From the journal of Steven H. Cullinane...
2008 January 01-31
Thursday, January 31, 2008 5:24 AM
Happy Birthday to a Dark Lady
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:
Jean Simmons (l.) and Deborah Kerr (r.)
and from the next day,
Jan. 18, 2008
... Todo lo sé por el lucero
que brilla en la diadema de la Muerte.
born January 18, 1867
Dark Lady and Bright Star
Time and Eternity
late John O'Hara
Friday, January 25, 2008 4:04 AM
ART WARS continued:
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
"I confess I do not believe in time.
I like to fold my magic carpet,
after use, in such a way
as to superimpose
part of the pattern
-- Nabokov, Speak, Memory
Figure by Coxeter
reminiscent of the
Ojo de Dios
Mexico's Sierra Madre
In memory of
of Art curator
who died on
| "the God's-eye
of the author"
-- Dorothy Sayers,
of the Maker
and free eye,
in all directions"
-- Vladimir Nabokov,
-- A Contrapuntal Theme
Monday, January 21, 2008 11:30 PM
Context-Sensitive Theology, continued:
"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:
- 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.
- 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.)
- André Weil: "God exists since mathematics is
consistent, and the Devil exists since we cannot prove it."
- 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.
Saturday, January 19, 2008 7:00 AM
A Death of Kings:
In Memory of
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
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."
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.
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.
Friday, January 18, 2008 12:00 PM
Friday, January 18, 2008 4:00 AM
Thursday, January 17, 2008 5:24 PM
For the Dark Lady:
"Mazur introduced the topic of prime numbers with a story from Don
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
Wednesday, January 16, 2008 12:25 PM
Christmas 2005 continued...
Geometry of the
Click on the image for a larger version
and an expansion of some remarks
quoted here on Christmas 2005
Sunday, January 6, 2008 1:00 AM
Eightfold Cube Illustrated
Friday, January 4, 2008 1:00 PM
n. itinerant seller or giver of books,
especially religious literature.
Now you has jazz.
-- Cole Porter, lyric for "High
set in Newport, Rhode Island, 1956
Friday, January 4, 2008 2:02 AM
The "greatest generation" theme from Art Wars-- April
7, 2003 continues in two obituaries from this morning's New
The first obituary says that Goldberg
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
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
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
Thursday, January 3, 2008 1:01 PM
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
Hardcover, US$27.95, 281 pages --
the Habermas-Lyotard debate (see  for an introduction) to the Sokal
hoax (), to recent atheist manifestos on the bestseller lists (e.g.,
) the question of foundations for intellectual thought and
especially for intellectual debate has never been more critical or
 M. Bérubé, What's Liberal about the Liberal Arts? Classroom
Politics and "Bias" in Higher Education, W. W. Norton, 2006.
 S. Harris, Letter to a Christian Nation, Knopf, 2006.
 A. Sokal and P. Bricmont, Fashionable Nonsense: Postmodern
Intellectuals' Abuse of Science, Picador, 1999.
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
"... 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.
the life of John Nash,
for whom the above
equilibrium is named.