From the journal of Steven H. Cullinane... 2007 June 01-15

Friday, June 15, 2007  10:31 PM

Annals of Art Education:

Geometry and Death

(continued from Dec. 11, 2006):

J. G. Ballard on "the architecture of death":

"... a huge system of German fortifications that included the Siegfried line, submarine pens and huge flak towers that threatened the surrounding land like lines of Teutonic knights. Almost all had survived the war and seemed to be waiting for the next one, left behind by a race of warrior scientists obsessed with geometry and death."

-- The Guardian, March 20, 2006

From the previous entry, which provided a lesson in geometry related, if only by synchronicity, to the death of Jewish art theorist Rudolf Arnheim:

"We are going to keep doing this until we get it right."

Here is a lesson related, again by synchronicity, to the death of a Christian art scholar of "uncommon erudition, wit, and grace"-- Robert R. Wark of the Huntington Library.  Wark died on June 8, a date I think of as the feast day of St. Gerard Manley Hopkins, a Jesuit priest-poet of the nineteenth century.

From a Log24 entry on the date of Wark's death--
Samuel Pepys on a musical performance (Diary, Feb. 27, 1668):
"When the Angel comes down"

"When the Angel Comes Down, and the Soul Departs," a webpage on dance in Bali:

"Dance is also a devotion to the Supreme Being."

Julie Taymor, interview:

"I went to Bali to a remote village by a volcanic mountain...."

The above three quotations were intended to supply some background for a link to an entry on Taymor, on what Taymor has called "skewed mirrors," and on a related mathematical concept named, using a term Hopkins coined, "inscapes."

They might form part of an introductory class in mathematics and art given, like the class of the previous entry, in Purgatory.

Wark, who is now, one imagines, in Paradise, needs no such class.  He nevertheless might enjoy listening in.

A guest teacher in
the purgatorial class
on mathematics
and art:

Olivier as Dr. Christian Szell

The icosahedron (a source of duads and synthemes)

"Is it safe?"


Friday, June 15, 2007  1:00 PM

ART WARS continued:

A Study in
Art Education

Rudolf Arnheim, a student of Gestalt psychology (which, an obituary notes, emphasizes "the perception of forms as organized wholes") was the first Professor of the Psychology of Art at Harvard.  He died at 102 on Saturday, June 9, 2007.

The conclusion of yesterday's New York Times obituary of Arnheim:

"... in The New York Times Book Review in 1986, Celia McGee called Professor Arnheim 'the best kind of romantic,' adding, 'His wisdom, his patient explanations and lyrical enthusiasm are those of a teacher.'"

A related quotation:

"And you are teaching them a thing or two about yourself. They are learning that you are the living embodiment of two timeless characterizations of a teacher: 'I say what I mean, and I mean what I say' and 'We are going to keep doing this until we get it right.'"

-- Tools for Teaching

Here, yet again, is an illustration that has often appeared in Log24-- notably, on the date of Arnheim's death:

The 3x3 square

Related quotations:

"We have had a gutful of fast art and fast food. What we need more of is slow art: art that holds time as a vase holds water: art that grows out of modes of perception and whose skill and doggedness make you think and feel; art that isn't merely sensational, that doesn't get its message across in 10 seconds, that isn't falsely iconic, that hooks onto something deep-running in our natures. In a word, art that is the very opposite of mass media. For no spiritually authentic art can beat mass media at their own game."

-- Robert Hughes, speech of June 2, 2004

"Whether the 3x3 square grid is fast art or slow art, truly or falsely iconic, perhaps depends upon the eye of the beholder."

-- Log24, June 5, 2004

If the beholder is Rudolf Arnheim, whom we may now suppose to be viewing the above figure in the afterlife, the 3x3 square is apparently slow art.  Consider the following review of his 1982 book The Power of the Center:

"Arnheim deals with the significance of two kinds of visual organization, the concentric arrangement (as exemplified in a bull's-eye target) and the grid (as exemplified in a Cartesian coordinate system)....

It is proposed that the two structures of grid and target are the symbolic vehicles par excellence for two metaphysical/psychological stances.  The concentric configuration is the visual/structural equivalent of an egocentric view of the world.  The self is the center, and all distances exist in relation to the focal spectator.  The concentric arrangement is a hermetic, impregnable pattern suited to conveying the idea of unity and other-worldly completeness.  By contrast, the grid structure has no clear center, and suggests an infinite, featureless extension.... Taking these two ideal types of structural scaffold and their symbolic potential (cosmic, egocentric vs. terrestrial, uncentered) as given, Arnheim reveals how their underlying presence organizes works of art."

-- Review of Rudolf Arnheim's The Power of the Center: A Study of Composition in the Visual Arts (Univ. of Calif. Press, 1982). Review by David A. Pariser, Studies in Art Education, Vol. 24, No. 3 (1983), pp. 210-213

Arnheim himself says in this book (pp. viii-ix) that "With all its virtues, the framework of verticals and horizontals has one grave defect.  It has no center, and therefore it has no way of defining any particular location.  Taken by itself, it is an endless expanse in which no one place can be distinguished from the next.  This renders it incomplete for any mathematical, scientific, and artistic purpose.  For his geometrical analysis, Descartes had to impose a center, the point where a pair of coordinates [sic] crossed.  In doing so he borrowed from the other spatial system, the centric and cosmic one."

Students of art theory should, having read the above passages, discuss in what way the 3x3 square embodies both "ideal types of structural scaffold and their symbolic potential."

We may imagine such a discussion in an afterlife art class-- in, perhaps, Purgatory rather than Heaven-- that now includes Arnheim as well as Ernst Gombrich and Kirk Varnedoe.

Such a class would be one prerequisite for a more advanced course-- Finite geometry of the square and cube.


Thursday, June 14, 2007  9:00 PM

Nine is a Vine:

A Time
for Remembering


June 9, the birthday of
Aaron Sorkin, a writer
mentioned in recent
Log24 entries, was also
the birthday of writer
Patricia Cornwell.

An illustration
from that date:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

Cornwell's first book was
a biography of
Ruth Bell Graham,
A Time for Remembering.

"Seven is heaven,
Eight is a gate,
Nine is a vine."


Thursday, June 14, 2007  4:00 PM

A Death, A Life...

A Flag for Sunset

"Kurt Waldheim, the former United Nations Secretary General and President of Austria whose hidden ties to Nazi organizations and war crimes was [sic] exposed late in his career, died today at his home in Vienna. He was 88." --The New York Times this afternoon

Related material:

From a story by
Leonard Michaels
linked to on
Aaron Sorkin's
birthday, June 9:

"Induction and analogy, in which he was highly gifted, were critical to mathematical intelligence.

It has been said that the unexamined life isn't worth living. Nachman wasn't against examining his life, but then what was a life? ....

... As for 'a life,' it was what you read about in newspaper obituaries. He didn't need one. He would return to California and think only about mathematics."

Mathematics:

1.  A quotation from George Polya,
     the author of
     Induction and Analogy
     in Mathematics

2.  A quotation from an anonymous
     Internet user signed
     "George Polya"--
     "Steven Cullinane is a Liar."

3.  L'Affaire Dharwadker continues
     (May 31, 2007)

4.  Geometry for Jews

The image “http://log24.com/theory/images/070614-Whirl.gif” cannot be displayed, because it contains errors.

"One two three four,
who are we for?"



Thursday, June 14, 2007  10:35 AM

For a Bright Star:

Trifecta

The image “http://www.log24.com/log/pix07/070614-Ariel.jpg” cannot be displayed, because it contains errors.

(Continued from 9/5/02)

Arts & Letters Daily (14 Jun 2007):


Every time an economic impact study comes out, you know the pigs are at the pastry cart. "Save your city by giving money to the arts!" Yeah, sure... more

Democracy can flourish in India only if every citizen resists the will to dominate and accepts the reality and equality of others... more

The American left has turned into a skittish, hysterical old lady who lives in the past, falls for pseudo-intellectual garbage, and runs from real conflict or responsibility... more


Thursday, June 14, 2007  2:00 AM

Gestalt, Part II

Unscholarly Notes

The time of the previous entry, 1:06:18, suggests both the date of Epiphany, 1:06, and Hexagram 18 of the I Ching: Ku, Work on what has been spoiled (Decay).

Epiphany: A link in the Log24 entries for Epiphany 2007 leads to Damnation Morning, which in turn leads to Why Me?, a discussion of the mythology of Spiders vs. Snakes devised by Fritz Leiber.  Spiders represent the conscious mind, snakes the unconscious.

On Hexagram 18: "The Chinese character ku represents a bowl in whose contents worms are breeding. This means decay." --Wilhelm's commentary

This brings us back to the previous entry with its mention of the date of Rudolf Arnheim's death: Saturday, June 9.  In Log24 on that date there was a link, in honor of Aaron Sorkin's birthday, to a short story by Leonard Michaels.  That link was suggested, in part,  by a review in the Sunday New York Times Book Review (available online earlier, on Friday). Here is a quote from that review related to the Hexagram 18 worm bowl:

"... what grabbed attention for his early collections was Michaels's gruesome, swaggering depiction of the sexual rampage that was the swinging '60s in New York-- 'the worm bucket,' as Michaels described an orgy."

Related material for meditation on this, the anniversary (according to Encyclopaedia Britannica) of the birth of author Jerzy Kosinski-- his novel The Hermit of 69th Street.

Kosinski was not unfamiliar with Michaels's worm bucket.  For related information, see Hermit (or at least a review).


In Leiber's stories the symbol of the Snakes is similar to the famed Yin-Yang symbol, also known as the T'ai-chi tu.  For an analysis of this symbol by Arnheim, see the previous entry.  See also "Sunday in the Park with Death" (Log24, Oct. 26, 2003):




"Ay que bonito es volar  
    A las dos de la mañana
...."
-- "La Bruja"


Thursday, June 14, 2007  1:06 AM

Gestalt, Part I

Scholarly Notes

In memory of
Rudolf Arnheim,
who died on
Saturday, June 9

"Originally trained in Gestalt psychology, with its emphasis on the perception of forms as organized wholes, he was one of the first investigators to apply its principles to the study of art of all kinds." --Today's New York Times

From the Wikipedia article on Gestalt psychology prior to its modification on May 31, 2007:

"Emergence, reification, multistability, and invariance are not separable modules to be modeled individually, but they are different aspects of a single unified dynamic mechanism.

For a mathematical example of such a mechanism using the cubes of psychologists' block design tests, see Block Designs in Art and Mathematics and The Kaleidoscope Puzzle."

The second paragraph of the above passage refers to my own work.

Some Gestalt-related work of Arnheim:

The image “http://www.log24.com/log/pix07/070614-Arnheim.gif” cannot be displayed, because it contains errors.

--  From p. 242 of
  "Perceptual Analysis of a
  Symbol of Interaction,"
  pp. 222-244 in
  Toward a Psychology of Art:
  Collected Essays
,
  Univ. of Calif. Press, 1966

Time of this entry:
1:06:18 AM ET.


Wednesday, June 13, 2007  6:29 PM

From Andrew Cusack:

A Flaming Cross
for Spain


Beatification of Martyrs of Spain

Click for details.

Related flaming crosses:

Nov. 19, 2004

and
 Nov. 21, 2004.

(This entry was actually made
just before noon on June 14.
 Its time, 6:29, was reserved
earlier in honor of
the date 6/29.)


Wednesday, June 13, 2007  12:00 PM

Endings

Tony:

Tony Soprano

One Notch Above

Maureen Dowd in today's New York Times on "Sopranos" creator David Chase:

"Mr. Chase, an apocalyptic tease, gave us a gimmicky and unsatisfying film-school-style blackout for an end to his mob saga, a stunt one notch above 'It was all a dream.'"

Related material:
the previous entry


Tuesday, June 12, 2007  11:07 PM

Because, because, because, because...

On Framing Science

"... Packaging is unavoidable.
Facts rarely, if ever, 
  speak for themselves."

-- Matthew C. Nisbet,  
American University
Assistant Professor
  of "Communication,"
on June 6, 2007, in

Framing Science

Frame this.

The Death of Mr. Wizard

Related material:
previous Log24 entries
of June 10-12



Tuesday, June 12, 2007  2:00 PM

Stage Space

Sky Fish

Sky Fish - A Logo for Philip K. Dick

Illustration from
LOGOS
(May 17, 2007)

From an obituary in today's New York Times:

"Lee Nagrin, a noted Off Broadway performance artist... died Thursday in Manhattan. She was 78....

She formed her own company, the Sky Fish Ensemble, in 1979 and presented performance-art pieces that tended to unspool like fairy tales, filled with mysterious, archetypal imagery. Her own presence was mysterious, too, both on and off the stage, often conjuring up the sense of a keen-eyed, all-seeing, benign witch.

She created some of those images midperformance, as when she traced a landscape along brown paper that ringed the stage space of Silver Whale Gallery, where much of her work was performed.

For her last piece, 'Behind the Lid,' she collaborated with the puppeteer Basil Twist on a story in which a woman looks back on her life through a dream. Performances are this month at the Silver Whale."

LEE NAGRIN AND BASIL TWIST’S
BEHIND THE LID

Tuesday - Sunday @ 8PM
June 3rd - June 28th
Silver Whale Gallery


"Silver Whale Gallery (21 Bleecker Street) proudly announces the world premiere of BEHIND THE LID, a new play by playwright/performer Lee Nagrin and puppeteer/performer Basil Twist that chronicles a woman looking back on her life through a dream; her memories expand, open and reveal while an intimate audience of 18 will travel with her through this hand made world. Audience members are guided by a young familiar through this older woman's life and dreams. They experience layer upon layer of the life of an American artist - Lee Nagrin. Basil Twist creates the puppetry and performs.

Tickets for BEHIND THE LID are $40. To purchase tickets, please call Smarttix.com at 212-868-4444 or for more information visit www.leenagrin.com on the Internet."

From Log24
on June 7, the date
of Nagrin's death
:

"... Packaging is unavoidable.
Facts rarely, if ever, 
  speak for themselves."

-- Matthew C. Nisbet,  
Assistant Professor
  of "Communication,"
June 6, 2007

From the
New York Lottery
on June 7, the date
of Nagrin's death:

Mid-day: 603
Evening: 805

Another opening of
another show.


Monday, June 11, 2007  12:00 AM

Another Midnight Special

Continued from June 7--

Second Billing, Part III:

Philosophy of
Communication


Obituaries: Richard Rorty, Ousmane Sembene

Pictures are more accessible
than words. See Logos
(May 17) and Torbellino
(June 10), as well as
the entries for June 8,
the date of Rorty's death.


Sunday, June 10, 2007  12:00 PM

Happy Birthday, Judy Garland

Torbellino
 
The image “http://www.log24.com/log/pix07/070610-Torbellino.jpg” cannot be displayed, because it contains errors.

Tornado and Rainbow over Kansas
,
NASA Picture of the Day for
June 13, 2005

WHAT MAKES IAGO EVIL? some people ask. I never ask. --Joan Didion

Iago states that he is not who he is. --Mark F. Frisch

La historia agrega que, antes o después de morir, se supo frente a Dios y le dijo: «Yo, que tantos hombres he sido en vano, quiero ser uno y yo». La voz de Dios le contestó desde un torbellino: «Yo tampoco soy; yo soñé el mundo como tú soñaste tu obra, mi Shakespeare, y entre las formas de mi sueño estabas tú, que como yo eres muchos y nadie». --Jorge Luis Borges


Sunday, June 10, 2007  2:00 AM

Garden of the Soul

Like a Melody

An excerpt from
The Miracle of the Bells
quoted in
A Mass for Lucero--

"'A pretty girl--          
 is like a melody---- !'
But that was always
Bill Dunnigan's      
Song of Victory....  
Thus thought the...
press agent for     
       'The Garden of the Soul.'"

"Ay que bonito es volar  
    A las dos de la mañana
...."
-- "La Bruja"

For a rendition by
Salma Hayek, click
on the picture below.



Related material:
Log24 entries for
May 18, 2007.


Saturday, June 9, 2007  9:00 AM

Happy Birthday, Aaron Sorkin

Cryptology

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

-- The Delphic Corporation


Friday, June 8, 2007  4:00 PM

ART WARS continued:

For the Author of
the Word "Inscape"
on His Feast Day

Samuel Pepys on a musical performance (Diary, Feb. 27, 1668):
"When the Angel comes down"

"When the Angel Comes Down, and the Soul Departs," a webpage on dance in Bali:

"Dance is also a devotion to the Supreme Being."

Julie Taymor, interview:

"I went to Bali to a remote village by a volcanic mountain...."

Under the Volcano:

"No se puede vivir sin amar.

Log24 on St. Peter's Day, 2004:

"And so to bed."

Friday, June 8, 2007  2:00 PM

Commencement week ends:

The Source
"Beautiful indeed
is the source of truth.
To measure the changes
     of time and space
the smartest are nothing."
-- The Emperor of Math

Forrest Gump plays ping-pong in China


Thursday, June 7, 2007  4:15 PM

What is Truth, continued:

Framing
truth

On "framing" and "spin"
in journalism:

"... Packaging is unavoidable.
Facts rarely, if ever, 
  speak for themselves."

-- Matthew C. Nisbet,  
Assistant Professor
  of "Communication,"
June 6, 2007

If they could, they might
say "We was framed!"

Facts cannot, of course,
speak for themselves
to those who do not
understand their language.

Example:


A picture that appeared in
Log24 on June 7, 2005:

Natural Transformation

Click for details.

Attempt to
frame the picture:


Analogies

"A functor is an analogy."
-- Anonymous

  The best mathematicians "see
analogies between analogies."
-- Banach, according to Ulam 

For further details,
click on the link
"Analogies" above.

See also the analogies in
the previous entry.


Thursday, June 7, 2007  11:30 AM

Final Arrangements, continued:

Masters of Chaos

From the May 6, 2007,
New York Times,
Charles McGrath on
Philip K. Dick:
His early novels, written in two weeks or less, were published in double-decker Ace paperbacks that included two books in one, with a lurid cover for each. "If the Holy Bible was printed as an Ace Double," an editor once remarked, "it would be cut down to two 20,000-word halves with the Old Testament retitled as 'Master of Chaos' and the New Testament as 'The Thing With Three Souls.'"
 
Masters of Chaos

Click to enlarge.

As for "the thing with
three souls"--


Part I:
"Educate, Empower, Entertain"
-- Motto of Yolanda King

Part II:
Three universities
(but not those of
Martin Myerson)--
Princeton, Harvard, Cambridge


Wednesday, June 6, 2007  11:07 AM

A Mathematical Narrative

It is now 3:07 AM
June 7 in New Zealand.
Today at Cullinane College:

Examination Day

The image “http://www.log24.com/log/pix05B/051003-Deceivers1.jpg” cannot be displayed, because it contains errors.

(For the college curriculum,
see the New Zealand
Qualifications Authority.)

If Cullinane College were Hogwarts--

Last-minute exam info:

The Lapis Philosophorum

"The lapis was thought of as a unity and therefore often stands for the prima materia in general."
-- Aion, by C. G. Jung

"Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe."
-- The Stars My Destination, by Alfred Bester

And from Bester's The Deceivers:

Meta Physics

"'... Think of a match.  You've got a chemical head of potash, antimony, and stuff, full of energy waiting to be released.  Friction does it.  But when Meta excites and releases energy, it's like a stick of dynamite compared to a match.  It's the chess legend for real.'

'I don't know it.'

'Oh, the story goes that a philosopher invented chess for the amusement of an Indian rajah.  The king was so delighted that he told the inventor to name his reward and he'd get it, no matter what.  The philosopher asked that one grain of rice be placed on the first square of the chessboard, two on the second, four on the third, and so on to the sixty-fourth.'

'That doesn't sound like much.'

'So the rajah said. ...'"

Related material:

Geometry of the I Ching


Tuesday, June 5, 2007  6:01 PM

Mathematics and Narrative, continued:

God, the Devil,
and a Bridge


"... just as God defeats the
devil: this bridge exists ..."
-- Andre Weil

The "Mathematical"
Bridge at Queens' College,
Cambridge:

Mathematical Bridge, Queens' College, Cambridge

Some related material
  might well be titled,
as in
the previous entry's
parody of a new book,

The Assault on Reason: A How-To Manual by Charles Matthews (former Fellow, Queens' College, Cambridge)

For details, see
Connecting Ideas
and
Blitzes at Wikipedia.

(The reference in the parody
book cover above is to
Charles Matthews,
Wikipedia administrator

  and former
Fellow of Queens' College.)


Tuesday, June 5, 2007  2:00 PM

Meanwhile, back at Harvard...

Devil in the Details

This morning was the
Princeton commencement.
Meanwhile...


(Altered) photo at right
courtesy of Kenneth L.

From the May 18 Harvard Crimson:

"Paul B. Davis ’07-’08, who contributed
to a collection of student essays
written in 2005 on the purpose
and structure of a Harvard education,
said that 'the devil is in the details'...."

For the details, see

Al Gore and the
Absence of Truth


(May 30, 2007).


Tuesday, June 5, 2007  11:08 AM

Whirligig continued...

Princeton:
A Whirligig Tour

Symbol from a
website on
"Presbyterian
Creedal Standards"

The above symbol
appeared here
on 11/8/02.

Related material:

1. The remarks of
Bradley Whitford

at Princeton's
Class Day yesterday:

The image “http://www.log24.com/log/pix07/070605-Whitford.jpg” cannot be displayed, because it contains errors.

2. An illustration from
Log 24 on 11/10/06:

Paul Robeson in
King Solomon's
Mines

Counterchange
symmetry


3. The Whirligig of Time
(1/5/03):

The image “http://www.log24.com/log/pix07/070605-Whirligig.jpg” cannot be displayed, because it contains errors.

4. Natalie Angier, priestess of Scientism
  (5/26/07), and her new book
The Canon: A Whirligig Tour of
the Beautiful Basics of Science
(available as a special from
Amazon.com):

Better Together Buy this book with
God Is Not Great:
How Religion Poisons Everything
by Christopher Hitchens today!

The Canon: A Whirligig Tour of the Beautiful Basics of Science God Is Not Great: How Religion Poisons Everything
Buy Together Today: $31.19

Customers who bought this item
also bought

God Is Not Great:
How Religion Poisons Everything
by Christopher Hitchens

5. Taking Christ to Studio 60


Sunday, June 3, 2007  9:29 PM

For Princeton's Class of 2007:

Dialogue

Albert Einstein--

"God does not play dice
with the universe."

Reply by the
New Jersey Lottery on
Sunday, June 3, 2007--

Mid-day 220, evening 939.

Related material


Review of a 2004 production
of a 1972 Tom Stoppard
play, "Jumpers"--

John Lahr on Tom Stoppard's play Jumpers


Sunday, June 3, 2007  10:31 AM

Today's Sermon:

Haunting Time

"Macquarrie remains one of the most
important commentators [on] ...
Heidegger's work. His co-translation
of Being and Time into English is
considered the canonical version."
-- Wikipedia

The Rev. John Macquarrie, Scottish Theologian, Dies at 87

The Rev. Macquarrie died on
May 28.  The Log24 entry
for that date contains the
following illustration:

A 4x4x4 cube

The part of the illustration
relevant to the death of
Macquarrie is the color.
From my reply to

a comment on the
May 28 entry:

"I checked out [Terence] McKenna and found this site on the aging druggie. I didn't like the hippie scene in the sixties and I don't like it now. Booze was always my drug of choice. Still, checking further, I found that McKenna's afterword to Dick's In Pursuit of Valis was well written."

From McKenna's afterword:

"Schizophrenia is not a psychological disorder peculiar to human beings. Schizophrenia is not a disease at all but rather a localized traveling discontinuity of the space time matrix itself. It is like a travelling whirl-wind of radical understanding that haunts time. It haunts time in the same way that Alfred North Whitehead said that the color dove grey 'haunts time like a ghost.'"

I can find no source for
any remarks of Whitehead
on the color "dove grey"
(or "gray") but Whitehead
did say that

"A colour is eternal.  It haunts time like a spirit.  It comes and it goes.  But where it comes it is the same colour.  It neither survives nor does it live.  It appears when it is wanted." --Science and the Modern World, 1925

The poetic remark of
McKenna on the color
"dove grey" may be
taken, in a schizophrenic
(or, similarly, a Christian) way,
 as a reference to the Holy Spirit.

My own remarks on the hippie
scene seem appropriate as a
response to media celebration
of today's 40th anniversary of
the beginning of the 1967
"summer of love."


Saturday, June 2, 2007  8:00 AM

Connecting Ideas

The Diamond Theorem
 
Four diamonds in a square
 
"I don't think the 'diamond theorem' is anything serious, so I started with blitzing that."

-- Charles Matthews at Wikipedia, Oct. 2, 2006

"The 'seriousness' of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of the mathematical ideas which it connects. We may say, roughly, that a mathematical idea is 'significant' if it can be connected, in a natural and illuminating way, with a large complex of other mathematical ideas."

-- G. H. Hardy, A Mathematician's Apology