Ready when you are, C. B. "Hurricane Gustav is bearing down on the Gulf Coast, a reminder of Hurricane Katrina in 2005 and the Bush administration's poor response. The storm was clearly on McCain's mind Saturday. 'You know, it just wouldn't be
appropriate to have a festive occasion while a near tragedy or a
terrible challenge is presented in the form of a natural disaster....'
McCain said in an interview taped for 'Fox News Sunday.'" --AP Aug. 30 birthday three years ago: The Gulf Coast, Aug. 29, 2005: President George W. Bush joins John McCain in a celebration of McCain's 69th birthday Posted 8/30/2008 at 6:28 PM |
Poetry and Politics* -- Movie-Teller "... maybe it was McCain's role as 'movie-teller' that
he cherishes most-- the man who used to narrate the plots of films to
his fellow PoWs in the compound. 'I must have told a hundred movies,'
says McCain. 'Of course I don't know a hundred movies-- I made them
up.'" -- The Guardian, quoted here on McCain's birthday, August 29, 2006. (McCain's birthday nine years earlier was the date of Judgment Day in "Terminator 2.") A story from McCain's "Hail Sarah!" -- Newsweek "At the still point, there the dance is." -- Four Quartets "... the Four Quartets themselves appear, in all their
complexity, as the poetry of simple civic virtue-- the poetry of a poet
trying to read the writing of the law that has become all but
illegible. This, you may say, has nothing to do with poetry. On the
contrary, it is one of the few truly hopeful signs that this civic
virtue could once more be realized poetically." -- Erich Heller, quoted hereon August 25, 2008 (Feast of St. Louis)
* Also known as smoke and mirrors. Posted 8/30/2008 at 9:00 AM |
Posted 8/28/2008 at 12:00 PM |
Associations for the writer known as UD
A related visual association of ideas -- ("The association is the idea" -- Ian Lee, The Third Word War) From UD Jewelry:
See also UD's recent A Must-Read and In My Day* as well as the five Log24 entries ending Sept. 20, 2002. More seriously: The date of The New Yorker issue quoted above is also the anniversary of the birth of Wallace Stevens and the date of death of mathematician Paul R. Halmos. Stevens's "space of horizons" may, if one likes, be interpreted as a reference to projective geometry. Despite the bleak physicist's view of mathematics quoted above, this discipline is-- thanks to Blaise Pascal-- not totally lacking in literary and spiritual associations. * Hey Hey Posted 8/28/2008 at 5:24 AM |
"One Shot" -- Keynote Address, Democratic National Convention
"You know, I spent 20 years in business. If you ran a company whose only strategy was to tear down the competition, it wouldn't last long. So why is this wisdom so hard to find in Washington? I know we're at the Democratic convention, but if an idea works, it really doesn't matter if it has an 'R' or 'D' next to it. Because this election isn't about liberal versus conservative. It's not about left versus right. It's about the future versus the past. In this election, at this moment in our history, we know what the problems are. We know that at this critical juncture, we have only one shot to get it right....Let me tell you about a place called Lebanon-- Lebanon, Virginia." -- Last night's keynote address at the Democratic National Convention
Posted 8/27/2008 at 6:23 AM |
The concluding paragraph of Erich Heller's 1953 essay, "The Hazard of Modern Poetry"-- "'The poetry does not matter.' These words from Mr. T.S. Eliot's Four Quartets acquire an all but revolutionary significance if we understand them not only in their particular context but also in the context of a period of poetry in which nothing mattered except poetry. Against this background the Four Quartets themselves appear, in all their complexity, as the poetry of simple civic virtue-- the poetry of a poet trying to read the writing of the law that has become all but illegible. This, you may say, has nothing to do with poetry. On the contrary, it is one of the few truly hopeful signs that this civic virtue could once more be realized poetically. For in speaking to the hazard of modern poetry I did not wish to suggest that the end had come for singers and skylarks. There will always be skylarks; perhaps even a few nightingales. But poetry is not only the human equivalent of the song of singing birds. It is also Virgil, Dante, and Hölderlin. It is also, in its own terms, the definition of the state of man." Posted 8/25/2008 at 3:23 AM |
Cross-Purposes Yesterday's entry, Absurdities, quoted Erich Heller: "All relevant objective truths are born and die as absurdities. They come into being as the monstrous claim of an inspired rebel and pass away with the eccentricity of a superstitious crank." The context for this remarkable saying is Heller's essay "The Hazard of Modern Poetry." (See p. 270 in the links below.) Discussing "the century of Pascal and Hobbes," he says (see the link to p. 269 below) that "... as for spiritual cunning, it was in the conceits of metaphysical poetry, in the self-conscious ambiguities of poetical language (there are, we are told, as many types of it as deadly sins), and in the paradoxes of Pascal's religious thought. For ambiguity and paradox are the manner of speaking when reality and symbol, man's mind and his soul, are at cross-purposes."Heller's description of "relevant objective truths" as "absurdities" seems to be an instance of such ambiguity and paradox. For further details, see The Disinherited Mind: Essays in Modern German Literature and Thought (Harvest paperback, 1975)-- "The Hazard of Modern Poetry" (pp. 263-300), Section 1, pages 263, 264, 265, 266, 267, 268, 269, 270, 271, 272. For material related to Pascal, see the five Log24 entries ending on D-Day, 2008. For material related to Hobbes, see the five Log24 entries ending on St. Patrick's Day, 2007. Posted 8/24/2008 at 7:00 AM |
Absurdities "All relevant objective truths are born and die as absurdities. They
come into being as the monstrous claim of an inspired rebel and pass
away with the eccentricity of a superstitious crank."-- Erich Heller, The Disinherited Mind Posted 8/23/2008 at 5:01 AM |
Tentative movie title: Blockheads The Kohs Block Design Intelligence Test Samuel Calmin Kohs, the designer (but not the originator) of the above intelligence test, would likely disapprove of the "Aryan Youth types" mentioned in passing by a film reviewer in today's New York Times. (See below.) The Aryan Youth would also likely disapprove of Dr. Kohs. Other related material: 1. Wechsler Cubes (intelligence testing cubes derived from the Kohs cubes shown above). See... Harvard psychiatry and...2. Wechsler Cubes of a different sort (Log24, May 25, 2008) 3. Manohla Dargis in today's New York Times: "... 'Momma’s Man' is a touchingly true film, part weepie, part comedy, about the agonies of navigating that slippery slope called adulthood. It was written and directed by Azazel Jacobs, a native New Yorker who has set his modestly scaled movie with a heart the size of the Ritz in the same downtown warren where he was raised. Being a child of the avant-garde as well as an A student, he cast his parents, the filmmaker Ken Jacobs and the artist Flo Jacobs, as the puzzled progenitors of his centerpiece, a wayward son of bohemia.... In American movies, growing up tends to be a job for either Aryan Youth types or the oddballs and outsiders...." 4. The bohemian who named his son Azazel: "... I think that the deeper opportunity, the greater opportunity film can offer us is as an exercise of the mind. But an exercise, I hate to use the word, I won't say 'soul,' I won't say 'soul' and I won't say 'spirit,' but that it can really put our deepest psychological existence through stuff. It can be a powerful exercise. It can make us think, but I don't mean think about this and think about that. The very, very process of powerful thinking, in a way that it can afford, is I think very, very valuable. I basically think that the mind is not complete yet, that we are working on creating the mind. Okay. And that the higher function of art for me is its contribution to the making of mind."5. For Dargis's "Aryan Youth types"-- From a Manohla Dargis See also, from August 1, 2008 (anniversary of Hitler's opening the 1936 Olympics) -- For Sarah Silverman -- and the 9/9/03 entry Olympic Style. Doonesbury, August 21-22, 2008: Posted 8/22/2008 at 5:01 AM |
For Madeleine L'Engle, wherever she may be The entries of yesterday (updated today) and the day before suggest a flashback to the five "Dungeons & Dragons" entries ending on March 6, 2008. For more about dungeons, see Jan. 7, 2007. For more about dragons, see Crystal and Dragon: The Cosmic Dance of Symmetry and Chaos in Nature, Art and Consciousness, by David Wade. Posted 8/20/2008 at 11:29 PM |
Three Times
Stevens does not say what object he is discussing. Another possibility --One possibility -- Bertram Kostant, Professor Emeritus of Mathematics at MIT, on an object discussed in a recent New Yorker: "A word about E(8). In my opinion, and shared by others, E(8) is the most magnificent 'object' in all of mathematics. It is like a diamond with thousands of facets. Each facet offering a different view of its unbelievable intricate internal structure." A more modest object -- the 4x4 square. Update of Aug. 20-21 -- Symmetries and Facets Kostant's poetic comparison might be applied also to this object. The natural rearrangements (symmetries) of the 4x4 array might also be described poetically as "thousands of facets, each facet offering a different view of... internal structure." More precisely, there are 322,560 natural rearrangements-- which a poet might call facets*-- of the array, each offering a different view of the array's internal structure-- encoded as a unique ordered pair of symmetric graphic designs. The symmetry of the array's internal structure is reflected in the symmetry of the graphic designs. For examples, see the Diamond 16 Puzzle. For an instance of Stevens's "three times" process, see the three parts of the 2004 web page Ideas and Art. * For the metaphor of rearrangements as facets, note that each symmetry (rearrangement) of a Platonic solid corresponds to a rotated facet: the number of symmetries equals the number of facets times the number of rotations (edges) of each facet-- The metaphor of rearrangements as facets breaks down, however, when we try to use it to compute, as above with the Platonic solids, the number of natural rearrangements, or symmetries, of the 4x4 array. Actually, the true analogy is between the 16 unit squares of the 4x4 array, regarded as the 16 points of a finite 4-space (which has finitely many symmetries), and the infinitely many points of Euclidean 4-space (which has infinitely many symmetries). If Greek geometers had started with a finite space (as in The Eightfold Cube), the history of mathematics might have dramatically illustrated Halmos's saying (Aug. 16) that "The problem is-- the genius is-- given an infinite question, to think of the right finite question to ask. Once you thought of the finite answer, then you would know the right answer to the infinite question."The Greeks, of course, answered the infinite questions first-- at least for Euclidean space. Halmos was concerned with more general modern infinite spaces (such as Hilbert space) where the intuition to be gained from finite questions is still of value. Posted 8/19/2008 at 8:30 AM |
No belief, no revelation:
An encounter with "492"--
Belief without revelation: Theology and human experience, and the experience of "272"--
Posted 8/18/2008 at 9:00 AM |
"Maybe Escher could have done it." Detail from Escher's Verbum ("In Touch with God") The title link of this entry leads, via a Log24 entry, to a story by Robert A. Heinlein. For those who, like Rick Warren (shown below in a current news page), prefer Jewish narratives, I recommend 1. Kesher Talk's "Dick Morris: Flaming Sword of Vengeance" 2. Eyes on the Prize 3. Triangulation. Posted 8/17/2008 at 6:20 AM |
Seeing the Finite Structure The following supplies some context for remarks of Halmos on combinatorics. From Paul Halmos: Celebrating 50 years of Mathematics, by John H. Ewing, Paul Richard Halmos, Frederick W. Gehring, published by Springer, 1991-- Interviews with Halmos, "Paul Halmos by Parts," by Donald J. Albers-- "Part II: In Touch with God*"-- on pp. 27-28: The Root of All Deep Mathematics Finite Structure on a Book Cover: Walsh Series: An Introduction to Dyadic Harmonic Analysis, by F. Schipp et al., Taylor & Francis, 1990 Halmos's above remarks on combinatorics as a source of "deep mathematics" were in the context of operator theory. For connections between operator theory and harmonic analysis, see (for instance) H.S. Shapiro, "Operator Theory and Harmonic Analysis," pp. 31-56 in Twentieth Century Harmonic Analysis-- A Celebration, ed. by J.S. Byrnes, published by Springer, 2001. Walsh Series states that Walsh functions provide "the simplest non-trivial model for harmonic analysis." The patterns on the faces of the cube on the cover of Walsh Series above illustrate both the Walsh functions of order 3 and the same structure in a different guise, subspaces of the affine 3-space over the binary field. For a note on the relationship of Walsh functions to finite geometry, see Symmetry of Walsh Functions. Whether the above sketch of the passage from operator theory to harmonic analysis to Walsh functions to finite geometry can ever help find "the right finite question to ask," I do not know. It at least suggests that finite geometry (and my own work on models in finite geometry) may not be completely irrelevant to mathematics generally regarded as more deep. * See the Log24 entries following Halmos's death. Posted 8/16/2008 at 8:00 AM |
Magister Ludi (The Glass Bead Game) is now available for download in pdf or text format at Scribd. "How far back the historian wishes to place the origins and antecedents
of the Glass Bead Game is, ultimately, a matter of his personal choice.
For like every great idea it has no real beginning; rather, it has
always been, at least the idea of it. We find it foreshadowed, as a dim
anticipation and hope, in a good many earlier ages. There are hints of
it in Pythagoras, for example, and then among Hellenistic Gnostic
circles in the late period of classical civilization. We find it
equally among the ancient Chinese, then again at the several pinnacles
of Arabic-Moorish culture; and the path of its prehistory leads on
through Scholasticism and Humanism to the academies of mathematicians
of the seventeenth and eighteenth centuries and on to the Romantic
philosophies and the runes of Novalis's hallucinatory visions. This
same eternal idea, which for us has been embodied in the Glass Bead
Game, has underlain every movement of Mind toward the ideal goal of a
universitas litterarum, every Platonic academy, every league of an
intellectual elite, every rapprochement between the exact and the more
liberal disciplines, every effort toward reconciliation between science
and art or science and religion. Men like Abelard, Leibniz, and Hegel
unquestionably were familiar with the dream of capturing the universe
of the intellect in concentric systems, and pairing the living beauty
of thought and art with the magical expressiveness of the exact
sciences. In that age in which music and mathematics almost
simultaneously attained classical heights, approaches and
cross-fertilizations between the two disciplines occurred frequently." Posted 8/14/2008 at 4:19 AM |
Posted 8/11/2008 at 9:00 PM |
"Duration is... not a state of rest, for mere
standstill is
regression. Duration is rather the self-contained and therefore
self-renewing movement of an organized, firmly integrated whole [click on link for an example], taking
place in accordance with immutable laws and beginning anew at every
ending." Globe at the Beijing 2008 Olympics Opening Ceremony The eight trigrams were perhaps implied in the opening's date, 8/8/8. Posted 8/10/2008 at 10:31 AM |
Posted 8/8/2008 at 8:08 AM |
From the last link within the last link of yesterday's entry: "Review the concepts of integritas, consonantia, and claritas in Aquinas...." Review also the properties of the number six that appears in today's date. For such properties, see the page of Log24 entries that end on September 6, 2006, with "Hamlet's Transformation." Happy Feast of the Transfiguration. Posted 8/6/2008 at 12:00 PM |
Published Today: The Last Theorem, a novel by Arthur C. Clarke and Frederik Pohl From the publisher's description: "The Last Theorem is a story of one man’s mathematical obsession, and a celebration of the human spirit and the scientific method. It is also a gripping intellectual thriller....For a similar third-world fantasy about another famous theorem, see the oeuvre of Ashay Dharwadker. Note the amazing conclusion of Dharwadker's saga (thus far)-- Dharwadker devises a proof of the four-color theorem that leads to... Grand Unification of the Standard Model with Quantum Gravity! For further background, see Ashay Dharwadker and Usenet Postings. Clarke lived in Sri Lanka (formerly Ceylon) from 1956 until his death last March. For another connection with Sri Lanka, see Posted 8/5/2008 at 2:02 PM |
Summer of '36 Another Opening -- Michael in the play "Dancing at Lughnasa" From the film "Contact"-- Jodie Foster and the
Posted 8/4/2008 at 9:57 AM |
This Hard Prize
"It was usually celebrated on the nearest Sunday to August 1st." --Chalice Centre Related material:
"Going up." -- Nanci Griffith Posted 8/3/2008 at 10:00 PM |
Note for a Triangle The triangle, a percussion instrument featured prominently in the Tom Stoppard play "Every Good Boy Deserves Favour" From a BBC News webpage last updated at 22:31 GMT (6:31 PM EDT) Sunday, 3 August 2008 -- Alexander Solzhenitsyn dies at 89 "Russian writer Alexander Solzhenitsyn, who exposed Stalin's prison system in his novels and spent 20 years in exile, has died near Moscow at the age of 89. The author of The Gulag Archipelago and One Day In The Life Of Ivan Denisovich, who returned to Russia in 1994, died of either a stroke or heart failure.
The Nobel laureate had suffered from high blood pressure in recent years. After returning to Russia, Solzhenitsyn wrote several polemics on Russian history and identity. His son Stepan was quoted by one Russian news agency as saying his father died of heart failure, while another agency quoted literary sources as saying he had suffered a stroke. He died in his home in the Moscow area, where he had lived with his wife Natalya, at 2345 local time (1945 GMT) [3:45 PM EDT], Stepan told Itar-Tass. Russian President Dmitry Medvedev sent his condolences to the writer's family, a Kremlin spokesperson said...." Related material: Today's 3 PM (EDT) entry. Posted 8/3/2008 at 7:20 PM |
Kindergarten Geometry Preview of a Tom Stoppard play presented at Town Hall in Manhattan on March 14, 2008 (Pi Day and Einstein's birthday): The play's title, "Every Good Boy Deserves Favour," is a mnemonic for the notes of the treble clef EGBDF. Review of the same play as presented at Chautauqua Institution on July 24, 2008: "Stoppard's modus operandi-- to teasingly introduce numerous clever tidbits designed to challenge the audience." "The leader of the band is tired And his eyes are growing old But his blood runs through My instrument And his song is in my soul." -- Dan Fogelberg "He's watching us all the time." -- Lucia Joyce
FinnegansWiki: Salmonson set his seel:Wikipedia: "George Salmon spent his boyhood in Cork City, Ireland. His father was a linen merchant. He graduated from Trinity College Dublin at the age of 19 with exceptionally high honours in mathematics. In 1841 at age 21 he was appointed to a position in the mathematics department at Trinity College Dublin. In 1845 he was appointed concurrently to a position in the theology department at Trinity College Dublin, having been confirmed in that year as an Anglican priest." Related material: Kindergarten Theology, Kindergarten Relativity, Arrangements for 56 Triangles. For more on the arrangement of triangles discussed in Finnegans Wake, see Log24 on Pi Day, March 14, 2008. Happy birthday, Martin Sheen. Posted 8/3/2008 at 3:00 PM |
Possible titles The Eye of Apollo See also the conclusion Posted 8/2/2008 at 3:52 PM |
Geometry and Death (continued from June 15, 2007) Today is the anniversary of the 1955 death of poet Wallace Stevens. Related material: A poem by Stevens, an essay on the relationships between poets and philosophers -- "Bad Blood," by Leonard Michaels -- and the Log24 entries of June 14-15, 2007. Posted 8/2/2008 at 2:02 PM |
Prattle There is an article in today's Telegraph on mathematician Simon Phillips Norton-- co-author, with John Horton Conway, of the rather famous paper "Monstrous Moonshine" (Bull. London Math. Soc. 11, 308–339, 1979). "Simon studies one of the most complicated groups of
all: the Monster. He is, still, the world expert on it .... Simon tells me he has a quasi-religious faith in the Monster. One day, he says, ... the Monster will expose the structure of the universe. ... although Simon says he is keen for me to write a book about him and his work on the Monster and his obsession with buses, he doesn't like talking, has no sense of anecdotes or extended conversation, and can't remember (or never paid any attention to) 90 per cent of the things I want him to tell me about in his past. It is not modesty. Simon is not modest or immodest: he just has no self-curiosity. To Simon, Simon is a collection of disparate facts and no interpretative glue. He is a man without adjectives. His speech is made up almost entirely of short bursts of grunts and nouns. This is the main reason why we spent three weeks together .... I needed to find a way to make him prattle." Those in search of prattle and interpretive glue should consult Anthony Judge's essay ""Potential Psychosocial Significance of Monstrous Moonshine: An Exceptional Form of Symmetry as a Rosetta Stone for Cognitive Frameworks." This was cited here in Thursday's entry "Symmetry in Review." (That entry is just a list of items related in part by synchronicity, in part by mathematical content. The list, while meaningful to me and perhaps a few others, is also lacking in prattle and interpretive glue.) Those in search of knowledge, rather than glue and prattle, should consult Symmetry and the Monster, by Mark Ronan. If they have a good undergraduate education in mathematics, Terry Gannon's survey paper "Monstrous Moonshine: The First Twenty-Five Years" (pdf) and book-- Moonshine Beyond the Monster-- may also be of interest. Posted 8/2/2008 at 6:23 AM |
A Two-Part Invention
for Sarah Silverman Part I: (Thanks to The Unapologetic Mathematician) The puzzle -- http://xkcd.com/457/
Part II:The moves --
(From this weblog's footprints today) Posted 8/1/2008 at 2:42 PM |
Posted 8/1/2008 at 2:56 AM |