Monday, July 31, 2006
“This epic poem was described by perhaps his closest friend, Poet Laureate Robert Bridges, as, ‘the dragon folded at the gate to forbid all entrance’ to the appreciation of his other works. More favorable is the opinion of the most thorough of Hopkins’s critics, W. H. Gardner, who described it as a great symphony or overture, introducing his other works and not forbidding them.”
— “Fr. Gerard Manley Hopkins: Priest and Poet,”
by Bro. Anthony Joseph
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For the feast of
St. Ignatius Loyola…
Final Arrangements,
continued:
“Now you has jazz.”
– High Society, 1956
— Today’s online New York Times
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Also from today’s
New York Times:
Kurt Kreuger
in the 1945 film
“Paris Underground.”
Kurt Kreuger,
a German-born actor
who reluctantly played
Nazi soldiers
in many films
about World War II,
died July 12 in
Beverly Hills, Calif.
He was 89.
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Log24, Wednesday,
July 12, 2006:
Band Numbers
“Some friends
of mine
are in
this band…”
— David
Auburn,
Proof
Seven is Heaven,
Eight is a Gate,
Nine is a Vine.
— The Prime Powers
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Related material:
A Log24 entry commemorating
the murder of six Jesuits
in El Salvador.
Sunday, July 30, 2006
“You can do what you want
Abe, but the next time you
see me comin’ you better run.”
Today’s online New York Times:
“On Highway 61 outside of
Natchez, Mississippi, stands
Campaign Song
“All things return to the One.
What does the One return to?”
— Zen koan, epigraph to
The Footprints of God,
by Greg Iles of
Natchez, Mississippi
“Literature begins with geography.”
— attributed to Robert Frost
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History
From “Today in History,” by The Associated Press–
On this date (July 30):
“In 1864, during the Civil War, Union forces tried to take Petersburg, Va., by exploding a mine under Confederate defense lines; the attack failed.”
“A nightmare” — Ulysses
Men ask the way to Cold Mountain.
Cold Mountain: there’s no through trail.
Saturday, July 29, 2006
Dark Fields
of the Republic
Today’s birthday: Ken Burns
Charley Reese on the republic:
“The republic died at Appomattox, and it’s been empire ever since.”
Charley Reese on Lincoln:
“Washington and Jefferson created the republic; Lincoln destroyed it.”
In closing…
A link in memory of Donald G. Higman, dead on Feb. 13, 2006, the day after Lincoln’s birthday:
On the Graphs of Hoffman-Singleton and Higman-Sims (pdf)
His truth is marching on.
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Big Rock
Thanks to Ars Mathematica, a link to everything2.com:
“In mathematics, a big rock is a result which is vastly more powerful than is needed to solve the problem being considered. Often it has a difficult, technical proof whose methods are not related to those of the field in which it is applied. You say ‘I’m going to hit this problem with a big rock.’ Sard’s theorem is a good example of a big rock.”
Another example:
Properties of the Monster Group of R. L. Griess, Jr., may be investigated with the aid of the Miracle Octad Generator, or MOG, of R. T. Curtis. See the MOG on the cover of a book by Griess about some of the 20 sporadic groups involved in the Monster:
The MOG, in turn, illustrates (via Abstract 79T-A37, Notices of the American Mathematical Society, February 1979) the fact that the group of automorphisms of the affine space of four dimensions over the two-element field is also the natural group of automorphisms of an arbitrary 4×4 array.
This affine group, of order 322,560, is also the natural group of automorphisms of a family of graphic designs similar to those on traditional American quilts. (See the diamond theorem.)
This top-down approach to the diamond theorem may serve as an illustration of the “big rock” in mathematics.
For a somewhat simpler, bottom-up, approach to the theorem, see Theme and Variations.
For related literary material, see Mathematics and Narrative and The Diamond as Big as the Monster.
“The rock cannot be broken.
It is the truth.”
— Wallace Stevens,
“Credences of Summer”
Comments Off on Saturday July 29, 2006
For a spider figure of
an (apparently) different sort,
see Log24 on the morning
after the demise of
Hunter S. Thompson,
and the links given there.
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Thursday, July 27, 2006
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Real Numbers:
720,
513
(NY Lottery today)
“Was there really a cherubim
waiting at the star-watching rock…?
Was he real?
What is real?”
— Madeleine L’Engle,
A Wind in the Door,
quoted at math16.com
7/20:
Real
5/13:
A Fold in Time
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Number Sense
The NY lottery numbers for yesterday, 7/26, Jung's birthday, were 726 (mid-day) and 970 (evening).
We may view these numbers as representing the Jungian "sheep" and Freudian "goats" of yesterday's entry Partitions.
For the Jungian coincidence of 726 with 7/26, recall the NY lottery number 911 that was drawn on 9/11 exactly a year after the destruction of the World Trade Center. For more on this coincidence, see For Hemingway's Birthday: Mathematics and Narrative Continued (July 21, 2006).
For 970, Google reveals a strictly skeptical (i.e., like Freud, not Jung) meaning: 970 is the first page of the article "Sources of Mathematical Thinking," in Science, 7 May 1999: Vol. 284. no. 5416, pp. 970 – 974.
That article has been extensively cited in the scholarly literature on the psychology of mathematics. Its lead author, Stanislas Dehaene, has written a book, The Number Sense.
What sense, if any, is made by 726 and 970?
The mid-day number again (see Hemingway's birthday) illustrates the saying
"Time and chance happeneth to them all."
The evening number again illustrates the saying
"Though truth may be very hard to find in the pages of most books, the page numbers are generally reliable."
— Steven H. Cullinane,
Zen and Language Games
These sayings may suit the religious outlook of Susan Blackmore, source (along with Matthew 25:31-46) of the sheep/goats partition in yesterday's entry on that topic. She herself, apparently a former sheep, is now a goat practicing Zen.
Update of later the same evening–
On Space, Time, Life, the Universe, and Everything:
Note that the "sheep" number 726 has a natural interpretation as a date– i.e., in terms of time, while the "goat" number 970 has an interpretation as a page number– i.e., in terms of space. Rooting, like Jesus and St. Matthew, for the sheep, we may interpret both of today's NY lottery results as dates, as in the next entry, Real Numbers. That entry may (or may not) pose (and/or answer) The Ultimate Question. Selah.
Comments Off on Thursday July 27, 2006
Wednesday, July 26, 2006
Venus at St. Anne’s
(Title of the closing chapter
of That Hideous Strength)
Symbol of Venus
and
Symbol of Plato
“What do they
teach them
at these schools?”
— C. S. Lewis
Today is the
feast of St. Anne.
Comments Off on Wednesday July 26, 2006
"Mistakes are inevitable and may be either in missing a true signal or in thinking there is a signal when there is not. I am suggesting that believers in the paranormal (called 'sheep' in psychological parlance) are more likely to make the latter kind of error than are disbelievers (called 'goats')."
— "Psychic Experiences:
Psychic Illusions,"
by Susan Blackmore,
Skeptical Inquirer, 1992
"… a drama built out of nothing
but numbers and imagination"
— Freeman Dyson, quoted in Log24
on the day Mosteller died
From Log24 on
Mosteller's last birthday,
December 24, 2005:
by Arturo Perez-Reverte
One by one, he tore the engravings from the book, until he had all nine. He looked at them closely. "It's a pity you can't follow me where I'm going. As the fourth engraving states, fate is not the same for all."
"Where do you believe you're going?"
Borja dropped the mutilated book on the floor with the others. He was looking at the nine engravings and at the circle, checking strange correspondences between them.
"To meet someone" was his enigmatic answer. "To search for the stone that the Great Architect rejected, the philosopher's stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso."
|
"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"
(Faust, Part Two)
— Carl Gustav Jung,
born on this date
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Monday, July 24, 2006
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Discourse Analysis
Edward Rothstein in today’s New York Times, reviewing Evil Incarnate (Princeton University Press):
“… the most decisive aspect of the myth is that it is, literally, a myth. Every single example of evil he gives turns out to be evil imagined: there is, he says, no evidence for any of it. Evil, he argues, is not something real, it is a ‘discourse,’ a ‘way of representing things and shaping our experience, not some force in itself.'”
Related material:
A review (pdf) by Steven G. Krantz of Charles Wells’s A Handbook of Mathematical Discourse (Notices of the American Mathematical Society, September 2004):
“Ambrose Bierce’s Devil’s Dictionary is a remarkable and compelling piece of writing because of its searing wit and sardonic take on life. Bierce does not define any new words. He instead gives deadly interpretations of very familiar words. Wells’s book does not fit into the same category of literary effort.”
For literary efforts perhaps more closely related to Bierce’s, see Mathematics and Narrative and the five Log24 entries ending on this date last year.
Comments Off on Monday July 24, 2006
Sunday, July 23, 2006
Dance of the Numbers, continued:
Partitions
Freeman Dyson on the role of the “crank” in the theory of partitions:
“‘Each step in the story is a work of art,’ Dyson says, ‘and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination.'”
— Erica Klarreich in
Science News Online, week of
June 18, 2005, quoted in
“In Honor of Freeman Dyson’s Birthday:
Dance of the Numbers“
(Log24, Dec. 15, 2005)
Paraphrase of Freeman Dyson’s remarks in The New York Review of Books, issue dated May 28, 1998:
“Theology is about words; science is about things.“
“What is 256 about?”
— Reply to Freeman Dyson,
(May 15, 1998)
A partial answer to that rhetorical question: 256 is the cardinality of the power set of an 8-set.
For the role played by 8-sets and by 23 (today’s date) in partitions of a different sort, see Geometry of the 4×4 Square.
Comments Off on Sunday July 23, 2006
Saturday, July 22, 2006
Mary Magdalene
(Portrait by Nikos Kazantzakis
and Martin Scorsese):
“Magdalene lay on her back, stark naked, drenched in sweat, her raven-black hair spread out over the pillow and her arms entwined beneath her head. Her face was turned toward the wall and she was yawning. Wrestling with men on this bed since dawn had tired her out.”
— Nikos Kazantzakis,
The Last Temptation of Christ
Comments Off on Saturday July 22, 2006
Friday, July 21, 2006
For Hemingway’s birthday:
Mathematics and Narrative, continued
“We know many little things about the relation between mathematics and narrative, but lack one big comprehensive insight.”
— John Allen Paulos (pdf)
“On Wednesday, Sept. 11, 2002– 9/11/02– the New York State lottery numbers were 911, an eerie coincidence that set many people to thinking or, perhaps more accurately, to not thinking.”
— John Allen Paulos
“Time and chance happeneth to them all.”
— Ecclesiastes 9:11
Comments Off on Friday July 21, 2006
Thursday, July 20, 2006
Bead Game
Those who clicked on Rieff’s concept in the previous entry will know about the book that Rieff titled Sacred Order/Social Order: My Life among the Deathworks.
That entry, from Tuesday, July 18, was titled “Sacred Order,” and gave as an example the following figure:
(Based on Weyl’s Symmetry)
For the use of this same figure to represent a theatrical concept–
“It’s like stringing beads on a necklace. By the time the play ends, you have the whole necklace.”
— see Ursprache Revisited (June 9, 2006).
Of course, the figure also includes a cross– or “deathwork”– of sorts. These incidental social properties of the figure (which is purely mathematical in origin) make it a suitable memorial for a theatre critic who died on the date of the previous entry– July 18– and for whom the American Theatre Wing’s design awards, the Henry Hewes Awards, are named.
“The annual awards honor designers… recognizing not only the traditional design categories of sets, costumes and lighting, but also ‘Notable Effects,’ which encompasses sound, music, video, puppets and other creative elements.” —BroadwayWorld.com
For more on life among the deathworks, see an excellent review of the Rieff book mentioned above.
Comments Off on Thursday July 20, 2006
Tuesday, July 18, 2006
Sacred Order
In memory of Philip Rieff, who died on July 1, 2006:
Related material:
and
For details, see the
five Log24 entries ending
on the morning of
Midsummer Day, 2006.
That essay says Rieff had "a dense, knotty, ironic style designed to warn off impatient readers. You had to unpack his aphorisms carefully. And this took a while. As a result, his thinking had a time-release effect." Good for him. For a related essay (time-release effect unknown), see
Hitler's Still Point: A Hate Speech for Harvard.
Comments Off on Tuesday July 18, 2006
Monday, July 17, 2006
Today is the feast of
St. James McNeill Whistler.
“Nature contains the elements of color and form of all pictures– as the keyboard contains the notes of all music– but the artist is born to pick, and choose, and group with science, these elements, that the result may be beautiful– as the musician gathers his notes, and forms his chords, until he brings forth from chaos, glorious harmony.”
— Whistler, “The Ten O’Clock“
Comments Off on Monday July 17, 2006
Sunday, July 16, 2006
Mathematics and Narrative
continued…
“Now, at the urging of the UC Berkeley cognitive linguist George Lakoff, liberal America’s guru of the moment, progressive Democrats are practicing to get their own reluctant mouths around some magical new vocabulary, in the hope of surviving and eventually overcoming the age of Bush.”
— Marc Cooper in The Atlantic Monthly, April 2005, “Thinking of Jackasses: The Grand Delusions of the Democratic Party”
Cooper’s “now” is apparently still valid. In today’s New York Times, the leftist Stanley Fish reviews Talking Right, by leftist Geoffrey Nunberg:
“… the right’s language is now the default language for everyone.
On the way to proposing a counterstrategy (it never really arrives), Nunberg pauses to engage in a polite disagreement with his fellow linguist George Lakoff, who has provided a rival account of the conservative ascendancy. Lakoff argues that Republicans have articulated– first for themselves and then for others– a conceptual framework that allows them to unite apparently disparate issues in a single coherent worldview … woven together not in a philosophically consistent framework but in a narrative ‘that creates an illusion of coherence.’
Once again, the Republicans have such a narrative– ‘declining patriotism and moral standards, the out-of-touch media and the self-righteous liberal elite … minorities demanding special privileges … disrespect for religious faith, a swollen government’– but ‘Democrats and liberals have not offered compelling narratives that could compete’ with it. Eighty pages later he is still saying the same thing. ‘The Democrats need a compelling narrative of their own.'”
Lakoff is the co-author of a book on the philosophy of mathematics, Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. From Wikipedia’s article on Lakoff:
“According to Lakoff, even mathematics itself is subjective to the human species and its cultures: thus ‘any question of math’s being inherent in physical reality is moot, since there is no way to know whether or not it is.’ Lakoff and Rafael E. Nunez (2000) argue at length that mathematical and philosophical ideas are best understood in light of the embodied mind. The philosophy of mathematics ought therefore to look to the current scientific understanding of the human body as a foundation ontology, and abandon self-referential attempts to ground the operational components of mathematics in anything other than ‘meat.'”
For a long list of related leftist philosophy, see The Thinking Meat Project.
Democrats seeking narratives may also consult The Carlin Code and The Prime Cut Gospel.
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Saturday, July 15, 2006
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Today’s birthday:
Linda Ronstadt is 60.
“Elegant as a slow blues.”
— Review of a writer
by Rolling Stone
Just send me black roses
White rhythm and blues
And somebody who cares when you lose
Black roses, white rhythm and blues
Black roses, white rhythm and blues
— Linda Ronstadt song
by J. D. Souther, from
Living in the USA, 1978
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Friday, July 14, 2006
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Thursday, July 13, 2006
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Longest Day’s Journey
BY BOB THOMAS, LOS ANGELES
July 13, 2006 (AP)– Red Buttons, the carrot-topped burlesque comedian who became a top star in early television and then in a dramatic role won the 1957 Oscar as supporting actor in “Sayonara,” died Thursday [July 13, 2006]. He was 87. —San Francisco Chronicle
Sayonara.
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Carpe Diem
From the new MySpace.com
weblog of Michio Kaku:
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Thursday, July 13, 2006
Hyperspace and a Theory of Everything
What lies beyond our 4 dimensions?
By Michio Kaku
When I was a child, I used to visit the Japanese Tea Garden in San Francisco. I would spend hours fascinated by the carp, who lived in a very shallow pond just inches beneath the lily pads, just beneath my fingers, totally oblivious to the universe above them.
I would ask myself a question only a child could ask: what would it be like to be a carp? |
A child, or Maurits Escher:
Three Worlds,
1955
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Today's birthday:
Harrison Ford
"The forest here at the bottom of the canyon is mostly pine, with a few aspen and broad-leafed shrubs. Steep canyon walls rise way above us on both sides. Occasionally the trail opens into a patch of sunlight and grass that edges the canyon stream, but soon it reenters the deep shade of the pines. The earth of the trail is covered with a soft springy duff of pine needles. It is very quiet here.
Mountains like these and travelers in the mountains and events that happen to them here are found not only in Zen literature but in the tales of every major religion."– Robert Pirsig
"… a point of common understanding between the classic and romantic worlds. Quality, the cleavage term between hip and square, seemed to be it. Both worlds used the term. Both knew what it was. It was just that the romantic left it alone and appreciated it for what it was and the classic tried to turn it into a set of intellectual building blocks for other purposes."– Robert Pirsig
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Wednesday, July 12, 2006
Band Numbers
“Some friends of mine
are in this band…”
— David Auburn, Proof
Seven is Heaven,
Eight is a Gate,
Nine is a Vine.
— The Prime Powers
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Tuesday, July 11, 2006
Not Crazy Enough?
Some children of the sixties may feel that today's previous two entries, on Syd Barrett, the Crazy Diamond, are not crazy enough. Let them consult the times of those entries– 2:11 and 8:15– and interpret those times, crazily, as dates: 2/11 and 8/15.
This brings us to Stephen King territory– apparently the natural habitat of Syd Barrett.
See Log24 on a 2/11, Along Came a Dreamcatcher, and Log24 on an 8/15, The Line.
From 8/15, a remark of Plato:
"There appears to be a sort of war of Giants and Gods going on…"
(Compare with the remarks by Abraham Cowley for Tom Stoppard's recent birthday.)
From 2/11, two links: Halloween Meditations and We Are the Key.
From Dreamcatcher (the film and the book):
For Syd Barrett as Duddits,
see Terry Kirby on Syd Barrett
(edited– as in Stephen King
and the New Testament—
for narrative effect):
"He appeared as the Floyd performed the song 'Shine On You Crazy Diamond.' It contains the words: 'Remember when you were young, you shone like the sun. Shine on you crazy diamond. Now there's a look in your eyes, like black holes in the sky.'
At first, they didn't recognise the man, whose head and eyebrows were shaved….
But this was the 'crazy diamond' himself: Syd Barrett, the subject of the song….
When Roger Waters saw his old friend, he broke down….
Rick Wright, the keyboards player, later told an interviewer:
… 'Roger [Waters] was in tears, I think I was; we were both in tears. It was very shocking… seven years of no contact and then to walk in while we're actually doing that particular track. I don't know – coincidence, karma, fate, who knows? But it was very, very, very powerful.'"
Remarks suitable for Duddits's opponent, Mister Gray, may be found in the 1994 Ph.D. thesis of Noel Gray.
"I refer here to Plato's utilisation in the Meno of graphic austerity as the tool to bring to the surface, literally and figuratively, the inherent presence of geometry in the mind of the slave."
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"In Tom Stoppard's new play 'Rock 'n' Roll,' showing in the West End, he [
Syd Barrett] is portrayed in the opening scene, and his life and music are a recurring theme."
— Terry Kirby, Syd Barrett: The Crazy Diamond, in The Independent of July 12
Keynote
"Each scene is punctuated with a rock track from such acts as the Velvet Underground, the Doors, the Rolling Stones, Bob Dylan and Pink Floyd. Songs by Floyd's lost founder, Syd Barrett, are the keynote for Stoppard's theme that rock music sounded the death knell for repression but also heralded a freedom filled with its own perils."
— Ray Bennett, today's review of a new play, "Rock 'n' Roll," by Tom Stoppard
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Pink Floyd co-founder
Syd Barrett dies
"Pink Floyd's 1975 track 'Shine On You Crazy Diamond,' from the album 'Wish You Were Here,' is widely believed to be a tribute to Barrett."– Reuters
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Monday, July 10, 2006
An obituary in this morning's New York Times suggests a flashback. The Times says that Paul Nelson, 69, a music critic once famously ripped off by the young Bobby Zimmerman, was found dead in his Manhattan apartment last Wednesday. Here is a Log24 entry for that date. (The obituary, by Jon Pareles, notes that Nelson "prized hard-boiled detective novels and film noir.")
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Sunday, July 9, 2006
Today’s birthday:
Tom Hanks, star of
“The Da Vinci Code”
Ben Nicholson
and the Holy Grail
Part I:
A Current Exhibit
A. Diamond Theory, a 1976 preprint containing, in the original version, the designs on the faces of Nicholson’s “Kufi blocks,” as well as some simpler traditional designs, and
B. “
Block Designs,” a web page illustrating design blocks based on the 1976 preprint.
Part III:
The Leonardo Connection
Part IV:
Nicholson’s Grail Quest
“I’m interested in locating the holy grail of the minimum means to express the most complex ideas.”
— Ben Nicholson in a 2005 interview
Nicholson’s quest has apparently lasted for some time. Promotional material for a 1996 Nicholson exhibit in Montreal says it “invites visitors of all ages to experience a contemporary architect’s search for order, meaning and logic in a world of art, science and mystery.” The title of that exhibit was “Uncovering Geometry.”
For web pages to which this same title might apply, see Quilt Geometry, Galois Geometry, and Finite Geometry of the Square and Cube.
* “Square Kufi” calligraphy is used in Islamic architectural ornament. I do not know what, if anything, is signified by Nicholson’s 6×12 example of “Kufi blocks” shown above.
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Saturday, July 8, 2006
For Kevin Bacon’s birthday
New Game:
Father, Son, and Holy Ghost
Roderick MacLeish, author of the classic Prince Ombra, died at 80 on Saturday, July 1, 2006. From an obituary:
“‘When I think back over my career, I know that my father was a tremendous inspiration,’ said his son, an attorney who represented abuse victims in a settlement with the Roman Catholic Archdiocese of Boston.”
Related material: Log24 entries of May 31 and June 1, 2006, and the remarks of Raymond Chandler on wainscoting in The Big Sleep. See also the following:
Friday, July 7, 2006
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Born (some say)
on this date:
Yul Brynner
Mate in 6
(White moves.)
(White: Ke8, Nd7, Be5,
b5, e4, f2. Black: Ke6.)
Log24, July 3, 2006:
“… There was a problem laid out on the board, a six-mover. I couldn’t solve it, like a lot of my problems. I reached down and moved a knight….
I looked down at the chessboard. The move with the knight was wrong. I put it back where I had moved it from. Knights had no meaning in this game. It wasn’t a game for knights.”
— Raymond Chandler, The Big Sleep, begun in the summer of 1938
Log24, July 2, 2006:
“Is a puzzlement!“
Log24, July 5, 2006:
“In this way we are offered a formidable lesson for every Christian community.”
— Pope Benedict XVI on Pentecost, June 4, 2006, St. Peter’s Square.
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Thursday, July 6, 2006
State and Church
Today’s birthdays:
George W. Bush and
Sylvester Stallone, born on
the same day 60 years ago.
Two birthday quotations from Kathleen Parker:
“Verily, I say unto you – Whatever.”
“No, wait, how about this: ‘Yo, Christ Buddy!‘”
— Orlando Sentinel
column written for release July 1, 2006
Parker’s column, on recent Presbyterian interpretations of the Holy Trinity, is titled
“I believe in Larry, Moe, and Curly Joe.”
What about Shemp?
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Mexican leftist’s
lead slips
in election recount
“The winner will take over from Fox on December 1, inheriting a divided nation and a fierce war against drug smuggling gangs.”
Muy buena suerte.
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What Song the Sirens Sang
“Wake you up in the
middle of the night
just to hear them say…”
“Suitcases filled with cash had changed hands in the four-star Hotel Hassler in Rome.”
— F. Mark Wyatt, recently deceased
career CIA officer,
quoted in this morning’s
New York Times
The New York Times, with its usual lack of clarity about dates, says Wyatt died “on Thursday.” Presumably this was Thursday a week ago– June 29, 2006, the Feast of Saint Peter.
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Wednesday, July 5, 2006
Solemn Dance
Virgil on the Elysian Fields:
Some wrestle on the sands, and some in play
And games heroic pass the hours away.
Those raise the song divine, and these advance
In measur'd steps to form the solemn dance.
(See also the previous two entries.)
Bulletin of the
American Mathematical Society,
July 2006 (pdf):
"The cover of this issue of the Bulletin is the frontispiece to a volume of Samuel de Fermat’s 1670 edition of Bachet’s Latin translation of Diophantus’s Arithmetica. This edition includes the marginalia of the editor’s father, Pierre de Fermat. Among these notes one finds the elder Fermat’s extraordinary comment [c. 1637] in connection with the Pythagorean equation x2 + y2 = z2, the marginal comment that hints at the existence of a proof (a demonstratio sane mirabilis) of what has come to be known as Fermat’s Last Theorem."
— Barry Mazur, Gade University Professor at Harvard
Mazur's concluding remarks are as follows:
"But however you classify the branch of mathematics it is concerned with, Diophantus’s
Arithmetica can claim the title of founding document, and inspiring muse, to modern number theory. This brings us back to the goddess with her lyre in the frontispiece, which is the cover of this issue. As is only fitting, given the passion of the subject, this goddess is surely Erato, muse of erotic poetry."
Mazur has admitted, at his website, that this conclusion was an error:
"I erroneously identified the figure on the cover as Erato, muse of erotic poetry, but it seems, rather, to be Orpheus."
"Seems"?
The inscription on the frontispiece, "Obloquitur numeris septem discrimina vocum," is from a description of the Elysian Fields in Virgil's Aeneid, Book VI:
His demum exactis, perfecto munere divae,
Devenere locos laetos, & amoena vireta
Fortunatorum nemorum, sedesque beatas.
Largior hic campos aether & lumine vestit
Purpureo; solemque suum, sua sidera norunt.
Pars in gramineis exercent membra palaestris,
Contendunt ludo, & fulva luctanter arena:
Pars pedibus plaudunt choreas, & carmina dicunt.
Necnon Threicius longa cum veste sacerdos
Obloquitur numeris septem discrimina vocum:
Jamque eadem digitis, jam pectine pulsat eburno.
PITT:
These rites compleat, they reach the flow'ry plains,
The verdant groves, where endless pleasure reigns.
Here glowing AEther shoots a purple ray,
And o'er the region pours a double day.
From sky to sky th'unwearied splendour runs,
And nobler planets roll round brighter suns.
Some wrestle on the sands, and some in play
And games heroic pass the hours away.
Those raise the song divine, and these advance
In measur'd steps to form the solemn dance.
There Orpheus graceful in his long attire,
In seven divisions strikes the sounding lyre;
Across the chords the quivering quill he flings,
Or with his flying fingers sweeps the strings.
DRYDEN:
These holy rites perform'd, they took their way,
Where long extended plains of pleasure lay.
The verdant fields with those of heav'n may vie;
With AEther veiled, and a purple sky:
The blissful seats of happy souls below;
Stars of their own, and their own suns they know.
Their airy limbs in sports they exercise,
And on the green contend the wrestlers prize.
Some in heroic verse divinely sing,
Others in artful measures lead the ring.
The Thracian bard surrounded by the rest,
There stands conspicuous in his flowing vest.
His flying fingers, and harmonious quill,
Strike seven distinguish'd notes, and seven at once they fill.
It is perhaps not irrelevant that the late Lorraine Hunt Lieberson's next role would have been that of Orfeo in Gluck's "Orfeo ed Euridice." See today's earlier entries.
The poets among us may like to think of Mazur's own role as that of the lyre:
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Entertainment
from today’s
New York Times
From the obituary of Lorraine Hunt Lieberson, who died at 52 on Monday, July 3, 2006, at her home in Santa Fe:
“If she rarely spoke of her private life, few artists have brought such emotional vulnerability to their work, whether it was her sultry portrayal of Myrtle Wilson, the mistress of wealthy Tom Buchanan in John Harbison’s ‘Great Gatsby,’ the role of her 1999 Metropolitan Opera debut, or her shattering performances several years ago in two Bach cantatas for solo voice and orchestra, staged by the director Peter Sellars, seen in Lincoln Center’s New Visions series, with the Orchestra of Emmanuel Music, Craig Smith conducting.
In Cantata No. 82, ‘Ich Habe Genug’ (‘I Have Enough’), Ms. Hunt Lieberson, wearing a flimsy hospital gown and thick woolen socks, her face contorted with pain and yearning, portrayed a terminally ill patient who, no longer able to endure treatments, wants to let go and be comforted by Jesus. During one consoling aria, ‘Schlummert ein, ihr matten Augen’ (‘Slumber now, weary eyes’), she yanked tubes from her arms and sang the spiraling melody with an uncanny blend of ennobling grace and unbearable sadness.”
Related Entertainment
from Nov. 6, 2003
Today’s birthday:
director Mike Nichols
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And now, from
the author of Sphere…
CUBE
He beomes aware of something else… some other presence.
"Anybody here?" he says.
I am here.
He almost jumps, it is so loud. Or it seems loud. Then he wonders if he has heard anything at all.
"Did you speak?"
No.
How are we communicating? he wonders.
The way everything communicates with everything else.
Which way is that?
Why do you ask if you already know the answer?
— Sphere, by Michael Crichton, Harvard '64
"… when I went to Princeton things were completely different. This chapel, for instance– I remember when it was just a clearing, cordoned off with sharp sticks. Prayer was compulsory back then, and you couldn't just fake it by moving your lips; you had to know the words, and really mean them. I'm dating myself, but this was before Jesus Christ."
— Baccalaureate address at Princeton, Pentecost 2006, reprinted in The New Yorker, edited by David Remnick, Princeton '81
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Monday, July 3, 2006
Culture War
The New York Times, August 6, 2003,
on its executive editor Bill Keller:
“‘It is past time for our magnificent coverage of culture and lifestyles, so essential to our present allure and to our future growth, to get the kind of attention we routinely bestow on hard news,’ Mr. Keller wrote in an e-mail message to the staff.”
The New York Times, June 25, 2006,
on art in Mexico:
“At the Hilario Galguera gallery, newly opened in a fortresslike, century-old building, was Damien Hirst’s gory new series ‘The Death of God– Towards a Better Understanding of Life Without God Aboard the Ship of Fools.’ He conceived the work at his part-time home in the Mexican surf town Troncones.”
Raymond Chandler in The Big Sleep:
“I went over to a floor lamp and pulled the switch, went back to put off the ceiling light, and went across the room again to the chessboard on a card table under the lamp. There was a problem laid out on the board, a six-mover. I couldn’t solve it, like a lot of my problems. I reached down and moved a knight, then pulled my hat and coat off and threw them somewhere. All this time the soft giggling went on from the bed, that sound that made me think of rats behind a wainscoting in an old house.
…………
I looked down at the chessboard. The move with the knight was wrong. I put it back where I had moved it from. Knights had no meaning in this game. It wasn’t a game for knights.”
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For Tom Stoppard on his birthday:
“For I remember when I began to read, and to take some pleasure in it, there was wont to lie in my mother’s parlour (I know not by what accident, for she herself never in her life read any book but of devotion), but there was wont to lie Spenser’s works; this I happened to fall upon, and was infinitely delighted with the stories of the knights, and giants, and monsters, and brave houses, which I found everywhere there (though my understanding had little to do with all this); and by degrees with the tinkling of the rhyme and dance of the numbers, so that I think I had read him all over before I was twelve years old, and was thus made a poet.”
— Abraham Cowley, Essays, 1668
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Requiem for a Clown
Into the Sunset, Part I:
Into the Sunset, Part II:
Requiem for a clown:
“At times, bullshit can only be
countered with superior bullshit.”
— Norman Mailer
See also 10/13.
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Sunday, July 2, 2006
Review:
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Related material:
The obituary of Jaap Penraat
in today’s New York Times—
“Hudson Talbott, a longtime friend of Mr. Penraat’s who wrote a children’s book about his experiences (Forging Freedom: A True Story of Heroism During the Holocaust) said his research indicated there was a daredevil aspect to the missions.
‘The feeling I get is that he just loved the idea of putting one over on the Nazis,’ Mr. Talbott said in an interview with The Albany Times Union. ‘It wasn’t a joke, or a game, but clearly there was something about fooling them that was an important aspect of this.'” –Douglas Martin in today’s New York Times
See also:
Log24, Jan. 6-8, 2006,
and
Jaap’s Puzzle Page.
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The Rock and the Serpent
In a search for a title to express
the contrast between truth and lies,
an analogy between the phrases
“Crystal and Dragon” and
“Mathematics and Narrative“
suggests a similar phrase,
“The Rock and the Serpent.”
A web search for related titles leads to a book by Alice Thomas Ellis:
Serpent on the Rock: A Personal View of Christianity. (See a review.)
(This in turn leads to an article on Ellis’s husband, the late Colin Haycraft, publisher.)
For an earlier discussion of Ellis in this weblog, see Three Eleanors (March 12, 2005).
That entry brings us back to the theme of truth and lies with its link to an article from the Catholic publication Commonweal:
Getting to Truth by Lying.
Christians who wish to lie more effectively may consult a book by the author of the Commonweal article:
For a more sympathetic view of
suffering stemming from
Christian narrative,
see
(Click on cover
for details. See also Log24
entries on Guy Davenport,
who wrote the foreword.)
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Saturday, July 1, 2006
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