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:

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:

Invariants 

"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 2x2 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.

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

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

-- 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:

Quilt Geometry

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!' "

Shape Note

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

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."

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

Quartet

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 Alexander Hammid

"... 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."

-- http://www.bach-cantatas.com/
Bio/Casals-Pablo.htm

Consacré

François Furet:

Chevalier de la Légion d'honneur

"Il a consacré l'essentiel de ses travaux à l'histoire de la Révolution française."

-- academie-francaise.fr/immortels

"St. Pierre-Toirac, in the Lot valley, has only minor entries in the Guide vert and the Guide bleu; because it has no hotel it is not in the red Michelin guide. The sole monument is a Romanesque church, a hybrid between a village church and the fortified churches of the region. It was, when we first visited, in very bad shape. François said he would see that it was restored, and so it eventually was."

-- David P. Jordan, François Furet: A Personal Reminiscence

See also an entry for Aug. 6,
 Feast of the Metamorphosis:

In memory of Rick James

Incense, Wine, Candles

Three's Not a Crowd

"Mr. James's wild rise came to an ignominious halt in 1993, when he was convicted of assaulting two women. The first attack occurred in 1991, when he and girlfriend Tanya Anne Hijazi restrained and burned a young woman with a hot crack pipe during a week-long cocaine binge at his house in West Hollywood.

He was free on bail when the second assault occurred in 1992, in his West Hollywood hotel room. A music executive, Mary Sauger, testified that she had gone to his room for a business meeting with Mr. James and Hijazi and that the couple beat her and held her prisoner for 20 hours. Mr. James could have been sentenced to life in prison had he been convicted of a torture charge."

Incense, wine, candles...

Some would say
bell, book, and candle
would be more appropriate.

Playing God:

The Color of
Collateral

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    

Communion

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
entry on Mr. Motley's
neighborhood.   

"... 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: