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.) 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. Posted 1/31/2008 at 5:24 AM |
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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:
Posted 1/26/2008 at 2:22 AM |
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 Posted 1/25/2008 at 5:01 PM |
"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:
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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:
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Oh, What Can It Mean? From the last entry in my Harvard weblog-- May 21, 2005: 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 Posted 1/20/2008 at 7:00 AM |
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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. Posted 1/19/2008 at 7:00 AM |
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Nativity ... Todo lo sé por el lucero puro que brilla en la diadema de la Muerte. -- Rubén Darío, born January 18, 1867 Posted 1/18/2008 at 4:00 AM |
"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: Desconvencida, 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) Posted 1/17/2008 at 5:24 PM |
Knight Moves: Geometry of the Eightfold Cube Click on the image for a larger version and an expansion of some remarks quoted here on Christmas 2005. Posted 1/16/2008 at 12:25 PM |
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The following illustration of how the eightfold cube works was redone. For further details, see Finite Geometry of the Square and Cube and The Eightfold Cube. Posted 1/6/2008 at 1:00 AM |
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colporteurn. itinerant seller or giver of books, Now you has jazz. -- Cole Porter, lyric for "High Society," Posted 1/4/2008 at 1:00 PM |
The "greatest generation" theme from Art Wars-- April 7, 2003 continues in two obituaries from this morning's New York Times: 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: Related material: Yesterday's entry The Revelation Game and an entry of April 7, 2003: April is Math Awareness Month. (The art, by Ingmar Bergman, was Posted 1/4/2008 at 2:02 AM |
Context-Sensitive Theology continued: 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. Also in the February Notices-- a review of a book, Superior Beings: If They Exist, How Would We Know?, in which the author In the 'Revelation Game,' for example, ... [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 for whom the above Posted 1/3/2008 at 1:01 PM |