Month: October 2008

  • Annals of Theology:

    Readings for
    Devil’s Night

    Pope Benedict XVI, formerly the modern equivalent of The Grand Inquisitor

    1. Today’s New York Times review
        of Peter Brook’s production of
       “The Grand Inquisitor”
    2. Mathematics and Theology
    3. Christmas, 2005
    4. Cube Space, 1984-2003

  • ART WARS, continued:

    From the Mountaintop

    Katherine Neville, author of perhaps the greatest bad novel of the twentieth century, The Eight, has now graced a new century with her sequel, titled The Fire. An excerpt:

    “Our family lodge had been built at about this same period in the prior
    century, by neighboring tribes, for my great-great-grandmother, a
    pioneering mountain lass. Constructed of hand-hewn rock and massive tree
    trunks chinked together, it was a huge log cabin that was shaped like
    an octagon– patterned after a hogan or sweat lodge– with many-paned
    windows facing in each cardinal direction, like a vast, architectural
    compass rose.
    ……..
    From here on the mountaintop, fourteen thousand feet atop the Colorado
    Plateau, I could see the vast, billowing sea of three-mile-high
    mountain peaks, licked by the rosy morning light. On a clear day like
    this, I could see all the way to Mount Hesperus– which the Diné call
    Dibé Nitsaa: Black Mountain. One of the four sacred mountains created
    by First Man and First Woman.

    Together with Sisnaajinii, white mountain (Mt. Blanca) in the east;
    Tsoodzil, blue mountain (Mt. Taylor) in the south, and Dook’o’osliid,
    yellow mountain (San Francisco Peaks) in the west, these four marked
    out the four corners of Dinétah– ‘Home of the Diné,’ as the Navajo call
    themselves.

    And they pointed as well to the high plateau I was
    standing on: Four Corners, the only place in the U.S. where four
    states– Colorado, Utah, New Mexico, and Arizona– come together at right
    angles to form a cross.”


    Related material
    (Oct. 14, 2004):

    The Eight

    Lest the reader of the previous entry mistakenly take Katherine Neville’s book The Eight
    more seriously than Fritz Leiber’s greatly superior writings on
    eightness, here are two classic interpretations of Leiber’s “spider” or
    “double cross” symbol:

    Greek: The Four Elements

    Aristotle:
    The 4 elements and
    the 4 qualities
    (On Generation and
    Corruption, II, 3
    )

    Chinese: The Eight Trigrams

    Richard Wilhelm:
    The 8 trigrams
    (Understanding
    the I Ching
    ,
    154-175)

    The eight-rayed star may be taken
    as representing what is known
    in philosophy as a “universal.”

    See also

    The Divine Universals,

    Plato, Pegasus, and the Evening Star,

    A Little Extra Reading, and

    Quine in Purgatory.

  • Annals of Religion, continued:

    Halloween
    Meditation

    for…

    Halloween Card from SuSu

    5:07:33 AM ET

    Denali

    Hexagram 33

    33 Retreat

    THE IMAGE

    Mountain under heaven:
    the image of RETREAT.
    Thus the superior man
    keeps the inferior man
    at a distance,
    not angrily
    but with reserve.

    “The mountain rises up under heaven, but owing to its nature it finally comes to a stop. Heaven on the other hand retreats upward before it into the distance and remains out of reach. This symbolizes the behavior of the superior man toward a climbing inferior; he retreats into his own thoughts as the inferior man comes forward. He does not hate him, for hatred is a form of subjective involvement by which we are bound to the hated object. The superior man shows strength (heaven) in that he brings the inferior man to a standstill (mountain) by his dignified reserve.” –Richard Wilhelm

  • Annals of Religion:

    Actual Being

    The New York Times Book Review online today has a review by Sam Tanenhaus of a new John Updike book.

    The title of the review (not the book) is “Mr. Wizard.”

    “John Updike is the great genial sorcerer of American letters. His output alone (60
    books, almost 40 of them novels or story collections) has been
    supernatural. More wizardly still is the ingenuity of his prose. He has
    now written tens of thousands of sentences, many of them tiny miracles
    of transubstantiation whereby some hitherto overlooked datum of the
    human or natural world– from the anatomical to the zoological, the
    socio-economic to the spiritual– emerges, as if for the first time, in
    the complete­ness of its actual being.”

    Rolling Stone interview with Sting, February 7, 1991:

    “‘I was brought up in a very strong Catholic community,’ Sting says. ‘My
    parents were Catholic, and in the Fifties and Sixties, Catholicism was
    very strong. You know, they say, “Once a Catholic, always a Catholic.”
    In a way I’m grateful for that background. There’s a very rich imagery
    in Catholicism: blood, guilt, death, all that stuff.’ He laughs.”

    http://www.log24.com/log/pix08A/081025-Sting.jpg

    RS 597, Feb. 7, 1991

    Last night’s 12:00 AM
    Log24 entry:

    Midnight Bingo

    From this date six years ago:


    It All Adds Up.

    From this morning’s newspaper,
    a religious meditation I had not
    seen last night:

    The image “http://www.log24.com/log/pix08A/081025-WizardOfIdSm.jpg” cannot be displayed, because it contains errors.

    Related material:

    Juneteenth through
    Midsummer Night, 2007

    and

    Church of the Forbidden Planet

  • Happy Picasso’s Birthday:

    Midnight Bingo

    From this date six years ago:

    It All Adds Up.

  • Cube Space, 1984-2003:

    The Cube Space” is a name given to the eightfold cube in a vulgarized mathematics text, Discrete Mathematics: Elementary and Beyond, by Laszlo Lovasz et al., published by Springer in 2003. The identification in a natural way of the eight points of the linear 3-space over the 2-element field GF(2) with the eight vertices of a cube is an elementary and rather obvious construction, doubtless found in a number of discussions of discrete mathematics. But the less-obvious generation of the affine group AGL(3,2) of order 1344 by permutations of parallel edges in such a cube may (or may not) have originated with me. For descriptions of this process I wrote in 1984, see Diamonds and Whirls and Binary Coordinate Systems. For a vulgarized description of this process by Lovasz, without any acknowledgement of his sources, see an excerpt from his book.

  • Terminator Prequel:

    Along Came
    a Spider

    Symmetry axes of the square

    A phrase from 1959
    (“Damnation Morning“),
    from Monday
    (“Me and My Shadow“),
    and from Sept. 28
    (“Buffalo Soldier“) –

    “Look, Buster,
    do you want to live?”

  • Concepts of Space:

    Euclid vs. Galois

    On May 4, 2005, I wrote a note about how to visualize the 7-point Fano plane within a cube.

    Last month, John Baez
    showed slides that touched on the same topic. This note is to clear up possible confusion between our two approaches.

    From Baez’s Rankin Lectures at the University of Glasgow:

    John Baez, drawing of seven vertices of a cube corresponding to Fano-plane points

    Note that Baez’s statement (pdf) “Lines in the Fano plane correspond to planes through the origin [the vertex labeled '1'] in this cube” is, if taken (wrongly) as a statement about a cube in Euclidean 3-space, false.

    The statement is, however, true of the eightfold cube, whose eight subcubes correspond to points of the linear 3-space over the two-element field, if “planes through the origin” is interpreted as planes within that linear 3-space, as in Galois geometry, rather than within the Euclidean cube that Baez’s slides seem to picture.

    This Galois-geometry interpretation is, as an article of his from 2001 shows, actually what Baez was driving at. His remarks, however, both in 2001 and 2008, on the plane-cube relationship are both somewhat trivial– since “planes through the origin” is a standard definition of lines in projective geometry– and also unrelated– apart from the possibility of confusion– to my own efforts in this area. For further details, see The Eightfold Cube.

  • A Riff for Dave:

    Me and My Shadow

    Thoughts suggested by Saturday’s entry–

    “… with primitives the beginnings
    of art, science, and religion coalesce in the undifferentiated chaos of
    the magical mentality….”

    – Carl G. Jung, “On the Relation of Analytical Psychology to Poetry,” Collected Works, Vol. 15, The Spirit in Man, Art, and Literature, Princeton University Press, 1966, excerpted in Twentieth Century Theories of Art, edited by James M. Thompson.

    For a video of such undifferentiated chaos, see the Four Tops’ “Loco in Acapulco.”

    “Yes, you’ll be goin’ loco
      down in Acapulco,

      the magic down there
      is so strong.”

    This song is from the 1988 film “Buster.”

    (For a related religious use of that name– “Look, Buster, do you want to live?”– see Fritz Leiber’s “Damnation Morning,” quoted here on Sept. 28.)

    Art, science, and religion are not apparent within the undifferentiated chaos of the Four Tops’ Acapulco video, which appears to incorporate time travel in its cross-cutting of scenes that seem to be from the Mexican revolution with contemporary pool-party scenes. Art, science, and religion do, however, appear within my own memories of Acapulco. While staying at a small thatched-roof hostel on a beach at Acapulco in the early 1960′s, I read a paperback edition of Three Philosophical Poets, a book by George Santayana on Lucretius, Dante, and Goethe. Here we may regard art as represented by Goethe, science by Lucretius, and religion by Dante. For a more recent and personal combination of these topics, see Juneteenth through Midsummer Night, 2007, which also has references to the “primitives” and “magical mentality” discussed by Jung.

    “The major
    structures of the psyche for Jung include the ego, which is comprised of
    the persona and the shadow. The persona is the ‘mask’ which the person
    presents [to] the world, while the shadow holds the parts of the self which
    the person feels ashamed and guilty about.”

    – Brent Dean Robbins, Jung page at Mythos & Logos

    As for shame and guilt, see Malcolm Lowry’s classic Under the Volcano, a novel dealing not with Acapulco but with a part of Mexico where in my youth I spent much more time– Cuernavaca.

    Lest Lowry’s reflections prove too depressing, I recommend as background music the jazz piano of the late Dave McKenna… in particular, “Me and My Shadow.”

    McKenna died on Saturday, the date of the entry that included “Loco in Acapulco.” Saturday was also the Feast of Saint Luke.