Reason and Rhyme
"Philosophers ponder the idea of identity: what it is to give something a name on Monday and have it respond to that name on Friday...." -- Bernard Holland in The New York Times Monday, May 20, 1996 Related material:
Evening: 557
See Dogma in the State of Grace, Is Nothing Sacred?, and, from page 557 of Webster's New World Dictionary, College Edition, 1960: "flower"
Birds, Beasts & Flowers
As performed by Presented at
St James's Palace, London, on 22nd November 1978 in the presence of Her Majesty, Queen Elizabeth The Queen Mother Posted 3/31/2006 at 9:00 PM |
Women's History Month continues... Ontology Alignment "He had with him a small red book of Mao's poems, and as he talked he squared it on the table, aligned it with the table edge first vertically and then horizontally. To understand who Michael Laski is you must have a feeling for that kind of compulsion." -- Joan Didion in the Saturday Evening Post, Nov. 18, 1967 (reprinted in Slouching Towards Bethlehem) "Or were you," I said. He said nothing. "Raised a Catholic," I said. He aligned a square crystal paperweight with the edge of his desk blotter. -- Joan Didion in The Last Thing He Wanted, Knopf, 1996 "It was Plato who best expressed-- who veritably embodied-- the tension between the narrative arts and mathematics.... Plato clearly loved them both, both mathematics and poetry. But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry. Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto. Let none ignorant of geometry enter. This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge. Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason. Mathematics is the threshold we cross to pass into the ideal, the truly real." -- Rebecca Goldstein, Mathematics and the Character of Tragedy Posted 3/31/2006 at 12:00 PM |
Posted 3/30/2006 at 8:24 PM |
Note: Carmichael's reference is to A. Emch, "Triple and multiple systems, their geometric configurations and groups," Trans. Amer. Math. Soc. 31 (1929), 25–42. "There is such a thing as a tesseract."
-- A Wrinkle in Time Posted 3/29/2006 at 8:00 PM |
Darkness at Noon,
continued It turns out that Medawar (see previous entry) also wrote a deeply hostile review of Koestler's The Act of Creation. (See Pluto's Republic.) There are plenty more like Medawar, so it may be that a further effort at documentation of Diamond Theory is needed. See this evening's entry, to follow. Posted 3/29/2006 at 12:00 PM |
A Prince of Darkness "What did he fear? It was not a fear or dread, It was a nothing that he knew too well. It was all a nothing and a man was a nothing too. It was only that and light was all it needed and a certain cleanness and order. Some lived in it and never felt it but he knew it all was nada y pues nada y nada y pues nada. Our nada who art in nada, nada be thy name thy kingdom nada thy will be nada in nada as it is in nada. Give us this nada our daily nada and nada us our nada as we nada our nadas and nada us not into nada but deliver us from nada; pues nada. Hail nothing full of nothing, nothing is with thee."
From a review of Teilhard de Chardin's The Phenomenon of Man:
"He's good." "Good? He's the fucking Prince of Darkness!" -- Paul Newman and Jack Warden in "The Verdict"
"This book is the outcome of a course given at Harvard first by G. W. Mackey...." -- Lynn H. Loomis, 1953, preface to An Introduction to Abstract Harmonic Analysis For more on Mackey and Harvard, see the Log24 entries of March 14-17. Posted 3/28/2006 at 4:00 PM |
A Living Church A skeptic's remark: "...the mind is an amazing thing and it can create patterns and interconnections among things all day if you let it, regardless of whether they are real connections." -- Xanga blogger "sejanus" A reply from G. K. Chesterton (Log24, Jan. 18, 2004): "Plato has told you a truth; but Plato is dead. Shakespeare has startled you with an image; but Shakespeare will not startle you with any more. But imagine what it would be to live with such men still living. To know that Plato might break out with an original lecture to-morrow, or that at any moment Shakespeare might shatter everything with a single song. The man who lives in contact with what he believes to be a living Church is a man always expecting to meet Plato and Shakespeare to-morrow at breakfast. He is always expecting to see some truth that he has never seen before." Mid-day: 024 Evening: 672 A meditation on Sunday's numbers -- From Log24, Jan. 8, 2005: 24 The Star "He looked at the fading light
-- Roderick MacLeish, Prince Ombra From Log24, Oct. 23, 2002: An excerpt from
Related material: 672 Astarte and The Venerable Bede (born in 672). 672 illustrated: The Venerable Bede and the Star of Venus The 672 connection is, of course, not a real connection (in the sense of "sejanus" above) but it is nevertheless not without interest. Postscript of 6 PM A further note on the above illustration of the 672 connection: The late Buck Owens (see previous entry for Owens, Reba, and the star of Venus) once described his TV series as "a show of fat old men and pretty young girls" (today's Washington Post). A further note on lottery hermeneutics: Those who prefer to interpret random numbers with the aid of a dictionary (as in Is Nothing Sacred?) may be pleased to note that "heehaw" occurs in Webster's New World Dictionary, College Edition, 1960, on page 672. In today's Washington Post, Richard Harrington informs us that "As a child, Owens worked cotton and maize fields, taking the name Buck from a well-liked mule...." Hee. Haw. Posted 3/27/2006 at 11:17 AM |
Rhinestone CowboyBy GREG RISLINGAssociated Press Writer LOS ANGELES -- Singer
Buck Owens, the flashy rhinestone cowboy who shaped the sound of
country music... died Saturday. He was 76. From Log24, Feb. 2, 2003: Head White House speechwriter Michael Gerson:
Related material: See the five Log24 entries ending with The Diamond as Big as the Monster (Dec. 21, 2005).
Note particularly the following:
From Fitzgerald's "Now," said John eagerly, "turn out your pocket and let's see what jewels you brought along. If you made a good selection we three ought to live comfortably all the rest of our lives."
Posted 3/26/2006 at 5:00 PM |
'Nauts (continued from Life of the Party, March 24) Exhibit A -- From (presumably) a Princeton student (see Activity, March 24): Exhibit B -- From today's Sunday comics: Exhibit C -- From a Smith student with the same name as the Princeton student (i.e., Dagwood's "Twisterooni" twin): Related illustrations ("Visual Stimuli") from the Smith student's game -- Literary Exercise: Continuing the Smith student's Psychonauts theme, compare and contrast two novels dealing with similar topics: A Wrinkle in Time, by the Christian author Madeleine L'Engle, and Psychoshop, by the secular authors Alfred Bester and Roger Zelazny. Presumably the Princeton student would prefer the Christian fantasy, the Smith student the secular. Those who prefer reality to fantasy -- not as numerous as one might think -- may examine what both 4x4 arrays illustrated above have in common: their structure. Both Princeton and Smith might benefit from an application of Plato's dictum: Posted 3/26/2006 at 2:02 PM |
Midnight in the Garden continued Questions posed by Roberta Smith in the New York Times of Jan. 13, 2006: "'What is art?' may be the art world's most relentlessly asked question. But a more pertinent one right now is, 'What is an art gallery?'" -- from "Who Needs a White Cube These Days?" An example that may help: London's White Cube gallery and its current Liza Lou exhibit, which is said to convey "a palpable sense of use, damage, lost time, lost lives." See the previous entry for details. On the brighter side, we have Clint Eastwood on the
"Midnight in the Garden of Good and Evil" soundtrack CD-- "Accentuate the positive"-- and an entry from last Christmas:
"Recollect what I have said to you, -- Horace Walpole,
Posted 3/26/2006 at 12:00 AM |
Built
In memory of Rolf Myller, who died on Thursday, March 23, 2006, at Mount Sinai Hospital in Manhattan: Myller was, according to the New York Times, an architect whose eclectic pursuits included writing children's books, The Bible Puzzle Book, and Fantasex: A Book of Erotic Games. He also wrote, the Times says, "Symbols and Their Meaning (1978), a graphic overview of children's nonverbal communication." This is of interest in view of the Log24 reference to "symbol-mongers" on the date of Myller's death. In honor of Women's History Month and of Myller's interests in the erotic and in architecture, we present the following work from a British gallery. This work might aptly be retitled "Brick Shithouse." Related material: (1) the artist's self-portrait and, in view of the cover illustration for Myller's The Bible Puzzle Book, (2) the monumental treatise by Leonard Shlain The Alphabet Versus the Goddess: The Conflict Between Word and Image. For devotees of women's history
Posted 3/25/2006 at 4:23 PM |
Women's History Month continues... Activity From the New York Times on the First of May, 1999:
Rota graduated from Some may prefer the following Related material: Oct. 21, 2002, April 30, 2005. Posted 3/24/2006 at 4:30 PM |
Life of the Party From Stephen King's Dreamcatcher: From Alfred Bester's The Demolished Man: Related material: "... it's going to be accomplished in steps, this establishment of the Talented in the scheme of things." -- Anne McCaffrey, Radcliffe '47, To Ride Pegasus Posted 3/24/2006 at 2:22 PM |
Dreaming Game A phrase from yesterday's entry: Lust und Freud. This phrase, together with the concluding song from the recent film "Good Night and Good Luck," suggests the following links (the first two from Sinatra's birthday, 2004):
One For His Baby,
Related material: "There were voices down the corridor, Posted 3/24/2006 at 2:45 AM |
Welcome to the
Hotel Hassler
Related material: Posted 3/23/2006 at 3:03 PM |
Happy Birthday, Hassler Whitney In honor of the late Hassler Whitney, mathematician and mountaineer, here is a link to the five Log24 entries ending with White, Geometric, and Eternal (Dec. 20, 2003). Related material: the five Log24 entries ending with The Meadow (Dec. 18, 2005) and the five Log24 entries ending with Strange Attractor (Jan. 7, 2006). The cross and the epiphany star in this last group of entries may interest the symbol-mongers among us. Those more interested in substance than in symbols may prefer the following (click to enlarge): This is apparently the original source for the figure I cited on Dec. 20, 2003, as from antiquark.com. The connection with Whitney is through the theory of matroids, which Whitney founded in 1935. See Hassler Whitney, "On the abstract properties of linear dependence," American Journal of Mathematics, vol. 57 (1935), 509-533, Collected Papers, vol. I, 147-171. Posted 3/23/2006 at 5:55 AM |
Former President of Dartmouth Dies From today's New York Times: "In one widely publicized episode, in 1988, he condemned The Dartmouth Review, a conservative student newspaper, for ridiculing blacks, gay men and lesbians, women and Jews." Posted 3/22/2006 at 4:30 AM |
"In a scathing attack on what they termed the 'Israel Lobby,' the Kennedy School's Stephen M. Walt and the University of Chicago's John J. Mearsheimer argued in a recent article that supporters of Israel have seized control of U.S. foreign policy, making it reflect Israel's interests more than those of the U.S." Posted 3/21/2006 at 6:25 PM |
Storyboard
From last year's Guy Fawkes Day entries: "Contrapuntal Themes in a Shadowland" and "Area Catholics Receive St. Thomas Aquinas Awards." From last year's Halloween season: The Judeo part: "It was like a 1930s comic book set in the future," [producer Joel] Silver says. "I can't say what it was, but there was something about it that made me think it would work as a movie." -- USA Today The Christian part: "Joseph Goebbels was brought up in a devoutly Catholic home. His parents hoped he would be a priest...." -- Catholic Nazi Leaders Flashback to March 18, 2003: "It's Springtime for Esther and Israel!" and to Grammy night, 2006:Esther Happy vernal equinox. Posted 3/20/2006 at 3:33 PM |
Readings for St. Joseph's Day Cut Numbers and In the Hand of Dante, both by Nick Tosches, and Symmetry, by Hermann Weyl: Related material: Kernel of Eternity (a Log24 entry of June 9, 2005) and the comment on that entry by ItAlIaNoBoI. Posted 3/19/2006 at 6:09 PM |
ART WARS:
From a site linked to in yesterday's St. Patrick's Day sermon as the keys to the kingdom: "In the western world, we tend to take for granted our
musical scale, formed of whole tone and
half tone steps. These steps are arranged in two ways: the major scale and the
minor."
"How strange the change from major to minor... Posted 3/18/2006 at 4:07 PM |
Dogma in the State of Grace "Words and numbers are of equal value, for, in the cloak of knowledge, one is warp and the other woof." -- The princesses Rhyme and Reason in The Phantom Tollbooth, by Norton Juster, 1961 (From a Sermon for St. Patrick's Day, 2001) The Pennsylvania midday lottery on St. Patrick's Day, 2006: 618.
Comparing, as in Philadelphia Stories, the Catholic style of Grace Kelly with the Protestant style of Katharine Hepburn, we conclude that Princess Rhyme might best be played by the former, Princess Reason by the latter.
Reason informs us that the lottery result "618" may
be regarded as naming
x2 - x - 1 = 0 Following the advice of Clint Eastwood (on the
"Midnight in the Garden of Good and Evil" soundtrack CD) to "accentuate
the positive," Reason notes that the other, positive, solution to this
equation, approximately 1.618, a number symbolized by the Greek letter
"phi," occurs in the following geometric diagram illustrating a
construction of the pentagon:
For further enlightenment, we turn to Rhyme, who
informs us that "618" may also be regarded as naming the date "6/18."
Consulting our notes, we find on 6/18, 2003, a reference to "claves," Latin for "keys," as in "claves regni caelorum."
We may tarry at this date, pleased to find that the keys to the kingdom involve rational numbers, rather than the irrational ratios suggested, paradoxically, by Reason.
Or we may, with Miles Davis, prefer a more sensuous incarnation of the keys: Alicia Keys "... it's going to be accomplished in steps, this establishment of the Talented in the scheme of things." -- Anne McCaffrey, Radcliffe '47, To Ride Pegasus Posted 3/17/2006 at 5:00 PM |
Mackey was born, according to Wikipedia, on Feb. 1, 1916. He died, according to Harvard University, on the night of March 14-15, 2006. He was the author of, notably, "Harmonic Analysis as the Exploitation of Symmetry -- A Historical Survey," pp. 543-698 in Bulletin of the American Mathematical Society (New Series), Vol. 3, No. 1, July 1980. This is available in a hardcover book published in 1992 by the A.M.S., The Scope and History of Commutative and Noncommutative Harmonic Analysis. (370 pages, ISBN 0-8218-9903-1). A paperback edition of this book will apparently be published this month by Oxford University Press (ISBN 978-0-8218-3790-7). From Oxford U.P.-- Contents
Related material: Posted 3/17/2006 at 2:28 AM |
Women's History Month
continues... Gallia est omnis divisa in partes tres, quarum unam incolunt Belgae, aliam Aquitani, tertiam qui ipsorum lingua Celtae, nostra Galli appellantur. -- Julius Caesar, De Bello Gallico Posted 3/15/2006 at 3:00 PM |
Club From today's Harvard Crimson: Two members of the Harvard Class of 2007 "scarf down pie at the Math Department's 'pi'-eating contest at 3:14 p.m. yesterday in celebration of Pi Day. Participants had three minutes and 14 seconds to eat as much pie as posssible."
Log24, Feb. 24, 2006: "What other colleges call fraternities, Princeton calls Eating Clubs." Posted 3/15/2006 at 2:24 PM |
Posted 3/14/2006 at 7:00 PM |
Fearful Symmetry and Minkowski Space-Time (For the tigers of Princeton, a selection suggested by the work of Richard Parker on Lorentzian lattices) Posted 3/14/2006 at 12:00 PM |
Click on pictures Posted 3/14/2006 at 12:00 AM |
Note the above description
Related material from Log24:
Religious Symbolism at Princeton, on the Nassau Church, Counting Crows on the Feast of St. Luke ("Fullness... Multitude"), The Quality of Diamond, in memory of Saint Hans-Georg Gadamer, who died at 102 four years ago on this date, and Diamonds Are Forever. Posted 3/13/2006 at 1:01 PM |
A Circle of Quiet From the Harvard Math Table page: "No Math table this week. We will reconvene next week on March 14 for a special Pi Day talk by Paul Bamberg."
From the April 2006 Notices of the American Mathematical Society, a footnote in a review by Juliette Kennedy (pdf) of Rebecca Goldstein's Incompleteness: 4 There is a growing literature in the area of postmodern commentaries of [sic] Gödel's theorems. For example, Régis Debray has used Gödel's theorems to demonstrate the logical inconsistency of self-government. For a critical view of this and related developments, see Bricmont and Sokal's Fashionable Nonsense [13]. For a more positive view see Michael Harris's review of the latter, “I know what you mean!” [9].... [9] MICHAEL HARRIS, “I know what you mean!,” http://www.math.jussieu.fr/~harris/Iknow.pdf. Following the trail marked by Ms. Kennedy, we find the following in Harris's paper: "Their [Sokal's and Bricmont's] philosophy of mathematics, for instance, is summarized in the sentence 'A mathematical constant like doesn't change, even if the idea one has about it may change.' ( p. 263). This claim, referring to a 'crescendo of absurdity' in Sokal's original hoax in Social Text, is criticized by anthropologist Joan Fujimura, in an article translated for IS*. Most of Fujimura's article consists of an astonishingly bland account of the history of non-euclidean geometry, in which she points out that the ratio of the circumference to the diameter depends on the metric. Sokal and Bricmont know this, and Fujimura's remarks are about as helpful as FN's** referral of Quine's readers to Hume (p. 70). Anyway, Sokal explicitly referred to "Euclid's pi", presumably to avoid trivial objections like Fujimura's -- wasted effort on both sides.32 If one insists on making trivial objections, one might recall that the theorem
What is the moral of all this French noise? Perhaps that, in spite of the contemptible nonsense at last summer's
Mykonos conference on mathematics and narrative, stories do have an important role to play in mathematics -- specifically, in the history of mathematics. Despite his disdain for Platonism, exemplified in his remarks on
the noteworthy connection of pi with the zeta function in the formula
given
above, Harris has performed a valuable service to mathematics by
pointing out the excellent historical work of Catherine Goldstein. Ms.
Goldstein has demonstrated that even a French nominalist can be a
first-rate scholar. Her essay on circles that Harris cites in a
French version is also available in English, and will repay the study of
those who, like Barry Mazur and other Harvard savants, are much too
careless with the facts of history. They should consult her
"Stories of the Circle," pp. 160-190 in A History of Scientific Thought, edited by Michel Serres, Blackwell Publishers (December 1995). For the historically-challenged mathematicians of Harvard, this
essay would provide a valuable supplement to the upcoming "Pi Day" talk
by Bamberg. For those who insist on limiting their attention to mathematics
proper, and ignoring its history, a suitable Pi Day observance might include
becoming familiar with various proofs of the formula, pictured
above, that connects pi with the zeta function of 2. For a survey,
see Robin Chapman, Evaluating Zeta(2)
(pdf). Zeta functions in a much wider context will be discussed at next
May's politically correct "Women in Mathematics" program at Princeton, "Zeta Functions All the Way" (pdf). Posted 3/12/2006 at 1:00 PM |
Seed
"This outer automorphism [of S6] can be regarded as the seed from which grow about half of the sporadic simple groups, starting with the Mathieu groups M12 and M24."
Feb. 28 (Mardi Gras), 2006.
Posted 3/11/2006 at 9:00 PM |
Posted 3/11/2006 at 12:00 PM |
Women's History Month continues...
Raiders of the Lost
Stone In honor of the upcoming program on Women and Mathematics at the Institute for Advanced Study and of Sharon Stone's 2005 lecture at Harvard's Memorial Church, here are links to reviews of two Sharon Stone classics: "King Solomon's Mines" (1985), said to be inspired by the 1981 box-office success of "Raiders of the Lost Ark," and "Diabolique" (1996), starring Stone as a teacher of mathematics at St. Anselm's School for Boys. For related material on St. Anselm and mathematics at Princeton, see Modal Theology and the April 2006 AMS Notices on Kurt Gödel. See also yesterday's entry and Log24, Jan. 1-15, 2006. Today's birthdays: Sharon Stone and Gregory La Cava. Posted 3/10/2006 at 7:59 PM |
x Posted 3/10/2006 at 12:00 AM |
Finitegeometry.org Update (Revised May 21, 2006) Finitegeometry.org now has permutable JavaScript views of the 2x2x2 and 4x4x4 design cubes. Solomon's Cube presented a claim that the 4x4x4 design cube retains symmetry under a group of about 1.3 trillion transformations. The JavaScript version at finitegeometry.org/sc/64/view/ lets the reader visually verify this claim. The reader should first try the Diamond 16 Puzzle. The simpler 2x2x2 design cube, with its 1,344 transformations, was described in Diamonds and Whirls; the permutable JavaScript version is at finitegeometry.org/sc/8/view/. Posted 3/9/2006 at 2:56 PM |
Women's History Month continues. Contender Miss O'Hara on the Oscars: "Cinderella Man: To me, this is the best film of 2005 (qualifier: I have not yet seen Walk the Line). Cinderella Man is a terrific film - maybe even a great one. It isn't flashy, it isn't brimming with special effects, porn stars, or snappy one-liners. But it is a terrific story, one that you feel good after watching. It's a slice of the true Golden Age of Hollywood - a solid story about good people that is well-acted by a superb cast. It's a very family-friendly film - although some of the boxing scenes may be too intense for little ones. I can't recommend this film highly enough, and am still furious that it was snubbed for the Oscars - then again, perhaps I shouldn't be. It would be an insult to the movie, the actors, and the writers to nominate this fine film with the dreck they are glorifying this year. Watch this movie. I guarantee you'll enjoy it." Posted 3/4/2006 at 10:34 AM |
"Her hair is Harlow gold...."
For Scarlett on James Merrill's birthday (which he shares with Jean Harlow)-- the Log24 links of Palm Sunday, 2004: Google's "sunlit paradigm" and my own "Lost in Translation." Posted 3/3/2006 at 9:26 PM |
3 pm Posted 3/3/2006 at 3:00 PM |
2:56:37 Posted 3/3/2006 at 2:56 PM |
Women's History Month continues. Global and Local:
One Small Step Audrey Terras, University of Maryland '64: We cannot discuss the proof here as it requires some knowledge of zeta functions of curves over finite fields. Charles Small, Harvard '64: The moral is that the zeta function exhibits a subtle connection between the "global" (topological, characteristic 0) nature of the curve and its "local" (diophantine, characteristic p for all but finitely many "bad" primes p) behaviour. The full extent of this connection only becomes apparent in the context of varieties more general than curves....
"Some friends of mine Posted 3/3/2006 at 1:00 PM |
In and Out John Updike in "Birthday, death-day -- For the Time Being: "in and out of time" Born on this date:Died on this date: Philip K. Dick Posted 3/2/2006 at 4:30 PM |
Father Figure
Women's History Month
continues... "My father is, of course, as mad as a hatter." -- Diana Rigg in "The Hospital," as transcribed at script-o-rama.com "A vesicle pisces* is the name that author Philip K. Dick gave to a symbol he saw (on February 2**, 1974) on the necklace of a delivery woman. PKD was probably conflating the names of two related symbols, the ichthys
consisting of two intersecting arcs resembling the profile of a fish...
used by the early Christians as a secret symbol, and the vesica piscis, from the centre of which the ichthys symbol can be drawn." -- Wikipedia Related material at Log24: Related material elsewhere: * Wikipedia's earliest online history for this incorrect
phrase is from 25 November, 2003, when the phrase was attributed to
Dick by an anonymous Wikipedia user, 216.221.81.98, who at that time apparently did not know the correct phrase, "vesica piscis," which was later supplied (16 February, 2004) by an anonymous user (perhaps the same as the first user, perhaps not) at a different IP address, 217.158.203.103. Wikipedia authors have never supplied a source
for the alleged use of the phrase by Dick. This comedy of errors would
be of little interest were it not for its strong resemblance to the writing
process that resulted in what we now call the Bible. ** Other accounts (for instance, Divine Invasions: A Life of Philip K. Dick,
by Lawrence Sutin, Carroll & Graf paperback (copyright 1989, republished on August 9, 2005),
page 210) say Dick's encounter was not on Groundhog Day (also known as Candlemas), but
rather on February 20, 1974. Posted 3/2/2006 at 1:06 PM |
Deaconess "Teach us to care and not to care." -- T. S. Eliot, "Ash Wednesday" Related material: Beth Israel Deaconess, The House of God, and, from Is Nothing Sacred?, the following quotations--
"I know what 'nothing' means."
"Nothing is random."
"692" -- Pennsylvania lottery,
"This hospital, like every other, Posted 3/1/2006 at 6:29 PM |
Women's History Month continues:
For Harrison Ford
and Meg Ryan, a quotation from Sir Walter Raleigh, via Susanna Moore and Elizabeth Tallent: Author Susanna Moore, Related material: An article in The Telegraph on the late Sybille Bedford (see also the previous entry), and On Glory Roads: A Pilgrim's Book About Pilgrimage, by Eleanor Munro Posted 3/1/2006 at 2:24 PM |
Posted 3/1/2006 at 12:00 AM |