Thursday, January 31, 2008

Thursday January 31, 2008

Filed under: General — m759 @ 5:24 AM
From G. K. Chesterton,
The Black Virgin
As the black moon
of some divine eclipse,
As the black sun
of the Apocalypse,
As the black flower
that blessed Odysseus back
From witchcraft; and
he saw again the ships.

In all thy thousand images
we salute thee.

Earlier in the poem….
Clothed with the sun
or standing on the moon
Crowned with the stars
or single, a morning star,
Sunlight and moonlight
are thy luminous shadows,
Starlight and twilight
thy refractions are,
Lights and half-lights and
all lights turn about thee.

From Oct. 16, 2007,
date of death of Deborah Kerr:

"Harish, who was of a
spiritual, even religious, cast
and who liked to express himself in
metaphors, vivid and compelling,
did see, I believe, mathematics
as mediating between man and
what one can only call God."
R. P. Langlands

From a link of Jan. 17, 2008
Time and Eternity:

Abstract Symbols of Time and Eternity

Jean Simmons and Deborah Kerr in Black Narcissus
Jean Simmons (l.) and Deborah Kerr (r.)
in "Black Narcissus" (1947)

and from the next day,
Jan. 18, 2008:

… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

Rubén Darío,
born January 18, 1867

Related material:

Dark Lady and Bright Star,
Time and Eternity,
Damnation Morning

Happy birthday also to
the late John O'Hara.

Monday, January 28, 2008

Monday January 28, 2008

Filed under: General — m759 @ 7:59 AM


Sunday, January 27, 2008

Sunday January 27, 2008

Filed under: General — m759 @ 4:28 AM


Saturday, January 26, 2008

Saturday January 26, 2008

Filed under: General — m759 @ 2:22 AM
Working Backward

Those who have followed the links here recently may appreciate a short story told by yesterday’s lottery numbers in Pennsylvania: mid-day 096, evening 513.

The “96” may be regarded as a reference to the age at death of geometer H.S.M. Coxeter (see yesterday morning’s links). The “513” may be regarded as a reference to the time of yesterday afternoon’s entry, 5:01, plus the twelve minutes discussed in that entry by presidential aide Richard Darman, who died yesterday.

These references may seem less fanciful in the light of other recent Log24 material: a verse quoted here on Jan. 18

… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

Rubén Darío,
born January 18, 1867

— and a link on Jan. 19 to the following:

The Lion, the Witch
and the Wardrobe:


“But what does it all mean?” asked Susan when they were somewhat calmer.

“It means,” said Aslan, “that though the Witch knew the Deep Magic, there is a magic deeper still which she did not know. Her knowledge goes back only to the dawn of Time. But if she could have looked a little further back, into the stillness and the darkness before Time dawned, she would have read there a different incantation. She would have known that when a willing victim who had committed no treachery was killed in a traitor’s stead, the Table would crack and Death itself would start working backward.”

Friday, January 25, 2008

Friday January 25, 2008

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

Time and the River

Harvard Class of 1964
Twenty-fifth Anniversary Report:

"At this writing (November, '88), President-elect Bush has just announced his intention to name me to his Cabinet and to nominate me as Director of the Office of Management and Budget. Given the state of play in Washington, I suppose I may find myself in premature retirement by the time this report is published.

That is not an entirely unattractive prospect. Kath (Kathleen Emmet, '64) and I live in an idyllic setting, overlooking the Little Falls of the Potomac, just twelve minutes upstream from the Capitol. She writes– she's now completing a book on American writers in Paris after World War II. Our children (Willy and Jonathan) do what healthy growing twelve- and seven-year-olds do. The river works its way peacefully over the falls and riffles around a woodsy island through the Chain Bridge narrows, and then on into the familar wide mud-basin of Washington– a wholly different world.

When I was an undergraduate, I asked all the adolescent questions. I still do: Why does the river flow the way it does? Why does one move downstream and back? The allure of such simple questions is as great for me today as when we talked of them so seriously and so long at the University Restaurant or the Casablanca, or on the steps of Widener. The only difference seems to be that I'm now a bit more willing to settle for answers that seem simpler, less profound, sometimes even trite. But only a bit."

— Richard Darman, who died today at 64

Friday January 25, 2008

Filed under: General — Tags: , — m759 @ 4:04 AM

Requiem for a Curator

"There is a pleasantly discursive treatment
of Pontius Pilate's unanswered question
'What is truth?'"

  — H. S. M. Coxeter, 1987,
book introduction quoted
as epigraph to
Art Wars

"I confess I do not believe in time.
I like to fold my magic carpet,
after use, in such a way
as to superimpose
one part of the pattern
upon another."

Nabokov, Speak, Memory


Figure by Coxeter
reminiscent of the
Ojo de Dios of
Mexico's Sierra Madre

In memory of
National Gallery
of Art curator
Philip Conisbee,
who died on
January 16:

"the God's-eye
 of the author"


— Dorothy Sayers,
    The Mind
    of the Maker

  "one complete
and free eye,
which can
simultaneously see
in all directions"

— Vladimir Nabokov,
    The Gift   

A Contrapuntal Theme

Friday January 25, 2008

Filed under: General — m759 @ 3:36 AM


Monday, January 21, 2008

Monday January 21, 2008

Filed under: General — m759 @ 11:30 PM
Serious Numbers

"When times are mysterious
Serious numbers will always be heard."

Paul Simon

Recent events in world financial markets suggest a return to this topic, considered here on October 13, 2007.

That day's entry, on mathematics and theology, may be of use to those who are considering, as their next financial move, prayer.

Some related material:

  1. The review in the Jan. 22 New York Times of a book by mathematics vulgarizer John Allen Paulos refuting arguments for the existence of God.

  2. Arguments in a less controversial area– for and against the consistency of elementary number theory:

    FOR: Kurt Gödel, Steven H. Cullinane, and John Dawson (See Log24– Nov. 30 and Dec. 2, 2005–  and "Gödel, Inconsistency, Provability, and Truth: An Exchange of Letters" (pdf), in the American Mathematical Society Notices of April 2006.)

    AGAINST: E. B. Davies, King's College London (See above.)

  3. André Weil: "God exists since mathematics is consistent, and the Devil exists since we cannot prove it."
  4. God: "605." (NY Lottery, mid-day Jan. 20, 2008) This can, of course, be interpreted as "6/05"– which is perhaps a reference to "God, the Devil, and a Bridge." Or perhaps not.

Monday January 21, 2008

Filed under: General — m759 @ 9:00 AM


Sunday, January 20, 2008

Sunday January 20, 2008

Filed under: General — m759 @ 7:00 AM
Oh, What Can It Mean?

From the last entry in my
Harvard weblog– May 21, 2005:

//www.log24.com/log/pix05/050521-Zeitung.jpg” cannot be displayed, because it contains errors.

Franken is best known as
the author of

Lies and the Lying Liars
Who Tell Them.

Today, more from the same newspaper:


AP Top Entertainment News
At 6:09 a.m. EST

‘Newhart’ Actress Suzanne Pleshette Dies
LOS ANGELES (AP) — Suzanne Pleshette, the husky-voiced star best known for her role as Bob Newhart’s sardonic wife on television’s long-running “The Bob Newhart Show,” has died at age 70….

‘Daydream Believer’ Songwriter Dies

SAN DIEGO (AP) — John Stewart, who wrote the Monkees’ hit “Daydream Believer” and became a well-known figure in the 1960s folk music revival as a member of The Kingston Trio, has died, according to the band’s Web site. He was 68….

“Oh, what can it mean
to a daydream believer
and a homecoming queen?”

Related material:
Buck Mulligan’s Introibo
and The Crimson Passion

“Thanks, old chap, he cried briskly.
That will do nicely. Switch off
the current, will you?”
Buck Mulligan

Sunday January 20, 2008

Filed under: General — m759 @ 6:23 AM


Saturday, January 19, 2008

Saturday January 19, 2008

Filed under: General — Tags: , — m759 @ 7:00 AM
In Memory of
Bobby Fischer

Edward Rothstein has a piece on Bobby Fischer in today’s New York Times.  The Rothstein opening:

“There may be only three human activities in which miraculous accomplishment is possible before adulthood: mathematics, music and chess.”

This echoes the opening of a classic George Steiner essay (The New Yorker, Sept. 7, 1968):

“There are three intellectual pursuits, and, so far as I am aware, only three, in which human beings have performed major feats before the age of puberty. They are music, mathematics, and chess.”

— “A Death of Kings,” reprinted in George Steiner: A Reader, Oxford University Press, 1984, pp. 171-178.

Despite its promising (if unoriginal) opening, the New York Times piece is mainly an attack on Fischer’s anti-Jewish stance.  Rothstein actually has little of interest to say about what he calls the “glass-bead games” of music, mathematics, and chess. For a better-written piece on chess and madness, see Charles Krauthammer’s 2005 essay in TIME. The feuilletons of Rothstein and Krauthammer do not, of course, come close to the genuinely bead-game-like writing of Steiner.

Related material on
chess and religion:
Magical Thinking
(December 7th, 2005)

Friday, January 18, 2008

Friday January 18, 2008

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

Front page top center, online NY Times: Bobby Fischer Dead at 64

Friday January 18, 2008

Filed under: General — Tags: — m759 @ 4:00 AM


… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

Rubén Darío,
born January 18, 1867

Thursday, January 17, 2008

Thursday January 17, 2008

Filed under: General — Tags: , — m759 @ 5:24 PM
Well, she was
   just seventeen…

"Mazur introduced the topic of prime numbers with a story from Don Quixote in which Quixote asked a poet to write a poem with 17 lines. Because 17 is prime, the poet couldn't find a length for the poem's stanzas and was thus stymied."

— Undated American Mathematical Society news item about a Nov. 1, 2007, event

Related material:

Jueves, Enero 17, 2008

Horses of a Dream
(Log24, Sept. 12, 2003)

Knight Moves
(Log24 yesterday–
anniversary of the
Jan. 16 publication
of Don Quixote)

Windmill and Diamond
(St. Cecilia's Day 2006)

Wednesday, January 16, 2008

Wednesday January 16, 2008

Filed under: General,Geometry — Tags: , , , , — m759 @ 12:25 PM
Knight Moves:
Geometry of the
Eightfold Cube

Actions of PSL(2, 7) on the eightfold cube

Click on the image for a larger version
and an expansion of some remarks
quoted here on Christmas 2005.

Monday, January 14, 2008

Monday January 14, 2008

Filed under: General — m759 @ 6:00 AM


Sunday, January 13, 2008

Sunday January 13, 2008

Filed under: General — m759 @ 12:00 PM


Sunday, January 6, 2008

Sunday January 6, 2008

Filed under: General,Geometry — Tags: — m759 @ 1:00 AM
The following illustration of
how the eightfold cube works
was redone.

How the eightfold cube works

For further details, see
Finite Geometry of
the Square and Cube
and The Eightfold Cube.

Saturday, January 5, 2008

Saturday January 5, 2008

Filed under: General — m759 @ 12:00 PM


Saturday January 5, 2008

Filed under: General — m759 @ 2:56 AM


Friday, January 4, 2008

Friday January 4, 2008

Filed under: General — m759 @ 1:00 PM
In memory of
LeRoy Schneck

From Log24 on
this date five years ago:


n. itinerant seller or giver of books,
especially religious literature.


Now you has jazz.

— Cole Porter, lyric for “High Society,”
set in Newport, Rhode Island, 1956

Friday January 4, 2008

Filed under: General — m759 @ 2:02 AM
The Harvest Continues

The “greatest generation” theme from Art Wars– April 7, 2003 continues in two obituaries from this morning’s New York Times:

NY Times obituaries: painter Michael Goldberg, military historian Gerald Astor

The first obituary says that Goldberg

“saw abstract painting… as ‘still the primary visual challenge of our time. It might get harder and harder to make an abstract image that’s believable, but I think that just makes the challenge greater.'”  The Times says that Goldberg was a veteran of Merrill’s Marauders in World War II (as well as of the last century’s art wars).

The second obituary notes that Astor’s books include A Blood-Dimmed Tide (a phrase from Yeats)– an account of the Battle of the Bulge– and a biography of Dr. Josef Mengele.

Both men died on Sunday, December 30, 2007. From Log24 on that date, an abstract image and a cinematic portrait of Dr. Mengele:

S. H. Cullinane,
Aug. 15, 2003

Dr. Mengele,
according to

Related material:

Yesterday’s entry
The Revelation Game
and an entry of April 7, 2003:

April is Math Awareness Month.
This year’s theme is “mathematics and art.”

(The art, by Ingmar Bergman, was
in honor of the April 7 birthday of
Francis Ford Coppola, director of
“Apocalypse Now.”)

Thursday, January 3, 2008

Thursday January 3, 2008

Filed under: General — m759 @ 1:01 PM
Context-Sensitive Theology

The Revelation Game 
New Year’s reading for
the tigers of Princeton

Two reviews from the February 2008 Notices of the American Mathematical Society:

From a review of

A Certain Ambiguity
(A Mathematical Novel)

by Gaurav Suri and Hartosh Singh Bal
Princeton University Press
Hardcover, US$27.95, 281 pages —

“From the Habermas-Lyotard debate (see [1] for an introduction) to the Sokal hoax ([4]), to recent atheist manifestos on the bestseller lists (e.g., [2]) the question of foundations for intellectual thought and especially for intellectual debate has never been more critical or urgent.”

[1] M. Bérubé, What’s Liberal about the Liberal Arts? Classroom Politics and “Bias” in Higher Education, W. W. Norton, 2006.
[2] S. Harris, Letter to a Christian Nation, Knopf, 2006.
[4] A. Sokal and P. Bricmont, Fashionable Nonsense: Postmodern Intellectuals’ Abuse of Science, Picador, 1999.

Danny Calegari of Caltech

Also in the February Notices– a review of a book, Superior Beings: If They Exist, How Would We Know?, in which the author

“.. uses elementary ideas from game theory to create situations between a Person (P) and God (Supreme Being, SB) and discusses how each reacts to the other in these model scenarios….

In the ‘Revelation Game,’ for example,
the Person (P) has two options:
1) P can believe in SB’s existence
2) P can not believe in SB’s existence
The Supreme Being also has two options:
1) SB can reveal Himself
2) SB can not reveal Himself….

… [and] goals allow us to rank all the outcomes for each player from best… to worst…. The question we must answer is: what is the Nash equilibrium in this case?”

The answer is what one might expect from the American Mathematical Society:

“… the dominant strategy for both is when SB does not reveal Himself and P does not believe in His existence.”

Other strategies are, of course, possible. See last year’s entries.

See also
the life of John Nash,


for whom the above
equilibrium is named.

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