Cullinane Journal 2008 August 01-15

From the journal of Steven H. Cullinane... 2008 August 01-15

Thursday, August 14, 2008 4:19 AM

A classic now online:

'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:

Ring Theory

Monday, August 11, 2008 9:00 PM

Finite Geometry note:

New Illustration
for the four-color
decomposition theorem:

Four-color decompostion applied to the 8-point binary affine space

Sunday, August 10, 2008 10:31 AM

Annals of Philosophy:

One Year Ago
in this journal --

Commentary by Richard Wilhelm
on I Ching Hexagram 32:

Hexagram 32, Duration, of the I Ching

Duration

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

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

Globe at opening of 2008 Beijing Olympics

Globe at the
Beijing 2008 Olympics
Opening Ceremony

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

Friday, August 8, 2008 8:08 AM

Happy 8/8/8:

Weyl on symmetry, the eightfold cube, the Fano plane, and trigrams of the I Ching

Click on image for details.

Wednesday, August 6, 2008 12:00 PM

Review:

From the last link within the last link of yesterday's entry:

"Review the concepts of integritas, consonantia, and claritas in Aquinas...."

Review also the properties of the number six that appears in today's date.

For such properties, see the page of Log24 entries that end on September 6, 2006, with "Hamlet's Transformation."

Happy Feast of the Transfiguration.

Tuesday, August 5, 2008 2:02 PM

Mathematics and Narrative, continued:

Published Today:

The Last Theorem, a novel by
Arthur C. Clarke and Frederik Pohl

From the publisher's description:

"The Last Theorem is a story of one man’s mathematical obsession, and a celebration of the human spirit and the scientific method. It is also a gripping intellectual thriller....

In 1637, the French mathematician Pierre de Fermat scrawled a note in the margin of a book about an enigmatic theorem: 'I have discovered a truly marvelous proof of this proposition which this margin is too narrow to contain.' He also neglected to record his proof elsewhere. Thus began a search for the Holy Grail of mathematics-- a search that didn’t end until 1994, when Andrew Wiles published a 150-page proof. But the proof was burdensome, overlong, and utilized mathematical techniques undreamed of in Fermat’s time, and so it left many critics unsatisfied-- including young Ranjit Subramanian, a Sri Lankan with a special gift for mathematics and a passion for the famous 'Last Theorem.'

When Ranjit writes a three-page proof of the theorem that relies exclusively on knowledge available to Fermat, his achievement is hailed as a work of genius, bringing him fame and fortune...."

For a similar third-world fantasy about another famous theorem, see the oeuvre of Ashay Dharwadker.

Note the amazing conclusion of Dharwadker's saga (thus far)--

Dharwadker devises a proof of the four-color theorem that leads to...

Grand Unification
of the Standard Model
with Quantum Gravity!

For further background, see

Ashay Dharwadker
and Usenet Postings.

Clarke lived in Sri Lanka (formerly Ceylon) from 1956 until his death last March.

For another connection with Sri Lanka, see

Location, Location, Location
(July 13, 2005) and
Bagombo Snuff Box
(May 7, 2006).

Monday, August 4, 2008 9:57 AM

Happy Birthday, Dennis Lehane:

Summer of '36

Another Opening
of Another Show

"When I cast my mind back to that summer of 1936 different kinds of memories offer themselves to me. We got our first wireless set that summer-- well, a sort of a set; and it obsessed us. And because it arrived as August was about to begin, my Aunt Maggie-- she was the joker of the family-- she suggested we give it a name. She wanted to call it Lugh after the old Celtic God of the Harvest. Because in the old days August the First was La Lughnasa, the feast day of the pagan god, Lugh; and the days and weeks of harvesting that followed were called the Festival of Lughnasa."

-- Michael in the play
"Dancing at Lughnasa"

From the film "Contact"--

Jodie Foster and the
opening of the 1936 Olympics

"Heraclitus.... says: 'The ruler
whose prophecy occurs at Delphi
oute legei oute kryptei,
neither gathers nor hides,
alla semainei, but gives hints.'"
-- An Introduction to Metaphysics,
by Martin Heidegger, Yale University
Press paperback, 1959, p. 170

Sunday, August 3, 2008 10:00 PM

Annals of Lughnasa:

This Hard Prize

Triangle (percussion instrument)

"Credences of Summer," VII,

by Wallace Stevens, from
Transport to Summer (1947)

"Three times the concentred
   self takes hold, three times
The thrice concentred self,
   having possessed
The object, grips it
   in savage scrutiny,
Once to make captive,
   once to subjugate
Or yield to subjugation,
   once to proclaim
The meaning of the capture,
   this hard prize,
Fully made, fully apparent,
   fully found."

Lughnasa -- An Irish harvest festival.

"It was usually celebrated on the nearest Sunday to August 1st." --Chalice Centre

Related material:

Dancing at Lughnasa, a play by Brian Friel
Natasha's Dance, an entry in this journal
Dancing at Lughnasa, an entry in this journal from August 3, 2003

"Going up."
-- Nanci Griffith

Sunday, August 3, 2008 7:20 PM

Every Good Boy Deserves...

Note for a Triangle

Triangle (percussion instrument)

The triangle,
a percussion instrument
featured prominently in
the Tom Stoppard play
"Every Good Boy
Deserves Favour"

From a BBC News webpage
last updated at 22:31 GMT
(6:31 PM EDT)
Sunday, 3 August 2008 --

Alexander Solzhenitsyn
dies at 89

"Russian writer Alexander Solzhenitsyn, who exposed Stalin's prison system in his novels and spent 20 years in exile, has died near Moscow at the age of 89.

The author of The Gulag Archipelago and One Day In The Life Of Ivan Denisovich, who returned to Russia in 1994, died of either a stroke or heart failure.

The Nobel laureate had suffered from high blood pressure in recent years.

After returning to Russia, Solzhenitsyn wrote several polemics on Russian history and identity.

His son Stepan was quoted by one Russian news agency as saying his father died of heart failure, while another agency quoted literary sources as saying he had suffered a stroke.

He died in his home in the Moscow area, where he had lived with his wife Natalya, at 2345 local time (1945 GMT) [3:45 PM EDT], Stepan told Itar-Tass.

Russian President Dmitry Medvedev sent his condolences to the writer's family, a Kremlin spokesperson said...."

Related material:

Today's 3 PM (EDT) entry.

Sunday, August 3, 2008 3:00 PM

Mathematics and Narrative, continued:

Kindergarten
Geometry

Preview of a Tom Stoppard play presented at Town Hall in Manhattan on March 14, 2008 (Pi Day and Einstein's birthday):

The play's title, "Every Good Boy Deserves Favour," is a mnemonic for the notes of the treble clef EGBDF.

The place, Town Hall, West 43rd Street. The time, 8 p.m., Friday, March 14. One single performance only, to the tinkle-- or the clang?-- of a triangle. Echoing perhaps the clang-clack of Warsaw Pact tanks muscling into Prague in August 1968.

The “u” in favour is the British way, the Stoppard way, "EGBDF" being "a Play for Actors and Orchestra" by Tom Stoppard (words) and André Previn (music).

And what a play!-- as luminescent as always where Stoppard is concerned. The music component of the one-nighter at Town Hall-- a showcase for the Boston University College of Fine Arts-- is by a 47-piece live orchestra, the significant instrument being, well, a triangle.

When, in 1974, André Previn, then principal conductor of the London Symphony, invited Stoppard "to write something which had the need of a live full-time orchestra onstage," the 36-year-old playwright jumped at the chance.

One hitch: Stoppard at the time knew "very little about 'serious' music… My qualifications for writing about an orchestra," he says in his introduction to the 1978 Grove Press edition of "EGBDF," "amounted to a spell as a triangle player in a kindergarten percussion band."

-- Jerry Tallmer in The Villager, March 12-18, 2008

Review of the same play as presented at Chautauqua Institution on July 24, 2008:

"Stoppard's modus operandi-- to teasingly introduce numerous clever tidbits designed to challenge the audience."

-- Jane Vranish, Pittsburgh Post-Gazette, Saturday, August 2, 2008

"The leader of the band is tired
And his eyes are growing old
But his blood runs through
My instrument
And his song is in my soul."

-- Dan Fogelberg

"He's watching us all the time."

-- Lucia Joyce

Finnegans Wake,
Book II, Episode 2, pp. 296-297:

I'll make you to see figuratleavely the whome of your eternal geomater. And if you flung her headdress on her from under her highlows you'd wheeze whyse Salmonson set his seel on a hexengown.¹ Hissss!, Arrah, go on! Fin for fun!

¹ The chape of Doña Speranza of the Nacion.

Log 24, Sept. 3, 2003:

Reciprocity

From my entry of Sept. 1, 2003:

"...the principle of taking and giving, of learning and teaching, of listening and storytelling, in a word: of reciprocity....

... E. M. Forster famously advised his readers, 'Only connect.' 'Reciprocity' would be Michael Kruger's succinct philosophy, with all that the word implies."

-- William Boyd, review of Himmelfarb, a novel by Michael Kruger, in The New York Times Book Review, October 30, 1994

Last year's entry on this date:

Today's birthday:
James Joseph Sylvester

"Mathematics is the music of reason."
-- J. J. Sylvester

Sylvester, a nineteenth-century mathematician, coined the phrase "synthematic totals" to describe some structures based on 6-element sets that R. T. Curtis has called "rather unwieldy objects." See Curtis's abstract, Symmetric Generation of Finite Groups, John Baez's essay, Some Thoughts on the Number 6, and my website, Diamond Theory.

The picture above is of the complete graph K₆... Six points with an edge connecting every pair of points... Fifteen edges in all.

Diamond theory describes how the 15 two-element subsets of a six-element set (represented by edges in the picture above) may be arranged as 15 of the 16 parts of a 4x4 array, and how such an array relates to group-theoretic concepts, including Sylvester's synthematic totals as they relate to constructions of the Mathieu group M₂₄.

If diamond theory illustrates any general philosophical principle, it is probably the interplay of opposites.... "Reciprocity" in the sense of Lao Tzu. See

Reciprocity and Reversal in Lao Tzu.

For a sense of "reciprocity" more closely related to Michael Kruger's alleged philosophy, see the Confucian concept of Shu (Analects 15:23 or 24) described in

Shu: Reciprocity.

Kruger's novel is in part about a Jew: the quintessential Jewish symbol, the star of David, embedded in the K₆ graph above, expresses the reciprocity of male and female, as my May 2003 archives illustrate. The star of David also appears as part of a graphic design for cubes that illustrate the concepts of diamond theory:

Click on the design for details.

Those who prefer a Jewish approach to physics can find the star of David, in the form of K₆, applied to the sixteen 4x4 Dirac matrices, in

A Graphical Representation
of the Dirac Algebra .

The star of David also appears, if only as a heuristic arrangement, in a note that shows generating partitions of the affine group on 64 points arranged in two opposing triplets.

Having thus, as the New York Times advises, paid tribute to a Jewish symbol, we may note, in closing, a much more sophisticated and subtle concept of reciprocity due to Euler, Legendre, and Gauss. See

The Jewel of Arithmetic and

The Golden Theorem.

FinnegansWiki:

Salmonson set his seel:

"Finn MacCool ate the Salmon of Knowledge."

Wikipedia:

"George Salmon spent his boyhood in Cork City, Ireland. His father was a linen merchant. He graduated from Trinity College Dublin at the age of 19 with exceptionally high honours in mathematics. In 1841 at age 21 he was appointed to a position in the mathematics department at Trinity College Dublin. In 1845 he was appointed concurrently to a position in the theology department at Trinity College Dublin, having been confirmed in that year as an Anglican priest."

Related material:

Kindergarten Theology,

Kindergarten Relativity,

Arrangements for
56 Triangles.

For more on the
arrangement of
triangles discussed
in Finnegans Wake,
see Log24 on Pi Day,
March 14, 2008.

Happy birthday,
Martin Sheen.

Saturday, August 2, 2008 3:52 PM

You Say Adieu, I Say...

Ready When
You Are, C. B.

(continued from
June 23, 2007)

Front page top center,
online New York Times,
3:12 PM Saturday, August 2, 2008:

http://www.log24.com/log/pix08/080802-OlympicsLogo.gif

http://www.log24.com/log/pix08/080802-NastiaLiukin.jpg

Finlay MacKay for The New York Times

PLAY MAGAZINE
The Great Endorsement Scramble

BY MIMI SWARTZ

For gold-medal hopefuls like Nastia Liukin, there’s just one big chance to make it as a marketing darling.

Possible titles
for the above photo:

The Eye of Apollo
or
The Hidden Sign.

See also the conclusion
of the Wallace Stevens
poem linked to in
the previous entry.

Saturday, August 2, 2008 2:02 PM

ART WARS continued:

Geometry and Death

(continued from
June 15, 2007)

Today is the anniversary
of the 1955 death of poet
Wallace Stevens.

Related material:

A poem by Stevens,

an essay on the
relationships between
poets and philosophers --
"Bad Blood," by
Leonard Michaels --

and

The ninefold square, a symbol of Apollo

the Log24 entries
of June 14-15, 2007.

Saturday, August 2, 2008 6:23 AM

Mathematics and...

Prattle

There is an article in today's Telegraph on mathematician Simon Phillips Norton-- co-author, with John Horton Conway, of the rather famous paper "Monstrous Moonshine" (Bull. London Math. Soc. 11, 308–339, 1979).

"Simon studies one of the most complicated groups of all: the Monster. He is, still, the world expert on it ....

Simon tells me he has a quasi-religious faith in the Monster. One day, he says, ... the Monster will expose the structure of the universe.

... although Simon says he is keen for me to write a book about him and his work on the Monster and his obsession with buses, he doesn't like talking, has no sense of anecdotes or extended conversation, and can't remember (or never paid any attention to) 90 per cent of the things I want him to tell me about in his past. It is not modesty. Simon is not modest or immodest: he just has no self-curiosity. To Simon, Simon is a collection of disparate facts and no interpretative glue. He is a man without adjectives. His speech is made up almost entirely of short bursts of grunts and nouns.

This is the main reason why we spent three weeks together .... I needed to find a way to make him prattle."

Those in search of prattle and interpretive glue should consult Anthony Judge's essay ""Potential Psychosocial Significance of Monstrous Moonshine: An Exceptional Form of Symmetry as a Rosetta Stone for Cognitive Frameworks." This was cited here in Thursday's entry "Symmetry in Review." (That entry is just a list of items related in part by synchronicity, in part by mathematical content. The list, while meaningful to me and perhaps a few others, is also lacking in prattle and interpretive glue.)

Those in search of knowledge, rather than glue and prattle, should consult Symmetry and the Monster, by Mark Ronan. If they have a good undergraduate education in mathematics, Terry Gannon's survey paper "Monstrous Moonshine: The First Twenty-Five Years" (pdf) and book-- Moonshine Beyond the Monster-- may also be of interest.

Friday, August 1, 2008 2:42 PM

Annals of Burlesque:

A Two-Part Invention
for Sarah Silverman

Part I:

(Thanks to
The Unapologetic Mathematician)

The puzzle --

http://www.log24.com/log/pix08A/080801-Puzzlement.png

http://xkcd.com/457/

Part II:

The moves --

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Australia Firefox	/607455961/annals-of-pr...	8/1/2008 11:31 AM
Australia Firefox	/50840880/item.html?	8/1/2008 11:30 AM
Australia Firefox	/13339976/item.html?	8/1/2008 11:29 AM
Australia Firefox	/444176348/item.html?	8/1/2008 11:26 AM
Australia Firefox	/537539006/gee-saint-pe...	8/1/2008 11:23 AM
Australia Firefox	/504856559/item.html?	8/1/2008 11:21 AM
Australia Firefox	/523541127/item.html?	8/1/2008 11:19 AM

(From this weblog's footprints today)

Friday, August 1, 2008 2:56 AM

One for my baby...

Front page, online New York Times, Friday, August 1, 2008, 2:16 AM

Click on image for context.

Time of entry: 2:56:04 AM.