometry key to the mystic hexagram of Pascal

Background: Inscapes and The 2-subsets of a 6-set are the points of a PG(3,2).

Related remarks: Classical Geometry in Light of Galois Geometry.

Saturday, April 6, 2013

Pascal via Curtis

Filed under: General,Geometry — Tags: , , , — m759 @ 9:17 am

Click image for some background.

IMAGE- The Miracle Octad Generator (MOG) of R.T. Curtis

Shown above is a rearranged version of the
Miracle Octad Generator (MOG) of R. T. Curtis
("A new combinatorial approach to M24,"
Math. Proc. Camb. Phil. Soc., 79 (1976), 25-42.)

The 8-subcell rectangles in the left part of the figure may be
viewed as illustrating (if the top left subcell is disregarded)
the thirty-five 3-subsets of a 7-set.

Such a view relates, as the remarks below show, the
MOG's underlying Galois geometry, that of PG(3,2), to
the hexagrammum mysticum  of Pascal.

On Danzer's 354 Configuration:

IMAGE- Branko Grünbaum on Danzer's configuration
 

"Combinatorially, Danzer’s configuration can be interpreted
as defined by all 3-sets and all 4-sets that can be formed
by the elements of a 7-element set; each 'point' is represented
by one of the 3-sets, and it is incident with those lines
(represented by 4-sets) that contain the 3-set."

— Branko Grünbaum, "Musings on an Example of Danzer's,"
European Journal of Combinatorics , 29 (2008),
pp. 1910–1918 (online March 11, 2008)

"Danzer's configuration is deeply rooted in
Pascal's Hexagrammum Mysticum ."

— Marko Boben, Gábor Gévay, and Tomaž Pisanski,
"Danzer's Configuration Revisited," arXiv.org, Jan. 6, 2013

For an approach to such configurations that differs from
those of Grünbaum, Boben, Gévay, and Pisanski, see

Classical Geometry in Light of Galois Geometry.

Grünbaum has written little about Galois geometry.
Pisanski has recently touched on the subject;
see Configurations in this journal (Feb. 19, 2013).

Tuesday, April 2, 2013

Baker on Configurations

Filed under: General,Geometry — Tags: , , — m759 @ 11:11 am

The geometry posts of Sunday and Monday have been
placed in finitegeometry.org as

Classical Geometry in Light of Galois Geometry.

Some background:

See Baker, Principles of Geometry , Vol. II, Note I
(pp. 212-218)—

On Certain Elementary Configurations, and
on the Complete Figure for Pappus's Theorem

and Vol. II, Note II (pp. 219-236)—

On the Hexagrammum Mysticum  of Pascal.

Monday's elucidation of Baker's Desargues-theorem figure
treats the figure as a 15420configuration (15 points, 
4 lines on each, and 20 lines, 3 points on each).

Such a treatment is by no means new. See Baker's notes
referred to above, and 

"The Complete Pascal Figure Graphically Presented,"
a webpage by J. Chris Fisher and Norma Fuller.

What is new in the Monday Desargues post is the graphic
presentation of Baker's frontispiece figure using Galois geometry :
specifically, the diamond theorem square model of PG(3,2).

See also Cremona's kernel, or nocciolo :

Baker on Cremona's approach to Pascal—

"forming, in Cremona's phrase, the nocciolo  of the whole."

IMAGE- Definition of 'nocciolo' as 'kernel'

A related nocciolo :

IMAGE- 'Nocciolo': A 'kernel' for Pascal's Hexagrammum Mysticum: The 15 2-subsets of a 6-set as points in a Galois geometry.

Click on the nocciolo  for some
geometric background.

Monday, December 24, 2012

Eternal Recreation

Memories, Dreams, Reflections
by C. G. Jung

Recorded and edited By Aniela Jaffé, translated from the German
by Richard and Clara Winston, Vintage Books edition of April 1989

From pages 195-196:

"Only gradually did I discover what the mandala really is:
'Formation, Transformation, Eternal Mind's eternal recreation.'*
And that is the self, the wholeness of the personality, which if all
goes well is harmonious, but which cannot tolerate self-deceptions."

* Faust , Part Two, trans. by Philip Wayne (Harmondsworth,
England, Penguin Books Ltd., 1959), p. 79. The original:

                   … Gestaltung, Umgestaltung, 
  Des ewigen Sinnes ewige Unterhaltung….

Jung's "Formation, Transformation" quote is from the realm of
the Mothers (Faust Part Two, Act 1, Scene 5: A Dark Gallery).
The speaker is Mephistopheles.

See also Prof. Bruce J. MacLennan on this realm
in a Web page from his Spring 2005 seminar on Faust:

"In alchemical terms, F is descending into the dark, formless
primary matter from which all things are born. Psychologically
he is descending into the deepest regions of the
collective unconscious, to the source of life and all creation.
Mater (mother), matrix (womb, generative substance), and matter
all come from the same root. This is Faust's next encounter with
the feminine, but it's obviously of a very different kind than his
relationship with Gretchen."

The phrase "Gestaltung, Umgestaltung " suggests a more mathematical
approach to the Unterhaltung . Hence

Part I: Mothers

"The ultimate, deep symbol of motherhood raised to
the universal and the cosmic, of the birth, sending forth,
death, and return of all things in an eternal cycle,
is expressed in the Mothers, the matrices of all forms,
at the timeless, placeless originating womb or hearth
where chaos is transmuted into cosmos and whence
the forms of creation issue forth into the world of
place and time."

— Harold Stein Jantz, The Mothers in Faust:
The Myth of Time and Creativity 
,
Johns Hopkins Press, 1969, page 37

Part II: Matrices

        

Part III: Spaces and Hypercubes

Click image for some background.

Part IV: Forms

Forms from the I Ching :

Click image for some background.

Forms from Diamond Theory :

Click image for some background.

Wednesday, November 7, 2012

Board

Filed under: General,Geometry — m759 @ 1:00 pm

In several posts now tagged Chessboard
an I Ching chessboard
image in which adjacent squares 
have the Karnaugh property

— has been replaced by a picture of
the original 1989 version in which
the Karnaugh property applies only to cells
that are adjacent in a cubic, not square,
arrangement—

I Ching chessboard (original 1989 arrangement)

Tuesday, November 6, 2012

Bend Sinister

Filed under: General — m759 @ 6:30 am

This morning's New York Times  obituaries—

These suggest a look at Solving Nabokov's Lolita Riddle ,
by Joanne Morgan (Sydney: Cosynch Press, 2005).

That book discusses Lolita as a character like Lewis Carroll's Alice.

(The Red Queen and Alice of course correspond to figures in
the first two thumbnails above.)

From the obituary associated with the third thumbnail above:

"Front-page headlines combined concision and dark humor." 

The title of this post, Bend Sinister , is not unlike such a headline.
It is the title of a novel by Nabokov (often compared with Orwell's 1984 )
that is discussed in the Lolita Riddle  book.

Related material— The bend sinister found in Log24 searches
for Hexagram 14 and for the phrase Hands-On

IMAGE- Magician's hands on his wand, viewed as a diagonal of a square

Monday, October 29, 2012

Opening Bell

Filed under: General — m759 @ 9:00 am

Related material:

Hexagram 29: Water

Hexagram 29 and the life of
Robert Palmer Dilworth, who
died on this date in 1993.

Sunday, September 16, 2012

Sermon

Filed under: General — m759 @ 11:00 am

"I'm 18."

— Spoken by a very beautiful girl
      in the summer of 1991

"Work on what has been spoiled [ Decay ]."

Hexagram 18

IMAGE- Matchbook with monogram ROT from 'North by Northwest'

Click image for some background.

Monday, July 2, 2012

Stiftung

Filed under: General,Geometry — m759 @ 9:00 pm

Heidegger, "Hölderlin and the Essence of Poetry,"
translated by Douglas Scott, in Existence and Being  ,
Regnery, 1949, pp. 291-316—

IMAGE- Page 304 of Heidegger's 'Existence and Being' - Heidegger's essay 'Hölderlin and the Essence of Poetry,' tr. by Douglas Scott, publ. by Henry Regnery Company, Chicago, in 1949

See also Hexagram 36.

Sunday, July 1, 2012

Coming to Meet

Filed under: General — m759 @ 10:30 pm

Hexagram 44:
Coming to Meet

"This hexagram indicates a situation in which
the principle of darkness, after having been eliminated,
furtively and unexpectedly obtrudes again from within
and below. Of its own accord the female principle
comes to meet the male. It is an unfavourable and
dangerous situation, and we must understand and
promptly prevent the possible consequences.

The hexagram is linked with the fifth month
[June-July], because at the summer solstice
the principle of darkness gradually becomes
ascendant again."

— Richard Wilhelm 

To counteract the principle of darkness—

The Uploading (Friday— St. Peter's Day, 2012),

Thor's Light Bulb Joke, and …

 .

Friday, June 22, 2012

Wand Work

Filed under: General — m759 @ 7:59 pm

The New York Times  today—
 "Reality and our perception of it are incommensurate…."

IMAGE- NY Times Wire item- 'Your Mind on Magic,' by Alex Stone

The above New York Times Wire  item from 3:35 PM ET today
mentions two topics touched on in today's earlier Log24 post
Bowling in Diagon Alley— magic (implied by the title) and
incommensurability. The connection in that post
between the two topics is the diagonal  of a square.

The  wire item shows one detail from a Times  illustration
of the linked article— a blindfolded woman.

Another detail from the same illustration—

IMAGE- Magician's hands on his wand, viewed as a diagonal of a square (or as Hexagram 14 in the box-style I Ching

Hands-on Wand Work

See also remarks on Magic in this journal and on Harry Potter.

I dislike both topics.

Tuesday, June 12, 2012

Meet Max Black (continued)

Filed under: General,Geometry — Tags: , — m759 @ 11:59 pm

Background— August 30, 2006—

The Seventh Symbol:

The image “http://www.log24.com/log/pix06A/060830-Algebra.jpg” cannot be displayed, because it contains errors.

In the 2006 post, the above seventh symbol  110000 was
interpreted as the I Ching hexagram with topmost and
next-to-top lines solid, not broken— Hexagram 20, View .

In a different interpretation, 110000 is the binary for the decimal
number 48— representing the I Ching's Hexagram 48, The Well .

“… Max Black, the Cornell philosopher, and 
others have pointed out how ‘perhaps every science
must start with metaphor and end with algebra, and
perhaps without the metaphor there would never
have been any algebra’ ….”

– Max Black, Models and Metaphors,
Cornell U. Press, 1962, page 242, as quoted
in Dramas, Fields, and Metaphors,
by Victor Witter Turner, Cornell U. Press,
paperback, 1975, page 25

The algebra is certainly clearer than either I Ching
metaphor, but is in some respects less interesting.

For a post that combines both the above I Ching
metaphors, View  and Well  , see Dec. 14, 2007.

In memory of scholar Elinor Ostrom,
who died today—

"Time for you to see the field."
Bagger Vance

Tuesday, June 5, 2012

Chinese Epiphany

Filed under: General,Geometry — m759 @ 4:38 am

References here yesterday to Epiphany 
and to Chinese logic suggest two observations—

First, a political interpretation of the number "64.89" 
from Monday's Shanghai stock market index
yielded the date  6/4 in 1989—

IMAGE- Google search on '64.89 Shanghai'

Second, an interpretation of 64.89 as the number  64 in 1989
(on the Feast of the Epiphany, January 6)—

Note of January 6, 1989 showing 
the 64 hexagrams in the von Franz style

No connection of the number  64 with the date  6/4 is implied.

Thursday, April 5, 2012

In the Details

Filed under: General — m759 @ 6:00 pm

An image from 62 years ago:

Click image for details.

For the religious significance of "62," see Strong Emergence Illustrated.

See also a related search.

Sunday, February 5, 2012

Sunday Morning

Filed under: General — Tags: — m759 @ 10:31 am

CBS Sunday Morning 's piece on
the number pi  today suggested…

Hexagram 20, Contemplation/View,
from the website Rightreading.com

Saturday, February 4, 2012

Ein Satz

Filed under: General — Tags: , — m759 @ 1:00 pm
 

 

4 × 5 =  ̲2̲0̲  .

 

Related material—

The link "Ten is a Hen"
in today's 10 AM post, and
Carl Schoettler on Barbara Wilson's
novel Gaudi Afternoon

"She's told a detective story without violence,
murder, mayhem, massacre, or even explicit sex
although there are a couple of sly double entendres.
She pays an homage to Dashiell Hammett
when Cassandra tells the gay saxophonist
 she's Brigid O'Shaughnessy.
Brigid O'Shaughnessy, of course, is the woman
Sam Spade won't play the sap for
in 'The Maltese Falcon.'"

Judy Davis, shown above in
"One Against the Wind," was the star
of the film version of Wilson's novel.

Sunday, October 23, 2011

Accentuate the Positive–

Filed under: General,Geometry — m759 @ 3:59 pm

A Date with Erin

http://www.log24.com/log/pix11C/111023-ErinBurnett.JPG

Related material suggested by today's
midday New York Lottery— 032 and 7537—

Richard Wilhelm
on I Ching  Hexagram 32:

Hexagram 32, Duration, of the I Ching

Duration

“Duration is… not a state of rest, for mere standstill
is regression. Duration is rather the self-contained
and therefore self-renewing movement of
an organized, firmly integrated whole
[click on link for an example], taking place
in accordance with immutable laws
and beginning anew at every ending.”

and the date 7/5/37—

http://www.log24.com/log/pix11C/111023-RisingSun7537.JPG

Wednesday, October 19, 2011

Puzzlement

Filed under: General,Geometry — m759 @ 4:10 pm

Midday NY lottery on Oct. 19, 2011— 043 and 7531.

The latter is the birth date (7/5/31) of Jerry Slocum,
Hughes Aircraft designer and puzzle enthusiast.

For the former, see Hexagram 43 in Geometry of the I Ching.

Thursday, October 6, 2011

Sequel

Filed under: General — m759 @ 9:29 pm

From post 4017 in this journal (do not click links)—

"Thanks to University Diaries  for an entry on Clancy Martin,
a philosophy professor in the 'show me' state, and his experiences with AA."

Neither link in this quote works anymore.
See instead Martin in the London Review of Books .

Lottery hermeneutics, however, still seems usable.

http://www.log24.com/log/pix11C/111006-NYlottery.jpg

Today's midday NY lottery "163" may be taken as a sequel
to both the page number "162" in today's noon post

http://www.log24.com/log/pix11C/111006-HumboldtsGift-PenguinUSA1996-P163.jpg

Humboldt's Gift , page 163 (Penguin Classics, 1996)

— and a sequel to University Diaries ' meditation today on the Nobel literature prize,
which includes a quote from the winner:

"At last my life returns. My name appears like an angel.
Outside the walls a trumpet signal blows…. It is I! It is I!"

Tomas Tranströmer, "The Name"

As for the evening NY numbers 014 and 5785, see Hexagram 14,
Not Even Wrong , and 5/7/85.

Friday, August 19, 2011

Crux

Filed under: General — Tags: — m759 @ 11:30 am

"Francis Bacon used the phrase instantia crucis,  'crucial instance,' to refer to something in an experiment that proves one of two hypotheses and disproves the other. Bacon's phrase was based on a sense of the Latin word crux,  'cross,' which had come to mean 'a guidepost that gives directions at a place where one road becomes two,' and hence was suitable for Bacon's metaphor."

The American Heritage® Dictionary of the English Language, Fourth Edition

Such a cross: St. Andrew's.  Some context—

http://www.log24.com/log/pix11B/110819-XMarksTheSpot.JPG

X Marks the Spot  scene, "The Last Crusade"

Related symbology for Dan Brown—

Neville's Labrys and Notes on Mathematics and Narrative.

Saturday, July 2, 2011

Mass Appeal

Filed under: General — m759 @ 3:57 am

A portrait reproduced here on October 11, 2007

The image “http://www.log24.com/log/pix07A/071011-vonNeumann.jpg” cannot be displayed, because it contains errors.

http://www.log24.com/images/IChing/hexagram45.gif

http://www.log24.com/images/IChing/Hexagram45-Massing.jpg

The above was suggested by yesterday's New York Lottery and by
items dated February  8, 1958 (date of receipt of an AMS Bulletin  article)
and February 1, 1953 (newspaper article on applied game theory).

(This covers three of the four relevant lottery numbers.
For the fourth, see 9/19 and recent discussions of
The End of Mr. Y  (Sunday Dinner and A Link for Sunrise)).

See also Saint  John Neumann.

Friday, June 3, 2011

Brightness at Noon (continued)

Filed under: General — m759 @ 12:00 pm

 

http://www.log24.com/images/IChing/hexagram55.gif

Hexagram 55
Abundance (Fullness)  

"Be not sad.
 Be like the sun at midday."

Sunday, May 22, 2011

Asterisk*

Filed under: General,Geometry — Tags: , — m759 @ 10:30 am

A year ago today—

2:02 AM EDT

   Art Space

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

http://www.log24.com/log/pix10A/100522-Clouseau.gif

Space: what you damn well have to see.
– James Joyce, Ulysses

10:31 AM EDT

Image-- The Case of the Lyche Gate Asterisk

* See Vonnegut.

Friday, May 20, 2011

Lottery Hermeneutics (continued)

Filed under: General — Tags: — m759 @ 3:09 pm

Recent New York Lottery numbers—

http://www.log24.com/log/pix11A/110520-RecentNYlottery.jpg

The interpretation of "056" in yesterday's
The Aleph, the Lottery, and the Eightfold Way
was not without interest, but the interpretation there
of "236" was somewhat lacking in poetic resonance.

For aspiring students of lottery hermeneutics,
here are some notes that may help. The "236" may
be reinterpreted as a page number in Stevens's
Collected Poems . It then resonates rather nicely
("answers when I ask," "visible and responsive")
with yesterday evening's "434"—

http://www.log24.com/log/pix11A/110520-StevensCP236And434-500w.jpg

For today's midday "022," see Hexagram 22: Grace in the context of the following—

http://www.log24.com/log/pix11A/110520-LaterPoetry-Hines141.jpg

As for yesterday afternoon's 609, see a particular Stevens-related page with that number…

IMAGE- Review of 'The Dome and the Rock'

For "a body of thought or poetry larger than the subject's," see The Dome of  the Rock.

Saturday, April 30, 2011

Sabato Tombstone

Filed under: General — m759 @ 8:28 pm

IMAGE- Sabato on his own tombstone in 'Angel of Darkness'

Related material:
  (Click images for details) —

IMAGE- The number 11 formed by twin switchblades, '12 Angry Men'

Exhibit B

IMAGE- Julie Taymor

Julie Taymor

  IMAGE- Hexagram 11: PEACE
Plato, Pegasus, and
the Evening Star

Monday, April 25, 2011

The Kristen Effect

Filed under: General — m759 @ 10:31 pm

From the author of The Abacus Conundrum

http://www.log24.com/log/pix10B/101206-AbacusConundrum.jpg

Harlan Kane's sequel to The Apollo Meme

THE KRISTEN EFFECT

IMAGE- Kristen Wiig, 'Cock and Bull Story'

"Thus the universal mutual attraction between the sexes is represented."
Hexagram 31

Friday, April 8, 2011

Concepts of Space

Filed under: General,Geometry — Tags: — m759 @ 7:35 pm

Part I — Roberta Smith in today's New York Times

"… the argument that painting may ultimately be about
little more than the communication of some quality of
light and space, however abstract or indirect."

– Review of "Rooms With a View" at the Met

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

http://www.log24.com/log/pix10A/100522-Clouseau.gif

Space: what you damn well have to see.
– James Joyce, Ulysses

Part II — Window from A Crooked House

"Teal lifted the blind a few inches. He saw nothing, and raised it a little more—still nothing. Slowly he raised it until the window was fully exposed. They gazed out at—nothing.

Nothing, nothing at all. What color is nothing? Don't be silly! What shape is it? Shape is an attribute of something . It had neither depth nor form. It had not even blackness. It was nothing ."

Part III — Not So Crooked: The Cabinet of Dr. Montessori

An April 5 Wall Street Journal  article on Montessori schools, and…

http://www.log24.com/log/pix11/110408-MontessoriCabinet.jpg

A cabinet from Dr. Montessori's own
explanation of her method

Part IV — Pilate Goes to Kindergarten and The Seven

Wednesday, March 16, 2011

Time and Chance (continued)

Filed under: General,Geometry — Tags: , — m759 @ 8:25 pm

Accidental Time and Space

New York Lottery today— midday 987, evening 522.

Time

The midday 987 may be interpreted as "…nine, eight, seven, …."—

"The countdown as we know it, 10-9-8-u.s.w.,
was invented by Fritz Lang in 1929 for
the Ufa film Die Frau im Mond . He put it into
the launch scene to heighten the suspense.
'It is another of my damned "touches,"' Fritz Lang said."

Gravity's Rainbow

Space

The evening 522 suggests the date 5/22. From that date last year

Art Space (2:02 AM EDT)

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

http://www.log24.com/log/pix10A/100522-Clouseau.gif

Space: what you damn well have to see.
– James Joyce, Ulysses

Wednesday, February 9, 2011

An Abstract Window

Filed under: General,Geometry — Tags: — m759 @ 12:00 pm

The sliding window in blue below

http://www.log24.com/log/pix11/110209-SymFrameBWPageSm.jpg

Click for the web page shown.

is an example of a more general concept.

Such a sliding window,* if one-dimensional of length n , can be applied to a sequence of 0's and 1's to yield a sequence of n-dimensional vectors. For example— an "m-sequence" (where the "m" stands for "maximum length") of length 63 can be scanned by a length-6 sliding window to yield all possible 6-dimensional binary vectors except (0,0,0,0,0,0).

For details, see A Galois Field

http://www.log24.com/log/pix11/110209-GaloisStamp.jpg

The image is from Bert Jagers at his page on the Galois field GF(64) that he links to as "A Field of Honor."

For a discussion of the m-sequence shown in circular form above, see Jagers's  "Pseudo-Random Sequences from GF(64)." Here is a noncircular version of the length-63 m-sequence described by Jagers (with length scale below)—

100000100001100010100111101000111001001011011101100110101011111
123456789012345678901234567890123456789012345678901234567890123

This m-sequence may be viewed as a condensed version of 63 of the 64 I Ching  hexagrams. (See related material in this journal.)

For a more literary approach to the window concept, see The Seventh Symbol (scroll down after clicking).

* Moving windows also appear (in a different way) In image processing, as convolution kernels .

Wednesday, January 26, 2011

Requiem for a Screenwriter*

Filed under: General — m759 @ 1:00 pm
 

Click for obit.

Background:

Hexagram 61
and

Still Point.

* Notably, of the film "Downfall" (Der Untergang ).
   "Has time rewritten every line?" —Streisand

Saturday, October 16, 2010

The Mandelbrot Numbers

Filed under: General — m759 @ 11:36 am
 

Benoît Mandelbrot died on Oct. 14.
 

NY Lottery Thursday, Oct. 14, 2010-- Midday 109, Evening 060

— New York Lottery on Thursday, Oct. 14, 2010

Related material on 109: See 1/09, 2009.
Related material on 060: See Hexagram 60 of the I Ching  and…

IMAGE-- Matt Damon stands where a door opens in 'Hereafter'

Margaret Atwood on Lewis Hyde's Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

Sunday, September 26, 2010

After the Fall

Filed under: General — m759 @ 10:09 am
 

The Harvard Crimson —

Magic of Numbers:
Summing Up the Fall

Published by Timothy J. Walsh on September 24, 2010 at 8:41AM

Each Thursday, The Crimson will compile a series of unique statistics
about Harvard's sports scene. Welcome to the Magic of Numbers—
without the problem sets. We'll do the math for you.

READY FOR SOME FOOTBALL

Saturday night's game… Harvard vs. Brown at Providence—

Harvard 14, Brown 29.

Related philosophy about divine providence—

http://www.log24.com/log/pix10B/100926-Hexagrams.png

See also, from 2002, a note on "light inclosed in the dark" versus the late Harvard philosopher Barbara Johnson.

For some context on Harvard and "the Magic of Numbers" see Summer Reading from 2007.

Saturday, August 14, 2010

Iconic Notation

Filed under: General — m759 @ 12:12 am

Continued from Friday the 13th

(Click to enlarge.)

http://www.log24.com/log/pix10B/100814-DBsm.jpg

Related material—

The image “http://www.log24.com/log/pix07A/070814-timejoin15.jpg” cannot be displayed, because it contains errors.
Cover art by Barclay Shaw reprinted from an earlier (1984) edition

IMAGE- Variations on Hexagram 14

A question from Ivan Illich
(founder of CIDOC, the Center for Intercultural Documentation,
in Cuernavaca, Mexico)—

"Who can be served by bridges to nowhere?"

For more about nowhere, see Utopia. See also http://outis.blogspot.com.

Tuesday, July 20, 2010

Midnight in the Garden continued

Filed under: General — m759 @ 12:00 am

Lottery hermeneutics for yesterday's numbers—

PA— Midday 711, Evening 039.

NY— Midday 440, Evening 704.

Simple interpretive methods— numbers as dates and as hexagram numbers— yield 7/11, hexagram 39, and 7/04.

The reader may supply his own interpretations of 7/11 and 7/04; for hexagram 39, see Wilhelm's commentary

"The hexagram pictures a dangerous abyss lying before us
  and a steep, inaccessible mountain rising behind us."

— and the cover of Cold Mountain

The image 
“http://www.log24.com/log/pix05A/050703-Cold.jpg” cannot be displayed, 
because it contains errors.

Adapted from cover of
German edition of Cold Mountain

This suggests revisiting The Edge of Eternity (July 5, 2005).

The hermeneutics of the NY midday 440 is more difficult. A Google search suggests that a Log24 post for Epiphany 2004, "720 in the Book," might yield a clue to the 440 riddle.

Image-- 'What is a closed-form number?'

By all means, let us 440.

Sunday, July 18, 2010

Today’s Sermon

Filed under: General — m759 @ 11:00 am

New York Lottery on Saturday, July 17, 2010—

Midday 049, Evening 613.

Related material:

Hexagram 49 and 6/13.

A quotation from this journal on 6/13

"Christianity offers the critic a privileged ontological window…."

Aaron Urbanczyk's 2005 review of Christ and Apollo 
   
by William Lynch, S.J., a book first published in 1960

Picture from today's New York Times  (page ST1 in New York edition)—

http://www.log24.com/log/pix10B/100718-LamWindow.jpg

Wednesday, June 16, 2010

Brightness at Noon

Filed under: General,Geometry — Tags: , , , — m759 @ 12:00 pm

David Levine's portrait of Arthur Koestler (see Dec. 30, 2009) —

Image-- Arthur Koestler by David Levine, NY Review of Books, Dec. 17, 1964, review of 'The Act of Creation'

Image-- Escher's 'Verbum'

Escher’s Verbum

Image-- Solomon's Cube

Solomon’s Cube

Image-- The 64 I Ching hexagrams in the 4 layers of the Cullinane cube

Geometry of the I Ching

See also this morning's post as well as
Monday's post quoting George David Birkhoff

"If I were a Leibnizian mystic… I would say that…
God thinks multi-dimensionally — that is,
uses multi-dimensional symbols beyond our grasp."

Geometry of Language

Filed under: General,Geometry — Tags: , — m759 @ 10:31 am

(Continued from April 23, 2009, and February 13, 2010.)

Paul Valéry as quoted in yesterday’s post:

“The S[elf] is invariant, origin, locus or field, it’s a functional property of consciousness” (Cahiers, 15:170 [2: 315])

The geometric example discussed here yesterday as a Self symbol may seem too small to be really impressive. Here is a larger example from the Chinese, rather than European, tradition. It may be regarded as a way of representing the Galois field GF(64). (“Field” is a rather ambiguous term; here it does not, of course, mean what it did in the Valéry quotation.)

From Geometry of the I Ching

Image-- The 64 hexagrams of the I Ching

The above 64 hexagrams may also be regarded as
the finite affine space AG(6,2)— a larger version
of the finite affine space AG(4,2) in yesterday’s post.
That smaller space has a group of 322,560 symmetries.
The larger hexagram  space has a group of
1,290,157,424,640 affine symmetries.

From a paper on GL(6,2), the symmetry group
of the corresponding projective  space PG(5,2),*
which has 1/64 as many symmetries—

(Click to enlarge.)

Image-- Classes of the Group GL(6,)

For some narrative in the European  tradition
related to this geometry, see Solomon’s Cube.

* Update of July 29, 2011: The “PG(5,2)” above is a correction from an earlier error.

Friday, June 4, 2010

ART WARS continued

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

Today's New York Times

Art Review

Painting Thin Air, Sometimes in Bright Blue

(“Yves Klein: With the Void, Full Powers”
  runs through Sept. 12 at the Hirshhorn.)

Related material—

Search this journal for klein + paris.

See also Art Space (May 22, 2010)—

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

http://www.log24.com/log/pix10A/100522-Clouseau.gif

Saturday, May 22, 2010

Art Space

Filed under: General,Geometry — Tags: , — m759 @ 2:02 am

From an interview with artist Josefine Lyche (see previous post) dated March 11, 2009—

Can you name a writer or book, fiction or theory that has inspired your works?
– Right now I am reading David Foster Wallace, which is great and inspiring. Others would be Aleister Crowley, Terence McKenna, James Joyce, J.L Borges, J.D Ballard, Stanislaw Lem, C. S. Lewis and Plato to mention some. Books, both fiction and theory are a great part of my life and work.

This journal on the date of the interview had a post about a NY Times  story, Paris | A Show About Nothing."

Related images—

 

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

http://www.log24.com/log/pix10A/100522-Clouseau.gif

Space: what you damn well have to see.
– James Joyce, Ulysses

Thursday, May 20, 2010

View

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

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

Related material:

A Handful of Dust
by J. G. Ballard

Friday, April 30, 2010

Bridge to Nowhere

Filed under: General — m759 @ 12:00 pm

(continued from April 26, 28, and 29):

http://www.log24.com/images/IChing/hexagram29.gif

Hexagram 29:
Water

http://www.log24.com/log/pix10A/100430-Commentary.jpg

http://www.log24.com/images/IChing/hexagram30.gif

Hexagram 30:
Fire

"Hates California,
it's cold and it's damp.
"

Image--'The Fire,' by Katherine Neville

Excerpt from The Fire,
by Katherine Neville —

"'Alaska's Aleutian Trench,' Key told us…. 'It's called the Ring of Fire because it boasts the largest collection of active volcanoes in the world.'….

'But you said that my father's not in Alaska…. So what does this Ring of Fire have to do with the place where we're actually going?'

'It's the Yellow Brick Road,' she told me."

Sarah Palin and friends-- Doonesbury, April 30, 2010

Thursday, January 21, 2010

Darkness at Noon

Filed under: General — m759 @ 12:00 pm

A NY Times review dated Jan. 20 has the headline

Trying to Paint the Deity by Numbers
Against a Backdrop of Jewish Culture

By JANET MASLIN

"…this novel’s bracing intellectual energy never flags. Though it is finally more a work of showmanship than scholarship, it affirms Ms. Goldstein’s position as a satirist…."

The title of the book under review is
36 Arguments for the
Existence of God: A Work of Fiction
.

Related "by the numbers" material–

From the I Ching, commentaries on the lines of Hexagram 36–

"Here the Lord of Light is in a subordinate place and is wounded by the Lord of Darkness…."

"The dark power at first held so high a place that it could wound all who were on the side of good and of the light. But in the end it perishes of its own darkness, for evil must itself fall at the very moment when it has wholly overcome the good, and thus consumed the energy to which it owed its duration."

http://www.log24.com/log/pix10/100121-IChing36.jpg


The Times review
of 36 Arguments notes that the book's chapters of fiction number 36, as do the 36 philosophical arguments in the book's title and appendix.

The reviewer– "So much for structure. It is not Ms. Goldstein’s strong suit…."

Some structure related to the above occurrence of 36 in the I Ching

http://www.log24.com/log/pix10/100121-Trigrams.jpg

Another example of eightfold symmetry:

http://www.log24.com/log/pix10/100121-LHCsm.jpg

The Large Hadron Collider

See also Angels & Demons in
Hollywood and in this journal.

Saturday, September 5, 2009

Saturday September 5, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 10:31 pm
For the
Burning Man

'The Stars My Destination,' current edition (with cover slightly changed)

(Cover slightly changed.)

 
Background —

 
SAT
 
Part I:

Sophists (August 20th)

Part II:

VERBUM
SAT
SAPIENTI

Escher's 'Verbum'

Escher's Verbum


Solomon's Cube



Part III:

From August 25th

Equilateral triangle on a cube, each side's length equal to the square root of two

"Boo, boo, boo,
  square root of two.
"

Saturday, August 29, 2009

Saturday August 29, 2009

Filed under: General — Tags: , — m759 @ 8:00 pm
Continued from
Father's Day
  last year–

Shoe cartoon, detail, Sunday, June 15, 2008

I Ching hexagram 48, The Well

"For further details,
 click on the well."

From the above link:

James Hillman

"The kind of movement Olson urges is
 an inward deepening of the image,
an in-sighting of the superimposed
 levels of significance within it.
This is the very mode that Jung
suggested for grasping dreams–
 not as a sequence in time,
but as revolving around
 a nodal complex."

And from Feb. 29, 2008:

http://www.log24.com/log/pix08/080229-Doonesbury3.jpg

and the following day:

Heraclitus: '...so deep is its logos'

— Heraclitus

Tuesday, July 28, 2009

Tuesday July 28, 2009

Filed under: General,Geometry — m759 @ 1:06 pm
Man and
His Symbols 101

Continued from July 21

A headline from yesterday:

US-China ties will shape
21st century: Obama

A headline from 2003,
with an epiphany from
twenty years ago:

The Tables of Time

JFK and chess at Chinatown picnic table

Peace Rune
Hexagram 11,
Jan. 6, 1989

Picnic Symbol 

Picnic site symbol,
British Sea Scouts

In related news:

Obama to hold picnic-table peace talk

Monday, July 27, 2009

Monday July 27, 2009

Filed under: General,Geometry — Tags: , — m759 @ 2:29 pm
Field Dance

The New York Times
on June 17, 2007:

 Design Meets Dance,
and Rules Are Broken

Yesterday's evening entry was
on the fictional sins of a fictional
mathematician and also (via a link
to St. Augustine's Day, 2006), on
the geometry of the I Ching* —

The eternal
combined with
the temporal:

Circular arrangement of I Ching hexagrams based on Singer 63-cycle in the Galois field GF(64)

The fictional mathematician's
name, noted here (with the Augustine-
I Ching link as a gloss) in yesterday's
evening entry, was Summerfield.

From the above Times article–
"Summerspace," a work by
 choreographer Merce Cunningham
and artist Robert Rauschenberg
that offers a competing
 vision of summer:

Summerspace — Set by Rauschenberg, choreography by Cunningham

Cunningham died last night.

John Cage, Merce Cunningham, Robert Rauschenberg in the 1960's

From left, composer John Cage,
choreographer Merce Cunningham,
and artist Robert Rauschenberg
in the 1960's

"When shall we three meet again?"

* Update of ca. 5:30 PM 7/27– today's online New York Times (with added links)– "The I Ching is the 'Book of Changes,' and Mr. Cunningham's choreography became an expression of the nature of change itself. He presented successive images without narrative sequence or psychological causation, and the audience was allowed to watch dance as one might watch successive events in a landscape or on a street corner."

Thursday, June 4, 2009

Thursday June 4, 2009

Filed under: General — Tags: , — m759 @ 1:24 pm

The Grasshopper
Lies Heavy

David Carradine dies at 72

“‘Oracle, why did you write
The Grasshopper Lies Heavy?
What are we supposed to learn?'”

— Philip K. Dick

She began throwing the coins.

I Ching Hexagram 61: Inner Truth

Click on image
for further details.

Thursday, April 23, 2009

Thursday April 23, 2009

Filed under: General,Geometry — Tags: , — m759 @ 10:00 am

 

The Geometry
of Language

(continued from April 16)

Background:

Professor Arielle Saiber with chess set

Click on the image for an
interview with the author of
Giordano Bruno and
the Geometry of Language
.

Related material:

Joyce on language —

The sigla of 'Finnegans Wake'

Bruno, Joyce, and coincidentia oppositorum

Cullinane on geometry —

Geometry of the I Ching (for comparison to Joyce's 'sigla')

Click on images for details.
 

Saturday, March 7, 2009

Saturday March 7, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 12:00 pm

One or Two Ideas
 
Today's birthday: Piet Mondrian
 
From James Joyce's A Portrait of the Artist as a Young Man:

he hearth and began to stroke his chin.

–When may we expect to have something from you on the esthetic question? he asked.

–From me! said Stephen in astonishment. I stumble on an idea once a fortnight if I am lucky.

–These questions are very profound, Mr Dedalus, said the dean. It is like looking down from the cliffs of Moher into the depths. Many go down into the depths and never come up. Only the trained diver can go down into those depths and explore them and come to the surface again.

–If you mean speculation, sir, said Stephen, I also am sure that there is no such thing as free thinking inasmuch as all thinking must be bound by its own laws.

–Ha!

–For my purpose I can work on at present by the light of one or two ideas of Aristotle and Aquinas.

–I see. I quite see your point.

Besides being Mondrian's birthday, today is also the dies natalis (in the birth-into-heaven sense) of St. Thomas Aquinas and, for those who believe worthy pre-Christians also enter heaven, possibly of Aristotle.

Pope Benedict XVI explained the dies natalis concept on Dec. 26, 2006:

"For believers the day of death, and even more the day of martyrdom, is not the end of all; rather, it is the 'transit' towards immortal life. It is the day of definitive birth, in Latin, dies natalis."

The Pope's remarks on that date
were in St. Peter's Square.
 
From this journal on that date,
a different square —
 
The Seventh Symbol:
 

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

The square may be regarded as
symbolizing art itself.
(See Nov.30 – Dec.1, 2008.)

In honor of
Aristotle and Aquinas,
here is a new web site,
illuminati-diamond.com,
with versions of the diamond shape
made famous by Mondrian

Cover of  Mondrian: The Diamond Compositions

— a shape symbolizing
possibility within modal logic
 as well as the potentiality of
 Aristotle's prima materia.

Wednesday, February 18, 2009

Wednesday February 18, 2009

Filed under: General — Tags: , , , , — m759 @ 11:30 am

Raiders of
the Lost Well

“The challenge is to
keep high standards of
scholarship while maintaining
showmanship as well.”

— Olga Raggio, a graduate of the Vatican library school and the University of Rome who, at one point in her almost 60 years with the Metropolitan Museum of Art, organized “The Vatican Collections,” a blockbuster show. Dr. Raggio died on January 24.

The next day, “The Last Templar,” starring Mira Sorvino, debuted on NBC.

Mira Sorvino in 'The Last Templar'
“The story, involving the Knights Templar, the Vatican, sunken treasure, the fate of Christianity and a decoding device that looks as if it came out of a really big box of medieval Cracker Jack, is the latest attempt to combine Indiana Jones derring-do with ‘Da Vinci Code’ mysticism.”

The New York Times

Sorvino in “The Last Templar”
at the Church of the Lost Well:

Mira Sorvino at the Church of the Lost Well in 'The Last Templar'

One highlight of Secretary of State Hillary Clinton’s first overseas trip will be a stop in China. Her main mission in Beijing will be to ensure that US-China relations under the new Obama administration get off to a positive start.”

— Stephanie Ho, Voice of America Beijing bureau chief, today

Symbol of The Positive,
from this journal
on Valentine’s Day:

'Enlarge' symbol from USA Today

“Stephanie started at the Voice of America as an intern in 1991. She left briefly to attend film school in London in 2000. Although she didn’t finish, she has always wanted to be a film school dropout, so now she’s living one of her dreams.

Stephanie was born in Ohio and grew up in California. She has a bachelor’s degree in Asian studies with an emphasis on Chinese history and economics, from the University of California at Berkeley.”

“She is fluent in
Mandrin Chinese.”
VOA

As is Mira Sorvino.

Chinese character for 'well' and I Ching Hexagram 48, 'The Well'

Those who, like Clinton, Raggio, and
Sorvino’s fictional archaeologist in
“The Last Templar,” prefer Judeo-
Christian myths to Asian myths,
may convert the above Chinese
“well” symbol to a cross
(or a thick “+” sign)
by filling in five of
the nine spaces outlined
by the well symbol.

In so doing, they of course
run the risk, so dramatically
portrayed by Angelina Jolie
as Lara Croft, of opening
Pandora’s Box.

(See Rosalind Krauss, Professor
of Art and Theory at Columbia,
for scholarly details.)

Rosalind Krauss

Krauss

Greek Cross, adapted from painting by Ad Reinhardt

The Krauss Cross

Thursday, December 18, 2008

Thursday December 18, 2008

Filed under: General — Tags: — m759 @ 1:00 pm
Polar Opposites

Susan Sontag in
this week's New Yorker:
"The mind is a whore."

Embedded in the Sontag
article is the following:

The New Yorker on Santa's use of the word 'ho'

I Ching hexagrams as a Singer 63-cycle, plus zero

Act One

South Pole:

David Mamet's book 'A Whore's Profession'

Hexagram 21 in the King Wen sequence

Shi Ho

Act Two

North Pole:

Susan Sontag

Hexagram 2 in the King Wen sequence

Kun

"If baby I'm the bottom,
you're the top."
Cole Porter   

Happy birthday,
Steven Spielberg.

Monday, December 1, 2008

Monday December 1, 2008

Filed under: General — Tags: , — m759 @ 8:48 pm
A Version of
Heaven's Gate

in memory of
G. H. Hardy,
who died on
this date in 1947

C. P. Snow on Hardy:

"He was living in some of the best intellectual company in the world– G.E. Moore, Whitehead, Bertrand Russell, Trevelyan, the high Trinity society which was shortly to find its artistic complement in Bloomsbury."

For a rather different artistic complement, see the previous entry.

See also
The Seventh Symbol:

Hexagram 20, a square frame, in the Cullinane box-style I Ching

Monday, October 27, 2008

Monday October 27, 2008

Filed under: General — m759 @ 5:07 am
Halloween
Meditation

for…

Halloween Card from SuSu

5:07:33 AM ET

Denali

Hexagram 33

33 Retreat

THE IMAGE

Mountain under heaven:
the image of RETREAT.
Thus the superior man
keeps the inferior man
at a distance,
not angrily
but with reserve.

“The mountain rises up under heaven, but owing to its nature it finally comes to a stop. Heaven on the other hand retreats upward before it into the distance and remains out of reach. This symbolizes the behavior of the superior man toward a climbing inferior; he retreats into his own thoughts as the inferior man comes forward. He does not hate him, for hatred is a form of subjective involvement by which we are bound to the hated object. The superior man shows strength (heaven) in that he brings the inferior man to a standstill (mountain) by his dignified reserve.” —Richard Wilhelm

Sunday, September 7, 2008

Sunday September 7, 2008

Filed under: General — Tags: — m759 @ 7:09 am
Bringing Change
to Washington

'Only I can bring change to Washington'-- LA Times, Sept. 7, 2008

First in War,
   First in Peace…

Quotations for
Chairman George

on February 22, 1999
(Washington’s Birthday)

I Ching Hexagram 49: The Image of Revolution

Fire in
the lake:
the image of Revolution

Thus the
superior man
Sets the calendar
in order
And makes the seasons clear.


Change for Washington:

'The Laws of Change: I Ching and the Philosophy of Life,' by Jack M. Balkin

For the details, see
yale.edu/lawweb:

“As important to Chinese civilization as the Bible is to Western culture, the I Ching or Book of Changes is one of the oldest treasures of world literature. Yet despite many commentaries written over the years, it is still not well understood in the English-speaking world. In this masterful [sic] new interpretation, Jack Balkin returns the I Ching to its rightful place….

Jack M. Balkin\

Jack M. Balkin

Jack M. Balkin is Knight Professor of Constitutional Law and the First Amendment at Yale Law School, and the founder and director of Yale’s Information Society Project. His books and articles range over many different fields….”

Wallace Stevens on 'the work of a comedian'

Sunday, August 10, 2008

Sunday August 10, 2008

Filed under: General,Geometry — m759 @ 10:31 am

One Year Ago
in this journal —

Commentary by Richard Wilhelm
on I Ching Hexagram 32:

Hexagram 32, Duration, of the I Ching

Duration

“Duration is… not a state of rest, for mere standstill is regression. Duration is rather the self-contained and therefore self-renewing movement of an organized, firmly integrated whole [click on link for an example], taking place in accordance with immutable laws and beginning anew at every ending.”


Richard Wilhelm's grave. Note the eight I Ching trigrams.

Richard Wilhelm’s grave:
Note the eight I Ching
trigrams surrounding
the globe.

Globe at opening of 2008 Beijing Olympics

Globe at the
Beijing 2008 Olympics
Opening Ceremony

The eight trigrams
were perhaps implied in
the opening’s date, 8/8/8.

Friday, August 1, 2008

Friday August 1, 2008

Filed under: General — m759 @ 2:56 am
Front page, online New York Times,  Friday, August 1, 2008, 2:16 AM

Click on image for context.

Time of entry: 2:56:04 AM.

Wednesday, July 9, 2008

Wednesday July 9, 2008

Filed under: General,Geometry — m759 @ 8:28 am
God, Time, Epiphany

8:28:32 AM

Anthony Hopkins, from
All Hallows' Eve
last year
:

"For me time is God,
God is time. It's an equation,
like an Einstein equation."

James Joyce, from
June 26 (the day after
AntiChristmas) this year
:

"… he glanced up at the clock
of the Ballast Office and smiled:
— It has not epiphanised yet,
he said."

Ezra Pound (from a page
linked to yesterday morning):

"It seems quite natural to me
that an artist should have
just as much pleasure in an
arrangement of planes
or in a pattern of figures,
  as in painting portraits…."

From Epiphany 2008:

An arrangement of planes:

http://www.log24.com/log/pix08/080709-Epiphany.gif

From May 10, 2008:

A pattern of figures:

 

Seven partitions of the 2x2x2 cube in 'Paradise of Childhood'

See also Richard Wilhelm on
Hexagram 32 of the I Ching:

 

"Duration is a state whose movement is not worn down by hindrances. It is not a state of rest, for mere standstill is regression. Duration is rather the self-contained and therefore self-renewing movement of an organized, firmly integrated whole, taking place in accordance with immutable laws and beginning anew at every ending. The end is reached by an inward movement, by inhalation, systole, contraction, and this movement turns into a new beginning, in which the movement is directed outward, in exhalation, diastole, expansion."

 

'The Middle-English Harrowing of Hell,' by Hulme, 1907, page 64, line 672: 'with this he gaf the gaste'

The Middle-English
    Harrowing of Hell…

    by Hulme, 1907, page 64

Sunday, June 15, 2008

Sunday June 15, 2008

Filed under: General — Tags: — m759 @ 7:00 am

A Cartoon Graveyard

Shoe cartoon,  Sunday, June 15, 2008

Click to enlarge.

Shoe cartoon, detail, Sunday, June 15, 2008

From Fathers' Day Meditation:

I Ching hexagram 48, The Well

For further details,
click on the well.

Sunday, June 8, 2008

Sunday June 8, 2008

Filed under: General — m759 @ 2:02 am
 
CHANGE
 TO BELIEVE IN
 


Part I:

NY Lottery June 7, 2008: Mid-day 925, Evening 016

Part II:

I Ching Hexagram 16

16

Thus the ancient kings made music
In order to honor merit,
And offered it with splendor
To the Supreme Deity,
Inviting their ancestors to be present.

When, at the beginning of summer, thunder– electrical energy– comes rushing forth from the earth again, and the first thunderstorm refreshes nature, a prolonged state of tension is resolved. Joy and relief make themselves felt. So too, music has power to ease tension within the heart and to loosen the grip of obscure emotions. The enthusiasm of the heart expresses itself involuntarily in a burst of song, in dance and rhythmic movement of the body. From immemorial times the inspiring effect of the invisible sound that moves all hearts, and draws them together, has mystified mankind. Rulers have made use of this natural taste for music; they elevated and regulated it. Music was looked upon as something serious and holy, designed to purify the feelings of men. It fell to music to glorify the virtues of heroes and thus to construct a bridge to the world of the unseen. In the temple men drew near to God with music and pantomimes (out of this later the theater developed). Religious feeling for the Creator of the world was united with the most sacred of human feelings, that of reverence for the ancestors. The ancestors were invited to these divine services as guests of the Ruler of Heaven and as representatives of humanity in the higher regions. This uniting of the human past with the Divinity in solemn moments of religious inspiration established the bond between God and man. The ruler who revered the Divinity in revering his ancestors became thereby the Son of Heaven, in whom the heavenly and the earthly world met in mystical contact. These ideas are the final summation of Chinese culture. Confucius has said of the great sacrifice at which these rites were performed: "He who could wholly comprehend this sacrifice could rule the world as though it were spinning on his hand."

—  Richard Wilhelm, commentary
    on Hexagram 16 of the I Ching

 

Part III:

The Dance

Song 'The Dance' performed by Tony Arata, who wrote it

See also 9/25.
 

Sunday, May 25, 2008

Sunday May 25, 2008

Filed under: General — Tags: , — m759 @ 8:28 am
"Caught up 
    in circles…"

— Song lyric,  
Cyndi Lauper

http://www.log24.com/log/pix08/080525-Alethiometer.jpg

Alethiometer from
"The Golden Compass"

 

The 64 hexagrams of the I Ching in a circular arrangement suggested by a Singer 63-cycle

The I Ching
as Alethiometer

Update:

See also this morning's
later entry, illustrating
the next line of Cyndi
Lauper's classic lyric
"Time After Time" —

"… Confusion is    
  nothing new."

Thursday, May 22, 2008

Thursday May 22, 2008

Filed under: General,Geometry — Tags: , — m759 @ 9:00 am
The Undertaking:
An Exercise in
Conceptual Art

I Ching hexagram 54: The Marrying Maiden

Hexagram 54:
THE JUDGMENT

Undertakings bring misfortune.
Nothing that would further.

The image “http://www.log24.com/log/pix08/080522-Irelandslide1.jpg” cannot be displayed, because it contains errors.

Brian O’Doherty, an Irish-born artist,
before the [Tuesday, May 20] wake
of his alter ego* ‘Patrick Ireland’
on the grounds of the
Irish Museum of Modern Art.”
New York Times, May 22, 2008    

THE IMAGE

Thus the superior man
understands the transitory
in the light of
the eternity of the end.

Another version of
the image:

Images of time and eternity in memory of Michelangelo
See 2/22/08
and  4/19/08.


Related material:

Michael Kimmelman in today’s New York Times

“An essay from the ’70s by Mr. O’Doherty, ‘Inside the White Cube,’ became famous in art circles for describing how modern art interacted with the gallery spaces in which it was shown.”

Brian O’Doherty, “Inside the White Cube,” 1976 Artforum essays on the gallery space and 20th-century art:

“The history of modernism is intimately framed by that space. Or rather the history of modern art can be correlated with changes in that space and in the way we see it. 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.”

An archetypal image

THE SPACE:

The Eightfold Cube: The Beauty of Klein's Simple Group

A non-archetypal image

THE ART:

Jack in the Box, by Natasha Wescoat

Natasha Wescoat, 2004
See also Epiphany 2008:

How the eightfold cube works

“Nothing that would further.”
— Hexagram 54

Lear’s fool:

 …. Now thou art an 0
without a figure. I am better
than thou art, now. I am a fool;
thou art nothing….

“…. in the last mystery of all the single figure of what is called the World goes joyously dancing in a state beyond moon and sun, and the number of the Trumps is done.  Save only for that which has no number and is called the Fool, because mankind finds it folly till it is known.  It is sovereign or it is nothing, and if it is nothing then man was born dead.”

The Greater Trumps,
by Charles Williams, Ch. 14

* For a different, Jungian, alter ego, see Irish Fourplay (Jan. 31, 2003) and “Outside the Box,” a New York Times review of O’Doherty’s art (featuring a St. Bridget’s Cross) by Bridget L. Goodbody dated April 25, 2007. See also Log24 on that date.

Tuesday, May 6, 2008

Tuesday May 6, 2008

Filed under: General — Tags: — m759 @ 11:07 am
In the Dreamtime
the Point Was Ten

From Play It As It Lays,
the paperback edition of 1990
(Farrar, Straus and Giroux) —

Page 170:                                             “… In her half sleep
the point was ten, the jackpot was on eighteen, the
only man that could ever reach her was the son of a
preacher man
, someone was down sixty, someone was
up, Daddy wants a popper and she rode a painted
pony let the spinning wheel spin
.

By the end of a week she was thinking constantly
about where her body stopped and the air began,
about the exact point in space and time that was the
difference between Maria and other. She had the sense
that if she could get that in her mind and hold it for

170


even one micro-second she would have what she had
come to get.”

 
For further details
see yesterday’s entries.”In her half sleep
the point was ten….”
Play It As It Lays

The Random House

Random House logo (color-reversed image)

signed first edition
of Norman Mailer’s
The Time of Our Time
(4 pounds, 1286 pages)
was published
ten years ago yesterday —

May 5, 1998:
Fireworks starburst
on the cover of
The Time of Our Time


Mailer's 'The Time of Our Time' May 5, 1998, cover with fireworks starburst

Also from May 5, 1998:
  File Photo in Mailer’s obituary —

(Photo by Bebeto Matthews
with Mailer obituary in

Toronto Globe and Mail)

with excerpt from the obituary,
by Richard Pyle

(Associated Press
Saturday, Nov. 10, 2007
at 8:20 AM EDT)

Norman Mailer, May 5, 1998 (with notes)

Related material:

Yesterday’s entries and
the time of this entry:
11:07:51 AM ET

CHANGE WE MAY BELIEVE IN sign, adapted from a current political campaign

I Ching hexagram 51: The Arousing (Shock, Thunder)

51

THE JUDGMENT

SHOCK brings success.   
Shock comes - oh, oh!    
Laughing words - ha, ha!

in light of…

 
A:  Mailer’s fireworks starburst
   on his book cover from
      ten years ago yesterday

B:  A real starburst in a story
from ten years ago today.

 

Monday, April 7, 2008

Monday April 7, 2008

Filed under: General,Geometry — m759 @ 11:07 pm
A year ago…

  (Holy Saturday, 2007) —

From Friedrich Froebel,
who invented kindergarten:

Froebel's Third Gift

For further details, see
Gift of the Third Kind
and
  Kindergarten Relativity.

Related material:

“… There was a problem laid out on the board, a six-mover. I couldn’t solve it, like a lot of my problems. I reached down and moved a knight…. I looked down at the chessboard. The move with the knight was wrong. I put it back where I had moved it from. Knights had no meaning in this game. It wasn’t a game for knights.”


— Raymond Chandler, The Big Sleep

Perhaps, instead,
a game for jumpers?

The image “http://www.log24.com/images/IChing/hexagram35.gif” cannot be displayed, because it contains errors.

See
Tom Stoppard’s Progress.

Sunday, April 6, 2008

Sunday April 6, 2008

Filed under: General — Tags: — m759 @ 2:12 am
For Sunrise

Charlton Heston as Ben-Hur in the New York Times online obituaries, morning of April 6, 2008

Click image to enlarge.

The above tableau, from this morning's
New York Times obituary page,
suggests the following meditations:

1. "Mickey Mouse will see you dead."
   — Robert Stone, A Flag for Sunrise
 
2. "Free!"
 
3. "I graduated in Alabama,
     Alaska, Arizona…."

These three meditations are
consistent with the fable of the
mice and the lion in The Lion,
The Witch, and the Wardrobe

and with the speech of
Aslan at the conclusion of
The Narnia Chronicles:

"The term is over: the holidays
have begun. The dream is
ended: this is the morning."

The rather depressing
"Death Notices" box
that has attracted
Charlton Heston's gaze
in the online obituaries
pictured above might
be replaced as follows:

A Hexagram for Charlton Heston-- Number 35: The sun rises above the earth

The Heston classic pictured
above is, let us recall,
based on a book titled
Ben-Hur: A Tale of
the Christ
.

"I know this man!"
— Charlton Heston

Time of this entry:
2:12:35.

Friday, February 29, 2008

Friday February 29, 2008

Filed under: General — m759 @ 11:32 am

I Have a
Dreamtime
 
http://www.log24.com/log/pix08/080229-Doonesbury3.jpg

Noting today that the time was 11:32 (AM ET),  a portentous number in Finnegans Wake, I decided to practice a bit of chronomancy (use of time for augury).  My weblog's server infomed me when I pressed "enter" that it thought the exact time was 11:32:39.  Consulting (as in Symmetry and Change in the Dreamtime) the I Ching for the meaning of (hexagram) 39, I found the following:

The hexagram pictures a dangerous abyss lying before us and a steep, inaccessible mountain rising behind us…. One must join forces with friends of like mind and put himself under the leadership of a man equal to the situation: then one will succeed in removing the obstacles.

For the abyss and the mountain, see the five log24 entries ending on July 5, 2005, with "The Edge of Eternity." As for "friends of like mind," see the previous entry's references to July 2005.  "The leadership of a man equal to the situation" is more difficult to interpret.  Perhaps it refers, as a politician recently noted, to "a king who took us to the mountain-top and pointed the way to the promised land." Or perhaps to a different king.

http://www.log24.com/log/pix08/080229-Obama.gif

Click on image for details.
Note the time: 11:32 (of 13:09).
The moment is that of the syllable
"mount" in the quotation above.

Saturday, February 23, 2008

Saturday February 23, 2008

Filed under: General,Geometry — Tags: , , , — m759 @ 12:00 pm
Jumpers

"An acute study of the links
between word and fact"
Nina daVinci Nichols

 
Thanks to a Virginia reader for a reminder:
 
Virginia /391062427/item.html? 2/22/2008 7:37 PM
 
The link is to a Log24 entry
that begins as follows…

An Exercise

of Power

Johnny Cash:
"And behold,
a white horse."

Springer logo - A chess knight
Chess Knight
(in German, Springer)

This, along with the "jumper" theme in the previous two entries, suggests a search on springer jumper.That search yields a German sports phrase, "Springer kommt!"  A search on that phrase yields the following:
"Liebe Frau vBayern,
mich würde interessieren wie man
mit diesem Hintergrund
(vonbayern.de/german/anna.html)
zu Springer kommt?"

Background of "Frau vBayern" from thePeerage.com:

Anna-Natascha Prinzessin zu Sayn-Wittgenstein-Berleburg 

F, #64640, b. 15 March 1978Last Edited=20 Oct 2005

     Anna-Natascha Prinzessin zu Sayn-Wittgenstein-Berleburg was born on 15 March 1978. She is the daughter of Ludwig Ferdinand Prinz zu Sayn-Wittgenstein-Berleburg and Countess Yvonne Wachtmeister af Johannishus. She married Manuel Maria Alexander Leopold Jerg Prinz von Bayern, son of Leopold Prinz von Bayern and Ursula Mohlenkamp, on 6 August 2005 at Nykøping, Södermanland, Sweden.

The date of the above "Liebe Frau vBayern" inquiry, Feb. 1, 2007, suggests the following:

From Log24 on
St. Bridget's Day, 2007:

The quotation
"Science is a Faustian bargain"
and the following figure–

Change

The 63 yang-containing hexagrams of the I Ching as a Singer 63-cycle

From a short story by
the above Princess:

"'I don't even think she would have wanted to change you. But she for sure did not want to change herself. And her values were simply a part of her.' It was true, too. I would even go so far as to say that they were her basis, if you think about her as a geometrical body. That's what they couldn't understand, because in this age of the full understanding for stretches of values in favor of self-realization of any kind, it was a completely foreign concept."

To make this excellent metaphor mathematically correct,
change "geometrical body" to "space"… as in

"For Princeton's Class of 2007"

Review of a 2004 production of a 1972 Tom Stoppard play, "Jumpers"–

John Lahr on Tom Stoppard's play Jumpers

Related material:

Knight Moves (Log24, Jan. 16),
Kindergarten Theology (St. Bridget's Day, 2008),
and

The image “My space -(the affine space of six dimensions over the two-element field
(Click on image for details.)

Wednesday, December 26, 2007

Wednesday December 26, 2007

Filed under: General — Tags: — m759 @ 12:00 pm
A Wonderful Life

Part I:
 
Language Games

 
on December 19:

 

http://www.log24.com/log/pix07A/071219-StanLilith.jpg

See also the noir entry on
"Nightmare Alley" for
Winter Solstice 2002,
as well as a solstice-related
commentary on I Ching
Hexagram 41, Decrease.

Part II:

Language Game
on Christmas Day

Pennsylvania Lottery
December 25, 2007:

PA Lottery Christmas Day: Mid-day 041 and 2911, Evening 173 and 0666
 

Part III:
 
A Wonderful Life

The Pennsylvania Lottery on Christmas at mid-day paired the number of the I Ching Hexagram 41, "Decrease," with the number 2911, which may be interpreted as a reference to I Chronicles 29:11
 
"Thine, O LORD is the greatness, and the power, and the glory, and the victory, and the majesty: for all that is in the heaven and in the earth is thine; thine is the kingdom, O LORD, and thou art exalted as head above all."

 

This verse is sometimes cited as influencing the Protestant conclusion of the Lord's Prayer:

"Thine is the kingdom, and the power, and the glory, forever" (Mt 6.13b; compare 1 Chr 29.11-13)….

This traditional epilogue to the Lord's prayer protects the petition for the coming of the kingdom from being understood as an exorcism, which we derive from the Jewish prayer, the Kaddish, which belonged at the time to the synagogical liturgy.

World Alliance of Reformed Churches

The Pennsylvania Lottery on Christmas evening paired 173 with the beastly number 0666.  The latter number suggests that perhaps being "understood as an exorcism" might not, in this case, be such a bad thing. What, therefore, might "173" have to do with exorcism?  A search in the context of the phrase "language games" yields a reference to Wittgenstein's Zettel, section 173:

http://www.log24.com/log/pix07A/071226-Zettel.jpg

From Charles L. Creegan, Wittgenstein and Kierkegaard:

Language-games give general guidelines of the application of language. Wittgenstein suggests that there are innumerably many language-games: innumerably many kinds of use of the components of language.24 The grammar of the language-game influences the possible relations of words, and things, within that game. But the players may modify the rules gradually. Some utterances within a given language-game are applications; others are 'grammatical remarks' or definitions of what is or should be possible. (Hence Wittgenstein's remark, 'Theology as grammar'25 – the grammar of religion.)

The idea of the 'form of life' is a reminder about even more basic phenomena. It is clearly bound up with the idea of language. (Language and 'form of life' are explicitly connected in four of the five passages from the Investigations in which the term 'form of life' appears.) Just as grammar is subject to change through language-uses, so 'form of life' is subject to change through changes in language. (The Copernican revolution is a paradigm case of this.) Nevertheless, 'form of life' expresses a deeper level of 'agreement.' It is the level of 'what has to be accepted, the given.'26 This is an agreement prior to agreement in opinions and decisions. Not everything can be doubted or judged at once.

This suggests that 'form of life' does not denote static phenomena of fixed scope. Rather, it serves to remind us of the general need for context in our activity of meaning. But the context of our meaning is a constantly changing mosaic involving both broad strokes and fine-grained distinctions.

The more commonly understood point of the 'Private Language Argument' – concerning the root of meaning in something public – comes into play here. But it is important to show just what public phenomenon Wittgenstein has in mind. He remarks: 'Only in the stream of thought and life do words have meaning.'27

24
Investigations, sec. 23.
25
Investigations, sec. 373; compare Zettel, sec. 717.
26
Investigations, p. 226e.
27
Zettel, sec. 173. The thought is expressed many times in similar words.

And from an earlier chapter of Creegan:

The 'possibility of religion' manifested itself in considerable reading of religious works, and this in a person who chose his reading matter very carefully. Drury's recollections include conversations about Thomas à Kempis, Samuel Johnson's Prayers, Karl Barth, and, many times, the New Testament, which Wittgenstein had clearly read often and thought about.25 Wittgenstein had also thought about what it would mean to be a Christian. Some time during the 1930s, he remarked to Drury: 'There is a sense in which you and I are both Christians.'26 In this context it is certainly worth noting that he had for a time said the Lord's Prayer each day.27

Wittgenstein's last words were: 'Tell them I've had a wonderful life!'28

25
Drury (1981) 'Conversations with Wittgenstein,' in Ludwig Wittgenstein: Personal Recollections, pp. 112ff.
26
Drury, 'Conversations,' p. 130.
27
Drury, 'Some notes,' p. 109.
28
Reported by Mrs. Bevan, the wife of the doctor in whose house Wittgenstein was staying. Malcolm, Memoir, p. 81.

Part IV:  

L'Envoi

For more on the Christmas evening
number of the beast, see Dec. 3:
  "Santa's Polar Opposite?" —

"Did he who made the Lamb
make thee?
"

Wednesday, December 19, 2007

Wednesday December 19, 2007

Filed under: General — Tags: — m759 @ 9:00 am
Tutelary Figures

An entry in memory of
Dr. Joseph L. Henderson,
Jungian analyst, who died
on Nov. 17 at 104

(An obituary appears in
today’s New York Times.)


Some remarks by Dr. Henderson
:

The myth of the hero is the most common and the best known myth in the world… classical mythology… Greece and Rome… Middle Ages… Far East… contemporary primitive tribes. It also appears in dreams… obvious dramatic… profound… importance. P. 101

… structurally very similar… universal pattern… over and over again… a tale of… miraculous… humble birth… early proof of superhuman strength… rapid rise to prominence… triumphant struggle with the forces of evil… fallibility to the sin of pride (hybris)… and his fall through betrayal or a “heroic” sacrifice that ends in his death. P. 101

… another important characteristic… provides a clue… the early weakness… is balanced by… strong “tutelary” figures… who enable him to perform the superhuman tasks that he cannot accomplish unaided. Theseus had Poseidon… Perseus had Athena… Achilles had Cheiron… the wise centaur, as his tutor. P. 101 

And Stan Carlisle had
Dr. Lilith Ritter
:

http://www.log24.com/log/pix07A/071219-StanLilith.jpg

See also the noir entry on
“Nightmare Alley” for
Winter Solstice 2002,
as well as a solstice-related
commentary on I Ching
Hexagram 41, Decrease.

Related material:

http://www.log24.com/log/pix07A/071219-Authors2.jpg

Dr. Dyane N. Sherwood and
Dr. Joseph L. Henderson, authors
of Transformation of the Psyche
(Routledge, Nov. 7, 2003)

Dr. Henderson is said to
have been, in his youth,
a student of Thornton Wilder
as well as of Dr. Jung.

Sunday, December 16, 2007

Sunday December 16, 2007

Filed under: General — Tags: , , — m759 @ 1:09 pm
 
Mad Phaedrus
Meets Mad Ezra

"Plato's Good was a fixed and eternal and unmoving Idea, whereas for the rhetoricians it was not an Idea at all. The Good was not a form of reality. It was reality itself, ever changing, ultimately unknowable in any kind of fixed, rigid way." –Phaedrus in Zen and the Art of Motorcycle Maintenance

This apparent conflict between eternity and time, fixity and motion, permanence and change, is resolved by the philosophy of the I Ching and by the Imagism of Ezra Pound.  Consider, for example, the image of The Well

as discussed here on All Saints' Day 2003 and in the previous entry.

As background, consider the following remarks of James Hillman in "Egalitarian Typologies Versus the Perception of the Unique," Part  III: Persons as Images

"To conceive images as static is to forget that they are numens that move.  Charles Olson, a later poet in this tradition, said:  'One perception must immediately and directly lead to a further perception… always, always one perception must must must move instanter, on another.' 80  Remember Lavater and his insistence on instantaneity for reading the facial image.  This is a kind of movement that is not narrational, and the Imagists had no place for narrative.  'Indeed the great poems to come after the Imagist period– Eliot’s The Waste Land and Four Quartets; Pound’s Cantos; Williams’s Paterson– contain no defining narrative.' 81  The kind of movement Olson urges is an inward deepening of the image, an in-sighting of the superimposed levels of significance within it. 82  This is the very mode that Jung suggested for grasping dreams– not as a sequence in time, but as revolving around a nodal complex.  If dreams, then why not the dreamers.  We too are not only a sequence in time, a process of individuation. We are also each an image of individuality."

   80  The New American Poetry (D. M. Allen, ed.) N.Y.: Evergreen, Grove, 1960, pp. 387-88. from Jones, p. 42.

81  Jones,* p. 40.

82  H. D. later turned narration itself into image by writing a novel in which the stories were "compounded like faces seen one on top of another," or as she says "superimposed on one another like a stack of photographic negatives" (Jones, p. 42).  Cf. Berry,** p. 63: "An image is simultaneous. No part precedes or causes another part, although all parts are involved with each other… We might imagine the dream as a series of superimpositions, each event adding texture and thickening to the rest."

    * Imagist Poetry (Peter Jones, ed.) London: Penguin, 1972

    ** The contrast between image simultaneity and narrative succession, and the different psychological effects of the two modes, is developed by Patricia Berry, "An Approach to the Dream," Spring 1974 (N. Y./Zürich: Spring Publ.), pp. 63, 68-71

Hillman also says that

"Jung’s 'complex' and Pound's definition of Image and Lavater's 'whole heap of images, thoughts, sensations, all at once' are all remarkably similar.  Pound calls an Image, 'that which presents an intellectual and emotional complex in an instant of time'… 'the Image is more than an Idea.  It is a vortex or cluster of fused ideas and is endowed with energy'… 'a Vortex, from which and through which, and into which, ideas are constantly rushing.' 79 Thus the movement, the dynamics, are within the complex and not only between complexes, as tensions of opposites told about in narrational sequences, stories that require arbitrary syntactical connectives which are unnecessary for reading an image where all is given at once."

79  These definitions of Image by Pound come from his various writings and can all be found in Jones, pp. 32-41.  Further on complex and image, see J. B. Harmer, Victory in Limbo: Imagism 1908-17, London: Secker & Warburg, 1975, pp. 164-68.

These remarks may help the reader to identify with Ada during her well-viewing in Cold Mountain (previous entry):

"She was dazzled by light and shade, by the confusing duplication of reflections and of frames. All coming from too many directions for the mind to take account of. The various images bounced against each other until she felt a desperate vertigo…."

If such complexity can be suggested by Hexagram 48, The Well, alone, consider the effect of the "cluster of fused ideas… endowed with energy" that is the entire 64-hexagram I Ching.
 

Related material: St. Augustine's Day 2006

Friday, December 14, 2007

Friday December 14, 2007

Filed under: General — Tags: , , — m759 @ 9:00 am

“Well, it changes.”

Nicole Kidman at a press conference
for the London premiere of
“The Golden Compass” on November 27:

Nicole Kidman'-- kittens and tiger

A related Log24 link from
that same date, November 27:

Deep Beauty

See also Zen and the Art of
Motorcycle Maintenance

“Plato hadn’t tried to destroy areté. He had encapsulated it; made a permanent, fixed Idea out of it; had converted it to a rigid, immobile Immortal Truth. He made areté the Good, the highest form, the highest Idea of all. It was subordinate only to Truth itself, in a synthesis of all that had gone before.That was why the Quality that Phaedrus had arrived at in the classroom had seemed so close to Plato’s Good. Plato’s Good was taken from the rhetoricians. Phaedrus searched, but could find no previous cosmologists who had talked about the Good. That was from the Sophists. The difference was that Plato’s Good was a fixed and eternal and unmoving Idea, whereas for the rhetoricians it was not an Idea at all. The Good was not a form of reality. It was reality itself, ever changing, ultimately unknowable in any kind of fixed, rigid way.”

— as well as Cold Mountain

Page 48: “It’s claimed that if
you take a mirror and look
backwards into a well, you’ll
see your future down in the water.”

“So in short order Ada found herself bent backward over the mossy well lip, canted in a pose with little to recommend it in the way of dignity or comfort, back arched, hips forward, legs spraddled for balance.  She held a hand mirror above her face, angled to catch the surface of the water below.

Ada had agreed to the well-viewing as a variety of experiment in local custom and as a tonic for her gloom. Her thoughts had been broody and morbid and excessively retrospective for so long that she welcomed the chance to run counter to that flow, to cast forward and think about the future, even though she expected to see nothing but water at the bottom of the well.

She shifted her feet to find better grip on the packed dirt of the yard and then tried to look into the mirror.  The white sky above was skimmed over with backlit haze, bright as a pearl or as a silver mirror itself.  The dark foliage of oaks all around the edges framed the sky, duplicating the wooden frame of the mirror into which Ada peered, examining its picture of the well depths behind her to see what might lie ahead in her life. The bright round of well water at the end of the black shaft was another mirror.  It cast back the shine of sky and was furred around the edges here and there with sprigs of fern growing between stones.

Ada tried to focus her attention on the hand mirror, but the bright sky beyond kept drawing her eye away.  She was dazzled by light and shade, by the confusing duplication of reflections and of frames. All coming from too many directions for the mind to take account of. The various images bounced against each other until she felt a desperate vertigo, as if she could at any moment pitch backward and plunge head first down the well shaft and drown there, the sky far above her, her last vision but a bright circle set in the dark, no bigger than a full moon.

Her head spun and she reached with her free hand and held to the stonework of the well.  And then just for a moment things steadied, and there indeed seemed to be a picture in the mirror.”

— and Log24 on December 3 —

I Ching Hexagram 48: The Well
The above Chinese character
stands for Hexagram 48, “The Well.”
For further details, click on the well.

Monday, December 3, 2007

Monday December 3, 2007

Filed under: General — Tags: — m759 @ 9:00 am

The image “http://www.log24.com/log/pix07A/071203-IChingResources.gif” cannot be displayed, because it contains errors.

The above logo is from
the I Ching Resources website.

http://www.log24.com/images/IChing/hexagram10.gif

Hexagram 10
Treading (Conduct)

Two Commentaries:

1.
The standard
Princeton University Press
Wilhelm/Baynes text

2.
An idiosyncratic interpretation
from one “Rhett Butler”
at I Ching Resources

Rhett describes his experience
with Hexagram 10 at the South Pole.
This pole, like the abode of Santa,
may serve to illustrate T. S. Eliot’s
remarks on “the still point of
the turning world.”

Related material:

Hitler’s Still Point,

The Still Point of
the Turning World:
Joan Didion and the
Opposite of Meaning

(Harper’s, Nov. 2005),

and
Chorus from the Rock
(Log24, Dec. 5, 2004).

Tuesday, August 21, 2007

Tuesday August 21, 2007

Filed under: General,Geometry — Tags: — m759 @ 8:14 am
In the Details

I Ching hexagram 14, box style

Symbol from the
box-style I Ching

Related material:
The five Log24 entries
ending on August 1

Lou Beach, Science and Magic, New York Times 8/21/07

Illustration by Lou Beach
in today's New York Times
article on science and magic

Related material:
A Wrinkle in Time 

Monday, August 20, 2007

Monday August 20, 2007

Filed under: General,Geometry — Tags: — m759 @ 8:01 am
An Epiphany
for Stephen King

From the front page of this
morning's online New York Times:

New York Times, 7:42 AM Aug. 20, 2007

In the details:

Stephen B. King, a Hallmark Cards creative director

Stephen B. King,
a Hallmark creative director,
with some of the new
greeting cards based
 on topical themes and humor.

From yesterday's Log24 entry:

Hallmark Card logo

When you care enough
to send the very best…

From a llnk to Aug. 1
in yesterday's entry:

Epiphany

Geometry of the I Ching (Box Style)

Box-style I Ching, January 6, 1989

(Click on image for background.)

Detail:

Detail of Box Style I Ching: Hexagram 14.

Related material:
Logos and Logic 
 and Diagon Alley.

Sunday, August 19, 2007

Sunday August 19, 2007

Filed under: General — m759 @ 8:19 am
Symmetry and Mirroring

Deutsche Bank Logo

Logo design by Anton Stankowski

"… at the beginning of the thirties… Stankowski began to work as a typographer and graphic designer in a Zurich advertising agency. Together with a group of friends– they were later to be known as the 'Zurich Concretists'– he explored the possibilities of symmetry and mirroring in the graphic arts. Stankowski experimented with squares and diagonals, making them the hallmarks of his art. Of his now world-famous logo for the Deutsche Bank— the soaring diagonal in the stable square– he proudly said in 1974: 'The company logo is a trade-mark that sends out a signal.'"

Deutsche Bank Collection

New York firefighters
killed at Deutsche Bank

From RTE News, Ireland:

Fire at Deutsche Bank Aug. 18, 2007

"Two New York fire fighters were killed while trying to douse a blaze in the former Deutsche Bank building in the city.

The fire broke out on 14th and 15th floors yesterday afternoon and spread to several floors before it was brought under control about five hours later.

The building had been heavily damaged during the 11 September, 2001 terrorist attacks.

The building, which was damaged by falling debris of the twin towers that had collapsed in 2001 when terrorists flew hijacked planes into them, was being 'deconstructed' to make way for construction of a new Freedom Tower."

Related material

From August 1
 
SPORTS OF THE TIMES

Restoring the Faith
After Hitting the Bottom

By SELENA ROBERTS
The New York Times
Published: August 1, 2007

What good is a nadir if it's denied or ignored? What's the value of reaching the lowest of the low if it can't buy a cheap epiphany?

 

Hallmark Card logo

When you care enough
to send the very best…

See also
"Cheap Epiphany, continued,"
from Aug. 3, as well as
A Writer's Reflections
(Aug. 14):

New Yorker cover, Aug. 20, 2007 (echoing Hexagram 14 in the box-style I Ching)

"Summer Reading,"
by Joost Swarte

Tuesday, August 14, 2007

Tuesday August 14, 2007

Filed under: General — Tags: , — m759 @ 12:00 pm
Philip K. Dick,
1928 – 1982

 
on the cover of
a 1987 edition of
his 1959 novel
Time Out of Joint:

The image “http://www.log24.com/log/pix07A/070814-timejoin15.jpg” cannot be displayed, because it contains errors.

Cover art by Barclay Shaw reprinted
from an earlier (1984) edition

Philip K. Dick as a
window wraith (see below)

The above illustration was suggested by yesterday's quoted New Yorker characterization by Adam Gopnik of Philip K. Dick–

"… the kind of guy who can't drink one cup of coffee without drinking six, and then stays up all night to tell you what Schopenhauer really said and how it affects your understanding of Hitchcock and what that had to do with Christopher Marlowe."

— as well as by the illustrations of Gopnik's characterization in Kernel of Eternity, and by the following passage from Gopnik's 2005 novel The King in the Window:

"What's a window wraith?"

"It's someone who once lived in the ordinary world who lives now in a window, and makes reflections of the people who pass by and look in."

"You mean you are a ghost?!" Oliver asked, suddenly feeling a little terrified.

"Just the opposite, actually. You see, ghosts come from another world and haunt you, but window wraiths are the world. We're the memory of the world. We're here for good. You're the ones who come and go like ghosts. You haunt us."

Related material: As noted, Kernel of Eternity, and also John Tierney's piece on simulated reality in last night's online New York Times. Whether our everyday reality is merely a simulation has long been a theme (as in Dick's novel above) of speculative fiction. Interest in this theme is widespread, perhaps partly because we do exist as simulations– in the minds of other people. These simulations may be accurate or may be– as is perhaps Gopnik's characterization of Philip K. Dick– inaccurate. The accuracy of the simulations is seldom of interest to the simulator, but often of considerable interest to the simulatee.

The cover of the Aug. 20 New Yorker in which the Adam Gopnik essay appears may also be of interest, in view of the material on diagonals in the Log24 entries of Aug. 1 linked to in yesterday's entry:

IMAGE- New Yorker cover echoing Hexagram 14 in the box-style I Ching

"Summer Reading,"
by Joost Swarte

Friday, August 10, 2007

Friday August 10, 2007

Filed under: General,Geometry — Tags: , , — m759 @ 10:31 am

The Ring of Gyges

10:31:32 AM ET

Commentary by Richard Wilhelm
on I Ching Hexagram 32:

“Duration is… not a state of rest, for mere standstill is regression.
Duration is rather the self-contained and therefore self-renewing
movement of an organized, firmly integrated whole, taking place in
accordance with immutable laws and beginning anew at every ending.”

Related material

The Ring of the Diamond Theorem

Jung and the Imago Dei

Log24 on June 10, 2007: 

WHAT MAKES IAGO EVIL? some people ask. I never ask. —Joan Didion

Iago states that he is not who he is. —Mark F. Frisch

“Not Being There,”
by Christopher Caldwell
,
from next Sunday’s
New York Times Magazine:

“The chance to try on fresh identities was the great boon that life online was supposed to afford us. Multiuser role-playing games and discussion groups would be venues for living out fantasies. Shielded by anonymity, everyone could now pass a ‘second life’ online as Thor the Motorcycle Sex God or the Sage of Wherever. Some warned, though, that there were other possibilities. The Stanford Internet expert Lawrence Lessig likened online anonymity to the ring of invisibility that surrounds the shepherd Gyges in one of Plato’s dialogues. Under such circumstances, Plato feared, no one is ‘of such an iron nature that he would stand fast in justice.’Time, along with a string of sock-puppet scandals, has proved Lessig and Plato right.”

“The Boy Who Lived,”
by Christopher Hitchens
,
from next Sunday’s
New York Times Book Review:

On the conclusion of the Harry Potter series:”The toys have been put firmly back in the box, the wand has been folded up, and the conjuror is discreetly accepting payment while the children clamor for fresh entertainments. (I recommend that they graduate to Philip Pullman, whose daemon scheme is finer than any patronus.)”

I, on the other hand,
recommend Tolkien…
or, for those who are
already familiar with
Tolkien, Plato– to whom
The Ring of Gyges” may
serve as an introduction.

“It’s all in Plato, all in Plato:
bless me, what do they
teach them at these schools!”
C. S. Lewis

Wednesday, August 1, 2007

Wednesday August 1, 2007

Filed under: General,Geometry — m759 @ 6:19 pm
Diagon Alley

From this morning:

IMAGE- I Ching Hexagram 14

This symbol from the
box-style I Ching is
echoed by a French ad for
the 2006 film "Scoop"–

The image “http://www.log24.com/log/pix07A/070801-scoop2.jpg” cannot be displayed, because it contains errors.

This film may be taken as
foreshadowing the afterlife
of the late Fleet Street
figure Richard Stott.

Stott, along with film
directors Ingmar Berman
and Michelangelo Antonioni,
died on Monday (July 30).

He is, we may suppose,
the mysterious third man
in Tuesday's remark by
the mayor of Rome
:

"With Antonioni dies not only
one of the greatest directors

The image “http://www.log24.com/log/pix07A/070801-Bergman.jpg” cannot be displayed, because it contains errors.

but also
a master of modernity."

The image “http://www.log24.com/log/pix07A/070801-Stott.jpg” cannot be displayed, because it contains errors.

Dogs and Lampposts,
by Richard Stott

The title of Stott's book
is from H. L. Mencken,
who is said to have felt
that the proper relationship
of a journalist to a politician
is that of a dog to a lamppost.

Wednesday August 1, 2007

Filed under: General,Geometry — Tags: — m759 @ 8:00 am
August First,
8:00:14 AM:

Cheap Epiphany

SPORTS OF THE TIMES

Restoring the Faith
After Hitting the Bottom

By SELENA ROBERTS
The New York Times
Published: August 1, 2007

What good is a nadir if it's denied or ignored? What's the value of reaching the lowest of the low if it can't buy a cheap epiphany?

 

Pennsylvania Lottery
on the Feast of
St. Ignatius Loyola:
 
PA Lottery July 31, 2007 - Mid-day 215, Evening 298

Restoring the Booze:
A Look at the 50's-

Grace and Bing in the Fifties

Another Epiphany:

Geometry of the I Ching (Box Style)

Box-style I Ching, January 6, 1989

(Click on image for background.)

Detail:

Detail of Box Style I Ching: Hexagram 14.

Related material:
Logos and Logic 
 and Diagon Alley.

"What a swell
  party this is."

— adapted from
     Cole Porter 

Monday, July 9, 2007

Monday July 9, 2007

Filed under: General,Geometry — m759 @ 11:59 pm
Harry Potter and
the Xbox 360

Harry Potter and the Order of The Phoenix for Xbox 360 “is based on the fifth book and is timed to coincide with the release of the movie of the same name…. The game consists of Harry walking around and talking to characters and performing spells and tasks in order to advance the plot. I jokingly considered calling this review ‘Harry Potter and the Order of the Random Tasks Needed to Advance the Plot.'” —July 9 review at Digital Joystick

Today’s lottery numbers
in the Keystone State:

Mid-day 220
Evening 034

Related material:
2/20 and
Hexagram 34 in the
box-style I Ching:

  The image �http://www.log24.com/theory/images/Box34.gif� cannot be displayed, because it contains errors.
 
The Power
of the Great

Let us hope that Harry fans remember the meaning of Hexagram 34 (according to Richard Wilhelm)– “Perseverance furthers” and “That is truly great power which does not degenerate into mere force but remains inwardly united with the fundamental principles of right and of justice. When we understand this point– namely, that greatness and justice must be indissolubly united– we understand the true meaning of all that happens in heaven and on earth.”

Related material:

If Cullinane College
were Hogwarts

(continued) and
the four entries
that preceded it
on July 5-6, 2007

Thursday, July 5, 2007

Thursday July 5, 2007

Filed under: General,Geometry — Tags: — m759 @ 7:11 pm

In Defense of
Plato’s Realism

(vs. sophists’ nominalism–
see recent entries.)

Plato cited geometry,
notably in the Meno,
in defense of his realism.
Consideration of the
Meno’s diamond figure
leads to the following:

The Eightfold Cube and its Inner Structure

Click on image for details.

As noted in an entry,
Plato, Pegasus, and
the Evening Star,

linked to
at the end of today’s
previous entry,
the “universals”
of Platonic realism
are exemplified by
the hexagrams of
the I Ching,
which in turn are
based on the seven
trigrams above and
on the eighth trigram,
of all yin lines,
not shown above:

Trigram of K'un, the Receptive

K’un
The Receptive

_____________________________________________

Update of Nov. 30, 2013:

From  a little-known website in Kuala Lumpur:
(Click to enlarge.)

The remarks on Platonic realism are from Wikipedia.
The eightfold cube is apparently from this post.

Wednesday, June 20, 2007

Wednesday June 20, 2007

Filed under: General,Geometry — Tags: , , , — m759 @ 1:06 am

Kernel

Mathematical Reviews citation:

MR2163497 (2006g:81002) 81-03 (81P05)
Gieser, Suzanne The innermost kernel. Depth psychology and quantum physics. Wolfgang Pauli's dialogue with C. G. Jung. Springer-Verlag, Berlin, 2005. xiv+378 pp. ISBN: 3-540-20856-9

A quote from MR at Amazon.com:

"This revised translation of a Swedish Ph. D. thesis in philosophy offers far more than a discussion of Wolfgang Pauli's encounters with the psychoanalyst Carl Gustav Jung…. Here the book explains very well how Pauli attempted to extend his understanding beyond superficial esotericism and spiritism…. To understand Pauli one needs books like this one, which… seems to open a path to a fuller understanding of Pauli, who was seeking to solve a quest even deeper than quantum physics." (Arne Schirrmacher, Mathematical Reviews, Issue 2006g)
 

An excerpt:

 

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

I do not yet know what Gieser means by "the innermost kernel." The following is my version of a "kernel" of sorts– a diagram well-known to students of anthropologist Claude Levi-Strauss and art theorist Rosalind Krauss:

The four-group is also known as the Vierergruppe or Klein group.  It appears, notably, as the translation subgroup of A, the group of 24 automorphisms of the affine plane over the 2-element field, and therefore as the kernel of the homomorphism taking A to the group of 6 automorphisms of the projective line over the 2-element field. (See Finite Geometry of the Square and Cube.)

Related material:

The "chessboard" of
   Nov. 7, 2006
(as revised Nov. 7, 2012)–

I Ching chessboard. Previous version replaced on Nov. 7, 2012, by original 1989 chessboard arrangement

I Ching chessboard

None of this material really has much to do with the history of physics, except for its relation to the life and thought of physicist Wolfgang Pauli— the "Mephistopheles" of the new book Faust in Copenhagen. (See previous entry.)

"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"

(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)
 

Thursday, June 14, 2007

Thursday June 14, 2007

Filed under: General — Tags: , — m759 @ 2:00 am
Unscholarly Notes

The time of the previous entry, 1:06:18, suggests both the date of Epiphany, 1:06, and Hexagram 18 of the I Ching: Ku, Work on what has been spoiled (Decay).

Epiphany: A link in the Log24 entries for Epiphany 2007 leads to Damnation Morning, which in turn leads to Why Me?, a discussion of the mythology of Spiders vs. Snakes devised by Fritz Leiber.  Spiders represent the conscious mind, snakes the unconscious.

On Hexagram 18: "The Chinese character ku represents a bowl in whose contents worms are breeding. This means decay." —Wilhelm's commentary

This brings us back to the previous entry with its mention of the date of Rudolf Arnheim's death: Saturday, June 9.  In Log24 on that date there was a link, in honor of Aaron Sorkin's birthday, to a short story by Leonard Michaels.  That link was suggested, in part,  by a review in the Sunday New York Times Book Review (available online earlier, on Friday). Here is a quote from that review related to the Hexagram 18 worm bowl:

"… what grabbed attention for his early collections was Michaels's gruesome, swaggering depiction of the sexual rampage that was the swinging '60s in New York– 'the worm bucket,' as Michaels described an orgy."

Related material for meditation on this, the anniversary (according to Encyclopaedia Britannica) of the birth of author Jerzy Kosinski— his novel The Hermit of 69th Street.

Kosinski was not unfamiliar with Michaels's worm bucket.  For related information, see Hermit (or at least a review).

In Leiber's stories the symbol of the Snakes is similar to the famed Yin-Yang symbol, also known as the T'ai-chi tu.  For an analysis of this symbol by Arnheim, see the previous entry.  See also "Sunday in the Park with Death" (Log24, Oct. 26, 2003):

"Ay que bonito es volar  
    A las dos de la mañana
…."
— "La Bruja"

Monday, May 28, 2007

Monday May 28, 2007

Filed under: General,Geometry — Tags: , , , , — m759 @ 5:00 pm
Space-Time

and a Finite Model

Notes by Steven H. Cullinane
May 28, 2007

Part I: A Model of Space-Time

The following paper includes a figure illustrating Penrose’s model of  “complexified, compactified Minkowski space-time as the Klein quadric in complex projective 5-space.”
 
The image “http://www.log24.com/log/pix07/070528-Twistor.jpg” cannot be displayed, because it contains errors.

Click on picture to enlarge.

For some background on the Klein quadric and space-time, see Roger Penrose, “On the Origins of Twistor Theory,” from Gravitation and Geometry: A Volume in Honor of Ivor Robinson, Bibliopolis, 1987.


Part II: A Corresponding Finite Model

 

The Klein quadric also occurs in a finite model of projective 5-space.  See a 1910 paper:

G. M. Conwell, The 3-space PG(3,2) and its group, Ann. of Math. 11, 60-76.

Conwell discusses the quadric, and the related Klein correspondence, in detail.  This is noted in a more recent paper by Philippe Cara:

The image “http://www.log24.com/log/pix07/070528-Quadric.jpg” cannot be displayed, because it contains errors.

 

As Cara goes on to explain, the Klein correspondence underlies Conwell’s discussion of eight heptads.  These play an important role in another correspondence, illustrated in the Miracle Octad Generator of R. T. Curtis, that may be used to picture actions of the large Mathieu group M24.


Related material:

The projective space PG(5,2), home of the Klein quadric in the finite model, may be viewed as the set of 64 points of the affine space AG(6,2), minus the origin.

The 64 points of this affine space may in turn be viewed as the 64 hexagrams of the Classic of Transformation, China’s I Ching.

There is a natural correspondence between the 64 hexagrams and the 64 subcubes of a 4x4x4 cube.  This correspondence leads to a natural way to generate the affine group AGL(6,2).  This may in turn be viewed as a group of over a trillion natural transformations of the 64 hexagrams.

Geometry of the I Ching.
“Once Knecht confessed to his teacher that he wished to learn enough to be able to incorporate the system of the I Ching into the Glass Bead Game.  Elder Brother laughed.  ‘Go ahead and try,’ he exclaimed.  ‘You’ll see how it turns out.  Anyone can create a pretty little bamboo garden in the world.  But I doubt that the gardener would succeed in incorporating the world in his bamboo grove.'”
— Hermann Hesse, The Glass Bead Game,
  translated by Richard and Clara Winston

Saturday, May 26, 2007

Saturday May 26, 2007

Filed under: General — m759 @ 1:09 pm

A Baffled Reader

A reader this morning commented on my first Xanga entry (July 20, 2002):

“To set one up (which I have not done because I don’t want anyone to know what I think),” … William Safire regarding “blogs”.

I still don’t know what you think.  Yet … I try, try, try.

Here’s one thing that I think– today– based on my “Hate Speech for Harvard,” on “Devil in the Details” (Log24, May 18 and 23), and, more recently, on

  1. last evening’s PA lottery number 005,
  2. the I Ching hexagram of the same number, and
  3. the New Yorker issue linked to at the end of the previous entry:
Revised New Yorker cover from 5/21/07
Revised version of the
New Yorker cover of 5/21/07
Commentary on the cover
by the PA lottery
on 5/25/07
in the form of the
evening number, 005.
In the I Ching, this
is the number of

HSU:
WAITING
(NOURISHMENT)

See also the previous entry
and Natalie Angier’s sneer
at a politician’s call for
prayer, which, she
said, involved the
“assumption that prayer is
some sort of miracle
Vicks VapoRub.”

Detail from the
5/21/07 New Yorker:

Detail, New Yorker cover, 5/21/07

THE IMAGE

Hexagram 5: Waiting (Nourishment)

Clouds rise up to heaven:
The image of WAITING.
Thus the superior man
eats and drinks,
Is joyous and
of good cheer.

AMEN.

Sunday, April 15, 2007

Sunday April 15, 2007

Filed under: General — m759 @ 10:18 am
The Sun
Also Rises
 
Ecclesiastes 1:5

Broken Symmetries by Paul Preuss

Hexagram 35
 
THE IMAGE
 
The sun rises over the earth:
The image of PROGRESS.
 
Classic of Change,
Hexagram 35
 
  10:18:35 AM ET
 
Related material:
 
Keillor Meets Thompson:
The Height of Folly
 
and
 
today’s New York Times
obituaries (previous entry)
 

Saturday, April 14, 2007

Saturday April 14, 2007

Filed under: General — m759 @ 10:31 pm
Entertainment Tonight

“What is the spirit of the bayonet?”

— United States Army
training question, 1964

A partial answer
in two parts:

Part I —

Another question —

“Know the one about
the Demiurge and the
Abridgment of Hope?”

— Robert Stone,
A Flag for Sunrise,
Knopf, 1981,
the final page, 439,
cited by page number
here this morning


Part II —

The image “http://www.log24.com/log07/saved/070414-PAlottery.jpg” cannot be displayed, because it contains errors.

Today’s numbers, in
this morning’s context,
strongly suggest
a look at
A Flag for Sunrise,
by Robert Stone,
Knopf, 1981,

page 431,
and at
Hexagram 34,

The Power of the Great,
in the context of a
Log24 entry for
October 8, 2005
.

There is no teacher
but the enemy.

— Orson Scott Card,
Ender’s Game

Related entertainment:
the previous entry
and the Vietnam memoir
Black Virgin Mountain.

Friday, April 6, 2007

Friday April 6, 2007

Filed under: General — m759 @ 2:56 pm
 Good Friday,
2:56:38 PM:

Fire Lake

Hexagram 38: Above, Fire; Below, Lake

Hexagram 38

Above, Fire;
Below, Lake

Thursday, March 8, 2007

Thursday March 8, 2007

Filed under: General,Geometry — m759 @ 1:00 pm
Day Without
Logic

The image “http://www.log24.com/log/pix06A/060804-DWA2.gif” cannot be displayed, because it contains errors.

Symbol of the Dec. 1
Day Without Art

This resembles the following symbol,
due to logician Charles Sanders Peirce,
of the logic of binary opposition:

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

(For futher details on the role
of this symbol in logic, see
Chinese Jar Revisited.)

On this, International Women’s Day,
we might also consider the
widely quoted thoughts on logic of
Harvard professor Barbara Johnson:

Nothing Fails Like Success, by Barbara Johnson

Detail:

Barbara Johnson, Nothing Fails Like Success, detail

“Instead of a simple ‘either/or’ structure,
deconstruction attempts to elaborate a discourse
that says neither “either/or”, nor “both/and”
nor even “neither/nor”, while at the same time
not totally abandoning these logics either.”

It may also be of interest on
International Women’s Day
that in the “box style” I Ching
(suggested by a remark of
Jungian analyst
Marie-Louise von Franz)
the symbol

The image “http://www.log24.com/theory/images/PeirceBox.bmp” cannot be displayed, because it contains errors.
 
denotes
Hexagram 2,
The Receptive.

Thursday March 8, 2007

Filed under: General,Geometry — m759 @ 9:00 am
Dia de la
Mujer Trabajadora

The image “http://www.log24.com/log/pix07/070308-Aldecoa.jpg” cannot be displayed, because it contains errors.

“Yo es que nací un 8 de marzo,
Día de la Mujer Trabajadora,
y no he hecho más que
trabajar toda mi vida.”

Josefina Aldecoa

For background on Aldecoa,
see a paper (pdf) by
Sara Brenneis:

“Josefina Aldecoa intertwines
history, collective memory
and individual testimony in her
historical memory trilogy…”

HISTORICAL MEMORY–

History:

The Triangle Shirtwaist Factory Fire in New York City on March 25, 1911, was the largest industrial disaster in the history of the city of New York, causing the death of 146 garment workers who either died in the fire or jumped to their deaths.

Propaganda, March 1977:

“On March 8, 1908, after the death of 128 women trapped in a fire at the Triangle Shirtwaist Factory in New York City, 15,000 women workers from the garment and textile industry marched echoing the demands of their sisters 50 years earlier…”

Propaganda, March 2006:

“First of all, on March 8th, 1857, a large number of factory workers in the United States took to the streets to demand their economic and political rights. The owners called the police who arrived immediately and opened fire, engaging in blind repression… Later on, in 1908, the same date of March 8th was once again a memorable date of struggle. On this day, capitalist bosses in Chicago set fire to a textile factory where over a thousand women worked. A very large number was terribly burnt. 120 died!”

Propaganda disguised as news, March 2007:

From today’s top story in 24 HoursTM, a commuter daily in Vancouver published by Sun Media Corporation:

Fight still on for equality

By Robyn Stubbs and Carly Krug

“International Women’s Day commemorates a march by female garment workers protesting low wages, 12-hour workdays and bad working conditions in New York City on March 8, 1857.

Then in 1908, after 128 women were trapped and killed in a fire at a New York City garment and textile factory, 15,000 women workers again took their protests to the street.”

Related historical fiction:

A version of the
I Ching’s Hexagram 19:

The image “http://www.log24.com/log/pix05B/051202-Hex19.jpg” cannot be displayed, because it contains errors.

Log24 12/3/05:

The image “http://www.log24.com/log/pix05B/051202-Axe.jpg” cannot be displayed, because it contains errors.

Katherine Neville, The Eight

    “What does this have to do with why we’re here?”
    “I saw it in a chess book Mordecai showed me.  The most ancient chess service ever discovered was found at the palace of King Minos on Crete– the place where the famous Labyrinth was built, named after this sacred axe.  The chess service dates to 2000 B.C.  It was made of gold and silver and jewels…. And in the center was carved a labrys.”
… “But I thought chess wasn’t even invented until six or seven hundred A.D.,” I added.  “They always say it came from Persia or India.  How could this Minoan chess service be so old?”
    “Mordecai’s written a lot himself on the history of chess,” said Lily…. “He thinks that chess set in Crete was designed by the same guy who built the Labyrinth– the sculptor Daedalus….”
    Now things were beginning to click into place….
    “Why was this axe carved on the chessboard?” I asked Lily, knowing the answer in my heart before she spoke.  “What did Mordecai say was the connection?”….
    “That’s what it’s all about,” she said quietly.  “To kill the King.”
 
     The sacred axe was used to kill the King.  The ritual had been the same since the beginning of time. The game of chess was merely a reenactment.  Why hadn’t I recognized it before?

Perhaps at the center of
Aldecoa’s labyrinth lurk the
  capitalist bosses from Chicago
who, some say, set fire
to a textile factory
on this date in 1908.

For a Freudian perspective
on the above passage,
see yesterday’s entry
In the Labyrinth of Time,
with its link to
John Irwin‘s essay

The False Artaxerxes:
Borges and the
Dream of Chess
.”

The image “http://www.log24.com/log/pix07/070307-Symbols.gif” cannot be displayed, because it contains errors.

Symbols
S. H. Cullinane
March 7, 2007

Today, by the way, is the
feast of a chess saint.

Friday, February 16, 2007

Friday February 16, 2007

Filed under: General — Tags: — m759 @ 6:16 am

The Judas Seat

Janet Maslin in today’s New York Times:

“The much-borrowed Brown formula involves some very specific things. The name of a great artist, artifact or historical figure must be in the book’s story, not to mention on its cover. The narrative must start in the present day with a bizarre killing, then use that killing as a reason to investigate the past. And the past must yield a secret so big, so stunning, so saber-rattling that all of civilization may be changed by it. Probably not for the better.

This formula is neatly summarized….”

Cover illustration
for
The Judas Seat:
The Narrative:

The Secret:

Part I

“Little ‘Jack’ Horner was actually Thomas Horner, steward to the Abbot of Glastonbury during the reign of King Henry VIII…. Always keen to raise fresh funds, Henry had shown a interest in Glastonbury (and other abbeys). Hoping to appease the royal appetite, the nervous Abbot, Richard Whiting, allegedly sent Thomas Horner to the King with a special gift. This was a pie containing the title deeds to twelve manor houses in the hope that these would deflect the King from acquiring Glastonbury Abbey. On his way to London, the not so loyal courier Horner apparently stuck his thumb into the pie and extracted the deeds for Mells Manor, a plum piece of real estate. The attempted bribe failed and the dissolution of the monasteries (including Glastonbury) went ahead from 1536 to 1540. Richard Whiting was subsequently executed, but the Horner family kept the house, so the moral of this one is: treachery and greed pay off, but bribery is a bad idea.” –Chris Roberts, Heavy Words Lightly Thrown: The Reason Behind the Rhyme

Part II

“The Grail Table has thirteen seats, one of which is kept vacant in memory of Judas Iscariot who betrayed Christ.” —Symbolism of King Arthur’s Round Table

“In medieval romance, the grail was said to have been brought to Glastonbury in Britain by Joseph of Arimathea and his followers. In the time of Arthur, the quest for the Grail was the highest spiritual pursuit.” —The Camelot Project

Part III

The Log24 entry
for the date–
February 13, 2007–
of the above Bible scholar’s death,

and the three entries preceding it:

“And what the dead had no speech for, when living,
they can tell you, being dead:
the communication of the dead is tongued with fire
beyond the language of the living.”

— T. S. Eliot, Four Quartets

Thursday, February 1, 2007

Thursday February 1, 2007

Filed under: General — Tags: — m759 @ 7:59 am
Change

The image “http://www.log24.com/theory/images/GF64-63cycleA495.gif” cannot be displayed, because it contains errors.

The above is from
Feb. 15, 2006.

"I don't believe in an afterlife, so I think this is it, and I'm trying to spend my time as best I can, and I'm trying to spend my time so I'm proud of what I've done, and I try not to do any things that I'm not proud of."

Jim Gray, 2002 interview (pdf)
 

Commencement Address (doc)
to Computer Science Division,
College of Letters and Science,
University of California, Berkeley,
by Jim Gray,
May 25, 2003:

"I was part of Berkeley's class of 1965. Things have changed a lot since then….

So, what's that got to do with you? Well, there is going to be MORE change…. Indeed, change is accelerating– Vernor Vinge suggests we are approaching singularities when social, scientific and economic change are so rapid that we cannot imagine what will happen next.  These futurists predict humanity will become post-human. Now, THAT! is change– a lot more than I have seen.

If it happens, the singularity will happen in your lifetime– and indeed, you are likely to make it happen."

 

I Ching, Hexagram 39

For other singular
sci-fi tales, click on
the above hexagram.


More from Gray's speech:

"I am an optimist. Science is a Faustian bargain– and I am betting on mankind muddling through. I grew up under the threat of atomic war; we've avoided that so far. Information Technology is a Faustian bargain. I am optimistic that we can have the good parts and protect ourselves from the worst part– but I am counting on your help in that."


"Not fare well,
But fare forward, voyagers."

— T. S. Eliot,
"The Dry Salvages"

Friday, January 26, 2007

Friday January 26, 2007

Filed under: General — Tags: — m759 @ 2:48 pm
 
IT
 
"… at last she realized
what the Thing on the dais was.
IT was a brain.
A disembodied brain…."
 
A Wrinkle in Time, by Madeleine L'Engle

"There could not be an objective test
that distinguished a clever robot
from a really conscious person."

— Daniel Dennett in TIME magazine,
issue dated Mon., Jan. 29, 2007

 

Daniel Dennett in his office

 

Daniel Dennett, Professor of Philosophy
and Director of the
Center for Cognitive Studies
at Tufts University,
in his office on campus.
(Boston Globe, Jan. 29, 2006.
Photo © Rick Friedman.)

Hexagram 39:
Obstruction

I Ching, Hexagram 39

The Judgment

Obstruction. The southwest furthers.
(See Zenna Henderson.) 
The northeast does not further.
 (See Daniel Dennett.)
It furthers one to see the great man.
 (See Alan Turing.)
Perseverance brings good fortune.

"If telepathy is admitted
it will be necessary
to tighten our test up."
 
Alan Turing, 1950
 
Amen.

Wednesday, January 3, 2007

Wednesday January 3, 2007

Filed under: General — m759 @ 11:32 am
The Wanderer:
 
11:32:56

“What on earth is
a concrete universal?”
Robert M. Pirsig  

Hexagram 56

“James Joyce meant Finnegans Wake to become a universal book. His universe was primarily Dublin, but Joyce believed that the universal can be found in the particular. ‘I always write about Dublin,’ he said to Arthur Power, ‘because if I can get to the heart of Dublin I can get to the heart of all the cities of the world’ (Ellmann 505). He achieved that goal in Ulysses by making Bloom a universal wanderer, the everyman trying to find his way in the labyrinth of the world.” —The Joyce of Science

Related material:

From A Shot at Redemption

The Past as Prologue:
Grand Rapids Revisited

Constantine (cartoon) and Donald Knuth

John Constantine,
cartoon character, and
Donald E. Knuth,
Lutheran mathematician

“…. recent books testify
further to Calvin College’s
unparalleled leadership
in the field of
Christian historiography….”

“I need a photo opportunity,
I want a shot at redemption.
Don’t want to end up a cartoon
In a cartoon graveyard.”

A photo opportunity —

Photo op for Gerald Ford

and a recent cartoon:

Cartoon of Gerald Ford with halo

History, said Stephen….

From Calvin College,
today’s meditation:

Tuesday, December 26, 2006

Tuesday December 26, 2006

Filed under: General,Geometry — Tags: — m759 @ 7:59 am

Today in History
by The Associated Press:

Today is Tuesday, Dec. 26, the 360th day of 2006. There are five days left in the year. The seven-day African-American holiday Kwanzaa begins today. This is Boxing Day.

Related material —

The Seventh Symbol:

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)

Sunday, December 24, 2006

Sunday December 24, 2006

Filed under: General,Geometry — m759 @ 7:15 am
The image “http://www.log24.com/log/pix06B/061224-Shoe2.gif” cannot be displayed, because it contains errors.

Hexagram 30,

Click on picture
for further details.

Roz Chast's Math Cliff

Click on picture
for further details.

Thursday, December 7, 2006

Thursday December 7, 2006

Filed under: General — m759 @ 3:30 am
From Here to Eternity

Time and Eternity

This morning’s New York Times:

Kenneth Taylor, 86,
a Key Pilot at Pearl Harbor,
Dies

In his honor,
“one brief shining moment”–
namely,

3:30:30,”

the time of this entry.

Hexagram 30
 
30

The Image

Image of Hexagram 30: Fire over Fire

That which is bright rises twice:
The image of Fire.

Tuesday, November 7, 2006

Tuesday November 7, 2006

Filed under: General,Geometry — Tags: — m759 @ 12:00 am
A Game of Chess

The image “http://www.log24.com/log/pix06B/061107-McQueen.jpg” cannot be displayed, because it contains errors.

"And these chessmen are men and women as they appear to themselves and to one another in this world. And the silver table is Time. And those who stand and watch are the immortal souls of these same men and women."

— C. S. Lewis,
The Great Divorce

I Ching chessboard

I Ching chessboard

Related material:

"At the still point,
there the dance is
"

and

Number and Time, by Marie-Louise von Franz
 

Sunday, October 29, 2006

Sunday October 29, 2006

Filed under: General — Tags: — m759 @ 1:00 am
Decrease
 
(Readings for the
Halloween season)


In 1692 on July 31, at the time of the Salem witchcraft trials, Increase Mather reportedly "delivered a sermon… in Boston in which he posed the question… 'O what makes the difference between the devils in hell and the angels of heaven?'"

Increase, the father of Cotton Mather, was president of Harvard from June 27, 1692, to Sept. 6, 1701.  His name is memorialized by Harvard's Mather House.

From Log24 on Jan. 15, 2003:

Locating Hell

"Noi siam venuti al loco ov' i' t'ho detto
            che tu vedrai le genti dolorose
    c'hanno perduto il ben de l'intelletto
."

Dante, Inferno, Canto 3, 16-18

"We have come to where
              I warned you we would find
Those wretched souls
              who no longer have 
The intellectual benefits of the mind."

Dante, Hell, Canto 3, 16-18

From a Harvard student's weblog:

Heard in Mather  I hope you get gingivitis You want me to get oral cancer?! Goodnight fartface Turd. Turd. Turd. Turd. Turd. Make your own waffles!! Blah blah blah starcraft blah blah starcraft blah starcraft. It's da email da email. And some blue hair! Oohoohoo Izod! 10 gigs! Yeah it smells really bad. Only in the stairs though. Starcraft blah blah Starcraft fartface. Yeah it's hard. You have to get a bunch of battle cruisers. 40 kills! So good! Oh ho ho grunt grunt squeal.  I'm getting sick again. You have a final tomorrow? In What?! Um I don't even know. Next year we're draggin him there and sticking the needle in ourselves. 

" … one more line/ unravelling from the dark design/ spun by God and Cotton Mather"

— Robert Lowell

 

 

To honor Harvard's Oct. 28 founding,
here are yesterday's numbers from
the state of Grace (Kelly, of Philadelphia):

The image “http://www.log24.com/log/pix06A/061028-PAlottery.jpg” cannot be displayed, because it contains errors.

Related material:

Log24 on 1/16,
and Hexagram 41,

The image “http://www.log24.com/images/IChing/hexagram41.gif” cannot be displayed, because it contains errors.

Decrease

The Image

At the foot of the mountain, the lake:
The image of Decrease.
Thus the superior man controls his anger
And restrains his instincts.

This suggests thoughts of
the novel Cold Mountain
 (see yesterday morning)
and the following from
Log24 on St. Luke's Day
this year:

The image �http://www.log24.com/log/pix05/050511-Montreat-logo.jpg� cannot be displayed, because it contains errors.

Lucero as portrayed by Megan Follows
Established in 1916,
Montreat College
is a private, Christian
college located in a
beautiful valley in the
Blue Ridge Mountains
of North Carolina.

From Nell:

The image �http://www.log24.com/log/pix05/050511-Nell-valleyview.jpg� cannot be displayed, because it contains errors.

"The valley spirit never dies…"

See also St. Luke's Day, 2004,
as well as a journal entry
prompted by both
the ignorant religion
of Harvard's past
and the ignorant scientism
of Harvard's present–
 Hitler's Still Point:
A Hate Speech for Harvard
.

This last may, of course, not
quite fit the description of
the superior man
controlling his anger
so wisely provided by
yesterday's lottery and
Hexagram 41.
Nobody's perfect.

Wednesday, October 11, 2006

Wednesday October 11, 2006

Filed under: General — m759 @ 11:07 am
Ticket Home

  

Yesterday’s Pennsylvania
Lottery numbers:

Mid-day 266
Evening 529

Related material:

The 266-Day Method

and

The Shining of May 29

(Wednesday, May 29, 2002)

Commentary on Hexagram 29:
“K’an represents…
the principle of light
inclosed in the dark.”

— Richard Wilhelm,
Translation of the I Ching

“How do we explain
the mathematical
if not by mathematics?”

  — Rhetorical question 
of Martin Heidegger

(Page 273 of Heidegger’s
Basic Writings,
edited by David Farrell Krell,
Harper Collins paperback, 1993)

Tuesday, September 26, 2006

Tuesday September 26, 2006

Filed under: General — m759 @ 8:48 am
Today’s Birthdays:
T. S. Eliot and Linda Hamilton

From Eliot’s
Ash Wednesday“–

“Prophesy to the wind,
    to the wind only for only
The wind will listen.
    And the bones sang chirping
With the burden of the grasshopper,
    saying….”         

The image “http://www.log24.com/log/pix06A/060926-Eliot.gif” cannot be displayed, because it contains errors.

From The Man in the High Castle:

“Juliana said, ‘Oracle, why did you write The Grasshopper Lies Heavy? What are we supposed to learn?’

‘You have a disconcertingly superstitious way of phrasing your question,’ Hawthorne said. But he had squatted down to witness the coin throwing. ‘Go ahead,’ he said; he handed her three Chinese brass coins with holes in the center. ‘I generally use these.’

She began throwing the coins; she felt calm and very much herself. Hawthorne wrote down her lines for her. When she had thrown the coins six times, he gazed down and said:

‘Sun at the top. Tui at the bottom. Empty in the center.’

‘Do you know what hexagram that is?’ she said. ‘Without using the chart?’

‘Yes,’ Hawthorne said.

‘It’s Chung Fu,’ Juliana said. ‘Inner Truth. I know without using the chart, too. And I know what it means.'”

The image “http://www.log24.com/log/pix06A/060926-Lady.gif” cannot be displayed, because it contains errors.

Our Lady of
Judgment Day

“One of the illusions is that the present hour is not the critical, decisive hour. Write it on your heart that every day is the best day in the year. No man has learned anything rightly until he knows that every day is Doomsday.”

Emerson, Ch. VII, “Works and Days,” in The Complete Works of Ralph Waldo Emerson, Vol. VII, Society and Solitude (1870)

Sunday, September 10, 2006

Sunday September 10, 2006

Filed under: General,Geometry — Tags: , , — m759 @ 4:00 am

And the
"
Meet Max Black"
Award goes to…

The image “http://www.log24.com/log/pix06A/060910-Obits.jpg” cannot be displayed, because it contains errors.

"For the Aeron and other designs,
Mr. Stumpf won this year’s
National Design Award
in Product Design
,
which is to be presented
posthumously on Oct. 18
by the Cooper-Hewitt
National Design Museum
in Manhattan."

— Today's New York Times

Stumpf died on August 30,
the date of the Log24 entry
"The Seventh Symbol."

Related material:

From
Geometry of the I Ching,
a chessboard:

I Ching chessboard (original 1989 arrangement)

From the
 National Design Museum:

The image “http://www.log24.com/log/pix06A/060910-DesignAwards.gif” cannot be displayed, because it contains errors.

 From Log24 on the
date of Stumpf's death,

The Seventh Symbol:

The image “http://www.log24.com/log/pix06A/060910-Box121.jpg” cannot be displayed, because it contains errors.

Pictorial version of
Hexagram 20,
Contemplation (View)

See also
Fearful Symmetry
and
Symmetry Framed.

Wednesday, August 30, 2006

Wednesday August 30, 2006

Filed under: General,Geometry — Tags: , — m759 @ 10:07 am
The Seventh Symbol:

A Multicultural Farewell

to a winner of the
Nobel Prize for Literature,
the Egyptian author of
The Seventh Heaven:
Supernatural Stories
 —

The image “http://www.log24.com/theory/images/GF64-63cycleA495.gif” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix06A/060830-SeventhSymbol.jpg” cannot be displayed, because it contains errors.

"Jackson has identified
the seventh symbol."
Stargate

Other versions of
the seventh symbol —

Chinese version:

The image “http://www.log24.com/log/pix06A/060830-hexagram20.gif” cannot be displayed, because it contains errors.

pictorial version:

The image “http://www.log24.com/log/pix06A/060830-Box.jpg” cannot be displayed, because it contains errors.

algebraic version:

The image “http://www.log24.com/log/pix06A/060830-Algebra.jpg” cannot be displayed, because it contains errors.

"… Max Black, the Cornell philosopher, and others have pointed out how 'perhaps every science must start with metaphor and end with algebra, and perhaps without the metaphor there would never have been any algebra' …."

— Max Black, Models and Metaphors, Cornell U. Press, 1962, page 242, as quoted in Dramas, Fields, and Metaphors, by Victor Witter Turner, Cornell U. Press, paperback, 1975, page 25

Monday, August 28, 2006

Monday August 28, 2006

Filed under: General,Geometry — Tags: — m759 @ 1:00 am
Today's Sinner:

Augustine of Hippo, who is said to
have died on this date in 430 A.D.

"He is, after all, not merely taking over a Neoplatonic ontology, but he is attempting to combine it with a scriptural tradition of a rather different sort, one wherein the divine attributes most prized in the Greek tradition (e.g. necessity, immutability, and atemporal eternity) must somehow be combined with the personal attributes (e.g. will, justice, and historical purpose) of the God of Abraham, Isaac, and Jacob."

Stanford Encyclopedia of Philosophy on Augustine

Here is a rather different attempt
to combine the eternal with the temporal:

 

The Eternal

Symbol of necessity,
immutability, and
atemporal eternity:

The image “http://www.log24.com/log/pix06A/060828-Cube.jpg” cannot be displayed, because it contains errors.

For details, see
finite geometry of
the square and cube
.

The Temporal

Symbol of the
God of Abraham,
Isaac, and Jacob:

The image “http://www.log24.com/log/pix06A/060828-Cloud.jpg” cannot be displayed, because it contains errors.

For details, see
Under God
(Aug. 11, 2006)

The eternal
combined with
the temporal:

 

Singer 63-cycle in the Galois field GF(64) used to order the I Ching hexagrams

Related material:

Hitler's Still Point and
the previous entry.
 

Friday, August 11, 2006

Friday August 11, 2006

Filed under: General — Tags: — m759 @ 11:07 pm

Under God

Adapted from August 7:

 The image “http://www.log24.com/log/pix06A/060811-Glyphs2.jpg” cannot be displayed, because it contains errors.

“Saomai, the Vietnamese name
for the planet Venus, was the
eighth major storm to hit China
during an unusually violent
typhoon season.”

AP online tonight 

Memorable Quotes 

Lieutenant Daniel Taylor:
Where the Hell is
this God of yours?
 
Forrest Gump:
[narrating]
It’s funny Lieutenant Dan
said that, ’cause right then,
God showed up.

 Wind and thunder:
the image of Increase.
Thus the superior man:
If he sees good,
he imitates it;
If he has faults,
he rids himself of them.

Hexagram 42 

For further details,
see
recent entries
(August 7-11)
and also

Symmetry and Change
In the Dreamtime
.

Update of 1:06 AM ET
from KHYI:

Mercy Now 
Written by Mary Gauthier

My father could use a little mercy now
The fruits of his labor
Fall and rot slowly on the ground
His work is almost over
It won’t be long and he won’t be around
I love my father, and he could use some mercy now

My brother could use a little mercy now
He’s a stranger to freedom
He’s shackled to his fears and doubts
The pain that he lives in is
Almost more than living will allow
I love my brother, and he could use some mercy now

My church and my country could use a little mercy now
As they sink into a poisoned pit
That’s going to take forever to climb out
They carry the weight of the faithful
Who follow them down
I love my church and country, and they could use some mercy now

Every living thing could use a little mercy now
Only the hand of grace can end the race
Towards another mushroom cloud
People in power, well
They’ll do anything to keep their crown
I love life, and life itself could use some mercy now

Yeah, we all could use a little mercy now
I know we don’t deserve it
But we need it anyhow
We hang in the balance
Dangle ‘tween hell and hallowed ground
Every single one of us could use some mercy now
Every single one of us could use some mercy now
Every single one of us could use some mercy now

Wednesday, August 9, 2006

Wednesday August 9, 2006

Filed under: General — m759 @ 10:00 pm

Night Listener
 
(See previous entry.)

Thanks to Natalie at
KHYI, 95.3 FM, Plano, Texas
(hard country music),
for just now playing
A Fine Line, by Radney Foster:

There’s a curve in the highway, just south of town
where a man has pulled over to figure life out
with only his concience and the lonesome sound
of diesels winding up grade
he’s got a wife and two kids, and they love him so
he’s got a woman down in georgia,
   and she’s startin’ to show
he’s damned if he leaves her,
   and he’s sure damned if he don’t
and he wonders how life got this way
cuase it’s a fine line in between right and wrong
yea he’s been crossing over that border
   way too long
he should’ve seen it coming at him
   right from the start
now there aint’ no escape from a broken heart
now the call of the highway is a powerful thing
like the pull of a lover, or a child in a swing
gave his heart to two women
   only one wears his ring
they’re both gonna have his babies now
so how do you confess,
   what words don’t explain
he never intended to cause this much pain
now he feels like a farmer
   who went praying for the rain
got more than he bargained from the clouds
[chorus]
he’ll turn his car around tonight,
   go home and try to face the truth
everyone involved’s getting hurt,
   now there aint nothing he can do
[chorus]

Wind and thunder:
the image of Increase.
Thus the superior man:
If he sees good,
he imitates it;
If he has faults,
he rids himself of them.

Hexagram 42

  (10:00:42 PM ET)

Update of 11:08 PM ET…

and, Natalie, for playing
Late Night Grande Hotel
just now, thanks big time.

Sunday, April 30, 2006

Sunday April 30, 2006

Filed under: General — m759 @ 1:11 am
Saturday Night
to Sunday Morning
John Kenneth Galbraith
died last evening
at 9:15 PM in
Cambridge, Mass.,
according to
news reports.
 
Related material:
  Hexagram 11
  Plato, Pegasus, and
  the Evening Star,
 
Time in the Rock.
The image “http://www.log24.com/log/pix06/060430-Galbraith.jpg” cannot be displayed, because it contains errors.
Brian Snyder/Reuters 

Galbraith
in 1998.

Wednesday, April 26, 2006

Wednesday April 26, 2006

Filed under: General — Tags: — m759 @ 3:09 pm
Charm
At Decision Time,
Colleges Lay On Charm
– Today’s New York Times

Also in today’s Times:

“‘Lestat,’ the maiden Broadway production of Warner Brothers Theater Ventures, is the third vampire musical to open in the last few years, and it seems unlikely to break the solemn curse that has plagued the genre. Directed by Robert Jess Roth from a book by Linda Woolverton, the show admittedly has higher aspirations and (marginally) higher production values than the kitschy ‘Dance of the Vampires’ (2002) and the leaden ‘Dracula: The Musical’ (2004), both major-league flops.” — Ben Brantley

Related material:

See Log24,
St. Patrick’s Day 2004:

“I faced myself that day with
the nonplused apprehension
of someone who has
come across a vampire
and has no crucifix in hand.”

— Joan Didion, “On Self-Respect,”
in Slouching Towards Bethlehem

“For every kind of vampire,
there is a kind of cross.”

— Thomas Pynchon,
  Gravity’s Rainbow

Hexagram 61: Inner Truth

Inner Truth,
Hexagram 61

See also

  Transylvania Bible School.

Wednesday, January 4, 2006

Wednesday January 4, 2006

Filed under: General,Geometry — Tags: , , — m759 @ 4:04 am
Dragon School

In memory of Humphrey Carpenter, author of The Inklings, who attended The Dragon School.  Carpenter died a year ago today.

From Log24 on Nov. 16, 2005:

 

Images

 

Adam Gopnik on C. S. Lewis in the New Yorker:

"Lewis began with a number of haunted images…."

"The best of the books are the ones… where the allegory is at a minimum and the images just flow."

"'Everything began with images,' Lewis wrote…."

The image “http://www.log24.com/log/pix05B/051116-Time.jpg” cannot be displayed, because it contains errors.

 

From Paul Preuss,
Broken Symmetries
(see previous entry):

"Mathematical relationships were enough to satisfy him, mere formal relationships which existed at all times, everywhere, at once.  It was a thin nectar, but he was convinced it was the nectar of the gods…."


From
Verbum Sat Sapienti?

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Escher's Verbum

The image “http://www.log24.com/theory/images/DTinvar246.jpg” cannot be displayed, because it contains errors.

Solomon's Cube


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Geometry of the I Ching

 

Tuesday, December 27, 2005

Tuesday December 27, 2005

Filed under: General — Tags: — m759 @ 12:11 pm
Dance of the Numbers
(continued)

The Pennsylvania lottery 
on St. Stephen's Day–

Midday: 105
Evening: 064

From a new
branch of theology, 
lottery hermeneutics:

See Log24, 1/05,
Death and the Spirit,

and the 64 hexagrams of
the box-style I Ching.

From the Wikipedia
article on hermeneutics:

"One prominent theme which arises in contemporary philosophical hermeneutics (i.e., the work of Hans-Georg Gadamer) is a serious calling into question of scientism. Scientism is the more or less unquestioned belief in the supremacy of the natural sciences when it comes to serving as models of knowledge. By calling scientism into question, hermeneutics is arguing for the legitimacy of (among other things) aesthetic, literary, spiritual, and philosophical knowledge, alongside (but not instead of) scientific knowledge."

Monday, December 26, 2005

Monday December 26, 2005

Filed under: General — Tags: — m759 @ 7:00 pm
Language Game on
Boxing Day

In the box-style I Ching
Hexagram 34,
The Power of the Great,
is represented by

  The image “http://www.log24.com/theory/images/Box34.gif” cannot be displayed, because it contains errors. .

Art is represented
by a box
(Hexagram 20,
Contemplation, View)

  The image “http://www.log24.com/theory/images/Box20.gif” cannot be displayed, because it contains errors. .

  And of course 
great art
is represented by
an X in a box.
(Hexagram 2,
The Receptive)

  The image “http://www.log24.com/theory/images/Box02.gif” cannot be displayed, because it contains errors. .

“… as a Chinese jar still   
Moves perpetually
 in its stillness”

“… at the still point,  
there the dance is.”

— T. S. Eliot 

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A Jungian on this six-line figure:

“They are the same six lines that exist in the I Ching…. Now observe the square more closely: four of the lines are of equal length, the other two are longer…. For this reason symmetry cannot be statically produced and a dance results.”
 
— Marie-Louise von Franz,
   Number and Time


For those who prefer
technology to poetry,
there is the Xbox 360.

(Today is day 360 of 2005.)

Sunday, December 11, 2005

Sunday December 11, 2005

Filed under: General — Tags: — m759 @ 10:00 pm
For Rita Moreno
on Her Birthday:

Sex and Art in
a Chinese Poem


In the box-style I Ching
Hexagram 34,
The Power of the Great,
is represented by

  The image “http://www.log24.com/theory/images/Box34.gif” cannot be displayed, because it contains errors. .

Art is represented
by a box
(Hexagram 20,
Contemplation, View)

  The image “http://www.log24.com/theory/images/Box20.gif” cannot be displayed, because it contains errors. .

  And of course 
great art
is represented by
an X in a box.
(Hexagram 2,
The Receptive)

  The image “http://www.log24.com/theory/images/Box02.gif” cannot be displayed, because it contains errors. .

The combination of these
three symbols may be viewed
as “Power in a  Box,” or,
according to some scholars,
“The Art of Great Sex.”
 
The image “http://www.log24.com/log/pix05/050310-hex.jpg” cannot be displayed, because it contains errors.

From Xinhua News Agency tonight:

Xbox 360 meets
cold shoulder in Japan
.

But in another time and place…

The image “http://www.log24.com/log/pix05B/051211-Rita21.jpg” cannot be displayed, because it contains errors.

 

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