Log24

Thursday, May 20, 2004

Thursday May 20, 2004

Filed under: General,Geometry — Tags: — m759 @ 7:00 am

Parable

"A comparison or analogy. The word is simply a transliteration of the Greek word: parabolé (literally: 'what is thrown beside' or 'juxtaposed'), a term used to designate the geometric application we call a 'parabola.'….  The basic parables are extended similes or metaphors."

— http://religion.rutgers.edu/nt/
    primer/parable.html

"If one style of thought stands out as the most potent explanation of genius, it is the ability to make juxtapositions that elude mere mortals.  Call it a facility with metaphor, the ability to connect the unconnected, to see relationships to which others are blind."

— Sharon Begley, "The Puzzle of Genius," Newsweek magazine, June 28, 1993, p. 50

"The poet sets one metaphor against another and hopes that the sparks set off by the juxtaposition will ignite something in the mind as well. Hopkins’ poem 'Pied Beauty' has to do with 'creation.' "

— Speaking in Parables, Ch. 2, by Sallie McFague

"The Act of Creation is, I believe, a more truly creative work than any of Koestler's novels….  According to him, the creative faculty in whatever form is owing to a circumstance which he calls 'bisociation.' And we recognize this intuitively whenever we laugh at a joke, are dazzled by a fine metaphor, are astonished and excited by a unification of styles, or 'see,' for the first time, the possibility of a significant theoretical breakthrough in a scientific inquiry. In short, one touch of genius—or bisociation—makes the whole world kin. Or so Koestler believes."

— Henry David Aiken, The Metaphysics of Arthur Koestler, New York Review of Books, Dec. 17, 1964

For further details, see

Speaking in Parables:
A Study in Metaphor and Theology

by Sallie McFague

Fortress Press, Philadelphia, 1975

Introduction
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7

"Perhaps every science must start with metaphor and end with algebra; and perhaps without metaphor there would never have been any algebra."

— attributed, in varying forms (1, 2, 3), to Max Black, Models and Metaphors, 1962

For metaphor and algebra combined, see

"Symmetry invariance in a diamond ring," A.M.S. abstract 79T-A37, Notices of the Amer. Math. Soc., February 1979, pages A-193, 194 — the original version of the 4×4 case of the diamond theorem.

Tuesday, February 17, 2004

Tuesday February 17, 2004

Filed under: General — m759 @ 4:35 pm

Hard Core

From USATODAY.com,
Posted 2/16/2004 11:16 PM

Diamond at heart of star
outweighs any on Earth

Astronomers announced Friday that a white dwarf star they’ve been studying is a chunk of crystallized carbon that weighs 5 million trillion trillion pounds. That’s the same as a diamond that is approximately 10 billion trillion trillion carats, or a one followed by 34 zeros.

Twinkle-twinkle indeed: An artist’s conception of the diamond core of a dead white-dwarf star.

Harvard-Smithsonian
Center for Astrophysics.

“It’s the mother of all diamonds,” said astronomer Travis Metcalfe, Harvard-Smithsonian Center for Astrophysics….

The biggest diamond on Earth is the 530-carat Star of Africa, part of the Crown Jewels of England. It was cut from a 3,100-carat gem*, the biggest ever found.

* The Cullinan diamond

Friday, January 9, 2004

Friday January 9, 2004

Filed under: General — m759 @ 7:20 am

Report to the
Joint Mathematics Meetings

“What was the lecture about,
Cosmo wanted to know.

‘It’s about solving equations
of the fifth degree,
which are supposed to be insoluble.'”

— Chapter 2 of
The Shadow Guests,
by Joan Aiken

For more material on insolubility
of fifth-degree equations
and on this winter’s
Joint Mathematics Meetings
(Phoenix, Jan. 7-10), see
the January 6 entry
720 in the Book.

For more material on Joan Aiken,
who died on January 4,
see the previous entry.

The number 720 is the order of
the symmetric group of degree 6.

For material related to
exceptional outer automorphisms
of this group and to
a song about Arizona, see

Skewed Mirrors.

Arizona Star:

“Shinin’ like a diamond
 she had tombstones
in her eyes.”

Tuesday, January 6, 2004

Tuesday January 6, 2004

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

720 in the Book

Searching for an epiphany on this January 6 (the Feast of the Epiphany), I started with Harvard Magazine, the current issue of January-February 2004.

An article titled On Mathematical Imagination concludes by looking forward to

“a New Instauration that will bring mathematics, at last, into its rightful place in our lives: a source of elation….”

Seeking the source of the phrase “new instauration,” I found it was due to Francis Bacon, who “conceived his New Instauration as the fulfilment of a Biblical prophecy and a rediscovery of ‘the seal of God on things,’ ” according to a web page by Nieves Mathews.

Hmm.

The Mathews essay leads to Peter Pesic, who, it turns out, has written a book that brings us back to the subject of mathematics:

Abel’s Proof:  An Essay
on the Sources and Meaning
of Mathematical Unsolvability

by Peter Pesic,
MIT Press, 2003

From a review:

“… the book is about the idea that polynomial equations in general cannot be solved exactly in radicals….

Pesic concludes his account after Abel and Galois… and notes briefly (p. 146) that following Abel, Jacobi, Hermite, Kronecker, and Brioschi, in 1870 Jordan proved that elliptic modular functions suffice to solve all polynomial equations.  The reader is left with little clarity on this sequel to the story….”

— Roger B. Eggleton, corrected version of a review in Gazette Aust. Math. Soc., Vol. 30, No. 4, pp. 242-244

Here, it seems, is my epiphany:

“Elliptic modular functions suffice to solve all polynomial equations.”

Incidental Remarks
on Synchronicity,
Part I

Those who seek a star
on this Feast of the Epiphany
may click here.

Most mathematicians are (or should be) familiar with the work of Abel and Galois on the insolvability by radicals of quintic and higher-degree equations.

Just how such equations can be solved is a less familiar story.  I knew that elliptic functions were involved in the general solution of a quintic (fifth degree) equation, but I was not aware that similar functions suffice to solve all polynomial equations.

The topic is of interest to me because, as my recent web page The Proof and the Lie indicates, I was deeply irritated by the way recent attempts to popularize mathematics have sown confusion about modular functions, and I therefore became interested in learning more about such functions.  Modular functions are also distantly related, via the topic of “moonshine” and via the  “Happy Family” of the Monster group and the Miracle Octad Generator of R. T. Curtis, to my own work on symmetries of 4×4 matrices.

Incidental Remarks
on Synchronicity,
Part II

There is no Log24 entry for
December 30, 2003,
the day John Gregory Dunne died,
but see this web page for that date.

Here is what I was able to find on the Web about Pesic’s claim:

From Wolfram Research:

From Solving the Quintic —

“Some of the ideas described here can be generalized to equations of higher degree. The basic ideas for solving the sextic using Klein’s approach to the quintic were worked out around 1900. For algebraic equations beyond the sextic, the roots can be expressed in terms of hypergeometric functions in several variables or in terms of Siegel modular functions.”

From Siegel Theta Function —

“Umemura has expressed the roots of an arbitrary polynomial in terms of Siegel theta functions. (Mumford, D. Part C in Tata Lectures on Theta. II. Jacobian Theta Functions and Differential Equations. Boston, MA: Birkhäuser, 1984.)”

From Polynomial —

“… the general quintic equation may be given in terms of the Jacobi theta functions, or hypergeometric functions in one variable.  Hermite and Kronecker proved that higher order polynomials are not soluble in the same manner. Klein showed that the work of Hermite was implicit in the group properties of the icosahedron.  Klein’s method of solving the quintic in terms of hypergeometric functions in one variable can be extended to the sextic, but for higher order polynomials, either hypergeometric functions in several variables or ‘Siegel functions’ must be used (Belardinelli 1960, King 1996, Chow 1999). In the 1880s, Poincaré created functions which give the solution to the nth order polynomial equation in finite form. These functions turned out to be ‘natural’ generalizations of the elliptic functions.”

Belardinelli, G. “Fonctions hypergéométriques de plusieurs variables er résolution analytique des équations algébrique générales.” Mémoral des Sci. Math. 145, 1960.

King, R. B. Beyond the Quartic Equation. Boston, MA: Birkhäuser, 1996.

Chow, T. Y. “What is a Closed-Form Number.” Amer. Math. Monthly 106, 440-448, 1999. 

From Angel Zhivkov,

Preprint series,
Institut für Mathematik,
Humboldt-Universität zu Berlin:

“… discoveries of Abel and Galois had been followed by the also remarkable theorems of Hermite and Kronecker:  in 1858 they independently proved that we can solve the algebraic equations of degree five by using an elliptic modular function….  Kronecker thought that the resolution of the equation of degree five would be a special case of a more general theorem which might exist.  This hypothesis was realized in [a] few cases by F. Klein… Jordan… showed that any algebraic equation is solvable by modular functions.  In 1984 Umemura realized the Kronecker idea in his appendix to Mumford’s book… deducing from a formula of Thomae… a root of [an] arbitrary algebraic equation by Siegel modular forms.”  

— “Resolution of Degree Less-than-or-equal-to Six Algebraic Equations by Genus Two Theta Constants“

Incidental Remarks
on Synchronicity,
Part III

From Music for Dunne’s Wake:

“Heaven was kind of a hat on the universe,
a lid that kept everything underneath it
where it belonged.”

— Carrie Fisher,
Postcards from the Edge

     

“720 in  
the Book”
and
“Paradise“

“The group Sp4(F2) has order 720,”
as does S6. — Angel Zhivkov, op. cit.

Those seeking
“a rediscovery of
‘the seal of God on things,’ “
as quoted by Mathews above,
should see
The Unity of Mathematics
and the related note
Sacerdotal Jargon.

For more remarks on synchronicity
that may or may not be relevant
to Harvard Magazine and to
the annual Joint Mathematics Meetings
that start tomorrow in Phoenix, see

Log24, June 2003.

For the relevance of the time
of this entry, 10:10, see

  1. the reference to Paradise
    on the “postcard” above, and
  2. Storyline (10/10, 2003).

Related recreational reading:

Labyrinth



The Shining

Shining Forth

Friday, January 2, 2004

Friday January 2, 2004

Filed under: General — m759 @ 4:28 pm

Music for Dunne’s Wake

“Heaven was kind of a hat on the universe,
a lid that kept everything underneath it
where it belonged.”

 — Carrie Fisher,
Postcards from the Edge

     

“720 in  
the Book”
and
“Paradise“

Musical Note: A Star is Born

Natalie Wood played a six-year-old
in “Miracle on 34th Street,”
six factorial equals 720,
and Wood was born on 7/20, 1938.

“How I love music.”

— John O’Hara, Hope of Heaven, 1938

For related metaphors, see
Immortal Diamond,
The Diamond Archetype, and
the first log24.net entry…
for July 20, 2002.

Friday January 2, 2004

Filed under: General — m759 @ 2:14 pm

Dunne's Wake:

What, and Give Up Show Biz?

"Dying is easy. Comedy is hard."

— Saying attributed to Edmund Gwenn, star of "Miracle on 34th Street," and also attributed to "Noel Coward, David Garrick, William Holden, Edmund Kean, Marcel Marceau, Groucho Marx, and Oscar Wilde."

See also yesterday's entry on the Dark Lady.  For more on Santa and the Dark Lady, see my archive for Aug.-Sept. 2002.

"Drink up, sweet.  You gotta go some.  How I love music.  Frère Jacques, Cuernavaca, ach du lieber August.  All languages.  A walking Berlitz.  Berlitz sounds like you with that champagne, my sweet, or how you're gonna sound."

— Hope of Heaven, by John O'Hara,
"another acidic writer to whom he
[John Gregory Dunne]
was often compared"
(Adam Bernstein, Washington Post)

For some context for the Hope of Heaven quotation, see Immortal Diamond: O'Hara, Hopkins, and Joyce, or click on the adding machine in yesterday's entry.

For more on miracles and the afterlife, see my archive for September 2002.

Saturday, September 13, 2003

Saturday September 13, 2003

Filed under: General — m759 @ 1:44 am

For the Man in Black

Lyrics:  Arizona Star

“Shinin’ like a diamond
 she had tombstones in her eyes.”

A picture: Salma Hayek and Julie Taymor

A book:  Dark Ladies, by Fritz Leiber

This offers a gentler form of the alcoholic experience than Malcolm Lowry’s classic Under the Volcano:

“I’ve had hallucinations from alcohol, too…. But only during withdrawal oddly, the first three days.  In closets and dark corners and under tables — never in very bright light — I’d see these black and sometimes red wires, about the thickness of telephone cords, vibrating, whipping around.  Made me think of giant spiders’ legs and such.  I’d know they were hallucinations — they were manageable, thank God.  Bright light would always wipe them out.”

— Fritz Leiber, “Our Lady of Darkness,” in Dark Ladies

Related entries:

The Feast of Kali, the Dark Lady, and

Architecture of Eternity,
my own “Once Upon a Time in Mexico.”

For a more serious Dark Lady portrait, see the site of artist John de la Vega.

Tuesday, September 9, 2003

Tuesday September 9, 2003

Filed under: General — m759 @ 4:04 pm

Story Theory

The conflict between the Euclidean, or “diamond” theory of truth, and the Trudeau, or “story” theory of truth, continues.

On this, Hugh Grant’s birthday, let us recall last year’s log24 entry for this date. On Roger Ebert’s review of the Hugh Grant film “Sirens” about the artist Norman Lindsay:

Ebert gets Pan wrong in this film; he says, “the bearded Lindsay is a Pan of sorts.” No. The “Pan of sorts” is in fact the girl who romps joyfully with the local boys and who later, with great amusement, uses her divine x-ray vision to view Tara Fitzgerald naked in church.

This year’s offering for Grant’s birthday is an illustrated prayer by a great defender of the religious, or “story,” theory of truth, Madeleine L’Engle:

Tara Fitzgerald

PATRICK’S RUNE

At Tara, in this fateful hour,
I place all heaven with its power.
And the sun with its brightness,
And the snow with its whiteness,
And the fire with all the strength it hath,
And the lightning with its rapid wrath,
And the winds with their swiftness along their path,
And the sea with its deepness,
And the rocks with their steepness,
And the earth with its starkness;
All these I place
By God’s almighty help and grace
Between myself and the powers of darkness.

From A Swiftly Tilting Planet
by Madeleine L’Engle

For an uncensored view, see my Harvard weblog.

Wednesday, September 3, 2003

Wednesday September 3, 2003

Filed under: General,Geometry — Tags: , , , — m759 @ 3:00 pm

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, 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 4×4 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 4×4 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.

Monday, August 18, 2003

Monday August 18, 2003

Filed under: General,Geometry — Tags: , — m759 @ 3:09 pm

Entries since Xanga’s
August 10 Failure:

Sunday, August 17, 2003  2:00 PM

A Thorny Crown of…

West Wing's Toby Ziegler

From the first episode of
the television series
“The West Wing“:

 

Original airdate: Sept. 22, 1999
Written by Aaron Sorkin

MARY MARSH
That New York sense of humor. It always–

CALDWELL
Mary, there’s absolutely no need…

MARY MARSH
Please, Reverend, they think they’re so much smarter. They think it’s smart talk. But nobody else does.

JOSH
I’m actually from Connecticut, but that’s neither here nor there. The point is that I hope…

TOBY
She meant Jewish.

[A stunned silence. Everyone stares at Toby.]

TOBY (CONT.)
When she said “New York sense of humor,” she was talking about you and me.

JOSH
You know what, Toby, let’s just not even go there.

 

Going There, Part I

 

Crown of Ideas

Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003.

From his New York Times obituary:

” ‘He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,’ said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe’s first big show at the Modern, ‘High & Low.’ ‘Art was always material first — it was never, ever bound by a thorny crown of ideas.’ ”

For a mini-exhibit of ideas in honor of Varnedoe, see

Fahne Hoch.

Verlyn Klinkenborg on Varnedoe:

“I was always struck by the tangibility of the words he used….  It was as if he were laying words down on the table one by one as he used them, like brushes in an artist’s studio. That was why students crowded into his classes and why the National Gallery of Art had overflow audiences for his Mellon Lectures earlier this year. Something synaptic happened when you listened to Kirk Varnedoe, and, remarkably, something synaptic happened when he listened to you. You never knew what you might discover together.”

Perhaps even a “thorny crown of ideas“?

“Crown of Thorns”
Cathedral, Brasilia

Varnedoe’s death coincided with
the Great Blackout of 2003.

“To what extent does this idea of a civic life produced by sense of adversity correspond to actual life in Brasília? I wonder if it is something which the city actually cultivates. Consider, for example the cathedral, on the monumental axis, a circular, concrete framed building whose sixteen ribs are both structural and symbolic, making a structure that reads unambiguously as a crown of thorns; other symbolic elements include the subterranean entrance, the visitor passing through a subterranean passage before emerging in the light of the body of the cathedral. And it is light, shockingly so….”

— Modernist Civic Space: The Case of Brasilia, by Richard J. Williams, Department of History of Art, University of Edinburgh, Scotland

 

Going There, Part II

Simple, Bold, Clear

Art historian Kirk Varnedoe was, of course, not the only one to die on the day of the Great Blackout.

Claude Martel, 34, a senior art director of The New York Times Magazine, also died on Thursday, August 14, 2003.

Janet Froelich, the magazine’s art director, describes below a sample of work that she and Martel did together:

“A new world of ideas”

Froelich notes that “the elements are simple, bold, and clear.”

For another example of elements with these qualities, see my journal entry

Fahne Hoch.

The flag design in that entry
might appeal to Aaron Sorkin’s
Christian antisemite:

 

Fahne,
S. H. Cullinane,
Aug. 15, 2003

Dr. Mengele,
according to
Hollywood

 

Note that the elements of the flag design have the qualities described so aptly by Froelich– simplicity, boldness, clarity:

They share these qualities with the Elements of Euclid, a treatise on geometrical ideas.

For the manner in which such concepts might serve as, in Gopnik’s memorable phrase, a “thorny crown of ideas,” see

“Geometry for Jews” in

ART WARS: Geometry as Conceptual Art.

See also the discussion of ideas in my journal entry on theology and art titled

Understanding: On Death and Truth

and the discussion of the word “idea” (as well as the word, and the concept, “Aryan”) in the following classic (introduced by poet W. H. Auden):

 

 

Saturday, August 16, 2003  6:00 AM

Varnedoe’s Crown

Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003.

From his New York Times obituary:

” ‘He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,’ said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe’s first big show at the Modern, ‘High & Low.’ ‘Art was always material first — it was never, ever bound by a thorny crown of ideas.’ “

For a mini-exhibit of ideas in honor of Varnedoe, see

Fahne Hoch. 

Verlyn Klinkenborg on Varnedoe:

“I was always struck by the tangibility of the words he used….  It was as if he were laying words down on the table one by one as he used them, like brushes in an artist’s studio. That was why students crowded into his classes and why the National Gallery of Art had overflow audiences for his Mellon Lectures earlier this year. Something synaptic happened when you listened to Kirk Varnedoe, and, remarkably, something synaptic happened when he listened to you. You never knew what you might discover together.”

Perhaps even a “thorny crown of ideas”?

“Crown of Thorns”
Cathedral, Brasilia

Varnedoe’s death coincided with
the Great Blackout of 2003.

“To what extent does this idea of a civic life produced by sense of adversity correspond to actual life in Brasília? I wonder if it is something which the city actually cultivates. Consider, for example the cathedral, on the monumental axis, a circular, concrete framed building whose sixteen ribs are both structural and symbolic, making a structure that reads unambiguously as a crown of thorns; other symbolic elements include the subterranean entrance, the visitor passing through a subterranean passage before emerging in the light of the body of the cathedral. And it is light, shockingly so….”

— Modernist Civic Space: The Case of Brasilia, by Richard J. Williams, Department of History of Art, University of Edinburgh, Scotland

Friday, August 15, 2003  3:30 PM

ART WARS:

The Boys from Brazil

It turns out that the elementary half-square designs used in Diamond Theory

 

also appear in the work of artist Nicole Sigaud.

Sigaud’s website The ANACOM Project  has a page that leads to the artist Athos Bulcão, famous for his work in Brasilia.

From the document

Conceptual Art in an
Authoritarian Political Context:
Brasilia, Brazil,

by Angélica Madeira:

“Athos created unique visual plans, tiles of high poetic significance, icons inseparable from the city.”

As Sigaud notes, two-color diagonally-divided squares play a large part in the art of Bulcão.

The title of Madeira’s article, and the remarks of Anna Chave on the relationship of conceptual/minimalist art to fascist rhetoric (see my May 9, 2003, entries), suggest possible illustrations for a more politicized version of Diamond Theory:

 

Fahne,
S. H. Cullinane,
Aug. 15, 2003

Dr. Mengele,
according to
Hollywood

 

Is it safe?

These illustrations were suggested in part by the fact that today is the anniversary of the death of Macbeth, King of Scotland, and in part by the following illustrations from my journal entries of July 13, 2003 comparing a MOMA curator to Lady Macbeth:

 

Die Fahne Hoch,
Frank Stella,
1959


Dorothy Miller,
MOMA curator,
died at 99 on
July 11, 2003.

 

Thursday, August 14, 2003  3:45 AM

Famous Last Words

The ending of an Aug. 14 Salon.com article on Mel Gibson’s new film, “The Passion”:

” ‘The Passion’ will most likely offer up the familiar puerile, stereotypical view of the evil Jew calling for Jesus’ blood and the clueless Pilate begging him to reconsider. It is a view guaranteed to stir anew the passions of the rabid Christian, and one that will send the Jews scurrying back to the dark corners of history.”

— Christopher Orlet

“Scurrying”?!  The ghost of Joseph Goebbels, who famously portrayed Jews as sewer rats doing just that, must be laughing — perhaps along with the ghost of Lady Diana Mosley (née Mitford), who died Monday.

This goes well with a story that Orlet tells at his website:

“… to me, the most genuine last words are those that arise naturally from the moment, such as

 

Joseph Goebbels

 

Voltaire’s response to a request that he foreswear Satan: ‘This is no time to make new enemies.’ ”

For a view of Satan as an old, familiar, acquaintance, see the link to Prince Ombra in my entry last October 29 for Goebbels’s birthday.

Wednesday, August 13, 2003  3:00 PM

Best Picture

For some reflections inspired in part by

click here.

Tuesday, August 12, 2003  4:44 PM

Atonement:

A sequel to my entry “Catholic Tastes” of July 27, 2003.

Some remarks of Wallace Stevens that seem appropriate on this date:

“It may be that one life is a punishment
For another, as the son’s life for the father’s.”

—  Esthétique du Mal, Wallace Stevens

Joseph Patrick Kennedy, Jr.

“Unless we believe in the hero, what is there
To believe? ….
Devise, devise, and make him of winter’s
Iciest core, a north star, central
In our oblivion, of summer’s
Imagination, the golden rescue:
The bread and wine of the mind….”

— Examination of the Hero in a Time of War, Wallace Stevens

Etymology of “Atonement”:

“Middle English atonen, to be reconciled, from at one, in agreement“

At One

“… We found,
If we found the central evil, the central good….
… we and the diamond globe at last were one.”

— Asides on the Oboe, Wallace Stevens

Tuesday, August 12, 2003  1:52 PM

Franken & ‘Stein,
Attorneys at Law

“Tue August 12, 2003 04:10 AM ET
NEW YORK (Reuters) – Fox News Network is suing humor writer Al Franken for trademark infringement over the phrase ‘fair and balanced’ on the cover of his upcoming book, saying it has been ‘a signature slogan’ of the network since 1996.”

Franken:
Fair?

‘Stein:
Balanced?

For answers, click on the pictures
of Franken and ‘Stein.

Saturday, August 9, 2003

Saturday August 9, 2003

Filed under: General — m759 @ 12:07 pm

Beware of…
Jews Peddling Stories:

An episode in the ongoing saga of the conflict between the "story theory of truth" and the "diamond theory of truth."

The following set of pictures summarizes some reflections on truth and reality suggested by the August 9, 2003, New York Times obituary of writer William Woolfolk, who died on July 20, 2003.

Woolfolk was the author of The Sex Goddess and was involved in the production of the comic book series The Spirit (see below).

The central strategy of the three Semitic religions — Judaism, Christianity, and Islam — is to pretend that we are all characters in a story whose author is God.  This strategy suggests the following Trinity, based on the work of William Woolfolk (The Sex Goddess and The Spirit) and Steven Spielberg ("Catch Me If You Can").  Like other Semitic tales, the story of this Trinity should not be taken too seriously.

 

William Woolfolk
Woolfolk as
a Jewish God

The Sex Goddess
Woolfolk's Story

 

Martin Sheen in Catch Me If You Can
The Father as
a Lutheran God

 

Amy Adams in Catch Me If You Can
The Father's
Story

DiCaprio as a doctor
The Son

DiCaprio and Adams
The Son's Story

Amy Adams, star of Catch Me If You Can
The Holy
Spirit

The Spirit, 1942
The Holy
Spirit's Story

 

A Confession of Faith:

Theology Based On the Film
"Catch Me If You Can":

The Son to God the Lutheran Father:

"I'm nothing really, just a kid in love with your daughter."

This is taken from a review of "Catch Me If You Can" by Thomas S. Hibbs.

For some philosophical background to this confession, see Hibbs's book

Shows About Nothing:
Nihilism in Popular Culture
from The Exorcist to Seinfeld.

By the way, today is the anniversary of the dropping on Nagasaki
of a made-in-USA Weapon of Mass Destruction, a plutonium bomb
affectionately named Fat Man.

Fat Man was a sequel to an earlier Jewish story,

Trinity.

Friday, June 27, 2003

Friday June 27, 2003

Filed under: General,Geometry — Tags: — m759 @ 6:16 pm

For Fred Sandback:
Time's a Round

The following entry of Feb. 25, 2003, was written for painter Mark Rothko, and may serve as well for minimalist artist Fred Sandback, also connected to the de Menil family of art patrons, who, like Rothko, has killed himself.

Plagued in life by depression — what Styron, quoting Milton, called "darkness visible" — Rothko took his own life on this date [Feb. 25] in 1970.  As a sequel to the previous note, "Song of Not-Self," here are the more cheerful thoughts of the song "Time's a Round," the first of Shiva Dancing: The Rothko Chapel Songs, by C. K. Latham.  See also my comment on the previous entry (7:59 PM).

Time’s a round, time’s a round,
A circle, you see, a circle to be.

— C. K. Latham

 

10/23/02

The following is from the cover of
"Finnegans Wake: a Symposium,"

a reprint of

Our Exagmination Round His Factification
for Incamination of Work in Progress,

 

Paris, Shakespeare and Company, 1929.

As well as being a memorial to Rothko and Sandback, the above picture may serve to mark the diamond anniversary of a dinner party at Shakespeare and Company on this date in 1928.  (See previous entry.)

A quotation from aaparis.org also seems relevant on this, the date usually given for the death of author Malcolm Lowry, in some of whose footsteps I have walked:

"We are not saints." 

— Chapter V, Alcoholics Anonymous

Sunday, June 22, 2003

Sunday June 22, 2003

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

Trance of the Red Queen

In memory of playwright George Axelrod, who died Saturday, June 21, 2003.

From the Chicago Sun-Times:

"In 1987, Mr. Axelrod was saluted at the New York Film Festival. He told the admiring crowd: 'I always wanted to get into the major leagues, and I knew my secret: luck and timing. I had a small and narrow but very, very sharp talent, and inside it, I'm as good as it gets.'

'The Manchurian Candidate,' in 1962, based on Richard Condon's novel about wartime brainwashing and subversive politics, may have been Mr. Axelrod's best achievement. He declared in 1995 that the script 'broke every rule. It's got dream sequences, flashbacks, narration out of nowhere . . . Everything in the world you're told not to do.'

He considered 'The Manchurian Candidate' a comedy…."

"Don't you draw the queen of diamonds,
     boy, she'll beat you if she's able.
You know the queen of hearts
     is always your best bet."

— The Eagles, "Desperado"

Another quotation that seems relevant:

"The hypnosis was performed by
the good and pious nuns…."

For the Diocese of Phoenix 

Confession in 'The Seventh Seal'

See entries of June 4 and June 15.

See also two items from Tuesday, June 17, 2003:

A 6/17 Arizona Daily Star article on Phoenix bishop Thomas O'Brien, and the 6/17 cartoon below.

 

Tony Auth, Philadelphia Inquirer,
June 17, 2003

For background, see Frank Keating in the New York Times, 6/17/03.

My entry of 5 PM EDT Saturday, June 14, 2003, which preceded the death involving Bishop O'Brien, may also be of interest.

Sunday, June 8, 2003

Sunday June 8, 2003

Filed under: General — m759 @ 3:04 am

Of Time and the River

Today is the feast day of Saint Gerard Manley Hopkins, “immortal diamond.”

“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”

— Thomas Wolfe, Of Time and the River

Thomas Wolfe

“entered the university at Chapel Hill at fifteen ‘an awkward, unhappy misfit.’ By the time he graduated, he was editor of the college newspaper….”

Jeff MacNelly, who died on this date in the Year of Our Lord 2000,

“in 1977 started drawing the comic strip ‘Shoe‘…. The strip was named in honor of the legendary Jim Shumaker, for whom MacNelly worked at the Chapel Hill Weekly.” 

From my Monday, June 2, 2003 entry:

Two quotations from “The Diamond Project“:

“We all know that something is eternal,” the Stage Manager says. “And it ain’t houses and it ain’t names, and it ain’t earth, and it ain’t even stars—everybody knows in their bones that something is eternal, and that something has to do with human beings.”
— John Lahr, review of “Our Town“ 

“Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave.  Its flashes are flashes of fire, a raging flame.”
— Song of Solomon

Here are some other thoughts from the same date, but a different time, fictional time, Faulkner time:

June Second, 1910

Where the shadow of the bridge fell I could see down for a long way, but not as far as the bottom. When you leave a leaf in water a long time after a while the tissue will be gone and the delicate fibers waving slow as the motion of sleep. They dont touch one another, no matter how knotted up they once were, no matter how close they lay once to the bones. And maybe when He says Rise the eyes will come floating up too, out of the deep quiet and the sleep, to look on glory.

— William Faulkner, The Sound and the Fury

The concluding link from my June 2, 2003, entry furnishes a clue to the timelessness of Quentin Compson‘s thoughts above:

Glory… Song of Songs 8. 7-8

From the King James Bible‘s rendition of the Song of Songs:

8:7  Many waters cannot quench love, neither can the floods drown it: if a man would give all the substance of his house for love, it would utterly be contemned.
8:8  We have a little sister, and she hath no breasts: what shall we do for our sister in the day when she shall be spoken for?

For Quentin Compson’s thoughts on his little sister Caddy, consult the online hypertext edition of

Monday, June 2, 2003

Monday June 2, 2003

Filed under: General — m759 @ 3:04 pm

Solomon’s Seal —

A follow-up to my May 28 entry,
“The Eightfold Way and Solomon’s Seal.”

From the New York Times of May (Mental Health Month) 31, 2003:

Martha Scott,
Original Emily in “Our Town,”
Dies at 88

By DOUGLAS MARTIN

Martha Scott, who created the role of the sweet, ethereal Emily in the original Broadway production of Thornton Wilder’s “Our Town” and was nominated for an Oscar for repeating it in the film version, died on Wednesday [May 28, 2003] in Los Angeles. She was 88.


United Artists

Martha Scott with William Holden
in the 1940 film of “Our Town.”

A quotation from Hemingway’s Death in the Afternoon:

“Madame, all stories, if continued far enough, end in death, and he is no true-story teller who would keep that from you.”

Two quotations from “The Diamond Project“:

“We all know that something is eternal,” the Stage Manager says. “And it ain’t houses and it ain’t names, and it ain’t earth, and it ain’t even stars—everybody knows in their bones that something is eternal, and that something has to do with human beings.”
— John Lahr, review of “Our Town” 

“Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave.  Its flashes are flashes of fire, a raging flame.”
— Song of Solomon

Monday, May 26, 2003

Monday May 26, 2003

Filed under: General,Geometry — m759 @ 4:25 am

Mental Health Month, Day 26:

Many Dimensions,
Part II — The Blue Matrix 

But seriously…

John Baez in July 1999:

"…it's really the fact that the Leech lattice is 24-dimensional that lets us compactify 26-dimensional spacetime in such a way as to get a bosonic string theory with the Monster group as symmetries."

Well, maybe.  I certainly hope so.  If the Leech lattice and the Monster group turn out to have some significance in theoretical physics, then my own work, which deals with symmetries of substructures of the Leech lattice and the Monster, might be viewed in a different light.  Meanwhile, I take (cold) comfort from some writers who pursue the "story" theory of truth, as opposed to the "diamond" theory.  See the following from my journal:

Evariste Galois and the Rock that Changed Things, and

A Time to Gather Stones Together: Readings for Yom Kippur.

See, too, this web page on Marion Zimmer Bradley's fictional

Matrices, or Blue Star-Stones, and

the purely mathematical site Diamond Theory, which deals with properties of the above "blue matrix" and its larger relatives.
 

Friday, April 25, 2003

Friday April 25, 2003

Filed under: General,Geometry — Tags: , , — m759 @ 7:59 pm

Mark

Today is the feast of Saint Mark.  It seems an appropriate day to thank Dr. Gerald McDaniel for his online cultural calendar, which is invaluable for suggesting blog topics.

Yesterday's entry "Cross-Referenced" referred to a bizarre meditation of mine titled "The Matthias Defense," which combines some thoughts of Nabokov on lunacy with some of my own thoughts on the Judeo-Christian tradition (i.e., also on lunacy).  In this connection, the following is of interest:

From a site titled Meaning of the Twentieth Century —

"Freeman Dyson has expressed some thoughts on craziness. In a Scientific American article called 'Innovation in Physics,' he began by quoting Niels Bohr. Bohr had been in attendance at a lecture in which Wolfgang Pauli proposed a new theory of elementary particles. Pauli came under heavy criticism, which Bohr summed up for him: 'We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that is not crazy enough.' To that Freeman added: 'When a great innovation appears, it will almost certainly be in a muddled, incomplete and confusing form. To the discoverer, himself, it will be only half understood; to everyone else, it will be a mystery. For any speculation which does not at first glance look crazy, there is no hope!' "

— Kenneth Brower, The Starship and the Canoe, 1979, pp. 146, 147

It is my hope that the speculation, implied in The Matthias Defense, that the number 162 has astonishing mystical properties (as a page number, article number, etc.) is sufficiently crazy to satisfy Pauli and his friend Jung as well as the more conventional thinkers Bohr and Dyson.  It is no less crazy than Christianity, and has a certain mad simplicity that perhaps improves on some of that religion's lunatic doctrines. 

Some fruits of the "162 theory" —

Searching on Google for muses 162, we find the following Orphic Hymn to Apollo and a footnote of interest:

27 Tis thine all Nature's music to inspire,
28 With various-sounding, harmonising lyre;
29 Now the last string thou tun'ft to sweet accord,
30 Divinely warbling now the highest chord….

"Page 162 Verse 29…. Now the last string…. Gesner well observes, in his notes to this Hymn, that the comparison and conjunction of the musical and astronomical elements are most ancient; being derived from Orpheus and Pythagoras, to Plato. Now, according to the Orphic and Pythagoric doctrine, the lyre of Apollo is an image of the celestial harmony…."

For the "highest chord" in a metaphorical sense, see selection 162 of the 1919 edition of The Oxford Book of English Verse (whose editor apparently had a strong religious belief in the Muses (led by Apollo)).  This selection contains the phrase "an ever-fixèd mark" — appropriately enough for this saint's day.  The word "mark," in turn, suggests a Google search for the phrase "runes to grave" Hardy, after a poem quoted in G. H. Hardy's A Mathematician's Apology.

Such a search yields a website that quotes Housman as the source of the "runes" phrase, and a further search yields what is apparently the entire poem:

Smooth Between Sea and Land

by A. E. Housman

Smooth between sea and land
Is laid the yellow sand,
And here through summer days
The seed of Adam plays.

Here the child comes to found
His unremaining mound,
And the grown lad to score
Two names upon the shore.

Here, on the level sand,
Between the sea and land,
What shall I build or write
Against the fall of night?

Tell me of runes to grave
That hold the bursting wave,
Or bastions to design
For longer date than mine.

Shall it be Troy or Rome
I fence against the foam
Or my own name, to stay
When I depart for aye?

Nothing: too near at hand
Planing the figured sand,
Effacing clean and fast
Cities not built to last
And charms devised in vain,
Pours the confounding main.

(Said to be from More Poems (Knopf, 1936), p. 64)

Housman asks the reader to tell him of runes to grave or bastions to design.  Here, as examples, are one rune and one bastion.

 


The rune known as
"Dagaz"

Represents
the balance point or "still point."


The Nike Bastion

 Dagaz: (Pronounced thaw-gauze, but with the "th" voiced as in "the," not unvoiced as in "thick") (Day or dawn.)

From Rune Meanings:

 Dagaz means "breakthrough, awakening, awareness. Daylight clarity as opposed to nighttime uncertainty. A time to plan or embark upon an enterprise. The power of change directed by your own will, transformation. Hope/happiness, the ideal. Security and certainty. Growth and release. Balance point, the place where opposites meet."

Also known as "the rune of transformation."

For the Dagaz rune in another context, see Geometry of the I Ching.  The geometry discussed there does, in a sense, "hold the bursting wave," through its connection with Walsh functions, hence with harmonic analysis.

 Temple of Athena Nike on the Nike Bastion, the Acropolis, Athens.  Here is a relevant passage from Paul Valéry's Eupalinos ou L'Architecte about another temple of four columns:

Et puis… Écoute, Phèdre (me disait-il encore), ce petit temple que j'ai bâti pour Hermès, à quelques pas d'ici, si tu savais ce qu'il est pour moi ! — Où le passant ne voit qu'une élégante chapelle, — c'est peu de chose: quatre colonnes, un style très simple, — j'ai mis le souvenir d'un clair jour de ma vie. Ô douce métamorphose ! Ce temple délicat, nul ne le sait, est l'image mathématique d'une fille de Corinthe que j'ai heureusement aimée. Il en reproduit fidèlement les proportions particulières. Il vit pour moi !

Four columns, in a sense more suited to Hardy's interests, are also a recurrent theme in The Diamond 16 Puzzle and Diamond Theory.

Apart from the word "mark" in The Oxford Book of English Verse, as noted above, neither the rune nor the bastion discussed has any apparent connection with the number 162… but seek and ye shall find.
 

Saturday, April 12, 2003

Saturday April 12, 2003

Filed under: General — Tags: — m759 @ 2:23 pm

2:23 PM
Sequel
to the previous two entries

"This world is not conclusion;
A sequel stands beyond…."
— Emily Dickinson

Today's birthday: dancer/actress Ann Miller.

"In 1937, she was discovered by Lucille Ball…."

Lucille Ball, Desi Arnaz,
and Ann Miller, cast photo
from Too Many Girls (1940)

"Just goes to show star quality shines through…."
— Website on Too Many Girls 

"It'll shine when it shines."
— Folk saying, epigraph to The Shining

"Shine on, you crazy diamond."
— Pink Floyd

"Well we all shine on…"
— John Lennon, "Instant Karma"

Monday, March 24, 2003

Monday March 24, 2003

Filed under: General — m759 @ 12:52 pm

Orwell’s question, according to
an admirer of leftist Noam Chomsky:

“When so much of the BS is right out in the open,
why is it that we know so little about it?
Why don’t we see what’s right in front of our eyes?”


Oscar
Deep Chomsky:
Lying, Truth-Telling,
and the Social Order
 
 
 
 
 Michael
 Moore

“First of all, I’d like to thank the Academy….”
— Quotation attributed to Plato

The New Yorker of March 31, 2003, discusses leftist academic Noam Chomsky.  The online edition provides a web page listing pro-Chomsky links.

Chomsky’s influence is based in part on the popularity of his half-baked theories on linguistics, starting in the 1950’s with “deep structure” and “transformational,” or “generative,” grammar.

Chomsky has abandoned many of his previous ideas and currently touts what he calls The Minimalist Program.

For some background on Chomsky’s recent linguistic notions, see the expository essay “Syntactic Theory,” by Elly van Gelderen of the Arizona State University English Department.  Van Gelderen lists her leftist political agenda on her “Other Interests” page.  Her department may serve as an example of how leftists have converted many English departments in American universities to propaganda factories.

Some attacks on Chomsky’s scholarship:

The Emperor’s New Linguistics

The New Grammarians’ Funeral

Beyond Chomsky

Could Chomsky Be Wrong? 

Forty-four Reasons Why the Chomskians Are Mistaken

Call for Papers, Chomsky 2003

Chomsky’s (Mis)Understanding of Human Thinking

Anatomy of a Revolution… Chomsky in 1962

…Linguistic Theory: The Rationality of Noam Chomsky

A Bibliography

Some attacks on Chomsky’s propaganda:

LeftWatch.com Chomsky page

Destructive Generation excerpt

The Sick Mind of Noam Chomsky

Partners in Hate: Noam Chomsky and the Holocaust Deniers

Chomsky and Plato’s Diamond

Like another purveyor of leftist nonsense, Jacques Derrida, Chomsky is fond of citing Plato as a precedent.  In particular, what Chomsky calls “Plato’s problem” is discussed in Plato’s Meno.  For a look at the diamond figure that plays a central role in that dialogue, see Diamond Theory.  For an excellent overview of related material in Plato, see Theory of Forms.

Wednesday, February 26, 2003

Wednesday February 26, 2003

Filed under: General — m759 @ 4:40 am

He Ain’t Heavy

Songwriter Tom Glazer, 88, died Friday, February 21, 2003.  From his New York Times obituary:

“Tom Glazer occasionally speculated about meeting St. Peter at the Pearly Gates and being asked what he accomplished in music.”

Glazer:

From the official Department of Defense
Korean War Commemoration website:

Title

Composer

America the Beautiful

W: Katherine Lee Baker,
M: Samuel A. Ward

The Battle Hymn
of the Republic

W: Julia Ward Howe,
M: Traditional

The Marine’s Hymn

W: Anonymous,
M: Jacques Offenbach

My Country ‘Tis of Thee

W: Samuel Francis Smith
M: Traditional

Old Soldiers Never Die

Tom Glazer

Sound Off

Willie Lee Duckworth

Stars and Stripes Forever

John Philip Sousa

Washington Post March

John Philip Sousa

West Point Suite

Darius Milhand

You’re a Grand Old Flag

George M. Cohan

Also from the New York Times:

“In 1957 he composed songs and background music for ‘A Face in the Crowd,’ a film directed by Elia Kazan.”

“His brother, who spelled his name Sidney Glazier, died in December. He produced the 1968 movie version of ‘The Producers.'”

St. Peter: 

Welcome to The Music Staff.

Wednesday, February 12, 2003

Wednesday February 12, 2003

Filed under: General,Geometry — m759 @ 3:00 am

Diamond Life
(Von Neumann’s Song, Part II)

A reader of yesterday’s entry “St. John von Neumann’s Song” suggested the relevance of little Dougie Hofstadter‘s book Gödel, Escher, Bach: An Eternal Golden Braid.  While the title of this work does continue the “golden” theme of my last three entries, Dougie is not playing in von Neumann’s league.  The nature of this league is suggested by yesterday’s citation of

Abstract Harmonic Analysis. 

For work that is more in von Neumann’s league than in Hofstadter’s, see the following

harmonic analysis abstract:

VECTOR-VALUED EXTENSIONS
OF SOME CLASSICAL THEOREMS
IN HARMONIC ANALYSIS

Maria Girardi and Lutz Weis

Abstract:
…. The approach used combines methods from Fourier analysis and the geometry of Banach spaces, such as R-boundedness.

A related paper by the same authors:

CRITERIA FOR R-BOUNDEDNESS
OF OPERATOR FAMILIES

Abstract:
…smooth operator-valued functions have a R-bounded range, where the degree of smoothness depends on the geometry of the Banach space.

Those who would like to make a connection to music in the charmingly childlike manner of Hofstadter are invited to sing a few choruses of “How do you solve a problem like Maria?“

Personally, I prefer the following lyrics:

Diamond life, lover boy;
We move in space with minimum waste and maximum joy.
City lights and business nights
When you require streetcar desire for higher heights.

No place for beginners or sensitive hearts
When sentiment is left to chance.
No place to be ending but somewhere to start.

No need to ask.
He’s a smooth operator….

Words and Music: Sade Adu and Ray St. John

Some may wish to alter the last five syllables of these lyrics in accordance with yesterday’s entry on another St. John.

Tuesday, January 21, 2003

Tuesday January 21, 2003

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

Diablo Ballet

Thanks to Meghan for the following:

not going, not coming,
rooted, deep and still
not reaching out, not reaching in
just resting, at the center
a single jewel, the flawless crystal drop
in the blaze of its brilliance
the way beyond.

— Shih Te (c. 730)

It turns out that Shih Te ("Foundling") was the sidekick of Han Shan ("Cold Mountain").  Here are some relevant links:

Thoughts of Robert Frost (see past two days' entries) lead to "Two Tramps in Mud Time," which in turn leads to Jack Kerouac and Gary Snyder splitting wood in The Dharma Bums.

This in turn leads, via a search on "Kerouac" and "axe," to the sentence

"There's the grace of an axe handle 
 as good as an Eglevsky ballet,"

in Big Sur. 

Kerouac taught me when I was 16 and he is still teaching me now that I am 60.

Searching for "Eglevsky ballet" leads to this site on André Eglevsky, his work, his life, and his children.  A further search leads to his daughter Marina Eglevsky, who stages dance for the Diablo Ballet.

Born to Dance

Marina Eglevsky and
the Diablo Ballet —
a rare and gifted
pas de deux

Those who feel the above is too "arty" for them may nevertheless appreciate the movie by the same name: "Born to Dance" (1936), starring Eleanor Powell and James Stewart.

In the larger metaphorical sense, of course, Powell and Eglevsky are both part of the same dance… at the "still point" described so well by Shih Te. 

"just resting, at the center
a single jewel…"

"At the still point,
there the dance is."
— T. S. Eliot

From Marshall's Jewelers, Tucson —

A Diamond-Cutter Sutra:

The ideal cut is a mathematical formula for cutting diamonds to precise angles and proportions to maximize the reflection and refraction of light. In addition to these ideal proportions, the polish and symmetry of the diamond is done to the highest standards also. Only then does it qualify to receive the American Gem Society (AGS) "triple zero" rating. A "zero" rating is the most perfect rating that the AGS gives evaluating the cut, polish, and symmetry of the diamond.

When a diamond receives the "zero" rating for each of these areas, (cut, polish, and symmetry), it gets three "zeros," hence the "triple zero" rating. Because of this attention to detail, it takes up to four times longer to cut a diamond to these standards than an "average" diamond.

You may choose to compromise on color or clarity but to ensure the most brilliant diamond you should not compromise on cut….

The "triple zero" ideal cut guarantees you a magnificent balance of brilliance, sparkle, and fire.

Postscript of 1/25/03:

See also the obituary of Irene Diamond, ballet patron, for whom the New York City Ballet's "Diamond Project" is named.  Diamond died on January 21, 2003, the date of the above weblog entry.

 

Monday, January 20, 2003

Monday January 20, 2003

Filed under: General — Tags: — m759 @ 5:00 pm

Shine On, Robinson Jeffers

"…be in nothing so moderate as in love of man, 
      a clever servant, insufferable master.
There is the trap that catches noblest spirits,
     that caught — they say — God, when he walked on earth."
— Shine, Perishing Republic, by Robinson Jeffers

Robinson Jeffers died at Big Sur, California, on January 20, 1962 — a year to the day after Robert Frost spoke at the Kennedy inauguration.

"The poetry of Robinson Jeffers shines with a diamond's brilliance when he depicts Nature's beauty and magnificence.   His verse also flashes with a diamond's hardness when he portrays human pain and folly."
— Gary Suttle  

"Praise Him, He hath conferred aesthetic distance
Upon our appetites, and on the bloody
Mess of our birthright, our unseemly need,
Imposed significant form. Through Him the brutes
Enter the pure Euclidean kingdom of number…."
— Howard Nemerov, 
   Grace To Be Said at the Supermarket 

"Across my foundering deck shone 
A beacon, an eternal beam. | Flesh fade, and mortal trash 
Fáll to the resíduary worm; | world's wildfire, leave but ash: 
In a flash, at a trumpet crash, 
I am all at once what Christ is |, since he was what I am, and 
Thís Jack, jóke, poor pótsherd, | patch, matchwood,
    immortal diamond, 
Is immortal diamond."
— Gerard Manley Hopkins,
    That Nature is a Heraclitean Fire and of the Comfort of the Resurrection

"In the last two weeks, I've been returning to Hopkins.  Even in the 'world's wildfire,' he asserts that 'this Jack, joke, poor potsherd, patch, matchwood, immortal diamond,/Is immortal diamond.' A comfort."
— Michael Gerson, head White House speechwriter,
    in Vanity Fair, May 2002, page 162

"There's none but truth can stead you.  Christ is truth."
— Gerard Manley Hopkins

"The rock cannot be broken.  It is the truth."
— Wallace Stevens 

"My ghost you needn't look for; it is probably
Here, but a dark one, deep in the granite…."
— Robinson Jeffers, Tor House

On this date in 1993, the inauguration day of William Jefferson Clinton, Audrey Hepburn died.

"…today, the Rock cries out to us, clearly, forcefully…."
— Maya Angelou, January 20, 1993

"So, purposing each moment to retire,
She linger'd still. Meantime, across the moors,
Had come young Porphyro, with heart on fire"
— John Keats, The Eve of St. Agnes (January 20), IX

Top view of
ordinary
diamond

Top view of
Hearts On Fire
diamond

Advertising Copy:

What you see with a Hearts On Fire diamond is an unequalled marriage of math and physics, resulting in the world's most perfectly cut diamond.

 

"Eightpointed symmetrical signs are ancient symbols for the Venus goddess or the planet Venus as either the Morning star or the Evening star."
— Symbols.com

"Set me as a seal upon your heart, as a seal upon your arm; for love is strong as death, passion fierce as the grave.  Its flashes are flashes of fire, a raging flame."
— Song of Solomon

"The last words from the people in the towers and on the planes, over and over again, were 'I love you.'  Over and over again, the message was the same, 'I love you.' …. Perhaps this is the loudest chorus from The Rock:  we are learning just how powerful love really is, even in the face of death."
— The Rev. Kenneth E. Kovacs

"Then I'll get on my knees and pray
We don't get fooled again."
— The Who 

See also my note, "Bright Star," of October 23, 2002.

 

Monday, December 16, 2002

Monday December 16, 2002

Filed under: General,Geometry — m759 @ 10:00 pm

Rebecca Goldstein
at Heaven’s Gate

This entry is in gratitude for Rebecca Goldstein’s
excellent essay
in The New York Times of December 16, 2002.

She talks about the perennial conflict between two theories of truth that Richard Trudeau called the “story theory” and the “diamond theory.” My entry of December 13, 2002, “Rhyme Scheme,” links the word “real” to an article in the Stanford Encyclopedia of Philosophy that contains the following:

“According to a platonist about arithmetic, the truth of the sentence ‘7 is prime’ entails the existence of an abstract object, the number 7. This object is abstract because it has no spatial or temporal location, and is causally inert. A platonic realist about arithmetic will say that the number 7 exists and instantiates the property of being prime independently of anyone’s beliefs, linguistic practices, conceptual schemes, and so on. A certain kind of nominalist rejects the existence claim which the platonic realist makes: there are no abstract objects, so sentences such as ‘7 is prime’ are false…”

This discussion of “sevenness,” along with the discussion of “eightness” in my December 14, 2002, note on Bach, suggest that I supply a transcription of a note in my paper journal from 2001 that deals with these matters.

From a paper journal note of October 5, 2001:

The 2001 Silver Cup Award
for Realism in Mathematics
goes to…
Glynis Johns, star of
The Sword and the Rose,
Shake Hands with the Devil, and
No Highway in the Sky.

Glynis Johns is 78 today.

“Seven is heaven,
Eight is a gate.”
— from Dealing with Memory Changes
as You Grow Older,
by Kathleen Gose and Gloria Levi

“There is no highway in the sky.”
— Quotation attributed to Albert Einstein.
(See Gotthard Günther’s website
“Achilles and the Tortoise, Part 2”.)

“Don’t give up until you
Drink from the silver cup
And ride that highway in the sky.”
—America, 1974

See also page 78 of
Realism in Mathematics
(on Gödel’s Platonism)
by Penelope Maddy,
Clarendon Press, Oxford, 1990
(reprinted, 2000).

Added 12/17/02: See also
the portrait of Rebecca Goldstein in
Hadassah Magazine
 Volume
78
Number 10
(June/July 1997).

For more on the Jewish propensity to
assign mystical significance to numbers, see
Rabbi Zwerin’s Kol Nidre Sermon.

For the significance of “seven” in Judaism, see
Zayin: The Woman of Valor.
For the significance of “eight” in Judaism, see
Chet: The Life Dynamic.

For the cabalistic significance of
“Seven is heaven, Eight is a gate,”
note that Zayin, Seven, signifies
“seven chambers of Paradise”
and that Chet, Eight, signifies
the “gateway to infinity.”

For the significance of the date 12.17, see
Tet: The Concealed Good.

Tuesday, October 8, 2002

Tuesday October 8, 2002

Filed under: General,Geometry — Tags: — m759 @ 4:08 am
Starflight Theme

On Graham Greene’s novel
The Human Factor:

“Greene, always the master of economy, never wrote a tighter or more beautifully focused novel.”
 — Steve Robertson

“The main character is Maurice Castle, the head of the Africa station for a branch of British intelligence….  [the] writing is sparse and neat rather than languid or flowery….”
— Kevin Holtsberry 

From Chapter I: 

“Castle could see that telling the truth this time had been an error of judgement, yet, except on really important occasions, he always preferred the truth.  The truth can be double-checked.”

On fiction and truth: 

Here is a short story that is
tight, focused, sparse, and neat.

The story is also true.

Mate in 2 
V. Nabokov, 1919

This problem embodies the “starflight” theme;
for details, see Tim Krabbé’s
 Open Chess Diary, entry 9.

As the example of Nabokov shows, a taste for truth (as in chess or geometry) may accompany a taste for fiction.  This applies also to Krabbé, as shown by the following reviews of his novel The Cave:

New York Times
“Krabbe’s carefully constructed narrative has a geometry so precise that the patterns buried under the surface emerge only in the final pages.”

Library Journal
“A diamond of a book- perfectly proportioned, multifaceted, and containing not one wasted word”

Monday, August 5, 2002

Monday August 5, 2002

Filed under: General,Geometry — Tags: , , — m759 @ 12:12 am

History, Stephen said….

— The Modern Word

— To really know a subject you've got to learn a bit of its history….

— John Baez, August 4, 2002

We both know what memories can bring;
They bring diamonds and rust.

—  Joan Baez, April 1975 

All sorts of structures that can be defined for finite sets have analogues for the projective geometry of finite fields….

Clearly this pattern is trying to tell us something; the question is what. As always, it pays to focus on the simplest case, since that's where everything starts.

— John Baez, August 4, 2002

In the beginning was the word….

— The Gospel according to Saint John

The anonymous author of John makes liberal use of allegory and double-entendre to illustrate this theme.

— The Gospel of John

Born yesterday: Logician John Venn. 

Venn considered three discs R, S, and T as typical subsets of a set U. The intersections of these discs and their complements divide U into 8 nonoverlapping regions….

— History of Mathematics at St. Andrews

Who would not be rapt by the thought of such marvels?….

— Saint Bonaventure on the Trinity

Sunday, August 4, 2002

Sunday August 4, 2002

Filed under: General,Geometry — m759 @ 2:52 pm

The Story Theory of Truth

versus

The Diamond Theory of Truth

One year ago today, Lorenzo Music, the voice of Carlton the doorman on Rhoda, died.  His eulogy from Valerie Harper:

 “Valerie’s heart is breaking, but Rhoda is certain that Carlton the doorman is giving St. Peter at the gate a run for his money.”

Today’s birthday: Logician John Venn. 

Appearing for the story theory…

Flannery O’Connor:

“In the long run, a people is known, not by its statements or statistics, but by the stories it tells. Fiction is the most impure and the most modest and the most human of the arts.”

Appearing for the diamond theory…

Mary McCarthy and G. H. Hardy:

From the Hollywood Investigator:

 On October 18, 1979, Mary McCarthy said on PBS’s Dick Cavett Show: “Every word she writes is a lie, including ‘and’ and ‘the.'”

Don’t forget “a,” as in “a people is known” —

“Greek mathematics is permanent, more permanent even than Greek literature.  Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.”

— G. H. Hardy in A Mathematician’s Apology

And a closing rebuttal from the story theory…

Martin Heidegger and Dean Martin: 

Words of wisdom from Martin Heidegger, Catholic Nazi:

“The nature of art is poetry.  The nature of poetry, in turn, is the founding of truth…. In the work, truth is thrown toward… an historical group of men.”

— Poetry, Language, Thought, page 75, translated by Albert Hofstadter, Harper & Row paperback, 1975

And from Dean Martin, avatar of anti-art :

That’s Amore:

– Artist: Dean Martin as sung on “Dean Martin’s Greatest Hits”
– Capitol 4XL-9389
– peak Billboard position # 2 in 1953
– from the movie “the Caddy” starring Dean, Jerry Lewis, and Donna Reed
– Words and Music by Harry Warren and Jack Brooks

(In Napoli where love is King, when boy meets girl, here’s what they say)

When the moon hits your eye like a big-a pizza pie,
That’s amore!
When the world seems to shine like you’ve had too much wine,
That’s amore!

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