October 22, 2002

  • Introduction to
    Harmonic Analysis


    From Dr. Mac's Cultural Calendar for Oct. 22:



    • The French actress Catherine Deneuve was born on this day in Paris in 1943....
    • The Beach Boys released the single “Good Vibrations” on this day in 1966.







    "I hear the sound of a
       gentle word


    On the wind that lifts
       her perfume
       through the air."


    — The Beach Boys


     

    In honor of Deneuve and of George W. Mackey, author of the classic 156-page essay, "Harmonic analysis* as the exploitation of symmetry† — A historical survey" (Bulletin of the American Mathematical Society (New Series), Vol. 3, No. 1, Part 1 (July 1980), pp. 543-698), this site's music is, for the time being, "Good Vibrations."

     

    For more on harmonic analysis, see "Group Representations and Harmonic Analysis from Euler to Langlands," by Anthony W. Knapp, Part I and Part II.

     

    * For "the simplest non-trivial model for harmonic analysis," the Walsh functions, see F. Schipp et. al., Walsh Series: An Introduction to Dyadic Harmonic Analysis, Hilger, 1990. For Mackey's "exploitation of symmetry" in this context, see my note Symmetry of Walsh Functions, and also the footnote below.

     

    † "Now, it is no easy business defining what one means by the term conceptual.... I think we can say that the conceptual is usually expressible in terms of broad principles. A nice example of this comes in form of harmonic analysis, which is based on the idea, whose scope has been shown by George Mackey... to be immense, that many kinds of entity become easier to handle by decomposing them into components belonging to spaces invariant under specified symmetries."

    -- The importance of mathematical conceptualisation,
    by David Corfield, Department of History and Philosophy of Science, University of Cambridge

October 21, 2002

  • Birthdays for a Small Planet


    Today's birthdays:



    The entry below, "Theology for a Small Planet," sketches an issue that society has failed to address since the fall of 1989, when it was first raised by the Harvard Divinity Bulletin.


    In honor mainly of Ursula K. Le Guin, but also of her fellow authors above, I offer Le Guin's solution. It is not new. It has been ignored mainly because of the sort of hateful and contemptible arrogance shown by



    • executives in the tradition of Henry Ford and later Ford Foundation and Ford Motors employees McGeorge Bundy and Robert McNamara (see yesterday's entry below for Ford himself), by
    • theologians in the tradition of the Semitic religions -- Judaism, Christianity, and Islam -- and by
    • self-proclaimed "shamans of scientism" like Michael Shermer in the tradition of Scientific American magazine.

    Here is an introduction to the theology that should replace the ridiculous and outdated Semitic religions.



    According to Le Guin,


    "Scholarly translators of the Tao Te Ching, as a manual for rulers, use a vocabulary that emphasizes the uniqueness of the Taoist 'sage,' his masculinity, his authority. This language is perpetuated, and degraded, in most popular versions. I wanted a Book of the Way accessible to a present-day, unwise, unpowerful, and perhaps unmale reader, not seeking esoteric secrets, but listening for a voice that speaks to the soul. I would like that reader to see why people have loved the book for 2500 years.


    It is the most lovable of all the great religious texts, funny, keen, kind, modest, indestructibly outrageous and inexhaustibly refreshing. Of all the deep springs, this is the purest water. To me it is also the deepest spring."

    Tao Te Ching: Chapter 6
    translated by Ursula K. Le Guin

    The valley spirit never dies
    Call it the mystery, the woman.

    The mystery,
    the Door of the Woman,
    is the root
    of earth and heaven.

    Forever this endures, forever.
    And all its uses are easy.

  • Theology for a Small Planet


    THE HARVARD DIVINITY BULLETIN for Fall 1989 contained a special section, "Theology for a Small Planet," with a number of short articles by divinity school faculty and others addressing environment and theology.


    From The Harvard Divinity Bulletin, XIX, 3 (1989):


    " While Angels Weep..."
    Doing Theology on a Small Planet


    Timothy C. Weiskel
    © Copyright, 1989, Timothy C. Weiskel


    ...We continue to strut and prance about with a sense of supreme self-importance as if all creation were put in place for our benefit....


    From where does such arrogance come? How can our beliefs be so far out of touch with our knowledge? How can we maintain such an inflated sense of personal, collective and species self-importance? ....


    The answer, in part, is that Western religious traditions have generated and sustained this petty arrogance.... 


    Western cultures have come to believe religiously in their own power, importance and capacity to dominate and control nature.


    Some religious groups have transcribed and elaborated creation myths which serve to ennoble and authorize this illusion of domination. In these myths a supreme and omnipotent God figure (usually portrayed as male) is said to have created humankind and enjoined this species to be "fruitful and multiply" and "subdue" the earth. Moreover, it is often a feature of these traditions that selected human groups come to feel entitled, empowered or specially ordained by such a God to be his "chosen people." Through their actions and history, it is believed, this God allegedly manifested his intent for the planet as a whole. In short, human groups created God in their own image and generated divine narratives that accorded themselves privileged status in the whole of creation....


    ...science itself has become the cornerstone of modern mankind's religiously held belief in human control. In our era, this kind of arrogant science, like the self-important religious traditions of the past, must be questioned....


    In short, we all stand in need of a theology for a small planet.

October 20, 2002

October 19, 2002

  • What is Truth?







    My state of mind
    before reading the
    New York Times


    My state of mind
    after reading the
    New York Times


    In light of the entry below ("Mass Confusion," Oct. 19, 2002), some further literary reflections seem called for. Since this is, after all, a personal journal, allow me some personal details...


    Yesterday I picked up some packages, delivered earlier, that included four books I had ordered. I opened these packages this morning before writing the entry below; their contents may indicate my frame of mind when I later read this morning's New York Times story that prompted my remarks. The books are, in the order I encountered them as I opened packages,



    • Prince Ombra, by Roderick MacLeish (1982, reprinted in August 2002 as a Tom Doherty Associates Starscape paperback)
    • Truth, edited by Simon Blackburn and Keith Simmons, from the Oxford Readings in Philosophy series (Oxford University Press, 1999, reprinted as a paperback, 2000)
    • The Savage and Beautiful Country, by Alan McGlashan (1967, reprinted in a revised and expanded edition in 1988 as a Daimon Verlag paperback)
    • Abstract Harmonic Analysis, by Lynn H. Loomis (Van Nostrand, 1953... a used copy)

    Taken as a whole, this quartet of books supplies a rather powerful answer to the catechism question of Pontius Pilate, "What is truth?"...


    The answer, which I pray will some day be delivered at heaven's gate to all who have lied in the name of religion, is, in Jack Nicholson's classic words,


    You can't handle the truth!  

  • Mass Confusion


    From Garrison Keillor's Writer's Almanac:


    "It's the birthday of [novelist] John le Carré, born David John Moore Cornwell, in Poole, England (1931).... His father was a con artist who wanted his two sons to be lawyers because he thought it would come in handy. He sent them to boarding school, where they learned to speak and act like members of the British upper-class, but when they went home they knew they might have to bail him out of jail, or spend the holidays with a bunch of crooks. He learned German and became a spy, but said he 'never did anything to alter the world order.'"


    From The New York Times of Oct. 19, 2002:


    "...victims of sexually abusive priests expressed despair and outrage yesterday at the Vatican's refusal to endorse the American bishops' zero tolerance policy....


    'This certainly sends the whole thing into wild confusion,' said Thomas C. Fox, publisher of The National Catholic Reporter, an independent newsweekly that helped uncover the church's sexual abuse problem nearly two decades ago. 'It seems we haven't moved anywhere in finding a resolution, and that makes it terribly, terribly painful. It's like this nightmare simply won't end.'"


    Other classic Catholic quotations...


    1.  "He ain't heavy, he's my brother."


    2.  "What is truth?"


    3.  "Writers often cry 'Truth! Truth at all costs!' Some are sincere. Others are hypocrites. They use the truth, distort it, exploit it, for an ulterior purpose. Let us consider the case of John Cornwell...."  -- Inside the Vatican 

    John Cornwell recently wrote a classic study of the Roman Catholic Church, Hitler's Pope* (Viking Press, October 1999).


    According to the Daily Catholic and to Inside the Vatican, Cornwell is the brother of of spy novelist John le Carré (born David Cornwell). An article in the Jerusalem Post, however, seems to say that the spy novelist had only one brother, whose name was in fact Tony, not John.  A Sydney Morning Herald article confirms this version of the Cornwell family history.  Finally, once one learns from the Sydney article that David Cornwell's father's name was Ronnie, a perfected Google search reveals a Literary Encyclopedia article that seems to demonstrate conclusively that the Roman Catholic sources cited above lied about John Cornwell's family background.  Of course, this may be wrong... Those who wish may investigate further.


    * (I personally prefer Hitler's own remarks on the Church's "static pole," but tastes differ.)

October 18, 2002

  • Readings for the Oct. 18
    Feast of St. Luke


    A fellow Xangan is undergoing a spiritual crisis. Well-meaning friends are urging upon her all sorts of advice. The following is my best effort at religious counsel, meant more for the friends than for the woman in crisis.


    Part I... Wallace Stevens 


    From Brewer's Dictionary of Phrase and Fable:


    Ox Emblematic of St. Luke. It is one of the four figures which made up Ezekiel's cherub (i. 10). The ox is the emblem of the priesthood....


       The dumb ox. St. Thomas Aquinas; so named by his fellow students at Cologne, on account of his dulness and taciturnity. (1224-1274.)
       Albertus said, “We call him the dumb ox, but he will give one day such a bellow as shall be heard from one end of the world to the other.” (Alban Butler.)


    From Wallace Stevens, "The Latest Freed Man":


    It was how the sun came shining into his room:
    To be without a description of to be,
    For a moment on rising, at the edge of the bed, to be,
    To have the ant of the self changed to an ox
    With its organic boomings, to be changed
    From a doctor into an ox, before standing up,
    To know that the change and that the ox-like struggle
    Come from the strength that is the strength of the sun,
    Whether it comes directly or from the sun.
    It was how he was free. It was how his freedom came.
    It was being without description, being an ox.


    Part II... The Rosy Cross


    Readings:



    • Brautigan, Richard, The Hawkline Monster, Simon and Schuster, 1974...
      Just for the pleasure of reading it... A compelling work of fiction on spiritual matters that includes a conversion to Rosicrucianism in its concluding chapter.
    • Browning, Vivienne (Betty Coley, ed).
      My Browning Family Album. With a Foreword by Ben Travers, and a Poem by Jack Lindsay Springwood, London, 1979...
      The Rosicrucian tradition in Australia (highly relevant background reading for the 1994 film "Sirens"). Includes a mention of Aleister Crowley, dark mage, who also figures (prominently) in....
    • Wilson, Robert Anton, Masks of the Illuminati, Pocket Books, April 1981...
      James Joyce and Albert Einstein join in a metaphysical investigation.

      "He recited from the anonymous Muses Threnody of 1648:
      For we be brethren of the Rosy Cross
      We have the Mason Word and second sight
      Things for to come we can see aright."

    Part III... Stevens Again


    A major critical work on Wallace Stevens that is not unrelated to the above three works on the Rosicrucian tradition:


    Leonora Woodman, Stanza My Stone: Wallace Stevens and the Hermetic Tradition, West Lafayette, Indiana: Purdue University Press, 1983


    From the Department of English, Purdue University:


    Leonora Woodman came to Purdue in 1976. In 1979, she became Director of Composition, a position she held until 1986.... At the time of her death in 1991, she was in the midst of an important work on modernist poetry, Literary Modernism and the Fourth Dimension: The Visionary Poetics of D.H. Lawrence, H.D., and Hart Crane.


    For more on Gnostic Christianity, see



    • Elaine Pagels, The Gnostic Gospels (Random House, 1979), and
    • Harold Bloom, Omens of Millenium: The Gnosis of Angels, Dreams, and Resurrection (Riverhead Books, 1996).

October 17, 2002

  • Slieve na mBan


    The view in the entry below is from Slievenamon or Slieve/Sliabh na mBan, a mountain in County Tipperary.


    From an interview with  Dr. Mary McAuliffe, an historian who specializes in women's history of the medieval period in Ireland:


    "It seems that there were no witchcraft trials in the Gaelic Irish areas. There isn't a tradition of witchcraft in the Gaelic Irish communities because people believed in magical women....  Another interesting thing about the... case was that it happened in Slieve na mBan, where the barrier between this world and the next is thinnest. Slieve na mBan means the 'mountain of women.'" 


    From Finn's Household in Part II Book I of


    Gods and Fighting Men

    The Story of the Tuatha De Danaan
    and of the Fianna of Ireland,

    arranged and put into English

    by Lady Augusta Gregory

    with a preface by W. B. Yeats

    [1904]

    "Where do you come from, little one, yourself and your sweet music?" said Finn. "I am come," he said, "out of the place of the Sidhe in Slieve-nam-ban...."


    Finn, again! -- James Joyce

  • To the Green Lady
     of Perelandra



    View from the slopes of Slieve na mBan


    In honor of the relationship between theology and literature, of the Green Lady of C. S. Lewis, and of... 


    John Flood BA, MA (NUI), Ph.D. (Dublin)
    Senior Lecturer. Formerly a tutor at the National University of Ireland, Maynooth, and Trinity College, Dublin, his Ph.D. was on the influence of the interpretation of the figure of Eve in Early Modern writing. His research interests include the Renaissance, George Orwell, J. R. R. Tolkien and the relationship between theology and literature.


    ... this site's music is now Caoine Cill Chais, The Lament for Kilcash.


October 16, 2002

  • Garden Party Revisited


    From the Archives:  On this date in 1992,







    "Sinead O’Connor was booed off the stage at a show honoring Bob Dylan at Madison Square Garden (famous for booing folks off the stage)....


    Click for ordering information.


    Sinead's new album.  The Gaelic title, "Sean-Nos Nua," means
    Old-Style New.


    The crowd was acting in disapproval of O’Connor’s tearing up a picture of Pope John Paul II on 'Saturday Night Live' October 3, 1992."


    Go mbeidh rincí fada ag gabháil timpeall,
    Ceol veidhlín is tinte cnámh.