Log24

Friday, March 7, 2025

2025: Space Odysseys

Filed under: General — Tags: — m759 @ 1:29 am

From a much more abstract space, an image from the
Log24 post Symmetry  of May 3, 2016 . . .

Webpage demonstrating symmetries of 'Solomon's Cube'

For a rotating 3D view from 2025, made with the help of AI, see . . .

Note that in the Design Cube image above, the six faces are viewed
as suspended in space on three pairs of parallel planes, with the observer
viewing the parallel images only from the three directions front to back,
right to left,
and top to bottom.  In the WebSim row of six faces, the images
are pictured as they might be seen by an observer whose viewpoints vary
as he himself floats in space around the cube.

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 .

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."

 

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

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“

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).

Sunday, May 29, 2016

The Ideogram Principle …

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

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

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.

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).

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

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.”

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