Sunday, August 30, 2015


Filed under: General,Geometry — Tags: , , — m759 @ 11:01 AM

"We tell ourselves stories in order to live." — Joan Didion

A post from St. Augustine's day, 2015, may serve to
illustrate this.

The post started with a look at a painting by Swiss artist
Wolf Barth, "Spielfeld." The painting portrays two
rectangular arrays, of four and of twelve subsquares, 
that sit atop a square array of sixteen subsquares.

To one familiar with Euclid's "bride's chair" proof of the
Pythagorean theorem, "Spielfeld" suggests a right triangle
with squares on its sides of areas 4, 12, and 16.

That image in turn suggests a diagram illustrating the fact
that a triangle suitably inscribed in a half-circle is a right 
triangle… in this case, a right triangle with angles of 30, 60,
and 90 degrees… Thus —

In memory of screenwriter John Gregory Dunne (husband
of Joan Didion and author of, among other things, The Studio
here is a cinematric approach to the above figure.

The half-circle at top suggests the dome of an observatory.
This in turn suggests a scene from the 2014 film "Magic in
the Moonlight."  

As she gazes at the silent universe above
through an opening in the dome, the silent
Emma Stone is perhaps thinking, 
prompted by her work with Spider-Man

"Drop me a line."

As he  gazes at the crack in the dome,
Stone's costar Colin Firth contrasts the vastness 
of the Universe with the smallness of Man, citing 

"the tiny field F2 with two elements."

In conclusion, recall the words of author Norman Mailer
that summarized his Harvard education —

"At times, bullshit can only be countered
with superior bullshit."

Friday, May 22, 2015

Colorful Tale

Filed under: General — m759 @ 11:01 AM

See a post of Nov. 17, 2011 — Void.

"We tell ourselves stories in order to live."
— Joan Didion, The White Album

See also John Gregory Dunne.

Friday, November 18, 2011

Plot Summary

Filed under: General — m759 @ 1:14 PM


IMDb Plot Summary for
Brainstorm (1983)

Brilliant researchers Lillian Reynolds and Michael Brace have developed a system of recording and playing back actual experiences of people. Once the capability of tapping into "higher brain functions" is added in, and you can literally jump into someone else's head and play back recordings of what he or she was thinking, feeling, seeing, etc., at the time of the recording, the applications for the project quickly spiral out of control. While Michael Brace uses the system to become close again to Karen Brace, his estranged wife who also works on the project, others start abusing it for intense sexual experiences and other logical but morally questionable purposes. The government tries to kick Michael and Lillian off the project once the vast military potential of the technology is discovered. It soon becomes obvious that the government is interested in more than just missile guidance systems. The lab starts producing mind torture recordings and other psychosis inducing material. When one of the researchers dies and tapes the experience of death, Michael is convinced that he must playback this tape to honor the memory of the researcher and to become enlightened. When another researcher dies during playback the tape is locked away and Michael has to fight against his former colleagues and the government lackeys that now run his lab in order to play back and confront the "scariest thing any of us will ever face"— death itself. Written by Eric van Bezooijen.

See also researcher John Gregory Dunne and "Lucero Puro" in this journal.

Thursday, November 17, 2011


Filed under: General — m759 @ 11:11 AM

From "Elegy to the Void," by Cathleen Schine, New York Review of Books , issue dated Nov. 24, 2011—

“We tell ourselves stories in order to live,” Didion famously wrote in The White Album . Blue Nights  is about what happens when there are no more stories we can tell ourselves, no narrative to guide us and make sense out of the chaos, no order, no meaning, no conclusion to the tale. The book has, instead, an incantatory quality: it is a beautiful, soaring, polyphonic eulogy, a beseeching prayer that is sung even as one knows the answer to one’s plea, and that answer is: No.

Blue Nights  is a sequel of sorts to The Year of Magical Thinking , Didion's story of the year following the death on December 30th, 2003, of her husband, fellow writer John Gregory Dunne.

Related material:




For some context, see

  1. Cosmic Banditos in this journal,
  2. the Fall 1997 newsletter of the Institute for Advanced Study,
  3. and Oppenheimer's Aria.

For a different link to that aria, see a journal entry dated December 28, 2003.
(Click link, scroll down.)

Wednesday, June 10, 2009

Wednesday June 10, 2009

Filed under: General — m759 @ 6:29 PM
Hello, Columbus

continued from
the two entries of
October 12, 2003:

Part I —
October 12, 2003 —

Vegas background for 'Play It As It Lays'

Above, an image from
Spinnin’ Wheel,
Spinnin’ True

Part II
  October 12, 2003 —

Stars of a film based on a novel, 'True Confessions,' by John Gregory Dunne

Above, an image from
Hello, Columbus

Part III —
June 10, 2009 —

Below, images from
a website:
 Images from a website on race, politics, and religion

“They all laughed at
    Christopher Columbus…”

Ira Gershwin  

Monday, October 10, 2005

Monday October 10, 2005

Filed under: General — m759 @ 10:00 AM

The image “http://www.log24.com/log/pix05B/051010-Yul2.jpg” cannot be displayed, because it contains errors.

“The crème de la crème
of the chess world in a
show with everything
 but Yul Brynner”

One Night in Bangkok

Mate in 2,
 V. Nabokov, 1919,
“Starflight” theme

Today is the feast of St. Yul Brynner,
who died on this date in 1985.

“Head bent down over the guitar,
he barely seemed to hum;
 ended “all come home”;
Yule– Yul log for the
Christmas-fire tale-spinner–
of fairy tales that can come true.
 Yul Brynner.”

— Marianne Moore,
“Rescue with Yul Brynner”

Related material:

Starflight, a year ago today

Pleiades, by Ivan Bunin, winner of the Nobel Prize for Literature in 1933, whose birthday is today

Natasha’s Dance (Log24, Jan. 8, 2004)

Star! by John Gregory Dunne (NY Review of Books, Jan. 15, 2004)

Sunday, December 5, 2004

Sunday December 5, 2004

Filed under: General — Tags: , , — m759 @ 3:00 PM

Chorus from
The Rock

Author Joan Didion is 70 today.

On Didion’s late husband, John Gregory Dunne:

“His 1989 memoir Harp includes Dunne’s early years in Hartford and his Irish-Catholic family’s resentment of WASP social superiority: ‘Don’t stand out so that the Yanks can see you,’ he wrote, ‘don’t let your pretensions become a focus of Yank merriment and mockery.'”

The Hartford Courant, August 4, 2002

From a Hartford Protestant:

The American Sublime

How does one stand
To behold the sublime,
To confront the mockers,
The mickey mockers
And plated pairs?

When General Jackson
Posed for his statue
He knew how one feels.
Shall a man go barefoot
Blinking and blank?

But how does one feel?
One grows used to the weather,
The landscape and that;
And the sublime comes down
To the spirit itself,

The spirit and space,
The empty spirit
In vacant space.
What wine does one drink?
What bread does one eat?

— Wallace Stevens

A search of the Internet for “Wallace Stevens”  + “The Rock” + “Seventy Years Later” yields only one quotation…

Log24 entries of Aug. 2, 2002:

From “Seventy Years Later,” Section I of “The Rock,” a poem by Wallace Stevens:

A theorem proposed
between the two —
Two figures in a nature
of the sun….

From page 63 of The New Yorker issue dated August 5, 2002:

“Birthday, death-day —
what day is not both?”
John Updike

From Didion’s Play It As It Lays:

Everything goes.  I am working very hard at not thinking about how everything goes.  I watch a hummingbird, throw the I Ching but never read the coins, keep my mind in the now.
— Page 8

From Play It As It Lays:

I lie here in the sunlight, watch the hummingbird.  This morning I threw the coins in the swimming pool, and they gleamed and turned in the water in such a way that I was almost moved to read them.  I refrained.
— Page 214

And the sublime comes down
To the spirit itself,
The spirit and space,
The empty spirit
In vacant space.

One heart will wear a Valentine.
— Sinatra, 1954

Thursday, January 8, 2004

Thursday January 8, 2004

Filed under: General — m759 @ 4:23 PM

Natasha's Dance

"… at the still point, there the dance is…."

"… to apprehend
 The point of intersection of the timeless
 With time, is an occupation for the saint…. "

— T. S. Eliot, Four Quartets

It seems, according to Eliot's criterion, that the late author John Gregory Dunne may be a saint.

Pursuing further information on the modular group, a topic on which I did a web page Dec. 30, 2003, the date of Dunne's death, I came across a review of Apostol's work on that subject (i.e., the modular group, not Dunne's death, although there is a connection).  The review:

"A clean, elegant,
absolutely lovely text…"

Searching further at Amazon for a newer edition of the Apostol text, I entered the search phrase "Apostol modular functions" and got a list that included the following as number four:

Natasha's Dance:
A Cultural History of Russia

which, by coincidence, includes all three words of the search.

For a connection — purely subjective and coincidental, of course — with Dunne's death, see The Dark Lady (Jan. 1, 2004), which concerns another Natasha… the actress Natalie Wood, the subject of an essay ("Star!") by Dunne in the current issue of the New York Review of Books.

The Review's archives offer another essay, on science and religion, that includes the following relevant questions:

"Have the gates of death
been opened unto thee?
Or hast thou seen the doors
of the shadow of death?"

From my December 31 entry:

In memory of
John Gregory Dunne,
who died on
Dec. 30, 2003

For further details, click
on the black monolith.

Tuesday, January 6, 2004

Tuesday January 6, 2004

Filed under: General,Geometry — 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.


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”


“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:


The Shining

Shining Forth

Sunday, January 4, 2004

Sunday January 4, 2004

Filed under: General — m759 @ 10:10 PM

Room 1010

Continuing the hotel theme of the previous entry….

John Gregory Dunne has a letter in the New York Review of Books of December 20 (St. Emil's Day in the previous entry), 1990.  In this letter, he reveals that he and his wife had at one time worked on a Grand Hotel screenplay based in Las Vegas.

For related material in memory of Dunne, see In Lieu of Rosebud, which contains entries for 10/10-10/12, 2002.

Mein Irisch Kind,
Wo weilest du?

Dancing at

Late Night
Grande Hotel

Big Time

Friday, January 2, 2004

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.

Thursday, January 1, 2004

Thursday January 1, 2004

Filed under: General — m759 @ 3:36 PM

The Dark Lady

"… though she has been seen by many men, she is known to only a handful of them.  You'll see her — if you see her at all — just after you've taken your last breath.  Then, before you exhale for the final time, she'll appear, silent and sad-eyed, and beckon to you.

She is the Dark Lady, and this is her story."

Mike Resnick

"… she played (very effectively) the Deborah Kerr part in a six-hour miniseries of From Here to Eternity…."

John Gregory Dunne on Natalie Wood
in the New York Review of Books
dated Jan. 15, 2004

Very  effectively.

Wednesday, December 31, 2003

Wednesday December 31, 2003

Filed under: General — m759 @ 8:00 PM

In memory of
John Gregory Dunne,
who died on
Dec. 30, 2003

For further details, click
on the black monolith.

See, too, last year's entries
for Dec. 30 and 31:

"… he might add under his breath,
like the professor in The Last Battle
who has passed on to the next life,
'It's all in Plato, all in Plato:
bless me, what do they teach them
at these schools!' "

Thursday, December 19, 2002

Thursday December 19, 2002

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


Bach at Heaven’s Gate

From a weblog entry of Friday, December 13, 2002:

Divine Comedy

Joan Didion and her husband
John Gregory Dunne
(author of
The Studio and Monster
wrote the screenplays for
the 1976 version of “A Star is Born”
and the similarly plotted 1996 film
Up Close and Personal.”

If the incomparable Max Bialystock 
were to remake the latter, he might retitle it
Distant and Impersonal.”
A Google search on this phrase suggests
a plot outline for Mel Brooks & Co.

From The Hollywood Reporter:

Producer Sidney Glazier dies
Dec. 18, 2002

Academy Award-winning producer
Sidney Glazier died early Saturday morning
[Dec. 14, 2002] of natural causes
at his home in Bennington, Vt. He was 86.
Glazier… is best known for producing
the 1968 film “The Producers.”
That film, which has since become a
Tony Award-winning Broadway play,
also marked comedian Mel Brooks’
directing debut.

In addition to “The Producers,”
Glazier produced…
the 1973 television drama “Catholics.”
[Based on a novel by Brian Moore]

His nephew is “Scrooged” screenwriter
Mitch Glazer.

(Josh Spector)

Recommended reading —


Art, Money, and Ego in the Making of
“Heaven’s Gate,”
the Film that Sank United Artists,

Second Edition,
by Steven Bach

From Newmarket Press:

Steven Bach was the senior vice-president and head of worldwide production for United Artists at the time of the filming of Heaven’s Gate…. Apart from the director and the producer, Bach was the only person to witness the evolution of Heaven’s Gate from beginning to end.”

See also my journal entry
“Back to Bach”
of 1:44 a.m. EST
Saturday, December 14, 2002.

Friday, December 13, 2002

Friday December 13, 2002

Filed under: General — m759 @ 5:24 PM

Shall we read? — The sequel

Two stories related to my recent entries on the death of Stan Rice (Sequel, 12/11/02) and the career of Jodie Foster (Rhyme Scheme, 12/13/02)  —

From BBC News World Edition,
Thursday, 12 December, 2002, 15:34 GMT

Entertainment Section

  • Poet Stan Rice dies

    Stan Rice, the poet, painter and husband of author Anne Rice, has died of brain cancer at the age of 60….

    He met his wife, the author of the Vampire Chronicles, when the pair studied journalism together.

  • Abba hit tops dance music poll

    Dancing Queen by Abba has been voted the top dancefloor tune of all time, according to viewers of cable music channel VH1.

That’s Entertainment!

See also my entry of December 5, 2002,
Key (for Joan Didion’s birthday):

I faced myself that day
with the nonplused apprehension
of someone who has come across a vampire
and has no crucifix in hand.

— Joan Didion, “On Self-Respect,”
in Slouching Towards Bethlehem

Divine Comedy

Didion and her husand John Gregory Dunne
(author of The Studio and Monster
wrote the screenplays for
the 1976 version of “A Star is Born”
and the similarly plotted 1996 film
Up Close and Personal.”

If the incomparable Max Bialystock 
were to remake the latter, he might retitle it
Distant and Impersonal.”
A Google search on this phrase suggests
a plot outline for Mel Brooks & Co. 

Saturday, October 12, 2002

Saturday October 12, 2002

Filed under: General — Tags: — m759 @ 3:26 PM

She's a…
Twentieth Century Fox

Columbus Day
Dinner Dance

Date: Sat Oct 12, 2002
Time: 6:30pm-???
Italian American Club
of Southern Nevada

2333 East Sahara Ave.,
Las Vegas, NV 89104
Live music by Boyd Culter's 5-Piece band, prime rib dinner, and dancing at the Italian-American Club of Southern Nevada. All are welcome to attend. Tickets are only $25 and must be purchased in advance.
Cost: $25.00
For More information
Call 457-3866  or visit  
Web Site

In honor of this dance, of Columbus, and of Joan Didion, this site's music for the weekend is "Spinning Wheel."  For the relevance of this music, see Chapter 65 (set in Las Vegas) of Didion's 1970 novel Play It As It Lays, which, taken by itself, is one of the greatest short stories of the twentieth century.

The photograph of Didion on the back cover of Play It (taken when she was about 36) is one of the most striking combinations of beauty and intelligence that I have ever seen.

She's the queen of cool
And she's the lady who waits.
The Doors, "Twentieth Century Fox," Jan. 1967

Play It As It Lays is of philosophical as well as socio-literary interest; it tells of a young actress's struggles with Hollywood nihilism.  For related material, see The Studio by Didion's husband, John Gregory DunneA review of Dunne's book:

"Not since F. Scott Fitzgerald and Nathanael West has anyone done Hollywood better."

High praise indeed.

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