Log24

Thursday, April 4, 2019

Expanding the Spielraum . . .

Filed under: General — Tags: — m759 @ 9:27 PM

Continues . . .

. . . with Stephen King.

Saturday, July 14, 2018

Expanding the Spiel

Filed under: General,Geometry — m759 @ 1:15 PM

(Continued)

Cube Dance

The walkerart.org passage above is from Feb. 17, 2011.

See also this  journal on Feb. 17, 2011

"…  Only by the form, the pattern,      
Can words or music reach
The stillness…."

— T. S. Eliot,
Four Quartets

For further details, see Time Fold.

Saturday, June 3, 2017

Expanding the Spielraum (Continued*)

Filed under: General,Geometry — Tags: — m759 @ 1:13 PM

Or:  The Square

"What we do may be small, but it has
 a certain character of permanence."
— G. H. Hardy

* See Expanding the Spielraum in this journal.

Wednesday, April 12, 2017

Expanding the Spielraum

Filed under: General,Geometry — Tags: , — m759 @ 9:48 AM

Cézanne's Greetings.

"Cézanne ignores the laws of classical perspective . . . ."

— Voorhies, James. “Paul Cézanne (1839–1906).”
In Heilbrunn Timeline of Art History .  New York:
The Metropolitan Museum of Art, 2000–. (October 2004)

Some others do not.

This is what I called "the large Desargues configuration
in posts of April 2013 and later.

Sunday, December 11, 2016

Expanding the Spielraum

Filed under: General — m759 @ 11:00 AM

(Continued)

Tony Stark's "little gray area" remark to Peter Parker 
in the previous post suggests an elementary calculation:

Compare to a remark from Wikipedia:

"This is the total area of
the 88 modern constellations 
in the sky."

— Wikipedia, Square degree

Wednesday, June 15, 2016

Expanding the Spielraum

Filed under: General — Tags: — m759 @ 2:40 PM

Continues

Rubik cube in the heading of the homepage of the Notices of the American Mathematical Society

"My AMS invited address at the SIAM Annual Meeting July 11–15
in Boston discusses the extension of eigenvectors and singular
vectors from matrices to higher order tensors."

Bernd Sturmfels in the June-July 2016 AMS Notices

See also Sturmfels in this  journal — for instance, in
"Expanding the Spielraum," a post of Feb. 3, 2015 —

Thursday, May 26, 2016

Expanding the Spielraum

Filed under: General — m759 @ 1:45 AM

(Continued)

The physicist Hendrik van Dam was mentioned in recent posts.

He reportedly died at 78 on February 11, 2013.

A post from that date, and a followup —

Saturday, April 9, 2016

Expanding the Spielfeld (continued)

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

"Mr. Conrad was relentless and rigorous in expanding
the parameters of the fields in which he worked."

The New York Times  today

See also Spielfeld in this  journal, as well as Conrad Moonshine.

Monday, October 26, 2015

Expanding the Seagram Spielraum

Filed under: General — m759 @ 11:20 PM

From the previous post, Expanding the Spielraum

"The knights and squires of nearby Ambras used to let their
steeds romp here, whence came the name Tummelplatz ." 

— Quelle: Ludwig von Hörmann, "Der Tummelplatz  bei Amras,"
in: Der Alpenfreund , 1. Band, Gera 1870, S. 72 – 73.

"Integrity, Craftsmanship, Tradition"

Expanding the Spielraum

Filed under: General — m759 @ 4:00 PM

(Continued)

Halloween meditation  on  the Tummelplatz  at Innsbruck

"Die Ritter und Knappen des nahegelegenen Ambras
pflegten hier ihre Rosse zu tummeln, woher sich auch
der Name Tummelplatz  schreibt."

"The knights and squires of nearby Ambras used to let their
steeds romp here, whence came the name Tummelplatz ." 

— Quelle: Ludwig von Hörmann, "Der Tummelplatz  bei Amras,"
in: Der Alpenfreund , 1. Band, Gera 1870, S. 72 – 73.

See as well Sigmund Freud, Erinnern, Wiederholen und Durcharbeiten
(1914) —

"Wir eröffnen ihm die Übertragung als den Tummel­platz ,
auf dem ihm gestattet wird, sich in fast völliger Freiheit
zu entfalten, und auferlegt ist, uns alles vorzuführen,
was sich an pathogenen Trieben im Seelenleben des
Analysierten verborgen hat."

"We admit it into the transference as a playground
in which it is allowed to expand in almost complete freedom
and in which it is expected to display to us everything in the
way of pathogenic instincts that is hidden in the patient's mind."

This passage has been discussed by later psychotherapists,
notably Russell Meares.  Dr. Meares, working from a translation
that has "playground" for Freud's Tummelplatz , uses Spielraum  
in place of Freud's own word.

For related material in this  journal, see Expanding the Spielraum.
An illustration from that search —

IMAGE- Concepts of Space

Friday, June 26, 2015

Expanding the Spielfeld*

Filed under: General — Tags: — m759 @ 2:45 PM

For TD Arena

See also Lincoln Alexander and posts in
this journal just before and on the date of
Alexander's death — Oct. 19, 2012.

* For the title, see Spielfeld posts.

Thursday, June 18, 2015

Expanding the Spielraum

Filed under: General — Tags: — m759 @ 2:25 PM

(Continued from Feb. 3, 2015)

IMAGE- Spielfeld (1982-83), by Wolf Barth

The above artist  Wolf Barth is not the same person
as the mathematician  Wolf Barth quoted in the 
previous post.  For further background on the artist, see
an article in Neue Zürcher Zeitung  from Nov. 15, 2013.

Saturday, April 18, 2015

Expanding the Spielraum

Filed under: General — Tags: — m759 @ 1:30 PM

Continues.

See also today's previous post and the new film "Beyond the Reach,"
filmed in northwest New Mexico —

IMAGE- Map of northwest New Mexico

Tuesday, February 3, 2015

Expanding the Spielraum

Filed under: General — Tags: , — m759 @ 11:00 AM

A short poem by several authors:

"The role of
the 16 singular points
on the Kummer surface
is now played by
the 64 singular points
on the Kummer threefold."

— From Remark 2.4 on page 9 of
"The Universal Kummer Threefold,"
by Qingchun Ren, Steven V Sam,
Gus Schrader, and Bernd Sturmfels,
http://arxiv.org/abs/1208.1229v3,
August 6, 2012 — June 12, 2013.

See also "Expanded Field" in this journal.

IMAGE- Concepts of Space

Illustration from "Sunday School," July 20, 2014.

Other Log24 background:  Kummer, Spielraum, Art Space.

Wednesday, December 4, 2019

Spielerei

Filed under: General — Tags: , , — m759 @ 7:18 PM

(See the title in this journal.)

Also on the above YouTube date — July 12, 2010 —

 

Nicht Spielerei

Filed under: General — Tags: , — m759 @ 10:22 AM

(See the title in earlier posts.)

Thursday, July 2, 2015

Deepening the Spielfeld

Filed under: General,Geometry — Tags: — m759 @ 3:27 AM

(Continued from Friday, June 26, 2015)

In memory of an architect —

Donald Wexler, an architect whose innovative steel houses
and soaring glass-fronted terminal at the Palm Springs
International Airport helped make Palm Springs, Calif.,
a showcase for midcentury modernism, died on Friday
[June 26, 2015] at his home in Palm Desert. He was 89.

William Grimes in this morning's New York Times

For a different sort of architecture in Palm Desert, see…

Hausdorff’s Spielraum

Filed under: General — Tags: — m759 @ 2:45 AM

Continued from January 31, 2015 .

Deepening the Spielraum

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

(A sequel to Expanding the Spielraum (Feb. 3, 2015))

"Knowledge, wisdom even, lies in depth, not extension."

Tim Parks in The New York Review of Books ,
     5 PM ET on June 26, 2015

See also Log24 posts on the following figure —

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

Friday, May 8, 2015

Spielraum

Filed under: General,Geometry — Tags: — m759 @ 9:30 AM

Review:

Illustrating the Spiegel-Spiel des Gevierts

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth. 
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by
Helen Lane 

 

Friday December 5, 2008

m759 @ 1:06 PM
 
Mirror-Play of
the Fourfold

For an excellent commentary
 on this concept of Heidegger,

View selected pages
from the book

Dionysus Reborn:

Play and the Aesthetic Dimension
in Modern Philosophical and
Scientific Discourse

(Mihai I. Spariosu,
Cornell U. Press, 1989)

Related material:
the logo for a
web page

Logo for 'Elements of Finite Geometry'

– and Theme and Variations.

Friday, February 6, 2015

The Annotated Spielraum

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

Comments on two sub-images from yesterday's
The Big Spielraum  (image, 1 MB) that may or
may not interest Emma Watson —

The Potter Sub-Image

This is from a link in a July 8, 2011, post:

The above "Childhood's End" link leads to
a midrash on the Harry Potter series:

"After pg. 759 in Harry Potter and the 
Deathly Hallows 
, my childhood ended."

The Carmichael Sub-Image

The number of the last page in the last Harry Potter
book is 759.  This number may, for those with
cabalistic tendencies, be interpreted as the
number 3*23*11 from a 1931 mathematics paper:

Thursday, February 5, 2015

The Big Spielraum

Filed under: General — Tags: — m759 @ 12:14 PM

From the Office for the Arts at Harvard:

Harvard Thinks Big VI

College Events Board

Location: Sanders Theatre, Memorial Hall,
45 Quincy Street, Cambridge
Parking: none

On Sale Date: 1/29/2015
How to get tickets: The Harvard Box Office
617-496-2222

Thursday 2/5 08:00 PM

Ticket Prices: Free. Harvard ID only.
2 tickets per person per ID.
Tickets valid until 7:45PM. 

Ticket Availability: Good 

The Harvard College Events Board presents Harvard Thinks Big VI, a night of big ideas and thinking beyond traditional boundaries. On Thursday February 5th at 8 pm in Sanders Theatre, 7 Harvard professors and lecturers will speak for ten minutes each to discuss a topic that intrigues and excites them. This annual event was first started in order to introduce the Harvard community to the fascinating research and developments from some of the greatest minds on campus. 

See as well The Big Spielraum  (1 MB).

Monday, February 2, 2015

Spielraum as Ω

Filed under: General,Geometry — Tags: , — m759 @ 6:29 PM
 

From "Origins of the Logical Theory of Probability: von Kries, Wittgenstein, Waismann," by Michael Heidelberger —

"Von Kries calls a range of objective possibilities of a hypothesis or event (under given laws) its Spielraum   (literally: play space), which can mean ‘room to move’, ‘leeway’, ‘latitude of choice’, ‘degree of freedom’ or ‘free play’ and ‘clearance’ – or even ‘scope’. John Maynard Keynes translated it as ‘field’, but the term ‘range’ has generally been adopted in English. Von Kries now holds that if numerical probability were to make any sense at all it must be through this concept of the Spielraum  . Von Kries’s theory is therefore called a ‘Spielraum  theory’ or ‘range theory of probability’."

— International Studies in the Philosophy of Science , Volume 15, Issue 2, 2001, pp. 177-188

See also the tag Points Omega
(Scroll down to January 11-12, 2015.)

Related material:

"Now, for example, in how far are
the six sides of a symmetric die
'equally possible' upon throwing?"

— From "The Natural-Range Conception
     of Probability," by Dr. Jacob Rosenthal,
     page 73 in Time, Chance, and
     Reduction: Philosophical Aspects of
     Statistical 
Mechanics , ed. by 
     Gerhard Ernst and Andreas Hüttemann, 
     Cambridge U. Press, 2010, pp. 71-90

Sunday, February 1, 2015

Spielraum III

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

From today's Super Bowl Halftime:

Click for image in context.

See also Spielraum  in this journal.

Saturday, January 31, 2015

Spielraum II

Filed under: General — Tags: — m759 @ 8:45 PM

For those who prefer Heidegger to Hausdorff:

Spielraum

Filed under: General — Tags: — m759 @ 1:27 PM

From the concluding paragraph of a new book by
mathematician Michael Harris:

"A team of eminent scholars is completing a definitive
edition of Hausdorff’s collected works—'unique
in the annals of mathematical publishing'— with the
care befitting the literary figure he undoubtedly was….
he is honored as, perhaps, the first modern
mathematician to give a name to what we have been
calling the 'relaxed field'— he called it the
'Spielraum  of thought'— and as a mathematician
who never lost his sensitivity to his chosen field’s
problematic attractions while remaining fully aware that
every veil lifted only reveals another veil."

— Harris, Michael, Mathematics without Apologies:
Portrait of a Problematic Vocation  
(2015-01-18) 
(pp. 324-325). Princeton U. Press. Kindle Edition. 

Related material:  Spiel ist nicht Spielerei .

Wednesday, December 23, 2020

Facets . . .

Filed under: General — Tags: , , — m759 @ 2:19 PM

Continued.

The book by Hesse has many facets ….” (Link added.)

— V. V. Nalimov, In the Labyrinths of Language ,
Ch. 1, “What Language Is,” p. 22.

Related philosophical speculation —

Thursday, October 29, 2020

The Art of the Possible: Weyl as Magister Ludi ?

Filed under: General — Tags: — m759 @ 3:54 AM

Johann A. Makowsky recently reviewed  Modernism, Fiction and Mathematics
by Nina Engelhardt.  Engelhardt is a  Wissenschaftliche Mitarbeiterin  at the
University of Stuttgart.  Makowsky is a professor emeritus of the computer science
department at the Technion-Israel Institute of Technology

The quotation below, by Makowsky not Engelhardt,  is from Notices of the
American Mathematical Society
, November 2020  (Vol. 67, No. 10, p. 1594) —

“Hermann Weyl was known for his inspiring lectures,
celebrating mathematics as a performing art. It is then likely
that he was both the model for the magister ludi celebrating
the Glass Bead Game, and the source of Hesse’s awareness of
modern mathematics as the art of the possible, rather than
the science of true nature.”

Possibly .

Consider also the diamond  as  Spielraum .

Monday, October 26, 2020

Theory

Filed under: General — Tags: , — m759 @ 11:37 AM

These news items suggest a review —

The above “Pynchon’s Paranoid History” page number  appeared
in this  journal on Groundhog Day, 2015 —

David Justice on a Zeta-related theory —

Friday, September 4, 2020

Force Field of Dreams

Filed under: General — Tags: — m759 @ 2:21 PM

(Continued from September 22, 2002.)

“As you read, watch for patterns. Pay special attention to
imagery that is geometric….” — “Pattern in The Defense

See as well Wednesday’s Smile,  and “Expanding the Spielraum .

Monday, March 16, 2020

Mathematics and Narrative* Continues:

Filed under: General — m759 @ 1:27 AM

Expanding the Spielraum

Mathematics:  See Tetrahedron vs. Square in this journal
(Notes on two different models of schoolgirl space ).

Narrative:  Replacing the square  from the above posts by
a related cube 

… yields a merchandising inspiration

Dueling Holocrons: 

Jedi Cube vs. Sith Tetrahedron

.

* See also earlier posts on Mathematics and Narrative.

Thursday, January 30, 2020

Poster Boy

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

Cover of 'The Institute,' a novel by Stephen King
                                                          Cover Design: Will Staehle / Unusual Co.

This post is in memory of "Wes Wilson, Psychedelic Poster Pioneer,"
who died at 82 on January 24, according to the NY Times  today. 
Related material — This  journal on January 24.

Wednesday, December 4, 2019

In Memoriam

Filed under: General — Tags: , , — m759 @ 12:35 PM

Also on the above date — October 28, 2013 —

Monday, December 2, 2019

“Show me all  the blueprints.”

Filed under: General — Tags: , — m759 @ 11:32 PM

Sunday, December 1, 2019

Dialogue

Filed under: General — Tags: , — m759 @ 10:09 PM

Space Song

Filed under: General — Tags: , — m759 @ 1:50 PM

From this journal on the above date — April 13, 2014 (Gray Space) —

Review of Seeing Gray , a book by pastor Adam Hamilton
of the United Methodist Church of the Resurrection
in Leawood, Kansas, a suburb of Kansas City—

“Adam Hamilton invites us to soulful gray space
between polarities, glorious gray space that is holy,
mysterious, complex, and true. Let us find within
our spirits the courage and humility to live and learn
in this faithful space, to see gray, to discern a more
excellent way.”

—Review by United Methodist Bishop Hope Morgan Ward

The above flashback was suggested by CBS Sunday Morning today —

See also Romanesque in this journal.

Saturday, October 12, 2019

Glass Beads

Filed under: General — Tags: — m759 @ 7:05 PM

(A sequel to the previous post, Marbles)

'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse

Click the book cover for some related posts.

Monday, September 23, 2019

First and Last Things

Filed under: General — Tags: — m759 @ 7:55 PM

“We shall now give a brief summary of the beginnings of the Glass Bead Game….

The Game was at first nothing more than a witty method for developing memory and ingenuity among students and musicians. And as we have said, it was played both in England and Germany before it was ‘invented’ here in the Musical Academy of Cologne, and was given the name it bears to this day, after so many generations, although it has long ceased to have anything to do with glass beads."

Friday, August 9, 2019

The Next Thing

Filed under: General — Tags: — m759 @ 10:00 AM

From posts tagged The Next Thing

an apt illustration can be found on the cover of
the 1943 first edition of Hesse's Glasperlenspiel 

http://www.log24.com/log/pix11/110203-Glasperlenspiel1943-Detail.jpg

See also Stevens's use of the phrase "heaven-haven"
in "Notes" (1942), the original plan of New Haven,
and related scholia in this journal.

http://www.log24.com/log/pix11/110203-Scholia.jpg

Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

– Rubén Darío

An academic work from 2003 discusses Stevens's "Notes"
as "a perfect geometric whole."

Note that "perfect" means "complete, finished, done."

 

Friday, April 5, 2019

A Definite Field

Filed under: General — m759 @ 10:45 AM

"We render the compulsion harmless, and indeed useful,
by giving it the right to assert itself in a definite field.
We admit it into the transference as a playground…."

— Sigmund Freud, 1914, "Remembering, Repeating,
and Working-Through" (See "Expanding the Spielraum,"
Oct. 26, 2015, in this  journal.)

An indefinite field —


A definite field —

A circular I Ching

Monday, October 22, 2018

Story Space

Filed under: General — Tags: — m759 @ 4:48 PM

A better term than "phase space" might be "story space."

See as well Expanding the Spielraum.

Tuesday, July 17, 2018

Space Art

Filed under: General — m759 @ 9:45 PM

Related material —

See too Ballet Blanc  and Expanding the Spiel.

A non -Paris review

Sunday, June 17, 2018

Bead Game Introduction

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

From The Abacus Conundrum

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

— Das Glasperlenspiel  (Hermann Hesse, 1943)

See also Web Audio Resources at GitHub.

Saturday, April 7, 2018

Sides

Filed under: General,Geometry — Tags: , , — m759 @ 11:47 AM

The FBI holding cube in "The Blacklist" —

" 'The Front' is not the whole story . . . ."

— Vincent Canby, New York Times  film review, 1976,
     as quoted in Wikipedia.

See also Solomon's Cube in this  journal.

IMAGE- 'Solomon's Cube'

Webpage demonstrating symmetries of 'Solomon's Cube'

Some may view the above web page as illustrating the
Glasperlenspiel  passage quoted here in Summa Mythologica 

“"I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above 4x4x4 design cube —

"I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created."

See also a related remark by Lévi-Strauss in 1955

"…three different readings become possible:
left to right, top to bottom, front to back."

Saturday, March 3, 2018

Thanking the Academy

Filed under: General — Tags: — m759 @ 11:05 PM

Blackboard Jungle , 1955 —

IMAGE- Richard Kiley in 'Blackboard Jungle,' with grids and broken records

“Every transition from major to minor in a sonata, every transformation
of a myth or a religious cult, every classical or artistic formulation was,
I realized in that flashing moment, if seen with a truly meditative mind,
nothing but a direct route into the interior of the cosmic mystery….”

— Hermann Hesse, The Glass Bead Game

“How strange the change from major to minor….”

— Cole Porter, “Every Time We Say Goodbye“

Thursday, August 24, 2017

Maori Chess

Filed under: General — m759 @ 2:44 PM

The Decepticons  date above, June 21, 2017, suggests an instance of
that date in this journal —

For the Church of Synchronology, a New York Times  item from  
the above death date, June 21, 2017 —

See as well Kurt Russell in Guardians of the Galaxy, Vol. 2

Some relevant context:  Expanding the Spielraum .

Sunday, June 4, 2017

Sequel to “The Square”* —

Filed under: General — m759 @ 3:03 PM

The Cube

CodePen logo, pictured here on May 28, 2017

From YouTube, "The Cube," published on April 6, 2016

Meanwhile, also on April 6, 2016, at 2:01 AM ET 

* See The Pinterest Directive and Expanding the Spielraum.

Friday, April 21, 2017

Music Box — The Theory

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

For the music box of the title, see the previous post.

See also Mazzola on the Glass Bead Game 
(Facebook date June 7, 2016)
and the Log24 post Symmetry (May 3, 2016).

Thursday, April 20, 2017

Point 8777*

Filed under: General — m759 @ 2:42 PM

Or:  Expanding the Spielraum, continued

Wikipedia on author Michael Connelly

Connelly had planned on following his father’s early choice of
career in building construction and started out at the 
University of Florida in Gainesville as a building construction major.
After earning grades that were lower than expected, Connelly went
to see Robert Altman’s film The Long Goodbye (1973) and was
enchanted by what he saw. The film, based on Raymond Chandler’s 
1953 novel of the same name, inspired Connelly to want to become
a mystery writer. Connelly went home and read all of Chandler's
works featuring Philip Marlowe, a detective in Los Angeles during
the 1940s and ‘50s, and decided to switch majors to journalism with
a minor in creative writing.[4] He was a student of Harry Crews.

[See also

https://blogs.wsj.com/speakeasy/2012/11/24/
the-teacher-michael-connelly-never-forgot/
.]

A 2002 novel by Connelly — City of Bones .

Two scenes from a 2014 TV pilot based on the 2002 novel —

The "Bosch" pilot does not state the address, but its location in the
Hollywood Hills suggests a review of Heinlein Lottery in this journal. 

"Bonedigger Bonedigger
 Dogs in the moonlight"
 — Paul Simon

* Title suggested by that of the previous post, "Point Zero."

Thursday, October 6, 2016

Poetics

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

Mirror Play

Filed under: General — Tags: — m759 @ 4:00 AM

See posts tagged Spiegel-Spiel.

"Mirror, Mirror …." —

A logo that may be interpreted as one-eighth of
a 2x2x2 array of cubes —

The figure in white above may be viewed as a subcube representing,
when the eight-cube array is coordinatized, the identity (i.e., (0, 0, 0)).

Friday, August 5, 2016

Sleight of Post

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

From an earlier Log24 post —

Friday, July 11, 2014

Spiegel-Spiel des Gevierts

Filed under: Uncategorized — m759 @ 12:00 PM 

See Cube Symbology.

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

Da hats ein Eck 

From a post of the next day, July 12, 2014 —

"So there are several different genres and tones
jostling for prominence within Lexicon :
a conspiracy thriller, an almost abstract debate
about what language can do, and an ironic
questioning of some of the things it’s currently used for."

Graham Sleight in The Washington Post 
     a year earlier, on July 15, 2013

For the Church of Synchronology, from Log24 on the next day — 

From a post titled Circles on the date of Marc Simont's death —

See as well Verhexung  in this journal.

Friday, June 3, 2016

Bruins and van Dam

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

A review of some recent posts on Dirac and geometry,
each of which mentions the late physicist Hendrik van Dam:

The first of these posts mentions the work of E. M. Bruins.
Some earlier posts that cite Bruins:

Sunday, May 29, 2016

The Ideogram Principle …

Filed under: General,Geometry — Tags: , , — m759 @ 4:23 PM

According to McLuhan

Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—

"The American mind is not even close to being amenable
to the ideogram principle as yet.  The reason is simply this.
America is 100% 18th Century. The 18th century had
chucked out the principle of metaphor and analogy—
the basic fact that as A is to B so is C to D.  AB:CD.   
It can see AB relations.  But relations in four terms are still
verboten.  This amounts to deep occultation of nearly all
human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  
Until stated and publicly recognized for what it is, poetry and
the arts can’t exist in America."

For context, see Cameron McEwen,
"Marshall McLuhan, John Pick, and Gerard Manley Hopkins."
(Renascence , Fall 2011, Vol. 64 Issue 1, 55-76)

A relation in four terms

A : B  ::  C : D   as   Model : Crutch  ::  Metaphor : Ornament —

See also Dueling Formulas and Symmetry.

Wednesday, May 18, 2016

Dueling Formulas

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

Jung's four-diamond formula vs. Levi-Strauss's 'canonical formula'

Note the echo of Jung's formula in the diamond theorem.

An attempt by Lévi-Strauss to defend his  formula —

"… reducing the life of the mind to an abstract game . . . ." —

For a fictional version of such a game, see Das Glasperlenspiel .

Sunday, May 8, 2016

Gesamtkunstwerke

Filed under: General — Tags: , , — m759 @ 10:00 PM

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

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

"Only connect." — Howards End

Tuesday, May 3, 2016

Symmetry

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

A note related to the diamond theorem and to the site
Finite Geometry of the Square and Cube —

The last link in the previous post leads to a post of last October whose
final link leads, in turn, to a 2009 post titled Summa Mythologica .

Webpage demonstrating symmetries of 'Solomon's Cube'

Some may view the above web page as illustrating the
Glasperlenspiel  passage quoted here in Summa Mythologica 

“”I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above web page* —

“I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created.”

Update of Sept. 5, 2016 — See also a related remark
by Lévi-Strauss in 1955: “…three different readings
become possible: left to right, top to bottom, front
to back.”

* For the underlying mathematics, see a June 21, 1983, research note.

Sunday, November 1, 2015

Transitions

Filed under: General — m759 @ 5:48 PM

Two transitions from last Monday, Oct. 26, 2015,
according to the online New York Times  today —

Leo P. Kadanoff, a physicist who provided critical insights into the transformations of matter from one state to another, died last Monday in Chicago. He was 78.

The cause was respiratory failure, said the University of Chicago, where he was a professor from 1978 until his retirement in 2003.

A member of the National Academy of Sciences and a fellow of the American Academy of Arts and Sciences, he received the National Medal of Science in 1999.

“He won basically every prize except the Nobel Prize, and many people thought he should have won the Nobel,” said Emil Martinec, a physics professor at the University of Chicago who directs the university’s Kadanoff Center for Theoretical Physics.

Dr. Kadanoff’s biggest scientific contribution came in the 1960s as scientists were trying to understand phase transitions, when matter changes from one form to another.

A Cornell chemist, Benjamin Widom, had come up with mathematical relationships that described behavior associated with second-order phase transitions, which include the boiling of water to steam at a particular temperature and pressure. But Dr. Widom did not have an underlying physical explanation for why these relationships existed.

Willis Carto, a reclusive behind-the-scenes wizard of the far-right fringe of American politics who used lobbying and publishing to denigrate Jews and other minorities and galvanize the movement to deny the Holocaust, died last Monday at his home in Virginia. He was 89.

His death was announced by The American Free Press, a newspaper he helped found.

Mr. Carto raised funds to finance a right-wing military dictatorship in the United States, campaigned to persuade blacks to voluntarily return to Africa and, most influentially, started newsletters, a journal and conferences of academics and others to deny the scale, and even the existence, of the Holocaust.

The Anti-Defamation League called him “one of the most influential American anti-Semitic propagandists” and “the mastermind of the hate network.”

His associates included neo-Nazis, Christian vigilantes, John Birch Society members and Ku Klux Klansmen, and his extreme views alienated mainstream conservatives. After William F. Buckley sued Mr. Carto for libel and won in 1985, Mr. Buckley said Mr. Carto epitomized “the fever swamps of the crazed right.’’

Related remarks:

Posts tagged "Steam," the post "On Ice-Breaking" from Oct. 27,
the post "Expanding the Seagram Spielraum" from Oct. 26, and
a 2008 article on the subject of the obituary at right above.

"Integrity, Craftsmanship, Tradition"

Monday, October 19, 2015

Zen and the Art

Filed under: General — Tags: — m759 @ 4:40 AM

According to René Guitart in May 2008 —

"In fact, in concrete terms, the Mathematical Pulsation  is
nothing else but the thing that everyone does when doing
mathematics, even the most elementary ones. It is a very
special gesture in understanding ('geste de pensée'), well
known by each mathematician. The mind have to go to
and fro between to antinomical postures: to have the
situation under control, to leave the door open. To master
and to fix (a clear unique meaning) or to neglect and to
change (toward other possible meanings). Because of the
similarity of the pulsation of inspiration and expiration in
breath with the pulsation of closing and opening phases
in mathematical thinking, at the end of [Guitart (2003/a)]
I suggested to consider the famous book 'Zen in the Art
of Archery' [Herrigel (1997)] as a true treatise in didactic
of mathematics: just you have to replace everywhere the
words 'archery' by 'mathematical proof'."

Related material: Heisenberg on Beauty and the previous post.

Update of 6:20 AM Oct. 19, 2015 —

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

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

For a version in English, see Summa Mythologica (Nov. 3, 2009).

Wednesday, June 24, 2015

Scoring Plan 9

Filed under: General — Tags: , — m759 @ 6:33 PM

In keeping with the resurrection themes of the
previous post and of "Plan 9 from Outer Space,"
here is a link to the soundtrack of "Field of Dreams."

Related material:

A post of March 11, 2014, on
truth, cornfields, and Rebecca Goldstein —
Dark Fields of the Republic.

R.I.P., James Horner.

Monday, June 22, 2015

Plato for Rebecca Goldstein

Filed under: General,Geometry — Tags: , — m759 @ 10:24 AM

"… geometry will draw the soul towards truth…." — Plato

Or not.

Sunday, June 21, 2015

High White Noon

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

(Continued)

You can't make this stuff up.

Sermon

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

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 —

 .

Thursday, April 30, 2015

Meditation on an Icon

Filed under: General — m759 @ 2:01 AM

IMAGE- Brian Bard on 'Heidegger's Reading of Heraclitus'

See also Legespiel  in this journal.

Saturday, April 18, 2015

The Southwest Furthers

Filed under: General — Tags: — m759 @ 2:01 PM

See Southwest + Furthers in this journal.

http://www.log24.com/log/pix11/110413-Compass.jpg

The Acme Corporation Presents…

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

Kyle Smith on April 15 in the New York Post —

"The ludicrous action thriller 'Beyond the Reach'
fails to achieve the Southwestern noir potency
of 'No Country for Old Men,' but there’s no denying
it brings to mind another Southwestern classic
about malicious pursuit: the Road Runner cartoons."

Related material: 

  1. Legespiel  Meets rfelspiel  in…
    Gift of the Third Kind
    (April 7, 2007), featuring Ellen Yi-Luen Do —

    Reinventing Froebel's Gifts

  2. the current home page of Ellen Yi-Luen Do,
    now at Georgia Tech, and…
  3. a page about her ACME Lab —

Welcome to ACME lab!
A Creativity Machine Environment!
aka ACME Creativity Machine Environment –
ACME Lab

Yes, the name is both confusing and has
many meanings. We like the acronym of ACME,
since it means the highest point, and also refers to
the fictional company in Looney Tunes, which is
A Company that Makes Everything!

We call it ACME Creativity Machine Environment –
yes, the acronym of this is ACME.

We like recursive ideas.

Saturday, February 28, 2015

Elegy with Stars

Filed under: General — Tags: , — m759 @ 10:00 PM

This evening's New York Times —

"William Thomas McKinley, a prolific American composer
whose music was infused with the jazz he had performed
since childhood, died on Feb. 3 at his home in Reading,
Mass. He was 76.

He died in his sleep, his son Elliott said."

"William Thomas McKinley: Elegy for Strings (2006)

[Elliott McKinley]  

137 views as of 9:45 PM ET Feb. 28, 2015

Published on Feb 11, 2015

Composed as an elegy and tribute for friends and family
that have passed, spurred by the passing of McKinley's
long time friend, drummer Roger Ryan. The performance
heard here is by the Seattle Symphony under the direction
of Gerard Schwarz. 

Photos by Elliott McKinley (Rho Ophiuchi nebula complex…
and the Pleiades…) shot at Cherry Springs State Park."

Related material from the date of McKinley's death —
Expanding the Spielraum.

Saturday, February 14, 2015

Valentine Dance

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

For Eliot and von Franz —

"A dance results."

— Marie-Louise von Franz
     in Number and Time

IMAGE- Halftime dance in 4x4 square, 2015 Super Bowl, with Katy Perry

Monday, February 9, 2015

Overarching Symmetry

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

Continued from earlier posts.

The Washington Post  online yesterday:

"Val Logsdon Fitch, the Nebraska rancher’s son who shared the Nobel Prize for detecting a breakdown in the overarching symmetry of physical laws, thus helping explain how the universe evolved after the Big Bang, died Feb. 5 in Princeton, N.J. He was 91.

His death was confirmed by Princeton University, where he had been a longtime faculty member and led the physics department for several years.

Dr. Fitch and his Princeton colleague James Cronin received the Nobel Prize in physics in 1980 for high-energy experiments conducted in 1964 that overturned fundamental assumptions about symmetries and invariances that are characteristic of the laws of physics."

— By Martin Weil

Fans of synchronicity may prefer some rather
ig -Nobel remarks quoted here  on the date
of Fitch's death:

"The Harvard College Events Board presents
Harvard Thinks Big VI, a night of big ideas
and thinking beyond traditional boundaries.
On Thursday February 5th at 8 pm in
Sanders Theatre …."

— Log24 post The Big Spielraum

Monday, March 17, 2014

Narratives

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

Or: The Confessions of Nat Tate

“A convincing lie is, in its own way, a tiny, perfect narrative.”
— William Boyd, “A Short History of the Short Story” (2006)

“A novel written in the first-person singular has certain powerful
narrative advantages, especially when it takes the form of a ‘confession.'”
— William Boyd, “Memoir of a Plagiarist” (1994)

IMAGE- 'Siri Hustvedt Interview: Fakes and Fiction'

IMAGE- 'Siri Hustvedt Interview: Fakes and Fiction'

From a Log24 post yesterday —

For Little Man Tate —

IMAGE- Wechsler block-design cubes and related WAIS-R manual

Related material — Wechsler in this journal and an earlier Siri Hustvedt
art novel, from 2003 —

Mark and Lucille, Bill and Violet, Al and Regina, etc., etc., etc. —

IMAGE- Siri Hustvedt on the name 'Wechsler' in 'What I Loved'

Wednesday, November 6, 2013

Bullshit Studies

Filed under: General — Tags: , — m759 @ 3:12 PM

The essay excerpted in last night's post on structuralism
is of value as part of a sustained attack by the late
Robert de Marrais on the damned nonsense of the late
French literary theorist Jacques Derrida—

Catastrophes, Kaleidoscopes, String Quartets:
Deploying the Glass Bead Game

Part I:  Ministrations Concerning Silliness, or:
Is “Interdisciplinary Thought” an Oxymoron?

Part II:  Canonical Collage-oscopes, or:
Claude in Jacques’ Trap?  Not What It Sounds Like!

Part III:  Grooving on the Sly with Klein Groups

Part IV:  Claude’s Kaleidoscope . . . and Carl’s

Part V:  Spelling the Tree, from Aleph to Tav
(While  Not Forgetting to Shin)

The response of de Marrais to Derrida's oeuvre  nicely
exemplifies the maxim of Norman Mailer that

"At times, bullshit can only be countered
with superior bullshit."

Thursday, August 8, 2013

Heaven’s Gate

Filed under: General — Tags: — m759 @ 3:01 PM

Yesterday's post Devil's Gate provided a dark view of life and culture.

A more cheerful view is provided by the late Gail Levin,
a maker of PBS "American Masters" documentaries
that included, notably, Jeff Bridges and Marilyn Monroe.

Levin reportedly died at 67 on July 31, 2013.*

An image from an interview with Levin —

The date in the image, July 19th, 2006, is the broadcast
date of the PBS "American Masters" program on Monroe.
A check for synchronicity shows there was no Log24 post
on that date.

See, however, posts for the day before— "Sacred Order"—
and the day after— "Bead Game."

A related quote from an article linked to in the latter—

"First world culture, which is 'pagan and in the majority
everywhere,' has as its defining characteristic
a 'primacy of possibility,' or pop— a broadly inclusive
concept that covers everything from the Aboriginal
dreamtime to Plato’s Forms."

Review by Jess Castle of Philip Rieff’s 
Sacred Order/Social Order, Vol. 1: My Life among the
Deathworks: Illustrations of the Aesthetics of Authority
,
University of Virginia Press, 2006. 256 pages, $34.95.

This quote may serve as the missing July 19, 2006, post.

Related material:  Dreamtime,  Possibility,  and Plato's Forms.

* See that date in this journal for two less famous American
  masters, artist Edward Valigursky and writer Robert Silverberg.

Friday, March 4, 2011

Ageometretos Medeis Eisito*

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

Your mission, should you choose to accept it…

IMAGE- Future Bead Game Master Joseph Knecht's mission to a Benedictine monastery

See also “Mapping Music” from Harvard Magazine , Jan.-Feb. 2007—

“Life inside an orbifold is a non-Euclidean world”

— as well as the cover story “The Shape of Music” from Princeton Alumni Weekly ,
Feb. 9, 2011, and “Bead Game” + music in this  journal (click, then scroll down).
Those impressed by the phrase “non-Euclidean” may also enjoy
Non-Euclidean Blocks and Pilate Goes to Kindergarten.

The “Bead Game” + music search above includes, notably, a passage describing a
sort of non-Euclidean abacus in the classic 1943 story “Mimsy Were the Borogoves.”
For a visually related experience, see the video “Chord Geometries Demo: Chopin
on a Mobius Strip” at a music.princeton.edu web page.

* Motto of the American Mathematical Society, said to be also the motto of Plato’s Academy.

Monday, February 21, 2011

The Abacus Conundrum*

From Das Glasperlenspiel  (Hermann Hesse, 1943) —

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

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

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

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

Thursday, February 3, 2011

Brightness at Noon (continued)

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

"The predicate of bright origin"

— A phrase of Wallace Stevens from "An Ordinary Evening in New Haven" (1950)

Perhaps the predicate Stevens means is "bright."

If so, an apt illustration can be found on the cover of
the 1943 first edition of Hesse's Glasperlenspiel

http://www.log24.com/log/pix11/110203-Glasperlenspiel1943-Detail.jpg

See also Stevens's use of the phrase "heaven-haven" in "Notes" (1942),
the original plan of New Haven, and related scholia in this journal.

http://www.log24.com/log/pix11/110203-Scholia.jpg

… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

– Rubén Darío

An academic work from 2003 discusses Stevens's "Notes" as
"a perfect geometric whole."

Note that "perfect" means "complete, finished, done."

Summa Mythologica, continued…

Filed under: General — Tags: , — m759 @ 10:30 AM

Yesterday's New York Lottery— Midday 392, Evening 946.

Catechism of the Catholic Church

392   Scripture speaks of a sin of these angels. This "fall" consists in the free choice of these created spirits, who radically and irrevocably rejected  God and his reign. We find a reflection of that rebellion in the tempter's words to our first parents: "You will be like God." The devil "has sinned from the beginning"; he is "a liar and the father of lies."

946   After confessing "the holy catholic Church," the Apostles' Creed adds "the communion of saints." In a certain sense this article is a further explanation of the preceding: "What is the Church if not the assembly of all the saints?" The communion of saints is the Church.

Some context related to last night's Rite of Change

Glasperlenspiel  Philosophy.

Those who prefer Dan Brown to Hermann Hesse may consult Fast Forward.

Tuesday, August 17, 2010

Riff Design

Filed under: General — Tags: , — m759 @ 5:09 AM

From yesterday

Call and Response

“One would call out, in the standardized abbreviations of their science, motifs or initial bars of classical compositions, whereupon the other had to respond with the continuation of the piece, or better still with a higher or lower voice, a contrasting theme, and so forth. It was an exercise in memory and improvisation….”

The Glass Bead Game

Today’s New York Times  has an obituary for Bernard Knox, classics professor. Knox died on July 22. On that date this journal happened to have a post, “Soul Riff,” featuring a professor— shown below. Click on the professor for a very relevant classical quotation.

The Soul Riff  post also contained the above secondary title—

Call and Response

Doonesbury 2/29/08-- Assignment: Identify Sources

For a response from the next day,
March 1, click on the professor
.

Sunday, August 15, 2010

The Game

Filed under: General — Tags: , , — m759 @ 11:07 PM
'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse

We shall now give a brief summary of the beginnings of the Glass Bead Game. It appears to have arisen simultaneously in Germany and in England. In both countries, moreover, it was originally a kind of exercise employed by those small groups of musicologists and musicians who worked and studied in the new seminaries of musical theory. If we compare the original state of the Game with its subsequent developments and its present form, it is much like comparing a musical score of the period before 1500, with its primitive notes and absence of bar lines, with an eighteenth-century score, let alone with one from the nineteenth with its confusing excess of symbols for dynamics, tempi, phrasing, and so on, which often made the printing of such scores a complex technical problem.

The Game was at first nothing more than a witty method for developing memory and ingenuity among students and musicians. And as we have said, it was played both in England and Germany before it was ‘invented’ here in the Musical Academy of Cologne, and was given the name it bears to this day, after so many generations, although it has long ceased to have anything to do with glass beads.

The inventor, Bastian Perrot of Calw, a rather eccentric but clever, sociable, and humane musicologist, used glass beads instead of letters, numerals, notes, or other graphic symbols. Perrot, who incidentally has also bequeathed to us a treatise on the Apogee and Decline of Counterpoint, found that the pupils at the Cologne Seminary had a rather elaborate game they used to play. One would call out, in the standardized abbreviations of their science, motifs or initial bars of classical compositions, whereupon the other had to respond with the continuation of the piece, or better still with a higher or lower voice, a contrasting theme, and so forth. It was an exercise in memory and improvisation quite similar to the sort of thing probably in vogue among ardent pupils of counterpoint in the days of Schütz, Pachelbel, and Bach — although it would then not have been done in theoretical formulas, but in practice on the cembalo, lute, or flute, or with the voice.

Bastian Perrot in all probability was a member of the Journeyers to the East. He was partial to handicrafts and had himself built several pianos and clavichords in the ancient style. Legend has it that he was adept at playing the violin in the old way, forgotten since 1800, with a high-arched bow and hand-regulated tension of the bow hairs. Given these interests, it was perhaps only natural that he should have constructed a frame, modeled on a child’s abacus, a frame with several dozen wires on which could be strung glass beads of various sizes, shapes, and colors. The wires corresponded to the lines of the musical staff, the beads to the time-values of the notes, and so on. In this way he could represent with beads musical quotations or invented themes, could alter, transpose, and develop them, change them and set them in counterpoint to one another. In technical terms this was a mere plaything, but the pupils liked it; it was imitated and became fashionable in England too. For a time the game of musical exercises was played in this charmingly primitive manner. And as is so often the case, an enduring and significant institution received its name from a passing and incidental circumstance. For what later evolved out of that students’ sport and Perrot’s bead-strung wires bears to this day the name by which it became popularly known, the Glass Bead Game.

Hermann Hesse

“For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.”

— “Albertus Secundus,” epigraph to The Glass Bead Game

From DownloadThat.com

(Click to enlarge.)

http://www.log24.com/log/pix10B/100815-ThePaletteSm.jpg

Wednesday, June 30, 2010

Field Dream

Filed under: General,Geometry — Tags: , , — m759 @ 10:23 AM

In memory of Wu Guanzhong, Chinese artist who died in Beijing on Friday

Image-- The Dream of the Expanded Field

“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

“The Chinese painter Wu Tao-tzu was famous because he could paint nature in a unique realistic way that was able to deceive all who viewed the picture. At the end of his life he painted his last work and invited all his friends and admirers to its presentation. They saw a wonderful landscape with a romantic path, starting in the foreground between flowers and moving through meadows to high mountains in the background, where it disappeared in an evening fog. He explained that this picture summed up all his life’s work and at the end of his short talk he jumped into the painting and onto the path, walked to the background and disappeared forever.”

Jürgen Teichmann. Teichmann notes that “the German poet Hermann Hesse tells a variation of this anecdote, according to his own personal view, as found in his ‘Kurzgefasster Lebenslauf,’ 1925.”

Tuesday, November 3, 2009

Summa Mythologica

Filed under: General,Geometry — Tags: , — m759 @ 10:10 PM

Book review by Jadran Mimica in Oceania, Vol. 74, 2003:

"In his classic essay of 1955 'The Structural Study of Myth' Levi-Strauss came up with a universal formula of mythopeic dynamics

[fx(a) : fy(b) :: fx(b) : fa-1(y)]

that he called canonical 'for it can represent any mythic transformation'. This formulation received its consummation in the four massive Mythologiques volumes, the last of which crystallises the fundamental dialectics of mythopoeic thought: that there is 'one myth only' and the primal ground of this 'one' is 'nothing'. The elucidation of the generative matrix of the myth-work is thus completed as is the self-totalisation of both the thinker and his object."

So there.

At least one mathematician has claimed that the Levi-Strauss formula makes sense. (Jack Morava, arXiv pdf, 2003.)

I prefer the earlier (1943) remarks of Hermann Hesse on transformations of myth:

"…in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created."

Saturday, April 25, 2009

Saturday April 25, 2009

Filed under: General — Tags: , — m759 @ 11:09 AM
April is Awareness Month

for both

Mathematics and Autism.

Welcome to the
Black Hole Café

"Our lifelong friendship made me not only an admirer of the depth, scholarship, and sheer energy of his mathematical work (and of his ceaseless activities as an editorial entrepreneur on behalf of mathematics) but one in awe of his status as the ultimate relaxed sophisticate."
 

The late Jacob T. Schwartz 
  on Gian-Carlo Rota

Psychoshop

by Alfred Bester
and Roger Zelazny:

His manner was all charm and grace; pure café society….

He purred a chuckle. "My place. If you want to come, I'll show you."

"Love to. The Luogo Nero? The Black Place?"

"That's what the locals call it. It's really Buoco Nero, the Black Hole."

"Like the Black Hole of Calcutta?"

"No. Black Hole as in astronomy. Corpse of a dead star, but also channel between this universe and its next-door neighbor."


"After Davis and Hersh,
it will be hard to uphold
the Glasperlenspiel
view of mathematics."
— Gian-Carlo Rota  

"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon  

http://www.log24.com/log/pix09/090425-AutismPuzzlePiece.jpg

AutismGear.com
 

Friday, March 20, 2009

Friday March 20, 2009

Filed under: General — Tags: — m759 @ 11:07 AM
Happy Birthday,
Holly Hunter

Epigraph to The Glass Bead Game:

Non entia enim licet quodammodo levibusque hominibus facilius atque incuriosius verbis reddere quam entia, veruntamen pio diligentique rerum scriptori plane aliter res se habet: nihil tantum repugnat ne verbis illustretur, at nihil adeo necesse est ante hominum oculos proponere ut certas quasdam res, quas esse neque demonstrari neque probari potest, quae contra eo ipso, quod pii diligentesque viri illas quasi ut entia tractant, enti nascendique facultati paululum appropinquant.
      
       — ALBERTUS SECUNDUS
           tract. de cristall. spirit.
           ed. Clangor et Collof. lib. I, cap. 28.

In Joseph Knecht’s holograph translation:.

For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.

Video -- 'The  Piano,' Part 11

Thursday, March 19, 2009

Thursday March 19, 2009

Filed under: General — Tags: — m759 @ 4:00 AM
An image from
 
Quintessence:
A Glass Bead Game

 
by Charles Cameron

Christ and the four elements, 1495

Christ and the Four Elements

This 1495 image is found in
The Janus Faces of Genius:
The Role of Alchemy
in Newton's Thought
,

by B. J. T. Dobbs,
Cambridge U. Press,
2002, p. 85

From
Kernel of Eternity:

Pauli's Dream Square from 'The Innermost Kernel'

From
Sacerdotal Jargon
at Harvard
:

The Klein Four-Group: The four elements in four colors, with black points representing the identity

From "The Fifth Element"
(1997, Milla Jovovich
    and Bruce Willis) —

The crossing of the beams:

The Fifth Element, crossing of the beams

Happy birthday, Bruce Willis.
 

Thursday, January 15, 2009

Thursday January 15, 2009

Filed under: General — Tags: — m759 @ 6:00 PM
Harvard, Magic,
and The New York Times

The New York Times Magazine for next Sunday:

The Edge of the Mystery, by Matt Bai–

“Weeks before the election of 1960, Norman Mailer, already an accomplished novelist, sat down to write his first major work of political journalism, an essay for Esquire in which he argued that only John F. Kennedy could save America… the only kind of leader who could rescue it, who could sweep in an era of what Mailer called ‘existential’ politics, was a ‘hipster’ hero– someone who welcomed risk and adventure, someone who sought out new experience, both for himself and for the country….

… Mailer essentially created a new genre for a generation of would-be literary philosophers covering politics….  By 1963, Mailer and other idealists were crushed to discover that Kennedy was in fact a fairly conventional and pragmatic politician, more Harvard Yard than Fortress of Solitude.”

The New York Times today:

Magic and Realism, by Roger Cohen–

“… what I want from the Obama administration is something more than Harvard-to-the-Beltway smarts. I want magical realism.”

Mailer and Cohen, taken together, suggest I should review two authors– Picard and Hesse– I encountered as a Harvard freshman in 1960.

Max Picard:

“In the ‘Prologue in Heaven’ in Goethe’s Faust a powerful silence is produced by the powerful word after each verse. There is an active, audible silence after every verse. The things that were moved into position by the word stand motionless in the silence, as if they were waiting to be called back into the silence and to disappear therein. The word not only brings the things out of silence; it also produces the silence in which they can disappear again.”

Goethe:

DER HERR:
Kennst du den Faust?

MEPHISTOPHELES:
Den Doktor?

DER HERR:
Meinen Knecht!

Online Etymology Dictionary:

knight
O.E. cniht “boy, youth, servant,” common W.Gmc. (cf. O.Fris. kniucht, Du. knecht, kneht “boy, youth, lad,” Ger. Knecht “servant, bondsman, vassal”), of unknown origin. Meaning “military follower of a king or other superior” is from c.1100. Began to be used in a specific military sense in Hundred Years War, and gradually rose in importance through M.E. period until it became a rank in the nobility 16c. The verb meaning “to make a knight of (someone)” is from c.1300. Knighthood is O.E. cnihthad M.H.G. “the period between childhood and manhood;” sense of “rank or dignity of a knight” is from c.1300. The chess piece so called from c.1440.

Further background on the word “Knecht”–

'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse

Epigraph to Magister Ludi
(Joseph Knecht’s translation):


“… For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.”

Thursday, August 14, 2008

Thursday August 14, 2008

Filed under: General,Geometry — Tags: — m759 @ 4:19 AM
'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse
Magister Ludi
(The Glass Bead Game)
is now available for
download in pdf or
text format at Scribd.

“How far back the historian wishes to place the origins and antecedents of the Glass Bead Game is, ultimately, a matter of his personal choice. For like every great idea it has no real beginning; rather, it has always been, at least the idea of it. We find it foreshadowed, as a dim anticipation and hope, in a good many earlier ages. There are hints of it in Pythagoras, for example, and then among Hellenistic Gnostic circles in the late period of classical civilization. We find it equally among the ancient Chinese, then again at the several pinnacles of Arabic-Moorish culture; and the path of its prehistory leads on through Scholasticism and Humanism to the academies of mathematicians of the seventeenth and eighteenth centuries and on to the Romantic philosophies and the runes of Novalis’s hallucinatory visions. This same eternal idea, which for us has been embodied in the Glass Bead Game, has underlain every movement of Mind toward the ideal goal of a universitas litterarum, every Platonic academy, every league of an intellectual elite, every rapprochement between the exact and the more liberal disciplines, every effort toward reconciliation between science and art or science and religion. Men like Abelard, Leibniz, and Hegel unquestionably were familiar with the dream of capturing the universe of the intellect in concentric systems, and pairing the living beauty of thought and art with the magical expressiveness of the exact sciences. In that age in which music and mathematics almost simultaneously attained classical heights, approaches and cross-fertilizations between the two disciplines occurred frequently.”

 — Hermann Hesse

Author’s dedication:

to the Journeyers
to the East

Related material:

The Ring of the Diamond Theorem

Ring Theory

Tuesday, July 8, 2008

Tuesday July 8, 2008

Filed under: General — Tags: , — m759 @ 3:33 AM
Translation
 

Yesterday's entry discussed T.E. Hulme— a co-founder, with Ezra Pound, of the Imagist school of poetry. Recent entries on randomness, using the New York Lottery as a source of examples, together with Hulme's approach to poetry discussed yesterday, suggest the following meditation– what Charles Cameron might call a "bead game."

Part I:

Ezra Pound on Imagism (from Gaudier-Brzeska,* 1916):

Three years ago in Paris I got out of a "metro" train at La Concorde, and saw suddenly a beautiful face, and then another and another, and then a beautiful child’s face, and then another beautiful woman, and I tried all that day to find words for what this had meant to me, and I could not find any words that seemed to me worthy, or as lovely as that sudden emotion. [….]

The "one image poem" is a form of super-position, that is to say, it is one idea set on top of another. I found it useful in getting out of the impasse in which I had been left by my metro emotion. I wrote a thirty-line poem, and destroyed it because it was what we call work "of second intensity." Six months later I made a poem half that length; a year later I made the following hokku-like sentence: —

"The apparition of these
    faces in the crowd:
 Petals, on a
    wet, black bough."

 

I dare say it is meaningless unless one has drifted into a certain vein of thought. In a poem of this sort one is trying to record the precise instant when a thing outward and objective transforms itself, or darts into a thing inward and subjective.

Part II:

Eleanor Goodman on translation (in a July 7, 2008, weblog entry, "Pound and Process: An Introduction"):

"… all translations exist on an axis. Indeed, they exist in a manifold of many axes intersecting. One axis is that of foreignness and familiarity. One axis is that of structural mimicry, another of melodic mimicry. And one axis is that of semantic fidelity."

Goodman's use of the word "manifold" here is of course poetic, not mathematical.

Part III:

New York Lottery, mid-day on July 7, 2008: 771.

Part IV:

A Google search on manifold 771 reveals that 771 is, according to Google's scanners, an alternate form (a "translation," via structural mimicry) of a script version of the letter M. (See Part V below.)

Part V:

Long version of a 
one-image poem —

"Random apparition:
  manifold translated."

This poem summarizes the
relationship (See Part IV above) of
the (apparently) random number 771
to the rather non-random concept of
a linear manifold:

Paul R. Halmos, Finite Dimensional Vector Spaces, Princeton, 1948-- Definition of linear manifold (denoted by script M)

[Such lines and planes have not
been, in mathematical language,
"translated."]

— Paul R. Halmos,
Finite Dimensional Vector Spaces,
Princeton University Press, 1948

Short version of the   
above one-image poem

 771:
Script M

* Gaudier-Brzeska created the artifact shown on the cover of Solid Objects, a work of literary theory by Douglas Mao. For more on that artifact and on the New York Lottery, see Sermon for St. Peter's Day. "It is not in the premise that reality/ Is a solid…." –Wallace Stevens

"I was like, Oh My God." —Poet Billy Collins at Chautauqua Institution, morning of July 7, 2008
 

Wednesday, June 25, 2008

Wednesday June 25, 2008

Filed under: General,Geometry — Tags: , — m759 @ 7:20 PM
The Cycle of
the Elements

John Baez, Week 266
(June 20, 2008):

“The Renaissance thinkers liked to
organize the four elements using
a chain of analogies running
from light to heavy:

fire : air :: air : water :: water : earth

They also organized them
in a diamond, like this:”

Diamond of the four ancient elements, figure by John Baez

This figure of Baez
is related to a saying
attributed to Heraclitus:

Diamond  showing transformation of the four ancient elements

For related thoughts by Jung,
see Aion, which contains the
following diagram:

Jung's four-diamond figure showing transformations of the self as Imago Dei

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

— Carl Gustav Jung

That the words Maximus of Tyre (second century A.D.) attributed to Heraclitus imply a cycle of the elements (analogous to the rotation in Jung’s diagram) is not a new concept. For further details, see “The Rotation of the Elements,” a 1995 webpage by one  “John Opsopaus.”

Related material:

Log24 entries of June 9, 2008, and

Quintessence: A Glass Bead Game,”
by Charles Cameron.

Sunday, May 25, 2008

Sunday May 25, 2008

Filed under: General,Geometry — Tags: — m759 @ 6:30 PM
Hall of Mirrors

Epigraph to
Deploying the Glass Bead Game, Part II,”
by Robert de Marrais:

“For a complete logical argument,”
Arthur began
with admirable solemnity,
“we need two prim Misses –”
“Of course!” she interrupted.
“I remember that word now.
And they produce — ?”
“A Delusion,” said Arthur.

— Lewis Carroll,
Sylvie and Bruno

Prim Miss 1:

Erin O’Connor’s weblog
“Critical Mass” on May 24:

Roger Rosenblatt’s Beet [Ecco hardcover, Jan. 29, 2008] is the latest addition to the noble sub-genre of campus fiction….

Curricular questions and the behavior of committees are at once dry as dust subjects and areas ripe for sarcastic send-up– not least because, as dull as they are, they are really both quite vital to the credibility and viability of higher education.

Here’s an excerpt from the first meeting, in which committee members propose their personal plans for a new, improved curriculum:

“… Once the students really got into playing with toy soldiers, they would understand history with hands-on excitement.”

To demonstrate his idea, he’d brought along a shoe box full of toy doughboys and grenadiers, and was about to reenact the Battle of Verdun on the committee table when Heilbrun stayed his hand. “We get it,” he said.

“That’s quite interesting, Molton,” said Booth [a chemist]. “But is it rigorous enough?”

At the mention of the word, everyone, save Peace, sat up straight.

“Rigor is so important,” said Kettlegorf.

“We must have rigor,” said Booth.

“You may be sure,” said the offended Kramer. “I never would propose anything lacking rigor.”

Smythe inhaled and looked at the ceiling. “I think I may have something of interest,” he said, as if he were at a poker game and was about to disclose a royal flush. “My proposal is called ‘Icons of Taste.’ It would consist of a galaxy of courses affixed to several departments consisting of lectures on examples of music, art, architecture, literature, and other cultural areas a student needed to indicate that he or she was sophisticated.”

“Why would a student want to do that?” asked Booth.

“Perhaps sophistication is not a problem for chemists,” said Smythe. Lipman tittered.

“What’s the subject matter?” asked Heilbrun. “Would it have rigor?”

“Of course it would have rigor. Yet it would also attract those additional students Bollovate is talking about.” Smythe inhaled again. “The material would be carefully selected,” he said. “One would need to pick out cultural icons the students were likely to bring up in conversation for the rest of their lives, so that when they spoke, others would recognize their taste as being exquisite yet eclectic and unpredictable.”

“You mean Rembrandt?” said Kramer.

Smythe smiled with weary contempt. “No, I do not mean Rembrandt. I don’t mean Beethoven or Shakespeare, either, unless something iconic has emerged about them to justify their more general appeal.”

“You mean, if they appeared on posters,” said Lipman.

“That’s it, precisely.”

Lipman blushed with pride.

“The subject matter would be fairly easy to amass,” Smythe said. “We could all make up a list off the top of our heads. Einstein–who does have a poster.” He nodded to the ecstatic Lipman. “Auden, for the same reason. Students would need to be able to quote ‘September 1939[ or at least the last lines. And it would be good to teach ‘Musee des Beaux Arts’ as well, which is off the beaten path, but not garishly. Mahler certainly. But Cole Porter too. And Sondheim, I think. Goya. Warhol, it goes without saying, Stephen Hawking, Kurosawa, Bergman, Bette Davis. They’d have to come up with some lines from Dark Victory, or better still, Jezebel. La Dolce Vita. Casablanca. King of Hearts. And Orson, naturally. Citizen Kane, I suppose, though personally I prefer F for Fake.”

“Judy!” cried Heilbrun.

“Yes, Judy too. But not ‘Over the Rainbow.’ It would be more impressive for them to do ‘The Trolley Song,’ don’t you think?” Kettlegorf hummed the intro.

Guernica,” said Kramer. “Robert Capa.” Eight-limbed asterisk

“Edward R. Murrow,” said Lipman.

“No! Don’t be ridiculous!” said Smythe, ending Lipman’s brief foray into the world of respectable thought.

“Marilyn Monroe!” said Kettlegorf.

“Absolutely!” said Smythe, clapping to indicate his approval.

“And the Brooklyn Bridge,” said Booth, catching on. “And the Chrysler Building.”

“Maybe,” said Smythe. “But I wonder if the Chrysler Building isn’t becoming something of a cliche.”

Peace had had enough. “And you want students to nail this stuff so they’ll do well at cocktail parties?”

Smythe sniffed criticism, always a tetchy moment for him. “You make it sound so superficial,” he said.

Prim Miss 2:

Siri Hustvedt speaks at Adelaide Writers’ Week– a story dated March 24, 2008

“I have come to think of my books as echo chambers or halls of mirrors in which themes, ideas, associations continually reflect and reverberate inside a text. There is always point and counterpoint, to use a musical illustration. There is always repetition with difference.”

A Delusion:

Exercise — Identify in the following article the sentence that one might (by unfairly taking it out of context) argue is a delusion.

(Hint: See Reflection Groups in Finite Geometry.)

A. V. Borovik, 'Maroids and Coxeter Groups'

Why Borovik’s Figure 4
is included above:

Euclid, Peirce, L’Engle:
No Royal Roads.

For more on Prim Miss 2
and deploying
the Glass Bead Game,
see the previous entry.

The image “http://www.log24.com/log/images/asterisk8.gif” cannot be displayed, because it contains errors. And now, perhaps, his brother Cornell Capa, who died Friday.

 Related material: Log24 on March 24– Death and the Apple Tree— with an excerpt from
George MacDonald, and an essay by David L. Neuhouser mentioning the influence of MacDonald on Lewis Carroll– Lewis Carroll: Author, Mathematician, and Christian (pdf).

Sunday May 25, 2008

Filed under: General,Geometry — Tags: , , — m759 @ 9:00 AM
Wechsler Cubes
“Confusion is nothing new.”
— Song lyric, Cyndi Lauper
Part I:
Magister Ludi

Hermann Hesse’s 1943 The Glass Bead Game (Picador paperback, Dec. 6, 2002, pp. 139-140)–

“For the present, the Master showed him a bulky memorandum, a proposal he had received from an organist– one of the innumerable proposals which the directorate of the Game regularly had to examine. Usually these were suggestions for the admission of new material to the Archives. One man, for example, had made a meticulous study of the history of the madrigal and discovered in the development of the style a curved that he had expressed both musically and mathematically, so that it could be included in the vocabulary of the Game. Another had examined the rhythmic structure of Julius Caesar’s Latin and discovered the most striking congruences with the results of well-known studies of the intervals in Byzantine hymns. Or again some fanatic had once more unearthed some new cabala hidden in the musical notation of the fifteenth century. Then there were the tempestuous letters from abstruse experimenters who could arrive at the most astounding conclusions from, say, a comparison of the horoscopes of Goethe and Spinoza; such letters often included pretty and seemingly enlightening geometric drawings in several colors.”

Part II:
A Bulky Memorandum

From Siri Hustvedt, author of Mysteries of the Rectangle: Essays on Painting (Princeton Architectural Press, 2005)– What I Loved: A Novel (Picador paperback, March 1, 2004, page 168)–

A description of the work of Bill Wechsler, a fictional artist:

“Bill worked long hours on a series of autonomous pieces about numbers. Like O’s Journey, the works took place inside glass cubes, but these were twice as large– about two feet square. He drew his inspiration from sources as varied as the Cabbala, physics, baseball box scores, and stock market reports. He painted, cut, sculpted, distorted, and broke the numerical signs in each work until they became unrecognizable. He included figures, objects, books, windows, and always the written word for the number. It was rambunctious art, thick with allusion– to voids, blanks, holes, to monotheism and the individual, the the dialectic and yin-yang, to the Trinity, the three fates, and three wishes, to the golden rectangle, to seven heavens, the seven lower orders of the sephiroth, the nine Muses, the nine circles of Hell, the nine worlds of Norse mythology, but also to popular references like A Better Marriage in Five Easy Lessons and Thinner Thighs in Seven Days. Twelve-step programs were referred to in both cube one and cube two. A miniature copy of a book called The Six Mistakes Parents Make Most Often lay at the bottom of cube six. Puns appeared, usually well disguised– one, won; two, too, and Tuesday; four, for, forth; ate, eight. Bill was partial to rhymes as well, both in images and words. In cube nine, the geometric figure for a line had been painted on one glass wall. In cube three, a tiny man wearing the black-and-white prison garb of cartoons and dragging a leg iron has

— End of page 168 —

opened the door to his cell. The hidden rhyme is “free.” Looking closely through the walls of the cube, one can see the parallel rhyme in another language: the German word drei is scratched into one glass wall. Lying at the bottom of the same box is a tiny black-and-white photograph cut from a book that shows the entrance to Auschwitz: ARBEIT MACHT FREI. With every number, the arbitrary dance of associations worked togethere to create a tiny mental landscape that ranged in tone from wish-fulfillment dream to nightmare. Although dense, the effect of the cubes wasn’t visually disorienting. Each object, painting, drawing, bit of text, or sculpted figure found its rightful place under the glass according to the necessary, if mad, logic of numerical, pictorial, and verbal connection– and the colors of each were startling. Every number had been given a thematic hue. Bill had been interested in Goethe’s color wheel and in Alfred Jensen’s use of it in his thick, hallucinatory paintings of numbers. He had assigned each number a color. Like Goethe, he included black and white, although he didn’t bother with the poet’s meanings. Zero and one were white. Two was blue. Three was red, four was yellow, and he mixed colors: pale blue for five, purples in six, oranges in seven, greens in eight, and blacks and grays in nine. Although other colors and omnipresent newsprint always intruded on the basic scheme, the myriad shades of a single color dominated each cube.

The number pieces were the work of a man at the top of his form. An organic extension of everything Bill had done before, these knots of symbols had an explosive effect. The longer I looked at them, the more the miniature constructions seemed on the brink of bursting from internal pressure. They were tightly orchestrated semantic bombs through which Bill laid bare the arbitrary roots of meaning itself– that peculiar social contract generated by little squiggles, dashes, lines, and loops on a page.”

Part III:
Wechsler Cubes(named not for
Bill Wechsler, the
fictional artist above,
but for the non-fictional
David Wechsler) —

From 2002:

Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale “block design” subtest.

Part IV:
A Magic Gallery
Log24, March 4, 2004

ZZ
WW

Figures from the
Kaleidoscope Puzzle
of Steven H. Cullinane:


Poem by Eugen Jost:
Zahlen und Zeichen,
Wörter und Worte

Mit Zeichen und Zahlen
vermessen wir Himmel und Erde
schwarz
auf weiss
schaffen wir neue Welten
oder gar Universen

 Numbers and Names,
Wording and Words

With numbers and names
we measure heaven and earth
black
on white
we create new worlds
and universes


English translation
by Catherine Schelbert
A related poem:

Alphabets
by Hermann Hesse

From time to time
we take our pen in hand
and scribble symbols
on a blank white sheet
Their meaning is
at everyone’s command;
it is a game whose rules
are nice and neat.

But if a savage
or a moon-man came
and found a page,
a furrowed runic field,
and curiously studied
lines and frame:
How strange would be
the world that they revealed.
a magic gallery of oddities.
He would see A and B
as man and beast,
as moving tongues or
arms or legs or eyes,
now slow, now rushing,
all constraint released,
like prints of ravens’
feet upon the snow.
He’d hop about with them,
fly to and fro,
and see a thousand worlds
of might-have-been
hidden within the black
and frozen symbols,
beneath the ornate strokes,
the thick and thin.
He’d see the way love burns
and anguish trembles,
He’d wonder, laugh,
shake with fear and weep
because beyond this cipher’s
cross-barred keep
he’d see the world
in all its aimless passion,
diminished, dwarfed, and
spellbound in the symbols,
and rigorously marching
prisoner-fashion.
He’d think: each sign
all others so resembles
that love of life and death,
or lust and anguish,
are simply twins whom
no one can distinguish…
until at last the savage
with a sound
of mortal terror
lights and stirs a fire,
chants and beats his brow
against the ground
and consecrates the writing
to his pyre.
Perhaps before his
consciousness is drowned
in slumber there will come
to him some sense
of how this world
of magic fraudulence,
this horror utterly
behind endurance,
has vanished as if
it had never been.
He’ll sigh, and smile,
and feel all right again.

— Hermann Hesse (1943),
Buchstaben,” from
Das Glasperlenspiel,
translated by
Richard and Clara Winston

Saturday, January 19, 2008

Saturday January 19, 2008

Filed under: General — Tags: , — m759 @ 7:00 AM
In Memory of
Bobby Fischer

Edward Rothstein has a piece on Bobby Fischer in today’s New York Times.  The Rothstein opening:

“There may be only three human activities in which miraculous accomplishment is possible before adulthood: mathematics, music and chess.”

This echoes the opening of a classic George Steiner essay (The New Yorker, Sept. 7, 1968):

“There are three intellectual pursuits, and, so far as I am aware, only three, in which human beings have performed major feats before the age of puberty. They are music, mathematics, and chess.”

— “A Death of Kings,” reprinted in George Steiner: A Reader, Oxford University Press, 1984, pp. 171-178.

Despite its promising (if unoriginal) opening, the New York Times piece is mainly an attack on Fischer’s anti-Jewish stance.  Rothstein actually has little of interest to say about what he calls the “glass-bead games” of music, mathematics, and chess. For a better-written piece on chess and madness, see Charles Krauthammer’s 2005 essay in TIME. The feuilletons of Rothstein and Krauthammer do not, of course, come close to the genuinely bead-game-like writing of Steiner.

Related material on
chess and religion:
Magical Thinking
(December 7th, 2005)

Thursday, May 31, 2007

Thursday May 31, 2007

Filed under: General,Geometry — Tags: — m759 @ 8:06 PM

Blitz by anonymous
New Delhi user

From Wikipedia on 31 May, 2007:

Shown below is a list of 25 alterations to Wikipedia math articles made today by user 122.163.102.246.

All of the alterations involve removal of links placed by user Cullinane (myself).

The 122.163… IP address is from an internet service provider in New Delhi, India.

The New Delhi anonymous user was apparently inspired by an earlier blitz by Wikipedia administrator Charles Matthews. (See User talk: Cullinane.)

Related material:

Ashay Dharwadker and Usenet Postings
and Talk: Four color theorem/Archive 2.
See also some recent comments from 122.163…
at Talk: Four color theorem.

May 31, 2007, alterations by
user 122.163.102.246:

  1. 17:17 Orthogonality (rm spam)
  2. 17:16 Symmetry group (rm spam)
  3. 17:14 Boolean algebra (rm spam)
  4. 17:12 Permutation (rm spam)
  5. 17:10 Boolean logic (rm spam)
  6. 17:08 Gestalt psychology (rm spam)
  7. 17:05 Tesseract (rm spam)
  8. 17:02 Square (geometry) (rm spam)
  9. 17:00 Fano plane (rm spam)
  10. 16:55 Binary Golay code (rm spam)
  11. 16:53 Finite group (rm spam)
  12. 16:52 Quaternion group (rm spam)
  13. 16:50 Logical connective (rm spam)
  14. 16:48 Mathieu group (rm spam)
  15. 16:45 Tutte–Coxeter graph (rm spam)
  16. 16:42 Steiner system (rm spam)
  17. 16:40 Kaleidoscope (rm spam)
  18. 16:38 Efforts to Create A Glass Bead Game (rm spam)
  19. 16:36 Block design (rm spam)
  20. 16:35 Walsh function (rm spam)
  21. 16:24 Latin square (rm spam)
  22. 16:21 Finite geometry (rm spam)
  23. 16:17 PSL(2,7) (rm spam)
  24. 16:14 Translation plane (rm spam)
  25. 16:13 Block design test (rm spam)

The deletions should please Charles Matthews and fans of Ashay Dharwadker’s work as a four-color theorem enthusiast and as editor of the Open Directory sections on combinatorics and on graph theory.

There seems little point in protesting the deletions while Wikipedia still allows any anonymous user to change their articles.

Cullinane 23:28, 31 May 2007 (UTC)

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

Monday, October 16, 2006

Monday October 16, 2006

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

Characters

Two items from a Wikipedia watchlist today:

1. User Loyola added a list of central characters to the article on The Glass Bead Game.

2. A dialogue between the Wikipedia characters Prof02 and Charles Matthews continues.

Item 2 seems almost to echo item 1.

The Bead Game, a classic novel by Hermann Hesse, is, in part, a commentary on German cultural history, and the Prof02-Matthews dialogue concerns the Wikipedia article on Erich Heller, a noted scholar of German cultural history.

Matthews is an expert on the game of Go. The Bead Game article says that

“The Game derives its name from the fact that it was originally played with tokens, perhaps analogous to those of an abacus or the game Go….

Although invented after Hesse’s death, Conway’s Game of Life can be seen as an example of a Go-like glass bead game with surprisingly deep properties; since it can encode Turing machines, it contains in some sense everything.”

For some related thoughts on cellular automata (i.e., Conway’s game) and Go, see The Field of Reason with its links Deep Game, And So To Bed.

For some related thoughts on Turing, see the November 2006 Notices of the American Mathematical Society (special issue on Turing).

For some related religious reflections, see Wolfram’s Theory of Everything and the Gameplayers of Zan, as well as the Log24 entries of last Halloween.

Thursday, July 20, 2006

Thursday July 20, 2006

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

Bead Game

Those who clicked on Rieff’s concept in the previous entry will know about the book that Rieff titled Sacred Order/Social Order: My Life among the Deathworks.

That entry, from Tuesday, July 18, was titled “Sacred Order,” and gave as an example the following figure:

The image “http://www.log24.com/log/pix06A/060604-Roots.jpg” cannot be displayed, because it contains errors.
(Based on Weyl’s Symmetry)

For the use of this same figure to represent a theatrical concept–

“It’s like stringing beads on a necklace. By the time the play ends, you have the whole necklace.”

— see Ursprache Revisited (June 9, 2006).

Of course, the figure also includes a cross– or “deathwork”– of sorts.  These incidental social properties of the figure (which is purely mathematical in origin) make it a suitable memorial for a theatre critic who died on the date of the previous entry– July 18– and for whom the American Theatre Wing’s design awards, the Henry Hewes Awards, are named.

“The annual awards honor designers… recognizing not only the traditional design categories of sets, costumes and lighting, but also ‘Notable Effects,’ which encompasses sound, music, video, puppets and other creative elements.” —BroadwayWorld.com

For more on life among the deathworks, see an excellent review of the Rieff book mentioned above.

 

Wednesday, August 17, 2005

Wednesday August 17, 2005

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

The image “http://www.log24.com/log/pix05B/050817-Ludi.jpg” cannot be displayed, because it contains errors.

    “The Game was at first nothing more than a witty method for developing memory and ingenuity among students and musicians.
     The inventor, Bastian Perrot of Calw… found that the pupils at the Cologne Seminary had a rather elaborate game they used to play. One would call out, in the standardized abbreviations of their science, motifs or initial bars of classical compositions, whereupon the other had to respond with the continuation of the piece, or better still with a higher or lower voice, a contrasting theme, and so forth. It was an exercise in memory and improvisation quite similar to the sort of thing probably in vogue among the ardent pupils of counterpoint in the days of Schütz, Pachelbel, and Bach….
     Bastian Perrot… constructed a frame, modeled on a child’s abacus, a frame with several dozen wires on which could be strung glass beads of various sizes, shapes, and colors….”

Hermann Hesse at The Glass Bead Game Defined

Tuesday, August 9, 2005

Tuesday August 9, 2005

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

Kaleidoscope

A new web page simplifies the Diamond 16 Puzzle and relates the resulting “kaleidoscope” to Hesse’s Bead Game.

Friday, March 11, 2005

Friday March 11, 2005

Filed under: General — Tags: — m759 @ 4:04 PM
Lucas Promises
a Darker ‘Star Wars’

See too:

The image “http://www.log24.com/log/pix05/050311-Mandate.jpg” cannot be displayed, because it contains errors.

Click on picture for details.

For some theological background
to this and the previous 8 entries,
see log24 Sept. 1-15, 2003,
which contains the following passage:

“I would like to say something more to you about cheerful serenity, the serenity of the stars and of the mind…. neither frivolity nor complacency; it is supreme insight and love, affirmation of all reality, alertness on the brink of all depths and abysses; it is a virtue of saints and of knights; it is indestructible and only increases with age and nearness to death. It is the secret of beauty and the real substance of all art.”

The Glass Bead Game

Star Wars Episode III opening date:

May 19

Friday, September 17, 2004

Friday September 17, 2004

Filed under: General — Tags: — m759 @ 3:57 PM

3:57:09…
Time is a Weapon

In memory of rock star and NRA member Johnny Ramone, who died on Wednesday, Sept. 15:

“You’ve got to ask yourself a question.”
Clint Eastwood as Dirty Harry

“At the end, when the agent pumps Neo full of lead, the agent is using a .357 Magnum. That gun only holds 9 bullets, but the agent shoots 10 shots at Neo. I don’t know where he got that gun.”

— Jesse Baumann,
    The Matrix: The Magic Bullet 

Manufacturer:
Ta’as Israel Industries,
Ramat Hasharon, Israel

Friday, August 01, 2003:

Fearful Meditation 

Ray Price - Time

TIME, Aug. 4, 2003

Ray Price — Time

“The Max D. Barnes-penned title track, with its stark-reality lyrics, is nothing short of haunting: ‘Time is a weapon, it’s cold and it’s cruel; It knows no religion and plays by no rules; Time has no conscience when it’s all said and done; Like a beast in the jungle that devours its young.’ That’s so good, it hurts! Price’s still-amazing vocals are simply the chilling icing on the cake.”

— Lisa Berg, NashvilleCountry.com

O fearful meditation!
Where, alack,
Shall time’s best jewel
from time’s chest lie hid?

— Shakespeare, Sonnet 65

Clue: click here.  This in turn leads to my March 4 entry Fearful Symmetry, which contains the following:

“Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery….”

— Hermann Hesse, The Glass Bead Game

“How strange the change from major to minor….”

— Cole Porter, “Every Time We Say Goodbye

Thursday, March 4, 2004

Thursday March 4, 2004

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

ZZ

Mit Zeichen und Zahlen
vermessen wir Himmel und Erde
schwarz
auf weiss
schaffen wir neue Welten
oder gar Universen
 
With numbers and names
we measure heaven and earth
black
on white
we create new worlds
and universes
 
— from “Zahlen und Zeichen,
  Wörter und Worte”
 
 

“Numbers and Names,
Wording and Words”

by Eugen Jost

English translation by Catherine Schelbert

Alphabets

From time to time we take our pen in hand
And scribble symbols on a blank white sheet
Their meaning is at everyone’s command;
It is a game whose rules are nice and neat.

But if a savage or a moon-man came
And found a page, a furrowed runic field,
And curiously studied lines and frame:
How strange would be the world that they revealed.
A magic gallery of oddities.
He would see A and B as man and beast,
As moving tongues or arms or legs or eyes,
Now slow, now rushing, all constraint released,
Like prints of ravens’ feet upon the snow.
He’d hop about with them, fly to and fro,
And see a thousand worlds of might-have-been
Hidden within the black and frozen symbols,
Beneath the ornate strokes, the thick and thin.
He’d see the way love burns and anguish trembles,
He’d wonder, laugh, shake with fear and weep
Because beyond this cipher’s cross-barred keep
He’d see the world in all its aimless passion,
Diminished, dwarfed, and spellbound in the symbols,
And rigorously marching prisoner-fashion.
He’d think: each sign all others so resembles
That love of life and death, or lust and anguish,
Are simply twins whom no one can distinguish …
Until at last the savage with a sound
Of mortal terror lights and stirs a fire,
Chants and beats his brow against the ground
And consecrates the writing to his pyre.
Perhaps before his consciousness is drowned
In slumber there will come to him some sense
Of how this world of magic fraudulence,
This horror utterly behind endurance,
Has vanished as if it had never been.
He’ll sigh, and smile, and feel all right again.

— Hermann Hesse (1943),
Buchstaben” from Das Glasperlenspiel,
translated by Richard and Clara Winston

See also the previous entry,
on the dream
of El Pato-lógico.

Saturday, November 22, 2003

Saturday November 22, 2003

Filed under: General — Tags: — m759 @ 2:45 PM

For Saint Cecilia’s Day

“Bastian Perrot… constructed a frame, modeled on a child’s abacus, a frame with several dozen wires on which could be strung glass beads of various sizes, shapes, and colors. The wires corresponded to the lines of the musical staff, the beads to the time values of the notes, and so on. … What later evolved out of that students’ sport and Perrot’s bead-strung wires bears to this day the name by which it became popularly known, the Glass Bead Game.”

Hermann Hesse, Das Glasperlenspiel

Compare and contrast:

Marpurg Model

Seifert Model

Wednesday, September 10, 2003

Wednesday September 10, 2003

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

4:04:08

The title refers to my entry of last April 4,

The Eight,

and to the time of this entry.

From D. H. Lawrence and the Dialogical Principle:

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

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



Philosophy



Fiction

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

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

See also

Plato, Pegasus, and the Evening Star.

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

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

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

Sunday, September 7, 2003

Sunday September 7, 2003

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

Horse Sense

Mathematicians are familiar with the emblem of Springer Verlag, the principal publisher of higher mathematics.

Ferdinand Springer, son of Julius Springer, founder of Springer Verlag, “was a passionate chess player and published a number of books on the subject. In 1881 this personal hobby and the name Springer led the company to adopt the knight in chess (in German, Springer) as its colophon.”

Hermann Hesse on a certain sort of serenity:

“I would like to say something more to you about cheerful serenity, the serenity of the stars and of the mind…. neither frivolity nor complacency; it is supreme insight and love, affirmation of all reality, alertness on the brink of all depths and abysses; it is a virtue of saints and of knights; it is indestructible and only increases with age and nearness to death. It is the secret of beauty and the real substance of all art.”

— From The Glass Bead Game

A saint and a knight, Jeanne d’Arc, was memorably portrayed by Milla Jovovich in The Messenger.

(Jovovich seems fated to play more-than-human characters in religious epics; see The Fifth Element.)

Another Springer, related to horses and to the accusation of witchcraft faced by Jeanne d’Arc, is Nancy Springer, the author of

The Hex Witch of Seldom.

Springer has written a number of books about horses, as well as other topics.

All of the above…. especially the parts having to do with mathematics and horses… was prompted by my redrawing today of a horse-shape within mathematics.  See my entry The Eight of April 4, 2003, and the horse-figure redrawn at right below.

 



Springer
Verlag



The
Messenger



A
7-Cycle

Believers in the story theory of truth may wish to relate the gifts of Jeanne d’Arc and of the girl in The Hex Witch of Seldom to the legend of Pegasus.  See, for instance,

Plato, Pegasus, and the Evening Star.

For another connection between mathematics and horses, see Sangaku.

Saturday, August 9, 2003

Saturday August 9, 2003

Filed under: General — Tags: — m759 @ 6:29 PM

Bibles

Today is the feast day of St. Hermann Hesse.  A quotation from a work by Hesse that is to some a sort of Bible:

“You treat world history as a mathematician does mathematics, in which nothing but laws and formulae exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.”

Father Jacobus, Benedictine priest, in The Glass Bead Game, ch. 4 (1943, translated 1960), by Hermann Hesse

A Benedictine Archbishop’s Apology:

“Archbishop Weakland described his feelings ‘at this moment’ as ‘remorse, contrition, shame and emptiness,’ also noting that ‘much self-pity and pride remain.’ He contended he ‘must leave that pride behind.’ “

A Mathematician’s Apology:

C.P. Snow in his introduction to A Mathematician’s Apology (also a Bible, or at least a book of a Bible, to some) quotes G. H. Hardy on hearing the chimes of Vespers:

“It’s rather unfortunate that some of the happiest hours of my life should have been spent within sound of a Roman Catholic church.”

A Bible for Benedictines:

The Encyclopedic Dictionary of Mathematics,
by the Mathematical Society of Japan,

is suitable reading for those Benedictines in Purgatory who have too lightly used words like “no reality” and “shallow” to describe mathematics.

For other remedial reading in the afterlife, see Midsummer Eve’s Dream and Quine in Purgatory.

Friday, August 1, 2003

Friday August 1, 2003

Filed under: General — Tags: , — m759 @ 1:40 PM

Fearful Meditation

Ray Price - Time TIME, Aug. 4, 2003

Ray Price — Time

“The Max D. Barnes-penned title track, with its stark-reality lyrics, is nothing short of haunting: ‘Time is a weapon, it’s cold and it’s cruel; It knows no religion and plays by no rules; Time has no conscience when it’s all said and done; Like a beast in the jungle that devours its young.’ That’s so good, it hurts! Price’s still-amazing vocals are simply the chilling icing on the cake.”

— Lisa Berg, NashvilleCountry.com

O fearful meditation! Where, alack,
Shall time’s best jewel from time’s chest lie hid?

— Shakespeare, Sonnet 65

Clue: click here.  This in turn leads to my March 4 entry Fearful Symmetry, which contains the following:

“Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery….”

— Hermann Hesse, The Glass Bead Game

“How strange the change from major to minor….”

— Cole Porter, “Every Time We Say Goodbye

Wednesday, July 23, 2003

Wednesday July 23, 2003

Filed under: General,Geometry — Tags: , , — m759 @ 4:17 PM

Being Pascal Sauvage

Pascal

“Voilà ce que je sais par une longue expérience de toutes sortes de livres et de personnes. Et sur cela je fais le même jugement de ceux qui disent que les géomètres ne leur donnent rien de nouveau par ces règles, parce qu’ ils les avaient en effet, mais confondues parmi une multitude d’ autres inutiles ou fausses dont ils ne pouvaient pas les discerner, que de ceux qui cherchant un diamant de grand prix

Diamant

parmi un grand nombre de faux, mais qu’ ils n’ en sauraient pas distinguer, se vanteraient, en les tenant tous ensemble, de posséder le véritable aussi bien que celui qui, sans s’ arrêter à ce vil amas, porte la main sur la pierre choisie que l’ on recherche, et pour laquelle on ne jetait pas tout le reste.”

— Blaise Pascal, De l’Esprit Géométrique

La Pensée Sauvage

“….the crowning image of the kaleido­scope, lavishly analogized to the mythwork in a three-hundred-word iconic apotheosis that served to put the wraps on the sustained personification of “la pensée sauvage” in the figure of the bricoleur, in an argument developed across two chapters and some twenty pages in his [Claude Lévi-Strauss’s] most famous book….”

— Robert de Marrais in
Catastrophes, Kaleidoscopes,
String Quartets:
Deploying the Glass Bead Game


Pascal Sauvage

Chiasmus

For more on pensée sauvage, see

“Claude Lévi-Strauss,

Chiasmus

and the Ethnographic Journey.”

Friday, March 21, 2003

Friday March 21, 2003

Filed under: General — Tags: , — m759 @ 9:29 AM

ART WARS:

Readings for Bach’s Birthday

Larry J. Solomon:

 

Symmetry as a Compositional Determinant,
Chapter VIII: New Transformations

In Solomon’s work, a sequence of notes is represented as a set of positions within a Latin square:

Transformations of the Latin square correspond to transformations of the musical notes.  For related material, see The Glass Bead Game, by Hermann Hesse, and Charles Cameron’s sites on the Game.

Steven H. Cullinane:

Orthogonal Latin Squares as Skew Lines, and

Map Systems

Dorothy Sayers:

“The function of imaginative speech is not to prove, but to create–to discover new similarities, and to arrange them to form new entities, to build new self-consistent worlds out of the universe of undifferentiated mind-stuff.” (Christian Letters to a Post-Christian World, Grand Rapids: Eerdmans, 1969, p. xiii)

— Quoted by Timothy A. Smith, “Intentionality and Meaningfulness in Bach’s Cyclical Works

Edward Sapir:

“…linguistics has also that profoundly serene and satisfying quality which inheres in mathematics and in music and which may be described as the creation out of simple elements of a self-contained universe of forms.  Linguistics has neither the sweep nor the instrumental power of mathematics, nor has it the universal aesthetic appeal of music.  But under its crabbed, technical, appearance there lies hidden the same classical spirit, the same freedom in restraint, which animates mathematics and music at their purest.”

 “The Grammarian and his Language,”
American Mercury 1:149-155, 1924

Tuesday, March 4, 2003

Tuesday March 4, 2003

Filed under: General — Tags: — m759 @ 9:25 PM

Fearful Symmetry

I just Googled this phrase and found the following site, which turns out to be related to my previous entry on the Bead Game and the death of John P. Thompson.

Fearful Symmetry:
The Music Master’s Lecture
,

by Daniel d’Quincy.

This in turn links to an excerpt from The Glass Bead Game that includes this passage: 

“I suddenly realized that in the language, or at any rate in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created.”

It is very easy to get dangerously confused about holiness, but here are some relevant quotes:

“You will have to allow me to digress a bit in order to bring ourselves to a sufficiently elevated perspective… I warn you, it will require an attitude of playfulness on your part. Our approach will aim more at sincerity than seriousness. The attitude I’m aiming at is best expressed, I suppose, in the playing of a unique game, known by its German name as Das Glasperlenspiel, and which we may translate as the Glass Bead Game.”

— Daniel d’Quincy, Fearful Symmetry 

“7:11”

— God himself said this, at least according to the previous entry and to my Jan. 28 entry, State of the Communion.

“Seven is heaven.”

— See my web page Eight is a Gate.

“An excellent example of a ‘universal’ in the sense of Charles Williams, Jung, or Plato is Hexagram 11 in China’s 3,000-year-old classic, the I Ching:

Hexagram 11

‘Heaven and earth unite:
 the image of PEACE.’ 
 (Wilhelm/Baynes translation,
 Princeton University Press, 1967)” 

— S. H. Cullinane, Plato, Pegasus, and the Evening Star

Thus we may associate the numbers 7 and 11 with the notions of heaven and peace; for a somewhat darker association of the time 7:11 with Kali as Time the Destroyer, see my last entry and also my previous entries

Fat Man and Dancing Girl (Feb. 18, 2003), and 

Time and Eternity (Feb. 1, 2003).

Sunday, March 2, 2003

Sunday March 2, 2003

Filed under: General — Tags: — m759 @ 10:20 PM

7:20 PM CALI Time

The Bus and the Bead Game:
 
The Communion of Saints as
 the Association of Ideas

On this date in 1955, “Bus Stop,” a play by William Inge, opened at the Music Box Theatre in New York City.

“I seemed to be standing in a bus queue by the side of a long, mean street.”

— C. S. Lewis, The Great Divorce, opening sentence

Today’s birthdays:

Sam Houston
Dr. Seuss
Kurt Weill
Mikhail Gorbachev
Tom Wolfe
Desi Arnaz
Jennifer Jones
Karen Carpenter

and many others.

Today is the feast day of  

St. Randolph Scott
St. Sandy Dennis
St. D. H. Lawrence, and
St. Charlie Christian.

“Your guitar, it sounds so sweet and clear…”

— Karen Carpenter singing “Superstar

“And if I find me a good man,
 I won’t be back at all.”

C. C. Rider lyrics

See (and hear) also “Seven Come Eleven,” played by St. Charlie Christian.

One might (disregarding separation in time and space — never major hindrances to the saints) imagine C. S. Lewis in Heaven listening to a conversation among the four saints listed above.  For more on the communion of saints, see my entry “State of the Communion” of Tuesday, Jan. 28, 2003.  This entry, quoting an old spiritual, concluded with “Now hear the word of the Lord”  — followed by this notation: 

 7:11 PM.

See also the N.Y. Times obituary of John P. Thompson of Dallas, former 7-Eleven chairman, who died, as it happened, on that very day (Jan. 28).  See also Karen Carpenter’s “first take luck.”

The sort of association of ideas described in the “Communion” entry is not unrelated to the Glasperlenspiel, or Glass Bead Game, of Hermann Hesse.  For a somewhat different approach to the Game, see

The Glass Bead Game,”

by John S. Wilson, group theorist and head of the Pure Mathematics Group at the University of Birmingham in England. Wilson is “not convinced that Hesse’s… game is only a metaphor.” Neither am I.

For the association-of-ideas approach, see the page cited in my “Communion” entry,

A Game Designer’s Holy Grail,”

and (if you can find a copy) one of the greatest forgotten books of the twentieth century,

The Third Word War,

by Ian Lee (A&W Publishers, Inc., New York, 1978).  As Lee remarks concerning the communion of saints and the association of ideas,

“The association is the idea.”
 

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