Log24

Saturday, June 13, 2015

The Holy Field

Filed under: General,Geometry — m759 @ 7:45 pm

( A Chinese designation for the 3×3 square )

Monday, September 22, 2014

A Holy Cross for Brooklyn

Filed under: General — m759 @ 12:00 pm

Saturday night’s 9  PM post:

“Once again, Harvard defeats Holy Cross.”

That post quoted Joseph Campbell describing a

“… matrix of the cosmic process, whether in the macrocosm
or in a microcosmic field of manifestation.”

Related material —

Macrocosm:

Microcosmic field of manifestation:

Tuesday, March 30, 2010

Lie Groups for Holy Week

Filed under: General,Geometry — Tags: — m759 @ 1:01 pm

Great line reading in 'Angels and Demons'- 'The God PARTICLE?'

Deep Down Things: The Breathtaking Beauty of Particle Physics, by Bruce A. Schumm, Johns Hopkins University Press, hardcover, Oct. 20, 2004, pp. 94-95–

"In the early 1960s, a physicist at the California Institute of Technology by the name of Murray Gell-Mann interpreted the patterns observed in the emerging array of elementary particles as being due to a symmetry….

Gell-Mann's eightfold way was perhaps the first conscious application of the results of the pure mathematical field of group theory and, in particular, the theory of 'Lie groups,' to a problem in physics."

From the preface–

"I didn't come up with the title for this book. For that, I can thank the people at the Johns Hopkins University Press…. my only reservation about the title is that… it implies a degree of literacy to which I can't lay claim."

Amen.

Remedial reading for those who might have fallen for Schumm's damned nonsense–

 "Quantum Mechanics and Group Theory I," by Dallas C. Kennedy

Group Theory and Physics, by Shlomo Sternberg

Saturday, March 20, 2010

Field Theory

Filed under: General — Tags: , — m759 @ 12:29 pm

Parker’s Wake

A continuation of Wednesday’s “Field of Dreams” link

Internet Movie Database comment

“The Kid From Left Field” is a wonderful baseball film made in the early fifties and breathes the nostalgia of that time period. Child actor Billy Chapin becomes a batboy for the woeful Bisons (a copy of the old St. Louis Browns) and proceeds to inform the players of how they can correct their individual problems. Unbeknownst to the team, Chapin’s wisdom is from his father, a washed-up player who has become a peanut vendor and lacks confidence and courage– in spite of his obvious baseball knowledge. Pretty soon, Chapin becomes the nine year old manager of the team with dramatic results that bind father to son; you can’t help but root for the Bisons! A baseball fantasy– but filled with much innocence and charm.

“…dramatic results that bind father to son….”

Not to mention the Holy Ghost. See Fess Parker, who died Thursday, in the “Left Field” film and in an essay by Roger Cooke in the April Notices of the American Mathematical Society

Life on the Mathematical Frontier: Legendary Figures and Their Adventures

http://www.log24.com/log/pix10/100320-Field.jpg

Fess Parker in
“The Kid from Left Field,” 1953

Possible associative links between recent Log24 posts and the baseball theme of the April AMS Notices

  1. The film “Field of Dreams” mentioned above is a resurrection story.
  2. Wednesday’s link to simultaneous multiple-level associations leads to the Gameplayers of Zan cover that also appears in Thursday’s post. That cover deals with a resurrection myth in Gameplayers.
  3. The Finnegans Wake resurrection myth is mentioned in Wednesday’s post “Spring Training.”

Associative links, though entertaining, have of course their limitations in logical argument.

A notable recent example– Jon Stewart’s parody of Glenn Beck.

Wednesday, June 5, 2024

For a future Michael Crichton*—  The Tachikawa Hint

Filed under: General — Tags: — m759 @ 9:22 am

Hat tip to Peter Woit for quoting the above  yesterday.

* See Crichton in this  weblog and the solar Apollo symbols
of CBS Sunday Morning, which this week featured Crichton.

As an Apollo symbol, I prefer the Chinese "holy field" —
a ninefold square.

Monday, April 18, 2022

Iconic Simplicity

Filed under: General — Tags: , — m759 @ 11:38 am

An illustration from posts tagged Holy Field GF(3) —

IMAGE- Elementary Galois Geometry over GF(3)

See also a Log24 search for "Four Gods."

Tuesday, August 10, 2021

Ex Fano Apollinis

Filed under: General — Tags: , , , , — m759 @ 9:41 am
 

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.


"As a Chinese jar . . . ."
     — Four Quartets

 

Rosalind Krauss
in "Grids," 1979:

"If we open any tract– Plastic Art and Pure Plastic Art  or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.

Or, to take a more up-to-date example…."

"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
– The Club Dumas , 1993

"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
– Robert Plant, 1971

The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.

An example of the universal— or, according to Krauss,
a "staircase" to the universal— is the ninefold square:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo,
  the field of Reason…."
– John Outram, architect    

The "Katz" of the August 7 post Art Angles
is a product of Princeton's
Department of Art and Archaeology.

 

ART —

 

The Lo Shu as a Finite Space
 

ARCHAEOLOGY —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71

Saturday, July 3, 2021

Here, There, and Chicago

Filed under: General — Tags: , — m759 @ 9:07 pm

The above phrase "the intersection of storytelling and visual arts"
suggests a review . . .

Storytelling —

Visual arts —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

– The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71

A Midrash for Michener —

IMAGE- Marie-Louise von Franz on the 'field' that represents 'the structural outlines of the collective unconscious'

For a connection of the above "Holy Field"
with pure mathematics, see Coxeter's Aleph.

Tuesday, October 17, 2017

Plan 9 Continues

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

See also Holy Field in this journal.

Some related mathematics —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Analysis of the Lo Shu structure —

Structure of the 3×3 magic square:

4  9  2
3  5  7    decreased by 1 is
8  1  6

3  8  1
2  4  6
7  0  5

In base 3 —

10  22  01
02  11  20
21  00  12

As orthogonal Latin squares
(a well-known construction) —

1  2  0     0  2  1
0  1  2     2  1  0
2  0  1     1  0  2 .

— Steven H. Cullinane,
October 17, 2017

Friday, December 9, 2016

Sacred Space (continued)

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

See Plan 9 in this journal.

 The 3x3 square 

Monday, June 20, 2016

Sacred Space

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

For further background to this morning's post Plan 9 Continues,
see posts tagged Sacred Space

The 3x3 square .

Friday, May 27, 2016

Plan 9

Filed under: General — m759 @ 9:00 am

http://m759.net/wordpress/?tag=holy-field-gf3

Sunday, October 18, 2015

Coordinatization Problem

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

There are various ways to coordinatize a 3×3 array
(the Chinese "Holy Field'). Here are some —

See  Cullinane,  Coxeter,  and  Knight tour.

Sunday, July 12, 2015

Characteristica Universalis

Filed under: General — m759 @ 7:00 pm

From Wikipedia —

"Many Leibniz scholars… seem to agree that he intended
his characteristica universalis  … to be a form of … 
ideographic language. This was to be based on a
rationalised version of the 'principles' of Chinese characters…."

See as well O Nine,  Chinese Calligraphy, and Holy Field.

Friday, July 10, 2015

Without Border

Filed under: General — Tags: , — m759 @ 3:18 pm

The previous post's Holy Field symbol, 
with border removed, becomes the
Chinese character for "well."

See also The Lost Well.

Thursday, July 9, 2015

Man and His Symbols

Filed under: General,Geometry — m759 @ 2:24 pm

(Continued)

A post of July 7, Haiku for DeLillo, had a link to posts tagged "Holy Field GF(3)."

As the smallest Galois field based on an odd prime, this structure 
clearly is of fundamental importance.  

The Galois field GF(3)

It is, however, perhaps too  small  to be visually impressive.

A larger, closely related, field, GF(9), may be pictured as a 3×3 array

hence as the traditional Chinese  Holy Field.

Marketing the Holy Field

IMAGE- The Ninefold Square, in China 'The Holy Field'

The above illustration of China's  Holy Field occurred in the context of
Log24 posts on Child Buyers.   For more on child buyers, see an excellent
condemnation today by Diane Ravitch of the U. S. Secretary of Education.

Tuesday, July 7, 2015

Haiku for DeLillo*

Filed under: General — Tags: — m759 @ 4:23 pm

A music video that opens with remarks by Lawrence Ferlinghetti
at the Last Waltz concert (Thanksgiving Day, Nov. 25, 1976):

"Our Father, whose art's in heaven…" —

For other religious remarks from the above upload date,
Sept. 9, 2011, see Holy Field GF(3).

Click the above "ripple" image for a Grateful Dead haiku
quoted here on Sunday, July 5, 2015.

For another meditation from the second upload date above,
March 19, 2012, see some thoughts on the word "field."

IMAGE- Japanese character for 'field'

* For the title, see an excerpt from Point Omega .

Saturday, June 20, 2015

Conceptual Art for Basel

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

The previous post's link to The Lindbergh Manifesto
and Thursday's post on Basel-born artist Wolf Barth 
suggest the following —

See as well a June 14 New York Times
piece on Art Basel.

The logo of the University of Basel 

suggests a review of The Holy Field —

 .

Tuesday, May 12, 2015

Writing Well*

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

See Stevens + New Haven.

* The above figure may be viewed as
the Chinese “Holy Field” or as the
Chinese character for “Well
inscribed in a square.

Thursday, February 19, 2015

The Bluebird of Happiness

Filed under: General — m759 @ 12:48 pm

(Chinese style)

Tuesday, November 18, 2014

The Abacus Conundrum…

Filed under: General — Tags: — m759 @ 1:44 am

Continues.

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

Prequel from 1961 (click image for context):

Detail that may be interpreted as the Chinese
3×3 "Holy Field" and a Chinese temple bell—

"Ting-a-ling." — Kurt Vonnegut.

Thursday, November 13, 2014

Progressive Matrix

Filed under: General,Geometry — Tags: , — m759 @ 6:00 am

Yesterday's post and recent Hollywood news suggest
a meditation on a Progressive Matrix —

Oct. 12-14, 2005:

'A Poem for Pinter,' conclusion: 'Tick Tick Hash.'

'The Interpreter'-- Sean Penn to Nicole Kidman-- 'My Card.'

Click to enlarge.

"My card."

Structurally related images —

A sample Raven's Progressive Matrices  test item
(such items share the 3×3 structure of the hash symbol above):

IMAGE- Raven's Progressive Matrices item with symbols from Cullinane's box-style I Ching

Structural background —

Tuesday, October 21, 2014

Art as a Tool

Filed under: General,Geometry — Tags: — m759 @ 12:35 pm

Two news items on art as a tool:

Two Log24 posts related to the 3×3 grid, the underlying structure for China’s
ancient Lo Shu “magic” square:

Finally, leftist art theorist Rosalind Krauss in this journal
on AntiChristmas, 2010:

Which is the tool here, the grid or Krauss?

Saturday, May 17, 2014

It’s Time for You to…

Filed under: General,Geometry — m759 @ 11:30 pm

See the Field

“There have long been rumors of a mythical Ninth Element
that grants ultimate power to the Wizard who masters it.
The Order of Magick says there is no such thing. But….”

— Website of Magicka: The Ninth Element Novel

William Worthy in Beijing —

This journal on the date of Worthy’s death,
May 4, 2014, had a link to…

    The Holy Field

Sunday, May 4, 2014

Geometry for Scarlett

Filed under: General,Geometry — Tags: , , — m759 @ 11:16 am

Scarlett Johansson stars in a new film, "Lucy," due to be
released on August 8, directed by Luc Besson, auteur  of
The Fifth Element  (1997). In other pop culture…

 "There have long been rumors of a mythical Ninth Element
that grants ultimate power to the Wizard who masters it.
The Order of Magick says there is no such thing. But…."

— Website of Magicka: The Ninth Element Novel

See also, in this journal, Holy Field as well as Power of the Center.

Wednesday, March 26, 2014

Grid

Filed under: General — m759 @ 12:00 pm

For some context, see Holy Field
and Krauss Grid.

Tuesday, July 16, 2013

Child Buyers

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

The title refers to a classic 1960 novel by John Hersey.

“How do you  get young people excited about space?”

— Megan Garber in The Atlantic , Aug. 16, 2012
(Italics added.) (See previous four posts.)

Allyn Jackson on “Simplicity, in Mathematics and in Art,”
in the new August 2013 issue of Notices of the American
Mathematical Society

“As conventions evolve, so do notions of simplicity.
Franks mentioned Gauss’s 1831 paper that
established the respectability of complex numbers.”

This suggests a related image by Gauss, with a
remark on simplicity—

IMAGE- Complex Grid, by Gauss

Here Gauss’s diagram is not, as may appear at first glance,
a 3×3 array of squares, but is rather a 4×4 array of discrete
points (part of an infinite plane array).

Related material that does  feature the somewhat simpler 3×3 array
of squares, not  seen as part of an infinite array—

Marketing the Holy Field

IMAGE- The Ninefold Square, in China 'The Holy Field'

Click image for the original post.

For a purely mathematical view of the holy field, see Visualizing GL(2,p).

Sunday, October 21, 2012

Multispeech

Filed under: General — m759 @ 9:00 pm

IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

     Click image above
     for some background.

IMAGE- Snow White Imprisoned- An image for the Snow Queen

IMAGE- Charlize Theron as Ravenna: 'She drifted.'

Saturday, June 2, 2012

Matrix Problem Revolutions

Filed under: General — m759 @ 1:28 am

(The sequel to yesterday's Matrix Problem Reloaded)

Wikipedia on the sci-fi weblog  io9.com

Newitz explained the significance of the name "io9":

"Well, io9s are input-output devices that let you see into the future.
They're brain implants that were outlawed because they drove
anyone who used one insane. We totally made that (device) up
to name the blog."

Jenna Wortham at wired.com, Jan. 2, 2008

From io9.com itself—

"Science fiction writer Ken MacLeod has another term for io9ers.
He calls them rapture fuckers.*"

— io9.com/explanations/

For the relevance of the term "revolutions" in this post's title, see
Wikipedia on Ken MacLeod.

I prefer to associate the number 9 with The Holy Field.

 

 

* MacLeod used this phrase in one of his novels, Newton's Wake.

Saturday, March 24, 2012

The David Waltz…

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

In Turing's Cathedral

"At the still point…" — T. S. Eliot

In memory of David L. Waltz, artificial-intelligence pioneer,
who died Thursday, March 22, 2012—

  1. The Log24 post of March 22 on the square-triangle theorem
  2. The March 18 post, Square-Triangle Diamond
  3. Remarks from the BBC on linguistic embedding
    that begin as follows—
         "If we draw a large triangle and embed smaller triangles in it,
          how does it look?"—
    and include discussion of a South American "tribe called Piranha" [sic ]
  4. The result of a Cartoon Bank search suggested by no. 3 above—
    (Click image for some related material.)
  5. A suggestion from the Cartoon Bank—
    IMAGE- 'Try our new grid view.'
  6. The following from the First of May, 2010

    The Nine Divisions of Heaven–

    Image-- Routledge Encyclopedia of Taoism, Vol. I, on the Nine Heavens, 'jiutian,' ed. by Fabrizio Pregadio

    Some context–

    IMAGE- The 3x3 ('ninefold') square as Chinese 'Holy Field'

    "This pattern is a square divided into nine equal parts.
    It has been called the 'Holy Field' division and
    was used throughout Chinese history for many
    different purposes, most of which were connected
    with things religious, political, or philosophical."

    – The Magic Square: Cities in Ancient China,
    by Alfred Schinz, Edition Axel Menges, 1996, p. 71

  7. The phrase "embedding the stone" —

Sunday, January 22, 2012

Year of the Dragon

Filed under: General — Tags: — m759 @ 3:33 pm

In China, the Year of the Dragon
has now begun. See Holy Field
in this journal.

Thursday, November 3, 2011

The China Conundrum

Filed under: General — m759 @ 5:48 pm
 
 

http://www.log24.com/log/pix11C/111103-3x3favicon-BlowupTo256w.bmp

The Holy Field

http://www.log24.com/log/pix11C/111103-ChinaConundrum-240w.jpg

"Buckle up!" — Harlan Kane, in the spirit of strategic stupidity.

Saturday, May 1, 2010

An Education

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

天鈞

 

Made famous by Ursula K. Le Guin
as the book title "Lathe of Heaven,"
this Chinese phrase, tianjun, apparently
means something more like "Scales of Heaven"–
an appropriate image for Law Day 2010.

Image--Scales (the legal symbol)

An anonymous forum user says that

"…if you switch the two characters around,
you get: 鈞天, which is one of
the nine heavens, more specifically,
the middle heaven."

This is supported by a
non-anonymous source:

"I follow A.C. Graham’s translation of
Juntian as 'Level Heaven (the innermost
of the nine divisions of heaven)';
he renders Juntian guangyue as
'the mighty music of the innermost heaven.'"

— "Music in the World of Su Shi (1037-1101):
Terminology
," by Stuart H. Sargent,
Colorado State University,
Journal of Sung-Yuan Studies 32 (2002), 39-81

The Nine Divisions of Heaven–

Image-- Routledge Encyclopedia of Taoism, Vol. I, on the Nine Heavens, 'jiutian,' ed. by Fabrizio Pregadio

Some context–

The 3x3 ('ninefold') square

"This pattern is a square divided into nine equal parts.
It has been called the 'Holy Field' division and
was used throughout Chinese history for many
different purposes, most of which were connected
with things religious, political, or philosophical."

The Magic Square: Cities in Ancient China,
by Alfred Schinz, Edition Axel Menges, 1996, p. 71

Sunday, September 22, 2024

Seattle Jam

Filed under: General — Tags: — m759 @ 9:11 am
 

CBS Sunday Morning today suggests a review of an old post featuring Pearl Jam. From that post . . .

Mathematics and Narrative, continued…

Out of What Chaos, a novel by Lee Oser

"This book is more or less what one would expect if Walker Percy wrote about a cynical rock musician who converts to Catholicism, and then Nabokov added some of his verbal pyrotechnics, and then Buster Keaton and the Marquis de Sade and Lionel Trilling inserted a few extra passages. It is a loving and yet appalled description of the underground music scene in the Pacific Northwest. And it is a convincing representation of someone very, very smart."

Matt Greenfield in The Valve

"If Evelyn Waugh had lived amid the American Northwest rock music scene, he might have written a book like this."

–Anonymous Amazon.com reviewer

A possible source for Oser's title–

"…Lytton Strachey described Pope's theme as 'civilization illumined by animosity; such was the passionate and complicated material from which he wove his patterns of balanced precision and polished clarity.' But out of what chaos did that clarity and precision come!"

Authors at Work, by  Herman W. Liebert and Robert H. Taylor, New York, Grolier Club, 1957, p. 16

Wednesday, August 18, 2021

What’s in a Name?

Filed under: General — Tags: — m759 @ 10:38 am

"Third Man – an elderly American railway bum,
a schizophrenic, speaks with a Southern drawl"

"Art to which I fix my celebrated signature."

— "Third Man" in Victor Snaith's play "Changing Stations"

"Snaithing  may thus be Smallfield . . . ."

Sunday, April 7, 2019

Block Talk

Filed under: General — Tags: — m759 @ 5:48 am

David Brooks in The New York Times  Sunday  Review   today

" 'In the deeps are the violence and terror of which psychology 
has warned us,' Annie Dillard writes in 'Teaching a Stone to Talk.' 
'But if you ride these monsters deeper down, if you drop with them
farther over the world’s rim, you find what our sciences cannot locate 
or name, the substrate, the ocean or matrix or ether which buoys
the rest, which gives goodness its power for good, and evil its power
for evil, the unified field: our complex and inexplicable caring for
each other.' "

Annie Dillard on the legendary philosopher's stone

“… if Holy the Firm is matter at its dullest, Aristotle’s materia prima ,
absolute zero, and since Holy the Firm is in touch with the Absolute
at base, then the circle is unbroken.  And it is…. Holy the Firm is
in short the philosopher’s stone.”

See also "The Thing and I."

Tuesday, October 11, 2016

Noto*

Filed under: General — m759 @ 12:00 pm
 

http://www.mirror.co.uk/news/world-news/
what-is-yom-kippur-2016-8946596

On the 10th day of the Jewish month of Tishri comes Yom Kippur, meaning the 'Day of Atonement'. It's the holiest day of the year.

To mark the 'Sabbath of Sabbaths', Jews fast for 25 hours and pray devoutly for most of the day, with five different sessions – Maariv, Shacharit, Musaf, Minchah and Neilah. [Link added.]

When is Yom Kippur?

Yom Kippur 2016 is a one day celebration. The holy event begins in the evening of Tuesday, October 11 and ends in the evening of Wednesday, October 12.

* For the title, see yesterday's post "Noto."   See also yesterday's
  "Saturday Dialectics." For further background, see an October 2 
  Rosh Hashanah piece in Politico Magazine  by Ben Wofford. 
  From "Saturday Dialectics" —

"You know that it would be untrue
You know that I would be a liar
If I was to say to you
Girl, we couldn't get much higher"

Song written by Robby KriegerThe Doors
(album produced by Paul A. Rothchild)

Saturday, June 11, 2016

Café Society

Filed under: General — m759 @ 9:00 pm

A post linked to here at 9 AM on May 27, 2016 —

Sunday, June 21, 2015

Sermon

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

Saturday, December 22, 2012

Web Links:

Filed under: General,Geometry — m759 @ 5:01 pm

Spidey Goes to Church

More realistically

  1. "Nick Bostrom is a Swedish philosopher at 
    St. Cross College, University of Oxford…."
  2. "The early location of St Cross was on a site in
    St Cross Road, immediately south of St Cross Church."
  3. "The church building is located on St Cross Road
    just south of Holywell Manor."
  4. "Balliol College has had a presence in the area since
    the purchase by Benjamin Jowett, the Master, in the 1870s
    of the open area which is the Balliol sports ground
    'The Master's Field.' "
  5. Leaving Wikipedia, we find a Balliol field at Log24:
  6. A different view of the same field, from 1950—
    .
  7. A view from 1974, thanks to J. J. Seidel — 
  8. Yesterday's Analogies.

Sunday, December 9, 2012

Eve’s Menorah

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

"Now the serpent was more subtle
than any beast of the field…."
Genesis 3:1

"“The serpent’s eyes shine
As he wraps around the vine….”
Don Henley

"Nine is a vine."
Folk rhyme

Part I

Part II

Part III

Halloween 2005

The image “http://log24.com/log/pix03/030109-gridsmall.gif” cannot be displayed, because it contains errors.

Click images for some background.

Saturday, April 28, 2012

Sprechen Sie Deutsch?

Filed under: General,Geometry — m759 @ 10:48 am

A Log24 post, "Bridal Birthday," one year ago today linked to
"The Discrete and the Continuous," a brief essay by David Deutsch.

From that essay—

"The idea of quantization—
the discreteness of physical quantities
turned out to be immensely fruitful."

Deutsch's "idea of quantization" also appears in
the April 12 Log24 post Mythopoetic

"Is Space Digital?" 

— Cover storyScientific American 
     magazine, February 2012

"The idea that space may be digital
  is a fringe idea of a fringe idea
  of a speculative subfield of a subfield."

— Physicist Sabine Hossenfelder 
     at her weblog on Feb. 5, 2012

"A quantization of space/time
 is a holy grail for many theorists…."

— Peter Woit in a comment 
      at his weblog on April 12, 2012

It seems some clarification is in order.

Hossenfelder's "The idea that space may be digital"
and Woit's "a quantization of space/time" may not
refer to the same thing.

Scientific American  on the concept of digital space—

"Space may not be smooth and continuous.
Instead it may be digital, composed of tiny bits."

Wikipedia on the concept of quantization—

Causal setsloop quantum gravitystring theory,
and 
black hole thermodynamics all predict
quantized spacetime….

For a purely mathematical  approach to the
continuous-vs.-discrete issue, see
Finite Geometry and Physical Space.

The physics there is somewhat tongue-in-cheek,
but the geometry is serious.The issue there is not
continuous-vs.-discrete physics , but rather
Euclidean-vs.-Galois geometry .

Both sorts of geometry are of course valid.
Euclidean geometry has long been applied to 
physics; Galois geometry has not. The cited
webpage describes the interplay of both  sorts
of geometry— Euclidean and Galois, continuous
and discrete— within physical space— if not
within the space of physics.

Thursday, April 12, 2012

Mythopoetic*

Filed under: General,Geometry — m759 @ 9:29 pm

"Is Space Digital?" 

Cover storyScientific American  magazine, February 2012

"The idea that space may be digital
  is a fringe idea of a fringe idea
  of a speculative subfield of a subfield."

— Physicist Sabine Hossenfelder
     at her weblog on Feb. 5, 2012

"A quantization of space/time
 is a holy grail for many theorists…."

— Peter Woit in a comment at his physics weblog today

See also 

* See yesterday's Steiner's Systems.

Saturday, April 7, 2012

Appeasing Epstein

Filed under: General — Tags: — m759 @ 7:14 pm

… On Holy Saturday

"'If only they could send us something grown-up… a sign or something.' 
And a sign does come from the outside. That night, unknown to the children,
a plane is shot down and its pilot parachutes dead to earth and is caught
in the rocks on the mountain. It requires no more than the darkness of night
together with the shadows of the forest vibrating in the signal fire to distort
the tangled corpse with its expanding silk 'chute into a demon that must
be appeased."

— Claire Rosenfield, 1961 essay about Lord of the Flies

Flies-related death from April 1

Edmund L. Epstein, Scholar Who Saved ‘Lord of the Flies,’ Dies at 80

See also Holy Saturday, 2004.

Thursday, January 26, 2012

Lamedvavnik

Filed under: General — m759 @ 9:57 am

NYT > Obituaries Dick Tufeld, Robot Voice in TV’s ‘Lost in Space,’ Dies at 85
    Wed Jan 25, 2012 23:42 from NYT Obituaries  By Bruce Weber

   "Mr. Tufeld possessed one of Hollywood’s most often-heard
   disembodied voices, especially from the 1950s through the 1970s."

In memoriam— A link from the date of Tufeld's death

Tuesday, January 10, 2012

Defining Form

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

(Continued from Epiphany and from yesterday.)

Detail from the current American Mathematical Society homepage

http://www.log24.com/log/pix12/120110-AMS_page-Detail.jpg

Further detail, with a comparison to Dürer’s magic square—

http://www.log24.com/log/pix12/120110-Donmoyer-Still-Life-Detail.jpg http://www.log24.com/log/pix12/120110-DurerSquare.jpg

The three interpenetrating planes in the foreground of Donmoyer‘s picture
provide a clue to the structure of the the magic square array behind them.

Group the 16 elements of Donmoyer’s array into four 4-sets corresponding to the
four rows of Dürer’s square, and apply the 4-color decomposition theorem.
Note the symmetry of the set of 3 line diagrams that result.

Now consider the 4-sets 1-4, 5-8, 9-12, and 13-16, and note that these
occupy the same positions in the Donmoyer square that 4-sets of
like elements occupy in the diamond-puzzle figure below—

http://www.log24.com/log/pix12/120110-DiamondPuzzleFigure.jpg

Thus the Donmoyer array also enjoys the structural  symmetry,
invariant under 322,560 transformations, of the diamond-puzzle figure.

Just as the decomposition theorem’s interpenetrating lines  explain the structure
of a 4×4 square , the foreground’s interpenetrating planes  explain the structure
of a 2x2x2 cube .

For an application to theology, recall that interpenetration  is a technical term
in that field, and see the following post from last year—

Saturday, June 25, 2011 

Theology for Antichristmas

— m759 @ 12:00 PM

Hypostasis (philosophy)

“… the formula ‘Three Hypostases  in one Ousia
came to be everywhere accepted as an epitome
of the orthodox doctrine of the Holy Trinity.
This consensus, however, was not achieved
without some confusion….” —Wikipedia

http://www.log24.com/log/pix11A/110625-CubeHypostases.gif

Ousia

Click for further details:

http://www.log24.com/log/pix11A/110625-ProjectiveTrinitySm.jpg

 

Sunday, June 19, 2011

Wednesday, January 6, 2010

Epiphany Revisited

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

January 06, 2007
ART WARS: Epiphany

Picture of Nothing
On Kirk Varnedoe’s
2003 Mellon Lectures,
Pictures of Nothing“–

“Varnedoe’s lectures were ultimately about faith, about his faith in the power of abstraction, and abstraction as a kind of anti-religious faith in itself….”

Related material:

The more industrious scholars will derive considerable pleasure from describing how the art-history professors and journalists of the period 1945-75, along with so many students, intellectuals, and art tourists of every sort, actually struggled to see the paintings directly, in the old pre-World War II way, like Plato’s cave dwellers watching the shadows, without knowing what had projected them, which was the Word.”

— Tom Wolfe, The Painted Word

Log24, Aug. 23, 2005:

“Concept (scholastics’ verbum mentis)–  theological analogy of Son’s procession  as Verbum Patris, 111-12″ — Index to Joyce and Aquinas, by William T. Noon, S.J., Yale University Press 1957,  second printing 1963, page 162

“So did God cause the big bang? Overcome by metaphysical lassitude, I finally reach over to my bookshelf for The Devil’s Bible. Turning to Genesis I read: ‘In the beginning there was nothing. And God said, ‘Let there be light!’ And there was still nothing, but now you could see it.'”
— Jim Holt, Big-Bang Theology, from Slate‘s “High Concept” department

'In the beginning' according to Jim Holt

“Bang.”

“…Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit. From their point of view, the grid is a staircase to the Universal….”

For properties of the “nothing” represented by the 3×3 grid, see The Field of Reason. For religious material related to the above and to Epiphany, a holy day observed by some, see Plato, Pegasus, and the Evening Star and Shining Forth.


Some Context:

Quaternions in Finite Geometry

Click to enlarge.

See also Nativity.

Thursday, December 3, 2009

Out of What Chaos

Filed under: General — Tags: — m759 @ 2:28 pm

Mathematics and Narrative, continued…

Out of What Chaos, a novel by Lee Oser

"This book is more or less what one would expect if Walker Percy wrote about a cynical rock musician who converts to Catholicism, and then Nabokov added some of his verbal pyrotechnics, and then Buster Keaton and the Marquis de Sade and Lionel Trilling inserted a few extra passages. It is a loving and yet appalled description of the underground music scene in the Pacific Northwest. And it is a convincing representation of someone very, very smart."

Matt Greenfield in The Valve

"If Evelyn Waugh had lived amid the American Northwest rock music scene, he might have written a book like this."

–Anonymous Amazon.com reviewer

A possible source for Oser's title–

"…Lytton Strachey described Pope's theme as 'civilization illumined by animosity; such was the passionate and complicated material from which he wove his patterns of balanced precision and polished clarity.' But out of what chaos did that clarity and precision come!"

Authors at Work, by  Herman W. Liebert and Robert H. Taylor, New York, Grolier Club, 1957, p. 16

Related material:

Unthought Known

Pearl Jam 'Backspacer' album released Sept. 20, 2009

and the

Catholic Analyst's Couch, White Cube Gallery, 2002

White Cube Gallery, 2002

Saturday, January 6, 2007

Saturday January 6, 2007

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


Picture of Nothing

On Kirk Varnedoe’s
2003 Mellon Lectures,
Pictures of Nothing“–

“Varnedoe’s lectures were ultimately
about faith, about his faith in
the power of abstraction,
and abstraction as a kind of
anti-religious faith in itself….”

The Washington Post

Related material:

The more industrious scholars
will derive considerable pleasure
from describing how the art-history
professors and journalists of the period
1945-75, along with so many students,
intellectuals, and art tourists of every
sort, actually struggled to see the
paintings directly, in the old
pre-World War II way,
like Plato’s cave dwellers
watching the shadows, without
knowing what had projected them,
which was the Word.”

— Tom Wolfe, The Painted Word

Log24, Aug. 23, 2005:

“Concept (scholastics’ verbum mentis)–
theological analogy of Son’s procession
as Verbum Patris, 111-12″

— Index to Joyce and Aquinas,
by William T. Noon, S.J.,
Yale University Press 1957,
second printing 1963, page 162

“So did God cause the big bang?
Overcome by metaphysical lassitude,
I finally reach over to my bookshelf
for The Devil’s Bible.
Turning to Genesis I read:
‘In the beginning
there was nothing.
And God said,
‘Let there be light!’
And there was still nothing,
but now you could see it.'”

— Jim Holt, Big-Bang Theology,
Slate‘s “High Concept” department

The image “http://www.log24.com/log/pix07/070106-Bang.jpg” cannot be displayed, because it contains errors.


“Bang.”

“…Mondrian and Malevich
are not discussing canvas
or pigment or graphite or
any other form of matter.
They are talking about
Being or Mind or Spirit.
From their point of view,
the grid is a staircase
to the Universal….”

Rosalind Krauss, “Grids”

For properties of the
“nothing” represented
by the 3×3 grid, see
The Field of Reason.

For religious material related
to the above and to Epiphany,
a holy day observed by some,
see Plato, Pegasus, and the
Evening Star
and Shining Forth.

Thursday, September 28, 2006

Thursday September 28, 2006

Filed under: General,Geometry — Tags: , — m759 @ 9:15 am
A Table

From the diary
of John Baez:

September 22, 2006

… Meanwhile, the mystics beckon:

Out beyond ideas of wrongdoing and rightdoing, there is a field. I’ll meet you there. – Rumi

September 23, 2006

I’m going up to San Rafael (near the Bay in Northern California) to visit my college pal Bruce Smith and his family. I’ll be back on Wednesday the 27th, just in time to start teaching the next day.

A check on the Rumi quote yields
this, on a culinary organization:

“Out beyond rightdoing and wrongdoing there is a field.  I’ll meet you there.”

This is the starting place of good spirit for relationship healing and building prescribed centuries ago in the Middle East by Muslim Sufi teacher and mystic, Jelaluddin Rumi (1207-1273).

Even earlier, the Psalmists knew such a meeting place of adversaries was needed, sacred and blessed:

“Thou preparest a table before me in the presence of mine enemies….” (23rd Psalm)

A Field and a Table:

The image “http://www.log24.com/theory/GF8-Table.gif” cannot be displayed, because it contains errors.

From “Communications Toolbox”
at MathWorks.com

For more on this field
in a different context, see
Generating the Octad Generator
and
“Putting Descartes Before Dehors”
in my own diary for December 2003.

The image “http://www.log24.com/log/pix06A/060928-Descartes.jpg” cannot be displayed, because it contains errors.
Descartes



Après l’Office à l’Église
de la Sainte-Trinité, Noël 1890

(After the Service at Holy Trinity Church,
Christmas 1890), Jean Béraud

Let us pray to the Holy Trinity that
San Rafael guides the teaching of John Baez
this year.  For related material on theology
and the presence of enemies, see Log24 on
  the (former) Feast of San Rafael, 2003.

Wednesday, July 5, 2006

Wednesday July 5, 2006

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

Solemn Dance
 
Virgil on the Elysian Fields:

  Some wrestle on the sands, and some in play
  And games heroic pass the hours away.
  Those raise the song divine, and these advance
  In measur'd steps to form the solemn dance.

(See also the previous two entries.)
 

Bulletin of the
American
Mathematical Society,
July 2006 (pdf):

The image “http://www.log24.com/log/pix06A/060705-Dioph1.gif” cannot be displayed, because it contains errors.

"The cover of this issue of the Bulletin is the frontispiece to a volume of Samuel de Fermat’s 1670 edition of Bachet’s Latin translation of Diophantus’s Arithmetica. This edition includes the marginalia of the editor’s father, Pierre de Fermat.  Among these notes one finds the elder Fermat’s extraordinary comment [c. 1637] in connection with the Pythagorean equation x2 + y2 = z2, the marginal comment that hints at the existence of a proof (a demonstratio sane mirabilis) of what has come to be known as Fermat’s Last Theorem."

— Barry Mazur, Gade University Professor at Harvard

Mazur's concluding remarks are as follows:
 

"But however you classify the branch of mathematics it is concerned with, Diophantus’s Arithmetica can claim the title of founding document, and inspiring muse, to modern number theory. This brings us back to the goddess with her lyre in the frontispiece, which is the cover of this issue. As is only fitting, given the passion of the subject, this goddess is surely Erato, muse of erotic poetry."

Mazur has admitted, at his website, that this conclusion was an error:

"I erroneously identified the figure on the cover as Erato, muse of erotic poetry, but it seems, rather, to be Orpheus."

"Seems"? 

The inscription on the frontispiece, "Obloquitur numeris septem discrimina vocum," is from a description of the Elysian Fields in Virgil's Aeneid, Book VI:

  His demum exactis, perfecto munere divae,
  Devenere locos laetos, & amoena vireta
  Fortunatorum nemorum, sedesque beatas.
  Largior hic campos aether & lumine vestit
  Purpureo; solemque suum, sua sidera norunt.
  Pars in gramineis exercent membra palaestris,
  Contendunt ludo, & fulva luctanter arena:
  Pars pedibus plaudunt choreas, & carmina dicunt.
  Necnon Threicius longa cum veste sacerdos
  Obloquitur numeris septem discrimina vocum:
  Jamque eadem digitis, jam pectine pulsat eburno.
PITT:

  These rites compleat, they reach the flow'ry plains,
  The verdant groves, where endless pleasure reigns.
  Here glowing AEther shoots a purple ray,
  And o'er the region pours a double day.
  From sky to sky th'unwearied splendour runs,
  And nobler planets roll round brighter suns.
  Some wrestle on the sands, and some in play
  And games heroic pass the hours away.
  Those raise the song divine, and these advance
  In measur'd steps to form the solemn dance.
  There Orpheus graceful in his long attire,
  In seven divisions strikes the sounding lyre;
  Across the chords the quivering quill he flings,
  Or with his flying fingers sweeps the strings.

DRYDEN:

  These holy rites perform'd, they took their way,
  Where long extended plains of pleasure lay.
  The verdant fields with those of heav'n may vie;
  With AEther veiled, and a purple sky:
  The blissful seats of happy souls below;
  Stars of their own, and their own suns they know.
  Their airy limbs in sports they exercise,
  And on the green contend the wrestlers prize.
  Some in heroic verse divinely sing,
  Others in artful measures lead the ring.
  The Thracian bard surrounded by the rest,
  There stands conspicuous in his flowing vest.
  His flying fingers, and harmonious quill,
  Strike seven distinguish'd notes, and seven at once they fill.

It is perhaps not irrelevant that the late Lorraine Hunt Lieberson's next role would have been that of Orfeo in Gluck's "Orfeo ed Euridice."  See today's earlier entries.

The poets among us may like to think of Mazur's own role as that of the lyre:

"You are the words,
I am the tune;
Play me."

Neil Diamond    

Sunday, June 18, 2006

Sunday June 18, 2006

Filed under: General — m759 @ 7:59 am
Father’s Day

For Mel Gibson,
who may or may not
see a parallel here.

IMDb Trivia for Music Box (1989)

  • After the movie was released, screenwriter Joe Eszterhas‘s own father Istvan Eszterhas was accused of war crimes in Hungary by printing anti-Semitic editorials and even organizing a book burning.
  • Both Kirk Douglas and Walter Matthau wanted to play the father….
Once a son,
now a father:

The image “http://www.log24.com/log/pix06A/060618-Eszterhas.gif” cannot be displayed, because it contains errors.

“He spent his earliest years in post WWII–refugee camps. He came to America and grew up in Cleveland–stealing cars, rolling drunks, battling priests, nearly going to jail. He became the screenwriter of the worldwide hits Basic Instinct, Jagged Edge, and Flashdance. He also wrote the legendary disasters Showgirls and Jade. The rebellion never ended, even as his films went on to gross more than a billion dollars at the box office and he became the most famous–or infamous–screenwriter in Hollywood. Joe Eszterhas is a complex and paradoxical figure: part outlaw and outsider combined with equal parts romantic and moralist. More than one person has called him ‘the devil.’ He has been referred to as ‘the most reviled man in America.’ But Time asked, ‘If Shakespeare were alive today, would his name be Joe Eszterhas?'”

Random House promotional material

And eventually to become
a holy ghost…

“Yea, though I walk
through the valley of death
I will fear no evil,
for I am the meanest
son of a bitch
in the valley.”

Karl Cullinane

in The Silver Crown,
by Joel Rosenberg

Monday, February 27, 2006

Monday February 27, 2006

Filed under: General — Tags: , , — m759 @ 9:26 am

Sudden View

From John O'Hara's Birthday:

"We stopped at the Trocadero and there was hardly anyone there.  We had Lanson 1926.  'Drink up, sweet.  You gotta go some.  How I love music.  Frère Jacques, Cuernavaca, ach du lieber August.  All languages.  A walking Berlitz.  Berlitz sounds like you with that champagne, my sweet, or how you're gonna sound.'"

— John O'Hara, Hope of Heaven, Chapter 11, 1938

"And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance."

Acts, Chapter 2, Verse 4

"Lps. The keys to. Given! A way a lone a last a loved a long the

PARIS,
1922-1939."

— James Joyce, conclusion of Finnegans Wake

"Using illustrative material from religion, myth, and culture, he starts with the descent of the dove on Jesus and ends with the poetic ramblings of James Joyce."

Review of a biography of the Holy Spirit

Monica Potts in today's New York Times on Sybille Bedford:

"Though her works were not always widely popular, they inspired a deeply fervent following of committed admirers, starting with her first published work, A Sudden View, in 1953. Later retitled A Visit to Don Otavio, it was an account of her journey through Mexico."

… "I addressed him.  'Is Cuernavaca not below Mexico City?'
    'It is low.'
    'Then what is this?'  Another summit had sprung up above a curve.
    'At your orders, the Three Marias.'
    'What are the Three Marias?'
    'These.'
    Later, I learned from Terry that they were the three peaks by the La Cima Pass which is indeed one of the highest passes in the Republic; and still later from experience, that before running down to anywhere in this country one must first run up some six or seven thousand feet.  The descents are more alarming than the climbs.  We hurtled towards Cuernavaca down unparapeted slopes with the speed and angle, if not the precision, of a scenic railway– cacti flashed past like telegraph poles, the sun was brilliant, the air like laughing gas, below an enchanting valley, and the lack of brakes became part of a general allegro accelerando."

— Sybille Bedford, A Sudden View, Counterpoint Press, Counterpoint edition (April 2003), page 77

"How continually, how startlingly, the landscape changed!  Now the fields were full of stones: there was a row of dead trees.  An abandoned plough, silhouetted against the sky, raised its arms to heaven in mute supplication; another planet, he reflected again, a strange planet where, if you looked a little further, beyond the Tres Marias, you would find every sort of landscape at once, the Cotswolds, Windermere, New Hampshire, the meadows of the Eure-et-Loire, even the grey dunes of Cheshire, even the Sahara, a planet upon which, in the twinkling of an eye, you could change climates, and, if you cared to think so, in the crossing of a highway, three civilizations; but beautiful, there was no denying its beauty, fatal or cleansing as it happened to be, the beauty of the Earthly Paradise itself."

— Malcolm Lowry, Under the Volcano, Harper Perennial Modern Classics, 1st Perennial Classics edition (May 1, 2000), page 10

Friday, June 10, 2005

Friday June 10, 2005

Filed under: General — m759 @ 1:25 am

From Andrew Cusack’s weblog:

April 21, 2005

‘For Christ and Liberty’

Though [it is] a purely Protestant institution (literally), I am rather fond of Patrick Henry College. Indeed, it takes some courage in this day and age to only admit students willing to sign a ten-point profession of Protestant Reformed faith. They also happen to have an old-fashioned ball featuring ‘English country dancing, delicacies such as cream puffs and truffles and leisurely strolls about the scenic grounds of the historic Selma Plantation’.

Anyhow, the college, whose motto is ‘For Christ and Liberty’, was visited [by] Anthony Esolen, a contributing editor to Touchstone magazine, who makes these comments:

Today I received a request to write a short article on Pope Benedict XVI from a club called the De Tocqueville Society, in a small college in Northern Virginia.

That such a request came was no surprise. Its provenance is, and cheeringly so. For this De Tocqueville Society is made up of a group of students at the new Patrick Henry College, founded by Mike Farris, the President of the Home School Legal Defense Association. More than ninety percent of the college’s students were homeschooled. If there’s a Roman Catholic in the bunch, I’ve yet to hear about it, and I’ve been to that campus twice to give lectures. [Note: Esolen does not seem to be aware that PHC requires its students to be Protestant.]

More on that in a moment. I could spend all evening singing the praises of PHC (as the students fondly call it), but let me share one discovery I made that should gratify Touchstone readers. The first time I spoke there, two years ago, I was stunned to meet young men and women who—who were young men and women. I am not stretching the truth; go to Purcellville and see it for yourselves if you doubt it; I believe my wife took a couple of pictures, just to quiet the naysayers. The young men stand tall and look you in the eye—they don’t skulk, they don’t scowl and squirm uncomfortably in the back chairs as they listen to yet another analysis of Rebecca of Sunnybrook Farm, or one of the healthier poems of Sylvia Plath. They’re frank and generous and respectful, but they hold their own in an argument, and they are eager to engage you in those. They are comfortable in their skins; they wear their manhood easily. And the young ladies are beautiful. They don’t wither away in class, far from it; but they wear skirts, they are modest in their voices and their smiles, they clearly admire the young men and are esteemed in turn; they are like creatures from a faraway planet, one sweeter and saner than ours.

Two years ago I spoke to them about medieval Catholic drama. They are evangelicals, half of them majors in Government, the rest, majors in Liberal Arts. They kept me and my wife in that room for nearly three hours after the talk was over. “Doctor Esolen, what you say about the habits of everyday life—to what extent is it like what Jean Pierre de Coussade calls ‘the sacrament of the present moment’?” “Doctor Esolen, do you see any connections between the bodiliness of this drama and the theology of Aleksandr Schmemann?” “Doctor Esolen, you have spoken a great deal about our recovery of a sense of beauty, but don’t you think that artists can also use the grotesque as a means of bringing people to the truth?” “You’ve suggested to us that Christians need to reclaim the Renaissance as our heritage, yet we are told that that was an age of the worship of man for his own sake. To what extent is the art of that period ours to reclaim?” And on and on, until nearly midnight.

The questions were superior to any that I have ever heard from a gathering of professors—and alas, I’ve been to many of those. I mean not only superior in their enthusiasm and their insistence, but in their penetrating to the heart of the problem, their willingness to make connections apparently far afield but really quite apropos, and their sheer beauty—I can think of no better word for it.

A few weeks ago I was in town for another talk, on the resurrection of the body. The Holy Father had passed away. At supper, ten or fifteen of the students packed our table, to ask questions before the talk. They were reverent and extraordinarily well informed; most especially they were interested in the Theology of the Body. The questions on that topic continued after the lecture, and I had the same experience I’d had before, but now without the surprise.

And these are the young people who are devoting an entire issue of their journal to the thought of Cardinal Ratzinger, now the new head of the Roman Catholic Church. They are hungry to know about him; in the next week or two they will do what our slatternly tarts and knaves, I mean our journalists, have never done and will not trouble themselves to do, and that is to read what Benedict XVI has said, read it with due appreciation for their differences with him, and due deference to a holy and humble man called by Christ to be a light not only to Roman Catholics but to all the nations.

These students don’t know it, but in their devotion to their new school (they are themselves the guards, the groundskeepers, the janitors; they ‘own’ the school in a way that is hard to explain to outsiders), they live the community life extolled by Leo XIII in Rerum Novarum; in their steadfastness to the truth they are stalwart participators in the quest set out by John Paul II in Fides et Ratio; in their welcoming of me and, God bless them, of the good Benedict XVI, they live in the true spirit of Lumen Gentium, that greathearted document of the council so often invoked for the lame tolerance of every betrayal of the ancient faith. And for what it’s worth, they are readers of Touchstone Magazine.

Be silent, Greeleys and Dowds of the world. These young people have you whipped, if for no other reason than that they believe in the One who is Truth, and who sets us free. How can I praise these my young brothers and sisters any more highly? God bless them and Patrick Henry College. And the rest of us, let’s keep an eye on them. We’ll be seeing quite a harvest from that seedbed!

Many of the points Esolen commends are things I hope will be found in the colleges of my university when I get around to starting it. I particularly admire that Patrick Henry College’s young men and women are just that, according to Esolen. This is all too often hard to achieve in modern American higher education, where students are quite often just elderly adolescents. (Though I suspect this has more to do with parents and family than education).

The absurdist drinking age that the Federal government underhandedly coerced each state into passing hinders maturity as well. Indeed, when I start the first college or colleges of the university I’m planning, each will have a private college bar which will serve anyone over the age of 16 or so. (Probably at the barman or barmaid’s discretion). Civil disobedience is the only solution.

Though the graduates Patrick Henry College provides will be Protestant (at least at the time of their graduation), I have no doubt that they will act as leaven to raise up the social and political life of our United States. I’m not particularly fond that they proudly advertise their commendation as “One of America’s Top Ten Conservative Colleges”. I’m not of the view that colleges ought to be ‘conservative’ or ‘liberal’ per se. They ought to be seen more as communities of inquisitive, curious, intelligent people united in the quest for truth. Labels like ‘conservative’ and ‘liberal’ are far too narrow and allow the simple-minded to pidgeon-hole things which are too complex for such monikers.

But anyhow, cheers for Patrick Henry College.

Posted by Andrew Cusack at April 21, 2005 05:25 PM

Monday, October 18, 2004

Monday October 18, 2004

Filed under: General — Tags: — m759 @ 3:33 pm

Counting Crows
on the Feast of St. Luke

"In the fullness of time,
educated people will believe
there is no soul
independent of the body,
and hence no life after death."

Francis Crick, who was awarded
a Nobel Prize on this date in 1962

"She went to the men on the ground and looked at them and then she found Inman apart from them. She sat and held him in her lap. He tried to talk, but she hushed him. He drifted in and out and dreamed a bright dream of a home. It had a coldwater spring rising out of a rock, black dirt fields, old trees. In his dream, the year seemed to be happening all at one time, all the seasons blending together.  Apple trees hanging heavy with fruit but yet unaccountably blossoming, ice rimming the spring, okra plants blooming yellow and maroon, maple leaves red as October, corn crops tasseling, a stuffed chair pulled up to the glowing parlor hearth, pumpkins shining in the fields, laurels blooming on the hillsides, ditch banks full of orange jewelweed, white blossoms on dogwood, purple on redbud.  Everything coming around at once.  And there were white oaks, and a great number of crows, or at least the spirits of crows, dancing and singing in the upper limbs.  There was something he wanted to say."

— Charles Frazier, Cold Mountain

"FullnessMultitude."
 

Sunday, May 2, 2004

Sunday May 2, 2004

Filed under: General — m759 @ 2:00 am

Trinity Test

Some background on the previous entry, Honorable Bird….

A note on the Michael Douglas film in that previous entry:

“This film is not to be confused with Japanese director Shohei Imamura’s BLACK RAIN, which was produced around the same time. Imamura’s film deals with the lives of a Japanese family who survived the nuclear-bombing of Hiroshima. The phrase ‘black rain,’ used in both films, refers to the deadly fallout caused by the detonation of an atomic weapon.”

For related material on the religion of Trinity, see Hiroshima Mayor Says US Worships Nukes, a news story quoted in Death of a Holy Man (8/10/03).  The phrase “holy man” there is from John Steinbeck, who once wrote a sentence saying that sons of bitches, viewed from another perspective, are holy men.

Here is the death of another holy man, Clayton S. White, a medical researcher who developed the field of blast biology — the study of how nuclear explosions affect people immediately and over time.  This holy man died on April 26, 2004.  A log24 entry of that date supplies an appropriate epitaph for the holy man, dead at 91, who has now joined his younger brother, the late Supreme Court Justice Byron R. White, in some region of the afterworld.

Thursday, November 6, 2003

Thursday November 6, 2003

Filed under: General,Geometry — Tags: — m759 @ 2:00 pm

Legacy Codes:

The Most Violent Poem

Lore of the Manhattan Project:

From The Trinity Site

“I imagined Oppenheimer saying aloud,
‘Batter my heart, three person’d God,”
unexpectedly recalling John Donne’s ‘Holy Sonnet [14],’
and then he knew, ‘ “Trinity” will do.’
Memory has its reasons.

‘Batter my heart’ — I remember these words.
I first heard them on a fall day at Duke University in 1963.
Inside a classroom twelve of us were
seated around a long seminar table
listening to Reynolds Price recite this holy sonnet….

I remember Reynolds saying, slowly, carefully,
‘This is the most violent poem in the English language.’ ”

Related Entertainment

Today’s birthday:
director Mike Nichols

From a dead Righteous Brother:

“If you believe in forever
Then life is just a one-night stand.”

Bobby Hatfield, found dead
in his hotel room at
7 PM EST Wednesday, Nov. 5, 2003,
before a concert scheduled at
Western Michigan University, Kalamazoo
.

From a review of The Matrix Revolutions:

“You’d have to be totally blind at the end
to miss the Christian symbolism….
Trinity gets a glimpse of heaven…. And in the end…
God Put A Rainbow In The Clouds.”

Moral of the
Entertainment:

According to Chu Hsi [Zhu Xi],

“Li” is
“the principle or coherence
or order or pattern
underlying the cosmos.”

— Smith, Bol, Adler, and Wyatt,
Sung Dynasty Uses of the I Ching,
Princeton University Press, 1990

Related Non-Entertainment

Symmetry and a Trinity
(for the dotting-the-eye symbol above)

Introduction to Harmonic Analysis
(for musical and historical background)

Mathematical Proofs
(for the spirit of Western Michigan
University, Kalamazoo)

Moral of the
Non-Entertainment:

“Many kinds of entity
become easier to handle
by decomposing them into
components belonging to spaces
invariant under specified symmetries.”

The importance of
mathematical conceptualisation

by David Corfield,
Department of History and
Philosophy of Science,
University of Cambridge

See, too,
Symmetry of Walsh Functions and
Geometry of the I Ching.

Wednesday, August 6, 2003

Wednesday August 6, 2003

Filed under: General — Tags: , , — m759 @ 10:23 am

Postmodern
Postmortem

“I had a lot of fun with this audacious and exasperating book. … [which] looks more than a little like Greil Marcus’s Lipstick Traces, a ‘secret history’ tracing punk rock through May 1968….”

— Michael Harris, Institut de Mathématiques de Jussieu, Université Paris 7, review of Mathematics and the Roots of Postmodern Thought, by Vladimir Tasic, Notices of the American Mathematical Society, August 2003

For some observations on the transgressive  predecessors of punk rock, see my entry Funeral March of July 26, 2003 (the last conscious day in the life of actress Marie Trintignant — see below), which contains the following:

“Sky is high and so am I,
If you’re a viper — a vi-paah.”
The Day of the Locust,
    by Nathanael West (1939)

As I noted in another another July 26 entry, the disease of postmodernism has, it seems, now infected mathematics.  For some recent outbreaks of infection in physics, see the works referred to below.

Postmodern Fields of Physics: In his book The Dreams of Reason, H. R. Pagels focuses on the science of complexity as the most outstanding new discipline emerging in recent years….”

— “The Semiotics of ‘Postmodern’ Physics,” by Hans J. Pirner, in Symbol and Physical Knowledge: The Conceptual Structure of Physics, ed. by M. Ferrari and I.-O. Stamatescu, Springer Verlag, August 2001 

For a critical look at Pagels’s work, see Midsummer Eve’s Dream.  For a less critical look, see The Marriage of Science and Mysticism.  Pagels’s book on the so-called “science of complexity” was published in June 1988.  For more recent bullshit on complexity, see

The Critical Idiom of Postmodernity and Its Contributions to an Understanding of Complexity, by Matthew Abraham, 2000,

which describes a book on complexity theory that, besides pronouncements about physics, also provides what “could very well be called a ‘postmodern ethic.’ “

The book reviewed is Paul Cilliers’s Complexity and Postmodernism: Understanding Complex Systems.

A search for related material on Cilliers yields the following:

Janis Joplin, Postmodernist

” …’all’ is ‘one,’ … the time is ‘now’ and … ‘tomorrow never happens,’ …. as Janis Joplin says, ‘it’s all the same fucking day.’

It appears that ‘time,’ … the linear, independent notion of ‘time’ that our culture embraces, is an artifact of our abstract thinking …

The problem is that ‘tomorrow never happens’ …. Aboriginal traditionalists are well aware of this topological paradox and so was Janis Joplin. Her use of the expletive in this context is therefore easy to understand … love is never having to say ‘tomorrow.’ “

Web page citing Paul Cilliers

“That’s the dumbest thing I ever heard.”

— Ryan O’Neal in “What’s Up, Doc?”

A more realistic look at postmodernism in action is provided by the following news story:

Brutal Death of an Actress Is France’s Summertime Drama

By JOHN TAGLIABUE

The actress, Marie Trintignant, died Friday [Aug. 1, 2003] in a Paris hospital, with severe head and face injuries. Her rock star companion, Bertrand Cantat, is confined to a prison hospital….

According to news reports, Ms. Trintignant and Mr. Cantat argued violently in their hotel room in Vilnius in the early hours of [Sunday] July 27 at the end of a night spent eating and drinking….

In coming months, two films starring Ms. Trintignant are scheduled to debut, including “Janis and John” by the director Samuel Benchetrit, her estranged husband and the father of two of her four children. In it, Ms. Trintignant plays Janis Joplin.

New York Times of Aug. 5, 2003

” ‘…as a matter of fact, as we discover all the time, tomorrow never happens, man. It’s all the same f…n’ day, man!’ –Janis Joplin, at live performance in Calgary on 4th July 1970 – exactly four months before her death. (apologies for censoring her exact words which can be heard on the ‘Janis Joplin in Concert’ CD)”

Janis Joplin at FamousTexans.com

All of the above fits in rather nicely with the view of science and scientists in the C. S. Lewis classic That Hideous Strength, which I strongly recommend.

For those few who both abhor postmodernism and regard the American Mathematical Society Notices

as a sort of “holy place” of Platonism, I recommend a biblical reading–

Matthew 24:15, CEV:

“Someday you will see that Horrible Thing in the holy place….”

See also Logos and Logic for more sophisticated religious remarks, by Simone Weil, whose brother, mathematician André Weil, died five years ago today.

Tuesday, May 27, 2003

Tuesday May 27, 2003

Filed under: General,Geometry — Tags: — m759 @ 5:01 am

Mental Health Month, Day 27:

Conspiracy Theory and
Solomon's Seal

In our journey through Mental Health Month, we have now arrived at day 27. This number, the number of lines on a non-singular cubic surface in complex projective 3-space, suggests it may be time to recall the following note (a sort of syllabus for an imaginary course) from August 1997, the month that the Mel Gibson film "Conspiracy Theory" was released.

Conspiracy Theory 101
August 13, 1997

Fiction:

(A) Masks of the Illuminati, by Robert Anton Wilson, Pocket Books, New York, 1981.  Freemasonry meets The Force (starring James Joyce and Albert Einstein).
(B) The Number of the Beast, by Robert A. Heinlein, Ballantine Books, New York, 1980.  "Pantheistic multiple solipsism" and transformation groups in n-dimensional space combine to yield "the ultimate total philosophy." (p. 438). 
(C) The Essential Blake, edited by Stanley Kunitz, MJF Books, New York, 1987.  "Fearful symmetry" in context.

Fact:

(1) The Cosmic Trigger, by Robert Anton Wilson, Falcon Press, Phoenix, 1986 (first published 1977).  Page 245 reveals that "the most comprehensive conspiracy theory," that of the physicist Sir Arthur Eddington, is remarkably similar to Heinlein's theory in (B) above.
(2) The Development of Mathematics, by E. T. Bell, 2nd. ed., McGraw-Hill, New York, 1945.  See the discussion of "Solomon's seal," a geometric configuration in complex projective 3-space.  This is as good a candidate as any for Wilson's "Holy Guardian Angel" in (A) above.
(3) Finite Projective Spaces of Three Dimensions, by J. W. P. Hirschfeld, Clarendon Press, Oxford, 1985.  Chapter 20 shows how to represent Solomon's seal in the 63-point 5-dimensional projective space over the 2-element field.  (The corresponding 6-dimensional affine space, with 64 points, is reminiscent of Heinlein's 6-dimensional space.)
 

See also China's 3,000-year-old "Book of Transformations," the I Ching, for more philosophy and lore of the affine 6-dimensional space over the binary field.

© 1997 S. H. Cullinane 

For a more up-to-date and detailed look at the mathematics mentioned above, see

Abstract Configurations
in Algebraic Geometry
,

by Igor Dolgachev.

"Art isn't easy." — Stephen Sondheim

Sunday, September 15, 2002

Sunday September 15, 2002

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

Evariste Galois and 
The Rock That Changed Things

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

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

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

A table of parallels

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

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

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

Dr. Berman, G’mar Chatimah Tova.

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