Shine On, Hermann Weyl


November 23, 2002

A Puzzlement

The Diamond 16 Puzzle presents a whole that is in some sense more than the sum of its parts, a whole that satisfies Joyce's aesthetic criteria: integritas, consonantia, claritas.

For a related puzzle of a more literary sort that reflects the fragmentary nature of experience, try to satisfy these criteria by fitting together the following pieces:

The following set of 5 weblog entries attempts a solution of this literary puzzle.


From the archives of Steven H. Cullinane's journal Log24.net ->


Saturday, November 09, 2002

Birthdate of Hermann Weyl

Weyl

Plato's Diamond

Result of a Google search Nov. 9, 2002...

Searched the web for weyl symmetry .
Result 1 of about 15,400... 

Category:  Science > Math > Algebra > Group Theory 

Weyl, H.: Symmetry.
Description of the book Symmetry by Weyl, H., published by Princeton University Press. ... pup.princeton.edu/titles/
865.html - 7k - Nov. 8, 2002

Sponsored Link

Symmetry Puzzle
New free online puzzle illustrates
the mathematics of symmetry.
m759.freeservers.com/puzzle.
html

Quotation from Weyl's Symmetry:

"Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect."

In honor of Princeton University, of Sylvia Nasar (see entries of Nov, 6), of the Presbyterian Church (see entry of Nov. 8), and of Professor Weyl (whose work partly inspired the website Diamond Theory), this site's background music is now Pink Floyd's


"Shine On, 
   You Crazy Diamond."
    
 

Updates of Friday, November 15, 2002:

In order to clarify the meaning of "Shine" and "Crazy" in the above, consult the following --

To accompany this detailed exegesis of Pink Floyd, click here for a reading by Marlon Brando.

For a related educational experience, see pages 126-127 of The Book of Sequels, by Henry Beard, Christopher Cerf, Sarah Durkee, and Sean Kelly (Random House paperback, 1990).

Speaking of sequels, be on the lookout for Annie Dillard's sequel to Teaching a Stone to Talktitled Teaching a Brick to Sing. 

  4:44 am


Friday, November 08, 2002

Religious Symbolism
at Princeton

In memory of Steve McQueen ("The Great Escape" and "The Thomas Crown Affair"... see preceding entry) and of Rudolf Augstein (publisher of Der Spiegel), both of whom died on November 7 (in 1980 and 2002, respectively), in memory of the following residents of

The Princeton Cemetery
of the Nassau Presbyterian Church
Established 1757

SYLVIA BEACH (1887-1962), whose father was pastor of the First Presbyterian Church, founded Shakespeare & Company, a Paris bookshop which became a focus for struggling expatriate writers. In 1922 she published James Joyce's Ulysses when others considered it obscene, and she defiantly closed her shop in 1941 in protest against the Nazi occupation.

KURT G�DEL (1906-1978), a world-class mathematician famous for a vast array of major contributions to logic, was a longtime professor at the Institute for Advanced Study, founded in 1930. He was a corecipient of the Einstein Award in 1951.

JOHN (HENRY) O'HARA (1905-1970) was a voluminous and much-honored writer. His novels, Appointment in Samarra (1934) and Ten North Frederick (1955), and his collection of short stories, Pal Joey (1940), are among his best-known works.

and of the long and powerful association of Princeton University with the Presbyterian Church, as well as the theological perspective of Carl Jung in Man and His Symbols, I offer the following "windmill," taken from the Presbyterian Creedal Standards website, as a memorial:

The background music Les Moulins de Mon Coeur, selected yesterday morning in memory of Steve McQueen, continues to be appropriate.

"A is for Anna."
-- James Joyce


  3:33 am


Thursday, November 07, 2002

16 Years Ago Today:

Endgame

Metaphor for Morphean morphosis,
Dreams that wake, transform, and die,
Calm and lucid this psychosis,
Joyce's nightmare in Escher's eye.

At the end there is a city
With cathedral bright and sane
Facing inward from the pity
On the endgame's wavy plane.

Black the knight upon that ocean,
Bright the sun upon the king.
Dark the queen that stands beside him,
White his castle, threatening.

In the shadows' see a bishop
Guards his queen of love and hate.
Another move, the game will be up;
Take the queen, her knight will mate.

The knight said "Move, be done.  It's over."
"Love and resign," the bishop cried.
"When it's done you'll stand forever
By the darkest beauty's side."

Dabo claves regni caelorum.  By silent shore
Ripples spread from castle rock.  The metaphor
For metamorphosis no keys unlock.

-- Steven H. Cullinane, November 7, 1986

Accompaniment from "The Thomas Crown Affair":
Michel Legrand, "Les Moulins de Mon Coeur"

Lyrics by Eddy Marnay:

Comme une pierre que l'on jette
Dans l'eau vive d'un ruisseau
Et qui laisse derri�re elle
Des milliers de ronds dans l'eau....


  5:24 am


Wednesday, November 06, 2002

The Times They Are A-Changin'

Trivia quiz on tonight's "West Wing" --

What do you feed a stolen goat?


  10:00 pm


Wednesday, November 06, 2002


Today's birthdays: Mike Nichols and Sally Field.

Who is Sylvia?
What is she? 

From A Beautiful Mind, by Sylvia Nasar:

Prologue

Where the statue stood
Of Newton with his prism and silent face,
The marble index of a mind for ever
Voyaging through strange seas of Thought, alone.
-- WILLIAM WORDSWORTH

John Forbes Nash, Jr. -- mathematical genius, inventor of a theory of rational behavior, visionary of the thinking machine -- had been sitting with his visitor, also a mathematician, for nearly half an hour. It was late on a weekday afternoon in the spring of 1959, and, though it was only May, uncomfortably warm. Nash was slumped in an armchair in one corner of the hospital lounge, carelessly dressed in a nylon shirt that hung limply over his unbelted trousers. His powerful frame was slack as a rag doll's, his finely molded features expressionless. He had been staring dully at a spot immediately in front of the left foot of Harvard professor George Mackey, hardly moving except to brush his long dark hair away from his forehead in a fitful, repetitive motion. His visitor sat upright, oppressed by the silence, acutely conscious that the doors to the room were locked. Mackey finally could contain himself no longer. His voice was slightly querulous, but he strained to be gentle. "How could you," began Mackey, "how could you, a mathematician, a man devoted to reason and logical proof...how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you...?"

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. "Because," Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, "the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously."

What I take seriously:

Introduction to Topology and Modern Analysis, by George F. Simmons, McGraw-Hill, New York, 1963 

An Introduction to Abstract Harmonic Analysis, by Lynn H. Loomis, Van Nostrand, Princeton, 1953

"Harmonic Analysis as the Exploitation of Symmetry -- A Historical Survey," by George W. Mackey, pp. 543-698, Bulletin of the American Mathematical Society, July 1980

Walsh Functions and Their Applications, by K. G. Beauchamp, Academic Press, New York, 1975

Walsh Series: An Introduction to Dyadic Harmonic Analysis, by F. Schipp, P. Simon, W. R. Wade, and J. Pal, Adam Hilger Ltd., 1990

The review, by W. R. Wade, of Walsh Series and Transforms (Golubov, Efimov, and Skvortsov, publ. by Kluwer, Netherlands, 1991) in the Bulletin of the American Mathematical Society, April 1992, pp. 348-359

Music courtesy of Franz Schubert.


2:22 pm


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