Log24

Sunday, June 17, 2018

Bead Game Introduction

Filed under: General — 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.

Sunday, November 12, 2017

Devil’s Music

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

From the groom in the previous post — Swedenborg Chapel

And from November 7 last year —

Monday, November 7, 2016

Subway Art for Times Square Church

Filed under: Uncategorized — m759 @ 9:11 PM 

Click images for related material.

http://www.log24.com/log/pix12/120108-CardinalPreoccupied.jpg

"The Cardinal seemed a little preoccupied today."

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).

Tuesday, November 12, 2013

Soundtrack

Filed under: General,Geometry — Tags: , — m759 @ 6:45 AM

IMAGE- 'Devil Music' from 'Kaleidoscopes- Selected Writings of H.S.M. Coxeter'

"DEVIL – MUSIC

20 pages of incidental music written at school
for G. K. Chesterton's play MAGIC

by D. Coxeter."

See also

Related material —  Chesterton + Magic in this journal.

Friday, March 4, 2011

Ageometretos Medeis Eisito*

Filed under: General,Geometry — 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*

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

From Das Glasperlenspiel  (Hermann Hesse, 1943) —

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

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

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

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

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

Thursday, August 14, 2008

Thursday August 14, 2008

Filed under: General,Geometry — 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

Sunday, May 25, 2008

Sunday May 25, 2008

Filed under: General,Geometry — 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 — 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)

Monday, December 24, 2007

Monday December 24, 2007

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

From Saturday's entry
(Log24, Dec. 22, 2007)
a link goes to–
The five entries of June 14, 2007.

From there, the link
"One Two Three Four,
Who Are We For?"
goes to–
Princeton: A Whirligig Tour
(Log24, June 5, 2007).

From there, the link
"Taking Christ to Studio 60"
goes to–
The five Log 24 entries
prior to midnight Sept. 18, 2006.

From there, the link
"Log24, January 18, 2004"
goes to–
A Living Church.

From there, the link
"click here"
goes to–
In the Bleak Midwinter
(Internet Movie Database)…

Tagline:

The drama. The passion. The intrigue… And the rehearsals haven't even started.

Plot Summary:

Out of work actor Joe volunteers to help try and save his sister's local church
for the community by putting on a Christmas production of Hamlet…

"… were it not that
  I have bad dreams."
— Hamlet

Related material:

The New York Times online
obituaries of December 22,

 Ike Turner's
 "Bad Dreams" album
(see Log24, July 12, 2004),

"Devil Music," a composition
by H. S. M. Coxeter,

and

King of Infinite Space.

Those desiring more literary depth
may consult the G. K. Chesterton
play "Magic" for which Coxeter
wrote his "Devil Music" and
the Ingmar Bergman film
"The Magician" said to have
been inspired by Chesterton.

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 — m759 @ 12:00 PM
At Cologne

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    “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

Friday, September 17, 2004

Friday September 17, 2004

Filed under: General — 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

Saturday, November 22, 2003

Saturday November 22, 2003

Filed under: General — 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

Friday, August 1, 2003

Friday August 1, 2003

Filed under: General — 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

Friday, March 21, 2003

Friday March 21, 2003

Filed under: General — 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 — 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 — 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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