Month: May 2003

  • Birthday Present


    Today is the birthday of Emile Mathieu.
    Here is a present.

  • Well Done


    "So tell me about the matrix reloaded... and what it's like to finish a job well done."


    -- Weblog entry by Harvard student, May 15, 2003


    The matrix reloaded: 


    See chapter VII, "Composition," in Chinese Calligraphy: An Introduction to Its Aesthetic and Technique, by Chiang Yee, Harvard University Press, first published April 21st, 1938.


    A job well done:



    "The Best is Yet to Come"
    -- Epitaph of Francis Albert Sinatra

  • Common Sense


    On the mathematician Kolmogorov:


    "It turns out that he DID prove one basic theorem that I take for granted, that a compact hausdorff space is determined by its ring of continuous functions (this ring being considered without any topology) -- basic discoveries like this are the ones most likely to have their origins obscured, for they eventually come to be seen as mere common sense, and not even a theorem."


    -- Richard Cudney, Harvard '03, writing at Xanga.com as rcudney on May 14, 2003


    That this theorem is Kolmogorov's is news to me.


    See



    The above references establish that Gelfand is usually cited as the source of the theorem Cudney discusses.  Gelfand was a student of Kolmogorov's in the 1930's, so who discovered what when may be a touchy question in this case.  A reference that seems relevant: I. M. Gelfand and A. Kolmogoroff, "On rings of continuous functions on topological spaces," Doklady Akad. Nauk SSSR 22 (1939), 11-15.  This is cited by Gillman and Jerison in the classic Rings of Continuous Functions.


    There ARE some references that indicate Kolmogorov may have done some work of his own in this area.  See here ("quite a few duality theorems... including those of Banaschewski, Morita, Gel'fand-Kolmogorov and Gel'fand-Naimark") and here  ("the classical theorems of M. H. Stone, Gelfand & Kolmogorov").


    Any other references to Kolmogorov's work in this area would be of interest.


    Naturally, any discussion of this area should include a reference to the pioneering work of M. H. Stone.  I recommend the autobiographical article on Stone in McGraw-Hill Modern Men of Science, Volume II, 1968.

  • Cubist Catechism


    For the birthday of Georges Braque


    From A Wrinkle in Time, by Madeleine L'Engle:


    "Now we will tesser, we will wrinkle again. Do you understand?"


    "No," Meg said flatly....


    "Oh, dear," Meg sighed. "I guess I am a moron. I just don't get it."


    "That is because you think of space only in three dimensions," Mrs. Whatsit told her....


    Meg sighed. "Just explain it to me."


    "Okay," Charles said. "What is the first dimension?"


    "Well -- a line."


    "Okay. And the second dimension?"


    "Well, you'd square the line. A flat square would be in the second dimension."

    "And the third?"

    "Well, you'd square the second dimension. Then the square wouldn't be flat any more. It would have a bottom, and sides, and a top."

    "And the fourth?"


    "Well, I guess if you want to put it into mathematical terms you'd square the square. But you can't take a pencil and draw it the way you can the first three."








    Braque

  • Operation Playmate:


    11:01 AM


    On this date in 1938, Louis Armstrong and his orchestra recorded "When the Saints Go Marching In."


    On this date in 1961, Saint Gary Cooper died.


    From my Jan. 2, 2003, entry:


    Faces of the Twentieth Century:
    The Harvest Continues


    "I walk, I lift up, I lift up heart, eyes,
    Down all that glory in the heavens
        to glean our Saviour;
    And, éyes, héart, what looks, what lips
        yet gave you a
    Rapturous love's greeting of realer,
        of rounder replies?"


    — Gerard Manley Hopkins,
       "Hurrahing in Harvest"









    Mary Brian



    Joe Foss


    "Cowboy, take me away.
    Fly this girl as high as you can
    into the wild blue."


    — The Dixie Chicks


    From my March 31, 2003, entry:


    "During the Gulf War, Playboy magazine's celebrated Centerfolds reached out to U.S. military men and women... with their 'Operation Playmate' project....


    Now, in light of the war in Iraq, 'Operation Playmate' has returned."


    Entertainment Weekly, May 2, 2003:



    Perhaps, in heaven, Dixie Chick Natalie "Mattress Dancing" Maines will provide terpsichorean instruction. 



    Etymology: Latin Terpsichor,
    from Greek Terpsikhor,
    from feminine of terpsikhoros,
    dance-loving : terpein, to delight
    + khoros, dance.


    See, too, my entry for Beltane (May 1), the day that death claimed the 13th Episcopal bishop of New York City.


    All of these events are not without interest, but it is not easy to fit them into one coherent story, as Robert Penn Warren once requested:



    "The name of the story will be Time,
    But you must not pronounce its name.
    Tell me a story of deep delight."


    It is perhaps relevant that, as T. S. Eliot well knew, there can be no dance except in time, and that the time of my May 1 entry is 5:13, today's date in another guise.  To paraphrase an Eliot line, 


    "Hurry up please, it's 5/13."

  • The Tony Nominations


    Dannie Abse quoting Robert Penn Warren:



    "The name of the story will be Time,
    But you must not pronounce its name.
    Tell me a story of deep delight."


     Dannie Abse


    Abse deserves a Tony Smith award¹ for his play Pythagoras.


    Frank Rich on Bush's Top Gun speech:



    "Only hours before President Bush's prime-time speech came news of what Variety headlined on Page 1 as 'Regime Change' in Hollywood — the departure of the [West Wing] creator, the writer Aaron Sorkin."


     George W. Bush


    President Bush deserves a Tony Smith award² for his performance aboard the aircraft carrier Abraham Lincoln.


     Madeleine L'Engle on the religion of Cubism:



    "There is such a thing as a tesseract."


     Madeleine L'Engle


    L'Engle, former librarian at the Cathedral of St. John the Divine in New York City, deserves a Tony Smith award³ for insisting on the existence of the tesseract, or 4-dimensional cube, as an object of conceptual art.


    L'Engle is perhaps the best defender of the religious, or "story," theory of truth, as opposed to the "diamond" theory of truth. (See my earlier May 12 entry, "Death and Truth," which deals with the bishop of L'Engle's cathedral.)


    ¹ See Tony Smith on mathematics.


    ² See Tony Smith on foreign policy.


    ³ See Tony Smith on conceptual art.

  • Epiphany 1941:
    Why We Fought









    Jan. 6, 1941

    Hepburn's father was disgusted and heartsick over her decision to become an actor. He thought it was a silly profession, closely allied to street walking.
    -- Heather Wilgar


    Not the way she did it.
    -- S. H. Cullinane


    Hepburn is 96 today.

  • Death and Truth


    Material related to my May 9, 2003, notes:



    1. Pilate, Truth, and Friday the Thirteenth
    2. The Diamond Theory of Truth
    3. Understanding

  • Day of the Mother Ship:

    A Close Encounter of the Third Level

    Today is also the feast day of Saint Zenna Henderson, who was born on All Saints' Day, 1917.   The Adherents.com website says she was a Mormon, but the printed reference work Contemporary Authors
    (written when she was still alive and could defend herself against any
    accusation of Mormonism) says she was a Methodist.  Maybe she was
    just one of The People -- i.e., a Person.

    "The concept of a person,
    which we find so familiar in its application to human beings, cannot be
    clearly and sharply expressed by any word in the vocabulary of Plato
    and Aristotle; it was wrought with the hammer and anvil* of theological disputes about the Trinity and the Person of Christ."

    -- Peter Geach, The Virtues, Cambridge U. Press, 1977, p. 75

    See also Terpsichore and the Trinity.

    * For a use of this phrase suited to Mental Health Month, see The Prisoner, Episode Ten.  See, too, Inaugural Address.

  • ART WARS:
    The Religion of Cubism


    In the dome of the Capitol at Washington, DC, a painting depicts The Apotheosis of Washington.  Personally, I prefer the following pair of pictures, which might be titled Apotheosis of the Cube.



    logo


    Die


    A New York Times article says Tony Smith's instructions for fabricating Die were as follows:


    "a six-foot cube of quarter-inch hot-rolled steel with diagonal internal bracing."


    The transparent cube in the upper picture above shows the internal diagonals.  The fact that there are four of these may be used to demonstrate the isomorphism of the group of rotations of the cube with the group of permutations on an arbitrary set of four elements.  For deeper results, see Diamond Theory.


    For an explanation of why our current president might feel that the cube deserves an apotheosis, see the previous entry, "The Rhetoric of Power."


    See, too, Nabokov's Transparent Things:


    "Its ultimate vision was the incandescence of a book or a box grown completely transparent and hollow.  This is, I believe, it: not the crude anguish of physical death but the incomparable pangs of the mysterious mental maneuver needed to pass from one state of being to another.  Easy, you know, does it, son."