Tuesday, August 31, 2004

Tuesday August 31, 2004

Filed under: General — m759 @ 7:31 PM

Symmetry and Change, Part 1…

Early Evening,
Shining Star

7:31:01 PM ET

Hexagram 01
The Creative:


The Image



The movement of heaven
is full of power.

Click on picture
for details.

The Clare Lawler Prize
for Literature goes to…

Under the Volcano,
Chapter VI:

“What have I got out of my life? Contacts with famous men… The occasion Einstein asked me the time, for instance. That summer evening…. smiles when I say I don’t know. And yet asked me. Yes: the great Jew, who has upset the whole world’s notions of time and space, once leaned down… to ask me… ragged freshman… at the first approach of the evening star, the time. And smiled again when I pointed out the clock neither of us had noticed.”

For the thoughts on time
of another famous man,
from Mexico, see the
Nobel Prize acceptance speech
of Octavio Paz,
In Search of the Present.”

Tuesday August 31, 2004

Filed under: General — m759 @ 10:01 AM


For student
Anthony Fonseca,
Harvard ’04-’05

Michael (Studio della Robbia, ca. 1475)

For teacher
Margaret Casey:

The Green and
Burning Tree
, by
Chesca Potter

For the Voice of Gollum,
Peter Woodthorpe:

For further details, click on
any of the pictures above.

… y eres tú y soy yo 
y es un caminarte en círculo 
dar a tus hechos dimensión de arco 
y a solas con tu impulso decirte la palabra.

Homero Aridjis

For Lucero:

dimensión de arco

(This last picture, taken by
Andrew from London,
was added at
11:30 AM ET Aug. 31, 2004.
For the excellent story that
accompanies the picture, see
Early Evening, the Light
Beginning to Fade

Monday, August 30, 2004

Monday August 30, 2004

Filed under: General — Tags: — m759 @ 4:01 PM


for Penelope Doob,
Radcliffe '64:

"How much story do you want?"
— George Balanchine

Monday August 30, 2004

Filed under: General,Geometry — m759 @ 12:07 PM


A Log24 entry of Aug. 17, 2004, on the
three Semitic (or “Abrahamic”) religions:


From Scotsman.com News
Mon., 30 Aug., 2004
11:43 AM (UK)

Ex-Priest Sentenced
for Disrupting Marathon

By Pat Hurst, PA News, in Athens

An ex-priest who lives in Britain was given a 12-month suspended sentence today for disrupting the men’s Olympic marathon in Athens.

Cornelius Horan, 57, a former Catholic priest living in London, appeared before a Greek judge this morning, local police said.

He was sentenced and released from custody but his whereabouts are unknown.

Irishman Horan, originally from Kerry, dashed from the sidelines to attack the marathon front-runner during yesterday’s event.

He told officers he staged the disruption to “prepare for the second coming”.

A police spokesman said: “He has got mental problems. He is not very well.

“His only explanation for his behaviour was that it was for the second coming.”

Horan also disrupted last year’s Silverstone Formula One Grand Prix by dashing across the track.

Leslie Broad, of Deunant Books, which publishes Mr Horan’s books on its website, said: “We publish two of his books on biblical prophecies and he seems to be fairly convinced that the second coming is due fairly shortly.

“After the incident at Silverstone, he did say he would never do anything like that again.

“He comes across as a shy, very intelligent and compassionate man but as is often the way with people who are very intelligent, it sometimes manifests itself in very strange ways.

“I think he found prison a fairly uplifting experience. He came out feeling that he had met a lot of people he wouldn’t normally have met, people who had committed serious crimes.”

Horan’s victim yesterday, Vanderlei De Lima, from Brazil, was at the head of the race just three miles from the finish.

Horan grabbed him and bundled him into spectators at the side of the road.

After a scuffle, the runner managed to get away, but he was clearly ruffled and finished third.

The Brazilian Olympic Committee put in an official complaint to the Greeks and at one point the final medal ceremony to be staged during the closing ceremony was in doubt.

Horan was arrested and taken to the General Police Division of Attica, where he stayed overnight.

Author biography
Deunant Books:

Father Cornelius (“Neil”) Horan


“Neil Horan was born in 1947, in Scartaglen, County Kerry, in the Republic of Ireland. After schooling in Ireland he was ordained a Catholic Priest in Saint Mary’s Cathedral, Killarney, in 1973.

He has served all his priestly life in the Southwark Diocese, covering London south of the River Thames and Kent, his first Parish being Bexley in Kent. His interest in Bible prophecy began when he attended a lecture in 1974, given by the Apostolic Fellowship of Christ, a group which had originated with the Christadelphians. Meaning ‘Brothers in Christ’, the Christadelphians were a small Church formed in 1861 by Dr John Thomas. Father Horan says he owes a debt of gratitude to the Christadelphian tradition for the understanding of the Bible which they gave him. He regards the Bible as the greatest Book in the world and has devoted his life to making it better known, especially the Prophecies.

He is not a prophet, considering himself to be merely an interpreter, has never received a Divine message or vision, and God has never spoken to him. He feels that he is right only in so far as he interprets the Book of Books correctly.

He is still a Catholic Priest, listed in the Catholic Directory under his full name of Cornelius Horan. Cornelius, a Centurian [sic] in the Roman army, was the first Christian convert; Father Horan is proud to bear that name and hopes to meet his famous namesake soon, when Jesus comes.”

A Glorious New World
by Father Neil Horan

“Are there passages in the Bible that foretell events that were, at the time it was written, far in the future? Father Neil Horan argues eloquently, knowledgeably and persuasively in this book, first published in 1985, that this is so. It is easy to scoff at predictions of events that were, according to the book, to have taken place a few years ago but which have not happened, but to do that would be wrong. With only the most subtle changes of emphasis in interpretation, it could just as easily be argued that events in the Middle East particularly have to a large degree fulfilled the prophecies for the years since 1985.

Then there are the events yet to come. They are, according to the author and his sources, to be the most significant in the history of mankind, and are going to happen soon. With a little thought, certain current-day world figures are a disconcertingly comfortable match for some of the characters who will act out the earth-shattering dramas to come. Even the most hardened cynic will get that prickly feeling down the back of his neck as he reads this book.

Taken together with Father Horan’s later work ‘Christ Will Soon Take Power From All Governments’ (also available from Deunant Books) the two books represent one of the most remarkable and significant bodies of work seen in this field for many, many years.”

Deunant Books on Theology

Ludwig Wittgenstein,
Philosophical Investigations:

373. Grammar tells what kind of object anything is. (Theology as grammar.)

Grammar and Geometry:
The Euclidean Proposition,
by J. B. Calvert:

For more on Wittgenstein, theology, and grammar, see the Log24

entries of Jan. 14, 2004.

Related material:

God Goes Hollywood,
by Jeremiah Cullinane

Sunday, August 29, 2004

Sunday August 29, 2004

Filed under: General — m759 @ 11:07 AM

Olympic Arc

Thomas Becker, president of Chautauqua Institution, on Friday, Aug. 27, 2004:

“I’m really proud of this lecture platform this year.  We started with Phil Wilcox on the first day of the season and finished with Sandra Day O’Connor.  The arc of participation between them was really amazing.”

Phil Wilcox: See 

Israel and Palestine:
Let’s Separate Myth from Reality

by Philip C. Wilcox, Jr., President,
Foundation for Middle East Peace,
Chautauquan Daily, June 28, 2004

Sandra Day O’Connor: See

The Majesty of the Law:
Reflections of a
Supreme Court Justice
by Sandra Day O’Connor

The O’Connor link above is to a page at the Chautauqua Bookstore.

For Justice O’Connor:

Reflections on Themis
(Log24, Aug. 17, 2004) 

For Wilcox:

The Zen of Abraham
(Same entry, different title.)

I personally was at Chautauqua only one day this season — Friday, the 13th of August.  My stops of course included the Chautauqua Bookstore, where I purchased the following:

Human cultural activity is mostly what Walker Percy astutely called “symbol-mongering.”  Of the three books above, the central one offers the best symbols.

My own version of a
Chautauqua “Versus” symbol:

The Line,
by S. H. Cullinane

For further details, see the

entries of Aug. 15, 2004.

For an “arc” symbol, see

Loretta’s Rainbow.

Saturday, August 28, 2004

Saturday August 28, 2004

Filed under: General,Geometry — m759 @ 5:01 PM

History of Mathematics

“… mathematicians often treat history with contempt (unsullied by any practice or even knowledge of it, of course).”

The Rainbow of Mathematics

On the history of the relationship between orthogonality (in the Latin-square sense) and skewness (in the projective-space sense)–

See the newly updated

Orthogonal Latin Squares as Skew Lines.

Sunday, August 22, 2004

Sunday August 22, 2004

Filed under: General — m759 @ 1:11 PM

A Matched Pair of Stories

From today’s Los Angeles Times:

The pitch that you
won’t see coming

With savvy consumers wary and weary of the old hard sell, advertising has shifted into covert mode.

From today’s New York Times:

Reverend Billy’s
Unholy War

Take that, Lucifer Media!

Thursday, August 19, 2004

Thursday August 19, 2004

Filed under: General — Tags: — m759 @ 5:01 AM

The Tiffany Code

5:01:58 AM ET:

A link for Jill St. John's birthday —

The Geometrics of Brilliance

Twinkle, twinkle…

Beach reading for
 brilliant redheads…

and for everyone else:

Click on pictures for details.

Thursday August 19, 2004

Filed under: General — m759 @ 3:09 AM

Angel of the
First Degree

June 24, 2002, at 8:22:21 PM:

A few words for M.C.C.

Honey Blonde
She’s as sweet as
  tupelo honey
She’s an angel
  of the first degree.
She’s as sweet as
  tupelo honey
Just like honey, baby,
  from the bee.
— Van Morrison, 1971

Elmer Bernstein, Film Composer, Dies at 82

Filed at 1:22 a.m. ET
Thursday, Aug. 19, 2004

LOS ANGELES (AP)– Elmer Bernstein, the versatile, Oscar-winning composer who scored such movie classics as “The Ten Commandments,” “The Magnificent Seven,”‘ “To Kill a Mockingbird,”‘ “The Great Escape” and “True Grit,” died Wednesday. He was 82.

Bernstein died in his sleep at his Ojai home.

That, M.C.C., is what
Fritz Leiber means by

The Big Time.

Thursday August 19, 2004

Filed under: General — Tags: — m759 @ 1:06 AM

Instantia Crucis

"Francis Bacon used the phrase instantia crucis, 'crucial instance,' to refer to something in an experiment that proves one of two hypotheses and disproves the other. Bacon's phrase was based on a sense of the Latin word crux, 'cross,' which had come to mean 'a guidepost that gives directions at a place where one road becomes two,' and hence was suitable for Bacon's metaphor."

The American Heritage® Dictionary of the English Language, Fourth Edition

The high notes hit by Harriet Wheeler, Jen Slocumb, and Alanis Morissette can, I am sorry to say, be excruciating. (See previous entry.) I greatly prefer the mellow tones of Mary Chapin Carpenter:

"I guess you're never really all alone,
        or too far from the pull of home,
An' the stars upon that painted dome
        still shine."

MCC, Grand Central Station

From an entry of 12/22/02:


As if

A white horse comes as if on wings.

— I Ching, Hexagram 22: Grace

See also

Plato, Pegasus, and the Evening Star,

Shining Forth, and

Music for Pegasus.

Carpenter's song quoted above
is from the album
Between Here and Gone,
released April 27, 2004.

Wednesday, August 18, 2004

Wednesday August 18, 2004

Filed under: General — m759 @ 11:25 PM

A Cross Between



“The only way to describe her voice is a cross between Harriet Wheeler of The Sundays & Alanis Morissette.”

Review of Jen Slocumb of Martha’s Trouble by Diane Matay

“Apostrophe Theory is a cross between.”

— Ian Lee, The Third Word War

Wednesday August 18, 2004

Filed under: General — m759 @ 11:07 AM

Dyer, Part II:

From Here to Eternity

“Dying, at its best, might be something like this.  Everything was a memory, and everything was still happening in some extended present, and everything was still to come.”

— Geoff Dyer, quoted (in part of an entry, Dyer, for yesterday– the day mathematician Shizuo Kakutani died) by Ruth Franklin in

Journey Without Maps

A Koan for Kakutani–
on a random walk, a bird, death, time, and eternity–

In a comment on the previous entry, a Xangan asks,

“How many drunk men could migrate to Argentina without a map?”

My answer:  At least one.

Wednesday August 18, 2004

Filed under: General — m759 @ 3:00 AM

Drunk Bird

T. Charles Erickson
Shizuo Kakutani
in the 1980’s

Kakutani died yesterday.

“A drunk man will find his way home, but a drunk bird may get lost forever.”

— Shizuo Kakutani, quoted by J. Chang in Stochastic Processes (ps), p. 1-19.  Chang says the quote is from an R. Durrett book on probability.


A random walk in d dimensions is recurrent if d = 1 or d = 2, but transient if d is greater than or equal to 3.

From a web page on Kylie Minogue:

Turns out she’s a party girl
who loves Tequila:
“Time disappears with Tequila.  
  It goes elastic, then vanishes.”

Kylie sings

From a web page on Malcolm Lowry’s classic novel Under the Volcano

The day begins with Yvonne’s arrival at the Bella Vista bar in Quauhnahuac. From outside she hears Geoffrey’s familiar voice shouting a drunken lecture this time on the topic of the rule of the Mexican railway that requires that  “A corpse will be transported by express!” (Lowry, Volcano, p. 43).

For further literary details in memory of Shizuo Kakutani, Yale mathematician and father of book reviewer Michiko Kakutani, see

Santa Versus the Volcano.

Of course, Kakutani himself would probably prefer the anti-Santa, Michael Shermer.  For a refutation of Santa by this high priest of Scientism, see

Miracle on Probability Street

(Scientific American, July 26, 2004). 

Wednesday August 18, 2004

Filed under: General — m759 @ 2:18 AM

Train of Thought

Kylie sings

“Oh, my Lolita. I have only words
to play with!” (Nabokov, Lolita)

“This is the best toy train set
a boy ever had!”
(Orson Welles, after first touring
RKO Studios, quoted in Halliwell)

“As the quotes above by Nabokov and Welles suggest, we need to be able to account for the specific functions available to narrative in each medium, for the specific elements that empirical creators will ‘play with’ in crafting their narratives.”

Donald F. Larsson

Tuesday, August 17, 2004

Tuesday August 17, 2004

Filed under: General — m759 @ 7:29 PM


Un train peut encacher un autre.

Modern Times:

ART WARS September 27, 2002 —

From the Bulletin of the American Mathematical Society, October 2002, p. 563:

“To produce decorations for their weaving, pottery, and other objects, early artists experimented with symmetries and repeating patterns.  Later the study of symmetries of patterns led to tilings, group theory, crystallography, finite geometries, and in modern times to security codes and digital picture compactifications.  Early artists also explored various methods of representing existing objects and living things.  These explorations led to…. [among other things] computer-generated movies (for example, Toy Story).”

— David W. Henderson, Cornell University

From an earlier Log24.net note: 

John Frankenheimer’s “The Train” —

Und was für ein Bild des Christentums
ist dabei herausgekommen?

Tuesday August 17, 2004

Filed under: General — m759 @ 7:11 PM


On an essay by Geoff Dyer:

“Dyer’s writing is searching and melancholic and sometimes profound. In the beautiful title essay, he has a fling with a girl named Kate on a beach in Thailand: for her it is a one-night stand, for him something more. ‘There is something about leaving a place on a small boat–something about the movement of the waves, the noise of the engine: it is like you are leaving your life behind and yet, since you are part of the life you have left behind, part of you is still there,’ he writes after they have said good-bye. ‘Dying, at its best, might be something like this. Everything was a memory, and everything was still happening in some extended present, and everything was still to come.'”

Journey Without Maps, by Ruth Franklin, The New Republic Online, posted Friday the 13th of August, 2004

 “The lord whose oracle is in Delphi neither indicates clearly nor conceals, but gives a sign.”
— Adolf H., The Left Hand of God, p. 50

Note the time in the Log24 illustration for Monday, August 16, 2004, and consult the entry for 12/05, 2003.

Tuesday August 17, 2004

Filed under: General — Tags: — m759 @ 12:00 AM

The Zen of Abraham

Today’s Zen Chautauqua, prompted by the fact that this is Abrahamic week at the real Chautauqua, consists of links to

The Matrix of Abraham,

Matrix of the Death God, and

Happy Birthday, Kate and Kevin.

The real Chautauqua’s program this week is, of course, Christian rather than Zen.  Its theme is “Building a Global Neighborhood: The Abrahamic Vision 2004.”  One of the featured performers is Loretta Lynn; in her honor (and, of course, that of Sissy Spacek), I will try to overcome the fear and loathing that the Semitic (i. e., “Abrahamic”) religions usually inspire in me.

To a mathematician, the phrase “global neighborhood” sounds like meaningless politico-religious bullshit —  a phrase I am sure accurately characterizes most of the discourse at Chautauqua this week.  But a Google search reveals an area of research — “particle swarm optimization” in which the phrase “global neighborhood” actually means something.  See

A Hybrid Particle Swarm
and Neural Network Approach
for Reactive Power Control,
by Paulo F. Ribeiro and
W. Kyle Schlansker

This article includes the following:

Given the sophistication of his writing, I am surprised at Schlansker’s Christian background:

A good omen for the future is the fact that Schlansker balances the looney Semitic (or “Abrahamic”) teachings of Christianity with good sound Aryan religion, in the form of the goddess Themis.

 Themis, often depicted as “Justice”

For those who must have an Abraham, Schlansker’s paper includes the following:

A Themis figure I prefer to the above:

For more on religious justice
at midnight in the garden of
good and evil, see the Log24
entries of Oct. 1-15, 2002.

For material on Aryan religion that is far superior to the damned nonsense at Chautauqua, New York, this week, see

Jane Ellen Harrison’s Themis: a Study of the Social Origins of Greek Religion, with an excursus on the ritual forms preserved in Greek tragedy by Gilbert Murray and a chapter on the origin of the Olympic games by F. M. Cornford.  Rev. 2nd ed., Cambridge, Cambridge U.P., 1927.

Those who prefer the modern religion of Scientism will of course believe that Themis is purely imaginary, and that truth is to be found in modern myths like that of Carl Sagan’s novel Contact, illustrated below.

Jodie Foster (an admirer of
Leni Riefenstahl) and the
opening of the 1936 Olympics

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

“The lord whose oracle is in Delphi neither indicates clearly nor conceals, but gives a sign.”
Adolf Holl, The Left Hand of God, Doubleday, 1998, p. 50

Monday, August 16, 2004

Monday August 16, 2004

Filed under: General — m759 @ 12:00 AM

Classic to Romantic

“Ben Webster is probably best known for his eloquent ballad playing. On JAZZ ‘ROUND MIDNIGHT, we are treated to no less than 15 ballads, all of which are performed superbly. Webster is one of the great jazz romantics….”

Sunday, August 15, 2004

Sunday August 15, 2004

Filed under: General — m759 @ 3:17 PM

The Line

Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, Ch. 6 (italics are mine):

“A classical understanding sees the world primarily as underlying form itself. A romantic understanding sees it primarily in terms of immediate appearance.”

The Sophist, by Plato:

STRANGER – We are far from having exhausted the more exact thinkers who treat of being and not-being. But let us be content to leave them, and proceed to view those who speak less precisely; and we shall find as the result of all, that the nature of being is quite as difficult to comprehend as that of not-being.

THEAETETUS – Then now we will go to the others.

STRANGER – There appears to be a sort of war of Giants and Gods going on amongst them; they are fighting with one another about the nature of essence.

THEAETETUS – How is that?

STRANGER – Some of them are dragging down all things from heaven and from the unseen to earth, and they literally grasp in their hands rocks and oaks; of these they lay hold, and obstinately maintain, that the things only which can be touched or handled have being or essence, because they define being and body as one, and if any one else says that what is not a body exists they altogether despise him, and will hear of nothing but body.

THEAETETUS – I have often met with such men, and terrible fellows they are.

STRANGER – And that is the reason why their opponents cautiously defend themselves from above, out of an unseen world, mightily contending that true essence consists of certain intelligible and incorporeal ideas; the bodies of the materialists, which by them are maintained to be the very truth, they break up into little bits by their arguments, and affirm them to be, not essence, but generation and motion. Between the two armies, Theaetetus, there is always an endless conflict raging concerning these matters.


— Translated by Benjamin Jowett

Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance, Ch. 18:

“The wave of crystallization rolled ahead. He was seeing two worlds, simultaneously. On the intellectual side, the square side, he saw now that Quality was a cleavage term. What every intellectual analyst looks for. You take your analytic knife, put the point directly on the term Quality and just tap, not hard, gently, and the whole world splits, cleaves, right in two…

The Line,
by S. H. Cullinane

hip and square, classic and romantic, technological and humanistic…and the split is clean. There’s no mess. No slop. No little items that could be one way or the other. Not just a skilled break but a very lucky break. Sometimes the best analysts, working with the most obvious lines of cleavage, can tap and get nothing but a pile of trash. And yet here was Quality; a tiny, almost unnoticeable fault line; a line of illogic in our concept of the universe; and you tapped it, and the whole universe came apart, so neatly it was almost unbelievable. He wished Kant were alive. Kant would have appreciated it. That master diamond cutter. He would see. Hold Quality undefined. That was the secret.”

What Pirsig means by “quality” is close to what Yagoda means, in the previous entry, by “style.”

Sunday August 15, 2004

Filed under: General — m759 @ 2:29 AM

In memory of Julia Child,
born on this date:

Elements of Style

“Born Julia McWilliams in 1912, she was the product of the best American genetic engineering, bouncing out of an old-money, privileged Pasadena childhood like a kind of WASP merry prankster….”

Dorothy Kalins in Newsweek, issue dated Aug. 23, 2004

When I read this, admiring the style of both Julia Child and Dorothy Kalins, I thought of a  blurb I’d seen yesterday in aldaily.com:

“If only academics had the wit and nerve to honor stylemore»

I didn’t click on the blurb then, but the spirit of Julia prompted me to click just now.  This is what I found, in an essay written while Child was still alive, as examples of style:

“Think of Michael Jordan and Jerry West each making a 20-foot jump shot, of Charlie Parker and Ben Webster playing a chorus of ‘All the Things You Are,’ of Julia Child and Paul Prudhomme fixing a duck à l’orange, or of Pieter Brueghel and Vincent van Gogh painting the same farmhouse.”

Ben Yagoda in Chronicle of Higher Education, issue dated Aug. 13, 2004

Thursday, August 12, 2004

Thursday August 12, 2004

Filed under: General,Geometry — Tags: — m759 @ 7:26 AM

Battle of Gods and Giants,
Part III:

The Invisible Made Visible

From today's New York Times:

"Leon Golub, an American painter of expressionistic, heroic-scale figures that reflect dire modern political conditions, died on Sunday in Manhattan. He was 82….

In the 1960's he produced a series, called 'Gigantomachies,' of battling, wrestling figures. They were based on classical models, including the Hellenistic Altar of Pergamon. But there was nothing idealized about them."

The Hellenistic Altar of Pergamon,
from  Battle of Gods and Giants:


Golub's New York Times obituary concludes with a quote from a 1991 interview:

"Asked about his continuing and future goal he said, 'To head into real!'"

From Tuesday's Battle of Gods and Giants:

This sort of mathematics illustrates the invisible "form" or "idea" behind the visible two-color pattern.  Hence it exemplifies, in a way, the conflict described by Plato between those who say that "real existence belongs only to that which can be handled" and those who say that "true reality consists in certain intelligible and bodiless forms."

Perhaps, if Golub is fortunate enough to escape from the afterlife version of Plato's Cave, he will also be fortunate enough to enter Purgatory, where there awaits a course in reality, in the form of…

Geometry for Jews.


Wednesday, August 11, 2004

Wednesday August 11, 2004

Filed under: General,Geometry — Tags: , — m759 @ 5:35 AM

Battle of Gods and Giants,
Part II:

Wonders of the Invisible World

Yesterday at about 5 PM I added a section titled "Invariants" to the 3:01 PM entry Battle of Gods and Giants.  Within this added section was the sentence

"This sort of mathematics illustrates the invisible 'form' or 'idea' behind the visible two-color pattern."

Now, at about 5 AM, I see in today's New York Times a review of a book titled The Invisible Century, by Richard Panek.  The reviewer, David Gelernter, says the "invisible" of the title refers to

"science that is done not by studying what you can see…. but by repairing instead to the privacy of your own mind, with the shades drawn and the lights off: the inner sanctum of intellectual history."

The book concerns the research of Einstein and Freud.  Gelernter says

"As Mr. Panek usefully notes, Einstein himself first called his work an 'invariant theory,' not a 'relativity theory.' Einstein does not say 'everything is relative,' or anything remotely like it."

The reader who clicks on the word "invariants" in Battle of Gods and Giants will receive the same information.

Gelernter's conclusion:

"The Invisible Century is a complex book about a complex topic. Mr. Panek's own topic is not so much invisibility, it seems to me, as a different kind of visibility, centering on mind-pictures revealed by introspection, which are just as sharp and clear as (for example) the mind-music Beethoven heard when he was deaf.

Inner visibility is a fascinating topic…."

As is synchronicity, a topic in the work of a greater man than Freud– Carl Jung.  The above remarks may be viewed as "synchronicity made visible."

All of this was, of course, foreshadowed in my web page "A Mathematician's Aesthetics" of August 2000:

C. G. Jung on Archetypes
and Visible Reality:

"All the most powerful ideas in history go back to archetypes. This is particularly true of religious ideas, but the central concepts of science, philosophy, and ethics are no exception to this rule. In their present form they are variants of archetypal ideas, created by consciously applying and adapting these ideas to reality. For it is the function of consciousness not only to recognize and assimilate the external world through the gateway of the senses, but to translate into visible reality the world within us."

— Carl Gustav Jung, "The Structure of the Psyche" (1927), in Collected Works Vol. 8, Structure and Dynamics of the Psyche, P. 342

Paul Klee on Visible Reality:

"Art does not reproduce the visible; rather, it makes visible…. My aim is always to get hold of the magic of reality and to transfer this reality into painting– to make the invisible visible through reality. It may sound paradoxical, but it is, in fact, reality which forms the mystery of our existence."

— Paul Klee, "Creative Credo" from The Inward Vision: Watercolors, Drawings, Writings. Abrams, not dated; published c. 1958.

Wallace Stevens on
the Visibility of Archetypes:

"These forms are visible
     to the eye that needs,
Needs out of the whole
     necessity of sight."

— Wallace Stevens, "The Owl in the Sarcophagus," (first publ. 1950) in
Collected Poetry and Prose, Library of America, 1997

Tuesday, August 10, 2004

Tuesday August 10, 2004

Filed under: General,Geometry — Tags: , — m759 @ 3:01 PM

Battle of Gods and Giants

In checking the quotations from Dante in the previous entry, I came across the intriguing site Gigantomachia:

"A gigantomachia or primordial battle between the gods has been retold in myth, cult, art and theory for thousands of years, from the Egyptians to Heidegger. This site will present the history of the theme. But it will do so in an attempt to raise the question of the contemporary relevance of it. Does the gigantomachia take place today? Where? When? In what relation to you and me?"

Perhaps atop the Empire State Building?

(See An Affair to Remember and  Empire State Building to Honor Fay Wray.)

Perhaps in relation to what the late poet Donald Justice called "the wood within"?

Perhaps in relation to T. S. Eliot's "The Waste Land" and the Feast of the Metamorphosis?

Or perhaps not.

Perhaps at Pergamon:

Perhaps at Pergamon Press:


"What modern painters are trying to do,
if they only knew it, is paint invariants."

— James J. Gibson in Leonardo
(Vol. 11, pp. 227-235.
Pergamon Press Ltd., 1978)

An example of invariant structure:

The three line diagrams above result from the three partitions, into pairs of 2-element sets, of the 4-element set from which the entries of the bottom colored figure are drawn.  Taken as a set, these three line diagrams describe the structure of the bottom colored figure.  After coordinatizing the figure in a suitable manner, we find that this set of three line diagrams is invariant under the group of 16 binary translations acting on the colored figure.

A more remarkable invariance — that of symmetry itself — is observed if we arbitrarily and repeatedly permute rows and/or columns and/or 2×2 quadrants of the colored figure above. Each resulting figure has some ordinary or color-interchange symmetry.

This sort of mathematics illustrates the invisible "form" or "idea" behind the visible two-color pattern.  Hence it exemplifies, in a way, the conflict described by Plato between those who say that "real existence belongs only to that which can be handled" and those who say that "true reality consists in certain intelligible and bodiless forms."

For further details, see a section on Plato in the Gigantomachia site.

Tuesday August 10, 2004

Filed under: General — m759 @ 5:24 AM

The Day Justice Died

But all things then were oracle and secret.
Remember the night when,
    lost, returning, we turned back
Confused, and our headlights
    singled out the fox?
Our thoughts went with it then,
    turning and turning back
   With the same terror,
                into the deep thicket
   Beside the highway,
                at home in the dark thicket.

I say the wood within is the dark wood….

Donald Justice, “Sadness”

In memory of Justice,
Dante excerpts:

Canto I

Nel mezzo del cammin di nostra vita
 mi ritrovai per una selva oscura,
 che la diritta via era smarrita.
Ahi quanto a dir qual era é cosa dura
 esta selva e selvaggia e aspra e forte
 che nel pensier rinova la paura!

Midway in the journey of our life
 I found myself in a dark wood,
 for the straight way was lost.
Ah, how hard it is to tell what that
 wood was, wild, rugged, harsh;
 the very thought of it renews the fear!

Canto III

Per me si va ne la città dolente,
 per me si va ne l’etterno dolore,
 per me si va tra la perduta gente.
Giustizia mosse il mio alto fattore;
 fecemi la divina podestate,
 la somma sapïenza e ‘l primo amore.
Dinanzi a me non fuor cose create
 se non etterne, e io etterno duro.
 Lasciate ogne speranza, voi ch’intrate.

Through me you enter the woeful city,
 through me you enter eternal grief,
 through me you enter among the lost.
Justice moved my high maker;
 the divine power made me,
 the supreme wisdom, and the primal love.
Before me nothing was created
 if not eternal, and eternal I endure.
 Abandon every hope, you who enter.

— Translation by Charles S. Singleton,
selection by Paul J. Viscuso

Justice moved my high maker…

From the day Justice died,
Friday, August 6, 2004,
The Feast of the Metamorphosis:

Monday, August 9, 2004

Monday August 9, 2004

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

Quilt Geometry

Monday August 9, 2004

Filed under: General — m759 @ 5:45 PM

Hollywood Ending

“… they will meet at the top of
the Empire State Building at 5 PM…
‘It’s the closest thing to Heaven
we have in New York City!’

Monday August 9, 2004

Filed under: General — m759 @ 4:00 AM

Shape Note

A variation on the theme of the previous entry, Quartet.

 The first
crossword puzzle:
The image “http://www.log24.com/log/pix04A/040715-Selim.gif” cannot be displayed, because it contains errors.

Derek Taunt

As in the previous entry, the illustration on the left is from a Log24 entry on the date of death of the person on the right.

Relevant quotations:

“It was rather like solving a crossword puzzle.”

— Derek Taunt, on breaking the Enigma Code

Four Quartets:

“… history is a pattern
Of timeless moments.”

Cambridge News obituary:

“He [Dr. Taunt] and Angela [his wife] founded the Friends of Kettle’s Yard when the Arts Council cut its grant in 1984 and together organised countless fundraising activities for the museum and gallery.”

“How do we relate to the past? How are our memories affected by the cultural context that shapes our present? How many, and what kind of narratives compete in the representation of a historical moment? Rear View Mirror sets out to explore these questions and examine the devices we use to reconstruct events and people through different lenses….”

— On a future Kettle’s Yard exhibition

Time past and time future
What might have been
      and what has been
Point to one end,
      which is always present.

Four Quartets

 “The diamonds will be shining,
no longer in the rough.”

Diamonds in the Rough

See the Log24 remarks on Jesus College— Taunt’s college– in a web page for June Carter Cash, The Circle is Unbroken.

Sunday, August 8, 2004

Sunday August 8, 2004

Filed under: General — Tags: , — m759 @ 6:08 AM


An illustration from July 26,
Jung’s birthday and the date
of Alexander Hammid’s death:


Jung’s Model
of the Self:

Four Quartets:

“… history is a pattern
Of timeless moments.”

Gerard Malanga, 2003


From today’s
New York Times

Alexander Hammid,
96, Filmmaker
Known for Many Styles,


Published: August 8, 2004

Alexander Hammid, a filmmaker whose body of work spanned the genesis of the experimental movement in Czechoslovakia, early anti-Nazi documentaries and soaring modern Imax spectacles, died on July 26 at his home in Manhattan. He was 96.

His work in the 1950’s and early 60’s involved his passion for the arts,  [including] … a collaboration on Gian Carlo Menotti’s opera “The Medium” and a documentary series of master classes by the cellist Pablo Casals….


“… legend has it, supported by Casals himself, that he was conceived when Brahms began his B-flat Major Quartet, of which Casals owned the original manuscript, and that he was born when Brahms completed its composition.”


Saturday, August 7, 2004

Saturday August 7, 2004

Filed under: General — m759 @ 3:00 PM

Playing God:

The Color of

John Lahr (Log24 on 1/26 2003):

“The play’s narrator and general master of artifice is the Stage Manager, who gives the phrase ‘deus ex machina’ a whole new meaning. He holds the script, he sets the scene, he serves as an interlocutor between the worlds of the living and the dead, calling the characters into life and out of it; he is, it turns out, the Author of Authors, the Big Guy himself. It seems, in every way, apt for Paul Newman to have taken on this role.”

“It’s not easy being green.”
Jill O’Hara    

Saturday August 7, 2004

Filed under: General — Tags: — m759 @ 4:07 AM


Ian Lee on the communion of saints and the association of ideas (in The Third Word War, 1978) 

"The association is the idea"

Herman Melville on the association of ideas:

"In me, many worthies recline, and converse."

Stephen Hunter yesterday on the protagonist of the new film Collateral:

"He dresses Italian, shoots German (suits by Versace, pistol by Heckler & Koch), talks like Norman Mailer's White Negro and improvises brilliantly."  

Anagram by Dante (Filipponi, that is) on the name of Gianni Versace:

Can Give a Siren

Sirens, true sirens verily be,
Sirens, waylayers in the sea.

— Herman Melville, quoted
early yesterday by stephenhoy

Siren and White Negro:

See Gates's essay on
Anatole Broyard and
the log24 Bastille Day
on Mr. Motley's

"… there are many associations of ideas which do not correspond to any actual connection of cause and effect in the world of phenomena…."

— John Fiske, "The Primeval Ghost-World," quoted in the Heckler & Coch weblog

And, finally, brilliance:

Fark News yesterday:

"Disrespectful look causes shootout in Houston. Gang telepathy classes enrolling soon."

Log24 entry of Sept. 28, 2003: 

Spirit of East St. Louis

Friday, August 6, 2004

Friday August 6, 2004

Filed under: General — m759 @ 8:00 PM


Friday August 6, 2004

Filed under: General — m759 @ 6:29 PM

Epistle and Hymns

In the spirit of Dave Barry’s Book of Bad Songs, we conclude our Hiroshima Day service with a link to The Epistle of Jeremiah and a deadly trinity of singers:

A Landmark

Neil Diamond–
I Am … I Said

Hoyt Axton–
Jeremiah Was a Bullfrog

Jill O’Hara–
It’s Not Easy Being Green

Friday August 6, 2004

Filed under: General — m759 @ 5:01 PM

Sermon for Hiroshima Day

In a comment, a Xangan recently made a pun on the name “Gennifer” (as in Flowers)… “geno-pher.”  I am still not sure what he meant, but I appreciate his prompting me to look up the etymology of gen words, one of which is…

genesis – O.E., from L. genesis, adopted as title of first book of Old Testament in Vulgate, from Gk. genesis “origin, creation, generation,” from gignesthai “to be born,” related to genos “race, birth, descent” (see genus). As such, it translated Heb. bereshith, lit. “in the beginning,” which was the first word of the text, taken in error as its title. Extended sense of “origin, creation” first recorded in Eng. 1604.

This ties in with the end of the previous entry, which recommended that the reader consult Log24 entries of Aug. 6, 2002.  Taking my own advice, I did so, and found that the current pope on Aug. 6, 1993, cited Genesis 1:26 —

And God said, Let us
make man in our image,
after our likeness….

Taking the chapter and verse numbers as also having deep religious significance, let us  consult the Log24 entries for 1/26 2003 and 1/26 2004.

In Our Image  

We find that 1/26 2003, and the entries on earlier days that lead up to it, deals with Paul Newman, Our Town, The Hustler, Super Bowl Sunday, and God.

After Our Likeness

We find that 1/26 2004 deals with God’s self-definition on Mount Sinai.  Lucifer also appears.  Karol Wojtyla would do well to click on the following link for an expert characterization of Lucifer:

hypocrite lecteur!
mon semblable, mon frère

Friday August 6, 2004

Filed under: General — m759 @ 2:29 AM

See, too, the Log24 entries
for August 6, 2002

Thursday, August 5, 2004

Thursday August 5, 2004

Filed under: General — Tags: — m759 @ 4:06 PM

In the beginning
the recursion?

"Words are events."
— The Walter J. Ong Project,
    quoted in Log24 on Aug. 25, 2003 

"Words are events."
— The Walter J. Ong Project,
    quoted in the Heckler & Coch weblog
    on July 17, 2004 as part of a section
    titled "Recursive, Wide, and Loopy"

Walter J. Ong was a Jesuit.  The Feast of St. Ignatius Loyola, founder of the Jesuit order, is celebrated on July 31 each year.

"Recursive, Wide, and Loopy 2", a Heckler & Coch entry dated July 31, 2004, leads to the following:

MSNBC, Jan. 15, 2004:

How humans got
the gift of gab

Why do other primates
lag behind in language?

"New research may help scientists dissect just what it is about the human brain that endows us with language.

Researchers have found that tamarin monkeys have some distinctly languagelike abilities but that they can’t quite master the more complex rules of human grammar. The findings appear in Friday’s issue of the journal Science, published by AAAS, the non-profit science society.

 The grammatical toolkit

'A relatively open question concerning language evolution is, "What aspects of the language faculty are shared with other animals, and what aspects are unique to humans?" ' said study author Marc Hauser of Harvard University.

To investigate, Hauser and W. Tecumseh Fitch of the University of St. Andrews, in Scotland, devised tests for cotton-top tamarin monkeys and human volunteers. Tamarins have been evolving separately from humans for approximately 40 million years –suggesting that any shared machinery in human and tamarin brains is old enough to be relatively common among primates.

Instead of trying to teach the monkeys real words, Hauser and Fitch generated strings of one-syllable words that followed various grammatical rules.

According to linguistics expert Noam Chomsky, the simplest type of grammar is a 'finite state grammar' or 'FSG,' which dictates which types of words go near each other in a sentence. In English, for example, an adjective like 'fast' must go directly in front of 'car,' the noun it's describing.

Building on previous experiments, Hauser and Fitch recorded word-strings that obeyed a specific FSG, in which any syllable spoken by a female voice was automatically followed by one from a male voice.

Audio: Listen to an FSG word-string.
(Requires Windows Media Player.)

After listening to a series of word-strings, the monkeys were able to distinguish between those that followed this rule and others that didn't. Human test subjects could tell the difference as well, implying that tamarins and humans may share at least some components of what Hauser called 'the universal toolkit underlying all languages.'

Mastering this type of grammar represents the ability to compute some simple statistics, something human infants accomplish early on as they learn to speak. This ability may not be specific to language, however.

'Either the same mechanism or some approximation of it is used in mathematics, vision, music and other activities,' Hauser said.

Upping the Complexity

The grammatical rules of real languages govern more than just the placement of neighboring words, as anyone who had to diagram sentences in English class may remember all too well.

One of the more complex types of grammar is known as a 'phrase structure grammar,' or PSG. These grammars involve relationships between words that aren't next to each other in a sentence and thus allow for a more complex range of expression. The 'if … then' construction is an example of a PSG.

The researchers generated a second set of word-strings that followed a PSG in which a pairing of syllables spoken by a female and a male could be embedded within another pairing. This grammar produces structures like [female [female, male] male].

Audio: Listen to a PSG word-string.
(Requires Windows Media Player)

After playing these recordings repeatedly to the monkeys, the researchers found that the animals didn't seem to notice the difference between word strings that obeyed the PSG and other strings that did not. In contrast, the human volunteers did notice the difference."

— Kathleen Wren

"The grammar or syntax of human language is certainly unique. Like an onion or Russian doll, it is recursive: One instance of an item is embedded in another instance of the same item. Recursion makes it possible for the words in a sentence to be widely separated and yet dependent on one another. 'If-then' is a classic example…. Are animals capable of such recursion? Fitch and Hauser have reported that tamarin monkeys are not capable of recursion. Although the monkeys learned a nonrecursive grammar, they failed to learn a grammar that is recursive. Humans readily learn both."

— David Premack (Science 2004 303:318, quoted in ScienceWeek)

These citations by Heckler & Coch show that inability to understand complex language is not limited to monkeys.

The examples given by Wren in the audio samples are of alternating female (Hi) and male (Lo) voices, thus —

FSG:  Hi Lo Hi Lo Hi Lo

PSG:  Hi Hi Hi Lo Lo Lo

As these examples show, neither monkeys nor humans heard the sound of parentheses (or square brackets) as Wren describes them:

"structures like [female [female, male] male]."

There of course is, in ordinary language (which does not include the monologues of Victor Borge), no such thing as the sound of parentheses.

Thus the research of Hauser and Fitch is not only invalid, but ridiculous.

This point is driven strongly home by the following two articles:

Greg Kochanski, Research Fellow,
 Oxford University Phonetics Lab

Is a Phrase Structure Grammar
the Important Difference
between Humans and Monkeys?


Mark Liberman, Professor,
University of Pennsylvania

Departments of Linguistics
and of Computer Science,
and co-director of the
Institute for Research
in Cognitive Science,
in his

Language Log,
January 17, 2004:

Hi Lo Hi Lo,
it's off to
formal language theory
we go

Wednesday, August 4, 2004

Wednesday August 4, 2004

Filed under: General — m759 @ 8:04 PM

Summering Forth

Everything that ever summered forth starts
in identical springs, or four-note variations
on that repeated theme: four seasons,
four winds, four corners, four-chambered heart…

— Richard Powers, “The Perpetual Calendar,”
    from The Gold Bug Variations, 1991

Wednesday August 4, 2004

Filed under: General — m759 @ 12:29 AM

Shell Beach

“It was a dark and stormy night….”

— Opening of A Wrinkle in Time, a classic novel by Madeleine L’Engle.

For those who seek religious significance in the name of Hurricane Alex:

Alex Proyas directs this futuristic thriller about a man waking up to find he is wanted for brutal murders he doesn’t remember. Haunted by mysterious beings who stop time and alter reality, he seeks to unravel the riddle of his identity.”

— Description of the 1998 film Dark City

See also ART WARS of June 19, 2002.

Tuesday, August 3, 2004

Tuesday August 3, 2004

Filed under: General — m759 @ 7:59 PM

Science and Fiction:

Attica to GATTACA

 “There is no gene for fate.”
— Vincent, a character in
   the 1997 film GATTACA

The film GATTACA was discussed in a Log24 entry for Saturday, July 31, 2004– the date of death of Frank Smith, also known as Big Black, a prominent figure in the events at Attica in 1971.  He died in Kinston, North Carolina, a town of about 24,000 about halfway between Raleigh and the Atlantic Ocean.

See today’s 6:01 AM entry for some details of Mr. Smith’s life.  In his memory, here are three links.

The first is to

Screening DNA:
Exploring the
Cinema-Genetics Interface,

by Stephen Nottingham

This online book, from which the above GATTACA quote was taken, discusses genetics in film more generally… Specifically, from Part 7 of Screening DNA:

In Star Wars Episode I: The Phantom Menace–

“Midi-chlorians are essentially genes for the force, which determine whether one will become either a Jedi or else a dark shadow of one. In particular, they evoke mitochondrian genes, as mitochondria once lived symbiotically in human cells. Mitochondria are a cell’s energy-producing ‘power plant,’ in which a positive mutation could lead to an individual having greater strength and stamina. Mitochondrial genes are also now known to control many critical stages in human development.“

The second link in memory of Mr. Smith, one he would probably prefer, is to another book, less academic in nature, that also deals with mitochondria:

A Wind in the Door,
by Madeleine L’Engle.

 Mr. Smith

From Chapter 3,
  “The Man in the Night”–

The stranger was dark, dark as night and tall as a tree, and there was something in the repose of his body, the quiet of his voice, which drove away fear.

Charles Wallace stepped towards him.  “Who are you?”

“A Teacher.”

Charles Wallace’s sigh was longing.  “I wish you were my teacher.”

“I am.” The cello-like voice was calm, slightly amused.

The third link is to the aforementioned


Tuesday August 3, 2004

Filed under: General — m759 @ 7:00 PM

Southern Strategy, Da Capo

From July 31:

“Why are you based in North Carolina?”

The Footprints of God


“Remembering speechlessly we seek the great forgotten language, the lost lane-end into heaven, a stone, a leaf, an unfound door. Where? When?”

Thomas Wolfe

At left:

Southern Strategy Galore. 

Meanwhile, at the Vatican:

ROME, July 31 — The Vatican issued a letter Saturday attacking the “distortions” and “lethal effects” of feminism.

Tuesday August 3, 2004

Filed under: General — m759 @ 6:01 AM

Death of Big Black

(Sequel to yesterday’s entry and to
the entries of Saturday, July 31,
feast day of St. Ignatius Loyola)

Current online information from The Free Press of Kinston, North Carolina: 

Frank Smith

Frank Smith, 70, of 2609 Brookhaven Drive, died Saturday, July 31, 2004, at Lenoir Memorial Hospital. Arrangements are incomplete at Swinson Funeral Home.

New York Times today:

In the Heat
of the Night

Frank Smith, who as an inmate leader at Attica prison was tortured by officers in the aftermath of the prisoner uprising of 1971 and then spent a quarter century successfully fighting for legal damages, died Saturday in Kinston, N.C. He was 71.

Mr. Smith, a huge man with a booming voice who was known as Big Black, figured large in the uprising at the Attica Correctional Facility, 30 miles east of Buffalo, during the second week of September 1971. He was chosen by other inmates to be chief of security with a principal responsibility to protect outsiders brought in to negotiate an end to the crisis. None were hurt.

(See previous entry.)

Monday, August 2, 2004

Monday August 2, 2004

Filed under: General — m759 @ 12:48 AM

and Truth

Bob Herbert, in today’s New York Times, on the central problem of democracy:

“It may well be that candidates can’t tell voters the truth and still win.”

Just figure that out,
did you, Bob?

Sunday, August 1, 2004

Sunday August 1, 2004

Filed under: General — m759 @ 2:22 PM

Poll Result

From USA Today
8/1/2004 1:20-1:30 PM

Bush 50%, Kerry 46%,

in a Friday-Saturday
poll of likely voters.

Before the Democratic convention, which ended Thursday night, Bush and Kerry were essentially tied.

From a July 12 Log24 entry:

Democratic Political Art:
Motherhood and Apple Pie

The image “http://www.log24.com/log/pix04A/040712-Ikex3.jpg” cannot be displayed, because it contains errors. 

“It was… a stunning result, the first time in the Gallup Poll since the 1972 Democratic convention that a candidate seemed to lose ground at his convention.”

— Susan Page, USA TODAY

Added at 10 PM ET Aug. 1:

The Susan Page story has been altered since 1:30 PM, and no longer calls the above “a stunning result.”  For the original story, see this Google Groups search.

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